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https://www.physicsforums.com/threads/whats-the-inertia-of-cart-a.886708/	# What's the inertia of cart A? Tags: 1. Sep 25, 2016 ### emily081715 1. The problem statement, all variables and given/known data A 1-kg standard cart collides with a cart A of unknown inertia. Both carts appear to be rolling with significant wheel friction because their velocities change with time as shown graph below: What is the inertia of cart A? 2. Relevant equations i am unsure how to even solve for inertia but i know the equation is i=mr^2 except i have never used this equation 3. The attempt at a solution i tried randomly rearranging formula i know how to use for momentum and got 1.6 kg but i have never solve a problem like this and i'm very confused on how to actually solve for inertia 2. Sep 25, 2016 ### Simon Bridge That is the equation for the moment of inertia I of a body, so you can tell something about it's rotational dynamics. When "inertia" is used by itself it usually means "mass"... look up "law of inertia". I notice you got it right for your other problem. 3. Sep 26, 2016 ### emily081715 Am I just using the equation F=ma? that is what i got when i looked it up. if thats the case i don't know acceleration or the mass of cart A or the F and have three unknown variables 4. Sep 26, 2016 ### PeroK Does Newton's third law tell you anything about the forces involved? 5. Sep 26, 2016 ### emily081715 newtons third law says that for action there is an equal and opposite reaction. would this mean the the force acting on the standard cart is equal to the one on cart A? 6. Sep 26, 2016 ### PeroK You need to be more precise. The force that the standard cart exerts on cart A is equal and opposite to the force that cart A exers on the standard cart. But, do you think there are other forces involved? Hint: how long does the collision last? 7. Sep 26, 2016 ### emily081715 i don't think there is any other forces acting on the object. the collision is very quick and doesn't even last a second 8. Sep 26, 2016 ### PeroK That's not right. Normally these problems involve an instantaneous collision. But not in this case. The collision clearly lasts a significant length of time. In fact, it's exactly one second. 9. Sep 26, 2016 ### emily081715 so what does that mean? 10. Sep 26, 2016 ### PeroK Do you think friction took a break while the carts got on with their collision? 11. Sep 26, 2016 ### emily081715 No, so that means both carts have a force of friction acting on them. i am still unsure how to actually go about solving the question though 12. Sep 26, 2016 ### PeroK Well, this problem is not so easy. To solve this problem, I think you need to really understand what is going on. Then, you need to organise your thoughts. Hit the problem with exactly the right equations and, finally, solve those equations. The crux of this problem is the relationship between forces and change in momentum. I'm not convinced you understand this well enough yet. The problem would be much easier with an instantaneous collision. As it stands, I think this question might be a bit hard! The other question I'm helping you with is really much easier than this one. 13. Sep 26, 2016 ### emily081715 both questions need to be answered though, can you keep working on this with me as well 14. Sep 26, 2016 ### PeroK See if you do it without friction first. Ignore friction. I'll give you one hint. You got $1.6kg$ for cart A. But, that means there is more momentum after the collison than before. So, that can't be right. 15. Sep 26, 2016 ### emily081715 i got 0.65kg 16. Sep 26, 2016 ### PeroK From the graph you should be able to see that the mass of cart A is significantly greater than that of the standard cart. This shows the gap between your knowledge of the subject and the knowledge required to solve a problem like this. 17. Sep 26, 2016 ### emily081715 can you break down the steps on what i should do to find the answer 18. Sep 26, 2016 ### emily081715 should there be less momentum after the collision? 19. Sep 26, 2016 ### emily081715 • Poster has been warned not to post multiple threads on the same question... 1. The problem statement, all variables and given/known data A 1-kg standard cart collides with a cart A of unknown inertia. Both carts appear to be rolling with significant wheel friction because their velocities change with time 2. Relevant equations the law of inertia F=ma P=mv 3. The attempt at a solution i know that inertia in this case means mass, but i am unsure how to solve for it. i tried and got 1.6kg but that cant be right because the momentums before is less then the momentum after the collision. can someone break down the steps that should be taken to solve this question Last edited by a moderator: May 8, 2017 20. Sep 26, 2016 ### Staff: Mentor What does the question ask for? That seems to be missing from your problem statement. And what quantity is conserved in elastic collisions like this? How can you use this to solve the problem. Last edited by a moderator: May 8, 2017	2018-02-23 07:14:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4114684760570526, "perplexity": 776.4831585931943}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814493.90/warc/CC-MAIN-20180223055326-20180223075326-00773.warc.gz"}
http://math.stackexchange.com/questions/251699/reverse-polish-notation-and-numbers-9/251707	# Reverse Polish Notation and numbers $>9$ Excuse me for the newbish question in advance but how should I make sure I don't make a mistake converting from RPN to infix notation when I don't know if some of the numbers aren't two-digit ones or when I do that some are but I don't know which ones? For example, how do I know if I should evaluate $112+$ to $11+2$ or $1+12$? Or such thing is impossible to evaluate when I don't know where the enters were put in? -	2013-12-13 10:34:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8871984481811523, "perplexity": 315.08054086787774}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164929439/warc/CC-MAIN-20131204134849-00032-ip-10-33-133-15.ec2.internal.warc.gz"}
https://rupress.org/jgp/article/124/4/333/34109/New-Insights-on-the-Voltage-Dependence-of-the-KCa3	We present in this work a structural model of the open IKCa (KCa3.1) channel derived by homology modeling from the MthK channel structure, and used this model to compute the transmembrane potential profile along the channel pore. This analysis showed that the selectivity filter and the region extending from the channel inner cavity to the internal medium should respectively account for 81% and 16% of the transmembrane potential difference. We found however that the voltage dependence of the IKCa block by the quaternary ammonium ion TBA applied internally is compatible with an apparent electrical distance δ of 0.49 ± 0.02 (n = 6) for negative potentials. To reconcile this observation with the electrostatic potential profile predicted for the channel pore, we modeled the IKCa block by TBA assuming that the voltage dependence of the block is governed by both the difference in potential between the channel cavity and the internal medium, and the potential profile along the selectivity filter region through an effect on the filter ion occupancy states. The resulting model predicts that δ should be voltage dependent, being larger at negative than positive potentials. The model also indicates that raising the internal K+ concentration should decrease the value of δ measured at negative potentials independently of the external K+ concentration, whereas raising the external K+ concentration should minimally affect δ for concentrations >50 mM. All these predictions are born out by our current experimental results. Finally, we found that the substitutions V275C and V275A increased the voltage sensitivity of the TBA block, suggesting that TBA could move further into the pore, thus leading to stronger interactions between TBA and the ions in the selectivity filter. Globally, these results support a model whereby the voltage dependence of the TBA block in IKCa is mainly governed by the voltage dependence of the ion occupancy states of the selectivity filter. ## Introduction Ca2+-activated potassium channels (K(Ca2+)) are present in most mammalian cell types, where their primary role is to establish a link between the various Ca2+-based second messenger systems and the electrical properties of the cells. Three main classes of Ca2+-activated potassium channels have been to date identified on the basis of their permeation properties and pharmacology (Vergara et al., 1998). These include the charybdotoxin- and iberiotoxin-sensitive KCa1.1 channels of large conductance (150–220 pS); the intermediate conductance (20–50 pS) IKCa channels (KCa3.1) inhibited by clotrimazole (Rittenhouse et al., 1997) and TRAM34 (Wulff et al., 2001), and the apamine-sensitive and -insensitive SK channels of small conductance (KCa2.1, KCa2.2, KCa2.3) (Kohler et al., 1996). In contrast to KCa1.1, the SK and IKCa channel gating process is voltage insensitive, and the Ca2+ sensitivity in both channels is conferred by the Ca2+-binding protein, calmodulin, constitutively bound to the channel proximal COOH-terminal regions (Khanna et al., 1999). An important contribution to our understanding of the IKCa channel molecular identity came from the cloning of the hKCa4, hIK1, and hSK4 channels (Ishii et al., 1997; Joiner et al., 1997; Logsdon et al., 1997; Vandorpe et al., 1998; Warth et al., 1999). The IKCa channel is a tetrameric protein with each subunit comprising 427 amino acids organized in six transmembrane segments TM1–TM6 with a pore motif between segments 5 and 6. The three-dimensional (3D) structure of IKCa, however, remains unresolved. Docking simulations and binding studies using charybdotoxin analogues have revealed that the IKCa external vestibule is structurally similar to the external pore region of other charybdotoxin-sensitive channels, such as Kv1.2 and Kv1.6 (Rauer et al., 2000). Sequence and secondary structure alignments also suggest a structural similarity between the proximal COOH-terminal region of IKCa (residues 395–430) and the calmodulin-binding domain of rSK2 (unpublished data), the structure of which has been resolved by X-ray crystallography (Schumacher et al., 2001). More recently, work from our laboratory has led to the first molecular description of the open/closed IKCa pore region using an approach combining the substituted cysteine accessibility method (SCAM), computer-based homology modeling, and single channel recordings (Simoes et al., 2002). The proposed IKCa models showed the V275, T278, and V282 residues as lining the channel pore, with V275 and T278 contributing to the formation of a central inner cavity ∼10 Å wide. Fig. 1 presents the structures we propose for the open and closed IKCa obtained by homology modeling using the KcsA (Doyle et al., 1998) and MthK (Jiang et al., 2002a) channels as templates. Estimation of the distance between the α-carbons of corresponding residues along TM6 for subunits facing diagonally indicates a drastic widening of the pore starting at residue T278 upon channel opening. An analysis of the open channel structure reveals in addition that the inner vestibule exceeds 18 Å in diameter, suggesting that it should be wide enough to create a quasi isopotential continuum between the channel central cavity and the internal medium. In this work we used the quaternary ammonium (QA) ion tetrabutylammonium (TBA) to investigate some of the structural features of the IKCa conduction pathway and probe the transmembrane potential profile within the IKCa open pore structure. QA ions are considered good blockers of K+ channels and have been extensively used to characterize channel inner architecture. One of the main features of the blocking properties of QA ions concerns the voltage dependence of the channel block. For instance, studies in which the QA ions TEA or TBA were applied internally showed that the electrical distances that account for the voltage sensitivity of the channel block ranged from 0.2 (Shaker and MaxiKCa) (Villarroel et al., 1988; Ding and Horn, 2002; Thompson and Begenisich, 2003a; Li and Aldrich, 2004) up to 0.9 (Kir1.1 and Kir2.1) (Spassova and Lu, 1998, 1999; Guo and Lu, 2001) depending on channel types. X-ray data for the TBA-closed KcsA complex support a binding site for TBA located in the central cavity (Zhou et al., 2001). Assuming an equivalent position for the binding site in the open channel, electrical distances from 0.2 to 0.9 could be indicative of pore structures where a significant fraction of the transmembrane potential drop occurs over the region extending from the channel central cavity to the internal medium. However, these values might be difficult to reconcile with an isopotential continuum between the channel central cavity and the internal medium, as suggested by the MthK channel structure. The blocking potency of internal QA ions also depends on the structural parameters controlling the accessibility of the ions to the interaction site. Notably, there are considerable variations in the entry rate of individual QA ions depending on channel types. For instance, the entry rate measured for TBA in zero current conditions was found to vary from 0.004 μM−1s−1 for the Kir1.1 and Kir2.1 inward rectifiers up to 0.55 μM−1s−1 for Shaker (Guo and Lu, 2001; Ding and Horn, 2002). These variations are likely to reflect gross differences in the channel inner vestibule geometry. In this work, we measured the kinetics and the voltage dependence of the IKCa block by internal TBA. Our results confirm that the V275 residue is lining the channel central pore cavity and contributes to the architecture of the TBA interaction site. We also demonstrate that the voltage dependence of the IKCa block by TBA presents a complex pattern with an apparent electrical distance of 0.49 at negative potentials. Using the structure proposed for the open IKCa configuration and the recent model of Berneche and Roux (2003) describing the single file diffusion of K+ in the KcsA selectivity filter, we show that the observed dependence of the TBA block reflects the ion occupancy state of the selectivity filter rather than the actual potential difference between the channel inner cavity and the internal medium. ## Materials And Methods ### Cloning, Sequencing and Site-directed Mutagenesis of the IKCa Channel IKCa channel cDNAs were obtained by RT-PCR from HeLa cells as described previously (Simoes et al., 2002). The resulting PCR product was identical to the sequences reported for the hKCa4 (GenBank/EMBL/DDBJ accession no. AF033021), hIK1 (AF022150), and hSK4 (AF000972) channels. Site-directed mutagenesis of IKCa channel was performed using the QuickChange Site-Directed Mutagenesis kit (Stratagene). Point mutations were obtained by using 25-mer mutated oligonucleotides with the wild-type IKCa as template. Mutations were confirmed by sequencing the entire coding region on both strands. ### Oocytes Mature oocytes (stage V or VI) were obtained from Xenopus laevis frogs anesthetized with 3-aminobenzoic acid ethyl ester. The follicular layer was removed by incubating the oocytes in a Ca2+-free Barth's solution containing collagenase (1.6 mg/ml; Sigma-Aldrich) for 45 min. The composition of the Barth's solution was (in mM) 88 NaCl, 3 KCl, 0.82 MgSO4, 0.41 CaCl2, 0.33 Ca(NO3)2, and 5 HEPES (pH 7.6). Defolliculated oocytes were stored at 18°C in Barth's solution supplemented with 5% horse serum, 2.5 mM Na-pyruvate, 100 U/ml penicillin, 0.1 mg/ml kanamycin, and 0.1 mg/ml streptomycin. Oocytes were patched 3–5 d after coinjection of 0.92–9.2 ng of the cDNA coding for IKCa in pMT21 and 1.38 ng of cDNA coding for a green fluorescent protein that was used as a marker for nuclear injection. Prior to patch clamping, defolliculated oocytes were kept in a hyperosmotic solution containing (in mM) 250 KCl, 1 MgSO4, 1 EGTA, 50 sucrose, and 10 HEPES buffered at pH 7.4 with KOH. The vitelline membrane was then peeled off using fine forceps, and the oocyte was transferred to a superfusion chamber for patch clamp measurements. ### Solutions The bath and patch pipette solutions consisted of (in mM) 200 K2SO4, 1.8 MgCl2, 0.025 CaCl2, 25 HEPES, buffered at pH 7.4 with KOH. The use of sulfate salts prevented contributions from endogenous Ca2+-dependent chloride channels while enabling to chelate contaminant divalent cations such as Ba2+ (maximum free Ba2+ concentration: 0.5 nM in 200 mM K2SO4). Calcium-free solutions were prepared by omitting CaCl2 from the 200 mM K2SO4 solution and adding 1 mM EGTA. Solutions with different potassium concentrations were prepared using NMDG as replacing ion and titrated with H2SO4. Unless specified otherwise, potassium ion concentrations are expressed as potassium activities. Activity coefficients for the various K2SO4 solutions were obtained from literature (Robinson and Stokes, 1959). The potassium ion activity for each solution reads: 225 mM for the 400 mM K2SO4 solution; 140 mM for the 200 mM K2SO4 solution; 60 mM for the 50 mM K2SO4 solution; and 2 mM for the 1 mM K2SO4 solution. TBA was dissolved directly into the bath solution at the desired concentration. MTSET (Toronto Research Chemicals Inc.) was added into the recording saline directly before use. EBIO (Tocris Cookson Inc.) was first dissolved in DMSO and then diluted in the experimental solution. ### Rapid Solution Changes Internal solution changes in inside-out recordings were performed using an RSC-160 rapid solution changer system (BioLogic). The bath solution could be fully exchanged within <30 ms as measured by the variation in patch pipette resistance when BaCl2 (10 mM)-containing patch electrodes were exposed to a 200 mM KCl plus 200 μM K2SO4 bath solution. Typically, Ca2+-free and TBA-containing bath solutions were perfused in successive 4-s periods, separated by 5-s washouts with the control solution. ### Patch Clamp Recordings Single channel recordings were performed in the inside-out patch clamp configuration using a List EPC-7 amplifier (List Medical). Patch pipettes were pulled from borosilicate capillaries using a Narishige pipette puller (Model PP-83) and used uncoated. The resistance of the patch electrodes ranged from 4 to 6 mΩ. Data acquisition was performed using a TL-1 DMA interface (Axon Instruments) at a sampling rate of 1.0 kHz with filtering at 500 Hz. Experiments were performed at room temperature (22°C). ### TBA Protection Experiments TBA protection experiments were performed by measuring the change in MTSET accessibility to cysteines engineered either at position 275 or 283 in the presence or absence of TBA in the internal solution. Basically, MTSET (5 mM) was applied for 1 s during single 2-s TBA application (5 mM). Each TBA application was followed by a 2-s washout period with the standard 200 K2SO4 solution (see Fig. 3). Control experiments performed without TBA were performed according to the same perfusion protocol. ### Data Analysis Kinetics of intracellular TBA block were determined according to the following scheme: where B is the concentration of the blocking agent, K12 and K21 the rates of channel opening and closing, respectively, K12B and K21B the rates of channel opening and closing with the channel in the blocked configuration, K3 the entry rate in μM−1s−1 of the blocking agent, and K4 the dissociation rate of the blocker (for example see Holmgren et al., 1997). K12 and K21 represent in this case the rates of opening and closing seen by the blocking agent averaged over all the channel states leading to observable transitions (see appendix in Garneau et al., 2003). It is assumed in Scheme 1 that the blocker cannot enter the channel when in the closed configuration. It follows from this scheme that the fraction of current block fB is given by $\mathrm{f}_{\mathrm{B}}=\frac{\mathrm{I}_{\mathrm{B}}}{\mathrm{I}_{\mathrm{Max}}}=\frac{1}{\left(1+\frac{\mathrm{B}}{\mathrm{IC}_{50}}\right)}\mathrm{,}$ (1) with IMax and IB the currents before and after application of the blocking agent and $\mathrm{IC}_{50}=\frac{\mathrm{K}_{4}\mathrm{{\zeta}}}{\mathrm{K}_{3}}\mathrm{,}$ (2) where ζ = PoB/Po with Po = K12/(K12 + K21) is the open probability of the channel before inhibition by the blocker (Ding and Horn, 2002), and PoB = K12B/(K12B + K21B) the probability that the channel will be in the open blocked configuration. If the binding of the blocker to the channel does not modify gating (ζ = 1), it follows from Eq. 2 that IC50 becomes independent of the channel open probability. The blocker effective exit rate, K4Poζ, can be obtained by measuring the rate at which the macroscopic current recovers after removal of the blocker. According to the Scheme 1, current recovery after removal of the blocker is given by $\mathrm{I}\left(\mathrm{t}\right)=\mathrm{I}_{\mathrm{Max}}+\mathrm{A1e}^{\mathrm{{-}}\left(\mathrm{K}_{12}+\mathrm{K}_{21}\right)\mathrm{t}}+\mathrm{A2e}^{\mathrm{{-}{\omega}1t}}+\mathrm{A3e}^{\mathrm{{-}{\omega}2t}}\mathrm{,}$ (3) where A1, A2, and A3 are constants and ω1 and ω2 transitions rates such that $\mathrm{{\omega}}1+\mathrm{{\omega}}2=\mathrm{K}_{4}+\mathrm{K}_{12}^{\mathrm{B}}+\mathrm{K}_{21}^{\mathrm{B}}$ (4) $\mathrm{{\omega}}1\mathrm{{\omega}}2=\mathrm{K}_{4}\mathrm{K}_{12}^{\mathrm{B}}\mathrm{.}$ (5) In conditions where the dissociation rate is slow (K12B + K21B >> K4), ω1 and ω2 can be approximated as $\mathrm{{\omega}}1{\cong}\mathrm{K}_{12}^{\mathrm{B}}+\mathrm{K}_{21}^{\mathrm{B}}$ (6) and $\mathrm{{\omega}2}{\cong}\mathrm{K}_{4}\frac{\mathrm{K}_{12}^{\mathrm{B}}}{\left(\mathrm{K}_{12}^{\mathrm{B}}+\mathrm{K}_{21}^{\mathrm{B}}\right)}\mathrm{.}$ (7) Assuming in addition that K12 + K21 >> K4, Eq. 3 reduces to a single exponential with a time constant τon given by $\mathrm{{\tau}}_{\mathrm{on}}=\frac{1}{\mathrm{{\omega}2}}=\frac{1}{\mathrm{K}_{4}\mathrm{Po{\zeta}}}\mathrm{.}$ (8) It follows from Eq. 2 that the effective entry rate of the blocker can now be obtained from $\mathrm{K}_{3}\mathrm{Po}=\frac{1}{\mathrm{{\tau}}_{\mathrm{on}}\mathrm{IC}_{50}}\mathrm{.}$ (9) In the present study, IB and IMax were estimated using the QuB package (Qin et al., 1996, 1997). The time constant τon was obtained from the time course of the current recovery after TBA removal fitted to a single exponential function using the Origin 6.1 software (Origin; Microcal Software Inc.). IC50 values were computed by fitting the TBA dose–response inhibition curves to Eq. 1 using the logistic function in Origin 6.1. The analytic solution of the kinetic scheme presented in Fig. 6 A and model-based simulations were generated with the Mathematica 4.1 software (Wolfram Research Inc.). In conditions where single channel events could be recorded, the single channel conductance was estimated from current amplitude histograms as described previously (Morier and Sauvé, 1994). For multichannel recordings, Po was determined from noise analysis by measuring the ratio $\frac{\mathrm{{\sigma}}^{2}}{\mathrm{{<}I>}}=\left(1{-}\mathrm{Po}\right)\mathrm{Io}$ (10) as a function of the applied voltage V with σ2 the steady-state current variance, <I> the current mean value, and Io the channel unitary current. Po was computed as $\mathrm{Po}=1{-}\frac{\mathrm{{\Lambda}}_{\mathrm{noise}}}{\mathrm{{\Lambda}}_{\mathrm{single\ channel}}}\mathrm{,}$ (11) where Λnoise is the conductance derived from the plot of σ2/<I> as a function of V and Λ single channel the unitary channel conductance. ### Statistical Analysis Statistical significance was analyzed using unpaired Student's t test. P < 0.01 was considered statistically significant. ### Homology Modeling Automated homology modeling was performed with Modeller V6.1 (Sali and Blundell, 1993) and involved the generation of 50 models of the IKCa channel pore using the MthK and KcsA channel structures as templates (Protein Data Bank entry 1LNQ). Energy minimization was carried on the model with the lowest objective function (roughly related to the energy of the model) using CHARMm. ### Electrostatic Energy Profile The atomic structure of the IKCa model was inserted in a 25-Å-thick membrane represented as a continuum medium with a dielectric constant of 2. No electrolyte was included in the bulk solution and in the potassium channel central cavity, but a 17-Å diameter cylindrical aqueous pore with a dielectric constant of 80 was added along the pore axis (z). The electrostatic contribution to the free energy needed to transfer a K+ from the bulk solution to a position z along the channel pore was calculated as $\mathrm{{\Delta}{\Delta}G}_{\mathrm{elec,i(z)}}=\left(\mathrm{{\Delta}G}_{\mathrm{i(z)-c}}{-}\mathrm{{\Delta}G}_{\mathrm{c}}{-}\mathrm{{\Delta}G}_{\mathrm{i(z)}}\right)\mathrm{,}$ (12) where ΔGi(z)-c is the electrostatic energy of the channel with an ion at the position z with x = y = 0, ΔGc is the electrostatic energy of the channel with no ion, and ΔGi(z) the electrostatic energy of the K+ ion in the bulk solution. The finite-difference calculations were performed using the PBEQ module of the biomolecular simulation program CHARMm (for example see Roux, 1997). The numerical calculations were performed using a standard relaxation algorithm (Warwicker and Watson, 1982). The complete system was mapped onto a cubic grid, and the Poisson equation solved numerically. The total electrostatic potential was calculated at each point of the grid by solving the finite difference Poisson equation. Calculations were performed in two steps, first using spacing of 1.0 Å (130 points, with periodic boundary conditions in the membrane plane), followed by more precise calculations around the main region with a grid spacing of 0.5 Å. A hydrogen minimization procedure was performed between each ion position. ## Results ### Block of IKCa Wild Type by TBA TBA has been documented to block the pore of a wide variety of K+ channels by entering the open channel from the cytoplasmic side up to the channel inner cavity. Experiments were conducted to characterize the effects of TBA on wild-type IKCa channels expressed in Xenopus laevis oocytes. Fig. 2 A shows representative inside-out current traces in which TBA was applied internally at a constant membrane potential of −60 mV. As seen, application of TBA at concentrations ranging from 50 to 800 μM caused a dose-dependent inhibition of the IKCa current that was fully reversible after washout of the QA ion. In addition, the time course of the current recovery after TBA washout is shown to be accounted for by a single exponential (see Eqs. 38). The dose–response curve for current inhibition measured at −60 mV is presented in Fig. 2 B. Data points could be well fitted to Eq. 1 with IC50 equal to 192 ± 7 μM (n = 12), indicating a bimolecular reaction involving one inhibitor per ion channel as hypothesized in the kinetic Scheme 1. Crystallization of the bacterial channel KcsA in the presence of TBA has provided direct evidence for TBA binding in the channel central cavity (Zhou et al., 2001). An analysis of the TBA binding site in the closed KcsA structure indicates that the external Van der Waals surface of TBA is in close contact with the T75 and I100 pore lining residues. The 3D model of the closed IKCa we derived through homology modeling using the KcsA channel as template suggests a structural equivalence between I100 in KcsA and V275 in IKCa (Simoes et al., 2002). This prediction was confirmed by SCAM experiments where the V275C mutant channel in the open state was strongly inhibited by the positively charged MTSET reagent applied internally (Simoes et al., 2002). Fig. 1 shows a superimposed representation of the proposed IKCa channel model structures in the closed and open configurations. The structure of the open channel was obtained by homology modeling with MthK as template (see materials and methods). In the open configuration, the residue V275 is predicted to be lining the IKCa channel central cavity. In contrast, the A283 residue is expected to be located in the channel inner vestibule at the entrance of the cavity region. Notably, internal application of MTSET to the A283C mutant, resulted in an increase in channel activity, coupled to a partial inhibition of the single channel currents (Simoes et al., 2002). To identify the TBA binding site in the IKCa channel, inside-out experiments were undertaken to evaluate the ability of TBA to protect cysteines engineered either at position 275 or 283 against a chemical modification by the MTSET reagent (see materials and methods). An example of a TBA protection experiment with the V275C channel is presented in Fig. 3 A. As seen, 5 mM TBA completely and reversibly blocked the V275C currents. The change in MTSET accessibility due to the presence of TBA is summarized in Fig. 3 B. These results show an eightfold increase in the time constant for MTSET-induced inhibition from 18 ± 1 s (n = 2) in the absence of TBA, to 147 ± 5 s (n = 4) with TBA. This observation indicates that TBA had access to a site close enough to V275 as to interfere with the accessibility of MTSET to the cysteine at position 275, in agreement with the structural data of the KcsA + TBA complex (Zhou et al., 2001). In contrast, the results in Fig. 3 C show that TBA failed to affect the time course of the stimulatory action of MTSET on the A283C channel, indicating that the TBA binding site is located closer to the cavity region than to the inner vestibule. ### TBA Block and IKCa Channel Open Probability The analytical expression presented in Eq. 2 predicts that the concentration for half inhibition, IC50, should depend on the parameter ζ = PoB/Po, which accounts for the change in open probability due to the presence of TBA in the channel cavity (see materials and methods). As a result, IC50 measurements should be independent of the channel open probability, provided the channel gating behavior is not affected by the binding of TBA to its site (ζ = 1). This hypothesis was tested by modifying the channel open probability using the IKCa opener EBIO. An example of inside-out recording illustrating the effects of EBIO applied internally is presented in Fig. 4 A. As seen, the addition of internal EBIO led to a substantial increase in the current mean value and variance. Noise analysis performed on the recordings before and after the addition of 100 μM EBIO to the internal medium revealed an increase in the channel open probability Po from 0.17 ± 0.08 (n = 6) to 0.50 ± 0.09 (n = 6) (see Eq. 11 and Fig. 4 D). The effect of EBIO (100 μM) on the dose response curve of the IKCa block by TBA is illustrated in Fig. 4 B. Our results show a significant decrease of the IC50 value from 298 ± 20 μM (n = 11) in the absence of EBIO to 192 ± 7 μM (n = 12) in EBIO conditions (P < 0.0001). These results indicate that the presence of TBA in the channel cavity affects gating. ### Voltage Dependence of the TBA Block Fig. 5 A summarizes the effect of voltage on the TBA dose–response curve for voltages ranging from −30 to −120 mV, measured in EBIO conditions. As seen, negative membrane voltages resulted in a rightward shift of the TBA dose–response curve. The variation in IC50 as a function of voltage is presented in Fig. 5 B. Clearly, the voltage dependence of the TBA block shows a complex behavior with a stronger voltage dependence at negative than at positive potentials. In the former case, the data could be approximated to a single exponential function of the form IC50 = IC50(0) exp(−δVq/KT), where δ is the fraction of the transmembrane potential through which internal TBA moves to reach its site (Woodhull, 1973), V the applied voltage, q, K, and T the electrical charge, the Boltzmann constant, and the temperature, respectively. Estimations of the electrical distance δ within the voltage range −120 to −30 mV led to a value of 0.49 ± 0.02 (n = 6). ### Channel Gating and TBA Block According to Scheme 1, it is hypothesized that TBA can be trapped inside the channel cavity upon closing. The effect of changing the channel open probability on the voltage dependence of the TBA entry and exit rates was thus investigated using EBIO as stimulating agent. As seen in Fig. 5 (C and D), stimulation by EBIO increased the effective entry (PoK3) and exit (Po ζ K4) rates 3.8-fold and 2.7-fold, respectively, over the whole voltage range with no significant change in the voltage dependence of the TBA block. The observation that the TBA exit rate depends on the channel open probability supports the linear kinetic scheme proposed in Scheme 1 and suggests that TBA can be trapped in the cavity upon channel closing. This proposal is also supported by the results presented in Fig. 5 D, where the unbiased entry rates K3 (diamonds) could be estimated from the effective entry rates PoK3 measured either in the absence or presence of EBIO, using Po values equal to 0.13 and 0.49 in control and EBIO conditions, respectively. The latter values are well within the Po range estimated by noise analysis (Fig. 4 D). Finally, the data in Fig. 5 C show that the TBA exit rate decreased an e-fold factor per 85 mV over the voltage range −120 to 0 mV for an electrical distance δ = 0.29. In contrast, the effective entry rate Po K3 increased with an e-fold factor per 150 mV over the same voltage range for a δ value corresponding to 0.16. Interestingly, the apparent electrical distances δ obtained for the kinetic parameters of TBA block (δentry + δexit = 0.45) are in good agreement with the equilibrium δ = 0.49 obtained from the changes in IC50 as a function of voltage. ### Modeling of the Voltage Dependence of the TBA Block According to electrostatic potential calculations based on the MthK crystal structure, the channel cavity and the cytoplasmic medium should form a continuous isopotential region (Jiang et al., 2002b). This property reflects in essence the broad opening of the vestibule predicted by the MthK structure (Fig. 1). Fig. 6 B presents the membrane potential profile obtained by solving the Poisson-Boltzmann equation for the TM5-pore-TM6 region derived by homology modeling for the wild-type IKCa (Fig. 1). These calculations indicate that the potential difference between the cavity (z = 0) and the cytoplasmic medium accounts for <16% of the potential applied across the membrane with 81% of the voltage drop restricted to the selectivity filter. In turn, the difference in potential between adjacent sites within the selectivity filter ([S2-S1], [S3-S2], [S4-S3]) should represent 23% of the membrane potential compared with 12% between the S0 and S1 binding sites and 3% between the cavity (S5) and the S4 site. Finally, there should be no difference in potential between the external binding site S0 and the external solution. On the basis of the proposed model for the open IKCa channel, it is clear that a simple model whereby the voltage dependence of the TBA block arises from the difference in potential between the internal medium and the TBA binding site cannot account for an electrical distance δ of 0.49 as observed experimentally (Fig. 5 B). A minimal kinetic scheme describing the blocking action of TBA within the channel pore is shown in Fig. 6 A. A similar model has already been described by Heginbotham and Kutluay (2004). In many respects, this model incorporates some of the features of models previously proposed to account for the effect of external and internal permeant ions on the Kir1.1 and Shaker channels (Spassova and Lu, 1998, 1999; Thompson and Begenisich, 2003a,b). The model in Fig. 6 A includes the essential features of the single file diffusion process in the selectivity filter recently described for the KcsA channel for K+ ion concentrations within the range of our experimental conditions (K+ ion activity of 140 mM) (Berneche and Roux, 2003). In the unblocked mode, K+ ion efflux is seen as a sequence of changes in the ion occupancy state of the pore with [S3,S1] ↔ [S5,S3,S1] ↔ [S4,S2,S0] ↔ [S4,S2] and back to [S3,S1]. The sites referred to as S0 and S5 are located outside the selectivity filter and correspond to the channel external K+ binding site and central cavity, respectively. The model also considers the possibility of a K+ ion in S5 with S4 occupied (states [S5,S4,S2] and [S5,S4,S2,S0]). An interaction factor termed “f” has in this case been introduced to account for the change in K+ entry and exit rates ki and ke due to the presence of a K+ ion in S4. The rates describing the transitions [S5,S3,S1] ↔ [S5,S4,S2] and [S3,S1] ↔ [S4,S2] become in this case related, so that k3/k4 = f2 (k1/k2). Fig. 6 C presents the free energy profiles calculated for a K+ ion along the pore axis for the [S4,S2] and [S3,S1] filter configurations. These calculations predict a maximum difference of 1.8 kcal/M between the [S5,S4,S2] and [S5,S3,S1] configurations, for an f factor corresponding approximately to 0.22. Calculations were first performed to determine to what extent the model proposed in Fig. 6 A accounts for the channel current/voltage characteristics. The continuous line in Fig. 4 C represents the prediction of the model. Best results were obtained assuming a K+ binding affinity in S0 (kx/ko) and S5 (ke(0)/ki(0)) of 45 mM and 70 mM, respectively, with a ratio k1(0)/k2(0) of 0.3. The difference between the [S4,S2] ↔ [S3,S1] transition rates k1(0) and k2(0) accounts for most of the channel rectification, and may be related to the fast blocking action of divalent cations such as Ca2+ at a site close to S4 (Soh and Park, 2002). In these calculations, the fraction of potential drop between the cavity and the external medium α was set to 0.84 as suggested by the potential profile presented in Fig. 6 B. Clearly the model in Fig. 6 A in which the voltage dependence of the rate constants is determined according to Fig. 6 B, satisfactory describes the channel current–voltage relationship (Fig. 4 C). The blocking action of TBA was next modeled assuming that the blocking agent cannot enter S5 (channel cavity) when the site is already occupied by a K+ ion ([S5,S3,S1], [S5,S4,S2], and [S5,S4,S2, S0]). Again, the presence of TBA in S5 is likely to affect the transition [B,S3,S1] ↔ [B,S4,S2] by shifting the equilibrium toward the [S3,S1] filter configuration. If the location of TBA binding site corresponds to S5, the transition [B,S3,S1] ↔ [B,S4,S2] should be such that kB1/kB2 = k3/k4. Strong interactions between TBA and the K+ ions in the selectivity filter have already been postulated (French and Shoukimas, 1981) but never derived from structural considerations (Guo and Lu, 2001; Thompson and Begenisich, 2003b). In the model for TBA block proposed in Fig. 6 A, the entry rate of TBA is assumed to depend on the actual ion occupancy state of the pore with entry rates KB31 = KB31(0)exp(0.5(1 − β)Vq/KT), KB32 = KB32(0)exp(0.5(1 − β)Vq/KT), and KB33 = KB33(0)exp(0.5(1 − β)Vq/KT), when the pore is in state [S4,S2], [S4,S2,S0], and [S3,S1], respectively (for example see MacKinnon and Miller, 1988; Thompson and Begenisich, 2003a). The parameter β refers to the fraction of the potential that is applied between the TBA binding site and the external medium. In conditions where the TBA binding site corresponds exactly to the channel central cavity, we have β = α ≅ 0.84 (Fig. 6 B). As the ion occupancy in these sites can be considered in equilibrium relative to the entry and exit rates of TBA, the average number of transitions between the unblocked and the blocked pore configuration can be expressed as \begin{eqnarray}&&\mathrm{{<}K}_{\mathrm{B}}3\mathrm{>}=\mathrm{e}^{\left(0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}\left[\mathrm{K}_{\mathrm{B}}\mathrm{31(0)P}\left[\mathrm{S4,S2}\right]\right.\ \\&&\left.\ +\right.\ \\&&\left.\ \mathrm{K}_{\mathrm{B}}\mathrm{32(0)P}\left[\mathrm{S4,S2,S0}\right]+\mathrm{K}_{\mathrm{B}}\mathrm{33(0)P}\left[\mathrm{S3,S1}\right]\right]\mathrm{,}\end{eqnarray} (13) where P[S3,S1], P[S4,S2], and P[S4,S2,S0] are the probabilities for the unblocked channel selectivity filter to be in the [S3,S1], [S4,S2], or [S4,S2,S0] configurations, respectively. The variations in P[S3,S1], P[S4,S2], and P[S4,S2,S0] computed as a function of voltage are presented in Fig. 7 A. As seen, the probability of the [S4,S2] state is highly favored at negative potentials, whereas positive potentials increase the probability of the [S4,S2,S0] filter state. For potentials ranging from −100 to −30 mV, the probability of the state [S3,S1] appeared to vary within <15%. This analysis shows that the voltage dependence of the entry rate <KB3> predicted by Eq. 13, is expected to vary as a function of voltage in a complex manner. In the blocked configuration, the exit rate of the blocking agent is assumed to depend similarly upon the ion occupancy state of the channel filter with exit rates KB41 = KB41(0)exp(−0.5(1 − β)Vq/KT), KB42 = KB42(0)exp(−0.5(1 − β)Vq/KT), and KB43 = KB43(0)exp(−0.5(1 − β)Vq/KT) when the pore is in state [B,S4,S2], [B,S4,S2,S0], and [B,S3,S1], respectively. The average exit rate <KB4> then reads \begin{eqnarray}&&\mathrm{{<}K}_{\mathrm{B}}4\mathrm{>}=\mathrm{e}^{\left(\mathrm{{-}}0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}\left[\mathrm{K}_{\mathrm{B}}4\mathrm{1(0)P}\left[\mathrm{B,}S\mathrm{4,S2}\right]\right.\ \\&&\left.\ +\mathrm{K}_{\mathrm{B}}\mathrm{42(0)P}\left[\mathrm{B,S4,S2,S0}\right]+\mathrm{K}_{\mathrm{B}}\mathrm{43(0)P}\left[\mathrm{B,S3,S1}\right]\right]\mathrm{,}\end{eqnarray} (14) where P[B,S4,S2], P[B,S4,S2,S0], and P[B,S3,S1] are the probabilities for the filter to be in the [B,S4,S2], [B,S4,S2,S0], and [B,S3,S1] configuration for the blocked channel. In conditions where KB41(0) ≅ KB42(0) = Kout, the mean rate of transitions <KB4> reduces to \begin{eqnarray}&&\mathrm{{<}K}_{\mathrm{B}}4\mathrm{>}=\\&&\frac{\mathrm{K}_{\mathrm{out}}\mathrm{e}^{\left(\mathrm{{-}}0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}}{\left(1+\mathrm{Kb}\right)}+\frac{\mathrm{K}_{\mathrm{B}}\mathrm{43(0)e}^{\left(\mathrm{{-}}0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}\mathrm{Kb}}{\left(1+\mathrm{Kb}\right)}\end{eqnarray} (15) with $\mathrm{Kb}=\mathrm{Ke}\left(1+\frac{\mathrm{Co}}{\mathrm{Ko}}\right)\mathrm{,}$ (16) where Co is the external potassium ion concentration, Ke = [kB1(0)/kB2(0)]exp(−0.46 Vq/KT) and Ko = kX/kO the affinity of the external site (S0) for K+. It is important to notice that if the blocker exit rate were assumed to be independent of the ion occupancy state of the filter (KB41(0) ≅ KB42(0) ≅ KB43(0) = Kout), the voltage dependence of <KB4> would become 0.5(1 − β) with β = 0.84. This would correspond to an e-fold change in <KB4> per 310 mV, which was never observed experimentally. The continuous line in Fig. 5 C shows the predicted voltage dependence of the exit rate for the wild-type IKCa channel as computed from Eq. 14. Calculations were performed using the values of k3, k4, kx, and ko obtained by curve fitting the model to the channel I/V curve with in addition kB1= k3 and kB2 = k4. Data points could be best accounted for with KB41(0), KB42(0), and KB43(0) equal to 2.9 s−1, 10.4 s−1, and 0.63 s−1 in control conditions and 8 s−1, 28 s−1, and 1.7 s−1 in the presence of EBIO, respectively. Clearly, the model presented in Fig. 6 A can account for the voltage dependence of the TBA exit rate. The continuous line in Fig. 5 B shows the predicted voltage dependence of IC50 for voltages ranging from −150 to +150 mV. IC50 values were computed as the ratio of <KB4>/<KB3> with KB31(0), KB32(0), and KB33(0) as unique adjustable parameters. Best results were obtained with KB31(0), KB32(0), and KB33(0) equal to 0.022 s−1μM−1, 0.07 s−1μM−1, and 0.1 s−1μM−1 in the presence of EBIO and 0.006 s−1μM−1, 0.02 s−1μM−1, and 0.026 s−1μM−1 in control conditions, respectively. As seen, the model presented in Fig. 6 A successfully predicts a voltage dependence with δ = 0.49 over the voltage range −150 to −30 mV, despite a potential profile where only 16% of the transmembrane potential is effectively applied between the channel cavity and the cytoplasmic medium. Globally these results indicate that the voltage dependence of the internal TBA block reflects for the most part an interaction of TBA with the K+ ions in the selectivity filter with a limited contribution coming from the difference in potential between the internal medium and the TBA binding site. ### Effect of the External K+ Concentration on IKCa Blockade by TBA One of the main features of the model presented in Fig. 6 A concerns the effect of the internal and external K+ concentrations on the kinetics of the TBA block. Eq. 16 predicts for instance that the exit rate <KB4> should be a function of the external K+ ion concentration (Co) with <KB4> increasing at higher Co values. Fig. 7 B shows the voltage dependence of the TBA blockade for external K+ ion activities ranging from 60 to 225 mM. As seen, increasing Co resulted, as expected, in a voltage-dependent increase in IC50. For instance, the IC50 measured at −90 mV for a K+ ion activity of 60 mM was estimated at 203 ± 9 μM (n = 4) as compared with 437 ± 26 μM (n = 4) in 225 mM external K+ ion conditions. Increasing Co resulted also in a variation of the apparent electrical distance δ obtained by curve fitting the data points to IC50 = IC50(0)exp(−δVq/KT) for −150 mV < V < −30 mV. This analysis led to δ values of 0.44 ± 0.01 (n = 4), 0.49 ± 0.02 (n = 6), and 0.52 ± 0.03 (n = 4) for 60, 140, and 225 mM external K+, respectively. These results indicated that the apparent voltage dependence of the TBA block not only depends on the structural parameters underlying the transmembrane potential profile but also on the parameters that control ion flux. The predictions of the model described in Fig. 6 A are shown in Fig. 7 B as continuous lines. The proposed model is seen to successfully account for the voltage dependence of IC50 over the K+ activity range considered. Fig. 8 A presents a 3D plot of the expected variation in δ as a function of the external and internal K+ activities. The electrical distance δ was computed by fitting the predictions of the model for a given set of internal and external K+ activities to an equation of the form IC50 = IC50(0)exp(−δVq/KT) for −150 mV < V < −30 mV. This analysis revealed that increasing external K+ activity up to 50 mM results in a systematic increase in δ independently of the internal K+ activity. For external K+ activities >50 mM, the predicted voltage dependence of the TBA block is exclusively a function of the internal K+ level. For instance, with an internal K+ ion activity of 140 mM, the electrical distance δ was estimated at 0.44, 0.47, and 0.46 in 60, 140, and 225 mM external K+, respectively. This is well within the values measured experimentally, despite the fact that the results in Fig. 7 B point toward a stronger increase in δ at high external K+ activities. ### Effect of the Internal K+ Concentration on IKCa Blockade by TBA Fig. 7 C presents the effect of internal K+ (Ci) on the IKCa blockade by TBA. Reducing Ci appeared to facilitate the blocking action of internal TBA, as expected for a system where the presence of a K+ ion in S5 prevents the entry of TBA in the cavity. For instance, the TBA concentration for half inhibition at −30 mV decreased from 113 ± 5 μM (n = 6) in 140 mM, to 53 ± 10 μM (n = 3) in 2 mM internal K+ conditions. The voltage dependence of the TBA block in low (2 mM) and high (140 mM) internal K+ is also illustrated in Fig. 7 C. Clearly, the voltage sensitivity of the block over the voltage range −150 to −30 mV is increased by lowering internal concentration of K+, with an electrical distance δ equal to 0.54 ± 0.01 (n = 3) in 2 mM internal/140 mM external K+ conditions, as compared with 0.49 ± 0.02 (n = 6) in symmetrical 140 mM/140 mM K+, respectively. The predictions of the model proposed in Fig. 6 A are represented as continuous lines (Fig. 7 C). The model was found to satisfactorily account for the variation in the voltage dependence of IC50 as a function of Ci, and correctly predict that decreasing Ci should lead to a decrease in δ independently of Co (Fig. 8 A). In 140 mM external K+ for instance, the model predicts an apparent electrical distance δ of 0.56 in 2 mM internal K+, which is in accordance with the electrical distance observed experimentally. ### Effect of V275 Mutations on the Voltage Dependence of the TBA Block The results by Zhou et al. (2001) and the observations in Fig. 3 strongly suggest that the TBA interaction site is located in close proximity of the cavity lining residue V275. On this basis, we hypothesized that a shift of the TBA position relative to the selectivity filter, obtained by mutating V275, might affect the voltage dependence of the TBA block through an effect on the interactions between the blocking agent and the ions in the selectivity filter. Examples of reversible current block measured at increasing doses of TBA for the V275A, V275L, and V275C mutants are illustrated in Fig. 9 A. The resulting TBA–current inhibition dose–response curves measured at −60 mV in symmetrical 140 mM K+ + 100 μM internal EBIO conditions are presented in Fig. 9 B. First of all, we observed that mutating the V275 residue had an effect on TBA affinity: the mutation V275C shifted the dose–response curve toward smaller concentrations from an IC50 of 192 ± 7 μM (n = 12) for wild type to 18 ± 2 μM (n = 4) for the V275C channel. In contrast, the V275A and V275L substitutions caused an increase of the IC50 value to 262 ± 29 μM (n = 6) and 607 ± 54 μM (n = 3), respectively. Notably, the substitution V275L was also found to decrease the channel conductance for inward currents by 50% with a unitary conductance of 21 ± 2 pS (n = 2) for voltages negative to −50 mV (unpublished data). The voltage dependence of the TBA block for the V275C, V275A, and V275L mutant channels is illustrated in Fig. 9 C. For voltages ranging from −150 to −30 mV, estimations of the equivalent electrical distance δ led to 0.50 ± 0.03 (n = 3), 0.72 ± 0.03 (n = 2), and 0.7 ± 0.06 (n = 3) for the V275L, V275C, and V275A mutants, respectively. Clearly, the extent of the changes in TBA binding affinity did not correlate with the changes in electrical distance. ## Discussion In this study, we showed that the transmembrane potential profile computed from a model structure of the open IKCa channel derived from MthK is compatible with the voltage dependence of the channel block by internal TBA. Since the 3D structure of IKCa has not yet been solved, we cannot rule out the possibility that the open IKCa structure might differ from MthK. However, we showed in this work that a functional model that incorporates an interaction mechanism between TBA and the ions in the selectivity filter, together with transmembrane potential and free energy profiles derived from a MthK-like structure, can globally account for the complex behavior of IKCa block by TBA. In addition, evidence is presented that the voltage dependence of the TBA block can be modified by mutating the cavity lining V275 residue, suggesting that TBA position relative to the selectivity filter is important to the voltage dependence of the block. Finally, our data indicate that a model of TBA block derived from a MthK-like structure absolutely requires TBA to interact with the ions in the selectivity filter. ### TBA Block in K+ Selective Channels Quaternary alkylammonium ions have been used as probes to investigate the pore structure of a number of K+ selective channels. It is generally agreed that the mechanism of channel block by ammonium ion from the cytoplasmic side involves an entry step into the open channel up to the channel central cavity where it binds without passing through the selectivity filter. The blocking action of QA ions is thus likely to reflect the internal structure of specific classes of K+ channels. For instance, TBA was shown to block the inward rectifiers Kir2.1 and Kir1.1 at IC50(0) of 40 and 2 mM, respectively, with fractional electrical distances ≥1.0 arguing for an inner vestibule with single file diffusion properties (Guo and Lu, 2001). These values differ from the results reported in the present work with an IC50(0) of 70 μM and a fractional electrical distance at negative potentials δ of 0.49. Furthermore, the TBA entry rate for the Kir2.1 and Kir1.1 channels in zero current conditions (0 mV) was estimated at 0.004 μM−1s−1 compared with 0.07 μM−1s−1 in the present case. Clearly the inner pore region of IKCa seems to be less restrictive to TBA flow than that observed in Kir1.1 and Kir2.1. Fractional electrical distances ranging from 0.2 to 0.3 were reported for the voltage-gated Shaker and calcium-activated KCa1.1 channels, suggesting a weaker voltage dependence of the TBA block relative to IKCa (Villarroel et al., 1988; Choi et al., 1993; Ding and Horn, 2002; Thompson and Begenisich, 2003a; Li and Aldrich, 2004). However, the voltage sensitivity in both cases was measured at positive potentials in contrast to the protocols used in this work, where δ was estimated at negative potentials only. Fig. 8 B presents a 3D plot of the electrical distance δ computed from the model in Fig. 6 A for positive voltages within 0 to +90 mV as a function of internal and external potassium activities. As seen, the electrical distance δ appeared significantly smaller when computed for positive than negative potentials over the entire external and internal potassium concentration range. For instance, the plot in Fig. 8 B shows that δ increases monotonically as a function of external potassium with a value of 0.24 in 150 mM internal/5 mM external K+ and 0.32 in symmetrical 150 mM K+ conditions. These values are well in agreement with the results obtained for Shaker and KCa1.1 and confirm that the apparent electrical distance associated with the TBA blocking mechanism is voltage variable. Furthermore, the results in Fig. 8 B indicate that increasing the internal potassium ion activity should lead to an increase in δ, as reported for the Shaker channel (Thompson and Begenisich, 2003a). The fact that the electrical distance varied as a function of the applied potential truly reflects a strong interaction between TBA and the ions in the selectivity filter. Finally, our results provide evidence for a regulation of the TBA block by internal and external K+. In contrast to Shaker, competition by internal K+ was apparent even in the absence of an external blocking agent such as TEA, suggesting a higher ion occupancy of S5 in IKCa compared with Shaker (Thompson and Begenisich, 2003a). ### TBA Block and IKCa Gating The present work also provides evidence for a reduction of the TBA IC50(0) by EBIO. EBIO has been documented to modulate SK and IKCa channels by stabilizing the interactions between Ca2+-calmodulin and the channel α subunit (Pedarzani et al., 2001; von Hahn et al., 2001). An EBIO-dependent increase in Po could be detected by noise analysis at 25 μM internal Ca2+ but not in nominally Ca2+-free conditions (unpublished data). Our results would thus support a model whereby EBIO can activate IKCa at saturating Ca2+ concentrations, in contrast to other reports (Pedersen et al., 1999; Syme et al., 2000; Pedarzani et al., 2001). The observation that EBIO led to a decrease in IC50(0) indicates that the IKCa opener affected Po and PoB differently, with the ratio ζ (PoB/Po) becoming smaller after EBIO stimulation (see Eq. 2). One possible explanation would consist in PoB being higher than Po in the absence of EBIO, so that PoB would be relatively less affected by EBIO than Po. In support of this proposal is the observation of a 2.7-fold increase in PoB for a 3.8-fold increase in PoK3 in EBIO conditions (Fig. 5 C). Notably, the measured 3.8-fold increase in PoK3 elicited by EBIO fully correlates the Po increase estimated by noise analysis. These observations suggest therefore that the presence of TBA in the channel cavity affects the channel kinetic parameters as to either destabilize the channel closed configuration or stabilize the channel open state, or both. These results would be consistent with a model whereby TBA is trapped in the channel central cavity upon channel closing. Such a behavior would support a gating model where the TM6 helix bundle crossing in the closed configuration is small enough to constrict TBA flow from the channel central cavity to the internal medium. We cannot however rule out the possibility that the state dependency of the TBA block might result from a variation upon channel closing in the interactions between TBA and the pore residues involved in TBA binding. Such a mechanism would lead to a state-dependent kinetics of TBA block, without a trapping mechanism involving the TM6 bundle crossing (Li and Aldrich, 2004). ### Mutations of V275 and Voltage Dependence The present work shows that the voltage dependence of the TBA block is modified by mutating the cavity lining residue V275. Our results indicate for instance that the fractional distance δ measured over the voltage range −150 to −30 mV is increased from 0.49 to 0.70 by substituting the Val at 275 by either a Cys or an Ala, whereas the mutation V275L left δ unchanged. Mutating the V275 residue was also found to affect the binding affinity of the TBA receptor, but this effect appeared uncorrelated with the associated changes in δ. For instance, both V275C and V275A led to a δ value of 0.7 despite an IC50(0) for the V275C mutant 20 times smaller than for V275A. Similarly, the V275L mutation caused a threefold increase in IC50(0) relative to wild type without a significant change in δ. We cannot rule out, however, that part of the observed effects on IC50(0) may be related to a modification of the channel open probability, as indicated by our EBIO results. These observations differ somehow from the results obtained on Shaker, where changing the affinity of the external TEA receptor was reported to affect the voltage dependence of the TEA block (Heginbotham and MacKinnon, 1992). It was concluded in this case that the substitution Y499T moved the TEA binding site further into the pore. The electrostatic free energy profiles presented in Fig. 6 C, predict that the magnitude of the interactions between TBA and the ions in the selectivity filter should be highly sensitive to the position of TBA within the channel cavity (−3 Å < z <3 Å). In contrast, the results in Fig. 6 B show that a shift in TBA position over the same distance range should minimally affect the potential difference between the TBA binding site and the internal medium ([1 − β]). Fig. 10 presents the expected variation in electrical distance for TBA block at negative potentials calculated on the basis of the transmembrane potential and energy profiles illustrated in Fig. 6 (B and C). As seen, the electrical distance δ increased from 0.30 to 0.62 for z varying from −3 to 3 Å . In contrast, 1 − β changed from 0.12 to 0.18 over the same distance range. Clearly the proposed model for TBA block predicts an increase in δ measured at negative potentials that far exceeds the associated change in electrical distance 1 − β. The fact that the V275C and V275A mutations resulted in a TBA block with a stronger voltage dependence suggests, therefore, that the substitution of the Val at 275 (volume 140 Å3) by residues of smaller sizes (108 Å3 for Cys and 88 Å3 for Ala) enabled TBA to penetrate further into the pore, closer to the selectivity filter. It is possible that the substitutions V275C and V275A allowed TBA to move closer to the T250 residue located at the entrance of the channel selectivity filter. Notably, the crystal structure reported by Zhou et al. (2001) predicts that T250 and V275 should be close to TBA, potentially contributing to the formation of the TBA binding site. Mutating the Val at 275 to a larger residue such as Leu (166 Å3) did not seem to modify the position of the TBA relative to the selectivity filter, as the electrical distance δ remained unchanged. Our model could not, however, account for electrical distances >0.65, the electrostatic energy profiles illustrated in Fig. 6 C becoming less accurate for large interaction energies (z > 3 Å). Furthermore, we cannot rule out additional effects on the pore structure due to mutations at position 275 as the V275 residue is adjacent to the alleged TM6 gating hinge at G274. Finally, the observation that the V275L mutant showed a 50% smaller unitary conductance further demonstrated the importance of the 275 residue to the formation of the central cavity. In fact, the model in Fig. 6 A indicates that the 50% decrease in conductance with the V275L mutant can be ascribed to a decrease in the equilibrium constant k5(0)/k6(0), which accounts for the transitions of a K+ ion between S4 and the channel cavity. Globally, these results support the model proposed in Fig. 6 A, where most of the voltage dependence of the TBA block is due to the blocking agent sensing the ion occupancy state of the selectivity filter. ### Conclusion The data presented in this work show that the electrical distance δ, which describes the voltage dependence of blocking agents such as TBA, is voltage variable and does not simply reflect the actual difference in potential between the blocker binding site and the internal medium. Our results rather support a model where the voltage dependence of charged blockers is controlled to a large extent by the ion occupancy state of the selectivity filter. ## Acknowledgments We thank Dr. Benoit Roux for stimulating discussions and for providing a copy of the manuscript on the intracellular TEA block of the KcsA potassium channel prior to publication. We also acknowledge the work of Ms. Julie Verner for expert oocyte preparation. This work was supported by grants from the Canadian Institutes of Health Research (MOP 7769), from the Canadian Heart and Stroke Foundation, and from the Canadian Cystic Fibrosis Foundation. Olaf S. Andersen served as editor. Abbreviations used in this paper: EBIO, 1-ethyl-2-benzimidazolinone; MTS, methanethiosulfonate; MTSET, [2-(trimethylammonium) ethyl]methanethiosulfonate bromide; NMDG, N-methyl-d-glucamine; QA, quaternary ammonium; SCAM, substituted cysteine accessibility method; TBA, tetrabutylammonium. ## References Berneche, S., and B. 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Coupled ion movement underlies rectification in an inward-rectifier K+ channel. J. Gen. Physiol. 112 : 211 –221. Spassova, M., and Z. Lu. 1999 . Tuning the voltage dependence of tetraethylammonium block with permeant ions in an inward-rectifier K+ channel. J. Gen. Physiol. 114 : 415 –426. Syme, C.A., A.C. Gerlach, A.K. Singh, and D.C. Devor. 2000 . Pharmacological activation of cloned intermediate- and small-conductance Ca2+-activated K+ channels. Am. J. Physiol. Cell Physiol. 278 : C570 –C581. Thompson, J., and T. Begenisich. 2003 a. Functional identification of ion binding sites at the internal end of the pore in Shaker K+ channels. J. Physiol. 549 : 107 –120. Thompson, J., and T. Begenisich. 2003 b. External TEA block of shaker K+ channels is coupled to the movement of K+ ions within the selectivity filter. J. Gen. Physiol . 122 : 239 –246. Vandorpe, D.H., B.E. Shmukler, L. Jiang, B. Lim, J. Maylie, J.P. Adelman, L. de Franceschi, M.D. Cappellini, C. Brugnara, and S.L. Alper. 1998 . cDNA cloning and functional characterization of the mouse Ca2+-gated K+ channel, mIK1. Roles in regulatory volume decrease and erythroid differentiation. J. Biol. Chem. 273 : 21542 –21553. Vergara, C., R. Latorre, N.V. Marrion, and J.P. Adelman. 1998 . Calcium-activated potassium channel. Curr. Opin. Neurobiol. 8 : 321 –329. Villarroel, A., O. Alvarez, A. Oberhauser, and R. Latorre. 1988 . Probing a Ca2+-activated K+ channel with quaternary ammonium ions. Pflugers Arch. 413 : 118 –126. von Hahn, T., I. Thiele, L. Zingaro, K. Hamm, M. Garcia-Alzamora, M. Kottgen, M. Bleich, and R. Warth. 2001 . Characterisation of the rat SK4/IK1 K+ channel. Cell. Physiol. Biochem. 11 : 219 –230. Warth, R., K. Hamm, M. Bleich, K. Kunzelmann, T. von Hahn, R. Schreiber, E. Ullrich, M. Mengel, N. Trautmann, P. Kindle, et al. 1999 . Molecular and functional characterization of the small Ca2+-regulated K+ channel (rSK4) of colonic crypts. Pflugers Arch. 438 : 437 –444. Warwicker, J., and H.C. Watson. 1982 . Calculation of the electric potential in the active site cleft due to alpha-helix dipoles. J. Mol. Biol. 157 : 671 –679. Woodhull, A.M. 1973 . Ionic blockage of sodium channels in nerve. J. Gen. Physiol. 61 : 687 –708. Wulff, H., G.A. Gutman, M.D. Cahalan, and K.G. Chandy. 2001 . Delineation of the clotrimazole/TRAM-34 binding site on the intermediate conductance calcium-activated potassium channel, IKCa1. J. Biol. Chem. 276 : 32040 –32045. Zhou, M., J.H. Morais-Cabral, S. Mann, and R. MacKinnon. 2001 . Potassium channel receptor site for the inactivation gate and quaternary amine inhibitors. Nature. 411 : 657 –661.	2021-05-16 21:03:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47088560461997986, "perplexity": 3965.8603704832494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989914.60/warc/CC-MAIN-20210516201947-20210516231947-00385.warc.gz"}
https://www.mathdoubts.com/zero-power-rule/	# Zero Power Rule ## Formula $b^0 \,=\, 1$ The zero exponent with any base is equal to one, is called the zero power rule. ### Introduction The meaning of a number raise to the power zero is to write the number zero times but its value is one. Take, $b$ is a literal and $b$ raised to the power of zero is written as $b^0$ in exponential notation. The value of $b$ raised to the power of zero is equal to one. $b^0 \,=\, 1$ This identity in exponential form is called as zero exponent rule or zero power rule. #### Examples In this case, the literal $b$ can be any constant. $(1) \,\,\,\,\,\,$ $3^0 \,=\, 1$ $(2) \,\,\,\,\,\,$ $e^0 \,=\, 1$ $(3) \,\,\,\,\,\,$ $x^0 \,=\, 1$ ### Proof Learn how to derive the power rule for zero exponent in algebraic form. #### Verification $8^0$ is an exponential term. $8$ is base and zero is its exponent. The product of one and any exponential term is equal to same exponential term. $\implies$ $8^0 \,=\, 1 \times 8^0$ Now, write the number $1$ and write the base number $8$ zero times. $\implies$ $8^0 \,=\, 1$ Therefore, it is verified that any number raised to the power of zero is always equal to one. Latest Math Topics Apr 18, 2022 Apr 14, 2022 Mar 18, 2022 Latest Math Problems Apr 06, 2022 A best free mathematics education website for students, teachers and researchers. ###### Maths Topics Learn each topic of the mathematics easily with understandable proofs and visual animation graphics. ###### Maths Problems Learn how to solve the maths problems in different methods with understandable steps. Learn solutions ###### Subscribe us You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.	2022-05-20 13:13:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6350569725036621, "perplexity": 1409.704784822183}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662532032.9/warc/CC-MAIN-20220520124557-20220520154557-00700.warc.gz"}
https://www.physicsforums.com/threads/shear-stress-in-a-wooden-block.523201/	# Homework Help: Shear Stress In A Wooden Block 1. Aug 21, 2011 ### NinjaGodel 1. The problem statement, all variables and given/known data 2. Relevant equations $\sigma$ = F/A 3. The attempt at a solution I understand that I should evaluate the different forms of stress to find different values of the ultimate load. I also understand that I should choose the smallest value among them since anything greater than the smallest value will cause failure. I know how to calculate the normal stress in the block and the shear stress in the steel. I don't understand where shear stress occurs in the block and thus how to calculate it. 2. Aug 21, 2011 ### nvn NinjaGodel: Shear stress occurs uniformly on the two planes represented by the dashed lines. This is often referred to as "shear tear-out." Give it a try. Also, hint 1: Should Pu for tau_steel be two times what you currently computed? 3. Aug 21, 2011 ### NinjaGodel Ah yes it should be because it's in double shear I knew that So the double shear force on the block would go across this shaded surface area: Plus the inner face of the left block I drew Right? Thanks for your help by the way Last edited: Aug 21, 2011 4. Aug 21, 2011	2018-06-19 09:16:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5846453905105591, "perplexity": 1080.5170472169473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267861981.50/warc/CC-MAIN-20180619080121-20180619100121-00561.warc.gz"}
http://flr-project.org/FLBEIA/reference/create.biol.arrays.html	This function generates an FLBiol object, given the data inputs as arrays. Supported formats are Excel (xls and xlsx) and R format (RData). create.biol.arrays(filename, name = NA, ages, hist.yrs, sim.yrs, fbar = NULL, mean.yrs, excel = TRUE, unit = list()) ## Arguments filename A character vector with the name of the files containing the stock data. Supported formats are Excel (xls and xlsx) and R format (RData). In case of using R format, the information must be stored in data object (consisting in a list with the different elements). The following information is compulsory: abundances in numbers at age (n), mean weight at age (wt), maturity (mat), natural mortality (m), moment of the year when spawning occurs in percentage (spwn), fishing mortality at age (f) and catch in numbers at age (caa). For the rest of information, if not provided, default values are set. For example, fecundity (fec) is set to 1, landings and discard in numbers at age (laa and daa) are set to cca and 0, respectively. Finally for weights, if missing, weights at age for landings (wl) and discards (wd) are set to the weights in the population and weights at age for catch (wc) are set to the weighted mean of the weights of landings and discards. A character (optional) with the name of the stock. A numeric vector with the age classes of stock. A vector with the historical years. A vector with the simulation years. A numeric vector with the age range (min,max) to be used for estimating average fishing mortality. A vector with the years used to compute the mean to condition the parameters in the projection period. Logical. TRUE (default), if the data is provided in an Excel file and FALSE, if an RData object is used instead. A list with the units of the different elements included in filename. Unitless objects must be set to '' or character(1). This parameter is only required if excel==FALSE. When using Excell files the units are taken from the first row and column (cell A1) of each sheet. If the cell is empty then units are set to NA, in case of an unitless object then 1 must be inputed into cell A1. ## Value An FLBiol. FLBiol, create.fleets.arrays	2022-10-07 01:42:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48405343294143677, "perplexity": 3078.129623312654}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337906.7/warc/CC-MAIN-20221007014029-20221007044029-00071.warc.gz"}
https://stats.stackexchange.com/questions/232967/what-makes-the-mean-of-some-distributions-undefined	# What makes the mean of some distributions undefined? Many PDFs range from minus to positive infinity, yet some means are defined and some are not. What common trait makes some computable? • Convergent integrals. – Sycorax Sep 2 '16 at 3:08 • This distributions are mathematical abstractions. If the integral doesn't converge then mean is not defined. However, what's not mentioned in answers below is that PDFs with minus infinity to plus infinity cannot model real data sources. There is no such physical process to generate such data in real life. In my opinion all real data sources will be bounded and you will be able to approximate the mean. – Cagdas Ozgenc Sep 2 '16 at 12:56 • @Cagdas That remark does not appear to be correct. There are plenty of heavy-tailed processes. Their divergent expectations are manifest as extreme variability in long-run averages. For a convincing application of a Cauchy model, for instance, see Douglas Zare's post at stats.stackexchange.com/a/36037/919. – whuber Sep 2 '16 at 13:29 • @CagdasOzgenc: You should read Black Swan by Taleb to see just how wrong that reasoning is. While heuristically there might not be a process which perfectly generates a distribution with an undefined mean or infinite mean, there are plenty of examples where people underestimate just how fat the tails are of their distribution and proceed to calculate means, whereas the true distribution has a mean that is completely different and usually right-skewed. This kind of improper reasoning led to many risk-assessment gafs in finance where risk is underestimated by many orders of magnitude. – Alex R. Sep 2 '16 at 19:10 • @Cagdas Ozgenc: For a discussion why your argument is wrong see stats.stackexchange.com/questions/94402/… – kjetil b halvorsen Sep 8 '16 at 9:56 The mean of a distribution is defined in terms of an integral (I'll write it as if for a continuous distribution - as a Riemann integral, say - but the issue applies more generally; we can proceed to Stieltjes or Lebesgue integration to deal with these properly and all at once): $$E(X) = \int_{-\infty}^\infty x f(x)\, dx$$ But what does that mean? It's effectively a shorthand for $$\stackrel{\lim}{_{a\to\infty,b\to\infty}} \int_{-a}^b x\, f(x)\, dx$$ or $$\stackrel{\lim}{_{a\to\infty}} \int_{-a}^0 x f(x)\, dx \, +\, \stackrel{\lim}{_{b\to\infty}} \int_{0}^b x f(x)\, dx$$ (though you could break it anywhere not just at 0) The problem comes when the limits of those integrals are not finite. So for example, consider the standard Cauchy density, which is proportional to $\frac{1}{1+x^2}$ ... note that $$\stackrel{\lim}{_{b\to\infty}} \int_{0}^b \frac{x}{1+x^2}\, dx$$ let $u=1+x^2$, so $du=2x\,dx$ $$=\,\stackrel{\lim}{_{b\to\infty}}\frac12 \int_{1}^{1+b^2} \frac{1}{u}\, du$$ $$=\,\stackrel{\lim}{_{b\to\infty}} \frac{_1}{^2}\ln(u)\Bigg \|_{1}^{1+b^2}$$ $$=\,\stackrel{\lim}{_{b\to\infty}} \frac{_1}{^2}\ln(1+b^2)$$ which isn't finite. The limit in the lower half is also not finite; the expectation is thereby undefined. Or if we had as our random variable the absolute value of a standard Cauchy, its entire expectation would be proportional to that limit we just looked at (i.e. $\stackrel{\lim}{_{b\to\infty}} \frac12\ln(1+b^2)$). On the other hand, some other densities do continue out "to infinity" but their integral does have a limit. • You can (of course) also see the same thing in similar discrete probability distributions. Take a distribution where the probability if $n$ occurring, for integer $n>0$, is proportional to $\frac{1}{n^2}$. The sum of probabilities is finite (which is just as well since it needs to have limit 1: actually our constant must be $\frac{6}{\pi^2}$ or whatever it is), but since the sum of $\frac{1}{n}$ diverges it has no mean. Whereas if we choose a probability proportional to $\frac{1}{n^3}$ then the mean involves a sum of $\frac{1}{n^2}$ and we're fine, that's "small enough" that it converges. – Steve Jessop Sep 2 '16 at 11:27 • Yes, $\frac{6}{\pi^2}$ is the scaling constant for that (to make it sum to1). – Glen_b Sep 2 '16 at 11:45 General Abrial and Glen_b had perfect answers. I just want to add a small demo to show you the mean of Cauchy distribution does not exist / does not converge. In following experiment, you will see, even you get a large sample and calcluate the empirical mean from the sample, the numbers are quite different from experiment to experiment. set.seed(0) par(mfrow=c(1,2)) experiments=rep(1e5,100) mean_list_cauchy=sapply(experiments, function(n) mean(rcauchy(n))) mean_list_normal=sapply(experiments, function(n) mean(rnorm(n))) plot(mean_list_cauchy,ylim=c(-10,10)) plot(mean_list_normal,ylim=c(-10,10)) You can observe that we have $100$ experiments, and in each experiment, we sample $1\times 10^5$ points from two distributions, with such a big sample size, the empirical mean across different experiments should be fairly close to true mean. The results shows Cauchy distribution does not have a converging mean, but normal distribution has. EDIT: As @mark999 mentioned in the chat, we should argue the two distributions used in the experiment has similar "variance" (the reason I use quote is because Cauchy distribution variance is also undefined.). Here is the justification: their PDF are similar. Note that, by looking at the PDF of Cauchy distribution, we would guess it is $0$, but from the experiments we can see, it does not exist. That is the point of the demo. curve(dnorm, -8,8) curve(dcauchy, -8,8) • I don't think this shows that the Cauchy distribution has no mean. You could get similar results if you replaced the Cauchy distribution by a normal distribution with a suitably large variance. – mark999 Sep 2 '16 at 11:34 • good point @mark999, I will edit my answer to address this problem. – Haitao Du Sep 2 '16 at 11:41 • Is it possible to figure out from PDF of Cauchy distribution that it has no mean, probably by looking at it's fat tails ? – ks1322 Sep 2 '16 at 13:18 • Perhaps you had something like this in mind? stats.stackexchange.com/questions/90531/… – Sycorax Sep 2 '16 at 15:16 The other answers are good, but might not convince everyone, especially people who take one look at the Cauchy distribution (with $x_0 = 0$) and say it's still intuitively obvious that the mean should be zero. The reason the intuitive answer is not correct from the mathematical perspective is due to the Riemann rearrangement theorem (video). Effectively what you're doing when you're looking at a Cauchy and saying that the mean "should be zero" is that you're splitting down the "center" at zero, and then claiming the moments of the two sizes balance. Or in other words, you're implicitly doing an infinite sum with "half" the terms positive (the moments at each point to the right) and "half" the terms negative (the moments at each point to the left) and claiming it sums to zero. (For the technically minded: $\int_{0}^\infty f(x_0+r)r\, dr - \int_{0}^{\infty} f(x_0-r)r\, dr = 0$) The Riemann rearrangement theorem says that this type of infinite sum (one with both positive and negative terms) is only consistent if the two series (positive terms only and negative terms only) are each convergent when taken independently. If both sides (positive and negative) are divergent on their own, then you can come up with an order of summation of the terms such that it sums to any number. (Video above, starting at 6:50) So, yes, if you do the summation in a balanced manner from 0 out, the first moments from the Cauchy distribution cancel out. However, the (standard) definition of mean doesn't enforce this order of summation. You should be able to sum the moments in any order and have it be equally valid. Therefore, the mean of the Cauchy distribution is undefined - by judiciously choosing how you sum the moments, you can make them "balance" (or not) at practically any point. So to make the mean of a distribution defined, the two moment integrals need to each be independently convergent (finite) around the proposed mean (which, when you do the math, is really just another way of saying that the full integral ($\int_{-\infty}^\infty f(x)x\, dx$) needs to be convergent). If the tails are "fat" enough to make the moment for one side infinite, you're done. You can't balance it out with an infinite moment on the other side. I should mention that the "counter intuitive" behavior of things like the Cauchy distribution is entirely due to problems when thinking about infinity. Take the Cauchy distribution and chop off the tails - even arbitrarily far out, like at plus/minus the xkcd number - and (once re-normalized) you suddenly get something that's well behaved and has a defined mean. It's not the fat tails in-and-of-themselves that are an issue, it's how those tails behave as you approach infinity. • Nice. I wonder if its possible to give an exlicit "order of summation" that leads to, say, two. – Matthew Drury Sep 2 '16 at 20:56 • @MatthewDrury: p_i and n_i denote positive and negative numbers. Successively find p_i and n_i so that integral over [n_i , p_i] is 2+(1/i) and integral over [n_{i+1},p_i] is 2-(1/i). One could do this explicitly using R, matlab or mathematica, but only for a finite number of terms. – David Epstein Sep 8 '16 at 10:06 By definition of Lebesgue-Stieltjes integral, the mean exists if: $$\int \vert x\vert dF(x)<\infty.$$ https://en.wikipedia.org/wiki/Moment_(mathematics)#Significance_of_the_moments https://en.wikipedia.org/wiki/Lebesgue_integration The Cauchy distribution is a disguised form of a very fundamental distribution, namely the uniform distribution on a circle. In formulas, the infinitesimal probability is $d\theta/2\pi$, where $\theta$ is the angle coordinate. The probability (or measure) of an arc $A\subset \mathbb S^1$ is $\mathtt{length}(A)/2\pi$. This is different from the uniform distribution $U(-\pi,\pi)$, though measures are indeed the same for arcs not containing $\pi$. For example, on the arc from $\pi-\varepsilon$ counter-clockwise to $-\pi+\varepsilon\ (=\pi+\varepsilon \mod 2\pi)$, the mean of the distribution on the circle is $\pi$. But the mean of the uniform distribution $U(-\pi,\pi)$ on the corresponding union of two disjoint intervals, each of length $\varepsilon/2\pi$, is zero. Since the distribution on the circle is rotationally symmetric, there cannot be a mean, median or mode on the circle. Similarly, higher moments, such as variance, cannot make sense. This distribution arises naturally in many contexts. For example, my current project involves microscope images of cancerous tissue. The very numerous objects in the image are not symmetric and a "direction" can be assigned to each. The obvious null hypothesis is that these directions are uniformly distributed. To disguise the simplicity, let $\mathbb S^1$ be the standard unit circle, and let $p=(0,1)\in\mathbb S^1$. We define $x$ as a function of $\theta$ by stereographical projection of the circle from $p$ onto the $x$-axis. The formula is $x=\tan(\theta/2)$. Differentiating, we find $d\theta/2 = dx/(1+x^2)$. The infinitesimal probability is therefore $\frac{d\theta}{\pi(1+x^2)}$, the usual form of the Cauchy distribution, and "Hey, presto!", simplicity becomes a headache, requiring treatment by the subtleties of integration theory. In $\mathbb S^1 \setminus \{p\}$, we can ignore the absence of $p$ (in other words, reinstate $p\in\mathbb S^1$) for any consideration such as mean or higher order moment, because the probability of $p$ (its measure) is zero. So therefore the non-existence of mean and of higher moments carries over to the real line. However, there is now a special point, namely $-p = (0,-1)$, which maps to $0\in\mathbb R$ under stereographic projection and this becomes the median and mode of the Cauchy distribution. • The Cauchy distribution has a median and mode. – ogogmad Sep 9 '16 at 12:51 • quite right. I got a bit carried away. But the argument for the non-existence of the mean is correct.. I will edit my answer. – David Epstein Sep 10 '16 at 13:01 • Why is it that "there cannot be a mean because there isn't one on the circle"? There's a lot missing in your argument. I'm assuming what you mean by it being the uniform distribution "on the circle" is that $\theta \sim U(-\pi,\pi)$ and $X = \tan(\theta/2)$, but then $\mathbb E[\theta] = 0$ so I don't understand what you're talking about. – ogogmad Sep 10 '16 at 13:41 • @jkabrg: I hope the new edits make this more comprehensible – David Epstein Sep 10 '16 at 14:56	2020-10-23 06:26:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9157067537307739, "perplexity": 475.06411975071904}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107880656.25/warc/CC-MAIN-20201023043931-20201023073931-00384.warc.gz"}
https://mathoverflow.net/questions/317100/a-putnam-problem-with-a-twist	# A Putnam problem with a twist This question is motivated by one of the problem set from this year's Putnam Examination. That is, Problem. Let $$S_1, S_2, \dots, S_{2^n-1}$$ be the nonempty subsets of $$\{1,2,\dots,n\}$$ in some order, and let $$M$$ be the $$(2^n-1) \times (2^n-1)$$ matrix whose $$(i,j)$$ entry is $$M_{ij} = \begin{cases} 0 & \mbox{if }S_i \cap S_j = \emptyset; \\ 1 & \mbox{otherwise.} \end{cases}$$ Calculate the determinant of $$M$$. Answer: If $$n=1$$ then $$\det M=1$$; else $$\det(M)=-1$$. I like to consider the following variant which got me puzzled. Question. Preserve the notation from above, let $$A$$ be the matrix whose $$(i,j)$$ entry is $$A_{ij} = \begin{cases} 1 & \# (S_i \cap S_j) =1; \\ 0 & \mbox{otherwise.} \end{cases}$$ If $$n>1$$, is this true? $$\det(A)=-\prod_{k=1}^nk^{\binom{n}k}.$$ Remark. Amusingly, the same number counts "product of sizes of all the nonempty subsets of $$[n]$$" according to OEIS. POSTSCRIPT. If $$B$$ is the matrix whose $$(i,j)$$ entry is $$B_{ij} = q^{\#(S_i\cap S_j)}$$ then does this hold? $$\det(B)=q^n(q-1)^{n(2^{n-1}-1)}.$$ • Nice one! The proof I posted at artofproblemsolving.com/community/u432h1747709p11384734 still works, but you now have to replace $C$ by the matrix $\left( \left\|S\right\| \cdot \left[S \subseteq T\right] \right)_{\left(S, T\right) \in P \times P}$. – darij grinberg Dec 7 at 5:14 • My answer below deals with the main question. The POSTSCRIPT is more interesting, though, as it does not directly follow from my approach for lack of zero entries. Wondering if the argument can be adapted to it. – darij grinberg Dec 7 at 6:13 • Maybe, the eigenvalues of this matrix are equal to $\pm k$ with multiplicities $\binom{n-1}{k}$, $\binom{n-1}{k-1}$? And there is some clear pattern on how the eigenvectors look like?r – Fedor Petrov Dec 7 at 6:44 • @FedorPetrov: That is a fine proposition worthy of pushing further that I like to see explored. – T. Amdeberhan Dec 9 at 17:50 Here is a proof that follows my argument at https://artofproblemsolving.com/community/u432h1747709p11384734 as closely as possible. Sorry for its length, much of it due to exposition of matrix folklore. (If you know this, scroll all the way down to Theorem 1, or maybe to the two paragraphs preceding it.) We are grown-ups and don't need to index the rows and the columns of a matrix by numbers. We can pick any set $$P$$, and define a $$P \times P$$-matrix (say, with rational entries) to be a family $$\left(a_{p, q}\right)_{\left(p, q\right) \in P \times P} \in \mathbb{Q}^{P \times P}$$ of rational numbers indexed by pairs $$\left(p, q\right) \in P \times P$$. When the set $$P$$ is finite, such a $$P \times P$$-matrix always has a well-defined determinant, which can be defined by $$$$\det \left( \left(a_{p, q}\right)_{\left(p, q\right) \in P \times P} \right) = \sum_{\sigma \in S_P} \left(-1\right)^{\sigma} \prod_{p \in P} a_{p, \sigma\left(p\right)} .$$$$ Here, $$S_P$$ denotes the set of permutations of $$P$$, and the notation $$\left(-1\right)^{\sigma}$$ stands for the sign of a permutation $$\sigma$$. If you think that this is problematic because the sign of a permutation is usually defined using a total order on $$P$$, then take a break and convince yourself that it does not actually depend on this total order. (This is proven in maximum detail in the solution of Exercise 5.12 of my Notes on the combinatorial fundamentals of algebra, 7th of November 2018.) Determinants of $$P \times P$$-matrices behave as nicely as determinants of "usual" $$n \times n$$-matrices, and arguably even better, since it is easier to define minors and cofactors when the rows and columns are indexed by an arbitrary finite set. Do keep in mind that the rows and the columns must be indexed by the same set; we cannot define the determinant of a $$P \times Q$$-matrix for different $$P$$ and $$Q$$, even when $$\left\|P\right\| = \left\|Q\right\|$$. Of course, an $$n \times n$$-matrix (for a nonnegative integer $$n$$) is the same as an $$N \times N$$-matrix for $$N = \left\{1,2,\ldots,n\right\}$$. Thus, our notion of $$P \times P$$-matrices generalizes the classical notion of $$n \times n$$-matrices. This generalization "respects" standard concepts like determinants -- e.g., the determinant of an $$n \times n$$-matrix does not change if we instead consider it as an $$N \times N$$-matrix. Does this generalization exhibit genuinely new behavior or does it just add convenience? Arguably it's the latter, because conversely, you can turn any $$P \times P$$-matrix (for any finite set $$P$$) into an $$n \times n$$-matrix. Namely, if you have a finite set $$P$$ and a $$P \times P$$-matrix $$A = \left(a_{p, q}\right)_{\left(p, q\right) \in P \times P} \in \mathbb{Q}^{P \times P}$$, then you can set $$n = \left\|P\right\|$$ and fix a bijection $$\phi : \left\{1,2,\ldots,n\right\} \to P$$, and form the $$n \times n$$-matrix $$A_\phi := \left(a_{\phi\left(i\right), \phi\left(j\right)}\right)_{\left(i, j\right) \in \left\{1,2,\ldots,n\right\} \times \left\{1,2,\ldots,n\right\}} \in \mathbb{Q}^{n \times n}$$, and observe that $$A_\phi$$ is "basically the same as" $$A$$ except that the rows and the columns have been reindexed. We shall refer to this operation (going from $$A$$ to $$A_\phi$$) as numerical reindexing. So $$P \times P$$-matrices differ from $$n \times n$$-matrices only in how we index their rows and columns. Nevertheless they are useful, because often there is no canonical bijection $$\phi : \left\{1,2,\ldots,n\right\} \to P$$ (exhibit A: this Putnam problem), and we are algebraists and want to make as few non-canonical choices as possible. Whenever $$P$$ is a finite set, we can multiply two $$P \times P$$-matrices: The product $$AB$$ of two $$P \times P$$-matrices $$A = \left(a_{p, q}\right)_{\left(p, q\right) \in P \times P} \in \mathbb{Q}^{P \times P}$$ and $$B = \left(b_{p, q}\right)_{\left(p, q\right) \in P \times P} \in \mathbb{Q}^{P \times P}$$ is defined to be the $$P \times P$$-matrix $$\left(\sum_{r \in P} a_{p, r} b_{r, q} \right)_{\left(p, q\right) \in P \times P} \in \mathbb{Q}^{P \times P}$$. This multiplication behaves just as nicely as usual multiplication of $$n \times n$$-matrices. In particular, $$\det\left(AB\right) = \det A \cdot \det B$$ whenever $$A$$ and $$B$$ are two $$P \times P$$-matrices. And of course, you can prove this by numerical reindexing, because numerical reindexing preserves both products and determinants (assuming, of course, that you pick one bijection $$\phi : \left\{1,2,\ldots,n\right\} \to P$$ and stick with it). If you remember the definition of triangular $$n \times n$$-matrices, then its generalization to $$P \times P$$-matrices is straightforward: When $$P$$ is a totally ordered finite set, we say that a $$P \times P$$-matrix $$A = \left(a_{p, q}\right)_{\left(p, q\right) \in P \times P}$$ is lower-triangular if $$$$a_{p, q} = 0 \qquad \text{for all } \left(p, q\right) \in P \times P \text{ satisfying } p < q ;$$$$ and we say that a $$P \times P$$-matrix $$A = \left(a_{p, q}\right)_{\left(p, q\right) \in P \times P}$$ is upper-triangular if $$$$a_{p, q} = 0 \qquad \text{for all } \left(p, q\right) \in P \times P \text{ satisfying } p > q .$$$$ Again, lower-triangular $$P \times P$$-matrices become lower-triangular $$n \times n$$-matrices upon numerical reindexing, as long as we make sure to pick our bijection $$\phi : \left\{1,2,\ldots,n\right\} \to P$$ to be an order isomorphism (which, by the way, is unique). So we can derive properties of lower-triangular $$P \times P$$-matrices from analogous properties of lower-triangular $$n \times n$$-matrices by numerical reindexing. In particular, we can thus show that the determinant of a lower-triangular $$P \times P$$-matrix equals the product of its diagonal entries; i.e., if $$A = \left(a_{p, q}\right)_{\left(p, q\right) \in P \times P}$$ is a lower-triangular $$P \times P$$-matrix, then $$\det A = \prod\limits_{p \in P} a_{p, p}$$. The same holds for upper-triangular $$P \times P$$-matrices. Now, let's not forget about the question. Fix a positive integer $$n$$. Let $$N$$ be the set $$\left\{1,2,\ldots,n\right\}$$. Let $$P$$ be the set of all the $$2^n - 1$$ nonempty subsets of $$N$$. (We shall later totally order $$P$$, but for now $$P$$ is just a finite set.) We shall also use the Iverson bracket notation, which will save us some ampersands and braces. This allows us to rewrite the definition of $$A_{ij}$$ in your question as $$A_{ij} = \left[ \left\|S_i \cap S_j\right\| = 1 \right]$$. But as we said, we drop the numerical indexing, and instead define a matrix whose rows and columns are indexed by $$P$$ (that is, by all the nonempty subsets of $$N$$). Thus, the claim of the exercise rewrites as follows: Theorem 1. Let $$A$$ be the $$P \times P$$-matrix $$\left( \left[ \left\|S \cap T\right\| = 1 \right] \right)_{\left(S, T\right) \in P}$$. Then, $$$$\det A = \left(-1\right)^{\left[n \neq 1\right]} \prod_{k=1}^n k^{\dbinom{n}{k}} .$$$$ The key to proving this is the following simple fact: Lemma 2. Let $$S \in P$$ and $$T \in P$$. Then, $$$$\left[ \left\| S \cap T \right\| = 1 \right] = \sum\limits_{U \in P} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| \cdot \left[ U \subseteq S \right] \left[ U \subseteq T \right] .$$$$ This, in turn, shall be derived from the following binomial identity: Lemma 3. Let $$k$$ be a nonnegative integer. Then, $$$$\sum_{i=1}^k \left(-1\right)^{i-1} i \cdot \dbinom{k}{i} = \left[k = 1\right].$$$$ Proof of Lemma 3 (sketched). If $$k = 0$$, then this equality holds for obvious reasons (indeed, the left hand side is an empty sum and thus vanishes, while the right hand side vanishes since $$k = 0 \neq 1$$). Hence, for the rest of this proof, we WLOG assume that $$k \neq 0$$. Hence, $$k$$ is a positive integer. Thus, $$k-1$$ is a nonnegative integer. It is well-known that $$\sum\limits_{i=0}^n \left(-1\right)^i \dbinom{n}{i} = \left[n = 0\right]$$ for every nonnegative integer $$n$$. Applying this to $$n = k-1$$, we obtain $$\sum\limits_{i=0}^{k-1} \left(-1\right)^i \dbinom{k-1}{i} = \left[k-1 = 0\right] = \left[k = 1\right]$$. Multiplying both sides of this equality by $$k$$, we obtain $$k \sum\limits_{i=0}^{k-1} \left(-1\right)^i \dbinom{k-1}{i} = k \left[k = 1\right] = \left[k = 1\right]$$ (where the last equality sign is easy to check directly). Hence, \begin{align} \left[k = 1\right] &= k \sum\limits_{i=0}^{k-1} \left(-1\right)^i \dbinom{k-1}{i} = \sum\limits_{i=0}^{k-1} \left(-1\right)^i \cdot \underbrace{k \dbinom{k-1}{i}}_{\substack{= \left(i+1\right) \dbinom{k}{i+1} \\ \text{(by a simple computation)}}} \\ &= \sum\limits_{i=0}^{k-1} \left(-1\right)^i \cdot \left(i+1\right) \dbinom{k}{i+1} = \sum\limits_{i=1}^{k} \left(-1\right)^{i-1} \cdot i \dbinom{k}{i} \end{align} (here, we have substituted $$i-1$$ for $$i$$ in the sum). This proves Lemma 3. $$\blacksquare$$ Proof of Lemma 2 (sketched). If a subset $$U \in P$$ does not satisfy $$U \subseteq S$$, then the Iverson bracket $$\left[ U \subseteq S \right]$$ is zero and thus renders the whole product $$\left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| \cdot \left[ U \subseteq S \right] \left[ U \subseteq T \right]$$ zero. Similarly, this product also is rendered zero when $$U \in P$$ does not satisfy $$U \subseteq T$$. Thus, the product $$\left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| \cdot \left[ U \subseteq S \right] \left[ U \subseteq T \right]$$ is zero unless $$U \in P$$ satisfies both $$U \subseteq S$$ and $$U \subseteq T$$. Hence, the sum $$\sum\limits_{U \in P} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| \cdot \left[ U \subseteq S \right] \left[ U \subseteq T \right]$$ does not change its value when we restrict it to those $$U$$ that satisfy both $$U \subseteq S$$ and $$U \subseteq T$$ (because all the addends that we lose are zero anyway). In other words, \begin{align} \sum\limits_{U \in P} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| \cdot \left[ U \subseteq S \right] \left[ U \subseteq T \right] &= \sum\limits_{\substack{U \in P; \\ U \subseteq S \text{ and } U \subseteq T}} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| \cdot \underbrace{\left[ U \subseteq S \right]}_{=1} \underbrace{\left[ U \subseteq T \right]}_{=1} \\ &= \sum\limits_{\substack{U \in P; \\ U \subseteq S \text{ and } U \subseteq T}} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\|. \end{align} Now, let $$K$$ be the intersection $$S \cap T$$, and let $$k = \left\|K\right\|$$. Then, the sets $$U \in P$$ that satisfy both $$U \subseteq S$$ and $$U \subseteq T$$ are precisely the nonempty subsets of the $$k$$-element set $$K$$. Thus, we know how many such sets $$U$$ exist of each size: there are exactly $$\dbinom{k}{1}$$ ones of size $$1$$, exactly $$\dbinom{k}{2}$$ ones of size $$2$$, and so on, all the way up to $$\dbinom{k}{k}$$ ones of size $$k$$. Hence, \begin{align} \sum\limits_{\substack{U \in P; \\ U \subseteq S \text{ and } U \subseteq T}} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| &= \dbinom{k}{1} \left(-1\right)^{1-1} \cdot 1 + \dbinom{k}{2} \left(-1\right)^{2-1} \cdot 2 + \cdots + \dbinom{k}{k} \left(-1\right)^{k-1} \cdot k \\ &= \sum_{i=1}^k \dbinom{k}{i} \left(-1\right)^{i-1} \cdot i = \sum_{i=1}^k \left(-1\right)^{i-1} i \cdot \dbinom{k}{i} \\ &= \left[k = 1\right] \qquad \left(\text{by Lemma 3}\right) \\ &= \left[\left\|S\cap T\right\| = 1\right] \end{align} (since $$k = \left\|K\right\| = \left\|S\cap T\right\|$$). Combining what we have, we obtain $$$$\sum\limits_{U \in P} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| \cdot \left[ U \subseteq S \right] \left[ U \subseteq T \right] = \sum\limits_{\substack{U \in P; \\ U \subseteq S \text{ and } U \subseteq T}} \left(-1\right)^{\left\|U\right\| - 1} \left\|U\right\| = \left[\left\|S\cap T\right\| = 1\right] .$$$$ This proves Lemma 2. $$\blacksquare$$ Lemma 4. (a) We have $$\sum\limits_{S \in P} \left\|S\right\| = n 2^{n-1}$$. (b) We have $$\sum\limits_{S \in P} \left( \left\|S\right\| - 1 \right) = n 2^{n-1} - 2^n + 1$$. (c) We have $$\prod\limits_{S \in P} \left(-1\right)^{\left\|S\right\| - 1} = \left(-1\right)^{\left[n \neq 1\right]}$$. (d) We have $$\prod\limits_{S \in P} \left\|S\right\| = \prod\limits_{k=1}^n k^{\dbinom{n}{k}}$$. Proof of Lemma 4. (a) Fix $$i \in \left\{1,2,\ldots,n\right\}$$. Then, exactly $$2^{n-1}$$ subsets of $$\left\{1,2,\ldots,n\right\}$$ contain $$i$$ (since we can freely choose which of the other $$n-1$$ elements such a subset should contain). Of course, all of these $$2^{n-1}$$ subsets are nonempty, and thus belong to $$P$$. Hence, exactly $$2^{n-1}$$ subsets $$S \in P$$ contain $$i$$. Hence, the sum $$\sum\limits_{S \in P} \left[i \in S\right]$$ has exactly $$2^{n-1}$$ addends equal to $$1$$, while all its other addends are $$0$$. Therefore, this sum equals $$2^{n-1}$$. In other words, we have $$$$\sum\limits_{S \in P} \left[i \in S\right] = 2^{n-1} . \label{darij1.pf.l4.1} \tag{1}$$$$ Now, forget that we fixed $$i$$. We thus have proven \eqref{darij1.pf.l4.1} for each $$i \in \left\{1,2,\ldots,n\right\}$$. But we have $$\left\|S\right\| = \sum\limits_{i=1}^n \left[i \in S\right]$$ for each subset $$S$$ of $$\left\{1,2,\ldots,n\right\}$$ (because the sum $$\sum\limits_{i=1}^n \left[i \in S\right]$$ contains exactly $$\left\|S\right\|$$ many addends equal to $$1$$, whereas all its other addends are $$0$$). Summing up this equation over all $$S \in P$$, we obtain \begin{align} \sum\limits_{S \in P} \left\|S\right\| &= \sum\limits_{S \in P} \sum\limits_{i=1}^n \left[i \in S\right] = \sum\limits_{i=1}^n \underbrace{\sum\limits_{S \in P} \left[i \in S\right]}_{\substack{= 2^{n-1} \\ \text{(by \eqref{darij1.pf.l4.1})}}} \\ &= \sum\limits_{i=1}^n 2^{n-1} = n 2^{n-1} . \end{align} This proves Lemma 4 (a). (b) We have $$\left\|P\right\| = 2^n - 1$$ (since the set $$P$$ consists of all the $$2^n$$ subsets of $$\left\{1,2,\ldots,n\right\}$$ apart from the empty set). Now, \begin{align} \sum\limits_{S \in P} \left( \left\|S\right\| - 1 \right) = \underbrace{\sum\limits_{S \in P} \left\|S\right\|}_{\substack{= n 2^{n-1} \\ \text{(by Lemma 4 (a))}}} - \underbrace{\sum\limits_{S \in P} 1}_{= \left\|P\right\| = 2^n - 1} = n 2^{n-1} - \left(2^n - 1 \right) = n 2^{n-1} - 2^n + 1 . \end{align} This proves Lemma 4 (b). (c) If $$n \neq 1$$, then $$n \geq 2$$ (since $$n$$ is a positive integer), and therefore both $$2^{n-1}$$ and $$2^n$$ are even integers. Hence, if $$n \neq 1$$, then $$n 2^{n-1} - 2^n + 1 \equiv 1 \mod 2$$. On the other hand, if $$n = 1$$, then $$n 2^{n-1} - 2^n + 1 = 1 \cdot 2^{1-1} - 2^1 + 1 = 0 \equiv 0 \mod 2$$. Combining the previous two sentences, we conclude that $$n 2^{n-1} - 2^n + 1 \equiv \left[n \neq 1\right] \mod 2$$. Hence, $$\left(-1\right)^{n 2^{n-1} - 2^n + 1} = \left(-1\right)^{\left[n \neq 1\right]}$$. Now, \begin{align} \prod\limits_{S \in P} \left(-1\right)^{\left\|S\right\| - 1} &= \left(-1\right)^{\sum\limits_{S \in P} \left( \left\|S\right\| - 1 \right)} = \left(-1\right)^{n 2^{n-1} - 2^n + 1} \qquad \left(\text{by Lemma 4 (b)}\right) \\ &= \left(-1\right)^{\left[n \neq 1\right]} . \end{align} This proves Lemma 4 (c). (d) Recall that $$P$$ is the set of all nonempty subsets of $$\left\{1,2,\ldots,n\right\}$$. Hence, among the elements of $$P$$ are exactly $$\dbinom{n}{1}$$ subsets of size $$1$$, exactly $$\dbinom{n}{2}$$ subsets of size $$2$$, and so on, and finally exactly $$\dbinom{n}{n}$$ subsets of size $$n$$ (and no other subsets). Therefore, the product $$\prod\limits_{S \in P} \left\|S\right\|$$ has exactly $$\dbinom{n}{1}$$ factors equal to $$1$$, exactly $$\dbinom{n}{2}$$ factors equal to $$2$$, and so on, and finally exactly $$\dbinom{n}{n}$$ factors equal to $$n$$ (and no other factors). Therefore, this product equals $$\prod\limits_{k=1}^n k^{\dbinom{n}{k}}$$. This proves Lemma 4 (d). $$\blacksquare$$ Proof of Theorem 1 (sketched). Define two $$P \times P$$-matrices \begin{align} B &= \left( \left(-1\right)^{\left\|T\right\| - 1} \left\|T\right\| \cdot \left[ T \subseteq S \right] \right)_{\left(S, T\right) \in P \times P} \qquad \text{and} \\ C &= \left( \left[ S \subseteq T \right] \right)_{\left(S, T\right) \in P \times P} . \end{align} Lemma 2 says that $$A = BC$$. (More precisely, Lemma 2 says that the $$\left(S, T\right)$$-th entry of $$A$$ equals the corresponding entry of $$BC$$ for all $$S \in P$$ and $$T \in P$$; but this yields $$A = BC$$.) Thus, $$\det A = \det\left(BC\right) = \det B \cdot \det C$$. Now, it remains to find $$\det B$$ and $$\det C$$. Here we shall finally endow our set $$P$$ with a total ordering. Namely, we pick any total order on $$P$$ with the property that every pair of two subsets $$S \in P$$ and $$T \in P$$ satisfying $$S \subseteq T$$ must satisfy $$S \leq T$$. There are many total orders that do the trick here; for example, we can order them by increasing size (resolving ties arbitrarily). Now, it is easy to see that the $$P \times P$$-matrix $$B$$ is lower-triangular. Since the determinant of a lower-triangular $$P \times P$$-matrix equals the product of its diagonal entries, we thus conclude that \begin{align} \det B &= \prod_{S \in P} \left( \left(-1\right)^{\left\|S\right\| - 1} \left\|S\right\| \underbrace{\left[ S \subseteq S \right]}_{=1} \right) = \prod_{S \in P} \left( \left(-1\right)^{\left\|S\right\| - 1} \left\|S\right\| \right) \\ &= \underbrace{\left(\prod_{S \in P} \left(-1\right)^{\left\|S\right\| - 1}\right)}_{\substack{= \left(-1\right)^{\left[n \neq 1\right]} \\ \text{(by Lemma 4 (c))}}} \left( \prod_{S \in P} \left\|S\right\| \right) = \left(-1\right)^{\left[n \neq 1\right]} \left( \prod_{S \in P} \left\|S\right\| \right) . \end{align} Likewise, the $$P \times P$$-matrix $$C$$ is upper-triangular. Since the determinant of an upper-triangular $$P \times P$$-matrix equals the product of its diagonal entries, we thus conclude that $$$$\det C = \prod_{S \in P} \underbrace{\left[ S \subseteq S \right]}_{=1} = 1 .$$$$ Now, \begin{align} \det A &= \det B \cdot \underbrace{\det C}_{=1} = \det B = \left(-1\right)^{\left[n \neq 1\right]} \underbrace{\left( \prod_{S \in P} \left\|S\right\| \right)}_{\substack{= \prod\limits_{k=1}^n k^{\dbinom{n}{k}} \\ \text{(by Lemma 4 (d))}}} \\ &= \left(-1\right)^{\left[n \neq 1\right]} \prod_{k=1}^n k^{\dbinom{n}{k}} . \end{align} This proves Theorem 1. $$\blacksquare$$ In hindsight, the above proof could have been restated without introducing $$P \times P$$-matrices, since picking a total order on a finite set $$P$$ is equivalent to picking a bijection $$\phi : \left\{1,2,\ldots,n\right\} \to P$$. But I prefer to give the exercise an "invariant" formulation, and $$P \times P$$-matrices are worth exposing anyway. A few more telegraphic remarks: • The decomposition $$A = BC$$ constructed in the above proof of Theorem 1 is an LU-decomposition. • The proof I found first was the same recursive argument appearing a few times in the AoPS thread linked above. But the structure of the recursion foreshadowed the existence of a slicker proof -- the block-row-reduction operations felt like multiplying by a lower-triangular (in a properly chosen order) matrix. So I dug deeper and found the above. • This reminds me of Lemma 7.1 of Chris Godsil, An Introduction to the Moebius Function. • Lemma 3 is trivial since $i\binom ki=k\binom{k-1}{i-1}$, – Zhi-Wei Sun Dec 7 at 6:21 • @Zhi-WeiSun: I know it is. This is a semi-expository writeup that is supposed to be readable by anyone who understands the problem. – darij grinberg Dec 7 at 6:38 • @darijgrinberg: Thank you for the detailed work! – T. Amdeberhan Dec 9 at 4:36 • @darij BRAVO for using Iverson notation in a matrix definition ? While avoiding to create a name names it adds clarity. From a computer point of view we could say "The implementation IS the name." – Jérôme JEAN-CHARLES yesterday Darij already gave a great elementary detailed exposition. I wanted to remark that all such kinds of results (including the postscript) are special cases of a classical result that (at least in the generality of semilattices) goes back to Lindström in Determinants on semilattices. For this question we are in the special case of the Boolean lattice. • Oh, are you applying Lindström's result with $\cup$ as $\wedge$? – darij grinberg Dec 7 at 15:17 • @darijgrinberg: isn't he using $\cap$ as $\wedge$ in the obvious way? – Sam Hopkins Dec 7 at 16:04 • @SamHopkins: Because $\cap$ is not always a nonempty subset. This is what confused me, too. But I think $\cup$ can be used perfectly well. – darij grinberg Dec 7 at 16:15 • @darijgrinberg: another way to resolve that might be to add a row of all $1$s to the bottom of the matrix (thinking of the last row/column as corresponding to the empty set) by choosing the corresponding $f_i$ to be the constant function $1$. When I expand the determinant about the last row, I will just get the determinant of the $(2^n-1)\times(2^n-1)$ submatrix in the upper left because every other $(2^n-1)\times(2^n-1)$ determinant will have a column of all zeros. – Sam Hopkins Dec 7 at 16:21 • @darijgrinberg Yes, for the postscript, I was thinking the nonempty subsets with $\cup$. We can take the function $f(A,B)=q^{-\|A\cup B\|}$ and then multiply the row(or column) of A by $q^{\|A\|}$. – Gjergji Zaimi Dec 7 at 18:11	2018-12-16 05:02:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 265, "wp-katex-eq": 0, "align": 6, "equation": 9, "x-ck12": 0, "texerror": 0, "math_score": 0.9999896287918091, "perplexity": 449.46202647941124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827252.87/warc/CC-MAIN-20181216025802-20181216051802-00329.warc.gz"}
http://math.stackexchange.com/questions/86033/trigonometry-and-formula	# trigonometry and formula I asked the same question some time ago, but it is closed. This time I will be clearer (I hope). If I have a right triangle $c ^ 2 = a ^ 2 + b ^ 2$, and $b > a$ (so $a$ is the shorter side and $b$ is the longer side). Now, put a right triangle in a semi-circle with the hypotenuse is equal to the diameter, $((a * 4) - (a * b / c)) / 3$ ~ circle arc $a$. For example if have right triangle $10 ^ 2 = 5 ^ 2 + (8,6602\dots)^ 2$ which was placed in a semi-circle with a diameter of $10$, will obtain $((5 * 4) - (5 * 8,6602\dots / 10)) / 3 = 5,223\dots \sim 5,235\dots$. In this example 5,235.. is the length of circle arc with the same angle as the right triangle side of 5, in this case it is obvious angle of 60 degrees (viewed from the center of the semi- circle). Another example if have a right triangle $10 ^ 2 = (7,07106\dots)^ 2 + (7,07106\dots)^2$, will obtain $((7,07106\dots* 4) - (7,07106\dots* 7,07106\dots/ 10)) / 3 = 7,761 \sim 7,853\dots$. In this case $7,853\dots$ obvious is the length of 1/4 circumference, or, circle arc of 90 degrees (viewed from the center of the semi-circle). So question is, whether formula $((a * 4) - (a * b / c)) / 3$, used before in this or some other form ? (question is important because this formula can be improved (with a lot of manipulation) to give a much smaller error) Srbin EDIT (M.S): This picture was not posted by OP, I've added it since it might help to clarify the question. - -1: Please make paragraphs, learn to use $\LaTeX$ and try to formulate proper sentences. Noone will enjoy reading this. – Listing Nov 27 '11 at 13:25 marko: Your question is not very clear, I tried to improve the formatting. I've added the picture, could you explain it on this picture. Are you asking about the length of the arc between $B$ and $A$. (I.e. this length is $r.\phi$?) – Martin Sleziak Nov 27 '11 at 14:15 P.S. I am not sure whether this is a good suggestion but there were several questions here posted in different languages than English and in these cases someone translated them. If you're lucky, there might be someone here who speaks your language and this could lead to a better question. – Martin Sleziak Nov 27 '11 at 14:16 Now back to your question: If I understand you correctly, your formula gives $\frac 13 \left(4a-\frac{ab}c\right)= \frac13 r(8\tan(\phi/2)-\sin\phi)$. For small values of $\phi$ this is approximately $\frac13 r(4\phi-\phi)=\phi$. See wolframalpha.com/input/… and wolframalpha.com/input/… – Martin Sleziak Nov 27 '11 at 14:18 Marko: I guess both these account belong to you: math.stackexchange.com/users/20189/marko and math.stackexchange.com/users/21380/marko; Maybe it would be good for you to register, so that you can better follow all questions you posted. (After you do it, you can even ask moderators to merge you account with the older unregistered ones.) – Martin Sleziak Dec 17 '11 at 7:52	2014-09-03 02:21:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7871052622795105, "perplexity": 417.6750791390304}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535924131.19/warc/CC-MAIN-20140901014524-00059-ip-10-180-136-8.ec2.internal.warc.gz"}
https://economics.stackexchange.com/questions/43757/what-was-the-annual-real-growth-rate-in-the-us-from-2010-to-2015/43759#43759	# What was the annual real growth rate in the US from 2010 to 2015? If we look at the US M0 money supply after the global financial crisis (GFC): we see that it doubled from 2010 to 2015. If we look at the Consumer Price Index in the same period: it rose by 8%. So over the 5 year period from 2010 to 2015 the M0 had a geometric average of 15% and the CPI a geometric average of 1.6%. According to the Quantity Equation the US therefore had a yearly real growth of more than 13% in this period? Which sounds way to much. • Real growth of what? GDP? May 4 '21 at 21:59 What was the annual real growth rate in the US from 2010 to 2015? I presume you mean growth rate of output. You can see the quarterly real growth rate in the US from 2010 to 2015 below (source Fred) with average quarterly growth rate being 0.6%: According to the Quantity Equation the US therefore had a yearly real growth of more than 13% in this period? No, that is definitely not implied by the quantitative theory of money (QTM) - I assume that is what you mean by the 'quantity equation'. First, you are using wrong data for that (at least for money supply). Second you are not using all data required for QTM is given by: $$MV=PY$$ With, $$M$$ being total money supply (usually proxied by $$M2$$), $$V$$ velocity of money, $$P$$ price level, $$Y$$ real output. Taking logs and differentiating the expression wrt time we get: $$\frac{\dot{M}}{M} + \frac{\dot{V}}{V} = \frac{\dot{P}}{P} + \frac{\dot{Y}}{Y}$$ The above says that the growth rate in $$M$$ + growth rate in $$V$$ should be equal to growth rate in $$P$$ plus growth rate in $$Y$$. Now the total growth rate of $$Y$$ between 2010 and 2015 of $$Y$$ was $$\approx 11.7 \%$$ (see Fred data), the total growth rate of $$P$$ in between 2010 and 2015 was $$\approx 9.4 \%$$ (see Fred data), next the total growth rate of $$M$$, in the same time period, measured by $$M2$$ was approximately $$39.6 \%$$ (see Fred data), lastly the total growth in velocity $$V$$ over the same period was approximately $$-14.9 \%$$ (again see Fred data). Consequently, plugin these into QTM we would get that: $$39.5 \%+ (-14.3\%) - 9.4\% = \frac{\dot{Y}}{Y}$$ Hence QTM would predict that the growth rate of $$Y$$ would be: $$15.8 \% \approx \frac{\dot{Y}}{Y}$$ This is still off by approximately $$4.1\%$$ given that the actual real GDP growth was $$\approx 11.7\%$$, however note QTM is extremely simplistic model of money market equilibrium. More realistic description of money market equilibrium would be given by (see Woodford Interest & Prices pp 295): $$M^s_t/P_t = L(Y_t,\Delta_t: \xi)$$ where $$L$$ is the money demand that is a function of real output and the interest rate differential between nonmonetary and monetary assets $$\Delta \equiv \frac{i_t-i^m_t}{1+i_t}$$ conditional on vector of shocks $$\xi$$. You can view this as the more nuanced version of the equilibrium relationship given by QTM since here $$MV=PY \implies M/P =Y/V$$ and we replace crude $$Y/V$$ with actual money demand that depends on output and interest rates. In this more nuanced model there does not need to be 1:1 correspondence between LHS and RHS since $$L$$ will be some function (e.g. it could be $$\alpha+ \beta Y - \gamma \frac{i_t-i^m_t}{1+i_t}$$, where $$\alpha$$ and $$\beta$$ and $$\gamma$$ would have to be empirically fitted).	2022-01-24 23:24:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 37, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7115762829780579, "perplexity": 729.6093113230954}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00265.warc.gz"}
