url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
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https://answerbun.com/tex-latex/button-in-the-bottom-of-all-pages-to-return-back-to-table-of-content/ | # Button in the bottom of all pages to return back to table of content
TeX - LaTeX Asked by Sidi Mohamed Merzougui on December 24, 2020
As the title said, I want to obtain Somthing like this, a button that send me back to the
toc :
The following might get you started. Just replace example-image with an image file of your button:
documentclass{article}
usepackage{blindtext} % just for dummy contents
usepackage{tikz}
usepackage{eso-pic}
usepackage{hyperref}
begin{document}
begin{tikzpicture}[remember picture,overlay]
node [rectangle, anchor=center, yshift=2cm]
(boxthepage) at
end{tikzpicture}}
phantomsection
hypertarget{mytableofcontents}{}
tableofcontents
blinddocument
end{document}
Correct answer by leandriis on December 24, 2020
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https://warwick.ac.uk/fac/sci/physics/research/astro/research/discs/news/ | # Research News & Highlights
Select tags to filter on
## Velocity-imaging the rapidly precessing planetary disc around the white dwarf HE 1349-2305 using Doppler tomography
##### Christopher J. Manser, Erik Dennihy, Boris T. Gänsicke, John H. Debes, Nicola P. Gentile Fusillo, J. J. Hermes, Mark Hollands, Paula Izquierdo, B. C. Kaiser, T. R. Marsh, Joshua S. Reding, Pablo Rodríguez-Gil, Dimitri Veras, David J. Wilson
The presence of planetary material in white dwarf atmospheres, thought to be accreted from a dusty debris disc produced via the tidal disruption of a planetesimal, is common. Approximately five per cent of these discs host a co-orbital gaseous component detectable via emission from atomic transitions - usually the 8600 Angstrom CaII triplet. These emission profiles can be highly variable in both morphology and strength. Furthermore, the morphological variations in a few systems have been shown to be periodic, likely produced by an apsidally precessing asymmetric disc. Of the known gaseous debris discs, that around HE1349-2305 has the most rapidly evolving emission line morphology, and we present updated spectroscopy of the CaII triplet of this system. The additional observations show that the emission line morphologies vary periodically and consistently, and we constrain the period to two aliases of 459±3d and 502±3d. We produce images of the CaII triplet emission from the disc in velocity space using Doppler tomography - only the second such imaging of a white dwarf debris disc. We suggest that the asymmetric nature of these velocity images is generated by gas moving on eccentric orbits with radially-dependent excitation conditions via photo-ionisation from the white dwarf. We also obtained short-cadence (~ 4 min) spectroscopy to search for variability on the time-scale of the disc's orbital period (~ hours) due to the presence of a planetesimal, and rule out variability at a level of ~ 1.4 per cent.
Mon 11 Oct 2021, 00:00 | Tags: White Dwarf Discs
## White dwarf planetary debris dependence on physical structure distributions within asteroid belts
##### Catriona H. McDonald, Dimitri Veras
White dwarfs which exhibit transit signatures of planetary debris and accreted planetary material provide exceptional opportunities to probe the material composition and dynamical structure of planetary systems. Although previous theoretical work investigating the role of minor body disruption around white dwarfs has focussed on spherical bodies, Solar System asteroids can be more accurately modelled as triaxial ellipsoids. Here we present an analytical framework to identify the type of disruption (tidal fragmentation, total sublimation or direct impact) experienced by triaxial asteroids approaching white dwarfs on extremely eccentric (e ~ 1) orbits. This framework is then used to identify the outcomes for simplified Main belt analogues of 100 bodies across five different white dwarf temperatures. We also present an empirical relationship between cooling age and effective temperature for both DA and DB white dwarfs to identify the age of the white dwarfs considered here. We find that using a purely spherical shape model can underestimate the physical size and radial distance at which an asteroid is subjected to complete sublimation, and these differences increase with greater elongation of the body. Contrastingly, fragmentation always occurs in the largest semi-axis of a body and so can be modelled by a sphere of that radius. Both fragmentation and sublimation are greatly affected by the body's material composition, and hence by the composition of their progenitor asteroid belts. The white dwarf temperature, and hence cooling age, can affect the expected debris distribution: higher temperatures sublimate large elongated asteroids, and cooler temperatures accommodate more direct impacts.
Tue 06 Jul 2021, 00:00 | Tags: White Dwarf Discs
## A review: planetary systems around white dwarfs
##### Dimitri Veras
White dwarf planetary science is a rapidly growing field of research featuring a diverse set of observations and theoretical explorations. Giant planets, minor planets, and debris discs have all been detected orbiting white dwarfs. The innards of broken-up minor planets are measured on an element-by-element basis, providing a unique probe of exoplanetary chemistry. Numerical simulations and analytical investigations trace the violent physical and dynamical history of these systems from au-scale distances to the immediate vicinity of the white dwarf, where minor planets are broken down into dust and gas and are accreted onto the white dwarf photosphere. Current and upcoming ground-based and space-based instruments are likely to further accelerate the pace of discoveries.
Fri 11 Jun 2021, 18:00 | Tags: White Dwarf Discs
## The post-main-sequence fate of the HR 8799 planetary system
##### Dimitri Veras, Sasha Hinkley
The noteworthy four-planet HR 8799 system teeters on the brink of gravitational instability and contains an A-type host star which is characteristic of the progenitors of the majority of known white dwarf planetary system hosts. Gozdziewski and Migaszewski (2020) have demonstrated that the system can retain all four planets for at least 1 Gyr along the main sequence if the planets evolve within an externally unperturbed 8:4:2:1 mean motion resonance configuration. Here we propagate forward their most stable fit beyond the main sequence, and incorporate external effects from Galactic tides and stellar flybys. We find that (i) giant branch mass loss always breaks the resonance, and usually triggers the ejection of two of the planets, (ii) stellar flybys and Galactic tides rarely break the resonance during the main-sequence and giant branch phases, but play a crucial role in determining the final planetary configurations around the eventual white dwarf host star, and (iii) the meanderings of the surviving planets vary significantly, occupying regions from under 1 au to thousands of au. The ubiquitous survival of at least one planet and the presence of the debris discs in the system should allow for dynamical pathways for the white dwarf to be metal-polluted.
Wed 05 May 2021, 00:00 | Tags: White Dwarf Discs
## ALMA imaging of the M-dwarf Fomalhaut C's debris disc
##### Patrick F. Cronin-Coltsmann, Grant M. Kennedy, Paul Kalas, Julien Milli, Cathie J. Clarke, Gaspard Duchêne, Jane Greaves, Samantha M. Lawler, Jean-François Lestrade, Brenda C. Matthews, Andrew Shannon, Mark C. Wyatt
Fomalhaut C (LP 876-10) is a low mass M4V star in the intriguing Fomalhaut triple system and, like Fomalhaut A, possesses a debris disc. It is one of very few nearby M-dwarfs known to host a debris disc and of these has by far the lowest stellar mass. We present new resolved observations of the debris disc around Fomalhaut C with the Atacama Large Millimetre Array which allow us to model its properties and investigate the system's unique history. The ring has a radius of 26 au and a narrow full width at half maximum of at most 4.2 au. We find a 3σ upper limit on the eccentricity of 0.14, neither confirming nor ruling out previous dynamic interactions with Fomalhaut A that could have affected Fomalhaut C's disc. We detect no 12CO J=3-2 emission in the system and do not detect the disc in scattered light with HST/STIS or VLT/SPHERE. We find the original Herschel detection to be consistent with our ALMA model's radial size. We place the disc in the context of the wider debris disc population and find that its radius is as expected from previous disc radius-host luminosity trends. Higher signal-to-noise observations of the system would be required to further constrain the disc properties and provide further insight to the history of the Fomalhaut triple system as a whole.
Tue 27 Apr 2021, 00:00 | Tags: Debris Discs
## Hiding Signatures of Gravitational Instability in Protoplanetary Discs with Planets
##### Sahl Rowther, Farzana Meru, Grant M. Kennedy, Rebecca Nealon, Christophe Pinte
We carry out three-dimensional smoothed particle hydrodynamics simulations to show that a migrating giant planet strongly suppresses the spiral structure in self-gravitating disks. We present mock Atacama Large Millimeter/submillimeter Array (ALMA) continuum observations that show that in the absence of a planet, spiral arms due to gravitational instability are easily observed. Whereas in the presence of a giant planet, the spiral structures are suppressed by the migrating planet resulting in a largely axisymmetric disk with a ring and gap structure. Our modeling of the gas kinematics shows that the planet's presence could be inferred, for example, using optically thin 13C16O. Our results show that it is not necessary to limit the gas mass of disks by assuming high dust-to-gas mass ratios in order to explain a lack of spiral features that would otherwise be expected in high-mass disks.
Thu 26 Nov 2020, 00:00 | Tags: Protoplanetary Discs
## Spirals, shadows and precession in HD 100453 - II. The hidden companion
##### Rebecca Nealon, Nicolás Cuello, Jean-François Gonzalez, Gerrit van der Plas, Christophe Pinte, Richard Alexander, François Ménard, Daniel Price
The protoplanetary disc HD 100453 exhibits a curious combination of spirals, shadows, and a relative misalignment between the observed outer disc and inferred inner disc. This disc is accompanied by a secondary star on a bound orbit exterior to the disc. In our companion paper, the orbit of the secondary was shown to be misaligned by 61° to the plane of the outer disc. Here, we investigate the properties of the inner companion and the origin of the misalignment between the inner and outer discs. In our proposed model, the misalignment observed between the outer and inner disc arises naturally as a result of the misaligned outer companion driving the outer disc to precess more rapidly than the inner disc.
Tue 01 Sep 2020, 00:00 | Tags: Protoplanetary Discs
## Planet Migration in Self-Gravitating Discs: Survival of Planets
##### Sahl Rowther, Farzana Meru
We carry out three-dimensional SPH simulations to study whether planets can survive in self-gravitating protoplanetary discs. The discs modelled here use a cooling prescription that mimics a real disc which is only gravitationally unstable in the outer regions. We do this by modelling the cooling using a simplified method such that the cooling time in the outer parts of the disc is shorter than in the inner regions, as expected in real discs. We find that both giant (> M_Sat) and low mass (< M_Nep) planets initially migrate inwards very rapidly, but are able to slow down in the inner gravitationally stable regions of the disc without needing to open up a gap. This is in contrast to previous studies where the cooling was modelled in a more simplified manner where regardless of mass, the planets were unable to slow down their inward migration. This shows the important effect the thermodynamics has on planet migration. In a broader context, these results show that planets that form in the early stages of the discs' evolution, when they are still quite massive and self-gravitating, can survive.
Thu 04 Jun 2020, 00:00 | Tags: Protoplanetary Discs
## The liftetimes of planetary debris discs around white dwarfs
##### Dimitri Veras and Kevin Heng
The lifetime of a planetary disc that orbits a white dwarf represents a crucial input parameter into evolutionary models of that system. Here we apply a purely analytical formalism to estimate lifetimes of the debris phase of these discs, before they are ground down into dust or are subject to sublimation from the white dwarf. We compute maximum lifetimes for three different types of white dwarf discs, formed from (I) radiative YORP break-up of exo-asteroids along the giant branch phases at 2-100 au, (II) radiation-less spin-up disruption of these minor planets at $\sim 1.5\phantom{\rule{negativethinmathspace}{0ex}}-\phantom{\rule{negativethinmathspace}{0ex}}4.5$ R, and (III) tidal disruption of minor or major planets within about R. We display these maximum lifetimes as a function of disc mass and extent, constituent planetesimal properties, and representative orbital excitations of eccentricity and inclination. We find that YORP discs with masses of up to 1024 kg live long enough to provide a reservoir of surviving cm-sized pebbles and m- to km-sized boulders that can be perturbed intact to white dwarfs with cooling ages of up to 10 Gyr. Debris discs formed from the spin or tidal disruption of these minor planets or major planets can survive in a steady state for up to, respectively, 1 or 0.01 Myr, although most tidal discs would leave a steady state within about 1 yr. Our results illustrate that dust-less planetesimal transit detections are plausible, and would provide particularly robust evolutionary constraints. Our formalism can easily be adapted to individual systems and future discoveries.
Mon 01 Jun 2020, 00:00 | Tags: White Dwarf Discs
## Heavy metal fragment survives destruction from dead star
##### Chris Manser et al.
Many white dwarf stars show signs of having accreted smaller bodies, implying that they may host planetary systems. A small number of these systems contain gaseous debris discs, visible through emission lines. We report a stable 123.4-minute periodic variation in the strength and shape of the Ca II emission line profiles originating from the debris disc around the white dwarf SDSS J122859.93+104032.9. We interpret this short-period signal as the signature of a solid-body planetesimal held together by its internal strength.
Sat 04 Apr 2020, 00:00 | Tags: White Dwarf Discs | 2021-10-26 12:55:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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": 0.5222301483154297, "perplexity": 3445.0370636207927}, "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/1634323587877.85/warc/CC-MAIN-20211026103840-20211026133840-00717.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-11-cumulative-review-exercises-page-1180/5 | ## Precalculus (6th Edition) Blitzer
The solution of the equation ${{\log }_{4}}\left( {{x}^{2}}-9 \right)-{{\log }_{4}}\left( x+3 \right)=3$ is $67$.
Consider the provided equation, ${{\log }_{4}}\left( {{x}^{2}}-9 \right)-{{\log }_{4}}\left( x+3 \right)=3$ Using, for $a>0$ and $b>0$, ${{\log }_{b}}a-{{\log }_{b}}c={{\log }_{b}}\left( \frac{a}{c} \right)$ \begin{align} & {{\log }_{4}}\left( \frac{{{x}^{2}}-9}{x+3} \right)=3 \\ & {{\log }_{4}}\left( \frac{\left( x-3 \right)\left( x+3 \right)}{x+3} \right)=3 \\ & {{\log }_{4}}\left( x-3 \right)=3 \end{align} Using,if for $a>0$ and $b>0$, ${{\log }_{b}}a=c$, then ${{b}^{c}}=a$ \begin{align} & {{\log }_{4}}\left( x-3 \right)=3 \\ & x-3={{4}^{3}} \\ & x-3=64 \\ & x=67 \end{align} Thus, the solution of the equation ${{\log }_{4}}\left( {{x}^{2}}-9 \right)-{{\log }_{4}}\left( x+3 \right)=3$ is $x=67$ | 2021-06-18 03:53:02 | {"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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 4721.8923929970115}, "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-2021-25/segments/1623487634616.65/warc/CC-MAIN-20210618013013-20210618043013-00177.warc.gz"} |
https://brilliant.org/practice/linear-diophantine-equations-level-3-4-challenges/?subtopic=diophantine-equations&chapter=linear-diophantine-equations | Number Theory
Linear Diophantine Equations: Level 3 Challenges
Solve the following cryptarithm:
$\begin{array} { l l l l l l } & & S & E & N & D \\ +& & M & O & R & E \\ \hline & M & O & N & E & Y \\ \end{array}$
and find the value of $S+E+N+D+M+O+R+Y.$
I am thinking of a four digit positive integer with distinct digits.
Of course, there's a total of $4!-1=23$ ways to rearrange the digits to form a new 4 digit positive integer.
If the sum of these other 23 numbers is 157193, what is the number that I was thinking of?
What is the smallest positive integer that can be written as the sum of 39 positive consecutive integers, the sum of 40 positive consecutive integers, and the sum of 41 positive consecutive integers?
Each circle has three or six neighbors, and the number placed in each blank circle must be the average of its neighbors. What is the largest of the five missing numbers?
Find the number of ordered pairs of positive integer solutions $(m, n)$ for $20m + 12n = 2012.$
× | 2019-12-15 19:43:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.6098616123199463, "perplexity": 259.2876474831082}, "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-2019-51/segments/1575541309137.92/warc/CC-MAIN-20191215173718-20191215201718-00434.warc.gz"} |
http://cms.math.ca/cmb/msc/14F35 | The Verdier Hypercovering Theorem This note gives a simple cocycle-theoretic proof of the Verdier hypercovering theorem. This theorem approximates morphisms $[X,Y]$ in the homotopy category of simplicial sheaves or presheaves by simplicial homotopy classes of maps, in the case where $Y$ is locally fibrant. The statement proved in this paper is a generalization of the standard Verdier hypercovering result in that it is pointed (in a very broad sense) and there is no requirement for the source object $X$ to be locally fibrant. Keywords:simplicial presheaf, hypercover, cocycleCategories:14F35, 18G30, 55U35 | 2015-05-26 07:51:52 | {"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": 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": 0.8282736539840698, "perplexity": 434.56286168348714}, "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-2015-22/segments/1432207928817.29/warc/CC-MAIN-20150521113208-00225-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://ptrrupprecht.github.io/Photon-yield-and-pulse-dispersion/ | # Photon yield and pulse dispersion
This case report was written by Peter Rupprecht in the lab of Rainer Friedrich.
# Technical note / case report
## Pulse dispersion, dielectric mirrors and fluorescence yield: A case report of a two-photon microscope
Peter Rupprecht
Lab of Rainer Friedrich, Friedrich Miescher Institute of Biomedical Research (FMI), Basel, Switzerland
Permanent email: p.t.r.rupprecht+dispersion(at)gmail.com
Key words: dispersion, dielectric mirror, photon yield, two-photon.
### Intended audience
Two-photon microscope users who are keen on understanding more about the technical details and especially about what can go wrong with two-photon microscopes.
### Summary
This case report describes how a two-photon microscope was found to come with a fluorescence yield that was lower than expected; how the underlying cause was found out in a systematic manner; and how the problem was solved. All approaches and solutions are specific for the microscope under question. However, I hope that this report (1) will inspire other people who are troubleshooting or optimizing their microscopes, (2) will help other people better understand two-photon microscopes and the relevance of technical details.
First, I will describe how the problem (too low photon yield) was identified. Before identification of the problem, the same microscope had been used without obvious hints that there was indeed an issue.
Next, I will describe the possible reasons underlying the problem and how the most likely cause (laser pulse dispersion) could be singled out.
Then, I will explain the tests that allowed to understand which optical component caused the laser pulse dispersion (degraded dielectric mirrors).
Finally, I will describe what was done to circumvent the problem and what else can be learnt from this experience.
### Disclaimer and peer review
This case report is not peer-reviewed and will not be submitted for publication in a peer-reviewed journal. If you find any errors or misleading descriptions, or if you think it would be helpful to cite or link to your or someone else's research article or homepage, just send me an (informal) email. I will of course acknowledge your contribution. This report is not a final version and I hope that input from other people will help improve it. Suggestions per email to p.t.r.rupprecht+dispersion(at)gmail.com.
Cite as:
### Quantitative comparison of photon yield across setups
In 2018, I was in the lucky situation to use a two-photon point scanning microscope that I had built myself in 2015 [Rupprecht et al., 2016] and therefore knew by heart. It was a microscope based on resonant scanners for video rate 2D imaging and a remote voice coil motor in the spirit of [Botcherby et al., 2008] for fast z-scanning. It was built on top of a galvo/galvo two-photon scanning Sutter scope built in 2007 and used most of the original components, like the MaiTai laser, the pockels cell, mirrors, (scan/tube) lenses and the dichroic. Therefore, there was no reason to assume there was a problem with any of those components.
The point spread function (PSF) of the microscope (ca. 3-4 μm FWHM in z) was okay, given that the beam underfilled the back aperture of the objective. In 2018, I tried to use the microscope for calcium imaging with the calcium-sensing dye OGB-1, which I injected in the (zebrafish) brain area of interest.
However, at some point I noticed that the amount of signal I could get from this setup (from now on called "setup A"; Fig. 1/left) was low when compared to results with a two-photon point scanning Sutter scope ("setup B"; Fig. 1/middle) that was equally built in 2007, used the same laser and an identical objective, with similar laser power below the objective (ca. 20 mW), and with only slightly better PSF (ca. 3 μm FWHM in z).
To compare the photon yields of the two setups quantitatively, I took advantage of a method suggested on the Labrigger blog (and tested some years ago by myself). This method calculates the gain $$g$$ of the imaging system, i.e., the conversion factor between photon count at the detector and the numerical pixel value saved to the image file. The method does so by exploiting the Poisson statistics (mean value $$\mu$$, variance $$\sigma^2$$) of fluorescent photon arrival at the PMT detector:
\begin{align} g&= \frac{\sigma^2}{\mu} \end{align}
Once determined, the gain factor $$g$$ allows to quantify the number of fluorescence photons arriving at the detector using the pixel values of the image. Mean and variance can be taken over the different pixels of the image of a spatially homogeneous sample (Labrigger post), or over the temporal trace of a spatially inhomogeneous but temporally stable fluorescent sample (my previous test). Here, I used the second method with a temporally stable sample, for which I used a cheap fluorescent plastic slide (Fig. 1/right).
As mentioned in the comments on the Labrigger blog post, this quantification can be contaminated by PMT offsets not accounted for (which I measured very carefully) and by multiplicative noise of the PMT cascade. Multiplicative noise adds up to the Poisson noise and therefore creates additional, non-poisson variance in the data, leading to a systematic error of the gain measurement. However, in this special case, where the same PMT type was used both with setup A and setup B at the same PMT gain setting, this systematic error was the same for both setups and could therefore, in a first approximation, be neglected.
The outcome of this quantitative comparison was devastating, indicating that setup A yielded roughly 8x fewer photons compared to setup B at the same conditions! What could be the reason for this huge difference?
The number of detected photons depends both on the number $$N_{photons}$$ of photons emitted by excited fluorophors and on the efficiency of the detection path. To test whether this low photon yield was due to the detection path, I simply exchanged the detection pathways of the two systems (including the PMTs, the objective, the dichroic and everything in-between). This was only possible because both systems were quasi-identical Sutter scopes, and the complete detection path could be mounted and unmounted as a whole. However, I observed only a minor change of the photon yield (+15-25%), ruling out a major difference of photon collection efficiencies between the two microscopes.
So what about the number of emitted fluorescence photons? $$N_{photons}$$ is influenced by several factors [So et al., 2000]:
\begin{align} N_{photons}&\sim \frac{P_0^2}{\tau_p f_p^2} \frac{\text{NA}^4}{\lambda_{exc}^2}, \end{align}
with the average power $$P_0$$ of the excitation laser, the laser pulse duration $$\tau_p$$, the pulse repetition frequency $$f_p$$, the numerical aperture NA of the system, the excitaton wavelength $$\lambda_{exc}$$, and a couple of factors that are omitted here.
For the two systems, the resolution (reflected by the NA) was roughly the same, as measured by the PSF (see above). Since the very same laser was used for both setups, the pulse repetition rate $$f_p$$ was the same for both setups, around 80 MHz, as was the excitation wavelength, $$\lambda_{exc}$$, at 920 nm. With the average power $$P_0$$ calibrated with a thermal power meter below the objective to be the same for both setups, this left the laser pulse width $$\tau_p$$ as the only remaining possible major difference.
The temporal pulse width of a classical Ti:Sa turnkey laser like the MaiTai (Spectra Physics) is just above 100 femtoseconds (fs) when the beam comes out of the laser. Since the product of temporal pulse width and spectral range cannot be below a physical limit (think of the uncertainty principle), these very short femtosecond pulses are actually colored, with a spectral range of ca. 10 nm. The spectral components, however, behave a bit differently depending on the wavelength, leading for example to chromatic aberrations in an imaging system. But also the temporal pulse shape can be affected since red photons travel faster through glass than blue photons. This dependence of the speed of light on the color of light is called dispersion. Many optical components like lenses or objectives therefore can lead to temporal dispersion of the pulse shape. In a typical two-photon point-scanning setup, the 100 fs-pulses coming out from the Ti:Sa laser will usually be dispersed into 300-600 fs-pulses below the objective. Following the equation above, this results in a 3-6-fold reduction of the fluorescence yield, while the average laser power remains unchanged.
Therefore I measured the pulse width of the laser pulses both right after the laser (or, to be precise, after the pockels cell) and below the objective. Usually, pulse widths are measured using an interferometer and therefore cannot be determined below the objective due to the diverging beam. However, the autocorrelator Carpe (from the company APE) that happened to sit somewhere in a lab cupboard is a device that is designed to perform exactly this task. To describe it very briefly, the Carpe inserts a variable optical delay into the beam path before the microscope, generating two output pulses that are closely spaced in time from one single input pulse. Using the nonlinear dependence of two-photon excitation, a two-photon excitation-based sensor after the microscope (that is, below the objective) can measure the overlap of the two delayed pulses. From the overlap, this device can calculate the pulse width of the original pulse. It is, therefore, a very clever physical implementation of an autocorrelation function (which is a bit broader than the pulse shape).
The device therefore does not directly show the pulse shape, but rather the autocorrelation function of the pulse shape. However, it automatically calculates the underlying pulse width. See the legend in Fig. 3 below for a more detailed explanation.
The Carpe autocorrelator is not super-intuitive to work with (for somebody new to this device), but the APE help service turned out to be very supportive, also for in-depth technical discussions. When I first measured the pulse width below the objective, I immediately knew that something was wrong (Fig. 3/right). Not only was the the pulse quite broad in time; in addition, the autocorrelator showed a non-linear distortion of the pulse shape with two heavy shoulders. Obviously, this would be highly detrimental to the fluorescence yield.
The waveform of the autocorrelation function in Fig. 3 suggests that there is not a single pulse, but two pulses. To illustrate this idea more clearly, Fig. 4 shows on the left side a pair of pulses (spaced by few 100 femtoseconds) and on the right side the resulting autocorrelation function. When the two pulses merge to a single one, the trident autocorrelation transforms into a single Gaussian-like shape.
This illustration hopefully makes it easier to understand what a given autocorrelation function means for the underlying temporal pulse shape.
But where did this unusual double-pulse come from?
### Possible reasons underlying femtosecond laser pulse distortion
After consultation with the confocal microscopy mailing list and with my PhD supervisor, I had collected a couple of candidate reasons for the strange pulse shape:
1. As mentioned already, the autocorrelation function in Fig. 3 could mean that there are two pulses that arrive shortly one after the other, instead of just one single pulse, as illustrated in Fig. 4. This could be due to an optical element or a coating that creates an internal reflection and therefore a second, delayed pulse.
2. The strange pulse measurement could be due to a measurement error or handling error of the Carpe autocorrelator.
3. According to a very experienced microscopy expert, this "pulse on a pedestal" shape of the autocorrelation functions is a "classic of higher order dispersion caused by large amounts of glass" or other optical elements.
4. Another explanation for the double pulse could be that slightly birefringent material could have been used in the pockels cell or in a polarizing beam splitter. Birefringent material consists of an anisotropic crystal that makes light polarized orthogonal and parallel to the so-called optical axis of this crystal travel faster and slower, respectively. This would result in the laser pulse being split up in two pulses with different polarizations that are delayed one with the respect to the other.
### Identification of the underlying problem
###### 1. A double-pulse due to a reflecting interface
As can be seen from the autocorrelation function in Fig. 3 (and as illustrated schematically in Fig. 4), the temporal spacing between the two pulses is around $$\Delta t = 250$$ fs. This permits to calculate the approximate physical distance across which the pulse must be reflected:
\begin{align} \Delta x = \Delta t \cdot c/2 = 250\cdot 10^{-15} \cdot 3\cdot 10^8/2\ m \approx 38\; \mu m \end{align}
Which is much shorter than the width of any optical element like a pockels cell or a lens, and much thicker then the thickness of e.g. a lens coating. This possibility can therefore be ruled out.
###### 2. A measurement error
I contacted an engineer of APE, the company that produces the Carpe autocorrelator. He excluded the possibility of a handling error.
###### 3. Dispersion by large amounts of glass
The setup, as described before [Rupprecht et al., 2016], uses a remote scanning unit, resulting in several centimeters of additional glass in the system. This could potentially lead to strong additional dispersion. I therefore removed all lenses (except for scan lens, tube lens and objective) from the microscope. The resulting pulse width was smaller. The shape, however, remained unchanged. Both scan lens, tube lens and objective were the same for the previously mentioned setup B and were therefore unlikely to be the culprit.
###### 4. A double-pulse due to birefringent material
Pulse-splitting by a birefringent material would mean that the resulting double pulse would consist of two pulses of orthogonal polarization. This means that a polarization filter held into the beam path would be able to block out one of the two pulses, depending on the insertion angle.
I used goggles leftover from a 3D cinema visit as polarizer. Inserting the polarization glasses into the beam path and rotating the filter reduced the total power of the transmitted light but did not change the temporal pulse shape. This ruled out the possibility that birefringeant material resulted in a double-pulse.
###### 5. Seemingly innocuous optical elements
Therefore something else was the culprit - one of those seemingly innocuous optical elements in the beam path. In total, there were 8 lenses and 3 other glass crystal-based optical elements, and in addition many mirrors of several different kinds. Some of the lenses and mirrors (like the tube lens and the scan lens and a couple of mirrors) could not be easily exchanged. Altogether, quite a daunting task to start with ...
To start with, I removed the entire remote scanning unit (described in [Rupprecht et al., 2016], but for this purpose it's just a big amount of glass), consisting of a polarizing beam splitter, three large-aperture Thorlabs achromats and a small gold mirror. This remote unit was inserted into the system just before the xy-scan unit, i.e., just before the "real" microscope beam path.
Upon removal of this unit, the original pulse shape (black in Fig. 6) was slightly changed - apparently due to linear dispersion - but still deformed in a similar way as before (red in Fig. 6). But this revealed everything I needed to know in order to find the culprit. Let's go into the details.
First, the autocorrelation function measured with the remote scan unit removed (red, dashed lines) was very similar to the original one (black, solid line), but compressed in time. This showed that the nonlinear dispersion responsible for the double-pulse must have happened before this point in the beam path. Why? If the nonlinear dispersion had been generated after this point in the beam path, the lag of the second pulse would have been unaffected by insertion or removal of linearly dispersing glass into the beam path (blue in Fig. 6). From these observations and thought experiments follows a straightforward rule to identify optical components that cause nonlinear dispersion with double pulses: insertion of simple glass with linear dispersion before and after the optical element under question.
At this point it was clear that the culprit was before the remote scanning unit in the beam path. Yet, there was basically no optical element before the remote scanning unit - except for mirrors.
In retrospect, it is an obvious case: dielectric mirrors. I sorted it out with help from the confocal microscopy mailing list, and all the relevant details have been summarized already by Labrigger in a blog post. In a nutshell, dielectric mirrors consist of many layers of coatings (Fig. 7) that basically act as interference filters, resulting in the reflection of the laser beam.
The dielectric mirrors in this setup were already older than 10 years. In addition, glue had been applied to the rear side of some of the mirrors. Both effects probably caused an irregular spacing of the interference layers of selected locations of some of the mirrors and therefore a highly nonlinear distortion of the temporal pulse shape. This effect was not due to all of the dielectric mirrors, but only 2 or 3 of them, with minor distortive contributions from the other mirrors. To make things a bit more complicated, the incidence angle onto each mirror mattered as well as the incident polarization, and a mirror that worked nicely for one incidence angle produced strong nonlinear dispersion for a different incidence angle.
As any interference effects, the distortions caused by these mirrors also turned out to be strongly wavelength-dependent. As shown below in Fig. 10, the temporal duration and shape of the laser pulse strongly depends on the wavelength (see again the Labrigger blog post for a bit more detail).
However, this strong dependence on the wavelength also allows to check for these pulse shape deformations with no need for a specialized autocorrelator: the deformation of the pulse shape is simply reflected by the fluorescence yield of a stable sample. I used the above-mentioned green plastic slide to record the fluorescence elicited by laser pulses at different wavelengths for both setups:
Of course, the fluorescence yield also depends on the wavelength because both the two-photon excitation cross section of the fluorophor and the output power of the Ti:Sa laser are wavelength-dependent. However, those dependencies are smooth (as for setup B in Fig. 8) and cannot explain the non-monotonous wavelength-dependence observed (setup A in Fig. 8). The result for setup A indicates that the laser pulse is strongly distorted at around 880 nm and 920 nm.
This simple experiment does not inform about the pulse shapes directly. But it is clear from the spectrum in Fig. 8 that "setup A" has an issue related to strong, nonlinear pulse dispersion.
How can we solve the problem?
### Solving the problem
To solve the problem, I replaced, as suggested by the confocal microsocopy mailing list, all dielectric mirrors with metal (gold) mirrors. Metal mirrors are coated with very few (protective) interference coatings and are therefore not strongly dispersive. They are actually not more expensive than dielectric mirrors, but are often replaced with dielectric mirrors because the latter offer higher reflectances than metal mirrors.
After replacing everything with gold mirrors, the laser pulse was quite long (FWHM of more than 500 fs), and the fluorescence yield was still by far lower in this setup (setup A) than in the previously mentioned setup B. Therefore, I measured the pulse width in this very impressive setup B, and it turned out to be just above 150 fs below the objective! At this point, I realized that setup B also used some old dielectric mirrors, which, however, did not lead to strange pulse-on-pedestal pulse shapes but instead - by chance - resulted in a highly compressed, optimized, short laser pulse. That was unexpected.
To match the superior performance of setup B, I first inserted a prism compressor (again from the company APE), which is designed to add negative dispersion to the laser pulse, ideally resulting in an optimal, short laser pulse at the sample. However, the alignment turned out to be quite tedious. The additional optical path inside of the prism compressor resulted in a diverging beam path, and I finally did not manage to make it work properly for all wavelengths. Plus, it did not seem to be entirely stable over days, and since I did not have much experience with pulse compressors, I would have taken me probably too long to solve this problem properly. Therefore I chose the quick-and-dirty solution: I switched back to dielectric mirrors.
As mentioned earlier, the pulse distortion for these mirrors is strongly wavelength-dependent, and also strongly dependent on the polarization and angle of the incident laser beam with respect to the mirrors. Since I wanted to use the system primarily around 930 nm, I arranged a couple of dielectric mirrors reflecting the laser beam before it entered the microscope. Then, I randomly exchanged mirrors, rotated them or changed the arrangement completely. This went on for several hours, until I arrived at a configuration with the desired short pulse width around 930 nm:
This technique of random mirror optimization turned out to be very efficient and by far less tedious than aligning an old-fashioned prism compressor. (I'd like to mention here that there are also chirped mirrors that can be used for pulse compression, which seem to be a bit easier to work with; Newport, Thorlabs.) I have to admit that this optimization process is only slighty based on an understanding of what happens and how which mirror contributes to pulse shaping, and pretty much based on simple serendipity - but it works.
Here is the (close-to-final) result of this random optimization process. The pulse width at 931 nm was around 180 fs (FWHM). Please use the drop-down menu in Fig. 10 (or arrow keys of your keyboard) to go through the wavelength-dependence of the pulse shapes. Due to the nonlinearities contributed by dielectric mirrors, this is not a Gaussian-like curve any more, but it seems to be very close.
### Conclusion
What I learned from this brief excursion in setup optimization: Dielectric mirrors can dramatically affect the pulse shape of femtosecond lasers (Figs. 3, 6, 10). Dielectric mirrors should be avoided for femtosecond laser pulses in general, especially if they are old; or they should be taken advantage of a) by choosing the best wavelength and/or b) by some sort of random mirror optimization (Fig. 10).
I realized that an autocorrelator can be necessary to understand a microscope based on pulsing lasers. However, recording the wavelength-dependent brightness of a stable object is an alternative source of information about temporal pulse deformations (Fig. 8).
Finally, I have realized that it is possible to work with a setup for years without understanding some of its oddities, and that it can take a lot of time to single down a strange behavior of an existing setup to a specific component or effect. All the more I'm glad that I've returned from this rabbit hole with some lessons learned!
### Acknowledgements
For helpful input and discussions, I'd like to thank Craid Brideau, Michael Giacomelli, Zdenek Svindrych, David Chen and Darry McCoy from the confocal microscopy mailing list, Darcy Peterka, Mateusz Ibek from APE Berlin, as well as Tommaso Caudullo and Rainer Friedrich for comments on an earlier version of this report. I'd also like to thank Andrew York for providing an excellent template for scientific publications via Github pages [York, 2017]. | 2021-06-13 23:04:26 | {"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": 2, "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": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46721652150154114, "perplexity": 1127.3550964461017}, "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-2021-25/segments/1623487611089.19/warc/CC-MAIN-20210613222907-20210614012907-00065.warc.gz"} |
https://docs.generic-mapping-tools.org/latest/supplements/geodesy/velo.html | # velo¶
Plot velocity vectors, crosses, and wedges
## Synopsis¶
gmt velo [ table ] -Jparameters -Rregion [ -Aparameters ] [ -B[p|s]parameters ] [ -Ecolor ] [ -Fcolor ] [ -Gcolor ] [ -L ] [ -N ] [ -Ssymbol/scale[/args ] ] [ -U[stamp] ] [ -V[level] ] [ -Wpen ] [ -X[a|c|f|r][xshift[u]] ] [ -Y[a|c|f|r][yshift[u]] ] [ -dinodata ] [ -eregexp ] [ -hheaders ] [ -iflags ] [ -ttransp ] [ -:[i|o] ] [ --PAR=value ]
Note: No space is allowed between the option flag and the associated arguments.
## Description¶
Reads data values from files [or standard input] and will plot velocity arrows on a map. Most options are the same as for plot, except -S.
## Required Arguments¶
table
One or more ASCII (or binary, see -bi[ncols][type]) data table file(s) holding a number of data columns. If no tables are given then we read from standard input.
-Jparameters (more …)
Select map projection.
-Rwest/east/south/north[/zmin/zmax][+r][+uunit]
west, east, south, and north specify the region of interest, and you may specify them in decimal degrees or in [±]dd:mm[:ss.xxx][W|E|S|N] format Append +r if lower left and upper right map coordinates are given instead of w/e/s/n. The two shorthands -Rg and -Rd stand for global domain (0/360 and -180/+180 in longitude respectively, with -90/+90 in latitude). Set geographic regions by specifying ISO country codes from the Digital Chart of the World using -Rcode1,code2,…[+r|R[incs]] instead: Append one or more comma-separated countries using the 2-character ISO 3166-1 alpha-2 convention. To select a state of a country (if available), append .state, e.g, US.TX for Texas. To specify a whole continent, prepend = to any of the continent codes AF (Africa), AN (Antarctica), AS (Asia), EU (Europe), OC (Oceania), NA (North America), or SA (South America). Use +r to modify the bounding box coordinates from the polygon(s): Append inc, xinc/yinc, or winc/einc/sinc/ninc to adjust the region to be a multiple of these steps [no adjustment]. Alternatively, use +R to extend the region outward by adding these increments instead [no extension]. Alternatively for grid creation, give Rcodelon/lat/nx/ny, where code is a 2-character combination of L, C, R (for left, center, or right) and T, M, B for top, middle, or bottom. e.g., BL for lower left. This indicates which point on a rectangular region the lon/lat coordinate refers to, and the grid dimensions nx and ny with grid spacings via -I is used to create the corresponding region. Alternatively, specify the name of an existing grid file and the -R settings (and grid spacing, if applicable) are copied from the grid. Appending +uunit expects projected (Cartesian) coordinates compatible with chosen -J and we inversely project to determine actual rectangular geographic region. For perspective view (-p), optionally append /zmin/zmax. In case of perspective view (-p), a z-range (zmin, zmax) can be appended to indicate the third dimension. This needs to be done only when using the -Jz option, not when using only the -p option. In the latter case a perspective view of the plane is plotted, with no third dimension.
-S
Selects the meaning of the columns in the data file and the figure to be plotted.
-Sevelscale/confidence/fontsize.
Velocity ellipses in (N,E) convention. velscale sets the scaling of the velocity arrows. This scaling gives inches (unless c, i, or p is appended). confidence sets the 2-dimensional confidence limit for the ellipse, e.g., 0.95 for 95% confidence ellipse. fontsize sets the size of the text in points. The ellipse will be filled with the color or shade specified by the -G option [default transparent]. The arrow and the circumference of the ellipse will be drawn with the pen attributes specified by the -W option. Parameters are expected to be in the following columns:
1,2: longitude, latitude of station (-: option interchanges order) 3,4: eastward, northward velocity (-: option interchanges order) 5,6: uncertainty of eastward, northward velocities (1-sigma) (-: option interchanges order) 7: correlation between eastward and northward components 8: name of station (optional).
-Snbarscale.
Anisotropy bars. barscale sets the scaling of the bars. This scaling gives inches (unless c, i, or p is appended). Parameters are expected to be in the following columns:
1,2: longitude, latitude of station (-: option interchanges order) 3,4: eastward, northward components of anisotropy vector (-: option interchanges order)
-Srvelscale/confidence/fontsize
Velocity ellipses in rotated convention. velscale sets the scaling of the velocity arrows. This scaling gives inches (unless c, i, or p is appended). confidence sets the 2-dimensional confidence limit for the ellipse, e.g., 0.95 for 95% confidence ellipse. fontsize sets the size of the text in points. The ellipse will be filled with the color or shade specified by the -G option [default transparent]. The arrow and the circumference of the ellipse will be drawn with the pen attributes specified by the -W option. Parameters are expected to be in the following columns:
1,2: longitude, latitude, of station (-: option interchanges order) 3,4: eastward, northward velocity (-: option interchanges order) 5,6: semi-major, semi-minor axes 7: counter-clockwise angle, in degrees, from horizontal axis to major axis of ellipse. 8: name of station (optional)
-Swwedgescale/wedgemag.
Rotational wedges. wedgescale sets the size of the wedges in inches (unless c, i, or p is appended). Values are multiplied by wedgemag before plotting. For example, setting wedgemag to 1.e7 works well for rotations of the order of 100 nanoradians/yr. Use -G to set the fill color or shade for the wedge, and -E to set the color or shade for the uncertainty. Parameters are expected to be in the following columns:
1,2: longitude, latitude, of station (-: option interchanges order) 3: rotation in radians 4: rotation uncertainty in radians
-Sxcross_scale
gives Strain crosses. cross_scale sets the size of the cross in inches (unless c, i, or p is appended). Parameters are expected to be in the following columns:
1,2: longitude, latitude, of station (-: option interchanges order) 3: eps1, the most extensional eigenvalue of strain tensor, with extension taken positive. 4: eps2, the most compressional eigenvalue of strain tensor, with extension taken positive. 5: azimuth of eps2 in degrees CW from North.
## Optional Arguments¶
-Aparameters
Modify vector parameters. For vector heads, append vector head size [Default is 9p]. See Vector Attributes for specifying additional attributes.
-B[p|s]parameters (more …)
Set map boundary frame and axes attributes.
-DSigma_scale
can be used to rescale the uncertainties of velocities (-Se and -Sr) and rotations (-Sw). Can be combined with the confidence variable.
-Efill
Sets the color or shade used for filling uncertainty wedges (-Sw) or velocity error ellipses (-Se or -Sr). [If -E is not specified, the uncertainty regions will be transparent.]
-Ffill
Sets the color or shade used for frame and annotation. [Default is black]
-Gfill
Specify color (for symbols/polygons) or pattern (for polygons) [Default is black]. Optionally, specify -Gpicon_size/pattern, where pattern gives the number of the image pattern (1-90) OR the name of a icon-format file. icon_size sets the unit size in inches. To invert black and white pixels, use -GP instead of -Gp. See the CookBook for information on individual patterns.
-L
Draw lines. Ellipses and fault planes will have their outlines drawn using current pen (see -W).
-N
Do NOT skip symbols that fall outside the frame boundary specified by -R. [Default plots symbols inside frame only].
-U[label][+c][+jjust][+odx/dy] (more …)
Draw GMT time stamp logo on plot.
-V[level] (more …)
Select verbosity level [c].
-W
Set pen attributes for velocity arrows, ellipse circumference and fault plane edges. [Defaults: width = default, color = black, style = solid].
-X[a|c|f|r][xshift[u]]
-Y[a|c|f|r][yshift[u]] (more …)
Shift plot origin.
-dinodata (more …)
Replace input columns that equal nodata with NaN.
-e[~]”pattern” | -e[~]/regexp/[i] (more …)
Only accept data records that match the given pattern.
-h[i|o][n][+c][+d][+rremark][+rtitle] (more …)
-icols[+l][+sscale][+ooffset][,][,t[word]] (more …)
Select input columns and transformations (0 is first column, t is trailing text, append word to read one word only).
-t[transp] (more …)
Set transparency level in percent.
-:[i|o] (more …)
Swap 1st and 2nd column on input and/or output.
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option (but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
--PAR=value
Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.
## Vector Attributes¶
Several modifiers may be appended to vector-producing options for specifying the placement of vector heads, their shapes, and the justification of the vector. Below, left and right refers to the side of the vector line when viewed from the start point to the end point of a segment:
+aangle sets the angle of the vector head apex [30].
+b places a vector head at the beginning of the vector path [none]. Optionally, append t for a terminal line, c for a circle, a for arrow [Default], i for tail, A for plain open arrow, and I for plain open tail. Further append l|r to only draw the left or right half-sides of this head [both sides].
+e places a vector head at the end of the vector path [none]. Optionally, append t for a terminal line, c for a circle, a for arrow [Default], i for tail, A for plain open arrow, and I for plain open tail. Further append l|r to only draw the left or right half-sides of this head [both sides].
+g-|fill turns off vector head fill (if -) or sets the vector head fill [Default fill is used, which may be no fill].
+hshape sets the shape of the vector head (range -2/2). Default is controlled by MAP_VECTOR_SHAPE [0].
+l draws half-arrows, using only the left side of specified heads [both sides].
+m places a vector head at the mid-point the vector path [none]. Append f or r for forward or reverse direction of the vector [forward]. Optionally, append t for a terminal line, c for a circle, a for arrow [Default], i for tail, A for plain open arrow, and I for plain open tail. Further append l|r to only draw the left or right half-sides of this head [both sides]. Cannot be combined with +b or +e.
+nnorm scales down vector attributes (pen thickness, head size) with decreasing length, where vector plot lengths shorter than norm will have their attributes scaled by length/norm [arrow attributes remains invariant to length]. For Cartesian vectors specify a length in plot units, while for geovectors specify a length in km.
+o[plon/plat] specifies the oblique pole for the great or small circles. Only needed for great circles if +q is given. If no pole is appended then we default to the north pole.
+p[-][pen] sets the vector pen attributes. If pen has a leading - then the head outline is not drawn. [Default pen is half the width of stem pen, and head outline is drawn]
+q means the input angle, length data instead represent the start and stop opening angles of the arc segment relative to the given point. See +o to specify a specific pole for the arc [north pole].
+r draws half-arrows, using only the right side of specified heads [both sides].
+t[b|e]trim[unit] will shift the beginning or end point (or both) along the vector segment by the given trim; append suitable unit (c, i, or p). If the modifiers b|e are not used then trim may be two values separated by a slash, which is used to specify different trims for the beginning and end. Positive trims will shorted the vector while negative trims will lengthen it [no trim].
In addition, all but circular vectors may take these modifiers:
+jjust determines how the input x,y point relates to the vector. Choose from beginning [default], end, or center.
+s means the input angle, length are instead the x, y coordinates of the vector end point.
Finally, Cartesian vectors may take these modifiers:
+zscale[unit] expects input dx,dy vector components and uses the scale to convert to polar coordinates with length in given unit.
## Examples¶
Note: Since many GMT plot examples are very short (i.e., one module call between the gmt begin and gmt end commands), we will often present them using the quick modern mode GMT Modern Mode One-line Commands syntax, which simplifies such short scripts.
The following should make big red arrows with green ellipses, outlined in red. Note that the 39% confidence scaling will give an ellipse which fits inside a rectangle of dimension Esig by Nsig.
gmt velo << END -h2 -R-10/10/-10/10 -W0.25p,red -Ggreen -L -Se0.2/0.39/18 -B1g1 -Jx0.4/0.4 -A1c+p3p+e -V -pdf test
#Long. Lat. Evel Nvel Esig Nsig CorEN SITE
#(deg) (deg) (mm/yr) (mm/yr)
0. -8. 0.0 0.0 4.0 6.0 0.500 4x6
-8. 5. 3.0 3.0 0.0 0.0 0.500 3x3
0. 0. 4.0 6.0 4.0 6.0 0.500
-5. -5. 6.0 4.0 6.0 4.0 0.500 6x4
5. 0. -6.0 4.0 6.0 4.0 -0.500 -6x4
0. -5. 6.0 -4.0 6.0 4.0 -0.500 6x-4
END
This example should plot some residual rates of rotation in the Western Transverse Ranges, California. The wedges will be dark gray, with light gray wedges to represent the 2-sigma uncertainties.
gmt velo << END -Sw0.4/1.e7 -W0.75p -Gdarkgray -Elightgray -h1 -D2 -Jm2.2i -R240./243./32.5/34.75 -Baf -BWeSn -pdf test
241.4806 34.2073 5.65E-08 1.17E-08
241.6024 34.4468 -4.85E-08 1.85E-08
241.0952 34.4079 4.46E-09 3.07E-08
241.2542 34.2581 1.28E-07 1.59E-08
242.0593 34.0773 -6.62E-08 1.74E-08
241.0553 34.5369 -2.38E-07 4.27E-08
241.1993 33.1894 -2.99E-10 7.64E-09
241.1084 34.2565 2.17E-08 3.53E-08
END
Kurt L. Feigl, Department of Geology and Geophysics at University of Wisconsin-Madison, Madison, Wisconsin, USA | 2019-11-13 07:54:01 | {"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": 0.6288319826126099, "perplexity": 7984.581166119044}, "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-2019-47/segments/1573496666229.84/warc/CC-MAIN-20191113063049-20191113091049-00473.warc.gz"} |
http://www.maths.kisogo.com/index.php?title=Equivalent_statements_to_compactness_of_a_metric_space | # Equivalent statements to compactness of a metric space
## Theorem statement
Given a metric space [ilmath](X,d)[/ilmath], the following are equivalent[1][Note 1]:
1. [ilmath]X[/ilmath] is compact
2. Every sequence in [ilmath]X[/ilmath] has a subsequence that converges (AKA: having a convergent subsequence)
3. [ilmath]X[/ilmath] is totally bounded and complete
## Proof
[ilmath]1)\implies 2)[/ilmath]: [ilmath]X[/ilmath] is compact [ilmath]\implies[/ilmath] [ilmath]\forall(a_n)_{n=1}^\infty\subseteq X\ \exists[/ilmath] a sub-sequence [ilmath](a_{k_n})_{n=1}^\infty[/ilmath] that coverges in [ilmath]X[/ilmath]
We see that every sequence in a compact space has a convergent subsequence.
[ilmath]2)\implies 3)[/ilmath]: Suppose for all sequences [ilmath](x_n)_{n=1}^\infty\subseteq X[/ilmath] that [ilmath] ({ x_n })_{ n = 1 }^{ \infty } [/ilmath] has a convergent subsequence [ilmath]\implies[/ilmath] [ilmath](X,d)[/ilmath] is a complete metric space and is totally bounded
Proof of completeness:
To show [ilmath](X,d)[/ilmath] is complete we must show that every Cauchy sequence converges. To do this:
Proof that [ilmath](X,d)[/ilmath] is totally bounded
TODO: Do this
TODO: Rest, namely: [ilmath]3\implies 1[/ilmath]
## Notes
1. To say statements are equivalent means we have one [ilmath]\iff[/ilmath] one of the other(s) | 2022-12-01 19:10:04 | {"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": 0.9476094841957092, "perplexity": 7273.665234918841}, "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/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00497.warc.gz"} |
https://grindskills.com/random-walk-kings-on-a-chessboard/ | # Random walk: kings on a chessboard
I have a question about the random walk of two kings in a 3×3 chessboard.
Each king is moving randomly with equal probability on this chessboard – vertically, horizontally and diagonally. Τhe two kings are moving independently from each other in the same chessboard. Both of them start in the same square, and then they move independently.
How could we find the probability in time $n$ both of them are in the same square, as $n$ goes to infinity?
Let’s exploit the symmetry to simplify the calculations.
The chessboard and its moves remain the same when the board is reflected vertically, horizontally, or diagonally. This decomposes its nine squares into three types, their orbits under this symmetry group. Correspondingly, each king can be in one of three “states”: a corner square ($C$), an edge square ($E$), or the central (“middle”) square ($M$). (A state ignores which particular square a king is on and tracks only its equivalence class under the group of symmetries.)
The following results are immediate:
• From a corner square, there are two transitions to edge squares and one transition to a middle square. Because the three transitions are equiprobable,
This gives a row $(0, 2/3, 1/3)$ in a transition matrix for the states $(C, E, M)$.
• From an edge square there are two transitions to corner squares, two to other edge squares, and one to the middle square. This gives a second row $(2/5, 2/5, 1/5)$ in a transition matrix.
• From the middle square there are four transitions to corner squares and four to middle squares. The third row of a transition matrix therefore is $(4/8, 4/8, 0) = (1/2, 1/2, 0)$.
In this graph representing this Markov chain, transition probabilities are represented both by edge thickness and color:
By inspection or otherwise, we find that a left eigenvector of its transition matrix
is $\omega = (3, 5, 2)^\prime$. This claim is easily checked by performing the multiplication: $\omega \mathbb{P} = 1 \omega.$ The eigenvalue manifestly is $1$. Because all states are connected, $\omega$ gives the limiting probabilities of each king being in each state; we only need to rescale its components to sum to unity:
(This is where we reap the benefits of exploiting the symmetry: instead of working with a nine by nine matrix of $81$ elements we only have to compute with a three by three matrix of $9$ elements. The reduction of the problem from nine states to three paid off quadratically by reducing the computational effort by a factor of $(9/3)^2 = 9$.)
The (limiting) chance that both kings are in a state $s$ of (limiting) probability $\omega_s$ is $\omega_s^2$ because the kings move independently. The chance that both kings are in the same cell is found by conditioning on the state: by symmetry, each cell in a given state has the same limiting probability, so if both kings are found in a state $s$ having $k_s$ cells, the chance they are both in the same cell is $1/k_s$. Whence the solution is | 2022-09-24 22:49:58 | {"extraction_info": {"found_math": true, "script_math_tex": 22, "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": 0.7286266088485718, "perplexity": 460.6802690948008}, "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-2022-40/segments/1664030333541.98/warc/CC-MAIN-20220924213650-20220925003650-00368.warc.gz"} |
https://leanprover-community.github.io/archive/stream/113489-new-members/topic/conceptual.20mathematical.20primer.20for.20tactics.3F.html | ## Stream: new members
### Topic: conceptual mathematical primer for tactics?
#### Chris M (Jun 16 2020 at 04:10):
I haven't used tactics yet in Lean, and starting to. Looking at the tutorial, some of them seem unnatural to me, and it's not "clicking" yet for me. Can you point to a practice that mathematicians perform within informal mathematical proofs, to which tactics are analogous? Is it possible to say "tactics are the formal version of ...."?
#### Jalex Stark (Jun 16 2020 at 06:29):
tactics are programs that build proof terms
#### Jalex Stark (Jun 16 2020 at 06:29):
in informal math we don't build proof terms, we argue that we could build a proof term if we tried
#### Jalex Stark (Jun 16 2020 at 06:30):
norm_num is a like a mathematician's a short calculation shows...
#### Utensil Song (Jun 16 2020 at 07:18):
I think it's a good idea to have such conceptual mathematical primer for tactics, I'll try to merge this idea into the cheat sheet idea here .
#### Matt Earnshaw (Jun 16 2020 at 15:52):
you may find it worthwhile to read at least the intro of Milner's paper that introduced the tactic idea, which gives a nice informal explanation https://royalsocietypublishing.org/doi/10.1098/rsta.1984.0067
If there are specific tactics that trouble you, feel free to ask about them. Some perhaps too obvious examples would be apply as recognising that when A -> B and we want to prove B then it suffices to prove A, and intro as introducing an arbitrary x : X when we want to prove a forall x : X
Last updated: May 13 2021 at 00:41 UTC | 2021-05-13 00:53:38 | {"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": 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": 0.45372673869132996, "perplexity": 2441.757834052417}, "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/1620243991413.30/warc/CC-MAIN-20210512224016-20210513014016-00535.warc.gz"} |
https://math.stackexchange.com/questions/1544408/mathematicians-who-overcame-academic-failure-to-achieve-success/1544452 | # Mathematicians who overcame academic failure to achieve success [closed]
Does anyone have any story of mathematicians who overcame "academic failure" or setbacks to achieve success later as a result of their perseverance? This is a soft question, that hopefully can inspire aspiring students.
New edit: I am especially interested in academic failure (e.g. failure of exams, failure in proof/ wrong proof, failure in getting academic jobs). This is to narrow down the question so it is not too broad. There is another related question on blind/disabled mathematicians which is very good: Who are some blind or otherwise disabled mathematicians who have made important contributions to mathematics?
My ideal accepted answer is a relatively less well known answer (so that we all learn something new), supported by factual evidence (e.g. a hyperlink to a page or a quote).
Some that I can list are:
1) Zhang Yitang, who worked in Subway (arguably a sort of a setback) but later proved a result related to the Twin Prime Conjecture.
2) Robion Kirby, who failed his oral Ph.D. qualifying examination (http://www-groups.dcs.st-and.ac.uk/history/Biographies/Kirby.html) but later proved the "torus trick".
Thanks! (Hope this question is on topic for Math Stackexchange..)
## closed as primarily opinion-based by Qiaochu Yuan, user149792, user642796Nov 25 '15 at 9:07
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
• I like this question, and find it interesting - However, do you think you can accept after only an hour of posting? (Though I do like the answer) – Chinny84 Nov 24 '15 at 15:50
• A good question. Perhaps one would need to define failure to be able to give a good answer. – mathreadler Nov 24 '15 at 17:06
• Euler did most of his work while being blind in one eye. In other fields, Beethoven wrote all his symphonies being deaf. – Lucian Nov 24 '15 at 17:44
• @Chinny84 My decision (accepted answer) is not final, it can change if I see a better answer. Do keep the answers coming! – yoyostein Nov 25 '15 at 0:02
• I've sometimes found I can think more clearly if I plug my ears (or have headphones with music) and close my eyes. But you can't really do that in a working kind of environment? It would look too silly, wouldn't it? – mathreadler Nov 29 '15 at 13:09
The analytic number theorist Hua Loo-Keng overcame abject poverty, handicappedness, political persecution; for more information refer to one of his faithful biography.
Charles Hermite overcame much too, but in different aspects; he failed nearly every math exam that he was to take.
To supplement, the analytic number theorist Chen Jing-Run, the man closest to Goldbach conjecture (who proved "1 + 2") and a student of Hua Loo-Keng, overcame unemployment, poverty, and political persecution; the serial political persecution done unto him was even more violent. But he survived anyway.
• Interesting! I learnt something new from your answer. +1 – yoyostein Nov 25 '15 at 0:09
• Where is the "academic failure" that the OP asks about in both your Chinese examples? – Alex M. Jun 22 '18 at 12:19
Srinivasa Ramanujan was such a mathematician. He failed to got admitted to college but he became one of the best mathematician of $20$th century.
Evariste Galois failed to enter to Ecole Polytechnique twice.
• Galois didn't really overcame his failure. – Asaf Karagila Nov 24 '15 at 15:20
• He didn't live long enough, but he did some of the brilliant works in mathematics, that's a huge success. – Kushal Bhuyan Nov 24 '15 at 15:29
• But it wasn't him who overcame the failure. It's his work. – Asaf Karagila Nov 24 '15 at 15:37
• I'd like to add that Galois got his famous work rejected three times by the Académie des Sciences comprising Cauchy, Fourier, Poisson. – GDumphart Nov 24 '15 at 16:08
• Yes, particularly Cauchy's behavior was unusual in both the case of Abel and Galois. – Kushal Bhuyan Nov 24 '15 at 16:11
Andrew Wiles with his Fermat proof is an example of massive struggle. He worked on the topic for 9 years and got demolished when presenting an erroneous proof after 7 years. There were several additional problems, but I forgot the details. You can read about it on Wiki and in much detail in the very accessible "Fermat's Last Theorem" by Simon Singh.
• It seems a bit strange to regard "Taking a long time and two chances to solve a more than 300 year old problem" as an instance of "academic failure". – Pete L. Clark Nov 29 '15 at 8:31 | 2019-05-26 21:28:17 | {"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": 0.6391825079917908, "perplexity": 1793.2114933150929}, "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-2019-22/segments/1558232259757.86/warc/CC-MAIN-20190526205447-20190526231447-00203.warc.gz"} |
https://alfter.us/wp/category/cancer/ | # Killing cancer by giving it polio
Word on the street is that the FDA has fast-tracked further research into a possible cure for cancer: (h/t AoSHQ)
A bold experiment to kill a vicious form of brain cancer has been granted breakthrough status by the Food and Drug Administration. Results in the earliest stage of testing have been so remarkable, the FDA wants to fast track the treatment to speed it to market.
The therapy uses the polio virus to attack glioblastoma. “60 Minutes” has been following patients in the clinical trial for the last two years.
One of those patients was Stephanie Lipscomb. In 2011, Lipscomb was a 20-year-old nursing student with headaches. A doctor told her she had a glioblastoma tumor the size of a tennis ball and that she had months to live.
She had 98 percent of the tumor removed. Then in 2012, the doctors told her the cancer had come back.
With recurrent glioblastoma, there were no options except the one that had never been tried. Lipscomb became the first volunteer for Duke University’s experiment with the polio virus.
Researchers took some polio virus and modified it with a bit of cold virus so that it can’t invade and reproduce in healthy tissue, but it can still invade and reproduce in cancer cells. Infected cancer cells then show up on the immune system’s radar as foreign cells that need to be eliminated:
Stephanie Lipscomb’s tumor shrank for 21 months until it was gone. Three years after the infusion, something unimaginable had happened.
An MRI in August of 2014 showed no active cancer cells at all.
# Be careful where you send your money
The worst kind of scam is one where you think you’re doing good when you donate, but your money instead goes to line the perp’s pockets.
After Tabitha’s death, I decided it’d be bad form to wish cancer on anyone…but these scumbags are such a tempting target. Maybe I’ll just wish for them to die in a fire instead:
4 Cancer Charities Are Accused of Fraud
There were subscriptions to dating websites, meals at Hooters and purchases at Victoria’s Secret — not to mention jet ski joy rides and couples’ cruises to the Caribbean.
# Make tumors glow to aid in their removal
An interesting new find that should improve the odds of surviving cancer by getting more of the tumor out:
Injectable Agent Illuminates Cancer During Surgery
Doctors have tested a new injectable agent that causes cancer cells in a tumor to fluoresce, potentially increasing a surgeon’s ability to locate and remove all of a cancerous tumor on the first attempt.
# Spinning for cancer
If you have a few bucks looking for a home, you could do worse than to help out my sister-in-law, who’s getting on one of those “spinning” stationary bikes for three hours to raise money to kick cancer in the teeth:
Yas-a-Thon 2015: Toni White’s Page
As most of you know, my sister, Tabitha Beatty Alfter, passed away from cancer on September 6, 2013, at 33 years old. Losing my sister has been the hardest thing I have ever had to endure and do not wish that anyone ever has to experience the pain to losing anyone they love to cancer. So, I am committed to do my part to work towards a cure.
# The sick shouldn’t have to beg for life-saving drugs
An effort is under way in a number of states to pass “right to try” laws that would widen the availability of experimental drugs to patients who’ve exhausted their other options. Here in Nevada, AB164 has passed the Assembly and is on its way to the Senate. The hope is that it’ll fend off more instances like the following:
The sick shouldn’t have to beg for life-saving drugs
Mikaela Knapp’s story is one such example.
At age 24, Mikaela was diagnosed with a deadly form of kidney cancer that migrated into her bones before she even knew she was sick. She went through every known treatment for the cancer in a matter of months — nothing worked. Mikaela’s high school sweetheart, Keith, heard about a drug in development that was successfully treating people with this same cancer. Like Josh, Mikaela wasn’t allowed to enroll in the clinical trial.
Mikaela and Keith launched a social media campaign to try to get access to the drug, but it wasn’t enough. The FDA didn’t help, the drug company didn’t bend and Mikaela didn’t get access to the drug.
She died on April 24, 2014.
Five months later, on Sept. 4, the FDA gave final approval to the drug that could have saved her life.
No family should have to launch a social media campaign or beg the government and drug companies on national television for the chance to save their child, their wife or their mother.
Dealing with cancer is bad enough. Being told you can’t have access to a potentially lifesaving drug because some faceless bureaucrat hasn’t signed off on it yet is not only frustrating, but it’s killing people needlessly. Is it guaranteed that the drugs in question will save people’s lives? No…but it’s one more shot against a disease that, left untreated, will kill.
# Is It Possible to Control Cancer Without Killing It?
Is It Possible to Control Cancer Without Killing It?
A novel therapy is in early trials aimed at bring a form of leukemia under control by trying to fix the damage done by cancer, rather than writing off the cancerous cells and trying to eradicate them:
The breakthrough is notable in part for the unconventional manner in which the drug attacks its target. There are many kinds of cancer, but treatments have typically combatted them in one way only: by attempting to destroy the cancerous cells. Surgery aims to remove the entire growth from the body; chemotherapy drugs are toxic to the cancer cells; radiation generates toxic molecules that break up the cancer cells’ DNA and proteins, causing their demise. A more recent approach, immunotherapy, coopts the body’s immune system into attacking and eradicating the tumor.
The Agios drug, instead of killing the leukemic cells—immature blood cells gone haywire—coaxes them into maturing into functioning blood cells. Cancerous cells traditionally have been viewed as a lost cause, fit only for destruction. The emerging research on A.M.L. suggests that at least some cancer cells might be redeemable: they still carry their original programming and can be pressed back onto a pathway to health.
It’s still too early to tell, but it’s yielded promising results so far. It remains to be seen if this would be an effective therapy for other sorts of cancer. According to the article, the standard treatment for acute myelogenous leukemia is a combination of two drugs: cytarabine (which is neurotoxic) and either daunorubicin or doxorubicin (both of which are cardiotoxic). The first round of Tabitha’s chemotherapy for metastatic uterine leiomyosarcoma included doxorubicin. Looking back, it appeared to have the most positive effect at rolling back the damage done by cancer, but her heart never worked quite the same afterward. Her resting pulse rate was closer to most people’s pulse rate while doing moderately vigorous exercise, and as time went on, it kept going up until it was about where mine is when I’m out for a run.
# On hashing, cancer, and symbols
Drinkers with a Satanic Cult Problem?
Hashers will recognize the symbol in the screengrab above. It got Flying Booger’s attention; after a few minutes’ googling, he found some wackjob website that tried linking cancer researchers, etc. to devil worship or some such nonsense. Said website raised his hackles a bit…can’t say I’d blame him, especially with one of his fellow Tucson hashers having recently gone into hospice care without anybody even knowing that he’d been sick.
This Saturday, it’ll be one year since my wife passed after putting up a hell of a fight against cancer. Her doctors tried every treatment feasible, including some experimental treatments. It was one of the rare cancers…probably something most of you wouldn’t have heard of. We hadn’t either, until we received the diagnosis after having been married all of two months. About all the docs could do was try what had worked with somewhat similar cancers in the past and hope for the best. At first, things looked promising, but the first course of treatment wasn’t sustainable over the long term due to cardiotoxicity and subsequent treatment regimens weren’t as successful at turning back the tide. All that said, I think everyone involved in my wife’s cancer treatment gave a best effort. It’s just such a damn tricky disease that a fair bit of the time (and more often than not, with this particular cancer), the best effort in the world still comes up short. I could be angry with the docs for that, but that would be counterproductive. It won’t bring Tabitha back, and it won’t help the docs help other patients avoid her fate.
The quacks and pseudoscience fearmongers (or “shit-stirrers,” as Flying Booger called them) who would send cancer patients off on wild-goose chases for “cures” that won’t do them any good (and would possibly do them harm) can go take a long walk off a short pier, as far as I’m concerned. Keeping a positive atttitude is one thing, but eschewing tested, peer-reviewed treatments for what some huckster on the radio at 2 AM is pushing isn’t going to do anybody any good. | 2017-02-25 02:11:30 | {"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": 0.24756020307540894, "perplexity": 4431.585716884178}, "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-2017-09/segments/1487501171646.15/warc/CC-MAIN-20170219104611-00131-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://dash.harvard.edu/handle/1/11004927 | # Nanophotonic Structures for Coupling to Quantum Emitters in the Visible
Title: Nanophotonic Structures for Coupling to Quantum Emitters in the Visible Author: Choy, Jennifer Tze-Heng Citation: Choy, Jennifer Tze-Heng. 2013. Nanophotonic Structures for Coupling to Quantum Emitters in the Visible. Doctoral dissertation, Harvard University. Full Text & Related Files: Choy_gsas.harvard_0084L_10990.pdf (14.55Mb; PDF) Abstract: This thesis is about the design, fabrication, and characterization of nanophotonic elements in the visible that can enhance light-matter interaction for single quantum emitters. We focus on two material systems: single photon sources based on the nitrogen-vacancy (NV) center in diamond with improved spontaneous emission rates and collection efficiencies, and passive TiO2 devices that comprise a potentially broadband (from the visible to the infrared), low loss photonics platform and that are suitable for probing and manipulating single colloidal quantum dots. We first discuss the requirements for using color center emission in bulk diamond crystals for potential applications in quantum information processing, and provide examples of using nanowire structures and planar resonators made in diamond for engineering the the NV center’s pump and collection efficiencies, and spontaneous emission rates, respectively. We also describe the integration of diamond with plasmonic structures. We have designed and implemented diamond-silver apertures for broadband enhancements of the spontaneous emission rates of NV centers. We show that shallow-implanted NV centers in diamond nanoposts provide a good system for controlling the NV center spontaneous emission rates, allowing for quenched emission with long lifetimes in the bare case, and enhanced emission with fast decay rates (corresponding to a Purcell factor of around 6) when coated with silver. We add plasmonic gratings around the diamond-silver apertures to improve the collection efficiency of the system, and observe over two-fold improvement in collection. We demonstrate the fabrication of chip-scale linear optical elements such as waveguides and racetrack resonators in low-loss $$TiO_2$$ thin films. The fabricated waveguides operate over a wide bandwidth with propagation losses from from 30 dB/cm in the visible to 4 dB/cm in the IR, while racetrack resonators can critically couple to waveg- uides and have quality factors as high as ~22000 in the red wavelengths. We present the fabrication of dielectric slot waveguides and their integration with colloidal quan- tum dots. Finally, we describe efforts to study and control charge transfer processes between quantum dots and $$TiO_2$$ on a single emitter level. Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11004927 Downloads of this work: | 2017-04-27 05:13:11 | {"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": 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": 0.30151522159576416, "perplexity": 3438.726130618042}, "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-2017-17/segments/1492917121869.65/warc/CC-MAIN-20170423031201-00632-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://angrystatistician.blogspot.com/ | ## Saturday, July 11, 2015
### Power Rankings: Looking at a Very Simple Method
One of the simplest and most common power ranking models is known as the Bradley-Terry-Luce model, which is equivalent to other famous models such the logistic model and the Elo rating system. I'll be referring to "teams" here, but of course the same ideas apply to any two-participant game.
Let me clarify what I mean when I use the term "power ranking". A power ranking supplies not only a ranking of teams, but also provides numbers that may be used to estimate the probabilities of various outcomes were two particular teams to play a match.
In the BTL power ranking system we assume the teams have some latent (hidden/unknown) "strength" $$R_i$$, and that the probability of $$i$$ beating $$j$$ is $$\frac{R_i}{R_i+R_j}$$. Note that each $$R_i$$ is assumed to be strictly positive. Where does this model structure come from?
Here are three reasonable constraints for a power ranking model:
1. If $$R_i$$ and $$R_j$$ have equal strength, the probability of one beating the other should be $$\frac{1}{2}$$.
2. As the strength of one team strictly approaches 0 (infinitely weak) with the other team fixed, the probability of the other team winning strictly increases to 1.
3. As the strength of one team strictly approaches 1 (infinitely strong) with the other team fixed, the probability of the other team winning strictly decreases to 0.
Note that our model structure satisfies all three constraints. Can you think of other simple model structures that satisfy all three constraints?
Given this model and a set of teams and match results, how can we estimate the $$R_i$$. The maximum-likelihood estimators are the set of $$R_i$$ that maximizes the probability of the observed outcomes actually happening. For any given match this probability of team $$i$$ beating team $$j$$ is $$\frac{R_i}{R_i+R_j}$$, so the overall probability of the observed outcomes of the matches $$M$$ occurring is $\mathcal{L} = \prod_{m\in M} \frac{R_{w(m)}}{R_{w(m)}+R_{l(m)}},$ where $$w(m)$$ is then winner and $$l(m)$$ the loser of match $$m$$. We can transform this into a sum by taking logarithms; $\log\left( \mathcal{L} \right) = \log\left(R_{w(m)}\right) - \log\left(R_{w(m)}+R_{l(m)}\right).$ Before going further, let's make a useful reparameterization by setting $$e^{r_i} = R_i$$; this makes sense as we're requiring the $$R_i$$ to be strictly positive. We then get $\log\left( \mathcal{L} \right) = r_{w(m)} - \log\left(e^{r_{w(m)}}+e^{r_{l(m)}}\right).$ Taking partial derivatives we get \begin{eqnarray*}
\frac{\partial \log\left( \mathcal{L} \right)}{\partial r_i} &=& \sum_{w(m)=i} 1 - \frac{e^{r_{w(m)}}}{e^{r_{w(m)}}+e^{r_{l(m)}}} + \sum_{l(m)=i} - \frac{e^{r_{l(m)}}}{e^{r_{w(m)}}+e^{r_{l(m)}}}\\
&=& \sum_{w(m)=i} 1 - \frac{e^{r_i}}{e^{r_i}+e^{r_{l(m)}}} + \sum_{l(m)=i} - \frac{e^{r_i}}{e^{r_{w(m)}}+e^{r_i}}\\
&=&0.
\end{eqnarray*} But this is just the number of actual wins minus the expected wins! Thus, the maximum likelihood estimators for the $$r_i$$ satisfy $$O_i = E_i$$ for all teams $$i$$, where $$O_i$$ is the actual (observed) number of wins for team $$i$$, and $$E_i$$ is the expected number of wins for team $$i$$ based on our model. That's a nice property!
If you'd like to experiment with some actual data, and to see that the resulting fit does indeed satisfy this property, here's an example BTL model using NCAA men's ice hockey scores. You can, of course, actually use this property to iteratively solve for the MLE estimators $$R_i$$. Note that you'll have to fix one of the $$R_i$$ to be a particular value (or add some other constraint), as the model probabilities are invariant with respect to multiplication of the $$R_i$$ by the same positive scalar.
### Getting Started Doing Baseball Analysis without Coding
There's lot of confusion about how best to get started doing baseball analysis. It doesn't have to be difficult! You can start doing it right away, even if you don't know anything about R, Python, Ruby, SQL or machine learning (most GMs can't code). Learning these and other tools makes it easier and faster to do analysis, but they're only part of the process of constructing a well-reasoned argument. They're important, of course, because they can turn 2 months of hard work into 10 minutes of typing. Even if you don't like mathematics, statistics, coding or databases, they're mundane necessities that can make your life much easier and your analysis more powerful.
Here are two example problems. You don't have to do these specifically, but they illustrate the general idea. Write up your solutions, then publish them for other people to make some (hopefully) helpful comments and suggestions. This can be on a blog or through a versioning control platform like GitHub (which is also great for versioning any code or data your use). Try to write well! A great argument, but poorly written and poorly presented isn't going to be very convincing. Once it's finished, review and revise, review and revise, review and revise. When a team you follow makes a move, treat it as a puzzle for you to solve. Why did they do it, and was it a good idea?
2. Pick any MLB team and review the draft picks they made in the 2015 draft for the first 10 rounds. Do you notice any trends or changes from the 2014 draft? Do these picks agree or disagree with the various public pre-draft player rankings? Which picks were designed to save money to help sign other picks? Identify those tough signs. Was the team actually able to sign them, and were the picks to save money still reasonably good picks? Do you best to identify which picks you thought were good and bad, write them down in a notebook with your reasoning, then check back in 6 months and a year. Was your reasoning correct? If not, what were your mistakes and how can you avoid making them in the future?
## Tuesday, March 3, 2015
### Who Controls the Pace in Basketball, Offense or Defense?
During a recent chat with basketball analyst Seth Partnow, he mentioned a topic that came up during a discussion at the recent MIT Sloan Sports Analytics Conference. Who controls the pace of a game more, the offense or defense? And what is the percentage of pace responsibility for each side? The analysts came up with a rough consensus opinion, but is there a way to answer this question analytically? I came up with one approach that examines the variations in possession times, but it suddenly occurred to me that this question could also be answered immediately by looking at the offense-defense asymmetry of the home court advantage.
As you can see in the R output of my NCAA team model code in one of my public basketball repositories, the offense at home scores points at a rate about $$e^{0.0302} = 1.031$$ times the rate on a neutral court, everything else the same. Likewise, the defense at home allows points at a rate about $$e^{-0.0165} = 0.984$$ times the rate on a neutral court; in both cases the neutral court rate is the reference level. Notice the geometric asymmetry; $$1.031\cdot 0.984 = 1.015 > 1$$. The implication is that the offense is responsible for about the fraction $\frac{(1.031-1)}{(1.031-1)+(1-0.984)} = 0.66$ of the scoring pace. That is, offensive controls 2/3 of the pace, defense 1/3 of the pace. The consensus opinion the analysts came up with at Sloan? It was 2/3 offense, 1/3 defense! It's nice when things work out, isn't it?
I've used NCAA basketball because there are plenty of neutral court games; to examine the NBA directly we'll have to use a more sophisticated (but perhaps less beautiful) approach involving the variation in possession times. I'll do that next, and I'll also show you how to apply this new information to make better game predictions. Finally, there's a nice connection to some recent work on inferring causality that I'll outline.
## Wednesday, February 11, 2015
### Baseball's Billion Dollar Equation
In 1999 Voros McCracken infamously speculated about the amount of control the pitcher had over balls put in play. Not so much, as it turned out, and DIPS was born. It's tough to put a value on something like DIPS, but if an MLB team had developed and exploited it for several years, it could potentially have been worth hundreds of millions of dollars. Likewise, catcher framing could easily have been worth hundreds of millions.
How about a billion dollar equation? Sure, look at the baseball draft. An 8th round draft pick like Paul Goldschmidt could net you a $200M surplus. And then there's Chase Headley, Matt Carpenter, Brandon Belt, Jason Kipnis and Matt Adams. The commonality? All college position players easily identified as likely major leaguers purely through statistical analysis. You can also do statistical analysis for college pitchers, of course, but ideally you'd also want velocities. These are frequently available through public sources, but you may have to put them together manually. We'll also find that GB/FB ratios are important. There's plenty of public data available. I've made yearly NCAA college baseball data available in my public baseball GitHub account; it covers 2002-2014, which is plenty of data for analysis. Older years are also available, but only in PDF format. So you'll either have to enter the data manually, use a service or do some high-quality automated OCR. My repository also includes NCAA play-by-play data from several sources, which among other things is useful for building catcher framing and defensive estimates. Also publicly available, and will be available in my GitHub over the next several days: 1. NAIA - roughly NCAA D2 level 2. NJCAA - junior college, same rules as NCAA 3. CCCAA - junior college 4. NWAACC - junior college Prospects come out of the NAIA and NCAA D2/D3 divisions every year, and with the free agent market valuing a single win at around$7M you want to make sure you don't overlook any player with talent. With JUCO players you'd like to identify that sleeper before he transfers to an NCAA D1 and has a huge year. Later you'll also want to analyze:
1. Summer leagues
2. Independent leagues
We'll start by looking at what data is available and how to combine the data sets. There are always player transfers to identify, and NCAA teams frequently play interdivision games as well as NAIA teams. We'll want to build a predictive model that identifies the most talented players uniformly across all leagues, so this will be a boring but necessary step.
### A Very Rough Guide to Getting Started in Data Science: Part II, The Big Picture
Data science to a beginner seems completely overwhelming. Not only are there huge numbers of programming languages, packages and algorithms, but even managing your data is an entire area itself. Some examples are the languages R, Python, Ruby, Perl, Julia, Mathematica, MATLAB/Octave; packages SAS, STATA, SPSS; algorithms linear regression, logistic regression, nested model, neural nets, support vector machines, linear discriminant analysis and deep learning.
For managing your data some people use Excel, or a relational database like MySQL or PostgreSQL. And where do things like big data, NoSQL and Hadoop fit in? And what's gradient descent and why is it important? But perhaps the most difficult part of all is that you actually need to know and understand statistics, too.
It does seem overwhelming, but there's a simple key idea - data science is using data to answer a question. Even if you're only sketching a graph using a stick and a sandbox, you're still doing data science. Your goal for data science should be to continually learn better, more powerful and more efficient ways to answer your questions. My general framework has been strongly influenced by George Pólya's wonderful book "How to Solve It". While it's directed at solving mathematical problems, his approach is helpful for solving problems in general.
"How to Solve It" suggests the following steps when solving a mathematical problem:
1. First, you have to understand the problem.
2. After understanding, then make a plan.
3. Carry out the plan.
4. Review/extend. Look back on your work. How could it be better?
Pólya goes into much greater detail for each step and provides some illustrative examples. It's not the final word on how to approach and solve mathematical problems, but it's very helpful and I highly recommend it. For data science, the analogous steps from my perspective would be:
1. What questions do you want to answer?
2. What data would be helpful to answer these questions? How and where do you get this data?
3. Given the question you want to answer and the data you have, which approaches and models are likely to be useful? This can be very confusing. There are always tradeoffs - underfitting vs overfitting, bias vs variance, simplicity vs complexity, information about where something came from vs what's it doing
4. Perform analysis/fit model.
5. How do you know if your model and analysis are good or bad, and how confident should you be in your predictions and conclusions? A very critical, but commonly treated lightly or even skipped entirely.
6. Given the results, what should you try next?
Let's follow Pólya and do an illustrative example next.
## Tuesday, February 10, 2015
### More Measles: Vaccination Rates and School Funding
I took a look at California's personal belief exemption rate (PBE) for kindergarten vaccinations in Part I. California also provides poverty information for public schools through the Free or Reduced Price Meals data sets, both of which conveniently include California's school codes. Cleaned versions of these data sets and my R code are in my vaccination GitHub.
We can use the school code as a key to join these two data sets. But remember, the FRPM data set only includes data about public schools, so we'll have to retain the private school data for PBEs by doing what's called a left outer join. This still performs a join on the school code key, but if any school codes included in the left data don't have corresponding entries in the right data set we still retain them. The missing values for the right data set in this case are set to NULL.
We can perform a left outer join in R by using "merge" with the option "all.x=TRUE". I'll start by looking at how the PBE rate varies between charter, non-charter public and private schools, so we'll need to replace those missing values for funding source after our join. If the funding source is missing, it's a private school. The FRPM data also denotes non-charter public schools with funding type "", so I'll replace those with "aPublic" for convenience. For factors, R will by default set the reference level to be the level that comes first alphabetically.
Here's a subset of the output. The addition of the funding source is an improvement over the model that doesn't include it, and the estimates for the odds ratios for funding source is the highest for directly funded charter schools, followed by locally funded charter schools and private schools. Remember, public schools are the reference level, so for the public level $$\log(\text{odds ratio}) = 0$$. Everything else being equal, our odds ratio estimates based on funding source would be: \begin{align*}
\mathrm{OR}_{\text{public}} &= e^{-3.820}\times e^{0} &= 0.022\\
\mathrm{OR}_{\text{private}} &= e^{-3.820}\times e^{0.752} &= 0.047\\
\mathrm{OR}_{\text{charter-local}} &= e^{-3.820}\times e^{1.049} &= 0.063\\
\mathrm{OR}_{\text{charter-direct}} &= e^{-3.820}\times e^{1.348} &= 0.085
\end{align*}
Converting to estimated PBE rates, we get: \begin{align*}
\mathrm{PBE}_{\text{public}} &= \frac{0.022}{1+0.022} &= 0.022\\
\mathrm{PBE}_{\text{private}} &= \frac{0.047}{1+0.047} &= 0.045\\
\mathrm{PBE}_{\text{charter-local}} &= \frac{0.063}{1+0.063} &= 0.059\\
\mathrm{PBE}_{\text{charter-direct}} &= \frac{0.085}{1+0.085} &= 0.078
\end{align*} | 2015-08-31 00:27:56 | {"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": 2, "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": 0.7489128708839417, "perplexity": 1177.4414596382358}, "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-2015-35/segments/1440644065464.19/warc/CC-MAIN-20150827025425-00075-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://bookdown.org/content/4857/conditional-manatees.html | # 8 Conditional Manatees
Every model so far in this book has assumed that each predictor has an independent association with the mean of the outcome. What if we want to allow the association to be conditional?…
To model deeper conditionality–where the importance of one predictor depends upon another predictor–we need interaction (also known as moderation). Interaction is a kind of conditioning, a way of allowing parameters (really their posterior distributions) to be conditional on further aspects of the data. The simplest kind of interaction, a linear interaction, is built by extending the linear modeling strategy to parameters within the linear model. So it is akin to placing epicycles on epicycles in the Ptolemaic and Kopernikan models. It is descriptive, but very powerful.
More generally, interactions are central to most statistical models beyond the cozy world of Gaussian outcomes and linear models of the mean. In generalized linear models (GLMs, Chapter 10 and onwards), even when one does not explicitly define variables as interacting, they will always interact to some degree. Multilevel models induce similar effects. (McElreath, 2020a, p. 238, emphasis in the original)
## 8.1 Building an interaction
“Africa is special” (p. 239). Let’s load the rugged data to see one of the reasons why.
data(rugged, package = "rethinking")
d <- rugged
rm(rugged)
# may as well load this, too
library(brms)
For this chapter, we’ll take our plot theme from the ggthemes package .
library(tidyverse)
library(ggthemes)
theme_set(
theme_pander() +
theme(text = element_text(family = "Times"),
panel.background = element_rect(color = "black"))
)
We’ll use the pander color scheme to help us make our first DAG.
library(ggdag)
dag_coords <-
tibble(name = c("R", "G", "C", "U"),
x = c(1, 2, 3, 2),
y = c(2, 2, 2, 1))
dagify(R ~ U,
G ~ R + U + C,
coords = dag_coords) %>%
ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
geom_dag_point(aes(color = name == "U"),
alpha = 1/2, size = 6, show.legend = F) +
geom_point(x = 2, y = 1,
size = 6, shape = 1, stroke = 3/4, color = palette_pander(n = 2)[2]) +
geom_dag_text(color = "black", family = "Times") +
geom_dag_edges() +
scale_colour_pander() +
theme_dag()
Let’s ignore Uv for now… Focus instead on the implication that $$R$$ and $$C$$ both influence $$G$$. This could mean that they are independent influences or rather that they interact (one moderates the influence of the other). The DAG does not display an interaction. That’s because DAGs do not specify how variables combine to influence other variables. The DAG above implies only that there is some function that uses $$R$$ and $$C$$ to generate $$G$$. In typical notation, $$G = f(R, C)$$. (p. 240) It’s generally not a good idea to split up your data and run separate analyses when examining an interaction. McElreath listed four reasons why: 1. “There are usually some parameters, such as $$\sigma$$, that the model says do not depend in any way upon continent. By splitting the data table, you are hurting the accuracy of the estimates for these parameters” (p. 241). 2. “In order to acquire probability statements about the variable you used to split the data, cont_africa, in this case, you need to include it in the model” (p. 241). 3. “We many want to use information criteria or another method to compare models” (p. 241). 4. “Once you begin using multilevel models (Chapter 13), you’ll see that there are advantages to borrowing information across categories like ‘Africa’ and ‘not Africa’” (p. 241). #### 8.1.0.1 Overthinking: Not so simple causation. Here’s the DAG for a fuller model for the data. dag_coords <- tibble(name = c("G", "R", "H", "C", "U"), x = c(1, 1.5, 2.5, 3.5, 1), y = c(3, 2, 2, 2, 1)) dagify(G ~ R + U + H, R ~ U, H ~ R + U + C, coords = dag_coords) %>% ggplot(aes(x = x, y = y, xend = xend, yend = yend)) + geom_dag_point(aes(color = name == "U"), alpha = 1/2, size = 6, show.legend = F) + geom_point(x = 1, y = 1, size = 6, shape = 1, stroke = 3/4, color = palette_pander(n = 2)[2]) + geom_dag_text(color = "black", family = "Times") + geom_dag_edges() + scale_colour_pander() + theme_dag() “The data contain a large number of potential confounds that you might consider. Natural systems like this are terrifyingly complex” (p. 241). In the words of the great Dan Simpson, “Pictures and fear–this is what we do [in statistics]; we draw pictures and have fear” (see here). ### 8.1.1 Making a rugged model. We’ll continue to use tidyverse-style syntax to wrangle the data. # make the log version of criterion d <- d %>% mutate(log_gdp = log(rgdppc_2000)) # extract countries with GDP data dd <- d %>% filter(complete.cases(rgdppc_2000)) %>% # re-scale variables mutate(log_gdp_std = log_gdp / mean(log_gdp), rugged_std = rugged / max(rugged)) Before we fit our first Bayesian models, let’s back track a bit and make our version of Figure 8.2. In the title, McElreath indicated it was a depiction of two linear regressions separated by whether the nations were African. A fairly simple way to make those plots is to simultaneously fit and plot the two regression models using OLS via the geom_smooth() function using the method = "lm" argument. After dividing the data with cont_africa, make each plot separately and then combine them with patchwork syntax. library(ggrepel) library(patchwork) # African nations p1 <- dd %>% filter(cont_africa == 1) %>% ggplot(aes(x = rugged_std, y = log_gdp_std)) + geom_smooth(method = "lm", formula = y ~ x, fill = palette_pander(n = 2)[1], color = palette_pander(n = 2)[1]) + geom_point(color = palette_pander(n = 2)[1]) + geom_text_repel(data = . %>% filter(country %in% c("Lesotho", "Seychelles")), aes(label = country), size = 3, family = "Times", seed = 8) + labs(subtitle = "African nations", x = "ruggedness (standardized)", y = "log GDP (as proportion of mean)") # Non-African nations p2 <- dd %>% filter(cont_africa == 0) %>% ggplot(aes(x = rugged_std, y = log_gdp_std)) + geom_smooth(method = "lm", formula = y ~ x, fill = palette_pander(n = 2)[2], color = palette_pander(n = 2)[2]) + geom_point(color = palette_pander(n = 2)[2]) + geom_text_repel(data = . %>% filter(country %in% c("Switzerland", "Tajikistan")), aes(label = country), size = 3, family = "Times", seed = 8) + xlim(0, 1) + labs(subtitle = "Non-African nations", x = "ruggedness (standardized)", y = "log GDP (as proportion of mean)") # combine p1 + p2 + plot_annotation(title = "Figure 8.2. Separate linear regressions inside and outside of Africa") Our first Bayesian model will follow the form \begin{align*} \text{log_gdp_std}_i & \sim \operatorname{Normal}(\mu_i, \sigma) \\ \mu_i & = \alpha + \beta \left (\text{rugged_std}_i - \overline{\text{rugged_std}} \right ) \\ \alpha & \sim \operatorname{Normal}(1, 1) \\ \beta & \sim \operatorname{Normal}(0, 1) \\ \sigma & \sim \operatorname{Exponential}(1). \end{align*} Here we compute $$\overline{\text{rugged_std}}$$. mean(ddrugged_std)
## [1] 0.2149601
A naïve translation of McElreath’s rethinking code into a brms::brm() formula argument might be log_gdp_std ~ 1 + (rugged_std - 0.215 ). However, this kind of syntax will not work outside of the non-linear syntax. Our approach will be to make a mean-centered version of rugged_std.
dd <-
dd %>%
mutate(rugged_std_c = rugged_std - mean(rugged_std))
Now fit the model.
b8.1 <-
brm(data = dd,
family = gaussian,
log_gdp_std ~ 1 + rugged_std_c,
prior = c(prior(normal(1, 1), class = Intercept),
prior(normal(0, 1), class = b),
prior(exponential(1), class = sigma)),
iter = 2000, warmup = 1000, chains = 4, cores = 4,
seed = 8,
sample_prior = T,
file = "fits/b08.01")
Did you notice the sample_prior = T argument? Because of that, we can now use the prior_samples() function to help us plot the prior predictive distribution for m8.1 and make our version of the left panel of Figure 8.3.
prior <- prior_samples(b8.1)
set.seed(8)
p1 <-
prior %>%
slice_sample(n = 50) %>%
rownames_to_column() %>%
expand(nesting(rowname, Intercept, b),
rugged_std_c = c(-2, 2)) %>%
mutate(log_gdp_std = Intercept + b * rugged_std_c,
rugged_std = rugged_std_c + mean(dd$rugged_std)) %>% ggplot(aes(x = rugged_std, y = log_gdp_std, group = rowname)) + geom_hline(yintercept = range(dd$log_gdp_std), linetype = 2) +
geom_line(color = palette_pander(n = 2)[2], alpha = .4) +
geom_abline(intercept = 1.3, slope = -0.6,
color = palette_pander(n = 2)[1], size = 2) +
labs(subtitle = "Intercept ~ dnorm(1, 1)\nb ~ dnorm(0, 1)",
x = "ruggedness",
y = "log GDP (prop of mean)") +
coord_cartesian(xlim = c(0, 1),
ylim = c(0.5, 1.5))
p1
Toward the bottom of page 243, McElreath wrote: “The slope of such a line must be about $$1.3 − 0.7 = 0.6$$, the difference between the maximum and minimum observed proportional log GDP.” The math appears backwards, there. Rather, the slope of our solid blue line is $$0.7 - 1.3 = -0.6$$. But anyway, “under the $$\beta \sim \operatorname{Normal}(0, 1)$$ prior, more than half of all slopes will have [an] absolute value greater than $$0.6$$” (p. 244).
prior %>%
summarise(a = sum(abs(b) > abs(-0.6)) / nrow(prior))
## a
## 1 0.55725
Our updated model is
\begin{align*} \text{log_gdp_std}_i & \sim \operatorname{Normal} (\mu_i, \sigma) \\ \mu_i & = \alpha + \beta \left (\text{rugged_std}_i - \overline{\text{rugged_std}} \right ) \\ \alpha & \sim \operatorname{Normal}(1, 0.1) \\ \beta & \sim \operatorname{Normal}(0, 0.3) \\ \sigma & \sim \operatorname{Exponential}(1). \end{align*}
Fit the model.
b8.1b <-
brm(data = dd,
family = gaussian,
log_gdp_std ~ 1 + rugged_std_c,
prior = c(prior(normal(1, 0.1), class = Intercept),
prior(normal(0, 0.3), class = b),
prior(exponential(1), class = sigma)),
iter = 2000, warmup = 1000, chains = 4, cores = 4,
seed = 8,
sample_prior = T,
file = "fits/b08.01b")
Now we’ll use prior_samples(b8.1b) to make the left panel of Figure 8.3 and present both panels together with a little patchwork syntax.
set.seed(8)
p2 <-
prior_samples(b8.1b) %>%
slice_sample(n = 50) %>%
rownames_to_column() %>%
expand(nesting(rowname, Intercept, b),
rugged_std_c = c(-2, 2)) %>%
mutate(log_gdp_std = Intercept + b * rugged_std_c,
rugged_std = rugged_std_c + mean(dd$rugged_std)) %>% ggplot(aes(x = rugged_std, y = log_gdp_std, group = rowname)) + geom_hline(yintercept = range(dd$log_gdp_std), linetype = 2) +
geom_line(color = palette_pander(n = 2)[2], alpha = .4) +
scale_y_continuous("", breaks = NULL) +
labs(subtitle = "Intercept ~ dnorm(1, 0.1)\nb ~ dnorm(0, 0.3)",
x = "ruggedness") +
coord_cartesian(xlim = c(0, 1),
ylim = c(0.5, 1.5))
p1 + p2 +
plot_annotation(title = "Simulating in search of reasonable priors for the terrain ruggedness example.",
theme = theme(plot.title = element_text(size = 12)))
Now check the summary for b8.1b.
print(b8.1b)
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: log_gdp_std ~ 1 + rugged_std_c
## Data: dd (Number of observations: 170)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 0.01 0.98 1.02 1.00 4316 2983
## rugged_std_c 0.00 0.06 -0.11 0.12 1.00 3677 2896
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.14 0.01 0.12 0.15 1.00 3938 3028
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
### 8.1.2 Adding an indicator variable isn’t enough.
When you’d like to allow a model intercept and slope to differ by levels of a dichotomous variable, a typical approach is to use a 0/1 coded dummy variable. In this section and throughout much of the text, McElreath opted to highlight the index variable approach, instead. We’ll follow along. But if you’d like to practice using brms to fit interaction models with dummy variables, see Section 7.1 of my (2020a) translation of McElreath’s (2015) first edition or Chapters 7 and beyond in my (2019) translation of Andrew Hayes’s (2017) text on mediation and moderation.
Make the index variable.
dd <-
dd %>%
mutate(cid = if_else(cont_africa == 1, "1", "2"))
In case you were curious, here’s a plot showing how the cid index works.
dd %>%
mutate(cid = str_c("cid: ", cid)) %>%
arrange(cid, country) %>%
group_by(cid) %>%
mutate(rank = 1:n()) %>%
ggplot(aes(x = cid, y = rank, label = country)) +
geom_text(size = 2, hjust = 0, family = "Times") +
scale_y_reverse() +
theme_void() +
facet_wrap(~ cid, scales = "free_x")
If you recall from the latter sections of Chapter 5, the conventional brms syntax can accommodate an index variable by simply suppressing the default intercept via the 0 + .... syntax. That will be our approach, here.
b8.2 <-
brm(data = dd,
family = gaussian,
log_gdp_std ~ 0 + cid + rugged_std_c,
prior = c(prior(normal(1, 0.1), class = b, coef = cid1),
prior(normal(1, 0.1), class = b, coef = cid2),
prior(normal(0, 0.3), class = b, coef = rugged_std_c),
prior(exponential(1), class = sigma)),
iter = 2000, warmup = 1000, chains = 4, cores = 4,
seed = 8,
file = "fits/b08.02")
Use add_criterion() and loo_compare() to compare b8.1b and b8.2 with the WAIC.
b8.1b <- add_criterion(b8.1b, "waic")
loo_compare(b8.1b, b8.2, criterion = "waic") %>% print(simplify = F)
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic waic se_waic
## b8.2 0.0 0.0 126.1 7.4 4.1 0.8 -252.3 14.8
## b8.1b -31.7 7.3 94.4 6.5 2.6 0.3 -188.8 13.0
Here are the WAIC weights.
model_weights(b8.1b, b8.2, weights = "waic") %>% round(digits = 3)
## b8.1b b8.2
## 0 1
Here is the summary for the model with all the weight, b8.2.
print(b8.2)
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: log_gdp_std ~ 0 + cid + rugged_std_c
## Data: dd (Number of observations: 170)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## cid1 0.88 0.02 0.85 0.91 1.00 4089 2944
## cid2 1.05 0.01 1.03 1.07 1.00 4491 2987
## rugged_std_c -0.05 0.05 -0.14 0.04 1.00 3484 2736
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.11 0.01 0.10 0.13 1.00 3981 3176
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Now extract the posterior draws, make a difference score for the two intercepts, and use tidybayes::qi() to compute the percentile-based 89% intervals for the difference.
post <-
posterior_samples(b8.2) %>%
mutate(diff = b_cid1 - b_cid2)
library(tidybayes)
qi(post$diff, .width = .89) ## [,1] [,2] ## [1,] -0.2004941 -0.1370836 Now it’s time to use fitted() to prepare to plot the implications of the model in Figure 8.4. nd <- crossing(cid = 1:2, rugged_std = seq(from = -0.2, to = 1.2, length.out = 30)) %>% mutate(rugged_std_c = rugged_std - mean(dd$rugged_std))
f <-
fitted(b8.2,
newdata = nd,
probs = c(.015, .985)) %>%
data.frame() %>%
bind_cols(nd) %>%
mutate(cont_africa = ifelse(cid == 1, "Africa", "not Africa"))
# what did we do?
head(f)
## Estimate Est.Error Q1.5 Q98.5 cid rugged_std rugged_std_c cont_africa
## 1 0.8999853 0.02380766 0.8493229 0.9514257 1 -0.200000000 -0.4149601 Africa
## 2 0.8977392 0.02231333 0.8501207 0.9451827 1 -0.151724138 -0.3666842 Africa
## 3 0.8954931 0.02093972 0.8501513 0.9397260 1 -0.103448276 -0.3184083 Africa
## 4 0.8932469 0.01971208 0.8517471 0.9355161 1 -0.055172414 -0.2701325 Africa
## 5 0.8910008 0.01865925 0.8511358 0.9314925 1 -0.006896552 -0.2218566 Africa
## 6 0.8887547 0.01781224 0.8504140 0.9274236 1 0.041379310 -0.1735808 Africa
Behold our Figure 8.4.
dd %>%
mutate(cont_africa = ifelse(cont_africa == 1, "Africa", "not Africa")) %>%
ggplot(aes(x = rugged_std, fill = cont_africa, color = cont_africa)) +
geom_smooth(data = f,
aes(y = Estimate, ymin = Q1.5, ymax = Q98.5),
stat = "identity",
alpha = 1/4, size = 1/2) +
geom_point(aes(y = log_gdp_std),
size = 2/3) +
scale_fill_pander() +
scale_colour_pander() +
labs(subtitle = "b8.2",
x = "ruggedness (standardized)",
y = "log GDP (as proportion of mean)") +
coord_cartesian(xlim = c(0, 1)) +
theme(legend.background = element_blank(),
legend.direction = "horizontal",
legend.position = c(.67, .93),
legend.title = element_blank())
Though adding our index variable cid to b8.2 allowed us to give the African nations a different intercept than the non-African nations, it did nothing for the slope. We need a better method.
#### 8.1.2.1 Rethinking: Why 97%?
Did you notice the probs = c(.015, .985) argument in our fitted() code, above? This is one of those rare moments when we went along with McElreath and used intervals other than the conventional 95%.
In the code block just above, and therefore also in Figure 8.4, I used 97% intervals of the expected mean. This is a rather non-standard percentile interval. So why use 97%? In this book, [McElreath used] non-standard percents to constantly remind the reader that conventions like 95% and 5% are arbitrary. Furthermore, boundaries are meaningless. There is continuous change in probability as we move away from the expected value. So one side of the boundary is almost equally probable as the other side. (p. 247)
Building off of McElreath’s “boundaries are meaningless” point, here we use a combination of summary = F within fitted() and a little tidybayes::stat_lineribbon() magic to re-imagine Figure 8.4. This time we use a sequence of overlapping semitransparent credible intervals to give the posterior a 3D-like appearance.
fitted(b8.2,
newdata = nd,
summary = F) %>%
data.frame() %>%
pivot_longer(everything()) %>%
bind_cols(
expand(nd,
iter = 1:4000,
nesting(cid, rugged_std))
) %>%
mutate(cont_africa = ifelse(cid == 1, "Africa", "not Africa")) %>%
ggplot(aes(x = rugged_std, y = value, fill = cont_africa, color = cont_africa)) +
stat_lineribbon(.width = seq(from = .03, to = .99, by = .03),
alpha = .1, size = 0) +
geom_point(data = dd %>%
mutate(cont_africa = ifelse(cont_africa == 1, "Africa", "not Africa")),
aes(y = log_gdp_std),
size = 2/3) +
scale_fill_pander() +
scale_colour_pander() +
labs(subtitle = "b8.2",
x = "ruggedness (standardized)",
y = "log GDP (as proportion of mean)") +
coord_cartesian(xlim = c(0, 1)) +
theme(legend.background = element_blank(),
legend.direction = "horizontal",
legend.position = c(.67, .93),
legend.title = element_blank())
### 8.1.3 Adding an interaction does work.
The 0 + ... syntax works fine when we just want to use an index variable to fit a model with multiple intercepts, this approach will not work for fitting brms models that apply the index variable to slopes. Happily, we have alternatives. If we’d like to use the cid index to make intercepts and slopes as in McElreath’s m8.3, we can use the brms non-linear syntax . Here it is for b8.3.
b8.3 <-
brm(data = dd,
family = gaussian,
bf(log_gdp_std ~ 0 + a + b * rugged_std_c,
a ~ 0 + cid,
b ~ 0 + cid,
nl = TRUE),
prior = c(prior(normal(1, 0.1), class = b, coef = cid1, nlpar = a),
prior(normal(1, 0.1), class = b, coef = cid2, nlpar = a),
prior(normal(0, 0.3), class = b, coef = cid1, nlpar = b),
prior(normal(0, 0.3), class = b, coef = cid2, nlpar = b),
prior(exponential(1), class = sigma)),
iter = 2000, warmup = 1000, chains = 4, cores = 4,
seed = 8,
file = "fits/b08.03")
Check the summary of the marginal distributions.
print(b8.3)
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: log_gdp_std ~ 0 + a + b * rugged_std_c
## a ~ 0 + cid
## b ~ 0 + cid
## Data: dd (Number of observations: 170)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## a_cid1 0.89 0.02 0.86 0.92 1.00 4808 3274
## a_cid2 1.05 0.01 1.03 1.07 1.00 6227 3439
## b_cid1 0.13 0.08 -0.02 0.28 1.00 5023 2991
## b_cid2 -0.14 0.06 -0.25 -0.03 1.00 4639 2559
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.11 0.01 0.10 0.12 1.00 4913 2940
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Success! Our results look just like McElreath’s. Now make haste with add_criterion() so we can compare the models by the PSIS-LOO-CV.
b8.1b <- add_criterion(b8.1b, "loo")
loo_compare(b8.1b, b8.2, b8.3, criterion = "loo") %>% print(simplify = F)
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic se_looic
## b8.3 0.0 0.0 129.6 7.3 5.0 0.9 -259.2 14.7
## b8.2 -3.5 3.2 126.1 7.4 4.1 0.8 -252.2 14.8
## b8.1b -35.2 7.5 94.4 6.5 2.6 0.3 -188.8 13.0
Here are the LOO weights.
model_weights(b8.1b, b8.2, b8.3, weights = "loo") %>% round(digits = 2)
## b8.1b b8.2 b8.3
## 0.00 0.03 0.97
We can get a Pareto $$k$$ diagnostic plot for b8.3 by feeding the results of the loo() function into plot().
loo(b8.3) %>%
plot()
Unlike in the text, our results suggest all the cases had Pareto $$k$$ values below the 0.5 threshold. We can confirm by rank ordering them and taking a look at the top values.
tibble(k = b8.3$criteria$loo$diagnostics$pareto_k,
row = 1:170) %>%
arrange(desc(k))
## # A tibble: 170 x 2
## k row
## <dbl> <int>
## 1 0.390 93
## 2 0.365 27
## 3 0.306 145
## 4 0.277 150
## 5 0.224 118
## 6 0.222 8
## 7 0.185 29
## 8 0.169 84
## 9 0.166 90
## 10 0.164 57
## # … with 160 more rows
Yep, no big issues, here.
#### 8.1.3.1 Bonus: Give me Student-$$t$$.
McElreath remarked: “This is possibly a good context for robust regression, like the Student-t regression we did in Chapter 7” (p. 249). Let’s practice fitting the alternative model using the Student-$$t$$ likelihood for which $$\nu = 2$$.
b8.3t <-
brm(data = dd,
family = student,
bf(log_gdp_std ~ 0 + a + b * rugged_std_c,
a ~ 0 + cid,
b ~ 0 + cid,
nu = 2,
nl = TRUE),
prior = c(prior(normal(1, 0.1), class = b, coef = cid1, nlpar = a),
prior(normal(1, 0.1), class = b, coef = cid2, nlpar = a),
prior(normal(0, 0.3), class = b, coef = cid1, nlpar = b),
prior(normal(0, 0.3), class = b, coef = cid2, nlpar = b),
prior(exponential(1), class = sigma)),
iter = 2000, warmup = 1000, chains = 4, cores = 4,
seed = 8,
file = "fits/b08.03t")
Use the LOO to compare this with the Gaussian model.
b8.3t <- add_criterion(b8.3t, c("loo", "waic"))
loo_compare(b8.3, b8.3t, criterion = "loo") %>% print(simplify = F)
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic se_looic
## b8.3 0.0 0.0 129.6 7.3 5.0 0.9 -259.2 14.7
## b8.3t -19.1 2.7 110.5 8.8 6.2 0.7 -221.0 17.5
The PSIS-LOO-CV comparison suggests the robust Student-$$t$$ model might be overfit. Just for kicks, we might make our own diagnostic plot to compare the two likelihoods by the Pareto $$k$$ values. To get a nice fine-grain sense of the distributions, we’ll employ the handy tidybayes::stat_dots() function which will display each value as an individual dot.
tibble(Normal = b8.3$criteria$loo$diagnostics$pareto_k,
Student-t = b8.3t$criteria$loo$diagnostics$pareto_k) %>%
pivot_longer(everything(),
values_to = "pareto_k") %>%
ggplot(aes(x = pareto_k, y = name)) +
geom_vline(xintercept = .5, linetype = 2, color = palette_pander(n = 5)[5]) +
stat_dots(slab_fill = palette_pander(n = 4)[4],
slab_color = palette_pander(n = 4)[4]) +
annotate(geom = "text",
x = .485, y = 1.5, label = "threshold", angle = 90,
family = "Times", color = palette_pander(n = 5)[5]) +
ylab(NULL) +
coord_cartesian(ylim = c(1.5, 2.4))
To close this exercise out, compare the $$\alpha$$ and $$\beta$$ parameters of the two models using fixef().
fixef(b8.3) %>% round(digits = 2)
## Estimate Est.Error Q2.5 Q97.5
## a_cid1 0.89 0.02 0.86 0.92
## a_cid2 1.05 0.01 1.03 1.07
## b_cid1 0.13 0.08 -0.02 0.28
## b_cid2 -0.14 0.06 -0.25 -0.03
fixef(b8.3t) %>% round(digits = 2)
## Estimate Est.Error Q2.5 Q97.5
## a_cid1 0.87 0.02 0.84 0.90
## a_cid2 1.05 0.01 1.02 1.07
## b_cid1 0.13 0.09 -0.02 0.33
## b_cid2 -0.20 0.07 -0.33 -0.07
### 8.1.4 Plotting the interaction.
The code for Figure 8.5 is a minor extension of the code we used for Figure 8.4. Other than which fit we use, the code we use for fitted() is the same for both plots. Two of the largest changes are the addition of labels with ggrepel::geom_text_repel() and using facet_wrap() to split the plot into two panels.
countries <- c("Equatorial Guinea", "South Africa", "Seychelles", "Swaziland", "Lesotho", "Rwanda", "Burundi", "Luxembourg", "Greece", "Switzerland", "Lebanon", "Yemen", "Tajikistan", "Nepal")
f <-
fitted(b8.3,
# we already defined nd, above
newdata = nd,
probs = c(.015, .985)) %>%
data.frame() %>%
bind_cols(nd) %>%
mutate(cont_africa = ifelse(cid == 1, "African nations", "Non-African nations"))
dd %>%
mutate(cont_africa = ifelse(cont_africa == 1, "African nations", "Non-African nations")) %>%
ggplot(aes(x = rugged_std, y = log_gdp_std, fill = cont_africa, color = cont_africa)) +
geom_smooth(data = f,
aes(y = Estimate, ymin = Q1.5, ymax = Q98.5),
stat = "identity",
alpha = 1/4, size = 1/2) +
geom_text_repel(data = . %>% filter(country %in% countries),
aes(label = country),
size = 3, seed = 8,
segment.color = "grey25", min.segment.length = 0) +
geom_point(aes(y = log_gdp_std),
size = 2/3) +
scale_fill_pander() +
scale_colour_pander() +
labs(x = "ruggedness (standardized)",
y = "log GDP (as proportion of mean)") +
coord_cartesian(xlim = c(0, 1)) +
theme(legend.position = "none") +
facet_wrap(~ cont_africa)
“Finally, the slope reverses direction inside and outside of Africa. And because we achieved this inside a single model, we could statistically evaluate the value of this reversal” (p. 250).
#### 8.1.4.1 Rethinking: All Greek to me.
We use these Greek symbols $$\alpha$$ and $$\beta$$ because it is conventional. They don’t have special meanings. If you prefer some other Greek symbol like $$\omega$$–why should $$\alpha$$ get all the attention?–feel free to use that instead. It is conventional to use Greek letters for unobserved variables (parameters) and Roman letters for observed variables (data). That convention does have some value, because it helps others read your models. But breaking the convention is not an error, and sometimes it is better to use a familiar Roman symbol than an unfamiliar Greek one like $$\xi$$ or $$\zeta$$. If your readers cannot say the symbol’s name, it could make understanding the model harder. (p. 249)
This topic is near and dear my heart. In certain areas of psychology, people presume symbols like $$\beta$$ and $$b$$ have universal meanings. This presumption is a mistake and will not serve one well beyond a narrow section of the scientific literature. My recommendation is whatever notation you fancy in a given publication, clearly define your terms, especially if there could be any confusion over whether your results are standardized or not.
## 8.2 Symmetry of interactions
If you’re unfamiliar with Buridan’s ass, here’s a brief clip to catch up up to speed. With that ass still on your mind, recall the model for $$\mu_i$$ from the last example,
$\mu_i = \alpha_{\text{cid}[i]} + \beta_{\text{cid}[i]} \left (\text{rugged_std}_i - \overline{\text{rugged_std}} \right ).$
With this model, it is equally true that that slope is conditional on the intercept as it is that the intercept is conditional on the slope. Another way to express the model is
\begin{align*} \mu_i & = \underbrace{(2 - \text{cid}_{i}) \left (\alpha_1 + \beta_1 \left [\text{rugged_std}_i - \overline{\text{rugged_std}} \right ] \right )}_{\text{cid}[i] = 1} \\ & \;\;\; + \underbrace{(\text{cid}_{i} - 1) \left (\alpha_2 + \beta_2 \left [\text{rugged_std}_i - \overline{\text{rugged_std}} \right ] \right )}_{\text{cid}[i] = 2}, \end{align*}
where the first term vanishes when $$\text{cid}_i = 2$$ and the second term vanishes when $$\text{cid}_i = 1$$. In contrast to the plots above, we can re-express this equation as saying “The association of being in Africa with log GDP depends upon terrain ruggedness” (p. 251, emphasis in the original). Here we follow McElreath’s Figure 8.6 and plot the difference between a nation in Africa and outside Africa, conditional on ruggedness.
fitted(b8.3,
newdata = nd,
summary = F) %>%
data.frame() %>%
pivot_longer(everything()) %>%
bind_cols(expand(nd,
iter = 1:4000,
nesting(cid, rugged_std))) %>%
select(-name) %>%
pivot_wider(names_from = cid, values_from = value) %>%
mutate(delta = 1 - 2) %>%
ggplot(aes(x = rugged_std, y = delta)) +
stat_lineribbon(.width = .95, fill = palette_pander(n = 8)[8], alpha = 3/4) +
geom_hline(yintercept = 0, linetype = 2) +
annotate(geom = "text",
x = .2, y = 0,
label = "Africa higher GDP\nAfrica lower GDP",
family = "Times") +
labs(x = "ruggedness (standardized)",
y = "expected difference log GDP") +
coord_cartesian(xlim = c(0, 1),
ylim = c(-0.3, 0.2))
This perspective on the GDP and terrain ruggedness is completely consistent with the previous perspective. It’s simultaneously true in these data (and with this model) that (1) the influence of ruggedness depends upon continent and (2) the influence of continent depends upon ruggedness.
Simple interactions are symmetric, just like the choice facing Buridan’s ass. Within the model, there’s no basis to prefer one interpretation over the other, because in fact they are the same interpretation. But when we reason causally about models, our minds tend to prefer one interpretation over the other, because it’s usually easier to imagine manipulating one of the predictor variables instead of the other. (pp. 251–252)
## 8.3 Continuous interactions
It’s one thing to make a slope conditional upon a category. In such a context, the model reduces to estimating a different slope for each category. But it’s quite a lot harder to understand that a slope varies in a continuous fashion with a continuous variable. Interpretation is much harder in this case, even though the mathematics of the model are essentially the same. (p. 252, emphasis in the original)
### 8.3.1 A winter flower.
Look at the tulips data, which were adapted from .
data(tulips, package = "rethinking")
d <- tulips
rm(tulips)
glimpse(d)
## Rows: 27
## Columns: 4
## $bed <fct> a, a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b, b, c, c, c, c, c, c, c, c, c ##$ water <int> 1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3, 3
## $shade <int> 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3 ##$ blooms <dbl> 0.00, 0.00, 111.04, 183.47, 59.16, 76.75, 224.97, 83.77, 134.95, 80.10, 85.95, 19.8…
### 8.3.2 The models.
Wrangle a little.
d <-
d %>%
mutate(blooms_std = blooms / max(blooms),
water_cent = water - mean(water),
shade_cent = shade - mean(shade))
With the variables in hand, the basic model is $$B = f(W, S)$$, where $$B$$ = blooms, $$W$$ = water, $$S$$ = shade, and $$f(\cdot)$$ indicates a function. We can also express this as $$W \rightarrow B \leftarrow S$$. Neither expression clarifies whether the effects of $$W$$ and $$S$$ are additive or conditional on each other in some way. We might express an unconditional (additive) model as
\begin{align*} \text{blooms_std}_i & \sim \operatorname{Normal}(\mu_i, \sigma) \\ \mu_i & = \alpha + \beta_1 \text{water_cent}_i + \beta_2 \text{shade_cent}_i \\ \alpha & \sim \operatorname{Normal}(0.5, 1) \\ \beta_1 & \sim \operatorname{Normal}(0, 1) \\ \beta_2 & \sim \operatorname{Normal}(0, 1) \\ \sigma & \sim \operatorname{Exponential}(1), \end{align*}
where $$\text{water_cent}_i = \left (\text{water}_i - \overline{\text{water}} \right )$$ and $$\text{shade_cent}_i = \left (\text{shade}_i - \overline{\text{shade}} \right )$$. Even though “the intercept $$\alpha$$ must be greater than zero and less than one,… this prior assigns most of the probability outside that range” (p. 254).
set.seed(8)
tibble(a = rnorm(1e4, mean = 0.5, sd = 1)) %>%
summarise(proportion_outside_of_the_range = sum(a < 0 | a > 1) / n())
## # A tibble: 1 x 1
## proportion_outside_of_the_range
## <dbl>
## 1 0.621
Tightening up the prior to $$\operatorname{Normal}(0, 0.25)$$ helps.
set.seed(8)
tibble(a = rnorm(1e4, mean = 0.5, sd = 0.25)) %>%
summarise(proportion_outside_of_the_range = sum(a < 0 | a > 1) / n())
## # A tibble: 1 x 1
## proportion_outside_of_the_range
## <dbl>
## 1 0.0501
Here are the ranges for our two predictors.
range(d$water_cent) ## [1] -1 1 range(d$shade_cent)
## [1] -1 1
Putting the same $$\operatorname{Normal}(0, 0.25)$$ prior on each would indicate a .95 probability each coefficient would be within -0.5 to 0.5. Since the total range for both is $$1 - (-1) = 2$$, that would imply either could account for the full range of blooms_std because $$0.5 \cdot 2 = 1$$, which is the full range of blooms_std. Our first model, then, will be
\begin{align*} \text{blooms_std}_i & \sim \operatorname{Normal}(\mu_i, \sigma) \\ \mu_i & = \alpha + \beta_1 \text{water_cent}_i + \beta_2 \text{shade_cent}_i \\ \alpha & \sim \operatorname{Normal}(0.5, 0.25) \\ \beta_1 & \sim \operatorname{Normal}(0, 0.25) \\ \beta_2 & \sim \operatorname{Normal}(0, 0.25) \\ \sigma & \sim \operatorname{Exponential}(1). \end{align*}
Fit the model.
b8.4 <-
brm(data = d,
family = gaussian,
blooms_std ~ 1 + water_cent + shade_cent,
prior = c(prior(normal(0.5, 0.25), class = Intercept),
prior(normal(0, 0.25), class = b, coef = water_cent),
prior(normal(0, 0.25), class = b, coef = shade_cent),
prior(exponential(1), class = sigma)),
iter = 2000, warmup = 1000, chains = 4, cores = 4,
seed = 8,
file = "fits/b08.04")
Check the model summary.
print(b8.4)
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: blooms_std ~ 1 + water_cent + shade_cent
## Data: d (Number of observations: 27)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.36 0.03 0.29 0.43 1.00 4448 2585
## water_cent 0.20 0.04 0.12 0.28 1.00 4299 2788
## shade_cent -0.11 0.04 -0.20 -0.03 1.00 4390 3062
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.18 0.03 0.13 0.24 1.00 3063 2786
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Using the $$\gamma$$ notation, we can express an interaction between water_cent and shade_cent by
\begin{align*} \mu_i & = \alpha + \color{#009E73}{\gamma_{1, i}} \text{water_cent}_i + \beta_2 \text{shade_cent}_i \\ \color{#009E73}{\gamma_{1, i}} & \color{#009E73}= \color{#009E73}{\beta_1 + \beta_3 \text{shade_cent}_i}, \end{align*}
where both $$\mu_i$$ and $$\gamma_{1, i}$$ get a linear model. We could do the converse by switching the positions of water_cent and shade_cent. If we substitute the equation for $$\gamma_{1, i}$$ into the equation for $$\mu_i$$, we get
\begin{align*} \mu_i & = \alpha + \color{#009E73}{\underbrace{(\beta_1 + \beta_3 \text{shade_cent}_i)}_{\gamma_{1, i}}} \text{water_cent}_i + \beta_2 \text{shade_cent}_i \\ & = \alpha + \color{#009E73}{\beta_1} \text{water_cent}_i + (\color{#009E73}{\beta_3 \text{shade_cent}_i} \cdot \text{water_cent}_i) + \beta_2 \text{shade_cent}_i \\ & = \alpha + \color{#009E73}{\beta_1} \text{water_cent}_i + \beta_2 \text{shade_cent}_i + \color{#009E73}{\beta_3} (\color{#009E73}{\text{shade_cent}_i} \cdot \text{water_cent}_i), \end{align*}
where $$\beta_3$$ is the interaction term which makes water_cent and shade_cent conditional on each other. If we use the same priors as before, we might write the full equation for our interaction model as
\begin{align*} \text{blooms_std}_i & \sim \operatorname{Normal}(\mu_i, \sigma) \\ \mu_i & = \alpha + \color{#009E73}{\beta_1} \text{water_cent}_i + \beta_2 \text{shade_cent}_i + \color{#009E73}{\beta_3 \text{shade_cent}_i} \cdot \text{water_cent}_i\\ \alpha & \sim \operatorname{Normal}(0.5, 0.25) \\ \beta_1 & \sim \operatorname{Normal}(0, 0.25) \\ \beta_2 & \sim \operatorname{Normal}(0, 0.25) \\ \beta_3 & \sim \operatorname{Normal}(0, 0.25) \\ \sigma & \sim \operatorname{Exponential}(1). \end{align*}
Fit the model.
b8.5 <-
brm(data = d,
family = gaussian,
prior = c(prior(normal(0.5, 0.25), class = Intercept),
prior(normal(0, 0.25), class = b, coef = water_cent),
prior(normal(0, 0.25), class = b, coef = shade_cent),
prior(normal(0, 0.25), class = b, coef = "water_cent:shade_cent"),
prior(exponential(1), class = sigma)),
iter = 2000, warmup = 1000, chains = 4, cores = 4,
seed = 8,
file = "fits/b08.05")
Check the summary.
print(b8.5)
## Family: gaussian
## Links: mu = identity; sigma = identity
## Data: d (Number of observations: 27)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.36 0.03 0.30 0.41 1.00 4147 2853
## water_cent 0.21 0.03 0.14 0.27 1.00 4603 2752
## shade_cent -0.11 0.03 -0.18 -0.04 1.00 4625 2673
## water_cent:shade_cent -0.14 0.04 -0.22 -0.06 1.00 4689 2968
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.14 0.02 0.11 0.19 1.00 3304 2710
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
The row for the interaction term, water_cent:shade_cent, indicates the marginal posterior is negative.
### 8.3.3 Plotting posterior predictions.
Now we’re ready for the top row of Figure 8.8. Here’s our variation on McElreath’s triptych loop code, adjusted for brms and ggplot2.
# loop over values of water_c and plot predictions
for(s in -1:1) {
# define the subset of the original data
dt <- d[d$shade_cent == s, ] # defining our new data nd <- tibble(shade_cent = s, water_cent = c(-1, 1)) # use our sampling skills, like before f <- fitted(b8.4, newdata = nd, summary = F) %>% data.frame() %>% set_names("-1", "1") %>% slice_sample(n = 20) %>% mutate(row = 1:n()) %>% pivot_longer(-row, names_to = "water_cent", values_to = "blooms_std") %>% mutate(water_cent = as.double(water_cent)) # specify our custom plot fig <- ggplot(data = dt, aes(x = water_cent, y = blooms_std)) + geom_line(data = f, aes(group = row), color = palette_pander(n = 6)[6], alpha = 1/5, size = 1/2) + geom_point(color = palette_pander(n = 6)[6]) + scale_x_continuous("Water (centered)", breaks = c(-1, 0, 1)) + labs(title = paste("Shade (centered) =", s), y = "Blooms (standardized)") + coord_cartesian(xlim = c(-1, 1), ylim = c(0, 1)) # plot that joint plot(fig) } We don’t necessarily need a loop. We can achieve all of McElreath’s Figure 8.8 with fitted(), some data wrangling, and a little help from ggplot2::facet_grid(). # augment the data points <- d %>% expand(fit = c("b8.4", "b8.5"), nesting(shade_cent, water_cent, blooms_std)) %>% mutate(x_grid = str_c("shade_cent = ", shade_cent), y_grid = fit) # redefine nd nd <- crossing(shade_cent = -1:1, water_cent = c(-1, 1)) # use fitted() set.seed(8) rbind(fitted(b8.4, newdata = nd, summary = F, nsamples = 20), fitted(b8.5, newdata = nd, summary = F, nsamples = 20)) %>% # wrangle data.frame() %>% set_names(mutate(nd, name = str_c(shade_cent, water_cent, sep = "_")) %>% pull()) %>% mutate(row = 1:n(), fit = rep(c("b8.4", "b8.5"), each = n() / 2)) %>% pivot_longer(-c(row:fit), values_to = "blooms_std") %>% separate(name, into = c("shade_cent", "water_cent"), sep = "_") %>% mutate(shade_cent = shade_cent %>% as.double(), water_cent = water_cent %>% as.double()) %>% # these will come in handy for ggplot2::facet_grid() mutate(x_grid = str_c("shade_cent = ", shade_cent), y_grid = fit) %>% # plot! ggplot(aes(x = water_cent, y = blooms_std)) + geom_line(aes(group = row), color = palette_pander(n = 6)[6], alpha = 1/5, size = 1/2) + geom_point(data = points, color = palette_pander(n = 6)[6]) + scale_x_continuous("Water (centered)", breaks = c(-1, 0, 1)) + scale_y_continuous("Blooms (standardized)", breaks = c(0, .5, 1)) + ggtitle("Posterior predicted blooms") + coord_cartesian(xlim = c(-1, 1), ylim = c(0, 1)) + theme(strip.background = element_rect(fill = alpha(palette_pander(n = 2)[2], 1/3))) + facet_grid(y_grid ~ x_grid) ### 8.3.4 Plotting prior predictions. In some of the earlier models in this book, we used the sample_prior = T argument within brm() to simultaneously sample from the posterior and prior distributions. As far as the priors go, we could then retrieve their draws from the prior_samples() function and plot as desired. And to be clear, we could use this method to remake Figure 8.8 with our brms fits. However, a limitation of the sample_prior = T method is it will not work if you’re trying to use a fitted()-oriented work flow. Happily, we have an alternative. Within brm(), set sample_prior = "only". The resulting fit object will be based solely on the priors. Here we’ll use this method within update() to refit the last two models. b8.4p <- update(b8.4, sample_prior = "only", iter = 2000, warmup = 1000, chains = 4, cores = 4, seed = 8, file = "fits/b08.04p") b8.5p <- update(b8.5, sample_prior = "only", iter = 2000, warmup = 1000, chains = 4, cores = 4, seed = 8, file = "fits/b08.05p") Now we can insert b8.4p and b8.5p into the fitted() function and plot the prior predictions we desire. set.seed(8) rbind(fitted(b8.4p, newdata = nd, summary = F, nsamples = 20), fitted(b8.5p, newdata = nd, summary = F, nsamples = 20)) %>% # wrangle data.frame() %>% set_names(mutate(nd, name = str_c(shade_cent, water_cent, sep = "_")) %>% pull()) %>% mutate(row = rep(1:20, times = 2), fit = rep(c("b8.4", "b8.5"), each = n() / 2)) %>% pivot_longer(-c(row:fit), values_to = "blooms_std") %>% separate(name, into = c("shade_cent", "water_cent"), sep = "_") %>% mutate(shade_cent = shade_cent %>% as.double(), water_cent = water_cent %>% as.double()) %>% # these will come in handy for ggplot2::facet_grid() mutate(x_grid = str_c("shade_cent = ", shade_cent), y_grid = fit) %>% # plot! ggplot(aes(x = water_cent, y = blooms_std, group = row)) + geom_hline(yintercept = 0:1, linetype = 2) + geom_line(aes(alpha = row == 1, size = row == 1), color = palette_pander(n = 6)[6]) + scale_size_manual(values = c(1/2, 1)) + scale_alpha_manual(values = c(1/3, 1)) + scale_x_continuous("Water (centered)", breaks = c(-1, 0, 1)) + scale_y_continuous("Blooms (standardized)", breaks = c(0, .5, 1)) + ggtitle("Prior predicted blooms") + coord_cartesian(xlim = c(-1, 1), ylim = c(-0.5, 1.5)) + theme(legend.position = "none", strip.background = element_rect(fill = alpha(palette_pander(n = 2)[2], 1/3))) + facet_grid(y_grid ~ x_grid) It was the aes() statement within geom_line() and the scale_size_manual() and scale_alpha_manual() lines that followed that allowed us to bold the one line in each panel. Relatedly, it was the set.seed() line at the top of the code block that made the results reproducible. What can we say about these priors, overall? They are harmless, but only weakly realistic. Most of the lines stay within the valid outcome space. But silly trends are not rare. We could do better. We could also do a lot worse, such as flat priors which would consider plausible that even a tiny increase in shade would kill all the tulips. If you displayed these priors to your colleagues, a reasonable summary might be, “These priors contain no bias towards positive or negative effects, and at the same time they very weakly bound the effects to realistic ranges.” (p. 260) ## 8.4Summary Bonus: conditional_effects() The brms package includes the conditional_effects() function as a convenient way to look at simple effects and two-way interactions. Recall the simple univariable model, b8.1b. b8.1b$formula
## log_gdp_std ~ 1 + rugged_std_c
We can look at the regression line and its percentile-based intervals like so.
conditional_effects(b8.1b)
If we feed the conditional_effects() output into the plot() function with a points = T argument, we can add the original data to the figure.
conditional_effects(b8.1b) %>%
plot(points = T)
We can further customize the plot. For example, we can replace the intervals with a spaghetti plot. While we’re at it, we can use point_args to adjust the geom_jitter() parameters and line_args() to adjust the line marking off the posterior median.
conditional_effects(b8.1b,
spaghetti = T,
nsamples = 200) %>%
plot(points = T,
point_args = c(alpha = 1/2, size = 1),
line_args = c(colour = "black"))
With multiple predictors, things get more complicated. Consider our multivariable, non-interaction model, b8.2.
b8.2$formula ## log_gdp_std ~ 0 + cid + rugged_std_c conditional_effects(b8.2) We got one plot for each predictor, controlling the other predictor at zero. Note how the plot for cid treated it as a categorical variable. This is because the variable was saved as a character in the original data set. b8.2$data %>%
glimpse()
## Rows: 170
## Columns: 3
## $log_gdp_std <dbl> 0.8797119, 0.9647547, 1.1662705, 1.1044854, 0.9149038, 1.0816501, 1.1909183, … ##$ cid <chr> "1", "2", "2", "2", "2", "2", "2", "2", "2", "1", "2", "1", "1", "2", "2", "2…
## $rugged_std_c <dbl> -0.07661760, 0.33760362, -0.09096781, -0.09000038, 0.21844851, -0.21399264, -… The results would have been similar had we saved cid as a factor. Things get more complicated with the non-linear interaction model, b8.3. b8.3$formula
## log_gdp_std ~ 0 + a + b * rugged_std_c
## a ~ 0 + cid
## b ~ 0 + cid
conditional_effects(b8.3)
The conditional_effects() function correctly picked up on how we used the a parameter to make two intercepts according to the two levels of cid. However, it did not pick up our intent to use the b parameter as a stand-in for the two levels of the slope for rugged_std_c. Instead, it only showed the slope for rugged_std_c == 1. In GitHub issue #925, Bürkner clarified this is because “brms will only display interactions by default if the interactions are explictely provided within linear formulas. brms has no way of knowing what variables in non-linear models actually interact.” However, the effects argument provides a workaround.
conditional_effects(b8.3, effects = "rugged_std_c:cid")
The conditional_effects() function defaults to expressing interactions such that the first variable in the term–in this case, rugged_std_c–is on the $$x$$-axis and the second variable in the term–cid, treated as an integer–is treated as a factor using different values for the fill and color of the trajectories. See what happens when we change the ordering.
conditional_effects(b8.3, effects = "cid:rugged_std_c")
Now our binary index variable cid is on the $$x$$-axis and the error bars for the effects are now depicted by three levels of the continuous variable rugged_std_c. By default, those are the mean $$\pm$$ one standard deviation. We might confirm those values like this.
b8.3$data %>% summarize(mean = mean(rugged_std_c), mean + 1 sd = mean(rugged_std_c) + sd(rugged_std_c), mean - 1 sd = mean(rugged_std_c) - sd(rugged_std_c)) %>% mutate_all(round, digits = 2) ## mean mean + 1 sd mean - 1 sd ## 1 0 0.19 -0.19 Now we might use b8.5, our interaction model with two continuous variables, to get a sense of how this behavior works in that context. b8.5$formula
## blooms_std ~ 1 + water_cent + shade_cent + water_cent:shade_cent
conditional_effects(b8.5, effects = "water_cent:shade_cent")
Once again, the three levels of the second variable in the interaction term, shade_cent, are the mean $$\pm$$ one standard deviation. If you’d like to set these to different values, such as -1, 0, and 1, define those within a list and feed that list into the int_conditions argument within conditional_effects(). We’ll do that in the next plot in a bit.
Though the paradigm of using the conditional_effects() and plot() functions allows users to augment the results with a variety of options, users to not have the full flexibility of ggplot2 with this approach. If you’re picky and want to augment the plot further with other ggplot2 settings, you need to:
• save the settings from conditional_effects() as an object,
• feed that object into plot(),
• set the plot argument to FALSE within the plot() function,
• index using bracket, and finally
• customize away with other ggplot2 functions.
Here’s an example of what that might look like.
p1 <-
conditional_effects(b8.5,
plot(p1,
points = T,
plot = F)[[1]] +
scale_fill_pander() +
scale_colour_pander() +
scale_x_continuous(breaks = -1:1) +
theme(legend.position = "none",
panel.grid.minor = element_blank()) +
facet_wrap(~ shade_cent, labeller = label_both)
I tend to prefer using other plotting methods when visualizing models, so we won’t be seeing much more from the conditional_effects() function in this ebook. But if you like method, you can find more ideas by checking out the conditional_effects section of the brms reference manual or searching for “conditional_effects” under the “brms” tag on the Stan Forums.
## Session info
sessionInfo()
## R version 4.0.4 (2021-02-15)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] tidybayes_2.3.1 patchwork_1.1.1 ggrepel_0.9.1 ggdag_0.2.3 ggthemes_4.2.4 forcats_0.5.1
## [7] stringr_1.4.0 dplyr_1.0.5 purrr_0.3.4 readr_1.4.0 tidyr_1.1.3 tibble_3.1.0
## [13] ggplot2_3.3.3 tidyverse_1.3.0 brms_2.15.0 Rcpp_1.0.6
##
## loaded via a namespace (and not attached):
## [1] readxl_1.3.1 backports_1.2.1 plyr_1.8.6 igraph_1.2.6
## [5] svUnit_1.0.3 splines_4.0.4 crosstalk_1.1.0.1 TH.data_1.0-10
## [9] rstantools_2.1.1 inline_0.3.17 digest_0.6.27 htmltools_0.5.1.1
## [13] viridis_0.5.1 rsconnect_0.8.16 fansi_0.4.2 magrittr_2.0.1
## [17] graphlayouts_0.7.1 modelr_0.1.8 RcppParallel_5.0.2 matrixStats_0.57.0
## [21] xts_0.12.1 sandwich_3.0-0 prettyunits_1.1.1 colorspace_2.0-0
## [25] rvest_0.3.6 ggdist_2.4.0.9000 haven_2.3.1 xfun_0.22
## [29] callr_3.5.1 crayon_1.4.1 jsonlite_1.7.2 lme4_1.1-25
## [33] survival_3.2-7 zoo_1.8-8 glue_1.4.2 polyclip_1.10-0
## [37] gtable_0.3.0 emmeans_1.5.2-1 V8_3.4.0 distributional_0.2.2
## [41] pkgbuild_1.2.0 rstan_2.21.2 abind_1.4-5 scales_1.1.1
## [45] mvtnorm_1.1-1 DBI_1.1.0 miniUI_0.1.1.1 viridisLite_0.3.0
## [49] xtable_1.8-4 stats4_4.0.4 StanHeaders_2.21.0-7 DT_0.16
## [53] htmlwidgets_1.5.2 httr_1.4.2 threejs_0.3.3 arrayhelpers_1.1-0
## [57] ellipsis_0.3.1 farver_2.0.3 pkgconfig_2.0.3 loo_2.4.1
## [61] dbplyr_2.0.0 utf8_1.1.4 labeling_0.4.2 tidyselect_1.1.0
## [65] rlang_0.4.10 reshape2_1.4.4 later_1.1.0.1 dagitty_0.3-1
## [69] munsell_0.5.0 cellranger_1.1.0 tools_4.0.4 cli_2.3.1
## [73] generics_0.1.0 broom_0.7.5 ggridges_0.5.2 evaluate_0.14
## [77] fastmap_1.0.1 processx_3.4.5 knitr_1.31 fs_1.5.0
## [81] tidygraph_1.2.0 pander_0.6.3 ggraph_2.0.4 nlme_3.1-152
## [85] mime_0.10 projpred_2.0.2 xml2_1.3.2 compiler_4.0.4
## [89] bayesplot_1.8.0 shinythemes_1.1.2 rstudioapi_0.13 curl_4.3
## [93] gamm4_0.2-6 reprex_0.3.0 tweenr_1.0.1 statmod_1.4.35
## [97] stringi_1.5.3 highr_0.8 ps_1.6.0 Brobdingnag_1.2-6
## [101] lattice_0.20-41 Matrix_1.3-2 nloptr_1.2.2.2 markdown_1.1
## [105] shinyjs_2.0.0 vctrs_0.3.6 pillar_1.5.1 lifecycle_1.0.0
## [109] bridgesampling_1.0-0 estimability_1.3 httpuv_1.5.4 R6_2.5.0
## [113] bookdown_0.21 promises_1.1.1 gridExtra_2.3 codetools_0.2-18
## [117] boot_1.3-26 colourpicker_1.1.0 MASS_7.3-53 gtools_3.8.2
## [121] assertthat_0.2.1 withr_2.4.1 shinystan_2.5.0 multcomp_1.4-16
## [125] mgcv_1.8-33 parallel_4.0.4 hms_0.5.3 grid_4.0.4
## [129] coda_0.19-4 minqa_1.2.4 rmarkdown_2.7 ggforce_0.3.2
## [133] shiny_1.5.0 lubridate_1.7.9.2 base64enc_0.1-3 dygraphs_1.1.1.6 | 2021-08-01 10:47:43 | {"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": 2, "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": 0.8678656220436096, "perplexity": 9923.244606816606}, "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/1627046154175.76/warc/CC-MAIN-20210801092716-20210801122716-00327.warc.gz"} |
https://www.eocharles.com/category/bible/luke-22/ | ## My body, my blood, given for you.
Luke 22:19
And he took bread and, having given praise, he gave it to them when it had been broken, saying, This is my body, which is given for you: do this in memory of me.
Luke 22:20
And in the same way, after the meal, he took the cup, saying, This cup is the new testament, made with my blood which is given for you.
## Be in communion with the Lord
And he took bread and, having given praise, he gave it to them when it had been broken, saying, This is my body, which is given for you: do this in memory of me.
Luke 22:19
And in the same way, after the meal, he took the cup, saying, This cup is the new testament, made with my blood which is given for you.
Luke 22:20 | 2022-05-27 02:56:03 | {"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": 0.8957655429840088, "perplexity": 2383.566872909896}, "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/1652662631064.64/warc/CC-MAIN-20220527015812-20220527045812-00424.warc.gz"} |
https://www.physicsforums.com/threads/molarity-notation.70138/ | # Molarity notation
1. Apr 5, 2005
### preet
What does the following notation (to the power of -1) mean? TiA
ex. $$[Na] = 0.050 mol L ^{-1}$$
2. Apr 5, 2005
### preet
I have another question (did not want to create a new thread):
"What is the ratio x:y when the equation below is properly balanced?"
$$xSn^{2+}(aq) + y Ag^{+}(aq) -> n Sn^{4+}(aq) + m Ag^{+}(s)$$
I've never seen a question like this before... an explanation or a link to a site or something would be greatly appreciated.
3. Apr 5, 2005
### pack_rat2
"L^-1" means "per liter." 0.05 mol/L is 0.05 M.
4. Apr 5, 2005
### dextercioby
For the first post,it's simply the unit 'liter' (which should be shortened 'l',not 'L' (that stands for length)) raised to the power "-1".
For the second,i'm sure u miss the negative ions...Silver ion is a spectator in a redox ionic reaction.I don't see a connection between "x" & "y".And next time use $\rightarrow$ (code \rightarrow).
Daniel.
5. Apr 5, 2005
### pack_rat2
Simply balance the equation and give the ratio of x to y. This is a re-dox reaction. They're usually solved using the method of "half-reactions."
6. Apr 5, 2005
### pack_rat2
Ooooops! I thought that was "Ag," not "Ag+"....and there is something wrong, here. Sn(+4) + 2Ag -> Sn(+2) + 2Ag(+) might be the reaction, but not what you have.
7. Apr 5, 2005
### dextercioby
That's what i said above and it seemed weird to me,too that "Ag" doesn't undergo either reduction or oxdation.
Daniel.
8. Apr 5, 2005
9. Apr 5, 2005
### dextercioby
$$Sn^{2+}_{(aq)} + Ag^{+}_{(aq)}\rightarrow Sn^{4+}_{(aq)}+Ag\downarrow$$
Now you can do the redox properly...
Daniel.
10. Apr 6, 2005
### Staff: Mentor
11. Apr 6, 2005
### dextercioby
Nope,it's incorrect.It's the same way they teach "k" instead of "K" for Kg...It's outrageous.
Daniel.
12. Apr 6, 2005
### Staff: Mentor
Have you read comment on the NIST page? L was adopted in 1979 and is internationally accepted. So it is correct.
IUPAC lists both forms just like NIST does:
http://www.iupac.org/reports/1993/homann/units51.html [Broken]
I was taught l 30 years ago and I am not advocating L - but it seems L is now accepted by all major institutions and I must agree with the fact that L is much less prone to be mistaken with 1 then l is. It doesn't mean I like it :)
Chemical calculators for labs and education
BATE - pH calculations, titration curves
Last edited by a moderator: Apr 21, 2017 at 2:22 PM
13. Apr 6, 2005
### pack_rat2
I usually use "L" for liter, and "ml" for milliliter. When on a computer or on the Net where certain specific fonts are employed, I *HATE* to use "l" because it looks too much like "I".
14. Apr 6, 2005
### dextercioby
I explained the reasoning with "l" vs."L".Capitals are used for physical quantities and multiples.Liter is not a part of the units which use capitals...I'm sorry for the French,but they're wrong.
Daniel.
15. Apr 7, 2005
### Staff: Mentor
m stands for mili and M for Mega - both are SI multiples.
s stands for second, K for Kelvin - both are base SI units.
So either I don't understand what you have written or you are not right
What I am aiming at is that there are no 'hard' rules.
And, while we can criticise units abbreviations defined by international organizations like IUPAC or CGPM we have no choice but to accept them (and to fight for changes if we think it is important)
Chemical calculators for labs and education
BATE - pH calculations, titration curves
16. Apr 7, 2005
### dextercioby
Sorry,i wasn't really precise.It happens from time time,i'm human,though.I may be wrog,occasionally.
Daniel.
17. Apr 13, 2005
### preet
Im sorry to bring this post up but I wanted to be sure that I was doing the redox equation right...
$$Sn^{2+}_{(aq)} + Ag^{+}_{(aq)}\rightarrow Sn^{4+}_{(aq)}+Ag$$
was the equation (sorry for my typo earlier)
And I needed to find the coeffecient on the left side of the equation (in front of tin and silver)... so..
*tin has lost two electrons
$$Sn^{2+}\rightarrow Sn^{4+}+ 2e^{-}$$
*silver has gained one electron (one atom of silver has gained one electron)
$$Ag^{+} + e^{-}\rightarrow Ag$$
*2 electrons were lost by tin so to balance that I multiply Ag by 2...
and the coeffecients are 1 in front of Sn and 2 in front of Ag? Is this right? TiA!
18. Apr 13, 2005
### dextercioby
Yes,it is correct...
Daniel. | 2017-04-24 15:21:35 | {"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": 0.4068574607372284, "perplexity": 5548.585228825692}, "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-2017-17/segments/1492917119637.34/warc/CC-MAIN-20170423031159-00376-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://stats.stackexchange.com/questions/13932/is-there-an-r-implementation-to-some-mixed-models-quantile-regression-statistica/13934 | Is there an R implementation to some mixed models quantile regression statistical procedure?
I would like to find some solution for performing a mixed effect model of quantile regression.
From my google searching, I was not able to find an R implementation for such a procedure (only warnings that "this is not for the faint hearted").
I would like to solve a simple situation where we have one x one y, and one "subject" variable.
Any suggestions on what to do with this?
-
Can you include a specification of the model you're trying to fit? In a comment to Gavin's answer, you mention several covariates. What model structure are you seeking? – Iterator Aug 6 '11 at 22:33
The extent to which one can answer your question depends on what sort of study you have in mind. Roger Koenker has done some work on quantile regression for longitudinal or panel data. Some details, a paper, and an early set of R code is available from Roger's website.
Do note the message on that webpage that it is now easier to do the methods discussed in the paper using qrss() in the quantreg package, shrinking fixed effects using the lasso penalty.
-
Hi Gavin. A study design: Let us say I have heights of kids and their parents - and I wish to estimate the 95 quantile of the kids height from the parents one. But the kids I have are also divided to kids from different countries, and I want countries to be a random effect. We might also want to account for gender and age, for example. Any further advice would be great. :) – Tal Galili Aug 6 '11 at 11:37
Recently, the lqmm package "Linear Quantile Mixed Models" has been uploaded on CRAN. Although I have never used it, the lqmm package seems to do what you want.
This presentation from the useR! 2011 conference shows some examples of the package. Here is a description of the package taken from the useR! 2011 conference abstracts:
Conditional quantile regression (QR) pertains to the estimation of unknown quantiles of an outcome as a function of a set of covariates and a vector of fixed regression coefficients. In the last few years, the need for extending the capabilities of QR for independent data to deal with clustered sampling designs (e.g., repeated measures) has led to several and quite distinct approaches. Here, I consider the likelihood-based approach that hinges on the strict relationship between the weighted L₁ norm problem associated with a conditional QR model and the asymmetric Laplace distribution (Geraci and Bottai, 2007).
In this presentation, I will illustrate the use of the R package lqmm to perform QR with mixed (fixed and random) effects for a two-level nested model. The estimation of the fixed regression coefficients and of the random effects' covariance matrix is based on a combination of Gaussian quadrature approximations and optimization algorithms. The former include Gauss-Hermite and Gauss-Laguerre quadratures for, respectively, normal and double-exponential (i.e., symmetric Laplace) random effects; the latter include a modified compass search algorithm and general purpose optimizers (optim and optimize). Modelling and inferential issues are detailed in Geraci and Bottai (2011) (a preliminary draft is available upon request). The package also provides commands for the case of independent data.
-
I've recently used lqmm too, and it does exactly what the OP wants. +1 – andrea May 12 '12 at 22:13 | 2013-05-25 12:19:31 | {"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": 0.5595592856407166, "perplexity": 970.6722198139232}, "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-2013-20/segments/1368705948348/warc/CC-MAIN-20130516120548-00014-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://tutorme.com/tutors/65087/interview/ | TutorMe homepage
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Linear Algebra
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Question:
If $$A$$ and $$B$$ are linear transformations (on the same vector space), then a necessary and sufficient condition that both $$A$$ and $$B$$ be invertible is that both $$AB$$ and $$BA$$ be invertible.
Sarah B.
Let us show that if $$V$$ is a vector space and $$A,B\in L(V,V)$$, then $$A,B$$ are invertible iff $$AB, BA$$ are invertible. To do this, lets show that if $$f:X\rightarrow Y, g:Y\rightarrow Z$$ and if $$g\circ f$$ is injective, then $$f$$ is injective and if $$g\circ f$$ is surjective then $$g$$ is surjective. First, let us suppose that $$g\circ f$$ is injective, but that $$f$$ is not. Then there exists $$x\neq y$$ in $$X$$ such that $$f(x)=f(y)$$. We then have that $$g(f(x))=g(f(y))$$, contradicting our assumptions that $$g\circ f$$ is injective. Thus $$f$$ must be injective. Now, let us suppose that $$g\circ f$$ is surjective but that $$g$$ is not. Then we have that $$g(f(X))\subseteq g(Y)\subset Z$$, which contradicts that $$g\circ f$$ is surjective. Thus, $$g$$ must be surjective. From what we just proved, we can show that if $$f,g: X\rightarrow X$$ and if $$g\circ f$$ and $$f\circ g$$ are bijections, then $$f$$ and $$g$$ are bijections. As $$g\circ f$$ is injective, we know that $$f$$ is injective and as $$f\circ g$$ is surjective, we know that $$f$$ is surjective. Thus $$f$$ is a bijection. Similarly, we have that as $$f\circ g$$ is injective, we have that $$g$$ is injective and as $$g\circ f$$ is surjective we know $$g$$ is surjective. And so we have that $$g$$ is a bijection. And so from all of this, we can see that if $$AB$$ and $$BA$$ are invertible (bijective), then so are $$A$$ and $$B$$. And, for the other direction, if $$A$$ and $$B$$ are invertible, then there exists matrices $$A^{-1}$$ and $$B^{-1}$$ such that $$AA^{-1}=I$$ and $$BB^{-1}=I$$. And so consider the matrices $$A^{-1}B^{-1} and B^{-1}A^{-1}$$. we then have that $$(AB)(B^{-1}A^{-1})=I$$ and $$(BA)(A^{-1}B^{-1})=I$$.
Calculus
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Question:
Prove that the series $$\sum_{n=1}^{\infty} (-1)^n \frac{x^2+n}{n^2}$$ converges uniformly in every bounded interval, but does not converge absolutely for any value on $$x$$.
Sarah B.