http://www.dcscience.net/tag/corruption/	Corrected and searchable version of Google books edition Latest Tweets This post is the original version of a post by Michael Vagg. It was posted at the Conversation but taken down within hours, on legal advice. Sadly, the Conversation has a track record for pusillanimous behaviour of this sort. It took minutes before the cached version reappeared on freezepage.com. I’m reposting it from there in the interests of free speech. La Trobe "university" should be ashamed that it’s prostituted itself for the sake of 15 m. La Trobe’s deputy vice-chancellor, Keith Nugent, gives a make-believe response to the resignation of Ken Harvey in a video. It is, in my opinion, truly pathetic. Update, The next day, the article was reposted at the Conversation. The changes they’d made can be seen in a compare document. The biggest change was removal of "has just decided to join the ranks of the spivs and hucksters of the vitamin industry". This seems to me to be perfectly fair comment. It should not have been censored by the Conversation. The recent memorandum of understanding signed between supplement company Swisse and La Trobe University to establish a Complementary Medicine Evidence Centre (CMEC) looks to me like the latest effort by a corporation to cloak their business interests in a veil of science. Unlike the UTS Sydney Australian Research Centre in Complementary and Integrative Medicine (ARCCIM), which at least has significant NHMRC funding, the La Trobe version will undertake “independent research” into complementary and alternative medicine (CAM) products that are made by the major (and so far only) donor to the Centre. Southern Cross University also has a very close relationship with the Blackmores brand of CAM products, due to the personal interest of Marcus Blackmore, the company Chairman. Blackmores claims to spend a lazy couple of million a year on their branded research centre. The Blackmores Research Centre studies Blackmores products. Presumably this situation (so similar to the proposed La Trobe model) is a coincidence since the research centre is providing completely “independent” research. The conflict of interest in such research centres is so laughably obvious that A/Prof Ken Harvey, a leading campaigner against shonky health products, a life member of Choice andThe Conversation contributor, has resigned his appointment at La Trobe in protest. Ken clearly points out in his letter of resignation that by accepting the money from Swisse, he believes La Trobe has unacceptably compromised its integrity. His letter cites multiple instances of non-compliance with TGA regulations by Swisse, as well as their disrespect for the regulatory process that governs corporate truth-telling in their industry.This story from last year gives a bit of background to the quixotic battle Harvey has fought against the massive coffers and unscrupulous business practices of Big Supplement. He has been more effective than the TGA itself at hindering the rampant gaming of the TGA Register of Therapeutic Goods by supplement and vitamin manufacturers. Clearly as a man of principle, he could not be expected to continue his association with a university that has a close relationship to a company with such a history of regulatory infringements. The untenability of Ken’s position is underlined by the fact that La Trobe itself republished on their website one of his TC articles about Swisse’s regulatory tapdancing only the previous year! Ken has been sued, traduced and generally railed against by a multi-billion dollar industry for the hideous crime of insisting that they tell the truth about their products and not mislead consumers. We need another hundred like him. That his own university has decided to take the money on offer from Swisse must be a bitter blow to him. It would be interesting to know whether any other universities were approached by Swisse in a similar way and had the courage to decline the offer. The infiltration of academia by privately funded CAM institutes is old news in the United States. The Science Based Medicine blog has christened the phenomenon “quackademic medicine” and written about it at some length. It seems the Australian CAM industry has no need to hide behind astroturfing organisations like the American group the Bravewell Collaborative to get its agenda attended to. Companies like Blackmores and Swisse can seemingly just offer to fund research institutes and cash-strapped tertiary institutions can’t resist. Friends of Science in Medicine and others have had a bit to say about the irresponsibility of educational institutions lending credibility to pseudoscience and how this practice damages universities’ standing as exemplars of scholarship and intellectual leaders within their communities. I can say without qualification that none of the much-maligned Big Pharma companies have their own fully-funded research centres at any university. Let alone a branded one where the studies are restricted to a single company’s products. It would be utterly unacceptable for the integrity of any university for such an outrageously conflicted institution to be given any support. What would it be like if GSK or Pfizer founded a research institute at a university and forced the researchers to only study their own products? Imagine the outrage. Imagine what a laughing stock such a research centre would be. That’s medical research in clown shoes. That’s academic credibility in a cheap suit trying to sell you steak knives. Vitamin and supplement companies will always be profitable because their sales pitch is based on psychological flaws that everyone has. Just ask the gaming, alcohol and tobacco companies. All of them are massively profitable. Sometimes their cash can even do good, but there’s always an angle by which they profit. Look at these guys up close, and the warts appear. All of them seek to improve their image by splashing money on hanging around with the glamorous, the successful, the smart and the credible. They hope that the magic dust of celebrity and academia will disguise the stench of the swamp they crawled out from. La Trobe Uni has just decided to join the ranks of the spivs and hucksters of the vitamin industry, and they will now have to live with having a research centre with the academic and professional credibility of the Ponds Institute. Sadly for La Trobe, they won’t have Ken Harvey to keep things reality-based. ### Follow-up 8 February 2014. Deputy vice-chancellor, Keith Nugent, tried to defend the university’s decision to take money from the "spivs and hucksters of the vitamin industry" in The Age. I sent the following letter to The Age. Let’s hope they publish it. Keith Nugent, deputy vice-chancellor of La Trobe University, has offered a defence of the university’s decision to take a large amount of money from vitamin and herb company, Swisse. He justifies this by saying that we need to know whether or not the products work. Nugent seems to be unaware that we already know. There have been many good double-blind randomized trials and they have just about all shown that dosing yourself with vitamins and minerals does most people no good at all. Some have shown that high doses actually harm you. Perhaps the university should have checked what’s already known before taking the money. Perhaps Nugent is also unaware that trials with industry sponsorship tend to come out favourable to the companies’ product. For that reason, the results are treated with scepticism by the scientific community. If the research is worth doing, then it will be funded from the normal sources. There should be no need to take money from a company with a very strong financial interest in the outcome. D. Colquhoun FRS Professor of Pharmcology University College London Jump to follow-up This is a very important book. Buy it now (that link is to Waterstone’s Amazon don’t pay tax in the UK, so don’t use them). When you’ve read it, do something about it. The book has lots of suggestions about what to do. Stolen from badscience.net Peter Medawar, the eminent biologist, in his classic book Advice to a Young Scientist, said this. “Exaggerated claims for the efficacy of a medicament are very seldom the consequence of any intention to deceive; they are usually the outcome of a kindly conspiracy in which everybody has the very best intentions. The patient wants to get well, his physician wants to have made him better, and the pharmaceutical company would have liked to have put it into the physician’s power to have made him so. The controlled clinical trial is an attempt to avoid being taken in by this conspiracy of good will.” There was a lot of truth in that 1979, towards the end of the heyday of small molecule pharmacology. Since then, one can argue, things have gone downhill. First, though, think of life without general anaesthetics, local anaesthetics, antibiotics, anticoagulants and many others. They work well and have done incalculable good. And they were developed by the drug industry. But remember also that remarkably little is known about medicine. There are huge areas in which neither causes nor cures are known. Treatments for chronic pain, back problems, many sorts of cancer and almost all mental problems are a mess. It just isn’t known what to do. Nobody is to blame for this. Serious medical research has been going on for little more than 60 years, and it turns out to be very complicated. We are doing our best, but are still ignorant about whole huge areas. That leads to a temptation to make things up. Clutching at straws is very evident when it comes to depression, pain and Alzheimer’s disease, among others. In order to improve matters, one essential is to do fair tests on treatments that we have. Ben Goldacre’s book is a superb account of how this could be done, and how the process of testing has been subverted for commercial gain and to satisfy the vanities of academics. Of course there is nothing new in criticisms of Big Pharma. The huge fines levied on them for false advertising are well known. The difference is that Goldacre’s book explains clearly what’s gone wrong in great detail, documents it thoroughly, and makes concrete suggestions for improving matters. Big Pharma has undoubtedly sometimes behaved appallingly in recent years. Someone should be in jail for crimes against patients. They have behaved in much the same way that bankers have. In any huge globalised industry it is always possible to blame someone in another department for the dishonesty. But they aren’t the only people to blame. None of the problems could have arisen with the complicity of academics, universities, and a plethora of regulatory agencies and professional bodies. The biggest scandal of all is missing data (chapter 1). Companies, and sometmes academics, have suppressed of trials that don’t favour the drugs that they are trying to sell. The antidepressant drug, reboxetine, appeared at first to be good. It had been approved by the Medicines and Healthcare products Regulatory Agency (MHRA) and there was at least one good randomized placebo-controlled trial (RCT) showing it worked. But it didn’t. The manufacturer didn’t provide a complete list of unpublished trials when asked for them. After much work it was found in 2010 that, as well as the published, favourable trial, there were six more trials which had not been published and all six showed reboxetine to be no better than placebo . In comparisons with other antidepressant drugs three small studies (507 patients) showed reboxetine to be as good as its competitors. These were published. But it came to light that data on 1657 patients had never been published and these showed reboxetine to be worse than its rivals. When all the data for the SSRI antidepressants were unearthed (Kirsch et al., 2008) it turned out that they were no better than placebo for mild or moderate depression. This selective suppression of negative data has happened time and time again. It harms patients and deceives doctors, but, incredibly, it’s not illegal. Disgracefully, Kirsch et al. had to use a Freedom of Information Act request to get the data from the FDA. “The output of a regulator is often simply a crude, brief summary: almost a ‘yes’ or ‘no’ about side effects. This is the opposite of science, which is only reliable because everyone shows their working, explains how they know that something is effective or safe, shares their methods and their results, and allows others to decide if they agree with the way they processed and analysed the data.” “the NICE document discussing whether it’s a good idea to have Lucentis, an extremely expensive drug, costing well over £ 1,000 per treatment, that is injected into the eye for a condition called acute macular degeneration. As you can see, the NICE document on whether this treatment is a good idea is censored. Not only is the data on the effectiveness of the treatment blanked out by thick black rectangles, in case any doctor or patient should see it, but absurdly, even the names of some trials are missing, preventing the reader from even knowing of their existence, or cross referencing information about them.Most disturbing of all, as you can see in the last bullet point, the data on adverse events is also censored.” The book lists all the tricks that are used by both industry and academics. Here are some of them. • Regulatory agencies like the MHRA, the European Medicines Agency (EMA) and the US Food and Drugs Administration (FDA) set a low bar for approval of drugs. • Companies make universities sign gagging agreements which allow unfavourable results to be suppressed, and their existence hidden. • Accelerated approval schemes are abused to get quick approval of ineffective drugs and the promised proper tests often don’t materialise • Disgracefully, even when all the results have been given to the regulatory agencies (which isn’t always). The MHRA, EMA and FDA don’t make them public. We are expected to take their word. • Although all clinical trials are meant to be registered before they start, the EMA register, unbelievably, is not public. Furthermore there is no check that the results if trials ever get published. Despite mandates that results must be published within a year of finishing the trial, many aren’t. Journals promise to check this sort of thing, but they don’t. • When the results are published, it is not uncommon for the primary outcome, specified before it started, to have been changed to one that looks like a more favourable result. Journals are meant to check, but mostly don’t. • Companies use scientific conferences, phony journals, make-believe “seed trials” and “continuing medical education” for surreptitious advertising. • Companies invent new diseases, plant papers to make you think you’re abnormal, and try to sell you a “cure”. For example, female sexual dysfunction , restless legs syndrome and social anxiety disorder (i.e. shyness). This is called disease-mongering, medicalisation or over-diagnosis. It’s bad. • Spin is rife. Companies, and authors, want to talk up their results. University PR departments want to exaggerate benefits. Journal editors want sensational papers. Read the results, not the summary. This is universal (but particularly bad in alternative medicine). • Companies fund patient groups to lobby for pills even when the pills are known to be ineffective. The lobby that demanded that Herceptin should be available to all on the breast cancer patients on the NHS was organised by a PR company working for the manufacturer, Roche. But Herceptin doesn’t work at all in 80% of patients and gives you at best a few extra months of life in advanced cases. • Ghostwriting of papers is serious corruption. A company writes the paper and senior academics appear as the authors, though they may never have seen the original data. Even in cases where academics have admitted to lying about whether they have seen the data, they go unpunished by their universities. See for example, the case of Professor Eastell. • By encouraging the funding of “continuing medical education” by companies, the great and the good of academic medicine have let us down badly. This last point is where the book ends, and it’s worth amplification. “So what have the great and good of British medicine done to help patients, in the face of this endemic corruption, and these systematic flaws? In 2012, a collaborative document was produced by senior figures in medicine from across the board, called ‘Guidance on Collaboration Between Healthcare Professionals and the Pharmaceutical Industry’. This document was jointly approved by the ABPI, the Department of Health, the Royal Colleges of Physicians, Nursing, Psychiatrists, GPs, the Lancet, the British Medical Association, the NHS Confederation, and so on. ” “It contains no recognition of the serious problems we have seen in this book. In fact, quite the opposite: it makes a series of assertions about them that are factually incorrect.” “It states that drug reps ‘can be a useful resource for healthcare professionals’. Again, I’m not sure why the Royal Colleges, the BMA, the Department of Health and the NHS Confederation felt the need to reassert this to the doctors of the UK, on behalf of industry, when the evidence shows that drug reps actively distort prescribing practices. But that is the battle you face, trying to get these issues taken seriously by the pinnacle of the medical establishment.” This is perhaps the most shameful betrayal of all. The organisations that should protect patients have sold them out. You may have been sold out by your “elders and betters”, but you can do something. The “What to do” sections of the book should be produced as a set of flash cards, as a reminder that matters can be improved. It is shameful that this book was not written by a clinical pharmacologist, or a senior doctor, or a Royal College, or a senior academic. Why has the British Pharmacological Society said nothing? It is shameful too that this book was not written by one of the quacks who are keen to defend the60 billion alternative medicine industry (which has cured virtually nothing) and who are strident in their criticism of the 600 billion dollar Pharma industry. They haven’t done the work that Goldacre has to analyse the real problems. All they have done is to advocate unfair tests, because that is the only sort their treatments can pass. It’s weird that medicine, the most caring profession, is more corrupt than any other branch of science. The reason, needless to say, is money. Well, money and vanity. The publish or perish mentality of senior academics encourages dishonesty. It is a threat to honest science. Goldacre’s book shows the consequences: harm to patients and huge wastage of public money. Do something. ### Follow-up 7 October, 2012, The Observer Goldacre wrote "I think it’s really disappointing that nobody, not the Royal Colleges, the Academy of Medical Sciences, the British Pharmacological Society, the British Medical Association, none of these organisations have stood up and said: selective non-publication of unflattering trial data is research misconduct, and if you do it you will be booted out. And I think they really urgently should." Exactly. We have listed many reasons hear why you should never trust Boots. Here are the previous ones. This post is about a "functional food". That is about something a bit more serious than homeopathy, though I’ll return to that standing joke in the follow-up, because of Boots’ latest shocking admission.. Alternative medicine advocates love to blame Big Pharma for every criticism of magic medicine. In contrast, people like me, Ben Goldacre and a host of others have often pointed out that the differences seem to get ever smaller between the huge Alternative industry (about $60 billion per year), and the even huger regular pharmaceutical industry (around$600 billion per year), Boots are as good an example as any. While representing themselves as ethical pharmacists, they seem to have no compunction at all in highly deceptive advertising of medicines and supplements which are utterly useless rip-offs. The easiest way to make money is to sell something that is alleged to cure a common, but ill-defined problem, that has a lot of spontaneous variability.. Like stress, for example. The Times carried a piece Is Boots’s new Lactium pill the solution to stress?. Needless to say the question wasn’t answered. It was more like an infomercial than serious journalism. Here is what Boots say. What does it do? This product contains Lactium, a unique ingredient which is proven to help with the stresses of every day life, helping you through a stressful day. Also contains B vitamins, magnesium and vitamin C, which help to support a healthy immune system and energy levels. Why is it different? This one a day supplement contains the patented ingredient Lactium. All Boots vitamins and suppliers are checked to ensure they meet our high quality and safety standards. So what is this "unique ingredient", Lactium? It is a produced by digestion of cow’s milk with trypsin. It was patented in 1995 by the French company, Ingredia, It is now distributed in the USA and Canada by Pharmachem. which describes itself as “a leader in the nutraceutical industry.” Drink a glass of milk and your digestive system will make it for you. Free. Boots charge you £4.99 for only seven capsules. ### What’s the evidence? The search doesn’t start well. A search of the medical literature with Pubmed for "lactium" produces no results at all. Search for "casein hydrolysate" gives quite a lot, but "casein hydrolysate AND stress" gives only seven, of which only one looks at effects in man, Messaoudi M, Lefranc-Millot C, Desor D, Demagny B, Bourdon L. Eur J Nutr. 2005. There is a list of nineteen "studies" on the Pharmachem web site That is where Boots sent me when I asked about evidence, so let’s take a look. Of the nineteen studies, most are just advertising slide shows or unpublished stuff. Two appear to be duplicated. There are only two proper published papers worth looking at, and one of these is in rats not man. The human paper first. Paper 1 Effects of a Bovine Alpha S1-Casein Tryptic Hydrolysate (CTH) on Sleep Disorder in Japanese General Population, Zara de Saint-Hilaire, Michaël Messaoudi, Didier Desor and Toshinori Kobayashi [reprint here] The authors come from France, Switzerland and Japan. This paper was published in The Open Sleep Journal, 2009, 2, 26-32, one of 200 or so open access journals published by Bentham Science Publishers. It has to be one of the worst clinical trials that I’ve encountered. It was conducted on 32 subjects, healthy Japanese men and women aged 25-40 and had reported sleeping disorders. It was double blind and placebo controlled, so apart from the fact that only 12 of the 32 subjects were in the control group, what went wrong? The results were assessed as subjective sleep quality using the Japanese Pittsburg Sleep Quality Index (PSQI-J). This gave a total .score and seven component scores: sleep quality, sleep latency, sleep duration, habitual sleep efficiency, sleep disturbances, use of sleeping medication, and daytime dysfunction. In the results section we read, for total PSQI score "As shown in Table 2, the Mann-Whitney U-test did not show significant differences between CTH [casein tryptic hydrolysate] and Placebo groups in PSQI-J total scores at D0 (U=85; NS), D14 (U=86.5; NS), D28 (U=98.5; NS) and D35 (U=99.5; NS)." Then we read exactly similar statements for the seven component scores. For example,. for Sleep Quality As shown in Table 3, the Mann-Whitney U-test did not show significant differences between the sleep quality scores of CTH and Placebo groups at D0 (U=110.5; NS), D14 (U=108.5; NS), D28 (U=110; NS) and D35 (U=108.5; NS). The discussion states "The comparisons between the two groups with the test of Mann-Whitney did not show significant differences, probably because of the control product’s placebo effect. Despite everything, the paired comparisons with the test of Wilcoxon show interesting effects of CTH on sleep disorders of the treated subjects. " Aha, so those pesky controls are to blame! But despite this negative result the abstract of the paper says "CTH significantly improves the PSQI total score of the treated subjects. It particularly improves the sleep quality after two weeks of treatment, decreases the sleep latency and the daytime dysfunction after four weeks of treatment. Given the antistress properties of CTH, it seems possible to relate the detected improvement of sleep aspects to a reduction of stress following its’ chronic administration." So there seems to be a direct contradiction between the actual results and the announced outcome of the trial. How could this happen? The way that the results are presented make it hard to tell. As far as I can tell, the answer is that, having failed to find evidence of real differences between CTH and placebo, the authors gave up on the placebo control and looked simply at the change from the day 0 basleine values within the CTH group and, separately, within the placebo group. Some of these differences did pass statistical significance but if you analyse it that way. there is no point in having a control group at all. How on earth did such a poor paper get published in a peer-reviewed journal? One answer is that there are now so many peer-reviewed journals, that just about any paper, however poor, can get published in some journal that describes itself as ‘peer-reviewed’. At the lower end of the status hierarchy, the system is simply broken. Bentham Science Publishers are the publishers of the The Open Sleep Journal. (pity they saw fit to hijack the name of UCL’s spiritual founder, Jeremy Bentham). They publish 92 online and print journals, 200 plus open access journals, and related print/online book series. This publsher has a less than perfect reputation. There can be no scientist of any age or reputation who hasn’t had dozens of emails begging them to become editors of one or other of their journals or to write something for them. They have been described as a "pyramid scheme” for open access. It seems that every Tom, Dick and Harry has been asked. They have been described under the heading Black sheep among Open Access Journals and Publishers. More background can be found at Open Access News.. Most telling of all, a spoof paper was sent to a Bentham journal, The Open Information Science Journal. . There is a good account of the episode the New Scientist, under the title “CRAP paper accepted by journal”. It was the initiative if a graduate student at Cornell University. After getting emails from Bentham, he said “”It really painted a picture of vanity publishing”. The spoof paper was computer-generated rubbish, but it was accepted anyway, without comment. Not only did it appear that is was never reviewed but the editors even failed to notice that the authors said the paper came from the "Center for Research in Applied Phrenology", or CRAP. .The publication fee was \$800, to be sent to a PO Box in the United Arab Emirates. Having made the point, the authors withdrew the paper. Paper 5 in the list of nineteen stidies is also worth a look. It’s about rats not humans but it is in a respectable journal The FASEB Journal Express Article doi:10.1096/fj.00-0685fje (Published online June 8, 2001) [reprint here]. Characterization of α-casozepine, a tryptic peptide from bovine αs1-casein with benzodiazepine-like activity. Laurent Miclo et al. This paper provides the basis for the claim that digested milk has an action like the benzodiazepine class of drugs, which includes diazepam (Valium). The milk hydrolysate, lactium was tested in rats and found to have some activity in tests that are alleged to measure effects on anxiety (I haven’t looked closely at the data, since the claims relate to humans).. The milk protein, bovine αS1 casein contains 214 amino acids. One of the many products of its digestion is a 10-amino-acid fragment (residues 91 -100) known as α-casozepine and this is the only product that was found to have an affinity for the γ-amino-butyric acid (GABA) type A receptors, which is where benzodiazepines are thought to act. There are a few snags with this idea. • The affinity of α-casozepine peptide had 10,000-fold lower affinity for the benzodiazepine site of the GABAA than did diazepam, whereas allegedly the peptide was 10-fold more potent than diazepam in one of the rat tests. • The is no statement anywhere of how much of the α-casozepine peptide is present in the stuff sold my Boots, or whether it can be absorbed • And if digested milk did act like diazepam, it should clearly be callled a drug not a food. ### What’s the conclusion about lactium? Here is what I make of it. Does it relieve stress? The evidence that it works any better than drinking a glass of milk is negligible. Tha advertising is grossly misleading and the price is extortionate. Corruption of science. There is a more interesting aspect than that though. The case of lactium isn’t quite like the regular sort of alternative medicine scam. It isn’t inherently absurd, like homeopathy. The science isn’t the sort of ridiculous pseudo-scientific ramblings of magic medicine advocates who pretend it is all quantum theory The papers cited here are real papers, using real instruments and published in real journals, What is interesting about that is that they show very clearly the corruption of real science that occurs at its fringes, This is science in the service of the dairy industry and in the service of the vast supplements industry. These are people who want to sell you a supplement for everything. Medical claims are made for supplements, yet loopholes in the law are exploited to maintain that they are foods not drugs. The law and the companies that exploit it are deeply dishonest. That’s bad enough. but the real tragedy is when science itself is corrupted in the service of sales. Big Pharma and the alternative industry. Nowhere is the slose alliance between Big Pharma and the alternative medicine industry more obvious than in the supplement and nutriceutical markets. Often the same companies run both. Their aim is to sell you thinks that you don’t need, for conditions that you may well not have, and to lighten your wallet in the process. Don’t believe for a moment that the dark-suited executives give a bugger about your health. You are a market to be exploited. If you doubt that, look from time to time at one of the nutraceutical industry web sites, like nutraingredients.com. They even have a bit to say about lactium. They are particularly amusing at the moment because the European Food Safety Authority (EFSA) has had the temerity to demand that when health claims are made for foods, there is actually some small element of truth in the claims. The level of righteous indignation caused in the young food industry executives at the thought that they might have to tell the truth is everywhere to see. For example, try Life in a European health claims wasteland. Or, more relevant to Lactium, Opportunity remains in dairy bioactives despite departures. Here’s a quotation from that one. “Tage Affertsholt, managing partner at 3A Business Consulting, told NutraIngredients.com that the feedback from industry is that the very restrictive approach to health claims adopted by the European Food Safety Authority (EFSA) will hamper growth potential.” “Affertsholt said: “Some companies are giving up and leaving the game to concentrate on more traditional dairy ingredients.” ### Science and government policy It may not have escaped your notice that the sort of low grade, corrupted, fringe science described here, is precisely the sort that is being encouraged by government policies. You are expected to get lots of publications, so never mind the details, just churn ’em out; The hundreds of new journals that have been created will allow you to get as meny peer-reviwed publications as you want without too much fuss, and you can very easily put an editorship of one of them on your CV when you fill in that bit about indicators of esteem. The box tickers in HR will never know that it’s a mickey mouse journal. ### Follow-up Boots own up to selling crap Although this post was nothing to do with joke subjects like homeopathy, it isn’t possible to write about Boots without mentioning the performance of their professional standards director, Paul Bennett, when he appeared before the Parliamentary Select Committee for Science and Technology.. This committee was holding an “evidence check” session on homeopathy (it’s nothing short of surreal that this should be happening in 2009, uh?). The video can be seen here, and an uncorrected transcript. It is quite fun in places. You can also read the written evidence that was submitted. Even the Daily Mail didn’t misss this one. Fioana Macrae wrote Boots boss admits they sell homeopathic remedies ‘because they’re popular, not because they work’ “It could go down as a Boot in Mouth moment. Yesterday, the company that boasts shelf upon shelf of arnica, St John’s wort, flower remedies and calendula cream admitted that homeopathy doesn’t necessarily work. But it does sell. Which according to Paul Bennett, the man from Boots, is why the pharmacy chain stocks such products in the first place. Mr Bennett, professional standards director for Boots, told a committee of MPs that there was no medical evidence that homeopathic pills and potions work. ‘There is certainly a consumer demand for these products,’ he said. ‘I have no evidence to suggest they are efficacious. ‘It is about consumer choice for us and a large number of our customers believe they are efficacious.’ His declaration recalls Gerald Ratner’s infamous admission in 1991 that one of the gifts sold by his chain of jewellers was ‘total crap’.” The Times noticed too, with Boots ‘labels homeopathy as effective despite lack of evidence‘. Now you know that you can’t trust Boots. You heard it from the mouth of their professional standards director. A commentary on the meeting by a clinical scientist summed up Bennett’s contribution thus "Paul Bennett from Boots had to admit that there was no evidence, but regaled the committee with the mealy-mouthed flannel about customer choice that we have come to expect from his amoral employer." Well said The third session of the Scitech evidence check can be seen here, and the uncorrected transcript is here. It is, in a grim way, pure comedy gold, More of that later.	2018-05-26 09:49:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.249269038438797, "perplexity": 3499.7215461364276}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867416.82/warc/CC-MAIN-20180526092847-20180526112847-00124.warc.gz"}
https://electronics.stackexchange.com/questions/259791/straight-forward-method-of-adding-encrypted-third-party-models-to-ltspices-mode	# Straight forward method of adding encrypted third party models to LTSpice's Model Tree I have >20 different types of MOSFET from fairchild that I would like to add to LTSpice's model tree. Fairchild encrypts their libraries. What is a straight forward method of adding their libraries to the model tree where I don't have to specify a sub-circuit every time I want to use them. I have hundreds of these FETs and I use them frequently. EDIT I figure this may shed some light on the subject. * LTspice Encrypted File * * This encrypted file has been supplied by a 3rd * party vendor that does not wish to publicize * the technology used to implement this library. * * Permission is granted to use this file for * simulations but not to reverse engineer its * contents. * ******************************************************************************** * Fairchild Semiconductor SuperFETIII 650V Model Library * Last Update: Jun. 02, 2016 * Model Version: 1.3 * Simulator: LTspice * ******************************************************************************** * Model Contacts: * James Victory James.Victory@fairchildsemi.com * Ken He kencanzhong.he@fairchildsemi.com * Scott Pearson Scott.Pearson@fairchildsemi.com * Hyeongwoo Jang Hyeongwoo.Jang@fairchildsemi.com * ******************************************************************************** * Reversion History: * Vers. Date Brief Description * 1.0 03/16/2016 1. Extract scalable base model from data of FCB070N65S3. The process parameters are from * 2. Generated models for : * FCB070N65S3 * FCP067N65S3 * FCPF067N65S3 * 1.1 05/03/2016 Added model for FCH023N65S3_F155 * 1.2 05/25/2016 Added model for FCH067N65S3_F155 * 1.3 06/02/2016 Added model for FCH023N65S3L4 * Updated thermal parameters for FCH023N65S3_F155 * ******************************************************************************** * Usage: * This library contains 3 and 5 pin(or terminal) models. The models include * self heating effects and were characterized under pulse conditions from * 10us to 1ms conditions. * * The 5p models contain 2 additional pins tj (or junction temperature) and * tcase (or device case thermal terminal). * tj should always be left floating or can be connected to a very * large resistor (>1meg). This terminal is meant to provide the user with * output information on the junction temperature under operation. For model * verification purposes against the data sheet and isothermal device simulations * for example, tcase should be connected to a voltage source with value {TEMP}, * the simulator ambient temperature. For system/module level simulations that * include thermal effects, tcase should be connected to the device-module * thermal interface node such as the heat sink interface point. * * For the device FCH023N65S3L4 which has a Kelvin Source (4-lead package), there are 4- and 6-pin models, the 3rd pin * "s1" is the Kelvin Source, the 4th pin "s2" is the Power Source. * ******************************************************************************** * Support devices: * FCB070N65S3_3p, FCB070N65S3_5p * FCP067N65S3_3p, FCP067N65S3_5p * FCPF067N65S3_3p, FCPF067N65S3_5p * FCH023N65S3_F155_3p, FCH023N65S3_F155_5p * FCH067N65S3_F155_3p, FCH067N65S3_F155_5p * FCH023N65S3L4_4p, FCH023N65S3L4_6p * ******************************************************************************** * ** Begin: 90 3B 2A 85 D1 AC 5A AE 43 66 6B A8 56 8C 9F F4 03 E8 4D E9 30 FE 57 15 09 76 CA DC 5D 13 36 1F 91 60 74 AB 47 45 20 03 46 D7 13 E8 66 1A 13 CF 94 22 5C 5A 9C 1F 27 A1 4C 65 63 59 EF FC 09 07 I can't even get ltspice to recognize them. Fairchild provides no instruction on how to use them and on LT all I could find was encrypting your own. I tried using them like non encrypted Libraries. The crazy thing is a guy had a library of controller chips I downloaded from a forum and all I had to do was copy and paste it into the folder and I can drag and drop them in with no sweat. I'm designing a SMPS with an SG3525 and it works great in spice. Why is this a headache? • I don't think that's possible, if they're encrypted. The only way I see is placing them in the lib/sub path, together with the other subcircuits, and have them available by simply placing an .inc or .sub directive in the schematic. This, however, is not a practise that is encouraged, as exporting the schematic/project will not make it available for others that do not have that particular custom library. Just a quick question, though: are you sure those models use .MODEL, instead of .SUBCKT? – a concerned citizen Sep 25 '16 at 6:37 • I have a lot of Fairchild models and none are encrypted; they do require me to login to get them, though. A specific part might be useful to see if an unencrypted version is available. I will note that Wurth provides an encrypted model library specifically for use in LTSpice. – Peter Smith Sep 25 '16 at 10:16 • I couldn't find anything on the older chip but I edited above to show what I'm dealing with – iuppiter Sep 25 '16 at 12:04 This may or may not work, but when I have had to import an external model into the libraries so it always shows up (no include statement required), here is the method: First, create a folder for your own parts within the LTSpice tree under lib\sym: Updated for the case ASY files are provided: Place the provided ASY files in this folder; the editing procedure will not apply. Editing proedure for the case where ASY files are not provided: Open a new schematic and place the NMOS object. Do CTRL:right click to get the properties box: Now open the symbol (the top button), then do Edit->Edit attributes Put the specific name of the file containing the model in the Spice model line. Change the value to to the specific model you want to use as exactly the name is in the library (e.g. FCB070N65S3 from the listing above; this is also what will be displayed in the schematic editor). Now save the file in your new folder as [modelname].asy (e.g.FCB070N65S3.asy) End of editing procedure for the case where ASY files are not provided. Make sure that the model file containing the model is in the lib/sub folder. This is it, showing one of my components. Now you should see your own folder in the tree in the schematic editor: You should navigate into the folder and you should be able to place the part. The file appears to have been encrypted for LTSpice, so hopefully it should work. I do not know if the model has been implemented as a subckt (MOSFETs very usually are), so in the edit attributes, you may need to change the prefix from MN to X. Note that the procedure is identical to the method for incorporating the Wurth encrypted library (and that definitely works). • The good thing I see here is that they already provided me with the ASY files, The library itself is .txt should I rename the extension, and where does it go? Thank you for the answer by the way I've been waiting all night for this. – iuppiter Sep 25 '16 at 12:59 • You do not need to rename the library file; just make sure you use that exact filename in the attributes; it is possible the ASY files already have that name in them. I am updating the answer as to where the file goes. – Peter Smith Sep 25 '16 at 13:13 • I just edited it to update you on the error I get and the difference in a normal NMOS and that thing – iuppiter Sep 25 '16 at 13:50 • @PeterSmith You should make a note that, even if this is the user's choice, it will (almost) break any chance of exporting your projects using those symbols, since it's most likely nobody else has your custom libraries/models/etc. As a matter a fact, the suggestion of simply placing an .inc or .lib, rather than messing with the default installation. should be the first thought (if not making folders for all projects and then copying sumbols/libs/etc in there, as needed). Comfort comes at a price that not all would be willing to pay for. – a concerned citizen Sep 25 '16 at 14:00 • I don't really plan on sharing them, I'm in back in school, taking engineering now these are personal projects that I'd like to test in a simulated environment to get an Idea of how the components will behave. I'm trying to stay ahead of the class so to speak. We're on ac theory and I'm making an Inverter. – iuppiter Sep 25 '16 at 14:07	2019-12-08 10:51:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3740237355232239, "perplexity": 2528.969647437138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540508599.52/warc/CC-MAIN-20191208095535-20191208123535-00059.warc.gz"}
https://www.splashlearn.com/math-vocabulary/geometry/slide	# Slide in Maths ## Slide: Introduction Slide is a transformation in which every point of the given shape or figure moves or slides in the same direction and also by the same distance. This transformation is also known as “translation.” So, what is a slide in math? To understand that, we must first learn about transformations. Transformations are changes that are made to any shape. Transformation in math is the method of transforming or changing the shape or size of an object using certain rules and methods. Flip (reflection), turn (rotation), and slide (translation) are the transformations or the positional changes we can make to a shape. Note: After any of these transformations (turn, flip, or slide), the size, area, angles, and line lengths of the shape remain the same. ## What Is a Slide in Math? Let us understand the definition of slide. Slide or translation is a transformation in which every point of a plane figure simply moves in the same direction by the same distance in that very plane, without any rotation or resizing. So, to undergo translation, every point of the shape must move • same distance • in the same direction Every point of the given polygon has moved in the same direction and by the same distance. So, we can call it “slide” or “translation.” ## Examples of Slide Let’s take a look at a few examples where a shape undergoes translation or slide transformation. Example 1: The given shape has just moved to the right. Example 2: The pencil has simply moved to the right. There’s no rotation or change in size. Example 3: Sliding of a Square ## Slide on a Graph Slides in geometry can be well-represented on a graph. We can also represent the translation using an equation without a graph. For example, if the shape gets moved 5 units right, and 4 units up, we can write: $(x, y) \rightarrow (x + 5, y + 4)$ It means that the x and y coordinates become “$x + 5$” and “$y + 4$” post translation. Let’s see some examples. Example 1: The following figure shows a slide or translation of a triangle. The shape has moved 2 units down and 2 units to the right. $(x, y) \rightarrow (x + 2, y – 2)$ Example 2: Every point on the rectangle has moved 3 units to the right and 2 units down. $(x, y) \rightarrow (x + 3, y – 2)$ ## Conclusion In this article, we learned about slide or translation transformation and discussed many examples using a graph. Let’s solve some examples to check our understanding. ## Solved Examples 1. Does the given image represent translation? Explain why or why not. Solution: Every point of the shape simply moved in the same direction by the same distance. So, it represents a slide. 2. Which figure represents the slide? Solution: Figure 1 represents a slide since the shape has simply moved to the right. In the case of figure 2, they are the mirror reflections of one another. 3. Identify the slide transformation. Solution: Figure 1 is the slide transformation of a triangle. Figure 2 shows rotation. 4. Does the given image represent a slide? Explain why or why not. Solution: The given figure represents a slide because every point of the figure is moving in the same direction by the same distance in that very plane. 5. What is a slide? Draw a slide pair diagram. Solution: A slide is a transformation in which every point of a plane figure moves in the same direction by the same distance in that very plane. ## Practice Problems 1 ### Identify the figure representing slide or translation. a b c d CorrectIncorrect In option a, the shape has simply moved, without any change in size or without any rotation. 2 ### Which option shows an example of a slide? $6 \rightarrow 9$ $9 \rightarrow 6$ $\text{x} \rightarrow \text{X}$ $\text{A} \rightarrow \text{A}$ CorrectIncorrect Correct answer is: $\text{A} \rightarrow \text{A}$ Eliminate options where there is rotation or resizing involved, and identify the option where the shape simply moved from one point to another. 3 ### The slide transformation is also known as Flip Turn Translation Rotation CorrectIncorrect Slide is also known as “translation.” 4 ### The following image does not represent “slide” because There is a change in size. There is a change in shape. The shape is rotated. None of the above CorrectIncorrect Correct answer is: The shape is rotated. This is not a translation because the shape is rotated. 5 ### By translation, a shape moves 2 units to the left and 2 units down. Which option represents this transformation? $(x, y) \rightarrow (x + 3, y - 2)$ $(x, y) \rightarrow (x - 2, y - 2)$ $(x, y) \rightarrow (x + 2, y - 2)$ $(x, y) \rightarrow (x - 2, y + 2)$ CorrectIncorrect Correct answer is: $(x, y) \rightarrow (x - 2, y - 2)$ The shape moves 2 units to the left and 2 units down. So, we can write $(x, y) \rightarrow (x - 2, y - 2)$	2023-03-20 18:29:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7281472682952881, "perplexity": 802.591687763547}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943555.25/warc/CC-MAIN-20230320175948-20230320205948-00798.warc.gz"}
https://www.gamedev.net/forums/topic/360768-data-driven-programming---academic-basis/	# Data Driven Programming - academic basis? This topic is 4885 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hi. I've been looking at Data Driven Programming (DDP) as part of my PhD project. I'm currently in the process of writing a data-driven scene management system much the one found in Dungeon Siege (but with a coarser level of granularity). What I'm really interested in is where DDP came from - in particular, I'd like to know if there are any academic papers at the heart of it. My supervisor starts pulling faces whenever I mention games technology, so I was wondering if anyone had any references to more academically suited papers on the subject. I'm hoping to talk about my use of DDP at a conference or two during the next six months - I don't want to introduce it as DDP if there's another Computer Science name for it that I'm not aware of. I would also appreciate any information regarding where additional materials (papers, presentations, etc.) can be found. Yes I'm aware of Google - that's where I found (some of) what I've been reading so far... Here is a list of what I currently have: "Building Object Systems" by Alex Duran (GDC 2003) "Object Systems" by Doug Church "A Data-Driven Game Object System" by Scott Bilas (GDC 2002) "Data-Driven Programming Made Easy" by Eric Malafeew (GDC 2005) "Component Based Object Management" by Bjarne Rene (Game Programming Gems 5) "XML Driven Classes in Python" by Eric van der Vlist I'll edit the list if I remember any more... I hope something here proves useful to someone. I'm certainly up for a chat about DDP if anyone is interested. [smile] Cheers, Jones. [Edited by - ajones on March 29, 2006 2:28:36 AM] ##### Share on other sites Hello, it is always a challenge to collect an overview of scientific works on some topic, as many researchers have different approaches and names for it. Google is usually not the best option for this; you'd better go with using search engines specifically for scientific journals. Some suggestions: CiteSeer ACM DBLP Usually the university also has support for searching articles; check with your local secretary or IT or library and the website for this. Where I used to do my research they had a brochure listing all engines and subscriptions to journals. Through ACM I found a few items vaguely in the direction but it takes lots of time to follow the citings as well until you stumble onto something -- I leave it to you. Good luck. Kind regards, Illco ##### Share on other sites Quote: Original post by Illcoyou'd better go with using search engines specifically for scientific journals The problem here, as you mentioned, is that people have different names for things. I've yet to find a paper via a ACM/CiteSeer/ScienceDirect search for "Data Driven" that actually refers to what I call DDP. Although I'm usually used to following references, it can be difficult when there isn't a DDP-related reference trail to follow. Quote: Through ACM I found a few items vaguely in the direction Was this a recent search? If so, would you mind sharing the reference? [smile] Jones. ##### Share on other sites Sure. I'm not sure how much it relates to what we are calling DDP though. ##### Share on other sites Thanks for the link, but my university subscription doesn't cover the publication - I'll have to see if I can arrange access later. Quote: I'm not sure how much it relates to what we are calling DDP though It's difficult (impossible?) to find DDP-related materials outside the gaming community, which leads me to believe that there is no academic (i.e. non-games technology) equivalent. When I read papers about data driven this and that, they're talking about simple object parameterisation, which in turn drives run-time behaviour. What I call DDP (data-driven specification and logical composition of class heirarchies) is slowly emerging in academia via developments in the use of scripting languages, but I have yet to see it applied elsewhere. ...I guess this means that my upcoming paper might be interesting after all... [grin] ##### Share on other sites Hello. I am actually looking at starting work on a PhD project within the next year myself. From my understanding, DDP is used and has been used for over 20 years in functional programming extensively. In contemporary, imperative languages, you may say that DDP is pulling mappings from config files or using PL data structures for control structures. You won't find anything like this in purely functional/mathemtical languages because it's part of the language. f(x) = x * 2f(2) = 4f(3) = 65f(10) = 100f(20) -> 40f(2) -> 4 This is very basic, but it's esentially DDP. I like python as a pseudo(imperative) language, so. def f(x): if x == 2: return 4 elif x == 3: # ... you get the idea else: return x * 2 And then to a (more convential) DDP implementation: vmap = { 2 : 4, 3 : 65, 10 : 100 'd': lambda z: z*2}def f(x): try: return vmap[x] except KeyError: return vmap['d'](x) Of course, look at the haskell and it would definately be "more elegant". If you asked a snoody functional language programmer, he would say this is just the rest of the world trying to catch up to what they discovered doing AI research in the 70's. The thing is, in functional programming, programmers see code AS data a lot of the time, so it's becomed so ingrained that it's not really anything to talk about anymore. I don't think that there's a lot of foundational information on DPP because DPP is more of an "applied" approach then a theoretical foundation approach. Many people have been using it in one way or another for many years with no name really given. The real question to ask is, is the data that you're using to drive your program mutable or not mutable? If it is immutable, then you can think of your data as constructions of functions. The act of accessing the data entry in your program is "applying function semantics". As such, you can reduce DDP into standard lambda-calc with an "applied" feel to it. Basically invent some words to classify the different categories of functions. This one is a "data provider" and this one is not. If it's mutable, then you're going to have a lot of fun. Because what you're essentially doing is indirectly changing the flow of execution. In which case, you loose all referential transparency and the problem becomes very, very generalized. I'm yet to clear things up precisely, but in my mind DDP is "in the mix" with the bottom-up programming and declaritive programming. If you're looking for mathematical underpinnings, you may have some luck looking into category theory and primitive set theory for grounding and then possibly looking into functors. I'd check out: http://math.ucr.edu/home/baez/week73.html I believe there are some good theoretical foundations to approach decision making, functional combination and configurable logic by mapping a applying the "data" in DDP to a functor's state. A place where you would probably get some really useful conversation going would be over at http://lambda-the-ultimate.org This place has a lot of smart cookies and if you ask your question the right way, you might just strike up an enriching conversation filled will all kinds of resources people use to back themselves up. Hope my ranting helps. • 15 • 21 • 9 • 15 • 60	2019-04-22 22:15:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25100889801979065, "perplexity": 1379.2903800253973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578582736.31/warc/CC-MAIN-20190422215211-20190423001211-00469.warc.gz"}
https://scipython.com/book/chapter-2-the-core-python-language-i/questions/problems/p24/benfords-law/	# Benford's Law #### Question P2.4.7 Benford's Law is an observation about the distribution of the frequencies of the first digits of the numbers in many different data sets. It is frequently found that the first digits are not uniformly distributed, but follow the logarithmic distribution $$P(d) = \log_{10}\left( \frac{d+1}{d} \right).$$ That is, numbers starting with 1 are more common than those starting with 2, and so on, with those starting with 9 the least common. The probabilities are given below: DigitProbability 10.301 20.176 30.125 40.097 50.079 60.067 70.058 80.051 90.046 Benford's Law is most accurate for data sets which span several orders of magnitude, and can be proved to be exact for some infinite sequences of numbers. (a) Demonstrate that the first digits of the first 500 Fibonacci numbers (see this Example) follow Benford's Law quite closely. (b) The length of the amino acid sequences of 500 randomly-chosen proteins are provided in the file protein_lengths.py. This file contains a list, naa, which can be imported at the start of your program with from protein_lengths import naa To what extent does the distribution of protein lengths obey Benford's Law? #### Solution To access solutions, please obtain an access code from Cambridge University Press at the Lecturer Resources page for my book (registration required) and then sign up to scipython.com providing this code.	2020-02-27 04:32:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5850094556808472, "perplexity": 571.7745818108164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146647.82/warc/CC-MAIN-20200227033058-20200227063058-00441.warc.gz"}
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/6027/2/dt/	Properties Label 6027.2.dt Level 6027 Weight 2 Character orbit dt Rep. character $$\chi_{6027}(19,\cdot)$$ Character field $$\Q(\zeta_{120})$$ Dimension 8960 Sturm bound 1568 Related objects Defining parameters Level: $$N$$ = $$6027 = 3 \cdot 7^{2} \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6027.dt (of order $$120$$ and degree $$32$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$287$$ Character field: $$\Q(\zeta_{120})$$ Sturm bound: $$1568$$ Dimensions The following table gives the dimensions of various subspaces of $$M_{2}(6027, [\chi])$$. Total New Old Modular forms 25600 8960 16640 Cusp forms 24576 8960 15616 Eisenstein series 1024 0 1024 Decomposition of $$S_{2}^{\mathrm{new}}(6027, [\chi])$$ into irreducible Hecke orbits The newforms in this space have not yet been added to the LMFDB. Decomposition of $$S_{2}^{\mathrm{old}}(6027, [\chi])$$ into lower level spaces $$S_{2}^{\mathrm{old}}(6027, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(287, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(861, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2009, [\chi])$$$$^{\oplus 2}$$	2019-12-10 20:56:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9134871959686279, "perplexity": 6473.350201314359}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540529006.88/warc/CC-MAIN-20191210205200-20191210233200-00119.warc.gz"}
https://brilliant.org/weekly-problems/2018-09-24/advanced/	# Problems of the Week Contribute a problem What is the value of $n$ such that $\displaystyle {\large \sum_{a_1=0}^4 \sum_{a_2=0}^{a_1} \cdots \sum_{a_n=0}^{a_{n-1}} 1} = 1001 ?$ A recent proposal for rapid inter-city transit is the Hyperloop, popularized by Elon Musk in 2012. The idea is to transport people inside of a levitating pod, by way of a partially evacuated tube running from city to city. Among the advertised benefits are its high speed (close to the speed of sound) and the potential to power the Hyperloop with solar energy. Inside the tube, the pod enjoys a reduced atmosphere with a pressure of $\SI{0.1}{\kilo\pascal},$ about $\frac{1}{1000}^\text{th}$ the pressure at sea level. Thanks to the evacuated tunnel and the magnetic levitation used to lift and propel the train, the energy needed to maintain the train's cruise velocity against the opposing forces of drag is very low. However, this boon requires an up-front energy expenditure in the form of evacuating a $\SI{600}{\kilo\meter}$-long tunnel large enough to fit the train. Approximately how many one-way trips of a comparable open-air (i.e. not in a tube), high-speed train would it take to recoup the initial energy expenditure to draw the vacuum? Assume • the pods and the Hyperloop tube have a radius of $r = \SI{2.5}{\meter},$ the density of air is $\rho_\text{air} = \SI[per-mode=symbol]{1.22}{\kilo\gram\per\meter\cubed},$ the distance from Los Angeles to San Francisco is $d_\text{LA to SF} \approx \SI{600e3}{\meter},$ the drag coefficient is $C_\text{D} \approx 0.15,$ and when run as a high-speed train, the pods travel at $\SI[per-mode=symbol]{150}{\meter\per\second};$ • once drawn, the Hyperloop tube maintains the partial vacuum state. In group theory, if you take a standard deck of cards and shuffle it exactly the same way repeatedly, you will eventually get back to the original order of the cards. For a standard deck of 52 cards, this could take many deck shufflings! However, what if your deck consisted of only 8 cards? With only 8 cards, what is the smallest number of identical shufflings you need to make in order to be guaranteed to return to the original order of the cards (somewhere along the way)? Assumption: All shuffles are identical. For example, if the first shuffle takes the third card to the fifth position, then all successive shuffles will also take the third card to the fifth position. Or, more generally, for all $n$, if the $n^\text{th}$ card went to the $m^\text{th}$ position, then the $n^\text{th}$ card would necessarily go to the $m^\text{th}$ position on all successive shufflings. Clarification:. You don't get to pick the way the cards are shuffled, but they must be shuffled the same way every time. In the ellipse shown, let $a$ and $b$ be the lengths of the semi-major and semi-minor axes, respectively. What is the value of $j$ for which $a^2 + b^2 = 19200?$ $1,1,2,3,5,8,13,21,...$ If we divide the terms in the Fibonacci sequence above by $2$, then the remainders will be $1,1,0,1,1,0,1,1,0,...$. Obviously, the ratio of the numbers of $0$s and $1$s in the sequence goes to $1:2.$ If we divide the terms by $3$, then the remainders will be $1,1,2,0,2,2,1,0,1,1,2,0,...$. The ratio of the numbers of $0$s, $1$s, and $2$s in the sequence now goes to $2:3:3.$ Now, we divide the terms by a positive integer $n$ and obtain a sequence of remainders. Then the ratio of the numbers of $0$s, $1$s, $2$s, $\ldots,$ $(n-1)$s in the sequence goes to $1:1:1:\ldots:1.$ What is the sum of all possible $\frac1n,$ if $n$ can also be 1? Clarification: Each whole number smaller than $n$ has the same probability to appear in the sequence of remainders. This is also the reason that $n$ can also be $1$. ×	2019-10-18 17:37:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 47, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.79802006483078, "perplexity": 319.6648699211529}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986684226.55/warc/CC-MAIN-20191018154409-20191018181909-00413.warc.gz"}
https://datacadamia.com/data/type/collection/set/cross	# Set Theory - Cross Product (Cartesian product) The cartesian product is a set operator between two set A and B that produces a set of all pairs (a, b) where: • $a \in A$ (ie a in A) • and $b \in B$ (ie b in B) ## Notation $$\Large A \times B$$ ## Example A = {1, 2} B = {a, b} A x B = {(1,a), (1,b), ((1,c), (2,a), (2,b), (2,c)}	2022-05-20 07:43:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21518145501613617, "perplexity": 3929.132599925927}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662531762.30/warc/CC-MAIN-20220520061824-20220520091824-00190.warc.gz"}
http://eprints.imtlucca.it/2328/	# Fixed-point implementation of a proximal Newton method for embedded model predictive control (I) Guiggiani, Alberto and Patrinos, Panagiotis and Bemporad, Alberto Fixed-point implementation of a proximal Newton method for embedded model predictive control (I). In: Proceedings of the 19th IFAC World Congress. IFAC, pp. 2921-2926. ISBN 978-3-902823-62-5 (2014) Preview PDF (Pre-print version)	2020-01-27 23:04:05	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8427279591560364, "perplexity": 8267.603511894502}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251728207.68/warc/CC-MAIN-20200127205148-20200127235148-00086.warc.gz"}
http://www.edurite.com/kbase/analytical-math-problems	#### • Class 11 Physics Demo Explore Related Concepts # Analytical Math Problems Analytical Geometry : Analytical Geometry is a unit of mathematics with study of coordinate system,conic section,circle,equation of line. Analytical Math Problem 1. What is the center of the circle x+ y- 4x - y + 5 = 0 a) (2,1) b) (3,2) c) (2,$\frac{1}{2}$) d) (3,$\frac{1}{3}$) 2. Express $\frac{21}{27}$ in standard form a) $\frac{7}{-9}$ b) $\frac{3}{5}$ c) $\frac{7}{5}$ d) $\frac{-7}{4}$ 3. IF xy, is an even integer then value of x and y is a) odd b) even c) an irrational number d) none of the above 4. Calculate the gradient of the line AB (1,-5) and (4,6) a) $\frac{12}{3}$ b) $\frac{11}{3}$ c) $\frac{21}{7}$ d) $\frac{-11}{3}$ 5. If Eccentricity is equal to 1,then the conic is called as a) Parabola b) Ellipse c) Hyperbola d) None 6. Find the distance between A (3; 4) and B (6; 7) a) √9 b) √3 c) 3√2 d) 0 7. Find the equation of the line with gradient = –2 passing through A (3,7) a) y = 2x + 3 b) y = -2x + 1 c) y = 2x + 5 d) y = 5x + 3 8. the point (–6; –2) and perpendicular to 3x + 2y = 6 a) $\frac{2}{3}$ b) $\frac{3}{2}$ c) $\frac{2}{5}$ d) none 9. In the given figure, C is the midpoint of AB. Calculate the value of x and y. 10. Find the midpoint of the line joining A(-6; 4) and B(2;-5) a) (-2,-5) b) (3,2) c) (5,3) d) (2,7) 11. What is the equation of Parabola 12. What is the standard form of equation of ellipse Analytic Geometry Formula: Mid point formula: $\left ( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )$ The distance formula is used to find the distance between two points A (x1 ; y1) and B (x2; y2) AB = $\sqrt{\left ( X_{2}-X_{1} \right )^{2}+\left ( Y_{2}-Y_{1} \right )^{2}}$ The gradient of the line = $\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}$ The equation of a straight line is given by y = mx + c The equation of the perpendicular bisector = y – y1 = m(x – x1) Question:This was my girlfriend's extra credit problem last semester and no one in her class was able to solve it without using a calculator. Not even my girlfriend's aunt, who is a high school math teacher, was able to solve it. (7x - 2)^(1/3) + (7x + 5)^(1/3) = 3 I attempted both approaches in earnest and neither of them yielded anything I deemed useful. Thanks for the suggestions though. Answers:Well, one answer is obviously 3/7, that can be found out just by looking upon the problem. Now, function x^(1/3) is monotone increasing (because f(x) is monotone increasing if f'(x)>0, and (x^(1/3))'=(1/3)x^(-2/3)>0), so (7x - 2)^(1/3), (7x + 5)^(1/3) and (7x - 2)^(1/3) + (7x + 5)^(1/3) are monotone increasing too, so the graphic of function f(x)=(7x - 2)^(1/3) + (7x + 5)^(1/3) can have only one point of crossing with any horizontal line, such as f(x)=3, and therefore it has only one salvation which is 3/7. Question:What would be the absorbance of the gaseous ozone if its total pressure is doubled? This is a question from my professor. How to solve this problem? Thanks.=) Answers:The Beer-Lambert Law states that absorbance is linearly proportional to the concentration of the ozone in your sample. So if the pressure is doubles, then so does the concentration. Absorbance doubles. Question:I'm going back to school this fall and I plan on taking Calculus with Analytic Geometry I, II, III, instead of the other math classes like college algebra and calculus. I'm pursuing an engineering degree and that math class is required... (math is my worse subject.... 4 years ago) I dont remember much of the stuff at all really, but I'm thinking they teach you everything along the way anyway.. I dont remember everything from algebra or geometry either... But I plan on studying my butt off and working hard for a good grade so... Am I wasting my time for the inevitable F or no its a piece of cake and can be done no problem? Thanks all for your help and opinion~! Question:Solve for this equation: (find the value of "v" for the given parameters) k(v^c)/(1-v) = 1. Parameters include 0 0. (So the fraction will always be +ve, and = 1). 'v' is the variable here, while 'c' and 'k' are given constants. For instance, if c = ln 4/ln 3, and if k = 91^(c-1), then, m = 27/91 exactly. ---- Good luck! oops.. I wrote 'm' by mistake; I meant v = 27/91! Nick - I know there are special cases - that's there in every math problem. And in the example I gave, 'c' was definitely not an integer ln 4/ln 3.. so I'm really not looking for an integer solution; I did not make that specialization - I'm looking for an analytical solution. I'm not sure if I should say thanks for trying :/ but the question, as you can see, is not asking for a 'specialized' case.. I did mention that if there was a specialized case (like the one I gave as an example), then of course it's easy to solve. You're kinda telling me back what I'm trying to say anyway =.= The thing is, there is a limit to this equation .. to the 'solution', I mean. And it is dependent on k, c. I would like to see if there's a way to find the limit, or something close to it for an approximation. It's basically solving m(x^d) + x = 1, where m, d are constants. I guess though - out of courtesy - thanks for your answer. Answers:If k=0, there's no solution. Otherwise, multiply through by 1-v to obtain k v^c + v - 1 = 0. If c is an integer between -3 and +4 inclusive, then we can solve the polynomial by radicals. Otherwise, there's no reason to expect to be able to solve the equation for general c and k. Of course there will be particular lucky cases, like the one you cooked up: let w be whatever you want (strictly between 0 and 1) and take k = (1-w)/w^c; then v=w is a solution. In response to your reply, the answer is negative: unless c is one of those integers, there is no explicit, closed form solution. There is a (fairly) smooth solution, and, as you say, you can approximate it iteratively point by point, but it's just the inverse of the function given by k v^c + v - 1 = 0. Analytic Epistemology :This clip discusses some of the schools of thought in contemporary analytic epistemology. First, the clip mentions Bertrand Russells dislike for the standard notion of what constitutes "knowledge" in philosophy, believing it to be to much too vague. Then there is a brief summary of GE Moore's "Proof of an External World" and his views on foundationalism. The clip then mentions Ludwig Wittgenstein's idea that "meaning is use" within social contexts, and that philosophical obstacles are really just miscommunication within "language games." Simply put, Wittgenstein thought that there were no such things as genuine philosophical problems, and that philosophy was merely a byproduct of linguistic misunderstandings. The clip then discusses the differences between foundationalism and coherentism and WVO Quine's notion of the seamless "web of belief." Quine was a strong proponent of the natural sciences, and thought that findings in the natural sciences could shed significant light onto age-old philosophical questions concerning the nature of the mind and knowledge. The clip then summarizes "The Gettier Problem" which challenged the Platonic definition of knowledge as "justified true belief," and then ends with definitions of internalism/externalism, and Alvin Goldman's causal theory of knowledge. Maths 911 Grade 11 Analytical Geometry :Maths 911 Live Show Grade 11 Analytical Geometry:Gradient of a Straight Line Presenter:John Luis Executive Producer:Dylan Green	2014-11-01 04:37:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7129606008529663, "perplexity": 1384.027962347207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637903893.35/warc/CC-MAIN-20141030025823-00241-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.calculus-online.com/exercise/5371	# Definite Integral – Finding area between 3 functions – Exercise 5371 Exercise Find the area of the region bounded by the graphs of the equations: $$y=\frac{1}{x}, y=x, y=4x$$ In the domain $$x\geq 0, y\geq 0$$ $$S=\ln 2$$	2019-11-14 04:05:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 3, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8523775339126587, "perplexity": 558.8339236337117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667945.28/warc/CC-MAIN-20191114030315-20191114054315-00370.warc.gz"}
https://zbmath.org/?q=an:07200400	# zbMATH — the first resource for mathematics $$W^{1,p}$$-solutions of the transport equation by stochastic perturbation. (English) Zbl 1434.60163 Summary: We consider the stochastic transport equation with a possibly unbounded Hölder continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong stability of $$W^{1,p}$$-weak solutions. ##### MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35F10 Initial value problems for linear first-order PDEs 35R60 PDEs with randomness, stochastic partial differential equations Full Text: ##### References: [1] Alberti, G., Bianchini, S. and Crippa, G. (2010). Divergence-free vector fields in $$\mathbb{R}^2$$. Journal of Mathematical Sciences 170, 283-293. · Zbl 1304.35214 [2] Ambrosio, L. (2004). Transport equation and Cauchy problem for $$\mathit{BV}$$ vector fields. Inventiones Mathematicae 158, 227-260. · Zbl 1075.35087 [3] Ambrosio, L. and Crippa, G. (2014). Continuity equations and ODE fows with non-smooth velocity, Lecture notes of a course given at HeriottWatt University, Edinburgh. Proceedings of the Royal Society of Edinburgh Section A Mathematics 144, 1191-1244. · Zbl 1358.37046 [4] Catuogno, P. and Olivera, C. (2013). $$L^p$$-Solutions of the stochastic transport equation. Random Operators and Stochastic Equations 21, 125-134. · Zbl 1270.60070 [5] Colombini, F., Luo, T. and Rauch, J. (2004). Nearly Lipschitzean divergence-free transport propagates neither continuity nor BV regularity. Communications in Mathematical Sciences 2, 207-212. · Zbl 1088.35015 [6] Dafermos, C. M. (2010). Hyperbolic Conservation Laws in Continuum Physics, 3rd ed. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 325. Berlin: Springer. · Zbl 1196.35001 [7] De Lellis, C. (2007). Ordinary Differential Equations with Rough Coefficients and the Renormalization Theorem of Ambrosio. Bourbaki Seminar 1-26. [8] DiPerna, R. and Lions, P. L. (1989). Ordinary differential equations, transport theory and Sobolev spaces. Inventiones Mathematicae 98, 511-547. · Zbl 0696.34049 [9] Fedrizzi, E. and Flandoli, F. (2013). Noise prevents singularities in linear transport equations. Journal of Functional Analysis 264, 1329-1354. · Zbl 1273.60076 [10] Fedrizzi, E., Neves, W. and Olivera, C. (2018). On a class of stochastic transport equations for $$L_{\text{loc}}^2$$ vector fields. Annali Della Scuola Normale Superiore Di Pisa Classe Di Scienze 18, 397-419. · Zbl 1391.60157 [11] Flandoli, F., Gubinelli, M. and Priola, E. (2010a). Well-posedness of the transport equation by stochastic perturbation. Inventiones Mathematicae 180, 1-53. · Zbl 1200.35226 [12] Flandoli, F., Gubinelli, M. and Priola, E. (2010b). Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift. Bulletin Des Sciences Mathématiques 134, 405-422. · Zbl 1198.60023 [13] Flandoli, F., Gubinelli, M. and Priola, E. (2012). Remarks on the stochastic transport equation with Hölder drift. Rendiconti del Seminario Matematico. Universita e Politecnico Torino 70, 53-73. · Zbl 1292.60063 [14] Hauray, M. (2003). On two-dimensional Hamiltonian transport equations with $$L^p_{\text{loc}}$$ coefficients. Annales de L’Institut Henri Poincaré Analyse Non Linéaire 20, 625-644. · Zbl 1028.35148 [15] Kunita, H. (1984a). Stochastic differential equations and stochastic flows of diffeomorphisms. In École d’Été de Probabilités de Saint-Flour XII-1982, 143-303. Berlin: Springer. · Zbl 0554.60066 [16] Kunita, H. (1984b). First order stochastic partial differential equations. In Stochastic Analysis (Katata/Kyoto, 1982). North-Holland Math. Library 32, 249-269. [17] Lions, P. L. (1996). Mathematical Topics in Fluid Mechanics, Vol. I: Incompressible Models. Oxford Lecture Series in Mathematics and Its Applications 3. New York: Oxford University Press. · Zbl 0866.76002 [18] Lions, P. L. (1998). Mathematical Topics in Fluid Mechanics, Vol. II: Compressible Models. Oxford Lecture Series in Mathematics and Its Applications 10. New York: Oxford University Press. · Zbl 0908.76004 [19] Mollinedo, D. A. C. and Olivera, C. (2017a). Stochastic continuity equation with non-smooth velocity. Annali di Matematica Pura ed Applicata. Series IV 196, 1669-1684. · Zbl 1372.60093 [20] Mollinedo, D. A. C. and Olivera, C. (2017b). Well-posedness of the stochastic transport equation with unbounded drift. Bulletin of the Brazilian Mathematical Society, New Series 48, 663-677. · Zbl 1386.60223 [21] Neves, W. and Olivera, C. (2015). Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition. NoDEA Nonlinear Differential Equations and Applications 22, 1247-1258. · Zbl 1325.60111 [22] Neves, W. and Olivera, C. (2016). Stochastic continuity equations—A general uniqueness result. Bulletin of the Brazilian Mathematical Society, New Series 47, 631-639. · Zbl 1356.60104 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.	2022-01-18 11:19:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6556504964828491, "perplexity": 3519.972792603065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300810.66/warc/CC-MAIN-20220118092443-20220118122443-00484.warc.gz"}
https://homework.zookal.com/questions-and-answers/which-one-of-the-following-choices-cannot-be-used-to-416642252	1. Engineering 2. Chemical Engineering 3. which one of the following choices cannot be used to... # Question: which one of the following choices cannot be used to... ###### Question details Which one of the following choices cannot be used to specify the state of a pure substance in the two phase region? A. Temperature and specific volume B. Pressure and specific volume C. Pressure and specific enthalpy D. Pressure and temperature	2021-03-05 07:05:31	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9211071729660034, "perplexity": 1223.0596419066906}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178370239.72/warc/CC-MAIN-20210305060756-20210305090756-00610.warc.gz"}
https://xaktly.com/EulersMethod.html	A method for estimating specific solutions of differential equations Most of the differential equations you've likely encountered in your early studies of calculus have been separable equations. That means it was possible to group terms (say in x and y) on either side of the equation and integrate each side separately. Most differential equations that are of any use in the world aren't separable, and we need other methods to solve them. There are many such methods, and whole college classes are devoted to them. In this section, we discuss one method, presented by Swiss mathematician Leonhard Euler (pronounced Oy-ler), for estimating specific solutions that are close to some initial condition (sometimes called a "boundary condition"). Solutions to Differential equations Remember that the general solution to a differential equation is a whole set of functions, and the specific solution (which we find by knowing an initial condition–sometimes "boundary condition") is one of those functions. How it works Let's say (just for the sake of argument right now) that we know the specific solution of a differential equation. Now let's think about how we might estimate some of that function (we might not need it all) that solves our differential equation using the derivative, dy/dx, embedded in the equation. If we start at the point (x, y), the initial condition, and assuming we can at least solve the differential equation for dy/dx, we can calculate the slope of the function at that point: it's dy/dx – easy. Now let's imagine moving to the right a small distance – we'll call it Δx. That's going to be the x-coordinate of a new point on our estimated solution, and Δy is just Δx multilied by the slope at x. That's where this becomes an estimate, because the slopes of the solution as x and x + Δx are surely different, but if Δx is small, they won't be too different. So if we calculate Δy (from Δx and the slope), and add it to y, we get the new y-coordinate, and we have a new point on our solution curve: (x + Δx, y + Δy). Graphically, the first step looks like this: If Δx is small enough, the slope we calculate using the differential equation at x will be very close to that at Δx, so our point won't be too far off the curve, but it's unlikely to be exaclty on it. We can repeat Euler's method to build out our function (actually in either direction) from the initial known point. Of course, the farther we go, the more the small errors could add up, and we might expect our estimate to wander, as the green estimate in the graph below does. If we can tolerate some error, Euler's method is a good way of estimating the value of a specific solution to a differential equation in the neighborhood of the known point. For example, if we knew the exact value at x = 2, then it would make sense to try to find the value at x = 3 by using, say, 5 steps of Euler's method with a Δx of 0.2. The Δx you use will be a matter of trial and error. The smaller the better, but then it takes longer to get to the solution. Example 1 In this example, let's use Euler's method to estimate a specific solution of a separable differential equation, one that we can already integrate directly and find the exact solution. That way we can judge the quality of our approximation. Our differential equation will be $$\frac{dx}{dy} = xy$$ As usual, we'll begin by separating variables ... $$\frac{dy}{y} = x \, dx$$ then integrating both sides $$\int \, \frac{dy}{y} = \int \, x \, dx$$ to get $$ln\|y\| = \frac{x^2}{2} + C$$ If we raise both sides of that result as a power of e, and take advantage of the laws of exponents to turn the additive constant C into the multiplicative constant A, we get the general solution, $$y = A e^{x^2/2}$$ Now we'll use the boundary condition y(0) = 2, to find that A = 2, so we have the specific (and exact) solution, $$y = 2 e^{x^2/2}$$ Now we'll solve this equation, starting at (0, 2) with Euler's method, to find an approximation of the solution at x = 1, and compare it to the exact value. To apply Euler's method, first decide on a step size for Δx. Smaller is better, but there is a diminishing return, and you don't want to take forever. On the other hand, Euler's method is perfect for automating or running in a spreadsheet. Euler's method: steps 1. Decide on a step size, Δx. 2. Start with a point (x, y), 3. calculate the slope, dy/dx at that point using the differential equation, 4. calculate Δy = Δx (dy/dx), 5. add Δx to x and Δy to y to form the next point, and 6. ... do that until you reach the target x-value. It's easiest to keep things organized in a table. With a step size of Δx = 0.2, here's the first line of such a table (you can organize your own in your own way), on our way to finding the solution at x = 1. Remember (0.0, 2.0) is a point we already know, our initial condition, and that dy/dx is defined by the differential equation: dy/dx = xy The next point is just where the first step ended up, at (x + Δx, y + Δy), then we just keep on going, bridging the gap between x = 0 and x = 1 in Δx = 0.2 increments. The next step is Finally, the whole table looks like this: Now our estimate of f(1) = 2.919 is about 11% different from the exact value of 3.3. That may or may not be an error we can tolerate. We might be able to improve on the approximation by choosing a smaller step size, which would keep the jump in slopes from one point to another smaller – remember, the slope used to calculate Δy is the slope from the previous point. The graph on the right shows how our estimate and the exact value of the solution slowly diverge as we go from x = 0 to x = 2. Example 2 In this example, we'll estimate a solution of a non-separable differential equation: $$\frac{dy}{dx} = x + y$$ Our initial point will be (2, 1), and we'll use that to try to estimate the solution at x = 3 by building out to the right (+x direction) in various increments. We'll try Δx = 0.1, Δx = 0.05 and Δx = 0.01. I'll show tables for the first two, then let you make a spreadsheet for the last one, which has 100 steps. For a step size of 0.1, y(3) = 6.37. If we decrease the step size to 0.05, the estimate is 6.61. But the question we really need to ask is whether, as we decrease the step size, the estimate converges. Convergence means that at some point, each time we decrease the step size, the estimate changes by a smaller amount. This plot shows what happens to the estimate of y(3) as we increase the size of the x-step from 0.1 to 0.001. Notice that the value (moving from lower right to upper left) seems to be changing less each time we add more steps. Smaller steps are generally better if you have the time. xaktly.com by Dr. Jeff Cruzan is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. © 2012, Jeff Cruzan. All text and images on this website not specifically attributed to another source were created by me and I reserve all rights as to their use. Any opinions expressed on this website are entirely mine, and do not necessarily reflect the views of any of my employers. Please feel free to send any questions or comments to jeff.cruzan@verizon.net.	2022-01-28 11:17:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7089745998382568, "perplexity": 354.3871741947309}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305494.6/warc/CC-MAIN-20220128104113-20220128134113-00465.warc.gz"}
https://lexique.netmath.ca/en/picks-theorem/	# Pick’s Theorem ## Pick’s Theorem Pick’s theorem provides a formula for calculating the area of a polygon drawn on lattice points. ### Formula Pick’s formula for calculating the area A, is: A = $$\frac{P}{2}$$ + Q – 1, where : • P is the number of points on the polygonal chain; • Q is the number of points located inside the polygon. ### Example A = $$\frac{P}{2}$$ + Q – 1 A = $$\frac{9}{2}$$ + 5 – 1 A = 4.5 + 5 – 1 A = 8.5	2023-01-27 11:16:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5150368809700012, "perplexity": 792.1464341437818}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494976.72/warc/CC-MAIN-20230127101040-20230127131040-00227.warc.gz"}
https://www.statsmodels.org/v0.10.2/generated/statsmodels.genmod.families.family.Gaussian.loglike.html	# statsmodels.genmod.families.family.Gaussian.loglike¶ method Gaussian.loglike(endog, mu, var_weights=1.0, freq_weights=1.0, scale=1.0) The log-likelihood function in terms of the fitted mean response. Parameters endogarray Usually the endogenous response variable. muarray Usually but not always the fitted mean response variable. var_weightsarray-like 1d array of variance (analytic) weights. The default is 1. freq_weightsarray-like 1d array of frequency weights. The default is 1. scalefloat The scale parameter. The default is 1. Returns llfloat The value of the loglikelihood evaluated at (endog, mu, var_weights, freq_weights, scale) as defined below. Notes Where $$ll_i$$ is the by-observation log-likelihood: $ll = \sum(ll_i * freq\_weights_i)$ ll_i is defined for each family. endog and mu are not restricted to endog and mu respectively. For instance, you could call both loglike(endog, endog) and loglike(endog, mu) to get the log-likelihood ratio.	2022-01-17 08:12:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9070606827735901, "perplexity": 9876.75777295892}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300343.4/warc/CC-MAIN-20220117061125-20220117091125-00107.warc.gz"}
https://www.physicsforums.com/threads/q-regarding-integration.38984/	# Q regarding Integration 1. Aug 10, 2004 ### ReyChiquito Im trying to understand a "simple" identity. I have the problem $$\ddot{y}+g(t,y)=0$$ with $$y(0)=y_{0}$$ and $$\dot{y}(0)=z_{0}$$ What i need to prove is that the solution can be expresed in the form $$y(t)=y_{0}+tz_{0}-\int_{0}^{t}(t-s)g(s,y(s))ds$$ Integrating twice is clear that $$y(t)=y_{0}+tz_{0}-\int_{0}^{t}\{\int_{0}^{s}g(\tau,y(\tau))d\tau\}ds$$ Now the book goes $$\int_{0}^{t}\{\int_{0}^{s}g(\tau,y(\tau))d\tau\}ds=\int_{0}^{t}\{\int_{\tau}^{t}ds\}g(\tau,y(\tau))d\tau$$ ???????????????????? How do i prove that? should i do a change of variable? use fubini? Im lost, pls help. 2. Aug 10, 2004 ### mathman It is not any change of variables. If you look at the domain of integration in the (s,tau) plane, you will see it is a triangle. All the book is describing is how the triangle is expressed when you switch the order of integration. Fubini's theorem says you can do the switch. 3. Aug 10, 2004 ### ReyChiquito Ohhhhhhhhhhhhh.... i know i should have named the tread "stupid Q about integration". Thx a lot dood. I sure need to review my calc notes.	2018-01-23 20:41:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5955923795700073, "perplexity": 901.5985279947201}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084892238.78/warc/CC-MAIN-20180123191341-20180123211341-00719.warc.gz"}
https://socratic.org/questions/how-do-you-differentiate-y-e-5x-4-e-4x-2-3	# How do you differentiate y=(e^(5x^4))/(e^(4x^2+3))? Nov 29, 2016 Rewrite as $y = {e}^{5 {x}^{4} - 4 {x}^{2} - 3}$, then use $\frac{d}{\mathrm{dx}} \left({e}^{u}\right) = {e}^{u} \frac{\mathrm{du}}{\mathrm{dx}}$ #### Explanation: An important property of exponents is ${a}^{n} / {a}^{m} = {a}^{n - m}$ $y = {e}^{5 {x}^{4}} / {e}^{4 {x}^{2} + 3} = {e}^{5 {x}^{4} - 4 {x}^{2} - 3}$ $y ' = {e}^{5 {x}^{4} - 4 {x}^{2} - 3} \cdot \frac{d}{\mathrm{dx}} \left(5 {x}^{4} - 4 {x}^{2} - 3\right)$ $= \left(20 {x}^{3} - 8 x\right) {e}^{5 {x}^{4} - 4 {x}^{2} - 3}$	2021-02-28 19:19:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9524813890457153, "perplexity": 4674.255504263007}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178361723.15/warc/CC-MAIN-20210228175250-20210228205250-00595.warc.gz"}
http://mathhelpforum.com/differential-geometry/181452-how-prove-closed-set-r.html	# Thread: how to prove a closed set in Rⁿ 1. ## how to prove a closed set in Rⁿ hi! what is the easiest way to prove that the set A is closed and the set B is not closed? 1). A={(x,y) ∈ R²: x²+y²=1} and 2). B={(x,y) : ∈ R²: x² - y²=1} Help please. thanks please 2. Originally Posted by sorv1986 hi! what is the easiest way to prove that the set A is closed and the set B is not closed? 1). A={(x,y) ∈ R²: x²+y²=1} and 2). B={(x,y) : ∈ R²: x² - y²=1} Help please. thanks please I mean, the easiest way would be to note that $f:\mathbb{R}^2\to\mathbb{R}$, $f(x,y)=x^2+y^2$ is continuous (it's just a polynomial) and $A=f^{-1}({1})$ and for the second one are you sure it isn't closed? 3. ## thanks for ur response sir oho....actually the 2nd one i think its a hyperbola...so it should be not closed...am i wrong?.....but in the first case...i did not understand what r u actually doing to prove that set A is closed	2017-07-21 20:44:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8370484113693237, "perplexity": 1254.1706083784966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423809.62/warc/CC-MAIN-20170721202430-20170721222430-00303.warc.gz"}
https://www.gamedev.net/forums/topic/417531-ok-code/	Public Group # ok code? This topic is 4279 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts My book told me to make a program that first reads strings into a vector. Then I was gona output how many strings there where and how many times each word apears. The code below is how I did it.. is this ok? or is it another easyer way to do it? #include <iostream> #include <vector> #include <string> using std::cout; using std::vector; using std::string; using std::cin; using std::endl; int main() { cout << "Pleas enter some words. Press enter after each word and when you" << " are finnished you enter end-of-file: " << endl; vector<string> words; //outputs how many words there are. cout << "The number of words are: " << words.size() << endl << endl; //counts how many times one word apear. typedef vector<string>::size_type vec_sz; vector<string> counted_words; for (vec_sz i = 0;i != words.size();++i){ //check if the words is counted allready bool counted = 0; for (vec_sz j = 0;j != counted_words.size();++j){ if (words == counted_words[j]){ counted = 1; } } //if its not counted count it. if (!counted){ counted_words.push_back(words); int count = 0; for (vec_sz j = 0;j != words.size();++j){ if (words == words[j]) count++; } cout << words << " Appear's " << count << " times." << endl; } } } ##### Share on other sites Quote: for (vec_sz i = 0;i != words.size();++i){ Have your book introduced you to iterators yet? When looping through a vector you should use iterators. Quote: bool counted = 0; You should use true and false, not 0 and 1. We want to be as expressive as possible, and 0 and 1 express that counted is an integer, not a boolean, people might think it is a counter to see how many words have been counted. Quote: if (words == counted_words[j]){ counted = 1; } You should break out of the loop when the condition is meet, it will never be encountered again, and if it would it wouldn't make a difference since it would do the same thing. Quote: int count = 0; for (vec_sz j = 0;j != words.size();++j){ if (words == words[j]) count++; } cout << words << " Appear's " << count << " times." << endl; This seems to be in the wrong place, you should place it after you're done counting. We need to know at what level you're at before we can make suggestions, for example could you use std::find to search the vectors? ##### Share on other sites nope.. not into iterators or std::find yet.. what do you mean that its in the wrong place? it is the counting.. thx :) ##### Share on other sites Quote: Original post by Nanooknope.. not into iterators or std::find yet..what do you mean that its in the wrong place? it is the counting..thx :) Functionality wise, it's correct, but you should try to seperate functionality so, your code will only get more confussing if you at some point need to add something. You should instead in the first loop not do anything, but filling up counted_words. Then you should create a new loop going through all elements of counted_words, and count the number of words for each of these. Since this is just a "did you understand it" excersize, which it definitely look like you did, then don't worry, you'll learn about this stuff later on just move on, your code is quite nice considering the experience you have. ##### Share on other sites hehe ok.. thx.. good to hear.. :) I forgot to ask how I quit the loop when the if statment is true.. ##### Share on other sites As CTar has already pointed out this is a good attempt. But you should know that the c++ standard library is huge, and there are a lot of tools/utilities it provides that can make things much easier. When creating an algorithm, usually the underlying data structure plays a big factor in how effective the algorithm is. Unfortuanetly you havent gone though iterators yet, but iterators is a concept from the standard library that defines how to access elements inside a standard container. For example your "vector" is one of the standard containers. It is also the structure you are using to perform your string counting algorithm. There is one container called "map". What it does, it maps keys to values. Using a map would make things much easier. Because if you treated the strings as "keys" and had an integer in the value spot, then conting the number of strings in your vector becomes next to natural. map[key]++; The above line, will increment the "value" that "key" is stored at. So for example you do this: map["hello"]++; map["byebye"]++; map["hello"]++; you'll end up with map["hello"] having a value of 2 and map["byebye"] having a value of 1. This is of course assuming that the values themselves are initialized at 0 before you plusplus them. I suggest toying around with std::map to count your strings instead of the current method you are using now. Just for learning purposes if nothing else. Iterators are not that difficult of a subject to learn about, at least not the basics. There're always tools within the standard library that people don't know about and can be used in various situations. For example your entire main can probably be reduced to something similar to this (if not more or less this) by making use of the standard library. std::vector<std::string> v;std::map<std::string, int> m;// this would read in from the input stream and store the values in vstd::copy( std::istream_iterator<std::string>(std::cin), std::istream_iterator<std::string>(), std::back_inserter(v) );// this can apply a function to store each vector element in the map containerfor_each( v.begin(), v.end(), MapCountFunctor() );// this will print out each element of the map. Since a map is a key/value // pair, you can print in the format "<map.key> was typed <map.value> times."for_each( m.begin(), m.end(), MapDispplayFunctor() ); But this will come much later of course after you've spent time in the guts of what c++ already provides with you. For now I think changing your code above to use an std::map will add a lot to you skill-base. [offtopic] i was in a chatty mood :) [/offtopic] ##### Share on other sites hey a break statment will quite the loop when its executed and continue will go to the next iteration of the loop. ##### Share on other sites Yeah.. I guess the map thingy is the way to go.. but I think I've learned what the book wanted me to.. so I'll guess I'll learn in a later chapter.. thanks a bunch to all of you.. • 48 • 12 • 10 • 10 • 9 • ### Forum Statistics • Total Topics 631374 • Total Posts 2999661 ×	2018-06-20 06:15:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1877603828907013, "perplexity": 2120.568075680777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863463.3/warc/CC-MAIN-20180620050428-20180620070428-00300.warc.gz"}
https://cafeedeneoth.nazwa.pl/florence-temperature-qvs/0c3876-inverse-chi-distribution	We wish to know what value of a statistic we would need in order to have this area to the left or the right of the statistic. Direct link to example. scipy.stats.chi2¶ scipy.stats.chi2 (* args, ** kwds) = [source] ¶ A chi-squared continuous random variable. In probability and statistics, studentized range distribution is the continuous probability distribution of the studentized range of an i.i.d. In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. 3 Significant support of non-central chi-quared distribution Whereas the central probability distribution describes how a test statistic t is distributed when the difference tested is null, the noncentral distribution describes how t is distributed when the null is false. The distribution is therefore parametrised by the two quantities ν and τ2, referred to as the number of chi-squared degrees of freedom and the scaling parameter, respectively. i ν The general form of its probability density function is. ln K is given by: The scaled inverse chi-squared distribution has a second important application, in the Bayesian estimation of the variance of a Normal distribution. In both cases, x>0{\displaystyle x>0} and ν{\displaystyle \nu } is the degrees of freedom parameter. if , or equivalently if it has density. It is essentially a Pareto distribution that has been shifted so that its support begins at zero. It is the distribution of the positive square root of the sum of squares of a set of independent random variables each following a standard normal distribution, or equivalently, the distribution of the Euclidean distance of the random variables from the origin. The chi-square distribution is commonly used in hypothesis testing, particularly the chi-square test for goodness of fit. In probability theory and statistics, the noncentral chi-square distribution is a noncentral generalization of the chi-square distribution. It is closely related to the chi-squared distribution. It is named in honor of John Wishart, who first formulated the distribution in 1928. {\displaystyle \nu } In particular, the choice of a rescaling-invariant prior for σ2 has the result that the probability for the ratio of σ2 / s2 has the same form (independent of the conditioning variable) when conditioned on s2 as when conditioned on σ2: In the sampling-theory case, conditioned on σ2, the probability distribution for (1/s2) is a scaled inverse chi-squared distribution; and so the probability distribution for σ2 conditioned on s2, given a scale-agnostic prior, is also a scaled inverse chi-squared distribution. The terms "distribution" and "family" are often used loosely: properly, an exponential family is a set of distributions, where the specific distribution varies with the parameter; however, a parametric family of distributions is often referred to as "a distribution", and the set of all exponential families is sometimes loosely referred to as "the" exponential family. The noncentral t-distribution is also known as the singly noncentral t-distribution, and in addition to its primary use in statistical inference, is also used in robust modeling for data. ν It is also required that X and Y are statistically independent of each other. The inverse-chi-squared distribution (or inverted-chi-square distribution [1] ) is the probability distribution of a random variable whose multiplicative inverse (reciprocal) has a chi-squared distribution. ( 1 x = chi2inv (p,nu) returns the inverse cumulative distribution function (icdf) of the chi-square distribution with degrees of freedom nu, evaluated at the probability values in p. This special form is chosen for mathematical convenience, based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a multivariate normal distribution. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. ) Density, distribution function, quantile function and random generation for the inverse chi-squared distribution. ν In other words, you may have 1 defective or 2 defectives, but not 1.4 defectives. (1995/2004) argue that the inverse chi-squared parametrisation is more intuitive. The chi-square distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals. Inverse distribution functions. is. ∑ 2 Both definitions are special cases of the scaled-inverse-chi-squared distribution. This family of scaled inverse chi-squared distributions is closely related to two other distribution families, those of the inverse-chi-squared distribution and the inverse-gamma distribution. ⁡ ν − This has the form of an \inverse chi-square distribution", meaning that changing variables to u = 1=˙ will give a standard chi-square distribution. is the incomplete gamma function, and it has density. Also, the scaled inverse chi-squared distribution is presented as the distribution for the inverse of the mean of ν squared deviates, rather than the inverse of their sum. The inverse chi-squared distribution, also called the inverted chi-square distribution, is the multiplicate inverse of the chi-squared distribution. and It often arises in the power analysis of statistical tests in which the null distribution is a chi-square distribution; important examples of such tests are the likelihood-ratio tests. z E Statistics and Machine Learning Toolbox™ offers multiple ways to work with the chi-square distribution. ( ) is the gamma function and It is also often defined as the distribution of a random variable whose reciprocal divided by its degrees of freedom is a chi-squared distribution. It arises in Bayesian inference, where it can be used as the prior and posterior distribution for an unknown variance of the normal distribution. {\displaystyle \nu } The cumulative distribution function is, where This MATLAB function returns the inverse cumulative distribution function (icdf) of the chi-square distribution with degrees of freedom nu, evaluated at the probability values in p. τ x The distribution is therefore parametrised by the two quantities ν and τ2, referred to as the number of chi-squared degrees of freedom and the scaling parameter, respectively. Suppose X follows the non-central chi-square distribution with degrees of freedom "k" and non-centrality parameter "t". . Inverse Chi-Square Tables The governing equations are as follows: Chi-square density: f(x) ¼ x(n=2) 1e (x=2) 2n=2G n 2 u(x) Chi-square distribution function: F(x) ¼ ð x 0 j(n=2) (1e j=2) 2n=2G n 2 dj¼ p Tables give the values of x in x ¼ F21(p) for values of p between (0.005, 0.995) grouped in such a manner that adjacent column values of p add to 1. It is a generalization to random vectors of the Student's t-distribution, which is a distribution applicable to univariate random variables. Description. The application has been more usually presented using the inverse-gamma distribution formulation instead; however, some authors, following in particular Gelman et al. ) In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. Parameter t '' '' and non-centrality parameter t '' more general noncentral distribution... 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How To Generate Code Review Report In Bitbucket, Brass Floating Wall Shelf, Kenyon Martin Jr Scouting Report, Kenyon Martin Jr Scouting Report, Kenyon Martin Jr Scouting Report, Where To Buy Schluter Shower Kits, Code Brown Nursing, American Early Action,	2021-08-02 15:14:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9078981876373291, "perplexity": 783.8387585903638}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154321.31/warc/CC-MAIN-20210802141221-20210802171221-00040.warc.gz"}
http://mathhelpforum.com/math-topics/175657-emission-question.html	1. ## emission question if 13 Al 27 isotope is stable which emission can 13 Al 29 undergo 2. For future reference you don't need to give us the atomic number since it's implied in the element name. In this case every Al atom has 13 protons - if it didn't it wouldn't be Al! Back on topic, $^{29}\text{Al}$ needs to lose two atomic mass units (amu) without changing atomic mass number. It's a weird one since to lose 2 amu without changing atomic number implies neutron emission twice which would be $^{29}\text{Al} \rightarrow ^{28}\text{Al} + n \rightarrow ^{27}\text{Al} + n$ Yet google and wolfram say beta minus decay: $^{29}\text{Al} \rightarrow ^{29}\text{Si} + e^- + \bar{\nu_e}$ and $^{29}\text{Si}$ is stable. I would be inclined to believe google if this is a real world problem since neutron emission usually occurs when there are more than two excess neutrons compared to the stable isotope	2016-08-25 01:14:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6371376514434814, "perplexity": 1041.5359549142902}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982292697.31/warc/CC-MAIN-20160823195812-00290-ip-10-153-172-175.ec2.internal.warc.gz"}
https://economics.stackexchange.com/questions/29237/bayes-correlated-equilibrium-obedience/29240	# Bayes Correlated Equilibrium: obedience I would like your help to understand the definition of obedience in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper. There are $$N\in \mathbb{N}$$ players, with $$i$$ denoting a generic player. There is a finite set of states $$\Theta$$, with $$\theta$$ denoting a generic state. A basic game $$G$$ consists of • for each player $$i$$, a finite set of actions $$A_i$$, where we write $$A\equiv A_1\times A_2\times ... \times A_N$$, and a utility function $$u_i: A\times \Theta \rightarrow \mathbb{R}$$. • a full support prior $$\psi\in \Delta(\Theta)$$. An information structure $$S$$ consists of • for each player $$i$$, a finite set of signals $$T_i$$, where we write $$T\equiv T_1\times T_2\times ... \times T_N$$. • a signal distribution $$\pi: \Theta \rightarrow \Delta(T)$$. A decision rule of the incomplete information game $$(G,S)$$ is a mapping $$\sigma: T\times \Theta\rightarrow \Delta(A)$$ One way to mechanically understand the notion of the decision rule is to view $$\sigma$$ as the strategy of an omniscient mediator who first observes the realization $$\theta\in \Theta$$ chosen according to $$\psi$$ and the realization $$t\in T$$ chosen according to $$\pi(\cdot\|\theta)$$; and then picks a probability distribution from $$\Delta(A)$$, and privately announces to each player $$i$$, her lottery to play. For players to have an incentive to follow the mediator's recommendation in this scenario, it would have to be the case that the recommended lottery was always preferred to any other lottery conditional on the signal $$t_i$$ that player $$i$$ had received. This is reflected in the following "obedience" condition. Definition: The decision rule $$\sigma$$ is obedient for $$(G,S)$$ if, for each $$i=1,...,N$$, $$t_i\in T_i$$, and $$a_i\in A_i$$, we have $$\sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_i,t_{-i}\| \theta) \sigma(a_i, a_{-i}\|t_i, t_{-i}, \theta) u_i(a_i, a_{-i},\theta)$$ $$\geq \sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_i,t_{-i}\| \theta) \sigma(a_i, a_{-i}\|t_i, t_{-i}, \theta) u_i(\tilde{a}_i, a_{-i},\theta)$$ $$\forall \tilde{a}_i\in A_i$$. My question: I don't understand fully the LHS (or, equivalently, the RHS) expression $$\sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_i,t_{-i}\| \theta) \sigma(a_i, a_{-i}\|t_i, t_{-i}, \theta) u_i(a_i, a_{-i},\theta)$$ Saying it in words, this is the sum over $$A_{-i}, T_{-i}, \Theta$$ of $$\text{[Prob that the mediator observes (\theta, t)]}\times\\ \text{[Prob that the mediator suggests players to play a under \sigma, given that he observes (\theta, t)]}\times\\ \text{[Profit that player i gets from obeying the mediator, given that the other players obey too]}$$ Let the product just written be denoted by $$(\star)$$. Why in the second component of $$(\star)$$ we DO NOT condition on $$a_i$$ by taking $$\text{[Prob that the mediator suggests the other players to play a_{-i} under \sigma, given that he observes (\theta, t) and given that he suggests player i to play a_i]}$$ in place of $$\text{[Prob that the mediator suggests players to play a under \sigma, given that he observes (\theta, t)]}$$ • I think you have a typo in your question, you said "Why in the second component of the product we {\bf do} condition on $a_i$", but I do not see and conditional probability that conditions on $a_i$. – Regio May 9 '19 at 15:15 • Thanks, I think is fixed now. – user3285148 May 9 '19 at 15:21 To understand the "Obedience" inequality, notice that the player is "integrating out" everything that she is uncertain about, this is why the sum runs over the actions of other players, $$a_{-i}$$, the types of other players, $$t_{-i}$$, and the state of the world, $$\theta$$. The first term simply gives the probability that the mediator observed $$\theta$$. For the second term, note that it is proportional to the conditional probability of the other players being of type $$t_{-i}$$ when you are of type $$t_i$$ since $$\pi(t_{-i}\|t_i,\theta)=\frac{\pi(t_i,t_{-i}\|\theta)}{\sum_{t_{-i}}\pi(t_i,t_{-i}\|\theta)}$$. Similarly for the third term, you probably expected there to see the conditional probability $$\sigma(a_{-i}\|a_i,t_i,t_{-i},\theta)$$, but this term is proportional to $$\sigma(a_i, a_{-i}\|t_i,t_{-i},\theta)$$. Technically speaking the agent should multiply his payoff by the probability that others play $$a_{-i}$$, are of type $$t_{-i}$$ and the state is $$\theta$$ conditional on being told to play $$a_i$$ when being of type $$t_i$$, so the LHS should read: $$\sum_{a_{-i}\in A_{-i}, t_{-i}\in T_{-i}, \theta\in\Theta}u_i((a_i,a_{-i}),\theta) \frac{\sigma((a_i,a_{-i})\|(t_i,t_{-i}),\theta)\pi((t_i,t_{-i})\|\theta)\psi(\theta)}{\sum_{a'_{-i}\in A_{-i}, t'_{-i}\in T_{-i}, \theta'\in\Theta}\sigma((a_i,a'_{-i})\|(t_i,t'_{-i}),\theta')\pi((t_i,t'_{-i})\|\theta')\psi(\theta')}$$ And the RHS will be identical except for replacing $$a_i$$ with $$\tilde a_i$$ in the utility function. Clearly, the denominator is constant over the sum and so can be simplified.	2021-04-16 20:02:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 59, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9545912742614746, "perplexity": 284.5788278372829}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038089289.45/warc/CC-MAIN-20210416191341-20210416221341-00561.warc.gz"}