We have that $$\sum |(-1)^n\frac{x^2+n}{n^2}|=\sum |\frac{x^2}{n^2}+\frac{1}{n}|\geq \sum |\frac{1}{n}|.$$ We cna see that the rightmost sum is the harmonic series, which diverges. Thus, by the comparison test we have that the leftmost series must also diverge.\ Now, to show that the series converges uniformly in every bounded interval $$[a,b]$$, let $$\epsilon >0$$ be given. Define $$X$$ to be $$\sup\{|a|,|b|\}$$. Define the partial sum $$f_m$$ to be $$f_m=\sum_{n=1}^m (-1)^n \frac{x^2+n}{n^2}.$$ We can rearrange this to get $$f_m=\sum_{n=1}^m (-1)^n \frac{1}{n}+x^2\sum_{n=1}^m (-1)^n \frac{1}{n^2}.$$ We know that the alternating harmonic series and $$\sum\frac{1}{n^2}$$ converges; thus, by the Cauchy criterion for convergence we can find $$N$$ such that $$p>q>N\Rightarrow |\sum_{n=q}^p (-1)^n\frac{1}{n}|<\frac{\epsilon}{2}$$ and we can find an $$M$$ such that $$p>q>M\Rightarrow |\sum_{n=q}^p (-1)^n\frac{1}{n^2}|<\frac{\epsilon}{2|X|^2}.$$ Thus, we can choose $$p>q>\max\{N,M\}$$ so that we have $$|f_p(x)-f_q(x)|=|\sum_{n=q}^p (-1)^n \frac{1}{n}+x^2\sum_{n=q}^p (-1)^n \frac{1}{n^2}|$$ $$\leq |\sum_{n=q}^p (-1)^n\frac{1}{n}|+|x^2\sum_{n=q}^p (-1)^n \frac{1}{n^2}|$$ $$\frac{\epsilon}{2}+\frac{\epsilon x^2}{2X^2}\leq \frac{\epsilon}{2}+\frac{\epsilon}{2}=\epsilon.$$
Algebra
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Question:
Let $$p$$ be a prime. Show that in $$\mathbb{Z}_p$$ we have $$(a+b)^p=a^p+b^p$$.
Sarah B.
We know that the order of $$\mathbb{Z}_p$$ is $$p$$. And as $$p$$ is a prime, we know that $$\mathbb{Z}_p$$ is a commutative ring. As the binomial expansion is valid in a commutative ring, we know that $$(a+b)^p=\sum_{k=0}^{p} \frac{p!}{k!(p-k)!} a^{p-k}b^k$$. For $$k=0$$ or $$k=p$$, we have that $$\frac{p!}{k!(p-k)!}=1$$. This means that $$(a+b)^p=a^p$$ for $$k=0$$, and $$(a+b)^p=b^p$$ for $$k=p$$. For any other value for $$k$$, we know that $$\frac{p!}{k!(p-k)!}$$ is an integer. This means that its' denominator, $$k!(p-k)!$$, divides $$p!$$. But since $$p$$ is a prime and $$p$$ is not a factor of $$k!(p-k)!$$, we can deduce that $$k!(p-k)!$$ divides $$(p-1)!$$. In other words, $$\frac{p!}{k!(p-k)!}=1$$ is a multiple of $$p$$ when $$k$$ is not $$0$$ or $$P$$. Thus, $$\frac{p!}{k!(p-k)!}=1\cong 0 \mod p$$. And so the only nonzero terms of $$(a+b)^p=\sum_{k=0}^{p} \frac{p!}{k!(p-k)!} a^{p-k}b^k$$ occur when $$k=0$$ and $$k=p$$, giving us that $$(a+b)^p=a^p+b^p$$.
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Contact Sarah | 2018-12-13 03:29:50 | {"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": 0.9682059288024902, "perplexity": 43.01158407493649}, "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/1544376824448.53/warc/CC-MAIN-20181213032335-20181213053835-00257.warc.gz"} |
https://www.physicsforums.com/threads/big-oh-notation-help.329112/ | # Big Oh notation help?
1. Aug 5, 2009
### AxiomOfChoice
Can someone please explain what it means to say something like
$$x = x_0 + \mathcal{O}(y)$$
?
2. Aug 5, 2009
### arildno
Nothing.
You must include in your expression a "as x goes to.."
Without that, it is meaningless.
3. Aug 5, 2009
### g_edgar
$\cos x = 1 + O(x^2)$ as $x \to 0$ means:
$$\frac{\cos x - 1}{x^2}$$
is bounded in some neighborhood of $0$ . | 2017-08-20 23:37:31 | {"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": 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": 0.6786022186279297, "perplexity": 4904.825532449785}, "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/1502886106996.2/warc/CC-MAIN-20170820223702-20170821003702-00126.warc.gz"} |
http://en.wikipedia.org/wiki/Binomial | # Binomial
In algebra, a binomial is a polynomial with two terms[1] —the sum of two monomials—often bound by parentheses or brackets when operated upon. It is the simplest kind of polynomial after the monomials.
## Operations on simple binomials
• The binomial $a^2 - b^2$ can be factored as the product of two other binomials.
$a^2 - b^2 = (a + b)(a - b).$
This is a special case of the more general formula: $a^{n+1} - b^{n+1} = (a - b)\sum_{k=0}^{n} a^{k}\,b^{n-k}$.
This can also be extended to $a^2 + b^2 = a^2 - (ib)^2 = (a - ib)(a + ib)$ when working over the complex numbers
• The product of a pair of linear binomials $(ax+b)$ and $(cx+d)$ is:
$(ax+b)(cx+d) = acx^2+adx+bcx+bd.$
• A binomial raised to the nth power, represented as
$(a + b)^n$
can be expanded by means of the binomial theorem or, equivalently, using Pascal's triangle. Taking a simple example, the perfect square binomial $(p+q)^2$ can be found by squaring the first term, adding twice the product of the first and second terms and finally adding the square of the second term, to give $p^2+2pq+q^2$.
• A simple but interesting application of the cited binomial formula is the "(m,n)-formula" for generating Pythagorean triples: for m < n, let $a=n^2-m^2$, $b=2mn$, $c=n^2+m^2$, then $a^2+b^2=c^2$. | 2013-12-10 04:51:10 | {"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": 0, "mathjax_asciimath": 0, "img_math": 14, "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": 0.9413483142852783, "perplexity": 259.166625395232}, "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-2013-48/segments/1386164009403/warc/CC-MAIN-20131204133329-00020-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://clay6.com/qa/48402/in-rule-method-the-null-set-is-represented-by | Want to ask us a question? Click here
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0 votes
# In rule method the null set is represented by
Can you answer this question?
## 1 Answer
0 votes
{x : x $\neq$ x}
Hence (D) is the correct answer.
answered Jun 24, 2014 | 2016-12-02 19:49:47 | {"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": 0.69319748878479, "perplexity": 2467.187604446358}, "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-2016-50/segments/1480698540563.83/warc/CC-MAIN-20161202170900-00202-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://zbmath.org/?q=ai%3Akucera.antonin+se%3A00004198 | zbMATH — the first resource for mathematics
A class of degrees of unsolvability for functions not possessing a fixed point. (Russian) Zbl 0711.03015
The paper is devoted to the study of the class F of degrees of unsolvability of functions f having no fixed points (i.e. such that $$\forall x(W_{f(x)}\neq W_ x)$$. The main result is that there exists a $$\Pi^ 0_ 1$$ class $${\mathcal A}$$ of sets such that F is equal to $$\{$$ dg(A): $$A\in {\mathcal A}\}$$.
Reviewer: R.Murawski
MSC:
03D30 Other degrees and reducibilities in computability and recursion theory 03D35 Undecidability and degrees of sets of sentences
Keywords:
degrees of unsolvability | 2021-01-21 06:41:31 | {"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": 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": 0.7370539307594299, "perplexity": 493.21879588273316}, "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/1610703522242.73/warc/CC-MAIN-20210121035242-20210121065242-00035.warc.gz"} |
https://forum.allaboutcircuits.com/threads/spd3303x-e-configure-lan-and-try-reading-firmware.167969/ | # SPD3303X-E configure LAN and try reading firmware ?
#### DarthVolta
Joined Jan 27, 2015
390
I have the SPD3303X-E and so I want to practice on it for when I get an AWG and scope. I'm on Windows 10, and I know very little about programing, LAN, firmware, hacking, LINUX, UNIX....although I'm enough of a tech geek to watch talks on some of this for fun.
What do I know so far, I got the Easypower and N.I. software installed and had Easypower running the PSU over USB and it works nicely.
So I un-hooked the USB and hooked up a LAN cable, and my PC and the PSU are blinking the LAN icon. The DCHP button is on, but the IP, NetMask, GateWay are all zero's. Is that supposed to be allowed ?
I ran IPCONFIG and found a device on the ethernet, so that must be it on my mobo. So I went into the PSU LAN settings and set it to what IP config said., it said nothing for gateway, so does that mean set 0's ? That's what I did.
Nothing in Win10 has said 'new LAN decive connected", where-as over USB it did some auto-setup.
So IDK if I need software for LAN ? I DL'ed some telnet program called Putty, and something else called busybox for a later step.
But for all I know all this is meant for LINUX.
For now I just what to try part of this
vt100
• Contributor
• Posts: 15
• Country:
Re: Siglent .ads firmware file format
« Reply #212 on: October 08, 2018, 03:13:09 am »
This process will obtain your license keys from a core dump of the scope application itself, in case you lost the paperwork after you purchased them (of course). No "guessing games" like the other software posted (although it was a fun intellectual exercise!)
Skill level: Easy/Moderate
Risk: Slim to none.
Steps:
1. download full armv7l version of busybox which has core dump enabled.
2. put version on thumb disk
3. reboot scope to known state
5. insert usb stick
6. copy busybox binary from usb to /tmp:
cp /usr/bin/siglent/usr/mass_storage0/U-disk/busybox-armv7l /tmp
7. unmount and remove usb
umount /usr/bin/siglent/usr/mass_storage/U-disk0
(and then remove usb stick)
8. identify and kill existing sds1000b.app
ps -ef | grep sds | awk '{printf "kill -9 %s\n", $1}' | ash 9. change to /tmp directory: cd /tmp 10. launch new busybox ash shell /tmp/busybox_armv7l ash (when you press enter it looks like nothing happens, but something does) 11. re-launch scope app in new busybox environment in background /usr/bin/siglent/sds1000b.app & 12. increase core dump ulimit to unlimited: ulimit -c unlimited you can verify new limit by typing ulimit -c and you should get a response "unlimited" 12. kill scope app again, telling OS to create a core dump of the app: ps -ef | grep sds | awk '{printf "kill -ABRT %s\n",$1}' | ash
13. wait a few seconds, and press enter once or twice. you should see:
[1]+ Aborted (core dumped) /usr/bin/siglent/sds1000b.app
if you do not, you did something wrong, go to step #3
14. verify core dump is in /tmp:
ls /tmp/core*
you should see something like this:
-rw------- 1 root root 377511936 Jan 1 00:14 /tmp/core
if not, you did something wrong, go to step #3
15. exit out of usb version of busybox shell
exit
(it will look like nothing happens when you press enter, but, something does)
16. re-launch Siglent scope application. See Step #11
17. insert usb drive
18. copy core dump to thumb drive
cp core /usr/bin/siglent/usr/mass_storage/U-disk0/coredump.bin
(this will take a minute or two, its a big file)
19. unmount usb stick and remove (see step #7)
20. Insert USB stick on Windows/Mac/Linux and open the coredump.bin file in your favorite hex editor.
21. Search for string "SDS1000X-E". Keep searching until you find the string next to either your scopeid (if you do not know your scope id, you can get it using the SCPI SCOPEID? command thru the web interface) or your serial number.
22. When you locate the entry with your scope ID, you will see a series of 5 16-character strings below it (one will look like a 32 character string, split it into half so you have two 16-character strings. These are your 100, 200, 50 and 70 mhz license keys, respectively. The one that appears twice is the license key your scope is currently licensed under.
23. You can license a different bandwidth by typing MCBD (license key) at the scope's SCPI web interface. It is necessary to reboot after you do this for everything to reset and take effect. You can verify the bandwidth by typing PRBD? through the SCPI web interface.
24. When you locate the entry with your serial number, you will see a series of (at least) 3 16-character strings. If you have any options already licensed, those keys will appear twice. if you have no options licensed, they only appear once. The keys are, respectively, AWG, WIFI and MSO.
25. You can license any options through the scope's SCPI interface using LCISL (option),(key) where (option) is AWG, WIFI or MSO and (key) is the 16-character key.
26. after doing so, even though the options are immediately licensed and active, I recommend a reboot for the new options to take effect.
27. Write keys down in a safe place so you do not lose them again.
Last edited: | 2020-05-30 09:39:20 | {"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": 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": 0.2547582685947418, "perplexity": 8278.887548626068}, "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-2020-24/segments/1590347407667.28/warc/CC-MAIN-20200530071741-20200530101741-00414.warc.gz"} |
https://math.stackexchange.com/questions/1813988/why-is-the-dot-product-defined-as-a-scalar-and-the-cross-product-a-normal-vector | # Why is the dot product defined as a scalar and the cross product a normal vector?
These are the definitions of the dot and cross products as I understand them:
The cross product provides a vector perpendicular to both input vectors with magnitude proportional to the area of the parallelogram traced out by the vectors.
a × b = ∥a∥∥b∥sinθ n
where n is the normal vector
The dot product provides a scalar proportional to the magnitudes of both vectors and the cosine of the angle between them (θ = 0° is pure magnitude multiplication whereas θ = 90° is 0).
a.b = ∥a∥∥b∥cosθ
Assuming I understand the definitions correctly, I don't see why the dot product is defined as a scalar and the cross product a vector. Why was the dot product not defined as a vector perpendicular to the input vectors with magnitude proportional to the cosine of the angles between them. Likewise why was the cross product not defined as a scalar representing the area of the parallelogram traced out between them?
For example:
a.b = ∥a∥∥b∥cosθ n
a × b = ∥a∥∥b∥sinθ
• Remember, the cross product is only defined in $\mathbb{R}^3$ while dot product is in $\mathbb{R}^n$. We cannot define the perpendicular in a general $n$-space because with 2 input vectors there are $n-2$ directions that are perpendicular to the inputs. – Cbjork Jun 5 '16 at 2:18
• I think you have it a little backwards. The dot product is not necessarily defined as being the product of the vectors magnitudes multiplied by the cosine of the angle between them and the cross product is not necessarily defined to be perpendicular etc. Rather, these two things are very nice, geometric, properties of the dot product and cross product. – Jared Jun 5 '16 at 2:19
• I pulled the definitions from wiki so they could be off. I've updated it for clarity. – Andyy K Jun 5 '16 at 2:28
The dot product is the special case of a more general concept, the inner product. If you have a vector space $V$ over the reals or the complex numbers, then an inner product is a map $f : V \times V \to \mathbb{C}$ or $f : V \times V \to \mathbb{R}$ which is conjugate symmetric, positive definite, and linear in its first argument. We usually write $f(u, v) = \langle u, v \rangle$, in which case these properties can be summed up as follows:
• Conjugate symmetry: $\overline{\langle u, v \rangle} = \langle v, u \rangle$, where $\bar{z}$ denotes complex conjugation. Note that this implies $\langle u, u \rangle$ is always real for any vector $u$.
• Positive definiteness: $\langle v, v \rangle \geq 0$ for any $v \in V$, with equality holding iff $v = 0$.
• Linearity in the first argument: $\langle \alpha u + \beta v, w \rangle = \alpha \langle u, w \rangle + \beta \langle v, w \rangle$ where $u, v, w \in V$ and $\alpha, \beta$ are in the field of scalars.
If $V = \mathbb{R}^n$, then we can fix a basis $B = \{ b_i \in \mathbb{R}, 1 \leq i \leq n \}$ and define $\langle b_i, b_i \rangle = 1$ and $\langle b_i, b_j \rangle = 0$ for $i \neq j$. Extending this to all of $\mathbb{R}^n$ by linearity gives us
$$\left \langle \sum_{k=1}^{n} c_k b_k, \sum_{j=1}^{n} d_j b_j \right \rangle = \sum_{1 \leq k, j \leq n} d_k c_j \langle b_i, b_j \rangle = \sum_{i=1}^{n} c_i d_i$$
where positive definiteness is readily verified. You will recognize this expression as the definition of the dot product. Indeed, if we take our basis $B$ to be the standard basis of $\mathbb{R}^n$, then this inner product is the dot product.
Why is this formalism more powerful? A result about the inner product is the Cauchy-Schwarz inequality, which says that $|\langle u, v \rangle| \leq |u| |v|$ where $|u| = \sqrt{\langle u, u \rangle}$. This tells us that
$$-1 \leq \frac{\langle u, v \rangle}{|u| |v|} \leq 1$$
assuming that our field of scalars is $\mathbb{R}$. We then see that the arccosine of this expression is well-defined, so we can define the angle between nonzero vectors $u$ and $v$ as
$$\theta = \arccos \left( \frac{\langle u, v \rangle}{|u| |v|} \right)$$
The properties we expect to be true are then easily verified. This notion extends to infinite dimensional vector spaces over $\mathbb{R}$, where defining angle is not at all obvious. It is then trivially true that we have $\langle u, v \rangle = |u| |v| \cos(\theta)$, since that is how $\theta$ was defined.
The cross product is an entirely separate concept which allows us to find a vector orthogonal to two given vectors in $\mathbb{R}^3$. In addition, its magnitude also gives the area of the parallelogram spanned by the vectors. These properties can be taken as the definition of the cross product (with appropriate care for orientation), or they can be derived as theorems starting from the algebraic definition.
• Thank you for your insightful response. I have a much clearer understanding now – Andyy K Jun 5 '16 at 14:13 | 2019-10-17 17:39:04 | {"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": 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": 0.9489034414291382, "perplexity": 104.48127273715967}, "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/1570986675598.53/warc/CC-MAIN-20191017172920-20191017200420-00110.warc.gz"} |
https://electronics.stackexchange.com/questions/166259/why-are-consumers-located-near-high-voltage-lines-typically-not-connected-to-tho | # Why are consumers located near high-voltage lines typically not connected to those lines but instead are connected through a lower high-voltage line?
A typical grid uses 110..500 kilovolts lines to deliver electricity to substations which lower that to 6..20 kilovolts and then lines with that lower voltage get to consumers where yet other substations are located which finally lower those 6-20 kilovolts to consumer voltage (100 or 230 volts or whatever the local standard is).
Those 110..500 kilovolt lines often pass through areas where those consumers are located. Consumers could be connected to those lines via transformers accepting say 110 kilovolts and outputting consumer voltage. Instead those lines run to faraway somewhere and then another powerline runs back with some lower voltage and a consumer is hooked to the latter. That's a lot of extra wiring.
What's the reason for this design? Why not hook consumers to the closest powerline?
• My guess is because it would cost more to ensure safety, with both installation and maintenance, for the highest voltage side. They probably try to keep the number of distribution points of the higher voltage as minimal as possible. The extra wiring probably isn't that great, since the lower high-voltage line would have to pass through the same distance anyway, to get to the same areas. – CL22 Apr 23 '15 at 12:16
• Insulation requirements are likely to impose a size below which you cannot build a 110kv transformer, whether down to 11kV or 240V, however little power you need from it. Which means a 110kv transformer will cost a lot. So the extra wiring involved in the 11kv circuit would be paid for by reducing the number of 110kv transformers needed. – Brian Drummond Apr 23 '15 at 12:34
• Why don't houses close to freeways have their own exit and entrance ramps, forcing the residents to wind through some irrelevant streets to reach the nearest freeway connector? – Kaz Apr 23 '15 at 20:12
• Why don't you just climb the powerline with two wired alligator clips to attach your house to the 110kV? – Alexander Apr 24 '15 at 13:14
• @sharptooth: Natural selection at work? – Li-aung Yip Apr 24 '15 at 13:49
HV (66kV - 500kV) is... difficult to deal with.
I will rattle off reasons I can think of from the top of my head.
All figures that follow (weights, dollars) are order-of-magnitude guesstimates.
# Clearances
Let's use 220kV as an example. The Australian HV substation standard AS 2067 nominates the following clearances required for 220kV equipment:
• Phase to earth - 2100mm. That is, no 220kV conductor may be within 2 metres of any earthed conductor (say, a transformer tank, or a steel pole.) Edit: Actually, I should have quoted the Non Flashover Distance (N) here.
• Phase to phase clearance - 2,415mm. That is, the 220kV aerial conductors must be at least 2.4m apart at all times.
• Horizontal safety clearance - 4,125mm. All live parts must be at least 4,125mm above any surface a person can stand on.
• Vertical safety clearance - 3,565 mm.
Which is to say there is no such thing as a 'compact' 220kV substation. (Well, there is; substations based on gas-insulated switchgear can be very compact, but you don't want to know how much they cost.)
The minimum size for a 220kV substation, containing the required equipment and maintaining all these clearances, is at least a 20m × 20m square, i.e. the size of a suburban block of land.
It would also have to have structures at least 4 metres high, which is hard to blend into the suburban landscape.
In addition to the above clearances required to prevent people getting directly electrocuted, you also have to contend with -
• Fire safety radius in case a transformer drops 10,000 litres of insulating oil and catches fire. From memory, at least 10 metres.
• Radius in case of electrical explosion. Typical threshold radius for receiving 'survivable' second-degree burns can exceed 10 metres for some energetic kinds of faults. Definitely no civilian housing allowed inside this radius.
# Protection
A fault on the 220kV network must be cleared rapidly, or it will drive the whole grid into an unstable state (i.e. blackout.) The 'critical fault clearing time' to avoid a blackout is usually much less than 1 second.
Very expensive protection schemes (line differential with optic fibre pilots, distance protection) are used to ensure this high speed of protection. These protection schemes must be installed at every terminal of the 220kV line.
Once we account for the cost of -
• 220kV circuit breakers - about $200,000 each, minimum three required per substation - two for the incoming/outgoing circuit continuing past the substation, and one for the T-off =$600,000
• two sets of three-phase protection current transformers rated 220kV, and "enough" continuous amps - about $50,000 a set (ballpark) =$100,000
• two sets of protection relays - each with a redundant duplicate - about $20,000 each =$80,000. (Note: duplicate "X" and "Y" protection is standard for HV substations.)
... we are up to about $780,000, just in protection equipment, per substation. And we haven't even started buying transmission line termination hardware, surge diverters, busbar, support structures, earthworks, fencing, concrete, control PLC's, control hut... (Compare 22kV distribution transformer protection, which is usually just a set of three-phase expulsion dropout fuses, total cost maybe$2,000.)
# Transformers
220kV transformers are large, by dint of all the insulation required inside them to prevent flashover. There is no such thing as a "small" 220kV transformer - the smallest one I have seen is rated 60 MVA and weighs about 10 tons.
Contrast typical pole-top transformers 22/0.415kV which are rated 500kVA or less. The weight is important because there is a maximum limit to what you can have on top of a wooden pole. I am no structural engineer, but you certainly wouldn't want to pole-mount anything more than a ton.
Is that enough reasons?
• (I had to suppress several waves of "holy crap, this is insane" while writing this answer. Well asked.) – Li-aung Yip Apr 23 '15 at 12:42
• One additional (massive) cost: maintenance. HV switchgear is pretty reliable, so you might only need to check things every 3, 5, or 10 years, but doing so is bloody expensive (especially if the work can't be performed live). Adding an order of magnitude more subs would send utilities broke. – sapi Apr 23 '15 at 23:29
• Just out of curiosity, how much does GIS substation cost? – l46kok Apr 24 '15 at 2:09
• @l46kok: I've never been involved with buying GIS so I don't know how much it costs, exactly. I do know there is a price premium involved. And many more moving parts to fail. – Li-aung Yip Apr 24 '15 at 2:11
• PS: we do use 'capacitive ballasts' of the kind you describe - they are called 'capacitive voltage transformers' and we use them to measure voltage on the line. They do fail, and the usual failure mode is to explode into large fragments at high speed. Not something you want in people's back yards. – Li-aung Yip Apr 24 '15 at 13:52
A major reason is that these lines are for long distance transmission and interconnecting large grids.
Imagine a highway. Mostly they have exits every few miles in built up areas, and sometimes more frequently than a mile in particularly strange cases, but for the most point they are intended to allow fast, efficient travel from long distances away. While there are clearly houses and businesses near highways, if each one had its own onramp and offramp, not only would the infrastructure resources be significant, but every time you have a problem with an onramp or offramp that ends up closing a section or a lane of the freeway for a period of time you impact many, many more people.
If you start building out more substations you increase the risk of down-time for the transmission line due to substation issues.
Further, smaller grids are actually connected to several larger grids with switches, which are then sometimes connected to more than one transmission line with switches. This allows a problem on any given line or grid to be routed around, and results in power loss that is localized to the problem. Transmission lines are harder and more costly to work on and repair, and are critical backbone infrastructure for national electrical grids. When power plants go offline for any reason, power plants much further away can take up the slack due to these lines.
Lastly, electrically they are phase balanced for the most efficient transmission of electricity. Individual substations and grids are designed so that the power factor is as close to 1 as possible. Lower power factors result in energy loss in the lines and transformers, which requires more substantial conductors. These lines are not meant for poorly matched AC loads. Industrial customers who connect to the higher voltage lines often have to add power factor correction if their plants are not properly balanced. Connecting a home or neighborhood more directly to a transmission line would require an even greater investment in the substation needed to service them so the transmission lines are unaffected. Other high voltage lines merge a lot of customers with poor power factor, but by mixing small industrial users (lots of motors) with home users (lots of switching power supplies) the substations can balance the power factor for a much lower cost and smaller facilities. Placing unbalanced loads directly on transmission lines would lead to more significant headaches than the power transmission coordinators already face.
They really are not designed for small consumers.
Imagine if we actually did this, and we had power lines run through a neighbourhood or alongside, and every house connected directly to these power lines rather than a substation, it'd be pretty silly
I drew a picture to demonstrate how silly it might be:
Fortunately, the Swedes built things far better than my drawing skills:
Those are telephone wires by the way, they can get somewhat close without terrible terrible things happening to the wires (and people nearby).
Now imagine those cables are heavy duty power line cables. Imagine you couldn't pack them so densely and had to give each line individual clearance. Imagine the additional supports for when tower blocks and apartment buildings block direct line of sight, additional structures along the way to support all the additional cabling and the weight and tension needed to hold it in place.
Imagine the impact all these heavy duty high voltage cables have on reception and radio transmissions, and the numerous micro substations for every house.
I drew another picture, it's a tiny village with power lines adjacent:
We could bury the power lines most of the way, but that's a lot of digging to lay pretty dangerous power lines, it's all going to get very expensive (which it already is).
A simple solution would be for several adjacent houses to share a cable and substation. Stations of sufficient size would be cheap enough to support entire neighbourhoods while saving on construction costs and reducing the number of cables. This is all starting to sound familiar...
I am thinking more that it's due to system protection. If you tap-off the transmission and successfully step it down to your house-hold voltage, it would be very expensive to the utility if a fault happens at your location.
Also it's cost effective to have a central system protecting the central transformer, and the main transmission line. Furthermore the cost of the transformer to step down the transmission line voltage from around 69Kv, 138Kv, and so on, to 120V would be crazy expensive to pursue.
So it has both technical and economical benefits to have the layout as it's today.
I think it's because the main goal of a high voltage line is transmission. This is because at high voltages the power lost caused by I2R is lower than using lower voltage (for the same Power [W], higher voltage => lower current)
Besides that, you can connect to high voltage line by using a transformers, maybe 500/0.4 kV, that would be unacceptably expnsive.
• Why would that be unacceptably expensive? – sharptooth Oct 23 '15 at 14:54
• Because a 500 kV transformer is too expensive, thinking in low loads, for example a neigborhood, that may require 100 kVA. Normally, 500kV power transformers are designed for a power of more than 150 MVA (= 150,000 kVA), to reach the lowest \$/kVA relation. Generally, for electrical machines, one of the main part of the total cost is because of the isolation requirements. Therefore, the higher is the voltage level the higher is the cost. – Bruno Y Oct 23 '15 at 15:12 | 2019-06-19 00:53:57 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4070543646812439, "perplexity": 2154.715970722501}, "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-2019-26/segments/1560627998879.63/warc/CC-MAIN-20190619003600-20190619025600-00163.warc.gz"} |
https://terahertztechnology.blogspot.com/ | ## Tuesday, April 20, 2021
### Abstract-Switchable generation of azimuthally- and radially-polarized terahertz beams from a spintronic terahertz emitter
Hiroaki Niwa, Naotaka Yoshikawa, Masashi Kawaguchi, Masamitsu Hayashi, and Ryo Shimano
(a) THz generation from a spintronic THz emitter. Transient spin current 𝐣s${\mathbf{j}}_{\mathrm{s}}$ generated upon photoexcitation converts into charge current 𝐣c${\mathbf{j}}_{\mathrm{c}}$ via the inverse spin Hall effect, which radiates THz electric field with the polarization perpendicular to the magnetization 𝐦̂ $\stackrel{^}{\mathbf{m}}$. (b) Schematic of the experimental setup. (c) and (d) Schematic presentation of generating azimuthal and radial polarization by converting HE21${\text{HE}}_{\text{21}}$ mode with different orientations, respectively.
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-29-9-13331&id=450178
We propose and demonstrate a method of generating two fundamental terahertz cylindrical vector beams (THz-CVBs), namely the azimuthally- and radially-polarized THz pulses, from a spintronic THz emitter. We begin by presenting that the spintronic emitter generates the HE21 mode, a quadrupole like polarization distribution, when placed between two magnets with opposing polarity. By providing an appropriate mode conversion using a triangular Si prism, we show both from experiment and numerical calculation that we obtain azimuthal and radial THz vector beams. The proposed method facilitates the access of CVBs and paves the way toward sophisticated polarization control in the THz regime.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
## Monday, April 19, 2021
### Graphene: Everything under control in a quantum material
The gated graphene sample device in which the graphene film acts as a channel between source and drain electrodes subjected to a constant potential difference of 0.2 mV. Image from Science Advances
https://www.sciencedaily.com/releases/2021/04/210408131501.htm
In a new study, a team of researchers demonstrates that graphene's nonlinearity can be very efficiently controlled by applying comparatively modest electrical voltages to the material.
How can large amounts of data be transferred or processed as quickly as possible? One key to this could be graphene. The ultra-thin material is only one atomic layer thick, and the electrons it contains have very special properties due to quantum effects. It could therefore be very well suited for use in high-performance electronic components. Up to this point, however, there has been a lack of knowledge about how to suitably control certain properties of graphene. A new study by a team of scientists from Bielefeld and Berlin, together with researchers from other research institutes in Germany and Spain, is changing this. The team's findings have been published in the journal Science Advances.
Consisting of carbon atoms, graphene is a material just one atom thick where the atoms are arranged in a hexagonal lattice. This arrangement of atoms is what results in graphene's unique property: the electrons in this material move as if they did not have mass. This "massless" behavior of electrons leads to very high electrical conductivity in graphene and, importantly, this property is maintained at room temperature and under ambient conditions. Graphene is therefore potentially very interesting for modern electronics applications.
It was recently discovered that the high electronic conductivity and "massless" behavior of its electrons allows graphene to alter the frequency components of electric currents that pass through it. This property is highly dependent on how strong this current is. In modern electronics, such a nonlinearity comprises one of the most basic functionalities for switching and processing of electrical signals. What makes graphene unique is that its nonlinearity is by far the strongest of all electronic materials. Moreover, it works very well for exceptionally high electronic frequencies, extending into the technologically important terahertz (THz) range where most conventional electronic materials fail.
In their new study, the team of researchers from Germany and Spain demonstrated that graphene's nonlinearity can be very efficiently controlled by applying comparatively modest electrical voltages to the material. For this, the researchers manufactured a device resembling a transistor, where a control voltage could be applied to graphene via a set of electrical contacts. Then, ultrahigh-frequency THz signals were transmitted using the device: the transmission and subsequent transformation of these signals were then analyzed in relation to the voltage applied. The researchers found that graphene becomes almost perfectly transparent at a certain voltage -- its normally strong nonlinear response nearly vanishes. By slightly increasing or lowering the voltage from this critical value, graphene can be turned into a strongly nonlinear material, significantly altering the strength and the frequency components of the transmitted and remitted THz electronic signals.
"This is a significant step forward towards implementation of graphene in electrical signal processing and signal modulation applications," says Prof. Dmitry Turchinovich, a physicist at Bielefeld University and one of the heads of this study. "Earlier we had already demonstrated that graphene is by far the most nonlinear functional material we know of. We also understand the physics behind nonlinearity, which is now known as thermodynamic picture of ultrafast electron transport in graphene. But until now we did not know how to control this nonlinearity, which was the missing link with respect to using graphene in everyday technologies."
"By applying the control voltage to graphene, we were able to alter the number of electrons in the material that can move freely when the electrical signal is applied to it," explains Dr. Hassan A. Hafez, a member of Professor Dr. Turchinovich's lab in Bielefeld, and one of the lead authors of the study. "On one hand, the more electrons can move in response to the applied electric field, the stronger the currents, which should enhance the nonlinearity. But on the other hand, the more free electrons are available, the stronger the interaction between them is, and this suppresses the nonlinearity. Here we demonstrated -- both experimentally and theoretically -- that by applying a relatively weak external voltage of only a few volts, the optimal conditions for the strongest THz nonlin-earity in graphene can be created."
"With this work, we have reached an important milestone on the path towards to using graphene as an extremely efficient nonlinear functional quantum material in devices like THz frequency converters, mixers, and modulators," says Professor Dr. Michael Gensch from the Institute of Optical Sensor Systems of the German Aerospace Center (DLR) and the Technical University of Berlin, who is the other head of this study. "This is extremely relevant because graphene is perfectly compatible with existing electronic ultrahigh-frequency semiconductor technology such as CMOS or Bi-CMOS. It is therefore now possible to envision hybrid devices in which the initial electric signal is generated at lower frequency using existing semiconductor technology but can then very efficiently be up-converted to much higher THz frequencies in graphene, all in a fully controllable and predictable manner."
## Friday, April 16, 2021
### Abstract-Diversified functions for a terahertz metasurface with a simple structure
Wei-Mang Pan and Jiu-Sheng Li
(a) Three-dimensional schematic diagram of terahertz metasurface with diversified functions, (b) Designed unit cell with the relevant geometric parameters
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-29-9-12918&id=450048
Here, we propose a new encoded metasurface with different predesigned coding sequences to dynamic manipulate terahertz wavefront and realize various functionalities including beam splitting, anomalous beam deflection, vortex beam generation, angle controlled single-beam deflection, angle controlled multi-beam deflection, angle-controlled vortex beam generation and multi-vortex beam generation. The far-field scattering patterns obtained by CST Microwave Studio demonstrate the behavior of the terahertz wave in each case and shows a high consistency with our theoretical prediction results. Due to the excellent properties of the diversified functionalities in a single structure at terahertz frequencies, the proposed encoded metasurface provides promising applications in terahertz multiple-input, multiple-output (MIMO) communication.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
## Thursday, April 15, 2021
### Abstract-Tunable and multifunctional terahertz devices based on one-dimensional anisotropic photonic crystals containing graphene and phase-change material
Xiangfei Gao, Zebin Zhu, Jing Yuan, and Liyong Jiang
Real part (a) and imaginary part (b) of the photonic bands of the graphene-Si 1D APC when kx = 0 and different chemical potentials are considered. (c) Corresponding transmission (T), reflection (R) and absorption (A) spectra of the graphene-Si 1D APC. The total layer number of 1D APC is 20. The green area represents the metallic band. The insets show the zoomed-in view for selected band gaps.
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-29-9-13314&id=450177
In the past few years, designing tunable and multifunctional terahertz devices has become a hot research area in terahertz science and technology. In this work, we report a study on one-dimensional anisotropic photonic crystals (1D APCs) containing graphene and phase-change material VO2. We numerically demonstrate the band-pass filtering, perfect absorption, comb-shaped extraordinary optical transmission and Fano-like resonance phenomenon in pure 1D APCs and 1D APCs with a VO2 defect layer under different conditions of a tangential wave vector. The performance of these phenomena in the terahertz region can be modulated by changing the chemical potential of graphene. The band-pass filter and perfect absorber functions of 1D APCs with a VO2 defect layer can be freely switched by changing the phase of VO2. We employ the equivalent-permittivity model and dispersion-relation equation to give reasonable explanations on these behaviors.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
## Wednesday, April 14, 2021
### Abstract-Electrical tunability of terahertz nonlinearity in graphene
Sergey Kovalev, Hassan A. Hafez, Klaas-Jan Tielrooij, Jan-Christoph Deinert, Igor Ilyakov, Nilesh Awari, David Alcaraz. Karuppasamy Soundarapandian, David Saleta, Semyon Germanskiy, Min Chen, Mohammed Bawatna, Bertram Green, Frank H. L. Koppens, Martin Mittendorff, Mischa Bonn, Michael Gensch, Dmitry Turchinovich,
Graphene is conceivably the most nonlinear optoelectronic material we know. Its nonlinear optical coefficients in the terahertz frequency range surpass those of other materials by many orders of magnitude. Here, we show that the terahertz nonlinearity of graphene, both for ultrashort single-cycle and quasi-monochromatic multicycle input terahertz signals, can be efficiently controlled using electrical gating, with gating voltages as low as a few volts. For example, optimal electrical gating enhances the power conversion efficiency in terahertz third-harmonic generation in graphene by about two orders of magnitude. Our experimental results are in quantitative agreement with a physical model of the graphene nonlinearity, describing the time-dependent thermodynamic balance maintained within the electronic population of graphene during interaction with ultrafast electric fields. Our results can serve as a basis for straightforward and accurate design of devices and applications for efficient electronic signal processing in graphene at ultrahigh frequencies.
## Monday, April 12, 2021
### Terahertz Imaging of Graphene Paves the Way to Optimization and Industrialization
Graphene Flagship researchers have developed a new measurement standard for the analysis of graphene and layered materials that could accelerate production and optimize device fabrication. Credit: Graphene Flagship
Graphene Flagship researchers have developed a new measurement standard for the analysis of graphene and layered materials that could accelerate production and optimize device fabrication.
X-ray scans revolutionized medical treatments by allowing us to see inside humans without surgery. Similarly, terahertz spectroscopy penetrates graphene films allowing scientists to make detailed maps of their electrical quality, without damaging or contaminating the material. The Graphene Flagship brought together researchers from academia and industry to develop and mature this analytical technique, and now a novel measurement tool for graphene characterization is ready.
The effort was possible thanks to the collaborative environment enabled by the Graphene Flagship European consortium, with participation by scientists from Graphene Flagship partners DTU, Denmark, IIT, Italy, Aalto University, Finland, AIXTRON, UK, imec, Belgium, Graphenea, Spain, Warsaw University, Poland, and Thales R&T, France, as well as collaborators in China, Korea and the US.
Graphene is often ‘sandwiched’ between many different layers and materials to be used in electronic and photonic devices. This complicates the process of quality assessment. Terahertz spectroscopy makes things easier. It images the encapsulated materials and reveals the quality of the graphene underneath, exposing imperfections at critical points in the fabrication process. It is a fast, non-destructive technology that probes the electrical properties of graphene and layered materials, with no need for direct contact.
The development of characterization techniques like terahertz spectroscopy is fundamental to accelerating large-scale production, as they guarantee that graphene-enabled devices are made consistently and predictably, without flaws. Quality control precedes trust. Thanks to other developments pioneered by the Graphene Flagship, such as roll-to-roll production of graphene and layered materials, fabrication technology is ready to take the next step. Terahertz spectroscopy allows us to ramp up graphene production without losing sight of the quality.
Terahertz spectroscopy penetrates graphene films allowing scientists to make detailed maps of their electrical quality, without damaging or contaminating the material. Credit: Peter Bøggild (Graphene Flagship / DTU)
“This is the technique we needed to match the high-throughput production levels enabled by the Graphene Flagship,” explains Peter Bøggild from Graphene Flagship partner DTU. “We are confident that terahertz spectroscopy in graphene manufacturing will become as routine as X-ray scans in hospitals,” he adds. “In fact, thanks to terahertz spectroscopy you can easily map even meter-scale graphene samples without touching them, which is not possible with some other state-of-the-art techniques.” Furthermore, the Graphene Flagship is currently studying how to apply terahertz spectroscopy directly into roll-to-roll graphene production lines, and speed up the imaging.
Collaboration was key to this achievement. Graphene Flagship researchers in academic institutions worked closely with leading graphene manufacturers such as Graphene Flagship partners AIXTRON, Graphenea and IMEC. “This is the best way to ensure that our solution is relevant to our end-users, companies that make graphene and layered materials on industrial scales,” says Bøggild. “Our publication is a comprehensive case study that highlights the versatility and reliability of terahertz spectroscopy for quality control and should guide our colleagues in applying the technique to many industrially relevant substrates such silicon, sapphire, silicon carbide, and polymers.” he adds.
Setting standards is an important step for the development of any new material, to ensure it is safe, genuine and will offer a performance that is both reliable and consistent. That is why the Graphene Flagship has a dedicated work-group focused on the standardization of graphene, measurement and analytical techniques and manufacturing processes. The newly developed method for terahertz spectroscopy is on track to become a standard technical specification, thanks to the work of the Graphene Flagship Standardisation Committee. “This will undoubtedly accelerate the uptake of this new technology, as it will outline how analysis and comparison of graphene samples can be done in a reproducible way,” explains Peter Jepsen from Graphene Flagship Partner DTU, who co-authors the study. “Terahertz spectroscopy is yet another step to increase the trust in graphene-enabled products,” he concludes.
Amaia Zurutuza, co-author of the paper and Scientific Director at Graphene Flagship partner Graphenea, says: “At Graphenea, we are convinced that terahertz imaging can enable the development of quality control techniques capable of matching manufacturing throughput requirements and providing relevant graphene quality information, which is essential in our path towards the successful industrialization of graphene.”
Thurid Gspann, the Chair of the Graphene Flagship Standardisation Committee, says: “This terahertz [spectroscopy] technique is expected to be widely adopted by industry. It does not require any particular sample preparation and is a mapping technique that allows one to analyze large areas in a time efficient way.”
Marco Romagnoli, Graphene Flagship Division Leader for Electronics and Photonics Integration, adds: “The terahertz spectroscopy tool for wafer-scale application is a state-of-the-art, high TRL system to characterize multilayer stacks on wafers that contain CVD graphene. It works in a short time and with good accuracy, and provides the main parameters of interest, such as carrier mobility, conductivity, scattering time and carrier density. This high-value technical achievement is also an example of the advantage of being part of a large collaborative project like the Graphene Flagship.”
Andrea C. Ferrari, Science and Technology Officer of the Graphene Flagship and Chair of its Management Panel, adds: “Yet again, Graphene Flagship researchers are pioneering a new characterization technique to facilitate the development of graphene technology. This helps us progress steadily on our innovation and technology roadmap and will benefit the industrial uptake of graphene in a wide range of applications.”
Reference: “Case studies of electrical characterisation of graphene by terahertz time-domain spectroscopy” by Patrick R Whelan, Binbin Zhou, Odile Bezencenet, Abhay Shivayogimath, Neeraj Mishra, Qian Shen, Bjarke S Jessen, Iwona Pasternak, David M A Mackenzie, Jie Ji, Cunzhi Sun, Pierre Seneor, Bruno Dlubak, Birong Luo, Frederik W Østerberg, Deping Huang, Haofei Shi, Da Luo, Meihui Wang, Rodney S Ruoff, Ben R Conran, Clifford McAleese, Cedric Huyghebaert, Steven Brems, Timothy J Booth, Ilargi Napal, Wlodek Strupinski, Dirch H Petersen, Stiven Forti, Camilla Coletti, Alexandre Jouvray, Kenneth B K Teo, Alba Centeno, Amaia Zurutuza, Pierre Legagneux, Peter U Jepsen and Peter Bøggild, 17 February 2021, 2D Materials. | 2021-04-21 04:56:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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": 0.4127781093120575, "perplexity": 3630.911737179524}, "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/1618039508673.81/warc/CC-MAIN-20210421035139-20210421065139-00545.warc.gz"} |
https://www.authorea.com/users/5754/articles/6087/_show_article | # Introduction to Decision Theory
Decision Theory: Dealing with choice among actions based on the desirability of their immediate outcomes; environment is thus episodic.
$$P(RESULT(a) = s'|\,a,e)$$
RESULT(a): random variable whose values are possible outcome states, given action a.
Probability of outcome s’, given evidence observations e.
$$EU(a|e) = \sum\limits_{s'} P(RESULT(a) = s'|\,a,e)U(s')$$
U(s): Utility function, a single number that expresses desirability of a state.
Average utility value of the outcomes, weighted by probability of outcome occuring.
$$action = \textrm{argmax}\: EU(a|e)$$
Maximum Expected Utility (MEU): Rational agent should choose the action that maximizes agent’s expected utility.
“If an agent acts so as to maximize a utility function that correctly reflects the performance measure, then the agent will achieve the highest possible performance score (averaged over all the possible environments.)”
# Utility Theory
## Constraints on Rational Preferences
Notation
• $$A \succ B$$ the agent prefers A over B
• $$A \sim B$$ the agent is indifferent between A and B
• $$A \succeq B$$ the agent prefers A over B or is indifferent between them.
A and B are not states, but a set out outcomes for each action–a lottery. A lottery $$L$$ with possible outcomes $$S_1,...,S_n$$ that occurs with probabilities $$p_1,...,p_n$$: $$L = [p_1,S_1;\,p_2, S_2;\, ... p_n, S_n].$$
Each outcome $$S_i$$ of a lottery can be either an atomic state or another lottery.
Preferences relations must require six constraints:
1. Orderability: Given any two lotteries, a rational agent must either prefer one to the other or rate them as equally preferable.
Exactly one of $$A \succ B$$, $$A \sim B$$, $$B \succ A$$
2. Transitivity: Given any three lotteries, if an agent prefers A to B and prefers B to C, then the agent must prefer A to C
3. Continuity: If some lottery B is between A and C in preference, then there is some probability p for which the rational agent will be indifferent between getting B for sure and the lottery that yields A with probability p and C with probability 1-p.
4. Substitutability: If an agent is indifferent between two lotteries A and B, then the agent is indifferent between two more complex lotteries that are the same except B is substitued for A in one of them. (This holds regardsless of the probabilities and the other outcome(s) in the lotteries.
5. Monotinicity: Suppose two lotteries have the same two possible outcomes, A and B. If an agent prefers A to B, then the agent must prefer the loterry that has a higher probability for A (and vice versa)
6. Decomposability: Compound lotteries can be reduced to simpler ones using the laws of probability. “No fun in gambling” rule: two consecutive lotteries can be compressed into a single equivalent lottery.
$$[p,A;\,1-p,[q,B;\,1-q,C]]\,\sim\,[p,A;\,(1-p)q,B;\,(1-p)(1-q),C].$$
## Preferences lead to utility
• Existence of a Utility Function: If an agent’s preferences obey the axioms of utility; then there exists a function $$U$$ such that $$U(A) > U(B)$$ if and only if A is preferred to B and U(A) = U(B) if and only iff the agent is indifferent between A and B.
$$U(A) > U(B) \Leftrightarrow A \succ B$$
$$U(A) = U(B) \Leftrightarrow A \sim B$$
• Expected Utility of a Lottery: The utility of a lottery is the sum of the probability of each outcome times the utility of that outcome.
$$U([p_1, S_1;...;p_n,S_n]) = \sum\limits_{i} p_iU(S_i).$$
# Utility Functions
A utility is a function that maps from lotteries to real numbers.
An agent can have any preferences that it wants; Preferences themselves cannot be irrational.
## Utility assessment and utility scales
• Pereference Elicitation: Process that involves presenting chocies to the agent and using the observed preferences to pin down the underlying utility function
• Normalized Utility: Establish a “best” utility and a “worst” utility. Normalized Utility use a scale with Worst = 0 and Best = 1.
• Use a Standard Lottery $$[p, util_{min};\,(1-p),util_{max}]$$ to assess utility of any paticular prize $$S$$. $$p$$ is adjusted until the agent is indifferent between $$S$$ and the standard lottery. Utility of $$S$$ is given by $$p$$. | 2017-06-28 12:25:17 | {"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": 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": 0.9672868847846985, "perplexity": 1116.110184557247}, "config": {"markdown_headings": true, "markdown_code": false, "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/1498128323680.18/warc/CC-MAIN-20170628120308-20170628140308-00438.warc.gz"} |
https://dominichosler.wordpress.com/2013/04/15/script-to-generate-standalone-latex-equations/ | Tags
Sometimes you will write a presentation in something that is not LaTeX or design a poster and you want to include equations. These equations you want to be nicely typeset with LaTeX, but they need to be standalone graphics.
This blog post describes a script which will take an input file of the LaTeX code for the equation and process it into either a bitmap (png) or vector (pdf) graphic.
I have previously blogged on this topic using a different method, here. However, I now prefer this method as it is easier to use and faster to do. It also uses much simpler files for the equations and makes it easier to get a coherent look across all the equations in your presentation or poster by using a common preamble.
This blog post is a guide to the script, and explains both how to use it and how it works.
Overview
There are a few stages to the process, first the script constructs a LaTeX file. Then the script processes this LaTeX file, producing the typeset equation as output. Then it crops the pdf and optionally converts to raster (png) graphics at high resolution. Finally it cleans up all the temporary files created.
Usage
The user must provide a LaTeX based input file containing the code to typeset the equation. This is standard LaTeX code when the packages amsmath,amssymb,bm,amsthm,bbold,latexsym,inputenc,fontenc, and mathrsfs are loaded. The user’s input file gets placed inside an equation environment so the user can get straight on to writing the equation.
When calling the script the user must provide an option flag to set the output to either -v (for vector, pdf, graphics) or -b (for bitmap, png, graphics).
The Input Files
The script then creates two temporary files to concatenate with the .texpart file to create the temporary .tex file. The contents of these files is as follows:
\documentclass{article}
\usepackage{amsmath,amssymb,bm,amsthm,bbold}
\usepackage{latexsym}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathrsfs}
\begin{document}
\pagestyle{empty}
\begin{equation*}
for part 1, and,
\end{equation*}
\end{document}
for part 3, with part 2 being provided by the .texpart file.
This is fairly standard for a stripped down document preamble. We use the empty pagestyle because it removes any page numbers and the starred equation environment to remove equation labels. We want the page to be completely empty apart from the equation. This will help the cropping program automatically determine the size to crop to. The part 1 file can be altered by adding or removing packages or providing any formatting specifications as the user desires.
The three files are put together using cat and >.
cat part1.temp $2 part3.temp > full.temp.tex The user input file will always be at$2 because the option flags count as an input.
Processing the file
The script runs lualatex using this command,
lualatex -interaction=batchmode full.temp.tex
Note the option -interaction=batchmode silences the main LaTeX run, and prevents it from stopping on errors or warnings. I use lualatex here because it has been recognised as the successor to pdflatex but it is possible to swap it out for any latex engine that produces a pdf output directly. It is even possible to swap it out for a set of commands that produce a pdf output indirectly, but for the purposes of this script I will treat it as creating a pdf file.
Option testing
The option to specify bitmap or vector graphics is interpreted by the script using getopts. This method is explained in the bash hackers wiki. This is used by putting it inside a loop and implementing the valid options with a case switch.
The loop is a while loop,
while getopts "vb" OPTION
do
commands-go-here
done
this loops over all options picking out v and b as valid options and storing the current one in the variable OPTION.
The case test is,
case $OPTION in v) commands-for-v-option ;; b) commands-for-b-option ;; \?) exit 1;; #This should never happen, as the getopts only selects valid options, but if something has gone wrong, it exits. esac The case tests the value of the variable OPTION and executes the appropriate set of commands. The test is inside a loop, so putting both options, -vb, will result in both sets of commands being executed in the order specified by the user. For this script, this is a desired effect, they are not mutually exclusive. Cropping the resulting pdf I use pdfcrop to crop the pdf to the exact size of the equation. It is available (with documentation) from ctan. The comand is, pdfcrop --margins 5 full.temp.pdf${2%\.*}.pdf
I use margins of 5 pixels because this gives an appropriately sized border to account for the fact that some character glyphs extend slightly beyond their bounding box.
The output file uses a parameter expansion on the input file the script is called on. This is to give the final output file the same name, but with the correct extension for the output. This particular parameter expansion removes everything after the final dot. After the parameter expansion, we then concatenate with .pdf to give the file name. If the user has chosen to output to png, I just crop to a standard filename of full.temp.cropped.pdf.
Converting to png
I use the bash command convert from the suite of software imagemagick, this command is described in full here. It is called with,
convert -density 500 full.temp.cropped.pdf ${2%\.*}.png I have set a density of 500 to make sure there is a high enough quality (dpi) for the equation to look good enough as a rasterised image. I again use a parameter expansion for this command, same as the pdfcrop command. Cleaning up temporary files Finally we delete all of the extra files created by this script using, rm part1.temp part3.temp full.temp.tex full.temp.aux full.temp.log full.temp.pdf Be warned that it doesn’t check modification times or anything, it will just remove any file in the current directory with these names. Also don’t run this script as root, you may harm your system. In the case of converting to png, the script will have already deleted the pdf interim. The full script #!/bin/bash # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This program was written by Dominic Hosler # There is a description of how it works on my blog https://dominichosler.wordpress.com # Please ask on the blog if you have any questions, thank you. # Script to take an input file containing LaTeX code for an equation. # It takes one optional argument, -v, to output the equations as vector graphics # (pdf) or -i, to output as raster (png). # The script will then remove the files it created (apart from the output file). #Create temporary files for latex file echo "Constructing LaTeX file" echo "\documentclass{article} \usepackage{amsmath,amssymb,bm,amsthm,bbold} \usepackage{latexsym} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{mathrsfs} \begin{document} \pagestyle{empty} \begin{equation*}" > part1.temp echo "\end{equation*} \end{document} " > part3.temp cat part1.temp$2 part3.temp > full.temp.tex
echo "Process the LaTeX file"
lualatex -interaction=batchmode full.temp.tex
#Test if the user has input the -v option (for vector) or -b (for bitmap)
while getopts "vb" OPTION
do
case $OPTION in v) #In the case of vector graphics, just crop the pdf with a small margin and output to correct filename. echo "Output set to vector graphics, pdf." pdfcrop --margins 5 full.temp.pdf${2%\.*}.pdf
;;
b) #In the case of bitmap graphics, crop the pdf with margin
echo "Output set to bitmap graphics, png."
pdfcrop --margins 5 full.temp.pdf full.temp.cropped.pdf
#Then convert to a png with a high resolution for rasterisation.
convert -density 500 full.temp.cropped.pdf \${2%\.*}.png
rm full.temp.cropped.pdf
;;
\?) exit 1;;
esac
done
#Cleanup temp files
echo "Cleanup temporary files"
rm part1.temp part3.temp full.temp.tex full.temp.aux full.temp.log full.temp.pdf
To use the above script you need to copy and paste it into a text file and make the file executable. Then to run, you need to have the file on your PATH variable or in the same directory.
Example usage file
We take the example of my favourite equation, which involves the five most important numbers, 0, 1, e, i and pi, and the four most important operations =, +, * and ^.
The example file, example.texpart is this:
e^{i \pi}+1=0
Yes, the usage file really is that simple. | 2018-02-22 05:00:27 | {"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": 0.75727778673172, "perplexity": 2391.1716645344063}, "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/1518891814002.69/warc/CC-MAIN-20180222041853-20180222061853-00607.warc.gz"} |
https://www.physicsforums.com/threads/even-degree-polynomial-show-p-x-geq-0-for-all-real-x.898778/ | # Even Degree Polynomial, show $p(x) \geq 0$ for all real x
1. Dec 31, 2016
### QuietMind
1. The problem statement, all variables and given/known data
Prove that if p(x) has even degree with positive leading coefficient, and $p(x) - p''(x) \geq 0$ for all real x, then $$p(x) \geq 0$$ for all real x
2. Relevant equations
N/A
Problem is from Art and Craft of Problem Solving, as an exercise left to the reader following a partial solution in the text. The text goes over a somewhat similar example: when we have a polynomial q(x) such that $q(x) - q'(x) \geq 0$. The text showed us that we can determine that q(x) must be of even degree with leading coefficient positive.
3. The attempt at a solution
I have thought about a few different possible strategies:
1) Show that p''(x) is always nonnegative. I'm not sure how to go about this strategy, or if this conjecture is even true.
2) Show that p(x) either has no zeroes, or only has zeroes that barely touch the x axis (therefore it lies on the upper half plane). If p(x) does have a zero at some point, say $x_0$ then $p(x_0) - p''(x_0) \geq 0$. If $p(x_0) = 0$ then $p''(x_0) = 0$. This is a necessary but not sufficient condition for an inflection point at $x_0$. This seems significant but how does this help me?
2. Dec 31, 2016
### Math_QED
And what did you achieve trying those strategies?
3. Dec 31, 2016
### QuietMind
I'm really not sure how to go about proving the first one, but the second derivative being zero should mean that the first derivative is not changing at $x_0$. This tells me that the first derivative is not changing at this point, but does this also tell me that the function never crosses the x axis (only barely touching it)?
Or are you telling me that I should be trying something else?
4. Dec 31, 2016
### PeroK
What can the second derivative be used to determine? Think elementary calculus.
5. Dec 31, 2016
### QuietMind
The second derivative determines the concavity of a function. At a zero of f(x), $x_0$ , the function has $f''(x_0) \leq 0$ . The problem is I don't know anything about the first derivative, so I can't use the second derivative test to say if a point is a local max/min. If the second derivative is zero, it may be an inflection point. Were you referring to concavity?
For any zero $x_0$ , either the second derivative must be 0 (function is linear at that point, might be inflection point) or negative (concave down). Also, I also know that the second derivative is positive as x tends to plus or minus infinity because it also is a even degree polynomial with positive leading coefficient. I'm wondering if it's impossible for these statements to be concurrently true. If all the zeroes of f(x) are concave down or linear, does this prevent the function from having the correct concavity at very large and very negative x?
6. Dec 31, 2016
### Ray Vickson
For large $|x|$ we must have $p(x) > 0$ because the large-$|x|$ behavior of $p(x)$ is governed by the leading term $c_{2n} x^{2n}$, with $c_{2n} > 0$ (stated in the problem, but also provable on its own from the condition $p'' \leq p$). If $p(x_0)< 0$ for some $x_0$, we will have $p(x) < 0$ for all $x$ in some interval $I$ that contains $x_0$. Since $p'' \leq p$ we have that $p''(x) < 0$ on the interval $I$; that is, $p$ is strictly concave on the interval $I$.
If we have $p'(x_1) < 0$ for some $x_1 \in I$, the function will be going down as $x$ increases from $x_1$, so will become increasingly negative. There is no way that we could have $p(x) > 0$ for some $x > x_1$---which we would need because we have $p(x) > 0$ for large enough $x$---because in order for that to happen the graph of $p(x)$ would need to "turn around" and start increasing again, and that would mean that $p(x)$ would need to pass through a minimum $x_2$ for which $p''(x_2) > 0$. In other words, $p$ would have to switch from being concave to being convex at some point where it was still < 0. But that is impossible because $p(x_2) < 0$ implies $p''(x_2) < 0$. So, our assumption that $p'(x_1) < 0$ for some $x_1 \in I$ leads to a contradiction, hence it cannot occur.
You can look at similar arguments if $p'(x_1) > 0$ for some $x_1 \in I$.
7. Dec 31, 2016
### QuietMind
I did out the argument for $p'(x_1) > 0$ for some $x_1 \in I$ by considering decreasing x from $x_1$. The derivative must be even more positive for these points, and because the second derivative is negative, this means that p(x) must approach negative infinity as x decreases from $x_1$. However, does one even have to consider this argument? I would expect that for the interval $I$ that you described, there must necessarily be a point $x_1$ with a negative derivative, because the function p(x) goes from zero, to some negative point $x_0$ and then back to zero. That would imply there must be a point with negative derivative, because polynomials are nice and smooth. So it technically shouldn't be necessary to consider $p'(x_1) > 0$ for some $x_1 \in I$, should it?
8. Jan 1, 2017
### Delta²
Ehm sorry for being slow (lol) but all we prove is that $p'(x)=0$ for x in some interval I, so doesn't that mean that $p(x)=c$ for all x in I? And since our function is polynomial doesn't that mean that $p(x)=c$ for all x in real line?????
is $p(x)=c>0$ the only polynomials that satisfy the conditions of this problem???
Last edited: Jan 1, 2017
9. Jan 1, 2017
### PeroK
I think you're making this too complicated. Just consider any local mimimum for the polynomial.
10. Jan 1, 2017
### Ray Vickson
Well, you can show that having $p(x) < 0$ on an interval $I$ leads to a contradiction (because $x_1 \in I$ and $p'(x_1) < 0$ or $x_1 \in I$ and $p'(x_1) > 0$ both lead to contradictions, and $p'(x_1) = 0$ implies that $p'(x_{1a}) > 0, p'(x_{1b}) < 0$ for some $x_{1a} < x_1 < x_{1b}$ in $I$. In other words, you cannot have $p(x) < 0$ on an interval $I$, so cannot have $p(x_0)< 0$ at any point $x_0$.
Basically we cannot have $p(x) < 0$ along with $p'(x) < 0$, $p'(x) = 0$ or $p'(x) > 0$ anywhere---in other words, we cannot have $p(x) < 0$ anywhere.
Last edited: Jan 1, 2017
11. Jan 1, 2017
### QuietMind
So in order to have the correct behavior at large positive or negative x, if the function crosses below the x axis, it must come back up and cross the x axis again. This guarantees that a local minimum must exist somewhere on this interval I where this function goes below the x axis, but if the second derivative is negative whenever p(x) < 0, then we cannot have a local minimum, only a maximum. Hence this is a contradiction, and we cannot have the function p(x) < 0.
I don't think p(x) has to be a constant, some function like $p(x) = x^4 + 12x^2 + 1000$ with $p''(x) = 12x^2 + 12$ should have $p(x)-p''(x) \geq 0$ for all real x. I made a mistake in an earlier post where I said that $p''(x_0)$ had to be 0.
12. Jan 1, 2017
### PeroK
Yes, that's the core of the argument. You can also argue simply that at any local minimum, $x_0$, we have $p(x_0) \ge p''(x_0) \ge 0$.
Note that the proposition holds for any function $f$ which is non-negative as $x \rightarrow \pm \infty$ and has $\forall \ x \ f(x) \ge f''(x)$.
13. Jan 2, 2017
### QuietMind
I think I see what you are saying with this holding for any function f, but I'm wondering if you'd need any additional constraint of it being "nice" and/or smooth. The argument hinges on if p(x) goes negative, there must necessarily be a local minimum at a negative value of p(x) to guarantee that the function curves back up. However, if a function goes negative and comes back up but doesn't have a local minimum (say a dirac delta valley or something very sharp like that) so the argument in my prior post using a local minimum wouldn't hold. This wouldn't happen for a polynomial, which tend to be "nice"/smooth, but I'm wondering what needs to be said about an arbitrary function f(x). Perhaps the existence of the second derivative of f(x) (or p(x) )for all x guarantee the function is "nice"/ smooth enough? I have no Real Analysis background yet, so this is an area that I have but a hazy understanding of.
14. Jan 2, 2017
### PeroK
The fact that $f$ is twice differentiable is enough. The Dirac Delta isn't a function. | 2018-02-23 13:33:39 | {"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": 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": 0.8589050769805908, "perplexity": 199.68411530247212}, "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/1518891814700.55/warc/CC-MAIN-20180223115053-20180223135053-00471.warc.gz"} |
https://www.habitus-rehabilitacja.pl/08-Mon/8311cae4af26.html | moment of inertia for power calculation of mill
moment of inertia for power calculation of mill
Angular Motion - Power and Torque
An electric motor runs with 3600 rpm with an measured power consumption of 2000 W. The moment created by the motor (without losses) can be calculated by rearranging (1) to. T = 30 P / (π n rpm) = 30 (2000 W) / (π (3600 rpm)) = 5.3 Nm. Moment Calculator. P - power (W) n m - rotations (rpm) Torque of a Body in Angular Motion. T = I α (2) where . I = moment of inertia (kg
How to Determine the Motor Size for Your Project? | RealPars
The larger inertia of the object, the greater force you need to change the velocity in a given time. The SI unit of measure for moment of inertia is “one kilogram-meter squared”. In equations, it is usually represented by the variable “I”.
How to Solve for the Moment of Inertia of Irregular or
The moment of inertia with respect to any axis in the plane of the area is equal to the moment of inertia with respect to a parallel centroidal axis plus a transfer term composed of the product of the area of a basic shape multiplied by the square of the distance between the axes. The Transfer formula for Moment of Inertia is given below. 6.
Design of a windmill for pumping water
p - Coefficient of power A s - Swept Area A B - Area of one blade V - Velocity U o - Speed of Wind - Density D - Diameter R - Radius - Tip Speed Ratio N - Number of Blades - Angular Velocity C t - Torque Coefficient İ - Mass Flux P w - Wind Power P T - Power Extracted From wind T - Torque g - Acceleration due to gravity Q - Flow rate
AC induction motor inertia: Difference between WK2 and WR2
Using inertia to determine torque and acceleration. The distinction between these two inertia equations, WR 2 and WK 2, is important because in AC induction motor applications, inertia is used to determine the motor torque required to achieve a desired speed within a given time.. T = acceleration torque (lb-ft) W = weight of load to be accelerated (lb)
Spindle power and torque limitations | Cutting Tool
The rotational counterpart to mass is moment of inertia (I), which has units of newton-meter-second 2, or equivalently kilograms-meters 2. Similar to it being more difficult to accelerate a massive object, the concept of moment of inertia expresses that it is more difficult to cause rotational acceleration for an object with a large mass or
A method for quick estimation of engine moment of inertia
A method for quick estimation of engine moment of inertia based on an experimental analysis of transient working process.pdf Rated power 40 kW @ 4000 In-cycle calculations
PDF Design of a Vertical-Axis Wind Turbine
ii Design of a Vertical-Axis Wind Turbine - Final Report 4 April 2014 Acknowledgements We would like to thank everyone who helped us realize this project including:
How can I calculate the rotational speed of a wind turbine?
Hi, I would like to calculate the rotational speed of a wind turbine with a power of 20 kw and average wind speed of 9 m / s. I want to know if there is a
PDF How to Size a Motor
With this load inertia calculation complete, it is possible to begin looking for an appro-priate motor to rotate the dial. The most common rules of thumb are to look for a motor whose rotor inertia is no less than 1/5 or 1/10 the load inertia. If the dial is large, this may be near impossible, and this is where a gearbox becomes important.
Moment of Inertia Formula and Other Physics Formulas
The general formula represents the most basic conceptual understanding of the moment of inertia. Basically, for any rotating object, the moment of inertia can be calculated by taking the distance of each particle from the axis of rotation (r in the equation), squaring that value (that's the r 2 term), and multiplying it times the mass of that particle. You do this for all
Motor Sizing Calculations
There are three factors to calculate when sizing a motor; Moment of Inertia, Torque, and Speed. Moment of Inertia. Moment of inertia is the measure of an object's resistance to changes in its rotation rate. When an object is just sitting without any motion, the moment of inertia is 0. When you try to make it move that mean you want to change the speed of the object from 0 to any,
Relation Between Torque And Moment Of Inertia - BYJU'S
Relationship between Torque and Moment of Inertia. For simple understanding, we can imagine it as Newton’s Second Law for rotation. Where torque is the force equivalent, a moment of inertia is mass equivalent and angular acceleration is linear acceleration equivalent. The rotational motion does obey Newton’s First law of motion.
electrical engineering - Quantifying inertia on the
This presentation goes into some of the details regarding how system inertia is calculated. Mechanical dynamics are modeled by the second-order differential equation: $J\frac{d^2\theta}{dt^2}=T_m - T_e$ $\theta$: angle (rad) of the rotor with respect to a stationary reference. $J$: moment of inertia. $T_m$: mechanical torque from the turbine.
10.5 Calculating Moments of Inertia - University Physics
Iparallel-axis = 1 2mdR2 + md(L + R)2. Adding the moment of inertia of the rod plus the moment of inertia of the disk with a shifted axis of rotation, we find the moment of inertia for the compound object to be. Itotal = 1 3mrL2 + 1 2mdR2 + md(L + R)2.
PDF Grid Code Frequency Response Working Group System Inertia
The maths behind inertia ∂f/∂t = Rate of change of frequency ∆P = MW of load or generation lost 2H = Two times the system inertia in MWs / MVA ∂f ∂t ∆P 2H = H = Inertia constant in MWs / MVA J = Moment of inertia in kgm2 of the rotating mass ω= nominal speed of rotation in rad/s MVA = MVA rating of the machine ½Jω2 MVA H = MVA | 2022-01-28 00:00:29 | {"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": 0.6334125995635986, "perplexity": 876.476258452016}, "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-2022-05/segments/1642320305317.17/warc/CC-MAIN-20220127223432-20220128013432-00064.warc.gz"} |
https://homework.cpm.org/category/CC/textbook/ccg/chapter/9/lesson/9.1.2/problem/9-24 | ### Home > CCG > Chapter 9 > Lesson 9.1.2 > Problem9-24
9-24.
At the band’s peak of popularity, a personally signed Black Diamond poster sold for $$500$. Three years later the band was almost forgotten and the poster was worth only$$10$. What were the annual multiplier and annual percent of decrease? Homework Help ✎
An exponential function is always of the form $y = ab^x$ | 2019-10-15 04:07:34 | {"extraction_info": {"found_math": true, "script_math_tex": 3, "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": 0.20677751302719116, "perplexity": 5418.938654775096}, "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/1570986655864.19/warc/CC-MAIN-20191015032537-20191015060037-00296.warc.gz"} |
https://math.answers.com/Q/A_score_set_has_a_mean_of_53_and_a_standard_deviation_of_5.6_If_each_score_was_multiplied_by_0.9_and_then_had_7_added_state_the_new_standard_deviation | 0
# A score set has a mean of 53 and a standard deviation of 5.6 If each score was multiplied by 0.9 and then had 7 added state the new standard deviation?
Wiki User
2011-09-26 13:10:06
Standard deviation is the spread of the data. If each score has 7 added, this would not affect the spread of the data - it would be just as evenly spaced or clumped up, but 7 greater. The only thing that would affect the spread is multiplying every data point by 0.9. This makes distances between the data points 0.9 times as big, and thus makes the standard deviation 0.9 times as big. The standard deviation was 5.6, and so now is 5.6x0.9 = 5.04
Wiki User
2011-09-26 13:10:06
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1190 Reviews | 2022-08-13 05:20:28 | {"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": 0.8039779663085938, "perplexity": 795.8680391624874}, "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/1659882571909.51/warc/CC-MAIN-20220813051311-20220813081311-00499.warc.gz"} |
https://repository.upenn.edu/edissertations/1261/ | ## Publicly Accessible Penn Dissertations
#### Title
A Random Walk in Representations
2014
Dissertation
#### Degree Name
Doctor of Philosophy (PhD)
Mathematics
The unifying objective of this thesis is to find the mixing time of the Markov chain on $S_n$ formed by applying a random $n$-cycle to a deck of $n$ cards and following with repeated random transpositions. This process can be viewed as a Markov chain on the partitions of $n$ that starts at $(n)$, making it a natural counterpart to the random transposition walk, which starts at $(1^n)$. By considering the Fourier transform of the increment distribution on the group representations of $S_n$ and then computing the characters of the representations, Diaconis and Shahshahani showed in \cite{DS81} that the order of mixing for the random transposition walks is $n\ln n$. We adapt this approach to find an upper bound for the mixing time of the $n$-cycle-to-transpositions shuffle. To obtain a lower bound, we derive the distribution of the number of fixed points for the chain using the method of moments. In the process, we give a nice closed-form formula for the irreducible representation decomposition of tensor powers of the defining representation of $S_n$. Along the way, we also look at the more general $m$-cycle-to-transpositions chain ($m \le n$) and give an upper bound for the mixing time of the $m=n-1$ case as well as characterize the expected number of fixed points in the general case where $m$ is an arbitrary function of $n$. | 2018-03-22 07:55:13 | {"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": 0.9522045254707336, "perplexity": 112.02947922193432}, "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-2018-13/segments/1521257647782.95/warc/CC-MAIN-20180322073140-20180322093140-00464.warc.gz"} |
http://mathhelpforum.com/differential-geometry/208908-vector-geometry-projectiles-print.html | # Vector Geometry: Projectiles
• December 2nd 2012, 11:30 AM
colinvt11
Vector Geometry: Projectiles
Hi guys, I am working on some Vector Geometry homework and have come across a problem that I don't know what to do for, any help would be greatly appreciated:
A spring catapult slings a boulder in the air from ground level with an initial speed of 280 feet per second and the boulder crashes back into the ground 7.7 seconds later. At what angle of elevation in degrees was the boulder slung into the air (in degrees)?
I know you would start with a = <0, -32> and v = <280cos(x), 280sin(x)> but I'm not quite sure where the problem goes from there, any help would be greatly appreciated.
• December 2nd 2012, 11:54 AM
topsquark
Re: Vector Geometry: Projectiles
Quote:
Originally Posted by colinvt11
Hi guys, I am working on some Vector Geometry homework and have come across a problem that I don't know what to do for, any help would be greatly appreciated:
A spring catapult slings a boulder in the air from ground level with an initial speed of 280 feet per second and the boulder crashes back into the ground 7.7 seconds later. At what angle of elevation in degrees was the boulder slung into the air (in degrees)?
I know you would start with a = <0, -32> and v = <280cos(x), 280sin(x)> but I'm not quite sure where the problem goes from there, any help would be greatly appreciated.
Call your variable $\theta$ to put it in the usual format.
There are a number of ways to approach this. The simplest is to use the equation
$\overrightarrow{s} = \overrightarrow{s_0} + \overrightarrow{v_0}t + \frac{1}{2} \overrightarrow{a} t^2$
where s is the final displacement <r, 0> (r is the range, an unknown), s_0 is the initial position <0, 0>, v_0 is the inital velocity, and a is the acceleration. This equation decouples into x and y equations. What you want is the y equation. This only has $\theta$ as a variable.
-Dan
PS: This should be in the Math subforum.
• December 2nd 2012, 02:19 PM
Soroban
Re: Vector Geometry: Projectiles
Hello, colinvt11!
Quote:
A spring catapult slings a boulder in the air from ground level with an initial speed of 280 ft/sec
and the boulder crashes back into the ground 7.7 seconds later.
At what angle of elevation was the boulder slung into the air (in degrees)?
The equations for projectile motion (for this problem) are:
. $\begin{array}{ccc}x &=& (280\cos\theta)t\qquad\;\; \\ y &=& (280\sin\theta)t - 16t^2 \end{array}$
$\text{When }\,t = 7.7,\;y \,=\,0.$
$\text{We have: }\:(280\sin\theta)(78.7) - 16(7.7^2) \:=\:0$
. . . . . . . . . . . . . $2156\sin\theta - 948.64 \:=\:0$
n . . . . . . . . . . . . . . . . . . . . . $\sin\theta \:=\:\frac{948.64}{2156} \:=\:0.44$
n . . . . . . . . . . . . . . . . . . . . . . . $\theta \:\approx\:26.1^o$
• December 2nd 2012, 04:27 PM
topsquark
Re: Vector Geometry: Projectiles
-Dan
• December 2nd 2012, 07:13 PM
colinvt11
Re: Vector Geometry: Projectiles
Thank you both very much, I was able to understand the problem from your descriptions!
• December 6th 2012, 08:47 PM
babynancy543
Re: Vector Geometry: Projectiles
Suppose that the equation of the line is:
r = (a1, b1, c1) + s(d1, d2, d3), where s is real
Suppose that the given point is: (a2, b2, c2)
We obtain the direction vector by considering the 2 points, e.g. (a2 - a1, b2 - b1, c2 - c1) = (e1, e2, e3). (a1 - a2, b1 - b2, c1 - c2) is also alright.
Equation of the plane is thus:
r = (a1, b1, c1) + s(d1, d2, d3) + t(e1, e2, e3) where s, t are reals.
or
r = (a2, b2, c2) + s(d1, d2, d3) + t(e1, e2, e3) where s, t are reals.
If you like to obtain the equation in scalar product form, it will be: r . n = a . n where
n = (d1, d2, d3) x (e1, e2, e3) and a = (a1, b1, c1) or (a2, b2, c2). | 2014-04-18 02:06:22 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "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": 0.7947320938110352, "perplexity": 815.0092492354667}, "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-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00566-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://mathandmultimedia.com/2014/03/page/2/ | ## Sexy Primes: What Are They?
You are probably shocked about the title and you will probably think that this is a joke. Well, it’s not. There are really sexy primes and in fact, there are some research about them.
Sexy primes are prime numbers which differ by 6. The pair (5,11) are examples of sexy primes, while (7,13,19) are triplet sexy primes. Quadruplet and quintuplet primes also exist and examples of them are (5,11,17,23) and (5,11,17,23,29) respectively. Sadly, there is only one quintuplet sexy prime.
“No, I am not a sexy Prime.”
Just like the search for twin primes, the search for sexy primes are also in progress (especially for single mathematicians). As of this writing, the greatest sexy prime pair found has 11,593 digits (the first number) and the greatest prime triplet has 5132 digits (the first number).
In September 2010, Ken Davis found the largest quadruplet sexy prime yet, a 1004-digit with p = 23333 + 1582534968299.
The proof that there is one quintuplet prime is quite easy. It only involves finding testing all the possible remainders of integers when divided by 5 (recall equivalence classes) and prove that one of $(p, p + 6, p + 12, p + 18, p + 24)$ is prime.
Reference: Wikipedia, Image Credit: Optimus Convoy, Devian Art
## Domain and Range on a Graphical Perspective
Two weeks ago, I discussed the basic concepts of domain and range which I presented in an ‘algebraic way.’ In this post, I would like to discuss these concepts from a graphical perspective.
The domain of a function $x$ is the set of points on the x-axis where if a vertical line is drawn, it will hit a point on the graph. Take for instance, in the linear function $f(x) = 2x$, we are sure that we can always hit a point wherever we draw a vertical line. In algebraic explanation, we can always find an $f(x)$ for every $x$. Therefore, we can conclude the that domain of $f$ is the set of real numbers. On the other hand, if we draw a horizontal line and it hits the graph, then it is part of the range of the graph. Clearly, the range of the $f$ is also the set of real numbers.
## What is the shape in three dimensions?
Got this problem from a seminar yesterday, and I think it’s a pretty good exercise for visualization. The bottom, side, and front views of an object is shown below.
How does the object look in three dimensions? There is a good discussion about this problem in StackExchange | 2019-08-24 05:15:52 | {"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": 0, "img_math": 7, "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": 0.713450014591217, "perplexity": 519.1770598229908}, "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/1566027319724.97/warc/CC-MAIN-20190824041053-20190824063053-00284.warc.gz"} |
http://icpc.njust.edu.cn/Problem/Pku/1220/ | # NUMBER BASE CONVERSION
Time Limit: 1000MS
Memory Limit: 10000K
## Description
Write a program to convert numbers in one base to numbers in a second base. There are 62 different digits: { 0-9,A-Z,a-z } HINT: If you make a sequence of base conversions using the output of one conversion as the input to the next, when you get back to the original base, you should get the original number.
## Input
The first line of input contains a single positive integer. This is the number of lines that follow. Each of the following lines will have a (decimal) input base followed by a (decimal) output base followed by a number expressed in the input base. Both the input base and the output base will be in the range from 2 to 62. That is (in decimal) A = 10, B = 11, ..., Z = 35, a = 36, b = 37, ..., z = 61 (0-9 have their usual meanings).
## Output
The output of the program should consist of three lines of output for each base conversion performed. The first line should be the input base in decimal followed by a space then the input number (as given expressed in the input base). The second output line should be the output base followed by a space then the input number (as expressed in the output base). The third output line is blank.
## Sample Input
8
62 2 abcdefghiz
10 16 1234567890123456789012345678901234567890
35 23 333YMHOUE8JPLT7OX6K9FYCQ8A
23 49 946B9AA02MI37E3D3MMJ4G7BL2F05
61 5 dl9MDSWqwHjDnToKcsWE1S
5 10 42104444441001414401221302402201233340311104212022133030
## Sample Output
62 abcdefghiz
2 11011100000100010111110010010110011111001001100011010010001
10 1234567890123456789012345678901234567890
35 333YMHOUE8JPLT7OX6K9FYCQ8A
35 333YMHOUE8JPLT7OX6K9FYCQ8A
23 946B9AA02MI37E3D3MMJ4G7BL2F05
23 946B9AA02MI37E3D3MMJ4G7BL2F05
61 dl9MDSWqwHjDnToKcsWE1S
61 dl9MDSWqwHjDnToKcsWE1S
5 42104444441001414401221302402201233340311104212022133030
5 42104444441001414401221302402201233340311104212022133030
10 1234567890123456789012345678901234567890
## Source
Greater New York 2002 | 2020-09-18 20:51:05 | {"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": 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": 0.3704173266887665, "perplexity": 1292.31861657933}, "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/1600400188841.7/warc/CC-MAIN-20200918190514-20200918220514-00387.warc.gz"} |
https://www.physicsforums.com/threads/doorframe-problem.462139/ | # Doorframe problem
A doorframe is twice as tall as it is wide. There is a positive charge on the top left corner and an equal but negative charge in the top right corner. What is the direction of the electric force due to these charges on a negatively charged dust mite in the bottom left corner of the doorframe?
So I know the how to divide into components and analyze in the x an y directions to figure out the net force in x an y direction. But the problem is the values I plugged in were not correct because it was wrong. my answer was 32 or so degree.
## The Attempt at a Solution
Any brave souls?
gneill
Mentor
Maybe show a little more of your attempt?
So I assumed that the positive charge at the top left corner is 1.602e-19C, an elementary charge. Likewise, the negative charge at the top right corner is assumed to be -1.602e-19C. The dust mite, although unspecified of its value, is negatively charged, so I assumed its charge to be -1.602e-19C. So the attractive electrostatic force between the mite and the positively charged particle is (0, 5.768e-29)=(Fx,Fy) assuming that the length along the side is 2m and the width is 1m. For the repulsive force between the mite and the negative charge, the angle made by the diagonal line, connecting the mite and the charge, and the length of the doorframe is arcsin(1/sqrt(5)) or 26.565degrees. The net electrostatic force between the negatively charged particle and the mite is 5.768e-29 N. So, using trigonometry, I get (Fx,Fy)=(-2.5795e-29,-5.159e-29). Then summing the forces, (Fx,Fy)=(-2.5795e-29, 6.0895e-30). Theta is then, atan(6.0895e-30/-2.5795e-29)+360= 346.717degrees. Any flaw in this?
gneill
Mentor
The net electrostatic force between the negatively charged particle and the mite is 5.768e-29 N. So, using trigonometry, I get (Fx,Fy)=(-2.5795e-29,-5.159e-29). Then summing the forces, (Fx,Fy)=(-2.5795e-29, 6.0895e-30). Theta is then, atan(6.0895e-30/-2.5795e-29)+360= 346.717degrees. Any flaw in this?
I think you should recheck the force due to the negative charge at the top right corner. You may have used the length of the door frame instead of the diagonal. Also, estimate the quadrant that the resultant should fall in by looking at your diagram; make sure that your calculated angle for the resultant agrees.
I really don't have an intuitive sense as to where the resultant electrostatic force will point to. So all I can rely on is calculation. So the right angle is 320.3868? The angle is actually atan(1/sqrt(5)). So using the angle, 24.095degrees, the ordered set of x and y component of electrostatic force vector is (-1.88e-29,-4.212e-29). So adding up all the x and y forces, the resultant force will have (-1.88e-29,1.556e-29). So taking arctangent;atan(1.556e-29/-1.88e-29)+360= 320.38degrees since it's in the fourth quadrant.
gneill
Mentor
I really don't have an intuitive sense as to where the resultant electrostatic force will point to. So all I can rely on is calculation. So the right angle is 320.3868? The angle is actually atan(1/sqrt(5)). So using the angle, 24.095degrees, the ordered set of x and y component of electrostatic force vector is (-1.88e-29,-4.212e-29). So adding up all the x and y forces, the resultant force will have (-1.88e-29,1.556e-29). So taking arctangent;atan(1.556e-29/-1.88e-29)+360= 320.38degrees since it's in the fourth quadrant.
The distance from the top right corner to the bottom left is greater than the distance from the top left corner to the bottom left (the diagonal is longer than the side). Since all charges have the same magnitude you expect the magnitude of the force with the shorter separation to be larger. Or, if you prefer, the one with the larger distance between them will be smaller.
The force between charges always lies along the line joining the charges.
So, if you were to sketch the forces on the charge at the lower left you'd have one pointing along the direction of the diagonal to the lower left (repulsive), and one, slightly larger, pointing straight up towards the upper left corner. If you "add" these vectors graphically on your sketch, where does the resultant end up? | 2021-02-28 19:51:01 | {"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": 0.8301528096199036, "perplexity": 431.5463995178332}, "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-20210228175250-20210228205250-00315.warc.gz"} |
http://tiku.21cnjy.com/?mod=quest&channel=4&cid=159&xd=2 | ## 考点：人生百味类
• “Everything happens for the best,” my mother said whenever things weren’t going my way. “Don’t worry, one day your luck will change.”
Mother was right, as I discovered after I had finished my college education. I had decided to try for a job in radio. One day, I wanted to host(主持) a sports program. I went to Chicago and knocked on the door of every station. But I got turned down every time.
In one station, a kind lady said my problem was that I hadn’t got enough experience. “ Get some work with a small station and work your way up,” she said.
I went back home. I couldn’t get a job there, either. Then my dad told me a businessman had opened a store and needed someone to help him. But again, I didn’t get the job.
I felt really down. “ Your luck will change,” Mom said to me. Dad lent me the car to help me to look for my job. I tried another radio station in Iowa. But the owner, a nice man, told me he had already had someone.
As I left his office, I asked, “How can someone be a sports announcer(播音员) if he can’t get a job in a radio station?”
I was waiting for the lift when I heard the man call. “ What did you mean? Do you know anything about football?” He put me in front of a microphone and asked me to try to imagine that I was giving my opinion on a football game, I succeeded.
On my way home, Mom’s words came back to me, “One day your luck will change, Son. And when it happens, it’ll feel doubly(加倍的) good because of all the hard work you’ve had.” At that moment I knew what just what she meant.
【小题1】 What’s the writer’s ideal (理想的) job? A．A sportsman [* _* K! X8 B8 ?& T) B% Z4 d- Q B．A shop assistant; L$A- @, R! X ' C．A sports announcer5 L) F3 \5 [* @- \& B$ O3 N0 C2 Q- I/ X D．A businessman4 \2 N5 e$i% ]/ b+ f. V 【小题2】Why didn’t the writer get the job in Chicago? A．because he was too young& S9 G3 W: h X: i: G B．Because he didn’t get college education( N8 ' T* I K# E C．Because he’s got a good-looking person2 F: ]& L8 X/ G1 G' \ D．Because he hadn’t got enough experience7 @% O/ @! i# [9 H 【小题3】Which of the following is true according to the article? A．You just need wait for some time, then luck will come.9 _+ W9 I1 X ^( P B．Luck will come if you try your best to do everything.' i" W! ?5 H; L; Q9 C．It’s important for you to wait for luck.1 S) U( c. L9 O- [4 ? D．You should trust your mother.) B N/ S4 ? _5 M$ \' d8 W( J
【小题4】The sentence “But I got turned down every time.” Means “______” A．But I was refused every time2 M# e! L+ S6 ^+ ? B．But I was successful every time+ N4 Q6 a4 e; a( @+ G- ^# b C．But I lost my way every time7 b i5 P0 4 R9 K( d D．But the door of every station was always closed$G$ U& ]1 E( A; U* a( d
【小题5】What’s the best title of this passage? A．Mother’s words3 E# V+ D+ U1 i0 U W+ Z( ?- h. [ B．Everything Happens For The Best- b. L3 a# K+ L C．No One Is Always Lucky+ Y: i6 W1 d* N: K. O3 I8 T& i/ E D．To Find A Job In Radio Is Difficult0 F9 ]& E4 d8 G; ?0 Z, U
• Have successful people ever felt sad? Do they have any "secrets" to success? The answers to these questions can be found in US president Barack Obama’s "back to school" speech. Here is a small part of his speech.
I know that sometimes, after watching TV, you may feel that you can be rich and successful without any hard work--that your ticket to success is through rapping (饶舌音乐) or basketball or being a TV star. But when chances come, you may not succeed.
The truth is, being successful is hard. And you may not succeed at everything the first time you try. That’s OK. Some of the most successful people in the world have had the most failures. JK Rowling’s first Harry Potter book was rejected(退稿)12 times before it finally came out. Michael Jordan lost hundreds of games and missed thousands of shots during his career (职业生涯). But he once said, "I have failed over and over and over again in my life. And that is why I succeed."
These people succeeded because they understand that you can’t let your failures beat you--you have to let them teach you. You have to let them show you what to do differently next time.
No one’s born being good at things. You become good at things through hard work. Don’t be afraid to ask questions. Don’t be afraid to ask for help when you need it.
And even when you’re struggling(挣扎), even when you’re discouraged(泄气), and you feel like other people have given up on you--don’t ever give up on yourself. Because when you give up on yourself, you give up on your country.
【小题1】Why does Barack Obama talk about JK Rowling and Michael Jordan in the second paragraph? A．To show that these two famous persons are different. e9 R6 W' I5 H# e. I6 Z B．To show that writing and sports are difficult skills. 5 a. Q% ]& h( b# E C．To show that the two persons were treated unfairly. # e$c) B4 [( f- M, R- E# X; D．To show that being successful is hard.2 U3 A- J8 L( i; a0 Q 【小题2】Barack Obama believes ____________ in his speech. A．you can be rich and successful without any hard work % B" j1 h8 j/ c; A8 U1 \ B．you may succeed at everything the first time you try 3 ^- C" W- I, B3 Q. ]( T C．you can’t let your failures beat you , e; [$ f/ Q# 2 ]- O5 ]* O D．you shouldn’t ask other people for help* 4 ? S3 T! N' O0 ^) d: J
【小题3】What does the underlined sentence mean? A．If you’re discouraged, you should give up on yourself. 7 E5 O9 B3 ]. M! e2 G$i1 O B．You should believe in yourself no matter how difficult it is.$ O9 ^4 W9 c# P5 _$Z C．When you’re struggling, you’ll feel like other people have given up on you. 0 i7 G$ N; A- e3 B5 H! C: L+ Y D．If you are not struggling or discouraged, you can give up on yourself.; B1 H* C- E5 P5 V
【小题4】What’s the best title of this small part of Mr. Obama’s speech? A．The way to succeed# d) Q- \& @7 L$F* O1 L: e0 G B．Failures can help you / X* A! X9 E2 H C．Don’t give up on yourself) ^# Y1 c3 d. Z" b" T) J D．Barack Obama’s success9 c6 W8 G) O2 c. E: • Last month the manager of a jewelry shop received a letter. As he was very busy then, the letter lay on his desk till tea-time. He opened it and a 10-pound note(票) fell out onto the desk. Within the note was a letter which said: Dear sir: In 1935 I got engaged(订婚). But unfortunately I lost my job. At the time a lot of people were out of work. Six months later I got a job again, but of course I was very short of money. I came to your shop to buy a wedding ring(婚戒). The assistant took out some rings for me to look at, but she was called away for a moment, and I put one of the rings in my pocket. When she came back, I said I didn’t know the size of my girl’s finger. So I left the shop without buying a ring. My wife died a short while ago and the fact that I never paid for the ring has been heavy in my heart all these years. At that time, the ring cost 2 pounds so I think it is 10 pounds at today’s price and I’m sending 10 pounds. Yours truly, A customer (顾客) 【小题1】When did the manager open the letter? A．In the morning B．When he received the letter C．At lunch time D．Till tea-time 【小题2】The customer didn’t write the letter until_____. A．he was dying B．his wife’s death C．he had enough money D．he got a job again 【小题3】What do you think of the customer’s paying for the ring at last? A．Honest B．Forgetful C．Dishonest D．Careless • This term we have a new teacher of English. His name is Mr Peterson. He comes from Australia, but now he lives in a tall building in Wuxi. He is not very tall and he is thin. He has a round（圆的）face and small blue eyes. He wears glasses and they make him look smart．He has dark（深的）brown hair． Mr Peterson works very hard. In class, he has many good ideas（想法）to make the class Very interesting. We all 1ike his class. After class, he always encourages us to speak more English. Sometimes, he plays games with us. He is very strong and he can play basketball and football very well. He is good at sports. Sometimes, he plays table tennis with us, but he doesn't play it very well. Mr Peterson loves living in China very much. He likes lots of things in China. He really loves eating Chinese food. He loves traveling in China, too. He is going to visit Xi'an next month. 【小题1】What does Mr Peterson do? Mr Peterson is _______. A．a doctor ]2 O3 A b# I0 ?6 D) L B．a teacher$ F, A8 R+ V0 J* V" B: ? C．a farmer4 R; F2 [" U: h& F5 O D．a worker2 ?$D9 K+ D& j 【小题2】We can not use _______ to describe（描述）Mr Peterson. A．tall+ 1 A; M' ], J- e/ R B．thin; A' S4 f7 P' O* C C．smart/ K' h! Z% M: Y D$ N D．hard—working（勤劳的）7 j* V. B# \6 Q2 b& a
【小题3】How many ball games is Mr Peterson good at? A．4$g- i8 f! j, i' B3 c) a7 L B．34 A% e& b& M! W* I* ? C．2$ U4 h$F% D6 K1 ?5 d+ Y1 d D．1/ b# J$ M6 K5 M( a# Q5 j. \3 I
【小题4】The underlined（画线的）word "encourage" means _______ in Chinese. A．阻止# f5 L9 b" c" R3 c. Q0 i% X$J( ? B．嘲笑: D: L7 Y Y6 F C．逼迫1 @$ U7 f/ ? @% S D．鼓励2 K% - V/ U+ T! S, I9 X4 \
【小题5】Which of the following is not true（正确）? A．Mr Peterson is a very good English teacher.% \7 f. ?0 Q& I4 D* S B．Mr Peterson likes playing computer games.: Z' K0 S+ a2 R# N' c0 ]7 e C．Mr Peterson is a very good football player.7 \- R% I- \% ]/ Z, Q9 j. E; b+ E D．Mr Peterson enjoys his life in China. P5 Z$C7 O3 I( i* j3 D" @ c • Bad days happen to us all. Often a day that starts out bad just continues to get worse. Sometimes there’s a “domino effect(多米诺效应)” with bad events. For example, you sleep through the alarm, so you’re stressed. And you will sit in the bad traffic, which will also make you late for work, etc. How can we turn a bad day to a good day? Here are some ideas that have worked for me: Smile a lot Smiling a lot will help you feel relaxed. Research has shown that smiling produces three useful chemicals which make us feel good. Talk to a good friend Keeping bad or unhappy things in your mind is not a good idea. Talking to someone who cares and listen really does help us feel better, too. Concentrate on your good things It’s hard to concentrate on how bad things are when you’re concentrating on how good things are! Think of 10 or more things you’re thankful for, and you’ll achieve a whole new outlook(人生观) on your day. Get some exercise If you can, go for a walk. Exercising will help you feel better. Excising can get your day back to be normal again. Make the day a challenge If you make yourself think of the day as a challenge, you’ll start to do all the things you can to make your day better. 根据材料内容选择最佳答案，并将其标号填入题前括号内。 【小题1】According to the passage, the “domino effect” is an effect that______. A．turns a good day to a bad day B．makes one person affect another C．turns bad things into good things D．gets one event to cause other similar events to happen 【小题2】Study shows that smiling produces three useful chemicals which make us feel______. A．terrible B．relaxed C．stressed D．worried 【小题3】According to the writer, if we consider a bad day as a challenge, we’ll ______. A．try our best to do things better B．give up doing things C．lose all our confidence D．have a terrible 【小题4】If the writer wants to feel better, how does the writer do? A．Quarrel with a good friend B．Concentrate on your good things C．Get some exercise D．Make the day a challenge 【小题5】Which of the following can be the best title for this passage? A．When we should smile a lot B．How to deal with problems C．How to turn a bad day around D．What we should concentrate on • Have you ever stayed in a hotel? Most Chinese hotels often provide guests with things like disposable(一次性的) toothbrushes, toothpaste, shampoo and slippers. Many guests like the idea because they don’t have to bring their own. But if you travel to Beijing, remember to bring these things of your own. That’s because some hotels in Beijing have no longer provided guests with these disposables (一次性用品). Many disposable things are made of plastic. People throw them away after only using them once. It’s a waste of natural resources (资源) and is very bad for the environment. In Beijing, people throw away about 19,000 tons of plastic bags and 1,320 tons of lunch bowls every year! Plastic can take 100 to 400 years to break down. So the less plastic we throw away, the better environment we will have. So, wherever you travel, bring your own things and use them again and again. Back at home and school, you can also do something to make our world a better place. Try to do these things in your daily life: Use cloth shopping bags, not plastic ones. After using a plastic bag, wash it out and let it dry. Then use it over and over again. Do not use paper cups. At your school canteen (餐厅), use your own bowls and chopsticks instead of disposable ones. 根据短文内容，判断正(T)误(F)。 【小题1】Many guests like to use disposable things because they are very convenient (方便的). 【小题2】Some Beijing hotels have no longer provided guests with free TV programmes. 【小题3】Plastic breaks down easily. 【小题4】After using a plastic bowl or a bag, we’d better throw it away, because it’s too dirty to use again. 【小题5】We should use less plastic things and protect our environment. • 阅读短文，选择正确答案（每题2分） A) LiYugang dresses like a woman and sings like a bird. He won the third prize in CCTV’s Star Road in 2006. He sings folk songs. However, he seems to have the spirit of Mei Lanfang. In fact, the young man had learnt something from Mei Lanfang’s students. People in China usually don’t like cross-dressing(反串). But people are really surprised at Li’s beauty and grace when he sings and dances. B) Do you know who invented QQ? It was Ma Huateng. He was born in Guangdong in 1971. He chose computer science when he entered Shenzhen University in 1989. He worked as a computer programmer for a company in Shenzhen for five years after he graduated in 1993. Later he left the company and started his own company in 1998. C) Yue Fei was a famous hero of Southern Song Dynasty. He was born in a poor family in Henan Province. He was very brave and won many battles with his soldiers. But Qin Hui killed Yue Fei for Mo Xuyou. Later a temple about Yue Fei was built in memory of him at the foot of Qixia Ling by the West Lake, in Hangzhou. 【小题1】Who did Li Yugang once learn from according to the passage? A．Mei Lanfang.) D3 d4 j6 E- I B．Mei Lanfang’s students.4 F0 S; V) d G0 L5 b3 A# e5 ^ C．Mei Yanfang’s students., F5 F# _* S, E5 J! f$ O$S3 c5 g D．Mei Lanfang’s friends.3 H+ M' f) R# Z; i( K( L9 A 【小题2】The underlined word “grace” means____________ in Chinese. A．粗犷3 O7 P* R2 h+ B" D) O+ N' j, A B．做作6 2 B' \ c1 j. A C．傲慢3 c. ^4 S0 g6 E( \& O+ g# ? D．优雅! ]) A" R8 ?; d* g1 \ 【小题3】From the passage, we know Yue Fei_____________. A．was not born in a rich family + a3 ]8 e: Z; h, S6 H: M B．was not brave- \; ?; O+ A; L9 R5 X C．killed Qin Hui; G1 Q" U: U+ _' ?4 a! M4 [8 a D．built a temple% b% h E- E% F9 i/ P 【小题4】Ma Huateng set up his own company when he was____________. A．180 L( ]& Y4 Q0 B. G: [5 N% X B．221 V" Z7 C* C) c' i& i/ j C．277 e7 U, i, d1 ^ D．42) i f G3 g* a+ Z7 g+ . Q 【小题5】 Which of the following is TRUE? A．Li Yugang invented QQ.2 S. D0 A$ Q9 H B．Ma Huateng used to work as a computer programmer for a company." M3 e1 C3 A+ S. R3 h: K C．Li Yugang won the first prize in CCTV’s Star Road.0 i) c9 C8 ]- E( M: c2 j0 H( h D．Yue Fei seldom won battles with his soldiers.0 O6 P" S) E& g# b
• Do you want to have a trip? Hope Farm can give you a nice experience this autumn.
On the farm, you can meet animals and take a walk through the garden and greenhouse. How about making friends with the plants there? Our teachers will tell you the differences or similarities of all the plants. You can also take a look at the honeybees, learn more about then and maybe even taste some honey! There is a hill beside the farm. Picking apples at the foot of the hill is an interesting activity. After that, how about climbing it with your friends? You are able to see the fantastic view at the top of the hill.
The price of each trip is $50 for a group of ten students. You can visit the traveling club in our school to order a trip. 【小题1】This passage introduces a trip for__________. A．poor families5 F. N Q+ \1 C* U: \+ h B．foreign travelers% i: O" b+ J' Y) G4 C C．students at school ) M9 B8 C9 h0 d1 Q/ a6 Y1 M2 f D．old people2 U0 C/ g, ?9 J2 G! b4 Y 【小题2】 You can __________at the foot of the hill. A．walk through the greenhouse' X T% P8 P- ^. ^ B．pick apples9 X5 V5 J! J0 2 Q% Z; i; U) N C．make friends with plants7 [; M/ A9 ?% K1 X6 f D．taste some honey& a6 H7 G2 d6 \ 【小题3】The underlined word “similarities” probably means “_________” in Chinese. A．类似处; a' T9 @4 G+ [* G B．益处& j C, i3 g2 h# D+ [0 @, A/ C C．异处1 B G7 Z* a- b; \' U8 K D．建议+ G7 J& [6 [5 H; b' H5 W 【小题4】 How much should you pay if your group has 20 people? A．$50 c- H/ \, \, g* ?( G B．$65- L ?0 j3 ^; i5 W& F. N. j# b C．$80$B6 L& Q B1 C0 \: W) e D．$100# c+ S1 ^' F2 \" N
• When I was a boy，I was a football fan．I always played football with some other boys in the backyard（后院）all the time．My mom was worried that I would get ill in the hot summer．
One day my brother gave me a new football．I came into the yard and played it excitedly．But suddenly，the ball flew through the window and nearly hit my dad．Dad said nothing．He took my football and cut it in half．
I didn’t cry because I knew how terrible my mistake was．I didn’t expect to get another football．But to my surprise，Dad bought me another one the next month and told me to be more careful．I was really thankful for my father’s forgiveness（宽恕）．He showed me that even when I made a mistake. He still loved me and gave me another chance．
Parents always give us their unconditional（无条件的）love and forgiveness．We should always give our love and forgiveness to them，too．
【小题1】The writer played football in the backyard all the time because _____． A．he was easy to get ill/ B. ^2 ^/ _+ ^/ N$A. O- Y! P B．he was a football fan1 ]: T& F- M* \5 D, P C．his father was a football player1 V- M* J8 V- D．his mother was worded about him) c7 e; Z& R# ]* C& ? 【小题2】The writer didn’t cry because _______． A．he knew his mistake5 L2 T5 6 e# G) e/ I6 O1 B' K B．his father cut the football in half9 U2 C9 M! V& S; L* P C．his father was very happy+ f F8 O# g4 U* A/ - D D．he nearly hit his father7 [, a3 _- S% O" I% T/ H+ [+ e0 J 【小题3】After his dad bought him another football，the writer ______． A．forgot his mistake$ U* M' G* V* A% ], N/ B4 H) W B．was angry# E) P/ U! ?) G1 Q ^ C．was thankful to his father$A. N; M8 B B- d7 f8 j) V8 \/ E D．didn’t like it/ ]" \# O5 i3 Z6 P, L4 ^, 9 [ 【小题4】What can we learn from the story? A．We should learn to play football．. Y8 H5 G( h* a0 [/ \9 _1 A+ U B．We should love our parents．2 J$ M: U8 R6 _ K$N6 a. f C．We should play football with our parents．1 8 X& E; J3 e5 g9 B2 D．We shouldn’t make mistakes．3 R6 U4 M- O- A D7 f+ G • Join us for an English Summer Camp in English ! 【小题1】__________can take part in the English Summer Camp. A．Students under 133 V0 d3 C, c3 K) i B．Students aged 16! Y5 h/ A1 W# V C．Students over 184 N( B+ T' V1 P. H( L D．All the students( U7 d5 : G! A- a& d- U4 d% d. S 【小题2】 You can go to register on__________. A．August 1st% g: _( c+ [* N5 a B．August 6th* E) b5 F: Y* N9 [# D' I& U i C．August 9th- Z; D9 b0 K1 A3 f) T( e, j/ S4 D+ D D．August 26th) @; S4 [( S2 H6 K% H 【小题3】You can _______by joining in the English Summer Camp A．visit the whole country2 O+ T1 N* ^7 _/ e B．become an experienced teacher8 E8 B R% _4 h- V# i` C．improve your Chinese6 h5 i: Z0 g# ^, D( D2 G6 [- R D．know about British customs; e" W2 H( @& j3 B9 ?$ Z+ b5 M3 O | 2018-07-16 21:49:24 | {"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": 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": 0.3036563992500305, "perplexity": 7014.04706384534}, "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-2018-30/segments/1531676589470.9/warc/CC-MAIN-20180716213101-20180716233101-00342.warc.gz"} |
http://mathoverflow.net/questions/68598/basic-questions-about-stacks-2 | I have again three basic questions about stacks.
1) When we consider categories fibered in groupoids, do we always mean small or essentially small groupoids? Especially I want to know if algebraic geometers always impose this condition when they talk about categories fibered in groupoids, especially stacks.
2) In the proof of Artin's criterion for algebraic spaces/stacks $X/S$ for every point $p \in X$ of finite type over $S$ a "local approximation" $X_p$ is constructed. Then $X = \coprod_p X_p$ does the job. But in order to show that this is actually a scheme in the given universe, we need that the points of finite type constitute a set. Perhaps I'm overlooking something trivial here, but I cannot see how we can use Artin's criterions to deduce this.
3) What is the current status of the book "Algebraic Stacks" by Kai Behrend, Brian Conrad, Dan Edidin, William Fulton, Barbara Fantechi, Lothar Göttsche und Andrew Kresch? I would love to read it as soon as it is completed.
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Regarding 1), the definition of a fibred category does not assume that the fibres are small, but in geometric examples they are (or at least are essentially small). For example, would you consider the groupoid of G-bundles on a fixed topological space to be a set? This groupoid is certainly essentially small once you have a classifying space BG. – David Roberts Jun 23 '11 at 12:42
Me again. The category GBund(X) of principal G-bundles on a fixed object X in a site (S,J) is equivalent to the hom-category Gpd_ana(X,_B_G) in the bicategory of internal groupoids, anafunctors and transformations (without loss of generality, assume S is a superextensive site - see nLab for definition - which is true in all geometric situations). Here _B_G is the groupoid with one object and morphisms G, and we consider X as a groupoid with only trivial morphisms. GBund(X) is essentially small when the axiom 'WISC' holds for J, again see nLab. But 'morally', if not actually, the 2-category.... – David Roberts Jun 23 '11 at 23:11
...of stacks in groupoids on (S,J) is equivalent to the bicategory of groupoids, anafunctors and transformations in S. Roughly speaking, all fibres of a stack are representable in this bicategory, and so given WISC, one knows that the fibres are essentially small. Oh, I should mention that really this is only expected to hold for geometric stacks (presentable by some space/scheme/what-have-you), but I guess that that is the case you are most interested in. – David Roberts Jun 23 '11 at 23:16 | 2015-08-05 02:47:02 | {"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": 0.8791495561599731, "perplexity": 336.78401662526795}, "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-2015-32/segments/1438043058631.99/warc/CC-MAIN-20150728002418-00252-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://aitopics.org/class/Technology/Information%20Technology?filters=taxnodes%3ATechnology%7CInformation+Technology&start=251140 | # Information Technology
### Learning the 2-D Topology of Images
We study the following question: is the two-dimensional structure of images a very strong prior or is it something that can be learned with a few examples of natural images? If someone gave us a learning task involving images for which the two-dimensional topology of pixels was not known, could we discover it automatically and exploit it? For example suppose that the pixels had been permuted in a fixed but unknown way, could we recover the relative two-dimensional location of pixels on images? The surprising result presented here is that not only the answer is yes but that about as few as a thousand images are enough to approximately recover the relative locations of about a thousand pixels. This is achieved using a manifold learning algorithm applied to pixels associated with a measure of distributional similarity between pixel intensities. We compare different topology-extraction approaches and show how having the two-dimensional topology can be exploited.
### Discriminative K-means for Clustering
We present a theoretical study on the discriminative clustering framework, recently proposed for simultaneous subspace selection via linear discriminant analysis (LDA) and clustering. Empirical results have shown its favorable performance in comparison with several other popular clustering algorithms. However, the inherent relationship between subspace selection and clustering in this framework is not well understood, due to the iterative nature of the algorithm. We show in this paper that this iterative subspace selection and clustering is equivalent to kernel K-means with a specific kernel Gram matrix. This provides significant and new insights into the nature of this subspace selection procedure. Based on this equivalence relationship, we propose the Discriminative K-means (DisKmeans) algorithm for simultaneous LDA subspace selection and clustering, as well as an automatic parameter estimation procedure. We also present the nonlinear extension of DisKmeans using kernels. We show that the learning of the kernel matrix over a convex set of pre-specified kernel matrices can be incorporated into the clustering formulation. The connection between DisKmeans and several other clustering algorithms is also analyzed. The presented theories and algorithms are evaluated through experiments on a collection of benchmark data sets.
### Theoretical Analysis of Heuristic Search Methods for Online POMDPs
Planning in partially observable environments remains a challenging problem, despite significant recent advances in offline approximation techniques. A few online methods have also been proposed recently, and proven to be remarkably scalable, but without the theoretical guarantees of their offline counterparts. Thus it seems natural to try to unify offline and online techniques, preserving the theoretical properties of the former, and exploiting the scalability of the latter. In this paper, we provide theoretical guarantees on an anytime algorithm for POMDPs which aims to reduce the error made by approximate offline value iteration algorithms through the use of an efficient online searching procedure. The algorithm uses search heuristics based on an error analysis of lookahead search, to guide the online search towards reachable beliefs with the most potential to reduce error. We provide a general theorem showing that these search heuristics are admissible, and lead to complete and epsilon-optimal algorithms. This is, to the best of our knowledge, the strongest theoretical result available for online POMDP solution methods. We also provide empirical evidence showing that our approach is also practical, and can find (provably) near-optimal solutions in reasonable time.
### The Epoch-Greedy Algorithm for Multi-armed Bandits with Side Information
We present Epoch-Greedy, an algorithm for multi-armed bandits with observable side information. Epoch-Greedy has the following properties: No knowledge of a time horizon $T$ is necessary. The regret incurred by Epoch-Greedy is controlled by a sample complexity bound for a hypothesis class. The regret scales as $O(T^{2/3} S^{1/3})$ or better (sometimes, much better). Here $S$ is the complexity term in a sample complexity bound for standard supervised learning.
### A probabilistic model for generating realistic lip movements from speech
The present work aims to model the correspondence between facial motion and speech. The face and sound are modelled separately, with phonemes being the link between both. We propose a sequential model and evaluate its suitability for the generation of the facial animation from a sequence of phonemes, which we obtain from speech. We evaluate the results both by computing the error between generated sequences and real video, as well as with a rigorous double-blind test with human subjects. Experiments show that our model compares favourably to other existing methods and that the sequences generated are comparable to real video sequences.
### GRIFT: A graphical model for inferring visual classification features from human data
This paper describes a new model for human visual classification that enables the recovery of image features that explain human subjects' performance on different visual classification tasks. Unlike previous methods, this algorithm does not model their performance with a single linear classifier operating on raw image pixels. Instead, it models classification as the combination of multiple feature detectors. This approach extracts more information about human visual classification than has been previously possible with other methods and provides a foundation for further exploration.
### On Ranking in Survival Analysis: Bounds on the Concordance Index
In this paper, we show that classical survival analysis involving censored data can naturally be cast as a ranking problem. The concordance index (CI), which quantifies the quality of rankings, is the standard performance measure for model \emph{assessment} in survival analysis. In contrast, the standard approach to \emph{learning} the popular proportional hazard (PH) model is based on Cox's partial likelihood. In this paper we devise two bounds on CI--one of which emerges directly from the properties of PH models--and optimize them \emph{directly}. Our experimental results suggest that both methods perform about equally well, with our new approach giving slightly better results than the Cox's method. We also explain why a method designed to maximize the Cox's partial likelihood also ends up (approximately) maximizing the CI. | 2019-10-22 21:28:51 | {"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": 0.39588093757629395, "perplexity": 668.7360872943856}, "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/1570987824701.89/warc/CC-MAIN-20191022205851-20191022233351-00046.warc.gz"} |
https://freeyork.org/entity/golden-ratio/ | # Golden ratio
The golden ratio is also called the golden section or golden mean. Other names include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number, and mean of Phidias. In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The figure on the right illustrates the geometric relationship. | 2019-10-18 04:57:35 | {"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": 0.90338534116745, "perplexity": 1044.472284627921}, "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-2019-43/segments/1570986677884.28/warc/CC-MAIN-20191018032611-20191018060111-00442.warc.gz"} |
https://socratic.org/questions/how-do-you-simplify-sqrt-x-3y-4 | # How do you simplify sqrt(x^3y^4)?
$\sqrt{{x}^{3} {y}^{4}} = \sqrt{{x}^{2} \cdot x \cdot {\left({y}^{2}\right)}^{2}}$
$= x {y}^{2} \sqrt{x}$ | 2019-09-18 23:55:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "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": 0.7834274172782898, "perplexity": 7258.775550151579}, "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-2019-39/segments/1568514573385.29/warc/CC-MAIN-20190918234431-20190919020431-00379.warc.gz"} |
https://brilliant.org/problems/inside-a-circle/ | # Inside a circle?
Geometry Level 2
How many points on or inside a circle of radius 1 consist of integer $$(x,y)$$ pairs only?
× | 2017-03-27 01:03:42 | {"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": 0.3751542270183563, "perplexity": 1279.9918711511546}, "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-2017-13/segments/1490218189316.33/warc/CC-MAIN-20170322212949-00565-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?p=3757758 | # Bosons and Fermions in a rigorous QFT
by kof9595995
Tags: bosons, fermions, rigorous
P: 679
Quote by DrDu Is there anybody who believes that a rigorous QED exists?
I'd like the ask the question again, if a rigorous QED doesn't exist, what would be underlying theory of perturbative QED?
P: 5,464
Quote by kof9595995 But here if you creat the Hilbert space using creation operators, it might not be the same with the true Hilbert space, then the best you can get is a perturbation theory.
At least in QM tis is not true.
Which states do I miss?
I can construct nearly arbitrary operators from the creation and annihilation operators; look at the method of coherent states, for example.
And please not that up to now we haven't defined the Hilbert space, neither for x and p, nor for the creation and annihilation operators! So if we need to change the entire Hilbert space for some reason we are not forced to do this by introducing creation and annihilation which are nothing else but linear combinations of x and p. There is physics behind it so far.
P: 679
Quote by tom.stoer At least in QM tis is not true. Which states do I miss? I can construct nearly arbitrary operators from the creation and annihilation operators; look at the method of coherent states, for example. And please not that up to now we haven't defined the Hilbert space, neither for x and p, nor for the creation and annihilation operators! So if we need to change the entire Hilbert space for some reason we are not forced to do this by introducing creation and annihilation which are nothing else but linear combinations of x and p. There is physics behind it so far.
I kinda get what you mean, but I think in QFT the situation is quite different, and I'm more curious about QFT senario.
In QM, before we define any operator, we set the full Hilbert space as all square-integrable functions, and we define how x and p (so are a and a+) act on this full Hilbert space, then according to the specific Hamiltonian we have, we can construct the subspace using a and a+, though the construction may not be as simple as harmonic oscillator case. I guess this is what you mean.
However in an interacting QFT, the true structure of the full Hilbert space is not clear yet, let alone defining how a and a+ act on the space. The normal treatment is to use the Hilbert space from free theory (a Fock space) and then do things perturbatively. And my point is, if the interaction actually destroys any existence of direct-product structure of the true Hilbert space, then whatever kind of Fock space you use will be just an approximation at best, and if this is the case, I think Fock space does necessarily imply a perturbative approach.
HW Helper
P: 1,334
Quote by kof9595995 I'd like the ask the question again, if a rigorous QED doesn't exist, what would be underlying theory of perturbative QED?
Lattice gauge theory or an asymptotically free gauge theory in a partial higgs phase can provide a UV completion of low energy QED.
Sci Advisor P: 8,788 Googling "Grassmann Osterwalder-Schrader" produced these papers which may be relevant. Jaffe, Constructive Quantum Field Theory "The Euclidean methods also apply to theories with fermions, at least for examples with interactions that are quadratic in the fermions. This is the case for free and for “Yukawa type” interactions, used extensively in physics." Benfatto, Falco, Mastropietro, Functional Integral Construction of the Thirring model "Proposed by Thirring half a century ago, the Thirring model is a Quantum Field Theory of a spinor field in a two dimensional space-time, with a self interaction ..."
P: 1,939
Quote by kof9595995 In QM, before we define any operator, we set the full Hilbert space as all square-integrable functions, and we define how x and p (so are a and a+) act on this full Hilbert space,
In modern QM, that's become kinda backwards. We start with an algebra of observable quantities which characterize the (class of) system being modelled, and then (try to) construct a unitary representation (i.e., construct a Hilbert space) in which those quantities are represented as operators on the Hilbert space. For many interesting case (like x,p) above, it turns out that a rigged Hilbert space is more convenient than an ordinary Hilbert space. See the early chapters of Ballentine for a more detailed exposition of all this.
However in an interacting QFT, the true structure of the full Hilbert space is not clear yet, let alone defining how a and a+ act on the space. The normal treatment is to use the Hilbert space from free theory (a Fock space) and then do things perturbatively. And my point is, if the interaction actually destroys any existence of direct-product structure of the true Hilbert space, then whatever kind of Fock space you use will be just an approximation at best, and if this is the case, I think Fock space does necessarily imply a perturbative approach.
That's essentially what renormalization tries to fix. At each order of perturbation, we adjust the space we're working with, either by adjusting the Hamiltonian, or applying a Bogoliubov-like transformation to the basic c/a operators (cf. Shirokov's approach: http://arxiv.org/abs/nucl-th/0102037[/url]).
BTW, the presence of interaction doesn't necessarily "destroy" direct-product structure. It simply means that the Hamiltonian can now mix stuff from different sectors.
P: 8,788
Quote by strangerep That's essentially what renormalization tries to fix. At each order of perturbation, we adjust the space we're working with, either by adjusting the Hamiltonian, or applying a Bogoliubov-like transformation to the basic c/a operators (cf. Shirokov's approach: http://arxiv.org/abs/nucl-th/0102037[/url]).
How does this tie in with the view that renormalization, say in QED, just preserves the important low energy terms, and that at high energies non-renormalizable terms or even new degrees of freedom should enter?
P: 679
Quote by strangerep BTW, the presence of interaction doesn't necessarily "destroy" direct-product structure. It simply means that the Hamiltonian can now mix stuff from different sectors.
But even the perturbative Hamiltonian can "mix stuff from different sectors". Let me elaborate my original point: my starting point is that in a mathematically rigorous QED, the equation of motion in my original post must be satisfied. However the perturbative approach definitely fails to satisfy it, because LHS and RHS are defined on independent sectors, so for example, if I sandwich (i.e. taking rayleigh quotient) both sides using photon states, then LHS is mostly nonzero but RHS is always 0. So to satisfy the equation, the true Hilbert space must somehow take Bosonic and Fermionic sector as one, but I can't proceed with the reasoning because I haven't acquired enough maths.
P: 679
Quote by Physics Monkey Lattice gauge theory or an asymptotically free gauge theory in a partial higgs phase can provide a UV completion of low energy QED.
But as far as I know, an constant issue of Lattice theory is about how to get to the continuum limit, and this isn't very well-established yet. And what I'm trying to argue is, QED is probably some limit of underlying bigger theory, but within this limit we should have a mathematically rigorous framework. Just like classical mechanics and quantum mechanics, the former is a limit of the latter, but still classical mechanics is a mathematically rigorous theory.
P: 8,788
Quote by strangerep That's essentially what renormalization tries to fix. At each order of perturbation, we adjust the space we're working with, either by adjusting the Hamiltonian, or applying a Bogoliubov-like transformation to the basic c/a operators (cf. Shirokov's approach: http://arxiv.org/abs/nucl-th/0102037[/url]).
Quote by atyy How does this tie in with the view that renormalization, say in QED, just preserves the important low energy terms, and that at high energies non-renormalizable terms or even new degrees of freedom should enter?
I took a look at Haag's "Local Quantum Physics". He describes both views of renormalization, but doesn't give any link between them. The view you describe is related to the "Algebriac QFT" formalism, while the latter Wilsonian view is related to the "Constructive QFT" formalism, which typically constructs a statistical field theory, and checks that it satisfies the Osterwalder-Schrader conditions in order to make it a Minkowski spacetime QFT.
P: 1,939
Quote by atyy I took a look at Haag's "Local Quantum Physics". He describes both views of renormalization, but doesn't give any link between them. The view you describe is related to the "Algebriac QFT" formalism, while the latter Wilsonian view is related to the "Constructive QFT" formalism, which typically constructs a statistical field theory, and checks that it satisfies the Osterwalder-Schrader conditions in order to make it a Minkowski spacetime QFT.
Which sections of Haag? There's some stuff in the early sections, but also in the later ch VIII.
(I should probably refresh my memory of Haag a bit more thoroughly, else I risk talking out of my rear... :-)
P: 1,939
Quote by kof9595995 [...] Let me elaborate my original point: my starting point is that in a mathematically rigorous QED, the equation of motion in my original post must be satisfied. However the perturbative approach definitely fails to satisfy it, because LHS and RHS are defined on independent sectors, so for example, if I sandwich (i.e. taking rayleigh quotient) both sides using photon states, then LHS is mostly nonzero but RHS is always 0. So to satisfy the equation, the true Hilbert space must somehow take Bosonic and Fermionic sector as one, [...]
This is an example of how the space of states in the free theory does not satisfactorily span the space of physical states in the full physical (interacting) theory.
The field operators in the exact form of Gauss' law correspond to the physical fields, not the free fields. Some approaches to QFT try to construct physical field operators perturbatively in terms of (increasingly-complicated) products of the free field operators. Among other things, this procedure must ensure that the new field operators still correspond to suitable Poincare unirreps with the physically correct spin, etc.
Do you recall the earlier thread where I talked about dressing the asymptotic electron states using coherent photon operators? After such dressing has been applied, the commutation relations are a bit different. E.g., the commutator between an electron operator and the electric field operator is no longer zero. Instead, it gives the usual Coulomb field of a charged electron. (This is all at low momenta, since the main task there was to deal with IR divergences.) A similar construction (of Dirac) also shows how to banish some parts of the unphysical EM gauge freedom.
At least one of the rigorous QFT results that I know proceeds via a related process of dressing transformations applied to the basic operators:
J. Glimm,
"Boson Fields with the $:Φ^4$: Interaction in Three Dimensions",
http://projecteuclid.org/DPubS?servi...cmp/1103840981
Warning: very few people can safely read that on an empty stomach...
P: 8,788
Quote by strangerep Which sections of Haag? There's some stuff in the early sections, but also in the later ch VIII. (I should probably refresh my memory of Haag a bit more thoroughly, else I risk talking out of my rear... :-)
In the second edition, the first sort of renormalization is in section 2.4, while the second type is in the section starting p323 "Algebraic Approach versus Euclidean Quantum Field Theory". I think that in his language "renormalization" always means the first type, because when discussing the second type he says something like it does away with renormalization (can't remember the exact words, I read it in the library, and am getting the section references from a search on Amazon).
P: 5,464
Quote by strangerep The field operators in the exact form of Gauss' law correspond to the physical fields, not the free fields. ... Do you recall the earlier thread where I talked about dressing the asymptotic electron states using coherent photon operators? After such dressing has been applied, the commutation relations are a bit different. ...
This is exactly what I had in mind in #3
Quote by tom.stoer The above mentioned field equation cannot be quantized directly b/c it has to be gauge fixed. In A°=0 at least for the time-indep. constraint (the Gauss law) this equaton is implemented on the physical Hilbert space. This does not require any "free field approach".
It is interesting that in the very end the physical fields can be decomposed using physical creation and annihilation operators spanning a physical Fock space. Now I understand where the confusion comes from; people seem to confuse Fock space with free particle Fock space plus perturbation theory. This (implicit) assumption is wrong of course.
A Fock space is nothing else but a direct sum of tensor products of copies of a single-particle Hilbert space H.
But it is not necessary that the Hilbert space H is spanned by free fields; any single particle Hilbert space with the correct creation and annihilation operator algebra is sufficient. So if it's possible to construct a suitable transformation from free to 'physical' or 'dressed' fields and a physical Hilbert space then the latter one can be decomposed into physical Fock states. This has been done in QCD in orer to study confinement in the canonical formulation (the problem with the construction of the physical Hilbert space is of course always the same: complete gauge fixing, taming Gribov ambiguities etc.; anyway - these problems do by no means spoil the Fock space approach using physical fields)
HW Helper
P: 1,334
Quote by kof9595995 But as far as I know, an constant issue of Lattice theory is about how to get to the continuum limit, and this isn't very well-established yet. And what I'm trying to argue is, QED is probably some limit of underlying bigger theory, but within this limit we should have a mathematically rigorous framework. Just like classical mechanics and quantum mechanics, the former is a limit of the latter, but still classical mechanics is a mathematically rigorous theory.
I would disagree about the continuum limit. We understand very well that the lattice theory flows to the continuum theory plus irrelevant operators. The essential properties of the low energy theory are there. For example, the heat capacity in lattice qed at low temperatures in the deconfined phase is proportional to $T^3$ just as you would get for free photons. Similarly, the long distance decay of gauge invariant correlation functions is exactly what you would expect for free photons. Lattice theories of qcd are also quite advanced, including fairly good numbers for hadron masses, although treating fermions dynamically is always troublesome because of the sign problem.
I also think it is interesting to note that classical electromagnetism is also not a rigorous theory, at least when thinking about point charges. Indeed, classical fluid dynamics and general relativity are also not known to be free of singularities.
P: 1,939
Quote by tom.stoer It is interesting that in the very end the physical fields can be decomposed using physical creation and annihilation operators spanning a physical Fock space.
...except that they might not satisfy exactly the same CCRs/CARs as in the free case.
Sci Advisor P: 5,464 I remember the 'dressing' and the 'gauge fixing by unitary transformations'; both approaches seem to be similar b/c they partially 'solve' some field equations. The first approach (dressing) changes the operator algebra; it can be solved explicitly in some 1+1 dim. field theories like the Schwinger model (here one formally solves the Dirac equation by exponentiation using a gauge field string with a path ordered product). The second approach does not change the operator algebra; the Gauss law is solved but b/c a unitary trf. is used, all operator algebras remain unchanged. This may be spoiled by regularization which requires gauge-invariant point splitting (I can only remember the two-dim. case). In the first case the interaction is "hidden" in the dressed fields; they create the physical Coulomb interaction, but the interaction term itself looks trivial algebraically. In the second case the interaction terms are constructed explicitly and in principle they can be expressed using physical Fock space operators. In the second case the (A°=0 & Coulomb gauge) Hamiltonian contains one piece which shows directly the color-electric Coulomb potential: $$H_C = g^2 \int d^3x \int d^3y \,\text{tr}\,J^{-1}(x)\,\rho(x)\,(-D\partial)^{-1}\,(-\partial^2)\,(-D\partial)^{-1}\,J(y)\,\rho(y)$$ with D = ∂ + gA, A being the gauge-fixed gluon field, J being the Fadeev-Popov determinant J = det(-D∂), ρ = ρ[q] + ρ[A] being the total color charge with quark and gluon contribution (w/o J, D and ρ[A] in HC the usual Coulomb gauge interaction in QED is recovered) | 2014-09-16 23:34:33 | {"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": 0.8449742197990417, "perplexity": 619.0435732459669}, "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-2014-41/segments/1410657120057.96/warc/CC-MAIN-20140914011200-00081-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
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As I'm sure you've all noticed, a lot of the stuff that gets posted here is - to put it delicately - fucking ridiculous. More backwards-ass shit gets posted to wallstreetbets than you'd see on a Westboro Baptist community message board. I mean, I had a look at the daily thread yesterday and..... yeesh. I know, I know. We all make like the divine Laura Dern circa 1992 on the daily and stick our hands deep into this steaming heap of shit to find the nuggets of valuable and/or hilarious information within (thanks for reading, BTW). I agree. I love it just the way it is too. That's what makes WSB great.
What I'm getting at is that a lot of the stuff that gets posted here - notwithstanding it being funny or interesting - is just... wrong. Like, fucking your cousin wrong. And to be clear, I mean the fucking your *first* cousin kinda wrong, before my Southerners in the back get all het up (simmer down, Billy Ray - I know Mabel's twice removed on your grand-sister's side). Truly, I try to let it slide. I do my bit to try and put you on the right path. Most of the time, I sleep easy no matter how badly I've seen someone explain what a bank liquidity crisis is. But out of all of those tens of thousands of misguided, autistic attempts at understanding the world of high finance, one thing gets so consistently - so *emphatically* - fucked up and misunderstood by you retards that last night I felt obligated at the end of a long work day to pull together this edition of Finance with Fuzzy just for you. It's so serious I'm not even going to make a u/pokimane gag. Have you guessed what it is yet? Here's a clue. It's in the title of the post.
That's right, friends. Today in the neighborhood we're going to talk all about hedging in financial markets - spots, swaps, collars, forwards, CDS, synthetic CDOs, all that fun shit. Don't worry; I'm going to explain what all the scary words mean and how they impact your OTM RH positions along the way.
We're going to break it down like this. (1) "What's a hedge, Fuzzy?" (2) Common Hedging Strategies and (3) All About ISDAs and Credit Default Swaps.
Before we begin. For the nerds and JV traders in the back (and anyone else who needs to hear this up front) - I am simplifying these descriptions for the purposes of this post. I am also obviously not going to try and cover every exotic form of hedge under the sun or give a detailed summation of what caused the financial crisis. If you are interested in something specific ask a question, but don't try and impress me with your Investopedia skills or technical points I didn't cover; I will just be forced to flex my years of IRL experience on you in the comments and you'll look like a big dummy.
TL;DR? Fuck you. There is no TL;DR. You've come this far already. What's a few more paragraphs? Put down the Cheetos and try to concentrate for the next 5-7 minutes. You'll learn something, and I promise I'll be gentle.
1. The Tao of Risk: Hedging as a Way of Life
The simplest way to characterize what a hedge 'is' is to imagine every action having a binary outcome. One is bad, one is good. Red lines, green lines; uppie, downie. With me so far? Good. A 'hedge' is simply the employment of a strategy to mitigate the effect of your action having the wrong binary outcome. You wanted X, but you got Z! Frowny face. A hedge strategy introduces a third outcome. If you hedged against the possibility of Z happening, then you can wind up with Y instead. Not as good as X, but not as bad as Z. The technical definition I like to give my idiot juniors is as follows:
Utilization of a defensive strategy to mitigate risk, at a fraction of the cost to capital of the risk itself.
Congratulations. You just finished Hedging 101. "But Fuzzy, that's easy! I just sold a naked call against my 95% OTM put! I'm adequately hedged!". Spoiler alert: you're not (although good work on executing a collar, which I describe below). What I'm talking about here is what would be referred to as a 'perfect hedge'; a binary outcome where downside is totally mitigated by a risk management strategy. That's not how it works IRL. Pay attention; this is the tricky part.
You can't take a single position and conclude that you're adequately hedged because risks are fluid, not static. So you need to constantly adjust your position in order to maximize the value of the hedge and insure your position. You also need to consider exposure to more than one category of risk. There are micro (specific exposure) risks, and macro (trend exposure) risks, and both need to factor into the hedge calculus.
That's why, in the real world, the value of hedging depends entirely on the design of the hedging strategy itself. Here, when we say "value" of the hedge, we're not talking about cash money - we're talking about the intrinsic value of the hedge relative to the the risk profile of your underlying exposure. To achieve this, people hedge dynamically. In wallstreetbets terms, this means that as the value of your position changes, you need to change your hedges too. The idea is to efficiently and continuously distribute and rebalance risk across different states and periods, taking value from states in which the marginal cost of the hedge is low and putting it back into states where marginal cost of the hedge is high, until the shadow value of your underlying exposure is equalized across your positions. The punchline, I guess, is that one static position is a hedge in the same way that the finger paintings you make for your wife's boyfriend are art - it's technically correct, but you're only playing yourself by believing it.
Anyway. Obviously doing this as a small potatoes trader is hard but it's worth taking into account. Enough basic shit. So how does this work in markets?
2. A Hedging Taxonomy
The best place to start here is a practical question. What does a business need to hedge against? Think about the specific risk that an individual business faces. These are legion, so I'm just going to list a few of the key ones that apply to most corporates. (1) You have commodity risk for the shit you buy or the shit you use. (2) You have currency risk for the money you borrow. (3) You have rate risk on the debt you carry. (4) You have offtake risk for the shit you sell. Complicated, right? To help address the many and varied ways that shit can go wrong in a sophisticated market, smart operators like yours truly have devised a whole bundle of different instruments which can help you manage the risk. I might write about some of the more complicated ones in a later post if people are interested (CDO/CLOs, strip/stack hedges and bond swaps with option toggles come to mind) but let's stick to the basics for now.
(i) Swaps
A swap is one of the most common forms of hedge instrument, and they're used by pretty much everyone that can afford them. The language is complicated but the concept isn't, so pay attention and you'll be fine. This is the most important part of this section so it'll be the longest one.
Swaps are derivative contracts with two counterparties (before you ask, you can't trade 'em on an exchange - they're OTC instruments only). They're used to exchange one cash flow for another cash flow of equal expected value; doing this allows you to take speculative positions on certain financial prices or to alter the cash flows of existing assets or liabilities within a business. "Wait, Fuzz; slow down! What do you mean sets of cash flows?". Fear not, little autist. Ol' Fuzz has you covered.
The cash flows I'm talking about are referred to in swap-land as 'legs'. One leg is fixed - a set payment that's the same every time it gets paid - and the other is variable - it fluctuates (typically indexed off the price of the underlying risk that you are speculating on / protecting against). You set it up at the start so that they're notionally equal and the two legs net off; so at open, the swap is a zero NPV instrument. Here's where the fun starts. If the price that you based the variable leg of the swap on changes, the value of the swap will shift; the party on the wrong side of the move ponies up via the variable payment. It's a zero sum game.
I'll give you an example using the most vanilla swap around; an interest rate trade. Here's how it works. You borrow money from a bank, and they charge you a rate of interest. You lock the rate up front, because you're smart like that. But then - quelle surprise! - the rate gets better after you borrow. Now you're bagholding to the tune of, I don't know, 5 bps. Doesn't sound like much but on a billion dollar loan that's a lot of money (a classic example of the kind of 'small, deep hole' that's terrible for profits). Now, if you had a swap contract on the rate before you entered the trade, you're set; if the rate goes down, you get a payment under the swap. If it goes up, whatever payment you're making to the bank is netted off by the fact that you're borrowing at a sub-market rate. Win-win! Or, at least, Lose Less / Lose Less. That's the name of the game in hedging.
There are many different kinds of swaps, some of which are pretty exotic; but they're all different variations on the same theme. If your business has exposure to something which fluctuates in price, you trade swaps to hedge against the fluctuation. The valuation of swaps is also super interesting but I guarantee you that 99% of you won't understand it so I'm not going to try and explain it here although I encourage you to google it if you're interested.
Because they're OTC, none of them are filed publicly. Someeeeeetimes you see an ISDA (dsicussed below) but the confirms themselves (the individual swaps) are not filed. You can usually read about the hedging strategy in a 10-K, though. For what it's worth, most modern credit agreements ban speculative hedging. Top tip: This is occasionally something worth checking in credit agreements when you invest in businesses that are debt issuers - being able to do this increases the risk profile significantly and is particularly important in times of economic volatility (ctrl+f "non-speculative" in the credit agreement to be sure).
(ii) Forwards
A forward is a contract made today for the future delivery of an asset at a pre-agreed price. That's it. "But Fuzzy! That sounds just like a futures contract!". I know. Confusing, right? Just like a futures trade, forwards are generally used in commodity or forex land to protect against price fluctuations. The differences between forwards and futures are small but significant. I'm not going to go into super boring detail because I don't think many of you are commodities traders but it is still an important thing to understand even if you're just an RH jockey, so stick with me.
Just like swaps, forwards are OTC contracts - they're not publicly traded. This is distinct from futures, which are traded on exchanges (see The Ballad Of Big Dick Vick for some more color on this). In a forward, no money changes hands until the maturity date of the contract when delivery and receipt are carried out; price and quantity are locked in from day 1. As you now know having read about BDV, futures are marked to market daily, and normally people close them out with synthetic settlement using an inverse position. They're also liquid, and that makes them easier to unwind or close out in case shit goes sideways.
People use forwards when they absolutely have to get rid of the thing they made (or take delivery of the thing they need). If you're a miner, or a farmer, you use this shit to make sure that at the end of the production cycle, you can get rid of the shit you made (and you won't get fucked by someone taking cash settlement over delivery). If you're a buyer, you use them to guarantee that you'll get whatever the shit is that you'll need at a price agreed in advance. Because they're OTC, you can also exactly tailor them to the requirements of your particular circumstances.
These contracts are incredibly byzantine (and there are even crazier synthetic forwards you can see in money markets for the true degenerate fund managers). In my experience, only Texan oilfield magnates, commodities traders, and the weirdo forex crowd fuck with them. I (i) do not own a 10 gallon hat or a novelty size belt buckle (ii) do not wake up in the middle of the night freaking out about the price of pork fat and (iii) love greenbacks too much to care about other countries' monopoly money, so I don't fuck with them.
(iii) Collars
No, not the kind your wife is encouraging you to wear try out to 'spice things up' in the bedroom during quarantine. Collars are actually the hedging strategy most applicable to WSB. Collars deal with options! Hooray!
To execute a basic collar (also called a wrapper by tea-drinking Brits and people from the Antipodes), you buy an out of the money put while simultaneously writing a covered call on the same equity. The put protects your position against price drops and writing the call produces income that offsets the put premium. Doing this limits your tendies (you can only profit up to the strike price of the call) but also writes down your risk. If you screen large volume trades with a VOL/OI of more than 3 or 4x (and they're not bullshit biotech stocks), you can sometimes see these being constructed in real time as hedge funds protect themselves on their shorts.
(3) All About ISDAs, CDS and Synthetic CDOs
You may have heard about the mythical ISDA. Much like an indenture (discussed in my post on $F), it's a magic legal machine that lets you build swaps via trade confirms with a willing counterparty. They are very complicated legal documents and you need to be a true expert to fuck with them. Fortunately, I am, so I do. They're made of two parts; a Master (which is a form agreement that's always the same) and a Schedule (which amends the Master to include your specific terms). They are also the engine behind just about every major credit crunch of the last 10+ years. First - a brief explainer. An ISDA is a not in and of itself a hedge - it's an umbrella contract that governs the terms of your swaps, which you use to construct your hedge position. You can trade commodities, forex, rates, whatever, all under the same ISDA. Let me explain. Remember when we talked about swaps? Right. So. You can trade swaps on just about anything. In the late 90s and early 2000s, people had the smart idea of using other people's debt and or credit ratings as the variable leg of swap documentation. These are called credit default swaps. I was actually starting out at a bank during this time and, I gotta tell you, the only thing I can compare people's enthusiasm for this shit to was that moment in your early teens when you discover jerking off. Except, unlike your bathroom bound shame sessions to Mom's Sears catalogue, every single person you know felt that way too; and they're all doing it at once. It was a fiscal circlejerk of epic proportions, and the financial crisis was the inevitable bukkake finish. WSB autism is absolutely no comparison for the enthusiasm people had during this time for lighting each other's money on fire. Here's how it works. You pick a company. Any company. Maybe even your own! And then you write a swap. In the swap, you define "Credit Event" with respect to that company's debt as the variable leg . And you write in... whatever you want. A ratings downgrade, default under the docs, failure to meet a leverage ratio or FCCR for a certain testing period... whatever. Now, this started out as a hedge position, just like we discussed above. The purest of intentions, of course. But then people realized - if bad shit happens, you make money. And banks... don't like calling in loans or forcing bankruptcies. Can you smell what the moral hazard is cooking? Enter synthetic CDOs. CDOs are basically pools of asset backed securities that invest in debt (loans or bonds). They've been around for a minute but they got famous in the 2000s because a shitload of them containing subprime mortgage debt went belly up in 2008. This got a lot of publicity because a lot of sad looking rednecks got foreclosed on and were interviewed on CNBC. "OH!", the people cried. "Look at those big bad bankers buying up subprime loans! They caused this!". Wrong answer, America. The debt wasn't the problem. What a lot of people don't realize is that the real meat of the problem was not in regular way CDOs investing in bundles of shit mortgage debts in synthetic CDOs investing in CDS predicated on that debt. They're synthetic because they don't have a stake in the actual underlying debt; just the instruments riding on the coattails. The reason these are so popular (and remain so) is that smart structured attorneys and bankers like your faithful correspondent realized that an even more profitable and efficient way of building high yield products with limited downside was investing in instruments that profit from failure of debt and in instruments that rely on that debt and then hedging that exposure with other CDS instruments in paired trades, and on and on up the chain. The problem with doing this was that everyone wound up exposed to everybody else's books as a result, and when one went tits up, everybody did. Hence, recession, Basel III, etc. Thanks, Obama. Heavy investment in CDS can also have a warping effect on the price of debt (something else that happened during the pre-financial crisis years and is starting to happen again now). This happens in three different ways. (1) Investors who previously were long on the debt hedge their position by selling CDS protection on the underlying, putting downward pressure on the debt price. (2) Investors who previously shorted the debt switch to buying CDS protection because the relatively illiquid debt (partic. when its a bond) trades at a discount below par compared to the CDS. The resulting reduction in short selling puts upward pressure on the bond price. (3) The delta in price and actual value of the debt tempts some investors to become NBTs (neg basis traders) who long the debt and purchase CDS protection. If traders can't take leverage, nothing happens to the price of the debt. If basis traders can take leverage (which is nearly always the case because they're holding a hedged position), they can push up or depress the debt price, goosing swap premiums etc. Anyway. Enough technical details. I could keep going. This is a fascinating topic that is very poorly understood and explained, mainly because the people that caused it all still work on the street and use the same tactics today (it's also terribly taught at business schools because none of the teachers were actually around to see how this played out live). But it relates to the topic of today's lesson, so I thought I'd include it here. Work depending, I'll be back next week with a covenant breakdown. Most upvoted ticker gets the post. *EDIT 1\* In a total blowout,$PLAY won. So it's D&B time next week. Post will drop Monday at market open.
##### Cryptosoft Review 2020-Is it a Scam?
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CryptoVibes recommends that you are doing demo trading before going to live to trade. Please note that the demo is for demonstrative purposes solely. The results you receive on the platform are primarily based on historical information and could therefore not mirror what you'll get in live trading. The Cryptp soft live trader comes with features to help you outline the amount of risk you are willing to require per trade. You wish to go through the demo account to familiarize with these features. As mentioned severally in this review, you do not want specialized skills to use this robot. Live trading with Cryptp soft involves determining the quantity of capital you plan to risk per trade and clicking the live button. Scan our review of Bitcoin Trader for one more straightforward to use the robot. *Remember all trading risks and you shouldn’t risk more then you'll be able to afford to lose. 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Like I said earlier, I actually have personally tested the Cryptp soft and found the success rate is about ninety sevenpercent. I don’t apprehend concerning you, but a ninety seven% probability of earning a profitable trade is TERRIBLY GOOD! I’ve never come across something like this trading software before. Keep reading, below are my Cryptp soft results for the past week or so… Watch over the Shoulder of a Professional Each Day and you'll be able to learn as you trade. Averaging 97% Winning Weeks With Cryptp soft— which suggests that more potential profits for you Cryptp soft Software Are Fully Transparent No previous experience with binary choices trading required Web-based mostly, no need for downloads, additionally works on phones, tablets You'll be able to Even Watch Cryptp soft Signals From Your Phone (iPhone Users — Photon Browser) If you are ready to begin making cash online with an on the spot edge, there has never been a better chance than currently. 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However, it's pertinent for cryptocurrency traders to verify if a particular trading software may be a scam or legit, which is also ? After subjecting the features of the Cryptp soft bot software to a series of tests, the software isn't a scam however legit. The Cryptp soft bot is believed to have successful rate of 85%, that is a lot of than the 80percent benchmark for average software. The Cryptp soft bot has helped cryptocurrency traders to make sensible profits, which has been documented as testimonies on the software’s website. Trading on the platform is straightforward and might not require experience. We had to verify the simplicity of the software, and we tend to discovered that the software is easy to navigate. The demo trading feature of the software makes it potential for brand new users to hold out trading activities in an exceedingly simulated atmosphere while not having to risk their investment. This any gives credence to the legitimacy of the software because it ensures that new users get accustomed to the features of the software before continuing to measure to trade As earlier stated, the Cryptp soft bot could be a high-tech program software that comes with exceptional options that makes it among the simplest cryptocurrency trading software in the blockchain market. The outstanding features of the Cryptp soft bot embody the subsequent: https://www.cryptoerapro.com/cryptosoft/ http://www.cryptoerapro.com/ https://twitter.com/cryptoerapro https://www.instagram.com/cryptoerapro/ https://www.pinterest.co.uk/cryptoerapro/ submitted by cryptoerapro to u/cryptoerapro [link] [comments]
##### YandereDev Email Response (pm for screenshot proof)
1.How do you feel about the overall health,community,and progress that you have made in Yandere Simulator over the past 6 years?
This is an extremely broad question that covers a large number of different topics. I'd prefer to answer more direct questions about more narrow subjects.
2.What were some major roadblocks in development that either stopped/slowed down your progress? How did you deal with these issues? Looking back,was there anything you would've changed in regards to your coping?
The major roadblocks are character assassination and nonstop daily harassment. I have no coping methods for dealing with either of these things.
Public humiliation is a very profitable entertainment industry. Even if you have no skills or talents whatsoever, you can quickly get millions of views by making a video where you ridicule someone. It's even easier to get views if you ridicule a YouTuber with lots of subscribers, because the YouTube algorithm will push your video to each of that person's followers.
I've been targeted by drama YouTubers who make trashy tabloid-style videos where they demonize and villify me, because they know that these videos will get them tons of attention and money. Nothing they say about me is true, and I can debunk every claim they've made. https://yanderesimulator.com/debunk/ Despite this, I still receive harassment dozens of times every hour of the day.
I dedicate over 10 hours of my day to Yandere Sim, 7 days a week, and I only take 1 day off per month, but people still call me lazy. People send me hateful messages every day on Discord, Reddit, Twitch, Twitter, and e-mail. Many people have been tricked into thinking that I'm an exaggerated caricature of who I actually am, and they take every opportunity to treat me like shit. No matter what I accomplish, there will always be a large number of people who will only focus on my mistakes and dedicate their time to smearing my reputation. I've been unhappy and depressed for the past 70 months, and every day only gets worse. The game that I created has destroyed my life, and I'm getting almost nothing out of it.
Being harassed on a daily basis has made me depressed, killed my enthusiasm for the project, and robbed me of all motivation. I have been harassed in various ways on a daily basis for the past several years. It is guaranteed that I will continue to be harassed every day for the rest of my life, and that the severity of the harassment will only continue to intensify. There is no reason to have any hope for the future. I don't even have a future anymore. The harassment isn't going to stop until I'm dead. Under these circumstances, I can no longer find a reason to keep living.
3. Towards the beginning of development, you said that you wanted to be the sole indie developer of Yandere Simulator. How have your opinions about this changed over time in relation to you reaching out to programmers/companies for help?
I don't remember saying that.
I'd be happy to work with a company.
I receive assistance from other programmers daily. This has been the norm for multiple years.
4. What are the top 3 regrets you have from developing Yandere Simulator. What are some things you think you do well?
A) The project's overly-ambitious scope
B) Prioritizing rapidly shoving things into the game as quickly as possible so that I could maintain a steady upload schedule for YouTube
C) Interacting with fans
5.Do you think that the backlash you have received is justified in any way,why or why not? From your perspective, what is the difference between harassment and constructive criticism?
100% unjustified.
Harassment = Insults, spam.
6.Do you ever watch any videos that people have against you to see what kinds of criticisms people have to help improve the game?
What do you think of these types of videos?
I do not watch trashy videos created by trashy people for a trashy audience.
7. On your current pace,what is a rough estimate of Yandere Simulators release date if you had to guess?
12 to 24 months, depending on severity of harassment.
1. What is your opinion of including more openly gay characters/adding the option to make Yandere Chan male stalking a male senpai? Will any trans/non-binary characters be added? Will such features ever come?
2. Have you ever considered the possibility of receiving legal allegations for selling merch that is solely based off the unity asset models? Are you planning of changing the merch once the artstyle is changed?
This is a preposterous suggestion. The characters depicted in the merchandise have nothing to do with the Unity Asset Store models. "Schoolgirl with black ponytail and black stockings" is not a Unity Asset, and is not something that I can be sued for.
3. Many players are uncomfortable with the whole panty mechanic and think that changing the “panty buffs” to other accessories would increase the appeal to other people. Will such things ever come?
Those people need to stop being babies.
4. What is the overall direction the game is going in? In the past you have stated that Yanderedev is a mix of Persona and Hitman. Some people would even say that a mix like this doesn’t work because they are contradictory. If you kill students,Then it’s like hitman,but then you sacrifice the dialogue and depth that the persona series has. What measures are you taking to balance these two game types to provide the best experience for the players?
1.Why is Osana listed as the fifth rivals Difficulty for the demo when you stated that you wanted to make a V slice to show the people in the Kickstarter what the game would be like? How hard are you planning of making the final rival?
It would be far easier to show you rather than tell you. Just wait until she is actually released.
2. What was the inspiration and thought process behind Raiburu and her being Osana’s invincible body guard? Wouldn’t having an invincible bodyguard limit the “Hitman” aspect of the game by making it so that you can only kill the rival at certain moments instead of awarding the players knowledge of the game by allowing them to kill her quickly and efficiently ?
You do not understand Raibaru as a gameplay mechanic. She just needs to be a simple speed-bump that prevents the player from charging straight at Osana at full speed. She exists to make the player solve a simple puzzle before they can kill Osana. Exactly like in Hitman, you shouldn't be allowed to charge straight at your target and kill them without consequence. That is Raibaru's purpose. You can get rid of Raibaru in less than 5 minutes.
3. In respect to Megami, what is your explanation of her apathetic nature towards other people? Is she more of someone who is secretly not as “dictatorly” in real life then in school or is there more behind her?
You do not understand Megami. Just wait and see.
4. What’s Megami's food preference?
Nutritious food.
Would you ever consider quitting Yandere simulator' even after all the funding you have received? What job would you undertake if you were to stop programming?
It is not an option.