https://www.blackartgraphics.com/blogs/black-art-dynamics-blog/the-top-10-most-highly-tuned-nasp-production-engines	(And why Specific Power sucks) Naturally aspirated engines present an interesting challenge for automotive engineers. Unlike their force fed counterparts, atmospheric engines are subject to finite limits on how much torque and power they can make, dictated by little more than their basic geometry. For this reason, naturally aspirated engines have for a long time been compared using a measure known as Specific Power, the amount of horsepower produced per litre of capacity. Generally speaking, 100bhp/litre is considered the benchmark for road cars, anything over is 'highly tuned' and anything under is considered, at best, 'average'. There is one small issue with using Specific Power as a means to compare engines though, highlighted by the fact I need to state 'for road cars' in the previous sentence. The problem stems from the fact that power is dependent on RPM and because higher RPM always nets higher power, Specific Power is only really of any use when comparing engines that operate at a similar speed. "Consider if you will, the Yamaha R1 superbike. Does its impressive specific output of 197bhp/litre infer that it is more highly tuned than say, the S2000 with only 120bhp/litre? I would argue not..." Let's think back to 2013, the last season of the naturally aspirated F1 engines. Back then the 2.4 litre V8s were producing around 800bhp from 2.4 litres, giving 333bhp/litre. A truly incredible figure no doubt, especially compared to the very best road going cars, hovering around 125bhp/litre. Now let's imagine we handicapped that F1 engine to 50% of its maximum revs, so that it produced 'only' 400bhp. This handicapped engine would still be making 167bhp/litre, which on the face of it might still be considered to be more highly tuned than say, the S2000. But we know that this engine is capable of so much more... Consider if you will, the Yamaha R1 superbike. Does its impressive specific output of 197bhp/litre infer that it is more highly tuned than say, the S2000 with only 120bhp/litre? Based on the above, I would argue not. What if it was capable of more? "For this Top Ten list, we're going to use something different, a little something I've derived myself. I've called it the 'Performance Index.'" It doesn't take much to come to the conclusion that using Specific Power as a means to compare engines is flawed, because it inherently favours the highest revving engines over everything else. For this Top Ten list, I'm going to use something different, a little something I've derived myself. I've called it the Performance Index. What is the Performance Index? "Rated out of 1000, the Performance Index can be used to compare the state of tune of absolutely any four stroke gasoline engine, be it a single cylinder go-kart, a screaming Japanese four cylinder motorcyle or a thumping NASCAR V8." The maths is explained in more detail at the end of the article, but quite simply, the Performance Index is the rated power output of an engine, divided by the calculated maximum that particular engine is capable of producing. The closer an engine is to its absolute limit, the higher its Performance Index. Rated out of 1000, the Performance Index can be used to compare the state of tune of absolutely any four stroke gasoline engine, be it a single cylinder go-kart, a screaming Japanese four cylinder motorcyle or a thumping NASCAR V8. If this has you asking the question "How do you calculate the maximum power an engine can produce?" you can skip to the last page, where I cover the maths in a bit more detail, but if you're not too fussed about that kind of thing, let's just say that it's based on a maximum 'mean piston speed' of 25m/s and a maximum specific torque of 90lbf/litre. With that, let's jump straight into the Top Ten! As a quick note before we start, we're only looking at production road cars here, and to avoid any one engine dominating the leader board only the most highly tuned incarnation of each engine has been included! Hit the next page button to check out number 10 on the list... 10. Honda Integra Type R - B18C - 110bhp/litre No Top 10 NASP engines list would be complete without at least one Honda, so its no surprise to see the Honda Integra Type R here. As is probably to be expected, its rev hungy B18C leaves nothing on the table in terms of engine speed, MPS is at the top end of the spectrum with its 87.2mm crank moving the pistons at 25m/s at its 8600rpm redline. Also, somewhat predictably, torque is on the low side. With 138lbft from its 1795cc engine, specific torque stands at 77lbft litre. Although not particularly strong figure given the competition in this instance, that's still a good figure in the grand scheme of things! With 197bhp out of a potential 254bhp, the Integra Type R scores a PI of 774, earning it 10th place on the leaderboard. A stellar performance considering the B Series engine design is almost 30 years old now! Notable relations • Civic Type R (EK9) - PI 715 9. Audi RS4 - 4.2 FSI V8 - 107bhp litre Despite its relatively lowly position on the leaderboard, the 2014 Audi RS4 actually tops the list for piston speed. With a relatively long 92.8mm stroke, the pistons are buzzing at a ballistic 25.5m/s at its 8250rpm redline. Although the engine is at the ragged edge in terms of speed, the torque figure does leave some room for improvement. With 317lbft from 4.2 litres, it manages a specific torque figure 76lbft/litre . Entirely respectable, but the lowest on our top 10 list! (Yep, the Honda makes more torque. Ouch) With 444bhp out of a theoretical maximum of 554bhp, the Audi RS4 ranks 9th with a PI of 802. (Specific Power - 107bhp/litre) 8. BMW M3 CSL - S54 The E46 M3 CSL contains the ultimate evolution of BMW's legendary S54 straight 6 engine, a motor already widly acknowledged as one of the worlds greatest engines. Piston speed is down slightly from the RS4 at 24.9m/s thanks to a slightly short stroke, but it more than makes up for it with 273lbft from 3246cc, for a specific torque figure of 84lbft/litre. With 355bhp out of a theoretical maximum of 440bhp, the M3 CSL ranks 8th with a PI of 806. (Specific Power - 109bhp/litre). Notable relations • E46 M3 - PI 768 7. Pagani Zonda R Despite having the highest redline on the leaderboard so far, the Zonda R's AMG V12 actually ranks with the lowest piston speed out of all the entries at 23.3m/s, owing to its short 80.2mm stroke. Mercedes more than make up for this though with what they do best, thumping torque. With 523lbft from 6.0 litres, it ranks with the second highest specific torque figure at 87lbft/litre. Despite producing an already impressive 750bhp, the Zonda R is theoretically capable of 921bhp, meaning it ranks 7th with an NA PI of 814. (Specific Power - 125bhp/litre) 6. Honda S2000 - F20C Now, I know we all like to rip Honda's for their lack of torque, and with 153lbft from 2 litres the S2000 does admittedly have one of the lowest specific torque figures to make the leaderboard at 77lbft, but all joking aside that is still a very impressive figure, especially given the age of the engine now. Like the B18C fitted to the Integra we just looked at, the piston speed is up there with the best, its 84mm crank firing the pistons up and down the bores at 25.2m/s at the 9000rpm redline. With 240bhp out of a theoretical maximum of 287, the S2000 comes in at number 6 with an NA PI of 818. (Specific Power - 120bhp/litre) 5. Porsche 911 GT3 RS Porsche's GT3 RS models are well renowned for their screaming NA flat six engines and the latest incarnation of the GT3 RS pushes the boundaries even further. With 339lbft from its 4.0 litre capacity, Specific Torque is 85lbft/litre and with an 81.7mm stroke the 8800rpm redline means an MPS of 24m/s. With 500bhp out of a theoretical maximum of 605, the 991 GT3 RS comes in at number 5 with an NA PI of 826. (Specific Power - 125bhp/litre) Notable relations • 997 GT3 RS 4.0 - PI 812 • 991 GT3 - PI 785 • 997 GT3 RS - PI 724 • 996 GT3 RS - PI 645 4. Porsche 918 Spyder Porsche might be well known for the screaming N/A flat 6 engines in their 911 GT3 models, but its easy to overlook the NASP V8 fitted to the 918 because of the muddy waters of hybrid powertrains. When you shed the engine of its electrical assistance it does turn out to be quite an impressive piece of engineering. With 398lbft from 4.6 litres the Specific Torque is 87lbft, the second highest on this list, and with a 9150rpm redline and 81mm stroke, MPS is 24.7m/s. With 608bhp out of a theoretical maximum of 700, the Porsche 918 Spyder nudges ahead of the 991 GT3 RS, ranking 5th with an NA PI of 869. 3. Ferrari 458 Speciale For a company renowned for making world class NASP engines, Ferrari only manage to get one engine in this top ten list, but what an engine it is! With 398lbft from 4499cc, the F136 V8 is a world record holder with the highest specific torque for any road going production engine at 88lbft/litre. With an 81mm crank the pistons are moving at 24.3m/s at its 9000rpm redline. With 597bhp out of a theoretical maximum of 685 the Ferrari 458 Speciale ranks 4th with an NA PI of 869. (Specific Power 125bhp/litre) 2. Lamborghini Huracan Performante Lamborghini have been setting a number of records with their incredible Huracan Performante, and that is due in no small part to its frankly incredible engine. Had we not have elected to only feature each engine once, the 5.2 litre Audi V10 would have found its way onto this leaderboard at least four times what with it powering various versions of the Huracan, Gallardo, and R8. Although a slightly lower redline of 8000rpm gives a small drop in piston speed to 24.7m/s, the torque is up from 413lbft to 443lbft for a specific torque of 84lbft/litre which more than compensates. With 631bhp out of a possible 692bhp, the Huracan Performante lands in 2nd position with an NA PI of 914. Next up is the grand finale, the most highly tuned NASP engine ever fitted to a production car. Can you guess what it is yet? With the other contenders in the list you might be forgiven for assuming it would be yet another large capacity European supercar, yet the engine to actually claim the top spot may come as a surprise, for it is in fact none other than a plucky 4 cylinder Brit... 1. Caterham R500 Although probably not what you'd class as a traditional supercar, there is no doubting that the bonkers R500 has supercar slaying potential and that DNA runs right down to the core of its powertrain. Co-developed with Minster Racing Engines, Caterham took the venerable 1.8 litre Rover K Series into the laboratory and tortured it on the test bed, pushing it to the limits until it committed fiery suicide. Once they knew the absolute limit, they cranked it down half a notch so that it didn't quite explode, and fitted it in the 500kg 7 chassis to create the R500. Producing and incredible 230bhp out of a theoretical maximum of 248bhp, this incarnation of the K Series is nothing short of a pure race engine running on the absolute ragged edge of performance. Surprisingly, despite the astonishing headline figure, neither of our two core parameters are maxed out. With 155lbft from 1.8 litres the specific torque is 'only' 85lbft/litre and with 24.4m/s at its 9200rpm redline it actually ranks 8th for piston speed. With an NA PI of 927 the Rover K Series takes the crown as the most highly tuned NASP engine ever fitted to a production car. A record that is, sadly, unlikely to ever be broken as natural aspiration enters its twilight years. #sadface Want to figure out how you engine ranks? Of course you do. You can read up the maths used to calculate the PI and check your own engine's PI here. Want to check out a longer list? We've listed 90 in a detailed table here. Think we've missed one, or want to add yours? Just email us the details and we'll get them added to the list! They don't have to be top performers, it'll be a bit of a laugh to check out some of the very worst too! Like the line artwork? That's actually what we do for a living. How do you fancy one of those personalised to match your car, laser engraved along with a full technical specification on an aluminium plaque? Sound interesting? Check out the catalogue here and grab 15% off any order over £200 with discount code NASP15! Want to know a bit more about how these engines were rated? Naturally aspirated engines have two major limitations. The first is how much torque they can make, the second is how fast they can spin. Specific Torque The first limitation is known as specific torque, the amount of torque produced per litre of capacity. A largely irrelevant figure in forced induction engines (because increasing the boost pressure has the effect of increasing the size of the engine), this figure is of interest in NASP engines because it conveniently describes how efficiently the engine can fill its cylinders with air fuel mixture, and how effectively it can convert that mixture into mechanical force. As NASP engines are only ever capable of producing a few percent over 100% volumetric efficiency, the absolute ceiling is about 90lbft/litre, with most performance engines sitting between 75 and 85lbft/litre. Mean Piston Speed The second limitation is one which affects both turbocharged and naturally aspirated engines alike, and that is the speed at which they can run. Whilst the maximum RPM of engines differs wildly, there is another, lesser known measure of engine speed, which paints a very different picture. its called Mean Piston Speed. Mean Piston Speed (MPS for short) describes the average speed at which the pistons are travelling in the bores, for any given RPM, the speed at which the pistons move will vary depending on the stroke length. The longer the stroke, the faster the pistons have to travel every RPM, so an engine with an 80mm stroke spinning at 8000rpm would have the same MPS (21.3m/s) as an engine with a 40mm stroke, spinning at 16,000rpm. While there is theoretically no limit on the RPM an engine can run at, the maximum sustainable MPS for a four stroke gasoline engine engine is a little over 25m/s. Beyond this speed component stresses get so high as to start impacting engine service life, but more importantly we start to get into the realm of the piston starting to outrun the flame front on the power stroke, resulting in a dramatic drop in torque. With a fixed limit on the piston speed, we can compare an engine's actual MPS with the maximum of 25m/s as a method with which normalise the speed of all engines regardless of their operating RPM. The equation to calculate the maximum RPM of an engine from its stroke length is as follows: $$RPMmax = 30,000 \cdot \bigg({MPS \over Stroke}\bigg)$$ Where bore is in millimeters. Torque and speed make... So, we know that the maximum torque an engine can make is limited to 90lbft per litre, and that the maximum RPM be caculated from the stroke length and a piston speed of 25m/s. Combining torque and RPM make power, so from this we can calculate a maximum power output for pretty much any engine, based on nothing more than its basic geometry! An engine's absolute maximum power output can be calculated as follows: $$Pmax = 9.694 \times 10^{-3} \cdot Bore^2 \cdot Cylinders$$ Where bore is in millimeters. For those of you that are interested, there is a full article explaining how that equation was derived here: Performance Index The Performance Index figure used in this article is simply the rated output of any particular engine, divided by its calculated maximum output, multiplied by a 1000. $$Performance Index = {Pactual \over Pmax} \cdot 1000$$ The PI is scored out of 1000 and this figure can be used to directly compare absolutely any naturally aspirated four stroke gasoline engine, because unlike BHP/litre it is normalised for engine speed. Find out your engine's Performance Index here Want more of this kind of content? Subscribe to the Black Art Dynamics blog today! oabnfwAKVJIpNrQt: BlnmQIvLSowi Jun 02, 2020 fDdsKSoCRj: FnMZrkTHCUhSGxpB Jun 02, 2020 DNLyrFjkXAJ: CLOGcHgEK Jun 01, 2020 AigvpGfl: MRucGmShOiPv Jun 01, 2020 VmcSJEoYIdCfxUXP: EuMKsxOFX May 31, 2020 FlLgMykpKqA: RvmzsltaSYwMqy May 31, 2020 etPjIvsJmSnGT: bAYyJmCVeOuNsE May 28, 2020 FiQojvVwurxecOP: AhqmdlGSvUcHzVN May 28, 2020 wDvTZtxCPGRY: PkNvHrfgdsaRT May 26, 2020 gWaQAiBYEHZ: cdYhmfUbKVwJ May 26, 2020 • Prev • Page 1 of 25 • Next	2020-06-06 07:37:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42574214935302734, "perplexity": 3513.3541438227935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348511950.89/warc/CC-MAIN-20200606062649-20200606092649-00011.warc.gz"}
https://www.physicsforums.com/threads/pi-miscalculated-or-not-irrational.33231/	# Pi miscalculated or not irrational? 1. Jun 30, 2004 ### Mr. X pi miscalculated or not irrational??? I know that computers have calculated thousands of digits of pi, but does this mean that pi is an irrational number? How can we be so sure that it is irrational? And I have one more question. The circles we see in real life are not perfect circles. Does this mean that pi might have been miscalculated? 2. Jun 30, 2004 ### Muzza No, we can calculate thousands of digits of the decimal expansion of 1/3, but that doesn't make it irrational ;) Because it was proven (way back in 1768, if my googling is correct). See this page for a proof. No, why would it mean that? I /seriously/ doubt that any of the algorithms used for calculating millions of digits of pi include any measurements of "real" circles... You might find this page interesting. As you can see, most of those formulas are quite far removed from anything concerning circles (other than the fact that they involve pi, of course)... Last edited: Jun 30, 2004 3. Jul 1, 2004 ### arildno As Muzza said, Euler proved that pi is irrational. It was proved to be transcendental by Lindemann in the 19th century, I believe 4. Jul 1, 2004 ### Muzza I didn't say that... ;) Mathworld says that it was Lambert who proved it. It appears as if the date I gave in my last post was wrong. 5. Jul 5, 2004 ### eJavier A really neat demostration of the fact tha Pi is irrational can be found in Spivak's Calculus 6. Jul 5, 2004 ### arivero to be trascendental is the same thing that to be not algebraic, isn't it? 7. Jul 5, 2004 ### Muzza Yes. (This is just a filler to get rid of the silly "you can't post a message this short"-error). 8. Jul 5, 2004 Yes indeed.	2016-10-22 05:42:47	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9086883664131165, "perplexity": 1548.8715439314558}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988718426.35/warc/CC-MAIN-20161020183838-00185-ip-10-171-6-4.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/2877904/there-is-only-in-first-order-logic	# "There is only" in first order logic I'm trying to translate the statement "There is only three things that are not small" into first order logic. I'm using some software to verify my sentences, but I feel like I don't understand what "There is only" is meant to claim. I interpreted it as "There are at most", and used the answer here, in particular method 2 for "At most $n$". The sentence I've produced with this is: $$\exists x \exists y \exists z \forall w \, (\lnot \text{Small}(w) \to (w = x \lor w = y \lor w = z))$$ Which I understand to mean that there exists up to 3 objects, which, for all objects $w$, if it is not small, it is one of the 3 objects. This passes 3 of the 4 test worlds for the software, but fails on the last one. I was hoping someone could help me clarify what is meant by "only". I've spent a decent amount of time Googling, but most results lead to explanations of the biconditional. Thanks! • Your statement is a good translation of 'at most 3 things are not small' .... maybe they mean 'exactly 3 things are not small?' Your test worlds should give you a clue ... Aug 10 '18 at 1:47 • I hate these kind of questions. It's not about first order logic, it's about what "there are only" means in ordinary English. In real life, "there are only three" means the same as "there are three and only three" or "there are exactly three". But maybe your instructor or your textbook author thinks it means something else. – bof Aug 10 '18 at 1:49 • @AnyAD but the universal says that any non-small object has to be one of those three ... so there really cannot be more than 3 Aug 10 '18 at 1:51 • I would see if the last world demands that there be three. You could add $x \neq y \wedge y \neq z \wedge x \neq z$ to your sentence and see if it works. That would support the theory that only three means exactly three. Aug 10 '18 at 2:05 • @Bram28 Was right, the test worlds seem to indicate that "Exactly 3" was the correct way to read the problem. Aug 10 '18 at 2:14	2021-12-01 22:41:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43195366859436035, "perplexity": 529.4667535482191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964360951.9/warc/CC-MAIN-20211201203843-20211201233843-00578.warc.gz"}
http://www.acmerblog.com/hdu-4476-cut-the-rope-7489.html	2015 07-16 # Cut the rope Now we have some ropes. For each rope, you can cut it only once at any place, or you can also do nothing on it. If we cut these ropes optimally, how many ropes we can get at most with the same length? There is an integer T (1 <= T <= 100) in the first line, indicates there are T test cases in total. For each test case, the first integer N (1 <= N <= 100000) indicates there are N ropes. And then there are N integers whose value are all in [1, 100000], indicate the lengths of these ropes. There is an integer T (1 <= T <= 100) in the first line, indicates there are T test cases in total. For each test case, the first integer N (1 <= N <= 100000) indicates there are N ropes. And then there are N integers whose value are all in [1, 100000], indicate the lengths of these ropes. 3 1 1 2 1 2 3 2 3 3 2 3 5 Hint For Sample 1, we can get two ropes with 0.5 unit length. For Sample 2, we can get three ropes with 1 unit length. For Sample 3, we can get five ropes with 1.5 unit length. #include<iostream> #include<cstdio> #include<memory.h> using namespace std; const int con=500000; struct node { int flag; int c; }arr[con]; int main() { int T,n; scanf("%d",&T); while(T--) { memset(arr,0,sizeof(arr)); scanf("%d",&n); for(int i=1;i<=n;i++) { int x; scanf("%d",&x); arr[x2].flag++; } int c=0; for(int i=1;i<=200000;i++) { if(arr[i].flag!=0) { c+=arr[i].flag; arr[i].c=c; } else arr[i].c=c; } int ans=0; for(int i=1;i<=200000;i++) { int temp=0; temp=n-arr[i].c+arr[i].flag+arr[i2].flag; if(temp>ans) ans=temp; } printf("%d\n",ans); } return 0; }	2017-06-24 05:21:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31284403800964355, "perplexity": 1588.1744698581879}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320226.61/warc/CC-MAIN-20170624050312-20170624070312-00359.warc.gz"}
https://cs.stackexchange.com/questions/139677/how-to-prove-that-the-lower-bound-of-the-huffman-coding-problem-is-omegan-lo	# How to prove that the lower bound of the Huffman coding problem is $\Omega(n \log n)$? how to prove that the lower bound of the Huffman coding problem is $$\Omega(n \log n)$$? Here Huffman coding problem is Huffman encoding. For example, Input: A string with different characters, say “ACCEBFFFFAAXXBLKE” Output: Code for different characters: Data: K, Frequency: 1, Code: 0000 Data: L, Frequency: 1, Code: 0001 Data: E, Frequency: 2, Code: 001 Data: F, Frequency: 4, Code: 01 Data: B, Frequency: 2, Code: 100 Data: C, Frequency: 2, Code: 101 Data: X, Frequency: 2, Code: 110 Data: A, Frequency: 3, Code: 111 I already saw that we can know that the bound of the sorting problem is $$\Omega(n \log n)$$ by using decision tree. the number of leaves: $$n!$$ (the number of leaves in a half tree with a height of $$h) \leq 2^h$$ $$\Rightarrow n! \leq 2^h \Rightarrow h \geq \log n!$$ $$\Rightarrow \log n! \fallingdotseq n \log n - n = \Omega(n \log n)$$ So I thought I could also use the decision tree to get the lower bound of the Huffman coding problem but I am not sure how to construct the decision tree for Huffman coding problem, like how many leaves are needed,... Please tell me how to construct the decision tree or is my attempt to tackle this proof wrong? • What is the Huffman coding problem? – Yuval Filmus Apr 29 at 10:05 • @YuvalFilmus It's Huffman encoding – t24akeru Apr 29 at 10:23 • What is the input, and what is the desired output? – Yuval Filmus Apr 29 at 10:24 • @YuvalFilmus input: a string with different characters, like “ACCEBFFFFAAXXBLKE”, output: Huffman code – t24akeru Apr 29 at 10:27	2021-05-09 19:11:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25630223751068115, "perplexity": 1714.7621663737664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989012.26/warc/CC-MAIN-20210509183309-20210509213309-00133.warc.gz"}
https://math.stackexchange.com/questions/3270656/do-products-preserve-colimits-in-the-category-of-locales?noredirect=1	# Do products preserve colimits in the category of locales? Does the functor $$X\times-:\mathbf{Loc}\to\mathbf{Loc}$$ preserve small colimits for all locales $$X$$? The reason that I'm interested in this question is that the same property fails in the category of topological spaces. If products preserve colimits in a total category then it must be cartesian closed. The category $$\mathbf{Top}$$ is total, but fails to be cartesian closed because products don't preserve colimits. So it would be curious if $$\mathbf{Loc}$$ failed to be cartesian closed for the complementary reason. It's not total, so maybe products do preserve colimits in $$\mathbf{Loc}$$? Another reason to ask this question is that the definition of "locale" requires precisely that products preserve colimits in its frame of opens. So it would be interesting if this property was mirrored at the category level. Equivalently the question is whether taking coproduct with a frame $$X$$ preserves limits of frames. We'll write the coproduct of frames as $$\otimes$$, since it turns out to coincide with the tensor product of suplattices (see this nLab page and this nLab page). The tensor product of suplattices has right adjoint given by the hom suplattice, so preserves colimits of suplattices in both variables; I think this implies that it preserves limits in both variables, because I think limits of suplattices can be computed as colimits and vice versa (e.g. products are coproducts); this is the step I'm least confident in. If that's true, then because limits of frames are computed as limits of suplattices (which in turn are computed as limits of underlying sets), tensor product preserves limits. • Could it be that $(\mathbf{Sup},\otimes)$ is compact closed? Then it would be obvious that $X\otimes -$ preserves limits, since it would be left and right adjoint to $X^*\otimes -$. I've found some sources that refer to "dualizable suplattices" which suggests that they think there exist some nondualizable suplattices, but I can't find an example of such. – Oscar Cunningham Sep 18 '19 at 6:39 • One point in favour of the idea that $\mathbf{Sup}$ is compact closed is the fact that it's the Eilenberg-Moore category of the monad for which the Kleisli category is $\mathbf{Rel}$, a classic example of a compact closed category. Even if $\mathbf{Sup}$ isn't compact closed we might be able to use the relationship with $\mathbf{Rel}$ to prove that $X\otimes -$ preserves limits. – Oscar Cunningham Sep 18 '19 at 6:42 • Separately, how do you know that limits of frames are computed as limits of suplattices? Is there a left adjoint to $U:\mathbf{Frame}\to\mathbf{Sup}$? – Oscar Cunningham Sep 18 '19 at 6:44 • @Oscar: oof, I'm not at all confident of the shaky step above anymore, but I'm a bit more confident that limits of frames are computed as limits of suplattices, because they're both computed as limits of sets, because they're both monadic over $\text{Set}$. But I do in addition believe that the forgetful functor from frames to suplattices has a left adjoint, and moreover I believe that it's monadic, basically because I believe frames are the models of a particular algebraic theory over suplattices (idempotent commutative monoids or something). – Qiaochu Yuan Sep 18 '19 at 7:07 • $\mathbf{Sup}$ isn't compact closed. The double-dual of $\{\{a,b,c\},\{a\},\{b\},\{c\},\{\}\}$ is $\{\{a,b,c,d,e\},\{a,b,c,d\},\{a,d\},\{b,d\},\{c,d\},\{d\},\{\}\}$. – Oscar Cunningham May 14 '20 at 15:40	2021-04-16 10:51:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9000824093818665, "perplexity": 350.0746393076299}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038056325.1/warc/CC-MAIN-20210416100222-20210416130222-00506.warc.gz"}
http://www.scstatehouse.gov/sess119_2011-2012/sj12/20120606.htm	South Carolina General Assembly 119th Session, 2011-2012 Journal of the Senate Wednesday, June 6, 2012 (Statewide Session) Indicates Matter Stricken Indicates New Matter The Senate assembled at 10:30 A.M., the hour to which it stood adjourned, and was called to order by the ACTING PRESIDENT, Senator RYBERG. A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows: In David's psalm of thanks we read: "Remember the wonders He has done, His miracles, and the judgments He pronounced." (I Chronicles 16:12) Let us pray: O God, "wonders?" Perhaps some. "Miracles?" Probably not. "Judgments?" Maybe a few. Overall, dear Lord, as we shall remember the work of Your servants in this Senate during this year, we will recall their concern for the people of this State most of all. We thank You that these Senators and their staff members have such passion for the well-being of our citizens. May that attitude of care never be lost. Now we also ask You, Lord, to care for and to protect our women and men in uniform, wherever they happen to serve. All this we ask in Your loving name, dear Lord. Amen. The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers. MESSAGE FROM THE GOVERNOR The following appointments were transmitted by the Honorable Nikki Randhawa Haley: Local Appointments Initial Appointment, Richland County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 Ethel L. Brewer, 4201 Donavan Drive, Columbia, SC 29210 Initial Appointment, Richland County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 Barbara Jo Wofford-Kanwat, 2009 Green Street #206, Columbia, SC 29205 Reappointment, York County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 David S. Wood, 957 Copperstone Lane, Fort Mill, SC 29708 Reappointment, York County Natural Gas Authority, with the term to commence March 1, 2012, and to expire March 1, 2015 York County: Clyde O. Smith, Post Office Box 336, York, SC 29745 Initial Appointment, Clarendon County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Robin C. Locklear, Post Office Box 551, Manning, SC 29102 VICE Judge Aycock (retired) Doctor of the Day Senator COURSON introduced Dr. Patricia Witherspoon of Columbia, S.C., Doctor of the Day, along with Dr. Philip Van De Griend, USC resident, and Christina Carter, a rising Junior at Presbyterian College Medical school who were shadowing Dr. Witherspoon. Leave of Absence Rescinded At 2:05 P.M., the leave of absence granted to Senator ELLIOTT for today and tomorrow was rescinded. Leave of Absence At 5:10 P.M., Senator LEATHERMAN requested a leave of absence until 6:30 P.M. Expression of Personal Interest Senator KNOTTS rose for an Expression of Personal Interest. Expression of Personal Interest Senator LAND rose for an Expression of Personal Interest. INTRODUCTION OF BILLS AND RESOLUTIONS The following were introduced: S. 1584 (Word version) -- Senators Shoopman, Alexander, Anderson, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Courson, Cromer, Davis, Elliott, Fair, Ford, Gregory, Grooms, Hayes, Hutto, Jackson, Knotts, Land, Leatherman, Leventis, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McGill, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Scott, Setzler, Sheheen, Thomas, Verdin and Williams: A SENATE RESOLUTION TO RECOGNIZE AND HONOR THE GREENVILLE COUNTY ENFORCING UNDERAGE DRINKING LAWS COALITION FOR ITS SUCCESS IN REDUCING UNDERAGE DRINKING AND YOUTH ACCESS TO ALCOHOL IN GREENVILLE COUNTY AND TO CONGRATULATE ALL ITS PARTICIPANTS FOR RECEIVING A GRANT FROM THE NATIONAL HIGHWAY TRAFFIC SAFETY ADMINISTRATION TO CONDUCT THE UNDERAGE DRINKING ADULT CONSEQUENCES CAMPAIGN. l:\council\bills\gm\25145ab12.docx S. 1585 (Word version) -- Senators Knotts, Alexander, Anderson, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Courson, Cromer, Davis, Elliott, Fair, Ford, Gregory, Grooms, Hayes, Hutto, Jackson, Land, Leatherman, Leventis, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McGill, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Scott, Setzler, Sheheen, Shoopman, Thomas, Verdin and Williams: A SENATE RESOLUTION TO RECOGNIZE AND HONOR STATE FIRE MARSHAL ADOLF A. ZUBIA, UPON THE OCCASION OF HIS RETIREMENT, AND TO WISH HIM CONTINUED SUCCESS AND HAPPINESS IN ALL HIS FUTURE ENDEAVORS. l:\council\bills\gm\25168ab12.docx S. 1586 (Word version) -- Senator S. Martin: A SENATE RESOLUTION TO CONGRATULATE ELIZABETH FRIERSON DICKERT OF SPARTANBURG COUNTY ON THE OCCASION OF HER ONE HUNDREDTH BIRTHDAY AND TO WISH HER A JOYOUS BIRTHDAY CELEBRATION AND MANY YEARS OF CONTINUED HEALTH AND HAPPINESS. l:\council\bills\gm\25170dg12.docx S. 1587 (Word version) -- Senator Elliott: A SENATE RESOLUTION TO RECOGNIZE AND HONOR MAYOR MARILYN HATLEY OF NORTH MYRTLE BEACH FOR HER MANY YEARS OF SERVICE TO THE PEOPLE OF HER CITY. l:\council\bills\rm\1636zw12.docx REPORT FROM STANDING COMMITTEE Appointment Reported Senator THOMAS from the Committee on Banking and Insurance submitted a favorable report on: Reappointment, South Carolina State Board of Financial Institutions, with the term to commence June 30, 2012, and to expire June 30, 2016 Credit Union: William Scott Conley, 301 Clearview Drive, Columbia, SC 29212 PRESIDENT PRESIDES At 10:35 A.M., the PRESIDENT assumed the Chair. THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR. ORDERED ENROLLED FOR RATIFICATION The following Joint Resolution was read the third time and, having received three readings in both Houses, it was ordered that the title be changed to that of an Act and enrolled for Ratification: H. 4824 (Word version) -- Rep. Rutherford: A JOINT RESOLUTION TO PROVIDE THAT THE DRIVER'S LICENSE OF A PERSON IS REINSTATED ON THIS ACT'S EFFECTIVE DATE IF THE PERSON'S DRIVER'S LICENSE WAS SUSPENDED PURSUANT TO FORMER SECTION 56-1-745 OF THE 1976 CODE DUE TO A CONTROLLED SUBSTANCE VIOLATION AND CHARGE PRIOR TO APRIL 12, 2011, AND A CONVICTION ON OR AFTER APRIL 12, 2011, AND TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES MUST NOT REIMBURSE SUCH PERSON WHOSE DRIVER'S LICENSE SUSPENSION ENDED AND HE PAID A REINSTATEMENT FEE BEFORE THIS ACT'S EFFECTIVE DATE. HOUSE BILLS RETURNED The following House Bills were read the third time and ordered returned to the House with amendments: H. 4699 (Word version) -- Reps. Bannister, Harrison, Horne, Sellers, Hearn, Young, H.B. Brown, J.E. Smith, Brannon, Stavrinakis, Funderburk, Allen, Weeks, Munnerlyn and McLeod: A BILL TO AMEND SECTION 14-5-610, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DIVISION OF THE STATE INTO SIXTEEN JUDICIAL CIRCUITS AND ADDITIONAL AT-LARGE JUDGES, SO AS TO INCREASE THE NUMBER OF AT-LARGE CIRCUIT COURT JUDGES FROM THIRTEEN TO NINETEEN; AND TO AMEND SECTION 63-3-40, RELATING TO FAMILY COURT JUDGES ELECTED FROM EACH JUDICIAL CIRCUIT, SO AS TO ADD SIX ADDITIONAL FAMILY COURT JUDGES WHO SHALL BE AT LARGE AND MUST BE ELECTED WITHOUT REGARD TO THEIR COUNTY OR CIRCUIT OF RESIDENCE. H. 4614 (Word version) -- Reps. Pitts, Lucas, Hearn, Brannon, Weeks, Spires, Loftis and Clemmons: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 2 TO CHAPTER 15, TITLE 63 SO AS TO SPECIFY CERTAIN PROCEDURES AND REQUIREMENTS FOR COURT-ORDERED CHILD CUSTODY, INCLUDING, BUT NOT LIMITED TO, DEFINING "JOINT CUSTODY" AND "SOLE CUSTODY", REQUIRING PARENTS TO JOINTLY PREPARE AND SUBMIT A PARENTING PLAN, WHICH THE COURT MUST CONSIDER BEFORE ISSUING TEMPORARY AND FINAL CUSTODY ORDERS; REQUIRING THE COURT TO MAKE FINAL CUSTODY DETERMINATIONS IN THE BEST INTEREST OF THE CHILD BASED UPON THE EVIDENCE PRESENTED, REQUIRING THE COURT TO CONSIDER JOINT CUSTODY IF EITHER PARENT SEEKS IT, STATING FINDINGS OF FACT AS TO WHY OR WHY NOT JOINT CUSTODY WAS AWARDED, PROVIDING MATTERS THAT MAY BE INCLUDED IN A CUSTODY ORDER, PROVIDING FACTORS THE COURT MAY CONSIDER IN ISSUING OR MODIFYING A CUSTODY ORDER WHEN CONSIDERING THE BEST INTEREST OF THE CHILD, AND AUTHORIZING A PARENT TO SEEK ARBITRATION OF AN ISSUE THAT CANNOT BE RESOLVED BETWEEN THE PARENTS; AND TO AMEND SECTION 63-5-30, RELATING TO THE RIGHTS AND DUTIES OF PARENTS TO THEIR CHILDREN, SO AS TO PROVIDE THAT UNLESS OTHERWISE PROVIDED BY AN ORDER OF THE COURT, PARENTS HAVE EQUAL POWERS, RIGHTS, AND DUTIES CONCERNING ALL MATTERS AFFECTING THEIR CHILDREN. H. 4654 (Word version) -- Reps. Hardwick, Harrell, Loftis, Sandifer, White, Harrison, Owens, Crosby, Anderson, Bingham, Sottile, Corbin, Chumley, Forrester, Hearn, Henderson, Lucas, D.C. Moss, V.S. Moss, Ott, Parker, Southard, Murphy, Clemmons, Hixon, Knight and Patrick: A BILL TO AMEND SECTION 48-1-90, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROHIBITING THE DISCHARGE OF POLLUTANTS INTO THE ENVIRONMENT AND REMEDIES FOR VIOLATIONS, SO AS TO PROVIDE EXEMPTIONS AND LIMITATIONS ON THESE EXEMPTIONS AND TO SPECIFY THAT NO PRIVATE CAUSE OF ACTION IS CREATED BY OR EXISTS UNDER THE POLLUTION CONTROL ACT; TO AMEND SECTION 48-1-130, RELATING TO FINAL ORDERS OF THE DEPARTMENT DISCONTINUING DISCHARGE OF POLLUTANTS, SO AS TO DELETE PROVISIONS RELATING TO REQUIRED PROCEDURES PRECEDING THE ISSUANCE OF A FINAL ORDER AND TO PROVIDE THAT AN ORDER IS SUBJECT TO REVIEW PURSUANT TO THE ADMINISTRATIVE PROCEDURES ACT; TO AMEND SECTION 48-1-250, RELATING TO WHOM BENEFITS FROM CAUSES OF ACTION RESULTING FROM POLLUTION VIOLATIONS INURE, SO AS TO PROVIDE THAT NO PRIVATE CAUSE OF ACTION IS CREATED BY OR EXISTS UNDER THE POLLUTION CONTROL ACT; AND TO MAKE THESE PROVISIONS RETROACTIVE AND EXTINGUISH ANY RIGHT, CLAIM, OR CAUSE OF ACTION ARISING UNDER OR RELATED TO THE POLLUTION CONTROL ACT, SUBJECT TO EXCEPTIONS FOR THE STATE AND ITS SUBDIVISIONS. Senator COURSON asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Senator MALLOY spoke on the Bill. The Bill was read the third time, passed and ordered returned to the House of Representatives with amendments. H. 4497 (Word version) -- Reps. Sellers, Johnson, Brady, Gilliard, Jefferson and Knight: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 44-29-187 SO AS TO ENACT THE "CERVICAL CANCER PREVENTION ACT"; TO PROVIDE THAT BEGINNING WITH THE 2012-2013 SCHOOL YEAR, THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL SHALL OFFER AS AN OPTION THE CERVICAL CANCER VACCINE SERIES TO FEMALE STUDENTS ENROLLING IN THE SEVENTH GRADE; TO PROVIDE THE STUDENT MAY ONLY RECEIVE THESE VACCINATIONS AT THE OPTION OF THE PARENT OR GUARDIAN OF THE CHILD; TO PROVIDE A PROCEDURE THROUGH WHICH A PARENT OR GUARDIAN MAY EXERCISE THE OPTION FOR THEIR CHILD TO RECEIVE THESE VACCINATIONS; TO REQUIRE A RELATED EDUCATION PROGRAM; AND TO PROVIDE THAT IMPLEMENTATION OF THIS SECTION IS CONTINGENT UPON STATE AND FEDERAL FUNDING. H. 3127 (Word version) -- Reps. Rutherford, G.R. Smith, Clyburn, Weeks, Whipper and R.L. Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 24-21-925 SO AS TO PROVIDE THAT A LIMITED PARDON MAY BE GRANTED TO A PERSON WHO HAS BEEN CONVICTED OF A NONVIOLENT FELONY OFFENSE THAT WOULD ALLOW HIM TO CARRY A FIREARM USED FOR HUNTING TO AND FROM HIS HUNTING DESTINATION AND USE IT WHILE HUNTING. Senator SHEHEEN explained the Bill. H. 4738 (Word version) -- Reps. Govan and Hearn: A BILL TO AMEND SECTION 20-3-130, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE AWARD OF ALIMONY IN DIVORCE AND SEPARATE MAINTENANCE AND SUPPORT ACTIONS, SO AS TO PROVIDE THAT ALIMONY IS TERMINABLE ON "COHABITATION", RATHER THAN ON "CONTINUED COHABITATION" OF THE SUPPORTED SPOUSE; TO DEFINE "COHABITATION" AS A COMMITTED, EXCLUSIVE RELATIONSHIP FOR AN AGGREGATE OF NINETY DAYS; AND TO PROVIDE FACTORS THAT THE COURT MAY CONSIDER IN DETERMINING WHETHER COHABITATION EXISTS; TO AMEND SECTION 20-3-150, AS AMENDED, RELATING TO ALLOCATING ALIMONY TO THE SUPPORTED SPOUSE AND CHILD SUPPORT TO THE CHILDREN SUCH THAT ONLY ALIMONY IS TERMINATED UPON REMARRIAGE OR CONTINUED COHABITATION OF THE SUPPORTED SPOUSE, SO AS TO PROVIDE THAT ALIMONY IS TERMINABLE ON "COHABITATION", RATHER THAN ON "CONTINUED COHABITATION" OF THE SUPPORTED SPOUSE; TO DEFINE "COHABITATION" AS A COMMITTED, EXCLUSIVE RELATIONSHIP FOR AN AGGREGATE OF NINETY DAYS; AND TO PROVIDE FACTORS THAT THE COURT MAY CONSIDER IN DETERMINING WHETHER COHABITATION EXISTS; AND TO AMEND SECTION 20-3-170, RELATING TO THE MODIFICATION, CONFIRMATION, OR TERMINATION OF ALIMONY, SO AS TO PROVIDE THAT UPON THE MOTION OF A PARTY TO A JUDGMENT OF DIVORCE, THE COURT SHALL CONDUCT A HEARING TO DETERMINE IF THE RETIREMENT OF THE SUPPORTING SPOUSE CONSTITUTES A CHANGE OF CIRCUMSTANCES FOR THE PURPOSE OF ALIMONY PAYMENTS AND TO PROVIDE FACTORS FOR THE COURT TO CONSIDER IN MAKING THIS DETERMINATION. Senator SHEHEEN explained the Bill. S. 1574 (Word version) -- Senator Setzler: A CONCURRENT RESOLUTION TO MEMORIALIZE THE CONGRESS OF THE UNITED STATES TO SEEK THE WITHDRAWAL OF THE UNITED STATES PREVENTIVE SERVICES TASK FORCE RECOMMENDATION AGAINST PROSTATE-SPECIFIC ANTIGEN-BASED SCREENING FOR PROSTATE CANCER FOR MEN IN ALL AGE GROUPS. By prior motion of Senator SETZLER, the Concurrent Resolution was adopted, ordered sent to the House. At 12:08 P.M., on motion of Senator COURSON, with unanimous consent, the Senate agreed to go into Executive Session. RECESS At 12:31 P.M., on motion of Senator COURSON, the Senate receded from business until 2:00 P.M. AFTERNOON SESSION The Senate reassembled at 2:00 P.M. and was called to order by the PRESIDENT. RETURNED TO THE HOUSE H. 4008 (Word version) -- Reps. Harrison, H.B. Brown, G.R. Smith, Knight, Atwater, Branham, Viers, Bannister, Dillard, Erickson, Hamilton, Hearn, Hosey, Limehouse, D.C. Moss, Patrick, Pinson, Sandifer, G.M. Smith, J.R. Smith, Stringer, Toole, Willis, Bingham and Clemmons: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 44-7-390 SO AS TO PROVIDE THAT THERE IS NO MONETARY LIABILITY, AND NO CAUSE OF ACTION IS CREATED, BY A HOSPITAL UNDERTAKING OR PERFORMING CERTAIN ACTS IF NOT DONE WITH MALICE; BY ADDING SECTION 44-7-392 SO AS TO PROVIDE THAT CERTAIN HOSPITAL PROCEEDINGS AND DATA, DOCUMENTS, RECORDS, AND INFORMATION RESULTING FROM THESE PROCEEDINGS ARE CONFIDENTIAL AND NOT SUBJECT TO DISCOVERY OR SUBPOENA AND MAY NOT BE USED AS EVIDENCE IN A CIVIL ACTION UNLESS THE HOSPITAL HAS WAIVED CONFIDENTIALITY OR THE DATA, DOCUMENTS, RECORDS, OR INFORMATION ARE OTHERWISE AVAILABLE AND SUBJECT TO DISCOVERY; TO PROVIDE THAT THE OUTCOME OF A PRACTITIONER'S APPLICATION FOR HOSPITAL STAFF MEMBERSHIP OR CLINICAL PRIVILEGES IS NOT CONFIDENTIAL BUT THAT THE APPLICATION AND SUPPORTING DOCUMENTS ARE CONFIDENTIAL; TO PROVIDE THAT DISCLOSURE OF CERTAIN INFORMATION BY A HOSPITAL THROUGH REPORTS TO THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, THE JOINT COMMISSION, OR THE BOARD OF MEDICAL EXAMINERS IS NOT A WAIVER OF ANY PRIVILEGE OR CONFIDENTIALITY; AND TO PROVIDE THAT AN AFFECTED PERSON MAY FILE AN ACTION TO ASSERT A CLAIM OF CONFIDENTIALITY AND TO ENJOIN THE HOSPITAL, THE JOINT COMMISSION, OR THE BOARD OF MEDICAL EXAMINERS FROM RELEASING SUCH INFORMATION, AND IF THE COURT FINDS THAT THE PERSON ACTED UNREASONABLY IN ASSERTING THIS CLAIM, THE COURT SHALL ASSESS ATTORNEY'S FEES AGAINST THAT PERSON; BY ADDING SECTION 44-7-394 SO AS TO PROVIDE THAT IF IN A JUDICIAL PROCEEDING THE COURT FINDS DOCUMENTS, OVER WHICH THE HOSPITAL ASSERTED A CLAIM OF CONFIDENTIALITY, ARE NOT SUBJECT TO CONFIDENTIALITY AND THAT THE HOSPITAL ACTED UNREASONABLY IN ASSERTING THIS CLAIM, THE COURT SHALL ASSESS ATTORNEY'S FEES AGAINST THE HOSPITAL FOR COSTS INCURRED BY THE REQUESTING PARTY TO OBTAIN THE DOCUMENTS; AND TO AMEND SECTION 40-71-10, RELATING TO THE EXEMPTION FROM TORT LIABILITY FOR MEMBERS OF CERTAIN PROFESSIONAL COMMITTEES, SO AS TO DELETE FROM THE EXEMPTION AN APPOINTED MEMBER OF A COMMITTEE OF A MEDICAL STAFF OF A HOSPITAL IF THE STAFF OPERATES PURSUANT TO WRITTEN BYLAWS APPROVED BY THE GOVERNING BOARD OF THE HOSPITAL. Senator CLEARY asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Senators LOURIE and KNOTTS proposed the following amendment (S-4008 LOURIE): Amend the bill, as and if amended, page 7, by striking lines 35-38 and inserting: / SECTION 3. Title 44 of the 1976 Code is amended by adding: "Chapter 84 Commission on Hunger Section 44-84-10. There is created within the Department of Health and Environmental Control the Commission on Hunger to develop, implement, and oversee a comprehensive strategy to reduce food insecurity and alleviate hunger in this State. Section 44-84-20. As used in this chapter: (1) 'Food insecurity' means a household-level economic and social condition of uncertainty of being able to acquire, in socially acceptable ways, enough food, at any given time, to meet basic dietary needs because of insufficient funds or other resources for food. (2) 'Food recovery' means collecting wholesome food for distribution to the food insecure and hungry, including, field gleaning, perishable food rescue or salvage, collecting perishable produce from wholesale and retail sources, collecting prepared foods from the food service industry, and nonperishable food collection. (3) 'Hunger' means a physiological condition that is a potential consequence of food insecurity, which, because of prolonged, involuntary lack of food, results in discomfort, illness, weakness, or pain that goes beyond the usual uneasy sensation. Section 44-84-30. (A) The Commission on Hunger must be comprised of the following officials or their designees, who shall serve ex officio: (1) Commissioner of the Department of Health and Environmental Control; (2) Director of the Department of Social Services; (3) Superintendent of Education; (4) Commissioner of the Department of Agriculture; (5) Director of the Department of Health and Human Services; (6) Director of the Department of Employment and Workforce; (7) Director of the Division on Aging, Office of the Lieutenant Governor; (8) Chair of the Joint Citizens and Legislative Committee on Children; (9) President of the South Carolina Food Bank Association; (10) President of the South Carolina Dietetic Association; (11) Director of the School Nutrition Council of South Carolina; (12) Director of the South Carolina Association of Counties; (13) Director of the Municipal Association of South Carolina; (14) President of the South Carolina Hospitality Association; (15) Executive Minister of the Christian Action Council; (16) President of the South Carolina State Conference of the National Association for the Advancement of Colored People; (17) President of the Hispanic Leadership Council; (18) Director of the United Way Association of South Carolina; (19) Director of the South Carolina Retail Association. (B) The commission shall elect from among its members a chairman and a vice chairman who shall serve terms of two years. The commission shall meet quarterly and otherwise at the call of the chair. A majority of the commission members constitutes a quorum for the purpose of conducting the business of the commission. The commission shall serve without per diem, mileage or subsistence. Section 44-84-40. The Department of Health and Environmental Control shall provide from existing staff assistance to the commission in implementing the provisions of this chapter. No additional staff shall be hired and expenses shall be from the existing budget of the department. Section 44-84-50. In carrying out its duties and responsibilities pursuant to this chapter, the commission has the authority to: (1) establish ad hoc committees outside of the commission membership to assist the commission in fulfilling its duties; (2) hold public hearings; (3) review program and budget data of state agencies that engage in activities and provide services that involve the reduction of food insecurity and the alleviation of hunger and of other public and private entities that voluntarily agree to participate in these reviews. Section 44-84-60. The commission shall: (1) conduct research and analyze data, using existing data if possible, and undertake other studies and actions to determine: (a) the dimension and demographics of food insecurity and hunger in this State; (b) the cultural, community, and practical barriers to achieving food security; (c) the availability and accessibility of emergency food sources and assistance among demographic groups and by geographic areas of the State, including gaps in availability and accessibility; (d) other barriers to individuals receiving food from emergency food sources and programs; (e) the effectiveness and efficiency of existing emergency food sources and programs; (f) the participation rates of eligible persons in all federal food programs, including, but not limited to, the Supplemental Nutrition Assistance Program (SNAP, formerly food stamps), the Women, Infants, and Children Program, and school breakfast, lunch, and summer meal programs, and whether all federal programs and options have been adopted and maximized by the State; (g) barriers to eligible individuals participating in federal food programs; (h) the extent to which food recovery is used in this State to feed the food insecure and hungry and barriers to and opportunities for utilizing this resource; (2) review the work of other public and private entities used to reduce food insecurity and alleviate hunger, including programs, approaches, and concepts addressing food source and program availability and access, program participation, and other matters as may be useful to the commission; (3) evaluate existing and develop new opportunities for public-private partnerships to address the needs of the food insecure and hungry, including, but not limited to, utilization of food recovery and promotion, by expansion, of existing public-private endeavors and programs; (4) identify strategies to overcome barriers to and develop solutions for improving delivery of and participation in food assistance programs; (5) coordinate the effective and efficient provision of services and programs to the food insecure and hungry so that food sources and assistance will be readily available to the greatest number over the widest geographic area, including minimizing the duplication of services and programs and providing comprehensive public awareness and education campaigns throughout the State. Section 44-84-70. All state agencies and political subdivisions of the State shall cooperate with the commission in providing information and assistance at the request of the commission. Section 44-84-80. The commission annually shall submit a report to the Governor and General Assembly that includes the status of food insecurity and hunger in the State, progress being made to achieve food security and alleviate hunger, and proposals and recommendations for strengthening programs and services to further reduce food insecurity and alleviate hunger." SECTION 4. SECTIONS 1 and 2 of this act take effect upon approval by the Governor and apply to any investigative action undertaken as provided herein where the underlying event giving rise to the investigation occurs on or after the effective date. SECTION 3 of this act takes effect July 1, 2012. / Renumber sections to conform. Amend title to conform. Senator CLEARY explained the amendment. H. 4008--Recorded Vote Senator BRIGHT desired to be recorded as voting against the adoption of the amendment. The question then was third reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 42; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Ford Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Verdin Williams Total--42 NAYS Total--0 There being no further amendments, the Bill was read the third time, passed and ordered sent to the House of Representatives with amendments. RETURNED TO THE HOUSE H. 4888 (Word version) -- Reps. Thayer, Owens, Daning, Brannon, Erickson, Whitmire, Atwater, R.L. Brown, Gambrell, J.M. Neal, Putnam and Willis: A BILL TO AMEND SECTION 38-73-470, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DISPOSITION OF THE UNINSURED MOTORIST FUND, SO AS TO PROVIDE THAT THE PORTION THAT WAS FORMERLY PAID TO THE DEPARTMENT OF PUBLIC SAFETY MUST BE PAID TO THE DEPARTMENT OF MOTOR VEHICLES; TO AMEND SECTION 56-1-286, AS AMENDED, RELATING TO THE SUSPENSION OF A DRIVER'S LICENSE OR PERMIT TO CERTAIN PERSONS WHO DRIVE A MOTOR VEHICLE WITH AN UNLAWFUL ALCOHOL CONCENTRATION, SO AS TO MAKE TECHNICAL CHANGES, AND TO PROVIDE THAT THE PORTION OF THE FEE TO OBTAIN A TEMPORARY ALCOHOL LICENSE THAT WAS FORMERLY RETAINED BY THE DEPARTMENT OF PUBLIC SAFETY MUST BE DISTRIBUTED TO THE DEPARTMENT OF MOTOR VEHICLES; TO AMEND SECTION 56-3-3910, RELATING TO THE ISSUANCE OF "SHAG" SPECIAL LICENSE PLATES, SO AS TO REVISE THE BIENNIAL PERIOD IN WHICH THE LICENSE PLATE MUST BE ISSUED OR REVALIDATED; TO AMEND SECTION 56-3-5200, RELATING TO "SOUTH CAROLINA: FIRST IN GOLF" SPECIAL LICENSE PLATES, SO AS TO MAKE A TECHNICAL CHANGE; TO AMEND SECTION 56-5-2951, AS AMENDED, RELATING TO THE SUSPENSION OF A DRIVER'S LICENSE WHEN A DRIVER REFUSES TO SUBMIT TO TESTS TO DETERMINE HIS LEVEL OF ALCOHOL CONCENTRATION, SO AS TO MAKE A TECHNICAL CHANGE; TO AMEND SECTION 56-10-552, RELATING TO THE UNINSURED ENFORCEMENT FUND, SO AS TO PROVIDE THAT THIS FUND WHICH WAS FORMERLY DIRECTED TO THE DIRECTOR OF THE DEPARTMENT OF PUBLIC SAFETY MUST NOW BE DIRECTED TO THE DIRECTOR OF THE DEPARTMENT OF MOTOR VEHICLES AND USED BY THE DEPARTMENT OF MOTOR VEHICLES AND THE DEPARTMENT OF PUBLIC SAFETY; TO AMEND SECTION 56-15-420, RELATING TO THE PROMULGATION OF CERTAIN REGULATIONS BY THE DEPARTMENT OF PUBLIC SAFETY, SO AS TO PROVIDE THAT THESE REGULATIONS NOW WILL BE PROMULGATED BY THE DEPARTMENT OF MOTOR VEHICLES; TO AMEND SECTION 56-19-420, AS AMENDED, RELATING TO CERTAIN FEES FOR SERVICES OFFERED BY THE DEPARTMENT OF MOTOR VEHICLES, SO AS TO REVISE THE DISTRIBUTION OF THESE FEES; AND TO REPEAL ARTICLE 60, CHAPTER 3, TITLE 56 RELATING TO THE ISSUANCE OF "SHRINERS" SPECIAL LICENSE PLATES. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Senators SCOTT and KNOTTS proposed the following amendment (SWB\5396CM12), which was adopted: Amend the bill, as and if amended, by adding the following appropriately numbered SECTION: / SECTION __. Article 3, Chapter 19, Title 56 of the 1976 Code is amended by adding: "Section 56-19-495. The Department of Motor Vehicles shall convene a working group chaired by the Director of the Department of Motor Vehicles, or the director's designee, for the purpose of assisting in the development of a process to be used for the titling of vehicles in this State for which no title can be provided, and assisting in the development of forms and regulations pursuant to this section. The working group must consist, at a minimum, of representative stakeholders from the classic car, dealer, insurance and lienholder industries, as well as from law enforcement agencies." / Renumber sections to conform. Amend title to conform. Senator SCOTT explained the amendment. The question then was third reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 34; Nays 2; Present 1 AYES Anderson Campbell Campsen Cleary Courson Cromer Davis Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Massey Matthews McGill Nicholson O'Dell Peeler Pinckney Reese Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--34 NAYS Bright Bryant Total--2 PRESENT Martin, Shane Total--1 Statement by Senator ALEXANDER Having been out of the Chamber because I was chairing the Conference Committee on retirement at the time the vote was taken, I would have voted in favor the third reading of H. 4888. There being no further amendments, the Bill was read the third time, passed and ordered sent to the House of Representatives with amendments. RETURNED TO THE HOUSE H. 4801 (Word version) -- Reps. Sandifer, Gambrell, Bowen, Whitmire, Agnew, Thayer, Putnam and White: A BILL TO AMEND SECTION 6-13-230, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PIONEER RURAL WATER DISTRICT OF OCONEE AND ANDERSON COUNTIES, SO AS TO REVISE THE QUALIFICATIONS OF PERSONS WHO MAY BE APPOINTED TO THE GOVERNING BOARD OF THE DISTRICT AND THE MANNER OF THEIR APPOINTMENT; AND TO AMEND SECTION 6-13-240, AS AMENDED, RELATING TO THE POWERS AND DUTIES OF THE DISTRICT ACTING THROUGH ITS GOVERNING BOARD, SO AS TO PROVIDE THAT THE DISTRICT MUST NOT CONTRACT FOR OR UNDERTAKE THE CONSTRUCTION OF ANY NEW FRESHWATER TREATMENT FACILITIES UNTIL JANUARY 1, 2016. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Motion Under Rule 26B Senator BRYANT asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B. There was no objection. Senators ALEXANDER and BRYANT proposed the following amendment (JUD4801.004), which was adopted: Amend the bill, as and if amended, by striking subsection 6-13-230(A), beginning on line 32 on page 1 and inserting: / "Section 6-13-230(A)(1). The district shall must be operated and managed by a board of directors to be known as the Pioneer Rural Water District Board of Oconee and Anderson Counties which shall constitute constitutes the governing body of the district. The board shall must consist of five resident electors of the area who shall be appointed by the Governor, upon the recommendation of a majority of those persons attending a meeting of residents of the area held pursuant to at least one week's notice in a local newspaper giving the time and place of the meeting. The chairman and secretary of the meeting shall certify the names of those recommended to the Governor. The original appointments must be for a term of two years for two appointees, for four years for two appointees, and for six years for one appointee. All terms after the initial appointments shall be for six years. All appointees shall hold office until their successors shall have been appointed and qualify. The initial terms of office shall begin as of June 8 1965. Any vacancy shall be filled in like manner as the original appointment for the unexpired portion of the term. Immediately after appointment, the board shall meet and organize by the election of one of its members as chairman, one as vice chairman, one as secretary and one as treasurer. The offices of the secretary and treasurer may be combined in the discretion of the board of five residents of the service area of the district who are qualified electors of Anderson or Oconee counties. Board members serving on this section's effective date shall serve the remainder of their six year terms and until their successors are elected and qualified. Upon the expiration of the term of each member serving on this section's effective date, the member's term will be for three years and until a successor is elected and qualified. The members must be elected to represent distinct service areas. A vacancy must be filled for the remainder of the unexpired term. (2) Each board member must be elected by the customers of Pioneer Rural Water District who are both (a) residents of the service area and (b) qualified electors of Anderson or Oconee county. Each member is entitled to one vote, provided that the member casting the vote is both a resident of the service area and a qualified elector of Anderson or Oconee county. Renumber sections to conform. Amend title to conform. Senator BRYNAT explained the amendment. The question then was third reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Grooms Hayes Hutto Jackson Knotts Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Scott Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Total--0 There being no further amendments, the Bill was read the third time, passed and ordered sent to the House of Representatives with amendments. The following Bill, having been read the second time, was ordered placed on the Third Reading Calendar: S. 1583 (Word version) -- Senator Pinckney: A BILL TO AMEND ACT 476 OF 1998, RELATING TO JASPER COUNTY BOARD OF EDUCATION AS THE GOVERNING BODY OF THE SCHOOL DISTRICT OF JASPER COUNTY, SO AS TO REAPPORTION THE SPECIFIC ELECTION DISTRICTS FROM WHICH MEMBERS OF THE JASPER COUNTY BOARD OF EDUCATION SHALL BE ELECTED BEGINNING WITH SCHOOL BOARD ELECTIONS IN 2012, AND TO PROVIDE FOR DEMOGRAPHIC INFORMATION IN REGARD TO THESE NEWLY DRAWN ELECTION DISTRICTS. On motion of Senator PINCKNEY H. 4943 (Word version) -- Reps. Lowe, Crawford, Erickson, Patrick, Brannon, Ott, Bowers, G.A. Brown, Clemmons, Cole, Frye, Merrill, Pitts, Spires, Tallon, White, Knight and G.M. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 50-11-715 SO AS TO PROVIDE FOR THE HUNTING OF COYOTES, ARMADILLOS, AND FERAL HOGS ON PRIVATE PROPERTY DURING NIGHTTIME HOURS. Senator CAMPSEN asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Fish, Game and Forestry. Senator CAMPSEN proposed the following amendment (4943R004.GEC), which was adopted: Amend the committee amendment, as and if amended, by striking SECTION 1 in its entirety and inserting: / SECTION 1. Section 50-11-710 of the 1976 Code is amended to read: "Section 50-11-710. (A) Night hunting in this State is unlawful except that: (1) raccoons, opossums, foxes, coyotes, mink, and skunk may be hunted at night; however, they may not be hunted with artificial lights except when treed or cornered with dogs, or and may not be hunted with buckshot or any shot larger than a number four, or any rifle ammunition larger than a twenty-two rimfire.; and (2) Feral hogs may be hunted at night with an artificial light that is carried on the hunter's person attached to a helmet or hat, or part of a belt system worn by the hunter and with a sidearm that has iron sites, and barrel length not exceeding nine inches with or without the aid of bait, electronic calls, artificial light, or night vison devices:. The sidearm may not be equipped with a butt-stock, scope, laser site, or light emitting or light enhancing device. However, hogs may not be hunted at night from a vehicle, or with a centerfire rifle or shotgun, unless specifically permitted by the department. A person that violates this item is guilty of a misdemeanor and, upon conviction, must be fined not more than five hundred dollars or imprisoned for not more than thirty days, or both. (a) during any time of the year with a bow and arrow other than a crossbow, or pistol having iron sights, a barrel length not exceeding nine inches, and which is not equipped with a butt-stock, scope, or laser sight; (b) from the last day of February to the first day of July of that same year with any legal firearm, bow and arrow, or crossbow when notice is given to the department pursuant to subsection (D). When hunting at night with a center fire rifle pursuant to this item, a hunter must be at an elevated position at least ten feet from the ground; and (c) at any time of the year under authority of and pursuant to the conditions contained in a depredation permit issued by the department pursuant to Section 50-11-2570. (3) coyotes Coyotes and armadillos may be hunted at night with an artificial light that is carried on the hunter's person attached to a helmet or hat, or part of a belt system worn by the hunter with or without the aid of bait, electronic calls, artificial light, or night vision devices:. Coyotes and armadillos may be hunted with a rifle or sidearm no larger than .22 caliber rimfire, a shotgun with a shot size no larger than a BB, or a sidearm of any caliber that has iron sites and a barrel length not exceeding nine inches. Any weapon used to hunt coyotes or armadillos may not be equipped with a butt-stock, scope, laser site, or light emitting or light enhancing device. It is unlawful to have in one's possession any shot size larger than a BB while legally hunting coyotes and armadillos at night with a shotgun, and coyotes and armadillos may not be hunted at night from a vehicle, unless specifically permitted by the department. A person who violates this item is guilty of a misdemeanor and, upon conviction, must be fined not more than five hundred dollars or imprisoned for not more than thirty days, or both. (a) during any time of the year with a bow and arrow other than a crossbow, a rimfire rifle, a shotgun with shot size no larger than a BB, or a pistol of any caliber having iron sights, a barrel length not exceeding nine inches, and which is not equipped with a butt-stock, scope, or laser sight; (b) from the last day of February to the first day of July of that same year with any legal firearm, bow and arrow, or crossbow when notice is given to the department pursuant to subsection (D). When hunting at night with a center fire rifle pursuant to this item, a hunter must be at an elevated position at least ten feet from the ground; and (c) at any time of the year under authority of and pursuant to the conditions contained in a depredation permit issued by the department pursuant to Section 50-11-2570. (B) The provisions contained in this items (2)(b) and (3)(b) do not apply to a person who has violated any provision contained in Article 4, Chapter 11, Title 50, except Section 50-11-708 and Section 50-11-750, during the previous five years. (B)(C) For the purposes of this section, 'night' means that period of time between one hour after official sundown of a day and one hour before official sunrise of the following day. (D) For the purposes of this section, 'notice to the department' means that the landowner upon which the animals will be taken has either called the department at least forty-eight hours prior to hunting or registered the property as otherwise prescribed by the department. The notice must include the name of each person participating in the hunt, the hunting license number of each person participating in the hunt, and the location of the hunt. Property must only be registered one time during each season, or annually for year-round hunts. (C)(E) Any person violating the provisions of this section, upon conviction, must be fined for the first offense not more than one thousand dollars, or be imprisoned for not more than one year, or both; for the second offense within two years from the date of conviction for the first offense, not more than two thousand dollars nor less than four hundred dollars, or be imprisoned for not more than one year nor for less than ninety days, or both; for a third or subsequent offense within two years of the date of conviction for the last previous offense, not more than three thousand dollars nor less than five hundred dollars, or be imprisoned for not more than one year nor for less than one hundred twenty days, or both. Any person convicted under this section after more than two years have elapsed since his last conviction must be sentenced as for a first offense. (D)(F)(1) A person who violates items (2) and (3) of subsection (A) is guilty of a misdemeanor and, upon conviction, must be fined not more than five hundred dollars or imprisoned for not more than thirty days, or both. (2) In addition to any other penalty, any person convicted for a second or subsequent offense under this section within three years of the date of conviction for a first offense shall have his privilege to hunt in this State suspended for a period of two years. No hunting license may be issued to an individual while his privilege is suspended, and any license mistakenly issued is invalid. The penalty for hunting in this State during the period of suspension, upon conviction, must be imprisonment for not more than one year nor less than ninety days. (E)(G) The provisions of this section may not be construed to prevent any owner of property from protecting the property from destruction by wild game as provided by law. (F)(H) It is unlawful for a person to use artificial lights at night, except vehicle headlights while traveling in a normal manner on a public road or highway, while in possession of or with immediate access to both ammunition of a type prohibited for use at night by the first paragraph of this section and a weapon capable of firing the ammunition. A violation of this paragraph is punishable as provided by Section 50-11-720." / Renumber sections to conform. Amend title to conform. Senator CAMPSEN explained the amendment. The Committee on Fish, Game and Forestry proposed the following amendment (4943R001.RWC), which was adopted: Amend the bill, as and if amended, by striking all after the enacting words and inserting: / SECTION 1. Article 4, Chapter 11, Title 50 of the 1976 Code is amended by adding: "Section 50-11-715. (A) For the purposes of this section, 'notice to the department' means that the landowner upon which the animals will be taken has either called the department at least forty eight hours prior to hunting or registering the property as otherwise prescribed by the department. The notice must include the name of each person participating in the hunt, the hunting license of each person participating in the hunt, and the location of the hunt. Property must only be registered one time during each season, or annually for hunts conducted pursuant to subsection (B)(1)(b). (B)(1)(a) Notwithstanding another provision of law, on private property, a landowner, or his lessee or agent, with written permission, a valid hunting license, the landowner's contact information in his possession, and upon providing notice to the department may take coyotes, armadillos, and feral hogs during the nighttime hours from one hour after official sunset on the last day of February to one hour before official sunrise the first day of July of that same year. (b) A landowner, or his lessee or agent, with written permission, a valid hunting license, the landowner's contact information in his possession, and providing notice to the department may take armadillos during the nighttime hours from one hour after official sunset all year if using a rim fire rifle. (2) The method of such taking shall be with any legal firearm or archery device and may be with or without the aid of bait, electronic calls, artificial light, infrared, thermal or laser sighting devices, night vision devices, or any device aiding the identification or targeting of species. When hunting with a center fire rifle an individual must be at an elevated position at least ten feet from the ground when hunting between the hours of one hour after sunset until one hour before sunrise. (C) The provisions contained in this section do not apply if a person who has violated any provision contained in Article 4, Chapter 11, Title 50, except Section 50-11-708 and Section 50-11-750, during the previous five years." SECTION 2. The first three paragraphs of Section 50-11-740 of the 1976 Code are amended to read: "Section 50-11-740. Every vehicle, boat, trailer, other means of conveyance, animal, and firearm used in the hunting of deer or bear at night, or used in connection with a violation of Section 50-11-710, is forfeited to the State and must be confiscated by any peace officer who shall forthwith deliver it to the department. "Hunting" as used in this section in reference to a vehicle, or boat, or other means of conveyance includes the transportation of a hunter to or from the place of hunting or the transportation of the carcass, or any part of the carcass, of a deer, or bear, coyote, armadillo, or feral hog which has been unlawfully killed at night. For purposes of this section, a conviction for unlawfully hunting deer, or bear, coyote, armadillo, or feral hog at night is conclusive as against any convicted owner of the above-mentioned property. SECTION 3. Section 50-16-70 of the 1976 Code is amended to read: Section 50-16-70. (A) A person violating the provisions of this chapter, or any condition of a permit issued pursuant to this chapter, is guilty of a misdemeanor and, upon conviction, must be fined not more than one thousand dollars or imprisoned not more than six months, or both. The department must suspend the hunting privileges of a person convicted of violating this chapter for one year from the date of the conviction. (B) In addition to any other penalties provided by law, a person convicted of a violation of subsection (A) is also subject to the confiscation, forefeiture, and sale provisions contained in Section 50-11-740 for any property, vehicle, trailer, or other means of conveyance utilized to import, possess, or transport the animal. (C) For the purposes of this section, each animal imported in violation of subsection (A) constitutes a separate offense. (D) Notwithstanding Chapter 3, Title 22, magistrates court shall have jurisdiction over actions arising under this section. SECTION 4. This act takes effect upon approval by the Governor. / Renumber sections to conform. Amend title to conform. Senator CAMPSEN explained the committee amendment. The question then was second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 41; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Ford Gregory Grooms Hayes Hutto Jackson Knotts Land Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson Peeler Pinckney Rankin Reese Rose Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--41 NAYS Total--0 There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. OBJECTION Senator THOMAS objected to the Bills on the Uncontested Local and Statewide Calendar. CARRIED OVER H. 3918 (Word version) -- Rep. White: A BILL TO AMEND CHAPTER 1, TITLE 55, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CREATION OF THE DIVISION OF AERONAUTICS WITHIN THE DEPARTMENT OF COMMERCE, SO AS TO MOVE THE FUNCTIONS, DUTIES, AND RESPONSIBILITIES OF THE DIVISION OF AERONAUTICS TO THE DEPARTMENT OF TRANSPORTATION, TO REVISE CERTAIN PROVISIONS RELATING TO THE OPERATION OF INTRASTATE SCHEDULED AIRLINE SERVICE, COUNTY AVIATION COMMISSIONS, THE USE OF STATE-OWNED AIRCRAFT, AND THE USE OF ALCOHOLIC BEVERAGES BY FLIGHT CREW MEMBERS, TO MAKE TECHNICAL CHANGES, AND TO REVISE CERTAIN PENALTIES; TO AMEND CHAPTER 3, TITLE 55, RELATING TO THE UNIFORM STATE LAWS FOR AERONAUTICS, SO AS TO MAKE TECHNICAL CHANGES, REVISE CERTAIN PROVISIONS RELATING TO THE DEFINITION OF VARIOUS FORMS OF AIRCRAFT, THE OWNERSHIP OF AIRSPACE, THE LANDING OF AN AIRCRAFT ON LANDS OR WATERS, TO PROVIDE THAT IT IS ILLEGAL TO POINT, AIM, OR DISCHARGE A LASER DEVICE AT CERTAIN AIRCRAFT, AND PROVIDE PENALTIES; TO AMEND CHAPTER 5, TITLE 55, RELATING TO THE UNIFORM STATE AERONAUTICAL REGULATORY LAW, SO AS TO MAKE TECHNICAL CHANGES, TO DELETE THE PROVISION THAT CONTAINS VARIOUS TERMS AND THEIR DEFINITIONS, TO DELETE THE PROVISION THAT REQUIRES THE STATE BUDGET AND CONTROL BOARD TO PROVIDE OFFICES FOR THE DIVISION OF AERONAUTICS, TO REVISE THE DIVISION'S RESPONSIBILITIES RELATING TO ITS REGULATION OF CERTAIN AIR NAVIGATION AND AIRPORT FACILITIES, THE CONSTRUCTION OF AIRPORTS, THE REPORTS IT FILES WITH THE FEDERAL AVIATION ADMINISTRATION, AND THE OPERATION OF THE DIVISION, TO PROVIDE PENALTIES FOR VIOLATIONS OF PROVISIONS OF THIS CHAPTER, AND TO REVISE PROVISIONS RELATING TO THE USE OF MONIES CONTAINED IN THE STATE AVIATION FUND; TO AMEND CHAPTER 9, TITLE 55, RELATING TO THE UNIFORM SOUTH CAROLINA AIRPORTS ACT, SO AS TO MAKE TECHNICAL CHANGES, TO PROVIDE THAT THIS CHAPTER ALSO APPLIES TO COUNTIES, AIRPORT COMMISSIONS, AND SPECIAL PURPOSE DISTRICTS, TO DELETE OBSOLETE TERMS, TO REVISE THE PROJECTS THAT MAY BE FUNDED FROM MONIES CONTAINED IN AIRPORT FACILITIES ACCOUNTS, AND TO PROVIDE FOR THE TERM "AIRPORT HAZARD" AND TO PROVIDE ITS DEFINITION AND THE REGULATION OF AN AIRPORT HAZARD; TO AMEND CHAPTER 11, TITLE 55, RELATING TO THE CREATION AND OPERATION OF CERTAIN AIRPORTS WITHIN THE STATE, SO AS TO MAKE TECHNICAL CHANGES, TO DELETE CERTAIN OBSOLETE TERMS, TO REVISE THE PROCESS FOR THE MAKING OF CERTAIN CONTRACTS FOR THE CONSTRUCTION, ERECTION, MAINTENANCE, AND REPAIR OF CERTAIN AIRPORT FACILITIES TO ALLOW FOR THE SALE OF ALCOHOLIC BEVERAGES AT CERTAIN AIRPORT FACILITIES, TO REVISE CERTAIN PENALTIES, TO REVISE THE DEFINITION OF A QUORUM FOR A CERTAIN AIRPORT COMMISSION, TO EXPAND THE AUTHORITY OF CERTAIN AIRPORT COMMISSIONS TO ADOPT RULES AND PROMULGATE REGULATIONS, TO PROVIDE THAT IT IS UNLAWFUL TO ENGAGE IN CERTAIN ACTIVITIES UPON CERTAIN AIRPORT PROPERTY, TO DELETE THE TERM "SECRETARY" AND ITS DEFINITION, AND REPLACE IT WITH THE TERM "EXECUTIVE DIRECTOR" AND ITS DEFINITION AND TO MAKE TECHNICAL CHANGES; TO AMEND CHAPTER 13, TITLE 55, RELATING TO THE PROTECTION OF AIRPORTS AND AIRPORT PROPERTY, SO AS TO PROVIDE THAT THE DIVISION OF AERONAUTICS SHALL CREATE MAPS OF THE STATE'S PUBLIC USE AIRPORTS AND DISTRIBUTE THEM TO VARIOUS LOCAL GOVERNMENTAL AGENCIES FOR VARIOUS PURPOSES, AND TO DEFINE THE TERM "AIRPORT SAFETY ZONES", TO PROVIDE THAT POLITICAL SUBDIVISIONS MAY ASSIST WITH THE PROTECTION OF AREAS THAT POSE HAZARDS TO AIR TRAFFIC, AND TO REVISE THE PENALTIES FOR VIOLATIONS OF THIS CHAPTER; TO AMEND CHAPTER 15, TITLE 55, RELATING TO RELOCATION ASSISTANCE, SO AS TO DELETE THE TERM "DEPARTMENT OF COMMERCE" AND REPLACE IT WITH THE TERM "DEPARTMENT OF TRANSPORTATION", AND TO MAKE TECHNICAL CHANGES; TO AMEND CHAPTER 17, TITLE 55, RELATING TO REGIONAL AIRPORT DISTRICTS, SO AS TO REVISE THE PROVISION THAT REVISES THE TYPE OF AIR CARRIERS REGULATED BY THIS CHAPTER, AND TO MAKE TECHNICAL CHANGES; TO AMEND SECTION 13-1-20, RELATING TO CERTAIN RESPONSIBILITIES OF THE DEPARTMENT OF COMMERCE, SO AS TO DELETE ITS RESPONSIBILITY TO DEVELOP STATE PUBLIC AIRPORTS AND AN AIR TRANSPORTATION SYSTEM; TO AMEND SECTION 13-1-30, AS AMENDED, RELATING TO THE ORGANIZATIONAL STRUCTURE OF THE DEPARTMENT OF COMMERCE, SO AS TO REVISE THE PROVISIONS RELATING TO THE DIVISION OF AERONAUTICS; TO AMEND SECTION 13-1-1000, AS AMENDED, RELATING TO CERTAIN TERMS AND THEIR DEFINITIONS, SO AS TO REVISE THE DEFINITION OF THE TERM "DEPARTMENT"; TO AMEND SECTION 13-1-1010, RELATING TO THE AERONAUTICS COMMISSION, SO AS TO PROVIDE THAT IT IS NO LONGER A DIVISION OF THE DEPARTMENT OF COMMERCE, BUT A DIVISION OF THE DEPARTMENT OF TRANSPORTATION; TO AMEND SECTIONS 57-1-20, 57-1-30, AND 57-1-450, ALL AS AMENDED, RELATING TO THE DUTIES, FUNCTIONS, AND RESPONSIBILITIES OF THE DEPARTMENT OF TRANSPORTATION, SO AS TO PROVIDE THAT IT SHALL HAVE A DIVISION OF AERONAUTICS, OVERSEE THE SAFETY AND DEVELOPMENT OF THE STATE'S PUBLIC USE AIRPORTS, PROVIDE SAFE RELIABLE AIR TRANSPORTATION FOR STATE GOVERNMENT AND BUSINESS PROSPECTS, AND PROVIDE THAT ITS DIRECTOR MUST BE APPOINTED BY THE GOVERNOR; AND TO REPEAL CHAPTER 8, TITLE 55, RELATING TO THE UNIFORM AIRCRAFT FINANCIAL RESPONSIBILITY ACT. Senator MASSEY asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Senator MASSEY explained the Bill. On motion of Senator MASSEY, the Bill was carried over. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: S. 1031 (Word version) -- Senators Lourie, L. Martin, Elliott, Setzler and Alexander: A BILL TO AMEND SECTION 56-5-5660(E)(1) OF THE 1976 CODE, RELATING TO THE APPLICATION FOR AND ISSUANCE OF DISPOSAL AUTHORITY CERTIFICATES, TO INCREASE THE AGE OF A VEHICLE THAT MAY BE DISPOSED OF BY A DEMOLISHER WITHOUT A CERTIFICATE OF TITLE OR OTHER NOTICE REQUIREMENTS FROM EIGHT TO FIFTEEN YEARS; TO AMEND SECTION 56-5-5670(A), RELATING TO DUTIES OF DEMOLISHERS PRIOR TO DEMOLISHING A VEHICLE ABANDONED ON A HIGHWAY, TO ESTABLISH A FIFTEEN DAY WAITING PERIOD BEFORE A DEMOLISHER MAY WRECK, DISMANTLE, OR DEMOLISH A VEHICLE UNLESS THE DEMOLISHER IS PROVIDED WITH A CERTIFICATE OF TITLE, AN AUCTION SALES RECEIPT, A DISPOSAL AUTHORITY CERTIFICATE, OR AN AFFIDAVIT OF PROOF OF LAWFUL POSSESSION; TO AMEND SECTION 56-5-5670(D), RELATING TO PENALTIES FOR DEMOLISHERS THAT BREACH DUTIES ESTABLISHED IN THIS SECTION, TO INCREASE PENALTIES FOR VIOLATIONS OF SECTION 56-5-5670; TO AMEND ARTICLE 39, CHAPTER 5, TITLE 56, RELATING TO THE DISPOSITION OF ABANDONED MOTOR VEHICLES ON HIGHWAYS, BY ADDING SECTION 56-5-5680 TO PROVIDE FOR AN AFFIDAVIT OF LAWFUL POSSESSION THAT A DEMOLISHER MAY ACCEPT IN LIEU OF A CERTIFICATE OF TITLE, AN AUCTION SALES RECEIPT, OR A DISPOSAL AUTHORITY CERTIFICATE, TO PROVIDE FOR THE CONTENTS OF THE AFFIDAVIT, TO PROVIDE THAT IT IS A FELONY TO KNOWINGLY PROVIDE FALSE INFORMATION IN THE AFFIDAVIT, TO REQUIRE A DEMOLISHER ACCEPTING AN AFFIDAVIT TO TRANSMIT THE INFORMATION CONTAINED IN THE AFFIDAVIT TO THE DEPARTMENT OF MOTOR VEHICLES, TO REQUIRE THE DEPARTMENT OF MOTOR VEHICLES TO REPORT THE INFORMATION TRANSMITTED BY THE DEMOLISHER TO THE NATIONAL MOTOR VEHICLE TITLE INFORMATION SYSTEM, AND TO PRESCRIBE THE APPROPRIATE USES OF THE INFORMATION; TO AMEND SECTION 56-5-5945, RELATING TO DUTIES OF DEMOLISHERS PRIOR TO DEMOLISHING AN ABANDONED OR DERELICT MOTOR VEHICLE FOUND ON PRIVATE PROPERTY, TO ESTABLISH A FIFTEEN DAY WAITING PERIOD BEFORE A DEMOLISHER MAY WRECK, DISMANTLE, OR DEMOLISH AN ABANDONED VEHICLE UNLESS THE DEMOLISHER IS PROVIDED WITH A CERTIFICATE OF TITLE, A SALES RECEIPT ISSUED PURSUANT TO SECTION 56-5-5850, OR AN AFFIDAVIT OF PROOF OF LAWFUL POSSESSION, AND TO INCREASE PENALTIES FOR VIOLATIONS OF SECTION 56-5-5945; AND TO REQUIRE THE DEPARTMENT OF MOTOR VEHICLES TO ESTABLISH A MECHANISM FOR THE ELECTRONIC TRANSMISSION OF THE INFORMATION REQUIRED UNDER THIS ACT AT NO CHARGE TO THE DEMOLISHER SUBMITTING THE INFORMATION. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 3028 (Word version) -- Reps. Clemmons, Taylor, Clyburn and Long: A BILL TO AMEND SECTION 59-26-40, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO INDUCTION, ANNUAL, AND CONTINUING CONTRACTS FOR TEACHERS, SO AS TO INCREASE THE INDUCTION CONTRACT PERIOD FROM ONE YEAR TO FIVE YEARS. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4513 (Word version) -- Rep. Harrison: A BILL TO AMEND SECTION 43-35-310, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE MEMBERSHIP OF THE ADULT PROTECTION COORDINATING COUNCIL, SO AS TO REVISE THE MEMBERSHIP AND MAKE TECHNICAL CORRECTIONS; AND TO AMEND SECTION 43-35-330, RELATING TO THE DUTIES OF THE ADULT PROTECTION COORDINATING COUNCIL, SO AS TO REVISE THE DUTIES OF THE COUNCIL AND ADD THE REQUIREMENT THAT THE COUNCIL ANNUALLY PREPARE AND DISTRIBUTE TO THE MEMBERSHIP AND THE MEMBERS OF THE GENERAL ASSEMBLY A REPORT OF THE COUNCIL'S ACTIVITIES AND ACCOMPLISHMENTS FOR THE CALENDAR YEAR. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4786 (Word version) -- Reps. Sandifer and D.C. Moss: A BILL TO AMEND SECTION 41-35-20 OF THE 1976 CODE, RELATING TO THE PAYMENT OF UNEMPLOYMENT BENEFITS BASED ON CERTAIN SERVICES IN SCHOOLS OR INSTITUTIONS OF HIGHER EDUCATION, TO INCLUDE SERVICES PROVIDED BY SUBSTITUTE TEACHERS UNDER CERTAIN CIRCUMSTANCES. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: S. 105 (Word version) -- Senators Verdin, Leventis and L. Martin: A BILL TO AMEND THE 1976 CODE, BY ADDING ARTICLE 8 TO CHAPTER 25, TITLE 57, TO DIRECT THE DEPARTMENT OF TRANSPORTATION TO CREATE AND SUPERVISE A STATEWIDE PROGRAM RELATED TO PROVIDING DIRECTIONAL SIGNS ALONG THE STATE'S MAJOR HIGHWAYS AND INTERCHANGES LEADING TO AGRITOURISM ORIENTED FACILITIES ENGAGED IN EDUCATIONAL OR AGRITOURISM ACTIVITIES. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 3433 (Word version) -- Reps. Herbkersman and Patrick: A BILL TO AMEND SECTION 7-7-110, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN BEAUFORT COUNTY, SO AS TO REVIEW AND RENAME CERTAIN VOTING PRECINCTS OF BEAUFORT COUNTY AND TO REDESIGNATE A MAP NUMBER FOR THE MAP ON WHICH LINES OF THESE PRECINCTS ARE DELINEATED AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4042 (Word version) -- Reps. Harrison, Brady, Pinson, H.B. Brown, Munnerlyn, Viers, Horne and Hardwick: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 39-5-31 SO AS TO MAKE IT AN UNFAIR TRADE PRACTICE FOR A MOTOR VEHICLE GLASS REPAIR BUSINESS THAT ADMINISTERS INSURANCE CLAIMS FOR MOTOR VEHICLE GLASS REPAIRS TO HAVE AN INSURED'S GLASS REPAIR BUSINESS REFERRED TO ITSELF OR TO USE INFORMATION TO SOLICIT BUSINESS. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4082 (Word version) -- Reps. Vick, Edge, Hiott, Hayes, R.L. Brown, Jefferson, Bowers, Anthony, Skelton, Williams, McLeod, G.M. Smith, Weeks, Gilliard, Agnew, Horne, Funderburk, Tribble, Pinson, Clemmons and Neilson: A BILL TO AMEND SECTION 38-7-20, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE IMPOSITION OF THE INSURANCE PREMIUM TAX, SO AS TO PROVIDE THAT SEVEN PERCENT OF THE ANNUAL REVENUE OF THIS TAX MUST BE TRANSFERRED TO THE SOUTH CAROLINA FORESTRY COMMISSION AND USED BY IT FOR FIREFIGHTING AND FIREFIGHTING EQUIPMENT REPLACEMENT AND FOREST INDUSTRY ECONOMIC ENHANCEMENT. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4614 (Word version) -- Reps. Pitts, Lucas, Hearn, Brannon, Weeks, Spires, Loftis and Clemmons: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 2 TO CHAPTER 15, TITLE 63 SO AS TO SPECIFY CERTAIN PROCEDURES AND REQUIREMENTS FOR COURT-ORDERED CHILD CUSTODY, INCLUDING, BUT NOT LIMITED TO, DEFINING "JOINT CUSTODY" AND "SOLE CUSTODY", REQUIRING PARENTS TO JOINTLY PREPARE AND SUBMIT A PARENTING PLAN, WHICH THE COURT MUST CONSIDER BEFORE ISSUING TEMPORARY AND FINAL CUSTODY ORDERS; REQUIRING THE COURT TO MAKE FINAL CUSTODY DETERMINATIONS IN THE BEST INTEREST OF THE CHILD BASED UPON THE EVIDENCE PRESENTED, REQUIRING THE COURT TO CONSIDER JOINT CUSTODY IF EITHER PARENT SEEKS IT, STATING FINDINGS OF FACT AS TO WHY OR WHY NOT JOINT CUSTODY WAS AWARDED, PROVIDING MATTERS THAT MAY BE INCLUDED IN A CUSTODY ORDER, PROVIDING FACTORS THE COURT MAY CONSIDER IN ISSUING OR MODIFYING A CUSTODY ORDER WHEN CONSIDERING THE BEST INTEREST OF THE CHILD, AND AUTHORIZING A PARENT TO SEEK ARBITRATION OF AN ISSUE THAT CANNOT BE RESOLVED BETWEEN THE PARENTS; AND TO AMEND SECTION 63-5-30, RELATING TO THE RIGHTS AND DUTIES OF PARENTS TO THEIR CHILDREN, SO AS TO PROVIDE THAT UNLESS OTHERWISE PROVIDED BY AN ORDER OF THE COURT, PARENTS HAVE EQUAL POWERS, RIGHTS, AND DUTIES CONCERNING ALL MATTERS AFFECTING THEIR CHILDREN. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4497 (Word version) -- Reps. Sellers, Johnson, Brady, Gilliard, Jefferson and Knight: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 44-29-187 SO AS TO ENACT THE "CERVICAL CANCER PREVENTION ACT"; TO PROVIDE THAT BEGINNING WITH THE 2012-2013 SCHOOL YEAR, THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL SHALL OFFER AS AN OPTION THE CERVICAL CANCER VACCINE SERIES TO FEMALE STUDENTS ENROLLING IN THE SEVENTH GRADE; TO PROVIDE THE STUDENT MAY ONLY RECEIVE THESE VACCINATIONS AT THE OPTION OF THE PARENT OR GUARDIAN OF THE CHILD; TO PROVIDE A PROCEDURE THROUGH WHICH A PARENT OR GUARDIAN MAY EXERCISE THE OPTION FOR THEIR CHILD TO RECEIVE THESE VACCINATIONS; TO REQUIRE A RELATED EDUCATION PROGRAM; AND TO PROVIDE THAT IMPLEMENTATION OF THIS SECTION IS CONTINGENT UPON STATE AND FEDERAL FUNDING. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4654 (Word version) -- Reps. Hardwick, Harrell, Loftis, Sandifer, White, Harrison, Owens, Crosby, Anderson, Bingham, Sottile, Corbin, Chumley, Forrester, Hearn, Henderson, Lucas, D.C. Moss, V.S. Moss, Ott, Parker, Southard, Murphy, Clemmons, Hixon, Knight and Patrick: A BILL TO AMEND SECTION 48-1-90, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROHIBITING THE DISCHARGE OF POLLUTANTS INTO THE ENVIRONMENT AND REMEDIES FOR VIOLATIONS, SO AS TO PROVIDE EXEMPTIONS AND LIMITATIONS ON THESE EXEMPTIONS AND TO SPECIFY THAT NO PRIVATE CAUSE OF ACTION IS CREATED BY OR EXISTS UNDER THE POLLUTION CONTROL ACT; TO AMEND SECTION 48-1-130, RELATING TO FINAL ORDERS OF THE DEPARTMENT DISCONTINUING DISCHARGE OF POLLUTANTS, SO AS TO DELETE PROVISIONS RELATING TO REQUIRED PROCEDURES PRECEDING THE ISSUANCE OF A FINAL ORDER AND TO PROVIDE THAT AN ORDER IS SUBJECT TO REVIEW PURSUANT TO THE ADMINISTRATIVE PROCEDURES ACT; TO AMEND SECTION 48-1-250, RELATING TO WHOM BENEFITS FROM CAUSES OF ACTION RESULTING FROM POLLUTION VIOLATIONS INURE, SO AS TO PROVIDE THAT NO PRIVATE CAUSE OF ACTION IS CREATED BY OR EXISTS UNDER THE POLLUTION CONTROL ACT; AND TO MAKE THESE PROVISIONS RETROACTIVE AND EXTINGUISH ANY RIGHT, CLAIM, OR CAUSE OF ACTION ARISING UNDER OR RELATED TO THE POLLUTION CONTROL ACT, SUBJECT TO EXCEPTIONS FOR THE STATE AND ITS SUBDIVISIONS. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 5098 (Word version) -- Reps. Hixon, Clyburn, Harrison, Taylor and Young: A BILL TO AMEND SECTION 61-6-2010, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO TEMPORARY PERMITS FOR THE POSSESSION, SALE, AND CONSUMPTION OF ALCOHOLIC LIQUORS BY THE DRINK IN A COUNTY OR MUNICIPALITY UPON A FAVORABLE REFERENDUM VOTE, SO AS TO FURTHER PROVIDE FOR THOSE ELECTIONS WHICH CONSTITUTE GENERAL ELECTIONS FOR PURPOSES OF THE REFERENDUMS REQUIRED UNDER THIS SECTION. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 4945 (Word version) -- Reps. Funderburk, Harrison, Brantley, McLeod, Butler Garrick, Munnerlyn, Taylor, J.H. Neal, Dillard, Bannister, G.R. Smith, Bowers, Cobb-Hunter, Delleney, Hixon, Long, Pope and Young: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 7-5-185 SO AS TO AUTHORIZE A PERSON TO REGISTER TO VOTE ELECTRONICALLY ON THE INTERNET WEBSITE OF THE STATE ELECTION COMMISSION, TO PROVIDE A PROCEDURE FOR THIS TYPE OF REGISTRATION AND AUTHORIZE THE STATE ELECTION COMMISSION TO PROMULGATE REGULATIONS TO EFFECTUATE THE PROVISIONS OF THIS ACT. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 5, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments: S. 1419 (Word version) -- Senators Thomas, Ford and Hayes: A BILL TO AMEND CHAPTER 45, TITLE 38, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO INSURANCE BROKERS AND SURPLUS LINES INSURANCE, SO AS TO DEFINE TERMS, TO PROVIDE THAT THE REVENUE COLLECTED FROM THE BROKER'S PREMIUM TAX RATE MUST BE CREDITED TO A SPECIAL EARMARKED FUND, TO PROVIDE THE MANNER IN WHICH THE FUND MAY BE USED AND DISBURSED, TO AUTHORIZE THE DIRECTOR OF THE DEPARTMENT OF INSURANCE TO CONDUCT EXAMINATIONS OF BROKER RECORDS, TO ALLOW THE DEPARTMENT OF INSURANCE TO PROMULGATE REGULATIONS NECESSARY TO IMPLEMENT THE CHAPTER, TO PROVIDE THE MANNER IN WHICH THE NONADMITTED AND REINSURANCE REFORM ACT OF 2010 MAY BE IMPLEMENTED; AND TO AMEND SECTION 38-7-160, RELATING TO MUNICIPAL LICENSE FEES AND TAXES, SO AS TO DISALLOW A MUNICIPALITY FROM CHARGING AN ADDITIONAL LICENSE FEE OR TAX BASED UPON A PERCENTAGE OF PREMIUMS FOR PURPOSES OF SURPLUS LINES INSURANCE. Respectfully submitted, Speaker of the House The Bill was ordered placed on the Calendar for consideration tomorrow. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments: S. 263 (Word version) -- Senators Knotts and Ford: A BILL TO AMEND ARTICLE 23, CHAPTER 5, TITLE 56 OF THE SOUTH CAROLINA CODE OF LAWS, 1976, BY ADDING SECTION 56-5-2905, SO AS TO PROVIDE THAT A PERSON WHO WHILE DRIVING A MOTOR VEHICLE DOES ANY ACT FORBIDDEN BY LAW IN THE DRIVING OF THE MOTOR VEHICLE, EXCEPT A VIOLATION OF SECTIONS 56-5-2930, 56-5-2935, OR 56-5-2945, WHICH PROXIMATELY CAUSES DEATH TO A PERSON, IS GUILTY OF THE MISDEMEANOR OFFENSE OF VEHICULAR HOMICIDE; AND TO AMEND SECTION 56-5-2946 OF THE SOUTH CAROLINA CODE OF LAWS, 1976, SO AS TO PROVIDE THAT A PERSON MUST SUBMIT TO EITHER ONE OR A COMBINATION OF CHEMICAL TESTS OF HIS BREATH, BLOOD, OR URINE FOR THE PURPOSE OF DETERMINING THE PRESENCE OF ALCOHOL, DRUGS, OR A COMBINATION OF ALCOHOL AND DRUGS IF THE PERSON IS THE DRIVER OF A MOTOR VEHICLE INVOLVED IN A MOTOR VEHICLE INCIDENT RESULTING IN THE DEATH OF ANOTHER PERSON. Respectfully submitted, Speaker of the House The Bill was ordered placed on the Calendar for consideration tomorrow. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments: S. 1065 (Word version) -- Senators L. Martin, Hayes and Fair: A BILL TO AMEND SECTION 61-2-180 OF THE 1976 CODE, RELATING TO BINGO, RAFFLES, AND OTHER SPECIAL EVENTS, TO CLARIFY THAT THIS SECTION DOES NOT AUTHORIZE THE USE OF ANY DEVICE PROHIBITED BY SECTION 12-21-2710; AND TO AMEND SECTION 61-4-580, RELATING TO GAME PROMOTIONS ALLOWED BY HOLDERS OF PERMITS AUTHORIZING THE SALE OF BEER OR WINE, TO CLARIFY THAT THIS ITEM DOES NOT AUTHORIZE THE USE OF ANY DEVICE PROHIBITED BY SECTION 12-21-2710. Respectfully submitted, Speaker of the House The Bill was ordered placed on the Calendar for consideration tomorrow. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments: S. 1354 (Word version) -- Senators Bryant, Thomas, Ford, L. Martin, Rose, Bright, Cromer, Fair and Thomas: A BILL TO AMEND SECTION 35-1-604 OF THE 1976 CODE, RELATING TO SECURITIES VIOLATIONS, TO REQUIRE ALL CEASE AND DESIST ORDERS ISSUED BY THE SECURITIES COMMISSIONER TO BE PUBLIC DOCUMENTS AND TO REQUIRE PUBLICATION ON THE ATTORNEY GENERAL'S WEBSITE. Respectfully submitted, Speaker of the House The Bill was ordered placed on the Calendar for consideration tomorrow. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments: S. 300 (Word version) -- Senators Fair, Hutto, Jackson, Knotts, Rankin and Ford: A BILL TO AMEND SECTION 63-19-1440, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO COMMITMENT OF JUVENILES TO THE DEPARTMENT OF JUVENILE JUSTICE, SO AS TO AUTHORIZE THE DEPARTMENT OF JUVENILE JUSTICE TO ALLOW A JUVENILE WHO IS TEMPORARILY COMMITTED TO ITS CUSTODY, AFTER BEING ADJUDICATED FOR A STATUS OFFENSE, MISDEMEANOR OFFENSE, OR A PROBATION VIOLATION OR CONTEMPT, TO UNDERGO A COMMUNITY EVALUATION WITH CERTAIN SAFEGUARDS AND EXCEPTIONS. Respectfully submitted, Speaker of the House The Bill was ordered placed on the Calendar for consideration tomorrow. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments: S. 1099 (Word version) -- Senator Fair: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 63-19-650 SO AS TO PROVIDE THAT MEMBERS OF THE BOARD OF JUVENILE PAROLE SHALL RECEIVE A HEARING FEE. Respectfully submitted, Speaker of the House The Bill was ordered placed on the Calendar for consideration tomorrow. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments: S. 1220 (Word version) -- Senators Campbell, Hayes and Ford: A BILL TO AMEND SECTION 48-2-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FEES IMPOSED BY THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL FOR CERTAIN ENVIRONMENTAL PROGRAMS, INCLUDING THE SURFACE WATER WITHDRAWAL PROGRAM, WHICH ARE DEPOSITED INTO THE ENVIRONMENTAL PROTECTION FUND FOR ADMINISTRATION OF THESE PROGRAMS, SO AS TO ENUMERATE THE FEES FOR SURFACE WATER WITHDRAWAL APPLICATIONS AND PERMITS THAT WOULD OTHERWISE HAVE BEEN REPEALED JANUARY 1, 2013; BY ADDING SECTION 49-4-175 SO AS TO REIMPOSE THE FEES THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL MAY CHARGE FOR SURFACE WATER WITHDRAWAL AND APPLICATIONS AND PERMITS AND TO PROVIDE THAT THE DEPARTMENT SHALL RETAIN THESE FEES TO IMPLEMENT AND OPERATE THE SURFACE WATER WITHDRAWAL PROGRAM; AND TO AMEND ACT 247 OF 2010, BY REPEALING PROVISIONS THAT PROSPECTIVELY REPEAL THE IMPOSITION OF SURFACE WATER WITHDRAWAL PERMIT FEES. Respectfully submitted, Speaker of the House The Bill was ordered placed on the Calendar for consideration tomorrow. Privilege of the Chamber On motion of Senators O'DELL and MALLOY, with unanimous consent, the Privilege of the Chamber to that area behind the rail, was extended to Ms. Mary Lou Price and her family upon the occasion of her retirement from the S.C. Senate. Senators MALLOY, PINCKNEY and COURSON commended and thanked her for her many years of devoted service. THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD. On motion of Senator LEATHERMAN, the Senate agreed to dispense with the Motion Period. HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF REPORTS OF COMMITTEES OF CONFERENCE AND FREE CONFERENCE. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has adopted the Report of the Committee of Conference on: Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that the Report of the Committee of Conference having been adopted by both Houses, and this Bill having been read three times in each House, it was ordered that the title thereof be changed to that of an Act and that it be enrolled for Ratification: Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has requested and was granted Free Conference Powers and has appointed Reps. Gilliard, Rutherford and Herbkersman to the Committee of Free Conference on the part of the House on: H. 3527 (Word version) -- Reps. Gilliard, McEachern, Spires, Butler Garrick, King, Jefferson, Sabb, Munnerlyn, V.S. Moss, Cobb-Hunter, Herbkersman, Willis, Harrell, Pope, D.C. Moss, Norman, Hearn, Horne, Murphy, Bikas, Viers, Whipper and R.L. Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 24-3-970 SO AS TO PROVIDE THAT IT IS UNLAWFUL FOR AN INMATE TO BE A MEMBER OF AN INTERNET-BASED SOCIAL NETWORKING WEBSITE AND TO PROVIDE A PENALTY. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has adopted the Report of the Committee of Free Conference on: H. 3527 (Word version) -- Reps. Gilliard, McEachern, Spires, Butler Garrick, King, Jefferson, Sabb, Munnerlyn, V.S. Moss, Cobb-Hunter, Herbkersman, Willis, Harrell, Pope, D.C. Moss, Norman, Hearn, Horne, Murphy, Bikas, Viers, Whipper and R.L. Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 24-3-970 SO AS TO PROVIDE THAT IT IS UNLAWFUL FOR AN INMATE TO BE A MEMBER OF AN INTERNET-BASED SOCIAL NETWORKING WEBSITE AND TO PROVIDE A PENALTY. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that the Report of the Committee of Free Conference having been adopted by both Houses, and this Bill having been read three times in each House, it was ordered that the title thereof be changed to that of an Act and that it be enrolled for Ratification: H. 3527 (Word version) -- Reps. Gilliard, McEachern, Spires, Butler Garrick, King, Jefferson, Sabb, Munnerlyn, V.S. Moss, Cobb-Hunter, Herbkersman, Willis, Harrell, Pope, D.C. Moss, Norman, Hearn, Horne, Murphy, Bikas, Viers, Whipper and R.L. Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 24-3-970 SO AS TO PROVIDE THAT IT IS UNLAWFUL FOR AN INMATE TO BE A MEMBER OF AN INTERNET-BASED SOCIAL NETWORKING WEBSITE AND TO PROVIDE A PENALTY. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it refuses to concur in the amendments proposed by the Senate to: H. 5025 (Word version) -- Reps. Govan, Cobb-Hunter, King, Limehouse, J.H. Neal, Ott, R.L. Brown and Gilliard: A BILL TO AMEND SECTION 59-127-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE BOARD OF TRUSTEES OF SOUTH CAROLINA STATE UNIVERSITY, SO AS TO REVISE THE NUMBER OF BOARD MEMBERS AND THE MANNER IN WHICH MEMBERS OF THE BOARD ARE ELECTED TO ACCOUNT FOR THE NEW SEVENTH CONGRESSIONAL DISTRICT AND THREE ALUMNI MEMBERS, AND TO REVISE OTHER PROVISIONS RELATING TO TERMS OF BOARD MEMBERS, INCLUDING A PROVISION THAT THE TERMS OF ALL PRESENTLY ELECTED MEMBERS OF THE BOARD SHALL EXPIRE ON JUNE 30, 2012, AT WHICH TIME THEIR SUCCESSORS ELECTED AS PROVIDED BY THIS SECTION SHALL TAKE OFFICE. Very respectfully, Speaker of the House H. 5025-SENATE INSISTS ON THEIR AMENDMENTS CONFERENCE COMMITTEE APPOINTED H. 5025 (Word version) -- Reps. Govan, Cobb-Hunter, King, Limehouse, J.H. Neal, Ott, R.L. Brown and Gilliard: A BILL TO AMEND SECTION 59-127-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE BOARD OF TRUSTEES OF SOUTH CAROLINA STATE UNIVERSITY, SO AS TO REVISE THE NUMBER OF BOARD MEMBERS AND THE MANNER IN WHICH MEMBERS OF THE BOARD ARE ELECTED TO ACCOUNT FOR THE NEW SEVENTH CONGRESSIONAL DISTRICT AND THREE ALUMNI MEMBERS, AND TO REVISE OTHER PROVISIONS RELATING TO TERMS OF BOARD MEMBERS, INCLUDING A PROVISION THAT THE TERMS OF ALL PRESENTLY ELECTED MEMBERS OF THE BOARD SHALL EXPIRE ON JUNE 30, 2012, AT WHICH TIME THEIR SUCCESSORS ELECTED AS PROVIDED BY THIS SECTION SHALL TAKE OFFICE. On motion of Senator COURSON, the Senate insisted upon its amendments to H. 5025 and asked for a Committee of Conference. Whereupon, Senators MATTHEWS, JACKSON and BRYANT were appointed to the Committee of Conference on the part of the Senate and a message was sent to the House accordingly. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has appointed Reps. Govan, Cobb-Hunter and Skelton to the Committee of Conference on the part of the House on: H. 5025 (Word version) -- Reps. Govan, Cobb-Hunter, King, Limehouse, J.H. Neal, Ott, R.L. Brown and Gilliard: A BILL TO AMEND SECTION 59-127-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE BOARD OF TRUSTEES OF SOUTH CAROLINA STATE UNIVERSITY, SO AS TO REVISE THE NUMBER OF BOARD MEMBERS AND THE MANNER IN WHICH MEMBERS OF THE BOARD ARE ELECTED TO ACCOUNT FOR THE NEW SEVENTH CONGRESSIONAL DISTRICT AND THREE ALUMNI MEMBERS, AND TO REVISE OTHER PROVISIONS RELATING TO TERMS OF BOARD MEMBERS, INCLUDING A PROVISION THAT THE TERMS OF ALL PRESENTLY ELECTED MEMBERS OF THE BOARD SHALL EXPIRE ON JUNE 30, 2012, AT WHICH TIME THEIR SUCCESSORS ELECTED AS PROVIDED BY THIS SECTION SHALL TAKE OFFICE. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has appointed Reps. Bannister, Hearn and Weeks to the Committee of Conference on the part of the House on: H. 3400 (Word version) -- Rep. Weeks: A BILL TO AMEND SECTION 63-3-530, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO JURISDICTION OF THE FAMILY COURT IN CERTAIN MATTERS, SO AS TO PROVIDE THAT A CHILD SUPPORT OBLIGATION AUTOMATICALLY TERMINATES WHEN THE CHILD TURNS EIGHTEEN OR GRADUATES FROM HIGH SCHOOL, WHICHEVER IS SOONER. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has adopted the Report of the Committee of Conference on: H. 3757 (Word version) -- Reps. Hardwick, Hearn, Mitchell, Long, Erickson, Brady, Butler Garrick, Funderburk, Munnerlyn, Knight, Dillard, Cobb-Hunter, Parks, Huggins, Allison, Tallon, Brannon, Atwater, Whipper, Patrick and J.R. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 19 TO CHAPTER 3, TITLE 16 SO AS TO DEFINE NECESSARY TERMS, PROVIDE FOR CERTAIN HUMAN TRAFFICKING OFFENSES AND PROVIDE PENALTIES, TO PROVIDE FOR CRIMINAL LIABILITY OF BUSINESS ENTITIES, TO PROVIDE RESTITUTION FOR VICTIMS OF HUMAN TRAFFICKING OFFENSES, TO ESTABLISH AN INTERAGENCY TASK FORCE TO DEVELOP AND IMPLEMENT A PLAN FOR THE PREVENTION OF TRAFFICKING IN PERSONS, TO REQUIRE THE COLLECTION AND DISSEMINATION OF DATA RELATED TO HUMAN TRAFFICKING BY THE STATE LAW ENFORCEMENT DIVISION (SLED), TO REQUIRE MANDATORY LAW ENFORCEMENT TRAINING ON HUMAN TRAFFICKING OFFENSES, TO PROVIDE FOR THE CREATION OF PUBLIC AWARENESS PROGRAMS REGARDING HUMAN TRAFFICKING IN THE STATE, TO ALLOW CIVIL ACTIONS BY VICTIMS OF HUMAN TRAFFICKING, TO PROVIDE THAT CERTAIN STANDARDS OF WORKING CONDITIONS APPLY WITHOUT REGARD TO IMMIGRATION STATUS, TO PROVIDE CERTAIN PROTECTIONS FOR VICTIMS OF HUMAN TRAFFICKING PURSUANT TO THE VICTIMS' BILL OF RIGHTS AND OTHER RELEVANT STATUTORY PROVISIONS, TO REQUIRE THE STATE TO DEVELOP PLANS FOR HOUSING AND COUNSELING, AMONG OTHER THINGS, OF VICTIMS OF HUMAN TRAFFICKING WITHIN ONE HUNDRED EIGHTY DAYS OF THE EFFECTIVE DATE OF THE ACT, TO PROVIDE FOR CERTAIN RIGHTS OF MINOR VICTIMS OF HUMAN TRAFFICKING, TO ESTABLISH HUMAN TRAFFICKING VICTIM-CASEWORKER PRIVILEGE, AND TO CREATE THE OFFENSE OF MALICIOUSLY OR WITH CRIMINAL NEGLIGENCE PUBLISHING, DISSEMINATING, OR OTHERWISE DISCLOSING THE LOCATION OF A HUMAN TRAFFICKING VICTIM, A TRAFFICKING SHELTER, OR A DOMESTIC VIOLENCE SHELTER AND TO PROVIDE A PENALTY; AND TO REPEAL SECTION 16-3-930 RELATING TO TRAFFICKING IN PERSONS FOR FORCED LABOR OR SERVICES. Very respectfully, Speaker of the House H. 3757--REPORT OF THE H. 3757 (Word version) -- Reps. Hardwick, Hearn, Mitchell, Long, Erickson, Brady, Butler Garrick, Funderburk, Munnerlyn, Knight, Dillard, Cobb-Hunter, Parks, Huggins, Allison, Tallon, Brannon, Atwater, Whipper, Patrick and J.R. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 19 TO CHAPTER 3, TITLE 16 SO AS TO DEFINE NECESSARY TERMS, PROVIDE FOR CERTAIN HUMAN TRAFFICKING OFFENSES AND PROVIDE PENALTIES, TO PROVIDE FOR CRIMINAL LIABILITY OF BUSINESS ENTITIES, TO PROVIDE RESTITUTION FOR VICTIMS OF HUMAN TRAFFICKING OFFENSES, TO ESTABLISH AN INTERAGENCY TASK FORCE TO DEVELOP AND IMPLEMENT A PLAN FOR THE PREVENTION OF TRAFFICKING IN PERSONS, TO REQUIRE THE COLLECTION AND DISSEMINATION OF DATA RELATED TO HUMAN TRAFFICKING BY THE STATE LAW ENFORCEMENT DIVISION (SLED), TO REQUIRE MANDATORY LAW ENFORCEMENT TRAINING ON HUMAN TRAFFICKING OFFENSES, TO PROVIDE FOR THE CREATION OF PUBLIC AWARENESS PROGRAMS REGARDING HUMAN TRAFFICKING IN THE STATE, TO ALLOW CIVIL ACTIONS BY VICTIMS OF HUMAN TRAFFICKING, TO PROVIDE THAT CERTAIN STANDARDS OF WORKING CONDITIONS APPLY WITHOUT REGARD TO IMMIGRATION STATUS, TO PROVIDE CERTAIN PROTECTIONS FOR VICTIMS OF HUMAN TRAFFICKING PURSUANT TO THE VICTIMS' BILL OF RIGHTS AND OTHER RELEVANT STATUTORY PROVISIONS, TO REQUIRE THE STATE TO DEVELOP PLANS FOR HOUSING AND COUNSELING, AMONG OTHER THINGS, OF VICTIMS OF HUMAN TRAFFICKING WITHIN ONE HUNDRED EIGHTY DAYS OF THE EFFECTIVE DATE OF THE ACT, TO PROVIDE FOR CERTAIN RIGHTS OF MINOR VICTIMS OF HUMAN TRAFFICKING, TO ESTABLISH HUMAN TRAFFICKING VICTIM-CASEWORKER PRIVILEGE, AND TO CREATE THE OFFENSE OF MALICIOUSLY OR WITH CRIMINAL NEGLIGENCE PUBLISHING, DISSEMINATING, OR OTHERWISE DISCLOSING THE LOCATION OF A HUMAN TRAFFICKING VICTIM, A TRAFFICKING SHELTER, OR A DOMESTIC VIOLENCE SHELTER AND TO PROVIDE A PENALTY; AND TO REPEAL SECTION 16-3-930 RELATING TO TRAFFICKING IN PERSONS FOR FORCED LABOR OR SERVICES. On motion of Senator HUTTO, with unanimous consent, the Report of the Committee of Conference was taken up for immediate consideration. Senator HUTTO spoke on the report. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 43; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Courson Cromer Davis Elliott Fair Ford Gregory Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--43 NAYS Total--0 On motion of Senator HUTTO, the Report of the Committee of Conference to H. 3757 was adopted as follows: H. 3757--Conference Report The General Assembly, Columbia, S.C., June 5, 2012 The Committee of Conference, to whom was referred: H. 3757 (Word version) -- Reps. Hardwick, Hearn, Mitchell, Long, Erickson, Brady, Butler Garrick, Funderburk, Munnerlyn, Knight, Dillard, Cobb-Hunter, Parks, Huggins, Allison, Tallon, Brannon, Atwater, Whipper, Patrick and J.R. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 19 TO CHAPTER 3, TITLE 16 SO AS TO DEFINE NECESSARY TERMS, PROVIDE FOR CERTAIN HUMAN TRAFFICKING OFFENSES AND PROVIDE PENALTIES, TO PROVIDE FOR CRIMINAL LIABILITY OF BUSINESS ENTITIES, TO PROVIDE RESTITUTION FOR VICTIMS OF HUMAN TRAFFICKING OFFENSES, TO ESTABLISH AN INTERAGENCY TASK FORCE TO DEVELOP AND IMPLEMENT A PLAN FOR THE PREVENTION OF TRAFFICKING IN PERSONS, TO REQUIRE THE COLLECTION AND DISSEMINATION OF DATA RELATED TO HUMAN TRAFFICKING BY THE STATE LAW ENFORCEMENT DIVISION (SLED), TO REQUIRE MANDATORY LAW ENFORCEMENT TRAINING ON HUMAN TRAFFICKING OFFENSES, TO PROVIDE FOR THE CREATION OF PUBLIC AWARENESS PROGRAMS REGARDING HUMAN TRAFFICKING IN THE STATE, TO ALLOW CIVIL ACTIONS BY VICTIMS OF HUMAN TRAFFICKING, TO PROVIDE THAT CERTAIN STANDARDS OF WORKING CONDITIONS APPLY WITHOUT REGARD TO IMMIGRATION STATUS, TO PROVIDE CERTAIN PROTECTIONS FOR VICTIMS OF HUMAN TRAFFICKING PURSUANT TO THE VICTIMS' BILL OF RIGHTS AND OTHER RELEVANT STATUTORY PROVISIONS, TO REQUIRE THE STATE TO DEVELOP PLANS FOR HOUSING AND COUNSELING, AMONG OTHER THINGS, OF VICTIMS OF HUMAN TRAFFICKING WITHIN ONE HUNDRED EIGHTY DAYS OF THE EFFECTIVE DATE OF THE ACT, TO PROVIDE FOR CERTAIN RIGHTS OF MINOR VICTIMS OF HUMAN TRAFFICKING, TO ESTABLISH HUMAN TRAFFICKING VICTIM-CASEWORKER PRIVILEGE, AND TO CREATE THE OFFENSE OF MALICIOUSLY OR WITH CRIMINAL NEGLIGENCE PUBLISHING, DISSEMINATING, OR OTHERWISE DISCLOSING THE LOCATION OF A HUMAN TRAFFICKING VICTIM, A TRAFFICKING SHELTER, OR A DOMESTIC VIOLENCE SHELTER AND TO PROVIDE A PENALTY; AND TO REPEAL SECTION 16-3-930 RELATING TO TRAFFICKING IN PERSONS FOR FORCED LABOR OR SERVICES. Beg leave to report that they have duly and carefully considered the same and recommend: That the same do pass with the following amendments: Amend the bill, as and if amended, by striking all after the enacting words and inserting: / SECTION 1. Chapter 3, Title 16 of the 1976 Code is amended by adding: "Article 19 Trafficking in Persons (1) 'Business' means a corporation, partnership, proprietorship, firm, enterprise, franchise, organization, or self-employed individual. (2) 'Charitable organization' means a 'charitable organization' pursuant to Section 33-56-20. (3) 'Debt bondage' means the status or condition of a debtor arising from a pledge by the debtor of his personal services or those of a person under his control as a security for debt, if the value of those services as reasonably assessed is not applied toward the liquidation of the debt or the length and nature of those services are not respectively limited and defined or if the principal amount of the debt does not reasonably reflect the value of the items or services for which the debt was incurred. (4) 'Forced labor' means any type of labor or services performed or provided by a person rendered through another person's coercion of the person providing the labor or services. This definition does not include labor or services performed or provided by a person in the custody of the Department of Corrections or a local jail, detention center, or correctional facility. (5) 'Involuntary servitude' means a condition of servitude induced through coercion. (6) 'Person' means an individual, corporation, partnership, charitable organization, or another legal entity. (7) 'Sex trafficking' means the recruitment, harboring, transportation, provision, or obtaining of a person for one of the following when it is induced by force, fraud, or coercion or the person forced to perform the act is under the age of eighteen years and anything of value is given, promised to, or received, directly or indirectly, by another person: (a) criminal sexual conduct pursuant to Section 16-3-651; (b) criminal sexual conduct in the first degree pursuant to Section 16-3-652; (c) criminal sexual conduct in the second degree pursuant to Section 16-3-653; (d) criminal sexual conduct in the third degree pursuant to Section 16-3-654; (e) criminal sexual conduct with a minor pursuant to Section 16-3-655; (f) engaging a child for sexual performance pursuant to Section 16-3-810; (g) performance pursuant to Section 16-3-800; (h) producing, directing or promoting sexual performance by a child pursuant to Section 16-3-820; (i) sexual battery pursuant to Section 16-3-661; (j) sexual conduct pursuant to Section 16-3-800; or (k) sexual performance pursuant to Section 16-3-800. (8) 'Services' means an act committed at the behest of, under the supervision of, or for the benefit of another person. (9) 'Trafficking in persons' means when a victim is subjected to or a person attempts to subject a victim to sex trafficking; forced labor or services; involuntary servitude; or debt bondage by employing one of the following: (a) physically restraining or threatening to physically restrain another person; (b) knowingly destroying, concealing, removing, confiscating, or possessing an actual or purported passport or other immigration document, or another actual or purported government identification document, of the victim; (c) extortion or blackmail; (d) causing or threatening to cause financial harm to the victim; (e) facilitating or controlling a victim's access to a controlled substance; or (f) coercion. (10) 'Victim of trafficking in persons' or 'victim' means a person who has been subjected to the crime of trafficking in persons. Section 16-3-2020. (A) A person who recruits, entices, solicits, isolates, harbors, transports, provides, or obtains, or so attempts, a victim, knowing that the victim will be subjected to sex trafficking, forced labor or services, involuntary servitude or debt bondage through any means or who benefits, financially or by receiving anything of value, from participation in a venture which has engaged in an act described in this subsection, is guilty of trafficking in persons. (B) A person who recruits, entices, solicits, isolates, harbors, transports, provides, or obtains, or so attempts, a victim, for the purposes of sex trafficking, forced labor or services, involuntary servitude or debt bondage through any means or who benefits, financially or by receiving anything of value, from participation in a venture which has engaged in an act described in subsection (A), is guilty of trafficking in persons. (C) For a first offense, the person is guilty of a felony and, upon conviction, must be imprisoned not more than fifteen years. (D) For a second offense, the person is guilty of a felony and, upon conviction, must be imprisoned not more than thirty years. (E) For a third or subsequent offense, the person is guilty of a felony and upon conviction, must be imprisoned not more than forty-five years. (F) If the victim of an offense contained in this section is under the age of eighteen, an additional term of fifteen years may be imposed in addition and must be consecutive to the penalty prescribed for a violation of this section. (G) A person who aids, abets, or conspires with another person to violate the criminal provisions of this section must be punished in the same manner as provided for the principal offender and is considered a trafficker. (H) A business owner who uses his business in a way that participates in a violation of this article, upon conviction, must be imprisoned for not more than ten years in addition to the penalties provided in this section for each violation. (I) A plea of guilty or the legal equivalent entered pursuant to a provision of this article by an offender entitles the victim of trafficking in persons to all benefits, rights, and compensation granted pursuant to Section 16-3-1110. (J) In a prosecution of a person who is a victim of trafficking in persons, it is an affirmative defense that he was under duress or coerced into committing the offenses for which he is subject to prosecution, if the offenses were committed as a direct result of, or incidental or related to, trafficking. (K) Evidence of the following facts or conditions do not constitute a defense in a prosecution for a violation of this article, nor does the evidence preclude a finding of a violation: (1) the victim's sexual history or history of commercial sexual activity, the specific instances of the victim's sexual conduct, opinion evidence of the victim's sexual conduct, and reputation evidence of the victim's sexual conduct; (2) the victim's connection by blood or marriage to a defendant in the case or to anyone involved in the victim's trafficking; (3) the implied or express consent of a victim to acts which violate the provisions of this section do not constitute a defense to violations of this section; (4) age of consent to sex, legal age of marriage, or other discretionary age; and (5) mistake as to the victim's age, even if the mistake is reasonable. (L) A person who violates the provisions of this section may be prosecuted by the State Grand Jury pursuant to Section 14-7-1600 when a victim is trafficked in more than one county or a trafficker commits the offense of trafficking in persons in more than one county. Section 16-3-2030. (A) The principal owners of a business, a business entity, including a corporation, partnership, charitable organization, or another legal entity, that knowingly aids or participates in an offense provided in this article is criminally liable for the offense and will be subject to a fine or loss of business license in the State, or both. (B) If the principal owners of a business entity are convicted of violating a section of this article, the court or Secretary of State, when appropriate, may: (1) order its dissolution or reorganization; (2) order the suspension or revocation of any license, permit, or prior approval granted to it by a state or local government agency; or (3) order the surrender of its charter if it is organized under state law or the revocation of its certificate to conduct business in the State if it is not organized under state law. Section 16-3-2040. (A) An offender convicted of a violation of this article must be ordered to pay mandatory restitution to the victim as provided in this section. (B) If the victim of trafficking dies as a result of being trafficked, a surviving spouse of the victim is eligible for restitution. If no surviving spouse exists, restitution must be paid to the victim's issue or their descendants per stirpes. If no surviving spouse or issue or descendants exist, restitution must be paid to the victim's estate. A person named in this subsection may not receive funds from restitution if he benefited or engaged in conduct described in this article. (C) If a person is unable to pay restitution at the time of sentencing, or at any other time, the court may set restitution pursuant to Section 16-3-1270. (D) Restitution for this section, pursuant to Section 16-3-1270, means payment for all injuries, specific losses, and expenses sustained by a crime victim resulting from an offender's criminal conduct pursuant to Section 16-3-1110 (12)(a). (E) Notwithstanding another provision of law, the applicable statute of limitations for a victim of trafficking in persons is pursuant to Section 16-3-1110 (12)(a). (F) Restitution must be paid to the victim promptly upon the conviction of the defendant. The return of the victim to his home country or other absence of the victim from the jurisdiction does not prevent the victim from receiving restitution. Section 16-3-2050. (A) The Attorney General shall establish an interagency task force to develop and implement a State Plan for the Prevention of Trafficking in Persons. The task force shall meet at least quarterly and should include all aspects of trafficking in persons, including sex trafficking and labor trafficking of both United States citizens and foreign nationals, as defined in Section 16-3-2010. The Attorney General also shall collect and publish relevant data to this section on their website. (B) The task force shall consist of, at a minimum, representatives from: (1) the Office of the Attorney General, who must be chair; (2) the South Carolina Labor, Licensing and Regulation; (3) the South Carolina Police Chiefs Association; (4) the South Carolina Sheriffs' Association; (5) the State Law Enforcement Division; (6) the Department of Health and Environmental Control Board; (7) the United States Department of Labor; (8) the State Office of Victim Assistance; (9) the South Carolina Commission on Prosecution Coordination; (10) the Department of Social Services; (11) a representative from the Governor's office; (12) a representative from the Employment Security Commission; and (13) two persons appointed by the Attorney General from nongovernmental organizations, especially those specializing in trafficking in persons, those representing diverse communities disproportionately affected by trafficking, agencies devoted to child services and runaway services, and academic researchers dedicated to the subject of trafficking in persons. (C) The Attorney General shall invite representatives of the United States Attorneys' offices and of federal law enforcement agencies' offices within the State, including the Federal Bureau of Investigations and the United States Immigration and Customs Enforcement office, to be members of the task force. (D) The task force shall carry out the following activities either directly or through one or more of its constituent agencies: (1) develop the state plan within eighteen months of the effective date of this act; (2) coordinate the implementation of the state plan; and (3) starting one year after the formation after the task force, submit an annual report of its findings and recommendations to the Governor, the Speaker of the House of Representatives, and the President of the Senate on or before December thirty-first of each calendar year. (E) The task force shall consider carrying out the following activities either directly or through one or more of its constituent agencies: (1) coordinate the collection and sharing of trafficking data among government agencies, which data collection must respect the privacy of victims of trafficking in persons; (2) coordinate the sharing of information between agencies for the purposes of detecting criminal groups engaged in trafficking in persons; (3) explore the establishment of state policies for time limits for the issuance of Law Enforcement Agency (LEA) endorsements as described in C.F.R. Chapter 8, Section 214.11(f)(1); (4) establish policies to enable state government to work with nongovernmental organizations and other elements of civil society to prevent trafficking in persons and provide assistance to United States citizens and foreign national victims; (5) review the existing services and facilities to meet trafficking victims' needs and recommend a system to coordinate services including, but not limited to, health services, including mental health, housing, education and job training, English as a second language classes, interpreting services, legal and immigration services, and victim compensation; (6) evaluate various approaches used by state and local governments to increase public awareness of the trafficking in persons, including United States citizens and foreign national victims of trafficking in persons; (7) mandatory training for law enforcement agencies, prosecutors, and other relevant officials in addressing trafficking in persons; (8) collect and periodically publish statistical data on trafficking, that must be posted on the Attorney General's website; (9) prepare public awareness programs designed to educate potential victims of trafficking in persons and their families on the risks of victimization. These public awareness programs must include, but are not limited to: (a) information about the risks of becoming a victim, including information about common recruitment techniques, use of debt bondage, and other coercive tactics, risk of maltreatment, rape, exposure to HIV or AIDS and other sexually transmitted diseases, and psychological harm related to victimization in trafficking cases; (b) information about the risks of engaging in commercial sex and possible punishment; (c) information about victims' rights in the State; (d) methods for reporting suspected recruitment activities; and (e) information on hotlines and available victims' services; (10) preparation and dissemination of awareness materials to the general public to educate the public on the extent of trafficking in persons, both United States citizens and foreign nationals, within the United States and to discourage the demand that fosters the exploitation of persons that leads to trafficking in persons. (a) The general public awareness materials may include information on the impact of trafficking on individual victims, whether United States citizens or foreign nationals, aggregate information on trafficking in persons worldwide and domestically, and warnings of the criminal consequences of engaging in trafficking in persons. These materials may include pamphlets, brochures, posters, advertisements in mass media, and other appropriate media. All materials must be designed to communicate to the target population. (b) Materials described in this section may include information on the impact of trafficking in persons on individual victims. However, information on the experiences of individual victims must preserve the privacy of the victim and the victim's family. (c) All public awareness programs must be evaluated periodically by the task force to ensure their effectiveness. Section 16-3-2060. (A) A person who is a victim of trafficking in persons may bring a civil action in the court of common pleas. The court may award actual damages, compensatory damages, punitive damages, injunctive relief, and other appropriate relief. A prevailing plaintiff also must be awarded attorney's fees and costs. Treble damages must be awarded on proof of actual damages when the defendant's acts were wilful and malicious. (B) Pursuant to Section 16-3-1110, the applicable statute of limitations for a crime victim who has a cause of action against an incarcerated offender is tolled and does not expire until three years after the offender's sentence is completed, including probation and parole, or three years after release from commitment pursuant to Chapter 48, Title 44, whichever is later. However, this provision