##### What should be hard in this game? What should be fun?
Hi all, I had iterations of this post in my head for several leagues and I am genuinely interested in other's people opinion as I changed my mind twice in the Harvest league about it. So what do I want to talk about - what makes this game fun? And is it complexity / difficulty or not? So what exactly am I getting at?
Let's compare the start of the league vs mirror-tier items in every slot because Harvest let significantly more people experience that. I personally hate levelling, maybe because I've done it so many times or maybe because it's not engaging. Some time ago there was a bump in campaign bosses difficulty and it has actually helped me to have more fun while running the same content again because I was challenged a bit and it didn't feel like an unnecessary chore. Feel free to disagree / write your opinion on that.
### Mapping
Next we have maps, I'm not a casual player so my expectations is to reach full atlas and T14+ every league and every character and usually I need to upgrade gear once from my starter "just hit maps" to progress to full atlas completion. Some leagues in this also started to become, a chore and I have mixed feelings about it. White maps just don't exist in my head, T8-T13s depending on the drops are nice because my gear is a bit weaker so I need to focus more on the screen, dodge more and actually interact with the game. I actually like to be ambushed by Betrayal content for that reason. But after some level of gearing I just run through maps and the most important stat for me is movement speed. It still can be fun because I can set some goals - this league I'm buying seeds in bulk and crafting just for the sake of creating items. But the gameplay itself is not engaging. And thus not fun of itself. This is where league mechanics make or break leagues for me, if it is all the same thing - different league I'm not having that much fun. But very important point - I know that many people do! Many people like to gear up their characters up to the level that the content is not difficult at all and they can autopilot tens or hundreds of maps.
After Delirium and pushing 100% delirious T19s I had loads of fun - I had content that was extremely rewarding to play the game. Not rewards-wide (that aside) but pure excitement from killing monsters - you know the thing you do in ARPGs ;) But this content is viewed as purely optional so not many players are fussed if they don't / can't do it. There is a lot of talk on this sub about Harvest is the first league a casual player can kill Sirus (not A8, just regular one). And that is one perspective, but what every boss in Red maps offered a similar thrill? Just as a thought experiment. Would you enjoy PoE if you had to upgrade your gear in a meaningful way between each tier between T11 and T16? I don't know how this would look like in terms of balancing / gearing options or other things but it is an interesting perspective.
### Bossing
So let's talk about bossing. Should any guardians / conquerors be challenging? Should you able to out gear them in a week? Two weeks? Later? What about Elder? Shaper? I know that many people would start a discussion now about the drops and how it is not profitable to run them, or fun to run them if you loose money or they don't drop anything. But shouldn't that be also connected? What if each of the conquerors was a really hard fight, but with guaranteed Conqueror Exalted orb? What if it was challenging but with the same drops as now? It's interesting that now there is a lot less discussion about Uber Elder compared to Sirus - I know about the feelings of the fight itself but I can't shake the impression that it's because Uber Elder is a "side content" while the game itself leads all players to Sirus. Almost nobody mentions Uber Atziri, even further to the side in terms of content. I really enjoyed that fight until reflect was too much (or in other words bullshit), you couldn't over gear for it easily unless you played a miner and just phased her out, so it was always challenging.
Going back to main villain - is the Uber Elder fight fun? Is it because of the mechanics only or drops? I have terrible Sirus RNG in Harvest, killed him 30+ times on A8 and got one woke orb, no woke gems, no other noteworthy drops. Still have the same amount of fun doing him - which is small but positive. I didn't do much of Uber Elder but the fight itself feels less random and it's always fun. I feel like also there is more things to care in that fight which makes it more engaging even without loot comparison. I also know that once I learned the Sirus fight I'm much more comfortable to go a bit under geared there but I don't want to try it with Uber Elder. How is it for you? Do you enjoy fights for the mechanics or drops? Or somewhere in between?
### Delve
Delve is interesting for me. If you don't start early in the league once you get going the first X levels are annoying because you are too strong and for the last couple of leagues the rewards for first levels are bad. So you are missing out on league content and grinding down just for future sake. Personally I would love if doing maps up to T16s would progress the mine to that monster level, especially with how rewarding recent leagues are. Afterwards I can say delve is fun for me because you are getting pushed towards getting better gear and at delving. Never personally reached 1000 or lover so maybe it's just one strategy or full immunity afterwards where it becomes a bit binary - either you can do it or not - would love to hear a perspective on that.
### Gearing
So you might expect at this point that I'm against Harvest crafting because it makes the game too easy. I'm not. I really like to make gear myself. I really like that I'm working towards something, that I'm progressing affix after affix. I really like that I don't need to trade or look for gear, I'd rather look for how to make it. But does being over-geared take enjoyment from other (core) parts of the game? For me it does. The solution I would look for is introducing more harder content rather than removing gearing options. Or expanding on gearing options - certain affixes that have 90, 95, 98 level requirement. If 400 pdps foil is enough to do all the content then maybe the solution is to make content that needs 550+pdps foil (or 600, or X), not to remove the ability to have 500+ pdps foil by more players? Because I think it boils down not only to "how easy" it is to gear. Not is it via crafting or trading, but what levels of gear is available vs how difficult is the content. Maybe this is a good place to ask a question to all the players who enjoy speed mapping - would you enjoy speed mapping yellow maps? Or white maps? Why not? Why are you aiming to casually map T16s and not double beyond, 100% delirious T16s? I don't want to sound elitist because I know that I would probably be pissed after years in red maps if I couldn't progress into them from one patch to another (looking at you PoE2). So what is your opinion on that? Also is gear your aim or means to enjoy other parts of the game?
That's it, I don't offer any wisdom or solutions, just asking questions. I hope for different answers just because so many people have different knowledge about this game and like different things about it.
##### Selling your Covered Call - Thoughts on How to Select Your Strike and Expiration
Congratulations! You are a bag holder of company XYZ which was thought to be the best penny stock ever. Instead of feeling sorry, you consider selling covered calls to help reduce your cost basis - and eventually get out of your bags with minimal loss or even a profit!
First - let's review the call option contract. The holder of the call option contract has the right but not the obligation to purchase 100 shares of XYZ at the strike price per share. This contract has an expiration date. We assume American style option contracts which means that the option can be exercised at any point prior to expiration. Thus, there are three parameters to the option contract - the strike price, the expiration date and the premium - which represents the price per share of the contract.
The holder of the call option contract is the person that buys the option. The writer of the contract is the seller. The buyer (or holder) pays the premium. The seller (or writer) collects the premium.
As an XYZ bag holder, the covered call may help. By writing a call contract against your XYZ shares, you can collect premium to reduce your investment cost in XYZ - reducing your average cost per share. For every 100 shares of XYZ, you can write 1 call contract. Notice that that by selling the contract, you do not control if the call is exercised - only the holder of the contract can exercise it.
There are several online descriptions about the covered call strategy. Here is an example that might be useful to review Covered Call Description
The general guidance is to select the call strike at the price in which you would be happy selling your shares. However, the context of most online resources on the covered call strategy assume that you either just purchased the shares at market value or your average cost is below the market price. In the case as a bag holder, your average cost is most likely over - if not significantly over - the current market price. This situation simply means that you have a little work to reduce your average before you are ready to have your bags called away. For example, you would not want to have your strike set at $2.50 when your average is above that value as this would guarantee a net loss. (However, if you are simply trying to rid your bags and your average is slightly above the strike, then you might consider it as the strike price). One more abstract concept before getting to what you want to know. The following link shows the Profit/Loss Diagram for Covered Call Conceptually, the blue line shows the profit/loss value of your long stock position. The line crosses the x-axis at your average cost, i.e the break-even point for the long stock position. The green/red hockey stick is the profit (green) or loss (red) of the covered call position (100 long stock + 1 short call option). The profit has a maximum value at the strike price. This plateau is due to the fact that you only receive the agreed upon strike price per share when the call option is exercised. Below the strike, the profit decreases along the unit slope line until the value becomes negative. It is a misnomer to say that the covered call is at 'loss' since it is really the long stock that has decreased in value - but it is not loss (yet). Note that the break-even point marked in the plot is simply the reduced averaged cost from the collected premium selling the covered call. As a bag holder, it will be a two-stage process: (1) reduce the average cost (2) get rid of bags. Okay let's talk selecting strike and expiration. You must jointly select these two parameters. Far OTM strikes will collect less premium where the premium will increase as you move the strike closer to the share price. Shorter DTE will also collect less premium where the premium will increase as you increase the DTE. It is easier to describe stage 2 "get rid of bags" first. Let us pretend that our hypothetical bag of 100 XYZ shares cost us$5.15/share. The current XYZ market price is $3/share - our hole is$2.15/share that we need to dig out. Finally, assume the following option chain (all hypothetical):
DTE Strike Premium Intrinsic Value Time Value
20 $2.5$0.60 $0.50$0.10
20 $5.0$0.25 $0$0.25
20 $7.5$0.05 $0$0.05
50 $2.5$0.80 $0.50$0.30
50 $5.0$0.40 $0$0.40
50 $7.5$0.20 $0$0.20
110 $2.5$0.95 $0.50$0.45
110 $5.0$0.50 $0$0.50
110 $7.5$0.25 $0$0.25
Purely made up the numbers, but the table illustrates the notional behavior of an option chain. The option value (premium) is the intrinsic value plus the time value. Only the $2.5 strike has intrinsic value since the share price is$3 (which is greater than $2.5). Notice that intrinsic value cannot be negative. The rest of the premium is the time value of the option which is essentially the monetary bet associated with the probability that the share price will exceed the strike at expiration. According to the table, we could collect the most premium by selling the 110 DTE$2.5 call for $0.95. However, there is a couple problems with that option contract. We are sitting with bags at$5.15/share and receiving $0.95 will only reduce our average to$4.20/share. On expiration, if still above $2.5, then we are assigned, shares called away and we receive$2.50/share or a loss of $170 - not good. Well, then how about the$5 strike at 110 DTE for $0.50? This reduces us to$4.65/share which is under the $5 strike so we would make a profit of$35! This is true - however 110 days is a long time to make $35. You might say that is fine you just want to get the bags gone don't care. Well maybe consider a shorter DTE - even the 20 DTE or 50 DTE would collect premium that reduces your average below$5. This would allow you to react to any stock movement that occurs in the near-term.
Consider person A sells the 110 DTE $5 call and person B sells the 50 DTE$5 call. Suppose that the XYZ stock increases to $4.95/share in 50 days then goes to$8 in the next 30 days then drops to $3 after another 30 days. This timeline goes 110 days and person A had to watch the price go up and fall back to the same spot with XYZ stock at$3/share. Granted the premium collected reduced the average but stilling hold the bags. Person B on the other hand has the call expire worthless when XYZ is at $4.95/share. A decision can be made - sell immediately, sell another$5 call or sell a $7.5 call. Suppose the$7.5 call is sold with 30 DTE collecting some premium, then - jackpot - the shares are called away when XYZ is trading at $8/share! Of course, no one can predict the future, but the shorter DTE enables more decision points. The takeaway for the second step in the 2-stage approach is that you need to select your profit target to help guide your strike selection. In this example, are you happy with the XYZ shares called away at$5/share or do you want $7.5/share? What is your opinion on the stock price trajectory? When do you foresee decision points? This will help determine the strike/expiration that matches your thoughts. Note: studies have shown that actively managing your position results in better performance than simply waiting for expiration, so you can adjust the position if your assessment on the movement is incorrect. Let's circle back to the first step "reduce the average cost". What if your average cost of your 100 shares of XYZ is$8/share? Clearly, all of the strikes in our example option chain above is "bad" to a certain extent since we would stand to lose a lot of money if the option contract is exercised. However, by describing the second step, we know the objective for this first step is to reduce our average such that we can profit from the strikes. How do we achieve this objective?
It is somewhat the same process as previously described, but you need to do your homework a little more diligently. What is your forecast on the stock movement? Since $7.5 is the closest strike to your average, when do you expect XYZ to rise from$3/share to $7.5/share? Without PR, you might say never. With some PR then maybe 50/50 chance - if so, then what is the outlook for PR? What do you think the chances of going to$5/share where you could collect more premium?
Suppose that a few XYZ bag holders (all with a $8/share cost) discuss there outlook of the XYZ stock price in the next 120 days: Person 10 days 20 days 30 days 40 days 50 days 100 days 120 days A$3 $3$3 $3$3 $4$4
B $4$4 $5$6 $7$12 $14 C$7 $7$7 $7$7 $7$7
Person A does not seem to think much price movement will occur. This person might sell the $5 call with either 20 DTE or 50 DTE. Then upon expiration, sell another$5 call for another 20-50 DTE. Person A could keep repeating this until the average is reduced enough to move onto step-2. Of course, this approach is risky if the Person A price forecast is incorrect and the stock price goes up - which might result in assignment too soon.
Person B appears to be the most bullish of the group. This person might sell the $5 call with 20 DTE then upon expiration sell the$7.5 call. After expiration, Person B might decide to leave the shares uncovered because her homework says XYZ is going to explode and she wants to capture those gains!
Person C believes that there will be a step increase in 10 days maybe due to major PR event. This person will not have the chance to reduce the average in time to sell quickly, so first he sells a $7.5 call with 20 DTE to chip at the average. At expiration, Person C would continue to sell$7.5 calls until the average at the point where he can move onto the "get rid of bags" step.
In all causes, each person must form an opinion on the XYZ price movement. Of course, the prediction will be wrong at some level (otherwise they wouldn't be bag holders!).
The takeaway for the first step in the 2-stage approach is that you need to do your homework to better forecast the price movement to identify the correct strikes to bring down your average. The quality of the homework and the risk that you are willing to take will dedicate the speed at which you can reduce your average.
Note that if you are unfortunate to have an extremely high average per share, then you might need to consider doing the good old buy-more-shares-to-average-down. This will be the fastest way to reduce your average. If you cannot invest more money, then the approach above will still work, but it will require much more patience. Remember there is no free lunch!
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I was scammed by a binary option website iq options to be exact. I lost about $250,000 to them. It was a really hard time for me because that was all i had and they tricked me into investing the money with a guarantee that i will make profit from the investment.. I was referred to Mr Gary, he’s a senior recovery specialist and he helped in recovering all my lost funds to me. I couldn’t believe at first that this was possible as i have lost all hope in contacting anyone on the internet, but i guess not everyone is bad after all. You can reach him on cybertechhub100 at gmail dot com. ''' Context Link Go1dfish undelete link unreddit undelete link Author: Manlikedrew submitted by removalbot to removalbot [link] [comments] ##### FutureICX AMA with nblaze (Midos) and the ICON Pilipinas Community Hello ICONists! Today we’re happy to outline and highlight the intricate components of FutureICX, our vision for the dapp’s future and the reason for its creation through this AMA with ICON Pilipinas. Many community members have highlighted questions they’d like answered and were happy to discuss the foundations of our project, our ideas and how FutureICX differentiates itself from other gamified trading applications within the blockchain sphere! We look forward to answering all of your questions! nblaze: Hey everyone! As most of you probably know I’m nblaze from ICON P-Rep team Midos and together with the P-Rep team Sharpn we have built the FutureICX.io app, which was released earlier this week. This has been quite a long and exciting journey which started almost a year ago and we are all very excited that we have finally been able to achieve such a successful app release with so much positive feedback coming in our direction. Jenny: How did you come up with the idea for FutureICX and how was this project started? nblaze: Well, as a long-term holder of ICX, I have always been fascinated by ICON’s system and was looking into ways to contribute to it. I began extensive research surrounding the best P-Rep teams to delegate my ICX to, but somehow this did not feel enough, and I wanted to do more for the chain (and respectively for my investment). After jumping through a lot of different plans and ideas, including lotteries, raffles, games, payment systems etc., I noticed that a lot of people in the trading channels love to make predictions; long story short, approximately half a year later I partnered with the Sharpn P-Rep team. We’re extremely grateful for a Grant that the ICON Foundation and the ICONation teams provided us and we continue to press forward with amazing results. Jay: Throughout the entire development journey, there's sure to be plenty of ups and downs experienced. What's one particular fond memory that stands out to you the most? nblaze: Oh, I would need to go all the way back to the planning phase of FutureICX. I had gone to bed pretty late one night as I was very excited about the Dapp idea, but somehow, I constantly kept hitting a brick wall in trying to figure out how it would work. No matter what I thought of, several hours of planning later I have thought of something critical that would be a major issue. That night I was tired and honestly becoming a bit discouraged that I would never find a system that would work. After going to sleep, I woke up approximately an hour later with a clear idea about the system that I would like to use for FutureICX. I had no sleep from this moment onwards, just got to my computer and worked on it all night. It was really an ‘Eureka’ moment that I'm quite fond of. Jenny: What are your plans, either near-term or longer-term now that FutureICX has been released? nblaze: Of course, we are still working on FutureICX’s current state and are making sure that everything is running well. The app is stable, and players are happy with it. We have already started making plans for our next development stage through and although I cannot share very much, I can tell you that we are aiming for 3 additional original trading games, additional trading pair predictions and maybe even different crypto payment options. Hopefully everything will go well, and we would be able to reach those targets (and who knows, maybe more). Twitter and Telegram follower questions theanerz: What is the Mission and Vision of FutureICX? nblaze: I like this question as it is simple and yet very complicated to answer. FutureICX is aiming to be a multi-purpose platform that could be used by a wide range of players. It could be used as a mean to get additional gains from trading, as a learning tool, as a proof-of-skill or even as a fun app that you can have fun and gamble on. It is also very beneficial to the ICON chain as it not only creates transactions, it could also be a replacement of the ‘exchange’ trading in which no ICX are leaving the system (thus reducing sell pressure and increasing the price of ICX) and finally as a tool which can reduce the circulating supply as the ICX tokens placed in predictions are locked until the outcome is processed. I wrote an article a few days ago about this exact topic – what has inspired us to make the app and what are the benefits of using it. Anyone interested can find it at this link: https://forum.icon.community/t/futureicx-io-vs-conventional-trading-article/1069 ricnnobre: FutureICX is a platform for traders and therefore a minimum of knowledge in technical analysis is needed to predict where the value of ICX is going. Doesn't that restrict the audience that will use the platform? nblaze: True, the platform is for the most part aimed at traders, however most people that trade in it are not professionals. This allows for beginner traders to have a tool where they can compete with a lot of similar skilled traders instead of professionals, whales and institutional traders and this makes FutureICX a good learning tool to use. The prediction times are also fixed so this eliminates second-guessing and reacting emotionally on a trade that you have already set. As you are not competing against the bank, this also gives the players the opportunity to progress with their prediction sizes as they get better and even potentially make a living out of this if they are good enough and hit their predictions on a regular basis. It can of course also be used as a fun gambling tool as a lot of traders seem to be using the exchanges for that anyway. RGerburt: DApps in which users spend money without obtaining any benefit causes loss of interest over time. Does FutureICX have any form of reward for traders who fail to succeed in their predictions? How to maintain the loyalty of users, mainly those who are not good traders? nblaze: We have put in great efforts in trying to be helpful to such players. FutureICX offers dividend returns (each 1 icx that you spend gives you 1 dividend point and the dividend points respectively give you a % of the dividend pool, which is 10% of the amount of ICX that all players spend, at the end of the week – you can see details of that on top of the main screen and in the ‘help’ section, which is the place where our system’s theory is located). One of our awards also gives returns to the player that has spent the most. If that doesn’t work, you can always go for an ‘influencer’ strategy and have your friends and followers generate dividends for you (every 1 icx spent by someone that registered via your affiliate link gives you 0.5 dividend points) lavicrep69: They call us Betlords of the Icon Pilipinas we are one of many supporters of FutureICX. I just would like to know, because for us statistics and achievements are really a big deal. I saw the "Tropies (Sniper, Marksman, Cannoneer, Monthly) and the ICX reward" that you will get from consistent playing/predicting. I’m just wondering if you have global ranking of top players on each trophy or tier like a data base link on blockchain that we can always check to improve our standing? And will we have a "copy prediction options?” I’m sure it will be a good idea coz we can follow players and see their statistics. nblaze: There are such options, but we are planning to expand on those. In your ‘Profile’ page you can see how many awards you have earned, the most recent ones and how much you have earned through them. The monthly awards are also giving a monthly ranking of the top 10 players and giving them rewards for it. However, we do understand that we will need to and will improve even more in this direction nhene00: The market today has a lot of development projects on the blockchain platform. One of the factors that makes the platform appealing to many users is its special features. So, what are the outstanding features and advantages of FutureICX to attract users and investors? nblaze: We truly believe that our app was designed in a really unique way. You have the exchanges, binary options and futures on one hand, you have the raffles, lotteries, casinos and games on the other. We try to be none of those and to provide a new experience to our players. We also think that we offer a unique system, created from scratch, that benefits a lot of different types of players and strategies. As every other platform though, we would need the users/community’s support and feedback in order to progress even further. We do not believe that this will be an issue with ICON’s community though. ThomaXMiller: How will the dividends/point system work? When will the$3000 Pool be distributed?
nblaze: You earn dividend points with every prediction that you and your affiliates make, and you get a % of all prediction amounts respectively to the amount of points that you have at the end of the week
CHARLoTTE9o: If it’s less risky and much more profitable for traders, how will you and the whole team benefit from this?
nblaze: The app has built in 5% commission, that is how we profit (you can see the full details in the 'help' page of the app). It is also not much more profitable for all traders of course; it simply provides better opportunities (according to our own deductions of course) than a normal exchange would.
Ketz23: DeFi is one of the hottest topics in the blockchain space right now. Can $ICX share your opinions on DeFi with us? Do you think that DeFi will disrupt the existing financial system? What is Unification approach towards the DeFi sector? nblaze: I don’t think that I’m qualified enough to give such comprehensive opinion in Defi in general I’m afraid. willydavec1: You mentioned earlier about gambling, more games to play, In this era where there are tons of cryptocurrency gambling addicts, do you have any plans to minimize their addiction? A good project needs to care for its users/gamblers/players. Do you have any plans for them, any limitations? For example, 1000 USD worth of loss, they must be restricted for a few hours, something like that. nblaze: I believe that it would be hard to get addicted to our app - its 1 prediction/day or week, that is not a major concern imo. Also please keep in mind that this is no gambling application - you are not playing against the house and you can easily be profitable long term. So, an 'addiction' could mean improving your trading skills and making a living out of this. Neajmik: The hardest thing about any business is not building a product. What is often the hardest is getting people to use the product. How will FUTUREICX team resolve this to make your project become mass adopted and be more attractive in investotraders eyes? nblaze: True, we are doing our best from the app's side - getting feedback, building a product that our players like, promoting it to the best of our abilities. I think that the rest is up to the actual players: if they like it, they will naturally promote the product. I also think that the affiliate system would help a lot with that as a player could earn by being a 'promoter' and not even playing a single game (although not playing would limit his potential gains). SiliLovers: How does it feel after the first daily prediction was resolved earlier? nblaze: Amazing. 2500 ICX placed in predictions on the first day, quite a bit of positive feedback, happy winners all around. I love it! lavicrep69: If I am an ICONist and use d’apps like ICONbet how will you convince me to play FutureICX if it was my first time? nblaze: We wouldn’t. We believe that ICONBet has their own player market and we have ours. The activities on both platforms are completely different so there will be no need to pull players from one to the other. ICONists could play easily play on both and be equally happy with their experience Neajmik: What are the ways that FUTUREICX generates profits to maintain your project and how can it benefit both investotraders and your project simultaneously? nblaze: We have a 5% commission for that, so we don’t actually aim to benefit from the players' losses, on the contrary, we try to limit them for the less experienced traders. That is why each prediction amount is split into: 80% into the selected reward period pool, 5% towards the weekly/monthly awards, 10% towards the dividends and 5% to our team so we can keep improving the Dapp. That gives players opportunities to gain, even if their prediction did not come true HiImGroot: What are your plans for global expansion; is FutureICX focusing on only trading at this time or are you focused on building and developing your Dapp for more quality experience with users? nblaze: We’re hoping that with the second phase of our app we will be able to go into different crypto markets as well. This is still a long shot of a plan and requires a lot of variables to piece together but if we are able to do this, that would generate ICX transactions (as our Dapp is fully based on the ICON chain) while we are processing predictions that are payed with other cryptocurrencies. matT325: Where do you see FutureICX 2 or 3 years from now? nblaze: As a large gamified trading platform with a lot of players, many more trading games and options and working with a lot of different chains and projects while generating icx transactions in the process. LadyCrows: To advertise a project, you need to provide benefits and features, security aspects of the project. How does FutureICX differ from other decentralized trading applications? nblaze: There are quite a bit, so I’m not sure that I can list all of them in one short message. We have multiple gain channels, tiered rewards, dividends, awards, independent affiliate gains, our Dapp is fully decentralized (so every transaction is secure and verifiable), we are using a decentralized oracle for results (fairness and security), our tx process time is short and recorded on the chain thanks to ICON as well. ThePredator11: Why did you choose this platform name "FutureICX? nblaze: This was entirely a team Sharpn contribution. I picked Midos as an app name - they suggested FutureICX and we went with it and kept Midos as the name of my P-Rep instead. CryptoHodler22: If you put in an amount of$ICX for a long term prediction you can't stake them. Is there a form of divided for long-term wages?
nblaze: That is absolutely correct – you would not receive any staking rewards for the duration of the prediction and that is the main reason that we have not set up a ‘monthly’ prediction or something like that. FutureICX is not aimed to make long-term holders to unstake their bags and come play. It is focused on the circulating ICX that instead of going to the exchanges, can come to ICX and have greater benefits from that.
In terms of if the players are not losing from locking their ICX into a prediction on FutureICX, instead of staking them, the staking rewards for 10 days are around 0.2% - with FutureICX the rewards start from 120% and you could earn up to 450%/day if you know what you are doing
I think that as with anything else, you have to balance your targets and decide what would be the best strategy for your money
Ramle13747634: What is the greatest risk that you've taken before you do the first move of making the FutureICX that was released recently? Is it worth it to take the risk?
nblaze: I think that building FutureICX was a very large risk in itself for me as in order for the project to see the light of day, I have personally spent almost an year working on it without any payment so far (while financing some parts of the app’s development out of my own pocket) and without any guarantees that I would be able to finish it. However I think that it was worth the risk and I would definitely do it again – I have not done this app to make money and have no delusions that it will make me rich or something. Im just happy that Im seeing it live and players loving it so far. This motivates me to develop FutureICX even further and provide even more fun experiences for the Iconists
Neajmik: You received a lot of questions related to utilities and technology, future vision etc. So now I want to ask what do you want to receive from the community?
nblaze: The greatest support that we can receive from the community is spreading the word about our app, about your opinion of it (good or bad it doesn’t matter – you are entitled of your own). At the end of the day, we have designed the app to be attractive to newcomers and to reward properly the proactive players assisting us with that task (via the affiliate bonuses), however our PR resources are limited and we would appreciate any help that we could get.
So if I have to summarize – talk with people, brag, show off, discuss, even rant about FutureICX to people, it will all be of help to us and will also earn you extra gains 😉.
# Introduction
Greetings, this is dumnem, also known as Theorchero, but you can call me Theo. I'm an experienced Tarkov player and I'm writing this guide to try and assist new Tarkov players learn the game, because it has one hell of a learning curve. We'll be going over a lot of different aspects of this guide, and it is going to be huge. Feel free to digest this in parts.
Additionally, this is a work in progress. I will write as much as I can in one Reddit post, but subsequent parts will be in additional comments. Google Docs Version (Note: Link is placeholder atm, but here is a sneak preview!)
Disclaimer: Tarkov recently updated to .12! That's a HUGE amount of information that I need to update. Please be patient! If there is anything I have gotten wrong or may have omitted, please let me know.
This is Primarily directed towards Tarkov Novices, but should be useful for even Tarkov Veterans. It hopefully includes everything you need to know to be able to go into a Raid equipped for success and to successfully extract with gear.
Want to play with friends? Want to have fun and learn Tarkov? Check out my discord here.
## Changelog
3/9/20:
• [Updated for .12]
• Money making strategies completed.
• Hideout section complete
• Tarkov Overview - What is Escape from Tarkov?
• Tarkov Resources - Useful links
• Tarkov's Maps
• Tarkov's Health System
• Tarkov's Hideout System
• Tarkov's Quest System and Progression
• Tarkov's Hotkeys to Know
• Getting Started
• Player Scavs
• What to Loot - How to get the most money per slot
• Stash Management - How to combat Gear Fear
• Tarkov Economy - How do I make money?
• What now?
# Tarkov Overview - What is Escape from Tarkov?
Escape from Tarkov is a tactical, realistic, FPS with MMO elements developed by Battlestate Games. It is currently in closed Beta. The game features several maps in which your primary character, your PMC, goes into Raids in order to find and salvage loot and useful equipment to survive and thrive in Tarkov. Death is very punishing in Tarkov. If you die you lose everything you had on you when you die (with the exception of what's inside your Container and your melee weapon) including any equipment you brought with you or what you found inside the Raid.
Enemies can be players (PMCs) or Scavengers ('Scavs') that are either controlled by AI or by players. Unlike many shooters, AI enemies in Tarkov are deadly - they can and will kill you on sight. They have recently been upgraded to act more intelligently, shoot more accurately, and react to situations on the map, such as investigating noise of gunfire or searching. It features beautiful and immersive environments, intricate and in-depth weapon modification system, a complex health system, dynamic and specific loot placement, and multiple options for engagement. Do you want to play slow and stealthy, to avoid fights, or set up a deadly ambush on an unwary foe? Or do you prefer raw combat, where only your quick wit, placements of shots, and tenaciousness determines who gets out alive? It's your Tarkov. You make the rules.
# Tarkov Resources - Useful links
I take no credit or responsibility for any of the content in these links. To the best of my knowledge, these are updated consistently and are accurate, but user beware.
# Quick-Reference Ammo Chart
An updated ammo chart can be found on the wiki.
# Tarkov Wiki
Absolutely fantastic resource. You can visit them here.
It is a massive collection of everything that we players have been able to find.
They contain trades, user-created maps, lists of ammo, parts, weapons, loot, etc. If it's in the game, it's on the Wiki, somewhere.
I highly recommend opening the wiki page for the Map that you plan on raiding in.
Factory
Customs
Woods
Shoreline
Interchange
Reserve
The Lab ('Labs')
# Map Keys and You
Huge collection of all the keys in the game. These are also on the wiki, but this page has them all on one page, and tries to inform the user if the key is worth keeping or using.
Check it out here.
# Tarkov's Weapon Compatibility Guide
Pretty self explanatory. Also includes a Key guide and a Mod guide.
Check it out here.
# HUGE Reference Bible by Veritas
Courtesy of Veritas (Send me his reddit username?), It's located here. (Open in new tab.) Contains: Detailed information about: Ammunition, Health, Firearms, Body Armor, Helmets, Rigs & Backpacks, Labs & Quest keys. Outdated! Needs to be updated for .12
# Offline Raids - Player Practice
Offline raids is a feature added for testing and learning purposes for both new and veteran players alike. It is an incredibly useful tool.
In an offline raid, your progress is not saved. This means you don't keep anything you find, keep any experience 'earned' if you successfully extract, or lose any gear when/if you die. To access OFFLINE Raids, head into a Raid normally until you see this screen. Then Check the box indicating that you want to do an OFFLINE raid and you're good to go! You even have a choice on whether or not to add AI. You can also control how many AI enemies spawn, fewer than normal or a great deal more! You can even make Scavs fight each other. (Framerates beware.)
You can control how many scavs spawn (if any) as well as a number of other paramaters. New players should use offline raids as a tool to practice shooting, controls, movement, etc.
# Tarkov's Maps
Tarkov features several maps - ranging from wide, beautiful vistas to ruined factory districts, to an abandoned laboratory where illegal experiments were being conducted. It is important to learn the maps you intend to play. In order to keep your gear, you must 'extract' at one of your designated exfiltration points. Not all extracts will be active every game, and some are conditional.
# Factory
Gate 3 Extract
A small, fast-paced map that was primarily created for PvP. Scavs spawn in all the time. Very close quarters, shotguns and SMGs tend to dominate here. PMCs can only access one Exit (Gate 3) without the Factory Exit Key. Good place to go if you need PMC kills as action is pretty much guaranteed. It is recommended NOT to bring in a lot of gear to Factory until you are experienced.
Factory Map in PvP is best played in Duos - due to the layout of the map, a Maximum of 6 PMCs may be present in the game. Due to the split spawn points, you effectively have 'sides' that have up to 3 spawn locations that are close together. This is why it is recommended to secure/scout enemy spawn locations. If you go in with a Duo, you at max have 2 players on your side for an even 2v2, and if played smartly you can eliminate them and know your 'side' is secure from aggression for the time being.
Upon loading in, scavs usually take a couple minutes to spawn, though this depends on the server in question and isn't super reliable. For new players, the best loadout in Factory is going to be a MP-153 Loadout - using just an MBSS (or similar bag) and ammo in your pocket to fight other players and Scavs. Scavs will often spawn with AKs and other 'vendorable' weapons, so is a good source of income.
Factory is also one of the best maps to Scav into, as Scavs can typically avoid the Exit camping strategy employed by a lot of weaker or newer players in order to secure gear, because they typically have extra exfiltrations whereas PMCs without the Factory Exit Key are stuck using Gate 3.
If you go in with a modicum of gear, it is recommended to keep at least a flashbang (Zarya) in your container. This will allow you to quickly slot it into an empty chest rig or pocket so you can throw it into the exit door, this will flash enemies and is cheap to do - the one time you survive because you flashed the 3 exit campers using shotguns will make this strategy extremely valuable.
# Customs
Extract map
A fairly large map that was recently expanded and is expected to receive an overhaul within a patch or two, due to the choke point design of the map. Essentially, players spawn either on 'warehouse' or 'boiler (stacks)' side. If you see a large red warehouse ('big red') near you (Customs Warehouse), then you spawned on the warehouse side. If you don't, you likely spawned near Boiler side. Players can also spawn in several places in the woods North of boilers.
This map has the most quests in the game. Geared players often come to customs to challenge other squads over Dorm loot and to fight a Scav boss. New players are usually trying to do one of several early quests, such as ‘Debut’ which tasks them with killing 5 scavs on Customs and acquiring 2 MR-133 shotguns (pump shotties) from their corpses. Construction is also a popular hotspot as it has a lot of scav spawns as well as the location for the Bronze Pocketwatch, which is Prapor’s second quest.
Customs itself does not offer very much loot on average. There are several spots which can contain decent, but the vast majority is located in a couple different locations.
Dorms is the best loot location for Customs. It has two sets, 2 story and 3 story dorms. They each have their own sections of good loot, but the best is considered to be 3 story dorms, due to the presence of the Marked Room. The marked room requires a marked key to open, and has a good chance to spawn rare loot, such as keytools, documents cases, weapons cases, and high-end weapons. Due to the nature of the high value of this room, it’s almost always contested and it’s one of the best rooms in the game to farm, albeit with difficulty to successfully extract with the loot found. Note, though the key required has a maximum amount of uses, it is a fairly cheap key, and worth buying if you like to run customs and go to Dorms.
Dorms also has a ton of early quests (Operation Aquarius, for one) with some keys being valuable to use, but most dorms keys aren’t worth that much on the market. There’s too many to list here, but make sure to check the Map Keys and You at the top of the guide to determine what the value of a particular key is.
Checkpoint (Military Checkpoint) is also a decent loot spot, though not nearly as good as Dorms. If you have the key, it has a grenade box and 2 ammo boxes which can spawn good ammo. The jacket in the blue car also can spawn good medical keys as well as medical items. It is very close to the gas station, so I’ll include that here as well.
The Gas Station is one of the possible spawn locations for the scav boss. It has loose food items, a weapon box in the side room, with two keyed rooms leading to a safe and a med bag and box. Also contains a couple registers and food spawns on the floor. The emercom key can spawn on the seat in the ambulance out front.
North of the gas station is the Antenna, which contains 3 weapon boxes, a tool box, and a med bag. Possible location for scav boss spawn, albeit rarely, and also spawns regular scavs, like checkpoint and gas station.
Beyond that, there’s scattered loot around the map in different places, but usually not enough to warrant going out of your way for. There’s also scav caches, mostly around the middle road outside construction and around the boiler area.
The scav boss for customs is 'Reshala.’ He has 5 guards that have above-average gear and can be tough to deal with solo. The guards tend to be more aggressive than normal scavs, so they can be a lot to handle but are vulnerable to fragmentation grenades or flashbangs due to their close proximity to one another. Reshala himself has a good chance to have one or more bitcoin in his pockets, as well as his unique Golden TT, which is required for a Jaegar quest and used in conjunction with other Golden TT's to purchase a Tactec, good plate carrier. Reshala may spawn either Dorms (either bldg), New Gas Station, or rarely the tower north of the gas station. Scav bosses are dangerous enemies with escorts that have above-average loot (sometimes great loot) and are hostile to everyone, Including player scavs. Scav guards will approach a player scav and basically tell them to leave the area, and if they walk closer towards the scav boss they turn hostile.
The ‘official’ spawn rate for Reshala is 35%.
# Woods
Woods Map with Exfil
A very large map that is mostly just a large forest, with the occasional bunker, and the Lumber Mill in the center. The Lumber Mill is the primary point of interest, as it contains a couple quest locations and is the primary location to farm Scavs, as Scavs killed on woods are a good source of end-game keys that are hard to find.
Since the map is so large and open, sniper rifles with scopes usually reign king here. You will see a lot of players with Mosin rifles as they are a cheap way to train the Sniper skill (for a quest later on) and are capable of killing geared players and scavs alike.
Overall, not usually very populated. An early quest from Prapor sends you here to kill a number of Scavs. A good map to learn the game, as although the loot is not fantastic, you can get experience with how the game runs and operates while fighting AI and possibly getting lucky with a key find off a scav.
As of .12, Woods now houses a Scav boss that acts as a Sniper scav. He is incredibly dangerous and usually carries a tricked-out SVDS. The 7.62x54 caliber is not to be underestimated. That caliber can and will wreck your shit through what most players are capable of wearing, especially early on in a wipe. He may also carry an AK-105, so he's going to be dangerous at both short and long ranges.
He has two guards, and he typically patrols the area around the Sawmill, and carries a key to a cache nearby full of goodies. His key is part of a quest for Jaegar.
Woods also has two bunkers, one of them being an extract and requiring a key. Both bunkers have some moderate loot in them, thus worth visiting, though not necessarily worth going out of your way for them. Several quests occur around the sawmill area, which contains a good couple keys that can spawn.
# Shoreline
Shoreline Map, with Loot, Exfil, etc
A very large map, notorious for its FPS hit. Generally speaking, one of the better maps for loot. The primary point of interest is the Resort, but scavs spawn there, and is primarily occupied by hatchlings (players only with hatchet, ie melee weapon) and geared players. Resort has great loot, but requires keys to access most of it.
A great map to learn though from new players as the outskirts still contains plenty of loot and combat opportunities with AI scavs. You can hit Villa, Scav Island, Weather station, Docks, etc and come out with a backpack full of valuable gear fairly easily. The Village (Not to be confused with villa) contains a lot of toolboxes which can contain lots of parts used to upgrade your Hideout.
Location of many quests, including a large quest chain where players are required to kill many, many, scavs on Shoreline. For this and other reasons, probably the best map for new players to learn the game with.
A good loot route is to hit the village (caches in it), scav island (2 med bags, 2 toolboxes, 2 weapon boxes, 1 cache), burning gas station (weapon boxes and a safe), pier (potential extract, 2 pcs 2 safes and lots of filing cabinets), and weather station. Scavs may spawn around these areas, but most players just head straight for resort anyway, so you are much less likely to encounter them, especially if you avoid Mylta power (most players hit it on the way to or leaving from the resort). Excellent route as a player scav as well.
# Interchange
Detailed map
Great, great loot area, but very complex map. Old computers might face unique struggles with this map. Features a mostly-binary exfil system like Shoreline, but.. kinda worse. Exfil camping is fairly common on this map, but usually avoidable. Huge map with multiple floors and many many different stores. Communication with teammates is a challenge on this map, but the map is also fantastically detailed.
This map features a lot of loot that depends on the kind of store you're in. It's a great place to farm rare barter materials which are valuable to sell on the Flea market or to use for quests or for hideout upgrades. An early quest (from Ragman) sends you here to kill a large amount of Scavs. I'd recommend getting Ragman to level 2 and accepting his quest asap when going to Interchange, as getting this quest done can take a while as it is and you want all scav kills to count towards progress.
Both the tech stores (Techlight, Techxo, Rasmussen) and department stores (Groshan, Idea, OLI) are the primary places to hit. There’s also Kiba (weapons store) as well as Emercom and Mantis. Players have different strategies, but this map is unique in the sense that it really rewards exploring. Most stores will have things you can grab that are worth quite a bit but are often overlooked. Very popular place to go in as a Player Scav.
# Reserve
Brand new map, chock full of loot. Has more complex extracts than other maps, save for Labs. Excellent place to farm rare barter items, computer parts, and especially military hardware. PMCs have limited extracts, most being conditional, and the ones that aren’t require activation of ‘power’ to turn on the extract, which alerts the map the extract has been opened and can spawn Raiders (more on them below.)
Additionally, has a scav boss by the name of Glukhar, who has multiple heavily armed guards. He has multiple spawn locations and can arrive with the train.
# The Lab ('Labs')
Here's a map.
DISCLAIMER: Labs, like much of Tarkov, is under constant development, so issues may be fixed or created without warning. Always check patch notes!
Labs is a very complex map compared to the rest of Tarkov. There is a great deal more exfiltrations but many of them have requirements or a sequence of events needed to be able to extract from them. It is recommended to read the Tarkov Wiki on Labs before raiding there.
## LABS IS NOT LIKE OTHER MAPS. READ THIS SECTION CAREFULLY.
Labs is a lucrative end-game raid location, comparable to 'dungeons' in other games. They are populated by tougher enemies that give greater rewards. In order to go to labs, you need to acquire a keycard, this functions like mechanical keys but instead of opening a door, they unlock your ability to select Labs for a raid.
They may be found in-raid in various locations, most notably in scavs backpacks, pockets, and in filing cabinets. They may be purchased from Therapist at LL4 for 189K Roubles. Labs are populated by a unique kind of AI enemy, Raiders.
# Raiders
Raiders are the Labs form of Scavs, or AI enemies. However, unlike other maps, they cannot contain player Scavs. Raiders have a much tougher than your average scav, they are capable of advanced tactics (such as flanking) and throw grenades and use other consumables as a player would. Once 'locked' onto you, they are typically capable of killing you very quickly, even if you are wearing high-end armor.
In Tarkov, Raiders act like the avatars of Death. They are clad in USEC and BEAR equipment, as they are effectively AI PMCs. Many changes have been made to labs and specifically how Raider AI works and to prevent exploits to easily farm them as well as bugs where they could be deadlier than intended.
A general rule of thumb is not to fight Raiders directly. They can and WILL kill you. Raiders can spawn with 7N9, or 'big boy' ammo. This ammunition type is incredibly lethal to players, even those wearing the toughest armor. If you get shot in the head, doesn't matter what kind of helmet, face shield, killa helmet, etc you are wearing, you will almost certainly die.
Because Raiders are controlled by AI, they have zero ping. They may also end to immediately respond as if you were aggressive even if they did not originally know you were there - ESP Raiders effectively will prone and return fire even as you ADS and put them in your sights.
This is why engaging a Raider must be done very, very carefully. There are a few strategies that you may employ, most commonly some form of baiting them towards an area and then killing them when they arrive. Players may accomplish this by generating noise - gunfire, melee weapon hitting walls, crates, etc, player deaths, players Mumbling (F1 by default) can all attract Raiders to investigate your area.
Due to the high power of Raiders, players often go in with minimal loadouts and seek to avoid conflict with other players, especially geared ones. Most players avoid PvP in Labs, though a good portion of the playerbase thoroughly enjoys hunting down poorly-geared players after they kill a few Raiders for them.
As such, players will lay prone in a hallway, or crouch in a room, and attract Raiders to enter their domicile by opening the door, and immediately headshotting them. Few Raiders actually wear helmets (though some do) so most players specialize in 'flesh ammo' or, ammunition that foregoes armor penetration in favor of raw damage in order to kill Raiders more reliably, because Raiders have slightly higher head health than PMCs do.
Raiders spawn with a great variety of equipment, weapons, armor, and materials such as medication or hideout parts. They tend to have chest armor and may have different helmets. Their pockets can contain Labs keycards, morphine, Ifaks, cash, and other items. They're always worth checking.
Raiders are a good source of grenades, they will often have F-1's and Zarya's in their rig or pockets that you can use to fight off players and Raiders alike.
Recently, changes have been made to Labs to make them less profitable so that other maps are more appealing. The cost and rarity of keycards increased, as well as reducing the frequency that raiders spawn, so that they come in more infrequent groups but also tighter in formation, while also lowering the overall output of individual Raiders, so that they are less likely to have a bunch of extra materials, such as grenades and other items.
Experience Farming on Labs
Labs is one of the best places to farm experience in the entire game. Killing a Raider with a headshot awards 1100 Experience. This does not include any looting, inspection (searching bodies), examine, streak, or other experience.
Killing a large sequence of Raiders gives additional bonus experience in the form of Streak rewards, usually 100 bonus exp per additional kill.
Surviving the raid multiplies all of these sources of experience by 1.5x
Changes coming to Labs
Disclaimer: I am not a BSG developer or employee. This is what I have seen on this subreddit and heard elsewhere. Some might be purely rumor, but other points are confirmed by Nikita Labs is undergoing constant changes. Nikita and BSG take feedback seriously, and always consider what the players are telling them. It known that Labs will eventually be accessed via the Streets of Tarkov map, and will require you to enter that map, make it to the labs entrance, and then extract from Labs to return to Streets of Tarkov and exfil from there as well. This will likely add an additional layer of risk to being ambushed for your goodies along your way out, as well as punishing damage taken in labs more severely. Additionally, keycards will have a limited number of uses, and may open more than one room.
The full extent of the changes coming is not known.
Remember, you can load a map in OFFLINE mode to practice against bots or to learn the map without fear of losing gear.
# Tarkov's Health System
Tarkov Wiki Article
Tarkov has a very advanced health system, and while it might seem overwhelming at first, you'll get the hang of it rather quickly. It features a very wide variety of effects and injury, including hydration, energy, blood pressure, blood loss, fractures, contusion, intoxication, exhaustion, tremors and more.
Not all of the Health System is implemented yet. Expect changes!
Your character (PMC, or otherwise) has a combined Health of 435. Each of his limbs have separate health. Taking damage to a limb that reduces it to 0 'blacks' that limb. Blacked limbs are a problem. They greatly impair the activities your PMC performs, and taking damage in a blacked limb amplifies the damage by a multiplier and spreads that damage among your other non-black limbs equally. You cannot heal a blacked limb without the use of a Surgical Kit.
Notes: Bloodloss applies damage to the affected limb and can be spread like other damage to a blacked limb. Treat immediately. Also causes significant dehydration! Bloodloss also helps level your Vitality skill, which in turn gives you experience towards your Health skill, which is necessary to reach level 2 of in order to improve your hideout.
Losing a limb applies additional effects. Fractures also apply these effects but not the damage amplification (Except for damage if running on fractured leg.) Fractures require specialized medical kits to heal.
Dehydration is what happens when your Hydration level reaches 0. You can view your Hydration level in your gear page, at the bottom left. Becoming dehydrated is extremely bad. You take constant damage. Taking dehydration damage can kill you if you have a black chest or head. Restoring hydration helps train Metabolism, which improves positive effects from food and drink.
Head/Chest: Bullet damage resulting in losing your head or chest is instant death. Note: Bloodloss resulting in your Head/Chest being black does not result in death, but any damage to them beyond that point will! A back chest will causes you to cough (much like your stomach!)
Painkillers: Prevents coughing that comes from your chest. Doesn't help otherwise.
Stomach: Massively increased rate of dehydration and energy loss. You must find liquids or exit the Raid soon. Additionally, your PMC will cough sputter loudly, attracting attention. A black stomach multiplies damage taken by 1.5 and redistributes that damage across your entire health pool.
Painkillers: Significantly reduces the frequency and volume of the coughs.
Arms: Makes activities like searching, reloading, etc, take additional time, as well as adding a sway, reducing accuracy. Arms have a .7x damage multiplier.
Painkillers: Reduces sway, removes debuff Pain.
Legs: Blacked legs cause your PMC to stumble and be unable to run. Blacked legs have a 1x damage multiplier.
Painkillers: Allows you to walk at full speed and to run.
WARNING: Running while your legs are blacked or fractured WILL DAMAGE YOU.
Health Items
Tarkov features many health items - 'Aid' items, which can be used to restore your characters health and to fix ailments or injuries he receives as the result of combat or mishaps. The two most important health conditions to consider are bloodloss and fractures, which have both been covered above. Some food items may have ancillary effects, such as losing hydration.
Since in the current patch the only ailments to worry about are bleeding and fractures, it changes which health items are most necessary. We'll go over them below.
## Health Restoration
Medical Items on Wiki
AI-2 medkit
The newb's medical kit. You receive several of these when you start Tarkov - they'll already be in your stash. Available from Level I Therapist, they are cheap and effective way of healing early in the game. They will not stop bloodloss. Because of this, you also need to bring bandages or a higher-grade medical kit. Affectionately called 'little cheeses' by the Tarkov community. Using it takes 2 seconds, and because of how cheap it is, it's often brought in by higher level players to supplement their healing without draining their main kit (which is capable of healing bloodloss or sometimes fractures). Due to its short use time, it's often very useful during combat as you can take cover and quickly recover damage taken to a vital limb. They're also useful as you can buy them from Therapist to heal yourself if you died in a raid.
Bandages
The newb's bloodloss solution. Available from Therapist at Level I. A better version, the Army Bandage is available at Level II, after a quest. Mostly obsolete after unlocking the Car Medical kit, but some players value them due to the Car's overall low health pool. Activating takes 4 seconds, and removes bloodloss to one limb.
Splint
The newb's solution to fractures. Cheap, takes five seconds to use, and takes up 1 slot. Fractures are much more common this patch, due to them being added back in the game from standard bullet wounds, not just drops. Available from Therapist at Level I, no quest needed. Can be used to craft a Salewa.
Alu Splint
More advanced form of the normal split. Works the same, but has up to 5 uses. Recommended to carry in your container if possible, due to frequency of fractures from gunfire.
CMS (Compact Medical Surgery) Kit
New medical item added in .12, fantastic item. Allows you to perform field surgery, removing the black limb state and allowing you to heal it beyond 0 hp. Takes 16 seconds to use, and cannot be cancelled so make sure you are safe if you are using it! Will reduce the maximum health of the limb it's used on by 40-55%, but will effectively remove all negative effects incurred by having a black limb. Highly recommended to carry in your container for emergencies. Can be bartered from Jaeger LL1, and purchased for roubles LL2.
Surv12 field surgical kit
Same as the compact surgical kit, but takes 4 seconds longer, and the health penalty is reduces to 10-20% max health of the limb. Considering this kit is 1x3, taking up a huge amount of space, it's probably not worth using. It's just too large. Better this than nothing, though.
Car Medical Kit
The newb's first real medical solution. Available LL1 as a barter (2 Duct Tape) and available for Roubles after completing Therapist's second quest. Has a larger health pool than AI-2's (220, vs AI-2's 100), and removes bloodloss. Takes up a 1x2 slot, so requires to be placed in a tactical rig in order to be used effectively. Cheap and fairly efficient, takes a standard 4 seconds to use. Rendered effectively obsolete when the Salewa is unlocked.
Often kept in a player's secure container as a backup health pool, before IFAKs are unlocked.
Salewa
Good medkit for use in mid and end-game. Contains 400 total health and can remove bloodloss. More rouble efficient form of a healing due to its high health pool, costs 13k roubles. Same size as the Car medical kit, so requires a tactical rig to use effectively. Because Tarkov does not currently have effects like Toxication in the game at the moment, this kit is favored by most players who go into a raid with at least a moderate level of gear. With a high health pool and relatively low cost, it's also a more efficient way of healing damage sustained while in raids. Unlocked at Therapist Level II after completing a level 10 Prapor quest, Postman Pat Part II. Required as part of Therapist's first quest, Shortage. This makes Salewas very valuable early on in a wipe as it gatekeeps the rest of Therapist's quests, most of which occur on Customs early on. Can be crafted in your meds station with a painkiller, splint, and bandage.
IFAK
Fantastic medical kit, and is the one preferred by most players. Features 300 health and the ability to remove bloodloss and a host of other negative effects that are not yet implemented into the game. It does not, however, remove fractures. Taking up only a single slot, it is favored by players in all stages of gear, and it is recommend to carry one in your Secure Container in case of emergencies. Is available at Therapist Level II for a barter (Sugar + Sodium), and may be purchased for Roubles at Level III after completing Healthcare Privacy, Part I. It is a fairly expensive kit, but due to its durability, its small size, and ability to remove bloodloss, it is a very common medical item used by players of all levels. Can be crafted in Lvl 2 medstation.
Grizzly
The 'big daddy' medical kit, boasting an impressive total health resource of 1800. It is also a very large kit, taking up 4 slots (2x2) - in order to be able to use this quickly, it would require specialized tactical rigs that feature a 2x2 slot. It removes all negative effects (some costing HP resource), including fractures. Used by highly-geared players who intend on staying in raids for an extended period of time, or by players with additional Secure Container space available in case of emergencies. It is available for barter at Therapist Level II, and purchase at Therapist Level 4. Due to its price point from Therapist at just under 23k Roubles and its healthpool of 1800, it is by far the most efficient method of healing from raid damage, at a 1.3 roubles per health, dramatically lower than other options available. Can be crafted in Lvl 3 medstation.
## Pain Management
Using any of these items results in your character being 'On Painkillers' which allows you to sprint on fractured and blacked legs, as well as reducing effects of fractures and blacked limbs, and removing the debuff Pain. Essentially, the only difference between most of these items are the speed of use, price, availability, and duration of the effect. Note that the Hideout has changed how some of these items are used, and because Tarkov is under constant development, it is very likely that these materials may be used to create higher-grade medkits or to upgrade your medstation. That being the case, it's best to hoard the unknown items for now as efficiently as possible until you know you don't need them.
Analgin Painkillers
The holy grail of pain medication. "Painkillers" have 4 total uses. The total duration is greater than Morphine and less risk of waste. Takes a short time to use, and is available from Therapist Level 1 for both barter and Roubles. Makes a loud, distinctive gulping noise. Can be used to craft Salewa kits.
Morphine
Quick application of painkillers. Favored by some highly geared players as it has greater usability in combat then it's typical counterpart, Painkillers. Has a longer duration, but only one use. It is required for a fairly early Therapist (and a late Peacekeeper) Quest, so it is recommend to hoard 10 of them, then sell the rest unless you intend on using them. They are worth a good amount to Therapist and take up little space so they are a valuable loot item. Available from Therapist for Roubles at Level 4, after completing Healthcare Privacy, Part 3.
Augmentin
Basically a cheaper Morphine. One use, 205s. Not recommended over Painkillers due to its cost. No current barter for this item, so usually it's just a fairly expensive, small loot item. Most likely a component of a medstation manufacturing process or upgrade. Keep it.
Ibuprofen
Powerful painkiller. Lasts 500 seconds and has 12 uses. This item is recommended as your long-term solution for painkillers. While it is valuable because it's used to trade for THICC items case, it's the cheapest component and is very useful as a painkiller. It has a long duration and a large amount of uses, so keep it in your container for use as a painkiller if your primary painkillers wear off. Don't use it completely up, though. Keep the 1/12 bottles for the trade.
Vaseline
Powerful medical item. Cannot be purchased from dealers. Has a maximum of 10 uses. Removes Pain, applies Painkillers for 500 seconds (8.3 minutes). Useful to keep in your container as an alternative to Painkillers, though it takes 6 seconds to use, which is longer than other painkillers. Used as part of a barter trade for the Medcase.
Golden Star Balm
Fairly useful medical item. It can remove Pain and Contusion (not a big deal of a debuff, goes away on its own shortly) and provides a small bonus to hydration and energy. It also removes toxication and Radiation exposure, both of which are not yet implemented into the game. Like Vaseline, has a maximum of 10 uses. Painkiller effect lasts for 10 minutes, and takes 7 seconds to apply. Recommended to take only if you are going on large maps and you have extra room in your container. Can be used with Ibuprofen and 5x Med parts to craft 7 Propital.
# Boolean data type
In computer science, the Boolean data type is a data type that has one of two possible values (usually denoted true and false) which is intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type is primarily associated with conditional) statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean condition evaluates to true or false. It is a special case of a more general logical data type (see probabilistic logic)—logic doesn't always need to be Boolean.
## Generalities
In programming languages with a built-in Boolean data type, such as Pascal) and Java), the comparison operators such as > and ≠ are usually defined to return a Boolean value. Conditional and iterative commands may be defined to test Boolean-valued expressions.
Languages with no explicit Boolean data type, like C90 and Lisp), may still represent truth values by some other data type. Common Lisp uses an empty list for false, and any other value for true. The C programming language uses an integer) type, where relational expressions like i > j and logical expressions connected by && and || are defined to have value 1 if true and 0 if false, whereas the test parts of if , while , for , etc., treat any non-zero value as true.[1][2] Indeed, a Boolean variable may be regarded (and implemented) as a numerical variable with one binary digit (bit), which can store only two values. The implementation of Booleans in computers are most likely represented as a full word), rather than a bit; this is usually due to the ways computers transfer blocks of information.
Most programming languages, even those with no explicit Boolean type, have support for Boolean algebraic operations such as conjunction (AND , & , * ), disjunction (OR , | , + ), equivalence (EQV , = , == ), exclusive or/non-equivalence (XOR , NEQV , ^ , != ), and negation (NOT , ~ , ! ).
In some languages, like Ruby), Smalltalk, and Alice) the true and false values belong to separate classes), i.e., True and False , respectively, so there is no one Boolean type.
In SQL, which uses a three-valued logic for explicit comparisons because of its special treatment of Nulls), the Boolean data type (introduced in SQL:1999) is also defined to include more than two truth values, so that SQL Booleans can store all logical values resulting from the evaluation of predicates in SQL. A column of Boolean type can also be restricted to just TRUE and FALSE though.
## ALGOL and the built-in boolean type
One of the earliest programming languages to provide an explicit boolean data type is ALGOL 60 (1960) with values true and false and logical operators denoted by symbols ' ∧ {\displaystyle \wedge } 📷' (and), ' ∨ {\displaystyle \vee } 📷' (or), ' ⊃ {\displaystyle \supset } 📷' (implies), ' ≡ {\displaystyle \equiv } 📷' (equivalence), and ' ¬ {\displaystyle \neg } 📷' (not). Due to input device and character set limits on many computers of the time, however, most compilers used alternative representations for many of the operators, such as AND or 'AND' .
This approach with boolean as a built-in (either primitive or otherwise predefined) data type was adopted by many later programming languages, such as Simula 67 (1967), ALGOL 68 (1970),[3] Pascal) (1970), Ada) (1980), Java) (1995), and C#) (2000), among others.
## Fortran
The first version of FORTRAN (1957) and its successor FORTRAN II (1958) have no logical values or operations; even the conditional IF statement takes an arithmetic expression and branches to one of three locations according to its sign; see arithmetic IF. FORTRAN IV (1962), however, follows the ALGOL 60 example by providing a Boolean data type (LOGICAL ), truth literals (.TRUE. and .FALSE. ), Boolean-valued numeric comparison operators (.EQ. , .GT. , etc.), and logical operators (.NOT. , .AND. , .OR. ). In FORMAT statements, a specific format descriptor ('L ') is provided for the parsing or formatting of logical values.[4]
## Lisp and Scheme
The language Lisp) (1958) never had a built-in Boolean data type. Instead, conditional constructs like cond assume that the logical value false is represented by the empty list () , which is defined to be the same as the special atom nil or NIL ; whereas any other s-expression is interpreted as true. For convenience, most modern dialects of Lisp predefine the atom t to have value t , so that t can be used as a mnemonic notation for true.
This approach (any value can be used as a Boolean value) was retained in most Lisp dialects (Common Lisp, Scheme), Emacs Lisp), and similar models were adopted by many scripting languages, even ones having a distinct Boolean type or Boolean values; although which values are interpreted as false and which are true vary from language to language. In Scheme, for example, the false value is an atom distinct from the empty list, so the latter is interpreted as true.
The language Pascal) (1970) introduced the concept of programmer-defined enumerated types. A built-in Boolean data type was then provided as a predefined enumerated type with values FALSE and TRUE . By definition, all comparisons, logical operations, and conditional statements applied to and/or yielded Boolean values. Otherwise, the Boolean type had all the facilities which were available for enumerated types in general, such as ordering and use as indices. In contrast, converting between Boolean s and integers (or any other types) still required explicit tests or function calls, as in ALGOL 60. This approach (Boolean is an enumerated type) was adopted by most later languages which had enumerated types, such as Modula, Ada), and Haskell).
## C, C++, Objective-C, AWK
Initial implementations of the language C) (1972) provided no Boolean type, and to this day Boolean values are commonly represented by integers (int s) in C programs. The comparison operators (> , == , etc.) are defined to return a signed integer (int ) result, either 0 (for false) or 1 (for true). Logical operators (&& , || , ! , etc.) and condition-testing statements (if , while ) assume that zero is false and all other values are true.
After enumerated types (enum s) were added to the American National Standards Institute version of C, ANSI C (1989), many C programmers got used to defining their own Boolean types as such, for readability reasons. However, enumerated types are equivalent to integers according to the language standards; so the effective identity between Booleans and integers is still valid for C programs.
Standard C) (since C99) provides a boolean type, called _Bool . By including the header stdbool.h , one can use the more intuitive name bool and the constants true and false . The language guarantees that any two true values will compare equal (which was impossible to achieve before the introduction of the type). Boolean values still behave as integers, can be stored in integer variables, and used anywhere integers would be valid, including in indexing, arithmetic, parsing, and formatting. This approach (Boolean values are just integers) has been retained in all later versions of C. Note, that this does not mean that any integer value can be stored in a boolean variable.
C++ has a separate Boolean data type bool , but with automatic conversions from scalar and pointer values that are very similar to those of C. This approach was adopted also by many later languages, especially by some scripting languages such as AWK.
Objective-C also has a separate Boolean data type BOOL , with possible values being YES or NO , equivalents of true and false respectively.[5] Also, in Objective-C compilers that support C99, C's _Bool type can be used, since Objective-C is a superset of C.
## Perl and Lua
Perl has no boolean data type. Instead, any value can behave as boolean in boolean context (condition of if or while statement, argument of && or || , etc.). The number 0 , the strings "0" and "" , the empty list () , and the special value undef evaluate to false.[6] All else evaluates to true.
Lua) has a boolean data type, but non-boolean values can also behave as booleans. The non-value nil evaluates to false, whereas every other data type always evaluates to true, regardless of value.
## Tcl
Tcl has no separate Boolean type. Like in C, the integers 0 (false) and 1 (true - in fact any nonzero integer) are used.[7]
Examples of coding:
set v 1 if { $v } { puts "V is 1 or true" } The above will show "V is 1 or true" since the expression evaluates to '1' set v "" if {$v } ....
The above will render an error as variable 'v' cannot be evaluated as '0' or '1'
## Python, Ruby, and JavaScript
Python), from version 2.3 forward, has a bool type which is a subclass) of int , the standard integer type.[8] It has two possible values: True and False , which are special versions of 1 and 0 respectively and behave as such in arithmetic contexts. Also, a numeric value of zero (integer or fractional), the null value (None ), the empty string), and empty containers (i.e. lists), sets), etc.) are considered Boolean false; all other values are considered Boolean true by default.[9] Classes can define how their instances are treated in a Boolean context through the special method __nonzero__ (Python 2) or __bool__ (Python 3). For containers, __len__ (the special method for determining the length of containers) is used if the explicit Boolean conversion method is not defined.
In Ruby), in contrast, only nil (Ruby's null value) and a special false object are false, all else (including the integer 0 and empty arrays) is true.
In JavaScript, the empty string ("" ), null , undefined , NaN , +0, −0 and false [10] are sometimes called falsy (of which the complement) is truthy) to distinguish between strictly type-checked and coerced Booleans.[11] As opposed to Python, empty containers (arrays , Maps, Sets) are considered truthy. Languages such as PHP also use this approach.
## Next Generation Shell
Next Generation Shell, has Bool type. It has two possible values: true and false . Bool is not interchangeable with Int and have to be converted explicitly if needed. When a Boolean value of an expression is needed (for example in if statement), Bool method is called. Bool method for built-in types is defined such that it returns false for a numeric value of zero, the null value, the empty string), empty containers (i.e. lists), sets), etc.), external processes that exited with non-zero exit code; for other values Bool returns true. Types for which Bool method is defined can be used in Boolean context. When evaluating an expression in Boolean context, If no appropriate Bool method is defined, an exception is thrown.
## SQL
Main article: Null (SQL) § Comparisons with NULL and the three-valued logic (3VL)#Comparisonswith_NULL_and_the_three-valued_logic(3VL))
Booleans appear in SQL when a condition is needed, such as WHERE clause, in form of predicate which is produced by using operators such as comparison operators, IN operator, IS (NOT) NULL etc. However, apart from TRUE and FALSE, these operators can also yield a third state, called UNKNOWN, when comparison with NULL is made.
The treatment of boolean values differs between SQL systems.
For example, in Microsoft SQL Server, boolean value is not supported at all, neither as a standalone data type nor representable as an integer. It shows an error message "An expression of non-boolean type specified in a context where a condition is expected" if a column is directly used in the WHERE clause, e.g. SELECT a FROM t WHERE a , while statement such as SELECT column IS NOT NULL FROM t yields a syntax error. The BIT data type, which can only store integers 0 and 1 apart from NULL, is commonly used as a workaround to store Boolean values, but workarounds need to be used such as UPDATE t SET flag = IIF(col IS NOT NULL, 1, 0) WHERE flag = 0 to convert between the integer and boolean expression.
In PostgreSQL, there is a distinct BOOLEAN type as in the standard[12] which allows predicates to be stored directly into a BOOLEAN column, and allows using a BOOLEAN column directly as a predicate in WHERE clause.
In MySQL, BOOLEAN is treated as an alias as TINYINT(1)[13], TRUE is the same as integer 1 and FALSE is the same is integer 0.[14], and treats any non-zero integer as true when evaluating conditions.
The SQL92 standard introduced IS (NOT) TRUE, IS (NOT) FALSE, IS (NOT) UNKNOWN operators which evaluate a predicate, which predated the introduction of boolean type in SQL:1999
The SQL:1999 standard introduced a BOOLEAN data type as an optional feature (T031). When restricted by a NOT NULL constraint, a SQL BOOLEAN behaves like Booleans in other languages, which can store only TRUE and FALSE values. However, if it is nullable, which is the default like all other SQL data types, it can have the special null) value also. Although the SQL standard defines three literals) for the BOOLEAN type – TRUE, FALSE, and UNKNOWN – it also says that the NULL BOOLEAN and UNKNOWN "may be used interchangeably to mean exactly the same thing".[15][16] This has caused some controversy because the identification subjects UNKNOWN to the equality comparison rules for NULL. More precisely UNKNOWN = UNKNOWN is not TRUE but UNKNOWN/NULL.[17] As of 2012 few major SQL systems implement the T031 feature.[18] Firebird and PostgreSQL are notable exceptions, although PostgreSQL implements no UNKNOWN literal; NULL can be used instead.[19]
Data typesUninterpreted
Numeric
Pointer)
Text
Composite
Other
Related topics
## References
1. "PostgreSQL: Documentation: 10: 8.6. Boolean Type". www.postgresql.org. Archived from the original on 9 March 2018. Retrieved 1 May 2018.
Categories:
• 📷
• 📷 | 2021-10-17 03:53:40 | {"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": 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": 0.2769624888896942, "perplexity": 2573.5123496627407}, "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/1634323585120.89/warc/CC-MAIN-20211017021554-20211017051554-00220.warc.gz"} |
https://uhra.herts.ac.uk/handle/2299/23308?show=full | dc.contributor.author Buisson, Lise du dc.contributor.author Marchant, Pablo dc.contributor.author Podsiadlowski, Philipp dc.contributor.author Kobayashi, Chiaki dc.contributor.author Abdalla, Filipe B. dc.contributor.author Taylor, Philip dc.contributor.author Mandel, Ilya dc.contributor.author Mink, Selma E. de dc.contributor.author Moriya, Takashi J. dc.contributor.author Langer, Norbert dc.date.accessioned 2020-10-22T11:30:01Z dc.date.available 2020-10-22T11:30:01Z dc.date.issued 2020-10-16 dc.identifier.citation Buisson , L D , Marchant , P , Podsiadlowski , P , Kobayashi , C , Abdalla , F B , Taylor , P , Mandel , I , Mink , S E D , Moriya , T J & Langer , N 2020 , ' Cosmic Rates of Black Hole Mergers and Pair-Instability Supernovae from Chemically Homogeneous Binary Evolution ' , Monthly Notices of the Royal Astronomical Society . https://doi.org/10.1093/mnras/staa3225 dc.identifier.issn 0035-8711 dc.identifier.other PURE: 22799134 dc.identifier.other PURE UUID: 80f5a346-5015-4c06-9ff1-bcb1bcf33af8 dc.identifier.other ArXiv: http://arxiv.org/abs/2002.11630v1 dc.identifier.other ORCID: /0000-0002-4343-0487/work/82470006 dc.identifier.uri http://hdl.handle.net/2299/23308 dc.description This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society. © 2020 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. dc.description.abstract During the first three observing runs of the Advanced gravitational-wave detector network, the LIGO/Virgo collaboration detected several black hole binary (BHBH) mergers. As the population of detected BHBH mergers grows, it will become possible to constrain different channels for their formation. Here we consider the chemically homogeneous evolution (CHE) channel in close binaries, by performing population synthesis simulations that combine realistic binary models with detailed cosmological calculations of the chemical and star-formation history of the Universe. This allows us to constrain population properties, as well as cosmological and aLIGO detection rates of BHBH mergers formed through this pathway. We predict a BHBH merger rate at redshift zero of $5.8 \hspace{1mm} \textrm{Gpc}^{-3} \textrm{yr}^{-1}$ through the CHE channel, to be compared with aLIGO's measured rate of ${53.2}_{-28.2}^{+55.8} \hspace{1mm} \text{Gpc}^{-3}\text{yr}^{-1}$, and find that eventual merger systems have BH masses in the range $17 - 43 \hspace{1mm} \textrm{M}_{\odot}$ below the pair-instability supernova (PISN) gap, and $>124 \hspace{1mm} \textrm{M}_{\odot}$ above the PISN gap. We further investigate the effects of momentum kicks during black hole formation, calculate cosmological and magnitude limited PISN rates and investigate the effects of high-redshift deviations in the star formation rate. We find that momentum kicks tend to increase delay times of BHBH systems, and our magnitude limited PISN rate estimates indicate that current deep surveys should be able to detect such events. Lastly, we find that our cosmological merger rate estimates change by at most $\sim 8\%$ for mild deviations of the star formation rate in the early Universe, and by up to $\sim 40\%$ for extreme deviations. en dc.language.iso eng dc.relation.ispartof Monthly Notices of the Royal Astronomical Society dc.subject astro-ph.HE dc.subject astro-ph.GA dc.subject astro-ph.SR dc.title Cosmic Rates of Black Hole Mergers and Pair-Instability Supernovae from Chemically Homogeneous Binary Evolution en dc.contributor.institution Centre for Astrophysics Research dc.contributor.institution School of Physics, Astronomy and Mathematics dc.description.status Peer reviewed rioxxterms.version AM rioxxterms.versionofrecord https://doi.org/10.1093/mnras/staa3225 rioxxterms.type Journal Article/Review herts.preservation.rarelyaccessed true
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http://robertmarkbramprogrammer.blogspot.com.au/2011_03_01_archive.html | ## Friday, March 18, 2011
### Using SELECT MAX(ID)+1 in an insert statement
I am working with the following Knowledge Tree table in MySQL - it holds reference data.
CREATE TABLE document_types_lookup (
id INT(10) NOT NULL,
name VARCHAR(100),
disabled BIT DEFAULT'0' NOT NULL
);
ALTER TABLE document_types_lookup ADD PRIMARY KEY (id);
I needed to insert a few thousand rows, but since there is no auto-increment field for the ID, I needed SQL that could increment ID for me - using SQL only, no script. I found a bug report (Allow INSERT...SELECT MAX(x)+1 from the same table) that had the below snippet that used select (max(id)+1) to increment ID for an insert.
insert into foo(lfd) select (max(lfd)+1) from foo;
And while I could get that statement by itself to work (inserting only ID into a record), I could not not adapt it to add the rest of the record values.
insert into
document_types_lookup(id, name, disabled)
values
(select (max(id)+1) from document_types_lookup, 'a name', false);
I always got the below error.
Executing:
insert into document_types_lookup(id, name, disabled) values (select (max(id)+1) from document_types_lookup, 'a name', false)
You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'select (max(id)+1) from document_types_lookup, 'a name', false)' at line 1
[Error Code: 1064]
[SQL State: 42000]
So, my work-around is to use two statements instead of one: an insert followed by an update, as below.
insert into
document_types_lookup(id)
select (max(id)+1) from document_types_lookup;
update
document_types_lookup
set
name = 'CORP_HMN_000_CA_',
disabled = false
where
name is null;
OK, see any problems with this script? You should - it's a dangerous script for two big reasons. Firstly, it isn't thread safe, i.e. using select (max(id)+1) in an insert is dangerous if there are multiple people updating the table at the same time. You have no guarantee that between the time you have selected max ID + 1 and the time the insert actually happens, a new record might have been inserted by someone else, meaning that when your insert statement finally hits, your max ID + 1 will not be unique anymore. You can solve this by locking the table before your insert and releasing it afterwards. The second reason that this is a dangerous script is because it assumes there will only ever be one record where name is null; it does this as I could think of no other way to determine what record I just inserted.
So, this script works only because a) I knew I was the only person who would be updating the table at that time and b) I knew name would have a value for all records other than the one I had just inserted.
## Monday, March 14, 2011
### UltraEdit macro for HTML/XML - auto-create closing tags
Here is another pair of UltraEdit macros that I use quite frequently - these two help me with creating container tags for HTML or XML; specifically, they automate the creation of the opening and closing tag: all I need to do is type out the tag name and run the macro with the cursor within (or at the left/right boundary of) the tag name.
For example, if I type out xmlTag and run the first macro, I will be left with the following: <xmlTag>|</xmlTag>. The I bar (|) indicates where the cursor is left when the macro finishes.
InsertMode
ColumnModeOff
HexOff
UltraEditReOn
Clipboard 9
IfSel
Cut
"<"
Paste
">"
Else
IfSel
Else
SelectWord
EndIf
StartSelect
Cut
"<"
Paste
">"
EndIf
Clipboard 0
Paste
Clipboard 9
"</"
Paste
">"
Clipboard 0
The second macro is the same except that it will paste whatever is in the clipboard at the time and leave the cursor at the end of the closing tag. For example, if I type and cut the following text: text in the clipboard, then type out xmlTag and run the second macro, I will be left with the following: <xmlTag>text in the clipboard</xmlTag>|. The I bar (|) indicates where the cursor is left when the macro finishes.
InsertMode
ColumnModeOff
HexOff
UltraEditReOn
Clipboard 9
IfSel
Cut
"<"
Paste
">"
Else
IfSel
Else
SelectWord
EndIf
StartSelect
Cut
"<"
Paste
">"
EndIf
Clipboard 0
Paste
Clipboard 9
"</"
Paste
">"
Clipboard 0
Note that both the macros above include instructions that are from another common UltraEdit macro I use, Alt+x to cut currently selected token (selected or if cursor is in the token).
IfSel
Else
SelectWord
EndIf
StartSelect
Cut
## Friday, March 11, 2011
### dotCMS thumbnail error: java.lang.IncompatibleClassChangeError
In our dotCMS 1.7 environments, we found - on just one environment (PROD, of all places!) - that image thumbnails were broken. For example, referencing the image itself worked fine: http://example.com/path/to/image.jpg, but referencing the thumbnail fails: http://example.com/thumbnail?inode=60732&w=75&h=50.
In the logs, I noticed the below error.
[07/03/11 04:39:53:053 EST] ERROR [/].[ThumbnailServlet]: Servlet.service() for
servlet ThumbnailServlet threw exception
java.lang.IncompatibleClassChangeError: Found class com.sun.image.codec.jpeg.JPEGImageEncoder, but interface was expected
at com.dotmarketing.util.Thumbnail.resizeImage(Thumbnail.java:114)
at com.dotmarketing.servlets.image.ThumbnailImage.service(ThumbnailImage.java:203)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:717)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:290)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at com.dotmarketing.filters.CMSFilter.doFilter(CMSFilter.java:104)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
After some Googling, I found the below description of the error on this page: 'Interface was expected' for JPEGImageEncoder.
Root Cause
If you found this error appears in the log file, the biggest possibility and maybe the only reason that this exception being thrown is you are using the OpenJDK instead of Sun JDK. Well, the exception message is obvious to tell you that the com.sun.image.codec.jpeg.JPEGImageEncoder is a class in OpenJDK whereas it is implemented as an interface in Sun JDK.
I then confirmed that PROD did indeed have a different JRE than the other environments. On DEV:
java -version
java version "1.6.0_21"
Java(TM) SE Runtime Environment (build 1.6.0_21-b06)
Java HotSpot(TM) Client VM (build 17.0-b16, mixed mode, sharing)
But on PROD:
java -version
java version "1.6.0_17"
OpenJDK Runtime Environment (IcedTea6 1.7.5) (rhel-1.16.b17.el5-x86_64)
OpenJDK 64-Bit Server VM (build 14.0-b16, mixed mode)
So... we had the wrong JDK. Overnight, we installed Java HotSpot on PROD, changed PATH and JAVA_HOME to point to the new JRA, and the issue was resolved.
I reported this issue on the dotCMS Yahoo group here: Thumbnails not showing - java.lang.IncompatibleClassChangeError. In a response to that post, Maria Ahues Bouza noted that dotCMS only supports Sun Java (Oracle now I guess) as it's defined on their technology requirements page.
## Thursday, March 10, 2011
### DOS Batch Script to upload file to multiple dotCMS environments via cadaver
Update: Friday 11 March 2011, 11:56:08 AM, added instructions for use with Eclipse. I also announced this script on the dotCMS Yahoo Group.
Friday 11 March 2011, 03:20:15 PM added section about STATUS_ACCESS_VIOLATION error.
In dotCMS, one of the most tedious activities for a developer is to use the dotCMS Admin UI to navigate to a file (.vtl for example), open it for editing, make your change and then publish the change. Depending on how snappy your environment is, everything bar the actual editing can take a minute or more. Now multiply that by the 30, 40, 50, 100 edits you might need to make in one work day, especially during a test-debug cycle.
It is for this reason that in my current project I have used .vtl files everywhere possible to store content/code that is a developer's responsibility. This means two things.
1. It is very easy to use Cadaver and a script to upload new and changed files.
2. I can use my favourite text editor or IDE to edit the VTL files.
1. Eclipse has a plugin for editing Velocity files: Veloeclipse. Unfortunately, apart from syntax highlighting and HTML auto-complete, none of the other functions seem to work since Galileo (at least), like auto-complete for macros or Velocity/Java objects.
2. UltraEdit has a wordfile for Velocity on its extras page (to allow for syntax highlighting).
Personally, I edit VTLs in UltraEdit and upload them using Cadaver scripts from Cygwin - and now from UltraEdit directly. Thanks to UltraEdit's ability to run DOS commands with a keyboard shortcut, I can upload the VTL file to all the dotCMS environments at the same time, without even alt+tabbing to Cygwin.
Prerequsites.
1. You are using a local project (directory structure) to store files (such as VTLs, JS, CSS etc) which you then upload to dotCMS. Your project directory structure must match the folder structure you are using in dotCMS (if not, stop reading this post because my script will not help you). It would also be really good if you are using a source control system (good like you being off Santa's nice list if you don't).
2. Have Cygwin installed and, um, be running Windows. :)
3. Make sure that your Cygwin install includes Cadaver. Cadaver is now included with Cygwin, so it should already be there if you recently installed/updated Cygwin. Make sure by entering the command cadaver. If you see command not found, then grab cadaver and unpack it into /usr/bin.
4. Make sure you have set up your .netrc file with credentials for each environment as described in my post Using webDAV and Cadaver with dotCMS.
5. Save the script below as a DOS batch file - into the root of your project directory - and edit only the section underneath the line :: Change these to suit your project.
• environmentLabelX and environmentX. Add as many environmentLabelX and environmentX pairs as you want - one for each environment you want files to be uploaded to. Make sure to increment X for each pair.
• max. Edit the line set max=3 to make the number match the number of environments you have just defined.
• PATH_SUFFIX. Within dotCMS, we have put all of our content inside a "root" directory that is not matched by our project directory structure. For example, our CSS file would be http://dev.example.com/rootDir/css/styles.css but in our project directory, this file would be found at PROJECT_DIR/css/styles.css. If you have such a root, store it in PATH_SUFFIX. Otherwise, leave it blank if you put all your files into the highest folder level within dotCMS.
6. This script can be used by itself (it is a DOS Batch after all, and the only argument it needs is the absolute path to the file being uploaded) or in conjunction with an editor/IDE that knows how to execute external commands. Both UltaEdit and Eclipse can do this. Below are the instructions for using the script with UltraEdit or Eclipse.
• To use it with UltraEdit, follow these instructions to add it to the Tool Configuration.
1. In the menu bar, select Advanced > Tool Configuraiton > Insert.
2. On the Command tab enter the following.
• Menu item name: Upload current file with Cadaver.
• Command line: C:\path\to\your\script.bat %f.
3. On the Options tab, enter the following.
• Program Type: DOS program.
• Tick "Save active file"
4. On the Output tab, enter the following.
• Command Output (DOS Commands): Output to list box.
• Tick "Show DOS box"
• Tick "Capture Output"
• Replace selected text with: No replace.
5. Now, after you have edited a VTL file (or CSS, JS etc) in UltraEdit, select Advanced > Upload current file with Cadaver or just use the keyboard shortcut UltraEdit gives to each of those (a control+shift+x shortcut).
• To use it with Eclipse, follow these instructions to add it as an external tool.
1. In the menu bar, select Run > External Tools > External Tools Configuration.
2. Click the icon for New Configuration.
3. Enter name: Upload current file with Cadaver.
4. Enter location: c:/path/to/your/batch.bat.
5. Enter arguments: \${resource_loc}.
6. Click close.
7. In the menu bar, select Run > External Tools > Oragnize Favourites...
8. Click add.
9. Tick the Launch Configuration you just created.
10. Click OK.
11. If you have multiple External Tools Favourites, you can change the order in which they appear here. This will affect the keyboard combination you use to access each one - changing the number used for the last key, 1-9 etc.
12. Click OK.
13. Now, after you have edited a VTL file (or CSS, JS etc) in Eclipse, select Run > External Tools > Upload current file with Cadaver or just use the keyboard combination Eclipse gives to each of those (Alt, R, E, 1-9).
And finally, here is the DOS Batch file.
:: Change these to suit your project.
set environmentLabel1=DEV
set environmentLabel2=Staging
set environmentLabel3=PROD
set environment1=http://dev.example.com/webdav/autopub/dev.example.com
set environment2=http://staging.example.com/webdav/autopub/staging.example.com
set environment3=http://prod.example.com/webdav/autopub/prod.example.com
SET MAX=3
SET PATH_SUFFIX=rootDir/
:: Do not change below here.
SET WORKING_DIR=%cd%
SET WORKING_DIR=%WORKING_DIR:\=/%
SET FILENAME=%~nx1
SET FULL_PATH=%~dp1
SET FULL_PATH=%FULL_PATH:\=/%
SET RELATIVE_PATH=!FULL_PATH:%WORKING_DIR%/=!
echo File: %1
echo FTP file name: %FILENAME%
echo Using relative path: %RELATIVE_PATH%
echo Using full path: %FULL_PATH%
For /L %%i in (1,1,%MAX%) Do (
echo.
echo.
echo.
echo.
echo =======================================================================
echo Transferring to !ENV_LABEL_%%i!
echo open !ENV_%%i! > %temp%\%~n0.cadaver
echo lcd %FULL_PATH% >> %temp%\%~n0.cadaver
echo cd %PATH_SUFFIX%%RELATIVE_PATH% >> %temp%\%~n0.cadaver
echo mput %FILENAME% >> %temp%\%~n0.cadaver
echo bye >> %temp%\%~n0.cadaver
1 [unknown (0xCA8)] cadaver 7944 exception::handle: Exception: STATUS_ACCESS_VIOLATION
It also leaves me with a cadaver.exe.stackdump just under 1MB. I can just re-run the command and clear up the stackdump, but I sure would like to know if there is a way to stop them from happening. | 2017-05-29 00:12:06 | {"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": 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": 0.35511335730552673, "perplexity": 6645.79987291084}, "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-2017-22/segments/1495463612003.36/warc/CC-MAIN-20170528235437-20170529015437-00058.warc.gz"} |
https://ece4uplp.com/maxwells-first-equation-in-electrostatics/ | # Maxwell’s First Equation in Electrostatics
From the Divergence theorem, we have
$\overrightarrow{\bigtriangledown&space;}.\overrightarrow{D}=&space;div&space;\overrightarrow{D}=(&space;\frac{\partial&space;D&space;_{x}}{\partial&space;x}+&space;\frac{\partial&space;D&space;_{y}}{\partial&space;y}+&space;\frac{\partial&space;D&space;_{z}}{\partial&space;z})$
$\lim_{dv->0}\frac{\oint_{s}\overrightarrow{D}.\overrightarrow{ds}}{dv}=\lim_{dv->0}(&space;\frac{\partial&space;D&space;_{x}}{\partial&space;x}+&space;\frac{\partial&space;D&space;_{y}}{\partial&space;y}+&space;\frac{\partial&space;D&space;_{z}}{\partial&space;z})$
${\oint_{s}\overrightarrow{D}.\overrightarrow{ds}}=\(&space;\frac{\partial&space;D&space;_{x}}{\partial&space;x}+&space;\frac{\partial&space;D&space;_{y}}{\partial&space;y}+&space;\frac{\partial&space;D&space;_{z}}{\partial&space;z})dv$
from Gauss’s law $\oint_{s}\overrightarrow{D}.\overrightarrow{ds}&space;=Q_{enclosed}$
${\oint_{s}\overrightarrow{D}.\overrightarrow{ds}}=\(&space;\frac{\partial&space;D&space;_{x}}{\partial&space;x}+&space;\frac{\partial&space;D&space;_{y}}{\partial&space;y}+&space;\frac{\partial&space;D&space;_{z}}{\partial&space;z})dv&space;=&space;Q_{enclosed}$
dividing it by $dv(or)&space;\Delta&space;v$ differential volume on both sides
$\frac{{\oint_{s}\overrightarrow{D}.\overrightarrow{ds}}}{dv}&space;=&space;\frac{Q_{enclosed}}{dv}$
by applying limit on both sides
$\lim_{dv->0}\frac{{\oint_{s}\overrightarrow{D}.\overrightarrow{ds}}}{dv}&space;=&space;\lim_{dv->0}&space;\frac{Q_{enclosed}}{dv}$
$div\overrightarrow{D}&space;=&space;\rho&space;_{v}$
$\overrightarrow{\bigtriangledown&space;}.\overrightarrow{D}&space;=&space;\rho&space;_{v}$
This equation is known as Maxwell’s first equation and is also known as point form of Gauss’s law /Differential form of Gauss’s law.
(No Ratings Yet) | 2019-05-21 03:30:14 | {"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": 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": 0.9673694372177124, "perplexity": 2867.9599786033586}, "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-2019-22/segments/1558232256215.47/warc/CC-MAIN-20190521022141-20190521044141-00006.warc.gz"} |
https://proxies-free.com/tag/complexity/ | data structures – Time complexity of algorithms
The first and the last statements are correct, while the second one is incorrect.
Statement 1
Denote by $$T_{min}$$ the actual running time of the algorithm $$A$$, in the best case, and $$T_{max}$$ in the worst case. By how we chose $$T_{min}$$ and $$T_{max}$$ it follows that $$T_{min}le T_{max}$$.
From our assumptions, $$T_{min}=Omega(g(n))implies T_{min}ge c_1g(n)$$. Also from our assumptions, $$T_{max}=O(f(n))implies T_{max}le c_2f(n)$$.
Combining them together we get:
$$c_1f(n)le T_{min} le T_{max} le c_2g(n)$$, which means that $$f(n)le frac{c_2}{c_1}g(n)implies f(n)=O(g(n))$$
Statement 2
Consider the following algorithm:
``````if lst(0) != 0:
for x in lst:
print(x)
``````
And consider the inputs $$I_1:=(0,1,2,3,…,n)$$ and $$I_2:=(1,2,3,…n+1)$$.
Clearly, the algorithm takes $$O(1)$$ time with input $$I_1$$, but $$Omega(n)$$ time with input $$I_2$$. Obvoiusly, $$nneq O(1)$$ and thus the statement is incorrect.
Statement 3
Repeat the proof of statement 1. Note that also $$T_{avg}le T_{max}$$ and thus the proof still holds.
time complexity – O(n^2) and O(nlogn) exercise
There is an exercise which says : Al and Bob are arguing about their algorithms. Al claims his O(n log n)-time method is always faster than Bob’s O(n^2)-time method. To settle the issue, they perform a set of experiments. To Al’s dismay, they find that if n<100, the O(n^2)-time algorithm runs faster, and only when n>= 100 is the O(n log n)-time one better. Explain how this is possible.
Can somene help me?
complexity theory – Classes of Functions Closed Under Polynomial Composition – Papadimitriou Exercise 7.4.4
I am studying Computation complexity using Papadimitrious’s book: “Computational Complexity”.
I am trying to do Problem 7.4.4:
“Let $$C$$ be a class of functions from nonnegative integers to nonnegative integers. We say that $$C$$ is closed under left polynomial composition if $$f(n) in C$$ implies $$p(f(n))=O(g(n))$$ for some $$g(n) in C$$, for all polynomials $$p(n)$$. We say that $$C$$ is closed under right polynomial composition if $$f(n) in C$$ implies $$f(p(n))=O(g(n))$$ for some $$g(n) in C$$, for all polynomials $$p(n)$$.
Intuitively, the first closure property implies that the corresponding complexity class is “computational model-independent”, that is, it is robust under reasonable changes in the underlying model of computation (from RAM’s to Turing machines, to multistring Turing machines, etc.) while closure under right polynomial composition suggests closure under reductions (see the next chapter).”
Which of the following classes of functions are closed under left polynomial composition, and which under right polynomial composition?
(a) – $${n^k: k > 0 }$$
(b) – $${k cdot n: k > 0 }$$
(c) – $${k^n : k > 0 }$$
(d) – $${2^{n^k} : k > 0 }$$
(e) – $${log^k n: k > 0 }$$
(f) – $${log n}$$
After understanding the definition of closed under left/right polynomial composition, I think I was able to solve items (a), (b), (c) and (f). However, I was not able to solve items (d) and (e).
My solution for item (a):
Closed Under Left Polynomial Composition: consider an arbitrary $$f(n) in C$$ and an arbitrary polynomial $$p(n)$$. Then, $$f(n)$$ is of the form $$n^{k’}$$, for some $$k’ > 0$$ and therefore $$p(f(n))$$ is a polynomial. Let $$k”$$ be the degree of the polynomial $$p(f(n))$$. Take $$g(n) = n^{k”} in C$$ and we have $$p(f(n)) = O(g(n))$$.
Closed Under Right Polynomial Composition: same reasoning.
My solution for item (b):
Not Closed Under Left Polynomial Composition: consider as a counterexample $$f(n) = n in C$$ and $$p(n) = n^2$$. Then, $$p(f(n)) = n^2$$. For every $$g(n) = k n in C$$ we have $$O(g(n)) = O(n)$$. Since $$n^2 neq O(n)$$ we conclude.
Not Closed Under Right Polynomial Composition: the previous counterexample applies.
My solution for item (c):
Closed Under Left Polynomial Composition: Consider an arbitrary $$f(n) = k_1^n$$ and a polynomial $$p(n)$$. Notice that $$p(f(n))$$ is a polynomial in $$k_1^n$$. For sufficiently large $$n$$, there exists some $$k_2$$ such that $$p(n) leq n^{k_2}$$ and therefore $$p(f(n)) leq (f(n))^{k_2} = (k_1^{n})^{k_2} = (k_1^{k_2})^n$$. Therefore, taking $$g(n) = (k_1^{k_2})^n in C$$ we obtain that $$p(f(n)) = O(g(n))$$.
Not Closed Under Right Polynomial Composition: Consider as a counterexample $$f(n) = 2^n$$ and $$p(n) = n^2$$. Then, $$f(p(n)) = 2^{n^2}$$, which is greater than $$g(n) = k^n$$, for every fixed value of $$k$$, if $$n$$ is sufficiently large. Therefore, $$f(p(n)) not in O(g(n))$$.
My solution for (f):
Not Closed Under Left Polynomial Composition: Consider as a counterexample $$f(n) = log n$$ and $$p(n) = n^2$$. Then, $$p(f(n)) = log^2 n$$. Also, $$g(n) in C$$ implies that $$g(n) = O(log n)$$. We have $$log^2 n not in O(log n)$$.
Closed Under Right Polynomial Composition: If $$f(n) in C$$ then $$f(n) = log n$$. Given an arbitrary polynomial $$p(n)$$, we have that there exists some $$k’$$ such that, for sufficiently large $$n$$, $$p(n) < n^{k’}$$. Then, for sufficiently large $$n$$:
$$f(p(n)) leq f(n^{k’}) = log n^{k’} = k’ log n = O(log n) = O(g(n)).$$
Can anyone help me with items (d) and (e)?
Thanks in advance. Of course, corrections/comments on the other items are also welcomed.
time complexity of AA^T
In the context of building of a cocitation weighted adjacency matrix, in terms of A using matrix operations.. what is the time complexity of AA^T?
algorithms – Time complexity of finding median in data stream
I was reading a solution to the problem in the title on leetcode and the article says that the time complexity of the following solution is O(n)
1. setup a data structure to hold stream value and insert new element in the right place using linear search or binary search
2. return median
my solution is as follows:
``````class MedianFinder:
def __init__(self):
"""
"""
self.arr = ()
def addNum(self, num: int) -> None:
idx = bisect.bisect_left(self.arr, num)
self.arr.insert(idx, num)
def findMedian(self) -> float:
# self.arr.sort()
if len(self.arr) % 2 != 0:
return self.arr(len(self.arr)//2)
else:
return (self.arr(len(self.arr)//2 -1) + self.arr(len(self.arr)//2 ))/2
``````
My question is about the time complexity of the push method. the binary search will take O(log n) to find the index. the insert will take O(n). but since the method will be called on the stream, will the complexity be O(n^2) or O(n) ?
Understanding of TIME COMPLEXITY in non deterministic and deterministic Turing Machines
If I assume that the complexity of an non-deterministic Turing machine N is T(n), where |w| = n, w: input string for N. What would be the time complexity of a deterministic Turing machine D equivalent to N?
logic – Complexity of pattern matching for modus ponens logical conclusions
Is a Turing machine with added the following contant-time operation equivalent (in the sense that polynomial time remains polynomial time and exponential time remains exponential time) to a (usual) Turing machine:
By predicates I will mean predicates in first-order predicate calculus. (Note that predicates may have free variables.)
• constant-time modus-ponens resolution (yes or no) and then adding $$y$$ to the end of this array if yes, for given predicates $$x$$ and $$y$$ and an array (or a linked list) of predicates. By definition of modus ponens, it’s yes, if and only if some element of the arrays is $$XRightarrow y$$ where $$X$$ is a pattern matching $$x$$.
Remark: The above operation is a part of the standard procedure of proof-checking is first-order predicate logic.
If the above hypothesis is false, then what is the running time upped bounds of the above operation in different kinds of Turning machine equivalents (such as Turing machine, Markov algorithms, von Neumann architecture with infinitely many infinitely big words of memory, etc.)?
BTW, is von Neumann architecture with infinitely many infinitely big words of memory a Turning machine equivalent? (I think yes, but not 100% sure.)
complexity theory – Constant-time adding an element?
Is a computer with infinite memory and infinite word size a Truing machine equivalent (in the sense that polynomial time remains polynomial time and exponential time remains exponential time) if we allow constant-time linked link element insertion (at the beginning of the list)?
I doubt this because element insertion requires memory allocation and allocation is usually not a constant-time operation.
complexity theory – Show that NL ⊆ P
$$textsf{PATH}$$ is in $$textsf{NL}$$, because to solve it, you just need to keep in memory the current vertex you are in, and guess (non-deterministicaly) the next one on the path until you reach your destination. Since you keep the current vertex $$v$$, numbered from $$0$$ to $$|V| – 1$$, you need a memory space corresponding to the binary encoding of $$v$$, which is at most $$1 + log_2(|V| – 1)$$. You also need to keep the potential adjacent vertex of $$v$$, next in the path.
All in all, a Turing Machine solving this problem would only need $$O(log |V|)$$ additionnal space memory (the memory of the graph and of the starting vertex and the destination vertex of the path you are guessing are not considered in the memory used, because they are part of the input).
$$textsf{PATH}$$ is $$textsf{NL}$$-hard, because to solve any $$textsf{NL}$$ problem, you have to determine if there exists a sequence of possible transitions from the initial configuration to an accepting configuration in the Turing Machine of the problem. If you consider a graph of the possible configurations (where there exists an edge from a configuration $$alpha$$ to a configuration $$beta$$ if and only if one can go from $$alpha$$ to $$beta$$ in one transition in the Turing Machine), then solving the $$textsf{NL}$$ problem is the same as solving $$textsf{PATH}$$ in the graph of possible configurations.
You then need to prove that the graph of configurations can be constructed in logarithmic additionnal space. This can be done, because if a non-deterministic Turing Machine works in space $$s(n)$$, then the number of possible configurations is $$2^{O(s(n))}$$. Considering the binary encoding of those configurations, one can determine if there exists an edge between two configurations in deterministic space $$O(s(n))$$.
Now, since $$textsf{PATH}$$ is solvable in polynomial time (with a graph traversal algorithm, for example), that means that any $$textsf{NL}$$ problem is solvable in polynomial time (via the $$textsf{NL}$$-completude of $$textsf{PATH}$$), so $$textsf{NL}subseteq textsf{P}$$. This stands true, because if a Turing Machine uses $$s(n)$$ space memory, then it has at most $$2^{O(s(n))}$$ configurations, and exploring all of them takes time $$2^{O(s(n))}$$. Since $$s(n) = log n$$ for problems in $$textsf{NL}$$, the total time is indeed $$n^{O(1)}$$.
can’t quit understand one step of the recurrence time complexity calculation
I solved the question T(n) = T(sqrt(n)) + 1 but can’t quit understand one step of the solution
I don’t understand the transition in (1).
how did we conclude that T(m) = T(m/2) + 1 from the previous step that m is in the power? | 2021-04-21 02:10:51 | {"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": 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": 120, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7764952182769775, "perplexity": 463.34871027040293}, "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-2021-17/segments/1618039503725.80/warc/CC-MAIN-20210421004512-20210421034512-00605.warc.gz"} |
https://www.zigya.com/study/book?class=11&board=ahsec&subject=Biology&book=Biology&chapter=Breathing+and+Exchange+of+Gases&q_type=&q_topic=Disorders+Of+Respiratory+System&q_category=&question_id=BIEN11007548 | ## Chapter Chosen
Breathing and Exchange of Gases
## Book Store
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CBSE Gujarat Board Haryana Board
## Previous Year Papers
Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12
What happens to respiratory process in man going up a hill ?
As altitude increases, the oxygen level in the atmosphere decreases. Therefore, as a man goes uphill, he will suffer from oxygen deficiency. This causes the amount of oxygen in the blood to decline. The respiratory rate increases to compensate for the decrease in the oxygen level of blood. Simultaneously, the rate of heart beat increases to increase the supply of oxygen to blood.
144 Views
By what amount the solubility of carbondioxide is more than the solubility of oxygen?
20 - 25 times
414 Views
Name the cavity having lungs.
Thoracic cavity.
448 Views
Oxygen is carried by haemoglobin as?
Oxyhaemoglobin.
415 Views
What is the partial pressure of oxygen in oxygenated blood ?
95 mm Hg
702 Views
70% of carbondioxide is transported as ?
Bicarbonate
360 Views | 2018-12-09 19:57:49 | {"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": 0.4032604694366455, "perplexity": 8474.12633927593}, "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/1544376823009.19/warc/CC-MAIN-20181209185547-20181209211547-00027.warc.gz"} |
https://www.mersenneforum.org/showthread.php?s=66563ba46bb17f07e889db9714f53f05&t=22756&goto=nextoldest | mersenneforum.org Prime95 Not using 100%
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2017-11-30, 23:48 #1 Thratrun Nov 2017 5 Posts Prime95 Not using 100% Hi, I'm using prime95 with a i7 6.7k 3.4ghz, with 4 workers (1 core each), and my cpu usage for prime95 is 56% most of the time, with 60-65% total CPU usage. Each core (including HT ones) is at 50% more or less.
2017-12-01, 03:21 #2 VBCurtis "Curtis" Feb 2005 Riverside, CA 117118 Posts That would be because hyperthread cores aren't real cores, but Windows doesn't know the difference. 8 * 50% = 4 * 100% = all 4 cores fully used.
2017-12-01, 09:13 #3
Thratrun
Nov 2017
5 Posts
Quote:
Originally Posted by VBCurtis That would be because hyperthread cores aren't real cores, but Windows doesn't know the difference. 8 * 50% = 4 * 100% = all 4 cores fully used.
Oh so everything is fine then? It is working at max?
2017-12-01, 12:25 #4
"Kieren"
Jul 2011
In My Own Galaxy!
2·3·1,693 Posts
You are running fine. If you turned off hyperthreading usage would be 100%. I keep HT on, but set affinity to run on one of each adjacent pair of cores. This assigns all physical cores.
EDIT:
Quote:
A 6700k should be running at 4GHz by default
Good point. I had not even noticed that detail. I have a 6700K which does quite well at 4.3GHz.
Last fiddled with by kladner on 2017-12-01 at 12:33
2017-12-01, 12:26 #5 henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 10111001100012 Posts A 6700k should be running at 4GHz by default
2017-12-01, 12:29 #6 kladner "Kieren" Jul 2011 In My Own Galaxy! 2·3·1,693 Posts Oops. Should have edited my previous post. Last fiddled with by kladner on 2017-12-01 at 12:30
2017-12-01, 12:37 #7
Thratrun
Nov 2017
1012 Posts
Quote:
Originally Posted by kladner You are running fine. If you turned off hyperthreading usage would be 100%. I keep HT on, but set affinity to run on one of each adjacent pair of cores. This assigns all physical cores. EDIT: Good point. I had not even noticed that detail. I have a 6700K which does quite well at 4.3GHz.
How do I set affinity? In each worker at the beginning it says "setting affinity worker on cpu core #1" (the #1 is the number of the worker)
Oh, mine is a 6700 not a 6700k, I said it wrong
EDIT: I didnt have 100% because i didnt have HT for LL, P-1, ECM (it said it wasn't recommended) but i activated it and now it shows 100%
Last fiddled with by Thratrun on 2017-12-01 at 13:11
2017-12-01, 14:46 #8 Thratrun Nov 2017 5 Posts However, after activating HT in prime95, the ms/iter for 3 of the workers are higher and the other stays more or less the same, so it looks like it works better without HT
2017-12-01, 18:36 #9
Dubslow
"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88
11100001101012 Posts
Quote:
Originally Posted by Thratrun However, after activating HT in prime95, the ms/iter for 3 of the workers are higher and the other stays more or less the same, so it looks like it works better without HT
This is true. Prime95 is very rare software that is written in hand-tuned x86 assembly -- the very, very large majority of software is not, and the compiled-to-assembly software generally isn't optimized enough to make full use of the hardware, which is the purpose of hyperthreading -- a second process can make use of silicon on one core that a first process simply can't use. Prime95 is the exception to the rule: its hand-tuned assembly is designed to use every bit of silicon to its maximum possible extent, so hyperthreading offers no additional value.
Even other software in use on other parts of this forum -- software with inline assembly included in the most critical computational loops , but still mostly written in C -- see a ~30% throughput gain with hyperthreading. Prime95 is very much different than nearly any other software in the world in this respect.
2017-12-02, 03:10 #10
"Kieren"
Jul 2011
In My Own Galaxy!
2×3×1,693 Posts
Quote:
Originally Posted by Thratrun How do I set affinity? In each worker at the beginning it says "setting affinity worker on cpu core #1" (the #1 is the number of the worker) Oh, mine is a 6700 not a 6700k, I said it wrong EDIT: I didnt have 100% because i didnt have HT for LL, P-1, ECM (it said it wasn't recommended) but i activated it and now it shows 100%
In local.txt:
Code:
[Worker #1]
Affinity=1,3,5,7
# Affinity=0,2,4,6
The second "Affinity" line is a commented example of another set of 'cores' that would use only physical cores.
Note that I run a single worker with 4 cores. If you have more workers, add sections as appropriate: [Worker #2] etc. Also that, in Windows at least, core numbers start with 0.
2017-12-02, 07:16 #11
GP2
Sep 2003
5×11×47 Posts
Quote:
Originally Posted by Dubslow This is true. Prime95 is very rare software that is written in hand-tuned x86 assembly -- the very, very large majority of software is not, and the compiled-to-assembly software generally isn't optimized enough to make full use of the hardware, which is the purpose of hyperthreading -- a second process can make use of silicon on one core that a first process simply can't use. Prime95 is the exception to the rule: its hand-tuned assembly is designed to use every bit of silicon to its maximum possible extent, so hyperthreading offers no additional value. Even other software in use on other parts of this forum -- software with inline assembly included in the most critical computational loops , but still mostly written in C -- see a ~30% throughput gain with hyperthreading. Prime95 is very much different than nearly any other software in the world in this respect.
Except Prime95 hasn't (yet) been tuned for Skylake, and therefore if you use Skylake you should try turning on hyperthreading (by adding HyperthreadLL=1 to local.txt) and doing benchmarks with and without this setting. For me it did make a difference.
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Sun Nov 28 17:47:06 UTC 2021 up 128 days, 12:16, 0 users, load averages: 1.44, 1.34, 1.24 | 2021-11-28 17:47:06 | {"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": 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": 0.37094807624816895, "perplexity": 4462.3333646730425}, "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/1637964358570.48/warc/CC-MAIN-20211128164634-20211128194634-00093.warc.gz"} |
https://aiuta.org/en/do-you-add-them-both-together-or-multiply-or-do-u-put-an-equal-sign-between-them-what-is-the-sum-o.41978.html | Mathematics
# Do you add them both together or multiply or do u put an equal sign between them? what is the sum of $\frac{-x+7}{2x+4}$ and$\frac{2x+5}{2x+4}$
### Answers
#### yassautumn
4 years ago
$\frac{-x+7}{2x+4} + \frac{2x+5}{2x+4}=\frac{x+12}{2x+4}$
4 years ago
#### Best answer
$\frac{-x+7}{2x+4}+\frac{2x+5}{2x+4} =\frac{-x+7+2x+5}{2x+4}=\frac{ x+12}{2x+4}$ | 2018-10-23 03:53:13 | {"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": 0.34338971972465515, "perplexity": 9231.974109442508}, "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-2018-43/segments/1539583516003.73/warc/CC-MAIN-20181023023542-20181023045042-00168.warc.gz"} |
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# Common Core Standard 8.G.C.9 Questions
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
You can create printable tests and worksheets from these questions on Common Core standard 8.G.C.9! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.
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What is the volume of a cylinder with a radius of 6 cm and a height of 10 cm? Use pi = 3.14.
1. 1130.4 $cm^3$
2. 1130 $cm^3$
3. 360.8 $cm^3$
4. 600 $cm^3$
Pi $(pi)$ is used when calculating which of the following?
1. area of a circle
2. volume of a sphere
3. volume of a cylinder
4. volume of a cone
5. all of the above
What is the volume of a cone with a radius of 3 feet and a height of 8 feet? (round to nearest tenth if needed)
1. 72.7 $ft^3$
2. 75.4 $ft^3$
3. 226 $ft^3$
4. 84.8 $ft^3$
What is the approximate volume of a cone with a height of 6 cm and a base radius of 2 cm? (Use $pi$ = 3.14).
1. 25 cubic centimeters
2. 23 cubic centimeters
3. 75 cubic centimeters
4. 38 cubic centimeters
A spherical water tower has a diameter of 32 feet. How much water can it hold?
1. 51,471 $ft^3$
2. 17,157 $ft^3$
3. 12,868 $ft^3$
4. 17,158 $ft^3$
What is the approximate volume of a cylinder with a radius of 5 in and a height of 4 in?
1. 63 inches cubed
2. 105 inches cubed
3. 251 inches cubed
4. 314 inches cubed
A conical sand pile has a diameter of 123 feet and a height of 61 feet. How much sand is in the pile?
1. 241,606 $ft^3$
2. 28,942 $ft^3$
3. 2,899,278 $ft^3$
4. 241,607 $ft^3$
A pencil has a diameter of 0.75 cm and a length of 20 cm. How much wood is in the pencil?
1. 26.5 $cm^3$
2. 8.8 $cm^3$
3. 35.3 $cm^3$
4. 6.3 $cm^3$
What is the formula for the volume of a sphere?
1. $V = l xx w xx h$
2. $V = 1/3pir^2h$
3. $V=pir^2h$
4. $V=4/3pir^3$
Ace Canning Company is redesigning its product. The new cans will have twice the radius, but the same height of the original cans. Which statement is true about the volume of the new cans compared to the volume of the original cans?
1. the volumes of the new and original cans will be equal
2. the volume of the new cans will be twice the volume of the original cans
3. the volume of the new cans will be four times the volume of the original cans
4. not enough information to determine
Which of the following will hold the greatest volume?
1. a sphere with a radius of 10 cm
2. a cube with a side length of 10 cm
3. a cone with a radius of 10 cm and a height of 10 cm
4. a cylinder with a radius of 10 cm and a height of 10 cm
What is the approximate volume of a sphere with a radius of 3 ft?
1. 14 cubic feet
2. 113 cubic feet
3. 339 cubic feet
4. 905 cubic feet
What is the formula for the volume of a cone?
1. $V = l xx w xx h$
2. $V = 1/3pir^2h$
3. $V=pir^2h$
4. $V=4/3pir^3$
1. $V = l xx w xx h$
2. $V = 1/3pir^2h$
3. $V=pir^2h$
4. $V=4/3pir^3$
1. $5.0 xx 10^4$ cubic miles
2. $10.0 xx 10^4$ cubic miles
3. $2.6 xx 10^11$ cubic miles
4. $2.1 xx 10^12$ cubic miles | 2017-03-29 01:34:02 | {"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": 0.6110666990280151, "perplexity": 907.1069539369715}, "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-2017-13/segments/1490218190134.67/warc/CC-MAIN-20170322212950-00284-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.cemc.uwaterloo.ca/pandocs/potw/2021-22/English/POTWA-21-A-N-28-S.html | # Problem of the Week Problem A and Solution Aquarium Issues
## Problem
Jacques got an aquarium for his birthday and wants to fill it with some guppies and tetras. Guppies are sold in groups of four and tetras are sold in groups of three. He can buy four guppies for $$\12$$, and three tetras for $$\7$$.
If Jacques spent exactly $$\50$$ on fish, how many of each fish did he buy?
## Solution
Since $$50$$ is not a multiple of $$12$$ or a multiple of $$7$$, then Jacques must have bought some of each fish in order to spend exactly $$\50$$. One way to solve this problem is to make a table to keep track of how much money it costs for multiples of four guppies, and how much of the $$\50$$ would be left to buy tetras.
Number of Guppies Cost for Guppies (in $) Money Leftover for Tetras (in$)
$$4$$ $$1\times 12=12$$ $$50 - 12 = 48$$
$$8$$ $$2\times 12=24$$ $$50 - 24 = 26$$
$$12$$ $$3\times 12=36$$ $$50 - 36 = 14$$
$$16$$ $$4\times 12=48$$ $$50 - 48 = 2$$
Now we look for a multiple of seven in the leftover money, because each group of tetras costs $$\7$$. The only multiple of seven in the leftover money is $$14$$. Since $$14 = 2 \times 7$$, Jacques must have bought two groups of tetras.
This means Jacques bought $$12$$ guppies and $$2 \times 3 = 6$$ tetras. | 2022-05-22 07:05:39 | {"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": 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": 0.24410639703273773, "perplexity": 809.6973242231883}, "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/1652662545090.44/warc/CC-MAIN-20220522063657-20220522093657-00664.warc.gz"} |
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[About The LaTeX Font Catalogue] Text handling with matplotlib's LaTeX support is slower than matplotlib's very capable mathtext, but is more flexible, since different LaTeX packages (font packages, math packages, etc.) typewriter Changing font styles in LaTeX . It was originally an answer to a question on stackexchange . Changing default font typeface. Home / Free Fonts / Decorative Cyrillic Free Fonts / Typewriter Cyrillic and Latin Typefaces. Trending Fonts Home > Tags > Typewriter Hello, you seem to have JavaScript turned off. « MIT Information Systems & Technology website. By default, in standard LaTeXclasses the serif typeface (a.k.a. I have a lot of founts, so I may be a bit misleading here. This is a property of the standard LaTeX typewriter font, Computer Modern, which is also inherited by derivates of Computer Modern such as Latin Modern and Computer Modern Unicode. 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Discussion about LaTeX 's general text formatting features ( e.g type to typewriter can be done two. | 2021-07-24 21:25:13 | {"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": 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": 0.9237895011901855, "perplexity": 7276.652767824124}, "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-2021-31/segments/1627046150308.48/warc/CC-MAIN-20210724191957-20210724221957-00580.warc.gz"} |
https://www.physicsforums.com/threads/question-about-buoyancy.784987/ | 1. Nov 30, 2014
### Graeme M
I recently posted a question about solids that led to a very productive discussion about solids, weight, gravity and pressure. I learned that many intuitive ideas I had about these concepts were wrong and I now have a better understanding as a result. However, in the course of my reading I came across the buoyant force.
Now of course at a general level I know what buoyancy is, but after reading a number of sources it became apparent that it’s much more complicated than I thought.
I now think I have a fair understanding of this force, but there are a few things I can’t get straight in my head, even after reading a lot.
Here’s my understanding, followed by my question. These points are at a very simplified level – that is, a homogeneous liquid, in this case water, with all other forces removed. I am talking about a static situation so I am disregarding flow, drags, and other complicating factors.
1. A submerged object displaces its volume in water.
2. The weight of the water displaced is equivalent to the upward buoyant force on the object.
3. The buoyant force arises from the difference in pressure between the top of the submerged object and the bottom of the submerged object.
4. The pressure in a column of water increases with depth and hence the buoyant force will increase with depth, all other factors remaining equal.
5. The apparent weight of a submerged object is reduced by the magnitude of the buoyant force. Because weight is a force, the net force applied to the object is the difference between its weight and the buoyant force.
6. If an object’s apparent weight is greater than the buoyant force, the object will sink. And vice versa – if less than the buoyant force, the object will rise.
The total apparent weight of a container of water and an object outside of the container of water is the sum of the two weights. If the object is placed in the container of water, the total weight of the container and water is increased by the weight of the object. However the apparent weight of the object, inside the container, is reduced by the buoyant force.
Assuming that the object’s mass and shape is such that the buoyant force is exactly equal to its weight and the object does not sink, the object’s apparent weight in the container will be zero. However, the total system weight of container, water and object is increased by the weight of the object.
What is happening here? The upward force exactly balances the downward force, yet there is still a nett downward force.
2. Nov 30, 2014
### Bystander
What is that "net downward force.?" Reread your excellent essay, and think carefully about all you've said.
3. Nov 30, 2014
### Staff: Mentor
Items 2 and 4 are inconsistent. Item 2 is correct, and item 4 is incorrect.
Regarding your question, if you added water to the container, the total weight of material in the container would increase. If instead you add an object to the container and the object is neutrally buoyant, this would be the same as adding water to the container.
Chet
4. Nov 30, 2014
### Staff: Mentor
We seem to get questions like this a lot. I wonder if schools are doing a poor job of teaching what "net force" is?
1. All forces always come in pairs, if you look hard enough. Typically when people talk of "net force" they are talking about the overall external forces on an object. And when they say the sum is non-zero, that just means they aren't counting the force from inertia and acceleration. So that has nothing to do with the situation here...
2. The internal forces on the floating object don't really need to be considered to determine the the external forces between the container and what is supporting it. You can sum them if you want, to find how the forces are transmitted through the container, but you really don't need to.
3. So if you do want to sum the forces, the upwards force on the object matches the downwards force on the water. Right. But that isn't a "net force" of zero because the two forces are acting on different things -- one acts on the water, the other on the object. Net force is all forces on one "object" summed together. So the water and object in it have other forces on them....
5. Nov 30, 2014
### Graeme M
Chestermiller, I get that in terms of weight for the whole container, adding water or a solid of same weight has the same effect.
However adding water results in no buoyant force whereas adding a solid object does. In the former case there is no other force involved, while in the latter there is but it doesn't matter whether it is nett up, down or neutral. The buoyant force affects apparent weight of the object, but not the whole system.
In other words, the buoyant force can be of any magnitude yet the total system weight is not changed. I can't get my head around that.
6. Nov 30, 2014
### Graeme M
Also, are you saying that my number 4 is wrong because the pressure differential between upper and lower surfaces remains the same regardless of depth and pressure? I did read on some science site somewhere that an object can sink until a point at which the buoyant force is sufficient to offset the weight, so that surely would arise from the change in pressure?
7. Nov 30, 2014
### Graeme M
russ_watters, you say
"So if you do want to sum the forces, the upwards force on the object matches the downwards force on the water. Right. But that isn't a "net force" of zero because the two forces are acting on different things -- one acts on the water, the other on the object. Net force is all forces on one "object" summed together. So the water and object in it have other forces on them...."
But the downwards force is on the object (gravity), and the upwards force is on the object (buoyancy). The upwards force isn't matching a downwards force on the water?
8. Nov 30, 2014
### Staff: Mentor
Incorrect. What do you think keeps a parcel of water at the surface from sinking?
Right.
That would be rare, but it would be because water isn't quite incompressible. So its density increases a little with depth. More common, though, is the opposite: as objects sink, they get compressed and become less buoyant. That's a problem for scuba divers: they have to continuously adjust their buoyancy to avoid sinking to the bottom or shooting to the surface.
Well sure it is: what force moves the water out of the way for the object to replace it?
9. Dec 1, 2014
### Graeme M
What keeps a parcel of water from sinking?
Hmmm... I wouldn't have thought of it like that! My thinking would say this. Water is a single thing much like a solid. The solid retains its form and shape from the bonds that hold its molecules/atoms in place. I understand that water is similar but that its bonds are not so resilient - that is, water molecules constantly create and break their bonds. So in effect water has the same form as a solid but its shape is flexible. What keeps the water at the top above the water at the bottom is the attractive/repelling forces. In fact I'd have thought that in the absence of currents etc, ie an entirely still column of water, there'd be no specific buoyany force as such, just the same forces that keep a solid together.
So... Are you saying that the buoyant force is simply the same force that keeps molecules/atoms apart? That is, repelling forces at the molecular level? So buoyancy is no more than the effect of two objects with defined form interacting.
That would explain how lowering an object into a container of water reduces the apparent weight of the object while increasing the apparent weight of the container of water. In effect, it would be similar to sliding say a brick across the upper surface of two other bricks - if a a scale were under each of the two lower bricks, the gaining brick will increase in weight proportionally to the rate at which the other brick loses weight.
10. Dec 1, 2014
### Staff: Mentor
No, that has nothing to do with buoyant force. The "parcel of water" thought experiment is simply for this: instead of pouring more water into the container, put the additional water in a plastic bag and put that bag into the container. What happens and why?
11. Dec 1, 2014
### Graeme M
OK... not sure I see the relevance. You have introduced a surface. A plastic bag filled with water is effectively no different to a solid object of equivalent mass. The water in the container cannot know that behind the surface lies more water. The bag filled with water will displace an equivalent volume of water in the container and the buoyant force will equal the weight of that volume of water. Providing your bag has thin walls, the total weight of the bag and water should be very similar to the buoyant force and the bag should float just under the surface. If though your bag has very thick walls, its overall weight may overcome the buoyant force and it will sink (here I am assuming something about the relative densities of plastic and water. And the shape of the bag.).
I don't see that tells me anything about the behaviour of a body of water.
12. Dec 1, 2014
### Sanky123
Good example
13. Dec 1, 2014
### Staff: Mentor
The point of the example is that the parcel of water behaves the same whether the bag is there or not. The bag is just an arbitrary boundary around an arbitrary volume of water, which has no impact on how you conceive the effects of buoyancy.
That idea becomes more useful when the parcel of water becomes warmer or cooler than its surrounding water and its net force changes. Or better yet, air in the atmosphere. Changes in buoyancy/density drive convection, which in the atmosphere drives the weather.
Last edited: Dec 1, 2014
14. Dec 1, 2014
### sophiecentaur
If you are having a problem with the concepts involved then perhaps you could work out a specific example (say a disc of wood of density 0.8) and a 1l beaker of water. (Choose some disc and beaker dimensions.) Put the two, side by side, on the platform of some scales. Now put the disc in the water.and, bearing in mind the total measured mass much be the same, work out the forces on the disc (once it has stopped moving) and the pressures in the water, at the new level. It's all got to work out so just find what you need to add to what to get it to balance. Actually, Archimedes' Principle is a half way house in the argument.
You have either discovered an Earth-shattering fact, hitherto unknown to mankind OR you have got your reasoning wrong, somewhere. Assume the latter. :)
15. Dec 1, 2014
### Staff: Mentor
Not that Russ needs my help, but I fully support what he is saying. The water surrounding the bag doesn't know whether there is a bag full of water there, a solid object of the same shape there, or water with no bag around it filling the same space. In all three situations, the hydrostatic pressure forces exerted by the surrounding water cause the same upward force on whatever is filling that space.
Chet
16. Dec 1, 2014
### Graeme M
Haha SophieCentaur, if ever I worked out an earth shattering fact no-one else had, it'd be the greatest miracle in history. I'm flat out figuring out how to get out the door each morning!
Now, to my mind there's a couple of things here, which may be just too hard for me to put into words. Chestermiller I disagree with what you say. Not because I am right and you are wrong, but because what you say makes no sense to me. Of course the problem is I just don't have the breadth of education, but I'm game to take a stab at this.
There is no 'parcel' of water. The buoyant force surely depends on there being a physical surface. If you just have water, there can be no surface - that is, if you examine any section of a still body of water it should look exactly the same as any other.
So the forces involved must be only those forces that inhabit any body. On the other thread, I learned that bonding forces - attractive/repelling - are what keep a solid, solid. A liquid has exactly the same internal forces at the molecular level, except (as I understand it) that the bonds are more short-lived. So in a way, a liquid is a very flexible solid.
What keeps water 'up' is the same thing that keeps the top of a solid 'up', surely? Ignoring currents and temperature and so on, a still cylindrical container of liquid must be broadly the same thing as a solid cylinder. Differences in density of the liquid just give rise to a different profile as the matter responds to gravity.
On the other thread I learned that the atmosphere has a pressure gradient as a response to gravity. So if we had two liquids mixed, one denser than the other, then the more dense will obviously sink to the bottom and the lighter one will be on top. But that is just a response to gravity is it not? It's not the buoyant force at work.
The imaginary parcel is just that. I can see how it's a useful model, but I think it's misleading. I can see how a solid object in a liquid can have a 'buoyant force' operating on it, but I cannot see how an arbitrary chunk of water in a body of water can have anything other than the normal molecular level forces acting on it.
17. Dec 1, 2014
### Khashishi
Regarding your original question, the mass of the full system clearly increases when you add more objects. The mass of the system is simply the sum of all the masses in the system. The apparent weight only matters when measuring the weight submerged in some fluid. If you put your scale outside of the fluid and measure the weight of the whole container, there is no buoyant force so you feel the full weight.
18. Dec 1, 2014
### nasu
It seems that at least part of your original problem relies on the assumption that the zero net force on the body is not compatible with the expected total weight.
In order to see that this is not realy a problem, you can take a step back and consider the following configuartion, which have nothing to do with buoyant forces.
1. What weight is measured by the spring scale?
2. What is the net force on the block on the right? (or on the left)
19. Dec 1, 2014
### A.T.
The total buoyant force on the solid object is just the sum of all molecular level forces exerted on it by the water.
20. Dec 1, 2014
### Staff: Mentor
OK GraemeM, I hear you. Let me first say that I still stand by what Russ and I have been saying and am confident in it, even regarding masses of liquid immersed within a larger body of the same liquid. However, I obviously have not done a good job of explaining the fundamentals of buoyancy to you. So, if it is all right with you, I would like to take a step backwards and, for now, confine attention exclusively to solid bodies of arbitrary shape immersed within a surrounding liquid. We will be focusing on determining the net force exerted by the surrounding liquid on the solid body. We are going to be doing some modeling to quantify the force. (Later we'll come back to fluid parcels).
I assume you are familiar with hydrostatics, and in particular, the equation for the fluid pressure p at a depth z below the air interface: $$p=p_a+\rho g z$$
where pa is the air pressure, ρ is the fluid density, and g is the acceleration of gravity.
Are you also familiar with Pascal's Law indicating that the pressure p acts equally in all directions at a given location in a fluid? This means that if there is an object immersed in a fluid, the pressure acts normal to the surface of the object at all locations on the surface.
I will continue after getting confirmation that you are comfortable with both these concepts.
Chet | 2017-11-21 14:34:42 | {"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": 0.4962710738182068, "perplexity": 418.65638021553855}, "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/1510934806388.64/warc/CC-MAIN-20171121132158-20171121152158-00243.warc.gz"} |
https://wiki.idec.io/team_wiki/operations/ | Common operations in MkDocs
In this section, please make sure you have the live server up and running.
You can refer to the previous page [Set up a Docker container for wiki editing] for the instructions.
Configure the wiki name
The default wiki name we give our template repository is "iDEC HQ Team Wiki Example".
To change it to a new name, use a plain text editor to open the file: mkdocs.yml
Look for the following configuration:
site_name: iDEC HQ Team Wiki Example
and change it to:
site_name: iDEC 2021 Mock Team Wiki
Refresh the live server, notice that 3 things should have changed:
• browser tab title
Attention
It is possible to change the favicon and icon of the wiki in mkdocs.yml.
However, if your team decide to use MkDocs for Material, or other static site generators with templates, we politely request that your use the iDEC favicon and logo, and keep our copyright statement. This is to show that your team wiki is part of iDEC. Thank you.
If you click on the "Protocol" or the "Notebook" link in the navigation menu, you will land on to a 404 - Not found page.
We will fix this now. Using an IDE or a text editor, open the mkdocs.yml file.
Look for the following configuration:
nav:
- Home: index.md
- Background: background.md
- Results: results.md
- Protocols: protocols.md
- Lab notebook: notebook.md
- Some useful features: useful_features.md
Danger
Failure to follow the proper use of whitespaces in each list item will result in links not being properly rendered.
Comparing this section with the navigation menu, you can see that, for each indented list item, the key (text before colon :) is the link label, and the value (text after colon) corresponds to the file path, which is relative to the docs/ folder.
The files for "Protocols" and "Notebook" actually exist - they are just sitting in the directory docs/documentation/.
.
└─docs
└─documentation
├─notebook.md
└─protocols.md
So the solution is to fix the mkdocs.yml file, nav section as follow:
nav:
- Home: index.md
- Background: background.md
- Results: results.md
- Protocols: documentation/protocols.md
- Lab notebook: documentation/notebook.md
- Some useful features: useful_features.md
If you have a lot of pages, you might want to group them together.
In the nav section inside the mkdocs.yml file, make the following change:
nav:
- Home: index.md
- Project:
- Background: background.md
- Results: results.md
- Documentation:
- Protocols: documentation/protocols.md
- Lab notebook: documentation/notebook.md
- Some useful features: useful_features.md
Return to the browser. The menu should now have 3 levels, and can collapsed or expanded at different levels.
Two important things to note in mkdocs.yml:
1. The subsection must have a header but without a file path1
2. Under the subsection, the list item is indented to the right by exactly 4 whitespaces
Tip
Structuring your Markdown file locations and the navigation menu in the same way is highly recommended, since it will help your collaborators / teammates to find the location of the file much more easily.
Note
The structure here is only for the illustration of increasing page depth. In general, we recommend that teams limit their wiki page depth to only 2 levels.
You will also notice that for your assigned team repository, your 2nd level pages are grouped under section headers instead. That is because we enabled the feature Navigation Sections in mkdocs.yml, which is more user-friendly when the total number of pages is small.
You will now add an image to the wiki, similar to how you would add figures for illustrations and results. Save a dummy image under the directory docs/img and name it as dummy.png
Then, edit docs/results.md, and add the following code underneath the existing texts:
{ width=800px }
Return to the browser. You should now see the image being shown on the "Results" page.
While the size of the figure was 600 pixels x 400 pixels, on the page it is stretched to 800 pixels in width. You can modify the image size by the attributes tag2 after the normal Markdown syntax for image insertion.
Self-practice
Why not try creating a page called "Our Team", list your iDEC teammates and add their photos?
In some cases you might have some information that are simply too long to be part of a webpage. Instead of displaying its full content, you might want to generate a link to the downloadable file instead. This can be done by placing the file somewhere under the docs folder and then pointing a hyperlink to it.
Inspect the directory docs and you will see:
.
└──docs
├─documentation
│ ├─notebook.md
│ └─protocols.md
└─notebooks
├─MCLONE001.pdf
└─EVOLVE001.pdf
Assuming these are exported electronic notebook files, you will now create links to them on the page
"Project -> Documentation -> Notebook", or,
http://localhost:8000/documentation/notebook/
Use a text editor and open docs/notebook.md, then insert the following lines underneath the existing content:
- [MCLONE001: Plasmid construction for DE of GFP](../notebooks/MCLONE001.pdf){: target="_blank" }
- [EVOLVE001: Directed evolution on GFP](../notebooks/EVOLVE001.pdf){: target="_blank" }
So for the relative path ../notebooks/MCLONE001.pdf, it works as follow: 1. Starts from docs/documentation where notebook.md is located 2. ../ = goes up 1 level to docs 3. notebooks/MCLONE001.pdf = goes into the notebooks folder and locate the MCLONE001.pdf file.
This relative path will work both on your location machine as well as the deployed GitHub Pages.
Return to the browser and go to "Notebook" page, you will now find two links. Click on any of them and you should see a new tab with the PDF file showing up.
Tip
Upload your files in formats that are OS-agnostic and not dependent on proprietary software. For example, use PDF instead of Word documents or Powerpoint files.
Embed a video
Use of multimedia faciliates scientific communication to the lay public. To embed a video, use of HTML is necessary.
You already have a cover image in the repository.
Then save the file as iDEC_video.mp4 under the docs/assets directory:
.
└──docs
├─assets
│ └─iDEC_video.mp4
└─img
└─video_cover.png
To embed this on the "Home" page, open a text editor, insert the following code into the end of the file docs/index.md and save the file.
<video controls width="600px" poster="img/video_cover.png">
<source src="assets/iDEC_video.mp4" type="video/mp4">
</video>
In the code above, the poster attribute in the <video> element has a relative path pointing to the cover image of the video.
The src attribute (which is a shorthand for "source") in the <source> element has a relative path pointing to the video itself.
Return to the browser and go to Home (localhost:8000), you will see the video being embedded.
Attention
Make sure each individual file (whether document or video) does not exceed 100 MB in size, which is the limit for hosting by GitHub. Also, you should keep the size of your repository within 1 GB.
1. Check out the Material for MkDocs reference on how to enable section index pages. This is however not recommended from a UX design perspective.
2. Material for MkDocs reference on images | 2022-12-07 20:56:31 | {"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": 0.341876745223999, "perplexity": 4536.847043244871}, "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-2022-49/segments/1669446711218.21/warc/CC-MAIN-20221207185519-20221207215519-00244.warc.gz"} |
http://mathoverflow.net/questions/127820/approximating-rational-generating-functions | # Approximating rational generating functions
Suppose we have a initial segment $x_1,\ldots,x_N$ (for reasonably large $N$) of a sequence of natural numbers $(x_i)$. We have reason to believe the generating function $\sum_{i=0}^\infty x_iX^i$ is rational. Are there any methods one could use to guess/approximate this generating function as a quotient of polynomials $P(X)/Q(X)$ with small degrees (relative to $N$).
-
## 1 Answer
This is called Padé approximation. There are several computer packages that can do that, in particular GFUN (Salvy and Zimmermann) for maple, Guess (Kauers) for mathematica, in FriCAS it's built-in (the function is called guessPade). You can access the latter also from sage, although very likely there is something built-in too.
- | 2015-03-06 22:00:36 | {"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": 0.744490385055542, "perplexity": 320.14315153531953}, "config": {"markdown_headings": true, "markdown_code": false, "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-2015-11/segments/1424936471203.9/warc/CC-MAIN-20150226074111-00305-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.gamedev.net/forums/topic/555233-noob-question-/ | # Noob question.. ,
This topic is 2996 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
// Hello planet #include <iostream> using namespace std; int main () { cout << "Hello World!"; return 0; } Whenever I try run this, it fails.. Is something wrong with the coding?
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It appears to be working fine,
although you may wish to write this line of code instead:
std::cout << "Hello World!"<<std::endl;
this just ensures that Hello World! is printed on a line separate from your terminal/cmd call line.
If it's still not working, check out how you are compiling the program.
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I don't think it fails, it just does it so fast that it just opens up and shuts down.
you might want something like this:
// Hello planet
#include <iostream>
using namespace std;
int main ()
{
cout << "Hello World!";
system("PAUSE");
return 0;
}
though I suggest you avoid using system("Pause") when ur programming for real because it takes a lot of memory or something. cin.get() would probably work better.
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How do you "try to run it"?
How does "it fail"?
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Yea that works fine. If you do the whole std::cout and std::endl then you won't need the line of code "using namespace std;"
I wouldn't use system("PAUSE")though.
Try using cin instead or if in visual studio you can do "Start without Debugging" under Debug. That should work (Just make sure it builds okay though)
As for failing, what are the errors? Or what happens?
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What do you have against system("pause"); ?
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I believe its cuz system("PAUSE"); is not very effecient in terms of speed and memory speed.
http://www.gidnetwork.com/b-61.html
it's a link describing why you should avoid it and alternate methods such as cin.get()
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Hmm, I thought the code was correct.
After trying to run at the bottom it says
"========== Build: 0 succeeded, 1 failed, 0 up-to-date, 0 skipped =========="
And nothing happens >,>
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Quote:
Original post by Mr_FayceHmm, I thought the code was correct.After trying to run at the bottom it says"========== Build: 0 succeeded, 1 failed, 0 up-to-date, 0 skipped =========="And nothing happens >,>
And what does it say above that? Why is it failing to build?
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Copy and pasted;
1>------ Build started: Project: fdsgafdg, Configuration: Debug Win32 ------
1>Compiling...
1>fdsgafdg.cpp
1>c:\users\mr_fayce\documents\visual studio 2008\projects\fdsgafdg\fdsgafdg\fdsgafdg.cpp(4) : warning C4627: '#include <iostream>': skipped when looking for precompiled header use
1>c:\users\mr_fayce\documents\visual studio 2008\projects\fdsgafdg\fdsgafdg\fdsgafdg.cpp(15) : fatal error C1010: unexpected end of file while looking for precompiled header. Did you forget to add '#include "stdafx.h"' to your source?
1>Build log was saved at "file://c:\Users\Mr_Fayce\Documents\Visual Studio 2008\Projects\fdsgafdg\fdsgafdg\Debug\BuildLog.htm"
1>fdsgafdg - 1 error(s), 1 warning(s)
========== Build: 0 succeeded, 1 failed, 0 up-to-date, 0 skipped ==========
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Turn off precompiled headers. The stadfx thing came up a few times when I was messing with sfml. I assume this is a windows console program? Anyway, turning off precompiled headers should work
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I haven't used Microsoft Visual cpp for a while, but I notice the compiler is complaining a lot about stdafx.h. I think there is an option to create a completely blank console project instead of using a precompiled header i.e. stdafx.h (I think it might be a checkbox in the new project dialogue). Try finding this then pasting your code into the new project and recompiling it.
Quote:
Original post by Atrix256What do you have against system("pause"); ?
system("PAUSE"); will only work on Windows, so it isn't portable. Also, the command "pause" just runs a program that waits for input to continue, so there is a possibility that this program can be replaced with malicious code.
I don't think that is very likely but it's still better practice to use something more like:
#include <iostream>#include <string>using namespace std;int main (){cout << "Hello World!" << endl;//system("PAUSE"); Don't use thiscout << "Press enter to terminate the program" << endl;std::string myString;getline(cin, myString);return 0;}
That said, for beginners it's generally fine to use system("PAUSE"); on their own machines until they get the hang of other methods. I'm only a beginner too :)
Hopefully this helps, good luck!
P.S. It's a good idea for you to get into the habit of placing your code in source tags when posting it (see the forum faq). Folk around these parts get cranky if you don't :)
[Edited by - chrisparton1991 on December 4, 2009 7:05:57 PM]
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I have a problem with cin.get()... If i have a cin >> VARIABLE right before it, it skips it... I just use system("PAUSE"); for now, but im not doing any complex programs yet... But yeah it always skips te cin.get(); whenever I use it like its not there...
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How can a pause be horribly inefficient in speed? I never understood that.
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Quote:
Original post by MAGIgullorksI have a problem with cin.get()... If i have a cin >> VARIABLE right before it, it skips it... I just use system("PAUSE"); for now, but im not doing any complex programs yet... But yeah it always skips te cin.get(); whenever I use it like its not there...
I think the reason it skips is because there is a return left in the stream. (The return you pressed earlier doesn't get removed automatically)
You should be able to remove the remaining return using cin.ignore(...), however using cin's operator >> is too low level when reading input from the users, you are better of using getline(cin, ...) instead. The getline function should take care of removing the remaining return as well.
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Quote:
Original post by CzarKirkHow can a pause be horribly inefficient in speed? I never understood that.
lol
The way I see it using system("PAUSE") is syntactically sluggish. A bit like shooting sparrows with a cannon. It will schedule a new process and it is not portable.
If you'r fine with all that I see no reason not to use it.
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Don't pause your program artificially at the end, in any manner. Learn to run it properly, instead. Use a batch script, run it from the command line, set a breakpoint on the last line, whatever is appropriate.
A pause makes for sloppy design because it's an extra step the user has to deal with. It makes it harder to integrate your program with others in batch scripts and looks ugly when the user *is* running the program from the command line (because it's unnecessary and doesn't make sense in context). Of course, none of these things are likely to matter for games, but it's good to take the opportunity to learn good design early.
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Quote:
Original post by pulpfist
Quote:
Original post by CzarKirkHow can a pause be horribly inefficient in speed? I never understood that.
lol
The way I see it using system("PAUSE") is syntactically sluggish. A bit like shooting sparrows with a cannon. It will schedule a new process and it is not portable.
If you'r fine with all that I see no reason not to use it.
The problem with system( "PAUSE" ) is that it is equivalent to opening a console and typing "pause" (try it!) But what if I, as an evil, malicious user created a file with something like
@format c: /quiet
called it "pause.bat" and placed it in the same folder as you're program?
Now, it is highly unlikely that this would actually happen, but it's a good idea to be defensive and there are better solutions to pausing (some of which has already been posted in this thread.)
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Quote:
Original post by Promethium
Quote:
Original post by pulpfist
Quote:
Original post by CzarKirkHow can a pause be horribly inefficient in speed? I never understood that.
lol
The way I see it using system("PAUSE") is syntactically sluggish. A bit like shooting sparrows with a cannon. It will schedule a new process and it is not portable.
If you'r fine with all that I see no reason not to use it.
The problem with system( "PAUSE" ) is that it is equivalent to opening a console and typing "pause" (try it!) But what if I, as an evil, malicious user created a file with something like*** Source Snippet Removed ***called it "pause.bat" and placed it in the same folder as you're program?
Now, it is highly unlikely that this would actually happen, but it's a good idea to be defensive and there are better solutions to pausing (some of which has already been posted in this thread.)
drobole@fluxbox:~$pause-bash: pause: command not founddrobole@fluxbox:~$
It's lack of portability saved me(!)
You have a good point though.
Reminds me of the old 'ls' hack from the days when root's PATH still contained the current directory (.) on linux systems | 2018-02-18 11:30:42 | {"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": 0.23382580280303955, "perplexity": 3607.7523817191254}, "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/1518891811830.17/warc/CC-MAIN-20180218100444-20180218120444-00682.warc.gz"} |
https://www.physicsforums.com/threads/how-to-find-the-domain-in-one-dimension.371538/ | # How to find the domain in one dimension
1. Jan 21, 2010
### tomfrank
1. The problem statement, all variables and given/known data
I am trying to find the domain of the following..
R^2 to R^3 of g(x,y) = (x-y,x+y,3*x)
R^3 to R of h(x,y,z) = x/(y+z)
2. Relevant equations
3. The attempt at a solution
I don't know how to start. I know how to find the domain in one dimension but how do you do it in 2 or 3 dimensions???
Thanks
Last edited: Jan 21, 2010
2. Jan 21, 2010
### Dick
Re: Domain
Your second function is actually R^3->R. Since they didn't tell you what the domain is, you just want to pick the domain of f:A->B to be all of the points in A where the function is defined.
3. Jan 21, 2010
### tomfrank
Re: Domain
so for the first one can just do from (-infinity to infinity) ????
can i just put in any value of x i want to?
4. Jan 21, 2010
### Staff: Mentor
Re: Domain
For the first one, your domain is not just R, the real line; it's the real plane, R2. For the second one, there is a restriction on y and z.
5. Jan 21, 2010
### Dick
Re: Domain
Basically, yes. But the domain isn't (-infinity,infinity), that's a subset of R. The domain should be a subset of R^2. How about saying it's ALL of R^2?
6. Jan 21, 2010
### tomfrank
Re: Domain
So the first one domain = R^2 the real plane
second one = is y+z not equal to '0'
is that right?
7. Jan 21, 2010
### Staff: Mentor
Re: Domain
Yes, pretty much. You can say it a little nicer as
$$\{(x, y, z)\in R^3 | y + z \neq 0\}$$.
8. Jan 21, 2010
### tomfrank
Re: Domain
that looks nice thanks | 2017-10-23 19:43:04 | {"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": 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": 0.49854981899261475, "perplexity": 1848.4610060867224}, "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-2017-43/segments/1508187826283.88/warc/CC-MAIN-20171023183146-20171023203146-00277.warc.gz"} |
https://www.gradesaver.com/textbooks/engineering/mechanical-engineering/engineering-mechanics-statics-and-dynamics-14th-edition/chapter-19-planar-kinetics-of-a-rigid-body-impulse-and-momentum-section-19-2-principle-of-impulse-and-momentum-problems-page-535/10 | ## Engineering Mechanics: Statics & Dynamics (14th Edition)
$t=0.6125s$
First we apply the principle of angular impulse and momentum to figure (1) $I_{\circ}\omega_1+\Sigma \int_{t_1}^{t_2} M_{\circ} dt=I_{\circ} omega_2~~~$[eq(1)] We know that $I_{\circ}=m_A k_{\circ}^2=(30)(0.125)^2=0.4688Kg\cdot m^2$ and $\omega_1=0$ $\omega_2=20 rad/s$ Similarly, $\int_{t_1}^{t_2} M_{\circ}= Frt=(0.15)Ft$ We plug in the known values in eq(1) to obtain: $0+0.15Ft=0.4688\times 20$ $Ft=62.5067N\cdot s$ Now, we apply the principle of angular impulse and momentum to figure (2) $m_Av_{B_1}+\Sigma \int_{t_1}^{t_2} M_{\circ} dt=m_Bv_{B_2}~~~$[eq(2)] Now, $v_{B_1}=r_B\omega_1=0$ and $v_{B_2}=r_B\omega_2=(0.15)(20)=3m/s$ Similarly, $\int_{t_1}^{t_2} M_{\circ} Pt-Ft=200t-62.5067$ We plug in the known values in eq(2) to obtain: $0+200t-62.5067=20(3)$ This simplifies to: $t=0.6125s$ | 2020-07-09 08:03:45 | {"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": 0.976991593837738, "perplexity": 311.3497212638861}, "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/1593655899209.48/warc/CC-MAIN-20200709065456-20200709095456-00570.warc.gz"} |
https://www.physicsforums.com/threads/probability-derangement-gambling-problem.843039/ | # [Probability] Derangement / gambling problem
Tags:
1. Nov 13, 2015
### goraemon
1. The problem statement, all variables and given/known data
Alice proposes to Bob the following game. Bob pays one dollar to play. Fifty balls marked 1, 2, . . . , 50 are placed in a big jar, stirred around, and then drawn out one by one by Zori, who is wearing a blindfold. The result is a random permutation (let's call it s) of the integers 1, 2, . . . , 50. Bob wins with a payout of two dollars and fifty cents if the permutation s is a derangement, i.e., s(i) =/= i for all i = 1, 2, . . . , n. Is this a fair game for Bob? If not, how should the payoff be adjusted to make it fair?
2. Relevant equations
Derangement formula: ∑(k=from 0 to n) [(-1)^k * C(n,k) * (n-k)!]
3. The attempt at a solution
I got this far:
Probability that any given random permutation is a derangement:
(num of all derangements) / (num of all permutations) = ∑(k=from 0 to n) [(-1)^k * C(n,k) * (n-k)!] / 50! ≈ 1/e
Then, computing the expected win/loss, given that he gains $2.50 (for a net profit of$2.50 - $1 -$1.50) if he wins, and is out \$1.00 if he loses:
1.5(1/e) - 1(1-1/e) ≈ -0.08. (so on average, he'll lose roughly 8 cents per play)
Solving for the adjusted payment amount so that he'll break even in the long run...
(p-1)(1/e) - 1(1-1/e = 0
Solving for p, we get: p ≈ e
First, is the above correct? Right now I settled for an approximate answer (e) as the derangement equation seemed too messy to compute an exact answer. Is there a simpler way to get an exact answer? Thanks.
2. Nov 13, 2015
### Ray Vickson
As Feller (Introduction to Probability Theory, Vol. I) points out, the probability that in a permutation of $n$ numbers exactly $k$ of the numbers match (that is, we have $s(i) = i$ for $k$ of the numbers from $1$ to $n$) is
$$P(k \; \text{matches}) = \frac{1}{k!} \left( \frac{1}{0!} - \frac{1}{1!} + \frac{1}{2!} - \cdots \pm \frac{1}{(n-k)!} \right).$$
In particular, for $k = 0$ and $n = 50$ we get your probability of a derangement (0 matches) as
$$P(\text{derangement}) = 1 - 1 + \frac{1}{2!} - \frac{1}{3!} + \cdots + \frac{1}{50!}$$
This, of course, is the first 51 terms in the series expansion of $e^{-1} = 1/e$, and because you have an alternating series, the error made in stopping the computation of $1/e$ at $1/50!$ is smaller than $1/51! \approx 0.6446959640\, 10^{-66}$. So, your error in replacing the answer by $1/e$ is not too bad. Admittedly, this is an approximation, but the error would only show up at the 66th or 67th decimal place, if that is what you were worrying about.
Last edited: Nov 14, 2015 | 2017-08-21 18:36:08 | {"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": 2, "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": 0.9179950952529907, "perplexity": 783.2469345640396}, "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/1502886109470.15/warc/CC-MAIN-20170821172333-20170821192333-00196.warc.gz"} |
http://ckms.kms.or.kr/journal/view.html?doi=10.4134/CKMS.c180290 | - Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
On the density of various shadowing properties Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 981-989 https://doi.org/10.4134/CKMS.c180290Published online July 31, 2019 Namjip Koo, Nyamdavaa Tsegmid Chungnam National University; Mongolian National University of Education Abstract : In this paper we deal with some shadowing properties of discrete dynamical systems on a compact metric space via the density of subdynamical systems. Let $f : X \to X$ be a continuous map of a compact metric space $X$ and $A$ be an $f$-invariant dense subspace of $X$. We show that if $f|_A:A\to A$ has the periodic shadowing property, then $f$ has the periodic shadowing property. Also, we show that $f$ has the finite average shadowing property if and only if $f|_A$ has the finite average shadowing property. Keywords : periodic shadowing, finite average shadowing, invariant dense subset MSC numbers : Primary 37C50, 54H20, 37B99 Downloads: Full-text PDF Full-text HTML | 2019-12-13 21:28:46 | {"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": 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": 0.4538903832435608, "perplexity": 1257.180567164054}, "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/1575540569146.17/warc/CC-MAIN-20191213202639-20191213230639-00544.warc.gz"} |
https://brilliant.org/problems/a-calculus-problem-by-siddharth-bhatt/ | # Is there an indefinite integral for this?
Calculus Level 4
$\large \displaystyle\int_0^{\infty}\frac{x^4e^x}{(e^x-1)^2} \, dx$
The integral above equals to $$\frac ab \pi^4$$ for coprime positive integers $$a,b$$ and that you're given $$\displaystyle \sum_{j=1}^\infty \frac1{j^4} = \frac{\pi^4}{90}$$.
Find $$a+b$$
× | 2017-01-21 17:49:38 | {"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": 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": 0.8681783676147461, "perplexity": 1116.1263289619094}, "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-2017-04/segments/1484560281162.88/warc/CC-MAIN-20170116095121-00092-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://in9design.com.br/i1sa3t/0c0ae6-latex-workshop-latex-recipes-location | # This is the default blog title
This is the default blog subtitle.