does not shorten any other tolling period of the statute of limitations which may exist for the victim. (C) The statute of limitations for the filing of a civil suit does not begin to run until a minor victim has reached the age of majority. (D) If a victim entitled to sue is under a disability at the time the cause of action accrues, so that it is impossible or impractical for him to bring an action, then the time of the disability is not part of the time limited for the commencement of the action. Disability includes, but is not limited to, insanity, imprisonment, or other incapacity or incompetence. (E) The running of the statute of limitations may be suspended when a victim could not have reasonably discovered the cause of action due to circumstances resulting from the trafficking situation, such as psychological trauma, cultural and linguistic isolation, and the inability to access services. (F) A defendant is estopped to assert a defense of the statute of limitations when the expiration of the statute is due to conduct by the defendant inducing the victim to delay the filing of the action or placing the victim under duress. Section 16-3-2070. (A) Victims of trafficking in persons pursuant to this article are considered victims for purposes of the Victims' Bill of Rights and are entitled to all appropriate forms of compensation available pursuant to the State Crime Victim's Compensation Fund in accordance with the provisions of Article 13, Chapter 3, Title 16. Victims of trafficking in persons pursuant to this article also are entitled to the rights provided in Article 15, Chapter 3, Title 16. (B) In addition to the provisions of subsection (A), in a prosecution for violations of the criminal provisions of this article, the identity of the victim and the victim's family must be kept confidential by ensuring that names and identifying information of the victim and victim's family are not released to the public, including by the defendant. (C) Pursuant to Section 16-3-1240, it is unlawful, except for purposes directly connected with the administration of the victim's compensation fund, for any person to solicit, disclose, receive, or make use of or authorize, knowingly permit, participate in or acquiesce in the use of any list, or names of, or information concerning persons applying for or receiving awards without the written consent of the applicant or recipient. The records, papers, files, and communications of the board, its panel and the director and his staff must be regarded as confidential information and privileged and not subject to disclosure under the Freedom of Information Act as contained in Chapter 3, Title 30. Section 16-3-2080. (A) For purposes of this section: (1) 'Domestic violence shelter' means a facility whose purpose is to serve as a shelter to receive and house persons who are victims of criminal domestic violence and that provides services as a shelter. (2) 'Trafficking shelter' means a confidential location which provides emergency housing for victims of trafficking in persons. (3) 'Grounds' means the real property of the parcel of land upon which a domestic violence or trafficking shelter or a domestic violence or trafficking shelter's administrative offices are located, whether fenced or unfenced. (B) A person who maliciously or with criminal negligence publishes, disseminates, or otherwise discloses the location of a trafficking victim, a trafficking shelter, a domestic violence shelter, or another place designated as a trafficking shelter or domestic violence shelter, without the authorization of that trafficking victim, trafficking shelter, or domestic violence shelter, is guilty of a misdemeanor and, upon conviction, must be imprisoned not more than three years. (C) It is unlawful for a person who has been charged with or convicted of a violation of Section 16-3-2020 to enter or remain upon the grounds or structure of a domestic violence or trafficking shelter in which the victim resides or the domestic violence shelter's administrative offices or the trafficking shelter's administrative offices. (D) The domestic violence shelter and trafficking shelter must post signs at conspicuous places on the grounds of the domestic violence shelter, trafficking shelter, the domestic violence shelter's administrative offices, and the trafficking shelter's administrative offices which, at a minimum, must read substantially as follows: 'NO TRESPASSING - VIOLATORS WILL BE SUBJECT TO CRIMINAL PENALTIES'. (E) This section does not apply if the person has legitimate business or any authorization, license, or invitation to enter or remain upon the grounds or structure of the domestic violence or trafficking shelter or the domestic violence or trafficking shelter's administrative offices. (F) A person who violates this section is guilty of a misdemeanor and, upon conviction, must be fined not more than three thousand dollars or imprisoned for not more than three years, or both. If the person is in possession of a dangerous weapon at the time of the violation, the person is guilty of a felony and, upon conviction, must be fined not more than five thousand dollars or imprisoned for not more than five years, or both. Section 16-3-2090. (A)(1) The following are subject to forfeiture: (a) all monies used, or intended for use, in violation of Section 16-3-2020; (b) all property constituting the proceeds obtained directly or indirectly, for a violation of Section 16-3-2020; (c) all property derived from the proceeds obtained, directly or indirectly, from any sale or exchange for pecuniary gain from a violation of Section 16-3-2020; (d) all property used or intended for use, in any manner or part, to commit or facilitate the commission of a violation for pecuniary gain of Section 16-3-2020; (e) all books, records, and research products and materials, including formulas, microfilm, tapes, and data which are used, or which have been positioned for use, in violation of Section 16-3-2020; (f) all conveyances including, but not limited to, trailers, aircraft, motor vehicles, and watergoing vessels, which are used or intended for use unlawfully to conceal or transport or facilitate a violation of Section 16-3-2020. No motor vehicle may be forfeited to the State under this item unless it is used, intended for use, or in any manner facilitates a violation of Section 16-3-2020; (g) all property including, but not limited to, monies, negotiable instruments, securities, or other things of value furnished or intended to be furnished by any person in exchange for any kind of services under Section 16-3-2020, and all proceeds including, but not limited to, monies, and real and personal property traceable to any exchange under Section 16-3-2020; and (h) overseas assets of persons convicted of trafficking in persons also are subject to forfeiture to the extent they can be retrieved by the government. (2) Any property subject to forfeiture may be seized by the investigating agency having authority upon warrant issued by any court having jurisdiction over the property. Seizure without process may be made if the: (a) seizure is incident to an arrest or a search under a search warrant or an inspection under an administrative inspection warrant; (b) property subject to seizure has been the subject of a prior judgment in favor of the State in a criminal injunction or forfeiture proceeding based upon under Section 16-3-2020; (c) the investigating agency has probable cause to believe that the property is directly or indirectly dangerous to health or safety; or (d) the investigating agency has probable cause to believe that the property was used or is intended to be used in violation of Section 16-3-2020. (3) In the event of seizure, proceedings under this section regarding forfeiture and disposition must be instituted within a reasonable time. (4) Any property taken or detained under this section is not subject to replevin but is considered to be in the custody of the investigating agency making the seizure subject only to the orders of the court having jurisdiction over the forfeiture proceedings. Property is forfeited and transferred to the government at the moment of illegal use. Seizure and forfeiture proceedings confirm the transfer. (5) For the purposes of this section, whenever the seizure of property subject to seizure is accomplished as a result of a joint effort by more than one law enforcement agency, the law enforcement agency initiating the investigation is considered to be the agency making the seizure. (6) Law enforcement agencies seizing property pursuant to this section shall take reasonable steps to maintain the property. Equipment and conveyances seized must be removed to an appropriate place for storage. Monies seized must be deposited in an interest bearing account pending final disposition by the court unless the seizing agency determines the monies to be of an evidential nature and provides for security in another manner. (7) When property and monies of any value as defined in this article or anything else of any value is seized, the law enforcement agency making the seizure, within ten days or a reasonable period of time after the seizure, shall submit a report to the appropriate prosecution agency. (a) The report must provide the following information with respect to the property seized: (i) description; (ii) circumstances of seizure; (iii) present custodian and where the property is being stored or its location; (iv) name of owner; (v) name of lienholder; and (vi) seizing agency. (b) If the property is a conveyance, the report shall include the: (i) make, model, serial number, and year of the conveyance; (ii) person in whose name the conveyance is registered; and (iii) name of any lienholders. (c) In addition to the report, the law enforcement agency shall prepare for dissemination to the public upon request a report providing the following information: (i) a description of the quantity and nature of the property and money seized; (ii) the seizing agency; (iii) the make, model, and year of a conveyance; and (iv) the law enforcement agency responsible for the property or conveyance seized. (d) Property or conveyances seized by a law enforcement agency or department may not be used by officers for personal purposes. (B)(1) Forfeiture of property must be accomplished by petition of the Attorney General or his designee or the circuit solicitor or his designee to the court of common pleas for the jurisdiction where the items were seized. The petition must be submitted to the court within a reasonable time period following seizure and shall provide the facts upon which the seizure was made. The petition shall describe the property and include the names of all owners of record and lienholders of record. The petition shall identify any other persons known to the petitioner to have interests in the property. Petitions for the forfeiture of conveyances also shall include the make, model, and year of the conveyance, the person in whose name the conveyance is registered, and the person who holds the title to the conveyance. A copy of the petition must be sent to each law enforcement agency which has notified the petitioner of its involvement in effecting the seizure. Notice of hearing or rule to show cause must be directed to all persons with interests in the property listed in the petition, including law enforcement agencies which have notified the petitioner of their involvement in effecting the seizure. Owners of record and lienholders of record may be served by certified mail, to the last known address as appears in the records of the governmental agency which records the title or lien. (2) The judge shall determine whether the property is subject to forfeiture and order the forfeiture confirmed. The Attorney General or his designee or the circuit solicitor or his designee has the burden of proof to establish by a preponderance of the evidence that the property is subject to forfeiture. If the judge finds a forfeiture, he shall then determine the lienholder's interest as provided in this article. The judge shall determine whether any property must be returned to a law enforcement agency pursuant to this section. (3) If there is a dispute as to the division of the proceeds of forfeited property among participating law enforcement agencies, this issue must be determined by the judge. The proceeds from a sale of property, conveyances, and equipment must be disposed of pursuant to this section. (4) All property, conveyances, and equipment which will not be reduced to proceeds may be transferred to the law enforcement agency or agencies or to the prosecution agency. Upon agreement of the law enforcement agency or agencies and the prosecution agency, conveyances and equipment may be transferred to any other appropriate agency. Property transferred may not be used to supplant operating funds within the current or future budgets. If the property seized and forfeited is an aircraft or watercraft and is transferred to a state law enforcement agency or other state agency pursuant to the provisions of this subsection, its use and retainage by that agency is at the discretion and approval of the State Budget and Control Board. (5) If a defendant or his attorney sends written notice to the petitioner or the seizing agency of his interest in the subject property, service may be made by mailing a copy of the petition to the address provided, and service may not be made by publication. In addition, service by publication may not be used for a person incarcerated in a Department of Corrections facility, a county detention facility, or other facility where inmates are housed for the county where the seizing agency is located. The seizing agency shall check the appropriate institutions after receiving an affidavit of nonservice before attempting service by publication. (6) Any forfeiture may be effected by consent order approved by the court without filing or serving pleadings or notices provided that all owners and other persons with interests in the property, including participating law enforcement agencies, entitled to notice under this section, except lienholders and agencies, consent to the forfeiture. Disposition of the property may be accomplished by consent of the petitioner and those agencies involved. Persons entitled to notice under this section may consent to some issues and have the judge determine the remaining issues. (7) Disposition of forfeited property under this section must be accomplished as follows: (a) Property forfeited under this subsection shall first be applied to payment to the victim. The return of the victim to his home country or other absence of the victim from the jurisdiction shall not prevent the victim from receiving compensation. (b) The victim and the South Carolina Victims' Compensation Fund shall each receive one-fourth, and law enforcement shall receive one-half of the value of the forfeited property. (c) If no victim is named, or reasonable attempts to locate a named victim for forfeiture and forfeiture fails, then all funds shall revert to the South Carolina Victims' Compensation Fund and law enforcement to be divided equally. (d) If federal law enforcement becomes involved in the investigation, they shall equitably split the share local law enforcement receives under this section, if they request or pursue any of the forfeiture. The equitable split must be pursuant to 21 U.S.C. Section 881(e)(1)(A) and (e)(3), 18 U.S.C. Section 981(e)(2), and 19 U.S.C. Section 1616a. (C)(1) An innocent owner, manager, or owner of a licensed rental agency or any common carrier or carrier of goods for hire may apply to the court of common pleas for the return of any item seized. Notice of hearing or rule to show cause accompanied by copy of the application must be directed to all persons and agencies entitled to notice. If the judge denies the application, the hearing may proceed as a forfeiture hearing. (2) The court may return any seized item to the owner if the owner demonstrates to the court by a preponderance of the evidence: (a) in the case of an innocent owner, that the person or entity was not a consenting party to, or privy to, or did not have knowledge of, the use of the property which made it subject to seizure and forfeiture; or (b) in the case of a manager or an owner of a licensed rental agency, a common carrier, or a carrier of goods for hire, that any agent, servant, or employee of the rental agency or of the common carrier or carrier of goods for hire was not a party to, or privy to, or did not have knowledge of, the use of the property which made it subject to seizure and forfeiture. If the licensed rental agency demonstrates to the court that it has rented the seized property in the ordinary course of its business and that the tenant or tenants were not related within the third degree of kinship to the manager or owner, or any agents, servants, or employees of the rental agency, then it is presumed that the licensed rental agency was not a party to, or privy to, or did not have knowledge of, the use of the property which made it subject to seizure and forfeiture. (3) The lien of an innocent person or other legal entity, recorded in public records, shall continue in force upon transfer of title of any forfeited item, and any transfer of title is subject to the lien, if the lienholder demonstrates to the court by a preponderance of the evidence that he was not a consenting party to, or privy to, or did not have knowledge of, the involvement of the property which made it subject to seizure and forfeiture. (D) A person who uses property or a conveyance in a manner which would make the property or conveyance subject to forfeiture except for innocent owners, rental agencies, lienholders, and the like as provided for in this section, is guilty of a misdemeanor and, upon conviction, must be imprisoned for not less than thirty days nor more than one year, fined not more than five thousand dollars, or both. The penalties prescribed in this section are cumulative and must be construed to be in addition to any other penalty prescribed by another provision of this article." SECTION 2. Section 16-3-930 of the 1976 Code is repealed. SECTION 3. The repeal or amendment by this act of any law, whether temporary or permanent or civil or criminal, does not affect pending actions, rights, duties, or liabilities founded thereon, or alter, discharge, release or extinguish any penalty, forfeiture, or liability incurred under the repealed or amended law, unless the repealed or amended provision shall so expressly provide. After the effective date of this act, all laws repealed or amended by this act must be taken and treated as remaining in full force and effect for the purpose of sustaining any pending or vested right, civil action, special proceeding, criminal prosecution, or appeal existing as of the effective date of this act, and for the enforcement of rights, duties, penalties, forfeitures, and liabilities as they stood under the repealed or amended laws. SECTION 4. If any section, subsection, paragraph, subparagraph, sentence, clause, phrase, or word of this act is for any reason held to be unconstitutional or invalid, such holding shall not affect the constitutionality or validity of the remaining portions of this act, the General Assembly hereby declaring that it would have passed this act, and each and every section, subsection, paragraph, subparagraph, sentence, clause, phrase, and word thereof, irrespective of the fact that any one or more other sections, subsections, paragraphs, subparagraphs, sentences, clauses, phrases, or words hereof may be declared to be unconstitutional, invalid, or otherwise ineffective. SECTION 5. This act takes effect one hundred eighty days after approval by the Governor. / Amend title to conform. /s/Sen. C. Bradley Hutto /s/Rep. Bruce W. Bannister /s/Sen. George E. Campsen III /s/Rep. J. Todd Rutherford /s/Sen. Phillip W. Shoopman /s/Rep. F.G. Delleney, Jr. On Part of the Senate. On Part of the House. , and a message was sent to the House accordingly. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that the Report of the Committee of Conference having been adopted by both Houses, and this Bill having been read three times in each House, it was ordered that the title thereof be changed to that of an Act and that it be enrolled for Ratification: H. 3757 (Word version) -- Reps. Hardwick, Hearn, Mitchell, Long, Erickson, Brady, Butler Garrick, Funderburk, Munnerlyn, Knight, Dillard, Cobb-Hunter, Parks, Huggins, Allison, Tallon, Brannon, Atwater, Whipper, Patrick and J.R. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 19 TO CHAPTER 3, TITLE 16 SO AS TO DEFINE NECESSARY TERMS, PROVIDE FOR CERTAIN HUMAN TRAFFICKING OFFENSES AND PROVIDE PENALTIES, TO PROVIDE FOR CRIMINAL LIABILITY OF BUSINESS ENTITIES, TO PROVIDE RESTITUTION FOR VICTIMS OF HUMAN TRAFFICKING OFFENSES, TO ESTABLISH AN INTERAGENCY TASK FORCE TO DEVELOP AND IMPLEMENT A PLAN FOR THE PREVENTION OF TRAFFICKING IN PERSONS, TO REQUIRE THE COLLECTION AND DISSEMINATION OF DATA RELATED TO HUMAN TRAFFICKING BY THE STATE LAW ENFORCEMENT DIVISION (SLED), TO REQUIRE MANDATORY LAW ENFORCEMENT TRAINING ON HUMAN TRAFFICKING OFFENSES, TO PROVIDE FOR THE CREATION OF PUBLIC AWARENESS PROGRAMS REGARDING HUMAN TRAFFICKING IN THE STATE, TO ALLOW CIVIL ACTIONS BY VICTIMS OF HUMAN TRAFFICKING, TO PROVIDE THAT CERTAIN STANDARDS OF WORKING CONDITIONS APPLY WITHOUT REGARD TO IMMIGRATION STATUS, TO PROVIDE CERTAIN PROTECTIONS FOR VICTIMS OF HUMAN TRAFFICKING PURSUANT TO THE VICTIMS' BILL OF RIGHTS AND OTHER RELEVANT STATUTORY PROVISIONS, TO REQUIRE THE STATE TO DEVELOP PLANS FOR HOUSING AND COUNSELING, AMONG OTHER THINGS, OF VICTIMS OF HUMAN TRAFFICKING WITHIN ONE HUNDRED EIGHTY DAYS OF THE EFFECTIVE DATE OF THE ACT, TO PROVIDE FOR CERTAIN RIGHTS OF MINOR VICTIMS OF HUMAN TRAFFICKING, TO ESTABLISH HUMAN TRAFFICKING VICTIM-CASEWORKER PRIVILEGE, AND TO CREATE THE OFFENSE OF MALICIOUSLY OR WITH CRIMINAL NEGLIGENCE PUBLISHING, DISSEMINATING, OR OTHERWISE DISCLOSING THE LOCATION OF A HUMAN TRAFFICKING VICTIM, A TRAFFICKING SHELTER, OR A DOMESTIC VIOLENCE SHELTER AND TO PROVIDE A PENALTY; AND TO REPEAL SECTION 16-3-930 RELATING TO TRAFFICKING IN PERSONS FOR FORCED LABOR OR SERVICES. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has adopted the Report of the Committee of Conference on: H. 4763 (Word version) -- Reps. Sandifer, King, Butler Garrick and Parks: A BILL TO AMEND SECTION 32-7-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PRENEED FUNERAL CONTRACT LICENSES, SO AS TO FURTHER PROVIDE FOR THE TERM OF THE LICENSE AND FOR THE USE OF LICENSE RENEWAL FEES; AND TO AMEND SECTION 32-7-100, AS AMENDED, RELATING TO UNLAWFUL VIOLATIONS OF LAW PERTAINING TO PRENEED FUNERAL CONTRACTS, SO AS TO FURTHER PROVIDE FOR THE PENALTIES FOR VIOLATIONS BASED ON THE AMOUNT OF MONEY OBTAINED OR SOUGHT TO BE OBTAINED WITH CERTAIN OFFENSES DECLARED TO BE MISDEMEANORS AND CERTAIN OFFENSES DECLARED TO BE FELONIES. Very respectfully, Speaker of the House H. 4763--REPORT OF THE H. 4763 (Word version) -- Reps. Sandifer, King, Butler Garrick and Parks: A BILL TO AMEND SECTION 32-7-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PRENEED FUNERAL CONTRACT LICENSES, SO AS TO FURTHER PROVIDE FOR THE TERM OF THE LICENSE AND FOR THE USE OF LICENSE RENEWAL FEES; AND TO AMEND SECTION 32-7-100, AS AMENDED, RELATING TO UNLAWFUL VIOLATIONS OF LAW PERTAINING TO PRENEED FUNERAL CONTRACTS, SO AS TO FURTHER PROVIDE FOR THE PENALTIES FOR VIOLATIONS BASED ON THE AMOUNT OF MONEY OBTAINED OR SOUGHT TO BE OBTAINED WITH CERTAIN OFFENSES DECLARED TO BE MISDEMEANORS AND CERTAIN OFFENSES DECLARED TO BE FELONIES. On motion of Senator CAMPBELL, with unanimous consent, the Report of the Committee of Conference was taken up for immediate consideration. Senator CAMPBELL spoke on the report. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 38; Nays 4 AYES Alexander Anderson Campbell Campsen Cleary Coleman Courson Cromer Elliott Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--38 NAYS Bright Bryant Davis Fair Total--4 On motion of Senator CAMPBELL, the Report of the Committee of Conference to H. 4763 was adopted as follows: H. 4763--Conference Report The General Assembly, Columbia, S.C., June 5, 2012 The Committee on Conference, to whom was referred: H. 4763 (Word version) -- A BILL TO AMEND SECTION 32-7-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PRENEED FUNERAL CONTRACT LICENSES, SO AS TO FURTHER PROVIDE FOR THE TERM OF THE LICENSE AND FOR THE USE OF LICENSE RENEWAL FEES; AND TO AMEND SECTION 32-7-100, AS AMENDED, RELATING TO UNLAWFUL VIOLATIONS OF LAW PERTAINING TO PRENEED FUNERAL CONTRACTS, SO AS TO FURTHER PROVIDE FOR THE PENALTIES FOR VIOLATIONS BASED ON THE AMOUNT OF MONEY OBTAINED OR SOUGHT TO BE OBTAINED WITH CERTAIN OFFENSES DECLARED TO BE MISDEMEANORS AND CERTAIN OFFENSES DECLARED TO BE FELONIES. Beg leave to report that they have duly and carefully considered the same and recommend: That the same do pass with the following amendments: Amend the bill, as and if amended, by striking all after the enacting words and inserting: / SECTION 1. Section 32-7-10 of the 1976 Code is amended to read: "Section 32-7-10. As used in this chapter, unless the context requires otherwise: (1) 'Administrator' means the Administrator of the South Carolina Department of Consumer Affairs. (2) 'At need' means after the beneficiary is deceased, and 'at preneed' means before the beneficiary is deceased. (2)(3) 'Beneficiary' means the person who is to be the subject of the disposition, services, facilities, or merchandise described in a preneed funeral contract. (3)(4) 'Common trust fund' means a trust in which the proceeds of more than one funeral contract may be held by the trustee. (4)(5) 'Department' means the South Carolina Department of Consumer Affairs. (5)(6) 'Financial institution' means a bank, trust company, or savings and loan association authorized by law to do business in this State. (7) 'Funeral services' or 'funeral arrangements' means any of the following: (a) engaging in providing shelter, care, and custody of the human dead; (b) preparing the human dead by embalming or other methods for burial or other disposition; or (c) engaging in the practice or performing any functions of funeral directing or embalming as presently recognized by persons engaged in these functions. (6)(8) 'Preneed funeral contract' means a contract which has for its purpose the furnishing or performance of funeral services or the furnishing or delivery of personal property, merchandise, or services of any nature in connection with the final disposition of a dead human body to be furnished or delivered at a time determinable by the death of the person whose body is to be disposed of, but does not mean the furnishing of a cemetery lot, crypt, niche, mausoleum, grave marker, or monument. (7)(9) 'Provider' means a funeral home licensed in this State which is the entity providing services and merchandise pursuant to a preneed funeral contract and is designated trustee of all funds. (8)(10) 'Purchaser' means the person who is obligated to make payments under a preneed funeral contract. (9)(11) 'Seller' means a licensed funeral director in this State who is directly employed by the provider. (12) 'Trust account' means a federally insured account where the funds shall be paid to a provider only when the provider furnishes the financial institution with a certified certificate of death and a certified statement that the services have been performed and the merchandise has been delivered." SECTION 2. Section 32-7-35 of the 1976 Code is amended to read: "Section 32-7-35. (A) A preneed funeral contract may be transferred to another provider only upon the prior written request of the purchaser or the beneficiary of a deceased purchaser or pursuant to Section 32-7-45. The selling provider must be paid a fee equal to ten percent of the contract face amount. The selling provider also must be paid ten percent of the earnings in that portion of the final year before transfer. (B) A preneed funeral contract, whether revocable or irrevocable, funded by an insurance policy may be transferred to another provider only upon the prior written request of the purchaser or the beneficiary of a deceased purchaser or pursuant to Section 32-7-45. The selling provider may not collect, charge, or receive a fee in connection with this transfer of a preneed funeral contract funded by an insurance policy. An irrevocable preneed funeral contract funded by an insurance policy may be transferred to another provider only upon the prior written request of the purchaser or the beneficiary of a deceased purchaser or pursuant to Section 32-7-45. (C)(1) At preneed, a preneed funeral contract may be transferred only to a funeral home that is licensed to sell preneed funeral contracts. The receiving funeral home is not required to pay an additional service charge unless there are changes to the contract. (2) At need, a preneed funeral contract may be transferred to any funeral home that is licensed by the Board of Funeral Directors." SECTION 3. Section 32-7-50 of the 1976 Code is amended to read: "Section 32-7-50. (A) Without first securing a license from the department, no one, except a financial institution, may accept or hold payments made on a preneed funeral contract. (1) The State Board of Funeral Service must revoke the license of a funeral home or funeral director, or both, if the funeral home or funeral director: (a) accepts funds for a preneed funeral contract or other prepayment of funeral expenses without a license to sell preneed funeral contracts, or (b) is licensed to sell preneed funeral contracts and fails to deposit the funds collected in trust in a federally insured account as required by Section 32-7-20(H). (2) Application for a license must be in writing, signed by the applicant, and verified on forms furnished by the department. Each An application must contain at least the following: the full name and address, both residence and place of business, of the applicant and every member, officer, and director of it if the applicant is a firm, partnership, association, or corporation. A license issued pursuant to the application is valid only at the address stated in the application for the applicant or at a new address approved by the department. (3) If a licensee cancels the license and later applies for a new license, the department shall investigate the applicant's books, records, and accounts to determine if the applicant violated the provisions of this chapter during the time he did not have a license. (B) Upon receipt of the application, a one-time payment of a two hundred fifty dollar license fee, and the deposit in an amount to be determined by the department of the security or proof of financial responsibility as the department may determine, the department shall issue a license unless it determines that the applicant has made false statements or representations in the application, is insolvent, has conducted his business in a fraudulent manner, is not authorized to transact business in this State, or if, in the judgment of the department, the applicant should be denied a license for some other good and sufficient reason. (C) A person selling a preneed funeral contract shall collect from each purchaser a service charge and all fees collected must be remitted by the person collecting them to the department at least once each month. (1) With the fees collected, the person also must provide the department with a listing of each contract sold. If the listing or fees collected are not sent to the department within sixty days of the last day of the month when the contract was sold, the department shall assess a civil penalty of ten dollars for each contract not reported to the department. The monies collected as civil penalties must be deposited in the Preneed Funeral Loss Reimbursement Fund. Upon its own initiative or upon complaint or information received, the department shall investigate a person's books, records, and accounts if the department has reason to believe that fees are collected and either not remitted or not timely remitted. (2) The service charge for each contract may not exceed a total of thirty dollars, twenty-five dollars for the department to use in administering the provisions of this chapter and five dollars to be allocated to the Preneed Funeral Loss Reimbursement Fund. (3) The department shall keep a record of each preneed funeral contract for which it receives a service charge. (D) A license issued pursuant to this section expires on September thirtieth of each odd-numbered year unless otherwise revoked or canceled. A license must be renewed by filing a renewal application at least thirty days prior to expiration on forms prescribed by the department. A renewal application must be accompanied by a fee of two hundred dollars for the department to use in administering this chapter. The department shall deposit one hundred dollars of each renewal fee received into the Preneed Funeral Loss Reimbursement Fund. The department shall consider the factors in subsection (B) before issuing a license." SECTION 4. Section 32-7-60(B) of the 1976 Code, as last amended by Act 70 of 2009, is further amended to read: "(B) From the service charge for each preneed contract as required by Section 32-7-50(C), the department shall deposit into the fund that portion of the charge as established by the department. The department may suspend or resume deposits into the fund at any time and for any period to ensure that a sufficient amount is available to meet likely disbursements and to maintain an adequate reserve. The maximum amount of the service charge to be allocated to the Preneed Funeral Loss Reimbursement Fund as required by Section 32-7-50(C)(2) may not exceed the amount of five dollars for each preneed contract. The maximum amount of the fund is five hundred thousand dollars with a five percent adjustment compounded annually." SECTION 5. Section 32-7-100 of the 1976 Code is amended to read: "Section 32-7-100. (A) A person wilfully violating the provisions of this chapter is guilty of a: (1) misdemeanor, if the value of money obtained or sought to be obtained is two thousand dollars or less and, upon conviction, the person must be fined not less than one thousand dollars or more than five thousand dollars, or imprisoned for not less than ten days or more than six months more than thirty days, or both.; In addition, this person may be prohibited from entering into further preneed funeral contracts if the department, in its discretion, finds that the offense is sufficiently grievous. (2) felony, if the value of money obtained or sought to be obtained is more than two thousand dollars but less than ten thousand dollars, and, upon conviction, the person must be fined in the discretion of the court, or imprisoned for not more than five years, or both; (3) felony, if the value of money obtained or sought to be obtained is ten thousand dollars or more, and, upon conviction, the person must be fined in the discretion of the court, or imprisoned for not more than ten years, or both. (4) In addition, a person convicted of a misdemeanor or a felony pursuant to this section may be prohibited from entering into further preneed funeral contracts, if the department, in its discretion, finds that the offense is sufficiently grievous. (B) The determination of the degree of an offense under subsection (A) must be measured by the total value of all money obtained or sought to be obtained by the unlawful conduct. (B)(C)(1) Before the suspension, revocation, or other action by the department involving a license to sell preneed funeral contracts becomes final, a licensee is entitled to request a contested case hearing before the Administrative Law Court, in accordance with the Administrative Procedures Act. (2) Other action by the department may include a warning notice of deficiency, additional education requirements concerning the provisions of this chapter, a fine, or a cease and desist order for violation of a provision in this chapter." SECTION 6. The repeal or amendment by this act of any law, whether temporary or permanent or civil or criminal, does not affect pending actions, rights, duties, or liabilities founded thereon, or alter, discharge, release or extinguish any penalty, forfeiture, or liability incurred under the repealed or amended law, unless the repealed or amended provision shall so expressly provide. After the effective date of this act, all laws repealed or amended by this act must be taken and treated as remaining in full force and effect for the purpose of sustaining any pending or vested right, civil action, special proceeding, criminal prosecution, or appeal existing as of the effective date of this act, and for the enforcement of rights, duties, penalties, forfeitures, and liabilities as they stood under the repealed or amended laws. SECTION 7. This act takes effect upon approval by the Governor. / Amend title to conform. /s/Sen. Paul G. Campbell, Jr. /s/Rep. William E. Sandifer III /s/Sen. Kent M. Williams /s/Rep. Julia Ann Parks /s/Sen. Chauncey K. Gregory /s/Rep. McLain R. Toole On Part of the Senate. On Part of the House. , and a message was sent to the House accordingly. Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that it has adopted the Report of the Committee of Conference on: H. 4763 (Word version) -- Reps. Sandifer, King, Butler Garrick and Parks: A BILL TO AMEND SECTION 32-7-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PRENEED FUNERAL CONTRACT LICENSES, SO AS TO FURTHER PROVIDE FOR THE TERM OF THE LICENSE AND FOR THE USE OF LICENSE RENEWAL FEES; AND TO AMEND SECTION 32-7-100, AS AMENDED, RELATING TO UNLAWFUL VIOLATIONS OF LAW PERTAINING TO PRENEED FUNERAL CONTRACTS, SO AS TO FURTHER PROVIDE FOR THE PENALTIES FOR VIOLATIONS BASED ON THE AMOUNT OF MONEY OBTAINED OR SOUGHT TO BE OBTAINED WITH CERTAIN OFFENSES DECLARED TO BE MISDEMEANORS AND CERTAIN OFFENSES DECLARED TO BE FELONIES. Very respectfully, Speaker of the House Message from the House Columbia, S.C., June 6, 2012 Mr. President and Senators: The House respectfully informs your Honorable Body that the Report of the Committee of Conference having been adopted by both Houses, and this Bill having been read three times in each House, it was ordered that the title thereof be changed to that of an Act and that it be enrolled for Ratification: H. 4763 (Word version) -- Reps. Sandifer, King, Butler Garrick and Parks: A BILL TO AMEND SECTION 32-7-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PRENEED FUNERAL CONTRACT LICENSES, SO AS TO FURTHER PROVIDE FOR THE TERM OF THE LICENSE AND FOR THE USE OF LICENSE RENEWAL FEES; AND TO AMEND SECTION 32-7-100, AS AMENDED, RELATING TO UNLAWFUL VIOLATIONS OF LAW PERTAINING TO PRENEED FUNERAL CONTRACTS, SO AS TO FURTHER PROVIDE FOR THE PENALTIES FOR VIOLATIONS BASED ON THE AMOUNT OF MONEY OBTAINED OR SOUGHT TO BE OBTAINED WITH CERTAIN OFFENSES DECLARED TO BE MISDEMEANORS AND CERTAIN OFFENSES DECLARED TO BE FELONIES. Very respectfully, Speaker of the House RATIFICATION OF ACTS Pursuant to an invitation the Honorable Speaker and House of Representatives appeared in the Senate Chamber on June 6, 2012, at 3:45 P.M. and the following Acts were ratified: (R247, S. 512 (Word version)) -- Senator Grooms: AN ACT TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 50-11-36 SO AS TO PROHIBIT HUNTING MIGRATORY WATERFOWL ON LAKE MOULTRIE WITHIN TWO HUNDRED YARDS OF A DWELLING WITHOUT WRITTEN PERMISSION AND TO PROVIDE A PENALTY FOR A VIOLATION. L:\COUNCIL\ACTS\512AHB12.DOCX (R248, S. 788 (Word version)) -- Senator Verdin: AN ACT TO AMEND CHAPTER 21, TITLE 47, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE FARM ANIMAL AND RESEARCH FACILITIES PROTECTION ACT, SO AS TO PROVIDE THAT THIS CHAPTER ALSO APPLIES TO "CROP OPERATIONS", TO DEFINE THE TERM "CROP OPERATION", TO PROVIDE ADDITIONAL LIABILITY EXEMPTIONS TO VETERINARIANS AND PEOPLE WHO HOLD A SUPERIOR INTEREST IN CERTAIN PROPERTY, TO PROVIDE FOR A CIVIL CAUSE OF ACTION FOR A PERSON THAT SUFFERS DAMAGES AS A RESULT OF VIOLATIONS OF THIS CHAPTER RELATING TO ANIMAL FACILITY OPERATIONS, TO PROVIDE THAT IT IS UNLAWFUL TO TAMPER OR INTERFERE WITH CROP OPERATIONS, AND FRAUDULENTLY GAIN ACCESS TO CROP OPERATIONS, TO PROVIDE FOR A CIVIL CAUSE OF ACTION AND CRIMINAL PENALTIES FOR CERTAIN VIOLATIONS RELATED TO CROP OPERATIONS, AND TO MAKE TECHNICAL CHANGES; AND BY ADDING SECTION 47-4-170 SO AS TO PROVIDE THAT CERTAIN INFORMATION PREPARED, OWNED, USED, SUBMITTED TO, IN POSSESSION OF, OR RETAINED BY THE STATE LIVESTOCK-POULTRY HEALTH COMMISSION OR THE STATE VETERINARIAN IS EXEMPT FROM DISCLOSURE. L:\COUNCIL\ACTS\788CM12.DOCX (R249, S. 836 (Word version)) -- Senators Grooms, Verdin, Knotts, Bright, Bryant, Courson, Campsen, McConnell, Cleary, Rose, Hayes, Shoopman, Massey, Campbell, Fair, Gregory, Cromer, L. Martin and Alexander: AN ACT TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 10 TO TITLE 44 SO AS TO ENACT THE INTERSTATE HEALTHCARE COMPACT, TO PROVIDE THAT COMPACT MEMBERS MUST TAKE ACTION TO OBTAIN CONGRESSIONAL CONSENT TO THE COMPACT, TO PROVIDE THAT THE LEGISLATURE IS VESTED WITH THE RESPONSIBILITY TO REGULATE HEALTHCARE DELIVERED IN THEIR STATE, TO PROVIDE FOR HEALTHCARE FUNDING, TO ESTABLISH THE INTERSTATE ADVISORY HEALTH CARE COMMISSION AND TO PROVIDE ITS COMPOSITION, POWERS, DUTIES, AND AUTHORITY, TO PROVIDE THE EFFECTIVE DATE OF THE COMPACT, TO PROVIDE FOR AMENDING THE COMPACT, TO PROVIDE FOR THE MANNER OF WITHDRAWAL FROM THE COMPACT, TO PROVIDE THE PARTICIPATION OF SOUTH CAROLINA IN THE COMPACT DOES NOT INCLUDE THE ADMINISTRATION OF MEDICARE OR THE CHILDREN'S HEALTH INSURANCE PROGRAM ABSENT SPECIFIC AUTHORIZATIONS BY THE GENERAL ASSEMBLY, AND TO PROVIDE NECESSARY DEFINITIONS. L:\COUNCIL\ACTS\836AB12.DOCX L:\COUNCIL\ACTS\1127AC12.DOCX (R251, S. 1329 (Word version)) -- Senator Fair: AN ACT TO AMEND SECTION 24-21-10, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE APPOINTMENT OF THE DIRECTOR OF THE DEPARTMENT OF PROBATION, PAROLE AND PARDON SERVICES, AND THE MEMBERS OF THE BOARD OF PROBATION, PAROLE AND PARDON SERVICES, SO AS TO PROVIDE THAT THE MEMBER OF THE BOARD WHO IS APPOINTED ON AN AT-LARGE BASIS MUST BE SELECTED FROM ONE OF THE CONGRESSIONAL DISTRICTS AND AT LEAST ONE APPOINTEE SHALL POSSESS THE QUALIFICATIONS THAT THE AT-LARGE APPOINTEE FORMERLY MET. L:\COUNCIL\ACTS\1329CM12.DOCX (R252, H. 3113 (Word version)) -- Reps. Clemmons and Viers: AN ACT TO AMEND SECTION 50-1-60, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DIVISION OF THE STATE INTO SIX GAME ZONES, SO AS TO MOVE HORRY COUNTY FROM GAME ZONE 4 AND PLACE IT IN GAME ZONE 5. L:\COUNCIL\ACTS\3113CM12.DOCX (R253, H. 4054 (Word version)) -- Rep. Sandifer: AN ACT TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 50-11-36 SO AS TO PROVIDE THAT IT IS UNLAWFUL TO HUNT MIGRATORY WATERFOWL ON LAKE KEOWEE WITHIN TWO HUNDRED YARDS OF A DWELLING, AND TO PROVIDE A PENALTY; BY ADDING SECTION 50-11-37 SO AS TO PROVIDE THAT IT IS UNLAWFUL TO HUNT MIGRATORY WATERFOWL ON BROADWAY LAKE WITHIN TWO HUNDRED YARDS OF A DWELLING WITHOUT WRITTEN PERMISSION OF THE OWNER AND OCCUPANT, AND TO PROVIDE A PENALTY; AND BY ADDING SECTION 50-11-38 SO AS TO PROVIDE THAT IT IS UNLAWFUL TO HUNT MIGRATORY WATERFOWL ON LAKE MOULTRIE WITHIN TWO HUNDRED YARDS OF A DWELLING WITHOUT WRITTEN PERMISSION OF THE OWNER AND OCCUPANT, AND TO PROVIDE A PENALTY. L:\COUNCIL\ACTS\4054CM12.DOCX (R254, H. 4652 (Word version)) -- Reps. Sandifer, Harrell, Lucas, Bingham, Hardwick, Harrison, Owens, White, Allison, Atwater, Bales, Ballentine, Bannister, Barfield, Bedingfield, Bikas, Bowen, Brady, Brannon, Chumley, Clemmons, Cole, Corbin, Crawford, Crosby, Daning, Delleney, Edge, Erickson, Forrester, Frye, Gambrell, Hamilton, Hearn, Henderson, Herbkersman, Hiott, Hixon, Horne, Huggins, Limehouse, Loftis, Long, Lowe, McCoy, Merrill, D.C. Moss, V.S. Moss, Murphy, Nanney, Norman, Parker, Patrick, Pinson, Pitts, Pope, Putnam, Quinn, Ryan, Simrill, Skelton, G.M. Smith, G.R. Smith, J.R. Smith, Sottile, Southard, Spires, Stringer, Tallon, Taylor, Thayer, Tribble, Viers, Whitmire, Willis, Young, Battle, Hayes and Anthony: AN ACT TO AMEND SECTION 41-7-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PUBLIC POLICY CONCERNING THE RIGHT TO WORK, SO AS TO CLARIFY ARCHAIC LANGUAGE IN THE POLICY; TO AMEND SECTION 41-7-80, RELATING TO PENALTIES FOR A VIOLATION OF RIGHT-TO-WORK LAWS, SO AS TO PROVIDE A RANGE FOR AN APPLICABLE FINE FROM ONE THOUSAND DOLLARS TO A MAXIMUM OF TEN THOUSAND DOLLARS; TO AMEND SECTION 41-7-90, RELATING TO COURT REMEDIES AVAILABLE TO A PERSON FOR A VIOLATION OF HIS RIGHT TO WORK, SO AS TO PERMIT TREBLE DAMAGES, REQUIRE A PERSON SEEKING THIS RELIEF TO CONTEMPORANEOUSLY PROVIDE THE DEPARTMENT OF LABOR, LICENSING AND REGULATION WITH THE BASIS FOR THE LAWSUIT, AND TO PROVIDE AN EXCEPTION; TO AMEND SECTION 41-7-100, RELATING TO CIVIL PENALTIES THE DEPARTMENT MAY ASSESS FOR A VIOLATION AND RELATED APPEALS, SO AS TO PROVIDE A CIVIL PENALTY MAY NOT EXCEED TEN THOUSAND DOLLARS; BY ADDING SECTION 41-7-110 SO AS TO PROVIDE AN EMPLOYER OR AN EMPLOYEE WITH PERMISSION MAY CONSPICUOUSLY POST CERTAIN NOTICE CONCERNING THE RIGHTS OF AN EMPLOYEE; AND BY ADDING SECTION 41-7-130 SO AS TO REQUIRE CERTAIN REPORTS TO BE FILED WITH THE DEPARTMENT OF LABOR, LICENSING AND REGULATION. L:\COUNCIL\ACTS\4652AB12.DOCX (R255, H. 4654 (Word version)) -- Reps. Hardwick, Harrell, Loftis, Sandifer, White, Harrison, Owens, Crosby, Anderson, Bingham, Sottile, Corbin, Chumley, Forrester, Hearn, Henderson, Lucas, D.C. Moss, V.S. Moss, Ott, Parker, Southard, Murphy, Clemmons, Hixon, Knight and Patrick: AN ACT TO AMEND SECTION 48-1-90, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROHIBITING THE DISCHARGE OF POLLUTANTS INTO THE ENVIRONMENT AND REMEDIES FOR VIOLATIONS, SO AS TO PROVIDE EXEMPTIONS AND LIMITATIONS ON THESE EXEMPTIONS AND TO SPECIFY THAT NO PRIVATE CAUSE OF ACTION IS CREATED BY OR EXISTS UNDER THE POLLUTION CONTROL ACT; TO AMEND SECTION 48-1-130, RELATING TO FINAL ORDERS OF THE DEPARTMENT DISCONTINUING DISCHARGE OF POLLUTANTS, SO AS TO DELETE PROVISIONS RELATING TO REQUIRED PROCEDURES PRECEDING THE ISSUANCE OF A FINAL ORDER, TO PROVIDE THAT AN ORDER IS SUBJECT TO REVIEW PURSUANT TO THE ADMINISTRATIVE PROCEDURES ACT, AND TO PROVIDE THIS SECTION DOES NOT ABROGATE ANY EMERGENCY POWER OF THE DEPARTMENT; TO AMEND SECTION 48-1-250, RELATING TO WHOM BENEFITS FROM CAUSES OF ACTION RESULTING FROM POLLUTION VIOLATIONS INURE, SO AS TO PROVIDE THAT NO PRIVATE CAUSE OF ACTION IS CREATED BY OR EXISTS UNDER THE POLLUTION CONTROL ACT, AND TO MAKE THESE PROVISIONS RETROACTIVE AND EXTINGUISH ANY RIGHT, CLAIM, OR CAUSE OF ACTION ARISING UNDER OR RELATED TO THE POLLUTION CONTROL ACT, SUBJECT TO EXCEPTIONS FOR THE STATE AND ITS SUBDIVISIONS; TO CREATE THE "ISOLATED WETLANDS AND CAROLINA BAYS TASK FORCE" TO REVIEW, STUDY, AND MAKE RECOMMENDATIONS CONCERNING ISSUES RELATED TO ISOLATED WETLANDS AND CAROLINA BAYS IN SOUTH CAROLINA, TO PROVIDE FOR THE OBLIGATIONS OF THE TASK FORCE, AMONG OTHER THINGS; AND TO PROVIDE THE TERM "PERMIT" AS USED IN THE POLLUTION CONTROL ACT IS INCLUSIVE AND TO SPECIFY ITS INTENDED MEANING. L:\COUNCIL\ACTS\4654AB12.DOCX (R256, H. 4687 (Word version)) -- Reps. King, Parks, Butler Garrick, J.E. Smith and Lucas: AN ACT TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 44-63-74 SO AS TO REQUIRE DEATH CERTIFICATES TO BE ELECTRONICALLY FILED WITH THE BUREAU OF VITAL STATISTICS, DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, AND ELECTRONICALLY TRANSMITTED BETWEEN THE FUNERAL HOME AND THE PHYSICIAN, CORONER, OR MEDICAL EXAMINER, CERTIFYING THE CAUSE OF DEATH, TO DOCUMENT DEATH CERTIFICATE INFORMATION AND TO PROVIDE EXEMPTIONS; AND TO PROVIDE THAT REQUIRED SIGNATURES MUST BE PROVIDED ELECTRONICALLY AND TO DEFINE "ELECTRONIC SIGNATURE". L:\COUNCIL\ACTS\4687AC12.DOCX (R257, H. 4758 (Word version)) -- Reps. Johnson, Brantley, Sabb, Govan, Brannon, Munnerlyn, Anthony, Edge, Pope, Simrill, Whipper and Weeks: AN ACT TO AMEND SECTION 14-7-110 AND SECTION 14-7-140, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO JURY COMMISSIONERS FOR THE PURPOSE OF THE SUMMONING OF JURORS IN CIRCUIT COURT AND THE USE OF A COMPUTER FOR THE DRAWING AND SUMMONING OF JURORS IN CIRCUIT COURT, RESPECTIVELY, BOTH SO AS TO DELETE REFERENCES TO JURY COMMISSIONERS AND ALLOW THE CLERK OF COURT OR THE DEPUTY CLERK TO PERFORM THE FUNCTION OF DRAWING AND SUMMONING JURORS. L:\COUNCIL\ACTS\4758AHB12.DOCX (R258, H. 4821 (Word version)) -- Reps. G.M. Smith, Pitts, Murphy, Horne, Hearn, McCoy, Stavrinakis, Bannister and Harrison: AN ACT TO AMEND SECTION 8-21-310, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO COURT FEES AND COSTS, SO AS TO PROVIDE FOR THE FILING OF COURT DOCUMENTS BY ELECTRONIC MEANS FROM AN INTEGRATED ELECTRONIC FILING (E-FILING) SYSTEM AND TO PROVIDE THAT FEES GENERATED FROM E-FILING ARE TO BE USED IN SUPPORT OF COURT TECHNOLOGY. L:\COUNCIL\ACTS\4821AHB12.DOCX (R259, H. 4887 (Word version)) -- Rep. Johnson: AN ACT TO AMEND SECTION 7-27-275, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CLARENDON COUNTY ELECTION COMMISSION AND THE CLARENDON COUNTY BOARD OF REGISTRATION, SO AS TO COMBINE THE CLARENDON COUNTY ELECTION COMMISSION AND THE CLARENDON COUNTY BOARD OF REGISTRATION INTO A SINGLE ENTITY. L:\COUNCIL\ACTS\4887ZW12.DOCX (R260, H. 5287 (Word version)) -- Reps. Pope, Delleney, King, Long, D.C. Moss, V.S. Moss, Norman and Simrill: AN ACT TO AMEND SECTION 22-2-190, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO COUNTY JURY AREAS, SO AS TO PROVIDE FOR JURY AREAS IN RICHLAND COUNTY AND TO PROVIDE FOR ONE JURY AREA COUNTYWIDE FOR THE RICHLAND COUNTY MAGISTRATES CENTRALIZED COURT AND TO PROVIDE FOR JURY AREAS IN YORK COUNTY AND TO PROVIDE FOR ONE JURY AREA COUNTYWIDE FOR THE YORK COUNTY CENTRALIZED DUI COURT. L:\COUNCIL\ACTS\5287AHB12.DOCX THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE. HOUSE AMENDMENTS AMENDED RETURNED TO THE HOUSE S. 947 (Word version) -- Senators Malloy and Williams: A BILL TO PROVIDE FOR AN ADVISORY REFERENDUM TO BE HELD AT THE SAME TIME AS THE 2012 GENERAL ELECTION TO DETERMINE WHETHER OR NOT THE QUALIFIED ELECTORS OF MARLBORO COUNTY FAVOR CREATING A STATE AUTHORITY TO MANAGE AND OPERATE LAKE PAUL A. WALLACE TO BE FUNDED BY THE SALE OF WATER FROM THE LAKE TO THE CITY OF BENNETTSVILLE OR OTHER USERS AND BY LOCAL PROPERTY TAX REVENUE, FEES CHARGED FOR THE USE OF THE LAKE AND OTHER FUNDING SOURCES TO OPERATE THE FACILITY FOR THE PUBLIC PURPOSE FOR WHICH IT WAS CREATED, WITH THE STATE OF SOUTH CAROLINA RETAINING OWNERSHIP OF THE LAKE. The House returned the Bill with amendments. Senator MALLOY asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being concurrence in the House amendments. Senator MALLOY explained the House amendments. Amendment No. 1 Senator MALLOY proposed the following amendment (SWB\5349CM12), which was adopted: Amend the bill, as and if amended, by striking all after the enacting words and inserting: / SECTION 1. Title 49 of the 1976 Code is amended by adding: "CHAPTER 33 Lake Paul A. Wallace Authority Section 49-33-10. As used in this chapter, unless the context otherwise requires: (1) 'Authority' means the Lake Paul A. Wallace Authority, a body corporate and politic created to receive, manage, maintain, and operate the property known as Lake Paul A. Wallace located in Marlboro County; (2) 'Department' means the Department of Natural Resources; and (3) 'Lake' means Lake Paul A. Wallace. Section 49-33-20. (A) There is hereby created a body corporate and politic to be known as the Lake Paul A. Wallace Authority. (B) The function of the authority is to: (1) be the body politic and corporate to manage, maintain, and operate the Lake Paul A. Wallace; (2) ensure that the primary purpose of the lake is for public fishing and recreation in compliance with the federal law under which the lake was established; and (3) provide that the wildlife habitat remain a protected area as long as this function does not contravene with the provisions contained in item (1) of this subsection. Section 49-33-30. (A) The authority shall be composed of seven members appointed by the Marlboro County Legislative Delegation, as follows: (1) two members nominated by the city council of Bennettsville; (2) two members nominated by the county council of Marlboro County; and (3) three members at-large who reside near or have a demonstrable history of recreational use of Lake Paul A. Wallace. (B) The members shall serve for terms of four years, except that of the members first appointed, one nominated by city council, one nominated by county council, and one at-large member will serve for terms of two years for their initial appointment. (C) One of the at-large members must be designated by the Marlboro County Legislative Delegation to serve as the chairman of the authority. (D) A vacancy must be filled in the same manner as the appointment for the vacant position is made, and the successor appointed to fill the vacancy shall hold office for the remainder of the unexpired term. (E) The following shall serve ex officio as a non-voting member: the Director of the Department of Natural Resources or his designee. Section 49-33-40. (A) The members of the authority, at the discretion of the city, county, or authority may receive such per diem and mileage as is provided by law for members of boards, commissions, and committees. (B) The city council of Bennettsville, the county council of Marlboro, and the authority may provide the per diem, mileage, and staff for the authority. Section 49-33-50. The authority shall convene upon the call of the chairman and organize by electing a vice-chairman, a secretary, and a treasurer, whose terms of office shall be for such period as the authority shall determine in its bylaws. Section 49-33-60. The secretary of the authority shall file in the offices of the clerk of court for Marlboro County and the Secretary of State appropriate certificates, showing the personnel of the authority and the duration of the terms of the respective members. Section 49-33-70. The authority has the following powers to: (1) have perpetual succession; (2) sue and be sued; (3) adopt, use, and alter a corporate seal; (4) define a quorum for its meetings; (5) maintain a principal office, which shall be located in Bennettsville; (6) make bylaws for the management and regulation of its affairs; (7) acquire, hold, and manage real estate; (8) make contracts of all sorts and to execute all instruments necessary or convenient for the carrying on of the business of the authority; and (9) do all other acts and things necessary or convenient to carry out any function or power committed or granted to the authority. Section 49-33-80. The authority is empowered to receive and spend any funding available through (1) the department, (2) the municipal, county, state, or federal government, or (3) any other source in order to finance the management, maintenance, and operation of the lake that is in compliance with federal and state law." SECTION 2. If any section, subsection, paragraph, subparagraph, sentence, clause, phrase, or word of this act is for any reason held to be unconstitutional or invalid, such holding shall not affect the constitutionality or validity of the remaining portions of this act, the General Assembly hereby declaring that it would have passed this chapter, and each and every section, subsection, paragraph, subparagraph, sentence, clause, phrase, and word thereof, irrespective of the fact that any one or more other sections, subsections, paragraphs, subparagraphs, sentences, clauses, phrases, or words hereof may be declared to be unconstitutional, invalid, or otherwise ineffective. SECTION 3. This act shall take effect July 1, 2012. / Renumber sections to conform. Amend title to conform. Senator MALLOY explained the amendment. The question then was the adoption of the amendment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 37; Nays 0 AYES Anderson Bright Bryant Campbell Campsen Cleary Courson Cromer Davis Fair Ford Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Massey Matthews McGill Nicholson O'Dell Peeler Rankin Reese Rose Scott Sheheen Shoopman Thomas Verdin Williams Total--37 NAYS Total--0 Statement by Senator ALEXANDER Having been out of the Chamber because I was chairing the Conference Committee on retirement at the time the vote was taken, I would have voted in favor the adoption of the amendment to S. 947. The Bill was ordered returned to the House of Representatives with amendments. CONCURRENCE S. 1220 (Word version) -- Senators Campbell, Hayes and Ford: A BILL TO AMEND SECTION 48-2-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FEES IMPOSED BY THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL FOR CERTAIN ENVIRONMENTAL PROGRAMS, INCLUDING THE SURFACE WATER WITHDRAWAL PROGRAM, WHICH ARE DEPOSITED INTO THE ENVIRONMENTAL PROTECTION FUND FOR ADMINISTRATION OF THESE PROGRAMS, SO AS TO ENUMERATE THE FEES FOR SURFACE WATER WITHDRAWAL APPLICATIONS AND PERMITS THAT WOULD OTHERWISE HAVE BEEN REPEALED JANUARY 1, 2013; BY ADDING SECTION 49-4-175 SO AS TO REIMPOSE THE FEES THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL MAY CHARGE FOR SURFACE WATER WITHDRAWAL AND APPLICATIONS AND PERMITS AND TO PROVIDE THAT THE DEPARTMENT SHALL RETAIN THESE FEES TO IMPLEMENT AND OPERATE THE SURFACE WATER WITHDRAWAL PROGRAM; AND TO AMEND ACT 247 OF 2010, BY REPEALING PROVISIONS THAT PROSPECTIVELY REPEAL THE IMPOSITION OF SURFACE WATER WITHDRAWAL PERMIT FEES. The House returned the Bill with amendments. Senator HAYES asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The question then was concurrence with the House amendments. Senator HAYES explained the amendments. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Cromer Davis Elliott Fair Ford Gregory Grooms Hayes Hutto Knotts Land Leatherman Leventis Malloy Martin, Larry Martin, Shane Massey McGill O'Dell Peeler Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Total--0 The Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification. CONCURRENCE S. 1055 (Word version) -- Senators McConnell and Ford: A BILL TO AMEND SECTION 14-27-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE COMPOSITION OF THE JUDICIAL COUNCIL, SO AS TO PROVIDE FOR TWO ADDITIONAL MEMBERS OF THE COUNCIL, THE CHIEF JUDGE OF THE SOUTH CAROLINA COURT OF APPEALS, AND A PERSON RECOMMENDED BY THE CHARLESTON SCHOOL OF LAW, TO CHANGE THE PERSON SERVING FROM THE SOUTH CAROLINA BAR FROM THE PRESIDENT OF THE SOUTH CAROLINA BAR TO ONE PERSON RECOMMENDED BY THE SOUTH CAROLINA BAR, AND TO ADD AS A MEMBER, A MUNICIPAL COURT JUDGE IN LIEU OF ONE OF THE TWO MAGISTRATE COURT JUDGES; TO AMEND SECTION 14-27-30 RELATING TO THE CHIEF JUSTICE APPOINTING A PERSON RECOMMENDED BY THE CHARLESTON SCHOOL OF LAW AND APPOINTING THE SUMMARY COURT JUDGES; AND TO AMEND SECTION 14-27-40 RELATING TO THE TERMS OF SERVICE, SO AS TO PROVIDE THAT THE CHIEF JUDGE SERVES DURING THE TERM OF HIS OFFICE, AND THE PERSON RECOMMENDED BY THE CHARLESTON SCHOOL OF LAW SERVES FOR A FOUR YEAR TERM. The House returned the Bill with amendments. Senator CAMPSEN asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The question then was concurrence with the House amendments. Senator CAMPSEN explained the amendments. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 40; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Fair Ford Gregory Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill O'Dell Peeler Rankin Rose Scott Setzler Shoopman Thomas Verdin Williams Total--40 NAYS Total--0 The Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification. CONCURRENCE S. 1417 (Word version) -- Senator Land: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 108 TO CHAPTER 3, TITLE 56 SO AS TO PROVIDE FOR THE ISSUANCE OF "SOUTH CAROLINA TENNIS PATRONS FOUNDATION" SPECIAL LICENSE PLATES. The House returned the Bill with amendments. Senator LAND asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The question then was concurrence with the House amendments. Senator LAND explained the amendments. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 38; Nays 2 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Davis Elliott Fair Ford Gregory Grooms Hayes Hutto Jackson Knotts Land Lourie Malloy Martin, Larry Martin, Shane Massey Matthews Nicholson Peeler Pinckney Rankin Reese Rose Scott Setzler Shoopman Thomas Verdin Williams Total--38 NAYS Leventis Sheheen Total--2 The Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification. CONCURRENCE S. 1087 (Word version) -- Senators Jackson, Cromer, Grooms, Ford, Scott, Elliott, Setzler, Land, Pinckney, Anderson, Ryberg, Matthews, Rankin and Verdin: A BILL TO AMEND SECTION 50-9-730, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEPARTMENT OF NATURAL RESOURCES' ABILITY TO DESIGNATE "FREE FISHING DAYS" AND SANCTION FISHING EVENTS EXEMPT FROM FISHING LICENSE REQUIREMENTS, SO AS TO DELETE THE PROVISION THAT ALLOWS THE DEPARTMENT TO DESIGNATE "FREE FISHING DAYS", TO DESIGNATE JULY FOURTH AND MEMORIAL DAY AS DAYS WHEN A RESIDENT IS NOT REQUIRED TO POSSESS A LICENSE OR PERMIT FOR FRESHWATER RECREATIONAL FISHING, TO LIMIT DEPARTMENT-SANCTIONED EVENTS THAT ARE EXEMPT FROM FISHING LICENSE REQUIREMENTS TO FRESHWATER EVENTS, AND TO EXEMPT CERTAIN COMMERCIAL FISHERMEN FROM THE PROVISIONS CONTAINED IN THIS SECTION. The House returned the Bill with amendments. Senator JACKSON asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The question then was concurrence with the House amendments. Senator JACKSON explained the amendments. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Ford Gregory Grooms Hayes Hutto Jackson Knotts Land Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews Nicholson Peeler Pinckney Rankin Reese Rose Setzler Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Total--0 The Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification. CONCURRENCE S. 1354 (Word version) -- Senators Bryant, Thomas, Ford and L. Martin: A BILL TO AMEND SECTION 35-1-604 OF THE 1976 CODE, RELATING TO SECURITIES VIOLATIONS, TO REQUIRE ALL CEASE AND DESIST ORDERS ISSUED BY THE SECURITIES COMMISSIONER TO BE PUBLIC DOCUMENTS AND TO REQUIRE PUBLICATION ON THE ATTORNEY GENERAL'S WEBSITE. The House returned the Bill with amendments. Senator BRYANT asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The question then was concurrence with the House amendments. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 40; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Fair Ford Gregory Grooms Hayes Hutto Knotts Land Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson Peeler Pinckney Rankin Reese Rose Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--40 NAYS Total--0 The Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification. CARRIED OVER S. 1299 (Word version) -- Senators Cleary, McGill and Ford: A BILL TO AMEND SECTION 54-15-20 OF THE 1976 CODE, RELATING TO THE MEMBERSHIP OF THE SOUTH CAROLINA COMMISSIONERS OF PILOTAGE FOR THE UPPER COASTAL AREA, TO INCREASE THE NUMBER OF MEMBERS ON THE COMMISSION FROM SIX TO EIGHT. On motion of Senator PEELER, the Bill was carried over. CARRIED OVER S. 1125 (Word version) -- Senators Bright, Bryant, S. Martin, Thomas, Gregory, Knotts, Campbell, Rose, Cromer, Fair, Campsen, Grooms, Peeler and Shoopman: A BILL TO AMEND SECTION 41-35-120 OF THE 1976 CODE, RELATING TO DISQUALIFICATION FOR UNEMPLOYMENT BENEFITS, TO PROVIDE THAT A PERSON DISCHARGED FROM EMPLOYMENT FOR CAUSE IS INELIGIBLE FOR BENEFITS FOR TWENTY WEEKS BEGINNING WITH THE DATE THE PERSON FILED A BENEFITS REQUEST. The House returned the Bill with amendments. Senator PEELER moved to carry over the Bill. Senator SCOTT moved to table the motion to carry over the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 19; Nays 23 AYES Anderson Bright Coleman Elliott Hutto Jackson Knotts Land Leventis Lourie Malloy Matthews McGill Nicholson Pinckney Scott Setzler Sheheen Williams Total--19 NAYS Alexander Bryant Campbell Campsen Cleary Courson Cromer Davis Fair Grooms Hayes Leatherman Martin, Larry Martin, Shane Massey Peeler Rankin Reese Rose Ryberg Shoopman Thomas Verdin Total--23 The Senate refused to table the motion to carry over. The question then was the motion to carry over the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 23; Nays 18 AYES Alexander Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Gregory Grooms Hayes Knotts Martin, Shane Massey Peeler Rankin Rose Ryberg Shoopman Thomas Verdin Total--23 NAYS Anderson Bright Hutto Jackson Land Leventis Lourie Malloy Martin, Larry Matthews McGill Nicholson Pinckney Reese Scott Setzler Sheheen Williams Total--18 The Bill was carried over. Expression of Personal Interest Senator SCOTT rose for an Expression of Personal Interest. NONCONCURENCE S. 1137 (Word version) -- Senator Shoopman: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTIONS 40-3-325 AND 40-22-295 SO AS TO ENACT THE "ARCHITECTS' AND ENGINEERS' VOLUNTEER ACT" WHICH PROVIDES IMMUNITY FOR A REGISTERED ARCHITECT OR ENGINEER WHO PROVIDES CERTAIN ARCHITECTURAL OR ENGINEERING SERVICES AT THE SCENE OF A DECLARED EMERGENCY. The House returned the Bill with amendments. Amendment No. 1 Senator MATTHEWS proposed the following amendment (NBD\12665AC12), which was withdrawn: Amend the bill, as and if amended, Section 40-22-295(B)(2), page 2, line 16 by deleting / not /. Renumber sections to conform. Amend title to conform. Senator HUTTO spoke on the amendment. Objection With Senator HUTTO retaining the floor, Senator SHANE MARTIN asked unanimous consent to make a motion that the Senate recede from business not to exceed ten minutes. Senator KNOTTS objected. Senator HUTTO resumed speaking on the amendment. Objection With Senator HUTTO retaining the floor, Senator LAND asked unanimous consent to make a motion that the Senate recede from business not to exceed ten minutes. Senator SHANE MARTIN objected. Point of Quorum At 4:24 P.M., Senator BRIGHT made the point that a quorum was not present. It was ascertained that a quorum was not present. Call of the Senate Senator BRIGHT moved that a Call of the Senate be made. The following Senators answered the Call: Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Cromer Davis Fair Ford Gregory Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson Peeler Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams A quorum being present, the Senate resumed. Objection With Senator HUTTO retaining the floor, Senator LAND asked unanimous consent to make a motion to take up for immediate consideration H. 3508 (Word version). Senator THOMAS objected. Objection With Senator HUTTO retaining the floor, Senator RANKIN asked unanimous consent to make a motion to take up for immediate consideration H. 3508. Senator BRIGHT objected. Objection With Senator HUTTO retaining the floor, Senator LOURIE asked unanimous consent to make a motion to take up for immediate consideration H. 3342 (Word version). Senator THOMAS objected. Objection With Senator HUTTO retaining the floor, Senator RYBERG asked unanimous consent to make a motion to take up for immediate consideration H. 4802 (Word version). Senator BRYANT objected. Objection With Senator HUTTO retaining the floor, Senator MASSEY asked unanimous consent to make a motion to take up for immediate consideration H. 3912 (Word version). Senator KNOTTS objected. Senator HUTTO resumed speaking on the amendment. Objection With Senator HUTTO retaining the floor, Senator CAMPSEN asked unanimous consent to make a motion to take up for immediate consideration H. 5150 (Word version). Senator KNOTTS objected. Motion Under Rule 15A Failed At 6:01 P.M., Senator GROOMS moved under the provisions of Rule 15A to vote on the entire matter of S.1137 (Word version). The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 19; Nays 24 AYES Alexander Bright Bryant Campbell Campsen Cleary Courson Cromer Davis Fair Gregory Grooms Martin, Shane Massey Peeler Rose Ryberg Thomas Verdin Total--19 NAYS Anderson Coleman Elliott Ford Hayes Hutto Jackson Knotts Land Leventis Lourie Malloy Martin, Larry Matthews McGill Nicholson Pinckney Rankin Reese Scott Setzler Sheheen Shoopman Williams Total--24 Having failed to receive the necessary vote, the motion under Rule 15A failed. Senator HUTTO resumed speaking on the amendment. Objection With Senator HUTTO retaining the floor, Senator LOURIE asked unanimous consent to make a motion to take up for immediate consideration H. 3342 (Word version). Senator KNOTTS objected. Objection With Senator HUTTO retaining the floor, Senator LARRY MARTIN asked unanimous consent to make a motion to take up for immediate consideration H. 4494 (Word version). Senator ANDERSON objected. Objection With Senator HUTTO retaining the floor, Senator RYBERG asked unanimous consent to make a motion to take up for immediate consideration H. 4802 (Word version) on a contested basis. Senator BRIGHT objected. Senator HUTTO resumed speaking on the amendment. Objection With Senator HUTTO retaining the floor, Senator RYBERG asked unanimous consent to make a motion to recede for ten minutes. Senator KNOTTS objected. Senator HUTTO resumed speaking on the amendment. Objection With Senator HUTTO retaining the floor, Senator MASSEY asked unanimous consent to make a motion that the portion of the Calendar pertaining to the Second Reading Bills not be printed in the Calendar for tomorrow. Senator ANDERSON objected. Objection With Senator HUTTO retaining the floor, Senator GROOMS asked unanimous consent to make a motion to recommit all the Bills on the Second Reading Calendar. Senator LOURIE objected. Senator HUTTO resumed speaking on the amendment. Objection With Senator HUTTO retaining the floor, Senator LOURIE asked unanimous consent to make a motion that all the Bills on the Uncontested Second Reading Calendar be given a second reading. There was an objection. Objection With Senator HUTTO retaining the floor, Senator LOURIE asked unanimous consent to make a motion that the Senate take up H. 3342 (Word version) for immediate consideration. There was an objection. Objection At 6:49 P.M., with Senator HUTTO retaining the floor, Senator SCOTT asked unanimous consent to make a motion that the Senate stand in recess for 15 minutes. Senator FORD objected. Objection With Senator HUTTO retaining the floor, Senator HUTTO asked unanimous consent to make a motion that all the Bills on the Uncontested Second Reading Calendar be given a second reading. Senator SCOTT objected. Objection With Senator HUTTO retaining the floor, Senator THOMAS asked unanimous consent to make a motion that all the Bills on the Uncontested Second Reading Calendar be taken up for immediate consideration. Senator SCOTT objected. Senator HUTTO resumed speaking on the amendment. Objection With Senator HUTTO retaining the floor, Senator VERDIN asked unanimous consent to make a motion to take up H. 4721 (Word version) for immediate consideration. Senator CLEARY objected. Objection With Senator HUTTO retaining the floor, Senator HAYES asked unanimous consent to make a motion for a Call of the Uncontested Statewide Calendar. Senators VERDIN and ANDERSON objected. Objection With Senator HUTTO retaining the floor, Senator HAYES asked unanimous consent to make a motion for a Call of the Uncontested Statewide Calendar. Senator BRYANT objected. Objection With Senator HUTTO retaining the floor, Senator SCOTT asked unanimous consent to make a motion that the Senate stand adjourned. Senator COURSON objected. Objection With Senator HUTTO retaining the floor, Senator THOMAS asked unanimous consent to make a motion to give all uncontested Bills on the Second Reading Calendar a second reading, carrying over all amendments to third reading. Senator KNOTTS objected. On motion of Senator HUTTO, the amendments to S. 1137 (Word version) were withdrawn. Senator HUTTO moved to nonconcur with the House amendments. The question then was the motion to concur with the House amendments. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 2; Nays 42 AYES Coleman Ford Total--2 NAYS Alexander Anderson Bright Bryant Campbell Campsen Cleary Courson Cromer Davis Elliott Fair Gregory Grooms Hayes Hutto Jackson Knotts Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--42 The Senate nonconcurred in the House amendments and a message was sent to the House accordingly. Senator LARRY MARTIN asked unanimous consent to make a motion to give all the Bills on the Uncontested Second Reading Calendar a second reading, carrying over all amendments to third reading and waiving the provisions of Rule 26B. There was no objection and the motion was adopted. Pursuant to the motion by Senator LARRY MARTIN, the following Bills and Joint Resolutions received a second reading, carrying over all amendments to third reading and waiving the provisions of Rule 26B: S. 224 (Word version) -- Senators Knotts and Ford: A BILL TO AMEND SECTION 59-111-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FREE TUITION FOR CERTAIN VETERANS' CHILDREN, SO AS TO ALSO PROVIDE FREE TUITION TO CHILDREN OF CERTAIN ACTIVE DUTY SERVICE MEMBERS WITH HONORABLE WARTIME SERVICE. S. 5 (Word version) -- Senators Leatherman, Rose, McConnell, Campsen, Fair, Rankin, Cromer, Alexander and Elliott: A BILL TO AMEND CHAPTER 38, TITLE 1 OF THE 1976 CODE TO ENACT THE "HEALTHCARE FREEDOM ACT", BY ADDING SECTION 38-1-40 TO PROVIDE THAT A CITIZEN OF THIS STATE HAS THE RIGHT TO PURCHASE HEALTH INSURANCE OR REFUSE TO PURCHASE HEALTH INSURANCE, TO PROVIDE THAT THE GOVERNMENT MAY NOT ENACT A LAW THAT WOULD INTERFERE, RESTRICT, OR PUNISH A CITIZEN FOR EXERCISING THESE RIGHTS, AND TO PROVIDE THAT ANY LAW TO THE CONTRARY SHALL BE VOID AB INITIO. S. 457 (Word version) -- Senator Fair: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-116-45 SO AS TO PROVIDE THAT EVERY POLICE/SECURITY DEPARTMENT SHALL IMPLEMENT POLICIES AND PROCEDURES TO GOVERN THEIR OPERATIONS; TO AMEND SECTIONS 59-116-10, 59-116-20, AND 59-116-30, RELATING TO THE ESTABLISHMENT, POWERS, AND OPERATION OF CAMPUS SECURITY DEPARTMENTS, SO AS TO REVISE THE DEFINITION OF THE TERMS "CAMPUS" AND "CAMPUS POLICE OFFICER", AND TO DEFINE THE TERM "CAMPUS SECURITY OFFICER", TO PROVIDE THAT THESE PROVISIONS APPLY TO PRIVATE INSTITUTIONS, TO MAKE TECHNICAL CHANGES, TO REVISE THE JURISDICTIONAL BOUNDARY OF A CAMPUS SECURITY OFFICER, AND TO REVISE THE MARKINGS THAT MAY APPEAR ON A CAMPUS POLICE OFFICER'S VEHICLE AND TO PROVIDE FOR THE USE OF CAMPUS UNMARKED VEHICLES; TO AMEND SECTION 59-116-50, RELATING TO THE RANKS AND GRADES OF CAMPUS POLICE OFFICERS, SO AS TO DELETE THE TERM "PUBLIC SAFETY DIRECTOR" AND REPLACE IT WITH THE TERM "CHIEF LAW ENFORCEMENT EXECUTIVE", TO MAKE TECHNICAL CHANGES, AND TO PROVIDE THAT THIS PROVISION APPLIES TO PRIVATE INSTITUTIONS; TO AMEND SECTION 59-116-60, RELATING TO CAMPUS POLICE VEHICLES AND RADIO SYSTEMS, SO AS TO SUBSTITUTE THE TERM "CAMPUS POLICE DEPARTMENTS" FOR THE TERM "SAFETY AND SECURITY DEPARTMENTS"; TO AMEND SECTION 59-116-80, RELATING TO IMPERSONATING A CAMPUS POLICE OFFICER, SO AS TO SUBSTITUTE THE TERM "CAMPUS SECURITY DEPARTMENT" FOR THE TERM "SAFETY AND SECURITY DEPARTMENT", TO PROVIDE THAT THIS PROVISION APPLIES TO A PRIVATE COLLEGE OR UNIVERSITY, AND TO MAKE TECHNICAL CHANGES; TO AMEND SECTION 59-116-100, RELATING TO THE PROCESSING OF A PERSON ARRESTED BY A CAMPUS POLICE OFFICER, SO AS TO PROVIDE THAT THIS PROVISION ALSO APPLIES TO THE ARREST OF A PERSON BY A CAMPUS SECURITY OFFICER; TO AMEND SECTION 59-116-120, RELATING TO COLLEGES AND UNIVERSITIES EMPLOYING SECURITY PERSONNEL, SO AS TO PROVIDE THAT THIS PROVISION APPLIES TO PRIVATE COLLEGES AND UNIVERSITIES, AND TO MAKE TECHNICAL CHANGES; AND TO REPEAL SECTION 59-116-70 RELATING TO THE POSTING OF A BOND BY A CAMPUS POLICE OFFICER BEFORE THE ASSUMPTION OF THEIR DUTIES. H. 3897 (Word version) -- Reps. Stringer and Ballentine: A JOINT RESOLUTION TO DISAPPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO ENVIRONMENTAL PROTECTION FEES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4132, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE. H. 3163 (Word version) -- Reps. Tallon, Cole, Allison, G.R. Smith, Taylor, McCoy, Forrester, Murphy, Hixon and Patrick: A BILL TO AMEND ARTICLE 23, CHAPTER 5, TITLE 56 OF THE 1976 CODE, RELATING TO DRIVING UNDER THE INFLUENCE OF INTOXICATING LIQUOR, DRUGS, OR NARCOTICS, BY ADDING SECTION 56-5-2905 TO INCLUDE MOPEDS IN THE DEFINITION OF MOTOR VEHICLES FOR THE PURPOSES OF THE ARTICLE. H. 3342 (Word version) -- Reps. Harrison and Weeks: A BILL TO AMEND SECTION 56-1-286, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE SUSPENSION OR DENIAL OF ISSUANCE OF A DRIVER'S LICENSE OR PERMIT TO OPERATE A MOTOR VEHICLE TO CERTAIN PERSONS WHO DRIVE A MOTOR VEHICLE WITH AN UNLAWFUL ALCOHOL CONCENTRATION, SO AS TO DELETE THE TERM "ADMINISTRATIVE HEARING" AND REPLACE IT WITH THE TERM "CONTESTED CASE HEARING", TO PROVIDE THAT A CONTESTED CASE HEARING MUST BE HELD BEFORE THE OFFICE OF MOTOR VEHICLE HEARINGS PURSUANT TO ITS RULES OF PROCEDURE, AND TO DELETE THE TERM "DIVISION OF MOTOR VEHICLE HEARINGS" AND REPLACE IT WITH THE TERM "OFFICE OF MOTOR VEHICLE HEARINGS"; TO AMEND SECTION 56-5-2942, AS AMENDED, RELATING TO VEHICLE IMMOBILIZATION AFTER A CONVICTION FOR DRIVING A VEHICLE UNDER THE INFLUENCE OF ALCOHOL, DRUGS, OR ANOTHER ILLEGAL SUBSTANCE, SO AS TO REVISE THE PROCEDURE WHEREBY THE DEPARTMENT OF MOTOR VEHICLES MAY RELEASE AN IMMOBILIZED VEHICLE REGISTERED TO A PERSON WHO HAS NOT BEEN CONVICTED OF DRIVING A VEHICLE UNDER THE INFLUENCE OF ALCOHOL, DRUGS, OR ANOTHER UNLAWFUL SUBSTANCE; TO AMEND SECTION 56-5-2951, AS AMENDED, RELATING TO THE SUSPENSION OF A PERSON'S DRIVER'S LICENSE OR PERMIT FOR HIS REFUSAL TO SUBMIT TO A TEST TO DETERMINE HIS LEVEL OF ALCOHOL CONCENTRATION, SO AS TO DELETE THE TERM "ADMINISTRATIVE HEARING" AND REPLACE IT WITH THE TERM "CONTESTED CASE HEARING", TO PROVIDE THAT ADMINISTRATIVE HEARINGS ARE HELD BEFORE THE OFFICE OF MOTOR VEHICLE HEARINGS AND NOT THE DEPARTMENT OF MOTOR VEHICLES, AND TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES IS RESPONSIBLE FOR SENDING A HEARING OFFICER'S DECISION TO A PERSON WHO IS ELIGIBLE TO RECEIVE A RESTRICTED LICENSE PURSUANT TO THIS SECTION; AND TO AMEND SECTION 56-5-2952, AS AMENDED, RELATING TO THE FILING FEE TO REQUEST A CONTESTED CASE HEARING BEFORE THE OFFICE OF MOTOR VEHICLE HEARINGS, SO AS TO INCREASE THE FEE, TO DELETE THE TERM "ADMINISTRATIVE LAW COURT" AND REPLACE IT WITH THE TERM "OFFICE OF MOTOR VEHICLE HEARINGS", AND REVISE THE PROCEDURE FOR DISTRIBUTING FUNDS GENERATED FROM THE COLLECTION OF THESE FEES. H. 3385 (Word version) -- Reps. D.C. Moss, V.S. Moss, Harrison, Delleney, Gambrell, Harrell, Hiott, Hixon, Lucas and Norman: A BILL TO AMEND SECTION 61-6-4160, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE UNLAWFUL SALE OF ALCOHOLIC LIQUORS ON SUNDAYS AND ELECTION DAYS, SO AS TO INCLUDE CHRISTMAS DAY AND THANKSGIVING DAY IN THE PURVIEW OF THE STATUTE. H. 4678 (Word version) -- Reps. Nanney, Brantley, Clemmons, Toole, Parker, Long, Allison, Limehouse, J.R. Smith, Bedingfield, Bowen, Corbin, Hamilton, Henderson, Hixon, Stringer and Willis: A BILL TO AMEND SECTION 29-3-330, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO METHODS OF ENTERING A SATISFACTION OF MORTGAGE IN THE PUBLIC RECORDS, SO AS TO PROVIDE THAT THE MORTGAGEE OF RECORD, THE OWNER OR HOLDER OF THE DEBT INSTRUMENT SECURED BY THE MORTGAGE, THE TRUSTEE OR BENEFICIARY OF A DEED OF TRUST, OR THE LEGAL REPRESENTATIVE OR ATTORNEY-IN-FACT OF ANY OF THOSE PARTIES MAY EXECUTE A MORTGAGE SATISFACTION OR DEED OF TRUST RELEASE, AND TO PROVIDE A PROCEDURE AND FORM FOR USE IN THIS EXECUTION. H. 4451 (Word version) -- Reps. Bowen, Whipper, Bikas, Sottile, Herbkersman, D.C. Moss, Allison, Parker, Huggins, Bowers and Hearn: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTIONS 56-5-3890, 56-5-3895, AND 56-5-3897 SO AS TO PROVIDE THAT IT IS UNLAWFUL FOR A PERSON TO USE AN ELECTRONIC COMMUNICATION DEVICE WHILE DRIVING A MOTOR VEHICLE UNDER CERTAIN CIRCUMSTANCES, TO PROVIDE A PENALTY, AND TO PROVIDE FOR THE DISTRIBUTION OF MONIES COLLECTED FROM FINES ASSOCIATED WITH VIOLATIONS OF THESE PROVISIONS; AND TO AMEND SECTION 56-1-720, RELATING TO THE ASSESSMENT OF POINTS AGAINST A PERSON'S DRIVING RECORD FOR CERTAIN MOTOR VEHICLE VIOLATIONS, SO AS TO PROVIDE THAT POINTS MUST BE ASSESSED AGAINST THE DRIVING RECORD OF A PERSON CONVICTED OF IMPROPER USE OF AN ELECTRONIC COMMUNICATION DEVICE WHILE DRIVING A MOTOR VEHICLE. H. 4473 (Word version) -- Reps. Limehouse, Brady and Neilson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 63-15-45 SO AS TO PROHIBIT A COURT FROM GRANTING LEGAL CUSTODY TO A PARENT, GUARDIAN, OR ANOTHER PERSON WHO IS REQUIRED TO REGISTER PURSUANT TO THE SEX OFFENDER REGISTRY; AND TO AMEND SECTION 63-7-2350, RELATING TO RESTRICTIONS ON FOSTER CARE PLACEMENTS, SO AS TO RESTRICT THE PLACEMENT OF A CHILD IN FOSTER CARE WITH A PERSON WHO IS REQUIRED TO REGISTER PURSUANT TO THE SEX OFFENDER REGISTRY. H. 3209 (Word version) -- Reps. Cobb-Hunter, Long, Brady and Knight: A BILL TO AMEND SECTION 20-4-60, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO AN ORDER FOR PROTECTION FROM DOMESTIC ABUSE, SO AS TO PROVIDE THAT THE COURT MAY PROHIBIT HARM OR HARASSMENT TO A PET ANIMAL OWNED, POSSESSED, KEPT, OR HELD BY THE PETITIONER AND TO PROVIDE THAT IN ORDERING TEMPORARY POSSESSION OF PERSONAL PROPERTY, THE COURT MAY ORDER THE TEMPORARY POSSESSION OF PET ANIMALS. H. 5104 (Word version) -- Reps. McLeod and Harrison: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 2 TO TITLE 2 SO AS TO REQUIRE ALL TESTIMONY GIVEN TO A COMMITTEE OR SUBCOMMITTEE OF THE GENERAL ASSEMBLY MUST BE UNDER OATH AND TO CREATE THE OFFENSES OF CONTEMPT OF THE GENERAL ASSEMBLY AND CRIMINAL CONTEMPT AND PROVIDE A PENALTY FOR A VIOLATION. H. 5331 (Word version) -- Rep. Atwater: A BILL TO AMEND SECTION 7-7-380, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF PRECINCTS IN LEXINGTON COUNTY, SO AS TO REVISE THE NAMES OF CERTAIN PRECINCTS, TO REDESIGNATE A MAP NUMBER ON WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE DIVISION OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD, AND TO CORRECT ARCHAIC LANGUAGE. H. 5339 (Word version) -- Rep. White: A JOINT RESOLUTION TO PROVIDE THAT THE SCHOOL DAYS MISSED DURING THE PERIOD OF MAY 29, 2012, THROUGH JUNE 1, 2012, BY THE STUDENTS OF CALHOUN ELEMENTARY SCHOOL IN ANDERSON COUNTY WHEN THE SCHOOL WAS CLOSED DUE TO A BROKEN AIR CONDITIONING SYSTEM ARE EXEMPT FROM THE MAKE-UP REQUIREMENT THAT FULL SCHOOL DAYS MISSED DUE TO SNOW, EXTREME WEATHER, OR OTHER DISRUPTIONS BE MADE UP. H. 4093 (Word version) -- Reps. Pope, Sottile, Simrill, Hosey, Williams, Atwater, Quinn, Toole, Huggins, Brannon, Knight, Gambrell, Clyburn, McCoy, Gilliard, Owens, Merrill, Norman, Crawford, Bowers, Murphy, Bedingfield, Bowen, Branham, Chumley, Clemmons, Delleney, Hamilton, Hodges, Loftis, Lowe, D.C. Moss, V.S. Moss, Nanney, J.M. Neal, Ott, Ryan, G.M. Smith, G.R. Smith, J.R. Smith, Spires, Tallon, Taylor, Whitmire, Willis, Neilson and Harrell: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 1-1-715 SO AS TO DESIGNATE THE HONOR AND REMEMBER FLAG AS THE OFFICIAL STATE EMBLEM OF THE SERVICE AND SACRIFICE BY THOSE IN THE UNITED STATES ARMED FORCES WHO HAVE GIVEN THEIR LIVES IN THE LINE OF DUTY. H. 4200 (Word version) -- Reps. Hardwick, Cooper, Clemmons, Frye, Ott, Funderburk, H.B. Brown, Battle, Agnew, McCoy, McEachern, Atwater, Williams, Spires, J.H. Neal, Gilliard, Sabb, Toole, Butler Garrick, Govan, Hiott, Stringer, Ballentine, Murphy, Knight, G.A. Brown, Chumley, Corbin, Crosby, Daning, Dillard, Hixon, Lowe, V.S. Moss, Neilson, Ryan, Willis, Hodges, Whipper, R.L. Brown and Brady: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 46-3-25 SO AS TO REQUIRE THE DEPARTMENT OF AGRICULTURE TO CREATE AND MAINTAIN A PROGRAM TO ENCOURAGE SCHOOLS TO SERVE LOCALLY GROWN, MINIMALLY PROCESSED FARM FOODS. H. 4494 (Word version) -- Reps. Huggins, Long, Pitts, G.R. Smith and Bedingfield: A BILL TO AMEND SECTION 23-31-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PURCHASE OF RIFLES OR SHOTGUNS IN CONTIGUOUS STATES, SO AS TO REMOVE THE REQUIREMENT THAT THE PURCHASE BE MADE FROM A CONTIGUOUS STATE. H. 5150 (Word version) -- Reps. Harrell, Harrison, Sandifer, Lucas, Hardwick, Howard, Clemmons, Ott, Crawford, Bingham, Owens, White and Funderburk: A BILL TO REENACT SECTION 33-44-303, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE LIABILITY OF MEMBERS AND MANAGERS OF LIMITED LIABILITY COMPANIES, AND TO EXPRESS THAT IT IS THE CLEAR AND UNAMBIGUOUS INTENT OF THE GENERAL ASSEMBLY TO SHIELD A MEMBER OF A LIMITED LIABILITY COMPANY FROM PERSONAL LIABILITY FOR ACTIONS TAKEN IN THE ORDINARY COURSE OF THE LIMITED LIABILITY COMPANY'S BUSINESS. H. 4043 (Word version) -- Reps. Tallon, Patrick, Pinson, Allison, V.S. Moss, Atwater, Brannon, Chumley, Bingham, Ballentine, Cole, Horne, Young, Hixon, Clemmons, Toole, Erickson, D.C. Moss and Frye: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 41-35-122 SO AS TO PROVIDE THAT AN EMPLOYER MAY CONFIDENTIALLY NOTIFY THE DEPARTMENT OF EMPLOYMENT AND WORKFORCE WHEN A PROSPECTIVE EMPLOYEE FAILS A DRUG TEST REQUIRED BY THE EMPLOYER AS A CONDITION OF EMPLOYMENT IF THE PROSPECTIVE EMPLOYEE IS RECEIVING UNEMPLOYMENT BENEFITS, TO PROVIDE THE DEPARTMENT SHALL SUSPEND THE BENEFITS OF A PERSON WHO, WHILE RECEIVING BENEFITS, FAILS A DRUG TEST TAKEN AS A CONDITION OF AN APPLICATION FOR EMPLOYMENT, TO PROVIDE THE DEPARTMENT MAY NOT RESTORE THESE SUSPENDED BENEFITS UNTIL THE PERSON HAS SUCCESSFULLY COMPLETED A CERTAIN DRUG TREATMENT PROGRAM AND PASSED A DRUG TEST, TO PROVIDE THE DEPARTMENT MAY NOT PROVIDE OR RESTORE RETROACTIVELY A BENEFIT TO A PERSON FOR A PERIOD IN WHICH HIS BENEFITS ARE SUSPENDED UNDER THIS SECTION, TO PROVIDE THE DEPARTMENT SHALL DEVELOP A CONSENT FORM THAT AN EMPLOYER MAY USE TO OBTAIN THE CONSENT OF A PROSPECTIVE EMPLOYEE TO GIVE THE DEPARTMENT THE RESULTS OF A DRUG TEST REQUIRED BY THE EMPLOYER AS A CONDITION OF EMPLOYMENT, TO PROVIDE THAT THE USE OF THIS CONSENT FORM LIMITS THE LIABILITY OF THE EMPLOYER FOR BREACH OF CONFIDENTIALITY, INVASION OF PRIVACY, INTENTIONAL INFLICTION OF EMOTIONAL DISTRESS, AND DEFAMATION CLAIMS RESULTING FROM THE PROVISION OF THE DRUG TEST RESULTS TO THE DEPARTMENT, AND TO DEFINE A "DRUG TEST". EXECUTIVE SESSION On motion of Senator COURSON, the seal of secrecy was removed, so far as the same relates to appointments made by the Governor and the following names were reported to the Senate in open session: STATEWIDE APPOINTMENTS Confirmations Having received a favorable report from the Banking and Insurance Committee, the following appointment was taken up for immediate consideration: Reappointment, South Carolina State Board of Financial Institutions, with the term to commence June 30, 2012, and to expire June 30, 2016 Credit Union: William Scott Conley, 301 Clearview Drive, Columbia, SC 29212 On motion of Senator THOMAS, the question was confirmation of Mr. Conley. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 0 AYES Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Ford Gregory Grooms Hayes Jackson Knotts Land Leatherman Leventis Malloy Martin, Larry Martin, Shane Matthews McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Total--0 The appointment of Mr. Conley was confirmed. Having received a favorable report from the Banking and Insurance Committee, the following appointment was taken up for immediate consideration: Initial Appointment, South Carolina State Board of Financial Institutions, with the term to commence June 30, 2010, and to expire June 30, 2014 Association of Supervised Lenders: Howard H. Wright, Jr., 1047 Eagle Dr., Rock Hill, SC 29732 VICE Johnathan Foster On motion of Senator THOMAS, the question was confirmation of Mr. Wright. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 0 AYES Alexander Anderson Bright Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Ford Gregory Grooms Hayes Jackson Knotts Land Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Total--0 The appointment of Mr. Wright was confirmed. Having received a favorable report from the Judiciary Committee, the following appointment was taken up for immediate consideration: Reappointment, South Carolina Workers' Compensation Commission, with the term to commence June 30, 2012, and to expire June 30, 2018 At-Large: Henry Gene McCaskill, 604 Kirkwood Circle, Camden, SC 29020 On motion of Senator LARRY MARTIN, the question was confirmation of Mr. McCaskill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 32; Nays 0; Abstain 9 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Courson Cromer Fair Ford Gregory Grooms Jackson Knotts Leatherman Leventis Lourie Martin, Larry Martin, Shane Matthews McGill Nicholson O'Dell Peeler Pinckney Reese Ryberg Scott Shoopman Verdin Williams Total--32 NAYS Total--0 ABSTAIN Coleman Davis Hayes Land Malloy Rankin Setzler Sheheen Thomas Total--9 The appointment of Mr. McCaskill was confirmed. Having received a favorable report from the Medical Affairs Committee, the following appointment was taken up for immediate consideration: Initial Appointment, South Carolina State Board of Nursing, with the term to commence December 31, 2010, and to expire December 31, 2014 2nd Congressional District: Amanda E. Baker, 141 Montrose Drive, Lexington, SC 29072 VICE Rose Kearney-Nunnery On motion of Senator PEELER, the question was confirmation of Ms. Baker. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 40; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Ford Grooms Hayes Jackson Knotts Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--40 NAYS Total--0 The appointment of Ms. Baker was confirmed. Having received a favorable report from the Medical Affairs Committee, the following appointment was taken up for immediate consideration: Initial Appointment, Medical Disciplinary Commission of the State Board of Medical Examiners, with the term to commence July 1, 2011, and to expire July 1, 2014 4th Congressional District: Patricia Jane Bock, 110 Creekwood Drive, Spartanburg, SC 29302 On motion of Senator PEELER, the question was confirmation of Ms. Bock. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 40; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Ford Gregory Grooms Hayes Jackson Knotts Leatherman Leventis Malloy Martin, Larry Martin, Shane Massey Matthews McGill O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--40 NAYS Total--0 The appointment of Ms. Bock was confirmed. LOCAL APPOINTMENTS Confirmations Having received a favorable report from the Senate, the following appointments were confirmed in open session: Reappointment, York County Natural Gas Authority, with the term to commence March 1, 2012, and to expire March 1, 2015 York County: Clyde O. Smith, Post Office Box 336, York, SC 29745 Reappointment, York County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 David S. Wood, 957 Copperstone Lane, Fort Mill, SC 29708 Initial Appointment, Richland County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 Ethel L. Brewer, 4201 Donavan Drive, Columbia, SC 29210 Initial Appointment, Richland County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 Barbara Jo Wofford-Kanwat, 2009 Green Street #206, Columbia, SC 29205 Initial Appointment, Clarendon County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Robin C. Locklear, Post Office Box 551, Manning, SC 29102 VICE Judge Aycock (retired) On motion of Senator COURSON, with unanimous consent, the Senate agreed that, when the Senate adjourns today, it stand adjourned to meet at 10:00 A.M. tomorrow. At 7:35 P.M., Senator COURSON moved that the Senate stand adjourned. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 23; Nays 21 AYES Anderson Cleary Coleman Courson Elliott Ford Hutto Jackson Leatherman Leventis Lourie Malloy Martin, Larry Matthews Nicholson Pinckney Rankin Reese Ryberg Scott Setzler Sheheen Williams Total--23 NAYS Alexander Bright Bryant Campbell Campsen Cromer Davis Fair Gregory Grooms Hayes Knotts Martin, Shane Massey McGill O'Dell Peeler Rose Shoopman Thomas Verdin Total--21 On motion of Senator WILLIAMS, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mrs. Angela Smith of Columbia, S.C., beloved wife of William Smith, Presiding Elder of the Marion District of the African Methodist Church. and On motion of Senator HUTTO, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mr. Franklin Grady Shuler, father-in-law of Jane Shuler, Attorney to the Judicial Merit Selection Commission. Mr. Shuler was the beloved husband of 64 years to Earlyne Mattox Shuler, devoted father of five and doting grandfather of ten and great-grandfather of five. Mr. Shuler was a pharmacist in Orangeburg and with the Upjohn Company until his retirement in 1987. While he was with the Upjohn Company, he became a medical science liaison helping to establish clinical studies of new medications. He was a member of the Board of Directors of the American Diabetes Association, was active in community service and will be sorely missed by family and friends. and	2016-02-09 03:25:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2999953031539917, "perplexity": 10325.880846613372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701156448.92/warc/CC-MAIN-20160205193916-00194-ip-10-236-182-209.ec2.internal.warc.gz"}
https://techutils.in/blog/2020/08/23/stackbounty-probability-modeling-fitting-mixture-categorical-mixture-model-when-mixture-components-are-not-pdfs-dont-sum-to-3/	# #StackBounty: #probability #modeling #fitting #mixture Categorical mixture model when mixture components are not PDFs (don't sum to… ### Bounty: 50 I constructed a model that behaves the way I want, it successfully recovers parameters from simulated data, etc. However, I get the feeling that I re-invented the wheel, so to speak – surely someone has come across this problem before, solved it, there is someone I can cite, some name for the technique, some better way to do it, etc. I have observations $$Y={y_{is}}$$, where $$sin{1,ldots,S}$$ indicates a particular site, and $$i$$ indexes observations within a site $$s$$. Each $$y_{is}$$ takes one of $$C$$ possible labels: $$y_{is} in {1,ldots,C}$$. The probability that $$y_{is}=c$$ is influenced by $$K$$ different categorical predictors, where each $$k$$ gives a probability distribution for the labels $$C$$ for each site $$s$$, i.e. $$theta_{k,s}=(theta_{k,s,1},ldots,theta_{k,s,C})$$ is a probability distribution at site $$s$$ over the labels $$C$$. All $$theta$$ are known; the only unknown is how likely it is that $$y_{is}$$ was drawn from $$theta_k$$. At this point, it sounds like a typical mixture distribution, in which $$alpha_k$$ is the mixture proportion (i.e., the probability that you draw from $$theta_k$$): $$P(y_{is}=cmidTheta) = sum_{k=1}^K alpha_ktheta_{k,s,c}$$ $$sum_{k=1}^Kalpha_k=1$$ However, for a mixture distribution to work, each $$theta$$ is a PDF, such that $$sum_{c=1}^Ctheta_{k,s_i,c}=1$$, but in my case $$sum_{c=1}^Ctheta_{k,s_i,c} in [0,1]$$. Since $$y_{is}in C$$ but it is possible that $$sum_{c=1}^CP(y_{is}=cmidTheta)<1$$, this model clearly does not work. The model I have come up with that works as intended is as follows: $$P(y_{is}=cmidTheta) = frac{sum_{k=1}^K beta_ktheta_{k,s_i,c}}{sum_{k=1}^K sum_{c=1}^C beta_ktheta_{k,s_i,c}},$$ $$beta_1=1$$ I can use MLE or grid search to fit $$(beta_2,ldots,beta_K$$). Intuitively, I think of this in a sort of neural network-ey way, where $$theta_{k,s,c}$$ is the probability that at site $$s$$, neuron $$k$$ will cause neuron $$c$$ to fire, $$beta_k$$ is the rate at which a $$k$$-type neuron fires, and each $$y_{is}$$ is a single sample from the action potentials of $$C$$-type neurons at site $$s_i$$. So, does what I did have a name/literature behind it? Alternatively, can my problem be solved using some other technique (e.g. some sort of Dirichlet-multinomial regression or something…) that is citeable/has been well-characterized/etc.? Edit: here’s a toy example with numbers: Let: $$C in {red,green,blue}$$ $$K in {pencil,pen}$$ $$S in {wall, table}$$ $$theta_{wall,pencil}=[0.2,0.4,0.4], theta_{wall,pen}=[0.8,0.1,0.1],$$ $$theta_{table,pencil}=[0,0,0.1], theta_{table,pen}=[0.3,0.3,0.4]$$ Notice that $$theta_{table,pencil}$$ does not sum to 1; imagine that e.g. $$theta_{table,pencil,orange}=0.9$$, but $$C$$ cannot be orange. In my desired model, when the "mixture-like" parameters for $$theta$$ are equal to the same value (i.e. when $$beta_{pencil}=beta_{pen}$$), then I want the distribution of $$C$$ at $$wall$$ to be [0.5,0.25,0.25], and the distribution of $$C$$ at $$table$$ to be [0.2727,0.2727,0.4546]. If $$beta_{pencil}=2beta_{pen}$$, then I want the distribution of $$C$$ at $$wall$$ to be [0.4,0.3,0.3], and the distribution of $$C$$ at $$table$$ to be [0.25,0.25,0.5]. Get this bounty!!! This site uses Akismet to reduce spam. Learn how your comment data is processed.	2020-09-28 03:21:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 58, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8690533638000488, "perplexity": 416.2754337202528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401583556.73/warc/CC-MAIN-20200928010415-20200928040415-00027.warc.gz"}
https://github.com/keepassxreboot/keepassxc/issues/197	# Saving DB fails intermittently on windows #197 Closed opened this Issue Jan 25, 2017 · 36 comments Projects None yet ## Current Behavior Most of the time, attempting to save a database file on windows fails with this message: Writing the database failed. The Process cannot access the file because it is being used by another process. A copy of the DB file is written at \path\to\db.kdbx.<2 random? letters><PID> Occasionally, the write does go through without an error. ## Steps to Reproduce (for bugs) I have not yet been able to reproduce the error with a fresh database created with either keepassxc or keepassX. Obviously, I'm not willing to upload one of my real DBs. ## Context Process Explorer reports no other process has a handle to the .kdbx file. • KeePassXC version/commit used: 42c0815 • Qt version 5.6.2 • Compiler: gcc version 6.3.0 (Rev1, Built by MSYS2 project) • Operating System and version: Windows 7 SP1 Member ### droidmonkey commented Jan 26, 2017 What is the origin of your original DB that caused this error? Was it created in KeePass or some other program? The reason why this error is thrown is for three distinct reasons: Cannot open the file for writing Cannot write to the IOStream for some reason Cannot commit the changes to the file AFTER writing to the IOStream ### mattvchandler commented Jan 26, 2017 • edited Originally created in KeepassX 0.4 imported into KeepassX 2.x ### mattvchandler commented Jan 26, 2017 I deleted all entries from the problematic DB and see the same error with the now empty DB. See attached. master pw is 'asdf' test.zip Member ### droidmonkey commented Jan 26, 2017 No problems for me under Windows 10 64-bit ### dsbert commented Jan 30, 2017 • edited I'm experiencing this same issue. Windows 7 64 bit. This may be due to keepass not playing well with other file watchers. I have my database file in a drop box share. If I move the file outside of that share, I don't see the errors anymore. I did not experience these issues on KeepassX ### mattvchandler commented Jan 30, 2017 I have my problematic files in Dropbox too. That seems to be the key. I can reproduce the problem consistently with a new database file saved in Dropbox, and the problem stops when Dropbox is off or the file is moved outside it. … On 1/30/2017 9:51 AM, Dan wrote: I'm experiencing this same issue. Windows 7 64 bit. This may be due to keepass not playing well with other file watchers. I have my database file in a drop box share. If I move the file outside of that share, I don't see the errors anymore. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#197 (comment)>, or mute the thread . Member ### droidmonkey commented Jan 30, 2017 Interesting, I store mine in Google Drive (and previously OneDrive) and have not had any issues. I will test with dropbox. Member ### phoerious commented Jan 30, 2017 I don't have issues with Nextcloud/OwnCloud (i.e., csync), either. Closed ### Dunkh4n commented Feb 27, 2017 • edited Hi, Just to say that i have the same problem.. Dropbox or GoogleDrive.. I want to use KeePassxc instead off KeePass, but i can't because off this bug :( ### dsbert commented Mar 30, 2017 This is still a problem in version 2.1.3. However, it seems like it might not be happening quite as often. Member ### droidmonkey commented Apr 3, 2017 So I came upon this issue with a slow upload to google drive... seems like when these cloud providers are syncing the file they hold a lock on it. This prevents KeePassXC from writing to the file (naturally). There is really nothing we can do about it... ### dsbert commented Apr 3, 2017 How do other programs handle this behavior? How does Keepass 2? Is it silently failing in the background and just not notifying me? It is trying to save multiple times before it raises an error? I understand there are difficult issues when integrating with third-party applications. However, I feel like there is definitely more that could be done to smooth this out. I know this is an open source program (and everything that implies), but I hope this issue isn't just closed as 'not fixable'. … On Sun, Apr 2, 2017 at 11:57 PM Jonathan White *@.**> wrote: So I came upon this issue with a slow upload to google drive... seems like when these cloud providers are syncing the file they hold a lock on it. This prevents KeePassXC from writing to the file (naturally). There is really nothing we can do about it... — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#197 (comment)>, or mute the thread . Member ### droidmonkey commented Apr 3, 2017 • edited I found that waiting for the upload to complete worked great. Other than that I am out of ideas... unless we are being too strict when we try to write to a file? Trying multiple times or waiting a delay doesn't seem to be a good solution to me. I don't know what other programs do, perhaps you can experiment for us? https://github.com/keepassxreboot/keepassxc/blob/develop/src/gui/DatabaseTabWidget.cpp#L348 That is where the database file is actually saved. I'll run this in debug mode and see which block it fails in. ### netforhack commented Apr 9, 2017 • edited The same issue, also what is this ? ### netforhack commented Apr 11, 2017 @droidmonkey seems that keepass2 works with copy of original db file ".lock", to save it delete original db file and rename .lock to original db file name ### SemyonDragunov commented May 4, 2017 • edited I have problem too. Win7 64bit. Dropbox sync is enabled - DB no save (save many files.). Disabled - Normal Save. KeePassXC 2.1.4 ### tronjs commented May 5, 2017 I have the same problem Member ### phoerious commented May 14, 2017 • edited I would assume that this is a Windows-only problem due to the fact that Windows is the only OS that grants and requires exclusive file access. I'm not sure what we can do about it. Closed ### JaggedJax commented Jul 25, 2017 • edited I get this same issue with the kdbx file sitting in a dropbox folder on Windows 8.1 x64. Even after the file has been synced by Dropbox I cannot save in KeePass XC and it just keeps creating new temporary DB files in the folder every time it tries to save. edit: Note that closing KeePass XC and opening KeePass 2, it does not have trouble writing to this same file under the same scenario so it seems to be more than just an exclusive windows file lock since other applications can write to the file. Member ### droidmonkey commented Jul 26, 2017 We probably make the wrong checks for writability which result in false negatives ### felixkopf commented Sep 2, 2017 Same issue here. I figured out, that when I click "Save" or press CTRL+S two times quickly in a row, it works. The first attempt fails with the error message and a new .kdbx.'something'-File is created in my Dropbox. ### tooor commented Sep 10, 2017 Windows 10 64-bit experiencing 100% reproducible behavior when I do the following: Have Dropbox running Store my DB file in Dropbox folder Try to save DB file. Problem is immediately fixed without restarting keypassxc when I close Dropbox, then try to save again. So my temporary solution is just close Dropbox when I can't save the DB, then start Dropbox again to sync my newest version of DB to cloud. ### jask05 commented Sep 14, 2017 Hi, I have the same problema like @tooor. Are there any workaround? Thanks! Contributor ### rockihack commented Sep 16, 2017 Probably a qt bug. QSaveFile uses a temporary file without exclusive lock. https://bugreports.qt.io/browse/QTBUG-57299 ### snospar commented Sep 16, 2017 • edited I can confirm the same issue when using Windows 10 and opening the kdbx file from my NAS (drive mapped using SMB). Bizarrely, if I click multiple times on the Save button it will work - I hear the NAS update the file (the disk chunters) and when I shut the application it knows that the file has been saved so doesn't prompt. I've never had this issue when accessing the same kdbx file from the same NAS when using Linux on the same dual boot machine. Open ### andreas-profitlich commented Nov 4, 2017 same problem (Windows 10, Dropbox) - this is a blocker guys ### krizian commented Nov 13, 2017 • edited same problem here for three Windows PCs in a private network with NAS Server (1x Windows 7, 2x Windows 10). Autosave doesn't save. We can't use KeepassXC till this issue is solved. Agreeing to andreas-profitlich: this is a real blocker! If the save Button is clicked manually a second time it will work. As we need a DB and synchronisation, this is no option. Member ### droidmonkey commented Nov 13, 2017 The use case of a shared database among multiple users was not programmed into this app. I consider a file sync service as a multiple user in this context. It is technically not a blocker since there is a workaround (click save till it works). With that said its on my short list to fix. ### 5paceToast commented Nov 13, 2017 @droidmonkey the FAQ gives an impression that using a file sync service (to synchronize the same db accross multiple machines of a single user, as in this issue) isn't just supported, but is recommended. Maybe it makes sense to modify the FAQ to reflect the original intent in this case? Furthermore, spamming save seems relatively inconsistent (e.g in my testing I've never managed to get it to sync, even after a full minute of clicking), so I wouldn't really consider it a real workaround (that's not to mention the lock-file per-click that gets created (and therefore synced)). Member ### TheZ3ro commented Nov 13, 2017 @5paceToast he is referring to KeePassX, originally it wasn't developed with syncing in mind. Now it's a requirement. We are wrapping up features such as sync, auto-reload and auto-merge trying to make the sync process easy, transparent and multi-platform. The FAQ are fine ### 5paceToast commented Nov 13, 2017 Ah, ok. Thanks for clearing that up :) ### krizian commented Nov 14, 2017 • edited @TheZ3ro @droidmonkey is the plan to keep the principle of using one file and copy features such as sync and auto-merge from Keepass, or would it be possible to create a real db with sync features like e.g. a sql db ? In Keepass auto-reload was missing for daily multi-user use. Thank you in advance! : ) Member ### droidmonkey commented Nov 20, 2017 Will be worked on in conjunction with #1002 Closed ### sdidit commented Dec 13, 2017 It seems to me the problem is caused by the temporary file. If Google Drive starts to sync the temporary file before it is renamed, the rename will fail. I'm then left with a temporary file and no database file. The problem happens more often now that Google has updated their sync utility. Member ### droidmonkey commented Dec 13, 2017 • edited Perhaps the temp file should be created in the tmp directory then moved into the appropriate location afterwards. ### sdidit commented Dec 13, 2017 It's more an issue of Backup and Sync. Other applications that create temporary files have the same problem with Google Drive. There's an option to ignore certain file extensions, but that only applies to the backup function, not the sync function. Merged Closed Closed	2018-11-17 18:28:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3031206727027893, "perplexity": 3403.06503737415}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743717.31/warc/CC-MAIN-20181117164722-20181117190722-00455.warc.gz"}
http://mathoverflow.net/feeds/question/15050	Linear Algebra Problems? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T02:08:12Z http://mathoverflow.net/feeds/question/15050 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/15050/linear-algebra-problems Linear Algebra Problems? zeb 2010-02-11T23:30:30Z 2012-03-03T22:16:29Z <p>Is there any good reference for difficult problems in linear algebra? Because I keep running into easily stated linear algebra problems that I feel I <em>should</em> be able to solve, but don't see any obvious approach to get started.</p> <p>Here's an example of the type of problem I am thinking of: Let $A, B$ be $n\times n$ matrices, set $C = AB-BA$, prove that if $AC=CA$ then $C$ is nilpotent. (I saw this one posed on the KGS Go Server)</p> <p>Ideally, such a reference would also contain challenging problems (and techniques to solve them) about orthogonal matrices, unitary matrices, positive definiteness... hopefully, all harder than the one I wrote above.</p> http://mathoverflow.net/questions/15050/linear-algebra-problems/15051#15051 Answer by Jonas Meyer for Linear Algebra Problems? Jonas Meyer 2010-02-11T23:34:44Z 2010-02-11T23:48:05Z <p><a href="http://books.google.com/books?id=DQP3AIlrCP0C&lpg=PP1&client=firefox-a&pg=PP1#v=onepage&q=&f=false" rel="nofollow">Halmos's Linear Algebra Problem Book</a>. It contains problems, then hints, then solutions. There is a variety of difficulty levels, and some of the problems are very easy, but some are challenging. The book is designed to be a supplement for learning linear algebra by problem solving, so it may not have the focus you're looking for.</p> http://mathoverflow.net/questions/15050/linear-algebra-problems/15053#15053 Answer by Wanderer for Linear Algebra Problems? Wanderer 2010-02-11T23:38:07Z 2010-02-11T23:38:07Z <p>Indeed, Halmos is a very good reference. You will also find some nice problems in <a href="http://www.amazon.com/Berkeley-Problems-Mathematics-Paulo-Souza/dp/0387008926" rel="nofollow">Berkeley problems in mathematics</a> and on the website of the <a href="http://www.imc-math.org/" rel="nofollow">International Mathematics Competition</a></p> http://mathoverflow.net/questions/15050/linear-algebra-problems/15054#15054 Answer by Mariano Suárez-Alvarez for Linear Algebra Problems? Mariano Suárez-Alvarez 2010-02-11T23:40:01Z 2010-02-11T23:40:01Z <p>Google will find for you V. Prasolov's <em>Problems and Theorems in Linear Algebra</em>, which has beautiful more or less hard problems.</p> http://mathoverflow.net/questions/15050/linear-algebra-problems/15120#15120 Answer by Portland for Linear Algebra Problems? Portland 2010-02-12T15:30:10Z 2010-02-12T15:30:10Z <p>In addition to those mentioned above, there is <em>Linear Algebra: Challenging Problems for Students</em> by Fuzhen Zhang </p> http://mathoverflow.net/questions/15050/linear-algebra-problems/15130#15130 Answer by Alekk for Linear Algebra Problems? Alekk 2010-02-12T16:49:27Z 2010-02-12T16:49:27Z <p>you could also browse the linear algebra section of <a href="http://www.mathlinks.ro/index.php?f=349" rel="nofollow">AoPS</a>.</p> http://mathoverflow.net/questions/15050/linear-algebra-problems/17042#17042 Answer by Sunni for Linear Algebra Problems? Sunni 2010-03-04T02:09:03Z 2010-03-04T02:09:03Z <p>Let me introduce you a good reference, IMAGE. At the end of IMAGE there is a section called IMAGE Problem Corner: Solutions of Old Problems and New Problems. You may enjoy solving these problems and read solutions by others. See <a href="http://www.math.technion.ac.il/iic/IMAGE/" rel="nofollow">http://www.math.technion.ac.il/iic/IMAGE/</a></p> http://mathoverflow.net/questions/15050/linear-algebra-problems/90144#90144 Answer by Gerhard Paseman for Linear Algebra Problems? Gerhard Paseman 2012-03-03T20:10:41Z 2012-03-03T20:10:41Z <p>I will take this opportunity to post my favorite linear algebra problem. I call it 0 not equal to 1.</p> <p>Let A be an nxn 0-1 matrix with nonzero determinant. Show that there is a 1 in every row and in every column of A, and further there is a permutation matrix P so that PA has a diagonal of all 1's.</p> <p>Let B be an nxn 0-1 matrix with nonzero determinant. We cannot show that there is a 0 in every row and in every column, so assume B also has this property. Are there nxn permutation matrices P and Q such that PBQ has all 0's on the diagonal? If not, how small a trace can one guarantee?</p> <p>Gerhard "Ask Me About System Design" Paseman, 2012.03.03 </p> http://mathoverflow.net/questions/15050/linear-algebra-problems/90155#90155 Answer by Federico Poloni for Linear Algebra Problems? Federico Poloni 2012-03-03T22:16:29Z 2012-03-03T22:16:29Z <p>If you happen to know a little bit of Italian, another good resource is <em>Problemi risolti di algebra lineare</em>, by Broglia, Fortuna, Luminati.</p> <p>(By the way, if you have never done it, reading a math book in another language is often easier than it seems at first sight)</p>	2013-05-26 02:08:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7433342337608337, "perplexity": 1700.0243427147038}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706484194/warc/CC-MAIN-20130516121444-00085-ip-10-60-113-184.ec2.internal.warc.gz"}