## latex workshop latex recipes location dez 30, 2020 Sem categoria
Just define your command along with its arguments using the following two configuration variables. Exclude log messages that matches the given regexp from the problems panel. The only difference being that I wanted the PDF preview to be displayed in an external editor. Once the root file is determined, it is parsed to discover all the files it includes using input, include, InputIfFileExists, subfile, import and subimport and the process goes on recursively. The tools in recipes can be defined in latex-workshop.latex.tools, in which each command is a tool. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. // By default, the first recipe is used to compile the project. It is possible to terminate the current compilation by calling Kill LaTeX compiler process from the Command Palette (command latex-workshop.kill) or calling Terminate current compilation from the TeX badge in the Build LaTeX project item. All LaTeX documents have a (non-blank) file that ends with .tex, which is the "main" file that has all of the text of the document. Move TypesetArg to types/mathjax-node/index.d.ts. Placing the code above to settings.json won't solve the problem. I got it working on Windows, on my Linux machine I am still facing some issues. The minimal time interval between two consecutive auto builds in milliseconds. Its default value is given by. An online LaTeX editor that's easy to use. Of course, as soon as I tried to compile a non-trivial sample document, compilation failed. Features for a targeted audience are available through extensions. Skip to main content. The non-interactive functions autobuild, autoclean and forward synctex rely on the value of the configuration variable latex-workshop.latex.rootFile.useSubFile to choose between the main file and the subfile. See here. Define which recipe is used by the Build LaTeX project command. The associated internal command latex-workshop.clean is bind to ctrl+alt+c. Upon building the project, LaTeX Workshop will parse the root file and figure out that xelatex should be used. From anecdotal evidence engineers tend to carefully evaluate a tool before including it into their standard toolkit. LaTeX log parser, with errors and warnings in LaTeX build automatically reported in VS Code. Notice that, in the property, only placeholders, e.g., %DIR%, take effect, and other variables, e.g., \$PATH, are not expanded. Intellisense, including completions for bibliography keys (\cite{}) and labels (\ref{}). add option to launch with a sample TeX file. Latex Workshop was able to find this one (the installer had automatically added it to the Path). For more details on glob patterns, see here. You must reload VSCode to take into account a change in this configuration. Head over to LaTeX Workshop and click install. download the GitHub extension for Visual Studio. Optionally display the compilation progress in a pop-up notification dialogue. When using auto-build and the file has not been compiled inside the extension yet, we use the first recipe with name (converted to lowercase) containing either jnw or jlweave. For a better handling of the last item, hitting Enter on a line only containing \item or \item[] actually deletes the content of the line. The former approach using \ has been deprecated. Are you on Windows? And is only for the pdf latex recipe. For non-perl users, the following texify toolchain from MikTeX may worth a try: The args and env parameters can contain symbols surrounded by %. It can also be called as a document preparation system. As discussed in 1932, this option breaks makeindex (this should be solved in the next release of latexmk). You can also override the PATH environment variable. Note that it must contain the file to proceed. Some letters have variants, which are available as @v + letter. If the messages displayed in the panel seem to be wrong, see the FAQ. Display warning messages in popup notifications. Jump to: navigation, search. LaTeX Workshop registers the following placeholders. We have to remove process.versions.electron to work around a bug of…, enable esModuleInterop in tsconfig.json, which is necessary to compil…, Surrounding selection with an environment, https://github.com/James-Yu/LaTeX-Workshop. I just recently set up VS Code + LaTeX pretty much how you described (via Latex-workshop). LaTeX Tutorial: How to use LaTeX. The alt+Enter is bind to the standard newline command. The env entry is a dictionary. It can be customized using the following configuration variables, Files associated to the jlweave language mode can be compiled using two different approaches, depending on how you would like code to be rendered, Using the Verbatim environment. LaTeX is a markup language used for writing documents such as papers, books, scientific articles, thesis, etc. . However, following the discussion in 1895 we decided that all paths should be relative to the root file directory. The manual of the extension is maintained as a wiki. Bonne lecture! This can be defined in latex-workshop.latex.autoBuild.run. When the current line starts with \item or \item[], hitting Enter automatically adds a newline starting in the same way. If such comments exist in the currently active editor, the referred file is set as root. Recipes are refered to by their names as defined in latex-workshop.latex.recipes. Pastebin is a website where you can store text online for a set period of time. I had the same problem and after looking like crazy on the internet I found the solution. The first one containing \begin{document} and which includes the file in the active editor is set as the root file. The preamble is used in "full blown" LaTeX, but not in the
Call Now Button | 2021-04-20 23:00:00 | {"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": 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": 0.8588729500770569, "perplexity": 2707.0084057454806}, "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-2021-17/segments/1618039491784.79/warc/CC-MAIN-20210420214346-20210421004346-00574.warc.gz"} |
https://socratic.org/questions/58d5c12c11ef6b7d8bf881b2 | # How do you solve the simultaneous equations x+y+z=-2, 2x+5y+2z=-10, -x+6y-3z=-16 ?
Mar 25, 2017
$\left(x , y , z\right) = \left(- 2 , - 2 , 2\right)$
#### Explanation:
Given:
$\left\{\begin{matrix}x + y + z = - 2 \\ 2 x + 5 y + 2 z = - 10 \\ - x + 6 y - 3 z = - 16\end{matrix}\right.$
Subtracting twice the first equation from the second, we get:
$3 y = - 6$
Dividing both sides by $3$ we find:
$y = - 2$
Adding the first and third equation together, we get:
$7 y - 2 z = - 18$
Substituting $y = - 2$ into this equation, we get:
$- 14 - 2 z = - 18$
Add $14$ to both sides to get:
$- 2 z = - 4$
Divide both sides by $- 2$ to get:
$z = 2$
Then putting $y = - 2$ and $z = 2$ in the first equation, we find:
$x - \textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} = - 2$
Hence:
$x = - 2$
Mar 25, 2017
Use the 3 equations to write an Augmented Matrix and then perform elementary row operations until you obtain an identity matrix.
#### Explanation:
Write the augmented matrix:
[ (1,1,1,|,-2), (2,5,2,|,-10), (-1,6,-3,|,-16) ]
Perform elementary row operations.
$- 2 {R}_{1} + {R}_{2} \to {R}_{2}$
[ (1,1,1,|,-2), (0,3,0,|,-6), (-1,6,-3,|,-16) ]
${R}_{2} / 3$
[ (1,1,1,|,-2), (0,1,0,|,-2), (-1,6,-3,|,-16) ]
${R}_{1} + {R}_{3} \to {R}_{3}$
[ (1,1,1,|,-2), (0,1,0,|,-2), (0,7,-2,|,-18) ]
$- 7 {R}_{2} + {R}_{3} \to {R}_{3}$
[ (1,1,1,|,-2), (0,1,0,|,-2), (0,0,-2,|,-4) ]
${R}_{3} / - 2$
[ (1,1,1,|,-2), (0,1,0,|,-2), (0,0,1,|,2) ]
${R}_{1} - {R}_{2} \to {R}_{1}$
[ (1,0,1,|,0), (0,1,0,|,-2), (0,0,1,|,2) ]
${R}_{1} - {R}_{3} \to {R}_{1}$
[ (1,0,0,|,-2), (0,1,0,|,-2), (0,0,1,|,2) ]
We have obtained an identity matrix and the right column contains the solution set:
$x = - 2 , y = - 2 , \mathmr{and} z = 2$ | 2019-10-23 00:12:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 32, "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": 0.7754637002944946, "perplexity": 5889.8955917752}, "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/1570987826436.88/warc/CC-MAIN-20191022232751-20191023020251-00165.warc.gz"} |
https://www.freemathhelp.com/forum/whats-new/latest-activity | # Latest activity
• Jomo reacted to MarkFL's post in the thread Series with Like.
I would probably choose to express the recursion in homogeneous form: 2a_{n+2}-3a_{n+1}+a_{n}=0 Then it's easy to see that the...
• MarkFL reacted to Jomo's post in the thread Series with Like.
Mark, don't worry as things are always weird looking for Denise. I myself prefer to think that an+1= (an+1)/2
• MarkFL replied to the thread Series.
I would probably choose to express the recursion in homogeneous form: 2a_{n+2}-3a_{n+1}+a_{n}=0 Then it's easy to see that the...
• Jomo reacted to MarkFL's post in the thread Distance between two points with Wow.
Hint: This is a bit of a trick question...consider the poles moving closer and closer to each other. :)
• Jomo reacted to MarkFL's post in the thread Distance between two points with Wow.
Yes, if the cable is 80 m long, and goes down 40 m and then back up 40 m, then the poles must be at the same location, or 0 m apart.
• Jomo replied to the thread Distance between two points.
I am impressed (OK shocked) that you know what a Catenary is.
• Jomo reacted to Denis's post in the thread Distance between two points with Like.
Well, hello to you too! Are you asking what the shape of the cable is? If so, go here: https://en.wikipedia.org/wiki/Catenary
• Jomo replied to the thread Series.
Mark, don't worry as things are always weird looking for Denise. I myself prefer to think that an+1= (an+1)/2
• MarkFL reacted to Denis's post in the thread Series with Haha.
Gets kinda weird using Mark's formula: 65, 33, 17 ,9 ,5 ,3 ,2 , 3/2, 5/4, 9/8, 17/16, ....
• Denis replied to the thread Series.
Gets kinda weird using Mark's formula: 65, 33, 17 ,9 ,5 ,3 ,2 , 3/2, 5/4, 9/8, 17/16, ....
• Jomo reacted to pka's post in the thread Stat help! with Like.
This a comment. I have no doubt that the problem means that we are to take the predictions as independent with probability 0.48...
• GetReal replied to the thread Modulus theory.
Using (a), since d|3 then we can see that the only divisors of n+1 and n^2+2 are multiples of 3. But because n is a multiple of 3, n+1...
• Hi guys, sometimes I find it hard to go to aspect of "superposition" of something , I mean for example v1+v2+v3+v4 which they are...
• Jomo reacted to Otis's post in the thread quadratic formula problem with Like.
4 × 12 = 48, not 36. 😎
• Ryan\$ replied to the thread Sin/Cos periodic 2*pi.
thanks alot!!!! | 2019-03-26 01:01:04 | {"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": 0.8062911033630371, "perplexity": 2424.7542703765384}, "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-2019-13/segments/1552912204736.6/warc/CC-MAIN-20190325234449-20190326020449-00522.warc.gz"} |
http://netprophetblog.blogspot.co.uk/2014/03/machine-march-madness-2014.html | ## Friday, March 7, 2014
Obviously the big news this year (in the area of machine prediction of the NCAA Tournament, anyway) is the Kaggle competition for $15,000. Oh, and there's the Quicken Loans competition for a$1 Billion. But if that's not enough to keep you busy this March, I'm pleased to announce the continuation of the Machine March Madness competitions. There's no money at stake, but this is the longest-running machine prediction competition, and let's face it -- if you're going to enter the Kaggle competition you might as well enter Machine March Madness, too. It's not much more work :-).
(My thanks to Danny and Lee for letting me keep the competition running.)
The rules are very informal. Your predictions must be based on a computer algorithm, but you can implement some parts manually as long as they're objective. For example, your method might include "Take the team with the higher Sagarin rating" which you just handled manually, but please limit these steps and avoid just using your subjective judgement. You can use any data you can find, including human-generated rankings like the AP poll.
The competition will be run as a Yahoo! Pool called "Machine March Madness" which you can find here. Scoring will be Fibonacci -- 2-3-5-8-13-21 -- which will make the competition a little bit less dependent on the final round(s) than the traditional scoring. To get the password to join the pool, email me (srt19170@gmail.com) with the name of your entry and a short description of your approach. Also, please join the Google Group for announcements and discussion.
Useful data can found in a couple of places. First, at the Kaggle competition data page. Secondly, you can look in this Google Group thread from last year for some pointer's to last year's data. Finally, I have fairly extensive data and will make it available as needed -- email me (or post in the Google Group) what you'd like to see.
Danny Tarlow's starter code from past years can be found here. A short tutorial I wrote on using RapidMiner to predict games can be found here. Finally, there have been several useful postings on ratings systems and predictions in the Kaggle forum | 2017-10-19 16:02:59 | {"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": 0.2100095897912979, "perplexity": 2336.4280157938033}, "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/1508187823350.23/warc/CC-MAIN-20171019160040-20171019180040-00755.warc.gz"} |
https://flaviocopes.com/linux-command-ln/ | The ln command is part of the Linux file system commands.
It’s used to create links. What is a link? It’s like a pointer to another file. A file that points to another file. You might be familiar with Windows shortcuts. They’re similar.
Hard links are rarely used. They have a few limitations: you can’t link to directories, and you can’t link to external filesystems (disks).
A hard link is created using
ln <original> <link>
For example, say you have a file called recipes.txt. You can create a hard link to it using:
ln recipes.txt newrecipes.txt
The new hard link you created is indistinguishable from a regular file:
Now any time you edit any of those files, the content will be updated for both.
If you delete the original file, the link will still contain the original file content, as that’s not removed until there is one hard link pointing to it.
Soft links are different. They are more powerful as you can link to other filesystems and to directories, but when the original is removed, the link will be broken.
You create soft links using the -s option of ln:
ln -s <original> <link>
For example, say you have a file called recipes.txt. You can create a soft link to it using:
ln -s recipes.txt newrecipes.txt
In this case you can see there’s a special l flag when you list the file using ls -al, and the file name has a @ at the end, and it’s colored differently if you have colors enabled:
Now if you delete the original file, the links will be broken, and the shell will tell you “No such file or directory” if you try to access it:
This command works on Linux, macOS, WSL, and anywhere you have a UNIX environment | 2022-05-24 08:38:08 | {"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": 0.19426584243774414, "perplexity": 2136.737778099665}, "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-2022-21/segments/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00695.warc.gz"} |
https://unapologetic.wordpress.com/2008/03/20/products-of-integrable-functions/?like=1&source=post_flair&_wpnonce=9a71b83933 | # The Unapologetic Mathematician
## Products of integrable functions
From the linearity of the Riemann-Stieltjes integral in the integrand, we know that the collection of functions that are integrable with respect to a given integrator over a given interval form a real vector space. That is, we can add and subtract them and multiply by real number scalars. It turns out that if the integrator is of bounded variation, then they actually form a real algebra — we can multiply them too.
First of all, let’s show that we can square a function. Specifically, if $\alpha$ is a function of bounded variation on $\left[a,b\right]$, and of $f$ is bounded and integrable with respect to $\alpha$ on this interval, then so is $f^2$. We know that we can specialize right away to an increasing integrator $\alpha$. This will work here (unlike for the order properties) because nothing in sight gets broken by subtraction.
Okay, first off we notice that $f(x)^2$ is the same thing as $|f(x)|^2$, and so they have the same supremum in any subinterval of a partition Then the supremum of $|f(x)|^2$ is the square of the supremum of $|f(x)|$ because squaring is an increasing operation that preserves suprema (and, incidentally, infima). The upshot is that $M_i(f^2)=M_i(|f|)^2$. Similarly we can show that $m_i(f^2)=m_i(|f|)^2$. This lets us write
$\displaystyle M_i(f^2)-m_i(f^2)=M_i(|f|)^2-m_i(|f|)^2=\left(M_i(|f|)+m_i(|f|)\right)\left(M_i(|f|)-m_i(|f|)\right)$
$\leq2M\left(M_i(|f|)-m_i(|f|)\right)$
where $M$ is an upper bound for $|f|$ on $\left[a,b\right]$. Riemann’s condition then tells us that $f^2$ is integrable.
Now let’s take two bounded integrable functions $f$ and $g$. We’ll write
$f(x)g(x)=\frac{1}{2}\left(\left(f(x)+g(x)\right)^2-f(x)^2-g(x)^2\right)$
and then invoke the previous result and the linearity of integration to show that the product $fg$ is integrable.
March 20, 2008 - Posted by | Analysis, Calculus
1. Typo: 2nd paragraph, 2nd line. I think you mean “…and if $f$ is bounded…”
Comment by Vishal | March 20, 2008 | Reply
2. I came across your blog, I dont know how to sound less strange but then again I am a strange person. Well most of my friends say that I am intresting, howvever that isnt the point. I cant tell you how much I love math I dont know why but it intrests me. I could sit through math problems for 5 hours before puting them down. I am only 18 and a senoir in high school but my math teachers dont understand that I want to learn more. I ask in Hopes that you may have time and would teach me. I will understand if you wouldn’t want to. I just want to learn “feed my mind” kind of thing. Write me either way Yes or no. So I will know.
thank you either way…. :-)
Comment by Kasey | March 21, 2008 | Reply
3. Kasey, I understand what you mean, and I’m sorry that your teachers aren’t in a better position to show you where to go next. If you don’t have easy access to a nearby college or university, you’re sort of stuck until you leave high school.
But from this distance I’m not in much of a position to guide you directly either. The best I can suggest is to go through my archives. Start here, and anything you don’t understand either try to find links back, or search for it in the bar on the right. Alternatively, there are some great mathematics texts out there you could try to get ahold of from Amazon or something. Actually, I’ll make a post tomorrow about that sort of thing, but I’ve got to head off to something else right now…
Comment by John Armstrong | March 21, 2008 | Reply
4. […] math books Yesterday, someone left a comment, which I’m reinterpreting a bit as a call for help in what to do for self-directed study of […]
Pingback by Classic math books « The Unapologetic Mathematician | March 22, 2008 | Reply
5. Vishal, I did not become interested in mathematics until I turned 21 or so.. I did not go to college, my background is in computer science (been coding since i was 9 years old). I taught myself mathematics by buying books and learning them myself.. it has been very expensive.. I spend on average about \$2000 a year on mathematics/statistics books and I choose to learn from advanced research oriented material rather than the basics as I believe it is worth it in the long run.
I suggest getting a copy of Maple and TexMacs for typesetting in a GUI very mathematical and professional looking papers.
Comment by Stephen Crowley | March 22, 2008 | Reply
6. Stephen, I think you’re meaning that towards Kasey.
Comment by John Armstrong | March 22, 2008 | Reply
7. My very first mathematics book was Measure Theory and Integration by MM Rao.
http://www.amazon.com/exec/obidos/ASIN/0824754018
Comment by Stephen Crowley | March 22, 2008 | Reply
8. John, you are right, my comment was directed towards Kasey.
Comment by Stephen Crowley | March 22, 2008 | Reply | 2016-02-09 07:31:08 | {"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": 0, "img_math": 23, "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": 0.820129930973053, "perplexity": 518.0795705946198}, "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-2016-07/segments/1454701156627.12/warc/CC-MAIN-20160205193916-00005-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://linearalgebras.com/solution-abstract-algebra-exercise-1-7-11.html | If you find any mistakes, please make a comment! Thank you.
## Exhibit Dih(8) as a subgroup of Sym(4)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.11
Write out the cycle decomposition of the eight permutations in $S_4$ corresponding to the elements of $D_8$ given by the action on the vertices of the square shown in the following figure.
Solution: The “flip” permutation, $s$, corresponds to the permutation $(2\ 4)$. The “rotation” corresponds to $(1\ 2\ 3\ 4)$. Now every other permutation is generated by these two, so we have the following.$$1 = 1$$ $$r = (1\ 2\ 3\ 4)$$ $$r^2 = (1\ 3)(2\ 4)$$ $$r^3 = (1\ 4\ 3\ 2)$$ $$s = (2\ 4)$$ $$sr = (1\ 4)(2\ 3)$$ $$sr^2 = (1\ 3)$$ $$sr^3 = (1\ 2)(3\ 4).$$ Note that these results are consistent with the fact that every nonpower of $r$ in $D_{2n}$ has order 2, and the only elements of order 2 in $S_m$ are products of disjoint 2-cycles.
#### Linearity
This website is supposed to help you study Linear Algebras. Please only read these solutions after thinking about the problems carefully. Do not just copy these solutions. | 2020-09-27 21:07:22 | {"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": 0.8661828637123108, "perplexity": 199.8955908526424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2020-40/segments/1600401578485.67/warc/CC-MAIN-20200927183616-20200927213616-00522.warc.gz"} |
https://qudt.org/vocab/quantitykind/RadiantFlux | $$\Phi = \frac{dQ}{dt}$$, where $$dQ$$ is the radiant energy emitted, transferred, or received during a time interval of the duration $$dt$$.
$$\phi$$ | 2022-07-04 14:35:34 | {"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": 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": 0.732232391834259, "perplexity": 365.1452602908673}, "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-2022-27/segments/1656104432674.76/warc/CC-MAIN-20220704141714-20220704171714-00389.warc.gz"} |
https://docs.analytica.com/index.php/Analytica_4.6 | # What's New in Analytica 4.6?
(Redirected from Analytica 4.6)
Analytica 4.6 was released on 24 May 2015. This page introduces the enhancements it adds to the previous Analytica 4.5 release.
## Summary of Whats's new in Analytica 4.6
66% Faster: Analytica 4.6 introduces several significant optimizations to speed up model evaluation. Their effect depends on the specifics of each model. A comparison of nine large customer models found that Analytica 4.6 runs the models from 7% slower to 4.52 times faster than Analytica 4.5, with an average of 1.66 times faster. Equivalently, it reduces average run time by about 40%. And that average excludes the tenth model (using iteration inside a dynamic loop) which runs 94 times faster!
Buttons, OnClick and OnChange Events: You can now create Buttons in Analytica Professional and Free 101 (previously you needed Enterprise). When you click a button (or Picture) it runs the OnClick event. When you change a user input variable, such as a Choice menu or Checkbox, it runs the OnChange event. You can specify any expression, including assignments to Global variables, to OnClick or OnChange attributes. These replace the Script Attribute, which is retained for forward compatibility. Unlike Script, which uses a special Typescript language, OnClick and OnChange accept standard Analytica syntax, offer Expression assist, input/output navigation, and the other advantages of the Definition.
Associating Colors with Index values: The Color Series Dialog (right-click on a colored line, bar, or key in a Graph) lets you set colors for values in an Index, not just a particular graph. Thus, you can set all graphs using, say, the Technologies Index, to use the same colors for each Technology. You can even set it an Index that a subset of the Technologies to use the same colors.
Graphing: Some other graphing additions include Waterfall charts, Heat maps, and hyperlinks from Variable names on a graph. By default, graphs usually include zero on each axis, unless it wouldn't make sense -- e.g. it won't show the year zero when plotting results for years 2010 to 2050.
COM to integrate with other applications: Analytica Enterprise and Optimizer support COM (Component Object Model), a widely used method to access other applications, including Microsoft Excel and other Office programs. This lets you access the full API (Application Programming Interface) for these applications. You can also write your own COM objects in C++, VB, C# and other languages, to add new functions to Analytica. You can call COM asynchronously, to support concurrent computation, including ADE to parallelize Analytica computations on multiple processors or remote servers.
Multitable: This new type of table lets you combine editable and computed cells (slices) in a single table, very useful for user interfaces.
Max open windows: By default, Analytica now displays up to 8 Diagram, Object, Table, and Graph windows. When you show another, it closes the least-recent Window. This much simplifies the previous scheme that could open vast number of windows, which were overwhelming and slowed user interaction. You can modify Max open windows in the Preferences dialog.
## Buttons, OnClick, and OnChange Events
• You can now create Buttons in Analytica Professional and Analytica Free 101 (previously, you needed Analytica Enterprise).
• You can specify any action as an expression in a Button's OnClick attribute. As you might guess, when you click the Button, it evaluates the expression.
• You can also add a expression in an OnChange attribute for any variable. If the variable is a user input, such as a Choice menu or Checkbox, it evaluates the OnChange expression when you change it.
• If it's not a user input, it evaluates the OnChange expression whenever the variable is evaluated.
• The expressions in OnClick and OnChange use the standard Analytica syntax used in a Definition.
• But, you can also include an assignment to a global variable in an OnClick in a Button or OnChange in a variable.
• Expression assist, input/output navigation, and other advantages of the Definition field are now available when editing the expressions in OnClick or OnChange.
• You can create an OnChange handler for any input variable, including text boxes. For edit tables, the event is run when the user finishes all cell edits, e.g., by clicking the green check. It isn't fired for each individual cell edits.
• You can use OnClick on Picture node. When a user clicks on the picture, your expression is evaluated and two variables, click_x and click_y can be used within your expression and give the coordinate of the click within your image.
• If you want to run one button from another button, you can use the button's identifier by itself as an expression from within OnClick or OnChange.
• OnChange handlers can be cyclic. For example, OnClick of Length_in_feet can set Length_in_meters, and OnClick of Length_in_meters can set Length_in_feet, allowing them to mutually synchronize each other when one is entered.
• The new OnClick and OnChange attributes replace the old Script attribute in Button, and user inputs with Checkboxes and Choice menus.
• OnClick and OnChange attributes use standard Analytica expressions, so you no longer have to learn the special Typescript syntax used by the Script attribute. They also support Expression Assist to make it easier to write the expressions.
• The Script attribute is now deprecated, meaning we discourage you from using it. But, any legacy models that use Scripts still work as they did before.
• If a button has an OnClick and Script attribute, it runs both. Or if a User input has both OnChange and Script, it runs both.
• The user interface won't show the Script attribute in an Object view or Attribute Panel unless it has an expression.
and take you to OnClick or OnChange instead, but it an object has a pre-existing Script attribute set, it will show that and take you there instead (e.g., with Ctrl+E).
• There are still a few things that can only be done through typescript. The most common are creating new objects and opening or closing user-interface windows. If you need to do any of these from a button, use the EvaluateScript function.
## Graphing
### Color Association with Indexes
You can now associate a custom color scheme with a particular index so that all graphs using that index in the Key have the same colors. For example, you can set the Technology index with Solar as yellow, Hydro as blue, Coal as black, etc. in all graphs with Technology as the Key index.
Right click on a point, line, or bar, or a key item in a graph, and select Change Series Color.... This gets you to the Color Series Dialog:
The new dropdown, Color to use for, lets you review and change the colors of all the Key labels in the same Change Series Color... dialog. So it's much faster to create or modify a color scheme.
After selecting the colors you want, select Apply these colors - To all graphs using Index Technology to associate this color series with the index so that all graphs using that Index as the color key use the same color sequence. You can also set the colors only for this graph, as the default for all graphs, or as a subset of another Index color sequence.
See Customization of Graph Colors for details.
### Varying color in 1-D graph
You can vary color in a 1-D graph, where the independent (Y) axis and color vary together. In this case, the position along the independent axis and the color are redundant; however, this can be particularly desirable when a standardized color scheme is used.
### Color varies by slice
When you have no graph key, the slicer now controls the color, so that as you toggle the slicer value, the color of the curve changes. When there are multiple slicer indexes, the first one with a color association is used. Hence, the color of the curve continues to reflect the slice being viewed.
### Computed Color Role
You can now assign a Color (or Key) role to a categorical comparison variable (or to the main value if it is categorical). You may also use a continuous variable if it has fewer than 50 values, in which case it is treated as categorical. This gives you a tremendous amount of control over the use of color, creating many opportunities for creative uses of color to communicate information. It gives you complete control over the color of every point, line or bar in a graph, and the color doesn't necessarily have to correspond to an index. See below for examples of creative uses of this flexibility.
This graph shows how to assign a computed categorical value (Staff development) to the color role.
#### Waterfalls
A waterfall graph is a variation of a stacked bar graph, in which stacking dimension is the same as a cluster dimension, or in which the stacking dimension varies with the independent axis and there are no clusters. The result view's "smart pivoting" normally prevents you from setting these roles to be the same. So, to show a waterfall graph, select Stacked and the new Waterfall checkbox on Graph Setup...
In a Waterfall style graph, negative values are not stacked separately from positive values, as they are in a pure stacked graph. The new example model "Waterfall chart.ana" illustrates this style of graph.
### Displaying a subset on a categorical axis
If you have a categorical axis with a lot of labels, you can display a subset by specifying the first and last to display from pulldown menus for Minimum and Maximum.
### Include Zero
It is usually misleading not to include zero on the Y-axis. Compare these two graphs of the number of burglaries in San José, CA. The one on the left doesn't include zero, and it seems to exaggerate the change over time.
Analytica now usually defaults to include zero -- except, when it would not make sense -- for example if the Y axis is years from 2010 to 2040, it makes little sense to include the year zero.
Axis and key labels on a graph can now be hyperlinks to objects in the model. This happens automatically when the element is a handle. The corresponding label displays in blue.
### Other graphing enhancements
• A graph doesn't display a data point whose value is Null or NaN, or, for a stacked graph, zero. It omits any item from the Key if none of its data points are displayed.
• Each item in the Graph Setup... dialog included a tooltip description.
• The filled area looks cleaner, when you select Area fill on the Chart type'.
## Influence Diagrams
• When you press just to the left (or right) of a node, it pops up a menu of the nodes input (output) variables. Now this list also shows aliases and user inputs (user outputs) for the variable with the name of the module that contains them. You can select one one of these from the popup menu to jump to its diagram.
Navigate from a variable to its input node Navigate from a variable to its aliases or output nodes Navigate from an alias to the original variable
Navigate from an output node to its variable Navigate from input node to its variable
• Now you can Undo (ctrl-Z) when you Delete (Delete) a node or set of nodes.
## Application Integration
• Analytica Enterprise and Optimizer users can now instantiate COM objects (Component Object Model) from external applications and call the methods on these objects. See COM Integration.
• You can use the workbook object returned from SpreadsheetOpen as a COM object, giving you full access to the entire Excel API An example here.
• You can call COM objects asynchronously, enabling concurrent computation.
• COM calls array-abstract automatically.
• You can use this mechanism to instantiate and call ADE instances.
• You can instantiate on remote computers and call their methods via DCOM. You may need to adjust Windows security settings appropriately to enable this.
• Many .NET libraries can be used via COM.
• Many applications support COM interfaces, and hence, this enables a very wide variety of opportunities to integrate with and make use of other application.
• Using C++, VB, C#, and a host of other programming languages, you can write your own COM objects. COM calls have low overhead, so it is possible to implement low-level functions efficiently in C to be used by your model.
## Evaluation Engine and Built-in Functions
• A new build-in function, Try(expr, catch:expr2), can be used to catch evaluation errors without Analytica stopping and reporting the error to the user. The new function Rethrow can be used from the catch expression to re-issue the error.
• The maximum number of dimensions for a single array has been increased in the 64-bit edition to 24. In Analytica 32-bit, the limit has not been changed, it is still 15. Keep in mind, however, that you will usually hit memory limits before this many dimensions.
• Speed-up using Evaluating Context: The evaluation engine can now detect several cases in which portions of a computation will not impact the final result, and in these cases will avoid computing the iterations that are used. In some cases, this can result in dramatically faster evaluation. For example, suppose x was a very large array, and you had this expression:
( Sin(x)^2 - CumNormal(x) )[I=10]
by recognizing the all I≠1 slices don't impact the final result, it can avoid evaluating the expense Sin and CumNormal for all slices other than I=10, as if you had instead written
Sin(x[I=10])^2 - CumNormal(x[I=10])
This comes into play often when there are two nestings of array abstraction active, but where only some variables had been restricted. One very important example of this in when there are multiple local variable declarations with explicit dimensionality declared, such as:
Var a[I] := F1();
Var b[J] := F2();
F3(a,b)
If it is the case that F1() is indexed by I,K, then everything in the scope of a needs to be iterated over K. If F2() is also indexed by K, then a nested iteration results. This new enhancement is now able to coordinate these, so that a single iteration over K results. In this example, this improves evaluation time from O(n^2) to O(n).
If you have intentional side-effects in your code, such as message boxes displayed to the user, data written to a file, or changes to local variables, this enhancement might alter your computation, since it may cause the code to go through fewer iterations. There are two ways to turn off this enhancement. You can turn it off globally by setting the EnableEvalContextUse system variable to 0. Or you can disable it within a single expression by using SetEvaluationFlag("EvaluationContext",0,expression).
The speed-up optimization is not applied to explicit FOR loops. So in For i1:=I Do For i2:=I Do F(i1,y2), F is called for every pair of I, n2 times, whereas in Var i1[]:=I Do Var i2[]:=I Do F(i1,i2), F is called only n times -- F(1,1), F(2,2), etc.
The final result of each of these would be the same in this example.
• Speed-up of Iterate nested in Dynamic. When an Iterate appears in a Dynamic loop, and implements a convergence algorithm than depends only on the current or recent time steps, evaluation in this case is now dramatically faster.
• A new parameter, «method» has been added to Dispatch. It provides alternatives for increment-constrained allocations when increments don't meet demand precisely.
• A new function, AddIndex, has been added. This returns an array having one or more additional indexes that you specify, with the array being constant over the new indexes. In normal situations, this is entirely unnecessary and even undesirable -- the Analytica philosophy is that an array only needs an index if its value vary over that index, which clearly is not the case for the result here. You never need to add an index prior to an array operation in Analytica expressions. There are, however, some esoteric cases where you do need to do this, often involving meta-inference.
• A new parameter, «extrapolationMethod», has been added to LinearInterp. With it you can specify that values are extrapolated using the nearest point (as in pre-4.6 releases), by extending the slope of the first or last segment, or by never extrapolating and returning null for values outside the data range. An important use is in piecewise-linear Optimization problems when you know that the solution does not appear in the extrapolated region. This extra info can lead to faster solves and greater numeric stability in the integer LP.
• You can now use cascading comparisons in expressions, such as If 0<=x<100 Then x Else Null.
• These have been supported in optimizer constraints, but this is a semantic change in syntax for expressions. Previously this would be parsed as If (0<=x)<100 Then..., which is not equivalent, whereas now this is equivalent to If 0<=x and x<100 Then....
• When Choice(Self,...) is evaluated, where the options are in the domain of the variable, the behavior has been changed so that the options are never evaluated, even if the «eval» parameter is specified to true. This is only relevant to the case where your domain contains handles to variables. This change avoids a domain-inconsistency that results otherwise.
• A new function, OpenURL, has been added. It opens the indicated web page in your browser.
## MultiTables
A MultiTable allows you to combine several edit tables (ideally with the same dimensionality) into a single view, and to also display computed columns in the same table. Edits to the edit-table columns change the source edit tables. Computed columns update immediately and cannot be edited. MultiTables and SubTables can be arbitrarily nested -- i.e., a SubTable can be source for a MultiTable, and a MultiTable can be a source for a SubTable.
A new control shows up in edit mode when viewing a MultiTable, which allows you to toggle between the "meta view" (the definitions of each "column") or the "cell view" (the actual data). Use the meta view to configure your multi-table, and use the cell view once it is set up. Keep in mind that in meta view, A means that A's definition should show, whereas Mid(A) means that A's computed result should be displayed.
The meta view The cell view
## User Interface
### Start up
The very first time you launch Analytica, it will inform you that if you are new to Analytica, the Tutorial is the best place to start.
### Elimination of buttons
When your variable is defined as call to Sequence or to a distribution function, it now shows the textual definition rather than those annoying buttons that would appear previously. Buttons in the definition field are now reserved for edit tables.
In Analytica 4.5 In Analytica 4.6
• You can rapidly see a description of a function by selecting its identifier in a Definition and pressing Ctrl+H (or selecting Find (Jump to) selection from the right-click context menu).
• Built-in functions have a link to their Wiki description in blue, as above.
• You can also jump straight to the wiki description for a built in function by selecting its identifier, right-click to see the context menu. and selecting "Wiki help on «name of function»".
• You can add a similar hyperlink for your own User-Defined Functions or Variable: Set the Att_WikiHelpURL attribute of the object to a URL. Then the link will appear in its object window, and in the right-mouse context menu when you select its identifier.
## Misc
• When you have some text selected when you press Ctrl+F, the select text is inserted into the text field of the Find dialog.
• You can adjust the column side of a table by double-clicking on the right edge of the column header cell.
• A new folder for the build-in functions was introduced, Application Integration. Functions that involve interactions with other applications (other than the Database functions) are now in this folder, including the new COM Integration functions, RunConsoleProcess and the Spreadsheet functions.
• The Shift+Ctrl+E shortcut opens the textual definition. Sometimes useful when Ctrl+E opens an edit table window.
### Window Management
• Max open windows is a new option on the Preference Dialog to control how many Analytica windows (of any kind) you can have open at once. If you are at this limit when opening a new window, it automatically closes the least-recently-used window. This much simplifies the previous somewhat confusing method, which often resulted in a vast number of windows being open which slowed down user interaction. This is a personal preference saved for you as a user, not stored with the model. Most users can simply ignore this now, and simply accept the default of 8 windows.
## Example Models
Some new example models have been included:
• Enterprise Model: (Business examples). A financial model of a hypothetical company than sells widgets. Forecasts sales and staffing needs into the future. Long used in Lonnie's introduction to Analytica webinar.
• Waterfall chart (Business examples). A very basic financial example, illustrating a type of graph called a Waterfall Chart.
• Vacation plan with PWL tax (Optimization Models): Illustrates the use of a piecewise-linear constraint in a linear program. Here, income tax rates are staged by bracket (as they are in the US tax code).
• Normally, when you install or upgrade Analytica and enter a key into the license dialog, it activates automatically. But, if your computer is not connected to the internet (or a firewall prevents it connecting to the activation server at AnalyticaOnline.com), you have to activate Analytica manually. We have simplified manual activation to make it more robust, to reduce the chance of mistakes, and to identify any problems that still occur.
• As before, use automatic activation if you can -- because it's much easier.
To activate manually an individual license in Analytica 4.6,
1. Double click the installer and go through installation screens (as before), but with activating.
2. Fill in the Manual Activation Form on the Lumina website and click "Submit".
3. When you receive the email with activation information, save the attached license file to a known directory.
4. Launch Analytica and open the Analytica Licensing Information dialog (Help→Update License...).
• You can now copy (ctrl-C) the Host id and User id from the bottom of this Analytica Licensing Information dialog, for example to paste it into the online Activation form.
• A new interface has been added, IAdeUICallbacks which allows you to implement callbacks that are called when Analytica functions requiring user input are evaluated. For Example: MsgBox(), ShowProgressBar(), ShowPdfFile(), OpenURL() More...
• A new Flags property has been added to CAEngine. It is a bit field. Currently only one bit is used:
1 = Allow hiding and unhiding of definitions. This is set to off by default, so that definitions that were hidden from Analytica Enterprise remains hidden.
## Backward Compatibility with Analytica 4.5
We always strive to make each release of Analytica backward compatible, so that models created with an earlier Analytica release will still work fine with the new release. But there is a remote chance that a change will impact an existing model. For example, if your model took advantage of a "bug" that is fixed in the new release. The situations that could possibly affect backward compatibility are quite rare, but we list them for completeness:
### Structured Optimization Library
If your model embeds the Structured Optimization Library (such as Use_opt_decisions() and Set_decisions_to_opt(), you should replace it with the new version of the library in 4.6 to make sure you get correct values. It fixes a bug that results in a gross inefficiency for optimization formulations with extrinsic indexes. The bug interacts with context speedup causing extrinsic indexes to be dropped by the assignment. We also recommend you use the new version even if you continue to use Analytica 4.5.
### Evaluation Context Speedup
This speed-up optimization can reduce the number of iterations that could rarely alter some results in these situations:
• Functions that generate random numbers appear within affected expressions. With fewer iterations, the random seed may be altered, so that the exact values appearing in Monte Carlo samples might change compared to Analytica 4.5.
• If a local variable with a scope broader that an iteration point is updated inside the iteration, the result of the computation might change. For example:
Var count := 0;
Index I := 1..3 Do (
Var i1[] := I;
Var i2[] := i1^2 + I;
count:=count + i2;
);
count
In Analytica 4.6 this returns 2 + 6 + 12 = 20, whereas in Analytica 4.5 it would return 60 due to the double iteration. This difference occurs because of the side-effect in which count is updated within the body of the second Var, but has a scope outside of this iteration.
• When there is a side-effect of a different nature, which occurs in an expression whose result for certain iteration values is not used. These side-effects might be the display of a MsgBox, writing to a file, interacting with an external application, or implementing a time delay through vacuous iteration.
If your legacy model is impacted by any of these conditions, you may disable this optimization for the whole model or for a particular expression. To disable it your whole model: 1. Press F12 to open the Typescript window. 2. Type: EnableEvalContextUse:0 Disabling globally is appropriate when the random seed is an issue for you; however, by doing so, you don't benefit from the speed-up in model evaluation time that might result from the optimization.
If you isolate a particular expression affected by this issue, you can disable the optimization just in that expression by nesting it inside SetEvaluationFlag:
SetEvaluationFlag("evaluationContext",0,
Var count := 0;
Index I := 1..3 Do (
Var i1[] := I;
Var i2[] := i1^2 + I;
count:=count + i2;
);
count
)
The change to how cascading comparisons are interpreted has the potential to "break" an expression. The situation where this occurs is extremely rare, and very unlikely to appear in your model, but it is nonetheless theoretically possible that an existing model might be impacted, and hence, it is listed here.
Suppose you wanted to test whether x is non-negative and y negative. The intuitive was of doing this would be:
If x>=0 and y<0 Then...
which presents no problem. But an arcane way of testing this same condition might be
If x<0 < (y<0) Then...
In earlier releases this would parse as (x<0) < (y<0). This arcane way of expressing this would be impacted by the new cascading comparisons, because it would now be parsed as x<0 and 0 < (y<0), which is not the same.
### Graph colors
In some Tornado charts, the colors for some of the bars may change when viewed in 4.6 compared to 4.5. Suppose you have an key index with items ['Low','Baseline','High'], and you set the bar origin to 'Baseline'. Analytica 4.5 uses the 1st color for 'Low' and the second color for 'High', whereas Analytica 4.6 uses the first color for 'Low' and the third color for 'High'. So the color used for 'High' will be different.
### Hiding or unhiding definitions in ADE
This note only impacts users of ADE.
ADE has been changed to issue an error by default if your attempt to change the Att__cloakDefn attribute of an object, whereas in 4.5 this was allowed. Setting this attribute to 1 hides definitions, to 0 unhides definitions. By default, if your code that calls ADE tries to change this attribute (e.g., using CAObject::SetAttribute or via typescript CAEngine::SendCommand, it will fail with an error. This is so that your applications that use models created in Analytica Enterprise that have hid certain definitions continue to hide these definitions from end users as intended. If you are creating code that allows people to build or configure models and want to allow hiding or unhiding, then set the 1 bit of CAEngine::Flags to allow it. | 2023-03-20 09:17:40 | {"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": 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": 0.3011114001274109, "perplexity": 2121.165215736862}, "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-2023-14/segments/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00755.warc.gz"} |
https://physics.stackexchange.com/questions/435464/how-to-find-the-degree-of-doping-in-a-material | # How to find the degree of doping in a material?
I find this term a bit mysterious, it appears that everyone is using it intuitively without proper definition (or at least I failed to find one).
So the Physics Glossary defines it as
In condensed matter physics, doping refers to the deliberate introduction of impurities into an extremely pure crystal. For example, a crystal of pure silicon might be doped with boron atoms that change the material's electrical properties, making it a more effective semiconductor.
But this definition doesn't help to use it in practice. Books like "Physics of Low-Dimensional Semiconductors" by Davies keep using this term a lot as "you can control something with doping" or "something is limited by doping". Professors assign problems mentioning "(...) find doping (...)".
What is doping in practice in this kind of context. Is it a number? Is it a function? What are its dimensions? If we have to find the degree of doping, what do we search for?
• Doping is a physical process. It isn't something you calculate or something that has a number associated with it like mass or momentum. You can quantify things about the doping, but that is different than doping itself being a number or having dimension. – Aaron Stevens Oct 19 '18 at 3:59
• I think that many books and articles like the following one explain what doping is: en.wikipedia.org/wiki/Doping_(semiconductor) – Samuel Weir Oct 19 '18 at 4:00
• I understand this is something more complicated than just a value, perhaps I should formulated my question as, if someone asks you to "find doping", what do you need to find? – Marek Oct 19 '18 at 4:57
• @Marek - "Find doping" means find the numerical value of the required doping for whatever physics problem was given to you. – Samuel Weir Oct 19 '18 at 5:03
• @SamuelWeir ok, so it is a value, and what are its dimensions? – Marek Oct 19 '18 at 5:09
In intrinsic crystalline silicon, there are approximately $$5×10^{22} \text{ atoms}/cm^3$$. Doping concentration for silicon semiconductors may range anywhere from $$10^{13} cm^{−3}$$ to $$10^{18} cm^{−3}$$.
The doping level is a concentration of dopants in a semiconductor - as such it has the unit $$[\frac{1}{cm^3}]$$, since it gives the number of dopant atoms per volume. | 2019-11-22 03:11:19 | {"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": 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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6534554958343506, "perplexity": 842.8396514407667}, "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-2019-47/segments/1573496671106.83/warc/CC-MAIN-20191122014756-20191122042756-00468.warc.gz"} |
http://math.stackexchange.com/questions/216837/product-of-normal-subgroups | # Product of Normal Subgroups
I'm trying to prove something regarding solvable groups, but I got stuck near the end with this problem: Let $K \unlhd H \leq G$ and $N \unlhd G$. I'm trying to prove that $NK \unlhd NH$. I've tried to do this through conjugation-invariance: $$(nh)^{-1}n'k(nh) = h^{-1}n^{-1}n'knh$$ but got stuck. I'd really appreciate a clue :)
-
Just continue: \begin{align} (nh)^{-1}n'k(nh) = h^{-1}n^{-1}n'knh & = h^{-1}n^{-1}n'h\cdot h^{-1}kh\cdot h^{-1}nh \\ &\in NKN \end{align} and as $N$ is normal, $KN=NK$ (because $kn=(knk^{-1})\cdot k$). | 2016-06-26 18:05:10 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999443292617798, "perplexity": 626.6446777185912}, "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-2016-26/segments/1466783395546.12/warc/CC-MAIN-20160624154955-00080-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://mathforums.com/tags/chebyshev/ | # chebyshev
1. ### Understanding a specific Chebyshev integral
I have a situation where I'm trying to understand the physics of a cooling tower. Part of the solution for the model I'm working with involves an integral: C = \int_{T_{low}}^{T_{high}} \frac{1}{\left(h' - h_a\right)} dT where h' is a slowly varying, monotonically increasing function with...
2. ### Chebyshev's Theorem
I have this problem: "In a distribution of 160 values with a mean of 72, at least 120 fall within the interval 67–77. Approximately what percentage of values should fall in the interval 62–82? Use Chebyshev’s theorem." If I knew what the standard deviation was, I would know how to do...
3. ### Gauss Chebyshev formula
Use Gauss Chebyshev formula with $n=3$ to approximate the value of the integral. $$\int \frac{x^4}{\sqrt{1-x^2}}dx$$ from -1 to 1. Also compare the result with true value, where the zeros and the corresponding weights of the following simple set of orthogonal polynomial is given as below...
4. ### Chebyshev's inequality
We`re throwing symetric cube for 720 times. Using Chebyshev's inequality show that the probability of throwed 4 is in the interval (100,140) How can i solve this one?
5. ### Chebyshev polynomials
These problems are about a useful class of polynomial called Chebyshev polynomials which are defined as: T_n(x)=cos(n cos^-^1x) (a) what are the domain(s) and range(s) of the functions? (b) give equivalent polynomial definitions for T_n(x) when n=0,1,2,3. That is show that the definition...
6. ### Euclidean vs Manhattan vs Chebyshev distance?
Imagine three points A,B and C. Is it possible AB>AC in Euclidean distance but AC>AB in Manhattan or Chebyshev distance? Or if AB>AC in one distance norm then AB>AC in any other distance norm? I will be grateful if you state your source(s). Thanks from Greece Pericles
7. ### Chebyshev's theorem
1. In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev's theorem to tell the probability that a number lies in the following interval. Round your results to the nearest whole percent. Less than 26 or more than 74
8. ### Chebyshev's theorem
Could anyone please kindly explain what this Chebyshev Theorem really tries to convey and its practical use ?? I am not getting it clearly its use and significance.. Thank you
9. ### Chebyshev polynomials / Odd Eigenvalues (12/04/06)
The following proof was given for the problem on Chebyshev polynomials: "Let z = e^(ix), and y = 2 cos(x) Then (z^n) is a polynomial in cos(x) and sin(x), say A( cos(x), sin(x) ) whose real part is cos (nx), but Re{A( cos(x), sin(x) ) contains only even powers of sin (x). Replacing... | 2020-04-05 13:26:21 | {"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": 0.8140071034431458, "perplexity": 1492.267962407247}, "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-2020-16/segments/1585371604800.52/warc/CC-MAIN-20200405115129-20200405145629-00358.warc.gz"} |
http://math.stackexchange.com/questions/208351/how-do-the-closed-subsets-in-the-product-topology-look-like | # How do the closed subsets in the product topology look like
I know that the open subsets in the product topology of $X=X_1\times X_2\times...\times X_3$, where $X_1,X_2,...,X_n$ topological spaces, are the union of subsets of X: $U_1\times U_2\times ...\times U_n$, where $U_1,U_2,...,U_n$ are open subsets of $X_1,X_2,...,X_n$ respectively.
I have a question, how the closed subsets look like? can I say that they are the union of the subsets of X: $F_1\times F_2 \times...\times F_n$, where $F_1,F_2,...,F_n$ are closed subsets of $X_1, X_2,..., X_n$ respectively? In fact, what they are?
thanks
-
Sets of the form $F_1\times\dots\times F_n$, with $F_j$ closed for $1\leq j\leq n$, are closed as their complement is open: it's $$\bigcup_{j=1}^n\left(\prod_{i=1}^{j-1}X_i\times (X_i\setminus F_i)\times \prod_{i=j+1}^nX_i\right).$$ But not all the closed sets have this form: form example, in the plane $\Bbb R^2$, the unit disk $\{(x_1,x_2)\in\Bbb R^2, x_1^2+x_2^2\leq 1\}$ cannot be written as a cartesian product. But closed sets are arbitrary intersection of sets of the form $F_1\times\dots\times F_n$, in the same way that an open subset for the product topology is an union of products of open sets.
when you said $F_j$ are you talking about every $F_j$? – user42912 Oct 9 '12 at 13:54
Yes, and I should say "the" $F_j$. – Davide Giraudo Oct 9 '12 at 13:59 | 2014-03-08 23:51:50 | {"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": 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": 0.9396158456802368, "perplexity": 104.9595976964578}, "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-2014-10/segments/1393999668222/warc/CC-MAIN-20140305060748-00095-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/118/2/88071/convergence-to-stable-laws-and-a-local-limit-theorem-for-stochastic-recursions | # Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty
## Convergence to stable laws and a local limit theorem for stochastic recursions
### Tom 118 / 2010
Colloquium Mathematicum 118 (2010), 705-720 MSC: Primary 60F05. DOI: 10.4064/cm118-2-21
#### Streszczenie
We consider the random recursion $X_{n}^{x}=M_nX_{n-1}^{x}+Q_n+N_n(X_{n-1}^{x})$, where $x\in\mathbb R$ and $(M_n, Q_n, N_n)$ are i.i.d., $Q_n$ has a heavy tail with exponent $\alpha>0$, the tail of $M_n$ is lighter and $N_n(X_{n-1}^{x})$ is smaller at infinity, than $M_nX_{n-1}^{x}$. Using the asymptotics of the stationary solutions we show that properly normalized Birkhoff sums $S_n^x=\sum_{k=0}^n X_k^x$ converge weakly to an $\alpha$-stable law for $\alpha\in(0, 2]$. The related local limit theorem is also proved.
#### Autorzy
• Mariusz MirekInstitute of Mathematics
University of Wrocław
Plac Grunwaldzki 2/4
50-384 Wrocław, Poland
e-mail
## Przeszukaj wydawnictwa IMPAN
Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.
Odśwież obrazek | 2021-07-27 18:34:13 | {"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": 0.9043456315994263, "perplexity": 5356.900676151142}, "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/1627046153474.19/warc/CC-MAIN-20210727170836-20210727200836-00079.warc.gz"} |
https://www.pololu.com/blog/engage-your-brain | # October 2022: still waiting for parts…
Posted by Jan on 15 October 2022
Wow, it’s been almost a year since my last update about how Pololu has been impacted by the global supply chain disruptions and chip shortages. And unfortunately, not much has improved. In today’s post, I will cover a few representative component stock histories and then go over other areas of our business that have been impacted and what we are doing to get through this situation.
### Some parts on order since 2020 still have not shipped
In the case of one important part I mentioned last year, we are still waiting for an order placed in late 2020 without having received anything since a partial shipment in March 2021! Here is what our internal stock chart looks like for that component:
When I wrote about this component in November of 2021, we still had 461 units in stock, and the manufacturer was giving me specific updates about where we were in line and how I could expect parts by Q1 2022 or maybe even by the end of 2021. Well, we are now getting close to the end of 2022, and they are not even giving me updates anymore on when I can expect these parts that I ordered in 2020! We have gone almost a year without being able to make or sell the products that use that chip.
### Some parts arrived in 2021 and early 2022, but we are out again
That first example of still waiting for an order from 2020 is not typical. Unfortunately, we are seeing more and more of this pattern:
This is a component we ran out of over the summer of 2021, but we received some shipments in August of that year, and then more in early February of this year. But since then, nothing, and we are about to run out again despite our attempts to carefully ration the parts. It’s been over 14 months since I placed my oldest unfilled order for these parts, and the current expected ship date is February 2023.
### Shifting demand clears out stock of alternative components
Another pattern we are seeing more of looks like this:
Here, we were in a pretty good stock situation at the beginning of the year on a component we didn’t use that many of. However, as we raised prices on other products or ran out of stock completely, our customers moved to some of our recommended alternatives and cleared us out of those, and hence the sudden dropoff of those parts in April of this year. The additional problem with components like these is that we did not have as many on order because our historical usage was not that high, so it might take an extra long time to get that back to decent stock levels.
### New “supply outlook” feature
We commonly use the same components in several different products. One of the main ways we are dealing with the shortages is to substantially reduce our inventory of completed products so that we can be sure the components we do have are going toward products that are getting sold immediately.
One big downside of reduced ready-to-sell inventory is that it’s difficult for customers to tell what is really, really unavailable because we’ve been out of parts for a year and what is actually available as soon as we make some more. To give you some automated guidance, we introduced a “supply outlook” feature to our website. Here is how that looks at the moment:
The calculations of what we can make are quite complicated given that we have thousands of different components going into thousands of different products, and the products (and the associated inventory) can be in various stages of production. Components stop being available once they are soldered onto a board, but that board might still go through many more processing steps before being ready and available for sale. The in stock and “in final production stages” quantities should be spot on, but we variously round down the “enough components” estimate to keep it conservative. The numbers can be outdated quickly since we are selling and making products all the time, but we regenerate those numbers several times a day to be as up-to-date as possible.
The supply outlook feature does not factor in components we have on order, though this year has proven that would be almost useless anyway (I’m not sure if I prefer the suppliers who give me no estimate of a ship date or those who have been saying “next week” for months). On our to-do list is to get more manual/human notes so that we can have updates like, “we are estimated to receive components in March 2024”.
I wish that last line was exaggeration. Unfortunately, I am getting more and more order confirmations with lead times of well over a year and estimated ship dates in late 2024. For parts I ordered early this year, we are approaching three-year lead time estimates for components.
### Supply chain issues impact other aspects of business
Although the chip shortages are the most nerve-wracking aspect of the current environment, other aspects of our business are also affected by the supply chain problems, and it’s getting more and more uncomfortable.
• Waiting more than 9 months for commercial air conditioners - One literal example is the air conditioners in our building. We have over fifty of them, and dozens of them are over twenty years old, meaning they are inefficient and reaching the end of their useful lives. We have had several on order since the beginning of the year, and at this point we are hoping that maybe they will arrive by the end of this year. Fortunately, we made it through the summer, but several units did die recently, and it’s not clear that we can even have them replaced by next summer.
• Waiting more than 6 months for window film - We started applying special solar-blocking films to our windows to help reduce the energy use by the ACs. That project started in late spring, and although part of it got done over the summer, most of it has been delayed by at least six months waiting for more of the film to get manufactured.
• 6-12 month lead time on compressors and nitrogen generators - We ordered a nitrogen-generation system earlier this year, and lead times on that are in the ballpark of a year as well. There are several components to the system and we get billed for them as they arrive, so I don’t think the manufacturer is holding back on any of them while waiting for the others. One component is a fairly standard (though nice) air compressor that I am expecting to use for the rest of manufacturing as our existing ones are getting kind of old. It’s scary to think some of our production or equipment could be out of commission for a year waiting for machines or components that normally are available within a few weeks.
### Outlook
We have been very fortunate at Pololu because we have a broad range of products and do our own design and production, so we have been able to adjust what we make based on what components are available. I don’t understand how more small manufacturers are not going out of business, though I am anecdotally starting to hear more about companies facing financial difficulties. Contract manufacturers in particular have it tough when they have to pay for the components they can get while waiting forever for the last few components and not getting paid until they can complete the final product.
My main hope is that just as we could not see how bad the shortages would be, we cannot see how close we are to the end. If it took two years to get a part that shipped today, it might be reasonable to estimate it will take two years to get a part we order now, or even to tack on an extra year for good measure, but eventually things will be better. I expect inventories everywhere are building up (ours are, just not of the last few critical parts!), and the coming global recession that seems to be forecasted from all sides (e.g. by the IPC) could accelerate chip manufacturers finally catching up to the extra demand from the last few years.
Since we are a small business, broader economic downturns can sometimes work in our favor. Our customer base is such a tiny portion of the world, and some of them could do well even if on average the global economy does not. If the slowdown leads to parts we need becoming available sooner, that might overall be better for us. Some of our best supplier relationships came out of the 2008 downturn, when companies started caring about our business after losing some of their bigger customers. We also got a good deal on renting part of the building we are in after it sat vacant for a couple of years, and that served us especially well as we gradually expanded to the whole building over the past ten years.
It’s unsettling that after two years of parts shortages, it does not seem to be getting any better. The situation might even be worse than it was a year ago, but we won’t really know until we are out of it and things are actually good again. I know it has been difficult for our customers, especially those who built our products into their own products or curricula and are counting on us to keep their operations moving. Please know that we are working very hard to keep our stock and production levels up with the minimal possible disruptions, and thank you very much for your continued business and support.
# November 2021 operations update: supply chain disruptions, price increases, and component rationing
Posted by Jan on 12 November 2021
Nearly two years of operations under the COVID-19 pandemic are behind us. Like many other businesses around the world, our biggest challenges have moved from direct health and safety concerns to secondary disruptions, most notably the supply chain issues and the global chip shortage that has been making news and shutting down factories since last year. Initially, we were relatively isolated from the shortages because we had maintained a high inventory, often stocking a year or more of critical components. However, as the disruptions dragged on, our reserves were depleted, and we have had to resort to increasingly drastic measures to keep operating at all.
I apologize to our customers who are frustrated by our worsening response times, price increases, and unavailability of products. I hope showing you some of what we are dealing with will make it easier to understand.
Here is a screenshot from our internal system showing the inventory history of a relatively unremarkable component (a small MOSFET) that we have been using for almost ten years now:
The stock history is representative for a typical component that we gradually put into more product designs so that the rate of usage keeps increasing and the amount of stock we keep on hand gradually increases, too. Usage of this part ramped up in 2018, to around 35 thousand pieces per year. We last received some shipments in mid-2020 that put us in a seemingly-secure place, but the situation became less comfortable as we got into 2021, and the past several months have been downright alarming since we might only have enough parts for two more months, while the estimated shipment dates for my orders are well into 2022. And this is with us putting the brakes on parts usage!
### Rationing
Slowing down component consumption is really not fun since our main options are just not making any of a product at all (sometimes we are forced into that option anyway once we run out of parts) or raising prices. Higher prices can make it confusing for customers to select among alternatives since we expect the more expensive product to generally be the better one. To help communicate that some products’ prices and availability are temporarily distorted, we added several rationing-related entries to our list of product status designations. You can see the status of each product along with stock and pricing information:
We initially focused on reducing volume discounts, and building the rationing designations into our system let us automatically exclude rationed items from sales and other special promotions. It has been almost six months since we started officially designating products as rationed, and unfortunately, what we expected to be a temporary measure for a few select items has gradually affected more and more products as component shipments keep getting delayed.
Here is the inventory history for another component, a more expensive and specialized part than the previous one:
There were already some supply issues with the part in 2017 that led us to keep slightly higher inventory of that component, and you can see the change in the pattern as we ramped up our rationing efforts. We buy the part on reels of 1,000 pieces, so the upward jumps in the graph are multiples of a thousand, and we used to use up fairly high quantities in each manufacturing run, so the downward jumps were fairly sizable, too. For instance, we might make five hundred of a product at a time and just put it all in stock on the website and not make more for a couple of months. Starting in the second quarter of this year, you can see how the inventory graph is a lot smoother as we made much smaller production runs to preserve flexibility in which products to use the components.
This strategy does help us maximize the usage of the parts we have on hand, but it comes with many costs. Production is less efficient since the machine setup is the same whether we are making twenty units of a product or a thousand units. We also have much more internal scrutinizing, planning, and checking of which products to make since accidentally making the wrong product is a much bigger problem than it used to be—it could now mean prolonged inability to make a different, otherwise unrelated product. It’s also more difficult on customers who do want to buy in bigger volumes since we used to have more stock available on our website, and customers could just order. Now, when we show 29 of a motor controller in stock and a customer needs 50, they have to talk to us about how soon we can make the additional 21. This also strains our support staff resources and reduces the service quality for all customers. And the sad thing is that we are doing a lot more work to produce and sell fewer products.
### What inventory do we do have?
You might be surprised to hear that our total inventory is actually at an all-time high. And apparently, that is fairly common, even among the biggest companies, including the main electronics distributors. When I was talking to my Arrow Electronics rep last month, he said his warehouse is full. I asked of what, and he said he didn’t know, but apparently not the parts he needs.
I spend a lot of time trying to understand what we do have. We have thousands of unique components, and on average we have thousands of each one, so we have many millions of components to keep track of. Most products use many different components, and most components get used in many different products. If we are missing one part out of fifty to make a product, we can’t make the product. And usage rates for the same component are different in different products; what are we supposed to do when we have five thousand left of a component that we use in a $5 product that used to sell thousands of units a month and in a$100 product that sells hundreds of units a month, and the earliest estimated delivery of more components is eight months out? So far, we have mostly raised the prices on the $5 product, sometimes very substantially, while not changing the price on the$100 product, and that lets us keep some finished products available to offer.
There are more and more components that have been on order for over a year now, and meanwhile estimated ship dates for new orders are well into 2023 (not 2022!). It’s a scary time to be an electronics manufacturer.
### Other cost increases
As I mentioned, we are going through a lot more effort to make fewer completed products, and that contributes to increased costs and higher prices independent of what we are doing with rationing. On top of that, prices for most of the components we have been using for a long time have risen substantially, even as our order volumes increase. Most increases have been in the 10% to 20% range, but several are 50% or more.
Then there are parts that we now buy in smaller quantities from catalog distributors like Digi-Key and Mouser (when we find stock there), and those prices can be several times higher. Some parts I bought a year ago for twelve cents each in quantities of fifty thousand are now costing 25 cents each in those bigger volumes, and if I order just a few hundred or a few thousand, they can cost a dollar each. If we just need one of those on a product we sell for $100, it’s not that big of a deal, but if there are three of those components on a product that used to cost$5, the price is going to have to go up, sometimes dramatically.
Non-electronics component and material costs are also going up, though those have generally been in the more modest 5% to 20% range, but shipping costs are up a lot, so that disproportionately affects heavier and bulkier items. We have had to reprice some of our stepper motors primarily because of the shipping costs to get them here, while we have thus far been able to avoid raising costs on our micro metal gearmotors (though volume discounts are smaller than they used to be). Most of our products involve at least some processing in the US, but we are able to ship some items directly from our China warehouse to other countries to reduce the impact of shipping costs and the tariffs on many products coming into the US from China.
The broader supply chain issues are a problem, too, even though it’s not as bad as with the chip shortages. Most of our mechanical parts, from injection molded plastic parts to motors and servos, come from China, and we are more directly involved in getting them shipped here (unlike the electronics parts, which are also mostly made overseas but which we buy from American distributors who deal with getting the parts into the US). Fortunately, most of our components are small and light so we ship a lot by air anyway, but we do ship heavier and bulkier items by boat and have had our share of days looking at all the ships waiting off the coast of California and wondering when ours would finally get to dock. It seems like regular delays by various carriers like FedEx and UPS are also getting worse, and we have now had at least a couple of instances where really important parts we were waiting months for made it to the US or even to Nevada and then got lost.
I have been writing mostly about components and how it affects electronics we manufacture, which is most of our business, but the other small manufacturers whose products we resell are in the same environment, and so we are seeing price increases and extended unavailability of products from them, too.
Delivery delays and other problems are affecting our shipments to our customers, too. Unfortunately, we are again mostly at the mercy of the large shipping companies and the general situation that has led to reduced service levels around the world. Many of the providers have suspended guarantees of delivery times or extended the times they say delivery will take. We have recently added UPS to our standard shipping offerings during checkout, so our customers at least have some more options in case one service is particularly bad in their area.
### When will it get better?
As I wrote a few years ago, we buy our electronics components through major authorized distributors, and we have so far not had to resort to going to secondary sellers and brokers (with the associated risks of ending up with counterfeit parts). From my talking to manufacturers’ representatives, my impression is that the semiconductor companies are just genuinely facing a combination of increased demand and reduced capacity as the pandemic interfered with their operations that are spread throughout the world. For example, ST was telling me about one motor driver that gets the silicon processed in Italy, then tested (still in silicon wafer form) in Singapore, and then chopped up and packaged in Malaysia. In this one instance, the silicon is done, and as operations resume in Malaysia, they should be able to get me some of the parts by the end of the year. But for other parts from the same company, such as microcontrollers, they don’t even have enough allocated to my general western North America region to meaningfully talk about where in the queue we are.
When I first heard predictions in early 2021 that the chip shortages would drag on through the end of the year, I didn’t really believe it. It’s increasingly clear that those predictions were right, but at least 2022 is not that far away anymore! And while we do have many orders with expected ship dates two years out (late 2023), we also have several with expected ship dates in early 2022 (and some parts have been trickling in, so it’s not as if we were completely choked off on all supply).
As we approach the holiday season when we traditionally have our biggest sale, we are assessing which products we can make and possibly discount. We have a few new releases this year that we are very excited about, but new products are especially difficult to ramp up, especially if they use new components we didn’t already have on order a year ago.
Despite the various challenges presented by the evolving pandemic and associated disruptions, we have generally been able to keep operating relatively smoothly this year. I know there are many small businesses of all types struggling or even having to shut down completely, and I am very grateful that we have avoided such extreme scenarios. Thank you to all of the employees at Pololu for so reliably keeping everything running, and thank you to all of our customers for your continued business. I wish everyone a safe and happy conclusion to the year and look forward to things improving on all fronts in 2022.
# 20 years since we shipped the first Pololu product
Posted by Jan on 9 April 2021
Today marks 20 years since we first shipped a Pololu product, on April 9, 2001! Join me for some reminiscing on where we were twenty years ago and for an update on how we are doing now, more than a year into the coronavirus pandemic.
I think I started Pololu in 2000. Probably in the fall, though I know for sure I was working on firmware for a servo controller (this one) over the summer of 2000. I had worked on other product ideas before that, too, but by November 2000 I had made the first board layout that had the name “Pololu” on it:
Here are a couple more pictures of the first prototypes, apparently taken on November 12, 2000. That “v1.2” was the version that became Pololu’s first product. I have seen the picture on that product page over the years, but I had forgotten that we still had to do microcontroller development with special windowed ceramic packages back then, with a separate UV eraser device you stuck the chip in for about ten minutes to erase it. (Production parts would then get made with microcontrollers in cheaper plastic packages that were only programmable once.)
The picture on the right shows Paul’s and my initials on the back side of that PCB design, and Paul registered the pololu.com domain on November 18, 2000. Here is a reconstruction, based on the Internet Archive, of how the Pololu web site probably looked in February 2001:
Candice, Paul, and I formally incorporated Pololu in early 2001, while Paul and I were still undergraduates living in dorm rooms (Candice had graduated a year earlier and was working at The MathWorks). Here are some pictures in the dorm in that time frame (how do we not have any better pictures?):
And then we get to April 9, 2001, for which we have the first recorded order. This is what pops up when we open System 2, our system for running most of the company:
When we started making that system in 2007, we imported the old data, including the fifteen orders we processed in 2001. Order number one was actually just a free sample to Mr. Hughes, my high school science teacher; we would get our first real sale to a paying customer on May 2.
Most of our time was devoted to school, though we did keep working on products we thought we would eventually release, especially when we could incorporate it into our classwork. This first prototype of our Orangutan robot controller (flash programmable microcontroller with a serial bootloader, plus integrated motor drivers) was also part of our final project for our 6.836: Embodied Intelligence class:
Paul and I were class of 2001, so we were close to done with our undergraduate degrees, and I was effectively a grad student that last semester of my fourth year. I skipped the graduation ceremony, but the lab I was working at was right next to the site anyway, and Paul spotted me one of his diplomas so I could feel a little more festive.
This was all still before the 9/11 terrorist attacks, which we experienced quite intensely because of the two flights originating from Boston. Paul had moved out of Massachusetts by then, and I had moved out of the dorms to an apartment in Watertown. Paul visited Candice and me there in February 2002, where we at least remembered to take a picture of our board of directors meeting:
I ended up skipping my second chance to be in the graduation ceremony and moved out of Massachusetts after wrapping up my master’s degree requirements by the end of May. You can see pictures from the next ten years of Pololu in my Ten years in Las Vegas update almost nine years ago.
Besides just focusing on Candice, Paul, and myself, I think it would be fun to look at where some of our other key people were twenty years ago, in 2001. There are fifteen of us still at Pololu who have been here at least ten years, which also means we have been working together since before we were at our current building. Unfortunately, not everyone has ready access to good pictures from 2001!
Ben had these two physical pictures that he scanned for me:
That second one is actually four years older, probably from May 1997, close to our high school graduation. I seem to be holding an RC transmitter and part of a robot arm.
Fang, meanwhile, was in college in China, and it would still be many years before she would even meet Paul:
David was also there for Paul’s graduation, so that must be when I first met him.
He would still go through most of high school and four years of college before moving out to join us in 2008. If you have used any of our USB products, you have benefited from his great work.
David’s college friend RyanTM also moved here from Illinois to join us later that year. These pictures from late 2000 were the closest he could find to 20 years ago:
Ryan gradually became involved in almost all aspects of Pololu, including our facilities and production; since the pandemic started, he has been working mostly remotely and has been able to focus more on our IT needs.
David’s and RyanTM’s college friend Kevin worked at Intel for two years before coming out to join us in 2010.
Kevin and RyanTM were in the same grade at the same high school, but they wouldn’t meet until their sophomore year in the fall of 2001.
Linnea has been with Pololu the longest out of people who were not my friends from school. She also finished college in 2001, at the University of Wisconsin, and moved to Las Vegas that year. She would join us six years later after responding to an ad for an office assistant/shipping clerk.
We had already filled the position she applied for, but we hired her as a laser cutting quoter; she then moved through various roles at Pololu and has now been our HR manager for many years.
Arthur, our operations manager, has also been with us since 2007. Here is his school picture from 20 years ago, when he was a seventh grader in California!
He recalls, “I moved to Vegas without any reason or real plan other than to get away, and when I got here I was totally NOT looking for a job right away. I really only applied here because ‘laser operator’ sounded so cool.”
You might recognize Emily from our videos; she has also had many roles in Pololu, from pick and place machine operator to product designer. She grew up in Vegas and was starting high school in 2000/2001. Here is one of her videos!
That last picture on the right is at the same climbing gym where Ben, Candice, Fang, Paul, and I eventually met her in 2008 when she was finishing up her physics degree at UNLV; she joined us in 2009.
Jennifer joined us in 2008 and effectively was the shipping department. She became the shipping manager as we grew, but she also became more and more involved in the non-technical customer service side. She has been dominating our Halloween costume contests for years, so it’s fitting that the only pictures she could find from 2001 were from Halloween.
We were already moving toward her working exclusively in customer service, and once the pandemic hit, that accelerated the transition; she has been working mostly remotely for the past year, with occasional visits in person just to make sure she can still help out in shipping if we need it.
RyanB is our current shipping manager, and he has been with us since early 2010. Here he is back in Minnesota in the summer of 2001:
You might recognize him on the forklift from some of my new equipment arrival posts like this one.
Damian is the youngest among those who have been at Pololu over ten years; here he is back in late 2001, “probably in fourth grade”:
He joined us in 2010 a year after finishing high school and is now in charge of our electronics production equipment and processes.
Rocky is the fifteenth person who has been with us since 2010 or earlier, and he started on the same day as Damian.
Rocky was working on his mechanical engineering degree at UNLV for his first many years at Pololu, and there were stretches where he was here part time, but he’s been here full time since he graduated in 2018, working on things like quality control and characterization of our gearmotors.
Pololu Valley – As I was looking through old pictures, I was hoping to find one of Candice and me at Pololu Valley in Hawaii. We were there in 2001, and it turns out that’s the last time Candice was in Hawaii (and I only went back once after that, due to a family emergency in 2008). Apparently I took all the pictures and selfies were not so much a thing yet.
The extra data in the picture files indicates this was the day after Christmas in 2001. I don’t remember if we were already thinking of moving to Las Vegas at that point, but I am sure I was not thinking that would be the last time we were there for the next twenty years; otherwise, I definitely would have taken better pictures!
### Pandemic recovery
We hit this twenty-year milestone soon after we passed the one-year anniversary of Nevada businesses getting shut down in response to the coronavirus, which happened on March 18. That makes reflecting on the past 20 years especially strange, with the world as it was just thirteen months ago seeming so foreign now. Life has its ups and downs, and we are not where I perhaps naively dreamed we would be by now, but I am also extremely grateful that we are still functioning at all. When I wrote that first blog post the weekend after the shutdowns started, I really thought we might not make it. I was telling everyone, even these long-term employees I just wrote about above, to go file for unemployment insurance because we wouldn’t be able to pay them.
It took me about five years to get over Dez dying, in the sense that it wasn’t on my mind all the time and that I could feel joyful and think about celebrating successes without flinching at the thought of some disaster blindsiding me. This feeling last March was not as bad, but it still really sucked. I mention these things because I do not want to seem indifferent to the pain and suffering for the millions around the world for whom this pandemic has been that life-shattering event. I also want to write down, before I forget it, how awful and terrifying my situation felt in March 2020, and to help convey the depth of the gratitude I feel toward those who helped Pololu make it this far.
I was already cautiously optimistic in my last update from late February, and since then there has been a very unexpectedly positive development: we started getting vaccinated at the beginning of March! Literally the day after I wrote in my internal company blog that it might still be a few months before we get our vaccines, Nevada opened up eligibility to manufacturing and other sectors applicable to Pololu. On March 3, I got my first shot!
And, two weeks ago, I got my second one! We have also been informally tracking how many of us have gotten the vaccines, and watching these counts go up has been a huge morale boost.
The chart is a lower bound since it only includes people who have shared more specific details for the purposes of generating the chart; I think the actual count of people who have gotten at least one shot is already past 40. There are just over fifty of us now, so that’s around 80%! And over half of us already have the second shot or a single dose of the Johnson & Johnson vaccine.
With the vaccination numbers similarly going up around the country and around the world, and with growing evidence that they work, it’s easy to be optimistic that the worst really is behind us this time. There’s a lot of work to be done, but we have a great team to do it. Thank you so very much to all the customers, suppliers, collaborators, and Pololu employees, past and present, who have kept us in business for 20 years, including this last very difficult year.
And thank you Ben, Fang, Paul, and Candice for doing this with me. I’ve gotten to work with my best friends for two decades, and practically speaking, for my whole life. Thank you for making it awesome!
# February 2021 coronavirus operations update
Posted by Jan on 23 February 2021
We are approaching a year since governments in the US started shutting down businesses in response to the pandemic, and by this time last year, the then-novel coronavirus was already causing what we naively considered to be severe disruption to our operations because of the restrictions that were implemented in China. (We have an office in Shenzhen, and many parts we use, such as bare printed circuit boards, come from China even when our China office is not involved).
The past year has been so filled with ups and downs that it’s difficult to recall how things were when. In my last update in mid-November, I almost wrote something about no one at Pololu having tested positive for COVID yet. That same week, we had several employees test positive as we were caught up in Nevada’s surge in cases. Nevada, like many other states, newly tightened restrictions on businesses and public gatherings, and we scaled back in-person staff to only those necessary on premises for basic operations. Over the holiday period, we had an additional 10-15 people who had been back return to being off-site, leaving around 30 on-site. Fortunately, we seem to have prevented any coronavirus transmission here, and those who did get sick have recovered without serious complications.
Nevada’s government-mandated “pause” was extended twice, and some of the restrictions finally began easing in mid-February. We did have some additional isolated COVID cases among our employees this year, but we have been able to maintain production and shipping throughout this time. It looks like new infection rates are coming down and vaccination rates are going up, which makes it easy to be optimistic that the worst is finally behind us. Like everyone else in the world, we don’t know what changes are still ahead and how close we are to full (or at least substantial) resumption of activities, but it was a big relief at least to make it through 2020, and now the first two months of 2021.
Looking back, we were fortunate to be where we were when the pandemic hit us. One major example is that we did some fairly substantial renovations from 2018-2019, and we spent most of 2019 with big holes in our floors and many areas of the building impassable. I had this hole outside my office starting in February 2019, and the stairs weren’t even usable until July (and they were finally finished even later)!