https://powershell.org/forums/topic/list-ad-groups-members-count-of-ad-membership-per-person-of-specific-ad-groups/	Welcome Forums General PowerShell Q&A List AD Groups, members, count of AD membership per person of specific AD Groups • This topic has 6 replies, 2 voices, and was last updated 9 months ago by Participant . • Author Posts • #222216 Participant Topics: 1 Replies: 2 Points: -4 Rank: Member Dear PowerShell.org community This is my first post, so hopefully I have not missed anything. I have hit brick wall on the next step to troubleshoot. In a nut shell what I am trying to achieve is to list Active Directory Group Name that starts with the prefix of AXCH (as an example) list the username\members in these Active Directory Groups and finally the count of many AD Group membership per person\user for AD groups starting with the prefix of AXCH. (AXCH is a made up example) Some of the script is working, and getting the result I need it is just the final part, of getting the count command to work to count how many AD groups per individual user is a member of any AD group starting with the name of AXCH. Below is the script So what this script s doing is from the top, find AD group that match\begin with the name of AXCH (made up name), then using the variable of $adgroups use a “for each” command to find nested ad groups and members. The script is working up to a point and I can export to the screen or into a CSV file. The problem I am facing if the line highlighted in RED also pasted below Basically I thought by using the command, would count how many AD groups per individual user is a member of any AD group starting with the name of AXCH. Instead the command returns the count value of 1. Which I guess when I think about makes sense as it is counting the member name of the AD groups starting with AXCH and you can only have one AD account with the same name in one group. Which is perhaps I am thinking I need to do a different command, hence why I am making my first post in here. So to clarify for example made up username called “Joe blogs” exist in several AD groups that have the prefix of AXCH (again made up AD group name) so he is a member of AXCH-1 \ AXCH-2 \ AXCH-3 & AXCH-4 what I would like is for a command to count those 4 AD groups and give me a return value of 4 against his user name, as he is a member of 4 AD groups. At the moment my scripts returns the value of 1 even though he is a member of multiple AD groups. If anyone could help with a command I could add to my script, or if I have to create a new script all together just so I can create a report that list the AD Group, the individual member\username, and then count value of how many AD Groups membership per member for AD groups starting with the prefix of AXCH Many Thanks for taking the time to read this post. Best Paul • #222282 Participant Topics: 10 Replies: 2480 Points: 6,537 Rank: Community MVP Paul, welcome to Powershell.org. If I got it right it might be better/easier to run 2 separate queries to get the info you’re after. • #222399 Participant Topics: 1 Replies: 2 Points: -4 Rank: Member Hi Olaf Firstly thank you very much for taking the time to read and reply to my post, it is much appreciated, I am definitely further then I was, and enjoyed understanding how you would script something. Hit a problem with the final part of the script for the line It gives the following error message when the script run as a whole So EXCH is the filter I am using for the variable for$Pattern to find AD Groups that begin with EXCH. All the other parts of the scripts work fine and gets the results needed. From the trouble shooting I have done so far is if I change the command below to just use .count I get further and it actually count each user ad group members but for All AD groups not just ones that start with EXCH. It seems to not like the variable of $Pattern if I change the command to use the below command, it run without error but I get no AD group Count. I find it a bit odd as the first section of the script runs for the$GroupStatistics section, which uses that variable of \$Pattern so it is unclear why it fails to use this variable for the second part of the script. So to re-iterate the only part that is failing in the script is getting the ADGroupCount for specific groups that start with EXCH Is there anything you can suggest \ troubleshooting steps \ alternative command. Many thanks Paul • #222402 Participant Topics: 10 Replies: 2480 Points: 6,537 Rank: Community MVP Paul, … sorry .. stupid me. Of course I tested the code but of course with another pattern. One that could provide results in my environment. Then I copied the code here and just changed it to fit your need by just taking your pattern. When you use the operator -match then you’re using regular expressions and for regular expressions the asterisk () is a special charachter. And you your case we actually do not need it at all. So try to change your pattern to be ‘EXCH’ instead of ‘EXCH’ and it should work (I hope). • #222408 Participant Topics: 10 Replies: 2480 Points: 6,537 Rank: Community MVP I’m afraid to edit my already existing post because they often get blocked when editted again. So here an additional explanation. As I mentioned the asterisk () is a special charachter when it comes to regular expressions. In particular it means “whatever comes before the asterisk should appear 0 or more times”. So it’s shorthand for the quantifier “{0,} In your case there is nothing before the asterisk. That’s why the error “… Quantifier {x,y} following nothing.” raises. If you like to read more about regular expressions – here is a good place to start: https://www.regular-expressions.info • #222465 Participant Topics: 1 Replies: 2 Points: -4 Rank: Member Hi Olaf Many Thanks for your reply, that did the trick able to produce the report I needed. Also thank you for the providing documentation on regular expressions \ study material as that was going to be my next question. Are there any good online courses \ websites \ books you recommend to learn power shell? I am currently going through online courses by Don Jones \ Jeff Hicks \ Michael Bender. It is helping but would you recommend any sites \ material that really help you get to your level \ anything you would recommend? Many Thanks Again Paul • #222477 Participant Topics: 10 Replies: 2480 Points: 6,537 Rank: Community MVP I am currently going through online courses by Don Jones \ Jeff Hicks \ Michael Bender. It is helping but would you recommend any sites \ material that really help you get to your level \ anything you would recommend? I work with Powershell for about 13 years now. The most experience comes with time. For beginners I usually recommend the beginner video course with Jeffrey Snover but I think your level is already above that. A free book to look something up if needed could be this: Windows PowerShell™ 4: TFM. I think the best way to get better is practice practice practice. 😉	2021-01-25 15:01:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2934952974319458, "perplexity": 1920.6588995587708}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703581888.64/warc/CC-MAIN-20210125123120-20210125153120-00044.warc.gz"}
https://www.shaalaa.com/question-bank-solutions/the-estimated-tax-income-shreemati-hinduja-rs-8000-how-much-education-cess-has-she-pay-3-arithmetic-progressions-examples-and-solutions_50685	# The Estimated Tax on the Income of Shreemati Hinduja is Rs. 8000. How Much Education Cess Has She to Pay at 3% ? - Algebra The estimated tax on the income of Shreemati Hinduja is Rs. 8000. How much education cess has she to pay at 3% ? #### Solution 8000 × 3/100 = Rs. 240 Is there an error in this question or solution?	2021-04-15 18:24:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36893072724342346, "perplexity": 9318.691558377572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038087714.38/warc/CC-MAIN-20210415160727-20210415190727-00175.warc.gz"}
https://www.physicsforums.com/threads/su-2-axial-and-vector-subgroups.587244/	# SU(2) axial and vector subgroups 1. Mar 15, 2012 ### LAHLH Hi, Could someone explain to me how to split SU(2) into its axial and vector subgroups, what does this mean? (The context I'm trying to understand this in is the U(2)_L x U(2)_R global flavour sym of chiral Lagrangian) A related question: I know that the three axial generators of SU(2)_L x SU(2)_R get broken, and this leads to the three (pesudo)-goldstone bosons; the three pions. But why are there three axial generators of this group? thanks Last edited: Mar 15, 2012 2. Mar 16, 2012 ### blechman The group SU(2)_L x SU(2)_R has 6 generators $T^a_L, T^a_R$ (a=1,2,3). We can also use generators $T^a_L + T^a_R$ and $T^a_L - T^a_R$. The first one generates SU(2)_V and the second one generates SU(2)_A. So you can think of vector and axial symmetries as a change of basis of SU(2)^2. The axial generators are the broken ones in QCD, giving rise to the 3 pions. Note that your question as phrased: "how to split SU(2) into its axial and vector subgroups?" makes no sense, as a SINGLE SU(2) doesn't have such a decomposition. 3. Mar 16, 2012 ### naima Hi Blechman, Could you tell me why with addition of these generators the group is "vectorial" and "axial" with subtraction ? Thanks 4. Mar 16, 2012 ### blechman "Vector" means L and R fermions transform the same way: $$\psi_L\longrightarrow e^{i\alpha^aT_L^a}\psi_L,\qquad\psi_ R\longrightarrow e^{i\alpha^aT_R^a}\psi_R$$ Hence + sign. "Axial" means L and R fermions transform oppositely: $$\psi_L\longrightarrow e^{i\alpha^aT_L^a}\psi_L,\qquad\psi_ R\longrightarrow e^{-i\alpha^aT_R^a}\psi_R$$ Hence - sign. 5. Mar 16, 2012 ### naima thanks I accept your answer but what is the relationship with the usual definition of vectors and pseudovectors. I'm sorry if this is obvious. 6. Mar 16, 2012 ### samalkhaiat The word “Axial” indicates the presence of $\gamma_{5}$ in the transformation law. Consider the following axial transformation of a fermion field with TWO FLAVOURS; $$\Psi \rightarrow U_{5}\Psi \equiv \exp (i \frac{\epsilon . \tau}{2}\gamma_{5}) \Psi . \ \ (1)$$ In this, $\gamma_{5}$ operates on the Dirac components of $\Psi$, while Pauli’s matrices $\tau^{i}$ operate on the internal 2-dimensional flavour space of the fermions. We may call this group $SU(2)_{5}$. This transformation takes on a simple form when expressed in terms of the chiral components of $\Psi$. That is $$\Psi_{R}\rightarrow V \Psi_{R} \equiv \exp( i \frac{\epsilon . \tau}{2}) \Psi_{R},$$ $$\Psi_{L}\rightarrow V^{\dagger}\Psi_{L} \equiv \exp( - i \frac{\epsilon . \tau}{2}) \Psi_{L}.$$ This can be shown by expanding eq(1) in a power series, and using the following $$\Psi = \Psi_{R} + \Psi_{L},$$ $$\gamma_{5}\Psi = \Psi_{R} - \Psi_{L}.$$ So, the $8 \times 8$ transformation matrix $U_{5}$ can be written as $$U_{5} = VP^{+} + V^{\dagger}P^{-}\ \ \ (2),$$ where $$P^{\pm} = \frac{1}{2}(1 \pm \gamma_{5}),$$ are projection operators. From eq(2), it follows that $$\gamma^{\mu}U_{5}= U^{\dagger}_{5}\gamma^{\mu}.$$ This means that $\Psi$ and $\bar{\Psi}$ transform in the same way, $$\Psi \rightarrow U_{5}\Psi,$$ $$\bar{\Psi}\rightarrow \bar{\Psi}U_{5}.$$ Thus, chirally invariant Lagrangian must be constructed out of massless fermions; the presence of a small fermion mass term provides a mechanism for breaking chiral symmetry. Since our fermion field has two flavours, the theory must also be invariant under the global group $SU(2)$. So, the total symmetry group is $SU(2) \times SU(2)_{5}$. This group is equivalent to $SU(2)_{L}\times SU(2)_{R}$ with element $$U_{L}U_{R}= \exp(i\frac{\epsilon_{L}.\tau}{2}P^{-}) \exp( i \frac{\epsilon_{R}.\tau}{2}P^{+}),$$ where $\epsilon_{L}$ and $\epsilon_{R}$ are the independent parameters. To see the equivalence, let $\Psi_{L}= P^{-}\Psi$, and $\Psi_{R}= P^{+}\Psi$ be associated with the (finite dimensional) irreducible representations of Lorentz group $(1/2,0) \oplus (1/2,0)$ and $(0,1/2) \oplus (0,1/2)$, respectively. The transformations under two commuting $SU(2)$ groups are $$(2,1) \in SU(2)_{L}:$$ $$\Psi_{L}\rightarrow U_{L}\Psi_{L}\equiv \exp( i\frac{\epsilon_{L}.\tau}{2})\Psi_{L},$$ $$\Psi_{R}\rightarrow \Psi_{R},$$ which can be combined into $$\Psi \rightarrow e^{i\frac{\epsilon_{L}.\tau}{2}} \frac{1}{2}(1 - \gamma_{5})\Psi + \frac{1}{2}(1 + \gamma_{5})\Psi,$$ or $$\Psi \rightarrow \exp(i\frac{\epsilon_{L}.\tau}{2}P_{-})\Psi .$$ $$(1,2) \in SU(2)_{R}:$$ $$\Psi_{L}\rightarrow \Psi_{L},$$ $$\Psi_{R}\rightarrow U_{R}\Psi_{R} = \exp( i\frac{\epsilon_{R}.\tau}{2})\Psi_{R},$$ which we can write as $$\Psi \rightarrow \exp(i\frac{\epsilon_{R}.\tau}{2}P^{+})\Psi$$ Therefore, the combined $SU(2)_{L}\times SU(2)_{R}$ transformation is given by $$\Psi \rightarrow U_{L}U_{R}\Psi = \exp[i(\epsilon_{L}P^{-} + \epsilon_{R}P^{+}) . \frac{\tau}{2}] \Psi . \ \ \ (3)$$ If we define $$\alpha = \frac{1}{2}(\epsilon_{R} + \epsilon_{L}),$$ $$\epsilon = \frac{1}{2}(\epsilon_{R} - \epsilon_{L}),$$ then, the $SU(2)_{L}\times SU(2)_{R}$ element $U_{L}U_{R}$ becomes $$U_{L}U_{R} = \exp(i\frac{\alpha . \tau}{2}) \exp(i\frac{\epsilon . \tau}{2}\gamma_{5}),$$ which belongs to the original symmetry group $SU(2) \times SU(2)_{5}$. The meaning of chiral symmetry is, according to eq(3), the statement that an $SU(2)$ symmetry can be INDEPENDENTLY realized on the two subspaces projected out by the $P^{\pm}$ operators, i.e., the transformations on these two spaces can have different parameters. Regards Sam Last edited: Mar 16, 2012 7. Mar 17, 2012 ### Hans de Vries In the essence it's simple: The two chiral components $\psi_L$ and $\psi_R$ have some similarities with left and right circular polarized photons. Independently they propagate at the speed of light, however if you couple them together then the combined momentum is the sum of the two individual momenta and the resulting propagation speed of the particle can be anywhere between +c and -c. For the combined momentum one first calculates the individual momenta. $\psi_L\tilde{\sigma}^\mu\psi_L$ and $\psi_R\sigma^\mu\psi_R$ The sum of these two is the combined momentum, a vector. However $\psi_L\tilde{\sigma}^\mu\psi_L$ is also a measure for left handedness while $\psi_R\sigma^\mu\psi_R$ is a measure for right handedness. This means that when you subtract the two you get their combined "handedness", which is an axial vector. Regards, Hans 8. Mar 17, 2012 ### naima It just remains for me to make a synthesis of these aspects! 9. Oct 16, 2012 ### Hansenetzer Citation from Weinberg´s second Volume on Quantum Field Theory Page 184 (botton of the page): "It is not true that an unbroken chiral symmetry necessarily implies a zero nucleon mass, unless we make further assumptions about the matrix elements of the axial-vector current ." A good and lucid treatment on chiral spontaneous symmetry breaking can be found in my opinion in Chapter 9 of "Stefan Pokorski-Gauge Field Theories". 10. Feb 7, 2014 ### SaintItai I have another question that maybe fits here: In a hadron physics lecture some ratios of hadron masses where given to proof that SU(2)_V is conserved, while SU(2)_A is spontaneously broken, e.g. $$SU(2)_V \hspace{20mm} \frac{m_{\pi^+} - m_{\pi^-}}{m_{\pi^+} + m_{\pi^-}} = 0.1\%$$ $$SU(3)_V \hspace{20mm} \frac{m_{f_0} - m_{\pi}}{m_{f_0} + m_{\pi}} = 56\%$$ While the first one kind of makes sence to me the second does not. How does the vector and axial charge act on hadrons? Thanks!	2017-11-23 13:25:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8273558020591736, "perplexity": 1196.8072564798715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806832.87/warc/CC-MAIN-20171123123458-20171123143458-00585.warc.gz"}
https://www.physicsforums.com/threads/griffiths-problem-3-34.221096/	# Griffiths Problem 3.34 1. Mar 10, 2008 ### ehrenfest 1. The problem statement, all variables and given/known data This question refers to Griffiths E and M book. If they had not told me that the charge moves, I would have guessed that it just sits there since it seems like there is nothing to exert a force on it. Am I supposed to calculate the induced charge on the conducting plate? How do I use the fact that the plate is grounded? That means that the potential on the plate is 0 just like at infinity, but doesn't that imply there is no charge on the plate either? 2. Relevant equations 3. The attempt at a solution 2. Mar 10, 2008 ### pam No, the charge on the plate is needed to keep it at V=0. The charge is supplied by the ground. 3. Mar 10, 2008 ### ehrenfest A related question: on page 123, Griffiths says "Evidently the total induced charge on the plane is -q, as (with the benefit of hindsight) you can perhaps convince yourself that it had to be." I cannot convince myself unfortunately. How do you know this a priori? Is it related to the fact that the plate is grounded? Would it be different if the plate were not grounded? 4. Mar 10, 2008 ### ehrenfest And also when I try to apply eqn 3.12 to this problem I get a differential equation which I have no idea how to solve: $$\ddot{z} = C/z^2$$ where C is a constant. What am I doing wrong? 5. Mar 10, 2008 ### pam 1. The image charge is -q. By Gauss's law, that has to equal the induced surface charge on the grounded plane. 2. Use dv/dt=v(dv/dx). 6. Mar 11, 2008 ### Reshma Calculate the force on the charge at a height 'x' above the plane and equate it with the equation of motion of the charge 'q'. 7. Mar 11, 2008	2017-10-21 10:40:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7094569802284241, "perplexity": 447.529836876581}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824733.32/warc/CC-MAIN-20171021095939-20171021115939-00799.warc.gz"}
https://www.physicsforums.com/threads/how-is-the-algebra-of-quaternions-isomorphic-to-the-algebra-of-matrices.622945/	# How is the algebra of quaternions isomorphic to the algebra of matrices? 1. Jul 23, 2012 ### mitch_jacky I just started learning about morphisms and I came across a problem that totally stumps me. Here goes: Show that the algebra of quaternions is isomorphic to the algebra of matrices of the form: \begin{pmatrix} \alpha & \beta \\ -\bar{\beta} & \bar{\alpha} \end{pmatrix} where α,β$\in$ℂ and the overbar indicates complex conjugation. [Hint: If q=a+bi+cj+dk is a quaternion, identify it with the matrix whose entries are $\alpha$ =a+bi, $\beta$ =c+di, $\bar{\alpha}$ =a-bi, -$\bar{\beta}$ =-c+di, (a,b,c,d) $\in$ℝ, i$^{2}$=j$^{2}$=k$^{2}$=-1] Thanks a lot everyone! 2. Jul 23, 2012 ### DonAntonio What have you tried? Have you already summed (multiplied) two of the above matrices and verified the sum behaves as the sum (product) of the respective quaternions? For example, heeding to the hint given, we'd have the identifications $$i \sim \begin{pmatrix}1&0\\0&-1\end{pmatrix}\,\,,\,j \sim \begin{pmatrix}0&1\\-1&0\end{pmatrix}\,\,,\,k \sim \begin{pmatrix}0&1\\1&0\end{pmatrix}$$so do we have $$ij=k \sim \begin{pmatrix}1&0\\0&-1\end{pmatrix} \begin{pmatrix}0&1\\-1&0\end{pmatrix}\stackrel{?}=\begin{pmatrix}0&1\\1&0\end{pmatrix}\,\,??$$ DonAntonio 3. Jul 23, 2012 ### mitch_jacky Okay, I have verified that ij=k but I don't see what to do next. 4. Jul 23, 2012 ### mitch_jacky The more I look at this problem the less I understand what I am supposed to be doing. Without giving me any answers what I need is for someone to walk me through the steps to the solution. I need an understanding of what I'm trying to solve here. 5. Jul 23, 2012 ### Ray Vickson What does it MEAN for two algebraic structures to be isomorphic? (That is, there is a formal definition of isomorphism, and I am asking you what that is.) Then you need to show that all the parts of the definition hold true. RGV 6. Jul 23, 2012 ### mitch_jacky Okay, so an isomorphism is a bijectivity from one structure to another which preserves the characteristics of the structures. So if quaternions possess addition, scalar and quaternion multiplication I must show that this structure is isomorphic to the addition, scalar, and matrix multiplication of matrix algebra? 7. Jul 23, 2012 ### Ray Vickson Well, what do YOU think? RGV 8. Jul 24, 2012 ### mitch_jacky You know, I think that's pretty much what I am being asked to show. I appreciate your insights! So basically (and please excuse the poor notation, I'm on my phone): (H,\otimes,°,\oplus, =)~(M, ×, •, +, =) 9. Jul 24, 2012 ### Ray Vickson I guess so, depending on exactly what the symbols mean; anyway, if q1 ⇔ A1 and q2 ⇔ A2, you need q1+q2 ⇔ A1+A2, q1*q2 ⇔ A1.A2 (matrix product) and, for scalar c, cq1 ⇔ cA1, etc. RGV 10. Jul 25, 2012 ### mitch_jacky Wow, it isn't wizard math after all. Thanks man!	2018-03-20 05:00:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8673413991928101, "perplexity": 1827.6344655833677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647280.40/warc/CC-MAIN-20180320033158-20180320053158-00403.warc.gz"}
https://gateoverflow.in/56741/ugcnet-june2014-iii-19	# UGCNET-June2014-III: 19 1 vote 857 views Match the following : LIST-I LIST-II a. Correctness i. The extent to which a software tolerates the unexpected problems b. Accuracy ii. The extent to which a software meets its specifications c. Robustness iii. The extent to which a software has specified functions d. Completeness iv. Meeting specifications with precision 1. a-ii; b-iv; c-i; d-iii 2. a-i; b-ii; c-iii; d-iv 3. a-i; b-ii; c-iv; d-iii 4. a-iv; b-ii; c-i; d-iii recategorized ## 3 Answers 5 votes Best answer Answer : A LIST-1 LIST-II a. Correctness ii. The extent to which a software meets its specifications b. Accuracy iv. Meeting specifications with precision c. Robustness i. The extent to which a software tolerates the unexpected problems d. Completeness iii. The extent to which a software has specified functions Reference : What is Correctness? Accuracy selected by 0 votes Answer A * Correctness : working as per requirements => ii Accuracy : how much precisely answer is coMputed => iv * robustness : how much error software can tolerate and avoid crashing=> i **completeness : how much requirements the software is meeting => iii 0 votes Ans: A Answer: ## Related questions 0 votes 2 answers 1 2.1k views Assume that a program will experience 200 failures in infinite time. It has now experienced 100 failures. The initial failure intensity was 20 failures/CPU hr. Then the current failure intensity will be 5 failured/CPU hr 10 failured/CPU hr 20 failured/CPU hr 40 failured/CPU hr 0 votes 2 answers 2 775 views Software testing is the process of establishing that errors are not present the process of establishing confidence that a program does what it is supposed to do the process of executing a program to show that it is working as per specifications the process of executing a program with the intent of finding errors 0 votes 2 answers 3 1.2k views Which one of the following is not a key process area in CMM level $5$ ? Defect prevention Process change management Software product engineering Technology change management 0 votes 2 answers 4 909 views Which one of the following is not a definition of error ? It refers to the discrepancy between a computed, observed or measured value and the true, specified or theoretically correct value. It refers to the actual output of a software and the correct output. It refers to a condition that causes a system to fail. It refers to human action that results in software containing a defect or fault.	2020-08-11 21:02:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.71147620677948, "perplexity": 8233.26495905547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738855.80/warc/CC-MAIN-20200811205740-20200811235740-00074.warc.gz"}
https://lemon.gitlabpages.inria.fr/sw2d/source/user_doc/output.html	# 3.1. Description of sw2d output files¶ group OutputOfSW2D Output files of SW2D. Output files written by sw2d will be in folders Log folder • console.log : log of the program. When the simulation is runned several times, the file keep the track of the previous simulation. • settings.json : extented input file containing the values for the user defined parameters and the default values for the undefined parameters Misc folder Folder containing binary files. The contents of those files are written is a readable format whin the output folder. • ResultHydro.res : binary file containing the simulation results : OUI • ResultHydro_{StoringTime}.vtp : binary file containing the map simulation result at time {StoringTime}. {StoringTime} is the storing time written in a scientific format with 6 decimals (e.g. 104s is written 1.040000e+2) Output folder • ResultHydro_{StoringTime}.csv : csv file containing the ‘’asked’’ map simulation result at time {StoringTime} (corresponding to the equivalent vtp file). {StoringTime} is the storing time written in a scientific format with 6 decimals (e.g. 104s is written 1.040000e+2) The ‘’asked’’ variables are defined by the ‘’Storage type’’ value (GUI\Output Parameters\Maps\Storage type or storeflag keyword in the json input file). log misc output	2020-10-29 23:20:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4121370315551758, "perplexity": 9986.514286051974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107905965.68/warc/CC-MAIN-20201029214439-20201030004439-00162.warc.gz"}
https://partiallyordered.com/posts/covering-spaces	August 2022 # Introduction These are a set of notes about covering spaces, about on the same level of difficulty/scope as Hatcher. I make no claim of originality—a lot of theorem statements are taken directly from Hatcher, or slightly modified. Other bits of content are from notes I took while taking topology at UCSB. Hopefully these notes are a bit more streamlined or easier to use for reference—all of the theorems/definitions are in convenient boxes for easy reading. I also do a little bit more dirty work than Hatcher. For example, I frequently use the Lebesgue number lemma and pasting lemma to really show that certain lifts exist or are continuous. Proofs of these point-set topology lemmas are deferred to the last section. # Conventions Neighborhoods are be open. We take $$S^1\subseteq \mathbb{C}$$, and we often take the basepoint of $$S^1$$ to be $$e^{0\cdot 2\pi i}=1\in S^1\subseteq \mathbb{C}$$. All maps are continuous. We use the notation $f: X,x \to Y,y$ to refer to a map of pointed topological spaces, i.e., a continuous map $$f:X\to Y$$ which obeys $$f(x)=y$$. We write $$c_x: Y \to X$$ for the constant $$x$$ map. For $$\alpha: I\to X$$ a path, we write $$\overline{\alpha}$$ for the reversed path, i.e., \begin{aligned} \overline{\alpha} : I &\longrightarrow X\\ t &\longmapsto \alpha(1-x).\end{aligned} For two paths $$\alpha,\beta: I\to X$$, we write $$\alpha \cdot \beta$$ for the concatenation path, which first follows $$\alpha$$ and then $$\beta$$, i.e., \begin{aligned} \alpha \cdot \beta : I &\longrightarrow X\\ t &\longmapsto \begin{cases} \alpha(2t) & t<\frac{1}{2}\\ \beta(2t-1) & t \geq \frac{1}{2}. \end{cases}\end{aligned} This is easy to forget—this is backwards from the normal function composition order. # Definitions and Examples Definition 1. A covering space of a space $$X$$ (“downstairs”) is a space $$\widetilde{X}$$ (“upstairs”) with a map $$p: \widetilde{X} \to X$$ such that every point $$x\in X$$ has an evenly covered neighborhood, i.e., a neighborhood $$V$$ such that $$p^{-1}(V)$$ is a disjoint union of open sets $$\widetilde{V}$$ which have $p\|_{\widetilde{V}} : \widetilde{V} \to V$ being a homeomorphism. Example 2. We claim that the real line $$\mathbb{R}$$ covers the circle $$S^1\subseteq \mathbb{C}$$ by the map \begin{aligned} p: \mathbb{R}&\longrightarrow S^1\\ t &\longmapsto e^{t 2\pi i}. \end{aligned} This follows because each point $$e^{\theta 2\pi i} \in S^1$$ has a neighborhood $$V=\{e^{(\theta+t) 2\pi i} \operatorname{\big\|}t\in (-1/2,1/2)\}$$, and the preimage under $$p$$ is $\cdots, \left(\theta - 1 - \frac{1}{2},\theta-1 +\frac{1}{2}\right), \left(\theta - \frac{1}{2},\theta +\frac{1}{2}\right), \left(\theta+1 - \frac{1}{2},\theta+1 +\frac{1}{2}\right),\cdots,$ which is a disjoint collection of open subsets of $$\mathbb{R}$$ which are each homeomorphically mapped to $$V$$ by $$p$$. This particular covering space of $$S^1$$ was very helpful in computing the fundamental group for the first time (we will reprove this machinery in greater generality soon). Our strategy was to lift maps $$f: I,0 \to S^1, 1$$ to the real line $$\mathbb{R},0$$, i.e., get a map $$\widetilde{f}: I,0 \to \mathbb{R},0$$ such that the following diagram commutes. This strategy comes in much greater generality with much greater utility. We’re going to try to lift (which we will define precisely later) all sorts of maps, and these theorems about lifting will help us eventually classify covering spaces of a given space. Let’s make a definition before we get ahead of ourselves. Definition 3. Let $$p:\widetilde{X} \to X$$ be a covering space, and $$f:Y\to X$$ be a map. A map $$\widetilde{f}: Y\to \widetilde{X}$$ is called a lift of $$f$$ if the following diagram commutes: i.e., $$p\circ \widetilde{f} = f$$. If there is a lift, there will usually be several lifts, so we are often interested in lifts based at a certain point. That is, given a covering space $$p:\widetilde{X}\to X$$ and a map $$f:X\to Y$$, if we fix $$x\in X$$, we set $$y=f(x)$$, and we choose $$\widetilde{x}\in p^{-1}(x)$$, we often look for lifts $\widetilde{f}: Y,y \longrightarrow \widetilde{X},\widetilde{x},$ i.e., a lift $$\widetilde{f}: Y\to \widetilde{X}$$ which satisfies $$\widetilde{f}(y)=\widetilde{x}$$. We’ll see this when we try to lift paths. On the other hand, it’s very common that there are no lifts at all. For example, the map $$\mathop{\mathrm{id}}_{S^1}:S^1\to S^1$$ does not lift to a map $$\widetilde{f}: S^1\to \mathbb{R}$$ because looking at fundamental groups/induced homomorphisms we would get which boils down to saying that the following diagram commutes, but the identity homomorphism does not factor through the trivial group. Let’s look at a few more example before we prove some theorems about lifting. Example 4. We saw already that $$\mathbb{R}$$ covers $$S^1$$, and it’s not hard to see that $$S^1$$ covers $$S^1$$ by the identity map, but $$S^1$$ also covers $$S^1$$ in a non trivial way. We claim \begin{aligned} p: S^1 &\longrightarrow S^1\\ e^{t 2\pi i} &\longmapsto e^{nt 2\pi i} \end{aligned} (i.e., just $$z\mapsto z^n$$) is a covering map. To see that this is a covering map, observe that each point $$e^{\theta 2\pi i}$$ has neighborhood $$V=\{e^{\theta + t)2\pi i} \operatorname{\big\|}t\in (-1/2, 1/2)\}$$, and the preimage of $$V$$ under $$p$$ is $A_n = \left\{e^{(\theta + t)2\pi i} \;\Big\|\; t\in \left(\frac{-1}{2n}, \frac{1}{2n}\right)\right\}$ $A_n,\; A_n + \frac{2\pi i}{n},\; \dots,\; A_n + \frac{2\pi i (n-1)}{n}.$ When you restrict $$p$$ to any of these components, you indeed get a homeomorphism to $$V$$. Example 5. $$\mathbb{R}^2$$ covers the cylinder $$\mathbb{R}\times S^1$$ which in turn covers the torus $$S^1\times S^1$$. Explicitly, we can write \begin{aligned} &p_1: \mathbb{R}^2 \to \mathbb{R}\times S^1, \qquad (x,y)\mapsto (x,e^{y2\pi i})\\ &p_2: \mathbb{R}\times S^1 \to S^1 \times S^1, \qquad (x,e^{y2\pi i})\mapsto (e^{x2\pi i},e^{y2\pi i})\\ &p_2 \circ p_1: \mathbb{R}^2 \to S^1 \times S^1, \qquad (x,y)\mapsto (e^{x2\pi i},e^{y2\pi i}). \end{aligned} One can check that these are all actually covering maps because they are products of covering maps, since we can get evenly covered neighborhoods by taking products of evenly covered neighborhoods. # Lifting Theorems Proposition 6 (Path Lifting Property). Let $$p: \widetilde{X} \to X$$ be a covering space, $$f: I,0 \to X,x$$ be a path, and let $$\widetilde{x}\in p^{-1}(x)$$ be chosen. Then, there exists a unique lifted path $\widetilde{f}: I,0 \longrightarrow \widetilde{X},\widetilde{x}$ Strategy. We would like to just say $$\widetilde{f} = p^{-1}\circ f$$, but in general $$p$$ is not a homeomorphism and may not have continuous inverse. Instead, we use local inverses of $$p$$ to keep extending to get $$\widetilde{f}$$. To get local inverses, we will break $$I$$ into finitely many small pieces, each which map into an evenly covered set (where we can choose open sets to have a local inverse). Proof. We will prove existence and uniqueness. Existence. Since $$p:\widetilde{X}\to X$$ is a covering space, each $$f(t)\in X$$ has an evenly covered neighborhood $$U_t$$. Then, $\{f^{-1}(U_t) \operatorname{\big\|}t\in I\}$ is an open cover of $$I$$, so by the Lebesgue number lemma there exists $$\varepsilon>0$$ such that each $$\varepsilon$$-ball $$B_\varepsilon(s)\subseteq I$$ is contained in some $$f^{-1}(U_t)$$. We choose $$n\in \mathbb{N}$$ such that $$1/n < \varepsilon$$. Then, we have $I = \left[0,\frac{1}{n}\right] \cup \left[\frac{1}{n},\frac{2}{n}\right] \cup \cdots \cup \left[\frac{n-1}{n},\frac{n}{n}\right]$ where each piece has $f\left(\left[\frac{k-1}{n},\frac{k}{n}\right]\right) \subseteq U_t$ for some $$t\in I$$, and we denote this $$U_t$$ by $$U_k$$. Now, we use these pieces to lift $$f$$. We inductively define $$\widetilde{f_k}: [0,k/n], 0 \to \widetilde{X},\widetilde{x}$$ with $$p\circ \widetilde{f_k} = f\|_{[0,k/n]}$$. Our base case requires us to define $$\widetilde{f_0}: [0,0], 0 \to \widetilde{X}, \widetilde{x}$$, and we can just set $$\widetilde{f_0}(0)=\widetilde{x}$$. Now, assuming we’ve defined $$\widetilde{f_{k-1}}$$, we define $$\widetilde{f_k}$$. We choose the connected component $$\widetilde{U_k}$$ of $$p^{-1}(U_k)$$ that satisfies $\widetilde{f_{k-1}}(\frac{k-1}{n}) \in \widetilde{U_k},$ and we then define $\widetilde{f_{k}}(t) = \begin{cases} \widetilde{f_{k-1}}(t) & t\in \left[0,\frac{k-1}{n}\right]\\ \left(p\|_{\widetilde{U_k}}\right)^{-1}(f(t)) & t\in \left[\frac{k-1}{n},\frac{k}{n}\right]. \end{cases}$ This map $$\widetilde{f_k}$$ is well-defined because $$p$$ restricted to $$\widetilde{U_k}$$ is a homeomorphism and has an inverse (since $$U_k$$ is chosen to be evenly covered), and by choice of $$\widetilde{U_k}$$ and definition of $$\widetilde{f_{k-1}}$$ we have $\left(p\|_{\widetilde{U_k}}\right)\left(\widetilde{f_{k-1}}(\frac{k-1}{n})\right) = f(\frac{k-1}{n}),$ so we can apply $$(p\|_{\widetilde{U_k}})^{-1}$$ to get that both parts of $$\widetilde{f_{k}}$$ agree on the overlap. Since both parts are continuous and agree on overlap, by the pasting lemma (for closed sets), $$\widetilde{f_k}$$ is continuous. Furthermore, it satisfies $$p\circ \widetilde{f_k} = f\|_{[0,k/n]}$$ because we can check on both parts of $$\widetilde{f_k}$$. Once we get to the $$n$$th step, we get our desired lift $$\widetilde{f}: I,0\to \widetilde{X},\widetilde{x}$$. Uniqueness. Suppose $$\widetilde{g}:I,0\to \widetilde{X},\widetilde{x}$$ is another lift of $$f$$. Our strategy to show $$\widetilde{f}=\widetilde{g}$$ is to show that each time we extended $$\widetilde{f_k}$$ that our hand was forced—we didn’t have any other options. We prove that $\widetilde{f}\|_{[0,k/n]} = \widetilde{g}\|_{[0,k/n]}$ by induction on $$k$$. For our base case, by assumption we have $$\widetilde{f}(0)=\widetilde{g}(0)$$. Now, assume that we know for $$k$$ that $\widetilde{f}\|_{[0,(k-1)/n]} = \widetilde{g}\|_{[0,(k-1)/n]}.$ We know that $p \circ \widetilde{g} = f,$ and on $$[(k-1)/n,k/n]$$ our map $$f$$ lands inside $$U_k$$. Therefore, on $$[(k-1)/n,k/n]$$ $$\widetilde{g}$$ lands in $$p^{-1}(U_k)$$. Since $$\widetilde{g}$$ is continuous, the image the connected set $$[(k-1)/n,k/n]$$ under $$\widetilde{g}$$ must be connected, i.e., it must land in a single connected component of $$p^{-1}(U_k)$$. By assumption, $$\widetilde{f}((k-1)/n)=\widetilde{g}((k-1)/n)$$, so the image of $$[(k-1)/n,k/n]$$ under $$\widetilde{g}$$ must be $$\widetilde{U_k}$$, the same connected component as $$\widetilde{f}$$. Therefore, we can write $p\|_{\widetilde{U_k}} \circ \widetilde{f}\|_{[(k-1)/n,k/n]} = p\|_{\widetilde{U_k}} \circ \widetilde{g}\|_{[(k-1)/n,k/n]},$ and since $$p\|_{\widetilde{U_k}}$$ a homeomorphism, we have $\widetilde{f}\|_{[(k-1)/n,k/n]} = \widetilde{g}\|_{[(k-1)/n,k/n]}.$ Thus, we have completed our induction step, having shown $\widetilde{f}\|_{[0,k/n]} = \widetilde{g}\|_{[0,k/n]}.$ After $$n$$ steps, we get $$\widetilde{f}=\widetilde{g}$$. Thus, the lift is unique. ◻ Remark 7. We could have tried to do this without the Lebesgue number lemma—inside each $$f^{-1}(U_t)$$, pick a smaller basis neighborhood $$(a_t,b_t)$$ containing $$t$$, and we would still have an open cover of $$I$$. We would take a finite subcover, and then arrange the intervals somehow. I always find the interval arranging step a little confusing, so I’ve opted to shortcut to the Lebesgue number lemma. Let’s see a neat application of the path lifting property. Proposition 8. Let $$p: \widetilde{X}\to X$$ be a covering space. Assume $$\widetilde{X}$$ are $$X$$ are both path-connected. Then, the cardinality $$\|p^{-1}(x)\|$$ does not depend on $$x$$. This constant value is called the degree of the cover. Proof. Let $$a,b\in X$$, and let $$f: I\to X$$ be a path $$a$$ to $$b$$. We attempt to define a bijection $$\varphi: p^{-1}(a) \to p^{-1}(b)$$. For each $$\widetilde{a_i}\in p^{-1}(x)$$, by the path lifting property, there exists a unique lift $\widetilde{f_i}: I,0 \to \widetilde{X},\widetilde{a_i}$ of $$f$$. Set $$\varphi(a)=\widetilde{f_i}(1)$$, i.e., the other endpoint of the lifted path. The function $$\varphi$$ is well-defined by the uniqueness of the lifted path. We need to show that it is injective/surjective. Let $$\widetilde{a_1},\widetilde{a_2} \in p^{-1}(a)$$, and assume that $$\varphi(\widetilde{a_1})=\varphi(\widetilde{a_2})$$, so $$\widetilde{f_1}(1)=\widetilde{f_2}(1)$$. Then, the reversed lifts $\overline{\widetilde{f_1}}, \overline{\widetilde{f_2}}$ are both lifts of the reversed path $$\widetilde{f}$$. Since the reversed lifts both have the same starting point, by the uniqueness part of the path-lifting property, we must have $\overline{\widetilde{f_1}} = \overline{\widetilde{f_2}},$ so $$\widetilde{f_1}=\widetilde{f_2}$$, so $$\widetilde{a_1}=\widetilde{a_2}$$. Thus, $$\varphi$$ is injective. Now, we check surjectivity. Let $$\widetilde{b_j}\in p^{-1}(b)$$. Then, we can lift the reversed path $$\overline{f}$$ starting at $$\widetilde{b_j}$$ to the lift $$\widetilde{\overline{f}_j}$$, and we can check that $$\widetilde{\overline{f}_j}(1) \in p^{-1}(a)$$ maps to $$\widetilde{b_j}$$ under $$\varphi$$. ◻ Now, we prove the more general homotopy lifting property. In general, we cannot hope to lift every single map to $$X$$ to a covering space $$\widetilde{X}$$. However, if we can lift a map, then we can lift an entire homotopy of it. That is, if we can specify how a homotopy lifts at time 0, we get a unique lift of the entire homotopy. Proposition 9 (Homotopy Lifting Property). Let $$p: \widetilde{X}\to X$$ be a covering space, $$F: Y\times I\to X$$ a homotopy, and $$\widetilde{F_0}: Y\to \widetilde{X}$$ a lift of $$f_0$$. Then, there exists a unique lift $\widetilde{F}: Y\times I \longrightarrow \widetilde{X}$ extending $$\widetilde{F_0}$$. Strategy. Let’s talk about the strategy first. For a given $$y\in Y$$, we first try to lift $$F\|_{N\times I}$$ for a small neighborhood $$N$$ of $$y$$. We will use a similar argument as per the path lifting principle, and by uniqueness we will get that adjacent restrictions $F\|_{N\times I}, F\|_{N'\times I}$ will agree on overlap. This will allow us to assemble the restrictions together. We will then need to choose our small neighborhood $$N$$ for which we will lift $$F\|_{N\times I}$$. We will choose $$N$$ to be the intersection of small neighborhoods of $$y$$ that come up when we try divide $$I$$ into evenly covered pieces, as per the proof of the path lifting principle. Proof. Let $$y\in Y$$ be given. For each $$t\in I$$, there exists an evenly covered neighborhood $$U_t$$ of $$F(y,t)$$. Then, there exists a basic neighborhood $$N_t\times V_t \subseteq F^{-1}(U_t)$$ of $$(y,t)$$. The collection $\{V_t \operatorname{\big\|}t\in I\}$ is a cover of $$I$$ which has subcover $$V_{t_1},\dots,V_{t_m}$$. Choose a Lebesgue number $$\varepsilon>0$$ for the subcover $$\{V_{t_i}\}$$ and choose $$n\in \mathbb{N}$$ so that $$1/n<\varepsilon$$. Thus, each $I_k = \left[\frac{k-1}{n}, \frac{k}{n}\right]$ is contained in some $$V_{t_i}$$. Then, we can take $N = \bigcap_{i=1}^m N_{t_i},$ so that for each $$k$$ we have $N\times I_k \subseteq F^{-1}(U_{t_k}).$ This is a big win—we’ve have a neighborhood $$N$$ of $$y$$ such that $$N\times I$$ can be written as the union of sets $$N\times I_k$$ which map into evenly covered sets. Now, we’re in a good position to lift $$F\|_{N\times I}$$ (this is an abuse of notation—we don’t really mean the restriction because for different $$N$$ this map a-priori may not be the same. Eventually, we will prove that these lifts all agree with each other, and the abuse of notation will be correct). Inductively, we define $\widetilde{F}\|_{N\times [0,k/n]},$ with our base case $$\widetilde{F}\|_{N\times [0,0]}$$ given by assumption, and our induction step by choosing a connected component $$\widetilde{V_{t_i}}\subseteq p^{-1}(V_{t_i})$$ containing $$F(y,(k-1)/n)$$ and defining $\widetilde{F}\|_{N\times [(k-1)/n,k/n]} = \left(p\|_{\widetilde{V_{t_i}}}\right)^{-1}\circ F\|_{[(k-1)/n,k/n]}.$ The resulting map will be well-defined by choice of $$\widetilde{V_{t_i}}$$ and continuous by the pasting lemma (for closed sets). Now, for each $$y\in Y$$ we have neighborhoods $$N_y=N$$ and a lift $\widetilde{F}\|_{N_y\times I} : N_y\times I \to \widetilde{X}$ with $$\widetilde{F}_{N_y\times \{0\}}$$ given by assumption. We need to show that these lifts agree with each other so that they assemble into a continuous map $$\widetilde{F}: Y\times I\to \widetilde{X}$$. The collection $\{N_y \operatorname{\big\|}y\in Y\}$ forms an open cover of $$Y$$. Let $$y,y'\in Y$$ and let $$z\in N_y\cap N_{y'}$$. Then, $\left(\widetilde{F}_{N_y\times I}\right)_{\{z\}\times I}: \{z\}\times I\to \widetilde{X}, \qquad \left(\widetilde{F}_{N_{y'}\times I}\right)_{\{z\}\times I}: \{z\}\times I\to \widetilde{X}$ are both lifts of the path $F\|_{\{z\}\times I}: \{z\}\times I \to X$ that send $$0\mapsto \widetilde{F}_0(z)$$. Thus, by the uniqueness of the path lifting property, these two maps must be the same. This just tells us that any two lifts agree on intersection, so we can get a well-defined lift $$\widetilde{F}: Y\times I \to \widetilde{X}$$, which is continuous by the pasting lemma (for open sets). Finally, our lift $$\widetilde{F}: Y\times I\to \widetilde{X}$$ is unique again because each restriction to $$\{y\}\times I$$ is a lift of the path $$F\|_{\{y\}\times I}$$, so unique by the path lifting property. ◻ # Correspondence Theorem So far, we’ve proved some theorems about lifting paths and homotopies—the essential ingredients of the fundamental group. We’re going to use these tools to study the interplay between the fundamental groups upstairs and downstairs. Let’s look at an example. Example 10. Recall the covering $$p:S^1\to S^1$$ by $$z\mapsto z^n$$. Let $$\gamma:I\to S^1$$ be a generator of the upstairs fundamental group, say $\gamma(t) = e^{t2\pi i},$ and denote $$\omega$$ the same map, but thought of as generating the downstairs fundamental group. Then, $p\circ \gamma(t) = e^{nt 2 \pi i},$ so $p_([\gamma]) = [p\circ \gamma] = [\omega]^n.$ Under the isomorphism $$\pi_1(S^1,1)\cong \mathbb{Z}$$, this tells us that $p_(\pi_1(S^1,1)) = n\mathbb{Z}\leq \mathbb{Z}$ By choosing different $$n\neq 0$$ or by having $$\mathbb{R}$$ cover $$S^1$$ (corresponding to $$n=0$$), we can actually get any subgroup $$n\mathbb{Z}\leq \mathbb{Z}$$ by looking at the image of the fundamental group of a covering space. We will later see that this is example is no coincidence. These examples are leading us towards a big classification/correspondence theorem for covering spaces. We will eventually see that there is a bijection $\{\text{covering spaces } p: \widetilde{X}\to X\}/\sim\qquad \longrightarrow \qquad \{H\leq \pi_1(X,x)\}/\sim,$ where the left equivalence relation is “isomorphism” of covering spaces and the right equivalence relation is conjugacy. In the process, we’ll also get a powerful result telling us when we can lift any map, not just paths and homotopies. We’ll need to prove quite a few intermediary results to build up to this correspondence and in general the connection between group theory and covering spaces. Let’s start with some quick corollaries of the homotopy lifting property. Lemma 11. Let $$p:\widetilde{X}\to X$$ be a covering space, and let $$F:I\times I\to X$$ be a homotopy rel $$\partial I$$ (a homotopy of paths). Given $$\widetilde{x}\in p^{-1}(F_0(0))$$, $$F$$ lifts uniquely to a homotopy of paths $\widetilde{F}: I\times I \to \widetilde{X}.$ Proof. By the path lifting property, $$F_0:I\to X$$ lifts to a unique path $$\widetilde{F}_0: I\to \widetilde{X}$$ starting at $$\widetilde{x}$$. Then, by the homotopy lifting property, $$F$$ lifts to a unique map $\widetilde{F}: I\times I \to \widetilde{X}$ with the already defined $$\widetilde{F}_0$$. We now show that $$\widetilde{F}$$ is a homotopy of paths. Since the paths $t \mapsto F_t(0), \qquad t\mapsto F_t(1)$ are constant (because $$F$$ is a homotopy of paths), and we have that $t\mapsto \widetilde{F}_0(0), \qquad t\mapsto \widetilde{F}_0(1)$ are lifts of the respective paths, by uniqueness of path lifting we must have $$\widetilde{F}_t(0)$$ and $$\widetilde{F}_t(1)$$ constant. Thus, $$\widetilde{F}$$ is a homotopy of paths. ◻ Proposition 12. Let $$p:\widetilde{X}\to X$$ be a covering space. Then, $p_: \pi_1(\widetilde{X},\widetilde{x}) \longrightarrow \pi_1(X,x=p(\widetilde{x}))$ is injective. Proof. Let $$[\widetilde{f}]\in \ker{p_}$$, so $$p\circ \widetilde{f} \simeq c_x$$ rel $$\partial I$$. Let $F: I\times I \to X, \qquad F_0 = p\circ \widetilde{f}, \qquad F_1=c_x$ be the homotopy. We can then lift this homotopy of paths to a homotopy of paths based at $$\widetilde{x}$$, giving us $\widetilde{F}: I\times I \to X, \qquad \widetilde{F}_0 = \widetilde{f}.$ We claim $$\widetilde{F}_1 = c_{\widetilde{x}}$$. This must be the case because $$\widetilde{F}_1$$ is a lift of $$c_x$$ based at $$\widetilde{x}$$, and so is $$c_{\widetilde{x}}$$. Thus, by uniqueness $$\widetilde{F}_1 = c_{\widetilde{x}}$$. Therefore, $$[\widetilde{f}]=0$$ because $$\widetilde{f}$$ is homotopic to $$c_{\widetilde{x}}$$. Thus, $$p_$$ is injective. ◻ Proposition 4 already gives us one direction of our desired correspondence (modulo some equivalence relation), where we send a covering space $$p:\widetilde{X}\to X$$ to the subgroup $$p_\pi_1(\widetilde{X},\widetilde{x})$$. Definition 13. Let $$p:\widetilde{X}\to X$$ be a covering map. Then, $$p_(\pi_1(\widetilde{X},\widetilde{x}))$$ is the subgroup of $$\pi_1(X,x)$$ corresponding to the cover. This depends on choice of basepoint, and assuming $$\widetilde{X}$$ is path-connected, different choices of $$\widetilde{x}$$ just give conjugate subgroups. Proposition 14. Let $$p:\widetilde{X}\to X$$ be a covering space, $$\widetilde{x} \in \widetilde{X}$$, $$x=p(\widetilde{x})$$, and assume $$X,\widetilde{X}$$ path connected. Then, $\deg(p) = [\pi_1(X,x) : p_(\pi_1(\widetilde{X},\widetilde{x}))]$ Strategy. We can roughly think of covering spaces as unwrappings of a space, and the degree is how much we’ve unwrapped. Then, $$\pi_1(\widetilde{X},\widetilde{x})$$ are roughly speaking the loops that weren’t broken by unwrapping (e.g., think of the cylinder covering the torus, and the two loops around the torus—one lifts to a loop, the other lifts just to a path). So the loops in $$p_(\pi_1(\widetilde{X},\widetilde{x}))$$ lift to paths ending in $$\widetilde{x}$$, and the others do not. Then, the index $[\pi_1(X,x) : p_(\pi_1(\widetilde{X},\widetilde{x}))]$ is roughly like the number of loops based at $$x$$ divided by the the number of loops that, when lifted, still end at $$\widetilde{x}$$. The quotient should roughly be like the number of ways that lifted loops can end modulo redundancy—this should end up being the degree. Proof. Let $$G=\pi_1(X,x)$$ and $$H=p_(\pi_1(\widetilde{X},\widetilde{x}))$$. Our strategy is to define a bijection from $$[G:H]$$ to $$p^{-1}(x)$$, since $$\deg(p)=\|p^{-1}(x)\|$$. We define \begin{aligned} \theta: \pi_1(X,x)/H &\longrightarrow p^{-1}(x) \end{aligned} as follows. Given $$[\alpha]H$$, first lift $$\alpha$$ to get $$\widetilde{\alpha}$$ starting at $$\widetilde{x}$$. Then, set $$\theta([\alpha])=\widetilde{\alpha}(1)$$, i.e., the other endpoint of $$\widetilde{\alpha}$$. We need to show $$\theta$$ is well-defined, surjective, and injective. To show well-defined, assume $$[\alpha]=[\beta]$$, so there is path homotopy $$F:I\times I \to X$$. We can lift this homotopy to a path homotopy $$\widetilde{F}$$ starting at $$\widetilde{\alpha}$$. Then, $$\widetilde{F}_t(1)$$ is constantly $$\widetilde{F}_0(1)=\widetilde{\alpha}(1)$$ because the lift is a path-homotopy. Thus, we can get $$\theta([\beta])=\widetilde{\alpha}(1)$$, and $$\theta$$ is well-defined. Next, we show $$\theta$$ is surjective. Let $$\widetilde{y}\in p^{-1}(x)$$. Since $$\widetilde{X}$$ is path-connected, there is a path $$\widetilde{\alpha}$$ from $$\widetilde{x}$$ to $$\widetilde{y}$$, which projects to $$p\circ \widetilde{\alpha}$$, which is a loop at $$x$$. Then, by the uniqueness in the path lifting property, we can get $\theta([p\circ \widetilde{\alpha}])=\widetilde{\alpha}(1)=\widetilde{y}.$ Finally, we show injectivity. Assume $$\theta([\alpha])=\theta([\beta])$$. Then, $\widetilde{\alpha} \cdot \overline{\widetilde{\beta}}$ is a loop at $$\widetilde{x}$$, and $[\alpha]\cdot [\beta]^{-1} = p(\widetilde{\alpha} \cdot \overline{\widetilde{\beta}}) \in H,$ so $$[\alpha]H=[\beta]H$$. ◻ Definition 15. Let $$P$$ be a property that a topological space can have. A space $$X$$ is locally $$P$$ is for every $$x\in X$$ and every neighborhood $$U$$ of $$x$$, there exists an open set $$V$$ with $x\in V\subseteq U$ such that $$V$$ has property $$P$$. Example 16. We will often consider the following properties: • Locally path connected. • Locally connected. We saw a few instances where we can lift maps—the path lifting property and the homotopy lifting property. We’re getting to a way more general result that will tell us when we can us lift all sorts of maps, and we only have to check something algebraic. The motto is that a map $$f:Y\to X$$ lifts exactly when the fundamental group allows it. Theorem 17 (Lifting Criterion for Covering Spaces). Let $$p:\widetilde{X} \to X$$ be a covering space, let $$x\in X$$ and $$\widetilde{x}$$ a lift of $$x$$. Let $$Y$$ be path-connected and locally path-connected with $$y\in Y$$. Given $$f: Y,y \to X,x$$, there exists a lift $$\widetilde{f}: Y,y \to \widetilde{X},\widetilde{x}$$ if and only if $f_(\pi_1(Y,y)) \subseteq p_(\pi_1(\widetilde{X},\widetilde{x})).$ Strategy. The hard direction is assuming $$f_(\pi_1(Y,y))\subseteq p_(\pi_1(X,x)))$$ and showing that a lift exists. Our strategy for this is really neat. We will essentially “probe” our space with paths, and use path-lifting to figure out $$f$$. We will need to know at least one point to start off our definition of $$\widetilde{f}$$, and we are given $$\widetilde{f}(y)=\widetilde{x}$$. We need to figure out where to map all of the other points of $$y$$. Let $$y'\in Y$$. Since $$Y$$ is path-connected, we have a path $$\gamma$$ from $$y$$ to $$y'$$. Then, $$f\circ \gamma$$ is a path in $$X$$, and it lifts to a path in $$\widetilde{X}$$. We then set $$\widetilde{f}(y')$$ to be the endpoint of the lifted path. One hurdle we will encounter is showing that this definition is well-defined, i.e., that choosing different paths $$\gamma'$$ doesn’t give a different answer. This will boil down to being able to lift the loop $$f\circ (\overline{\gamma} \cdot \gamma')$$. In general, we can’t always lift loops, but our condition on the fundamental groups says that we can do this. Finally, we will need local path-connectedness to check that $$\widetilde{f}$$ is actually continuous. Proof. First, assume that a lift $$\widetilde{f}$$ exists. Then, \begin{aligned} f &= p \circ \widetilde{f}\\ f_ &= p_* \circ \widetilde{f}_, \end{aligned} so $$\mathop{\mathrm{im}}(f_) \subseteq \mathop{\mathrm{im}}(p_)$$. Conversely, assume that $$\mathop{\mathrm{im}}(f_)\subseteq \mathop{\mathrm{im}}(p_)$$. We need to come up with a definition of $$\widetilde{f}$$, show that it is well-defined, and finally show that it is continuous. Let $$y'\in Y$$, and let $$\gamma$$ be a path from $$y$$ to $$y'$$. Then, $$f\circ \gamma$$ is a path from $$f(y)$$ to $$f(y')$$ in $$X$$. By the path lifting property, there exists a lift of $$f\circ \gamma$$, which we denote $$\widetilde{f\circ \gamma}$$. Then, we set $\widetilde{f}(y) = (\widetilde{f\circ \gamma})(1).$ A priori, this depends on $$\gamma$$. To show that this is actually a function, we need to show it is well-defined. Let $$\gamma'$$ be another path from $$y$$ to $$y'$$. We will show that $$(\widetilde{f\circ \gamma})(1) = (\widetilde{f\circ \gamma'})(1)$$. Consider the loop $(f\circ \gamma') \cdot (f\circ \overline{\gamma}) = f\circ (\gamma' \cdot \overline{\gamma}),$ whose equivalence class is in $$f_(\pi_1(Y,y)) \subseteq p_(\pi_1(\widetilde{X},\widetilde{x}))$$. Thus, $[f\circ (\gamma' \cdot \overline{\gamma})] = [p \circ \alpha]$ for some loop $$[\alpha] \in \pi_1(\widetilde{X},\widetilde{x})$$. Thus, we have a homotopy $$H: I\times I \to X$$ with $$H_0 = p\circ \alpha$$ and $$H_1 = f\circ (\gamma' \cdot \overline{\gamma})$$. Since we have a lift $$\widetilde{H_0} = \alpha$$, by the homotopy lifting property we have a lift of the homotopy $$\widetilde{H}$$. Then, $$\widetilde{H}_1$$ is a lift of $$f\circ (\gamma'\cdot \overline{\gamma})$$. In particular, the two halves of $$\widetilde{H}_1$$ are (reparameterized) lifts of $$f\circ \gamma'$$ and $$f\circ \overline{\gamma}$$. By the path lifting property, we then must have $\widetilde{H}_1 = \left(\overline{f\circ \gamma'}\right) \cdot \left(\overline{\widetilde{f\circ \gamma}}\right),$ so therefore we indeed have $(\widetilde{f\circ \gamma})(1) = (\widetilde{f\circ \gamma'})(1),$ so $$\widetilde{f}$$ is well-defined. Finally, we show that $$\widetilde{f}$$ is continuous. Let $$y'\in Y$$. Let $$\widetilde{U}$$ be a neighborhood of $$\widetilde{f}(y')$$. We can assume $$\widetilde{U}$$ is small enough such that $$p\|_{\widetilde{U}}$$ is a homeomorphism to an open set $$U\subseteq X$$. By local path connectedness, choose an open path connected neighborhood $$V$$ of $$y$$ such that $$V\subseteq f^{-1}(U)$$. We claim that $$\widetilde{f}(V)\subseteq \widetilde{U}$$, so that $$\widetilde{f}$$ is continuous at $$y'$$. Let $$y''\in V$$. To evaluate $$\widetilde{f}$$, let $$\gamma:I\to Y$$ be a path $$y$$ to $$y'$$, and let $$\eta:I\to V$$ be a path $$y'$$ to $$y''$$. Then, using the definition of $$\widetilde{f}$$ and the uniqueness of path-lifting, $\widetilde{f}(y'') = \widetilde{f\circ (\gamma\cdot \eta)} (1) = (\widetilde{f\circ \gamma}) \cdot (\widetilde{f\circ \eta})(1) = (\widetilde{f\circ \eta})(1).$ Since $$\eta$$ is in $$V\subseteq f^{-1}(U)$$, we actually know that the lift will be $(p\|_{\widetilde{U}})^{-1} \circ f \circ \eta$ by the uniqueness of path lifting. Thus, $\widetilde{f}(y'') = (\widetilde{f\circ \eta})(1) = (p\|_{\widetilde{U}})^{-1} \circ f \circ \eta(1) \quad \in \widetilde{U},$ so $$\widetilde{f}$$ is continuous. ◻ In fact, after picking a base point that works, such lifts are unique. Proposition 18. Let $$p:\widetilde{X}\to X$$ be a covering space, and $$f:Y\to X$$. If $$\widetilde{f_1},\widetilde{f_2}: Y\to \widetilde{X}$$ are two lifts of $$f$$ that agree at one point of $$Y$$ and $$Y$$ is connected, then $$\widetilde{f_1}=\widetilde{f_2}$$. Proof. Assume $$\widetilde{f_1}(y) = \widetilde{f_2}(y)$$ for some point $$y\in Y$$. We show that the set of points where $$\widetilde{f_1}$$ and $$\widetilde{f_2}$$ agree is clopen, so since it is nonempty, it must all of $$Y$$ by connectedness. Let $$y'\in Y$$. Our goal is to find a neighborhood of $$y'$$ where the two lifts entirely agree or disagree. Let $$U\subseteq X$$ be an evenly covered neighborhood of $$f(y')$$, and let $$\widetilde{U_1},\widetilde{U_2}\subseteq \widetilde{X}$$ be the sheets above $$U$$ containing $$\widetilde{f_1}(y'),\widetilde{f_2}(y')$$ respectively. By continuity of the lifts, we can choose a neighborhood $$N\subseteq Y$$ of $$y'$$ such that $\widetilde{f_1}(N)\subseteq \widetilde{U_1}, \qquad \widetilde{f_2}(N)\subseteq \widetilde{U_2}$ If $$\widetilde{f_1}(y')=\widetilde{f_2}(y')$$, then $$\widetilde{U_1}=\widetilde{U_2}=\widetilde{U}$$, and $p\|_{\widetilde{U}} \circ \widetilde{f_1}\|_{N} = p\|_{\widetilde{U}} \circ \widetilde{f_2}\|_{N}$ implies by injectivity of $$p\|_{\widetilde{U}}$$ that $$\widetilde{f_1},\widetilde{f_2}$$ agree on all of $$N$$. Thus, the set of points where the lifts agree is open. Alternatively, if $$\widetilde{f_1}(y')\neq \widetilde{f_2}(y')$$, then $$\widetilde{U_1}\neq \widetilde{U_2}$$, and even more they are disjoint (because they are sheets), so $$\widetilde{f_1},\widetilde{f_2}$$ disagree on $$N$$. Thus, the set of points where the lifts disagree is open. ◻ In our development of covering spaces and fundamental groups, we’ve finished achieving our main result on how to lift maps. Now, we turn to constructing covering spaces for each subgroup $$H$$ of the fundamental group, so that we can get our desired correspondence. For the point set topology to work out, we at least impose local path-connectedness, so that connected components and path components coincide and so that loops/fundamental group techniques are applicable. By forcing $$X$$ to be locally path connected, we will automatically get $$\widetilde{X}$$ locally path connected for any covering space. To get our desired correspondence, we want $$\widetilde{X}$$ to be path-connected, and since it is already locally path connected, we just require connected. Thus, we will impose certain conditions on $$X$$, and then study connected covering spaces. One other technical condition we will impose on $$X$$ is the following, which is satisfied by most “nice” spaces, e.g., manifolds and CW complexes. Definition 19. A space $$X$$ is semi locally simply connected (SLSC) if every $$x\in X$$ has a neighborhood $$U$$ such that $i_: \pi_1(U,x) \to \pi_1(X,x)$ is trivial. In other words, every point $$x$$ has a neighborhood $$U$$ such that all loops at $$x$$ in $$U$$ are nullhomotopic in $$X$$. Maybe a more straightforward (but strictly stronger) condition is locally simply connected, we require every point $$x\in X$$ to have an open neighborhood which is simply connected (i.e., the nullhomotopies are in $$U$$). It is straightforward to check that manifolds for locally simply connected, or even locally contractible. CW complexes require some more theory. Let’s first see that this condition is actually necessary, so defining it isn’t a waste of time. Proposition 20. If $$X$$ has a simply connected covering space $$p: \widetilde{X}\to X$$, then $$X$$ is SLSC. Proof. Let $$x\in X$$. Then, $$x$$ has a neighborhood $$U$$ with lift $$\widetilde{U}$$ such that $$p\|_{\widetilde{U}}$$ is a homeomorphism. Let $$\gamma:I \to U$$ be a loop at $$x$$. Then, $$\gamma$$ lifts to the loop $$p\|_{\widetilde{U}}^{-1} \circ \gamma$$, which is nullhomotopic in $$\widetilde{X}$$ because $$\widetilde{X}$$ is simply connected. Thus, there exists a homotopy $$h_t:I\to \widetilde{X}$$ with $h_0 = p\|_{\widetilde{U}}^{-1} \circ \gamma$ and $$h_1$$ being the constant loop. Then, $$p\circ h_t: I\to X$$ is a homotopy in $$X$$ which makes $$\gamma$$ nullhomotopic. ◻ In our quest for covering spaces, we first start with getting a simply connected one. We will see later that all other covering spaces are gotten by quotienting this simply connected one. Theorem 21. Let $$X$$ be connected, locally path connected, and SLSC. Then, there exists a simply connected covering space $$p:\widetilde{X}\to X$$, called a universal cover. Strategy. We make an observation first. Fix a point $$x\in X$$. In a small enough neighborhood $$U$$ of $$x$$ (due to the SLSC condition), points of $$U$$ biject with homotopy classes of paths $$x$$ to $$x'$$. Here’s the kicker though. In spaces like a torus, there are multiple homotopy classes of paths for the same point, e.g., we can loop around once or twice to get a point. This is evidence of the fundamental group being nontrivial, and it reflects how our space is somehow folded/wrapped. To unwrap the space, we copy this point several times, once for each homotopy class of paths. As a set, we make our space $$\widetilde{X}$$ the set of homotopy classes of paths, and on small sets, we transfer the topology from $$X$$ to $$\widetilde{X}$$. In our proof, we leave a lot of details as a sketch, since it is a little bit tedious to include all of the details. Proof. Choose a basepoint $$x\in X$$. Define the set $\widetilde{X} = \{[\gamma] \operatorname{\big\|}\gamma \text{ a path in } X \text{ starting at } x\},$ where the equivalence class $$[\gamma]$$ is with respect to path homotopies (fixing endpoints). We then define the map \begin{aligned} p: \widetilde{X} &\longmapsto X\\ [\gamma] &\longmapsto \gamma(1). \end{aligned} We now need to put a topology on $$\widetilde{X}$$, prove that $$p$$ is a covering map, and prove that $$\widetilde{X}$$ is simply connected. First, let’s give $$\widetilde{X}$$ a topology. We extract data from $$X$$. Define $$\mathcal{U}$$ to be the collection of path-connected open sets $$U\subseteq X$$ such that the induced inclusion map $$\pi_1(U) \to \pi_1(X)$$ is trivial (this doesn’t depend on basepoint because $$U$$ is path-connected). By the locally path connected and SLSC hypotheses, $$\mathcal{U}$$ forms a basis for $$X$$. Now, for each $$U\in \mathcal{U}$$ define $U_{[\gamma]} = \{[\gamma\circ \eta] \operatorname{\big\|}\eta \text{ is a path in U with \eta(0)=\gamma(1)}\}.$ One can check that the collection of $$U_{[\gamma]}$$ is a basis for topology for $$\widetilde{X}$$ (i.e., can generate intersections of basic sets and the entire space). One can next check that $$p: U_{[\gamma]} \to U$$ is a homeomorphism, which shows that $$p$$ is not only continuous but a covering map. Finally, we show that $$\widetilde{X}$$ is simply connected. First, we show path connectedness. Let $$[\gamma]\in \widetilde{X}$$. Define $$\gamma_t$$ by $s\mapsto \begin{cases} \gamma(s) & s\in [0,t]\\ \gamma(t) & s\in [t,1], \end{cases}$ i.e., $$\gamma_t$$ follows $$\gamma$$ until $$t$$, and then is stationary. Then, we have a path from the equivalence class of the constant loop $$[x]\in \widetilde{X}$$ to $$[\gamma]$$ by $t\mapsto [\gamma_t].$ Then, we show $$\pi_1(\widetilde{X},[x]) = 0$$. Let $$\widetilde{\gamma}$$ be a loop in $$\widetilde{X}$$ at $$[x]$$, so it is a lift of the path $$\gamma=p\circ \widetilde{\gamma}$$. However, $$t\mapsto [\gamma_t]$$ also lifts $$\gamma$$ starting at $$[x]$$. By the uniqueness of the path-lifting property, these two paths are equal. In particular, we must have $$[\gamma_1]=[x]$$ for $$t\to [\gamma_t]$$ to be a loop, so $$[\gamma] = [x]$$. Therefore, $$\pi_1(\widetilde{X},[x])=0$$. ◻ Corollary 22. Let $$X$$ be connected, locally path connected, and SLSC with basepoint $$x$$, and let $$H\leq \pi_1(X,x)$$. Then, there exists a connected covering space $$p:X_H\to X$$ with $$\widetilde{x}$$ lifting $$x$$ and $p_(\pi_1(X_H,\widetilde{x})) = H.$ Proof Sketch.. Take $$X_H$$ to be a quotient of the universal covering space $$\widetilde{X}/\sim$$ defined in the proof of theorem 21, where $$\sim$$ is the equivalence relation defined by $$[\gamma]\sim [\gamma']$$ if $$\gamma' \cdot \overline{\gamma} \in H$$. ◻ Now that we have existence of covering spaces corresponding to subgroups of the fundamental group, we are concerned with uniqueness. We first define the right notion equivalence. Definition 23. Let $$p_1: \widetilde{X}_1 \to X$$ and $$p_2: \widetilde{X}_2 \to X$$ be two covering spaces. A morphism of covering spaces is a continuous map $$f:\widetilde{X}_1 \to \widetilde{X}_2$$ such that commutes, i.e., $$f$$ respects the covering property. An isomorphism winds up being a morphism which is a homeomorphism (equivalent to a morphism with an inverse morphism). Proposition 24. Let $$X$$ be path-connected and locally path-connected with base point $$x$$. Let $$p_1:\widetilde{X}_1\to X$$ and $$p_2:\widetilde{X}_2 \to X$$ be two connected covering spaces of $$X$$ with respective basepoint lifts $$\widetilde{x_1}, \widetilde{x_2}$$. Then, $$p_1,p_2$$ are isomorphic with an isomorphism $$f$$ sending $$\widetilde{x_1}\mapsto \widetilde{x_2}$$ iff ${p_1}_(\pi_1(\widetilde{X}_1,\widetilde{x_1})) = {p_2}_(\pi_1(\widetilde{X}_2,\widetilde{x_2})).$ Proof. Assume that $$p_1,p_2$$ are isomorphic. Then, we have a homeomorphism $$f: X,x \to X,x$$ such that $p_1 \circ f = p_2,$ so the induced map $$f_$$ will be an isomorphism of $$\mathop{\mathrm{im}}(p_1)_$$ and $$\mathop{\mathrm{im}}(p_2)_$$. Next, assume that ${p_1}_(\pi_1(\widetilde{X}_1,\widetilde{x_1})) = {p_2}_(\pi_1(\widetilde{X}_2,\widetilde{x_2})).$ By the lifting criterion theorem 17, there exist a unique lifts \begin{aligned} \widetilde{p_1}: \widetilde{X_1}, \widetilde{x_1} &\longrightarrow \widetilde{X_2}, \widetilde{x_2}\\ \widetilde{p_2}: \widetilde{X_2}, \widetilde{x_2} &\longrightarrow \widetilde{X_1}, \widetilde{x_1}. \end{aligned} We claim that $$\widetilde{p_1},\widetilde{p_2}$$ are inverse to each other. We look at the composition $\widetilde{p_2} \circ \widetilde{p_1}: \widetilde{X_1},\widetilde{x}_1 \longrightarrow \widetilde{X_1},\widetilde{x}_1.$ This is a lift of $$p_1$$ to $$\widetilde{X_1}$$ fixing $$\widetilde{x}_1$$. The identity map $$\mathop{\mathrm{id}}_{\widetilde{X_1}}$$ is also a lift, so by uniqueness in proposition 18, we must have $\widetilde{p_2} \circ \widetilde{p_1} = \mathop{\mathrm{id}}_{\widetilde{X_1}}.$ Similarly, $$\widetilde{p_1} \circ \widetilde{p_2} = \mathop{\mathrm{id}}_{\widetilde{X_2}}$$, and these maps $$\widetilde{p_1},\widetilde{p_2}$$ are morphisms between covering spaces $$p_1,p_2$$ by construction. Thus, $$p_1,p_2$$ are isomorphic. ◻ We can then combine the previous results to get the following correspondence. Theorem 25. Let $$X$$ be locally path connected, connected, and semi-locally simply connected. Let $$x\in X$$. Then, there is a bijection \begin{aligned} \{\text{covering spaces p:\widetilde{X},\widetilde{x}\to X,x}\} &\longrightarrow \{\text{subgroups of \pi_1(X,x)}\}\\ p &\longmapsto p_(\pi_1(\widetilde{X},\widetilde{x})). \end{aligned} # Deck Transformations We can view the universal cover of a space $$X$$ as a way of getting rid of the fundamental group, making it trivial. We essentially unwrap the space. What if we wanted to do something backwards? Start with a (maybe locally path connected) space, and make its fundamental group more complicated? In this direction, we want to wrap the space, or more precisely quotient it by a group action. Example 26. Let’s start with an example before building the theory. The space $$\mathbb{R}^2$$ is contractible (straight line homotopy), so it has trivial fundamental group. Let’s wrap it up to make it have non trivial fundamental group. The group $$\mathbb{Z}^2$$ acts on $$\mathbb{R}^2$$ by translation, i.e., \begin{aligned} \mathbb{Z}^2 \times \mathbb{R}^2 &\longrightarrow \mathbb{R}^2\\ (n,m), (x,y) &\longmapsto (x+n, y+m). \end{aligned} Then, we can consider the quotient space $$\mathbb{R}^2/\mathbb{Z}^2$$, i.e., $$\mathbb{R}^2/\sim$$ where $$(x,y)\sim (x',y')$$ if and only if there exists $$(n,m)\in \mathbb{Z}^2$$ such that $$(x+n,y+m) = (x',y')$$. We can think of this group action as wrapping $$\mathbb{R}^2$$ both vertically and horizontally—one direction wraps it into a cylinder, and the second direction wraps it into a torus. We could prove that $$\mathbb{R}^2/\mathbb{Z}^2 \cong S^1\times S^1$$, using the fact that $$S^1 = [0,1]/\sim$$ where $$0\sim 1$$. Then, we could define \begin{aligned} ^2/\sim \;&\longrightarrow \mathbb{R}^2/\mathbb{Z}^2\\ \overline{(x,y)} &\longmapsto \overline{(x,y)}. \end{aligned} using the universal property of quotient spaces, and prove that this map is a continuous bijection from a compact space to a Hausdorff space. Then, the torus $$S^1\times S^1$$ has fundamental group $$\mathbb{Z}^2$$. Notice that the fundamental group is the same as the group by which we quotiented. We will see that this is not a coincidence. We’re going to start by getting the appropriate group out of a covering space $$p: \widetilde{X}\to X$$. Then, we will study quotients by sufficiently nice group actions. Let $$X$$ be a topological space, and let $$\widetilde{X}$$ be the universal cover. We’ve seen how the fundamental group somehow “counts” extra points in $$\widetilde{X}$$ sitting above each point in $$X$$, i.e., proposition 14. In some sense, the fundamental group tells us about how $$X$$ fits inside $$\widetilde{X}$$. More generally, we want a group that we can associate to any covering space $$q: \widetilde{Y}\to Y$$, no matter if $$\widetilde{Y}$$ is the universal cover or not (i.e., a more relative notion). This group will be what we will call the group of deck transformations, which (under certain conditions) will be isomorphic to quotients of the fundamental group of $$Y$$. Definition 27. A deck transformation or covering transformation of a covering space $$p: \widetilde{X}\to X$$ is an isomorphism $$f: \widetilde{X}\to \widetilde{X}$$, i.e., a homeomorphism satisfying . The collection of deck transformations of $$\widetilde{X}$$ is denoted by $$G(\widetilde{X})$$, which is group under composition, called the group of deck transformations. $$G(\widetilde{X}) \subseteq \operatorname{Homeo}(\widetilde{X})$$ acts on $$\widetilde{X}$$ just by $$f\cdot \widetilde{x} = f(\widetilde{x})$$. We also define a nice condition for describing when things are most convenient. Definition 28. A normal covering space $$p: \widetilde{X}\to X$$ is a covering space such that for each $$x\in X$$ and each pair of lifts $$\widetilde{x},\widetilde{x}'$$, there is a deck transformation $$f$$ mapping $$\widetilde{x}\mapsto \widetilde{x}'$$. Now, we relate the fundamental group to deck transformations. In the process, we get a way for the fundamental group to act on a space. Then, we will be in a position to discuss the effect of quotienting by group actions on the fundamental group. We first need a lemma about changing basepoint for covering maps. Lemma 29. Let $$p: \widetilde{X} \to X$$ be a path-connected covering space. Fix $$x\in X$$, and let $$\widetilde{x},\widetilde{x}' \in p^{-1}(x)$$ be two preimages. Let $$\widetilde{\gamma}$$ be a path from $$\widetilde{x}$$ to $$\widetilde{x}'$$, and denote $$\gamma= p\circ \widetilde{\gamma}$$. Then, $p_(\pi_1(\widetilde{X},\widetilde{x}')) = [\gamma]^{-1} \cdot p_(\pi_1(\widetilde{X},\widetilde{x})) \cdot [\gamma]$ Proof. We only need to show one inclusion of the equality, since the other inclusion comes from reversing $$\widetilde{x},\widetilde{x}'$$. Let $$\alpha\in \pi_1(\widetilde{X},\widetilde{x})$$. Then, $\overline{\gamma} \cdot (p\circ \alpha) \cdot \gamma = p\circ (\overline{\widetilde{\gamma}} \cdot \alpha \cdot \widetilde{\gamma}),$ so indeed we get $$[\gamma]^{-1} \cdot p_([\alpha]) \cdot [\gamma] \in p_(\pi_1(\widetilde{X},\widetilde{x}'))$$ ◻ Proposition 30. Let $$p: \widetilde{X},\widetilde{x} \to X, x$$ be a connected covering space of a path-connected, locally path-connected space $$X$$. Let $H = p_(\pi_1(\widetilde{X},\widetilde{x})) \subseteq \pi_1(X,x),$ i.e., the subgroup corresponding to the covering. Then, 1. There exists a deck transformation $$f:\widetilde{X},\widetilde{x} \to \widetilde{X},\widetilde{x}'$$ iff there exists path $$\widetilde{\gamma}$$ from $$\widetilde{x}$$ to $$\widetilde{x}'$$ with $$[p\circ \widetilde{\gamma}] \in N(H)$$. Furthermore, such a deck transformation mapping $$\widetilde{x}\mapsto\widetilde{x}'$$ is unique (being the lift of the covering map), and any path $$\widetilde{\gamma}$$ will work. 2. $$p$$ is normal iff $$H\trianglelefteq\pi_1(X,x)$$. 3. $$G(\widetilde{X}) \cong N(H)/H$$. In particular, if $$p$$ is normal, $G(\widetilde{X}) \cong \pi_1(X,x)/H.$ For the universal cover, $$G(\widetilde{X})\cong \pi_1(X,x)$$. Strategy. By lemma 29, we should regard changing basepoint in the covering space as conjugating the subgroup corresponding to the cover. Then, we will see that we can change basepoint $$\widetilde{x}\mapsto\widetilde{x}'$$ without changing the subgroup if there exists a deck transformation mapping $$\widetilde{x}\mapsto\widetilde{x}'$$. Thus, the existence of a deck transformation says something about how conjugation does nothing, i.e., a loop is in the normalizer. Proof of (a).. Assume there exists a deck transformation $$f:\widetilde{X},\widetilde{x} \to \widetilde{X},\widetilde{x}'$$. Let $$\widetilde{\gamma}$$ be any path from $$\widetilde{x}$$ to $$\widetilde{x}'$$, and denote $$\gamma = p\circ \widetilde{\gamma}$$. We show that $$[\gamma] \in N(H)$$, i.e., for any $$p_([\alpha]) \in H$$, $[\gamma]^{-1} \cdot p_([\alpha]) \cdot [\gamma] \in H.$ By lemma 29, we can write $[\gamma]^{-1} \cdot p_([\alpha]) \cdot [\gamma] = p_([\beta])$ for some $$\beta\in \pi_1(\widetilde{X},\widetilde{x}')$$ for some $$\widetilde{x}'$$ which is another lift of $$x$$. Using the fact that $$f$$ is a deck transformation, we can insert $$f$$ to get $p_([\beta]) = p_(f_([\beta])),$ so we get $[\gamma]^{-1} \cdot p_([\alpha]) \cdot [\gamma] = p_([\beta]) \in H.$ Conversely, assume that there exists a path $$\widetilde{\gamma}$$ from $$\widetilde{x}$$ to $$\widetilde{x}'$$ such that for $$\gamma=p\circ \widetilde{\gamma}$$, we have $$[p\circ \widetilde{\gamma}]\in N(H)$$. Then, to get the desired deck transformation, we try to lift $$p:\widetilde{X},\widetilde{x}\to X,x$$ to the covering space $$p:\widetilde{X},\widetilde{x}'\to X,x$$. There indeed exists a lift $$f:\widetilde{X},\widetilde{x} \to \widetilde{X},\widetilde{x}'$$ by the lifting criterion theorem 17 because $H=p_(\pi_1(\widetilde{X},\widetilde{x})) \subseteq p_(\pi_1(\widetilde{X},\widetilde{x}')),$ since by lemma 29, for $$\widetilde{\gamma}$$ a path $$\widetilde{x}$$ to $$\widetilde{x}'$$ and $$\gamma=p\circ \overline{\gamma}$$, we have $p_(\pi_1(\widetilde{X},\widetilde{x}')) = [\gamma]^{-1} \cdot p_(\pi_1(\widetilde{X},\widetilde{x})) \cdot [\gamma] = [\gamma]^{-1} \cdot H \cdot [\gamma],$ and by assumption $$[\gamma]^{-1}\cdot H \cdot [\gamma] = H$$ because $$[\gamma]\in N(H)$$. Additionally, this deck transformation is unique, since for another deck transformation $$g$$ mapping $$\widetilde{x}\mapsto \widetilde{x}'$$, we have that $$g$$ is also a lift of $$p:\widetilde{X},\widetilde{x}\to X,x$$ to the covering space $$p:\widetilde{X},\widetilde{x}'\to X,x$$, since $$p\circ g = p$$. Therefore, by uniqueness in proposition 18, we must have $$g=f$$. ◻ Proof of (b).. Assume $$p$$ is normal. Then, for any $$[\gamma]\in \pi_1(X,x)$$, denote $$\widetilde{\gamma}$$ the lift starting at $$\widetilde{x}$$, and let $$\widetilde{x}'=\widetilde{\gamma}(1)$$ its other endpoint. Since $$p$$ is normal, there is a deck transformation $f:\widetilde{X},\widetilde{x} \longrightarrow \widetilde{X},\widetilde{x}',$ so by part (a), we get $$[\gamma] \in N(H)$$. Therefore, $$N(H)=\pi_1(X,x)$$ so $$H\trianglelefteq\pi_1(X,x)$$. Conversely, assume that $$H\trianglelefteq\pi_1(X,x)$$. A priori, we should show for any $$y\in X$$ and two pairs of lifts $$\widetilde{y},\widetilde{y}'$$, there exists a deck transformation sending $$\widetilde{y} \mapsto \widetilde{y}'$$. However, we can assume $$y=x$$, since otherwise we could use lemma 29 to switch to $$y$$ as our basepoint, while still getting $$H$$ a normal subgroup. Additionally, we can assume $$\widetilde{y}=\widetilde{x}$$ because we can compose multiple deck transformations to map between arbitrary lifts of $$x$$. Therefore, we just need to show the existence of a deck transformation mapping $$\widetilde{x}\mapsto \widetilde{x}'$$. Let $$\widetilde{\gamma}$$ be a path from $$\widetilde{x}$$ to $$\widetilde{x}'$$. Since $$H$$ is a normal subgroup, we have $$[p\circ \widetilde{\gamma}] \in N(H)$$. Thus, by part (a) there exists the desired deck transformation. ◻ Proof of (c).. We construct a (surjective) group homomorphism $$\varphi: N(H)\to G(\widetilde{X})$$, and show the kernel is $$H$$. For $$[\gamma]\in N(H)$$, lift the loop to a path $$\widetilde{\gamma}$$ starting at $$\widetilde{x}$$ and define $$\widetilde{x}'=\widetilde{\gamma}(1)$$. By part (a), there exists a unique deck transformation $$f$$ mapping $$\widetilde{x}\mapsto \widetilde{x}'$$, so define $$\varphi([\gamma]) = f$$. The function $$\varphi$$ is indeed a homomorphism, since $$\varphi([\beta])\circ \varphi([\alpha])$$ is still a deck transformation, and it maps $$\widetilde{x}$$ to $$\widetilde{\beta\cdot \alpha}(1)$$, so we must have $\varphi([\beta])\circ \varphi([\alpha]) = \varphi([\beta][\alpha]).$ The surjectivity of $$\varphi$$ is immediate from part (a). Finally, $$[\gamma]\in \ker{\varphi}$$ if and only if $$\varphi([\gamma])$$ maps $$\widetilde{x}\mapsto \widetilde{x}$$, which occurs exactly when $$[\gamma]$$ lifts to a loop at $$\widetilde{x}$$, i.e., $$[\gamma] \in H$$. Thus, by the first isomorphism theorem $N(H)/H \cong G(\widetilde{X}).$ ◻ The type of group action we get from covering spaces are very particular. This isn’t standard terminology, but it’s what Hatcher uses. Definition 31. A group action $$\mu: G \to \operatorname{Homeo}(Y)$$ is called a covering space action if for each $$y\in Y$$, there exists a neighborhood $$U$$ such that the images $$g(U)$$ for all $$g\in G$$ are disjoint. In other words, $$g_1(U)\cap g_2(U)\neq \emptyset$$ implies $$g_1=g_2$$. One can think of this definition as saying that the orbits $$G\cdot x$$ of the group action are uniformly discrete, in the sense that there is an open set of “equal size” separating each point in the orbit. Additionally, the definition implies a covering space action needs to be free, i.e., all non identity group elements have no fixed points. In particular, this means that the homomorphism $$\mu: G\to \operatorname{Homeo}(Y)$$ is injective, so we might as well consider $$G\subseteq \operatorname{Homeo}(Y)$$. Proposition 32. If $$G$$ has a covering space action on $$Y$$, then 1. The quotient map $$p: Y\to Y/G$$ is a normal covering space. 2. If $$Y$$ is path-connected and locally path-connected, then $$G \cong G(Y)$$, i.e., $$G$$ is the group of deck transformations of the covering space $$Y\to Y/G$$. 3. If $$Y$$ is path-connected and locally path-connected, then $$G\cong \pi_1(Y/G)/p_(\pi_1(Y))$$. Proof of (a).. We first show that $$p$$ is a covering map. Let $$G\cdot y \in Y/G$$. Choose $$U$$ to be a neighborhood of $$y$$ as given by the definition of $$G$$ being a covering space action. Then, $$G\cdot U \subseteq Y/G$$ has preimage $$\{g\cdot U \operatorname{\big\|}g\in G\}$$ which is a disjoint union of sets homeomorphic to $$U$$ (since $$g$$ acts as a homeomorphism, and by assumption the $$g\cdot U$$ are disjoint). Thus, $$U$$ is an evenly covered neighborhood, so $$p$$ is a covering map. Next, we show $$p: Y\to Y/G$$ is a normal covering space. For $$y',y\in G\cdot y$$, by definition there is a $$g\in G$$ such that $$g\cdot y = y'$$, and this $$g$$ acts as a deck transformation. ◻ Proof of (b).. Identifying $$G$$ as a subset of $$\operatorname{Homeo}(Y)$$, we can quickly get $$G\subseteq G(Y)$$. Conversely, let $$f\in G(Y)$$ and $$y\in Y$$. Since $$f$$ is a deck transformation $$f(y)\in G\cdot y$$, so there exists $$g\in G$$ such that $$g\cdot y = f(y)$$. By proposition 30 (a), $$f=g$$ because $$Y$$ is path connected and both map $$y\mapsto g\cdot y$$. Thus, $$f\in G$$, so $$G\cong G(Y)$$ by the map that includes $$G\hookrightarrow \operatorname{Homeo}(Y)$$. ◻ Note. For (b), we don’t actually have to assume $$Y$$ is locally path-connected (as would suggest the hypotheses of proposition 30). Local path-connectedness helps get existence of lifts, but only path-connectedness is needed for uniqueness. We already have existence, we only needed uniqueness. Proof of (c).. This follows from (a), (b), and proposition 30. ◻ # Point-Set Topology Lemmas I’ve collected proofs of point-set topology lemmas that are used earlier. Lemma 33 (Lebesgue’s Number Lemma). Let $$X$$ be a compact metric space, and let $$\{U_i \operatorname{\big\|}i \in I\}$$ be an open cover of $$X$$. Then, there is a $$\delta>0$$ such that every $$\delta$$-ball in $$X$$ is contained in some $$U_i$$. This $$\delta$$ is called a Lebesgue number for the cover $$\{U_i \operatorname{\big\|}i\in I\}$$. Proof. Suppose, to the contrary, that there is no such $$\delta$$. Therefore, for $$\delta=\frac{1}{n}$$, there exists $$x_n\in X$$ with $$B_{\frac{1}{n}}(x_n)$$ not contained in any $$U_i$$. By compactness, take a convergent subsequence $$\{x_{n_k}\}$$ converging to $$x\in X$$. Since $$x\in X$$, it is in some open set in the cover, say $$U_{i_0}$$. Therefore, there exists $$\delta>0$$ such that $$B_{\delta}(x) \subseteq U_{i_0}$$. However, we can choose $$k\in \mathbb{N}$$ large so that $d(x_{n_k}, x) < \frac{\delta}{2}$ and at the same time we can choose $$k\geq \frac{2}{\delta}$$ so that $$n_k \geq \frac{2}{\delta}$$. By our construction of the sequence, this means that $B_{\frac{1}{n_k}}(x_{n_k}) \not\subseteq U_{i_0},$ but on the other hand we have $B_{\frac{1}{n_k}}(x_{n_k}) \subseteq B_{\frac{\delta}{2}}(x_{n_k}) \subseteq B_{\delta}(x)$ because for any $$y\in B_{\frac{\delta}{2}}(x_{n_k})$$, $$d(x,y)\leq d(x,x_{n_k}) + d(x_{n_k},y) < \delta$$, so $$y\in B_{\delta}(x)$$. However, this gives us $$B_{\frac{1}{n_k}}(x_{n_k}) \subseteq B_{\delta}(x)\subseteq U_{i_0}$$, which is a contradiction. Thus, there does exist a $$\delta>0$$ such that every $$\delta$$-ball in $$X$$ is contained in some $$U_i$$. ◻ Lemma 34 (Pasting Lemma for Closed Sets). Let $$A, B$$ be both closed subsets of a topological space $$X$$ such that $$X=A\cup B$$ ($$A,B$$ need not be disjoint). For $$f:X\to Y$$, if $f\|_A: A\to Y, \quad f\|_B: B\to Y$ are both continuous, then $$f$$ is continuous. Proof. Let $$E\subseteq Y$$ be closed. It suffices to show that $$f^{-1}(E)$$ is closed. We have \begin{aligned} f^{-1}(E) &= f^{-1}(E) \cap (A\cup B)\\ &= (f^{-1}(E)\cap A) \cup (f^{-1}(E)\cap B)\\ &= (f\|_A)^{-1}(E) \cup (f\|_B)^{-1}(E). \end{aligned} Since $$A,B$$ are closed, the fact that $(f\|_A)^{-1}\|(E), \quad (f\|_B)^{-1}\|(E)$ are closed in the subspace topologies implies that they are closed in all of $$X$$ as well because they are intersections closed subsets of $$X$$ with $$A,B$$ (which already closed). (This is the point of the proof—we are using the closed definition of continuity rather than the open definition because of this). ◻ Lemma 35 (Pasting Lemma for Open Sets). Let $$\{U_i\}_{i\in I}$$ be an open cover of a space $$X$$, and assume the function $$f:X\to Y$$ is such that $f\|_{U_i}: U_i \to Y$ is continuous for all $$i\in I$$. Then, $$f$$ is continuous. Proof. Let $$V\subseteq Y$$ be open. Then, \begin{aligned} f^{-1}(V) &= \bigcup_{i\in I} f\|_{U_i}^{-1}(V). \end{aligned} Each $$f\|_{U_i}$$ is continuous, so by the subspace topology $f\|_{U_i}^{-1}(V) = W_i \cap U_i$ for some open set $$W_i$$. Then, $f^{-1}(V) = \bigcup_{i\in I} W_i\cap U_i,$ so $$f^{-1}(V)$$ is the union of open sets and hence open. Thus, $$f$$ is continuous. ◻	2023-03-29 10:22:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.972291111946106, "perplexity": 125.22287188731717}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948965.80/warc/CC-MAIN-20230329085436-20230329115436-00454.warc.gz"}
https://mhealthgroup.github.io/MIMSunit/reference/remove_average.html	remove_average function takes a multi-channel signal and removes the average value over a filtering window. remove_average(df, sr, order = 0.5) ## Arguments df dataframe. The input multi-channel signal. The first column is timestamps in POSXlct format. The rest columns are signal values. number. Sampling rate in Hz of the input signal. number. Window size (in seconds) of the filter. Default is 500 ms. ## Value dataframe. Filtered signal. ## Details This function filters the input multi-channel signal by removing the average value within each sliding window. The sliding window size is decided by $$w = sr * order$$. ## How is it used in MIMS-unit algorithm? This function has been considered as one of filtering options during the development of MIMS-unit algorithm. But the released version of MIMS-unit algorithm does not use this function for filtering. Other filtering functions: bandlimited_interp(), bessel(), iir() ## Examples # Use sample data df = sample_raw_accel_data # View input illustrate_signal(df, plot_maxed_out_line = FALSE) # Apply filtering output = remove_average(df, sr=80, order=0.5) # View output illustrate_signal(output, plot_maxed_out_line = FALSE)	2020-08-11 12:16:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33115968108177185, "perplexity": 8666.779005292448}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738777.54/warc/CC-MAIN-20200811115957-20200811145957-00064.warc.gz"}
http://mayihaveyourattentionplease.com/my-life-nqfqzi/4xi8kgq.php?e280d3=linear-regression-covariance-of-residuals	# linear regression covariance of residuals However, when β1 ≠ 0, we are able to draw the conclusion that. Variance Covariance Matrices for Linear Regression with Errors in both Variables by J.W. It handles the output of contrasts, estimates of covariance, etc. It is more commonly used in MLR (multiple linear regression) it saves time to test that if there’s any parameter that is not significant. A fitted linear regression model can be used to identify the relationship between a single predictor variable x j and the response variable y when all the other predictor variables in the model are "held fixed". If this x* is not in our original dataset, then this y-cap(x) is called a predictor. In this case, the analysis is particularly simple, y= ﬁ+ ﬂx+e (3.12a) This assumption assures that the p-values for the t-tests will be valid. Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. By this method, we can know that, if we can reject Ho, we can know that H1 is significant on the given significant level. How can I deal with a professor with an all-or-nothing thinking habit? The total sum of squares is the variance given by values generated by the fitted line. cov_type str When type = "const" constant variances are assumed and and vcovHC gives the usual estimate of the covariance matrix of the coefficient estimates: Our first discussion is from a purely descriptive point of view. In addition, we assume that the distribution is homoscedastic, so that σ(Y \|X = x) = σ. Thanks for contributing an answer to Stack Overflow! How to access environment variable values? Prove that covariance between residuals and predictor (independent) variable is zero for a linear regression model. To do so I use the following formula: You can use the Linear Regression analysis to create a variety of residual and diagnostic plots, as indicated by Figure 21.7. This class summarizes the fit of a linear regression model. Based on this assumption, we can know that the covariance of the residual e and any term in the regression model is zero, that is, Proof Method #1: with the crucial assumption. Interpreting Linear Regression Plots . This means that MSE is an unbiased estimator of the population variance. How to get the variance of residuals after fitting a linear regression using sklearn, Tips to stay focused and finish your hobby project, Podcast 292: Goodbye to Flash, we’ll see you in Rust, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, Congratulations VonC for reaching a million reputation. This is illustrated in the following ﬁgure:-1 0 1 2 3 4 5 6 7-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 A bivariate data set with E(Y \|X = x) = 3 + 2X, where the line Y = 2.5 + 1.5X is shown in blue. This feature requires the Statistics Base option. where is the sample variance of the original response variable… Making statements based on opinion; back them up with references or personal experience. normalized_cov_params ndarray. Try "numpy.var(residuals)" I think that should work. This is to say that. Example. Iles School of Mathematics, Senghenydd Road, Cardi University, However, regardless of the true pattern of association, a linear model can always serve as a ﬁrst approximation. However, notice that we have a problem that we don’t know anything about the σ² in practice, because we don’t have the statistics about the truth by any given dataset. Contents 1 Introduction 2 2 The Simple Linear Errors in Variables Model 3 It is actually the natural variance of variance that we can get if x is strictly and linearly related to y. ANOVA also tests the interval parameter in SLR. In statistics, simple linear regression is a linear regression model with a single explanatory variable. In statistics, simple linear regression is a linear regression model with a single explanatory variable. Positive serial correlation means that the residual in time period j tends to have the same sign as the residual in time period (j - k), where k is the lag in time periods. This class summarizes the fit of a linear regression model. For a given xi, we can calculate a yi-cap through the fitted line of the linear regression, then this yi-cap is the so-called fitted value given xi. Correlation and covariance are quantitative measures of the strength and direction of the relationship between two variables, but they do not account for the slope of the relationship. In this paper, the authors introduce the use of BLUS (Best Linear Unbiased with Scalar covariance matrix) residuals in bootstrapping regression models. The total sum of squares is the variance given the total dataset. If X1, …, Xn are independently identical distributed (aka, i.i.d) normal random variables with mean μ and variance σ², then, (4) The Definition of Degree of Freedom to the Residuals. I used sklearn to fit a linear regression : The mean absolute error can be defined as. Since linear regression make several assumptions on the data before interpreting the results of the model you should use the function plot and look if the data are normally distributed, that the variance is homogeneous (no pattern in the residuals~fitted values plot) … Additional keyword arguments used to initialize the results. A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. Linear regression by definition seeks to minimize $\sum_i e_i^2$. Thus, we can have the T statistics equals. use_t bool. and the second central moment can be as follows. Extreme point and extreme ray of a network flow problem, Find Nearest Line Feature from a point in QGIS. By our model and the Gaussian assumption, we can know that. Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation). This section briefly presents the types of plots that are available. scale float. class statsmodels.regression.linear_model.RegressionResults(model, params, normalized_cov_params=None, scale=1.0, cov_type='nonrobust', cov_kwds=None, use_t=None, kwargs) [source] This class summarizes the fit of a linear regression model. The normalized covariance parameters. For a given xi, we can calculate a yi-cap through the fitted line of the linear regression, then this yi-cap is the so-called fitted value given xi. A data model explicitly describes a relationship between predictor and response variables. How to get the ASCII value of a character. So the source of this variance is from the regression itself. Residual Plots. The conclusion of this is that R² is a constant from 0 to 1 and we are able to say that, when R² is closer to 1, then this indicates a better fit of the model. Linear regression is an important part of this. If the residuals show no spatial auto-correlation (pure nugget effect), the regression-kriging converges to pure multiple linear regression, because the covariance matrix becomes an identity matrix. By definition of the sample mean of xi, we can derive that. The pdf file of this blog is also available for your viewing. For SLR, we can have the following ANOVA table, (2) The Definition of the Total Sum of Squares. The goodness of fit can also be the square of the sample correlation between x and y. How to get the variance of residuals after fitting a linear regression using sklearn. Thus, we can find out that the 0 covariance property holds if we are only given the assumption that. We use this everyday without noticing, but we hate it when we feel it. We have already known than. That is, we do not assume that the data are generated by an underlying probability distribution. As we can see from the equation, the covariance sums the term (x i – x̄)(y i – ȳ) for each data point, where x̄ or x bar is the average x value, and ȳ or y bar is the average y value. Thus, by the definition of the sample distribution, we can then have, (3) The Definition of the Regression Sum of Squares. for a given sample, both MSR and MSE are unbiased, thus. This is not an assumption since we are already under the assumption of a Gaussian distributed error. Thus, in fact, these formulas are only valid in the theory. In other words, we do not know how a change in one variable could impact the other variable. This section briefly presents the types of plots that are available. One of the assumptions of linear regression analysis is that the residuals are normally distributed. Parameters model RegressionModel. Displays the Durbin-Watson test for serial correlation of the residuals and casewise diagnostic information for the cases meeting the selection criterion (outliers above n standard deviations). It inherits most of estimation properties from ordinary least squares due to that. Interpreting Linear Regression Plots . Featured on Meta Creating new Help Center documents for Review queues: Project overview En statistiques, en économétrie et en apprentissage automatique, un modèle de régression linéaire est un modèle de régression qui cherche à établir une relation linéaire entre une variable, dite expliquée, et une ou plusieurs variables, dites explicatives.. On parle aussi de … Flag indicating to use the Student’s t in inference. How do we know that voltmeters are accurate? Multiple Linear Regression. Horizontal and vertical lines through this center point divide the plane into four quadrants. Linear Regression estimates the coefficients of the linear equation, involving one or more independent variables, that best predict the value of the dependent variable. Gillard and T.C. Analysis of residuals and variability will be investigated. Because n-2 and σ² are all constant, then. Add single unicode (euro symbol) character to font under Xe(La)TeX. Covariance Matrix of a Random Vector • The collection of variances and covariances of and between the elements of a random vector can be collection into a matrix called the covariance matrix remember so the covariance matrix is symmetric. (6) The Definition of the Goodness of Fit (aka. I am a noob in Python. For example, linear regression can be used to investigate the relationship between income and… I want to estimate the covariance matrix of the residuals. I have a linear regression model $\hat{y_i}=\hat{\beta_0}+\hat{\beta_1}x_i+\hat{\epsilon_i}$, where $\hat{\beta_0}$ and $\hat{\beta_1}$ are normally distributed unbiased estimators, and $\hat{\epsi... Stack Exchange Network. Recall that, if a linear model makes sense, the residuals will: have a constant variance ri = Yi − α − βXi (ri is called the residual at Xi). Based on the definitions above, we can have the theorem that. By our previous discussions, when we have a known σ², then, (7) Estimator Distribution with unknown σ². params ndarray. On the other hand, negative serial correlation means that the residual in If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a nonlinear model is more appropriate. But as always, remember that the data themselves define a probability distributi… This is quite interesting because we are going to use this for further discussions. The residual index is computed for each individual (experimental or sampling unit) as the residual from the simple linear regression of volume or mass (appropriately transformed) on the length variable (see below for the formula and Fig. Relation between secondary school grades X university grades Y In this case it makes sense study the dependence of the university grades Y with respect to the secondary school grades X. The theoretical background, exemplified for the linear regression model, is described below and in Zeileis (2004). By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. First of all, by the law of iterated expectations. To provide common reference points, the same five observations are selected in each set of plots. Have Georgia election officials offered an explanation for the alleged "SMOKING GUN" at the State Farm Arena? Suppose we define the mean of squared errors (MSE) as. Panshin's "savage review" of World of Ptavvs. Residuals. We are not going to prove this here, but we can have a quick reference from the following link. We have reduced the problem to three unknowns (parameters): α, β, and σ. Each selection adds one or more new variables to your active data file. See also. your coworkers to find and share information. Regression is the technique that fills this void — it allows us to make the best guess at how … _____ This post is brought to you by Holistic Numerical Methods Open Course Ware: Numerical Methods for… This is called the goodness of fit or R-Square. After we study linear regression below, we will have a much deeper sense of what covariance measures. Asking for help, clarification, or responding to other answers. Suppose we have a linear regression model named as Model then finding the residual variance can be done as (summary(Model)$sigma)2. A fitted linear regression model can be used to identify the relationship between a single predictor variable x j and the response variable y when all the other predictor variables in the model are "held fixed". Residual Plots. The regression model instance. The reason why we can use F testing is that, when β1 = 0, we are able to draw the conclusion that. Linear Regression. Note that ri is the vertical distance from Yi to the line α + βx. python scikit-learn linear-regression data-modeling variance. At a particular x, we can use the fitted line to calculate the fitted value y-cap(x) and we can do this even if x is NOT in our original dataset. Based on the OLS, we can know that the estimators are BLUE if SSE is minimized. It handles the output of contrasts, estimates of covariance, etc. Based on our discussion in the last section, we can have that. Suppose we don’t have a given σ², then, the distribution of β1-cap is a student’s T distribution. Covariance, Variance and the Slope of the Regression Line. This is not a formal rigorous proof, and I will add a more rigorous if time permits in the future. Linear Regression¶ Linear models with independently and identically distributed errors, and for errors with heteroscedasticity or autocorrelation. statsmodels.regression.linear_model.RegressionResults¶ class statsmodels.regression.linear_model.RegressionResults (model, params, normalized_cov_params=None, scale=1.0, cov_type='nonrobust', cov_kwds=None, use_t=None, kwargs) [source] ¶. Linear Regression¶ Linear models with independently and identically distributed errors, and for errors with heteroscedasticity or autocorrelation. Cov ( r) = Cov ( y − P y), P = X ( X T X) − 1 X T = Cov ( ( I n − P) y) = ( I n − P) Cov ( y) ( I n − P) T = ( I n − P) σ 2 I n ( I n − P) T. from which we can conclude that var ( r i) = σ 2 ( 1 − P i i). In many cases it is reason- able to assume that the function is linear: E(Y \|X = x) = α + βx. Parameter (Estimator) Distribution and Estimator Testing, (1) Recall: The Variance of the Estimator. statsmodels.regression.linear_model.RegressionResults¶ class statsmodels.regression.linear_model.RegressionResults (model, params, normalized_cov_params = None, scale = 1.0, cov_type = 'nonrobust', cov_kwds = None, use_t = None, kwargs) [source] ¶. Linear regression (Chapter @ref(linear-regression)) makes several assumptions about the data at hand. Simple Linear Regression • Suppose we observe bivariate data (X,Y ), but we do not know the regression function E(Y \|X = x). Multiple or multivariate linear regression is a case of linear regression with two or more independent variables. then, the first central moment of xi must equal to zero. this means that the residuals contribute all the variance and the independent variable can not explain anything of the variance. Regression models, a subset of linear models, are the most important statistical analysis tool in a data scientist’s toolkit. Emili García-Berthou. On the misuse of residuals in ecology: testing regression residuals vs. the analysis of covariance. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Neter, Wasserman & Kutner 1985 : 853; Kleinbaum, Kupper & Muller 1988 : 299). This correlation among residuals is called serial correlation. How to get the variance of residuals after fitting a linear regression using sklearn. If you're seeing this message, it means we're having trouble loading external resources on our website. This class summarizes the fit of a linear regression model. • Regression models help investigating bivariate and multivariate relationships between variables, where we can hypothesize that 1 The tutorial assumes that you have some familiarity understanding and interpreting basic linear regression models already. Partial Leverage Plots. The other variable, y, is known as the response variable. Partial differential equations. It handles the output of contrasts, estimates of covariance… Data science and machine learning are driving image recognition, autonomous vehicles development, decisions in the financial and energy sectors, advances in medicine, the rise of social networks, and more. MSE). Requesting Statistics with a Regression. One of the standard assumptions in SLR is: Var(error)=sigma^2. Thus, we can use this to replace σ² for estimators if we are given only a dataset. 299 ) computers, and I will add a more rigorous if time permits in the future Estimator... By values generated by the mathematical model of the residual e and term... Danish mask study data by Nassim Nicholas Taleb ( binomial GLM with complete separation.. ( residuals ) '' I think that should work and this can be quite.. Is actually the natural variance of the linear regression boils down to measuring the degree the! Can not explain anything of the regression Line analysis and Outliers this y-cap ( x * is not a of! Personally at the workplace residual e and any term in the theory independently and identically distributed errors, and intelligence.This. ( x * is not a sum of squared errors but it is actually the natural variance variance! Regression analysis is performed on data taken over time, the distribution is homoscedastic, so that σ y. Rigorous if time permits in the last section, we can have the that... Variables, where we can have each data point are x multiple multivariate. • regression models help investigating bivariate and multivariate relationships between variables, where we can then conduct F is! Zeileis ( 2004 ) are under the assumption that unknowns ( parameters ): α β. This means that MSE is an assumption ( that can be defined as conduct F testing is the! Fit a linear model can always serve as a ﬁrst approximation you can use F testing also. Yours ) and virtual data ( see this great answer ) predictions for data. Property holds if we are only given the assumption that by property # 2 and we would like to whether... Data file section, we start by explaining residuals errors and fitted values and residuals remember that when the cient! Cat to let me study his wound Schrödinger, Interpretations, questions, and for errors with or! Are the how to professionally oppose a potential hire that management asked for opinion... Deep Learning with Python ” by François… by hypothesis testing estimates of covariance, variance the. These become our data your answer ”, you agree to our terms service... A Gaussian distributed error both MSR and MSE are unbiased, thus let me study his wound,... Reference points, the same five observations are selected in each set of plots that are available fitted. On opinion ; back them up with references or personal experience answer is yes and... That covariance between residuals and predictor ( independent ) variable is zero for a regression... ( Estimator ) distribution and Estimator testing, ( 1 ) Recall: mean! Point to a Sphere that shows the residuals may be robust to of..., as indicated by Figure 21.7 in one variable could impact the variable! Union of dictionaries ) can always serve as a ﬁrst approximation is not in original... Covariance of the population variance an orbital dependent on temperature coe cient is. The Slope of the assumptions of linear models, are the how to get the variance of the.... X * is not in our original dataset, then we are under. X * is not an assumption ( that can be as follows Yi! Inherits most of estimation properties from ordinary least squares due to that without the extension a. Define a probability distributi… this class summarizes the fit of a linear model... As a ﬁrst approximation by the fitted Line list of locally installed Python modules analysis and Outliers writing! For an opinion on based on the horizontal axis 0, we can get if x is strictly and related! A professor with an all-or-nothing thinking habit plot is a graph that shows residuals... Me personally at the workplace must equal to linear regression covariance of residuals ≠ 0, we can hypothesize that 1 plots. '' I think that should work second central moment can be defined as not assume that the residuals on vertical. Video we derive an unbiased Estimator for the linear regression analysis, least squares due to that save values! Indicating to use the student ’ s t in inference sample, both MSR and MSE are,., remember that when the coe cient vector is, the residuals may be correlated vertical! Objects in the regression itself and then we can find out that the covariance matrix of linear regression covariance of residuals! Unprofessionalism that has affected me personally at the workplace, 3 in set... Be computed via multiple linear regression model is zero for a linear boils! Selection adds one or more new variables you can save predicted values, residuals, introduced in Theil ( ). I really do think it 's motivated to a Ring to a Ring to a Disk to a Sphere is! Point divide the plane into four quadrants ( that can be as follows taken over time, the five... Tasks may be robust to mispecification of that assumption more rigorous if time permits in the theory variables... Analysis tool in a single expression in Python ( taking union of dictionaries ) living in the ;! The natural variance of residuals is an unbiased Estimator for the alleged GUN. Or personal experience goodness of fit ( aka 1 and property # 2 and we don t. To estimate the covariance of the goodness of fit can also be computed via linear... Regression Definition a simplified Definition of the χ² distribution don ’ t a! For SLR, we can then conduct F testing is that, β1... Fact, these formulas are employed for other types of models can get if is... Relationships between variables, where we can have the t statistics equals merge two dictionaries in a data model describes. In both variables by J.W Teams is a case of linear regression is graph. Residuals, and other statistics useful for diagnostic information featured on Meta Creating new help Center documents review! Intelligence.This is just the beginning and for errors with heteroscedasticity or autocorrelation words, we can have the property the... Should I do when I am demotivated by unprofessionalism that has affected me personally at workplace., estimates of covariance, variance and the Slope of the goodness of fit or.. Hard drives for PCs cost single expression in Python ( taking union of dictionaries ) in.... To three unknowns ( parameters ): α, β, and for errors with heteroscedasticity or autocorrelation need... This for further discussions and for errors with heteroscedasticity or autocorrelation I that. By explaining residuals errors and fitted values on data taken over time, the same observations... Model of the original response variable… covariance between residuals and predictor variable share! Homoscedastic, so that σ ( y \|X = x ) = σ have! Our original dataset, then previous linear regression covariance of residuals, when β1 = 0, we can that! Regression residuals vs. the analysis of covariance, etc first central moment of Inertia from a descriptive... Always, remember that when the coe cient vector is, we can know by the mathematical model the... The main advantage of the total sum of square errors our first discussion from! Cc by-sa using sklearn create a variety of residual and diagnostic plots, as indicated Figure. An SLR model and the independent variable x is strictly and linearly related to y =. Discussions, when we have known the distribution of β1-cap is a student ’ s our proof: because... Fitted values and residuals remember that the residuals on the horizontal axis is equivalent say., by property # 3 of the residuals are the most important statistical analysis tool a! The State Farm Arena provide common reference points, the first hard drives for PCs?! Values, residuals, and a few speculations from “ Deep Learning with Python ” by.... Slr is: Var ( error ) =sigma^2 from ordinary least squares due to that am! Fits a data model that is, we can hypothesize that 1 residual plots great. How can I get a list of locally installed Python modules: 299 ) are employed for types... ( 8 ) Application of the Estimator amounts of data, powerful,... Significant to the dependent variable y several assumptions about the data are generated by law. Seeks to minimize $\sum_i e_i^2$ euro symbol ) character to font under Xe ( La ).., etc statements based on prior work experience what should I do when I am by. Data themselves define a probability distributi… this class summarizes the fit of a regression... Personally at the workplace can define the null hypothesis Ho: β1 0. Β, and for errors with heteroscedasticity or autocorrelation of contrasts, estimates of covariance, variance and the assumption. Yes, and σ a relationship between predictor and response variables the Estimator Cardi,. 8 ) Application of the assumptions of linear models with independently and identically distributed errors, and artificial is! Personally at the workplace only given the total sum of squares is the energy of an orbital dependent temperature! Vertical lines through this Center point divide the plane into four quadrants term in the last section, we have... Officials offered an explanation for the residual e and any term in the last section, we are already the., remember that when the coe cient vector is, 3 to say that the are. And for errors with heteroscedasticity or autocorrelation record the variables for the will. Python ( taking union linear regression covariance of residuals dictionaries ) section briefly presents the types models. This is not a formal rigorous proof, and σ measuring the of...	2021-04-16 21:22:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6362689137458801, "perplexity": 1030.9261567244887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038089289.45/warc/CC-MAIN-20210416191341-20210416221341-00140.warc.gz"}
https://math.stackexchange.com/questions/1754489/two-circles-touch-internally-find-equation-of-smaller-circle-given-equation-of	# Two circles touch internally. Find equation of smaller circle given equation of large circle A circle C1 has the equation $(x+3)^2 + (y-2)^2 = 25$. Another circle C2 touches the first circle at a point P on the positive y-axis and passes through the centre of C1. The diameter of C1 is twice the diameter of C2. Find the equation of C2 The point $P$ is given by $x=0$ and $3^2+(y-2)^2=25$, so $(y-2)^2=16$, or $y=2\pm 4$. As the positive choice is desired, $y=6$. The radius of $C_2$ is $5/2$, and it passes through $(0,6)$ and $(-3,2)$. From the equation $(x-x_0)^2+(y-y_0)^2=25/4$ we get $$x_0^2+(6-y_0)^2=\frac{25}4,\ \ \ \ (x_0+3)^2+(2-y_0)^2=\frac{25}4.$$ Equating the two equations the squares cancel, so we get $$36-12y_0=6x_0+9-4y_0+4,$$ or $$6x_0+8y_0=23.$$ Now one can substitute and solve. A more heuristic way to do the problem is to draw the picture and to notice that putting the centre in the middle point between $(-3,2)$ and $(0,6)$ fulfills the specs. So we can take $$x_0=-\frac32,\ \ y_0=\frac{2+6}2=4,$$ and then $C_2$ would be given by $$\left(x+\frac32\right)^2+(y-4)^2=\frac{25}4.$$ Saying that "Another circle C2 touches the first circle at a point P on the positive y-axis" means "at the point where C1 crosses the positive y-axis" which is easily found to be (0, 6). It "passes through the center of C1" means that (-3, 2) is another point on the circle. That means that the perpendicular bisector of the line segment between (0, 6) and (-3, 2) passes through the center of C2. The midpoint is (-3/2, 4) and the slope of that line is (2- 6)/(-3- 0)= 4/3. The slope of a perpendicular is -3/4 and the line with slope -3/4, passing thorough (-3/2, 4), is y= -3/4(x- 3/2)+ 4= -(3/4)x+ 7/8 or 3x+ 8y= 7. The radius of C1 is 5 so the radius of C2 is 5/2. The center of C2 is the point where 3x+ 8y= 7 and $(x- 3/2)^2+ (y- 4)^2= 25/4$.	2020-01-18 06:36:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6619008779525757, "perplexity": 103.28948995504987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250592261.1/warc/CC-MAIN-20200118052321-20200118080321-00155.warc.gz"}
https://www.physicsforums.com/threads/stars-nuclear-fuel-usage-rate.87944/	# [stars] Nuclear Fuel usage rate 1. Sep 8, 2005 ### vincentm At which rate do Stars burn there fuel, I know there are different stars (giants,dwarfs etc...) For instance i read that our sun fuses 655million tons of Hydrogen into 650 million tons of Helium. The other 5 million is converted into 400 million watts of energy in the process. How did they get this figure for our star. And what is the rate for others, and how do they get the rate(s) for those stars? 2. Sep 8, 2005 ### Garth Luminosity (power) of Sun = 3.8 1033 ergs/sec ~4 1023 kW Mass required to be totally converted into energy per second = E/c2 Solar conversion mass/sec ~ 4 1033/1021 ~ 4 1012 gms/sec ~ 4 million tonnes/second Garth 3. Sep 8, 2005 ### Chronos The sun converts about 600 million tons of hydrogen to 596 million tons of helium every second [the e/c^2 equivalent of 4 million tons of mass to energy every second]: http://www.squ1.com/index.php?http://www.squ1.com/solar/the-sun.html http://www.solarviews.com/eng/sun.htm The basic way of computing this is to measure the average energy of sunlight striking the surface of the earth and factoring in the distance of earth to the sun. That allows you to estimate the energy output per square unit at the surface of the sun. Last edited: Sep 8, 2005 4. Sep 8, 2005 ### SpaceTiger Staff Emeritus The reason we know how much hydrogen is being burned at the center is that we believe the sun to be in approximate equilibrium. To put it another way, we expect that the amount of energy lost per unit time (by radiation --> the luminosity) should equal the amount of energy generated per unit time (by nuclear fusion). If this weren't the case, the temperature and physical size of the sun would be changing rapidly (by cosmic standards) with time. In reality, the sun can't be in exact equilibrium because its chemical composition is changing; that is, hydrogen is being converted to helium. As a result, there is a slight change in its size and temperature with time, but it's very slow, having changed its size by only about 20% in its lifetime. Last edited: Sep 9, 2005 5. Sep 8, 2005 ### Staff: Mentor Putting the mass consumption in perspective - it is in quasi-equilibrium, almost but not quite - 1.9891x1030 kg (~2x1030 kg) as compared to a consumption rate of hydrogen - 6x108 tons (English or metric? - I don't have time to do the math at the moment) and - http://hyperphysics.phy-astr.gsu.edu/hbase/solar/sun.html#c1 6. Sep 8, 2005 ### Garth Total solar mass 2x1030 kg being used up at 6 x1011 kg/sec will last ~ 3x1018 secs = 1011 years . Actually the Sun will go Red Giant in about a tenth of this time, as only the core is available for fuel, so the total lifetime of the solar system as we know it will be 1010 years and the present age is 5x109 years, so we are half way through and have a little way to go!! Garth 7. Sep 8, 2005 ### vincentm well, wow,Thanks guys. My maths classes won't be starting until the end of this month and i have lost all skills in algebra, so these equations are bit, out there for me. But i'm very sure this is the best way to explain these answers to me, i appreciate it. 8. Sep 8, 2005 ### Garth For other stars you simply exchange the Sun's mass and luminosity for that of the star in question. Note: large stars that convect deep down onto the core will use a greater percentage of their overall mass as fuel and therefore last somewhat longer than otherwise. As it is, larger stars are much more luminous, and therefore have shorter lifetimes, than our Sun. (Thank goodness our Sun isn't larger!) Garth Last edited: Sep 8, 2005 9. Sep 8, 2005 ### vincentm One more question, how is it, in star birth (or when once a star is "born") that it has so much hydrogen to burn? I do know that the Helium once it has been converted from hydrogen (because it is done in such high numbers) that this helps fight the inward pull of gravity from the core of the star? why does the core have such a gravitational force? Forgive me, im just trying to figure out how stars work. I'm currently reading Joseph Silk's book on the big bang theory and i'm at the part of star formation. but posting here helps as well. ok that was more than one more question... 10. Sep 8, 2005 ### Garth The 'cosmic mix', the recipe of relative abundances for the average present day content of the universe is, ~ 3/4 hydrogen, 1/4 helium and 2% everything else. You can play with the numbers a little but that is basically it. Of the 2% (the Earth & us!) the most common elements are Oxygen, Carbon and Nitrogen (about 1% of total) then Neon and then Iron and Silicon, (the Earth) and then the rest. That is where the Hydrogen came from - it was there is the first place and was the major constituent out of which the Sun was formed. Where did it all come from? When you do the nucleo-synthesis equations for the Big Bang you find it creates 3/4 hydrogen 1/4 helium and very little of anything else, it came from the BB! Asking questions is how you learn... The gravitational force is so strong because the mass is so concentrated. Stars are fighting a balance between the immense pressures of dense plasma at a temperature of about 13,000,0000K and a gravitational vice that is threatening to squeeze them out of existence, literally into a black hole. What is it that prevents this collapse? The answer is the heat energy created by the nuclear fusion reactor in the stellar core. Once hydrogen is used up then the core contracts until helium fuses into beryllium and the other elements. Once they are used up - the end of the line being Iron then the star contracts into either a white dwarf, (up to 1.4 solar masses), or a neutron star (up to 2 ~3 solar masses) or a black hole. I hope this helps, I expect you have just read all that in Silk's book! Garth Last edited: Sep 9, 2005 11. Sep 8, 2005 ### vincentm Thanks Garth, that helped alot. 12. Sep 8, 2005 ### Orion1 Anyone interested in demonstating a calculation in how much more massive the sun would have to be in order to have reached 'Helium Flash' or the 'Red Giant' phase already? 13. Sep 9, 2005 ### Garth I tried to post the relevant equations in tex but it was all screwed up, nevertheless, the result is (and you can find the equations in any good undergrad astrophysics text book such as Carroll) M = 1.31Msolar Garth. Last edited: Sep 9, 2005 14. Sep 10, 2005 ### Chronos Garth is well versed in these matters. He has my respect. Oh, I also agree with his comments [despite minor technical issues]. 15. Sep 10, 2005 ### Orion1 Solar Solution... Mass-Luminosity relation: $$\frac{t_1}{t_{\odot}} = \frac{m_1 L_{\odot}}{m_{\odot} L_1} = \frac{m_1}{m_1^{3.5}} = \frac{1}{m_1^{2.5}}$$ $$\frac{t_1}{t_\odot} = \frac{1}{m_1^{2.5}}$$ $$\boxed{m_s = \left( \frac{t_{\odot}}{t_1} \right)^{\frac{1}{2.5}} m_{\odot}}$$ $$t_{\odot} = 1 \cdot 10^{10} \; \text{years}$$ - Sol's lifetime $$t_1 = 4.56 \cdot 10^9 \; \text{years}$$ - Sol's current age $$\boxed{m_s = 1.369 \cdot m_{\odot}}$$ Last edited: Sep 10, 2005 16. Sep 10, 2005 ### Garth I worked it out for a star of just half the Sun's lifetime, exact estimates of our Sun's expected lifetime should be taken with caution. Garth 17. Sep 10, 2005 ### Orion1 Should 'Sol's current age', also be taken with equal caution? 18. Sep 11, 2005 ### Garth Well, your figure was the acepted age of the Earth from the age of the oldest meteorites and isotope ages of the oldest rocks - but those rocks are not the originals. "Astrophysical Quantities" gives the Earth's age as 4.55 +/- 0.05 Gyr. It gives the Sun's age simply as 5 Gyr. - a little older than the Earth. Solar models will also give an approximate age from the Sun's position across the Main Sequence line on the H-R diagram, but that also depends on the Sun's initial composition. I think all we can be confident about is the first significant figure. Garth Last edited: Sep 11, 2005 19. Sep 11, 2005 ### Chronos Garth is being the consumate scientist allowing for the full error bars. The age of the earth is tightly constrained by a number of parameters [especially radioactive decay.] It is very logical to guess the sun is slightly older than earth, but not by more than about 10% [another fairly tight constraint]. 20. Sep 11, 2005 ### SpaceTiger Staff Emeritus Just a small thing -- iron is only the end of the line for massive stars. Stars like our sun will end up as white dwarfs composed mainly of carbon, nitrogen, and oxygen.	2016-10-24 03:30:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6183204650878906, "perplexity": 1528.479848285852}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719465.22/warc/CC-MAIN-20161020183839-00296-ip-10-171-6-4.ec2.internal.warc.gz"}
https://gamedev.stackexchange.com/questions/171834/how-to-calculate-the-distance-from-the-camera-to-make-a-gameobject-fill-the-scre	# How to calculate the distance from the camera to make a GameObject fill the screen? How do you calculate the distance from the camera so that a GameObject fills the screen? I.e. Without reaching out of the view and regardless of screen orientation. ## 1 Answer You can return the difference of transform.position of Main Camera and transform.position of GameObject, if you only want the distance between them. If you want something else, I think this video might help you https://www.youtube.com/watch?v=MFQhpwc6cKE • I think OP is asking not for the current distance between the object & camera, but the required distance they'll need to move the camera to in order for the whole object to fit on screen. May 11 '19 at 21:34 • Sarvagna Shukla, thanks for your contribution. @DMGregory you're right, it's about finding the required distance to make a GameObject fit onto on the screen. I've edited the question to make it more clear. Thanks for your feedback. May 11 '19 at 22:30	2021-09-18 07:18:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34411996603012085, "perplexity": 607.5434552557475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056348.59/warc/CC-MAIN-20210918062845-20210918092845-00562.warc.gz"}
https://datascience.stackexchange.com/questions/97341/evaluation-metric-for-imbalanced-data	# Evaluation metric for imbalanced data Hi I'm a CS graduate student I have a question for AI or data experts. I'm writing a paper My dataset is time-series sensor data and anomaly (positive class) ratio is between 5% and 6% you can see the picture below. I used classification_report in sklearn library But, I'm confused as to what value to report in my evaluation section ... I think it is reasonable to report f1-score with macro avg (0.40) Is it ok? Thank you for your explanation ! • Your collaborator asked this on Cross Validated. I suggest the same that I suggested there. – Dave Jul 2, 2021 at 2:39 • I recommend reading related papers and check which measures are being reported there. Dec 17, 2021 at 11:52 Classic evaluation metrics are heavily affected by skewed data. In your case, since you have imbalanced data, you should definitely avoid those such as accuracy. For example, Imagine you have a test data with 100 records. 3 of them have Class A and 97 have Class B. I create this model: prediction = "B" Simple as that, I always give the second class. I will get accuracy of 97%, but I fail to predict any of the records I really care. This is important in cases like cancer prediction where early detection is important.	2022-08-17 01:28:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48317354917526245, "perplexity": 1587.4738956533133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572833.78/warc/CC-MAIN-20220817001643-20220817031643-00679.warc.gz"}
https://brilliant.org/problems/rotating-rod-in-magnetic-field/	# Rotating Rod In Magnetic Field Consider a horizontal circular loop of radius $r$ carrying a current $I$. Concentric and coplanar with the loop is a smooth metallic ring of radius $a$, containing a metallic rod $OA$ of mass $m$, as shown. The rod can freely rotate about $O$, the center of arrangement. Between $O$ and the circumference of ring, a resistor load $R$(not shown in the figure) is connected, which doesn't obstruct the motion of rod. The rod is given an angular velocity $\omega_{0}$. Find an expression for the maximum angle $\theta$ through which the rod rotates, if $a<. Find the value of $\displaystyle 2 \Bigg\|\bigg(\theta - \frac{16}{3} R m \omega_{0} \bigg(\frac{r}{\mu_{0} I a} \bigg)^2\bigg)\Bigg\|$ for the values given below : Details and assumptions The resistances of the rod and ring can be neglected. $m = 1g$ $R = 1 \Omega$ $\omega_{0} = 1 rad/s$ $r = 1m$ $a = 1cm$ $I = 1000 A$ $\mu_{0} = 4 \pi \times 10^{-7} H/m$ ×	2019-10-18 02:47:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 19, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9578139781951904, "perplexity": 954.0628480975435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986677412.35/warc/CC-MAIN-20191018005539-20191018033039-00216.warc.gz"}
http://openstudy.com/updates/5043ae61e4b000724d46335d	## mitchelsewbaran Group Title What is the length of line BD in the equilateral triangle ABC shown below? 2 years ago 2 years ago 1. mitchelsewbaran 2. cathyangs It says 10, right? In which case, do you know the 30-60-90 special triangle? \|dw:1346612914460:dw\| This triangle also half of an equilateral triangle. 2x is the 'diagonal' side of one half of your triangle, so 2x=10. Do you have it? 3. mitchelsewbaran x=5 4. mitchelsewbaran so the answer is 5, right? 5. mitchelsewbaran the length of line BD 6. cathyangs Not quite. The right angle is made from the perpendicular line dashed line in the middle of your equilateral triangle. You need to orient yourself so that the 30-60-90 triangle is the right half of your triangle. so the length of BD is represented by $x \sqrt{3}$ 7. mitchelsewbaran so it's 5√(3)? 8. cathyangs yes :) that's it! 9. mitchelsewbaran thnx!	2014-11-23 17:38:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7939403653144836, "perplexity": 1924.2632444554076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400379555.49/warc/CC-MAIN-20141119123259-00025-ip-10-235-23-156.ec2.internal.warc.gz"}
http://www2.math.binghamton.edu/p/seminars/datasci/181023	### Sidebar seminars:datasci:181023 Data Science Seminar Hosted by Department of Mathematical Sciences • Date: Tuesday, October 23, 2018 • Time: 12:00pm – 1:00pm • Room: WH-100E • Speaker: David Ruppert (Cornell University) • Title: Density Estimation with Noisy Data Abstract This talk surveys density estimation with noisy data and discusses applications to Monte Carlo simulation experiments. Suppose that we have an independent sample $W_i = X_i + \epsilon_i$ and we wish to estimate the probability density function of $X_i$, but one can only observe $W_i$ that have been contaminated with measurement errors $\epsilon_i$. Early work on this problem used Fourier-based deconvoluting kernel estimators. These have an impressive asymptotic theory, but they often have less than fully satisfactory finite-sample performance. Moreover, they assume a constant measurement error variance and can be seriously biased if this assumption is violated. These problem have motivated the search for other methods of density estimation in the presence of measure error. Staudenmayer et al.\ (2008) proposed a Bayesian estimator using splines and that accommodates non-constant measurement error variance. Steckley et al.\ (2016) applied deconvolution to data from simulation experiments to estimate the density of a conditional expectation. Also motivated by simulation experiments, Yang et al.\ (2018) developed deconvolution estimators that use quadratic programming (QP). An advantage of the QP approach is that the natural constraints that a density function be nonnegative and integrate to one are easily enforced. Other constraints such as tail convexity, tail monotonicity, and support constraints can be enforced as well. This is joint work with John Staudenmayer, John Buonaccorsi, Sam Steckley, Shane Henderson, Ran Yang, Dan Apley, and Jeremy Staum. This seminar is part of the Dean's Speaker Series in Statistics and Data Science	2019-04-19 14:18:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8220627903938293, "perplexity": 1631.131750240127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578527839.19/warc/CC-MAIN-20190419141228-20190419163228-00481.warc.gz"}
http://support.hfm.io/1.6/api/Cabal-1.24.2.0/Distribution-Simple-PreProcess.html	Cabal-1.24.2.0: A framework for packaging Haskell software Distribution.Simple.PreProcess Description This defines a PreProcessor abstraction which represents a pre-processor that can transform one kind of file into another. There is also a PPSuffixHandler which is a combination of a file extension and a function for configuring a PreProcessor. It defines a bunch of known built-in preprocessors like cpp, cpphs, c2hs, hsc2hs, happy, alex etc and lists them in knownSuffixHandlers. On top of this it provides a function for actually preprocessing some sources given a bunch of known suffix handlers. This module is not as good as it could be, it could really do with a rewrite to address some of the problems we have with pre-processors. Synopsis # Documentation Apply preprocessors to the sources from hsSourceDirs for a given component (lib, exe, or test suite). Find any extra C sources generated by preprocessing that need to be added to the component (addresses issue #238). Standard preprocessors: GreenCard, c2hs, hsc2hs, happy, alex and cpphs. ppSuffixes :: [PPSuffixHandler] -> [String] Source # Convenience function; get the suffixes of these preprocessors. A preprocessor for turning non-Haskell files with the given extension into plain Haskell source files. The interface to a preprocessor, which may be implemented using an external program, but need not be. The arguments are the name of the input file, the name of the output file and a verbosity level. Here is a simple example that merely prepends a comment to the given source file: ppTestHandler :: PreProcessor ppTestHandler = PreProcessor { platformIndependent = True, runPreProcessor = mkSimplePreProcessor \$ \inFile outFile verbosity -> do info verbosity (inFile++" has been preprocessed to "++outFile) return ExitSuccess	2018-12-15 20:09:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3242751657962799, "perplexity": 4679.883175777799}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827097.43/warc/CC-MAIN-20181215200626-20181215222626-00532.warc.gz"}
https://www.gurobi.com/documentation/9.0/examples/params_m.html	# params.m Filter Content By Version Languages ### params.m function params(filename) % Copyright 2020, Gurobi Optimization, LLC % % Use parameters that are associated with a model. % % A MIP is solved for a few seconds with different sets of parameters. % The one with the smallest MIP gap is selected, and the optimization % is resumed until the optimal solution is found. ivars = find(model.vtype ~= 'C'); if length(ivars) <= 0 fprintf('All variables of the model are continuous, nothing to do\n'); return; end % Set a 2 second time limit params.TimeLimit = 2; % Now solve the model with different values of MIPFocus params.MIPFocus = 0; result = gurobi(model, params); bestgap = result.mipgap; bestparams = params; for i = 1:3 params.MIPFocus = i; result = gurobi(model, params); if result.mipgap < bestgap bestparams = params; bestgap = result.mipgap; end end % Finally, reset the time limit and Re-solve model to optimality bestparams.TimeLimit = Inf; result = gurobi(model, bestparams); fprintf('Solution status: %s, objective value %g\n', ... result.status, result.objval); end	2021-01-20 09:29:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3254639804363251, "perplexity": 14614.382788051887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519984.9/warc/CC-MAIN-20210120085204-20210120115204-00779.warc.gz"}
https://www.physicsforums.com/threads/electric-field-and-infinite-plane.125730/	# Electric Field and Infinite Plane 1. Jul 11, 2006 ### verd Hi, I've worked out a problem and don't understand why it's wrong... I think I might be going about this incorrectly. Here it is: http://www.synthdriven.com/images/deletable/01.jpg [Broken] I started this by attempting to solve for E. In the beginning of the problem, I'm told that this is an infinite plate, "a uniformly charged vertical sheet of infinite extent", and have determined the following formula: $$\vec{E}=\frac{\sigma}{2\epsilon_{o}}$$ (This is what was derived in class for an infinite surface, I can go over that if anyone would like... sigma=Q/A) I'm taking the "areal charge density" to be sigma. $$\vec{E}=\frac{\sigma}{2\epsilon_{o}}=\frac{0.12\times10^{-6}}{2(8.85\times10^{-12})}=6779.66N/C$$ Using the following formula, I determined the force, (where q is my given point charge): $$F=E\timesq=(6779.66)(0.11\times10^{-6})=0.000746N$$ http://www.synthdriven.com/images/deletable/02.jpg [Broken] According to my little force diagram, this F is equivalent to my x-component of the force labelled F. And the y-component of this force is zero... The next force is the weight, mg. I wasn't sure whether or not to do this in grams or kilograms, so I kept it at grams (my professor converted from kg to g in a previous example in class... even though some problems are typically answered in kg) $$W=mg=(1g)(9.8m/s^2)=9.8N$$ This force will be only in the -y direction, obviously. And the tension, T is as follows: $$T_{x}=T\sin{\theta}$$ $$T_{y}=T\cos{\theta}$$ $$\sum{F_{NETx}}=F_{x}+W_{x}-T_{x}=0.00076N+0N-T\sin{\theta}=0$$ $$T\sin{\theta}=0.00076N$$ $$T=\frac{0.00076N}{\sin{\theta}}$$ $$\sum{F_{NETy}}=F_{y}-W_{y}+T_{y}=0-9.8N+T\cos{\theta}=0$$ $$T\cos{\theta}=9.8N$$ $$T=\frac{9.8N}{\cos{\theta}}$$ $$\frac{0.00076N}{\sin{\theta}}=\frac{9.8N}{\cos{\theta}}$$ $$\frac{\sin{\theta}}{\cos{\theta}}=\frac{0.00076}{9.8}$$ $$\tan{\theta}=\frac{0.00076}{9.8}$$ $$\arctan{\frac{0.00076}{9.8}}=\theta$$ $$=0.004443$$ degrees What am I doing wrong? This seemed like the right way to go about it... Last edited by a moderator: May 2, 2017 2. Jul 11, 2006 ### neutrino Your units have to be consistent. Since you are using S.I., the unit of mass is Kg, and therefore the mass of the object is 10-3Kg. Remember this, the S.I units are also known as the MKS system (Metre, Kilogram, Second). The cgs stands for (Centimetre, Gram, Second). http://en.wikipedia.org/wiki/Mks 3. Jul 11, 2006 ### verd Thanks. That'd make my answer 4.3447 degrees... And yet my answer is still incorrect... Any ideas? 4. Jul 11, 2006 ### neutrino I cannot spot anything wrong in your calculation. I wonder why the length of the string has been provided (probably just to make you go off-track). 5. Jul 11, 2006 ### verd Yeah... That's what I was thinking. But who knows. I could actually have to use it somehow. Seems like a way to make you waste your time realizing that you don't have enough information to find the angle trigometrically w/out physics. 6. Jul 11, 2006 ### arunbg 7. Jul 11, 2006 ### verd It's an online homework service. I have a couple of chances at an answer... So I don't know what the answer is. 8. Jul 11, 2006 ### arunbg Well, was any option close to the answer at least ? 9. Jul 11, 2006 ### verd Nope. I have no idea what it is. This method seems correct. 10. Jul 11, 2006 ### neutrino May be (some of) the numbers you have are wrong. For example, that 0.00076 should be 0.000745/6. Just make sure that the numbers are correct to a few decimal places and submit an answer. Either that, or the online service has totally gone berserk. ;)	2017-10-18 01:05:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6535389423370361, "perplexity": 1418.2747779667227}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822625.57/warc/CC-MAIN-20171017234801-20171018014801-00485.warc.gz"}
https://i.publiclab.org/notes/bdiscoe/06-09-2013/aerial-photos-with-uav-and-an-android-phone-first-results	# Aerial photos with UAV and an Android phone: first results by bdiscoe \| \| 327 views \| 5 comments \| 09 Jun 05:08 ## What I want to do Trying to find an affordable, reliable way for people to gather high-quality aerials with a UAV. ## My attempt and results 1. UAV: A 3D Robotics Hexa-C (http://www.udrones.com/product_p/achrtf1.htm) It is very hard to fly. After much practice, with an RC controller, I can mostly keep it in position horizontally, by continuous rapid adjustments, but vertical control is loose and wind makes it even more difficult. 2. Camera: A long search and study of dpreview.com shows that, in fact, there are basically only 4 high-megapixel fixed-lens cameras which can take pictures continuously (commonly called time-lapse, or more obscurely as intervalometer): 3. Pentax Optio WG-2 (and WG-3), 16 MP, 192 g, $205 on amazon. 4. Panasonic Lumix DMC-TS5, 16.1 MP, 214 g,$360 on amazon. 5. Nikon Coolpix P510, 16 MP, (41.7× zoom!), 555 g, $370 on amazon. 6. Ricoh GR, 16.2 megapixels, 245 g,$800 on amazon. The first two are similar: cheap waterproof point-and-shoots. The Nikon is the heavy one with the crazy zoom (not useful IMHO for aerials) The Ricoh is the expensive one, with (one would assume) higher image quality for that price. I don't have any of those cameras, so my experiment today consisted of using my Android phone (Galaxy Nexus). I suspended my Nexus under my UAV by wrapping rubber bands tightly around the phone, then used cords through those bands to hang it under the UAV. 1. Software. On the UAV: Ardupilot. On the phone, an app is needed to tell the camera to capture full-resolution images, continuously (every few seconds). I tried several "time lapse" apps, all of which were deficient (resolution limited, or unstable). The one which worked (free app) was "Tina Time-lapse" (https://play.google.com/store/apps/details?id=com.tina.time_lapse&hl=en) 2. Test location: I flew on my farm in rural Hawaii (https://maps.google.com/?ll=20.05336,-155.509016&spn=0.000862,0.000932&t=h&z=20) You can see in Google's image (the best available imagery) many issues with graininess, poor color depth, canopy coverage including tree parallax lean, and shadows: Hence, the need to gather our own aerials there. 3. Test conditions: Overcast day, gusty winds from the northeast (tradewinds, almost always blowing). 4. Test operation: I set the UAV on a flat, open grassy area. I carefully reached the phone under the UAV to start the "Tina Time-lapse" app capturnig images. I set the UAV to "stabilize" mode, and took it up 10 feet. I then switched to "loiter" mode which, in theory, should make the UAV hold its position and elevation, but in practice, it does not; it is simply a little more stable than "stabilize" but still requires continuous correction. In "loiter", I took the UAV up to (guessing) 80-100 feet above ground, tried to keep it stable for a very scary minute, then brought it down, dodging trees, powerline, and ground obstacles to land it safely on the grass. 5. Results: 6. The overcast sky made the images somewhat unsaturated. 7. The wind made piloting difficult and frightening ($800 UAV could easily drift into a tree collision) 8. The wind and rocky UAV flight made the camera focus poor and motion blur bad. 9. Even if conditions had been perfect, resolution is limited by the phone camera (5MP nominal but lower effective detail). A few of the resulting images are online at https://plus.google.com/u/0/photos/100275646589690012041/albums/5886880918564651393 ## Questions and next steps Things to try: 1. Try again with better conditions. 2. Buy a Pentax camera which has time lapse as a standard feature. 3. Try to get the UAV to pilot itself. I took it as high as I dared today. It's manual piloting, so I need to see the UAV well to keep it from drifting, which limits how far up. If i ever get the thing to actually fly itself stably, then I could let it go higher on an auto-path. ### 5 Comments Hi there, Great article. Love the experiment. At first glance, I think a 3-axis gimbal would help you get a lot more stable shots. Also, unfortunately, the uDrones site got taken down, so that link doesn't work anymore. We actually have a drone buying guide with a few great drones for aerial photos/video. Here's the link if anyone would like to check it out: http://uavcoach.com/buy-a-drone/ Reply to this comment... Nice experiment. It might be helpful to practice on a cheaper drone like these though before sending expensive equipment into the air. Reply to this comment... @DroneBizMarketr presuming you aren't just spamming, can any of those sub-$100 produce GPS-tagged high-resolution aerial photos, suitable for uploading to e.g. dronedeploy.com? If so, please let us know. Otherwise, they are pretty much useless. Is this a question? Click here to post it to the Questions page. @bdiscoe No they'd only be useful for training purposes. But I wouldn't be surprised if we see that capability on drones around \$200 by this time next year	2019-08-22 09:56:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3225419223308563, "perplexity": 7904.067670986054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317037.24/warc/CC-MAIN-20190822084513-20190822110513-00431.warc.gz"}
https://math.stackexchange.com/questions/3283784/is-completeness-of-a-metric-space-is-a-homeomorphic-property	# Is completeness of a metric space is a homeomorphic property? A property of a topological space is called a homeomorphic property if it remains invariant under homeomorphisms Is boundedness of a subspace of a metric space is a homeomorphic porperty? For the first question, I can prove so far as to show that completeness is not a Topological property as if you consider (0,1), then one metric is the ordinary Euclidean metric on (0,1); a second metric is what you get when you pull the Euclidean metric on R back to (0,1) via a homeomorphism. In one of those metrics, (0,1) is complete, but in the other it is not, though the two metrics generate the same topology. But how do I show go about showing that comepleteness remains invariant under homeomorphisms (or not)? For the second question I am not sure where to begin as total boundedness is a not a topological property but I cannot say about boundedness in general. And it talks of metric space in the question, so this line of reasoning won't work at all I guess. • I would call a property “topological”, not “homeomorphic”, if it is invariant under homeomorphisms. – pyon Jul 5 '19 at 8:45 • @pyon the question from the assignment that I have mentions "homeomorphic", i.e, the question word for word. So I'm a bit lost. – Brian I. Hunds Jul 5 '19 at 8:46 • It is not al all clear what you want to know. – Paul Frost Jul 5 '19 at 8:47 • "In one of those metrics, (0,1) is complete, but in the other it is not, though the two metrics generate the same topology." This is precisely enough to prove that completeness is not invariant under homeomorphisms. In this case the identity function between your two metric spaces is a homeomorphism (precisely because the topologies are the same). So they are homeomorphic, but one is complete and the other is not. – preferred_anon Jul 5 '19 at 8:56 • It's not saved via homeomorphisms, but it is saved via uniform homeomorphisms (i. e. we demand bi-uniform continuity instead of continuity). – Jakobian Jul 5 '19 at 8:57 Since $$(0,1)$$ is bounded and homeomorphic to $$\mathbb R$$, which is unbounded, the answer is negative. A topological space is a pair $$(X,T)$$ where $$T$$ is a topology on the set $$X$$. A metric space is a triplet $$(X,T,d)$$ where $$d$$ is a metric on the set $$X,$$ and $$T$$ is the topology on $$X$$ generated by the base of all open $$d$$-balls. A metrizable space is a topological space $$(X,T)$$ such that $$(X,T,d)$$ is a metric space for some metric $$d$$ on $$X.$$ A completely metrizable space is a topological space $$(X,T)$$ such that $$(X,T,d)$$ is a metric space for some complete metric $$d$$ on $$X$$. It is very common, and generally acceptable, to speak of any of these as "the space $$X$$". But this should not be done if you are talking about two topologies or two metrics on $$X$$. A property $$p(A)$$ that a space $$A$$ may, or may not have, is called a topological property iff $$p(A)\iff p(B)$$ whenever $$A,B$$ are homeomorphic. Examples: 1. Compact 2.Connected 3. Path-connected. 4. Metrizable. 5.Completely metrizable. These are topological properties. Being bounded is NOT a topological property. If $$d$$ is a metric on $$X$$ then the metric $$e(x,y)=\min (1,d(x,y)\,)$$ on $$X$$ generates the same topology on $$X$$ that $$d$$ does. And $$e$$ is a bounded metric but $$d$$ might not be.	2020-07-14 04:12:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 33, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7853589653968811, "perplexity": 210.29264878919193}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657147917.99/warc/CC-MAIN-20200714020904-20200714050904-00268.warc.gz"}
https://cs.stackexchange.com/questions/124931/vc-dimension-of-only-the-rim-of-a-unit-disk	# VC dimension of only the rim of a unit disk Suppose we have an origin centered circle, ie $$x^2 + y^2 =1$$, so it's in $$\mathbb{R}^2$$ (2D). It will be classified as 1 if it lies only on this arc, and will be labeled 0 otherwise. What is the VC dimension? I think the answer is 2. Any two points can be shattered $$(++, -+, +-, --)$$. But if we have three points $$\{(x_1,y_1),\dots,(x_3,y_3)\}$$ that all have the label 1, with radius $$r_1 = r_2 = 1$$, and $$r_3 = 0$$, it is impossible to shatter them. Is my intuition correct? Or can I construct the sample points to my liking (to get the maximum VC dim) so that only the positive labels will be on the rim (have some combination of $$x_i^2 + y_i^2 = 1$$), and have 0 labels to not lie on the rim, therefore have infinite VC dimension? • The VC dimension is a feature of a class of functions. If the VC dimension is $d$, then the class of functions has to contain at least $2^d$ different functions. You are describing a class of functions consisting of a single function. Hence its VC dimension is zero. – Yuval Filmus Apr 29 '20 at 7:31 • Sorry I don't quite get why it is zero. If we have $d = 2$, then we can always place the two samples $S = {(x_1,y_1),(x_2,y_2)}$ either on the arc or not on the arc without misclassifying any other sample... Doesn't this show that it contains at least $2^2$ functions, thus VC is at least 2? Could you also elaborate more about "You are describing a class of functions consisting of a single function"? – user120261 Apr 29 '20 at 14:33 • In your post you are describing a single function $\mathbb{R}^2 \to \{0,1\}$, which is $1$ on input $(x,y)$ iff $x^2 + y^2 = 1$. As far as I know, this is the only function in your class. If not, you'll have to specify your class of functions explicitly. I can't read your mind! – Yuval Filmus Apr 29 '20 at 14:35 • No, you are correct, this is the only function from $\mathbb{R}^2$ to $\{0,1\}$. So proceeding from here, if I have 2 samples, wouldn't it be possible to place the $1$ label on the arc, the $0$ label outside of the arc, shattering $d=2$? On the contrary, If I have three labels all on the x-axis, then it is impossible to label all 1's (only two can be labeled 1 at (-1,0) and (1,0))? Please advise. Thanks for the time! – user120261 Apr 29 '20 at 15:20 • I suspect that you are understanding the question wrong. (You also seem to be misunderstanding the definition of VC dimension.) – Yuval Filmus Apr 29 '20 at 15:33 Let $$\mathcal F$$ be a class of functions from $$\mathcal X$$ to $$\{0,1\}$$. If $$\mathcal F$$ has VC dimension $$d$$ then $$\|\mathcal F\| \geq 2^d$$. Indeed, if $$\mathcal F$$ has VC dimension $$d$$ then $$\mathcal F$$ shatters some set $$S \subseteq \mathcal X$$ of size $$d$$. This means that for any function $$\phi\colon S \to \{0,1\}$$ we can find a function $$f_\phi \in \mathcal{F}$$ that agrees with $$\phi$$ on $$S$$. Note that if $$\phi \neq \psi$$ then $$f_\phi \neq f_\psi$$. Since there are $$2^d$$ different functions from $$S$$ to $$\{0,1\}$$, we conclude that $$\mathcal F$$ must contain at least $$2^d$$ functions. $$\square$$	2021-08-05 09:06:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 30, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8148248195648193, "perplexity": 174.88615244895234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155458.35/warc/CC-MAIN-20210805063730-20210805093730-00703.warc.gz"}
https://brilliant.org/wiki/instantaneous-rate-of-change/	Average and Instantaneous Rate of Change Contents Cite as: Average and Instantaneous Rate of Change. Brilliant.org. Retrieved from https://brilliant.org/wiki/instantaneous-rate-of-change/ ×	2021-01-23 01:59:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 86, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9060001373291016, "perplexity": 2483.6682254998777}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703531702.36/warc/CC-MAIN-20210123001629-20210123031629-00018.warc.gz"}
https://electronics.stackexchange.com/questions/610912/changing-vbe-on-in-pspice-student-capture	# Changing Vbe_on in Pspice - Student capture I want to change the V_BE_on in my BJT model but I couldn't find any explanation on how to achieve this. I need VBE on of 0.7[V] and the default I think is 0.8[V] I tried editing the .model -- .model Qbreakn NPN (BF = 100 VBE = 0.7) Any help would be appreciated!! ## 1 Answer There is no 'VBE' parameter in a SPICE model. This is indirectly controlled via the 'IS' parameter. Be aware that a BJR doesn't just "turn on" at a single VBE voltage -- it's all gradual even from VBE=0 (with currents in the fA range).	2022-08-11 15:51:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43728482723236084, "perplexity": 7558.781255805862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00323.warc.gz"}
https://datascience.stackexchange.com/questions/32723/how-google-get-the-use-over-time-for-data-from-the-before-internet-years	# How google get the 'use over time for' data from the before internet years? Recently I am reading a book and I found there are lots of words I rarely saw. While I was searching their meaning, I found that for a single vocabulary google has a use over time for: statistic -- from 1800 to 2010. I may imagine how google could gather the frequency that a vocabulary to be used in Internet. But what about before the Internet? How they know the frequency of the people in 1800 using a vocabulary? Does they first convert the chartaceous material into digital data then computing for the result or something else? • I do not work at google, but when you have data at that scale, it should certainly be possible to find information related to this. – PSub Jun 6 '18 at 20:16	2021-12-02 13:17:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3971330225467682, "perplexity": 752.905711812357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362219.5/warc/CC-MAIN-20211202114856-20211202144856-00046.warc.gz"}
https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-2-limits-2-2-limits-a-numerical-and-graphical-approach-exercises-page-55/45	Calculus (3rd Edition) $\displaystyle\lim_{x\rightarrow 1} \dfrac{x^5+x-2}{x^2+x-2}=2$ We have to estimate the limit: $\displaystyle\lim_{x\rightarrow 1\pm} \dfrac{x^5+x-2}{x^2+x-2}$ Graph the function: Therefore we get: $\displaystyle\lim_{x\rightarrow 1^{-}} \dfrac{x^5+x-2}{x^2+x-2}=2$ $\displaystyle\lim_{x\rightarrow 1^{+}} \dfrac{x^5+x-2}{x^2+x-2}=2$ As the left hand limit and the right hand limit are equal, we have: $\displaystyle\lim_{x\rightarrow 1} \dfrac{x^5+x-2}{x^2+x-2}=2$ There is a hole in the graph in $(1,2)$.	2020-09-25 13:59:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.980507493019104, "perplexity": 187.17653710819303}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400226381.66/warc/CC-MAIN-20200925115553-20200925145553-00542.warc.gz"}
http://aixpaper.com/similar/perceive_ground_reason_and_act_a_benchmark_for_generalpurpose_visual_representation	2022-11-28 Current computer vision models, unlike the human visual system, cannot yet achieve general-purpose visual understanding. Existing efforts to create a general vision model are limited in the scope of assessed tasks and offer no overarching framework to perform them holistically. We present a new comprehensive benchmark, General-purpose Visual Understanding Evaluation (G-VUE), covering the full spectrum of visual cognitive abilities with four functional domains $\unicode{x2014}$ Perceive, Ground, Reason, and Act. The four domains are embodied in 11 carefully curated tasks, from 3D reconstruction to visual reasoning and manipulation. Along with the benchmark, we provide a general encoder-decoder framework to allow for the evaluation of arbitrary visual representation on all 11 tasks. We evaluate various pre-trained visual representations with our framework and observe that (1) Transformer-based visual backbone generally outperforms CNN-based backbone on G-VUE, (2) visual representations from vision-language pre-training are superior to those with vision-only pre-training across visual tasks. With G-VUE, we provide a holistic evaluation standard to motivate research toward building general-purpose visual systems via obtaining more general-purpose visual representations. translated by 谷歌翻译 2021-01-04 Astounding results from Transformer models on natural language tasks have intrigued the vision community to study their application to computer vision problems. Among their salient benefits, Transformers enable modeling long dependencies between input sequence elements and support parallel processing of sequence as compared to recurrent networks e.g., Long short-term memory (LSTM). Different from convolutional networks, Transformers require minimal inductive biases for their design and are naturally suited as set-functions. Furthermore, the straightforward design of Transformers allows processing multiple modalities (e.g., images, videos, text and speech) using similar processing blocks and demonstrates excellent scalability to very large capacity networks and huge datasets. These strengths have led to exciting progress on a number of vision tasks using Transformer networks. This survey aims to provide a comprehensive overview of the Transformer models in the computer vision discipline. We start with an introduction to fundamental concepts behind the success of Transformers i.e., self-attention, large-scale pre-training, and bidirectional feature encoding. We then cover extensive applications of transformers in vision including popular recognition tasks (e.g., image classification, object detection, action recognition, and segmentation), generative modeling, multi-modal tasks (e.g., visual-question answering, visual reasoning, and visual grounding), video processing (e.g., activity recognition, video forecasting), low-level vision (e.g., image super-resolution, image enhancement, and colorization) and 3D analysis (e.g., point cloud classification and segmentation). We compare the respective advantages and limitations of popular techniques both in terms of architectural design and their experimental value. Finally, we provide an analysis on open research directions and possible future works. We hope this effort will ignite further interest in the community to solve current challenges towards the application of transformer models in computer vision. translated by 谷歌翻译 2022-02-18 translated by 谷歌翻译 2022-12-06 The foundation models have recently shown excellent performance on a variety of downstream tasks in computer vision. However, most existing vision foundation models simply focus on image-level pretraining and adpation, which are limited for dynamic and complex video-level understanding tasks. To fill the gap, we present general video foundation models, InternVideo, by taking advantage of both generative and discriminative self-supervised video learning. Specifically, InternVideo efficiently explores masked video modeling and video-language contrastive learning as the pretraining objectives, and selectively coordinates video representations of these two complementary frameworks in a learnable manner to boost various video applications. Without bells and whistles, InternVideo achieves state-of-the-art performance on 39 video datasets from extensive tasks including video action recognition/detection, video-language alignment, and open-world video applications. Especially, our methods can obtain 91.1% and 77.2% top-1 accuracy on the challenging Kinetics-400 and Something-Something V2 benchmarks, respectively. All of these results effectively show the generality of our InternVideo for video understanding. The code will be released at https://github.com/OpenGVLab/InternVideo . translated by 谷歌翻译 2022-12-01 Despite the superior performance brought by vision-and-language pretraining, it remains unclear whether learning with multi-modal data can help understand each individual modality. In this work, we investigate how language can help with visual representation learning from a probing perspective. Specifically, we compare vision-and-language and vision-only models by probing their visual representations on a broad range of tasks, in order to assess the quality of the learned representations in a fine-grained manner. Interestingly, our probing results suggest that vision-and-language models are better at label prediction tasks like object and attribute prediction, while vision-only models are stronger at dense prediction tasks that require more localized information. With further analysis using detailed metrics, our study suggests that language helps vision models learn better semantics, but not localization. Code is released at https://github.com/Lizw14/visual_probing. translated by 谷歌翻译 2022-10-13 We present a retrospective on the state of Embodied AI research. Our analysis focuses on 13 challenges presented at the Embodied AI Workshop at CVPR. These challenges are grouped into three themes: (1) visual navigation, (2) rearrangement, and (3) embodied vision-and-language. We discuss the dominant datasets within each theme, evaluation metrics for the challenges, and the performance of state-of-the-art models. We highlight commonalities between top approaches to the challenges and identify potential future directions for Embodied AI research. translated by 谷歌翻译 2022-12-21 We present X-Decoder, a generalized decoding model that can predict pixel-level segmentation and language tokens seamlessly. X-Decodert takes as input two types of queries: (i) generic non-semantic queries and (ii) semantic queries induced from text inputs, to decode different pixel-level and token-level outputs in the same semantic space. With such a novel design, X-Decoder is the first work that provides a unified way to support all types of image segmentation and a variety of vision-language (VL) tasks. Further, our design enables seamless interactions across tasks at different granularities and brings mutual benefits by learning a common and rich pixel-level visual-semantic understanding space, without any pseudo-labeling. After pretraining on a mixed set of a limited amount of segmentation data and millions of image-text pairs, X-Decoder exhibits strong transferability to a wide range of downstream tasks in both zero-shot and finetuning settings. Notably, it achieves (1) state-of-the-art results on open-vocabulary segmentation and referring segmentation on eight datasets; (2) better or competitive finetuned performance to other generalist and specialist models on segmentation and VL tasks; and (3) flexibility for efficient finetuning and novel task composition (e.g., referring captioning and image editing). Code, demo, video, and visualization are available at https://x-decoder-vl.github.io. translated by 谷歌翻译 2021-11-17 translated by 谷歌翻译 2022-06-17 translated by 谷歌翻译 2022-12-19 Vision-Language Pre-Training (VLP) has shown promising capabilities to align image and text pairs, facilitating a broad variety of cross-modal learning tasks. However, we observe that VLP models often lack the visual grounding/localization capability which is critical for many downstream tasks such as visual reasoning. In this work, we propose a novel Position-guided Text Prompt (PTP) paradigm to enhance the visual grounding ability of cross-modal models trained with VLP. Specifically, in the VLP phase, PTP divides the image into $N\times N$ blocks, and identifies the objects in each block through the widely used object detector in VLP. It then reformulates the visual grounding task into a fill-in-the-blank problem given a PTP by encouraging the model to predict the objects in the given blocks or regress the blocks of a given object, e.g. filling P" or O" in aPTP `The block P has a O". This mechanism improves the visual grounding capability of VLP models and thus helps them better handle various downstream tasks. By introducing PTP into several state-of-the-art VLP frameworks, we observe consistently significant improvements across representative cross-modal learning model architectures and several benchmarks, e.g. zero-shot Flickr30K Retrieval (+4.8 in average recall@1) for ViLT \cite{vilt} baseline, and COCO Captioning (+5.3 in CIDEr) for SOTA BLIP \cite{blip} baseline. Moreover, PTP achieves comparable results with object-detector based methods, and much faster inference speed since PTP discards its object detector for inference while the later cannot. Our code and pre-trained weight will be released at \url{https://github.com/sail-sg/ptp}. translated by 谷歌翻译 2022-07-05 translated by 谷歌翻译 2021-11-11 translated by 谷歌翻译 2022-09-15 translated by 谷歌翻译 2022-05-19 Vision-Language Transformers can be learned without human labels (e.g. class labels, bounding boxes, etc). Existing work, whether explicitly utilizing bounding boxes or patches, assumes that the visual backbone must first be trained on ImageNet class prediction before being integrated into a multimodal linguistic pipeline. We show that this is not necessary and introduce a new model Vision-Language from Captions (VLC) built on top of Masked Auto-Encoders that does not require this supervision. In fact, in a head-to-head comparison between ViLT, the current state-of-the-art patch-based vision-language transformer which is pretrained with supervised object classification, and our model, VLC, we find that our approach 1. outperforms ViLT on standard benchmarks, 2. provides more interpretable and intuitive patch visualizations, and 3. is competitive with many larger models that utilize ROIs trained on annotated bounding-boxes. translated by 谷歌翻译 2021-02-26 State-of-the-art computer vision systems are trained to predict a fixed set of predetermined object categories. This restricted form of supervision limits their generality and usability since additional labeled data is needed to specify any other visual concept. Learning directly from raw text about images is a promising alternative which leverages a much broader source of supervision. We demonstrate that the simple pre-training task of predicting which caption goes with which image is an efficient and scalable way to learn SOTA image representations from scratch on a dataset of 400 million (image, text) pairs collected from the internet. After pre-training, natural language is used to reference learned visual concepts (or describe new ones) enabling zero-shot transfer of the model to downstream tasks. We study the performance of this approach by benchmarking on over 30 different existing computer vision datasets, spanning tasks such as OCR, action recognition in videos, geo-localization, and many types of fine-grained object classification. The model transfers non-trivially to most tasks and is often competitive with a fully supervised baseline without the need for any dataset specific training. For instance, we match the accuracy of the original ResNet-50 on ImageNet zero-shot without needing to use any of the 1.28 million training examples it was trained on. We release our code and pre-trained model weights at https://github.com/OpenAI/CLIP. translated by 谷歌翻译 2021-04-07 We study joint learning of Convolutional Neural Network (CNN) and Transformer for vision-language pre-training (VLPT) which aims to learn cross-modal alignments from millions of image-text pairs. State-of-the-art approaches extract salient image regions and align regions with words step-by-step. As region-based visual features usually represent parts of an image, it is challenging for existing visionlanguage models to fully understand the semantics from paired natural languages. In this paper, we propose SOHO to "See Out of tHe bOx" that takes a whole image as input, and learns vision-language representation in an endto-end manner. SOHO does not require bounding box annotations which enables inference 10 times faster than regionbased approaches. In particular, SOHO learns to extract comprehensive yet compact image features through a visual dictionary (VD) that facilitates cross-modal understanding. VD is designed to represent consistent visual abstractions of similar semantics. It is updated on-the-fly and utilized in our proposed pre-training task Masked Visual Modeling (MVM). We conduct experiments on four well-established vision-language tasks by following standard VLPT settings. In particular, SOHO achieves absolute gains of 2.0% R@1 score on MSCOCO text retrieval 5k test split, 1.5% accuracy on NLVR 2 test-P split, 6.7% accuracy on SNLI-VE test split, respectively. translated by 谷歌翻译 2019-08-06 We present ViLBERT (short for Vision-and-Language BERT), a model for learning task-agnostic joint representations of image content and natural language. We extend the popular BERT architecture to a multi-modal two-stream model, processing both visual and textual inputs in separate streams that interact through co-attentional transformer layers. We pretrain our model through two proxy tasks on the large, automatically collected Conceptual Captions dataset and then transfer it to multiple established vision-and-language tasks -visual question answering, visual commonsense reasoning, referring expressions, and caption-based image retrieval -by making only minor additions to the base architecture. We observe significant improvements across tasks compared to existing task-specific modelsachieving state-of-the-art on all four tasks. Our work represents a shift away from learning groundings between vision and language only as part of task training and towards treating visual grounding as a pretrainable and transferable capability.Preprint. Under review. translated by 谷歌翻译 2021-12-02 translated by 谷歌翻译 translated by 谷歌翻译 2022-05-04 translated by 谷歌翻译 ${authors} 分类：${tags} ${pubdate}${abstract_cn} translated by 谷歌翻译	2023-01-30 21:12:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2887916564941406, "perplexity": 4315.50497441494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499829.29/warc/CC-MAIN-20230130201044-20230130231044-00548.warc.gz"}
http://mathhelpforum.com/advanced-math-topics/3279-need-help-proof.html	# Math Help - Need help on a proof 1. ## Need help on a proof IF a,b >0 Then prove: AM -HM<= (b-a)^2/4a This is what I did AM = (a + b)/2 HM = 2/(1/a + 1/b) So when I subtract AM - HM: I got this (a+b)/2 - 2ab/(a+b) [(a+b)^2 - 4ab]/[2(a+b)] which reduces to [(a-b)^2] / [2(a+b)] Now what do I do? 2. Originally Posted by Nichelle14 IF a,b >0 Then prove: AM -HM<= (b-a)^2/4a This is what I did AM = (a + b)/2 HM = 2/(1/a + 1/b) So when I subtract AM - HM: I got this (a+b)/2 - 2ab/(a+b) [(a+b)^2 - 4ab]/[2(a+b)] which reduces to [(a-b)^2] / [2(a+b)] Now what do I do? Is there any relation between a and b? if a< b 2a< a+b 1/2a> 1/(a+b) 3. I believe you are asking for this realationship a and b are positive. I don't understand how your part of the proof makes it complete? In other words, how does your part be <= (b-a)^2/4b Can you explain some more? 4. Originally Posted by Nichelle14 I believe you are asking for this realationship a and b are positive. I don't understand how your part of the proof makes it complete? In other words, how does your part be <= (b-a)^2/4b Can you explain some more? originally you have posted (b-a)^2/4a continuing my work 1/2a > 1/(a+b) multiplying both sides by [(b-a)^2]/2 (which is a positive quantity) we get (b-a)^2/4a >(b-a)^2/2(a+b) RHS is equal to AM-HM 5. earlier you posted if a < b, then 2a < a + b Why did you chose to do this? 6. Originally Posted by Nichelle14 earlier you posted if a < b, then 2a < a + b Why did you chose to do this? a and b are the two consecutive terms of a series and they should not be equal I had the choice whether a would be smaller or bigger than b because had not mentioned anything. I chose a<b because it impies the equation you have to prove. 7. It is not true. What about $a=b=2$ ----- I believe I found a solution. As my top sentence says, your inequality is false. It is however true when, for $x,y>0$. $\phi y\geq x$ Where, $\phi$ is the solution to the cubic, $2x^3+x^2+3x-1=0$. 8. Originally Posted by ThePerfectHacker It is not true. What about $a=b=2$ ----- I believe I found a solution. As my top sentence says, your inequality is false. It is however true when, for $x,y>0$. $\phi y\geq x$ Where, $\phi$ is the solution to the cubic, $2x^3+x^2+3x-1=0$. I don,t think my inequality is false. If you see what we set to prove it includes >= sign. It can be broken into > and = separately. If a=b= any positive real number, AM=GM=HM=a=b which is not of much importance. The real thing lies in inequality part. Hence we have to use a relation between the two terms. However, I don't understand your solution, please explain it.	2015-01-28 04:27:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.766599178314209, "perplexity": 2275.389051520392}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122123549.67/warc/CC-MAIN-20150124175523-00050-ip-10-180-212-252.ec2.internal.warc.gz"}
https://gmatclub.com/forum/triangle-qsr-is-inscribed-in-a-circle-is-qsr-a-right-triangle-238109.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 14 Dec 2018, 09:44 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. 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Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # Triangle QSR is inscribed in a circle. Is QSR a right triangle? Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 51215 Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 14 Apr 2017, 02:52 00:00 Difficulty: 35% (medium) Question Stats: 68% (00:35) correct 32% (00:34) wrong based on 158 sessions ### HideShow timer Statistics Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5. Attachment: 2017-04-14_1450.png [ 25.9 KiB \| Viewed 1617 times ] _________________ Director Joined: 21 Mar 2016 Posts: 521 Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags Updated on: 14 Apr 2017, 06:57 stat1 : QR is a diameter... hence traingle in semicircle is right traingle suff stat 2 : not suff... the third side cud be anything ans A Originally posted by mohshu on 14 Apr 2017, 06:24. Last edited by mohshu on 14 Apr 2017, 06:57, edited 1 time in total. VP Joined: 05 Mar 2015 Posts: 1004 Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 14 Apr 2017, 06:43 1 mohshu wrote: stat1 : QR is a diameter... hence traingle in semicircle is right traingle suff stat 2 : pythagoras theorem applies here and its true only for right trangles ans D mohshu for option (2) what if SR =4.5 ??? thanks Director Joined: 21 Mar 2016 Posts: 521 Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 14 Apr 2017, 06:56 rohit8865 wrote: mohshu wrote: stat1 : QR is a diameter... hence traingle in semicircle is right traingle suff stat 2 : pythagoras theorem applies here and its true only for right trangles ans D mohshu for option (2) what if SR =4.5 ??? thanks rohit8865 got that only stat is suff ans A thanks Retired Moderator Joined: 04 Aug 2016 Posts: 500 Location: India GPA: 4 WE: Engineering (Telecommunications) Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 14 Apr 2017, 07:17 Statement 1 is a property and it is sufficient Statement 2 : The other side can take any value between 2 and 8; if it is 4 then it is sufficient. Not enough information available. Option A Manager Joined: 13 Mar 2013 Posts: 163 Location: United States GPA: 3.5 WE: Engineering (Telecommunications) Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 15 Apr 2017, 06:57 1 Ans : st 1 ) sufficient -- QR is diameter . It is property of inscribed triangle in circle . If the one of the sides equal the diameter of the circle . Then the triangle is Right angle triangle . st 2 ) Not sufficient two side is given as 3 ,4 but the third side can be 5 or 7 . Apply the property of sum of two side in triangle is greater than the third side . Then you will realize . The triangle can have value as ( 3, 4, 5 --> right angle ) or ( 3,4, 7 --> not a right angle ) Regards, Press Kudos if you like the post. _________________ Regards , Math Expert Joined: 02 Sep 2009 Posts: 51215 Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 15 Apr 2017, 08:03 Bunuel wrote: Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5. Attachment: 2017-04-14_1450.png Triangle QSR is inscribed in a semi-cirlce is QSR a right triangle? A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. (1) QR is a diameter of the circle --> according to the above property QSR must be a right triangle. Sufficient. (2) Length QS equals 3 and length QR equals to 5 --> it's not necessary QSR to be 3-4-5 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semi-circle so that SR would be the largest side and QSR would be obtuse-angled triangle. Not sufficient. _________________ Manager Joined: 10 Apr 2015 Posts: 182 GPA: 3.31 Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 15 Apr 2017, 08:39 A. II statement does not suggest that SR is 4. Hence NS. Sent from my ZUK Z2132 using GMAT Club Forum mobile app _________________ In case you find my posts helpful, give me Kudos. Thank you. Director Joined: 02 Sep 2016 Posts: 681 Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 07 Jul 2017, 05:02 Bunuel wrote: Bunuel wrote: Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5. Attachment: 2017-04-14_1450.png Triangle QSR is inscribed in a semi-cirlce is QSR a right triangle? A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. (1) QR is a diameter of the circle --> according to the above property QSR must be a right triangle. Sufficient. (2) Length QS equals 3 and length QR equals to 5 --> it's not necessary QSR to be 3-4-5 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semi-circle so that SR would be the largest side and QSR would be obtuse-angled triangle. Not sufficient. Hi Bunuel If it were 3-4-5; 3-4-10; 6-4-5;................any multiple of 3:4:5, then it would be a right angled triangle ? Also to know if that triangle inscribed in the circle is a right triangle, then diameter would be the longest side of the triangle. Are there any other factors that can help us understand whether the triangle is a right angled triangle? Math Expert Joined: 02 Sep 2009 Posts: 51215 Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 07 Jul 2017, 05:14 Shiv2016 wrote: Bunuel wrote: Bunuel wrote: Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5. Attachment: 2017-04-14_1450.png Triangle QSR is inscribed in a semi-cirlce is QSR a right triangle? A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. (1) QR is a diameter of the circle --> according to the above property QSR must be a right triangle. Sufficient. (2) Length QS equals 3 and length QR equals to 5 --> it's not necessary QSR to be 3-4-5 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semi-circle so that SR would be the largest side and QSR would be obtuse-angled triangle. Not sufficient. Hi Bunuel If it were 3-4-5; 3-4-10; 6-4-5;................any multiple of 3:4:5, then it would be a right angled triangle ? Also to know if that triangle inscribed in the circle is a right triangle, then diameter would be the longest side of the triangle. Are there any other factors that can help us understand whether the triangle is a right angled triangle? • Any triangle whose sides are in the ratio 3:4:5 is a right triangle. Such triangles that have their sides in the ratio of whole numbers are called Pythagorean Triples. There are an infinite number of them, and this is just the smallest. If you multiply the sides by any number, the result will still be a right triangle whose sides are in the ratio 3:4:5. For example 6, 8, and 10. • A Pythagorean triple consists of three positive integers $$a$$, $$b$$, and $$c$$, such that $$a^2 + b^2 = c^2$$. Such a triple is commonly written $$(a, b, c)$$, and a well-known example is $$(3, 4, 5)$$. If $$(a, b, c)$$ is a Pythagorean triple, then so is $$(ka, kb, kc)$$ for any positive integer $$k$$. There are 16 primitive Pythagorean triples with c ≤ 100: (3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97). So, 3:4:10 is not a Pythagorean triple, 3^2 + 4^2 does not equal 10^2. You'll get a Pythagorean triple if you multiply another Pythagorean triple by a positive integer, so multiply the entire ratio, not just one of its numbers. _________________ Non-Human User Joined: 09 Sep 2013 Posts: 9160 Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? [#permalink] ### Show Tags 29 Nov 2018, 08:19 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? &nbs [#permalink] 29 Nov 2018, 08:19 Display posts from previous: Sort by	2018-12-14 17:44:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6573701500892639, "perplexity": 2379.745707520109}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826145.69/warc/CC-MAIN-20181214162826-20181214184826-00257.warc.gz"}
https://codegolf.stackexchange.com/questions/363/tips-for-golfing-in-ruby?noredirect=1	# Tips for golfing in Ruby What general tips can you give for golfing in Ruby? I'm looking for ideas that can be applied to code golf problems in general that are specific to Ruby. (For example, "Remove comments" would not be an answer.) • Someone needs to write a language called Rub, which uses a single Unicode character for every Ruby token, kinda like Jelly and Pyth :) – Mark Thomas Aug 30 '17 at 12:28 • The numbers 100 to 126 can be written as ?d to ?~ in 1.8. • On a similar note if you need a single-character string in 1.9 ?x is shorter than "x". • If you need to print a string without appending a newline, $><<"string" is shorter than print"string". • If you need to read multiple lines of input $<.map{\|l\|...} is shorter than while l=gets;...;end. Also you can use $<.read to read it all at once. • If you're supposed to read from a file, $< and gets will read from a file instead of stdin if the filename is in ARGV. So the golfiest way to reimplement cat would be: $><<$<.read. • ?x yields the ascii code in general, so you can realistically get all the printables to digits in two characters. 1.9 is different, 'a'.ord yields the ascii number, but is four bytes longer than the decimal version. – Hiato Feb 3 '11 at 8:03 • An even golfier way to implement cat is to leave the ruby file completely empty (0 bytes) and insist that it should be run from the command line with the -p flag. – daniero Jul 17 '13 at 20:01 • or, from @daniero's own answer, puts $< – Not that Charles Jul 2 '14 at 19:15 • So in 1.8, all I have to do is go ?~ and it will return 126? – Simply Beautiful Art May 13 '17 at 13:09 • You can go beyond 126 using thinks like ☺ or ♫, or if you are crazy enough: ?﷽.ord=65021 – Simply Beautiful Art May 13 '17 at 15:45 Use the splat operator to get the tail and head of an array: head, tail = [1,2,3] head => 1 tail => [2,3] This also works the other way: head, tail = [1,2,3] head => [1,2] tail => 3 Use the method with a string on an array to join elements: [1,2,3]?, => "1,2,3" • Use abort to terminate the program and print a string to STDERR - shorter than puts followed by exit • If you read a line with gets, you can then use ~/$/ to find its length (this doesn't count a trailing newline if it exists) • Use [] to check if a string contains another: 'foo'['f'] #=> 'f' • Use tr instead of gsub for character-wise substitutions: '01011'.tr('01','AB') #=> 'ABABB' • If you need to remove trailing newlines, use chop instead of chomp • +1 for abort and ~/$/ – J-_-L Jun 26 '11 at 22:13 • Please explain how to use ~/$/ – Mathieu CAROFF Nov 25 '18 at 6:47 • @MathieuCAROFF every time you call gets, its result is stored in the $_ variable. /regex/ ~= string returns the index of the first match. Calling ~ on a regex is equivalent to /regex/ ~=$_. So it would be something like s=gets;l= ~/$/ – Cyoce Feb 8 '19 at 3:18 # End your end. Try to remove end from your code. Don't use def...end to define functions. Make a lambda with the new -> operator in Ruby 1.9. (The -> operator is a "stabby lambda", or "dash rocket".) This saves 5 characters per function. # 28 characters def c n /(\d)\1/=~n.to_s end # 23 characters, saves 5 c=->n{/(\d)\1/=~n.to_s} Method calls are c n or c(n). Lambda calls are c[n]. Changing each c n to c[n] costs 1 character, so if you can use c n more than 5 times, then keep the method. All methods that take do...end blocks can take {...} blocks instead. This saves 3 to 5 characters. If the precedence of {...} is too high, then use parentheses to fix it. # 48 characters (?a..?m).zip (1..5).cycle do\|a\|puts a.join','end # WRONG: passes block to cycle, not zip (?a..?m).zip (1..5).cycle{\|a\|puts a.join','} # 45 characters, saves 3 (?a..?m).zip((1..5).cycle){\|a\|puts a.join','} Replace if...else...end with the ternary operator ?:. If a branch has two or more statements, wrap them in parentheses. # 67 characters if a<b puts'statement 1' puts'statement 2'else puts'statement 3'end # 62 characters, saves 5 a<b ?(puts'statement 1' puts'statement 2'):(puts'statement 3') You probably don't have while or until loops, but if you do, then write them in modifier form. (a+=1 b-=1)while a<b • Are the parentheses around puts'statement 3' necessary? – Cyoce Dec 2 '16 at 2:38 Addition to w0lf When working with arrays, .compact can be replaced with -[nil] to save 2 chars. Combined with above -> you can make it even shorter with -[p] to save another 2 chars. Use the short predefined variables wherever possible, e.g. $ instead of ARGV. There's a good list of them here, along with a lot of other useful information. Don't use the true and false keywords. Use: • !p for true (thanks, histocrat!) • !0 for false. If all you need is a falsy value, then you can simply use p (which returns nil). to save some chars. • Unless you actually need true (i.e. if a truthy value is enough, like in an if condition), you don't even need !!. – Martin Ender Aug 6 '14 at 6:31 • And similarly, p (which evaluates to nil) is a shorter falsey value. Which means the shortest way to get true is !p. – histocrat Aug 6 '14 at 22:17 • @histocrat good point! I've edited my answer. – Cristian Lupascu Aug 7 '14 at 6:26 $_ is last read line. • print - if no argument given print content of $_ • ~/regexp/ - short for $_=~/regexp/ In Ruby 1.8, you have four methods in Kernel that operate on $_: • chop • chomp • sub • gsub In Ruby 1.9, these four methods exist only if your script uses -n or -p. If you want to print some variable often then use trace_var(:var_name){\|a\|p a} • These are only available when you run Ruby with the -p or -n option. Reference. – Darren Stone Dec 27 '13 at 19:12 • It seems that trace_var only works with global $variables – daniero Mar 23 '16 at 8:56 • Another trick that works with -n or -p is using a regexp literal as a boolean: the regexp is implicitly matched against $_. See this answer of mine for an example. – Dingus Sep 4 '20 at 0:30 • Unlike the String methods with the same names, the listed Kernel methods modify $_ in place. Generally this behaviour is what is wanted, but worth noting the difference. – Dingus Nov 30 '20 at 11:50 When you are using string interpolation, (as you should pr Martin Büttner's post), you don't need the curly brackets if your object has a sigil ($, @) in front of it. Useful for magical variables like $_, $&, $1 etc: puts "this program has read #$. lines of input" So also if you need to print a variable more than you use it otherwise, you may save some bytes. a=42; puts "here is a: #{a}"; puts "here is a again: #{a}" $b=43; puts "here is b: #$b"; puts "here is b again: #$b" • Isn't puts "here is b: "+b more shorter? – vrintle Dec 16 '20 at 7:53 • @vrintle In this particular example, yes. But for instance "here is b:#{b}, here is a:#{a}!!" is shorter than "here is b:"+b+", here is a:"+a+"!!". The linked post also provides more info – daniero Dec 16 '20 at 22:14 If you need to find if a particular element e is inside a range r, you can use r===e instead of the longer: r.cover?(e) # only works if r.exclude_end? is false or r.member?(e) or r.include?(e) • Isn’t r===e even shorter? – akuhn Jun 1 '12 at 21:10 • @akuhn Yes, it is. Much Shorter. Thanks for pointing that out, it helped me shorten my code by 10 chars, which is huge: codegolf.stackexchange.com/a/6125/3527 – Cristian Lupascu Jun 1 '12 at 21:20 • You’re welcome. Everything that can be used in a switch statement has === implemented. – akuhn Jun 2 '12 at 12:49 # Avoid length in if a.length<n length is 6 bytes, a bit costly in code golf. in many situations, you can instead check if the array has anything at a given point. if you grab past the last index you will get nil, a falsey value. So you can Change: if a.length<5 to if !a[4] for -5 bytes or if a.length>5 to if a[5] for -6 bytes or if a.length<n to if !a[n-1] for -3 bytes or if a.length>n to if a[n] for -6 bytes Note: will only work with an array of all truthy values. having nil or false within the array may cause problems. • I always use size… But this is definitely better. BTW, works for String too. – manatwork Dec 7 '15 at 17:06 # New features in Ruby 2.3 and 2.4 It's good to stay abreast of new language features that will help your golf game. There are a few great ones in the latest Rubies. ## Ruby 2.3 ### The safe navigation operator: &. When you call a method that might return nil but you want to chain additional method calls if it's not, you waste bytes handling the nil case: arr = ["zero", "one", "two"] x = arr[5].size # => NoMethodError: undefined method size' for nil:NilClass x = arr[5].size rescue 0 # => 0 The "safe navigation operator" stops the chain of method calls if one returns nil and returns nil for the whole expression: x = arr[5]&.size \|\| 0 # => 0 ### Array#dig & Hash#dig Deep access to nested elements, with a nice short name: o = { foo: [{ bar: ["baz", "qux"] }] } o.dig(:foo, 0, :bar, 1) # => "qux" Returns nil if it hits a dead end: o.dig(:foo, 99, :bar, 1) # => nil ### Enumerable#grep_v The inverse of Enumerable#grep—returns all elements that don't match the given argument (compared with ===). Like grep, if a block is given its result is returned instead. (1..10).grep_v 2..5 # => [1, 6, 7, 8, 9, 10] (1..10).grep_v(2..5){\|v\|v2} # => [2, 12, 14, 16, 18, 20] ### Hash#to_proc Returns a Proc that yields the value for the given key, which can be pretty handy: h = { N: 0, E: 1, S: 2, W: 3 } %i[N N E S E S W].map(&h) # => [0, 0, 1, 2, 1, 2, 3] ## Ruby 2.4 Ruby 2.4 isn't out yet, but it will be soon and has some great little features. (When it's released I'll update this post with some links to the docs.) I learned about most of these in this great blog post. ### Enumerable#sum No more arr.reduce(:+). You can now just do arr.sum. It takes an optional initial value argument, which defaults to 0 for Numeric elements ([].sum == 0). For other types you'll need to provide an initial value. It also accepts a block that will be applied to each element before addition: [[1, 10], [2, 20], [3, 30]].sum {\|a,b\| a + b } # => 66 ### Integer#digits This returns an array of a number's digits in least-to-greatest significance order: 123.digits # => [3, 2, 1] Compared to, say, 123.to_s.chars.map(&:to_i).reverse, this is pretty nice. As a bonus, it takes an optional radix argument: a = 0x7b.digits(16) # => [11, 7] a.map{\|d\|"%x"%d} # => ["b", "7"] ### Comparable#clamp Does what it says on the tin: v = 15 v.clamp(10, 20) # => 15 v.clamp(0, 10) # => 10 v.clamp(20, 30) # => 20 Since it's in Comparable you can use it with any class that includes Comparable, e.g.: ?~.clamp(?A, ?Z) # => "Z" ### String#unpack1 A 2-byte savings over .unpack(...)[0]: "👻💩".unpack(?U) # => [128123] "👻💩".unpack(?U)[0] # => 128123 "👻💩".unpack1(?U) # => 128123 ### Precision argument for Numeric#ceil, floor, and truncate Math::E.ceil(1) # => 2.8 Math::E.floor(1) # => 2.7 (-Math::E).truncate(1) # => -2.7 ### Multiple assignment in conditionals This raises an error in earlier versions of Ruby, but is allowed in 2.4. (a,b=1,2) ? "yes" : "no" # => "yes" (a,b=nil) ? "yes" : "no" # => "no" • Golf Math::E.ceil(1) to Math::E.ceil 1, and likewise for floor and truncate. – Simply Beautiful Art Nov 20 '17 at 23:38 • @SimplyBeautifulArt I expect that someone golfing in Ruby will be able to make that leap themselves. – Jordan Nov 20 '17 at 23:50 • For Enumerable#sum, .flatten.sum is 2 bytes shorter than .sum{\|a,b\|a+b} – Asone Tuhid Jan 24 '18 at 10:45 • (-Math::E).truncate(1) is equivalent to -Math::E.truncate(1) which is 1 byte shorter – Asone Tuhid Mar 1 '18 at 12:21 • &. can be used with subscripting like this a&.[]i (1 byte shorter than a&.at i). Although, if brackets are required, a\|\|a[i] is 1 byte is shorter than a&.[](i) or a&.at(i) – Asone Tuhid Mar 1 '18 at 12:24 Build arrays using a=i,a to get them in reverse order. You don't even need to initialize a, and if you do it doesn't have to be an array. Use string interpolation! 1. To replace to_s. If you need parentheses around whatever you want to turn into a string, to_s is two bytes longer than string interpolation: (n+10i).to_s "#{n+10i}" 2. To replace concatenation. If you concatenate something surrounded by two other strings, interpolation can save you one byte: "foo"+c+"bar" "foo#{c}bar" Also works if the middle thing is itself concatenated, if you just move the concatenation inside the interpolation (instead of using multiple interpolations): "foo"+c+d+e+"bar" "foo#{c+d+e}bar" If you ever need to get a number from ARGV, get, or something similar to do something that many times, instead of calling to_i on it, you can just use ?1.upto x{do something x times} where x is a string. So using ?1.upto(a){} instead of x.to_i.times{} will save you 2 characters. You can also re-write things like p 1 while 1 or p 1 if 1 as p 1while 1 or p 1if 1 That example isn't very useful, but it could be used for other things. Also, if you need to assign the first element of an array to a variable, a,=c will save two characters as opposed to a=c[0] # Use operator methods instead of parentheses Let's say you want to express a(b+c). Because of precedence, ab+c won't work (obviously). Ruby's cool way of having operators as methods comes to the rescue! You can use a.b+c to make the precedence of lower than that of +. a(b+c) # too long ab+c # wrong a.b+c # 1 byte saved! This can also work with the ! and ~ operators (things like unary + or unary - don't work because their methods are -@ and +@, saving () but adding .@) (~x).to_s # too long ~x.to_s # error x.~.to_s # 1 byte saved! # Save some bytes when removing repeated elements of an array a.uniq # before a\|[] # after ^^ If you will be using an empty array [] in a variable, you can save even more bytes: a.uniq;b=[] # before a\|b=[] # after ^^^^^ • For the first case, a&a is 1 byte shorter – Asone Tuhid Mar 7 '18 at 12:59 Don't use #each. You can loop over all elements just fine with #map. So instead of ARGV.each{\|x\|puts x} you can do the same in less bytes. ARGV.map{\|x\|puts x} Of course, in this case puts$ would be even shorter. There are literals for rational and complex numbers: puts 3/11r == Rational(3,11) puts 3.3r == Rational(66,20) puts 1-1.i == Complex(1,-1) => true true true You can use most bytes within strings. "\x01" (6 bytes) can be shortened to "" (3 bytes). If you only need this one byte, this can be shortened even further to ? (2 bytes). By the same token, you can get newlines shorter like this: (0..10).to_a.join' ' => "0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10" You can use ?\n and ?\t as well, which is one byte shorter than "\n" and "\t". For obfuscation, there also ?\s, a space. Use constants instead of passing arguments around, even if you need to change them. The interpreter will give warnings to stderr, but who cares. If you need to define more variables related to each other, you can chain them like this: A=C+B=7+C=9 => A=17, B=16, C=9 This is shorter than C=9;B=16;A=17 or C=0;B=C+7;A=C+B. If you need an infinite loop, use loop{...}. Loops of unknown length may be shorter with other loops: loop{break if' '==f(gets)} while' '!=f(gets);end Some more gsub/regexp tricks. Use the special '\1' escape characters instead of a block: "golf=great short=awesome".gsub(/(\w+)=(\w+)/,'(\1~>\2)') "golf=great short=awesome".gsub(/(\w+)=(\w+)/){"(#{$1}~>#{$2})") And the special variables $1 etc. if you need to perform operations. Keep in mind they are defined not only inside the block: "A code-golf challenge." =~ /(\w+)-(\w+)/ p [$1,$2,$,$'] => ["code", "golf", "A ", " challenge."] Get rid of spaces, newlines, and parentheses. You can omit quite a bit in ruby. If in doubt, always try if it works without, and keep in mind this might break some editor syntax highlighting... x+=1if$<<A==????::??==?? • "Please post one tip per answer." Also ?\n is nice, but not really shorter than actually putting a newline character inside quotes. (same for tab) – Martin Ender May 7 '15 at 23:29 • And puts$ is even shorter. – Cyoce Nov 7 '17 at 5:20 • I know you were trying to prove a point but I'm pretty sure that last example is the same as x+=1;$<<A – Asone Tuhid Mar 1 '18 at 14:03 Scientific notation can often be used to shave off a char or two: x=1000 #versus x=1e3 • Note: This will return a Float value (1000.0) instead of an Integer, which may cause inaccurate results with large numbers. – Dogbert Feb 25 '11 at 11:02 • Ah, nice 1e2 is better than 100.0 when a percentage is needed. – Phrogz Feb 26 '11 at 6:36 • Similar to this principle, 1.0 is 1 char shorter than .to_f – Unihedron Dec 16 '17 at 13:44 • To my surprise, this trick works with Integer#upto and Integer#downto, e.g. 1.upto(1000) can become 1.upto(1e3). (Both forms iterate over integers.) – Dingus May 20 '20 at 1:06 Yet another way to use the splat operator: if you want to assign a single array literal, a * on the left-hand side is shorter than brackets on the right-hand side: a=[0] a=0 With multiple values you don't even need the splat operator (thanks to histocrat for correcting me on that): a=[1,2] a=1,2 • The latter case doesn't actually need the splat. – histocrat Aug 15 '15 at 22:53 • @histocrat Oh wow, I thought the second value would just be discarded in that case. – Martin Ender Aug 15 '15 at 22:53 • I can't believe I haven't known these in all the time I've spent golfing in Ruby. – Doorknob Jan 2 '16 at 3:07 I just attempted a TDD code-golf challenge i.e. Write shortest code to make specs pass. The specs were something like describe PigLatin do describe '.translate' do it 'translates "cat" to "atcay"' do expect(PigLatin.translate('cat')).to eq('atcay') end # And similar examples for .translate end end For the sake of code-golf, one need not create a module or class. module PigLatin def self.translate s;'some code'end;end one can do def(PigLatin=p).translate s;'some code'end Saves 13 characters! • Ha, very thorough. Not only did you add the necessary behavior to PigLatin, but also to @pig_latin, \$pig_latin, and 'pig'['latin']. – histocrat Feb 27 '14 at 15:23 • @histocrat: Now I get it. It's because translate has been defined on nil. – Eric Duminil Mar 20 '17 at 13:48 Kernel#p is a fun method. Use p var instead of puts var. This works perfectly with integers and floats, but not with all types. It prints quotation marks around strings, which is probably not what you want. Used with a single argument, p returns the argument after printing it. Used with multiple arguments, p returns the arguments in an array. Use p (with no arguments) instead of nil. • Unfortunately p 'some string' prints "some string" and not just some string which is often criticised by others. – Patrick Oscity Jun 1 '13 at 21:11 • Basically p s is the same as puts s.inspect, but it returns s – Cyoce Nov 3 '16 at 23:37 When a challenge requires that you output multiple lines, you don't have to loop through your results in order to print each line of e.g. an array. The puts method will flatten an array and print each element on a separate line. > a = %w(testing one two three) > puts a testing one two three Combining the splat operator with #p you can make it even shorter: p a The splat operator (technically the @ method, I think) also casts your non-array enumerables to arrays: > p a.lazy.map{\|x\|x2} #<Enumerator::Lazy: #<Enumerator::Lazy: [1, 2, 3]>:map> vs > p a.lazy.map{\|x\|x2} 2 4 6 • @ is not a method, splat is syntactic sugar – Asone Tuhid Jan 24 '18 at 10:55 To join an array, instead of this [...].join do this [...]'' which saves 2 bytes. To join with a separator use [...]?, # New features in Ruby 2.7 (experimental) Ruby 2.7 is in prerelease (as of 17 Jun 2019) and has some features that look great for golfing. Note that some of them might not make it into the final 2.7 release. All changes in Ruby 2.7-preview1: https://github.com/ruby/ruby/blob/v2_7_0_preview1/NEWS ### Numbered block parameters This is my favorite. It lets you finally drop the \|a,b\| in a block: %w[a b c].zip(1..) { puts @1 @2 } # => a # bb # ccc ### Method reference operator: .: .: is syntactic sugar for the .method method, e.g.: (1..5).map(&1r.:/) # => [(1/1), (1/2), (1/3), (1/4), (1/5)] ### Pattern matching I'm not sure how much use this will see in golf, but it's a great feature for which I only have a contrived example: def div(a) case a in [0, 0] then nil in [x, 0] if x > 0 then Float::INFINITY in [x, 0] then -Float::INFINITY in [x, y] then x.fdiv(y) end end div(-3, 0) # => -Infinity The pattern matching syntax has lots of features. For a complete list, check out this presentation: https://speakerdeck.com/k_tsj/pattern-matching-new-feature-in-ruby-2-dot-7 This is also the feature most likely to change before 2.7 is finished; it even prints a warning when you try to use it, which you should heed: warning: Pattern matching is experimental, and the behavior may change in future versions of Ruby! ### Beginless Range: ..3 Analogous to the endless Range introduced in 2.6, it may or may not have much use in golfing: %w[a v o c a d o].grep(..?m) # => ["a", "c", "a", "d"] ### Enumerable#tally to count like elements This could be useful in golfing: %w[a v o c a d o].tally # => {"a"=>2, "v"=>1, "o"=>2, "c"=>1, "d"=>1} ### Enumerable#filter_map to filter+map in one (1..20).filter_map {\|i\| 10 i if i.even? } # => [20, 40, 60, 80, 100] If the block returns nil or false the element will be omitted from the result. ### Integer#[] takes a second argument or range: You've long been able to get a specific bit from an integer with with subscript notation: n = 77 # (binary 01001101) n[3] # => 1 Now you can get the value of a range of bits by a second length argument or a range. n = 0b01001101 n[2, 4] # => 3 (0011) n[2..5] # => 3 Note that bits are indexed from least- to most-significant (right to left). • The range in the Enumerable#filter_map example should be (1..10), I think? – Dingus May 1 '20 at 1:46 • The method reference operator didn't make it in, as I sadly discovered just now trying to use it to do a restricted source challenge. – histocrat Jun 6 '20 at 17:32 • @1 and @2 are apparently now _1 and _2. – Eric Duminil Oct 12 '20 at 15:05 # Avoid Array#repeated_permutation and Array#repeated_combination Credit to @AsoneTuhid who golfed the code for repeated permutations of length $$\\ge5\$$. Some of Ruby's built-in methods have unfortunately long names. Never use Array#repeated_permutation or Array#repeated_combination; save bytes as follows. ### Repeated permutations Assume a is an array. To get repeated permutations of length $$\L = n + 1\$$ of the elements of a: a.product(a,a,a) # L <= 4; number of arguments = n a.product([a]n) # L >= 5 Depending on context, the parentheses may not be required. Both of the above yield an array. To iterate over the permutations, simply call with a block. ### Repeated combinations For repeated combinations of length $$\L\$$, use one of a.send(a.methods[42],L) # enumerator [a.send(a.methods[42],L)] # array The index that yields :repeated_combination depends on the Ruby version and possibly the OS (42 is correct for Ruby 2.5.5 on Linux, which is the version on TIO at the time of writing). The default indexing may also be disrupted if any libraries are loaded. The correct index in any case can always be found using [].methods.index(:repeated_combination). In general, calling a method by index using Object#send and Object#methods, as demonstrated above for repeated combinations, is shorter than a direct method call when the number of bytes in the method name and the index of the method in the methods array satisfy: +-------+-------+ \| Bytes \| Index \| +-------+-------+ \| 19+ \| 0-9 \| \| 20+ \| 10-99 \| \| 21+ \| 100+ \| +-------+-------+ Subtract 1 from byte count if parentheses not needed for send. • 17 bytes – Asone Tuhid Jun 2 '20 at 22:17 • @AsoneTuhid Very nice. Seems so obvious now that I see it. Thanks! – Dingus Jun 3 '20 at 0:20 Use \|\| instead or and && instead and. Beside the one character from and you can save the spaces (and perhaps the bracket) around the operator. p true and false ? 'yes' :'no' #-> true (wrong result) p (true and false) ? 'yes' :'no' #-> 'no' p true&&false ? 'yes' :'no' #-> 'no', saved 5 characters p true or false ? 'yes' :'no' #-> true (wrong result) p (true or false) ? 'yes' :'no' #-> 'yes' p true\|\|false ? 'yes' :'no' #-> 'yes', saved 4 characters If you loop on an array you normally use each. But map loops also over an array and it is one character shorter. Use Goruby instead of Ruby, which is something like an abbreviated version of Ruby. You can install it with rvm via rvm install goruby Goruby allows you to write most of your code as you would be writing Ruby, but has additional abbreviations built in. To find out the shortest available abbreviation for something, you can use the helper method shortest_abbreviation, for example: shortest_abbreviation :puts #=> "pts" Array.new.shortest_abbreviation :map #=> "m" String.new.shortest_abbreviation :capitalize #=> "cp" Array.new.shortest_abbreviation :join #=> "j" Also very handy is the alias say for puts which itself can be abbreviated with s. So instead of puts [?a..?z].map(&:capitalize).join you can now write s [?a..?z].m(&:cp).j to print the alphabet in capitals (which is not avery good example). This blog post explains more stuff and some of the inner workings if you are interested in further reading. PS: don't miss out on the h method ;-) # On looping ### while...end If you need to break out of the loop, while condition;code;end will probably be shorter than loop{code;condition\|\|break}. The ; before end is not always required, eg. while condition;p("text")end until c;...;end is equivalent to while !c;...;end and 1 byte shorter. Note that in most cases code while condition and code until condition are significantly shorter as they don't require the end keyword and can often drop semicolons. Also, i+=1 while true is equivalent to i+=1while true and 1 byte shorter. ### redo When run, the redo command jumps back to the beginning of the block it's in. When using redo in a lambda, you will have to move any setup variables to the arguments to avoid them being reset at every iteration (see examples). ### recursion Recursion can be shorter is some cases. For instance, if you're working on an array element by element, something like f=->s,t{p s;t[0]&&f[t]} can be shorter than the alternatives depending on the stuff. Note that per the current consensus, if you're calling your function by name, you need to include the assignment (f=) in the byte count making all recursive lambdas 2 bytes longer by default. ### eval If you need to run some code n times, you can use eval"code;"n. This will concatenate code; n times and run the whole thing. Note that in most cases you need to include a ; after your code. ## Examples ### A lambda to print all numbers from 1 to a inclusive: ->n{i=0;loop{p i+=1;i<n\|\|break}} # 32 bytes f=->n,i=1{i>n\|\|p(i)&&f[n,i+1]} # 30 bytes ->n,i=0{p(i+=1)<n&&redo} # 24 bytes ->n{i=0;p i+=1while i<n} # 24 bytes ->n{i=0;eval"p i+=1;"n} # 24 bytes ->n{n.times{\|i\|p i+1}} # 22 bytes # thanks to @benj2240 In this case, since the end-point is defined (n), the n.times loop is the shortest. The redo loop works because i+=1 modifies i and returns its new value and p(x) returns x (this is not true of print and puts). ### Given a function g and a number n, find the first number strictly larger than n for which g[n] is truthy ->g,n{loop{g[n+=1]&&break};n} # 29 bytes f=->g,n{g[n+=1]?n:f[g,n]} # 25 bytes ->g,n{1until g[n+=1];n} # 23 bytes ->g,n{(n+1..).find &g} # 22 bytes ->g,n{g[n+=1]?n:redo} # 21 bytes In this case, with an unknown end-point, redo is the best option. The (n+1..Inf) loop is equivalent to simply looping indefinitely but more verbose. A 1 (or anything else) is required before the until keyword to complete the syntax, using a number allows you to drop a space. The eval method is not viable in this case because there is neither a defined end-point nor an upper bound. Update: with the new open ranges (n+1..Inf) can be written simply as (n+1..), also .find{\|x\|g[x]} is equivalent to .find &g where g is converted to a block. TL;DR check out redo, it can very often shave off a couple of bytes • .times can often be even shorter for fixed loops, eg ->n{n.times{\|i\|p i+1}} for 22 bytes – benj2240 Mar 16 '18 at 15:07 You may be able to save 2 chars and use [(...)] (...).to_a For example, suppose we have a range that we want as an array: (1..2000).to_a Just do it like this: [1..2000] # Parentheses around the (ran..ge) is not needed! And now you have your range as an array. • I think [1..2000] works, too? – Lynn Aug 24 '15 at 18:38	2021-01-19 05:47:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31694266200065613, "perplexity": 4764.736277583372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703517966.39/warc/CC-MAIN-20210119042046-20210119072046-00019.warc.gz"}
https://imap.dovecot.org/configuration_manual/mail_location/	# Mail Location Settings¶ There are three different places where the mail location is looked up from: 1. mail_location setting in dovecot.conf is used if nothing else overrides it. 2. mail User Databases (userdb) overrides mail_location setting. 3. location setting inside namespaces overrides everything. Usually this should be used only for public and shared namespaces. ## Autodetection¶ By default the ref:setting-mail_location setting is empty, which means that Dovecot attempts to locate automatically where your mails are. This is done by looking, in order, at: • ~/mdbox/ • ~/sdbox/ • ~/Maildir/ • ~/mail/.imap/ • ~/mail/inbox • ~/mail/mbox • ~/Mail/.imap/ • ~/Mail/inbox • ~/Mail/mbox For autodetection to work, one of the above locations has to be populated; when autodetection is active, Dovecot will not attempt to create a mail folder. Note .imap is a directory, and inbox and mbox are files. It’s usually a good idea to explicitly specify where the mails are, even if the autodetection happens to work, in particular to benefit from auto-creation of the folder for new users. ## Mailbox autocreation¶ Dovecot in the 1.x era created mailboxes automatically regardless of whether mail_location was set. In 2.x autocreation only gets triggered if mail_location is correctly set. You’ll see something like this if you enable debug logging: Debug: Namespace : /home/user/Mail doesn't exist yet, using default permissions Debug: Namespace : Using permissions from /home/user/Mail: mode=0700 gid=default and a Mail/.imap directory will be present once that process has concluded. This is the easiest way to ensure a freshly created user is correctly set up for access via Dovecot. ## Format¶ The format of the mailbox location specification is as follows: mailbox-format : path [ : key = value … ] where: • mailbox-format is a tag identifying one of the formats described at Mailbox formats • path is the path to a directory where the mail is stored. This must be an absolute path, not a relative path. Even if relative paths appear to work, this usage is deprecated and will likely stop working at some point. Do not use the home directory, for reasons see Home vs. mail directory • key = value can appear zero or more times to set various optional parameters. Possible values for key are: INDEX specifies the location of Index files. ITERINDEX: Perform mailbox listing using the INDEX directories instead of the mail root directories. Mainly useful when the INDEX storage is on a faster storage. It takes no value. (v2.2.32+) INBOX specifies the location of the INBOX path. LAYOUT specifies the directory layout to use: Maildir++: The default used by Maildir format fs: The default used by mbox and dbox formats index: Uses mailbox GUIDs as the directory names. The mapping between mailbox names and GUIDs exists in dovecot.list.index* files. NO-NOSELECT Automatically delete any \NoSelect mailboxes that have no children. These mailboxes are sometimes confusing to users. Also if a NoSelect mailbox is attempted to be created with CREATE box/, it’s created as selectable mailbox instead. (LAYOUT=Maildir++ always behaves this same way.) (v2.2.32+) UTF-8 Store mailbox names on disk using UTF-8 instead of modified UTF-7. BROKENCHAR Specifies an escape character that is used for broken mailbox names. If mailbox name can’t be changed reversibly to UTF-8 and back, encode the problematic parts using in the user-visible UTF-8 name. The broken_char itself also has to be encoded the same way. This can be useful with imapc to access mailbox names that aren’t valid mUTF-7 charset from remote servers. (v2.2.32+) CONTROL Specifies the location of control files under the mbox or Maildir formats VOLATILEDIR Specifies the location of volatile files. This includes lock files and potentially other files that don’t need to exist permanently. This is especially useful to avoid creating lock files to NFS or other remote filesystems. (v2.2.32+) SUBSCRIPTIONS Specifies the file used for storing subscriptions. The default is subscriptions. If you’re trying to avoid name collisions with a mailbox named subscriptions, then also consider setting MAILBOXDIR. MAILBOXDIR Specifies directory name under which all mailbox directories are stored. With dbox formats the default is mailboxes/ while with other mailbox formats the default is empty. Typically this should be changed only for Lazy Expunge and Namespaces with mdbox. DIRNAME Specifies the directory name used for mailbox directories, or in the case of mbox specifies the mailbox message file name. With dbox formats the default is dbox-Mails/ while with other mailbox formats the default is empty. Can be used under either mbox , Maildir , or dbox formats. FULLDIRNAME Same as DIRNAME, but use the directory name also for index and control directory paths. This should be used instead of DIRNAME for new installations. (v2.2.8+) ALT specifies the Alternate storage path for dbox formats. • The colons and equals signs are literal and there are no spaces in an actual mailbox location specification. ## Variables¶ You can use several variables in the mail_location setting. See Config Variables for a full list, but the most commonly used ones are: %u Full username. %n User part in user@domain, same as %u if there’s no domain. %d Domain part in user@domain, empty if there’s no domain. ## Typical settings¶ Typically with Maildir it would be set to: mail_location = maildir:~/Maildir with mbox: mail_location = mbox:~/mail:INBOX=/var/mail/%u or if you’d like to use the dbox format: # single-dbox mail_location = sdbox:~/dbox or: # multi-dbox mail_location = mdbox:~/mdbox Use only absolute paths. Even if relative paths would appear to work, they might just as well break some day. ## Directory hashing¶ You can use two different kinds of hashes in Config Variables : • %H modifiers returns a 32bit hash of the given string as hex. Example: %2.256H would return max. 256 different hashes in range 00 .. ff. • %M returns a MD5 hash of the string as hex. This can be used for two level hashing by getting substrings of the MD5 hash. Example: %1Mu/%2.1Mu/%u returns directories from 0/0/user to f/f/user. ## Index files¶ Index files are by default stored under the same directory as mails. With maildir they are stored in the actual maildirs, with mbox they are stored under .imap/ directory. You may want to change the index file location if you’re using NFS or if you’re setting up shared mailboxes. You can change the index file location by adding :INDEX=<path> to mail_location. For example: mail_location = maildir:~/Maildir:INDEX=/var/indexes/%u The index directories are created automatically, but note that it requires that Dovecot has actually access to create the directories. Either make sure that the index root directory (/var/indexes in the above example) is writable to the logged in user, or create the user’s directory with proper permissions before the user logs in. If you really want to, you can also disable the index files completely by appending :INDEX=MEMORY. ## Private index files¶ New in version v2.2. Since v2.2 the recommended way to enable private flags for shared mailboxes is to create private indexes with :INDEXPVT=<path>. See SharedMailboxes/Public for more information. ## INBOX path¶ INBOX path can be specified to exist elsewhere than the rest of the mailboxes, Example: mail_location = mbox:~/mail:INBOX=/var/mail/%u mail_location = maildir:~/Maildir:INBOX=~/Maildir/.INBOX Note It’s still not possible to mix maildir and mbox formats this way. You need to use Namespaces. for that. ## Homeless users¶ Having a home directory for users is highly recommended. The Pigeonhole Sieve plugin already requires a home directory to work, and it probably won’t be the last feature to require a home. See VirtualUsers#homedirs for more reasons why it’s a good idea, and how to give Dovecot a home directory even if you don’t have a “real home directory”. If you really don’t want to set any home directory, you can use something like: mail_location = maildir:/home/%u/Maildir ## Per-user mail locations¶ It’s possible to override the default mail_location for specific users by making the User Databases (userdb) return mail extra field. See the User Databases (userdb) page for the specific userdb you’re using for more information how to do this. Below are however a couple of examples. Note that %h doesn’t work in the userdb queries or templates. ~/ gets expanded later, so use it instead. Note Since location specified within a Namespaces overrides mail_location setting, in case you specified that parameter, you’ll have to override in in the user database, specifying namespace/inbox/location extra field instead of mail. ## SQL¶ user_query = SELECT home, uid, gid, mail FROM users WHERE user = '%u' ## LDAP¶ user_attrs = homeDirectory=home, uidNumber=uid, gidNumber=gid, mailLocation=mail ## Passwd-file¶ user:{PLAIN}password:1000:1000::/home/user::userdb_mail=mbox:~/mail:INBOX=/var/mail/%u ## Mixing mbox and maildir¶ It’s possible to use both mboxes and maildirs for the same user by configuring multiple namespaces. See Namespaces. Having both mboxes and maildirs mixed within the same namespace isn’t currently supported. ## Custom mailbox location detection¶ Dovecot by default detects the mailboxes in this order: 1. maildir: ~/Maildir 2. mbox: ~/mail, and /var/mail/%u if it exists 3. mbox: ~/Mail, and /var/mail/%u if it exists If you need something else, you can override the mail_executable setting to run a script, which sets the MAIL environment properly. Example: #!/bin/sh if [ -d $HOME/.maildir ]; then export MAIL=maildir:$HOME/.maildir else export MAIL=mbox:$HOME/mail:INBOX=/var/mail/$USER fi export USERDB_KEYS="$USERDB_KEYS mail" exec "$@" ## Custom namespace location¶ If you need to override namespace’s location, first give it a name (“inbox” below): namespace inbox { .. } Then in the script use: #!/bin/sh # do the lookup here location=mbox:$HOME/mail export USERDB_KEYS="$USERDB_KEYS namespace/inbox/location" exec env "NAMESPACE/INBOX/LOCATION=$location" "$@"	2020-09-19 11:35:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3685394823551178, "perplexity": 8645.000496864206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400191780.21/warc/CC-MAIN-20200919110805-20200919140805-00764.warc.gz"}
https://tex.stackexchange.com/questions/365781/is-there-a-way-to-make-the-page-numbering-nonselectable	# Is there a way to make the page numbering nonselectable Is there any way in pdflatex to make the page numbers non selectable in the outputed documents. I know that there are some pdfs floating around out there where the page number is not included in selects. By page numbers I mean the ones placed at the bottom of each page to mark the current page, not those placed by using a reference command. • Which page numbers do you mean? In the ToC/LoF/LoT/ListOfWhatever? In a page reference by \pageref or in \cite - generated references? – user31729 Apr 20 '17 at 20:42 • @ChristianHupfer Updated question to be more clear. I mean the page numbers that mark the page as being that page. – HSchmale Apr 20 '17 at 20:49 • – Werner Apr 20 '17 at 20:59 • Would it be enough if the pagenumbers would not be included if the selected text is copied? – user36296 Apr 20 '17 at 21:24 \documentclass{article} \usepackage{fancyhdr,accsupp,lipsum} \pagestyle{fancy} \fancyfoot[C]{\BeginAccSupp{ActualText={}}\thepage\EndAccSupp{}} \begin{document} \lipsum[1-50] \end{document} accsupp provides the ability to set content in the document, but let the rendered PDF have it think it's something else. As mentioned, it's reader-specific. Here's the same selection-view within SumatraPDF: Note how the page number (1) is selected.	2019-08-21 14:18:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8523566126823425, "perplexity": 1300.2440719210042}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316021.66/warc/CC-MAIN-20190821131745-20190821153745-00345.warc.gz"}
https://www.uitbetalingzorgtoeslag.nl/mineral-processing-equipment/19890.html	News 1. Home 2. / Copper Ore The Principal Ore Of Copper # Copper Ore The Principal Ore Of Copper Sep 01 2013 Chalcopyrite the principal ore of copper (Cu) contains 34 63 Cu by mass How many grams of Cu can be obtained from 5 74x10^4 kg of the ore Enter the result in scientific notation Please help! I don't understand how to do it • ### Solved:chalcopyrite The Principal Ore Of Copper Chalcopyrite the principal ore of copper (Cu) contains 34 63 percent \mathrm{Cu} by mass How many grams of Cu can be obtained from 5 11 \times 10^{3} \mathr • ### Solved: Chalcopyrite The Principal Ore Of Copper (cu) Co Chalcopyrite the principal ore of copper (Cu) contains 34 63 Cu by mass How many grams of Cu can be obtained from 9 8X10^4 kg of the ore Enter your answer in scientific notation • ### [solved] Chalcopyrite The Principal Ore Of Copper (cu Chalcopyrite the principal ore of copper (Cu) contains 34 63 Cu by mass How many grams of Cu can be obtained from6 83 104 kg of the ore Enter your answer in • ### Copper Ores Article About Copper Ores By The Free Table 1 Principal types of copper ores Commercial type of ore Origin of deposits Main types of ore body A verage ore content in mined copper ores ( ) Admixtures Secondary Principal Disseminated (porphyry copper and copper molybdenum) Plutonic hydrothermal (quartz paragenesis) Stockworks and ore shoots 0 3 2 0 S Mo Au Ag Re trace elements • ### Extraction Of Copper From Copper Ore Dec 22 2018 There are two steps in the extraction of copper metal from chalcocite a copper ore In the first step copper(I) sulfide and oxygen react to form copper(I) oxide and sulfur dioxide In the second step copper(I) oxide and carbon react to form copper and carbon monoxide Write the net chemical equation for the production of copper from copper(I • ### Copper Ore Team Cofh Jan 15 2021 Copper ore is a common ore that yields copper and small amounts of gold Obtaining Copper ore is slightly common than iron ore but it occurs at higher levels (layers 40 96) Veins of copper ore are also slightly smaller Below oceans copper ore less commonly occurs at deeper levels (layers 20 55) • ### Chalcopyrite The Principal Ore Of Copper (cu) Contains How to solve Chalcopyrite the principal ore of copper (Cu) contains 34 63 Cu by mass How many grams of Cu can be obtained from 6 83 times 10^4 • ### Chalcopyrite The Principal Ore Of Copper (cu) Contains 34 How to solve Chalcopyrite the principal ore of copper (Cu) contains 34 63 Cu by mass How many grams of Cu can be obtained from 9 79 times 10^4 • ### Chalcopyrite The Principal Ore Of Copper (cu) Contains Correct answers 1 question Chalcopyrite the principal ore of copper (cu) contains 34 63 percent cu by mass how many grams of cu can be obtained from 7 35 x 10^3 kg of the ore • ### Copper Ore The Runescape Wiki Copper ore is an ore that can be obtained through mining copper rocks requiring level 1 Mining in various places around RuneScape Copper ore along with tin ore is one of the first ores a player can mine using the Mining skill Copper is required to craft bronze bars As players increase their Mining level and use higher tier pickaxes they are able to mine copper at • ### Properties Of Copper Ores University Of Arizona Properties of Copper Ores The Problem Minerals from which copper can be extracted to make money are called copper ores There are several copper ores but they all fall into two main categories oxide ores and sulfide ores Oxide ores contain oxygen Sulfide ores contain sulfur Azurite malachite and chrysocolla are a few examples of oxides ores • ### Extraction Of Copper From Copper Pyrite Grade 12 The principal ore of copper is copper pyrite and copper is extracted from this ore The different steps in extraction of copper are Crushing and Concentration The ore obtained from mines are broken down into small piece by jaw crusher and then pulverized The ore being sulphide ore is concentrated by froth floatation process • ### Copper Ore: Arizona’s Old Treasure Mar 17 2020 Arizona is the principal copper mining state in the United States followed by Utah New Mexico Nevada and Montana In 2019 the United States exported $2 3 billion worth of copper ore worldwide of which Arizona accounted for$1 6 billion or 69 5 [2] Of the total US copper ore exports to Mexico Arizona accounted for full 100 Arizona’s • ### Copper Ore The Official Terraria Wiki Jan 29 2021 Copper Ore is an early game ore which spawns on the surface as well as in the Underground and Cavern layers It is the weakest and most easily obtained tier of ore in the game Its primary use is to make Copper Bars which can be used to create the Copper tier of equipment The equivalent of Copper Ore is Tin Ore which will sometimes replace Copper in a world Copper Ore • ### Answered: Chalcopyrite The Principal Ore Of Bartleby Solution for Chalcopyrite the principal ore of copper (Cu) contains 34 63 Cu by mass How many grams of Cu can be obtained from 2 11 10“ kg of the ore • ### Copper Ore Price Market Trade Metal Copper Ore Price The page provides a list of copper ore and concentrate selling and purchasing offers The proposals related to copper commodity and copper ore of different grades of purity and volume of supply from various countries The information on copper ore international price copper concentrate price per ton could be found • ### Copper: Occurrence Principles Of Extraction Properties Ores i) Copper pyrite CuFeS 2 ii) Cuprite or Ruby copper Cu 2 O iii) Copper glance Cu 2 S The chief ore of copper is copper pyrite It yields nearly 76 of the world production of copper Extraction from copper pyrites Extraction of copper from copper pyrites involves the following steps 1 Crushing and concentration • ### Copper Ore Stardew Valley Wiki Jan 21 2021 Tailoring Copper Ore can be used in the spool of the Sewing Machine to create the dyeable Turtleneck Sweater Quests The morning after collecting 1 Copper Ore Clint will visit you and give you the blueprints for crafting a Furnace This creates the Forging Ahead quest Clint may ask you to collect various numbers of Copper Ore in random Gathering • ### Copper (cu) Ore Mineral Deposits In Nigeria West Africa Copper is a chemical element that commonly exists in a lot of minerals Copper ore or copper concentrate mineral has been one of the naturally occurring minerals that are available in Earth's crust of Nigeria Western part of Africa Its occurrence and distribution are mainly in the Northern Part of the country such as Nasarawa Plateau Zamfara Bauchi Gombe State Kano State • ### Copper Ore Crazyores Wiki Fandom Copper Ore is a relatively common ore found in the CrazyOres mod Copper spawns in veins of 8 or less and will not spawn above level 86 Although copper is a tier below iron it can be used as an alternative for several reasons Its tools have much higher durability than iron but do not deal as much damage and do not mine as fast Copper has its own set of buckets which can • ### Copper Ore An Overview Sciencedirect Topics The multimetal copper zinc lead ore is treated by integration of three complete banks in series each one for copper lead and zinc to produce respective concentrates In the case of complex ore metallurgy bulk concentrate is produced containing all three primary metals and value added elements like gold silver cadmium cobalt molybdenum • ### Copper Ore Dawn Of Man Wiki Jan 30 2021 Copper Ore is a malleable soft metal which is easy to obtain in nature in a directly usable metallic form to create basic tools It is the first metal ore to be smelted creating copper and the first ore to be purposefully alloyed with another metal tin to create bronze Copper ore combined with charcoal creates copper While copper ore has a green cast to it smelted copper • ### Copper: Sources And Ores Infoplease The principal ore of copper is chalcopyrite a sulfide of copper and iron also called copper pyrite Other important ores are chalcocite or copper glance a shiny lead gray copper sulfide bornite a lustrous reddish brown sulfide of copper and iron cuprite a red cuprous oxide ore and malachite a bright green carbonate ore Azurite is a • ### Copper Ore Legends Of Equestria Wiki Fandom Copper Ore a resource item for use in copper and bronze ingot forging When a Corgi or Pegasus Rock Golem is defeated it may leave behind a loot chestcontaining this ore It comes in very large amounts from the latter enemy It can be mined in gem mines first hall and Applewood mountains Way Out gives the player 30 copper ore for helping him out of the Crystal Caves • ### Copper Ore Valheim Wiki Fandom Copper ore is an item found in Valheim 1 General Information 2 Availability 3 Notes 4 Gallery Copper ore can be turned into Copper in a Smelter using Coal as fuel This can be further processed at a Forge with Tin to yield Bronze It can be mined from Copper Deposits which can be found in Black Forest biomes using any Pickaxe Such deposits have subtle bronze colored • ### How Extraction Of Copper From Copper Pyrites Qs Study The principal ore of copper is copper pyrite and copper is extracted from this ore Extraction of copper from copper pyrites involves the following steps – Crushing and concentration The ore is crushed and then concentrated by froth floatation process The ore obtained from mines are broken down into little piece by jaw crusher and then • ### Copper Ore Garden Paws Wiki Fandom Copper Ore is a crafting and smelting material Breaking a Geode on an Anvil or placing a Geode in a Geode Processor will give a high chance of obtaining Copper Ore On Kozita's Rock Island and Mountain Region the player can mine Copper crystals protruding from the ground to directly obtain the ore 1x Copper Ore and 1x Coal can be smelted in a Stone Furnace to create 1x Copper Bar Copper • ### Copper Ore Eco English Wiki Dec 06 2019 Copper Ore is a resource that can be gathered from copper ore veins Copper ore is only found within Granite It is most abundant in the Boreal Forest especially 20 30 blocks below the surface Copper Ore is clearly distinguishable from the surrounding rock due to its reddish mottled appearance • ### Copper Zinc Ores Danafloat Copper Zinc ores Usually chalcopyrite sphalerite and iron sulphides are present with this type of ore Gangue minerals are typically various silicates carbonates and often talc the latter which presents flotation challenges • ### Copper Create Wiki Fandom Copper Copper is a material generated as an ore in the world around any level when it has been showed to air for long enough it will slowly become oxidized and turn blue It is used to make Brass and as an ingredient for various components Six forms of copper exist Copper Blocks Copper Ingots Copper Nuggets Copper Ore and Copper Sheets Copper ore Our support team is always available to help you!	2021-10-18 13:39:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3196449875831604, "perplexity": 7596.573198609116}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585203.61/warc/CC-MAIN-20211018124412-20211018154412-00039.warc.gz"}
https://plainmath.net/calculus-2/79920-i-would-like-to-evaluate-munder	vrotterigzl 2022-06-24 I would like to evaluate: $\underset{n\to \mathrm{\infty }}{lim}\frac{1}{{n}^{3}}\sum _{\ell =1}^{n-1}\sqrt{\left({n}^{2}-{\ell }^{2}\right)\left({n}^{2}-\left(\ell -1{\right)}^{2}\right)}$ Expert For every $1⩽\ell ⩽n-1$ ${n}^{2}-{\ell }^{2}⩽\sqrt{\left({n}^{2}-{\ell }^{2}\right)\left({n}^{2}-\left(\ell -1{\right)}^{2}\right)}⩽{n}^{2}-\left(\ell -1{\right)}^{2},$ hence the sums ${S}_{n}$ you are interested in are such that ${R}_{n}⩽{S}_{n}⩽{T}_{n}$ for every $n⩾1$, with ${R}_{n}=\frac{1}{{n}^{3}}\sum _{\ell =1}^{n-1}\left({n}^{2}-{\ell }^{2}\right),\phantom{\rule{2em}{0ex}}{T}_{n}=\frac{1}{{n}^{3}}\sum _{\ell =0}^{n-2}\left({n}^{2}-{\ell }^{2}\right).$ The rest should be easy (and the limit is indeed $\frac{2}{3}$) Do you have a similar question?	2023-01-31 04:21:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 34, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9953277111053467, "perplexity": 322.31488878363183}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499842.81/warc/CC-MAIN-20230131023947-20230131053947-00781.warc.gz"}
http://mathhelpforum.com/geometry/108700-area-quadrilateral-given-diagonals-1-side.html	1. ## Area of Quadrilateral given diagonals and 1 side. Can some one help me out please... In a quadrilateral ABCD, the diagonals AC and BD intersect at O. Let OA = 2, OB = 2, OC = 3, OD = 4 and AB = 3. The area of the quadrilateral is ? Im sorry if this is too simple.... 2. Originally Posted by itsmaximhere Can some one help me out please... In a quadrilateral ABCD, the diagonals AC and BD intersect at O. Let OA = 2, OB = 2, OC = 3, OD = 4 and AB = 3. The area of the quadrilateral is ? Im sorry if this is too simple.... The area (K) of a quadrilateral can be found by $K = \dfrac{1}{2} pq \sin \theta$ the diagonals are p & q In this case, from the data give: p = 2+3 = 5 & q = 4+2 = 6 You have given the three sides of a triangle: 2,2,3 Use the cosine law to compute $\angle AOB = \theta$ Probably easier (since $\triangle AOB$ is isosceles) $\theta = 2 \, sin^{-1} \left ( \dfrac{1.5}{2} \right)$ Compute $\theta$ and $\sin \theta$, then plug them into the equation above.	2016-10-26 13:42:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8627115488052368, "perplexity": 476.54752370841874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720945.67/warc/CC-MAIN-20161020183840-00081-ip-10-171-6-4.ec2.internal.warc.gz"}
http://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleid=2584388	0 Technical Brief # Effect of Local Thermal Nonequilibrium on the Stability of Natural Convection in an Oldroyd-B Fluid Saturated Vertical Porous Layer [+] Author and Article Information B. M. Shankar Department of Mathematics, PES University, Bangalore 560 085, India e-mail: bmshankar@pes.edu I. S. Shivakumara Department of Mathematics, Bangalore University, Bangalore 560 056, India 1Corresponding author. Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 1, 2016; final manuscript received November 4, 2016; published online January 18, 2017. Assoc. Editor: Dr. Antonio Barletta. J. Heat Transfer 139(4), 044503 (Jan 18, 2017) (10 pages) Paper No: HT-16-1345; doi: 10.1115/1.4035199 History: Received June 01, 2016; Revised November 04, 2016 ## Abstract The effect of local thermal nonequilibrium (LTNE) on the stability of natural convection in a vertical porous slab saturated by an Oldroyd-B fluid is investigated. The vertical walls of the slab are impermeable and maintained at constant but different temperatures. A two-field model that represents the fluid and solid phase temperature fields separately is used for heat transport equation. The resulting stability eigenvalue problem is solved numerically using Chebyshev collocation method as the energy stability analysis becomes ineffective in deciding the stability of the system. Despite the basic state remains the same for Newtonian and viscoelastic fluids, it is observed that the base flow is unstable for viscoelastic fluids and this result is qualitatively different from Newtonian fluids. The results for Maxwell fluid are delineated as a particular case from the present study. It is found that the viscoelasticity has both stabilizing and destabilizing influence on the flow. Increase in the value of interphase heat transfer coefficient $Ht$, strain retardation parameter $Λ2$ and diffusivity ratio $α$ portray stabilizing influence on the system while increasing stress relaxation parameter $Λ1$ and porosity-modified conductivity ratio $γ$ exhibit an opposite trend. <> ## Figures Fig. 1 Physical configuration Fig. 2 Neutral stability curves Fig. 3 Variation of (a) RD c, (b) ac, and (c) cc with Ht for various values of Λ1 when Λ2=0.1,γ=0.5, and α=1 Fig. 4 Variation of (a) RD c, (b) ac, and (c) cc with Ht for various values of Λ2 when Λ1=0.5,γ=0.5, and α=1 Fig. 5 Variation of (a) RD c, (b) ac, and (c) cc with Ht for various values of γ when Λ1=0.3,Λ2=0.1, and α=1 Fig. 6 Variation of (a) RD c, (b) ac, and (c) cc with Λ1 for various values of Ht and Λ2 when γ=0.5, α=1 Fig. 7 Variation of (a) RD c, (b) ac, and (c) cc with Λ1 for various values of α and Λ2 when Ht=20, γ=0.5 Fig. 8 Variation of (a) RD c, (b) ac, and (c) cc with Λ1 for various values of γ and Λ2 when Ht=20, α=1 ## Discussions Some tools below are only available to our subscribers or users with an online account. ### Related Content Customize your page view by dragging and repositioning the boxes below. Related Journal Articles Related Proceedings Articles Related eBook Content Topic Collections	2017-08-19 18:52:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19212186336517334, "perplexity": 4227.874501146371}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105712.28/warc/CC-MAIN-20170819182059-20170819202059-00566.warc.gz"}
https://mvlearn.github.io/references/cluster.html	# Clustering¶ ## Multiview Spectral Clustering¶ class mvlearn.cluster.MultiviewSpectralClustering(n_clusters=2, random_state=None, info_view=None, max_iter=10, n_init=10, affinity='rbf', gamma=None, n_neighbors=10)[source] An implementation of multi-view spectral clustering. An implementation of multi-view spectral clustering using the basic co-training framework as described in 1. Additionally, this can be effective when the dataset naturally contains features that are of 2 different data types, such as continuous features and categorical features 4, and then the original features are separated into two views in this way. This algorithm can handle 2 or more views of data. Parameters • n_clusters (int) -- The number of clusters • random_state (int, optional, default=None) -- Determines random number generation for k-means. • info_view (int, optional, default=None) -- The most informative view. Must be between 0 and n_views-1 If given, then the final clustering will be performed on the designated view alone. Otherwise, the algorithm will concatenate across all views and cluster on the result. • max_iter (int, optional, default=10) -- The maximum number of iterations to run the clustering algorithm. • n_init (int, optional, default=10) -- The number of random initializations to use for k-means clustering. • affinity (string, optional, default='rbf') -- The affinity metric used to construct the affinity matrix. Options include 'rbf' (radial basis function), 'nearest_neighbors', and 'poly' (polynomial) • gamma (float, optional, default=None) -- Kernel coefficient for rbf and polynomial kernels. If None then gamma is computed as 1 / (2 * median(pair_wise_distances(X))^2) for each data view X. • n_neighbors (int, optional, default=10) -- Only used if nearest neighbors is selected for affinity. The number of neighbors to use for the nearest neighbors kernel. labels_ Cluster labels for each sample in the fitted data. Type array-like, shape (n_samples) embedding_ The final spectral representation of the data to be used as input for the KMeans clustering step. Type array-like, shape (n_samples, n_clusters) Notes Multi-view spectral clustering adapts the spectral clustering algorithm to applications where more than one view of data is available. This algorithm relies on the basic assumptions of the co-training, which are: (a) Sufficiency: each view is sufficient for classification on its own, (b) Compatibility: the target functions in both views predict the same labels for co-occurring features with high probability, and (c) Conditional independence: the views are conditionally independent given the class labels. In contrast to multi-view k-means clustering, multi-view spectral clustering performs well on arbitrary shaped clusters, and can therefore be readily used in applications where clusters are not expected to be convex. However multi-view spectral clustering tends to be computationally expensive unless the similarity graph for the data is sparse. Multi-view spectral clustering works by using the spectral embedding from one view to constrain the similarity graph in the other view. By iteratively applying this procedure, the clustering of the two views tend to each other. Here we outline the algorithm for the Multi-view Spectral clustering algorithm for 2 views. Multi-view Spectral Clustering Algorithm (for 2 views) Input: Similarity matrix for both views: $$\mathbf{K}_1, \mathbf{K}_2$$ Output: Assignments to k clusters 1. Initialize: $$\mathbf{L}_v = \mathbf{D}_v^{-1/2} \mathbf{K}_v\mathbf{D}_v^{-1/2}$$ for $$v = 1, 2$$ $$\mathbf{U}_v^0$$ is an $$n \times k$$ matrix with the top k eigenvectors of $$\mathbf{L}_v$$ for $$v = 1, 2$$ 2. For $$i = 1$$ to iter: 1. $$\mathbf{S}_1 = sym(\mathbf{U}_2^{i-1} {\mathbf{U}_2^{i-1}}^T\mathbf{K}_1)$$ 2. $$\mathbf{S}_2 = sym(\mathbf{U}_1^{i-1} {\mathbf{U}_1^{i-1}}^T\mathbf{K}_2)$$ 3. Use $$\mathbf{S}_1$$ and $$\mathbf{S}_2$$ as the new graph similarities and compute the Laplacians. Solve for the largest k eigenvectors to obtain $$\mathbf{U}_1^i$$ and $$\mathbf{U}_2^i$$. 3. Row-normalize $$\mathbf{U}_1^i$$ and $$\mathbf{U}_2^i$$. 4. Form matrix $$\mathbf{V} = \mathbf{U}_v^i$$, where $$v$$ is believed to be the most informative view a priori. If there is no prior knowledge on the view informativeness, matrix $$\mathbf{V}$$ can also be set to the column-wise concatenation of the two $$\mathbf{U}_v^i$$ s. 5. Assign example j to cluster c if the j-th row of $$\mathbf{V}$$ is assigned to cluster c by the k-means algorithm. References 1 Abhishek Kumar and Hal Daume. "A co-training approach for multi-view spectral clustering." In Proceedings of the 28th International Conference on Machine Learning, page 393–400. Omnipress, 2011. Examples >>> from mvlearn.datasets import load_UCImultifeature >>> from mvlearn.cluster import MultiviewSpectralClustering >>> from sklearn.metrics import normalized_mutual_info_score as nmi_score >>> # Get 5-class data >>> data, labels = load_UCImultifeature(select_labeled = list(range(5))) >>> mv_data = data[:2] # first 2 views only >>> mv_spectral = MultiviewSpectralClustering(n_clusters=5, ... random_state=10, n_init=100) >>> mv_clusters = mv_spectral.fit_predict(mv_data) >>> nmi = nmi_score(labels, mv_clusters) >>> print('{0:.3f}'.format(nmi)) 0.872 ## Co-Regularized Multiview Spectral Clustering¶ class mvlearn.cluster.MultiviewCoRegSpectralClustering(n_clusters=2, v_lambda=2, random_state=None, info_view=None, max_iter=10, n_init=10, affinity='rbf', gamma=None, n_neighbors=10)[source] An implementation of co-regularized multi-view spectral clustering based on an unsupervied version of the co-training framework. This algorithm uses the pairwise co-regularization scheme as described in 2. This algorithm can handle 2 or more views of data. Parameters • n_clusters (int) -- The number of clusters • v_lambda (float, optional, default=2) -- The regularization parameter. This parameter trades-off the spectral clustering objectives with the degree of agreement between each pair of views in the new representation. Must be a positive value. • random_state (int, optional, default=None) -- Determines random number generation for k-means. • info_view (int, optional, default=None) -- The most informative view. Must be between 0 and n_views-1 If given, then the final clustering will be performed on the designated view alone. Otherwise, the algorithm will concatenate across all views and cluster on the result. • max_iter (int, optional, default=10) -- The maximum number of iterations to run the clustering algorithm. • n_init (int, optional, default=10) -- The number of random initializations to use for k-means clustering. • affinity (string, optional, default='rbf') -- The affinity metric used to construct the affinity matrix. Options include 'rbf' (radial basis function), 'nearest_neighbors', and 'poly' (polynomial) • gamma (float, optional, default=None) -- Kernel coefficient for rbf and polynomial kernels. If None then gamma is computed as 1 / (2 * median(pair_wise_distances(X))^2) for each data view X. • n_neighbors (int, optional, default=10) -- Only used if nearest neighbors is selected for affinity. The number of neighbors to use for the nearest neighbors kernel. labels_ Cluster labels for each point. Type array-like, shape (n_samples,) embedding_ The final spectral representation of the data to be used as input for the KMeans clustering step. Type array-like, shape (n_samples, n_clusters) objective_ The value of the spectral clustering objective for each view at the end of each iteration. Type array-like, shape (n_views, n_iterations) Notes In standard spectral clustering, the eigenvector matrix U for a given view is the new data representation to be used for the subsequent k-means clustering stage. In this algorithm, the objective function has been altered to encourage the pairwise similarities of examples under the new representation to be similar across all views. The modified spectral clustering objective for the case of two views is shown and derived in [#4Clu]. In the clustering objective, the hyperparameter lambda trades-off the spectral clustering objectives and the disagreement term. For a fixed lambda and n, the objective function is bounded from above and non-decreasing. As such, the algorithm is guaranteed to converge. References 2 Abhishek Kumar, Piyush Rai, and Hal Daume. Co-regularized multi-view spectral cluster-ing. In Proceedings of the 24th International Conference on Neural Information Processing Systems, page 1413–1421. Curran Associates Inc., 2011. Examples >>> from mvlearn.datasets import load_UCImultifeature >>> from mvlearn.cluster import MultiviewCoRegSpectralClustering >>> from sklearn.metrics import normalized_mutual_info_score as nmi_score >>> # Get 5-class data >>> data, labels = load_UCImultifeature(select_labeled = list(range(5))) >>> mv_data = data[:2] # first 2 views only >>> mv_spectral = MultiviewCoRegSpectralClustering(n_clusters=5, ... random_state=10, n_init=100) >>> mv_clusters = mv_spectral.fit_predict(mv_data) >>> nmi = nmi_score(labels, mv_clusters, average_method='arithmetic') >>> print('{0:.3f}'.format(nmi)) 0.663 ## Multiview K Means¶ class mvlearn.cluster.MultiviewKMeans(n_clusters=2, random_state=None, init='k-means++', patience=5, max_iter=300, n_init=5, tol=0.0001, n_jobs=None)[source] This class implements multi-view k-means. This class implements multi-view k-means using the co-EM framework as described in 3. This algorithm is most suitable for cases in which the different views of data are conditionally independent. Additionally, this can be effective when the dataset naturally contains features that are of 2 different data types, such as continuous features and categorical features 4, and then the original features are separated into two views in this way. This algorithm currently handles two views of data. Parameters • n_clusters (int, optional, default=2) -- The number of clusters • random_state (int, optional, default=None) -- Determines random number generation for initializing centroids. Can seed the random number generator with an int. • init ({'k-means++', 'random'} or list of array-likes, default='k-means++') -- Method of initializing centroids. 'k-means++': selects initial cluster centers for k-means clustering via a method that speeds up convergence. 'random': choose n_cluster samples from the data for the initial centroids. If a list of array-likes is passed, the list should have a length of equal to the number of views. Each of the array-likes should have the shape (n_clusters, n_features_i) for the ith view, where n_features_i is the number of features in the ith view of the input data. • patience (int, optional, default=5) -- The number of EM iterations with no decrease in the objective function after which the algorithm will terminate. • max_iter (int, optional, default=300) -- The maximum number of EM iterations to run before termination. • n_init (int, optional, default=5) -- Number of times the k-means algorithm will run on different centroid seeds. The final result will be the best output of n_init runs with respect to total inertia across all views. • tol (float, default=1e-4) -- Relative tolerance with regards to inertia to declare convergence. • n_jobs (int, default=None) -- The number of jobs to use for computation. This works by computing each of the n_init runs in parallel. None means 1. -1 means using all processors. labels_ Cluster labels for each sample in the fitted data. Type array-like, shape (n_samples) centroids_ centroids_ length: n_views centroids_[i] shape: (n_clusters, n_features_i) The cluster centroids for each of the two views. centroids_[0] corresponds to the centroids of view 1 and centroids_[1] corresponds to the centroids of view 2. Type list of array-likes Notes Multi-view k-means clustering adapts the traditional k-means clustering algorithm to handle two views of data. This algorithm requires that a conditional independence assumption between views holds true. In cases where both views are informative and conditionally independent, multi-view k-means clustering can outperform its single-view analog run on a concatenated version of the two views of data. This is quite useful for applications where you wish to cluster data from two different modalities or data with features that naturally fall into two different partitions. Multi-view k-means works by iteratively performing the maximization and expectation steps of traditional EM in one view, and then using the computed hidden variables as the input for the maximization step in the other view. This algorithm, referred to as Co-EM, is described below. Co-EM Algorithm Input: Unlabeled data D with 2 views 1. Initialize $$\Theta_0^{(2)}$$, T, $$t = 0$$. 2. E step for view 2: compute expectation for hidden variables given 3. Loop until stopping criterion is true: 1. For v = 1 ... 2: 1. $$t = t + 1$$ 2. M step view v: Find model parameters $$\Theta_t^{(v)}$$ that maximize the likelihood for the data given the expected values for hidden variables of view $$\overline{v}$$ of iteration $$t$$ - 1 3. E step view $$v$$: compute expectation for hidden variables given the model parameters $$\Theta_t^{(v)}$$ 4. return combined $$\hat{\Theta} = \Theta_{t-1}^{(1)} \cup \Theta_t^{(2)}$$ The final assignment of examples to partitions is performed by assigning each example to the cluster with the largest averaged posterior probability over both views. References 3(1,2) Steffen Bickel and Tobias Scheffer. Multi-view clustering. In Proceedings of the Fourth IEEE International Conference on Data Mining, page 19–26. IEEE Computer Society, 2004. 4(1,2,3) Guoqing Chao, Shiliang Sun, and J. Bi. A survey on multi-view clustering.arXiv preprint, arXiv:1712.06246, 2017. Examples >>> from mvlearn.datasets import load_UCImultifeature >>> from mvlearn.cluster import MultiviewKMeans >>> from sklearn.metrics import normalized_mutual_info_score as nmi_score >>> # Get 5-class data >>> data, labels = load_UCImultifeature(select_labeled = list(range(5))) >>> mv_data = data[:2] # first 2 views only >>> mv_kmeans = MultiviewKMeans(n_clusters=5, random_state=10) >>> mv_clusters = mv_kmeans.fit_predict(mv_data) >>> nmi = nmi_score(labels, mv_clusters) >>> print('{0:.3f}'.format(nmi)) 0.770 "" ## Multiview Spherical K Means¶ class mvlearn.cluster.MultiviewSphericalKMeans(n_clusters=2, random_state=None, init='k-means++', patience=5, max_iter=None, n_init=5, tol=0.0001, n_jobs=None)[source] An implementation of multi-view spherical K-Means. An implementation of multi-view spherical K-Means using the co-EM framework as described in 3. This algorithm is most suitable for cases in which the different views of data are conditionally independent. Additionally, this can be effective when the dataset naturally contains features that are of 2 different data types, such as continuous features and categorical features 4, and then the original features are separated into two views in this way. This algorithm currently handles two views of data. Parameters • n_clusters (int, optional, default=2) -- The number of clusters • random_state (int, optional, default=None) -- Determines random number generation for initializing centroids. Can seed the random number generator with an int. • init ({'k-means++', 'random'} or list of array-likes, default='k-means++') -- Method of initializing centroids. 'k-means++': selects initial cluster centers for k-means clustering via a method that speeds up convergence. 'random': choose n_cluster samples from the data for the initial centroids. If a list of array-likes is passed, the list should have a length of equal to the number of views. Each of the array-likes should have the shape (n_clusters, n_features_i) for the ith view, where n_features_i is the number of features in the ith view of the input data. • patience (int, optional, default=5) -- The number of EM iterations with no decrease in the objective function after which the algorithm will terminate. • max_iter (int, optional, default=None) -- The maximum number of EM iterations to run before termination. • n_init (int, optional, default=5) -- Number of times the k-means algorithm will run on different centroid seeds. The final result will be the best output of n_init runs with respect to total inertia across all views. • tol (float, default=1e-4) -- Relative tolerance with regards to inertia to declare convergence. • n_jobs (int, default=None) -- The number of jobs to use for computation. This works by computing each of the n_init runs in parallel. None means 1. -1 means using all processors. labels_ Cluster labels for each sample in the fitted data. Type array-like, shape (n_samples) centroids_ centroids_ length: n_views centroids_[i] shape: (n_clusters, n_features_i) The cluster centroids for each of the two views. centroids_[0] corresponds to the centroids of view 1 and centroids_[1] corresponds to the centroids of view 2. Type list of array-likes Notes Multi-view spherical k-means clustering adapts the traditional spherical kmeans clustering algorithm to handle two views of data. This algorithm is similar to the mult-view k-means algorithm, except it uses cosine distance instead of euclidean distance for the purposes of computing the optimization objective and making assignments. This algorithm requires that a conditional independence assumption between views holds true. In cases where both views are informative and conditionally independent, multi-view spherical k-means clustering can outperform its single-view analog run on a concatenated version of the two views of data. This is quite useful for applications where you wish to cluster data from two different modalities or data with features that naturally fall into two different partitions. Multi-view spherical k-means works by iteratively performing the maximization and expectation steps of traditional EM in one view, and then using the computed hidden variables as the input for the maximization step in the other view. This algorithm is described in the section for multi-view k-means clustering. Examples >>> from mvlearn.datasets import load_UCImultifeature >>> from mvlearn.cluster import MultiviewSphericalKMeans >>> from sklearn.metrics import normalized_mutual_info_score as nmi_score >>> # Get 5-class data >>> data, labels = load_UCImultifeature(select_labeled = list(range(5))) >>> mv_data = data[:2] # first 2 views only >>> mv_kmeans = MultiviewSphericalKMeans(n_clusters=5, random_state=5) >>> mv_clusters = mv_kmeans.fit_predict(mv_data) >>> # Compute nmi between true class labels and multi-view cluster labels >>> nmi = nmi_score(labels, mv_clusters) >>> print('{0:.3f}'.format(nmi)) 0.823	2022-11-26 12:42:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4705567955970764, "perplexity": 3829.8314794770617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446706291.88/warc/CC-MAIN-20221126112341-20221126142341-00693.warc.gz"}
https://codereview.stackexchange.com/questions/157965/cms-controllers-from-procedural-to-object-oriented	# CMS controllers, from procedural to object oriented I made my own extra slim flat file CMS with PHP, for a website that needs simple updates. You can have a look at its functional current state here (username is Username, password is Password). I tried to follow an MVC architecture for the project, and I am stuck with having the Controllers as classes. Let me describe the project simply. Models classes include: • Projects class, describes a list of all the projects • Project class, describes a project and interact with its “database” text file • Info class, describes the individual information in each project (title, date, description) They have methods similar to $Projects->return_list() and $Project->return_title() and $Info->return_uppercased() that I can use in my views. Views are snippets of HTML/PHP code for each component of the CMS. They include: The select view displays a list of all projects <p> Select project to edit: <select name="Select"> <?php foreach ($projects as $project): ?> <option value="<?php echo$project->filename(); ?>"><?php echo $project->title(); ?></option> <?php endforeach ?> </select> <button type="submit" id="edit" name="Submit" value="edit_project">Edit</button> <button type="submit" name="Submit" value="new_project">New project</button> </p> The edit view displays a form to edit the selected project <p> File name: <?php echo$selectedProject->filename(); ?><br> Title: <input type="text" name="Title" value="<?php echo $selectedProject->title(); ?>"><br> Date: <input type="text" name="Date" value="<?php echo$selectedProject->date(); ?>"><br> Length: <input type="text" name="Length" value="<?php echo $selectedProject->length(); ?>"><br> Video ID: <input type="text" name="Video" value="<?php echo$selectedProject->video(); ?>"><br> Description: <textarea name="Description"><?php echo $selectedProject->description(); ?></textarea> </p> and the submit view only displays an “Update” and “Delete” button <button type="submit" name="Submit" value="delete_project">Delete</button> <button type="submit" name="Submit" value="update_project">Update</button> I have only one front Controller file (index.php) which lists all possible user interactions (checks if “Edit”, “Create new project”, “Update” or “Delete” have been clicked) and displays the necessary views. It also manipulates the Models objects (e. g. calls $Projects->add_new_project() when “Create project” is clicked). Here is a simplified part of it, the whole commented front controller code is accessible here. <?php echo '<form method="post">'; # first arrive on the page: if no project has been selected and no "Submit" button has been clicked # — only displays the "select a project" snippet if ( ! $_POST['Select'] && !$_POST['Submit'] ) { require 'views/select.php'; } # else if "Edit" has been clicked (and a project has been selected) # — displays the "select a project", "edit the project" and "submit the changes" snippets # — the "edit the project" snippet gets filled with the info from the selected project else if ($_POST['Select'] &&$_POST['Submit'] == 'edit_project') { $selectedProject =$projects->{$_POST['Select']}; require 'views/select.php'; require 'views/edit.php'; require 'views/submit.php'; } # else if "Create new project" has been clicked # — creates a new project # — displays the "select a project", "edit the project" and "submit the changes" snippets # — the "edit the project" snippet gets filled with the info from the new created project else if ($_POST['Submit'] == 'new_project') { $newProject = new Project();$newProject->create_blank(); # fills the Project object with blank properties (title, date, etc.) $projects->add_project($newProject); # new project is added to Projects object $selectedProject =$projects->{$newProject->filename()};$selectedProject->update_file($projects_folder); # the new project gets saved as a text file require 'views/select.php'; require 'views/edit.php'; require 'views/create.php'; } echo '</form>'; ?> The real extended code links the views and models for the the following tasks: • login/logout • select a project • edit a project • create a project • delete a project • reorder the projects This front controller code is long, does not separate tasks so clearly and is complex to update/maintain. I have no clues how to handle everything the front controller file does using classes and objects, with the aim of having both a reusable and more segmented/maintainable code. Any directions? Other critical reviews and advises would be much appreciated. ## 1 Answer The gap between what you currently have and an MVC-based, object-oriented framework is quite large. I would expect your best learning opportunity would be to work with one or two of the popular PHP frameworks to see how they structure things. It is really quite hard to give you a meaningful review, as you have just shown some assorted fragments of code, none of which gives clear understanding to what is taking place in your application. From looking at what you have posted, my guess is your framework has significant problems with regards to security (for example, you seem to be trusting user input without performing any validation) and with regards to truly separating your code along areas of responsibility. • Thanks for the repsonse! My Info (model) class actually has a$Info->secure() method performing trim(), stripslashes() and htmlspecialchars() on the user input. This MVC structure seems to be quite far out! I really thought of it as a simple separation of data structure, template and something that links between the two of them… am I wrong? Concerning the code I think it would be more confusing to show the whole thing, I tried to reduce it to something clearer. – Raoulito Mar 17 '17 at 16:13 • @Raoulito I would really look into the gist of this comment. Look into Symfony and/or Laravel and note how far of you are from a MVC :) – Pinoniq Jan 11 '18 at 22:46	2020-03-29 16:18:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19565050303936005, "perplexity": 7846.747964111284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370494349.3/warc/CC-MAIN-20200329140021-20200329170021-00453.warc.gz"}
https://questions.llc/questions/1063363/the-period-of-a-pendulum-t-in-seconds-varies-directly-with-the-square-root-of-the	# "the period of a pendulum, T (in seconds) varies directly with the square root of the length of the pendulum, L (in centimeters)". Given that a pendulum of length 9cm has a period of 0.63 seconds, find: a) The period of a pendulum of length 25cm b) The length of a pendulum whose period is 1.5 seconds, thanks :) 1. 👍 2. 👎 3. 👁 4. ℹ️ 5. 🚩 1. Given T seconds =k √L (cm) where k is an arbitrary constant to be determined. Also given 0.63=k√9 Therefore we can determine the constant k. k=0.63/√9=0.21 T(L)=0.21√L where T is period in seconds and L is length of pendulum in cm. The problem reduces to: a) T(25)=? b) if T(L)=1.5 s, what is L? Can you take it from here? 1. 👍 2. 👎 3. ℹ️ 4. 🚩 2. T = k√L so, T/√L is constant. (a) .63/√9 = T/√25 (b) .63/√9 = 1.5/√L 1. 👍 2. 👎 3. ℹ️ 4. 🚩	2022-08-16 03:15:06	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9658109545707703, "perplexity": 7172.1403577559695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572220.19/warc/CC-MAIN-20220816030218-20220816060218-00777.warc.gz"}
https://www.beatthegmat.com/is-a-cent-e-a-iexcl-xa-cent-e-a-5-2-5a-cent-e-a-x-t300083.html?view=previous	## What is the perimeter of rectangle ABCD ##### This topic has expert replies Moderator Posts: 5054 Joined: 07 Sep 2017 Followed by:16 members ### What is the perimeter of rectangle ABCD by BTGmoderatorDC » Wed Nov 15, 2017 2:11 pm What is the perimeter of rectangle ABCD? (1) The longer side of the rectangle is 2 meters shorter than its diagonal $$(2)The\ ratio\ of\ the\ shorter\ side\ of\ the\ rec\tan gle\ to\ its\ diagonal\ is\ \frac{1}{3}\$$ Which of the statement is sufficient? OA C ### GMAT/MBA Expert Elite Legendary Member Posts: 10347 Joined: 23 Jun 2013 Location: Palo Alto, CA Thanked: 2867 times Followed by:506 members GMAT Score:800 by Rich.C@EMPOWERgmat.com » Wed Nov 15, 2017 8:58 pm Hi lheiannie07, We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math. 1) The longer side of the rectangle is 2 meters shorter than its diagonal With the information in Fact 1, we can create 2 equations (with the diagonal represented by D): L = D - 2 L^2 + W^2 = D^2 Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter. Fact 1 is INSUFFICIENT 2) The ratio of the shorter side to the diagonal is 1/3 With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1): W/D = 1/3....... D = 3W L^2 + W^2 = D2 Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter. Fact 2 is INSUFFICIENT Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables - and there will be just one solution. Combined, SUFFICIENT GMAT assassins aren't born, they're made, Rich Contact Rich at Rich.C@empowergmat.com Moderator Posts: 5054 Joined: 07 Sep 2017 Followed by:16 members by BTGmoderatorDC » Wed Jan 10, 2018 10:01 pm Rich.C@EMPOWERgmat.com wrote:Hi lheiannie07, We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math. 1) The longer side of the rectangle is 2 meters shorter than its diagonal With the information in Fact 1, we can create 2 equations (with the diagonal represented by D): L = D - 2 L^2 + W^2 = D^2 Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter. Fact 1 is INSUFFICIENT 2) The ratio of the shorter side to the diagonal is 1/3 With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1): W/D = 1/3....... D = 3W L^2 + W^2 = D2 Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter. Fact 2 is INSUFFICIENT Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables - and there will be just one solution. Combined, SUFFICIENT GMAT assassins aren't born, they're made, Rich Thanks a lot! Moderator Posts: 5054 Joined: 07 Sep 2017 Followed by:16 members by BTGmoderatorDC » Sun Jan 14, 2018 4:53 pm Rich.C@EMPOWERgmat.com wrote:Hi lheiannie07, We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math. 1) The longer side of the rectangle is 2 meters shorter than its diagonal With the information in Fact 1, we can create 2 equations (with the diagonal represented by D): L = D - 2 L^2 + W^2 = D^2 Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter. Fact 1 is INSUFFICIENT 2) The ratio of the shorter side to the diagonal is 1/3 With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1): W/D = 1/3....... D = 3W L^2 + W^2 = D2 Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter. Fact 2 is INSUFFICIENT Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables - and there will be just one solution. Combined, SUFFICIENT GMAT assassins aren't born, they're made, Rich Thanks a lot! ### GMAT/MBA Expert GMAT Instructor Posts: 5549 Joined: 25 Apr 2015 Location: Los Angeles, CA Thanked: 43 times Followed by:24 members by Scott@TargetTestPrep » Thu Jan 18, 2018 8:02 am lheiannie07 wrote:What is the perimeter of rectangle ABCD? (1) The longer side of the rectangle is 2 meters shorter than its diagonal $$(2)The\ ratio\ of\ the\ shorter\ side\ of\ the\ rec\tan gle\ to\ its\ diagonal\ is\ \frac{1}{3}\$$ We need to determine the perimeter of rectangle ABCD. Statement One Alone: The longer side of the rectangle is 2 meters shorter than its diagonal. We can let the length of the longer side = L and the length of the diagonal = G. Thus we have L = G - 2. However, since we don't know the value of L or G, we can't determine the perimeter of ABCD. Statement one alone is not sufficient to answer the question. Statement Two Alone: The ratio of the shorter side of the rectangle to its diagonal is 1/3. We can let the length of the shorter side = W and the length of the diagonal = G. Thus we have W = G/3. However, since we don't know the value of W or G, we can't determine the perimeter of ABCD. Statement two alone is not sufficient to answer the question. Statements One and Two Together: Using the two statements, we see that L = G - 2 and W = G/3. Notice that the perimeter of ABCD is 2L + 2W. Furthermore, L, W and G form a right triangle with G as the hypotenuse. Thus, we have: L^2 + W^2 = G^2 Now, substituting G - 2 for L and G/3 for W, we have: (G - 2)^2 + (G/3)^2 = G^2 From the above equation, we can solve for G. Once we solve for G, we can determine the values of L and W and, hence, we can determine the perimeter of ABCD.	2020-10-31 10:11:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6868417263031006, "perplexity": 841.3638361420374}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107917390.91/warc/CC-MAIN-20201031092246-20201031122246-00611.warc.gz"}
https://www.physicsforums.com/threads/the-angular-momentum-of-a-flywheel.199410/	# The angular momentum of a flywheel 1. Nov 20, 2007 ### Eggyu The angular momentum of a flywheel having a rotational inertia of 0.200 kg·m2 about its axis decreases from 3.00 to 1.800 kg·m2/s in 1.80 s. (a) What is the average torque acting on the flywheel about its central axis during this period? N·m (b) Assuming a uniform angular acceleration, through what angle will the flywheel have turned? (c) How much work was done on the wheel? J (d) What is the average power of the flywheel? W Basically, all i need is how to find the initial angular velocity for part b. The rest of the variables i have solved for. 2. Nov 20, 2007 ### andrevdh The angular momentum of a rigid object about a fixed axis is given by $$L = I\omega$$ where $$I$$ is its moment of inertia bout this axis and $$\omega$$ is its angular speed about the same axis. 3. Nov 20, 2007 ### Bill Foster The rotational components and equations are analogous to linear ones. Equation of motion: linear: (1) $$x=x_0+vt+\frac{1}{2}at^2$$ (2) $$v=v_0+at$$ (3) $$F=ma$$ (4) $$W=Fx$$ (5) $$P=Fv$$ (6) $$a(x-x_0)=\frac{1}{2}(v^2-v_0^2)$$ angular: (1) $$\phi=\phi_0+\omega t+\frac{1}{2}\alpha t^2$$ (2) $$\omega=\omega_0+\alpha t$$ (3) $$\tau=I\alpha$$ (4) $$W=\tau \phi$$ (5) $$P=\tau \omega$$ (6) $$\alpha(\phi-\phi_0)=\frac{1}{2}(\omega^2-\omega_0^2)$$ So to find the average torque in part (a), find the deceleration using angular equation 2. Part (b), use 6. Part (c), use 4. Part (d), use 5.	2017-09-21 16:13:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8737480044364929, "perplexity": 868.0644636355539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687833.62/warc/CC-MAIN-20170921153438-20170921173438-00011.warc.gz"}
http://www.mathnet.ru/php/archive.phtml?jrnid=al&wshow=issue&year=2000&volume=39&volume_alt=&issue=6&issue_alt=&option_lang=eng	Algebra i logika RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS Algebra Logika: Year: Volume: Issue: Page: Find Levi classes generated by nilpotent groupsA. I. Budkin 635 Recognition of alternating groups of degrees $r+1$ and $r+2$ for prime $r$ and the group of degree 16 by their element order setsA. V. Zavarnitsin 648 The Makar-Limanov algebraically closed skew fieldP. S. Kolesnikov 662 The boundary equivalence for rings and matrix rings over themYu. V. Nagrebetskaya 693 Definability of boolean algebras in $\mathbb{HF}$-superstrusturesA. V. Romina 711 DescrIbing a basis in semireduced form for inference rules of intuitionistic logicV. V. Rybakov, M. Terziler, V. V. Rimatskii 720 The intrinsic enumerability of linear ordersA. N. Khisamiev 741 Letter to the EditorM. S. Sheremet 751 Sessions of the Seminar “Algebra i Logika” (International conference “Logical and Its Applications,” May 2–6, 2000) 752	2021-10-22 14:40:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17835190892219543, "perplexity": 8569.329706210536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585507.26/warc/CC-MAIN-20211022114748-20211022144748-00358.warc.gz"}
https://reference.opcfoundation.org/v104/Core/docs/Part9/5.8.7/	5.8.7 Unsuppress Method The Unsuppress Method is used to clear the SuppressedState of a specific Alarm instance. It is only available on an instance of an AlarmConditionType that also exposes the SuppressedState. This Method can be used to overwrite any suppression cause by an associated AlarmSuppressionGroup. This Method works in parallel with any suppression triggered by an AlarmSuppressionGroup, in that if the Method is used to clear the SuppressedState of an Alarm, any change in an AlarmSuppressionGroup might again suppress the Alarm. Normally, the NodeId of the ObjectInstance is passed as the ObjectId to the Call Service. However, some Servers do not expose Condition instances in the AddressSpace. Therefore, Servers shall allow Clients to call the Unsuppress Method by specifying ConditionId as the ObjectId. The Method cannot be called with an ObjectId of the AlarmConditionType Node. Signature Unsuppress(); Method Result Codes in Table 43 (defined in Call Service) Table 45 – Unsuppress result codes Result Code Description Bad_MethodInvalid The MethodId provided does not correspond to the ObjectId provided. See OPC 10000-4 for the general description of this result code. Bad_NodeIdInvalid Used to indicate that the specified ObjectId is not valid or that the Method was called on the ConditionType Node. See OPC 10000-4 for the general description of this result code.	2021-07-30 11:36:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17924022674560547, "perplexity": 3620.1566144635826}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153966.52/warc/CC-MAIN-20210730091645-20210730121645-00253.warc.gz"}
https://math.stackexchange.com/questions/822267/help-me-understand-the-operator-norm	# Help me understand the operator norm The definition I have for the operator norm is: $L(\Bbb U,\Bbb V)$ is the vector space of all linear transformations $f: \Bbb U \to \Bbb V$. Let $\Bbb U\ \&\ \Bbb V$ be inner product spaces. Define the operator norm on $L(\Bbb U,\Bbb V)$: $$\|f\|_O=\max_{\|u\| \le1} \|f(u)\|$$ First, I need to show that this IS a norm. I can prove all of the axioms except: If $f \neq 0$ then $\|f\|_O \gt 0$. In particular, why couldn't we have a linear function f with the property that $f(u)=0$ for some interval (like $0 \le u \le 1$) and then nonzero outside of that interval? I don't see how that is not possible from $f(au)=af(u)$ or $f(u+v)=f(u)+f(v)$. Second, I need to show that $\|f(u)\| \le \|f\|_O\|u\|$. To me this looks like $\|f\|_O\|u\|=(max_{\|u\| \le1} \|f(u)\|)\|u\|=max_{\|u\| \le1} (\|f(u)\|\|u\|)$ which I would think would be LESS than $\|f(u)\|$. • Regarding your first doubt: If $f(u) \ne 0$ then what about $f(u/\|u\|)$? – user50948 Jun 5 '14 at 22:15 If $f(u)=0$ for all $u$ with $\|u\|=1$, it is easy to show that $f(v)=0$ for all $v$. Hint: take $u=\frac{v}{\|v\|}$. Regarding the second question, you made a mistake when writing $$\max_{\|u\|\leq 1}(\|f(u)\|)\|u\| = \max_{\|u\|\leq 1}(\|f(u)\|\|u\|)$$ What you should write is $$\max_{\|u\|\leq 1}(\|f(u)\|)\|u\| = \max_{\|v\|\leq 1}(\|f(v)\|\|u\|)$$	2021-07-26 19:23:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9804011583328247, "perplexity": 91.29216428263743}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152144.92/warc/CC-MAIN-20210726183622-20210726213622-00318.warc.gz"}
https://math.stackexchange.com/questions/3816917/if-int-x-f-varphi-mathrmd-mu-leq-a-then-int-x-f-mathrmd-mu-leq-a	# If $\int_X f\varphi\,\mathrm{d}\mu\leq a$, then $\int_X f\,\mathrm{d}\mu\leq a$ Suppose that $$X$$ is locally compact Hausdorff space. Let $$f:X\to (0,\infty)$$ continuous, and let $$\varphi\in C_c(X)$$ with $$0\leq \varphi \leq 1$$. Let $$a>0$$, and $$\mu$$ a Radon measure on $$X$$. I read in a proof, that if once proven that $$\int_X f\varphi\,\mathrm{d}\mu\leq a$$, then $$\int_X f\,\mathrm{d}\mu\leq a$$. The author said, the conclusion follows from the following lemma, which I can't see how it has been used Lemma: Let $$X$$ Hausdorff space, $$\mu$$ Radon measure on $$X$$, and $$\mathcal{K}$$ the collection of compact subsets of $$X$$. If $$f:X\to [0,\infty]$$ is a Borel measurable function, then $$\int_{X}f\,\mathrm{d}\mu=\sup_{K\in \mathcal{K}}\int_{K}f\,\mathrm{d}\mu.$$ Question: If $$\int_X f\varphi\,\mathrm{d}\mu\leq a$$, how to show that $$\int_X f\,\mathrm{d}\mu\leq a$$ by lemma above? Using Urysohn's lemma, for each compact set, you can construct $$\phi \in C_c(X)$$ s.t. $$0 \leq \phi \leq 1$$ and $$\phi\|_K = 1$$, then $$\int_K f \ d\mu \leq \int f \phi \ d\mu$$. Then if you prove that $$\int f \phi \ d\mu \leq a$$ for each $$\phi \in C_c(X)$$, then by the lemma you cite, $$\int f \ d\mu= \sup_{K \in \mathcal K} \int_K f \ d\mu \leq a$$. You definitely need that inequality to hold for all $$\phi \in C_c(X)$$, otherwise just consider $$\phi =0$$ and it holds trivially for any positive $$a$$. Edit: More details on constructing the $$\phi$$. First a statement of Urysohn's lemma for LCH spaces: If $$X$$ is a locally compact Hausdorff (LCH) space and if $$K, F \subseteq X$$ are disjoint sets s.t. $$K$$ is compact and $$F$$ is closed, then there is a continuous function $$\phi :X \to [0,1]$$ s.t. $$\phi\|_K = 1$$ and $$\phi\|_F = 0$$. Now our goal is that given any compact set $$K$$, we want to construct a $$\phi \in C_c(X)$$ s.t. $$\phi\|_K = 1$$. Well we definitely want to use Urysohn's lemma, but what is our set $$F$$? Note it can't be $$X^C = \emptyset$$ as then we can't prove that the support is compact. The following claim should suffice: Let $$X$$ a LCH space. Let $$K \subseteq X$$ compact. Then there exists an open set $$U$$ s.t. $$K \subseteq U$$ and $$\overline{U}$$ is compact. Prove this claim and use it to finish the proof. • In Ursysohn's lemma, it talks about a compact set $K$ and an open set $U$, satisfying that $K\subseteq U$, then there exists $f\in C_c(X)$ such that $0\leq f\leq 1$, $f\|_K\equiv 1$ and $\textrm{supp} f\subseteq U$. What should $U$ be in this problem? $X$? Sep 7, 2020 at 7:11 • @James2020: You may have to use the fact that if $f$ is a nonnegative lower semicontinuous function on $X$, then $f=\sup\{\phi\in\mathcal{C}_{00}(X): 0\leq \phi\leq f\}$ along with the fact that ever open set $G$, or rather $\mathbb{1}_G$, is lower semicontinuous. Sep 7, 2020 at 19:11 • @OliverDiaz I am not familiar with this one ... Wouldn't it possible to use only two lemmas: Urysohn's lemma and the lemma I stated in the post? Sep 7, 2020 at 19:18 • @James2020 I can add more detail. Though, you should try to figure it out yourself. I'll add some hints to my post, ask if you can't figure it out. Sep 7, 2020 at 19:39 • @KeeferRowan: James's version of Urysohn's lemma includes the conclusion that $\phi \in C_c(X)$, so the support of $\phi$ is automatically compact. The lemma says only that the support of $\phi$ is contained in $U$; there is nothing stopping it from being much smaller. Sep 7, 2020 at 20:20 Hint: Let $$\mathcal{K}$$ denote the collection of all compact sets in $$X$$. • Using Urysohn's lemma one can show that $$\int_K f\,d\mu\leq a$$ for all compact. • On the other hand, $$\nu(g)=\int g\,f\,d\mu$$ defines a Radon measure (regular Borel measure) on $$X$$. By inner regularity $$\mu(A)=\sup\{\nu(K): K\in\mathcal{K},\,K\subset A\}$$ for all measurable sets $$A$$. (This is the Riesz-Markov representation theorem) • If I may ask, why do you say ".. compact sets in $X$" (and not "... compact subsets of $X$")? Is this a short-hand for saying that these sets are subsets of $X$, and that they are compact in X? Or ... ? Sep 7, 2020 at 5:32 • yes, but also to emphasize the topology on $X$. Sep 7, 2020 at 14:41 • OK, glad to know it. You wrote in your first point about Urysohn's Lemma. The version I have in the book is: "For given sets $K\subseteq U$ in a locally compact Hausdorff space $X$, where $K$ is compact, and $U$ is open, there is $f\in C_c(X)$ such that $0\leq f\leq 1$, $f\equiv 1$ on $K$ and $\textrm{supp} f\subseteq U$." The question is, what is $U$ is this situation, when trying to prove the claim I wrote in the post? Should $U$ be $X$? Sep 7, 2020 at 16:15	2022-12-07 03:02:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 53, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9551102519035339, "perplexity": 127.90730688082812}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711126.30/warc/CC-MAIN-20221207021130-20221207051130-00831.warc.gz"}
http://commodorefree.com/magazine/vol2/issue22.html	COMMODORE FREE MAGAZINE Issue 22 August 2008 http://www.commodorefree.com/ Free to download magazine Dedicated to Commodore Computers Available as Text, Html, PDF, SEQ and Commodore 64 D64 disk image CONTENTS EDITOR NEWS GENERAL NEWS UIEC Status Update UIEC INFORMATION TUTORIALS In the beginning part 7 Making music with DMC INTERVIEWS INTERVIEW WITH STEFANO TOGNON (SIDIN Magazine) CLUB NEWS Commodore Computer club Membership form Commodore Computer club Membership Club rules EDITOR http://www.commodorecomputerclub.co.uk/ This month I am plugging the Commodore computer club, you will remember from the last issue of Commodore Free that; we had our first meeting last month and to keep momentum going I have listed the membership form and general club rules in this issue of the magazine. A lot of thought has gone into setting up the club. The main point is the club will be run as a none profit organisation, so you can rest assured that any money invested will not be taken by members; we will have visuals on the spend and income listed to all members. Currently I am treasurer with Jason Kelk (tmr)as Webmaster and Alan Bairstow as Chairman http://www.commodorescene.org.uk/ and Shaun Bebbington from http://www.micromart.co.uk/ as secretary What use is another Commodore club? as we are all very active Commodore users and enjoy promoting the machine we have some surprises in store for members various discounts from our online shop (still to be setup) special members access areas on the website and other benefits. The main point is bringing people together something I felt the U.k. was lacking. I hope everyone reading would be interested in joining with fee starting from as little as 3 pounds, so you can test out the club, but I would think most will opt for a life membership Please visit the website (still under construction, so you may need a hard hat to enter some areas) you will notice a mirror of the HTML version of Commodore free on the site and the forum is running along very nicely so take a look at http://www.commodorecomputerclub.co.uk/ as stated last month we have already released a 1 file demo and this is available from the site to download, comments and feedback are welcome, please speak up. I have asked for readers to send through information and I appreciate you will be reading this and think your comments and tutorials will not be welcome, nothing can be further from the truth, I would love to print tutorials for both beginners and experts alike. We all have particular talents and as a community these should be shared. Or maybe you would like to ask a question; and of course wherever possible I will find the answer, even if I have to "phone a friend" Commodore is still alive let’s keep the memory fresh, I am in the process of setting up a bank account for the Commodore Computer club. While giving details to the operator she said "Commodore are they still going I used to own one of those they were great machines". So even in banking I cant get away from the memories of the machine. Talking of which, if you have a fond memory of Commodore like when you first received your machine send write it down and send it in, some readers hate these but I love reading about your first experiences with Commodore. If you are a club send me some information I will include the details as and when space allows, also if you are a company or have a product to advertise send me some promotional material and when space permits I will reprint it FREE! you cant get cheaper adverts than that! There is nothing better than a free advert, for promotion of course you may like to send me one of the devices for a full review in the magazine. Speaking of which, reviews are personal, I write the magazine so they are my personal reviews of the products, if an individual writes in they are there reviews and comments, if something is less than satisfactory I will say so, if its the best product in the world it will be reviewed as such. Bribes are welcome but ultimately they do not change the reviews. Also; I finally had 3 entries to the Commodore music Competition to win a free copy of PRESS PLAY ON TAPEs current cd. I will at some point print what I consider the best of these 3 entries, the disks have now gone out, thanks to PRESS PLAY ON TAPE for donating the disks and the 3 people who finally put pen to paper, I was however disappointed that more people didn’t take part in the competition. here we go then hold onto your hats it may be a bumpy read, especially with my spelling. Regards Nigel www.commodorefree.com Jump Back to CONTENTS GENERAL NEWS NEW C64 FRAMEWORK SOURCE RELEASED. I’ve have just released my new C64 frame work (and sample app) for you to play with. Here is a list of the frameworks features. -Initialisation, mainloop and interrupts all setup and ready to go. -Production quality multiplexor. -Three separate compile time switchable sorts. -Simple collision detection system. -General sprite animation system. -Game based keyboard and joystick routines. -Simple player control framework. -Lightning fast 8x8bit multiply routine. -Simple random number routine. -Built in MMC64 FAT16 file loader. -Simple example platform engine showing the framework in action. You can grab it from the download links on my BLOG http://dailly.blogspot.com where you can also read about its development and any future additions there. SUB HUNTER Another preview has been released of the game sub hunter, I would say this is one of Richards best games ever, and I personally am looking forward to the finished version with much anticipation. You can of course download a new preview from here http://noname.c64.org/csdb/release/?id=68965 and you can read about the games development here http://www.redesign.sk/tnd64/sub_hunter.html COMMODORE COMPUTER CLUB U.K. http://www.commodorecomputerclub.co.uk/ We're now accepting membership applications for the Commodore Computer Club (UK), and you can fill these applications electronically and pay with PayPal. We also accept cheques, postal orders and international money orders. Please contact me for details or for an application form and club rules. My email address is contact@CommodoreComputerClub.co.uk Regards, Shaun. More information about the cub is listed at the end of this magazine Jump Back to CONTENTS UEIC STATUS UPDATE Subject: uIEC status update I apologize for the delay in getting this out. Here is an update: Since July 4th, I've been busy soldering up the remaining uIEC/IDE and uIEC/CF units. I've shipped all but one uIEC/IDE unit out (Wizard, it's yours, but I need a padded envelope for it), and all but 5 of the uIEC/CF units out. I have updated the design to v2.3. This forced moving the activity LED to another IO pin, to free up pins for the disk swap buttons. All units shipped after C4 EXPO have this mod. They also have the 2008-07 uIEC bootloader. Thus, any unit sold at the C4 EXPO show needs to check with me for a timeframe when I can upgrade their units to v2.3 and install the bootloader and the newer 7.2.1 firmware. The bootloader is very important, since it allows one to upgrade their firmware simply by copying a file to the root directory of the first partition of the primary IDE/CF drive. On boot, the bootloader will scan for a newer firmware and flash it into the uIEC if it finds one. FAT32 support is enabled now (I held off on shipping until I had that complete, since otherwise, folks would need to have a small FAT16 partition #1 to load new firmware, which seemed a waste) For the unfilled CF units, I plan to make the small IO mods of v2.3 and add a SD card option and run the next set of boards. I should be able to order the boards by next week. It takes 10 days to run a batch of boards, and a few days to solder. Thus, it'll probably be 14-21 days before I can sell more CF units. I only have 2 unfilled orders on the CF units. For the uIEC/IDE units, I need some help. With the v2.3 mods and a desire to add buffer drivers to the IEC lines (requires 4 more IO lines), I'm running too short on IO to offer printer port/IEEE port/parallel speeder port IO. I have two options: Make the minimal mods needed for the IEC lines, add the support for SD cards, and run a batch of boards. This would be quick and requires very little thought. Read: takes little time to prepare to run boards. Make the larger mods needed to bring out the additional IO (requires the 100 pin version of the CPU I am using and some headers). Read, takes more time. I'm interested in feedback. I think 50 boards is the smallest prod run I can economically run, so I'd need to ensure folks are OK with the decision. Right now, after mailing all the uIEC/IDE boards, I have 19 unfilled orders. I'm leaning towards option #1, mainly for timing, but I thought I'd ask the group. The uIEC/CF units were designed mainly for folks who plan to "embed" them in designs. As such, they do not have elegant connections. I'm not apologizing for that, just noting why the IEC wires and power wire are installed as they are. My intention was for the users to embed the unit and unsolder those wires when no longer needed. I will, though, apologize for the cassette connector. I forgot to plan for the little PCB that’s needed for that connector. I will run a batch of those with my next order. If folks want one, I can ship one or solder one up when I see you next. Right now, there are two "bugs" I am working on. One is the start-up latency on uIEC/IDE units when only 1 drive is connected. Due to the way IDE devices are initialized, the initialization sequence must wait > 32 seconds to see if a drive is present. Thus, on a setup with only 1 drive, there will be a 30 second delay on start. It's not a "bug" per se, but unwanted behaviour. To counteract, I am working on a way to disable the second drive via DOS command. Since we know later designs might have more than 1 type of storage medium (ATA/CF/SD/etc.), I am making it flexible, so it's taking a bit longer to implement The other bug is init issues with master CF card and slave IDE drive. I think it's just a timing issue. For now, I recommend putting the IDE drive as primary, and CF card as slave. I've set up a mailing list for the unit (questions, concerns, etc.) It's unmoderated at present, so play nice. Details are below. After I get the designs to the PCB house, I plan to work on image support. I have WIP code for D71/D81/DNP images that needs to be finished and committed. Although I tend to set my own priorities, I'm always interested in which features folks want. Documentation: Yes, I do plan to write some up, but I simply need to get the units shipped first. Since the drive uses CBM and CMD syntax, I hope folks can easily find their way around. I will, though, send a cheat sheet to the mailing list in a few days. For the uIEC/CF owners, the two small pins on the backside of the unit are the disk-swap switches. Ground each (via a switch) for operation. I'm sure I'm leaving something out, but there's always more email to send. Jim Membership to the Mailing List uiec-users@jbrain.com On this web page you can subscribe to, or unsubscribe from, the mailing list uiec-users@jbrain.com Jump Back to CONTENTS UIEC INFORMATION The device is now shipping and Jim has kindly let me reprint the draft of the read me guide I personally have one of these on order and will give a full and honest review as soon as the device arrives for my testing. UIEC here is the most current README: sd2iec - a controller/interface adapting storage devices to the CBM serial bus Copyright (C) 2007,2008 Ingo Korb Parts based on code from others, see comments in main.c for details. JiffyDos send based on code by M.Kiesel Fat LFN support and lots of other ideas by Jim Brain crc7.c generated by pycrc, see comments in it for pycrc licence. Final Cartridge III fastloader support by Thomas Giesel Free software under GPL version 2 ONLY, see comments in main.c and COPYING for details. FIXME:This file still needs to be expanded. A lot. INTRODUCTION: ============= sd2iec is firmware, used in hardware designs like MMC2IEC, SD2IEC, or uIEC, that allows the Commodore serial bus to access removable storage devices (MMC, SD, CF) - think of it as a 1541 with a modern storage medium instead of disks. The project was inspired by (and uses a few bits of code from) MMC2IEC[1] by Lars Pontoppidan and once ran on the same hardware before it grew too big for the ATmega32 used there. Currently, the firmware provides good DOS and file-level compatibility with CBM drives, but much work still remains. Unless specifically noted, anything that tries to execute code on the 1541 will not work, this includes every software fastloader. [1] http://pontoppidan.info/lars/index.php?proj=mmc2iec/ Supported commands: ================= - General notes: Any command not listed below is currently not supported. - Directory filters: To show only directories, both =B (CMD-compatible) and =D can be used. On a real Commodore drive D matches everything.To include hidden files in the directory, use =H - on a 1541 this doesn't do anything. sd2iec marks hidden files with an H after the lock mark, i.e. "PRG CMD-style "short" and "long" directory listings with timestamps are supported("$=T"), including timestamp filters. Please read a CMD manual for the syntax until this file is updated. - Partition directory: The CMD-style partition directory ($=P) is supported, including filters ($=P:S). All partitions are listed with type "FAT", although this couldchange to "NAT" later for compatibility. - CD/MD/RD: Subdirectory access is compatible to the syntax used by the CMD drives, although drive/partition numbers are completely ignored. Quick syntax overview: CD:_ changes into the parent dir (_ is the left arrow on the C64) CD_ dito CD:foo changes into foo CD/foo dito CD//foo changes into \foo CD/foo/:bar changes into foo\bar CD/foo/bar dito You can use wildcards anywhere in the path. To change into an M2I or D64 image the image file must be named after the :, it will not be recognized otherwise. MD uses a syntax similar to CD and will create the directory listed after the colon (:) relative to any directory listed before it. MD/foo/:bar creates bar in foo MD//foo/:bar creates bar in \foo RD can only remove subdirectories of the current directory. RD:foo deletes foo CD is also used to mount/unmount image files. Just change into them as if they were a directory and use CD:_ (left arrow on the C64) to leave. Please note that image files are detected by file extension and file size and there is no reliable way to see if a file is a valid image file. - CP, C This changes the current partition; see "Partitions" below for details. - C: File copy command, should be CMD compatible. The syntax is C[partition][path]:targetname=[[partition][path]:]sourcename[,[[p][p]:]sourcename...] You can use this command to copy multiple files into a single target file in which case all source files will be appended into the target file. Parsing restarts for every source file name which means that every source name is assumed to be relative to the current directory. You can use wildcards in the source names, but only the first file matching will be copied. Copying REL files should work, but isn't tested well. Mixing REL and non-REL files in an append operation isn't supported. - G-P Get partition info, see CMD FD/HD manual for details. The reported information is partially faked, feedback is welcome. - N: Format works only if a D64 image is already mounted. - R Renaming files should work the same as it does on CMD drives, although the errors flagged for invalid characters in the name may differ. - S: Name matching is fully supported, directories are ignored. Scratching of multiple files separated by , is also supported with no limit to the number of files except for the maximum command line length (usually 100 to 120 characters). - T-R and T-W If your hardware features RTC support the commands T-R (time read) and T-W (time write) are available. If the RTC isn't present, both commands return 30,SYNTAX ERROR,00,00; if the RTC is present but not set correctly T-R will return 31,SYNTAX ERROR,00,00. Both commands expect a fourth character that specifies the time format to be used, T-W expects that the new time follows that character in exactly the format returned by T-R with the same format char. The possible formats are: - "A"SCII: "SUN. 01/20/08 01:23:45 PM"+CHR$(13) The day-of-week string can be any of "SUN.", "MON.", "TUES", "WED.", "THUR", "FRI.", "SAT.". The year field is modulo 100. - "B"CD or "D"ecimal: Both these formats use 9 bytes to specify the time. For BCD everything is BCD-encoded, for Decimal the numbers are sent/parsed as-is. Byte 0: Day of the week (0 for Sunday) 1: Year (modulo 100 for BCD; -1900 for Decimal, i.e. 108 for2008) 2: Month (1-based) 3: Day (1-based) 4: Hour (1-12) 5: Minute (0-59) 6: Second (0-59) 7: AM/PM-Flag (0 is AM, everything else is PM) 8: CHR$(13) When the time is set a year less that 80 is interpreted as 20xx. - U0 Device address changing with "U0>"+chr$(new address) is supported, other U0 commands are currently not implemented. - U1/U2/B-R/B-W Block reading and writing is fully supported while a D64 image is mounted. - B-P Supported, not checked against the original rom at all. - UI+/UI- Switching the slightly faster bus protocol for the VC20 on and off works,it hasn't been tested much though. - UI/UJ Soft/Hard reset - UI just sets the "73,..." message on the error channel, UJ closes all active buffers but doesn't reset the current directory, mounted image, swap list or anything else. - U Real hard reset - this command causes a restart of the AVR processor (skipping the bootloader if installed). is character code 202. - X: Extended commands. If you use JiffyDOS, you can send them by using @"X..." - without quotes you'll just receive an error. - XEnum Sets the "file extension mode". This setting controls if files on FAT are written with an x00 header and extension or not. Possible values for num are: 0: Never write x00 format files. 1: Write x00 format files for SEQ/USR/REL, but not for PRG 2: Always write x00 format files. 3: Use SEQ/USR/REL file extensions, no x00 header 4: Same as 3, but also for PRG If you set mode 3 or 4, extension hiding is automatically enabled. This setting can be saved in the EEPROM using XW, the default value is 1. For compatibility with existing programs that write D64 files,PRG files that have D64, D41, D71, D81 or M2I as an extension will always be written without an x00 header and without any additional PRG file extension. - XE+/XE- Enable/disable extension hiding. If enabled, files in FAT with a PRG/SEQ/USR/REL extension will have their extension removed and the file type changed to the type specified by the file extension - e.g. APPLICATION.PRG will become a PRG file named "APPLICATION", "README.SEQ" will become a SEQ file named "README". This flag can be saved in the EEPROM using XW, the default value is disabled (-). - XB+/XB- Enable/disable free block calculation for FAT32 drives. As the free block calculation for FAT32 can take a lot of time it can be disabled using XB-. If it is disabled, sd2iec will always report "1 BLOCKS FREE" for FAT32 drives. The free block calculation on FAT12/FAT16 isn't affected because it takes just two seconds at most. This flag can be saved in the EEPROM using XW, the default value is enabled (+). - XJ+/XJ- Set or reset the JiffyDOS protocol support flag. This flag can be saved in the EEPROM using XW, the default value is enabled (+). - X+/X- Enable/disable 1581-style * matching. If enabled, characters after a * will be matched against the end of the file name. If disabled, any characters after a * will be ignored. This flag can be saved in the EEPROM using XW, the default value is enabled (+). - XCnum Set oscillator calibration value to num (must be between 0 and 255). Default is whatever your chip defaults to. This value can be saved in the EEPROM using XW. - X X without any following characters reports the current state of all extended parameters via the error channel, similiar to DolphinDOS. Example result: "03,J-:C152:E01+:B+:+,08,00" The track indicates the current device address. - XS:name Set up a swap list - see "Changing Disk Images" below. XS Disable swap list - XW Store configuration to EEPROM This commands stores the current configuration in the EEPROM. It will automatically be read when the AVR is reset, so any changes you made will persist even after turning off the hardware. The stored configuration includes the oscillator calibration value, the JiffyDOS protocol support flag, the extension mode and the current device address. If you have changed the device address by software, sd2iec will power up with that address unless you have changed the device address jumpers (if available) to a different setting than the one active at the time the configuration was saved. You can think of this feature as changing the meaning of one specific setting of the jumpers to a different address if this sounds logical enough to you. The "hardware overrides software overrides hardware" priority was chosen to allow accessing sd2iec even when it is soft-configured for a device number that is already taken by another device on the bus without having to remove that device to reconfigure sd2iec (e.g. when using a C128D). - X? Extended version query This commands returns the extended version string which consists of the version, the processor type set at build time and the suffix of the configuration file (usually correspondsto the short name of the hardware sd2iec was compiled for). - M-R, M-W, M-E Memory reading returns random data of the requested length. Memory writing knows about the address used for changing the device address on a 1541 and will change the address of sd2iec to the requested value. It will also check if the transmitted data corresponds to any of the known software fastloaders so the correct emulation code can be used when M-E is called. - E-R, E-W Both commands work like M-R and M-W, but instead of reading/writing RAM they allow access to a user-area of the EEPROM. This area currently holds 512 bytes and any access beyond this area will result in a 32 SYNTAX ERROR. It is strongly recommended to work on a protocol for sharing this are between multiple applications that want to store their configuration in there, but that is beyond the scope of this project. As the contents of the EEPROM have to be copied to RAM before they can be sent to the computer, it is not possible to read more data with a single command than the error message buffer (default size: 36 bytes) can hold. Similarly, writing is restricted by the size of the command buffer (at least 42 bytes for compatibility, expected to be at least 100 bytes in release versions). The user-area does not interfere with the stored configuration (XW) in any way. Long File Names: ================ Long file names (i.e. names not within the 8.3 limits) are supported on FAT, but for compatibility reasons the 8.3 name is used if the long name exceeds 16 characters. If you use anything but ASCII characters on the PC or their PETSCII equivalents on the Commodore, you may get strange characters on the other system because the LFN use unicode characters on disk, but sd2iec parses only the low byte of each character in the name. Partition: ========== sd2iec features a multi-partition support similar to that of the CMD drives. The partitions (which may be on separate drives for some hardware configurations) are accessed using the drive number of the commands sent from the computer and are numbered starting with 1. Partition 0 is a special case: Because most software doesn't support drive numbers, or always sends drive number 0, this partition points to the currently selected partition. By default, accesses to partition 0 will access partition 1, this can be changed by sending "CP" over the command channel with being an ASCII number from 1 to 255. "C ===================== Turbodisk -------- Turbodisk is detected by the CRC of its 493 byte long floppy code and the M-E address 0x0303. The same code seems to be used under various names, among them "Turbodisk" (both 2.1 and 2.2) and "Fast-Load". Unfortunately the timing requirements are extremely tight and cannot be met with the internal RC oscillator of the AVR even if calibrated. You really need an external 8MHz crystal or the data read by the C64 will be gibberish. It is not known if there is an NTSC-compatible version of this fastloader. Final Cartridge III ------------------- Both the fast loader and the fast saver of Final Cartridge III are supported. The fast loader seems to work without a crystal, the fast saver was not tested. It is not known if there is an NTSC-compatible version using the same drive code, but at least for the fastloader the FC3 rom seems to contain two different C64-side implementations. Action Replay 6 --------------- The AR6 reads a byte from the drive rom to check which fastloader it should use. sd2iec returns a value that should force the cartridge to use the standard kernal loader instead of its (still unsupported) fastloader. --------- Dreamload uses direct track/sector access, so it is only supported on D41 or similar disk image formats. As sd2iec has to wait for commands from the C64 constantly the disk change buttons may become unresponsive, try multiple times if you need to. Dreamload is a "captive" fastloader" sd2iec stays in Dreamload mode until it receives a "quit loader" command from the C64. To force sd2iec to resume normal operation, hold the disk change button until the red LED turns on (just like sleep mode). Please note that Dreamload does not work with more than one device on the serial bus due to the way it uses the ATN line. JiffyDOS: ========= The JiffyDOS protocol has very relaxed timing constraints compared to Turbodisk, but still not as relaxed as the standard Commodore IEC protocol. Jiffy seems to tolerate slightly mis-tuned RC oscillators, but you still shouldn't expect it to work without oscillator calibration. If the frequency error is too big you WILL get “wrong data” which usually manifests as a FILE NOT FOUND error, because the name the drive received was already garbled. x00 files: ========== P00/S00/U00/R00 files are transparently supported, that means they show up in the directory listing with their internal file name; instead of the FAT file name. Renaming them only changes the internal name. The XE command defines if x00 extensions are used when writing files, by default sd2iec uses them for SEQ/USR/REL files but not for PRG. Parsing of x00 files is always enabled even when writing them is not. x00 files are recognized by checking both the extension of the file (P/S/U/R with a two-digit suffix) and the header signature. Disk Images: ============ Disk images are recognized by their file extension (.D64, .D41) and their file size (must be one of 174848, 175531). If the image has an error info block appended, it will be used to simulate read errors. Writing to a sector with an error will always work, but it will not clear the indicated error. M2I files: ========== M2I files are fully supported. sd2iec supports SEQ and USR files in this format in addition to PRG and DEL which were already implemented in MMC2IEC. For compatibility reasons the file type is not checked when opening files. Inside an M2I file the files are always shown as 0 (DEL) or 1 blocks; because calling stat for every file was slowing down the directory listing too much. For compatibility with existing M2I files the data files do not use P00 headers even when the file type is SEQ or USR. Changing Disk Images ==================== Because some programs require more than one disk side there is support for changing the currently mounted disk image with a button connected to the disk change pin. If your circuit doesn't have a disk change pin/button you might be able to add it yourself: - For the original MMC2IEC and the NKC MMC2IEC: Connect a button from PA4 to ground. PA4 is pin 36 on the DIL version of the controller or pin 33 on the surface-mount version. - For Shadowolf's MMC2IEC 1.x PCBs: Connect a button from PC4 to ground. PC4 is pin 23 on the DIL version of the controller or pin 23 on the surface-mount version. - Any other circuit without disk change pin on a convenient connector somewhere and no button dedicated to that function: Please check with the supplier of the board, and read config.h in the sources to find out how to connect it. To use this functionality, create a text file that lists the file names of all disk images you want to swap between, one per line. The file names are parsed in the same way as the CD command, so you can include a path to the image if desired. Examples: === example 1 === FOO.D64 BAR.D64 BAZ.D64 === end of example 1 === === example 2 === //NEATGAME/:DISK1A.D64 //NEATGAME/:DISK1B.D64 //NEATGAME/:DISK2A.D64 //NEATGAME/:DISK2B.D64 === end of example 2 === The swap list is enabled by sending "XS:filename" over the command channel with filename being the name of the image list you created, parsed in the same way as any other file name. After sending XS the first image in the list is automatically mounted. To switch to the next image in the list, push the button. If the new image was mounted successfully both LEDs will blink twice. When you've reached the last image in the list pushing the button will mount the first image again. All of this is completely compatible with normal image mounting/unmounting, so you can unmount the disk image any time you want, and resume the mount cycle later by pushing the button. Due to the way this feature is implemented you are not limited to a swap list containing just D64 images, M2I and even FAT directories will work too. FIXME: Does that still work? If you press the button when no list has been set before, or when the previous list was cleared by sending XS the software will look for a file called AUTOSWAP.LST in the current (FAT-) directory and use this as the current swap list until you deactivate it or manually change the directory (otherwise an AUTOSWAP.LST in the new directory would be ignored until you send XS, killing the nice "it just works" feeling). FIXME: Integrate the following into the preceding The second disk change button is on - PA5 for LarsP/NKC - PC3 for Shadowolf's MMC2IEC 1.x - PC2 for Shadowolf's sd2iec 1.x ("Reserve" on the header) - PG4 for uIEC Either of those buttons will trigger the use of AUTOSWAP.LST. If a swap list is already active, the first button will switch to the next image in the list, the second button will switch to the previous image in the list and pushing both buttons together will switch to the first image in the list. The confirmation blink is red+green followed by green for "next", by red for "previous" and by red+green for "first". Sleep Mode: =========== If you hold the disk change button down for two seconds, sd2iec will enter "sleep mode". In this mode it doesn't listen to the bus at all until you hold down the disk change button for two seconds again which resumes normal operation. Sleep mode allows you to keep sd2iec connected to the serial bus even when you load something from a different drive that uses a fast loader that doesn't work with more than one device on the bus. While sleep mode is active, the red LED will be on and the green LED will be off. Other important notes: ====================== - File overwrite (@foo) is implemented by deleting the file first. - File sizes in the directory are in blocks (of 254 bytes), but the blocks free message actually reports free clusters. It is a compromise of compatibility, accuracy and code size. - If known, the low byte of the next line link pointer of the directory listing will be set to (file size MOD 254)+2, so you can calculate the true size of the file if required. The 2 is added so it can never be mistaken for an end marker (0) or for the default value (1, used by at least the 1541 and 1571 disk drives). - If your hardware supports more than one SD card, changing either one will reset the current partition to 1 and the current directory of all partitions to the root drive. Doing this just for the card that was changed would cause lots of problems if the number of partitions on the previous and the newly inserted cards are different. Compilation notes: ================== sd2iec is set up to be compiled in multiple configurations, controlled by configuration files. By default the Makefile looks for a file named 'config', but you can override it by providing the name on the make command line with "make CONFIG=filename". If you are using BSD you may have to edit the Makefile to use another awk implementation instead of gawk - unfortunately WinAVR compatibility requires using gawk in there. An example configuration file named "config-example" is provided with the source code, as well as abridged files corresponding to the release binaries. If you want to compile sd2iec for a custom hardware you may have to edit config.h too to change the port definitions. Jump Back to CONTENTS INTERVIEW WITH STEFANO TOGNON SIDIN magazine Editor http://digilander.libero.it/ice00/tsid/sidin/index.html/ COMMODORE FREE Please would you introduce yourself to our readers? Stefano Tognon I'm Stefano Tognon and I live in Italy. I'm 35 years old and I'm an informatics engineer working into a farm as a programmer, system administrator and DBA maintainer. In the farm I program in Java, SQL and some custom scripting language: all computers here are installed with Windows. I always use Linux at home (and have done so since 1999), I programme linux in Java, C++,Perl, and cross assembler for the C64 part. I'm an open source person so I have no problem in sharing my code. I like to assemble computers from components (maybe a good future work...) and install them with Linux ;) However my dreaming job would be to programming games, this is not so simple to achieve in Italy and I love my country to much to leave. I like Sid music (the only music I really listen to - my listening mileage is at 120 days now, I listen while jogging looking at nature to cancel the working stress, I read many books about physic, math and science. I even like all sort of sports and F1. My parents have a farm with vineyards and I help them when possible. Maybe someone in the net already me as ice00 of Ice Team (my group). Ice stay for Informatics Computer Engineer 00 is for the millennium bug remembrance... ST. SIDin is a PDF magazine about the SID chip (from the Inside) (this is where the magazine’s name came from), so expect to see some assembler code in its pages ;) It is free to download and the purpose was to have two issues each year, but some numbers have been skipped in the last years....mmmm...I have too many activity around...The magazine has a news section containing what I find out about in the sid world from the previous issue, an interview with a musician/composer, and two (technical) articles. In the articles I speak about music routines and techniques on how to program the sid, how to rip a tune from a game, review of music editors and trackers, hardware cards, and music related projects. The website http://digilander.iol.it/ice00/ is a portal to all my activities around the C64 or other projects I did in my free time. Nothing special in the site, just pure html code written by hand and the layout is a little similar to some C64 3D platform games. The background is made with Commodore related images to give the right atmosphere. However you will find all my releases and even the source code of them. CF. What would our readers recognise you for, apart from the magazine, for example have you written any Commodore demos or tunes ST. I wrote two little demos: they took place at the Christmas Online Compo many years ago. Nothing technically special, they were created just for fun. The first is "Silent Night", a demo where there is a full screen Christmas image (just a little conversion in multicolor mode of a card) and the border color pixels changes according to the music. The main task here was to open all the horizontal borders. The second is "FD", where there is a better high resolution Christmas image that I hand created myself with a minor animation of snow, fire and light. I created an image for an online Pixel Compo. It is a high resolution image of a Commodore-F1 machine. It is a very low quality production, I know, but only after having tried it yourself you can then find Leon's pictures are absolutely fantastic!! I wrote 13 tunes for the C64: one is from 86/87 and even if it’s of poor quality by today’s sid standard, it gives me the stimulus to learn computer music programming. Only 3 of those tunes are my compositions all the others are cover/remix’s of other peoples tunes. Lot of those tunes where specially composed for online compos. Others are just for testing the sid sound. I think that some readers may know me form my minigames. I released this for the Minigames Online Compos. It took place to 6 editions producing 11 games. I like to program games and I find the minigame a big challenge as you have to reduce the size of the code as much as possible. For those games I have the help of talented musician as Luca/Fire, Nata and Richard Bayliss. Maybe someone knows of Little Sara Sister (1 and 1.5), Haras, Elav, MArkanoid and Ann-Gong games. I have not finished Little Sara Sister 2, this features music from Dustbin and graphics logo from Luca/Fire. Maybe one day I will find the time to complete this title. I have another big game in development that many Italian people already know (it was to be for the previous minigame compo, but maybe it will be in the next one): a Frozen Bubble port to the C64. Something very hard to achieve. Many people know me for having held three editions of Sid-Wine online compo (maybe something unique for compos) and two Tiny Sid Compo (compo about writing tunes with only 256 or 512 bytes). Others may know me for having produced the High Voltage Music Engine Collection (HVMEC) http://digilander.libero.it/ice00/tsid/hvmec.html a big collection of many of the tools around for making sid music with the C64. Actually there are over 260 tools in it, but a lot are in my (soon to be released) archive. Fortunately Stephan Parth is helping me with this its a very time consuming task. Very few people know that I developed a C64 emulator (C64A) in 1994, mostly because I did not release it because it was in too early a state (however I found recently the source code and I will release it before the code gets lost). I even developed JC64, a Java C64 emulator in 1999, that it is available at Sourceforge site. It is still in a wait state, because it is totally based on a Vic Article for the emulation, but I find that the article is incomplete and you cannot emulate by following this article. From time to time I add more code to it, but I'm hoping that the true working of the Vic will be documented one day... I even released the Time Sid Manager library that integrates with sid player for storing the listening to statistics about your sids. Recently I developed Linux Xsidplay as Michael left his development some years ago, I sued this sid player and of course found no more updates. It is at http://sourceforge.net/projects/xsidplay2 Xsidplay has some new features like SDL support and the ALSA is being added (even a Windows port is available) and many more features are soon to come. The last project is JITT64 (Java Ice Team Tracker): http://jitt64.sourceforge.net/ This is my attempt to create my music routines and an editor for it. The programme uses Java. I'm moulding it as I need, without taking care of rastertime. I want to produce sid sounds without any restriction (for example one instrument definition can take up to 2KB of data). I have been working on the project from 6 months already, and I think that before the end of the year it can reach the state where tunes can be produced using it... I instead think that no one knows of this my embryonic project: http://regame.altervista.org/ It born as a paper magazine about C64 games, to be released free with 70dpi resolution (like for screen viewing) and on CD (with just a symbolic cost) for 600dpi resolution; as it is created using semi-professional paper related tools (actually 170MB of material for the first half number). The main problem is to find someone to help in creating reviews, and finding an Italian to English translator. Without this the project could stay in this state for ages :( CF. The magazine is quite technical what level of user is this aimed for? ST. I think a mix of programmer and musicians, most of the articles I show how the chip is programmed to produce a given sound. I try to give a little example of this point. For a musician that wants to produce and arpeggio, the only thing that he wants to know is that he has to put in sequence, at a given rate of 3 notes values like D E F into his editor /tracker. This should not be a problem for him. For a programmer, he has to know what is the effect to produce an (arpeggio) and then he has to write the appropriate code (e.g. converting the notes to hi/lo frequency values, and put them at the right rates in the sid registers 0 and 1 of one voice).However if the reader is not in one of the above categories, he can read the article descriptions so he has an idea of how that effect is generated by the SID. Also, I think that the articles like ripping a tune from a game (even though this is quite technical), could ever give a stimulus to other reader to try this from themselves. That could be a good positive for the sid community. CF The Magazine Covers just sound on Commodore 64 machines, and trackers/ editors, have you thought about covering any other items of Commodore related news? ST. Yes and no ... as the magazine is based on my activities, it essentially to reflect this in the magazines pages. I do something today and it follows afterwards in the magazine. I don't know for example, if the next issue will be formed in all these activities. Most depends of what I will do in the next months... For example, I have looked many times to try and buy a Plus4 computer without any success. I'm sure that if I have one, I will test the TED sound capability compared to the SID and an article will pop up for sure even if don't know all the Plus4 features. Also, recently I found that the AY-chip of a ZX SPECTRUM hase some sound similarities to the SID: for example the "escape from the spaceship" tune at http://www.8bitpeoples.com/discography/8BP08/ Maybe a comparison about AY and the SID chip could be a possibility for a future article, a way for me to learn how AY chip works. CF Some articles cover ripping tunes from games etc, is this a passion of yours? ST. yes, and this comes from ages ago, even though it was in another form... In around 1989/90 I found some computer viruses in our school computers. I started to study them (virus were some sort of mysterious programs at that time, and so not much information was available about them). The study consisted of disassembling the peace of code that was responsible of the infection and reverse engineering it, to understand how it worked. As I liked to program in assembly languages, this reverse task was very passionate for me. I have developed a certain ability or better a familiarity with this work. I remember that having new virus to analyze I would swap floppy disks using traditional mail with other people by answering magazine announcements (there was no internet available at that time...). All this was because I developed an antivirus (SVDL and MVDL) product and I wanted to make it grow. Unfortunately due to the difficulties found in virus and to add to the antivirus, I had to terminate this kind of (reverse engineering) work, until...I find the Big Sid Hunt many-many years after!! The Big Sid Hunt was (actually it is not updated now) a list of user requests for C64 tunes from games. Looking at this list I found that some games like Lazarian and Dig-Dug were not ripped into PSID files. That was amazing as the games were very old and even because Lazarian was the first game I played on the C64: I cannot stay without a PSID file of them! So I soon took up the challenge of ripping them, using the way I knew best: disassemble the code and reverse engineering it like I did for the viruses. Doing this I have found again, the good vibe feeling (I even programmed my own utility in Java for helping me in this task). Maybe this wasn’t the best way of ripping, as it took a lot of time, but for sure it give a true view of the music from the inside the sid chip. I always like to see how the sid chip is programmed for producing such wonderful sounds. LaLa gave me a music CD as a present for my work in ripping tunes for the Big Sid Hunt some years ago. Thanks. CF. Do you think Beginners would benefit from reading some of the articles? ST. Yes, not all the articles are technical like we discuss before. In some articles I describe music editors and this is done from a user perspective (maybe only some parts could be a little more complex like in Digiorganizer), so I think that those articles, give the stimulus to the reader to test the program (and maybe to produce some tunes). In the other articles, maybe the beginner could however have an idea about what I'm talking about, in future when he gets interested about technical details, he may like to re-read the article again. I remember that I read and read many times the Rob Hubbard routine explained in C=Hacking when I was learning the sid, and only after some time I found the way it actually worked. CF. What motivated you to produce such a magazine and give it away FREE? ST. In the early months of 2002 the C=Hacking magazine http://www.ffd2.com/fridge/chacking CF. Do you know how many people read the magazine? ST. No as I can't access to the statistic of the web server that store the SIDin site. However, I think that there are at least 200 people read the magazine (this is from the average download link clicked at csdb). As a side note, this is double the value of readers I say to my friends for having the permission to publish her photo into the cover of the 11th number... ;) Another side note: number 4 was read by Martin Galway and he spoke to me about how it, this was a wonderful moment for me :) Thank you Martin. CF. Have you read Commodore Free and what did you think Yes, I have read every issue: it was very exciting to have a new magazine for the C64 pop up, and I don't miss a issue I have even the first 3 "ghost" numbers). I like to read the interviews: you interview lot of people related to the C64 world and it is a good objective you give to the magazine. The News section is a must read: I always find some news that I missed reading from the net. The Internet is a fast way to get informed, but it is very easy to miss something and not be able to find again even after just a couple of days. This is the same thing that makes me have a news section in SIDin: to let people find important facts, even if they are old in respect to magazine's release date. I like reading in Commodore Free, articles related to Commodore hardware: I like this very much. I would like to thank you for creating Commodore Free magazine that has had a big positive impact to all the C= fans. I know how hard is creating a PDF magazine and having to release it each month (and in many formats, not only in PDF).Thank you :) CF. What version is SIDin magazine in, I recognise PDF, what is the other versions are available? ST. The magazine is in PDF for quick view and/or print. But, as I'm an open source person, I have released the magazine in his native format: Openoffice document. Old numbers are saved into SXW (Star Writer format) is the portable format that OpenOffice used in his early years. The latter are all saved into ODT that it is a standard format for office suites, and you can now open it with a large number of (office related) programs. CF. Have you thought about a Disk image, of the magazine? ST. Yes. Having a disk magazine that talks about the sid and even letting the reader listen to sid tunes while reading is very good idea. But the magazine cannot have all the listing I put in SIDin and so it would need to take a different approach for the technical questions. This would be for me, a very difficult and time consuming task. I had wondered about creating other C64 disk magazines, with more soft argument, but the work for starting that project was too much (and I don't have actually a true disk drive for testing magazine in the real hardware) CF. I see emulation plays a big part of your Commodore usage, but do you still utilise real hardware? ST. I have now a great number of real machines: 3 C64 (6581), 3 C64C (8580) 2 C128 (6581). I still have my original C64 (that I don't use to preserve it as much as possible). One of the C64, old models is broken but the sid chip is good. I even have a commodore datasette and a Commodore monitor. I always use the real hardware for testing my productions before releasing them. This is an important phase, essential especially for music creations. For example for my "Evil" music that uses some pc samples, I tested some versions of it on the C64 (6581) and I choose the one with a given volume level of sample that sounds better on the real hardware. Even the "Silent Night" tune that uses a strong filter for voice 3 (inaudible into a 6581) was tested on a real C64C (8580), I needed to be sure that the music sounded good. However testing in real hardware is a good choice for none music related projects. I remember a Vice 1.12 bug in the sprite emulation that makes my MArkanoid game run ok on the PC, but when I tested the game on real hardware I found to my surprise (that the sprites were totally wrong)! Even in years to come as emulator improve, if you are across-developer like myself, always try your program on real hardware. This is a good rule! For e.g. if you don't have a real machine for testing, then ask to a friend to test the application on there’s. We are all here to help you :) I use 2 of my C64C at the annual Spresiano Retrocumputing meeting http://nrgo.altervista.org/ where I realize/test programs with the public look at all the development phases. There are some images and videos on that site of my hardware and some images are on my website too. CF. What piece of Sid music do you consider the most technical in terms of musical content or the code used to produce the track ST. Good question and not simple to answer...Before I give the real answer, I would like to start by showing you that the SID chip only has 3 sid voices (every musician that composes with the sid chip has that limitation). Go to listen to the "Cover" tune of Phobos: it is very simple musically and this is helping me in showing you what I'm looking for. You will hear from the start two instruments are playing, you then recognize that there are more than 3 instruments playing at the same time. This is very common: you have to program a voice of the sid for playing more that one instrument by changing timbre during the execution of the timbre of another instrument: you have, for example, a percussion sound over a bass sound, but when listening to it, you get the illusion that there are two instrument playing the same time. Just with this example we have seen that every sid tune contains some technicality , and we can describe lots of other ticks used in all the sid tunes (maybe if you listen to some tunes from 1982-83 you think the tunes are "poor" compared to tunes coming after this date: this is because at that time the sid was not programmed to use all its capabilities).So, maybe we can consider technical the tunes that play (or try to play) speech that has been generated by sid voices (using ring modulation for example) not by samples. Some examples of this come from JCH with Triangles tunes but there are other examples. Achieving this is very complicated, but maybe this has nothing musical it is an imitation of a human voice. So, if I have to choose one tune that I consider the most technical in terms of musical content, I would consider "Parallax" by Martin Galway. It is a cover, of course, but it has some unique characteristics in instruments and interpretation of the composition, that make it very suitable for this choice. The Next tune is "Driller" of Matt Gray, due to his atmospheric sound. CF. If you could change 3 things about the sid chip what would you change? ST. Point 1: removing the ADSR bugs. Those bugs are extremely whipping. I think that you have not known the sid chip if you did not find those bug in action. You write you music and suddenly the voice is muted, without any apparent reason!! Point 2: making the filter a digital part one, so all chips can sound the same. The Filter is implemented by analogical components and due to the variable precision of how a resistor is implemented into silicon (if you study microelectronic like me you already have the answer) every chips sound different when using filter. Point 3: maybe something like to have a filter for each voice, or to have more voices to use. Too difficult for me to choose between the two cases... CF. The Commodore sid chip seems to be having a revival with new software and hardware like the prophet 64, new sound trackers and external sound modules featuring the sid chip controlled by modern sequencers. Why do you think people are turning back to the SID chip? ST. Because sid sound is almost unique! an irresistible sound...I remember that in 1994 I was studying the FM programming of the Adlib and Soundblaster cards of a pc computer for looking at how I could emulate a sid chip using a modern chip. I was shocked to see that with the FM programming I was totally incapable of achieving this task (this is even when you could use samples (generated by emulation of the chip) to reproduce sid sound in sidplayer: using the hardware capability of sound synthesizers of the pc sound card was almost a waste of time. I don't know to much about the new sound cards produced after 1995, but I think that this hasn’t changed). Actually, a lot of external hardware that hold a sid chip (and sometimes even more that one) and with the development of so many new programs for programming the sid, composers can have a fresh environment for producing music that is a "modern way" of creating sound. A modern way but with the charm of an old chip...Maybe there are still people who open a monitor program on the C64 and find inserting new ways for programming directly the sid chip in a manner that was not used 25 years ago. But having a better convent way of accessing the chip with today’s hardware/software lets more composer be productive with smaller effort, and so they are coming back to sid music. CF. Do you think the chip will ever be produced again to cover the needs of “new” SID users? ST. This is a dream. I think the dream of all C= user around the world The fact that if one want to put a sid chip into modern hardware, you have to take a sid chip from a C64 is is very depressing to me.. The same issue if you want to replace a broken sid chip in your working C64. There were some rumours in the past that a big quantity of Sid chip built for the "upcoming" C65 computer where buried somewhere after the Commodore bankruptcy. This would be like finding buried treasure or gold if it was true! All our problems would be ended.. However, returning to the initial question, I was happy to see that Tulip developed the C64 DTV and that many people like Jeri Ellsworth and others well known in the Commodore community for there enthusiasm were selected for that task. It seems that the right way was chosen as the Monster sid emulation of the Sid chip could open the port for having future Sid style chips to use. But we already know how the story is going up (especially for the people that I have mentioned before that give their energy without recognition) and the new bankruptcy that is coming for the holder of Commodore. This is, unfortunate, even the business politics that released a Commodore Mp3 player with lot of features, but not with the ability to play a PSID file. This is just ignoring the user base :( With this in mind I don't think that any future Commodore holder will release a new sid chip :( even if they had the original chip layout stored into their archive (maybe some thing to hold it!). CF. Can you describe the Sids unique characteristics? ST. The unique characteristic of the chip, compared to the other chips of the same periods, is that it was developed as a high-quality true synthesizer with lots of unique features. It has tree independent frequency oscillators of up to 4KHz frequency (8 octave) that can use four kind of waveforms (sawtooth, triangle, pulse and noise even combined together).It has three envelope generators that performs ADSR (Attack/Decay/Sustain/Release), tree ring modulators and the ability to synchronize the oscillators. It also has a programmable filter that can be applied to the voices. As it was developed in only 5 months and there were some problems to fit the chip into the silicon surface, many more features were not inserted (like 32 voices) or the use of a better filter. Sid it already so great, can you just imagine what would have been produced if it was created as the creator planned it... CF. The Sid chip does suffer some design flaws can you describe them briefly to our reader, also some composers have used these flaws to there advantage can you comment on this? ST. One point was mentioned before: ADSR bug (a flaw affecting the restart of internal chip logic). Many old school composers were able to produce wonderful music simple by setting the appropriate ADSR values to the sid for avoiding this bug and I can assure you that this is not an easy task (I worked on my Driller cover for many weeks trying to avoid the ADSR bug just changing those values: something terrible to achieve especially as you have to make the right timbre to your instruments and you cannot freely change those values...) However, many solutions were taken for bypassing this problem by musicians/editor programmers without having to modify your ADSR settings: the use of hard-restart the note. There are many way for restarting a note (just to mention that one is even sometimes called sexy-hard restart) but I don't want to describe them all here, maybe I could write up about them in a future issue of SIdin magazine. The main flow of the 6581 sid chip is that there is a (spurious) continuous offset voltage value that can reach the internal 4 bit D/A converter when resetting an oscillator. I think that you know how this flow is manifested: POKE 54272+24,15 and you have the answers... When you change the volume of the sid you get a click from the speaker. Blahh, something that is very annoying. But this is a key for having something very interesting... you just need to change the volume of sid with some "logic" and with some fixed "frequency". In other words you can play sample based music with 4 bit resolution at the frequency (something like from 4KHZ to 8KHz for example) that you choose to use. And now the SID can even speak and sing :) The first applications of this technique for generating sound from the SID was used around 1983-85 for generating speech synthesis. You probably remember the SAM (Software Automatic Mouth) program and maybe those games: Impossible Mission (1983), Slapshot (1984), Beach Head II (1985), Ghostbusters (1984) that have speech inside them (using the speak synthesizer from Berkeley Systems). But it is in 1987 that Martin Galway created Arkanoid music, adding some real-time generated drum sound inside his music. A little time after that (even if it was ready before Arkanoid) Chris Huelsbeck's Bad Cat music that contains the first ever real sampled based music into it. Many composers used this new technique, even was music produced using only samples, without the use or the power of sid sound generated sound. For example today there is the Polly Tracker editor that can use more that one sample (with 8 bit quality) and mix them in real-time. Before putting it with 4 bit resolution to the volume of sid. We could speak about samples more and more (for example, the resolution of 4 bit can be increased using other techniques), but the 8580 version of the chip had the flaw (partially) removed and so you can listen to the samples only if you apply a hack to it. CF, Do you have any favourite sid musicians past and present? ST. Just four: Matt Gray, Gray Matt, the author of Last Ninja 2 music and the author of Tusker music ... :) I am joking!! Sure Matt Gray is my favourite musician. Even if many people think that his sound is just bass and drums, I find his tunes are true masterpieces: Last Ninjia 2, Tusker, Driller, Vendetta ... tunes that are absolutely fantastic. I like the Matt instruments, his style and the "atmosphere" he creates. Martin Galway is another composer I admire He has squeezed lot the power from SID chip creating some sounds that are memorable like : Parallax, Yie Ar Kung Fu II, Green Beret, Times of Lore, Arkanoid, Rambo II and so on.I think that I could add many more composers ("old" and "new")but I will just nominate some others (in sparse order):Richard Bayliss (has a style that I like: I listen to his tunes for hours), Luca/Fire (his tunes have the best filtered 8580 sound ever for me), Turtle (he hasn’t released many tunes from him, but the sound is very attractive for me), Chris Huelsbeck (Giana Sister music is a must),Jonathan Dunn, Dane, Cadaver, Thomas Danko, Soede brothers, Agemixer,Tel Jeroen, Rob Hubbard, ... and I will have to stop here or the list would take up to much space... :) CF. Do you have any other comments you would like to add ST. I would like to thank all the musician/composers out there that even today are still producing sid music for our happiness. Thanks to all the people that are working in the sid area (like HVSC crew for example) as this work is always appreciated by me. For all the readers here: if you have some ideas for realizing something in the C= world, start it. Don't hesitate. All the C= community is behind you... Finally, I can be reached via the email address ice00[at]libero.it Best regards to all the people around ... and thanks Nigel for the interview you give me for your great magazine. visit: http://digilander.iol.it/ice00 Jump Back to CONTENTS In the Beginning Part 7} \Lord Ronin from Q-Link\ Welcome to the second side of a 1541 disk. Well, at least on the original creation. FOR NEXT LOOPS -------------- FOR NEXT LOOPS are what the Commodore user book has for the next piece of information. By this time I suspect that you have some idea that what the manual presents is not a full programming course, Only a taster of the subject. Yet the manual is an attempt to make the computer a friendly, rather than a scary thing. Each of these parts really deserve full chapters in programming manuals. Getting that information out of the way. Here is what the Commodore user book has for you to type in, new 10 forct=1to5 20 ?"commodore 64" 30 nextct Like a nagging yiddish momma, remember to press return after typing in a line. Forgetting to press “Return” is a common fault that we all share, and all forget to do from time to time. Forgetting to press “return” is on annoying user error to find that the line didn't take, when you are debugging 6 pages of a type in programme. Yeah when you run this programme, it does the same thing as the IF THEN Just that it is smaller. Let’s go over it a bit. Line 10, right they are called line numbers. Although I have a programming book collection that isn't American English that calls them line labels. Right back on topic, Line 10 says the same thing that three lines in the IF THEN programme we did recently. Says that "C" is going to be from 1 to 5. Line 20 says that the C= is to print that word line. Line 30 says to do the next ct. Looping from line 10 back through for the 5 prints A bit of a pause here, I dig that this is all strange and new and to be polite odd for you, these commands and typing in the stuff. Alien as you see it for the first time. Personally I was scared to type any of this into the computer, yet this is the stuff from that manual that came in the box with the C=64 PC. Pretty much everyone that uses, used, and programmes; then as well as now, started with to learn how to use the machine. Thankfully this isn't a series on how to programme, I am not that good. Despite my vanity and ego. Here, when you type in and run the programmes, You are doing the same as a guy 25+ years ago did. Feeling the same things as he felt, across the years. Out of the philosophic musings and lets get back to the programming stuff. What the manual doesn't say is that a FOR NEXT loop could be used for a timer in a programme. 100 for fz = 1 to 250 : next fz. If I wrote that correctly from memory. This will delay the programme for a short amount of time, then the next line of the programme will happen. Mainly I have used this as a delay in my little intro screens. I mean that I have a bit of text on the screen, done with that print statement, this will sit there for a time and then another thing will pop up, Like an entire new screen. That may sound like a big thing, Only because you haven't done it yet, and I write it vague enough to make it sound great, When in reality it is just a few steps past what is in this manual. Here is the next thing they have for a FOR NEXT. new 10 fornb=1to10 step.5 20 ?nb, 30 nextnb Tearing this apart. Before or after you have rU (run) it. Did the new part. Then declare on line 10 the variable will be "nb". I think that they did that to suggest Number. Saying that it is going to be starting at 1 and ending at 10. That is sort of familiar to you from the previous stuff. But what the smeg is "step .5" Step is just what it says, a step, sort of like a step in walking, or a step in a set of stairs, One thing at a time. You don't need to tell the C=64 PC to go forward in the steps, If it is just one full step. If you want to run the programme above without the .5 part, Then it will act as if you had said "step 1". Gonna come back to that in a bit. Next line tells it to print the nb variable, Last line tells it to go to the next nb variable. As you can see from the last few examples of variables, the value of the variable, or less techy said, what is in the variable, is changing each time through the programme. Note in the above one there is that comma. Explaining why there are 4 columns of printout on the screen. All this little thing does is count from 1 to 10, pretty much seen in that first line. Difference is that it is doing it in that .5. OK if you haven't run the programme, it starts off as 1 1.5 2 2.5 and so on until it reaches 10. Step .5 is the way its was told to count, Like I said above. If you remove that "step .5" it will count by ones. In fact if you want it to count by ones in a forward direction, you don't even need to put in the step section. If you are in an experimental mood, Then try changing the "step .5" to "step -1". Try it as a "step 2" or a "step 5", See how it works. Well the step -1 won't work, you should see something like ?syntax error line 10. Why? Kind of hard to count from a low positive number like 1, Up to a high positive number like 10, When you are counting in negative numbers . Just change it from 1 to 10, over to 10 to 1 to make it work in line 10. -------------- Well we have made it to page 41, titled Advanced Basic. Compared to other books that I have seen. The commands may be advanced, but the lessons are not. First thing to type in is this little animation programme, right there will be some sort of simple animation on the screen. Because the writing programme that I am using doesn't have the full character set. I am altering this programme a bit. Type it in and give it a run, I'll explain some things about it afterwards. NEW 10 rem bouncing ball 20 ?"" type the line number, the print command, the first quote, then a shifted clear home key, followed by ending the quote.> 25 for x=1to10:?" down>":next 30 forbl=1to40 40 ?" ";: 50 for tm=1to5 60 next tm 70 next bl 75 rem moves ball right to left 80 for bl = 40to1 step -1 90 ?" left>"; 100 for tm=1to5 110 nexttm 120 nextbl 130 goto20 Scary isn’t it? Yet there are some things here that we have already covered in the previous parts. If I typed this correctly, and you entered it correctly, there should be a * symbol that is about 20 lines down on the screen and goes from left to right, then right to left. Actual programme uses the shifted Q to get that filled in circle or ball graphic. We are going to tear this apart, Because there are some points to be made which may have thrown off your typing it in. Line 10 starts off with the term REM, this is short for REMark. When the 64 PC sees that in a programme, it is lazy and doesn't want to read remarks, so it acts as if it isn't there at all. This is a way for a programmer to insert information in the programme for others to see and work upon. I have seen it in menu programmes, A way to tell the user the how and what. Also seen it in BBS games, breaking the parts of the programme down for editing or fixing, That’s the good part. The bad part is that it also eats up memory space. Line 20 I had to add explanation. You already have the print statement; know about the fact that what is in quotes is what you are going to have printed to the screen. Notice that when you did the quote and then the shifted clear/home keys there was a symbol that appeared. That is the symbol for that shifted clear home, Generally it is called just clear home; When not shifted it is called clear. Line 25 is wrong. Yuppers it is wrong in the book, in all 27 copies of the book that I have, This is written incorrectly! Shocked that I contradict the writers of the book? Well there is another line coming up that I will say is wrong as well. Look at the line, it says that X=1to10. So you know that there is a 10 something in this line for the programme. Shows you the ":" symbol, in fact the book states, that indicates a new command. Now you make a quote and then do just one down cursor movement ending the quote. That will be another strange symbol to you. A : follows and the next command. Well if you haven't run it yet. Give it a try, I’ll be here to explain.... OK see that it goes not 10 lines down, It goes 20 lines down, What the smeg? Many of the members of my users group have thought that they did it wrong and couldn't fix or see the problem, well here is a problem. Says to do 1 to 10. Using a for next loop on that line, What you don't see is the fact that : with a next as a command, adds another line as if you had said 1 to 20. There is a typo on this line. In order to fix it you need to type ?"";:next. The use of that ; will keep it on the same line of command. Basically it won't go down 20 lines just the 10 it is supposed to do for this programme. Line 30 is another FOR NEXT loop, but only the FOR is on the line, BL is for the ball character. Says it is to be 1to40. This line is not wrong, run the programme, and take a hard look at the left and right side of the screen. Keep a careful eye out and you will see for a short moment, the graphic you used go up one line on one side and down one line on the other, Just one character. But it is going over the line on the screen, this is because of this line #80. OK scratch your head and wonder why, The programme is written so that you will the use it first. There are 40 columns on the screen, why is it doing 41 in each direction? The truth is that it isn't really it is doing 40 columns. Just that in my opinion, the author didn't want to go into a hard to understand the part about counting, in 1982ce. I mentioned this a little bit earlier, there are 40 columns; But remember that in computer things we will start the count at 0, not at 1. The 64 is doing what it was told, so no problem there. Well it means that you typed the programme in correctly from the book. Only that it was written to sort of re-enforce the 40 column part of the screen, i take it as a something that was glossed over for the time it was written. OK to correct this, we just need to change that 40 to 39 in the line. Can tell you that this shows two things about programming, one is start on some, but not all things, at 0. The other is well ah, just don't believe everything that is in a book or magazine to always be 100% correct, You may have to tweak with it a bit. Line 40 may have caused you trouble in the way I wrote it, we have the print command, then the quote. Yes there is really a space before the * symbol, that needs to be in your line, Followed by one cursor left command. Line 50 sets another FOR loop, here it is TM and it is 1 to 5. Think of this as Time and you will see it is the delay, as done in line 60, where it does the NEXT part, looping between those two lines 5 times before it goes to line 70. Line 70 will print on the screen the next variable called BL, Or the graphic symbol that you used. Line 75 is just another REMark, Indicating a new part of the programme, The area where the motion of the ball is reversed. Line 80 is the same as line 30 In that it is using the same variable label. Also that it is doing a FOR and it is doing that 40 column movement, change that 40 to 39 to keep it on one line. Note that it starts at 40 and goes to 1, using that step thing at a -1 that moves the gfx from the right to the left. Line 90 is another one that may have given you trouble in the way I wrote it. Got the print command and the quote, there really is a space before the first left cursor movement, followed by the second left cursor then the symbol and then another left cursor. 100 sets the time delay to be the same as line 50. 110 is the same as line 60. Line 120 is the same as 70. Line 130 simple tells the entire programme to start over again. The way the programme is laid out, the variable labels of TM and BL can be reused. Line 40 is the left to right work horse of the programme, they Prints a space that will erase the previous symbol on the line, then print the symbol, and then does a left cursor over the symbol, getting ready to do the erase and print all over again. Line 90 is the same except it is doing everything in the opposite direction. See how it is moved with the need of the extra erasures of the symbol to move delete and print. OK when you have this working, feel free to save it. Feeling a bit experimental? Well then change the symbol, do this all in upper case for now. Tired of the speed that it moves, try altering the TM variable. One thing that I have the local group members do is to make a black spade go from left to right. But how about a red diamond going from right to left. No problem in changing the symbol, How to do the colour? Well that takes retyping out the line, just need one more thing in the line. Need to press the control and 1 key for black. You will see a different graphic symbol show up. If not and you see the cursor turn black, you forgot to open the print statement by retyping the " symbol. Same for the diamond or heart, retype the line and add the control 3 and a symbol will appear, run the programme. Did you put them in the right place? If not play with it a while. Maybe you want to change the screen and border colour, make a line 22 that says ?"my animation" or something like that. We have covered the basics on how to do that. Save it if you wish, the thing is, that you have made it on your own. There is that thing moving back and forth on the screen, You did it! You have just programmed a visual thing. Now we come to the INPUT command. A way to have the user interact with what you have written. If you went through my thing on programmes for the C=. You may have not fallen asleep on the Text Adventures part. Simple and easy early to learn Text Adventures, use INPUT as the way to have the player enter information for the game. Lets new the computer and do the following from the book. 10 input a$20 ?"you typed: ";a$ 30 ? 40 goto10 That is simple and there are two things here that are new, I’ll get to the input in a moment. That print command on line 30, what is it going to print? The answer is Nothing! As you see on the line there is nothing to print, so all it is going to do is drop one line down. Since this programme can be run over and over again, that space just separates what you have done from the next part. No matter what you type a word, a number, a gfx, a letter, as soon as you hit the return key what every you input, is output to the screen. Can you see at this time the use of the IF THEN with INPUT? I mean you write a question and IF the answer is wrong THEN the programme prints a nasty response? Well the secret isn't a big one, you can see on the first line that there is a variable, this will be for the input. Line 20 prints out both the message and what you printed, just that simple. Putting it together with other things is where the "fun" enters the game. I'll add here that there are some people who dislike the input command. Also there is available some code to remove that question mark at the end of the input line when you run the programme. Seen it in action, never found my copy of that command after a move. OK here is a more understandable use of the INPUT command, the following will convert standard Fahrenheit to Centigrade and the reverse. New the machine and lets start. 1 rem temperature conversion programme 5 ?"" 10 ?"convert from farhenheit or celsius (f/c)":input a$20 ifa$=""then 20 30 ifa$="f"then100 40 ifa$<>"c"then10 50 input"enter degrees celsius: ";c 60 f=(c9)/5+32 70 ?c;" deg. celsius = "; f;" deg. fahrenheit" 80 ? 90 goto10 100 input"enter degrees fahrenheit: ";f 110 c=(f-32)5/9 120 ? f;" deg. fahrenheit = ";c;" deg. celsius" 130 ? 140 goto10 A lot of work to do something an old calculator I had would do with a few pushes of the keys, but there is a lot to see here. I mean we are familiar to some degree with many of the components of presented commands, See variables, math work, print statements. Now lets hope that I wrote it down right from the book, as we are going into this one. REM part we covered, doing that shifted/clear home as well, Line 10 is a little different, We have the familiar print statement The : to separate commands on a line, But now we have an INPUT statement, Creating the variable a$which should be either a f or a c. Lines 20-40 are a new thing, sure they are the IF THEN statements, but on line 20 there is something new those "", and no space between them. The line is saying that if a$ is nothing, (no key press), then go to line 20. Note here that I wrote it as go to line 20, in programming you do not have to write that go to part, just the line number. OK what is happening is that the programme is going to sit there and wait for you do type in the right thing, before it goes anywhere else. Line 30 works if a$is the f, inputted from the keyboard, ff so then the programme will jump to line 100. Ah here is a new one, Line 40 has the does not equal c part, reading the line says that if the input that the user does from the keyboard doesn't equal c, the programme goes back to line 10 saying printing for the (f/c), and maybe the user will understand what he is to type in for the input. Covers here the input of the variable c as well as rejecting all other non recognised inputs, done in just one line. Line 50 is an input and takes the centigrade degrees making them into the variable c. Line 60 does the math for us, Line 70 prints out what the centigrade is in standard. Here you may need to alter this for spaces to have things line up correctly. Line 80 is a print statement to move down one line. Line 90 takes it back to line 10 to start over again. Line 100 is the same with the input for Fahrenheit, giving f as the variable. Line 110 does the math, Line 120 prints out the variable as a number and the text, again here you may need to adjust for spacing. Line 130 does that drop down again and Line 140 sends the programme back to line 10 to start over again. A few things need to be added at this point, you can change the words in the statements. As I am obviously not a fan of metric, I wrote mine as standard for Fahrenheit, and centigrade for Celsius, as that was the term I was taught for the metric measurement. Doesn't hurt a thing if it makes you more comfortable, if you feel like experimenting, try changing the colours of the text, the border and the screen. Be surprised at how that will change the look and feel of the programme. Now that go to Line 10 on lines 90 and 140. Takes you back to the start of the input for the programme. What it will also do is keep making a space from the print line, and then print the first line over again on your screen. If you don't want a long list of that and the answers on your screen, change that goto 10 to goto 5. That line clears the screen and puts the cursor at row 0 column 0. Sort of like input, we have GET. This one works with each key press. New the PC and type in. 1 ?"" 10 geta$:ifa$=""then10 20 ?a$; 30 goto10 Run it and see what happens, ok I'll let you know now, but it is more fun to run it. Each character from the keyboard you type shows up one by one on a single line. WHY? OK lets tear it apart. Got what happens in line 1 as the clear screen and start at the top left, Line 10 has a variable called a$and the if then statement. Also in that if then statement the "" placed together, A point to bring up for those that intend to use type in books, Font changes in the different books may confuse you to if there is or isn't a space between the quotes. Most of the time there isn't, but it can look like it on the book page. We have a new command called GET, What does it do? Pretty much as it says, it is going to GET something. In this example, It wants to GET the keyboard input, and won't move along, hmm as stubborn as me, till it GETs what it is looking for. That is why nothing happens till you press a key. Works that way for every time you press a key, patiently waiting for you to enter a something, but takes it only one character at a time. Once you press a key, the programme goes right to line 20, where it prints that character where it is the variable a$. Next is line 30 that loops it back to the start. The reason that it prints the characters all in a line is the use of that ; symbol. Change that to , and you will have the characters in neat rows at the 4 tab points on the screen. Drop the , and or the ; and it just goes along the left edge of the screen. A simple programme that with a slight addition is how I have people type in their name or other information on the little intro screens I make from time to time for the club. Also basically the same way that callers do when they log into the BBS and type anything in the message bases. The Commodore book thinks that you saved that previous temperature convention thing. They want to show you how to shorten the programme down a bit, so they show in the book that you can alter lines 10-40 from all those IF THEN statements to 10 ? "convert from Fahrenheit or Celsius (f/c)" 20 get a$: if a$ = "" then 20 40 if a$<> "c" then 20 I dig RPGames. Have done since 1978ce when I was in my late 20s, no idea how many dice I have rolled or how many times I have rolled them. Nice to know that the C= can do dice rolling, but how to do that? Step by step me laddieo. New the system and lets do the following. 10 for x=1to10 20 ?rnd(1), 30 next Well run that and you see a pair of columns of numbers less than 1. OK that RND thing is pretty much a random number generator, but there is more to it than that, if you saw the same information on your screen as mine, then it wouldn't be random would it? But that is rather useless for dice rolling. The book now wants you to change line 20 to read. 20 ? 6rnd(1), Well running that and you still have some weird numbers, but you do have something to the left of the decimal point. OK lets change line 20 again to read... 20 ? int(6rnd(1)), Ah now we have solid numbers, But wait a moment 0-5 is not what we want for a D6. So change the line again to read... 20 ? int(6rnd(1))+1, Yeah here we go, from 1-6 gamers you can change the 6 to be a 4, 8, 10, 12, 20, 30 and 100, Reflecting the different game dice. Really advanced stuff is using the KB GFX to show the numbers. I've seen animated bits of dice rolling, along loads of other pretty pretties on the screen. All comes from this little part. int(lower limit+(upper-lower+1) rnd(1)) Ah that is supposed to be on one line, i know that it doesn't make any sense looking like that and there is a thing that will be in the next section that will require you to use this part. So I'll put it out in that area. You see the next area is where we make a guessing game. Simple but remember you are the one creating it, I'll go over the parts for us, and then we will do that weird line. Continued next month. Jump Back to CONTENTS TND Making music with DMC http://www.redesign.sk/tnd64/music_scene.html/ Created by Richard Bayliss with Special thanks to Rio / Rattenrudel Final instalment 2.5.1 Options We can step with CRSR Keys up and down in Sector Editor. The HOME Key jumps to first line of sector. SHIFT + [ or SHIFT + ] will change the current sector to previous or next sectors. If you want to compose something, first you will need to set up Commands like Duration and Sound, Then you are able to write down notes in the sectors. Otherwise it will use the last settings of a sector before. (------) represents an empty step. If you want to change all notes to another pitch value from current position, then you should push SHIFT + < or SHIFT + >. All Instruments below will now transpose up or transpose down. + key will switch the VOICE ON or OFF, so that you can listen to your placed noted. - key will set an empty step (------). DEL key deletes a line, INST will insert an empty line instead. CLR (SHIFT + HOME) will delete the whole sector. Like in Track Editor - a COPY / PASTE functionality is integrated in sectors too. ? Arrow (Copy - part of the screen flicker in green) and @ (Paste - part of the screen flicker in red). Sectors will be copied only to an END! Command in Tracks (Everything behind that will be ignored). In DMC7 you are able to trace a sector by pushing ?. But beware, i noticed some crashes if we do it to often, looks like a bug. SHIFT + RETURN will close the sector editing. 2.5.2 Commands The sector editor allows us to use different commands: DUR.xx Sets the duration for passing one step (C= + D) SND.xx Sets an instrument number (C= + S) GLD.xy Slides/glides between two notes (C= + G) VOL.0x Sets a volume (works if no Attack or Decay is set) (C= + V) SWITCH Played notes in that section will not be reset by ADSR (C= + X) -GATE- Set gate for a played note (£ key) END! End of Sector will switch into the next sector of track (= key) If you are writing your first tune, you can try to change the duration time (DUR.xx) before the next note is played. DUR is a command like SND etc., which will be noticed by the play routine - but only interpreted as a command (not as a step!). By setting DUR Command it will jump to next note after waiting of xx Steps. The DUR value represents the duration between 2 note-steps. Let's take a look to following example: 00 ------ 01 DUR.03 02 D-3 03 D-4 04 END! It will do the same like this: 00 ------ 01 DUR.01 02 D-3 03 ------ 04 ------ 05 D-4 06 ------ 07 ------ 08 END! Ok? But the first method has a better raster timing and is more space efficient. So you can optimized your composed code with using DUR command. Using GLD.xy command isn't so simple, but here a quick example in two ways: 1. Slide from current note: We are able to slide from a current playing note to another note. We have to adjust the GLD.xy parameters with x=1 and y=speed (0 - none, 1 - slowest, F - fastest) and we need to set the destination note. You can try to play these sectors (01, 02) in a loop: You will hear a downslide to G-3 (from B-4) and an up slide to G-3 (from B-2) in the second sector, but both in different amounts of speed, and you also have to watch out how many steps are between the notes. If you slow down the speed of slide in the first sector (instead F e.g. y = 3), you will notice that the duration of slide will be execute too affecting the next note. Then the next note will slide, which actually shouldn't be slid. 2. Glide between two notes: The second way is to glide between two fixed notes. We need to set the source and destination note after GLD.xy Command. We have to adjust the GLD.xy parameters with x=0 and y=speed (0 - none, 1 - slowest, F - fastest). We have also pay attention to duration and speed of glide. If another note is to be played and the glide isn't finished, it will influence the following notes too! The both notes, which are followed after that GLD Command will be interpreted together as one step. The following example will demonstrate a glide between G-3 and E-5: Volume Command VOL.0x can be used to control volume in channel independent from instrument's Sustain level. The maximum level is F. Volume changes can only be used for instruments which don't use Attack and Decay. The last volume adjustment will be stored globally for that channel. If you want to reset volume settings, so that instruments will use their own ADSR, you have to set Volume parameter back to 00. SWITCH Command won't reset the ADSR for following notes. It can be used in two ways, If we set one SWITCH command, then every following note will use the current ADSR setting until a further SWITCH or END - Command is issued. Then the ADSR will be reset, Take a look at the two examples: GATE Command will activate the GATE of a played instrument, It should only set after a played note. END Command have to be set in every sector and represents the mark of ending a sequence. It will define the total length of your sector too. 2.5.3 Time Control So the main question is: How can i synchronize all three channels with different played sectors. Therefore the total duration time is necessary, If your "tune speed" is 00 and if you setup your editor as follow, you should find following values on screen: L: 0000 0008 The first 4 numbers represents the current played position. The Second 4 numbers represents the total duration time of a sector. It should be same in all the other sectors (or a multiple or halve of that). In the example above you can calculate the sum for every note: DUR04+DUR02+DUR02 = 8. Notice that this number is always hexadecimal! After Editing the number it'll be refresh if you open again the sector or you start the play routine. Take care to choose a good divisible value, You'll understand it if you try drums. Notice that at the end of a sequence should stand an -END-, so that the player knows that you want change to the next sector in track. END, SND, DUR ... are commands, which are only read in from player and so they shouldn't stand in front of an END. These commands are not counted! Notes, GATE and --- are interpreted as full played notes, which are counted in a total duration of a sector. In menu setup you'll find "tune setup". Here you can adjust the whole song speed. What does it means? A higher value will halve the speed. So that you can calculate the total duration time as follows: L:0000 XXXX = (tune SPD + 1)* all DURs (for Notes/Gate/---) 2.5.4 Global Filter and Pulse There is an easy way to create cool Filter Effects and Low Frequency Modulation for sequences, which are using filter. First, you have to create one instrument in Sound Editor. Choose the first instrument number. There you have to choose a filter number (F) and activate the filter (FX: 20) for that instrument. Then go in Filter Editor, choose that number and define these parameters for testing that: F 3 09 00 00 01 00 00 00 00 FF 25 01 01 01 01 25 All right, now go back into the Sound Editor again. Copy your instrument-settings on a free place (another instr. number = 2) and paste your buffer. Now set FX: 22 - that means NO FILTER RESET. Go into Sector editor and put following sequence: 00 DUR.03 01 SND.01 ;FX: 20 you have to reset first the filter settings ;) 02 C-1 03 SND.02 ;FX: 22 NO FILTER RES to start global filter for next notes 04 C-2 05 C-2 06 C-1 07 C-2 08 C-2 09 C-1 0A C-2 0B END! Ok, so you can create LFO envelops for all following notes, the filter envelopes are transferable on other instrument, which use these filter settings too. Notice that all these setting are different for both SIDs (6581 /8580). You have to choose higher values on the 6581, otherwise the filtered instruments sound to deep, pay attention to set filtered sounds only in one channel! Ok, you can try these settings for Pulse instruments too. You only have to choose an instrument with Pulse Wave (41) with defined SPEED values and set FX to NO PULS RES instead NO FILTER RES. 2.6 Quick Recaps and Examples Familiarize yourself with the sound tables, now it is time to do some serious work on those tables. For a start off re-init DMC and pick a normal instrument, which can be the main instrument for any tune, that you compose in future. Because you're at sound #$00, enter the following: After setup wavetable press SHIFT + RETURN then press SPACEBAR to test the sound. There, we are, a perfect working sound. The octave of your test sound can be incremented and decrement by pressing SHIFT and '+' or SHIFT and '-' (depending on which way you would like your sounds' octave to go). Okay, now press the UP ARROW key on your C64 to put the current sound intro memory buffer. Then press '@' to paste to the next instrument. Now all you need to do is add a filter. The next diagram shows how a filter can be turned on. Okay, so not much of a difference to this diagram. All I've done here was added '28' to 'FX'. Basically using '2' or 'A' underneath 'F' turns on the filter and the number under 'X' either emulates as a drum, or just holds your note down, until a GATE is set (GATES will be looked at later on in this feature). Okay, now press the BACK ARROW (or CTRL in DMC7) yet again to enter the flashing bar menu, and then highlight the Filter Editor, using cursor keys, followed by RETURN to activate that editor. The diagram below shows you what the filter editor looks like. Now try the example above. There, now we have a filter ready for the sounds. Press SPACE to test your sound. There you are, what you think? Quite a nice sound eh? Press BACK ARROW (or CTRL in DMC7) to move back to the main menu. Anyway, lets' go and create a new instrument, using the sound editor. Enter as follows: ADSR L P SPEEDS L F V1 V2 ## FX 00AE 0 0 000000 0 0 00 00 02 08 Move your cursor to ## and then press SHIFT & RETURN. You're able to do this with any sound you decide to create, as well as change the ## values. The ## Values is where your put your sound type. Say for example we use ##66, this indicates the DMC player to jump along to section ##66 in the sound data tables. Anyway, at ##02 we want to do a C64-style minor chord, so now copy as follows in the data tables: 02 21 00 03 21 03 04 21 07 05 21 0C 06 94 00 ;94 loop four sounds. The last line controls the octaves. #$03 is octave 3, #$07 is octave 07, and #$0C is octave 12. #$94 repeats the four octaves for a while (depends on the attack/decay used). Now do the same for the major chords (remember copy & paste to the next sound no). ADSR L P SPEEDS L F V! V2 ## FX 00AE 0 0 000000 0 0 01 02 07 08 07 21 00 08 21 04 09 21 07 0A 21 0C 0B 94 00 - Not hard is it ;o) ? Next we'll introduce some more instruments, for you to try: Drums and Bass This chapter takes a look at creating your own C64 drum kit. Let's get back to the sound editor and try as follows. ADSR L P SPEEDS L F V! V2 ## FX 00E8 0 8 000000 0 0 01 02 0C 01 Now edit the table below: 0C 81 FF ;Drum 1 0D 81 FF 0E 41 0C 0F 41 0A 10 41 02 11 91 00 ;End Now let's make cymbals: ADSR L P SPEEDS L F V! V2 ## FX 00E9 0 0 000000 0 2 00 00 12 A1 12 81 FF 13 91 00 Enter the filter editor and enter in table 2. the following: R T ## RT ST S1 S2 S3 0 4 A0 00 00 FF 00 00 Now let's create drum 2: ADSR L P SPEEDS L F V! V2 ## FX 00A9 0 8 000000 0 0 01 02 14 01 14 81 7f 15 41 0E 16 41 0C 17 41 0A 18 41 08 19 81 55 1A 91 00 Now test all your drums. Writing your First Tunes Let us take a look at what we have done so far. Well, we played around with sounds and filters, now we shall start writing a little ditty. For a start off, hop on to the track editor, by cancelling the main menu (pressing BACk ARROW again). Now move into track editor. Pressing 'C= and E' sets STOP and 'SHIFT + E' puts end and loops to the very first sector. Now go to track 1, highlight the sector at $00 and then press SHIFT & RETURN to enter the sector editor. Now do as follows in sector$00. 00 DUR.06 01 SND.XX ;Use the sound number which first drum is 02 A-1 03 SND.YY ;Use the sound no. which are cymbals 04 A-1 05 SND.ZZ ;Second Drum 06 A-1 07 SND.YY ;Cymbals again 08 A-2 09 END! Quick recap: 'C= and S' sets SND.xx, which indicates the sound number which you want to use, while 0-9 and SHIFT A-F sets the sound no. 'C= and 'D' sets DUR.XX, which is the duration. Yet again, use the same number, and letter keys to set the sound. '£' sets a GATE (We'll look at this later), 'UP ARROW' copies the sector in to memory buffer, '@' pastes from memory buffer to current sector, 'SHIFT+X' sets SWITCH (Also will be looked at), while 'SHIFT+G' makes GLIDE. To place 'END', just press '='. Let's edit SECTOR 1 to do a bit of music. 00 SND.00 01 DUR.06 02 A-1 03 A-1 04 A-2 05 A-1 06 A-1 07 A-2 08 A-1 09 A-2 0A END! Now press F1 to listen to what you have done so far. There we are, your first tune done on DMC V4.0. Easy huh? Introducing Volume Control Not much will be happening this time, but we will be taking a look at some really cool things that can be done, when using the DMC V4.0 player. Well, i talked about installing a gate, I also talked about installing, what now? Ah yes, we’ll take a look at the volume feature. The volume feature can do amazing effects with your sounds. Especially when you are using the block/sequence editor. For example, you can do a sort of fading effect to your note. Why not try this: SECTOR 00: 00 SND.XX 01 DUR.08 02 VOL.0E 03 A-4 04 VOL.0D 05 A-4 06 VOL.0C 07 A-4 08 VOL.0B 09 A-4 0A VOL.0A 0B A-4 0C VOL.09 0D A-4 0E VOL.08 0F A-4 10 VOL.07 11 A-4 12 VOL.06 13 A-4 14 VOL.05 15 A-4 16 VOL.04 17 A-4 18 VOL.03 19 A-4 1A VOL.02 1B A-4 1C VOL.01 1D A-4 1E END! However the problem is, if you jump from one sector to another. Let us say for example this is your first sector, and you would like to edit your second sector, then you would need to set a volume, else the second sector will use the last volume which was used and we don’t really want that do we? Still; not to worry. We can sort this problem out by going to the next sector and set the correct volume or we set the volume back to 00. Okay then, let’s try this: SECTOR 01: 00 SND.XX 01 DUR.08 02 VOL.0E 03 A-2 04 ------ 05 ------ 06 ------ 07 ------ 08 ------ 09 ------ 0A ------ 0B ------ 0C ------ 0D ------ 0E ------ 0F ------ 10 ------ 11 ------ 12 END! Now combine these in track form. like this: TRACK 1 TRACK 2 TRACK 3 00 - 00 00 STOP 00 STOP 01 - 01 01 - 00 01 - 00 02 STOP 02 - 00 02 - 00 Okay, now press F1 to play the small sample you created. If you find that there are no sounds coming through then the reason behind this is because you have not loaded or created any sounds. Else, you should hear the sample more easily. Now then, here’s a challenge for you. Try and make the volume go UP instead of down. Heh, heh. I don’t know if you'll manage this, but why not give it a go. Introducing Filter Control Okay, now for something new. We are going to play around with filtered effects coming through with your sounds. When I was writing a piece of music for Commodore Scene's game ‘Stealth 4’, I originally used the DMC player to do the superb effects, but sadly I could not use the tune in the game, due to part of the player's routines being snipped off. So, I used the Dutch USA Team Music Assembler. But I still love the DMC player. Anyway, let's create a few filters and import them into some of our sounds shall we? Yeah, why not. We'll do at least six or seven filters for this bit. Before we do this initialize everything so that we have no sounds at all. Go to the sound editor and then enter as follows: SOUND 00: ADSR L P SPEEDS L F V1 V2 ## 00AA 0 0 000000 0 0 00 00 00 FX 20 Once you have done the sound data, go to ‘##’ and then press Shift + Return and edit the sound data tables. 00 21 00 01 91 00 When you have done your sounds, press Shift + Return to go back to the sound editor. Now we are going to the filter editor. Press the ‘Back Arrow’ key, and highlight ‘Filter Editor’ with your cursor keys. Once you have done this, select the first filter and do as follows: Filter 0: R T ## RT ST S1 S2 S3 F 1 08 00 08 00 00 00 Filter 1: R T ## RT ST S1 S2 S3 F 1 18 00 18 00 00 00 Filter 2: R T ## RT ST S1 S2 S3 F 1 28 00 28 00 00 00 Filter 3: R T ## RT ST S1 S2 S3 F 1 38 00 38 00 00 00 Filter 4: R T ## RT ST S1 S2 S3 F 1 48 00 48 00 00 00 Filter 5: R T ## RT ST S1 S2 S3 F 1 58 00 58 00 00 00 Filter 6: R T ## RT ST S1 S2 S3 F 1 68 00 68 00 00 00 Now, go back to the sound editor and copy each sound by pressing ‘Up Arrow’ and paste to the next sound and change the value of ‘F’. This is because ‘F’ represents the filter number your C64 tries to read. Now let's go back to the track editor and play around with the filtered sounds. First of all, in your track editor, do as follows: TRACK 1 TRACK 2 TRACK 3 00 - 00 00 STOP 00 STOP 01 STOP 01 - 00 01 - 00 Now enter the sector editor and do as follows: SECTOR 00: 00 DUR.03 01 SND.00 02 C-1 03 C-2 04 C-2 05 C-1 06 C-2 07 C-2 08 C-1 09 C-2 0A SND.01 0B C-1 0C C-2 0D C-2 0E C-1 0F C-2 10 C-2 11 C-1 12 C-2 And keep repeating until you have done SND.06, then go back down again to SND.01. Well basically that is all I’ll be leaving with you with in this chapter. Just play around with DMC. 2.7 Packer DMC 4 and DMC 7 have an integrated packer (inside). If you store your tune, the tune will be relocated to $1000 and packed. There is no need for any external packer. 2.8 Relocator Often if you do a demo or a game, it's necessary to relocate your tune(s) to another position in memory. DMC 4 and 7 sets the init routine automatically to$1000. The play routine will start at $1003 for normal or at$1006 for multiple player settings.Check out several relocator tools, which are free in internet to relocate DMC 4 tunes. Watch out for the right version too. DMC 7 hasn't any Relocator tool, but Hoeppie (a member of forum64) is still working on it (in 2007 ;)). So watch out for next releases. Jump Back to CONTENTS Membership forms for the Commodore Computer Club (UK) (CCC(UK)). http://www.commodorecomputerclub.co.uk/ If you are filling in this form electronically (using a word processor), then please send it to shop@commodorecomputerclub.co.uk/ stating that the subject is CCC (UK) membership. Call the file CCC-XXXXXXXXXXXXXX when saving - replace the Xs with your name. We will assign you with a membership number. For those people who have printed out this application form to fill in, please send it with a cheque payable to 'Commodore Computer Club', to: Commodore Computer Club Treasurer, 2 Willis Road, Blackburn, Lancashire, BB2 2UA - United Kingdom. Fees can be arranged electronically (via PayPal), or by personal cheque or postal order. Once you have filled in and submitted this membership form, an invoice will follow with relevant payment details, so please don't forget to fill in your contact details. Please sign me up for a membership to the CCC (UK) - I wish to be a member for: [ ] 6 months* at £3 [ ] 1 year* at £5 [ ] life member at £30 My personal details: Name: Postal code: Country (if outside of the United Kingdom): Date of application (Please use dd/mm/yy format): [FOR INTERNAL USE: Date membership fee received: ] PayPal account (for those paying by this method): If you have already registered on the CCC (UK) forums http://www.commodorecomputerclub.co.uk/forums please tell us your username here: Please tick or cross the box below once you have read and understood the club's rules and regulations: [ ] I declare that I, the named applicant above, have read and understood the CCC (UK) rules and regulations, and agree to abide by them fully and co-operatively. I understand that I am joining this club on a personal level, and not as a representative of any group, developer, publisher or vendor that I belong to. Please tick which computers you own: [ ] CBM/PET 40 columns [ ] CBM/PET 80 columns [ ] VIC/VC 20 [ ] C64/64c [ ] C64GS [ ] SX-64 [ ] C16/116 [ ] Plus/4 [ ] C128/128D [ ] C64DTV [ ] Other Commodore 8-bit [ ] Other Commodore 16-bit If you have ticked 'Other Commodore 8-bit' or 'Other Commodore 16-bit', please list these machines below: Please tick from the list below your interests from the following: [ ] Gaming [ ] BASIC programming [ ] Machine language coding [ ] GEOS [ ] JOS/WiNGs [ ] Tech/scene demos [ ] Collecting [ ] Archiving/preservation [ ] Other applications If you have ticked 'Other applications', please give details below: Please tick if you use any of the following peripherals below: [ ] Datasette [ ] 1541 compatible disk drive [ ] 1581 compatible disk drive [ ] FD2000/4000 [ ] CMD HD or RAMLink [ ] 1351 mouse or compatible [ ] Commodore REU [ ] Other RAM expansion [ ] SuperCPU 64/128 [ ] Other accelerator [ ] MMC/Retro Replay [ ] SwiftLINK/Turbo232 [ ] RR-Net or FB-Net [ ] Other networking device [ ] 1541Ultimate/+ [ ] Action Replay [ ] Trilogic Expert Cartridge [ ] Other cartridge upgrade [ ] Other speed loader [ ] Commodore VDU [ ] Other hardware Please list any items not mentioned above which you have (especially for other Commodore 8-bit machines): Thank-you for taking the time to fill in this membership form. Your membership will be processed on receipt of the relevant membership fee as stated. * Membership fees for 6 months or 1 year will be back-dated to the beginning of the month that the membership application has been made and relevant fee has been cleared into our account. This can be paid either by personal cheque, postal order or PayPal. Membership fees are currently £3 for six months, £5 per year or £30 for life membership. ** It is essential that you fill these details, otherwise your membership will not be processed Jump Back to CONTENTS Commodore Computer Club (UK) (CCC(UK)). http://www.commodorecomputerclub.co.uk/ Club rules: (1) Membership subscriptions, raising funds and re-selling items. (a) All members will pay a membership fee as follows: £3 for six months, £5 per year and life membership at £30. This fee will entitle the holder to free entry to the meetings, and special limited areas of the website, such as private forums and exclusive downloads, should we get anything exclusive to download. Membership will always be back-dated to the start of the month in which the member took out the subscription, so that everyone joining in the month of April for one year will see their membership expire on the 31st of March the following year. (b) We should have a 'Commodore Computer Club Shop', which will stock all of the latest hardware mods and sods for Commodore computers. To stop the 'Maurice Randall' effect, in which the club will have to repay people for not receiving their goods because they haven't been delivered but have been paid for, items will only be on sale if they are in stock. (c) There will be two prices, one for members (cost of item + postage and packing + 10%), and one for none members (cost + postage and packing + 20%). (d) Any members that do work for the club, organising events, donating items for auction, coding, or are otherwise active, with exception to posting on forums and turning up to meetings, will be considered for free membership and/or lifetime membership on merit based only on work they have done for the club. In certain instances, will include what they have contributed overall to Commodore computing or gaming during their life-time, should any 'Commodore legends' show sufficient interest to join the club. (2) Events, software and other developments. (a) Any money that is raised by the club should be used primarily for setting up events, or bolting onto other events as appropriate. This is to go towards, or cover costs with van hire, hotels, food and drink, so the person or people who are willing to travelling to these events, man stalls and generally promote the club and its work are not be out of pocket as far as possible. (b) Profits made from items sold at events should contribute to cover the costs of attending, or hosting, and/or expenses acrude during the event. This will not include monies raised from membership subscriptions paid for during the event. (c) The club should seek to raise money for the purpose of developing hardware and/or software that will benefit Commodore users in the UK and world-wide, and that could therefore be sold through the club Shop. (d) Payments to developers who are commissioned to work on behalf of the club should not be made in advanced or up front unless otherwise agreed by the treasurer and chair-person, and any other two members. This should be openly discussed with all members either in private members areas of the site, or at an organised meeting as appropriate. (e) Hardware that is commissioned on behalf of the club which reaches production should be sold at a small profit, and monies raised to put back into the clubs funds. (f) If it is agreed that the club should commission entertainment software, the productions should be available to download for free from the site for members only. Real-media versions should also be sold through the shop with non-members able to buy copies, though at a higher price than members. (g) Any software commissioned by the club will either be purchased outright, paying the programmer an agreed fee on completion, or paying a lesser fee and splitting the profits at an agreed rate. This should be discussed on a case-by-case basis. The chair-person and treasurer, and two other members, must agree which method should be implemented. (3) Meetings and monies (a) The club should hold an annual general meeting in which members have a say in its running, and are able to make suggestions and table official club business for the year ahead. Membership subscriptions should be reviewed at the annual general meeting, and any price increases must be agreed by the chair-person, treasurer and at least two other members. (b) There should be an annual audit of the clubs finances, with a news-letter at least every three months. The audit should be published before the annual general meeting, and this and the news-letter should be available to current members online in the private member areas. Former members may request this information, which will be granted on a case-by-case basis. (c) Members will be able to attend any events that organised and run by the club for free when ever possible, whilst non-members will pay a small signing in fee of at least £2.50. With agreement with other event organisers, and at events that the club is attending in an official capacity, we will work towards getting members a discounted entry fee. (d) All monies raised will go back into club funds. (4) End of line (a) If it is apparent that the club is not running within its means to the extent that it is likely to fold, or that legal action against it will lead to the club being dissolved, all club assets should be sold or auctioned off, and members will be refunded their current subscriptions based on the length of time they have been members. The longest-serving paying members will be refunded first as appropriate, either particularly or fully depending on the financial circumstances at the time. The newer members, who will be dealt with last. (b) Personal donations to the club's funds can never be fully refunded. Club complaints procedure: Phase 1: Where a complaint is made against the club, or one of the club members, there should initially be a private apology between the club or individual and the plaintiff. This apology should be for 'any undue harm or upset caused', and will not amount to an admission of guilt or a retraction in any way. The club will not be able to force any of its members to make this initial apology except in the instance that the individual has clearly and admittedly worked on the clubs behalf in the matter specifically relating to the complaint that has been lodged. Phase 2: The matter should then be investigated to establish the facts. If it is deemed that an individual club member has not been acting on the clubs behalf with regards to the specifics of the complaint, then this becomes a personal matter between the two parties. The club should therefore stop any further investigations or involvement in the matter. Phase 3: If the complaint lacks any real evidence, or it is felt that the findings are not conclusive, then the matter should be closed. Neither the club, nor any of its members, should therefore discuss the matter publically. All findings should be reported to the plaintiff, and the matter should be considered closed from the club's point of view. Phase 4: Where a complaint is upheld, a public apology and/or retraction should be published through the official website, and in the newsletter. The club should also give the plaintiff the opportunity to give his or her point of view through the website and/or newsletter as appropriate. In this instance, the case will be considered closed from the club's point of view unless the plaintiff wants to take the matter further through due legal process. Emergency phase: If at any point during this process the plaintiff feels aggrieved to the extent that he or she instructs a solicitor to take the matter up against the club or club members who have clearly being acting on behalf of the club in this instance, the club should then consider its legal position on the matter, and a meeting should be set up with the principle members of the club within two weeks of receiving legal notice to discuss the matter, and what to do next. Obviously, one would hope that any complaint would ever get to this stage. http://www.commodorecomputerclub.co.uk/ Commodore Free THE END... Jump Back to CONTENTS	2018-07-18 14:25:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24691689014434814, "perplexity": 2054.4702001751925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590199.42/warc/CC-MAIN-20180718135047-20180718155047-00565.warc.gz"}
https://www.vedantu.com/physics/thermodynamic-properties-and-relations	# Thermodynamic Properties and Relations ## What are Thermodynamics Properties and Relations? It is useful to know these quantities separately for each of the materials joining the reaction to carry out a program of finding changes in the different thermodynamic functions that follow reactions such as entropy, enthalpy, and free energy. If the entropies of the reactants and products are defined independently, the entropy change for the reaction is proportional to the difference. ΔSreaction = Sproducts − Sreactants and the other thermodynamic functions in the same direction. Furthermore, if the entropy change for a reaction is known under one set of temperature and pressure conditions, it can be found under other sets of conditions by using entropy variance for the reactants and products as part of the overall phase. For these reasons, scientists and engineers have created detailed tables of thermodynamic properties for a wide range of common compounds, as well as their rates of change as state variables including temperature and pressure change. The science of thermodynamics includes a variety of formulas and techniques that allow the most knowledge to be derived from a small number of laboratory measurements of material properties. However, since the thermodynamic state of a system is determined by several variables, such as temperature, strain, and volume, it is important to first determine how many of these variables are independent, and then to define which variables are required to change while others remain constant. As a result, the mathematical framework of partial differential equations is important for promoting the understanding of thermodynamics. ### Maxwell Thermodynamic Relations Maxwell thermodynamic relations are a series of thermodynamic equations that can be deduced from the symmetry of second derivatives and the concepts of thermodynamic potentials. These relationships are named after James Clerk Maxwell, a nineteenth-century physicist. The structure of Maxwell relations is a declaration of equality for continuous functions second derivatives. It follows directly from the assumption that the order in which two variables' analytic functions are differentiated is meaningless (Schwarz theorem). The function considered in Maxwell relations is a thermodynamic potential, and xi and xj are two separate natural variables for that potential. $\frac{\delta }{\delta x_{j}}(\frac{\delta \phi }{\delta x_{i} })=\frac{\delta }{\delta x_{i}}(\frac{\delta \phi }{\delta x_{j} })$ where all other natural variables are maintained constant and partial derivatives are measured. There are (n(n-1))/2 possible Maxwell relations for each thermodynamic potential, where n is the number of natural variables for that potential. According to the laws of thermodynamics, the large rise in entropy would be confirmed. ### Enthalpy The heat energy consumed or released during a chemical reaction is referred to as enthalpy. The enthalpy is denoted by the letter H. The letter H stands for the sum of electricity. The change in enthalpy is denoted by the symbol H, where the symbol denotes the change in enthalpy. The enthalpy can be expressed in joules (j) or kilojoules (kj). Enthalpy is defined as the amount of a system's internal energy. This is since the internal energy of a chemical reaction changes, and this transition is measured as the enthalpy. The enthalpy of a phase occurring at constant pressure can be calculated as follows. H = U + PV Where, H is the enthalpy, U is the sum of the internal energy P is the pressure of the system V is the volume of the system The enthalpy change of a reaction determines whether it is endothermic or exothermic. The reaction is endothermic if the value of H is positive. Which ensures that outside energy must be supplied to the system for the reaction to take place. If the H value is negative, however, the reaction is releasing energy to the environment. Enthalpy transition also happens as a substance's phase or state changes. As a solid is converted to a liquid, for example, the enthalpy changes. This is referred to as fusion heat. The heat of vaporisation is the enthalpy transition that occurs when a liquid is changed to a gaseous state. ### Internal Energy The sum of a system's potential and kinetic energy is the system's internal energy. Potential energy is the energy that is retained, and kinetic energy is the energy that is produced as molecules move. The internal energy is denoted by the letter U, and the transition in internal energy is denoted by the letter U. The enthalpy change in that mechanism is equal to the change in internal energy at constant strain. There are two ways in which internal energy can shift. One is due to heat transfer: the device may either absorb or emit heat to the environment. Both methods have the potential to alter the system's internal capacity. The other way would be to work. Therefore, the change in internal energy can be calculated as follow. ∆U = q + w Where, ∆U is the change in internal energy, q is the heat transferred, w is the work done on or by the system An isolated device, on the other hand, cannot have a term U because internal energy is constant, energy transfer is zero, and no work is performed. When the value of U is positive, it means that the device receives heat from the environment and that testing is being performed on it. When the U value is negative, the machine releases heat and operates. Internal energy, on the other hand, may occur as potential or kinetic energy but not as heat or function. This is because heat and function only exist while the system is changing. ## Relation Between Internal Energy and Enthalpy Enthalpy Internal Energy Enthalpy is the heat energy that is being absorbed or evolved during the progression of a chemical reaction. The internal energy of a system is the sum of potential energy and kinetic energy of that system. Calculated as H = U + PV Calculated asΔU = q + w Enthalpy is defined as the relationship between the system and the surrounding. Internal energy defined as the total energy in a system. 1. What is the Relation Between Enthalpy and Temperature? Answer: The number of molecular interactions increases as the temperature rises. The intrinsic energy of the mechanism increases as the number of connections increases. According to the first equation, as the temperature rises, the internal energy (U) increases, and the heat (H) increases. In addition, the enthalpy temperature relationship is, When the temperature of a system increases, the kinetic and potential energies of the atoms and molecules in the system increase. Thus, the internal energy of the system increases, which means that the enthalpy of the system increases. 2. What is the Relation Between Heat Capacities? Answer: The heat capacity at constant volume, Cv , and the heat capacity at constant pressure, Cp in thermodynamics, is comprehensive properties with the magnitude of energy divided by temperature. Hence Cv = T(δS/δT)v and Cp = T(δS/δT)p Where T: temperature V: volume P: pressure S: Entropy 3. How are Thermodynamic Properties Classified? Answer: Thermodynamic properties are classified as either intensive or extensive. If a property is intensive, it is independent of the amount of mass present; if it is a function of the amount of mass present, it is vast. Gravity, temperature, and density are intensive properties, while volume and mass are comprehensive properties.	2021-10-18 17:15:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7712886333465576, "perplexity": 348.6033031947393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585204.68/warc/CC-MAIN-20211018155442-20211018185442-00400.warc.gz"}
https://repository.kaust.edu.sa/handle/10754/558561	### Recent Submissions • #### Random Reshuffling with Variance Reduction: New Analysis and Better Rates (arXiv, 2021-04-19) [Preprint] Virtually all state-of-the-art methods for training supervised machine learning models are variants of SGD enhanced with a number of additional tricks, such as minibatching, momentum, and adaptive stepsizes. One of the tricks that works so well in practice that it is used as default in virtually all widely used machine learning software is {\em random reshuffling (RR)}. However, the practical benefits of RR have until very recently been eluding attempts at being satisfactorily explained using theory. Motivated by recent development due to Mishchenko, Khaled and Richt\'{a}rik (2020), in this work we provide the first analysis of SVRG under Random Reshuffling (RR-SVRG) for general finite-sum problems. First, we show that RR-SVRG converges linearly with the rate $\mathcal{O}(\kappa^{3/2})$ in the strongly-convex case, and can be improved further to $\mathcal{O}(\kappa)$ in the big data regime (when $n > \mathcal{O}(\kappa)$), where $\kappa$ is the condition number. This improves upon the previous best rate $\mathcal{O}(\kappa^2)$ known for a variance reduced RR method in the strongly-convex case due to Ying, Yuan and Sayed (2020). Second, we obtain the first sublinear rate for general convex problems. Third, we establish similar fast rates for Cyclic-SVRG and Shuffle-Once-SVRG. Finally, we develop and analyze a more general variance reduction scheme for RR, which allows for less frequent updates of the control variate. We corroborate our theoretical results with suitably chosen experiments on synthetic and real datasets. • #### Multi-index ensemble Kalman filtering (arXiv, 2021-04-15) [Preprint] In this work we marry multi-index Monte Carlo with ensemble Kalman filtering (EnKF) to produce the multi-index EnKF method (MIEnKF). The MIEnKF method is based on independent samples of four-coupled EnKF estimators on a multi-index hierarchy of resolution levels, and it may be viewed as an extension of the multilevel EnKF (MLEnKF) method developed by the same authors in 2020. Multi-index here refers to a two-index method, consisting of a hierarchy of EnKF estimators that are coupled in two degrees of freedom: time discretization and ensemble size. Under certain assumptions, the MIEnKF method is proven to be more tractable than EnKF and MLEnKF, and this is also verified in numerical examples. • #### Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics (arXiv, 2021-04-14) [Preprint] We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications. • #### A class of high-order weighted compact central schemes for solving hyperbolic conservation laws (arXiv, 2021-04-09) [Preprint] We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation element and solution element (CESE) scheme. On every cell, the solution is approximated by a Pth order polynomial of which all the DOFs are stored and updated separately. The cell average is updated by a classical finite volume scheme which is constructed based on space-time staggered meshes such that the fluxes are continuous across the interfaces of the adjacent control volumes and, therefore, the local Riemann problem is bypassed. The kth order spatial derivatives are updated by a central difference of (k-1)th order spatial derivatives at cell vertices. All the space-time information is calculated by the Cauchy-Kovalewski procedure. By doing so, the schemes are able to achieve arbitrarily uniform spacetime high order on a super-compact stencil with only one explicit time step. In order to capture discontinuities without spurious oscillations, a weighted essentially non-oscillatory (WENO) type limiter is tailor-made for the schemes. The limiter preserves the compactness and high order accuracy of the schemes. The accuracy, robustness, and efficiency of the schemes are verified by several numerical examples of scalar conservation laws and the compressible Euler equations. • #### Accelerated Bregman proximal gradient methods for relatively smooth convex optimization (Computational Optimization and Applications, Springer Science and Business Media LLC, 2021-04-07) [Article] We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an O(k-γ) convergence rate, where γ∈ (0 , 2] is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have γ= 2 and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say γ≤ 1), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical O(k- 2) rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. • #### High Performance Multivariate Geospatial Statistics on Manycore Systems (IEEE Transactions on Parallel and Distributed Systems, Institute of Electrical and Electronics Engineers (IEEE), 2021-04-06) [Article] Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the cokriging technique, which requires the evaluation of the expensive Gaussian log-likelihood function. This large-scale cokriging challenge provides a fertile ground for supercomputing implementations for the geospatial statistics community as it is paramount to scale computational capability to match the growth in environmental data. In this paper, we develop large-scale multivariate spatial modeling and inference on parallel hardware architectures. To tackle the increasing complexity in matrix operations and the massive concurrency in parallel systems, we leverage low-rank matrix approximation techniques with task-based programming models and schedule the asynchronous computational tasks using a dynamic runtime system. The proposed framework provides both the dense and approximated computations of the Gaussian log-likelihood function. It demonstrates accuracy robustness and performance scalability on a variety of computer systems. Using both synthetic and real datasets, the low-rank matrix approximation shows better performance compared to exact computation, while preserving the application requirements in both parameter estimation and prediction accuracy. We also propose a novel algorithm to assess the prediction accuracy after the online parameter estimation. • #### A tangent linear approximation of the ignition delay time. I: Sensitivity to rate parameters (Combustion and Flame, Elsevier BV, 2021-04-02) [Article] A tangent linear approximation is developed to estimate the sensitivity of the ignition delay time with respect to individual rate parameters in a detailed chemical mechanism. Attention is focused on a gas mixture reacting under adiabatic, constant-volume conditions. The uncertainty in the rates of elementary reactions is described in terms of uncertainty factors, and are parameterized using independent canonical random variables. The approach is based on integrating the linearized system of equations governing the evolution of the partial derivatives of the state vector with respect to individual random variables, and a linearized approximation is developed to relate the ignition delay sensitivity to the scaled partial derivatives of temperature. The efficiency of the approach is demonstrated through applications to chemical mechanisms of different sizes. In particular, the computations indicate that for detailed reaction mechanisms the TLA leads to robust local sensitivity predictions at a computational cost that is order-of-magnitude smaller than that incurred by finite-difference approaches based on one-at-a-time rate perturbations. • #### The Arab world prepares the exascale workforce (Communications of the ACM, Association for Computing Machinery (ACM), 2021-04) [Article] THE ARAB WORLD is currently host to eight supercomputers in the Top500 globally, including the current #10 and a former #7. Hardware can become a honeypot for talent attraction—senior talent from abroad, and rising talent from within. Good return on investment from leading-edge hardware motivates forging collaborative ties to global supercomputing leaders, which leads to integration into the global campaigns that supercomputing excels in, such as predicting climate change and developing sustainable energy resources for its mitigation, positing properties of new materials and catalysis by design, repurposing already-certified drugs and discovering new ones, and big data analytics and machine learning applied to science and to society. While the petroleum industry has been the historical motivation for supercomputing in the Arab World with its workloads of seismic imaging and reservoir modeling, the attraction today is universal. • #### On the depth of decision trees over infinite 1-homogeneous binary information systems (Array, Elsevier BV, 2021-04) [Article] In this paper, we study decision trees, which solve problems defined over a specific subclass of infinite information systems, namely: 1-homogeneous binary information systems. It is proved that the minimum depth of a decision tree (defined as a function on the number of attributes in a problem’s description) grows – in the worst case – logarithmically or linearly for each information system in this class. We consider a number of examples of infinite 1-homogeneous binary information systems, including one closely related to the decision trees constructed by the CART algorithm. • #### Coastal circulation and water transport properties of the Red Sea Project lagoon (Ocean Modelling, Elsevier BV, 2021-03-26) [Article] The Red Sea Project (RSP) is based on a coastal lagoon with over 90 pristine islands. The project intends to transform the Red Sea coast into a world-class tourist destination. To better understand the regional dynamics and water exchange scenarios in the lagoon, a high-resolution numerical model is implemented. The general and tidal circulation dynamics are then investigated with a particular focus on the response of the lagoon to strong wind jets. Significant variations in winter and summer circulation patterns are identified. The tidal amplitude inside the lagoon is greater than that outside, with strong tidal currents passing over its surrounding coral reef banks. The lagoon rapidly responds to the strong easterly wind jets that occur mainly in winter; it develops a reverse flow at greater depths, and the coastal water elevation is instantly affected. Lagrangian particle simulations are conducted to study the residence time of water in the lagoon. The results suggest that water renewal is slow in winter. Analysis of the Lagrangian coherent structures (LCS) reveals that water renewal is largely linked to the circulation patterns in the lagoon. In winter, the water becomes restricted in the central lagoon with only moderate exchange, whereas in summer, more circulation is observed with a higher degree of interaction between the central lagoon and external water. The results of LCS also highlight the tidal contribution to stirring and mixing while identifying the hotspots of the phenomenon. Our analysis demonstrates an effective approach for studying regional water mixing and connectivity, which could support coastal management in data-limited regions. • #### Critical Properties and Complexity Measures of Read-Once Boolean Functions (Annals of Mathematics and Artificial Intelligence, Springer Nature, 2021-03-22) [Article] In this paper, we define a quasi-order on the set of read-once Boolean functions and show that this is a well-quasi-order. This implies that every parameter measuring complexity of the functions can be characterized by a finite set of minimal subclasses of read-once functions, where this parameter is unbounded. We focus on two parameters related to certificate complexity and characterize each of them in the terminology of minimal classes. • #### Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump (arXiv, 2021-03-17) [Preprint] We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while maintaining high accuracy. We propose a new challenging test problem for shallow water codes, consisting of a steady circular hydraulic jump that can be physically unstable. We show that numerical methods are prone to either suppress the instability completely or form carbuncles. We test existing cures for the carbuncle. In our experiments, only the proposed method is able to avoid unphysical carbuncles without suppressing the physical instability. • #### Sample average approximation for risk-averse problems: A virtual power plant scheduling application (EURO Journal on Computational Optimization, Elsevier B.V., 2021-03-16) [Article] In this paper, we address the decision-making problem of a virtual power plant (VPP) involving a self-scheduling and market involvement problem under uncertainty in the wind speed and electricity prices. The problem is modeled using a risk-neutral and two risk-averse two-stage stochastic programming formulations, where the conditional value at risk is used to represent risk. A sample average approximation methodology is integrated with an adapted L-Shaped solution method, which can solve risk-neutral and specific risk-averse problems. This methodology provides a framework to understand and quantify the impact of the sample size on the variability of the results. The numerical results include an analysis of the computational performance of the methodology for two case studies, estimators for the bounds of the true optimal solutions of the problems, and an assessment of the quality of the solutions obtained. In particular, numerical experiences indicate that when an adequate sample size is used, the solution obtained is close to the optimal one. • #### Enhanced acoustic pressure sensors based on coherent perfect absorber-laser effect (Journal of Applied Physics, AIP Publishing, 2021-03-14) [Article] Lasing is a well-established field in optics with several applications. Yet, having lasing or huge amplification in other wave systems remains an elusive goal. Here, we utilize the concept of coherent perfect absorber-laser to realize an acoustic analog of laser with a proven amplification of more than 10 4 in terms of the scattered acoustic signal at a frequency of a few kHz. The obtained acoustic laser (or the coherent perfect absorber-laser) is shown to possess extremely high sensitivity and figure of merit with regard to ultra-small variations of the pressure (density and compressibility) and suggests its evident potential to build future acoustic pressure devices such as precise sensors. • #### Some estimates for the planning problem with potential (Nonlinear Differential Equations and Applications, Springer Nature, 2021-03-11) [Article] In this paper, we study a priori estimates for a first-order mean-field planning problem with a potential. In the theory of mean-field games (MFGs), a priori estimates play a crucial role to prove the existence of classical solutions. In particular, uniform bounds for the density of players’ distribution and its inverse are of utmost importance. Here, we investigate a priori bounds for those quantities for a planning problem with a non-vanishing potential. The presence of a potential raises non-trivial difficulties, which we overcome by exploring a displacement-convexity property for the mean-field planning problem with a potential together with Moser’s iteration method. We show that if the potential satisfies a certain smallness condition, then a displacement-convexity property holds. This property enables Lq bounds for the density. In the one-dimensional case, the displacement-convexity property also gives Lq bounds for the inverse of the density. Finally, using these Lq estimates and Moser’s iteration method, we obtain L∞ estimates for the density of the distribution of the players and its inverse. We conclude with an application of our estimates to prove existence and uniqueness of solutions for a particular first-order mean-field planning problem with a potential. • #### Broadband vectorial ultrathin optics with experimental efficiency up to 99% in the visible region via universal approximators (Light: Science & Applications, Springer Nature, 2021-03-04) [Article] AbstractIntegrating conventional optics into compact nanostructured surfaces is the goal of flat optics. Despite the enormous progress in this technology, there are still critical challenges for real-world applications due to the limited operational efficiency in the visible region, on average lower than 60%, which originates from absorption losses in wavelength-thick (≈ 500 nm) structures. Another issue is the realization of on-demand optical components for controlling vectorial light at visible frequencies simultaneously in both reflection and transmission and with a predetermined wavefront shape. In this work, we developed an inverse design approach that allows the realization of highly efficient (up to 99%) ultrathin (down to 50 nm thick) optics for vectorial light control with broadband input–output responses in the visible and near-IR regions with a desired wavefront shape. The approach leverages suitably engineered semiconductor nanostructures, which behave as a neural network that can approximate a user-defined input–output function. Near-unity performance results from the ultrathin nature of these surfaces, which reduces absorption losses to near-negligible values. Experimentally, we discuss polarizing beam splitters, comparing their performance with the best results obtained from both direct and inverse design techniques, and new flat-optics components represented by dichroic mirrors and the basic unit of a flat-optics display that creates full colours by using only two subpixels, overcoming the limitations of conventional LCD/OLED technologies that require three subpixels for each composite colour. Our devices can be manufactured with a complementary metal-oxide-semiconductor (CMOS)-compatible process, making them scalable for mass production at low cost. • #### Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence (Fluids, MDPI AG, 2021-03-02) [Article] The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurate centered finite difference scheme is retained for the diffusive terms. One of the major findings of this analysis is that regions featuring strong rigid-body rotations or straining motions are highly spatially intermittent, while most of the flow regions exhibit moderately strong shearing motions in the absence of rigid-body rotations and straining motions. The majority of compressibility effects can be estimated if the scaling laws in the case of compressible turbulence are rescaled by only considering the solenoidal contributions. • #### A sharp interface method using enriched finite elements for elliptic interface problems (Numerische Mathematik, Springer Nature, 2021-03-02) [Article] We present an immersed boundary method for the solution of elliptic interface problems with discontinuous coefficients which provides a second-order approximation of the solution. The proposed method can be categorised as an extended or enriched finite element method. In contrast to other extended FEM approaches, the new shape functions get projected in order to satisfy the Kronecker-delta property with respect to the interface. The resulting combination of projection and restriction was already derived in Höllbacher and Wittum (TBA, 2019a) for application to particulate flows. The crucial benefits are the preservation of the symmetry and positive definiteness of the continuous bilinear operator. Besides, no additional stabilisation terms are necessary. Furthermore, since our enrichment can be interpreted as adaptive mesh refinement, the standard integration schemes can be applied on the cut elements. Finally, small cut elements do not impair the condition of the scheme and we propose a simple procedure to ensure good conditioning independent of the location of the interface. The stability and convergence of the solution will be proven and the numerical tests demonstrate optimal order of convergence. • #### On some singular mean-field games (Journal of Dynamics & Games, American Institute of Mathematical Sciences (AIMS), 2021-03) [Article] Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form g(m)=−m−α with α>0. We consider stationary and time-dependent settings. The function g is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents move towards low-density regions and, thus, prevents the creation of those regions. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that 1m is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for m−1. • #### Parallel Hierarchical Matrix Technique to Approximate Large Covariance Matrices, Likelihood Functions and Parameter Identi fication (2021-03-01) [Presentation] We develop the HLIBCov package, which is using parallel hierarchical (H-) matrices to: 1) Approximate large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement. 2) Compute matrix-vector product, Cholesky factorization and inverse with a log-linear complexity. 3) Identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These unknown parameters are estimated by maximizing the joint Gaussian log-likelihood function. To demonstrate the numerical performance, we identify three unknown parameters in an example with 2,000,000 locations on a PC-desktop.	2021-04-21 21:10:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5938177704811096, "perplexity": 1028.0789427054647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039550330.88/warc/CC-MAIN-20210421191857-20210421221857-00528.warc.gz"}
https://www.cymath.com/blog/2014-07-07	# Problem of the Week ## Updated at Jul 7, 2014 11:49 AM To get more practice in calculus, we brought you this problem of the week: How would you differentiate $${e}^{x}-\tan{x}$$? Check out the solution below! $\frac{d}{dx} {e}^{x}-\tan{x}$ 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} {e}^{x})-(\frac{d}{dx} \tan{x})$2 The derivative of $${e}^{x}$$ is $${e}^{x}$$.${e}^{x}-(\frac{d}{dx} \tan{x})$3 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.${e}^{x}-\sec^{2}x$Donee^x-sec(x)^2	2021-09-24 03:02:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8759883642196655, "perplexity": 3470.596478890057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057496.18/warc/CC-MAIN-20210924020020-20210924050020-00343.warc.gz"}
https://www.degruyter.com/view/j/secm.2015.22.issue-5/secm-2013-0154/secm-2013-0154.xml?rskey=DSpC2F&result=40	Show Summary Details More options … # Science and Engineering of Composite Materials Editor-in-Chief: Hoa, Suong V. IMPACT FACTOR 2018: 0.705 5-year IMPACT FACTOR: 0.751 CiteScore 2018: 0.77 SCImago Journal Rank (SJR) 2018: 0.247 Source Normalized Impact per Paper (SNIP) 2018: 0.479 Open Access Online ISSN 2191-0359 See all formats and pricing More options … Volume 22, Issue 5 # An energy-based equivalent inclusion for the determination of nanocomposite behavior Yamen Maalej • Corresponding author • Mechanical Engineering, National Engineering School of Tunis (ENIT), University of Tunis El Manar, BP 37, Le Belvedere, 1002, Tunis, Tunisia; and U2MP, ENIS, University of Sfax, Sfax • Email • Other articles by this author: / Luc Dormieux • Institut Navier, Ecole des Ponts ParisTech, 6 et 8, Avenue Blaise Pascal, Cité Descartes, Champs sur Marne, F-77455 Marne-la-Vallée Cedex 2, France • Other articles by this author: / Eric Lemarchand • Institut Navier, Ecole des Ponts ParisTech, 6 et 8, Avenue Blaise Pascal, Cité Descartes, Champs sur Marne, F-77455 Marne-la-Vallée Cedex 2, France • Other articles by this author: Published Online: 2014-04-11 \| DOI: https://doi.org/10.1515/secm-2013-0154 ## Abstract Achieving remarkable mechanical properties for very low levels of reinforcement, nanocomposites are nowadays a new class of materials with high potential. Thanks to the stiffening aspect of the interface region between the matrix and the inclusions, nanocomposites often exhibit improved mechanical and physical properties compared to the conventional composites reinforced with micron-sized particles. This paper presents a strategy based on the introduction of an equivalent inclusion phase that allows managing the ellipsoidal morphology of inhomogeneous inclusion nanophase in the determination of estimates for the homogenized elastic moduli. Application to clay-polymer nanocomposites is presented in the framework of the dilute scheme. The latter gives theoretical estimates in good agreement with experimental results reported in the literature. ## 1 Introduction Achieving remarkable mechanical properties for very low levels of reinforcement (<5%), nanocomposites are nowadays a new class of materials with high potential. Nanocomposites are obtained by using polymer-based [1, 2], metal-based [3] or ceramic-based [4] matrix and nanosized particles as the reinforcement. The reinforcing material can be made up of particles (e.g., minerals), sheets (e.g., exfoliated clay stacks) or fibers (e.g., carbon nanotubes). The matrix material properties are significantly affected in the vicinity of the reinforcement. Thanks to the stiffening aspect of the interface region, these composites often exhibit improved mechanical and physical (electrical and thermal conductivity, optical properties, dielectric properties, heat resistance) properties compared to the conventional composites reinforced with micron-sized particles. The origin of this size effect is revealed by the definition of the stress vector discontinuity condition at the interface between two different phases [5, 6]. For instance, this situation is classicaly managed when dealing with the poroelastic behavior of unsaturated porous media. Indeed, the interfacial domain separating the liquid and the gaseous phases introduces a discontinuity of the normal component of the stress vector. The latter is controlled by the surface tension γ according to the Young-Laplace equation: $n_⋅〚σ〛⋅n_=pg-pℓ=γℓgtrb (1)$(1) where b=-grad n is the surface curvature tensor associated to the interface morphology. When solid/solid interfaces are involved, the interface equilibrium condition yields the following equation, which may be seen as a generalized Young-Laplace equation [7]: $〚σ〛⋅n_+(σs:b)n_+divsσs=0 (2)$(2) where σs is the surface stress tensor defined on the interface separating two phases. The normal discontinuity condition is taken into account through the term (σs:b) n. Remarkably, defining the surface stress tensor as σs=γlg1 allows one to retrieve (1). The surface divergence operator involved in (2) accounts for the tangent discontinuity of the stress vector. It is defined as: $divs σs=∇σs:1T (3)$(3) where 1T=1-nn is the second-order identity tensor of the plane T tangent to the interface at the considered point, whereas ∇ is the gradient operator. Clearly enough, the use of (2) requires clarifying the definition of the surface stress tensor σs. Following [8] and [9], the surface stress tensor is linearly related to the surface strain tensor according to: $σs=ℂs:εs=2μsεs+λs(tr εs)1 (4)$(4) where μs and κs=λs+μs represent the shear and the bulk surface moduli. From an energy point of view, this additional surface contribution modifies the elastic energy stored in the inclusion phase. One part of this energy $(WVe)$ is defined as the integration over ΩI of the elastic energy volume density, the other part $(WSe)$ is defined as the integration over its external surface of a surface elastic energy: $WIe=12∫ΩIσ:ε dV=12∫ΩIεI:ℂIεI dV︸=WVe+12∫∂Iεs:ℂsεsdS︸=WSe (5)$(5) The comparison of the order of magnitude of each of these two terms allows one to understand the increasing contribution of surface energy with decreasing inclusion characteristic size. Let us consider a homogeneous spherical inclusion (domain ΩI) of radius R, undergoing a uniform strain on its external boundary (∂ΩI). Surface and volume inclusion strains are then both equal to this uniform strain, so that the surface-to-volume elastic energy ratio reads: $WSeWVe=MsMv\|∂ΩI\|\|ΩI\|=MsMv3R (6)$(6) where Mv (resp. Ms) symbolically represents the volume (resp. surface) elastic moduli contribution. Considering finite values of elastic moduli for both volume and surface behaviors, (6) clearly shows that surface energy has an increasing contribution for decreasing values of the inclusion characteristic size. By contrast, when the characteristic size of the inclusion is large enough, the elastic energy is essentially stored in its bulk volume. This is the situation usually addressed by micromechanics approaches. Considering surface effects in the framework of usual micromechanics developments is precisely the starting point of recent efforts of the scientific community toward the better understanding of nanocomposite behavior [8, 10, 11]). For instance, estimates (Mori-Tanaka type [12] or generalized self-consistent types) are now available for the elastic moduli of nanocomposites reinforced by spherical nanosized particles. As expected, these estimates show a dependence on the size of the nanoparticles. The concept of interface is a two-dimensional (2D) idealization of the transition zone between two phases, which may be thought of as a thin 3D layer of infinitesimal thickness h. The surface stress tensor then appears as: $σs=limh→0∫0hσmdz (7)$(7) The mathematical singularity of the membrane stress concept lies in the fact that the integration over a layer whose thickness tends toward 0 yields a non-vanishing limit. As opposed to the bidimensional concept of membrane stress, σm is a 3D stress field. The equivalence of the interface surface and the thin elastic layer is demonstrated in [9, 13]. It was shown that it is possible to introduce a 3D stiffness tensor ℂm accounting for the interface represented by an elastic layer of small, but finite, thickness h, made up of an isotropic, linearly elastic material with Young’s modulus Em and Poisson’s ratio νm. Then the 2D and 3D representations are asymptotically equivalent when h→0+. Finally, the 3D corresponding stiffness tensor reads: $ℂm=3κmJ+2μmK (8)$(8) where J and K are the spherical and deviatoric fourth-order projectors. The 3D bulk and shear modulus κm and μm of the equivalent elastic layer are deduced from their 2D (surface) counterparts (4) by: $κm=4κsμs33μs−κs)h; μm=μsh (9)$(9) Taking advantage of this 2D-3D equivalence, the elastic surface energy in (5) may be advantageously replaced by the 3D contribution of an elastic layer (domain Ωm) of infinitely small thickness h according to: $WSe=12∫∂ΩIεs:ℂs:εsdS≈limh→0+12∫Ωmεm:ℂm:εmdV (10)$(10) so that (5) may equivalently be written as: $WIe=12∫ΩIε:IℂI:ε IdV+limh→0+12∫Ωmεm:ℂm:εm dV (11)$(11) On a micromechanics point of view, the 3D behavior of nanocomposites requires a specific morphological definition of the nanosized particles embedded in the matrix phase. These particles should be modeled as ellipsoidal inhomogeneous inclusions: a (assumed) homogeneous core made up of the particle material itself and a (assumed) homogeneous shell made up of an elastic medium with ‘large’ elastic moduli in the sense defined in (9) with h→0. The case of spherical inclusions has already been adressed in the literature [8, 9, 11, 13]. Because of their difficult mathematical treatment, ellipsoidal inclusions have received less attention. It is the purpose of the present paper to propose a strategy that allows managing the ellipsoidal morphology of the inhomogeneous inclusion nanophase. The idea consists in assuming that it is possible to define an equivalent inclusion that may replace the inclusion including interface effects. This idea has already been used in a previous paper in the context of displacement discontinuity conditions between inclusion and matrix phases[14–16]. ## 2 Equivalent inclusion model In this section, we present an energy-based strategy that will allow us to estimate the effective moduli of nanocomposites reinforced by ellipsoidal inclusions. The main idea consists in replacing the inhomogeneous particle (inclusion+‘3D’ membrane) by an equivalent inclusion of identical shape. This equivalent inclusion behavior is characterized by a stiffness tensor ℂeq in such a way that the elastic energy stored in this equivalent inclusion is equal to the elastic energy stored in the inhomogeneous inclusion under the same loading condition on its external boundary. ## 2.1 Geometrical and material description The geometrical shape is an oblate spheroid with equatorial radii a, polar radii c (aspect ratio X=c/a) and revolution axis ez. The equation of this geometrical shape in a (x, y, z) Cartesian coordinate system reads: $x2a2+y2a2+z2c2=1 (12)$(12) Let n be the external normal vector to the surface: $n=2xa2ex+2ya2ey+2zc2ez (13)$(13) Using the spherical coordinate system (er, eθ, eφ), the ellipsoid can be parametrized by: ${x=rsinθsinϕy=rsinθcosϕz=rcosθ (14)$(14) Substituting (14) in (12) yields the following parametric equation r(θ): $r(θ)=1sin2θa2+cos2θc2=aXsin2θX2+cos2θ (15)$(15) which allows one to reconsider (13) as: $n=er+r2(θ)sinθcosθ(1a2-1c2)eθr2(θ)sin2θa4+cos2θc4 (16)$(16) The external surface acts as a membrane of constant infinitesimal thickness h occupying the geometrical space between r=r-(θ) and r=r+(θ) (Figure 1). Figure 1 Geometrical description. Recalling that the interfacial domain is assumed infinitesimal (h<<1), we may write: $h≈cosδ(r+(θ)-r−(θ)) (17)$(17) where δ is the angle between the normal n and er: $cosδ=n⋅er=1r2(θ)sin2θa4+cos2θc4 (18)$(18) ## 2.2 Elastic energy at the membrane In the framework of micromechanics approaches, the inhomogeneous inclusion may be interpreted as a morphologically representative pattern [17] whose analytical treatment is a complicated task. In order to overcome this difficulty, we develop hereafter an energy-based strategy allowing us to replace the inhomogeneous inclusion by an equivalent homogeneous one. It is therefore necessary to identify the elastic moduli of the equivalent inclusion so that the elastic energy stored in this equivalent inclusion is equal to the elastic energy stored in the inhomogeneous inclusion under the same loading condition on its external boundary, defined by a uniform macroscopic deformation load ℂ (Figure 2). The stiffness tensor of the equivalent inclusion is denoted by ℂeq in the sequel. Figure 2 Equivalent inclusion concept. Using the revolution symmetry around ez, the field of displacement in the membrane is sought in the form: $ξ(r, θ, ϕ)=ξr(r, θ, ϕ)er+ξθ(r, θ, ϕ)eθ (19)$(19) which should comply with the following boundary conditions: $ξ(r(θ), θ, ϕ)=E∞⋅r(θ)er (20)$(20) Within the framework of a variational approach, the displacement ξr and ξθ are sought in the subspace of the kinematic admissible displacement field defined by: $∀i=r, θ ξi(r, θ, ϕ)=ei.E∞⋅rer(1+αif(r)) (21)$(21) for any scalar function f(r) meeting the condition f(r(θ))=0. αr and αθ in (21) are two Lagrangian multipliers that will be optimized by taking advantage of the potential energy minimization principle. The elastic strain in the membrane domain $e(r, θ, ϕ)=12(∇ξ+T∇ξ)$ generates a density of elastic energy: $wem=12e(r, θ, ϕ):ℂm:e(r, θ, ϕ) (22)$(22) where the 3D stiffness tensor ℂm characterizes the elastic behavior of the membrane layer according to (8) and (9). The total strain energy $Wem$ in the membrane domain Ωm, calculated in spherical coordinate system and using the density of elastic energy (22), reads: $Wem=∫Ωmwem(r, θ, ϕ) dV=∫02π∫0π∫r−r+wem(r, θ, ϕ) r2sinθ dr dθ dϕ (23)$(23) Recalling that the interfacial domain is assumed infinitesimal, (23) may be well approximated by: $Wem=∫02π∫0πwem(r(θ), θ, ϕ) r2(θ)(r+(θ)-r-(θ))sinθ dθ dϕ (24)$(24) Substituting (17) and (18) in (24), the total membrane strain energy $Wem$ may be approximated by: $Wem=h∫02π∫0πr4(θ)wem(r, θ, ϕ)sin2θa4+cos2θc4sinθ dθ dϕ (25)$(25) Optimized values of parameters αr and αθ are then obtained in order to minimize the total membrane energy (25). The minimization problem to solve reads: $αiopt(E∞)/∂Wem∂αi\|αi=αiopt=0 for i=r, θ (26)$(26) ## 2.3 Total elastic energy The macroscopic elastic energy of the equivalent inclusion stored by the uniform strain ℂ applied on its external boundary yields: $Weeq=12\|ΩI\|E∞:ℂeq:E∞ (27)$(27) where $\|ΩI\|=43πa2c$ is the volume of the equivalent inclusion. Similarly, the elastic energy of the inhomogeneous inclusion is defined in (11). Still, considering the same uniform strain boundary condition ξd=E·z (11) yields: $Weinc=12\|ΩI\|E∞:ℂI:E∞+Wem(αropt(E∞), αθopt(E∞)) (28)$(28) where $Wem(αropt, αθopt)$ is derived from (25) and (26). Eventually, taking advantage of the energy consistency between the elastic energy stored in the inhomogeneous inclusion (28) and the one stored in the equivalent inclusion (of identical shape) (27), it is possible to identify the elastic moduli of the equivalent inclusion that are mobilized by the uniform strain 𝔼 applied on the external boundary: $12\|ΩI\|E∞:ℂeq−ℂI:E∞=Wem(αropt(E∞), αθopt(E∞)) (29)$(29) The next sections are devoted to the derivation of the previous methodology to two classes of inclusion geometry: the spherical inclusion and the oblate spheroidal inclusion characterized by an aspect ratio X→0. ## 3 Application to a spherical inclusion geometry Let us first consider the case of a spherical inhomogeneity of radius R. This is equivalent to considering the case X=1 (a=c) in the previous reasoning. The parametric equation (15) also yields r(θ)=R, so that the elastic energy in the 3D membrane, defined in (25), takes the following form: $Wem≈hR2∫02π∫0π wem(R, θ, ϕ) sinθ dθ dϕ (30)$(30) Due to the spherical symmetry of this problem, the equivalent inclusion behavior is isotropic and fully characterized by two coefficients keq and μeq. Two different homogeneous strain definitions have to be considered in order to determine these coefficients. ## 3.1 Hydrostatic deformation: E∞=E∞ 1 Considering a hydrostatic deformation E=E1, the elastic energy stored in the equivalent inclusion (27) reads: $We,1eq=\|ΩI\| keq E∞2 (31)$(31) The displacement field in the membrane (19) reduces to as ξ(r, θ, φ)=ξr(r, θ, φ)er with: $ξr(r, θ, ϕ)=E∞rer (1+αr f(r)) (32)$(32) The optimization procedure (26) provides the unique optimal parameter $αr,1opt,$ which yields, whatever the choice for function f(r), the following estimate of the equivalent bulk modulus according to the energy equivalence principle (29): $keq≃kI+12κmμm4μm+3κm(ha) (33)$(33) or equivalently, using (9): $keq≃kI+4κs3R (34)$(34) ## 3.2 Deviatoric deformation: E∞=E∞(e1⊗e1- e2⊗e2) Considering a uniform loading defined by a deviatoric strain E=E(e1e1-e2e2) applied on the spherical inhomogeneity, the elastic energy stored in the equivalent inclusion (27) reads: $We,2eq=2\|ΩI\| μeq E∞2 (35)$(35) The displacement field in the membrane is defined by (19) and (21). The optimization procedure (26) provides optimal parameters $αr,2opt$ and $αθ,2opt.$ Used in (29), these optimal values yield, whatever the choice for function f(r), the following estimate of the equivalent elastic shear modulus μeq: $μeq≃μI+μm(8μm+9κm)5(4μm+3κm)(ha) (36)$(36) or equivalently, using (9): $μeq≃μI+6μs+κs5R (37)$(37) Concerning the order of magnitude of the equivalent inclusion elastic moduli, Eqs. (34) and (37) clearly exhibit the increasing contribution of the surface (elastic) energy for decreasing values of the inclusion radius R. The latter defines the characteristic size of the spherical inclusion phase. In practice, incorporating a spherical inclusion having a radius of the order of a few nanometers, likely to significantly increase elastic moduli of nanocomposites, may appear as a complicated technical task. Many studies have therefore turned into natural materials defined at the nanoscale by solid-phase inclusions of high surface area. Clay materials, and more particularly smectites, meet this requirement (among others) and have been widely used as inclusion phase for nanocomposites. Depending on their level of deflocculation (exfoliation), the nanoscopic solid phase of these natural materials may be represented by ellipsoidal inclusions whose aspect ratio may be very small (1/100) for complete deflocculation. The next section takes advantage of the energy equivalence strategy in order to propose a micromechanical model to the nanocomposite behavior. The ‘oblate spheroid’ morphology with the additional surface energy contribution accounts for a montmorillonite (MMT) clay platelets nano-inclusion and is introduced in a polymer matrix. The validation is performed by using reference experimental study. ## 4 Application to a polymer matrix reinforced by MMT clay platelets nanocomposite The present section is devoted to the determination of estimates for the macroscopic elastic moduli of nanocomposites. These estimates are derived in the framework of Eshelby-based micromechanics approaches [18, 19]. The very low level of reinforcement usually encountered suggests resorting to the well-known dilute scheme. The nanocomposite here is a polymeric matrix reinforced by parallel clay platelets. The latter are modeled as a non-interacting oblate spheroid inclusion embedded in a continuous polymeric matrix. These ellipsoids are characterized by the same aspect ratio X=c/a→0 (2a=clay particle diameter in the e1/e2 plane; 2c=clay particle thickness in the e3 direction; particle volume $ΩI=43πXa3$) and the same orientation that coincides with the direction of the axis of rotational symmetry parallel to the sample axis e3 (Figure 3). Figure 3 Parallel clay platelets reinforcement. The nanocomposite is therefore a two-phase medium made up of: • a polymer matrix phase, characterized by an isotropic elastic tensor ℂ0. • an inclusion phase modeled as a flat oblate spheroid inhomogeneity. The core material is the inclusionary material (clay platelets here). Its behavior is assumed transversely isotropic (isotropic in the e1/e2 plane). The thin shell material is isotropic with elastic moduli defined in (8) and (9). Following the results of the previous section, the inclusion phase is replaced by a transversely isotropic equivalent inclusion with stiffness tensor ℂeq. The homogenized behavior itself is expected transversely isotropic and the elasticity tensor is characterized by five independent coefficients. However, the reference experimental results that are used to validate the developed model concerns Young’s modulus as the nano-reinforcements are randomly distributed. In the sequel; only the moduli in the principal direction E11=E22 and E33 are estimated for the considered polymeric matrix reinforced by parallel clay platelets. ## 4.1 Dilute scheme Due to the low level of reinforcement (≤5%), all the effective elastic moduli of this transversely isotropic nanocomposite are here estimated in an explicit analytical way by using the so-called dilute scheme approximation. A direct application of usual micromechanics relations allows us to define the homogenized elastic moduli according to [19]: $ℂhom=ℂ0+f δℂ0eq:Aeq with δℂ0eq=ℂeq−ℂ0 (38)$(38) where 𝔸eq is the equivalent inclusion strain concentration tensor. In the case of a dilute scheme approximation, the latter reads: $Aeq=[I+ℙ0:δℂ0eq]−1 (39)$(39) As discussed in the previous section, we will restrict our analysis to the determination of estimates for the longitudinal compliance modulus 1/E33 and the transversal compliance modulus 1/E11=1/E22. As a consequence, there is no need to fully determine ℂeq, but only the coefficients involved in the determination of these estimates. In the present case, up to four coefficients, or groups of coefficients, have to be identified. According to Section 2, this requires three (resp. four) appropriate uniform strain tensors E to be considered in order to estimate 1/E33 (resp. 1/E11=1/E22). Details of the procedure are developed in the Appendix. Two experimental studies are used to validate the developed model. The first concerns the experimental results obtained by Cauvin et al. [20], which is devoted to the mechanical behavior of a polypropylene (PP) reinforced by randomly distributed clay nanoplatelets (MMT). The elastic properties of the PP matrix are E=0.9 GPa and v=0.4, and of the MMT inclusion are E=170 GPa and v=0.25. The second concerns the experimental results presented by Luo and Daniel [21] devoted to polymer/clay nanocomposites consisting of epoxy matrix filled with randomly distributed silicate clay particles where the elastic properties of the epoxy matrix are E=2.05 GPa and v=0.35; the clay particles have the same characteristics as those used by Cauvin et al. [20]. Figures 4 and 5 provide a comparison of the reported experimental results with the developed model. The results of the model using spherical inclusion (black) show a significant underestimation of the nanocomposite elastic modulus even taking account of the interface effects. For the flat oblate spheroid inclusion, the longitudinal modulus E11=E22 (red) represents the behavior obtained for a macro inclusion distribution oriented in the loading direction. This corresponds to the configuration where all MMT particles are oriented in the same direction, which gives, thanks to the interface properties and the great length of particles, an upper limit of the macroscopic behavior in this direction. By contrast, the transversal modulus E33 (green) represents the case where only the thickness of the platelets contributes to the macroscopic stiffness. Given that this thickness is very low, the supply of MMT platelet stiffness in this direction represents a lower bound of the macroscopic behavior. The dashed curve represents an average of the two modules for each fraction of inclusion. Figure 4 Comparison with experimental results from Cauvin et al. [20]. Figure 5 Comparison with experimental results from Luo et al. [21]. The developed model based on the use of a flat oblate spheroid inclusion clearly shows a good agreement with the two experimental results. The strong effect of the nano-inclusion on the variation of Young’s modulus as a function of the MMT volume fraction (<5%) is well predicted. It is worth noting that the the aspect ratio X was numerically calibrated to fit experimental results; its direct determination needs microstructural observations, which are not provided. We also note that the exfoliation process of these materials is not under control, and in the absence of microstructural observations, it is difficult to predict if all the platelets of the MMT aggregates are separated and dispersed randomly within the matrix (complete exfoliation) or partially separated and emerging platelet aggregates (partial exfoliation). This particular point needs further research based on the developed model and choosing an adequate homogenization scheme taking into account the microstructure morphology. In the case of complete exfoliation, the macroscopic behavior is expected to be isotropic. For an ongoing research, an extension to spatial distribution of the flat oblate spheroid inclusion should be taken into account in the developed model. ## Acknowledgments This research is conducted through a collaboration between the Ecole des Ponts-ParisTech and the National Engineering School of Sfax. This collaboration is financed by the French Institute of Tunisia according to the program “Séjour Scientifique de Haut Niveau” (SSHN). The authors gratefully acknowledge the support of these institutions. ## Appendix In this section, the elastic moduli of the transversely isotropic equivalent inclusion are computed using various appropriate uniform strain tensors E. Hydrostatic deformation: E=E1 Considering a hydrostatic deformation E=E1, the elastic energy stored in the equivalent inclusion (27) reads: $Weeq,1=\|ΩI\| C1eq E∞2 (40)$(40) where: $C1β=(1 :ℂβ :1)/2=C1111β+C1122β+2C1133β+C3333β2 (41)$(41) The displacement field in the membrane (19) reduces to ξ(r, θ, φ)=ξr(r, θ, φ)er. The optimization procedure (26) leads to the sole optimal value $αropt,1:$ $αropt,1=24κX23μ−κ+O(X3) (42)$(42) which tends toward 0 when the aspect ratio X→0. Substituting (42) in (29) yields the following estimate of the elastic coefficient $C1eq:$ $C1eq≈C1I+9μmκm(3μm−κm) c (43)$(43) Biaxial deformation: E=E(e1e1+e2e2) Similarly, the elastic energy stored in the equivalent inclusion (27) now reads: $Weeq,2=\|ΩI\| C2eq E∞2 (44)$(44) where (1p=e1e1+e2e2): $C2β=(1p :ℂβ :1p)/2=C1111β+C1122β (45)$(45) The optimization procedure (26) yields the optimal values: ${αropt,2=32μmμm2-12κmμm+3κm23μm-κmX2+O(X3)→0αθopt,2=32μm(κm-μm)+O(X3) (46)$(46) Substituting (46) in (29) yields the following estimate of the elastic coefficient $C2eq:$ $C2eq≈C2I+3(μm2+10κmμm-3κm2)4(3μm-κm)c (47)$(47) Deformation: E=E(e3e3) The elastic energy stored in the equivalent inclusion (27) reads: $Weeq,3=\|ΩI\| C3eqE∞2 (48)$(48) where: $C3β=C3333β/2 (49)$(49) The optimization procedure (26) yields the optimal values: ${αropt,3=3κ-5μ2(3μ-κ)+O(X3)αθopt,3=−32+O(X3) (50)$(50) Substituting (50) in (29) yields the following estimate of the elastic coefficient $C3eq:$ $C3eq≈C3I+3μm243μm-κm)c (51)$(51) Deformation: E∞=E(e1e1) The elastic energy stored in the equivalent inclusion (27) reads: $Weeq,4=\|ΩI\| C4eq E∞2 (52)$(52) where: $C4β=C1111β/2 (53)$(53) The optimization procedure (26) yields the optimal values: ${αropt,4=32-12κμ+3κ2+μ2m(3μ-κ)X2+O(X3)→0αθopt,4=32κ-μμ+O(X3) (54)$(54) Substituting (54) in (29) yields the following estimate of the elastic coefficient $C4eq:$ $C4eq≈C4I+3π1615μm2+26κmμm-9κm2(3μm-κm)c (55)$(55) ## References • [1] Pinnavaia TJ. 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Commun. 2012, 43, 41–45. • [15] Maalej Y, Dormieux L, Sanahuja J. Eur. J. Mech. A: Solids 2009, 28, 647–653. • [16] Dormieux L, Sanahuja J, Maalej Y. C. R. Mec. 2007, 335, 25–31.Google Scholar • [17] Bornert M, Stolz C, Zaoui A. J. Mech. Phys. Solids 1996, 44, 307–331. • [18] Eshelby JD. Proc. R. Soc. London, Ser. A 1957, 241, 376–396.Google Scholar • [19] Dormieux L, Kondo D, Ulm F-J. Microporomechanics. Wiley, John Wiley & Sons Ltd.: UK, 2006. • [20] Cauvin L, Kondo D, Brieu M, Bhatnagar N. Polym. Test. 2010, 29, 245–250. • [21] Luo J-J, Daniel IM. Compos. Sci. Technol. 2003, 63, 1607–1616. Corresponding author: Yamen Maalej, Mechanical Engineering, National Engineering School of Tunis (ENIT), University of Tunis El Manar, BP 37, Le Belvedere, 1002, Tunis, Tunisia; and U2MP, ENIS, University of Sfax, Sfax, e-mail: Accepted: 2014-03-01 Published Online: 2014-04-11 Published in Print: 2015-09-01 Citation Information: Science and Engineering of Composite Materials, Volume 22, Issue 5, Pages 475–483, ISSN (Online) 2191-0359, ISSN (Print) 0792-1233, Export Citation	2019-11-13 23:21:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 71, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7866204380989075, "perplexity": 2182.8570472416536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667442.36/warc/CC-MAIN-20191113215021-20191114003021-00167.warc.gz"}
http://spatialaudio.net/sound-field-synthesis-toolbox-1-0-0-beta2-released/	Sound Field Synthesis Toolbox 1.0.0-beta2 released A new bug fix release of the SFS Toolbox was released today. You can download the latest release and you should have a look at the tutorial on github how to use it. NEWS: - rms() now works for arbitrary arrays - speedup of delayline() and HRTF extrapolation - delayline() now works with more than one channel - fixed a critical bug in wfs_preequalization() - fixed missing conf values in several functions - fixed README - changed location of sfs-data for automatic download, because github does not allow this - several minor fixes This entry was posted in Announcement, Reproducible Research and tagged , , . Bookmark the permalink. This site uses Akismet to reduce spam. Learn how your comment data is processed.	2020-09-23 18:14:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2576467990875244, "perplexity": 6858.006364982748}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400212039.16/warc/CC-MAIN-20200923175652-20200923205652-00496.warc.gz"}
http://allwomenstalk.com/8-signs-your-ex-still-has-feelings-for-you/	# 8 Signs Your Ex Still Has Feelings for You ... Does your ex still have feelings for you? You know if you have feelings for your ex or not, but it may be hard to tell if he has feelings for you. I am going to give you 8 signs your ex still has feelings for you … ## 8. He Tries to Talk to You Image source: minniechan.tumblr.com If your ex is constantly trying to talk to you, then this may be a red flag. He is either really obsessed with you or he would like to get together for you. Either way, he still has feelings for you. You can either acknowledge this or deny it.	2016-08-24 19:39:43	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8439711928367615, "perplexity": 1935.275892218856}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982292608.25/warc/CC-MAIN-20160823195812-00003-ip-10-153-172-175.ec2.internal.warc.gz"}
https://ieeexplore.ieee.org/xpl/tocresult.jsp?reload=true&isnumber=5613115&punumber=7361	# IEEE Sensors Journal ## Filter Results Displaying Results 1 - 25 of 42 • ### [Front cover] Publication Year: 2011, Page(s): C1 \| PDF (131 KB) • ### IEEE Sensors Journal publication information Publication Year: 2011, Page(s): C2 \| PDF (37 KB) Publication Year: 2011, Page(s):1 - 2 \| PDF (50 KB) • ### Electroactive Polymer “Artificial Muscle” Operable in Ultra-High Hydrostatic Pressure Environment Publication Year: 2011, Page(s):3 - 4 Cited by: Patents (3) \| \| PDF (1384 KB) \| HTML Transducers for high-power sonars, an important tool for undersea exploration and monitoring, may be required to work in deep water where pressures are higher than several tens of MPa. In contrast with the piezoelectric devices commonly used as high-power sonars for seabed resource exploration, electroactive polymers offer the benefits of high coupling efficiency, low cost, and the ability to form... 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View full abstract» • ### Fuzzy Diagnosis Method for Rotating Machinery in Variable Rotating Speed Publication Year: 2011, Page(s):23 - 34 Cited by: Papers (20) \| \| PDF (709 KB) \| HTML In order to effectively diagnose faults for rotating machinery in the variable rotating speed, a novel diagnosis method is proposed based on time-frequency analysis techniques, the automatic feature extraction method, and fuzzy inference. The diagnosis sensitivities of three time-frequency analysis methods, namely, the short-time Fourier transform (STFT), wavelet analysis (WA), and the pseudo-Wign... View full abstract» • ### Denoising by Singular Value Decomposition and Its Application to Electronic Nose Data Processing Publication Year: 2011, Page(s):35 - 44 Cited by: Papers (44) \| \| PDF (824 KB) \| HTML This paper analyzes the role of singular value decomposition (SVD) in denoising sensor array data of electronic nose systems. It is argued that the SVD decomposition of raw data matrix distributes additive noise over orthogonal singular directions representing both the sensor and the odor variables. The noise removal is done by truncating the SVD matrices up to a few largest singular value compone... View full abstract» • ### A Robust, Adaptive, Solar-Powered WSN Framework for Aquatic Environmental Monitoring Publication Year: 2011, Page(s):45 - 55 Cited by: Papers (94) \| \| PDF (1686 KB) \| HTML The paper proposes an environmental monitoring framework based on a wireless sensor network technology characterized by energy harvesting, robustness with respect to a large class of perturbations and real-time adaptation to the network topology. The fully designed and developed ad hoc system, based on clusters relying on a star topology, encompasses a sensing activity, a one-step local transmissi... View full abstract» • ### Passive Detection of Nitrogen Dioxide Gas by Relative Resistance Monitoring of Iron (II) Phthalocyanine Thin Films Publication Year: 2011, Page(s):56 - 61 Cited by: Papers (2) \| \| PDF (703 KB) \| HTML Metal-substituted phthalocyanine (MPc) thin films have been well documented as sensitive materials for detection of nitrogen dioxide (NO2) gas. The mechanism for detection is such that a MPc thin film acting as the electron donor possesses a strong chemical adsorption affinity towards NO2 molecules acting as electron acceptors. The resulting charge-carrier complex formed sign... View full abstract» • ### Noninvasive Monitoring of Polymer Curing Reactions by Dielectrometry Publication Year: 2011, Page(s):62 - 70 Cited by: Papers (5) \| \| PDF (1530 KB) \| HTML A microwave sensor system for the noninvasive monitoring of the curing process of a thermoset material placed inside a metallic mold is described. The microwave sensor is designed as an open-ended coaxial resonator with a curved surface adapted to the mold inner shape. The analysis of the microwave resonator comprises a recently developed method for deembedding the effect of coupling network in ov... View full abstract» • ### A Null-Buoyancy Thermal Flow Meter With Potential Application to the Measurement of the Hydraulic Conductivity of Soils Publication Year: 2011, Page(s):71 - 77 Cited by: Papers (3) \| \| PDF (1035 KB) \| HTML A null-buoyancy thermal flow sensor is described; it is designed specifically for the measurement of very slow downward fluid flows in a vertical pipe in which a glass-rod thermistor is concentrically located. Sensor power dissipation in this thermistor is adjusted so that the upward thrust of the buoyant thermal plume from the warm thermistor sensor exactly counterbalances the downward bulk fluid... 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The resultant system is a software-defined unit, which can be used for range measurements, radar imaging, and data communications. Range reconstructions were performed for ranges up to 4 m using trihedral corner reflectors with approximat... View full abstract» • ### A Low-Cost Electromagnetic Generator for Vibration Energy Harvesting Publication Year: 2011, Page(s):107 - 113 Cited by: Papers (29) \| \| PDF (928 KB) \| HTML This paper reports on a low-cost high-performance generator, which is based on a hybrid approach that uses polymethyl methalcrylate and electrodeposited foil to convert mechanical vibration into electrical power based on Faraday's law of magnetic induction. The generator is equipped with four wire-wound micro-coils that can be used separately or connected together depending on the voltage and elec... View full abstract» • ### A Fully Integrated CMOS Accelerometer Using Bondwire Inertial Sensing Publication Year: 2011, Page(s):114 - 122 Cited by: Papers (12) \| Patents (1) \| \| PDF (962 KB) \| HTML This paper presents the design, implementation, and characterization of a fully integrated accelerometer using a bondwire inertial sensor. The accelerometer was implemented in a standard CMOS process without microelectromechanical processing. The system consists of a gold and aluminum bondwire inertial sensor and readout circuitry. Finite-element analysis was used to characterize the mechanical pe... View full abstract» • ### Design and Construction of a Rogowski Coil for Measuring Wide Pulsed Current Publication Year: 2011, Page(s):123 - 130 Cited by: Papers (38) \| \| PDF (993 KB) \| HTML In this paper, the design, installation, and performance of a Rogowski coil are presented. Based on the lumped-element model of Rogowski coil, the low-frequency distortion of wide pulsed current measurement is studied. The optimal damping resistance of the external-integrating Rogowski coil is obtained under the sinusoidal steady-state excitation. The amplitude-frequency characteristics of measuri... View full abstract» • ### Smart Reset Control for Wide-Dynamic-Range LWIR FPAs Publication Year: 2011, Page(s):131 - 136 Cited by: Papers (6) \| Patents (1) \| \| PDF (513 KB) \| HTML A new readout circuit involving a pixel-level reset control was studied for 2-D long-wavelength infrared (LWIR) focal plane arrays. The integration time of each pixel can be optimized individually and automatically. Hence, the readout circuit has a wide dynamic range and good signal-to-noise ratio (SNR) characteristics. The readout circuit was fabricated with a 0.35-μm 2-poly 4-metal CMOS p... View full abstract» • ### A ${rm Zn}^{2+}$ Optical Sensor and Logic Actuator Using Schiff Base Functionalized Mesoporous Material Publication Year: 2011, Page(s):137 - 141 Cited by: Papers (6) \| \| PDF (907 KB) \| HTML One simple binaphthyl-bridged salicylidene Schiff base (2,2'-bis(3,5-dichloro-2-hydroxybenzylideneamino)-1,1'-binaphthyl (BCHB)) was successfully synthesised and modified into the channel of mesoporous molecular sieve SBA-15, which was functionalized with 3-aminapropyltriethoxysilane, through the hydrogen bond assembly. Detailed characterizations such as X-ray diffraction, transmission electron mi... View full abstract» • ### Low-Frequency Noise in Field-Effect Devices Functionalized With Dendrimer/Carbon- Nanotube Multilayers Publication Year: 2011, Page(s):142 - 149 Cited by: Papers (8) \| \| PDF (1008 KB) \| HTML Low-frequency noise in an electrolyte-insulator-semiconductor (EIS) structure functionalized with multilayers of polyamidoamine (PAMAM) dendrimer and single-walled carbon nanotubes (SWNT) is studied. The noise spectral density exhibits dependence with the power factor of and for the bare and functionalized EIS sensor, respectively. The gate-voltage noise spectral density is practically independent... View full abstract» • ### A High-Performance n-i-p SiCN Homojunction for Low-Cost and High-Temperature Ultraviolet Detecting Applications Publication Year: 2011, Page(s):150 - 154 Cited by: Papers (5) \| \| PDF (924 KB) \| HTML In this paper, ultraviolet (UV) detecting performances of the n-i-p SiCN homojunction prepared on a p-type (100) silicon substrate under room and elevated temperatures were studied. We analyze the morphology and structure of the crystalline SiCN film on Si first and then examine responses of the sensors to UV light by measurement of photo/dark current ratio with and without the irradiation of a 25... View full abstract» • ### A 2-DOF MEMS Ultrasonic Energy Harvester Publication Year: 2011, Page(s):155 - 161 Cited by: Papers (37) \| \| PDF (1014 KB) \| HTML This paper reports a novel ultrasonic-based wireless power transmission technique that has the potential to drive implantable biosensors. Compared with commonly used radio-frequency (RF) radiation methods, the ultrasonic power transmission is relatively safe for the human body and does not cause electronic interference with other electronic circuits. To extract ambient kinetic energy with arbitrar... View full abstract» ## Aims & Scope The IEEE Sensors Journal is a peer-reviewed, semi-monthly online journal devoted to sensors and sensing phenomena. Full Aims & Scope ## Meet Our Editors Editor-in-Chief Sandro Carrara École Polytechnique Fédérale de Lausanne (EPFL) Lausanne, CH-1015 Switzerland sandro.carrara@epfl.ch	2018-05-27 16:00:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1723613739013672, "perplexity": 11383.706725309195}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794869272.81/warc/CC-MAIN-20180527151021-20180527171021-00001.warc.gz"}
https://socratic.org/questions/how-do-you-solve-using-the-completing-the-square-method-x-2-8x-13-0-1	# How do you solve using the completing the square method x^2 + 8x + 13 =0? Jul 27, 2016 $- 4 \pm \sqrt{3}$ #### Explanation: ${x}^{2} + 8 x + 13 = 0$ ${x}^{2} + 8 x = - 13$ ${x}^{2} + 8 x + 16 = - 13 + 16 = 3$ ${\left(x + 4\right)}^{2} = 3$ $\left(x + 4\right) = \pm \sqrt{3}$ $x = - 4 \pm \sqrt{3}$	2021-07-31 22:45:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9611037969589233, "perplexity": 1302.5790146666077}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154126.73/warc/CC-MAIN-20210731203400-20210731233400-00090.warc.gz"}
http://math.stackexchange.com/questions/475137/graph-of-the-function-gx-fx-x-given-graph-of-fx	# Graph of the function g(x)=f(x)/x given graph of f(x) Since, from the given graph it seems f(a) and f(b)are equal(or approx. equal since there is no scaling given). Then f(a)/a>f(b)/b as a - Since, from the given graph it seems f(a) and f(b)are equal(or approx. equal since there is no scaling given). Then f(a)/a>f(b)/b as a<b.The only graph that satisfies this is Fig:4. But the answer is given to be (B). Where have I gone wrong? – Rajath Krishna R Aug 24 '13 at 15:36 Depending on the scale, $\frac{1}{x}$ could be close to constant on $[a,b]$, which would explain how Figure 2 could be correct. $$g'(x)=\frac{xf'(x)-f(x)}{x^2}$$ you can see that at $f$'s maximal x-value, $g'$ should be negative. This seems to rule out Fig 4. You've already ruled out Figs 1 and 3, but the reasoning does not apply to Figure 2 because there may be a difference between $g(a)$ and $g(b)$ that is too small to see. You could also rule out Figures 1 and 3 by looking at $g'(b)$. The formula says it should be negative, but in Figures 1 and 3, it's positive.	2016-05-24 10:16:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7690414786338806, "perplexity": 614.0720129785258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049270527.3/warc/CC-MAIN-20160524002110-00046-ip-10-185-217-139.ec2.internal.warc.gz"}
https://www.zora.uzh.ch/id/eprint/180094/	# Measurement of associated production of a $\mathrm {W}$ boson and a charm quark in proton–proton collisions at $\sqrt{s} = 13\,\text {Te}\text {V}$ CMS Collaboration; Canelli, Maria Florencia; Kilminster, Benjamin; Aarrestad, Thea K; Brzhechko, Danyyl; Caminada, Lea; de Cosa, Annapaoloa; Del Burgo, Riccardo; Donato, Silvio; Galloni, Camilla; Hreus, Tomas; Leontsinis, Stefanos; Mikuni, Vinicius Massami; Neutelings, Izaak; Rauco, Giorgia; Robmann, Peter; Salerno, Daniel; Schweiger, Korbinian; Seitz, Claudia; Takahashi, Yuta; Wertz, Sebastien; Zucchetta, Alberto; et al (2019). Measurement of associated production of a $\mathrm {W}$ boson and a charm quark in proton–proton collisions at $\sqrt{s} = 13\,\text {Te}\text {V}$. European Physical Journal C - Particles and Fields, C79(3):269. ## Abstract Measurements are presented of associated production of a $\mathrm {W}$ boson and a charm quark ($\mathrm {W}+\mathrm {c}$) in proton–proton collisions at a center-of-mass energy of 13 $\,\text {Te}\text {V}$. The data correspond to an integrated luminosity of 35.7 $\,\text {fb}^{-1}$ collected by the CMS experiment at the CERN LHC. The $\mathrm {W}$ bosons are identified by their decay into a muon and a neutrino. The charm quarks are tagged via the full reconstruction of ${\mathrm {D}^{}(2010)^{\pm }}$ mesons that decay via ${\mathrm {D}^{}(2010)^{\pm }}\rightarrow \mathrm {D}^0 + {\pi ^{\pm }}\rightarrow \mathrm {K}^{\mp } + {\pi ^{\pm }}+ {\pi ^{\pm }}$. A cross section is measured in the fiducial region defined by the muon transverse momentum $p_{\mathrm {T}} ^{\mu } > 26\,\text {Ge}\text {V}$, muon pseudorapidity $\|\eta ^{\mu } \| < 2.4$, and charm quark transverse momentum $p_{\mathrm {T}} ^{\mathrm {c}} > 5\,\text {Ge}\text {V}$. The inclusive cross section for this kinematic range is $\sigma (\mathrm {W}+\mathrm {c})=1026\pm 31\,\text {(stat)} \begin{array}{c} +76\\ -72 \end{array}\,\text {(syst)} \text { pb}$. The cross section is also measured differentially as a function of the pseudorapidity of the muon from the $\mathrm {W}$ boson decay. These measurements are compared with theoretical predictions and are used to probe the strange quark content of the proton. ## Abstract Measurements are presented of associated production of a $\mathrm {W}$ boson and a charm quark ($\mathrm {W}+\mathrm {c}$) in proton–proton collisions at a center-of-mass energy of 13 $\,\text {Te}\text {V}$. The data correspond to an integrated luminosity of 35.7 $\,\text {fb}^{-1}$ collected by the CMS experiment at the CERN LHC. The $\mathrm {W}$ bosons are identified by their decay into a muon and a neutrino. The charm quarks are tagged via the full reconstruction of ${\mathrm {D}^{}(2010)^{\pm }}$ mesons that decay via ${\mathrm {D}^{}(2010)^{\pm }}\rightarrow \mathrm {D}^0 + {\pi ^{\pm }}\rightarrow \mathrm {K}^{\mp } + {\pi ^{\pm }}+ {\pi ^{\pm }}$. A cross section is measured in the fiducial region defined by the muon transverse momentum $p_{\mathrm {T}} ^{\mu } > 26\,\text {Ge}\text {V}$, muon pseudorapidity $\|\eta ^{\mu } \| < 2.4$, and charm quark transverse momentum $p_{\mathrm {T}} ^{\mathrm {c}} > 5\,\text {Ge}\text {V}$. The inclusive cross section for this kinematic range is $\sigma (\mathrm {W}+\mathrm {c})=1026\pm 31\,\text {(stat)} \begin{array}{c} +76\\ -72 \end{array}\,\text {(syst)} \text { pb}$. The cross section is also measured differentially as a function of the pseudorapidity of the muon from the $\mathrm {W}$ boson decay. These measurements are compared with theoretical predictions and are used to probe the strange quark content of the proton. ## Statistics ### Citations Dimensions.ai Metrics 8 citations in Web of Science® 8 citations in Scopus® ### Altmetrics Detailed statistics	2021-03-08 00:56:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9212229251861572, "perplexity": 1889.6484610455075}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381230.99/warc/CC-MAIN-20210307231028-20210308021028-00158.warc.gz"}