And our production area looks much better today than it did for most of 2019:
And while it’s still sad to see how empty and underutilized our breakroom has been for the past year, it still beats the piles of dirt we had inside less than a year before.
2020 was stressful enough as it was, and I am very grateful we wrapped up the remodeling by the time the pandemic hit. I feel so sorry for all the businesses who made similar recent investments before the pandemic and then had their businesses completely shut down. At least we are still able to use the space, and I hope it will eventually see more use as it gets safer to have more people in the building.
So, where does that leave us going forward? I’m reminded of a false “proof” by induction, that I can carry infinite weight because I know I can carry some weight and for any weight I can carry, I can carry one gram more. It’s easy to take it for granted and get lulled into complacency that since we’ve made it this far, we’ll make it forever. (That keeps being true until it’s not.) However, I do want to recognize that while in some sense we lost a year, in many ways, we are in a better place than we were a year ago. One way we are acknowledging this is to update our donation requests to be less about our survival. I am hesitant to completely remove those requests and declare victory since that would be an unwarranted arrogance, so I would rather reframe the donation requests as an invitation to support us if you like what we do, similar to how you might donate to content creators on YouTube or Patreon.
Our operations are still stretched fairly thin since we have about 30% fewer people doing almost the same amount of work as we did a year ago. Some things are more difficult to do now than before, but we also have a more experienced core team and we keep working on our processes to do things better. Our emphasis is on normal production and order fulfillment, which I hope has gone well enough that most customers will not have noticed any changes. New challenges, including component shortages and other supply chain disruptions, keep cropping up, but that was also true of just normal life before the pandemic, too. Some of our extra support and special services like product customizations have been affected, but we will work on improving those and on more effective ways to address the very broad range of challenges our customers face.
Thank you to everyone who has supported us and helped us get through this past year. We hope the worst is behind us, and we will keep working hard to contribute to a better future for all of us.
# Our newest robot, 3pi+, is here—Arduino-compatible, USB, encoders, full IMU and more!
Posted by Jan on 23 November 2020
I am thrilled to announce the release of our newest robot, the 3pi+! This new platform is a major upgrade from the original 3pi robot we introduced twelve years ago. At 97 mm, the diameter is just 1mm larger than the original, and the general concept of a tiny, fast robot powered by four AAA batteries and two micro metal gearmotors remains the same. However, just about everything has been redesigned from the ground up to add the extra features everyone has been asking for.
First off, the 3pi+ is now a platform that encompasses a range of products, not just one particular robot. This is enabled primarily by the chassis now being an independent structure rather than being a specific circuit board with motors strapped on:
The chassis incorporates the battery holders, motor mounts, and ball caster. An outer bumper skirt is removable and the motors can instead be held in by separate clips (also included in the kit). The left-most picture shows the chassis with motors installed but without the bumper skirt or motor clips, and the next two pictures show the motor clips installed:
Making the chassis separate from any electronics means that you can use it with your own electronics and that we can make various versions with different capabilities and microcontrollers.
## 3pi+ 32U4
The first full 3pi+ robot we are launching is the 3pi+ 32U4, which is based on an Arduino-compatible ATmega32U4 microcontroller from Microchip (formerly from Atmel). Like the original 3pi, the 3pi+ 32U4 has five integrated downward-looking reflectance sensors, making the robot a great starting point for line following and line-maze events.
The 3pi+ 32U4 offers many major improvements over the original 3pi, including:
• ATmega32U4 microcontroller with Arduino-compatible bootloader can be programmed directly through a USB connection
• Quadrature encoders on both motors for closed-loop position and speed control
• Full 9-axis IMU (three-axis gyro, accelerometer, and compass)
• Full wrap-around bumper to protect electronics from collisions
• Two bump sensors on the front
The 3pi+ 32U4 is also available with three motor options for different usage scenarios:
3pi+ 32U4 Version Products Micro Metal Gearmotor Top Speed Comments
Standard Edition assembled or kit 30:1 MP 6V 1.5 m/s great all-around balance between controllability and speed, with top theoretical speed above that of the original 3pi
Turtle Edition assembled or kit 75:1 LP 6V 0.4 m/s longest battery life, easiest to control, appropriate for swarm robot projects or classrooms where you might not want robots flying around the floor (or desktop) too quickly
Hyper Edition assembled or kit 15:1 HPCB 6V ~4 m/s ridiculous speed, which can definitely be fun. But, controlling that speed can be difficult, which can make the robot more prone to self-destruction (or at least self-inflicted damage), so we recommend this only for advanced users
These three 3pi+ 32U4 motor options are available in assembled or kit form, and for those who want to do your own thing, the parts are available separately so that you can pick some other motor or gear ratio.
Normally we would have an introductory special for this big of a new product release, but since we are about to launch our annual Black Friday and Cyber Monday sale, you can get a great discount on the new 3pi+ there!
# November 2020 update after 8 months of operations under coronavirus
Posted by Jan on 16 November 2020
This week marks eight months since business shutdowns began in Nevada in response to the coronavirus pandemic. Here is an update about how we have been surviving at Pololu since my last detailed post in April, when we got our PPP loan.
We managed to reach a record sales quarter for Q1 despite the last few weeks being under the Nevada emergency measures and February onward being disrupted by the shutdowns affecting our China operations. Sales really dropped in April and even more in May, leading to Q2 sales ending up the worst since 2013. The money we received in April from the PPP loan allowed us to keep paying those employees who were still working and to cover health insurance and other benefits for the rest. We submitted our PPP loan forgiveness application in early July on the day our bank released their application and kept in constant contact with our bank rep while we maintained core operations with a minimal staff.
The initial loan application had been approved very quickly, so we were hoping to get a resolution on the forgiveness similarly quickly to let us know where we stood regarding how much we would be in debt. We made some tough staffing decisions in July and August, and that turned out to be a very good move because the loan forgiveness process ended up taking a lot longer. We started the year with around 80 employees, and by the end of August, we had reduced that to around 55, of which about ten work only remotely. Everyone else has now formally quit or been laid off, with some hope that most of them could eventually return once the pandemic is under control.
Q3 brought several special high-volume sales, including components going into coronavirus testing equipment around the world, which helped Q3 sales inch past our Q1 sales for a new all-time record sales quarter. Perhaps some of that was also impacted by orders delayed from Q2 and from schools buying more kits for the resumption of classes in the fall. It sure felt like things were going in a good direction, which I guess is how a lot of the world felt.
The news did not stay good for long as sales dropped a lot again in October, falling below our April low (but not getting as bad as May) as the new wave of COVID cases swept Europe and brought in renewed shutdowns in many countries there. November has so far also been weak as the coronavirus continues to surge across the globe.
We got one bit of good news for Pololu last week when our PPP loan forgiveness went through! We did not get our whole loan forgiven, but it was over 90% of the loan amount, which is a substantial amount of money that covers a lot of our losses from Q2 and lets us approach the end of the year with a bit of cash reserves instead of being in a hole. It’s a huge relief knowing we should be able to ride out the holiday season without having to do further layoffs.
We are of course working hard to do more than just to get by for another few months. Some of the staff we brought back in the summer are working on new and exciting products, including resumption of projects we had been working on long before the coronavirus hit. We have not even done proper announcements of some of the items that are already released, including our 3-channel wide field of view (FOV) distance sensor module.
That was a very challenging project that I still intend to write about in a separate blog post. Right now, I have one more product to tease that we are pushing to release in time for the holidays!
Speaking of the holidays, normally we would be gearing up for our biggest sale of the year, our Black Friday/Cyber Monday sale that has run from the Wednesday before Thanksgiving through the following Monday. This also made that period very busy for our shipping and manufacturing departments. Since we are working with a reduced staff this year and many people are already stretched thin covering multiple roles, we will be scaling back the intensity of the sale and running it longer in the hopes of distributing the load on those departments. Last year, we introduced a design-your-own-doorbuster promotion, and that was pretty fun to run, so we’ll try to do that again (though we’ll probably be less open to selling things at a loss just to be in the holiday spirit).
Only six more weeks of this crazy year to go! I am so grateful to everyone who has helped us get this far, from all the customers who kept ordering to the employees who stuck with me through the scariest times to everyone who has made a donation. Thank you very much and stay healthy and safe, everybody!
# First new products under emergency operations - new servo wheels!
Posted by Jan on 7 May 2020
We are into May, and after almost 8 weeks of shutdowns and emergency operations, most of the world’s attention seems to be moving toward reopening and how to return to some semblance of normal, or at least longer-term sustainable operations. With no particular medical solution even on the horizon, it’s clear that we have a long way to go, and a city like Las Vegas is going to be hurt especially hard and for a long time by changes people will adopt until they are comfortable flying for fun again. Pololu has managed to hold up much better than I initially feared during the first week of mandated shutdowns, and I am especially grateful to all of our customers and staff members who have worked hard to get us this far.
It is with this backdrop of gratitude for making it this far while realizing we still have a long way to go that I am especially excited to announce our first new products released since the pandemic hit!
In all, we have eight new wheels for micro and standard sized servos. These are red and white versions of the four sizes we released in black back in January. Since we are operating with a minimum staff on site, we don’t have many actual pictures of the new wheels in action, so I will use the pictures with older black wheels for the rest of the post.
We have small, 40 mm and 60 mm sizes that are compatible with micro servo splines with 20 teeth and a 4.8 mm diameter and can be used with the following continuous rotation servos that we carry:
We have larger 70 mm and 90 mm sizes that are compatible with standard servo splines with 25 teeth and a 5.8 mm diameter and can be used with the following continuous rotation servos we carry:
If you plan on using the wheels with a servo not listed above, be sure to check your servo’s specifications for compatibility as servo splines are not standardized.
I was never especially fond of continuous-rotation servos, but there’s no denying that they’re often a quick and relatively simple way to get something moving, both from the electronics side (since the motor controller is built into the servo) and the software side. I am a fan of building your own unique robots, so I am happy we now have a range of size and color choices to give you more problem-solving options and variety in your robots.
Like many of our plastic products, these wheels were designed by us in Las Vegas and then injection molded in China. Since we already had the design and molds finished before we released the black versions, these new products are not the most new from a design perspective. We made the black ones first, and red and white were supposed to follow shortly after the Chinese New Year holiday. As we all got reminded, things don’t always go according to plan. And now, what should have been a minor new product has additional sentimental meaning as our first new product since the coronavirus upended our lives and a symbol of our determination to carry on.
We had been announcing new products along with introductory discounts for the last few years, and I wavered for a bit about doing extra discounts for these wheels. Shipping costs have gone up dramatically, and we’re trying to raise whatever money we can, so extra discounts are not the first thing I felt like doing. But the whole point is that we do want to celebrate at least a little! So, hooray for the continuation of the new product discount tradition:
## Other ways you can help (mostly copied from last post):
### Pay now, ship later
We have added a feature to our online checkout system to allow for orders to be placed with a “pay now, ship later” option that lets you authorize us to charge the payment for an order as soon as it comes in, possibly well ahead of when the order would actually ship. We started working on this feature at a time when we thought complete shutdown of our operations was imminent, when it might have been weeks or even months before we could reopen. As I wrote at the top of this update, we have been able to ship all orders, and I expect to continue shipping, but this option still allows us to prioritize shipments and reduce stress with orders that come in later in the day and can get shipped the next day. We have already received dozens of orders with this option selected, and it is also encouraging just to see that our customers are trying to help us out. Thank you to all of you who have selected that option!
### Order non-soldered versions of products, or the higher-stock versions
We offer a few of our products with some of the optional (but usually used) through-hole connectors soldered in. If you are able to solder, please consider ordering the non-soldered versions if there is plentiful stock of them. We do all of the through-hole soldering by hand, and most of our manual assemblers were older or otherwise in the higher-risk population for COVID-19, so they are not currently working here. And if you’re at home doing a non-critical project, now is a good time to do a little extra soldering, right?
On a related note, it’s a little bit easier for us if you order the item that has more stock. Each product page has links to relevant parametric comparison tables that can help you identify similar products that might have more available stock:
If your application could get by with either an item of which we have 300 in stock or one of which we have 12 units, please get the product that we have much more of. It’s probably a more popular version that we make more often, and it keeps the less popular version available for those who might really need it.
### Help each other on our forum
We have had to severely cut back on our technical support. If you are one those people with extra time on your hands now and are familiar with any of our products, please consider helping out our other customers on our forum.
### Ask others to help us out
If you know anybody that could afford to help us out, please let them know and ask them to contribute.
### Other suggestions and ideas
Part of the reason I have been going into more details in some areas of these updates is so you might be able to better give us advice about how we could make things better. Maybe you’re also working at a small business facing similar challenges, and you have some good suggestions. Maybe your uncle has a vacant building nearby. One suggestion I’ve heard repeatedly is about gift certificates, which we are looking into; if you know of particularly good ways of implementing that or things to be careful about, please let us know.
# COVID-19 impact update: still hanging on after three weeks
Posted by Jan on 6 April 2020
Monday, 13 April 2020 update – we got our PPP loan!
## After 3 weeks of emergency operations, we are still shipping all orders!
Today, April 6, marks the beginning of our fourth week of emergency operations. We are still hanging on, and it looks like we will be able to maintain operations similar to those of the past three weeks (i.e. continue shipping all orders with a minimal staff on site) at least through the end of April, by which point I hope some of the emergency loans we have applied for might start coming in.
## Thank you for your continued donations 🙏
We are very grateful for the many donations that continue to come in. As we trim our expenses, those donations become a larger fraction of what we need to get by. I know it’s asking so much for donations with no strings attached, and it means a great deal at a time when we are scrambling to make ends meet. To the many of you making us special proposals and suggestions, thank you and please keep them coming. We do not have the resources now to reply to them individually, but they do affect what we are considering offering and how we continue to operate.
If you can, please consider donating to help Pololu make it. We have set up item 2400 for donating in $1 increments. ## Please help reduce overwhelming workload (for those of us who can work) We are especially grateful for any routine orders that do not require special considerations. We are also happy to help with emergency orders involving efforts to fight the pandemic. For smaller, non-emergency inquiries, please understand that we are trying to maintain most of our usual operations with a much more limited staff while having to take on a lot of extra work (new HR issues for navigating layoffs vs. waiting for possible stimulus funds, coming up with new operating/safety procedures, rerouting incoming and outgoing packages among constantly changing rules for each country and carrier, etc.). Please help us reduce our workload by cutting back on non-critical inquiries. For regular orders, prices and stock are all on the web site. Tracking numbers are included in shipment confirmation emails. Invoices are available on the website when you log in. For technical support, please consider our forum. ## Emergency loan updates One of the most common questions or recommendations we get is about applying for emergency loans. We applied for an SBA economic injury disaster loan (EIDL) almost two weeks ago and followed up with the$10k advance application provided by the new CARES Act. We have been working with our bank all weekend to apply for the new Paycheck Protection Program loan, the applications for which have just started becoming available. My understanding is that the SBA is also scrambling as it is suddenly charged with processing more than 10x what they usually do over the whole year over the next several weeks. We received some confirmation about the EIDL loan being received but there’s been no visible progress on that, and in general, it’s difficult to know what to expect in terms of if, when, and how much we might be able to receive in emergency loans.
Given that uncertainty, it is especially urgent for us to cut costs where we can and to bring in whatever money we can to keep covering basic expenses. We are definitely hoping we qualify for some assistance and that it will come soon, so we are doing everything we can to keep all those applications moving forward while also trying to maintain operations independent of any guarantee of anything coming from that.
## Employee update
We received a few responses questioning our treatment of employees while asking for donations. They are far outnumbered by positive responses, and I suspect the negative responses come from people who have little appreciation of the realities of running a small business, especially amid this level of disruption. Nevertheless, I believe more people might be wondering about what we are doing, and I am proud of our response given the circumstances, so I would like to highlight what we have done so far.
Some of the responses questioned the “over half of our staff is unpaid in one way or another” phrasing. We had about 75 employees at the beginning of March, and over half of them are now either laid off, on unpaid leave, or volunteering to take a pay cut. This is just a basic reality of payroll being by far our biggest expense, and if people cannot come in to work and money stops coming in, there is nothing to pay them from. We are doing everything we can to keep Pololu in a viable state so that there is something for everyone to come back to in a few weeks or months.
Here is some of the rest of our response:
• Prior to any Nevada mandates, we began staggering our workbenches, improving sanitizing procedures, and set up some employees for working remotely.
• Within the first day of the Nevada governor’s emergency business closure declaration, we set up an emergency forum for all employees to be able to communicate without being on site. I have been posting there almost daily to keep everyone in the loop on our operations and outlook.
• We contacted all employees to make sure we had their contact information and understood their preferences about working (different people have different preferences based on their living arrangements, risk factors for COVID-19, etc.).
• We are maintaining health insurance and similar benefits for everyone who had them, including paying the employees’ portion for those who could not work and were out of paid time off (PTO). Some employees who were scheduled to begin getting coverage through Pololu are still getting added to our plans.
• We paid out remaining PTO to those laid off.
• We are maintaining PTO for those on unpaid leave and those still working.
• We paid full amounts due to those still able to work (excluding those volunteering for pay cuts).
• We are continuing safety assessments for on-site operations, including providing face masks for all on-site staff.
• We are working on improving remote connection and work capability.
## How you can help
### Make a donation
If you can, please consider donating to help Pololu make it. We have set up item 2400 for donating in \$1 increments.
### Pay now, ship later
We have added a feature to our online checkout system to allow for orders to be placed with a “pay now, ship later” option that lets you authorize us to charge the payment for an order as soon as it comes in, possibly well ahead of when the order would actually ship. We started working on this feature at a time when we thought complete shutdown of our operations was imminent, when it might have been weeks or even months before we could reopen. As I wrote at the top of this update, we have been able to ship all orders, and I expect to continue shipping, but this option still allows us to prioritize shipments and reduce stress with orders that come in later in the day and can get shipped the next day. We have already received dozens of orders with this option selected, and it is also encouraging just to see that our customers are trying to help us out. Thank you to all of you who have selected that option!
### Order non-soldered versions of products, or the higher-stock versions
We offer a few of our products with some of the optional (but usually used) through-hole connectors soldered in. If you are able to solder, please consider ordering the non-soldered versions if there is plentiful stock of them. We do all of the through-hole soldering by hand, and most of our manual assemblers were older or otherwise in the higher-risk population for COVID-19, so they are not currently working here. And if you’re at home doing a non-critical project, now is a good time to do a little extra soldering, right?
On a related note, it’s a little bit easier for us if you order the item that has more stock. Each product page has links to relevant parametric comparison tables that can help you identify similar products that might have more available stock:
If your application could get by with either an item of which we have 300 in stock or one of which we have 12 units, please get the product that we have much more of. It’s probably a more popular version that we make more often, and it keeps the less popular version available for those who might really need it.
### Help each other on our forum
We have had to severely cut back on our technical support. If you are one those people with extra time on your hands now and are familiar with any of our products, please consider helping out our other customers on our forum.
### Ask others to help us out
If you know anybody that could afford to help us out, please let them know and ask them to contribute.
### Other suggestions and ideas
Part of the reason I have been going into more details in some areas of these updates is so you might be able to better give us advice about how we could make things better. Maybe you’re also working at a small business facing similar challenges, and you have some good suggestions. Maybe your uncle has a vacant building nearby. One suggestion I’ve heard repeatedly is about gift certificates, which we are looking into; if you know of particularly good ways of implementing that or things to be careful about, please let us know.
## Thank you all for your support. Stay safe and healthy, everybody!
Monday, 13 April 2020 update – we got our PPP loan!
(702) 262-6648
Same-day shipping, worldwide | 2022-12-01 06:12:15 | {"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": 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": 0.19490104913711548, "perplexity": 1278.533883166928}, "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/1669446710801.42/warc/CC-MAIN-20221201053355-20221201083355-00101.warc.gz"} |
https://tex.stackexchange.com/questions/121663/parenthesis-around-year | # parenthesis around year
I tried to put the date in parenthesis and the result ist quite weird. I just want to have the year in this form: (2005) and instead (. 2005) is printed.
\begin{filecontents*}{test.bib}
@ARTICLE{Andreasen2005,
author = {Nancy C Andreasen and William T Carpenter and John M Kane and Robert
A Lasser and Stephen R Marder and Daniel R Weinberger},
title = {Remission in schizophrenia: proposed criteria and rationale for consensus.},
journal = {Am J Psychiatry},
year = {2005},
volume = {162},
pages = {441--449},
number = {3},
month = {3}
}
\end{filecontents*}
\documentclass[
12pt,
DIV10,
ngerman,
a4paper,
]{scrreprt}
\usepackage[ngerman]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[
bibstyle=test, citestyle=test
]{biblatex}
\bibliography{test.bib}
\begin{document}
\cite{Andreasen2005}
\printbibliography
\end{document}
and my test.bbx-file
% $Id: test.bbx,v 0.1 2013/06/28 19:09:07 lehman unstable$
\ProvidesFile{test.bbx}
[\abx@bbxid $Id: test.bbx,v 0.1 2013/06/28 19:09:07 lehman unstable$]
\newbibmacro*{begentry}{}
\newbibmacro*{finentry}{\finentry}
\DeclareBibliographyDriver{article}{%
\usebibmacro{bibindex}%
\usebibmacro{begentry}%
\usebibmacro{author/translator+others}%
\setunit{\labelnamepunct}\newblock
\usebibmacro{title}%
\newunit\newblock
\usebibmacro{byauthor}%
\newunit\newblock
\usebibmacro{bytranslator+others}%
\newunit\newblock
\printfield{version}%
\newunit\newblock
\usebibmacro{journal+issuetitle}%
\newunit
\usebibmacro{byeditor+others}%
\newunit
\usebibmacro{note+pages}%
\newunit\newblock
\usebibmacro{date}
\setunit{\bibpagerefpunct}\newblock
\usebibmacro{pageref}%
\usebibmacro{finentry}}
\newbibmacro*{journal+issuetitle}{%
\usebibmacro{journal}%
\iffieldundef{series}
{}
{\newunit
\printfield{series}%
\usebibmacro{volume}%
\usebibmacro{issue}%
\newunit}
\newbibmacro*{volume}{%
\printfield{volume}%
}
\newbibmacro*{issue}{%
\iffieldundef{issue}
{}
{\printtext[parens]{%
{\printfield{issue}%
\newunit}}
\newbibmacro*{series+number}{%
\printfield{series}%
\printfield{number}%
\newunit}
\newbibmacro*{note+pages}{%
\printfield{note}%
\setunit{\bibpagespunct}%
\printfield{pages}%
\newunit}
\renewbibmacro*{date}{\mkbibparens{\printdate}}
\endinput
and my test.cbx-file
% $Id: test.cbx,v 1.7 2011/11/13 19:09:07 lehman stable$
\ProvidesFile{test.cbx}
[\abx@cbxid $Id: verbose-inote.cbx,v 1.7 2011/11/13 19:09:07 lehman stable$]
\providebool{bbx:subentry}
\DeclareFieldFormat{entrysetcount}{\mknumalph{#1}}
\newbibmacro*{cite}{%
\printtext[bibhyperref]{%
\printfield{prefixnumber}%
\printfield{labelnumber}%
\ifbool{bbx:subentry}
{\printfield{entrysetcount}}
{}}}
\DeclareCiteCommand{\cite}[\mkbibbrackets]
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\usebibmacro{cite}}
{\multicitedelim}
{\usebibmacro{postnote}}
\AtEveryBibitem{\clearfield{month}}
\endinput
• See §4.11.7.2 of the biblatex manual. Unit punctuation is not handled synchronously. There's an example almost identical to yours there. Jun 29, 2013 at 0:31
• okay it's working. i just had to replace \renewbibmacro*{date}{\mkbibparens{\printdate}} by \DeclareFieldFormat{parens}{\mkbibparens{#1}} and \renewbibmacro*{date}{\printtext[parens]{\printdate}} in test.bbx Thank you very much Alan!
– ingo
Jun 29, 2013 at 1:31
• Since you solved your own problem (I just pointed you to the right place) you should turn your comment into an actual answer. You'll have to wait a day or so before you accept it (which you should, by clicking on the checkmark beside the answer). Jun 29, 2013 at 1:36
• ok, i'll do it.
– ingo
Jun 29, 2013 at 2:04
• Ah now I understand this portal. There are questions, comments, answers and patient Alans:-) Now it should be okay.
– ingo
Jun 29, 2013 at 3:32
Unfortunately, as a guest I can't comment on the solution posted above. But I'd like to note that this solution will cause the 'mergedate=basic' option to stop working as expected. Using this instead:
\DeclareFieldFormat{parens}{\mkbibparens{#1}}
\renewbibmacro*{date}{%
\iffieldundef{month}
{}
{\printtext[parens]{\printdate}}}%
when using 'mergedate=basic' will be fine. For any other option one should take a look at authoryear.bbx file and adopt the according lines of code.
• Needless to say that DeclareFieldFormat{parens}{\mkbibparens{#1}} is only ever necessary if you do not load a biblatex standard style (or one not based on biblatex.def). So with normal authoryear styles that line can be dropped, as it exactly corresponds to the definition in biblatex.def. Aug 25, 2015 at 9:54
The Solution:
Replace
\renewbibmacro*{date}{\mkbibparens{\printdate}}
by
\DeclareFieldFormat{parens}{\mkbibparens{#1}}
\renewbibmacro*{date}{\printtext[parens]{\printdate}}
and this is the new test.bbx-file:
% $Id: test.bbx,v 0.1 2013/06/28 19:09:07 lehman unstable$
\ProvidesFile{test.bbx}
[\abx@bbxid $Id: test.bbx,v 0.1 2013/06/28 19:09:07 lehman unstable$]
\newbibmacro*{begentry}{}
\newbibmacro*{finentry}{\finentry}
\DeclareBibliographyDriver{article}{%
\usebibmacro{bibindex}%
\usebibmacro{begentry}%
\usebibmacro{author/translator+others}%
\setunit{\labelnamepunct}\newblock
\usebibmacro{title}%
\newunit\newblock
\usebibmacro{byauthor}%
\newunit\newblock
\usebibmacro{bytranslator+others}%
\newunit\newblock
\printfield{version}%
\newunit\newblock
\usebibmacro{journal+issuetitle}%
\newunit
\usebibmacro{byeditor+others}%
\newunit
\usebibmacro{note+pages}%
\newunit\newblock
\usebibmacro{date}
\setunit{\bibpagerefpunct}\newblock
\usebibmacro{pageref}%
\usebibmacro{finentry}}
\newbibmacro*{journal+issuetitle}{%
\usebibmacro{journal}%
\iffieldundef{series}
{}
{\newunit
\printfield{series}%
\usebibmacro{volume}%
\usebibmacro{issue}%
\newunit}
\newbibmacro*{volume}{%
\printfield{volume}%
}
\newbibmacro*{issue}{%
\iffieldundef{issue}
{}
{\printtext[parens]{%
{\printfield{issue}%
\newunit}}
\newbibmacro*{series+number}{%
\printfield{series}% | 2022-05-22 17:23:26 | {"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": 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": 0.7123774886131287, "perplexity": 3632.266937832448}, "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/1652662545875.39/warc/CC-MAIN-20220522160113-20220522190113-00484.warc.gz"} |
https://www.rdocumentation.org/packages/VGAM/versions/1.1-6/topics/cqo | VGAM (version 1.1-6)
# cqo: Fitting Constrained Quadratic Ordination (CQO)
## Description
A constrained quadratic ordination (CQO; formerly called canonical Gaussian ordination or CGO) model is fitted using the quadratic reduced-rank vector generalized linear model (QRR-VGLM) framework.
## Usage
cqo(formula, family = stop("argument 'family' needs to be assigned"),
data = list(), weights = NULL, subset = NULL,
na.action = na.fail, etastart = NULL, mustart = NULL,
coefstart = NULL, control = qrrvglm.control(...), offset = NULL,
method = "cqo.fit", model = FALSE, x.arg = TRUE, y.arg = TRUE,
contrasts = NULL, constraints = NULL, extra = NULL,
smart = TRUE, ...)
## Arguments
formula
a symbolic description of the model to be fit. The RHS of the formula is applied to each linear predictor. Different variables in each linear predictor can be chosen by specifying constraint matrices.
family
a function of class "vglmff" (see vglmff-class) describing what statistical model is to be fitted. This is called a VGAM family function''. See CommonVGAMffArguments for general information about many types of arguments found in this type of function. Currently the following families are supported: poissonff, binomialff (logitlink and clogloglink links available), negbinomial, gamma2. Sometimes special arguments are required for cqo(), e.g., binomialff(multiple.responses = TRUE).
data
an optional data frame containing the variables in the model. By default the variables are taken from environment(formula), typically the environment from which cqo is called.
weights
an optional vector or matrix of (prior) weights to be used in the fitting process. Currently, this argument should not be used.
subset
an optional logical vector specifying a subset of observations to be used in the fitting process.
na.action
a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The factory-fresh'' default is na.omit.
etastart
starting values for the linear predictors. It is a $$M$$-column matrix. If $$M = 1$$ then it may be a vector. Currently, this argument probably should not be used.
mustart
starting values for the fitted values. It can be a vector or a matrix. Some family functions do not make use of this argument. Currently, this argument probably should not be used.
coefstart
starting values for the coefficient vector. Currently, this argument probably should not be used.
control
a list of parameters for controlling the fitting process. See qrrvglm.control for details.
offset
This argument must not be used.
method
the method to be used in fitting the model. The default (and presently only) method cqo.fit uses iteratively reweighted least squares (IRLS).
model
a logical value indicating whether the model frame should be assigned in the model slot.
x.arg, y.arg
logical values indicating whether the model matrix and response matrix used in the fitting process should be assigned in the x and y slots. Note the model matrix is the LM model matrix.
contrasts
an optional list. See the contrasts.arg of model.matrix.default.
constraints
an optional list of constraint matrices. The components of the list must be named with the term it corresponds to (and it must match in character format). Each constraint matrix must have $$M$$ rows, and be of full-column rank. By default, constraint matrices are the $$M$$ by $$M$$ identity matrix unless arguments in the family function itself override these values. If constraints is used it must contain all the terms; an incomplete list is not accepted. Constraint matrices for $$x_2$$ variables are taken as the identity matrix.
extra
an optional list with any extra information that might be needed by the family function.
smart
logical value indicating whether smart prediction (smartpred) will be used.
further arguments passed into qrrvglm.control.
## Value
An object of class "qrrvglm".
## Warning
Local solutions are not uncommon when fitting CQO models. To increase the chances of obtaining the global solution, increase the value of the argument Bestof in qrrvglm.control. For reproducibility of the results, it pays to set a different random number seed before calling cqo (the function set.seed does this). The function cqo chooses initial values for C using .Init.Poisson.QO() if Use.Init.Poisson.QO = TRUE, else random numbers.
Unless I.tolerances = TRUE or eq.tolerances = FALSE, CQO is computationally expensive with memory and time. It pays to keep the rank down to 1 or 2. If eq.tolerances = TRUE and I.tolerances = FALSE then the cost grows quickly with the number of species and sites (in terms of memory requirements and time). The data needs to conform quite closely to the statistical model, and the environmental range of the data should be wide in order for the quadratics to fit the data well (bell-shaped response surfaces). If not, RR-VGLMs will be more appropriate because the response is linear on the transformed scale (e.g., log or logit) and the ordination is called constrained linear ordination or CLO.
Like many regression models, CQO is sensitive to outliers (in the environmental and species data), sparse data, high leverage points, multicollinearity etc. For these reasons, it is necessary to examine the data carefully for these features and take corrective action (e.g., omitting certain species, sites, environmental variables from the analysis, transforming certain environmental variables, etc.). Any optimum lying outside the convex hull of the site scores should not be trusted. Fitting a CAO is recommended first, then upon transformations etc., possibly a CQO can be fitted.
For binary data, it is necessary to have enough' data. In general, the number of sites $$n$$ ought to be much larger than the number of species S, e.g., at least 100 sites for two species. Compared to count (Poisson) data, numerical problems occur more frequently with presence/absence (binary) data. For example, if Rank = 1 and if the response data for each species is a string of all absences, then all presences, then all absences (when enumerated along the latent variable) then infinite parameter estimates will occur. In general, setting I.tolerances = TRUE may help.
This function was formerly called cgo. It has been renamed to reinforce a new nomenclature described in Yee (2006).
## Details
QRR-VGLMs or constrained quadratic ordination (CQO) models are estimated here by maximum likelihood estimation. Optimal linear combinations of the environmental variables are computed, called latent variables (these appear as latvar for $$R=1$$ else latvar1, latvar2, etc. in the output). Here, $$R$$ is the rank or the number of ordination axes. Each species' response is then a regression of these latent variables using quadratic polynomials on a transformed scale (e.g., log for Poisson counts, logit for presence/absence responses). The solution is obtained iteratively in order to maximize the log-likelihood function, or equivalently, minimize the deviance.
The central formula (for Poisson and binomial species data) is given by $$\eta = B_1^T x_1 + A \nu + \sum_{m=1}^M (\nu^T D_m \nu) e_m$$ where $$x_1$$ is a vector (usually just a 1 for an intercept), $$x_2$$ is a vector of environmental variables, $$\nu=C^T x_2$$ is a $$R$$-vector of latent variables, $$e_m$$ is a vector of 0s but with a 1 in the $$m$$th position. The $$\eta$$ are a vector of linear/additive predictors, e.g., the $$m$$th element is $$\eta_m = \log(E[Y_m])$$ for the $$m$$th species. The matrices $$B_1$$, $$A$$, $$C$$ and $$D_m$$ are estimated from the data, i.e., contain the regression coefficients. The tolerance matrices satisfy $$T_s = -\frac12 D_s^{-1}$$. Many important CQO details are directly related to arguments in qrrvglm.control, e.g., the argument noRRR specifies which variables comprise $$x_1$$.
Theoretically, the four most popular VGAM family functions to be used with cqo correspond to the Poisson, binomial, normal, and negative binomial distributions. The latter is a 2-parameter model. All of these are implemented, as well as the 2-parameter gamma.
For initial values, the function .Init.Poisson.QO should work reasonably well if the data is Poisson with species having equal tolerances. It can be quite good on binary data too. Otherwise the Cinit argument in qrrvglm.control can be used.
It is possible to relax the quadratic form to an additive model. The result is a data-driven approach rather than a model-driven approach, so that CQO is extended to constrained additive ordination (CAO) when $$R=1$$. See cao for more details.
In this documentation, $$M$$ is the number of linear predictors, $$S$$ is the number of responses (species). Then $$M=S$$ for Poisson and binomial species data, and $$M=2S$$ for negative binomial and gamma distributed species data.
Incidentally, Unconstrained quadratic ordination (UQO) may be performed by, e.g., fitting a Goodman's RC association model; see uqo and the Yee and Hadi (2014) referenced there. For UQO, the response is the usual site-by-species matrix and there are no environmental variables; the site scores are free parameters. UQO can be performed under the assumption that all species have the same tolerance matrices.
## References
Yee, T. W. (2004). A new technique for maximum-likelihood canonical Gaussian ordination. Ecological Monographs, 74, 685--701.
ter Braak, C. J. F. and Prentice, I. C. (1988). A theory of gradient analysis. Advances in Ecological Research, 18, 271--317.
Yee, T. W. (2006). Constrained additive ordination. Ecology, 87, 203--213.
qrrvglm.control, Coef.qrrvglm, predictqrrvglm, calibrate.qrrvglm, model.matrixqrrvglm, vcovqrrvglm, rcqo, cao, uqo, rrvglm, poissonff, binomialff, negbinomial, gamma2, lvplot.qrrvglm, perspqrrvglm, trplot.qrrvglm, vglm, set.seed, hspider, trapO.
## Examples
Run this code
# NOT RUN {
# Example 1; Fit an unequal tolerances model to the hunting spiders data
hspider[,1:6] <- scale(hspider[,1:6]) # Standardized environmental variables
set.seed(1234) # For reproducibility of the results
p1ut <- cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
Auloalbi, Pardlugu, Pardmont, Pardnigr, Pardpull,
Trocterr, Zoraspin) ~
WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
fam = poissonff, data = hspider, Crow1positive = FALSE,
eq.tol = FALSE)
sort(deviance(p1ut, history = TRUE)) # A history of all the iterations
if (deviance(p1ut) > 1177) warning("suboptimal fit obtained")
S <- ncol(depvar(p1ut)) # Number of species
clr <- (1:(S+1))[-7] # Omits yellow
lvplot(p1ut, y = TRUE, lcol = clr, pch = 1:S, pcol = clr,
las = 1) # Ordination diagram
legend("topright", leg = colnames(depvar(p1ut)), col = clr,
pch = 1:S, merge = TRUE, bty = "n", lty = 1:S, lwd = 2)
(cp <- Coef(p1ut))
(a <- latvar(cp)[cp@latvar.order]) # Ordered site scores along the gradient
# Names of the ordered sites along the gradient:
rownames(latvar(cp))[cp@latvar.order]
(aa <- Opt(cp)[, cp@Optimum.order]) # Ordered optimums along the gradient
aa <- aa[!is.na(aa)] # Delete the species that is not unimodal
names(aa) # Names of the ordered optimums along the gradient
trplot(p1ut, which.species = 1:3, log = "xy", type = "b", lty = 1, lwd = 2,
col = c("blue","red","green"), label = TRUE) -> ii # Trajectory plot
legend(0.00005, 0.3, paste(ii$species[, 1], ii$species[, 2], sep = " and "),
lwd = 2, lty = 1, col = c("blue", "red", "green"))
abline(a = 0, b = 1, lty = "dashed")
S <- ncol(depvar(p1ut)) # Number of species
clr <- (1:(S+1))[-7] # Omits yellow
persp(p1ut, col = clr, label = TRUE, las = 1) # Perspective plot
# Example 2; Fit an equal tolerances model. Less numerically fraught.
set.seed(1234)
p1et <- cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
Auloalbi, Pardlugu, Pardmont, Pardnigr, Pardpull,
Trocterr, Zoraspin) ~
WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
poissonff, data = hspider, Crow1positive = FALSE)
sort(deviance(p1et, history = TRUE)) # A history of all the iterations
if (deviance(p1et) > 1586) warning("suboptimal fit obtained")
S <- ncol(depvar(p1et)) # Number of species
clr <- (1:(S+1))[-7] # Omits yellow
persp(p1et, col = clr, label = TRUE, las = 1)
# Example 3: A rank-2 equal tolerances CQO model with Poisson data
# This example is numerically fraught... need I.toler = TRUE too.
set.seed(555)
p2 <- cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
Auloalbi, Pardlugu, Pardmont, Pardnigr, Pardpull,
Trocterr, Zoraspin) ~
WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
poissonff, data = hspider, Crow1positive = FALSE,
I.toler = TRUE, Rank = 2, Bestof = 3, isd.latvar = c(2.1, 0.9))
sort(deviance(p2, history = TRUE)) # A history of all the iterations
if (deviance(p2) > 1127) warning("suboptimal fit obtained")
lvplot(p2, ellips = FALSE, label = TRUE, xlim = c(-3,4),
C = TRUE, Ccol = "brown", sites = TRUE, scol = "grey",
pcol = "blue", pch = "+", chull = TRUE, ccol = "grey")
# Example 4: species packing model with presence/absence data
set.seed(2345)
n <- 200; p <- 5; S <- 5
mydata <- rcqo(n, p, S, fam = "binomial", hi.abundance = 4,
eq.tol = TRUE, es.opt = TRUE, eq.max = TRUE)
myform <- attr(mydata, "formula")
set.seed(1234)
data = mydata)
sort(deviance(b1et, history = TRUE)) # A history of all the iterations
lvplot(b1et, y = TRUE, lcol = 1:S, pch = 1:S, pcol = 1:S, las = 1)
Coef(b1et)
# Compare the fitted model with the 'truth'
cbind(truth = attr(mydata, "concoefficients"), fitted = concoef(b1et))
# Example 5: Plot the deviance residuals for diagnostic purposes
set.seed(1234)
p1et <- cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
Auloalbi, Pardlugu, Pardmont, Pardnigr, Pardpull,
Trocterr, Zoraspin) ~
WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
poissonff, data = hspider, eq.tol = TRUE, trace = FALSE)
sort(deviance(p1et, history = TRUE)) # A history of all the iterations
if (deviance(p1et) > 1586) warning("suboptimal fit obtained")
S <- ncol(depvar(p1et))
par(mfrow = c(3, 4))
for (ii in 1:S) {
tempdata <- data.frame(latvar1 = c(latvar(p1et)),
sppCounts = depvar(p1et)[, ii])
tempdata <- transform(tempdata, myOffset = -0.5 * latvar1^2)
# For species ii, refit the model to get the deviance residuals
fit1 <- vglm(sppCounts ~ offset(myOffset) + latvar1, poissonff,
data = tempdata, trace = FALSE)
# For checking: this should be 0
# print("max(abs(c(Coef(p1et)@B1[1,ii],Coef(p1et)@A[ii,1])-coef(fit1)))")
# print( max(abs(c(Coef(p1et)@B1[1,ii],Coef(p1et)@A[ii,1])-coef(fit1))) )
# Plot the deviance residuals
devresid <- resid(fit1, type = "deviance")
predvalues <- predict(fit1) + fit1@offset
ooo <- with(tempdata, order(latvar1))
plot(predvalues + devresid ~ latvar1, data = tempdata, col = "red",
xlab = "latvar1", ylab = "", main = colnames(depvar(p1et))[ii])
with(tempdata, lines(latvar1[ooo], predvalues[ooo], col = "blue"))
}
# }
`
Run the code above in your browser using DataCamp Workspace | 2022-09-30 18:35:16 | {"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": 2, "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": 0.41599327325820923, "perplexity": 6643.294204292525}, "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-2022-40/segments/1664030335504.22/warc/CC-MAIN-20220930181143-20220930211143-00002.warc.gz"} |
http://mathhelpforum.com/calculus/37423-limit-problems.html | 1. limit problems
On Monday our teacher surprised us by telling us that we have a quiz on wednesday. Tonight she gave us homework, and I went through all of the questions, but there were ton of stuff I didn't see before. So I tried doing it on my own, but it got kinda crazy. So here they are. Sorry for not using latex, but I just don't got the time to learn the complex latex codes at the moment. I'll try to learn them after my midterm, which is next week.
1c) lim x-->0 (sin3X)/5X
e) lim x-->0 x cscx
g) lim x-->0 (1-cos2X)/X
i) lim x-->(pie/2) (((pie/2)-x)/(cosx)
2.Differentiate y with respect to X (I think we have to simplify which makes me )
2a)y= ((tan^4)(3x)
c)y=secx^2
d) y=(cot^2)2X/(1+x^2)
f) y=2sec(squareroot X)
h) y=cos^2(tanx)
i) y=1/(sin(x-sinx)
3. A triangle has adjacent sides of 4cm and 6cm. Prove that the traingle has a maximum area when the angle enclosed by these sides is 90degree.
4. A rain gutter is to be constructed wfrom a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle (theata). How should theata be chosen so the gutte will carry the maximum amount of water.
-----
On another sheet
A rectangular shet of iron 300 cm wide is to be bent to form a gutter whose cross section is the arc of a circle. What radius will give the gutter the maximum carrying capacity.
Thats all folks.
2. Hi
Originally Posted by Mr. Edward
1c) lim x--> (sin3X)/5X
e) lim x--> x cscx
g) lim x--> (1-cos2X)/X
i) lim x--> (((pie/2)-x)/(cosx)
$x\to ?$
For this four limits, think about the definition of the derivative : $f'(t)=\lim_{h\to0}\frac{f(t+h)-f(t)}{h}$
For example, for the first one (I guess $x\to 0$) :
$\lim_{x\to0}\frac{\sin(3x)}{5x}=\lim_{x\to0} \frac{1}{5}\cdot\frac{\sin(3(0+x))-\sin(3\cdot0)}{x}=\frac{1}{5}\cdot 3\cdot \cos(0)=\ldots$
because the derivative of $x\mapsto \sin(3x)$ is $x\mapsto3\cos(3x)$
3. Originally Posted by Mr. Edward
On Monday our teacher surprised us by telling us that we have a quiz on wednesday. Tonight she gave us homework, and I went through all of the questions, but there were ton of stuff I didn't see before. So I tried doing it on my own, but it got kinda crazy. So here they are. Sorry for not using latex, but I just don't got the time to learn the complex latex codes at the moment. I'll try to learn them after my midterm, which is next week.
1c) lim x--> (sin3X)/5X
e) lim x--> x cscx
g) lim x--> (1-cos2X)/X
i) lim x--> (((pie/2)-x)/(cosx)
2.Differentiate y with respect to X (I think we have to simplify which makes me )
2a)y= ((tan^4)(3x)
c)y=secx^2
d) y=(cot^2)2X/(1+x^2)
f) y=2sec(squareroot X)
h) y=cos^2(tanx)
i) y=1/(sin(x-sinx)
3. A triangle has adjacent sides of 4cm and 6cm. Prove that the traingle has a maximum area when the angle enclosed by these sides is 90degree.
4. A rain gutter is to be constructed wfrom a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle (theata). How should theata be chosen so the gutte will carry the maximum amount of water.
-----
On another sheet
A rectangular shet of iron 300 cm wide is to be bent to form a gutter whose cross section is the arc of a circle. What radius will give the gutter the maximum carrying capacity.
Thats all folks.
For the limit problems, it would help if you stated what x is approaching. I'm going to assume for the first limit problem that $x \to 0$. So what is the limit of $\frac{\sin{(3x)}}{5x}$ as x approaches 0?
Well, that expression is equal to:
$\frac{3}{5}\cdot \frac{\sin{(3x)}}{3x}$. And you should remember that the limit of $\frac{\sin{\theta}}{\theta}$ as theta approaches 0 is 1. Hence:
$\frac{3}{5}\cdot \frac{\sin{(3x)}}{3x} \to \frac{3}{5}$.
4. For the differentiation problems, use the chain rule:
$\frac{d}{dx} f(g(x)) = g'(x)\cdot f'(g(x))$.
I'll give you a hint on the first of these: $\frac{d}{dx} \tan{x} = \sec ^2{x}$.
5. I am sorry about that I fixed it now.
6. Originally Posted by Mr. Edward
1c) lim x-->0 (sin3X)/5X
e) lim x-->0 x cscx
g) lim x-->0 (1-cos2X)/X
i) lim x-->(pie/2) (((pie/2)-x)/(cosx)
You can use L'Hospital's rule (if this is unfamiliar to you, you should be able to find it by looking it up in the index of your book)
1c) $\lim_{x\to 0} \frac {sin(3x)}{5x} ~~~~=~~~~ \lim_{x\to 0} \frac {3cos(3x)}{5} ~~~~=~~~~ \frac 35 cos(0) ~~~~=~~~~ \frac 35$
e) $\lim_{x\to 0} x ~cscx ~~~~=~~~~ \lim_{x\to 0} \frac x{sin~x} ~~~~$ (use L'Hospital's here) $= \lim_{x\to 0} \frac 1{cos~x} ~~~~=~~~~ \frac x{cos 0} ~~~~=~~~~ 1$
i) $\lim_{x\to \pi /2} \frac {\pi /2 -x}{cos ~x}~~~~$ (use L'Hospitals here) $~~ = \lim_{x\to \pi /2} \frac {-1}{-sin ~x} ~~~~=~~~~ \frac {1}{sin ~\pi /2}~~~~=~~~~1$
Originally Posted by Mr. Edward
2.Differentiate y with respect to X (I think we have to simplify which makes me )
2a)y= ((tan^4)(3x)
c)y=secx^2
d) y=(cot^2)2X/(1+x^2)
f) y=2sec(squareroot X)
h) y=cos^2(tanx)
i) y=1/(sin(x-sinx)[/tex]
These are applications of the chain rule
2a) $y = [tan(3x)]^4$
$y\prime = 4[tan(3x)]^3 * \left( \frac d{dx} tan(3x)\right)$
$y\prime = 4[tan(3x)]^3 * sec^2(3x) * \left(\frac d{dx}3x\right)$
$y\prime = 4[tan(3x)]^3 * sec^2(3x) * 3$
$y\prime = 12~tan^3(3x)~sec^2(3x)$
----------
For this one, I'm assuming you know that square root means to the power of 1/2, and that a power of -1/2 means 1 over the square root. I found especially when I was first doing derivatives, that keeping everything in fraction form (and using negative fractions instead of doing 1 over some expression) made things much simpler and prevented errors.
f) $y=2~sec(x^{1/2})$
$y\prime=2 ~sec(x^{1/2})~tan(x^{1/2}) * \left( \frac d{dx}x^{1/2}\right)$
$y\prime=2 ~sec(x^{1/2})~tan(x^{1/2}) * \frac 12 x^{-1/2} * \left(\frac d{dx} x\right)$
$y\prime=2 ~sec(x^{1/2})~tan(x^{1/2}) * \frac 12 x^{-1/2}$
$y\prime= \frac{sec(\sqrt{x})~tan(\sqrt{x})}{\sqrt{x}}$
------------
i) $y=\frac 1{sin(x-sin~x)}$
$y=[sin(x-sin~x)]^{-1}$
$y\prime=-[sin(x-sin~x)]^{-2} * \left( \frac d{dx} sin(x-sin~x) \right)$
$y\prime=-[sin(x-sin~x)]^{-2} * cos(x-sinx) \left( \frac d{dx} (x-sin~x) \right)$
$y\prime=-[sin(x-sin~x)]^{-2} * cos(x-sinx) ~(1-cos~x)$
$y\prime=-\frac{cos(x-sinx) ~(1-cos~x)}{sin^2(x-sin~x)}$
$y\prime=-\frac{cos(x-sinx) -cos~x~cos(x-sinx))}{sin^2(x-sin~x)}$
Was gonna do the others, but it just started storming :/ | 2016-12-09 13:47:49 | {"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": 0, "img_math": 0, "codecogs_latex": 35, "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": 0.9275699257850647, "perplexity": 1575.9319666239817}, "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-2016-50/segments/1480698542712.12/warc/CC-MAIN-20161202170902-00327-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=59&t=39178&p=132560 | ## pKa and pKb uses
Acidity $K_{a}$
Basicity $K_{b}$
The Conjugate Seesaw $K_{a}\times K_{b}=K_{w}$
Joonsoo Kim 4L
Posts: 61
Joined: Fri Sep 28, 2018 12:29 am
### pKa and pKb uses
What's the point of calculating pKa and pKb? I understand that they can determine the relative strength of an acid/base, but isn't that possible by just using Ka and Kb?
lizziemcguire
Posts: 3
Joined: Fri Sep 28, 2018 12:15 am
### Re: pKa and pKb uses
I have the same question. Also if anyone has an equalization example problem that would be great :)
Jewelyana3A
Posts: 31
Joined: Fri Sep 28, 2018 12:24 am
### Re: pKa and pKb uses
It is sort of a relationship between going from one to another. Remember that when there is a p in front of the value it means that there is a -log. pKa is the -log of Ka. It is for when the problem may provide one and you have to get to the other. | 2019-12-15 11:52:54 | {"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": 0.5822205543518066, "perplexity": 3787.578265457356}, "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/1575541307813.73/warc/CC-MAIN-20191215094447-20191215122447-00529.warc.gz"} |
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# A 10-by-6 inch piece of paper is used to form the lateral surface of a
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A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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10 Jan 2011, 19:00
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A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A. The volume of the cylinder with height 10 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 6.
B. The volume of the cylinder with height 6 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
C. The volume of the cylinder with height 10 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 6.
D. The volume of the cylinder with height 6 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 10.
E. The volume of the cylinder with height 6 is $$\frac{240}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
[Reveal] Spoiler: OA
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Last edited by Bunuel on 02 Jan 2017, 04:55, edited 2 times in total.
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Simple math
1. Answer choices asking about difference in volumes
2. Find volume (pi)*r^2*h of each
case a: 2(pi)r =10 and h = 6 --> (pi)r^2*h = (pi) [10/2*(pi)]^2 * 6 = 25*6/(pi) = 150/pi
case b: 2(pi)r =6 and h = 10 --> (pi)r^2*h = (pi) [6/2*(pi)]^2 * 10 = 9*10/(pi) = 90/pi
3. Difference is 60/pi
4. So [case a volume] when h = 6 is greater than [case b volume ] when h = 10, by 60/(pi)
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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28 Jul 2011, 12:24
baker2145 wrote:
Here's the question:
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.
B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.
C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.
D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.
E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.
I am having difficulty with this one: Please help and explain, if answer if B or E, WHY it is (#/pi) and not #pi, considering pi(r-squared)(h) is the volume formula
Thanks,
6 or 10 will be circumference ...so 2 * pi* r = 6 or 10 and hence r = #/pi....and difference would be 60/pi [applying the volume formula and taking the difference] ...would go with B
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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28 Jul 2011, 12:58
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when the paper is folded with the 10 as the height .. 6 will be the circumference not the radius.. so 2*pi*r = 6 -> r = 3/ pi.. then its pretty straightforward.. pi ( r1*r1*h1 - r2*r2*h)
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28 Jul 2011, 13:05
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baker2145 wrote:
Here's the question:
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.
B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.
C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.
D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.
E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.
I am having difficulty with this one: Please help and explain, if answer if B or E, WHY it is (#/pi) and not #pi, considering pi(r-squared)(h) is the volume formula
Thanks,
Hopefully, you have some intuition about which of the possible cylinders is going to have the greater volume. Because the volume of a cylinder is directly proportional to the height and directly proportional to the square of the radius, the size of the radius has the greatest effect on the volume of the cylinder. Given this intuition we can eliminate A and C.
The answer given already is correct, but I'm going to provide some more details in term of calculation
Cylinder with height 10 and circumference 6:
$$2pi(r) = 6$$
$$r = \frac{3}{(pi)}$$
$$V = (pi)(\frac{3}{pi})^2(10)$$
$$V = \frac{90}{pi}$$
Cylinder with height 6 and circumference 10:
$$2pi(r) = 10$$
$$r = \frac{5}{(pi)}$$
$$V = (pi)(\frac{5}{pi})^2(6)$$
$$V = \frac{150}{pi}$$
150-90 = 60
So, B.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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31 Jul 2011, 23:32
Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 6 and 10 are the circumference of the base and not the radius. B is the right answer.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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28 Feb 2013, 13:24
mun23 wrote:
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
(A)The volume of the cylinder with height 10 is 60 / cubic inches greater than the volume of the cylinder with height 6.
(B)The volume of the cylinder with height 6 is 60 / cubic inches greater than the volume of the cylinder with height 10.
(C)The volume of the cylinder with height 10 is 60 cubic inches greater than the volume of the cylinder with height 6.
(D)The volume of the cylinder with height 6 is 60 cubic inches greater than the volume of the cylinder with height 10.
(E)The volume of the cylinder with height 6 is 240 / cubic inches greater than the volume of the cylinder with height 10.
Radius of 1 cylinder 6*10 (l*h) is 2pi r1 = 6
Radius of 2 cylinder 10*6 (l*h) is 2pi r2 = 10
Volume of cylinder is pi r square * h
Volume of 1 cylinder = 90/pi
volume of 2 = 150/pi
Difference = 60/pi
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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21 Jun 2014, 03:32
Bunuel , can you please explain this problem. I am not able to understand the difference between Option B and D. According to me option D should be correct but its not.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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gauravsoni wrote:
Bunuel , can you please explain this problem. I am not able to understand the difference between Option B and D. According to me option D should be correct but its not.
The difference is that B says "$$\frac{60}{\pi}$$", while D says: "$$60\pi$$". Formatted the original post to make it clearer.
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A. The volume of the cylinder with height 10 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 6.
B. The volume of the cylinder with height 6 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
C. The volume of the cylinder with height 10 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 6.
D. The volume of the cylinder with height 6 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 10.
E. The volume of the cylinder with height 6 is $$\frac{240}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
We can make 2 cylinders:
With height of 6 and the radius of the base of $$r=\frac{5}{\pi}$$ (from $$2\pi{r}=10$$ --> $$r=\frac{5}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{150}{\pi}$$.
With height of 10 and the radius of the base of $$r=\frac{3}{\pi}$$ (from $$2\pi{r}=6$$ --> $$r=\frac{3}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{90}{\pi}$$.
The volume of the first one is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the second one.
Answer: B.
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22 Jun 2014, 01:23
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Bunuel wrote:
gauravsoni wrote:
Bunuel , can you please explain this problem. I am not able to understand the difference between Option B and D. According to me option D should be correct but its not.
The difference is that B says "$$\frac{60}{\pi}$$", while D says: "$$60\pi$$". Formatted the original post to make it clearer.
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A. The volume of the cylinder with height 10 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 6.
B. The volume of the cylinder with height 6 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
C. The volume of the cylinder with height 10 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 6.
D. The volume of the cylinder with height 6 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 10.
E. The volume of the cylinder with height 6 is $$\frac{240}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
We can make 2 cylinders:
With height of 6 and the radius of the base of $$r=\frac{5}{\pi}$$ (from $$2\pi{r}=10$$ --> $$r=\frac{5}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{150}{\pi}$$.
With height of 10 and the radius of the base of $$r=\frac{3}{\pi}$$ (from $$2\pi{r}=6$$ --> $$r=\frac{3}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{90}{\pi}$$.
The volume of the first one is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the second one.
Answer: B.
Thanks Bunuel, I thought of using the width of the rectangle as the radius, now i see that its actually the circumference of the circular base. Thanks for the clarification.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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21 Sep 2014, 00:03
HI Bunuel,
Can you pls explain how can i know its the circumference of the base? Thank you very much.
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vietnammba wrote:
HI Bunuel,
Can you pls explain how can i know its the circumference of the base? Thank you very much.
When you roll a paper into a cylinder one of the dimensions of the paper becomes the height of the cylinder and the another forms circumference of the base:
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21 Sep 2014, 00:30
I get it now, thank you
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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08 Jan 2016, 19:31
we have 2 possible cylinders:
h=10, or h=6.
now, with radius, it is more tricky.
We know that Circumference is 2piR.
now, if h=10, then 2piR=6, or R=3/pi
if h=6, then 2piR=10, or 5/pi.
volume is pi*r^2*h.
1. h=10, r=3/pi. volume is 90/pi
2. h=6, r=5/pi. volume is 150/pi.
we can eliminate right away A, C, and E. - A, B because the cylinder with h=6 is greater. E because the difference is 60/pi and not 240/pi.
D is incorrect because it tells 60pi, when actually it is 60/pi.
B thus is the correct answer.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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22 May 2017, 19:16
ajit257 wrote:
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A. The volume of the cylinder with height 10 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 6.
B. The volume of the cylinder with height 6 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
C. The volume of the cylinder with height 10 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 6.
D. The volume of the cylinder with height 6 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 10.
E. The volume of the cylinder with height 6 is $$\frac{240}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
The trick of this problem is to realize that 6in or 10in, the given length and width, are not the radius of the folded piece of paper; they are the circumference. So you need to solve for the circumference of each (5/pi and 3/pi, respectively). Then you plug them into the volume formula (piR^2H) to arrive at 150/pi - 90/pi.
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A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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10 Nov 2017, 19:25
V = pi(5/pi)^2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)^2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to cross-cancel the pi out?
Last edited by OCDianaOC on 11 Nov 2017, 08:09, edited 1 time in total.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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11 Nov 2017, 01:37
OCDianaOC wrote:
V = pi(5/pi)*2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)*2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to cross-cancel the pi out?
The volume formula is $$volume=\pi{r^2}h$$. Notice that r there is squared not multiplied by 2.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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11 Nov 2017, 08:08
Bunuel wrote:
OCDianaOC wrote:
V = pi(5/pi)*2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)*2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to cross-cancel the pi out?
The volume formula is $$volume=\pi{r^2}h$$. Notice that r there is squared not multiplied by 2.
I'm aware of that. Sorry, I put "*" hoping to imply it meant squared since I couldn't find another symbol for that on my keyboard. Let me rephrase,
V = pi(5/pi)^2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)^2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to cross-cancel the pi out?
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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11 Nov 2017, 08:15
OCDianaOC wrote:
Bunuel wrote:
OCDianaOC wrote:
V = pi(5/pi)*2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)*2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to cross-cancel the pi out?
The volume formula is $$volume=\pi{r^2}h$$. Notice that r there is squared not multiplied by 2.
I'm aware of that. Sorry, I put "*" hoping to imply it meant squared since I couldn't find another symbol for that on my keyboard. Let me rephrase,
V = pi(5/pi)^2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)^2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to cross-cancel the pi out?
$$\pi$$ there is also gets squared.
h = 6 and $$r=\frac{5}{\pi}$$:
$$volume=\pi{r^2}h=\pi*(\frac{5}{\pi})^2*6=\pi*\frac{25}{\pi^2}*6=\frac{150}{\pi}$$.
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]
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11 Nov 2017, 09:12
Oh! That's what I was missing! Thanks Brunel... so we multiple out straight across (squaring num and denom) then cancel out the extra pi from numerator and denominator!
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Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink] 11 Nov 2017, 09:12
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# A 10-by-6 inch piece of paper is used to form the lateral surface of a
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Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2017-12-11 23:04:52 | {"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": 0.7345497012138367, "perplexity": 1570.9362625744984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2017-51/segments/1512948514113.3/warc/CC-MAIN-20171211222541-20171212002541-00219.warc.gz"} |
http://mathoverflow.net/questions/120753/asking-about-a-quasicommutative-semigroup/120902 | Honestly, I have been looking for an a finite Quasicommutative semigroup by surfing the web, but I could't. May I ask here to give me an example for such this kind of semigroup. I tried to built one of them by using GAP, but it fails. Thank you so much. I am new to it.
-
I don't understand the problem. A semigroup is called quasicommutative if for all elements $a,b$ there is some $r \geq 1$ such that $ab=b^r a$. In particular every commutative semigroup is also quasicommutative, and there are lots of examples. Or are you looking for a finite quasicommutative semigroup which is not commutative? – Martin Brandenburg Feb 4 '13 at 11:19
Dear Martin, I know that and I have found out that the Clifford (1961) made a methd to constuct them, but I ask for a sample. I though maybe someone gave me an example. In fact, my question is not a problem, but it is asking for a finite quasicommutative semigroup. I have none of them in my hand to work. Sorry if I get the time of all users. Thanks. – Babak S. Feb 4 '13 at 12:24
I want it non-commutative. – Babak S. Feb 4 '13 at 12:25
I've worked in semigroups for 15 years and never saw this definition. One can easily construct artificial examples but I don't know offhand a natural example that is noncommutative. – Benjamin Steinberg Feb 4 '13 at 16:45
@Martin and @Sorouh: Is it right the definition written above for quasicommutativity? I have found some online references where it is required $ab=(ba)^r$ instead of $ab=b^r a$. – boumol Feb 4 '13 at 18:09
The simple examples are Hamiltonian groups. Then you can construct Clifford semigroups from them.
-
Thanks Boris for the time. I think, I should focus to Clifford's paper again, however it is very old one. – Babak S. Feb 5 '13 at 18:20
Babak, in your semigroups all idempotents are central. There are some articles on semigrous with commuting idempotents, e.g. C.Ash, Finite semigroups with commuting idempotents, J. of the Australian Math. Society (1987). Maybe they will be useful for you. – Boris Novikov Feb 5 '13 at 18:51
The following is (for me) a bit much for a series of comments. EDIT: It is also not appropriate as an answer. The fun begins when I alternate quantifiers and turn the intended property into a semigroup identity. In an actual quasicommutative semigroup, $ab=b^3a$ would not say anything about b having torsion. Even in the finite semigroup case, there is no justification for saying that all nontrivial powers are rth powers. I leave the comedy of inferences for those who like to see how easy and wrong it can be to deduce something from a single conflation of (for all)(exists) and (exists)(for all). END EDIT. It might interest one who wants to construct an example.
The propety as described by Martin Brandenburg is a semigroup identity that implies $b^2=b^{r+1}$. Further, one finds that for $i>1$, $b^i=c^r$ for some $c$ and that $r$th powers commute with everything in the semigroup. An attempt at a reduced form for words on k letters in such a semigroup (this part needs checking before taking seriously) is something like wp where w is a squarefree word (so w does not have abcabc or similar subwords) on some subset S of the k letters and p is possibly the empty word and otherwise is an $r$th power involving only powers of the letters not in S. The subsemigroup of square or higher powers will be commutative.
If the above is correct, I see finite noncommutative examples looking like a small set of extra elements adjoined to a commutative semigroup, where the square of any extra element lies in the commutative semigroup. Not being a semigroup theorist, I sympathize with the original poster and his/her plight. | 2015-11-30 04:25:52 | {"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": 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": 0.8539122939109802, "perplexity": 515.4096850192489}, "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-2015-48/segments/1448398460982.68/warc/CC-MAIN-20151124205420-00137-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://piping-designer.com/index.php/properties/relativistic-mechanics/490-universal-gravitational-constant | Universal Gravitational Constant
Written by Jerry Ratzlaff on . Posted in Relativity
Universal Gravitational Constant
The universal gravitational constant ( $$G$$ ) is the proportionality constant used in Newton's Law of Universal Gravitation.
$$G = 6.67384 \; \left( 10^{-11} m^3 kg^{-1} s^{-2} \right) \; = \; 6.67384 \; \left( 10^{-11} Nm^2 kg^{-2} \right)$$ | 2018-04-26 09:26:05 | {"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": 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": 0.995553195476532, "perplexity": 2654.0664616637505}, "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-2018-17/segments/1524125948125.20/warc/CC-MAIN-20180426090041-20180426110041-00217.warc.gz"} |
http://hellhammer.belegarth.com/viewtopic.php?f=3&t=434 | It is currently Mon Jan 17, 2022 10:34 am
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Hey everybody
Author Message
Joined: Sun May 13, 2012 8:35 pm
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Hey everybody
I just registered for the forums, I wanted to say hi. I am really excited to be a barreler, and I can't wait to see everybody again at geddon.
Sun May 13, 2012 8:44 pm
Joined: Thu Feb 19, 2009 11:40 am
Posts: 247
Re: Hey everybody
First challenge: teach me something.
Sun May 13, 2012 8:47 pm
Joined: Sun Apr 19, 2009 1:24 pm
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Location: Esgaroth
Re: Hey everybody
Second Challenge: What sort of Cupcake do I like?
Third Challenge: Make that cupcake for me!
Set
GO!GO!GO!EXPLODE!
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'ey...sup.
Postal wrote:
i would be more than happy with one hell hammer member being picked up a year. fuck our friends i want family members.
Squire to Sir Angelus of Numenor
Guardian of Esgaroth
Sword of Shaolin
Sun May 13, 2012 8:53 pm
Joined: Sun May 13, 2012 8:35 pm
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Re: Hey everybody
Fucking Magnets, how do they work:
To a good approximation:
B = (mu_0 / 4pi) (mu/r^3)
Vak, chocolate cupcakes with strawberry frosting?
Sun May 13, 2012 8:56 pm
Joined: Tue Feb 24, 2009 3:09 pm
Posts: 150
Re: Hey everybody
And you're first assignment under me, you're sponsor, don't look like a fucking kite the next time I see ya but keep the Russian hat, that shit is ballin.
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shithawks fellas......SHITHAKWS
Sun May 13, 2012 9:09 pm
Joined: Sun Feb 22, 2009 1:18 pm
Posts: 548
Re: Hey everybody
Wolfenstein3d wrote:
Fucking Magnets, how do they work:
To a good approximation:
B = (mu_0 / 4pi) (mu/r^3)
I'm sold
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urrthing I do, I do it big
Sun May 13, 2012 9:11 pm
Joined: Thu Feb 19, 2009 11:40 am
Posts: 247
Re: Hey everybody
I'm on board for part of that, but only up to calc 1 & physics 1 (cause I'm a deadbeat scumbag college dropout).
I need a bit more hand-holding (cause fuck you if you think I'm going to wikipedia).
WHAT IS B
WHAT IS MU_SUBWHATEVER
WHY FOURPI
WHAT IS A TESLA
WAS I RIGHT ABOUT MU_SUBWHATERVER? WHAT IS THAT ANYWAYS?
Basically, assume I have nothing except a solid knowledge of SI units, significant figures and a host of physical and chemical laboratory testing apparati.
Sun May 13, 2012 9:34 pm
Joined: Sun May 13, 2012 8:35 pm
Posts: 12
Re: Hey everybody
Bodmin- I'm on it, your right that new garb is definitely in order.
Derian-
B is the magnetic field created by a permanent magnet (for example, a fridge magnet). The unit for magnetic field is the Tesla, and for reference the Earth's magnetic field is about 20 microTesla.
mu_0 is the permeability of free space. Its just a number, although it is important because it turns out to be related to the speed of light.
The four pi comes the field being spread out over the surface of a sphere basically. The surface area of a sphere goes as 4 pi r^2.
The mu (without the _0) is the magnetic moment of the magnet (How "magnetic" it is.) You can either measure it for a specific magnet to find what it is, or try and determine it by looking at the properties of what the magnet is made from.
For a single magnet, everything besides the 1/r^3 is constant. The important thing is that magnets don't interact with each other strongly for very far.
Sun May 13, 2012 10:41 pm
Joined: Thu Feb 19, 2009 11:40 am
Posts: 247
Re: Hey everybody
Quote:
A particle carrying a charge of 1 coulomb and passing through a magnetic field of 1 tesla at a speed of 1 meter per second perpendicular to said field experiences a force of 1 newton, according to the Lorentz force law. As an SI derived unit, the tesla can also be expressed as
\mathrm{T\ =\ V\ s\ m^{-2}\ =\ N\ A^{-1}m^{-1}\ =\ Wb\ m^{-2}\ =\ kg\ C^{-1}s^{-1}=\ kg\ A^{-1}s^{-2}\ =\ N\ s\ C^{-1}m^{-1}}
Sun May 13, 2012 10:47 pm
Joined: Thu Feb 19, 2009 11:40 am
Posts: 247
Re: Hey everybody
Final question: How do I calculate the magnetic field generated from the winding/rotor interaction in my 1987 Oldsmobile Calais. Furthermore, how would I calculate the cost:energy discrepancy between charging the battery outright via a mechanism with 100% outlet->output efficiency (assuming a sample rate of $0.15/kWh) vs. purchasing a gasoline/ethanol blend of 87 AKI octane rating fuel at$3.40/gallon assuming optimal lubrication, exhaust efficiency and engine RPM:fuel consumption ratio.
Sun May 13, 2012 11:01 pm
Joined: Sun May 13, 2012 8:35 pm
Posts: 12
Re: Hey everybody
Well, you could approximate your alternator as a simple inductor, in which case the formula for the field would be B = mu_0 N I / L. mu_0 is the same as before, N is the number of windings, I is the current that flows through, and L is the length of the alternator. However, it is further complicated by the wires being wrapped around an iron core, which will increase the field.
As for the second question, I you need to find the energy density of 87 octane. Wikipedia gives 9.7 kW·h/L, so using $3.40/gallon, you would get$0.09 KwH. However, that assumes you can get 100% of the energy out of your fuel in your engine, which is physically impossible regardless of the engine design. At the temperatures cars run at, the maximum possible efficiency is about 25%, which means in terms of the energy you can actually use, you would be looking at \$0.36 KwH. So, the battery at this point is looking about twice as efficient. There are of course many complications. One thing to consider is that car engines are not designed to get as much energy as possible out of the fuel, but instead designed to get lots of horsepower out of the fuel.
Sun May 13, 2012 11:47 pm
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Posts: 278
Re: Hey everybody
Fuckin nerds
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Shiv wrote:
Yeah, well I love Jay. Probably even more than you love life.
Mon May 14, 2012 6:33 am
Joined: Thu Feb 19, 2009 11:40 am
Posts: 247
Re: Hey everybody
Hahahah, what the fuck. I have no idea what was going on in my head last night.
Well played, W:3D, well played indeed.
Mon May 14, 2012 8:22 am
Joined: Sat Feb 21, 2009 2:12 pm
Posts: 278
Re: Hey everybody
Derian wrote:
Hahahah, what the fuck. I have no idea what was going on in my head last night
I got this: Booze
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Shiv wrote:
Yeah, well I love Jay. Probably even more than you love life.
Mon May 14, 2012 7:46 pm
Joined: Thu Feb 19, 2009 11:40 am
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Re: Hey everybody
Well, clearly.
Mon May 14, 2012 8:03 pm
Prince of Stench
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Location: cedar falls ia
Re: Hey everybody
Jay wrote:
Fuckin nerds
Mon May 14, 2012 9:33 pm
Joined: Tue Mar 17, 2009 11:14 am
Posts: 18
Re: Hey everybody
Well well well Wolfenstein. Congrats on being a barreller. Do you have your PhD yet?
Tue May 15, 2012 8:15 am
Joined: Sun May 13, 2012 8:35 pm
Posts: 12
Re: Hey everybody
Thanks Kazi. I don't have the PhD, but I am doing essentially my master's defense on June 4th. I probably won't get the PhD until spring/summer 2015 at the earliest.
Tue May 15, 2012 9:35 am
Joined: Sat Feb 21, 2009 5:36 pm
Posts: 40
Re: Hey everybody
Most awesome thing i've read all week.
I miss you guys.
Tue May 15, 2012 5:05 pm
Joined: Sun Feb 22, 2009 10:07 am
Posts: 22
Re: Hey everybody
but as far as your alternator goes you also hafto take into account what is hear by to it wen doing your math to find the output of energy. due to the wiring and other mettle objects and the unshielded nature of an alternator you lose production and or gane it depending on the gage of wire by creating an magnetioce field wen that field passes threw wire it creates electricity and that can interfier with the production of energy.
Mon Jun 11, 2012 1:30 pm
Joined: Sun Feb 22, 2009 10:07 am
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Re: Hey everybody
also i am sad we dident get to hang out and talk at geadon and hope that nose of yours is alright
Mon Jun 11, 2012 1:34 pm
Joined: Sun May 13, 2012 8:35 pm
Posts: 12
Re: Hey everybody
Yeah, I think its gradually getting better. I can't really feel much with the drugs, they seem to be working. I'll know more when I see the doctor on Wednesday.
Mon Jun 11, 2012 2:00 pm
Joined: Sun Feb 22, 2009 2:06 pm
Posts: 243
Location: roamer - far frozen north
Re: Hey everybody
Keep us updated man and heal quickly. <3
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Young Gun
Vak wrote:
we are a collection of stone killers, with a swag that says it just as loudly as our voice
Wed Jun 13, 2012 12:34 am
Joined: Sun May 13, 2012 8:35 pm
Posts: 12
Re: Hey everybody
Went to the doctor today, I have an in place fracture, which apparently just needs time and rest. I'm still incredibly not mobile, but feeling pretty good. I did not have to take the medication today.
Wed Jun 13, 2012 5:00 pm
Joined: Sun May 13, 2012 8:35 pm
Posts: 12
Re: Hey everybody
Also, he said I should be healed and feeling better (and able to fight!) in a week.
Wed Jun 13, 2012 5:11 pm
Joined: Sun Feb 22, 2009 2:06 pm
Posts: 243
Location: roamer - far frozen north
Re: Hey everybody
Sorry this is so belated but I'm glad to hear good news. Hope you're still healing up well and feeling better. =)
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Young Gun
Vak wrote:
we are a collection of stone killers, with a swag that says it just as loudly as our voice
Thu Jun 21, 2012 4:26 pm
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Search for: | 2022-01-17 16:34:21 | {"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": 0.35181930661201477, "perplexity": 4404.220956948459}, "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/1642320300574.19/warc/CC-MAIN-20220117151834-20220117181834-00657.warc.gz"} |
https://www.reliccastle.com/resources/629/ | # Prize Wheels N/A
Pokémon Essentials Version
This script lets you create Prize Wheels that players can spin to win one of ten prizes! Your prize pool can be Pokemon, items, money, or a mix of the three!
(Yes I got this idea from Webkinz/Neopets what are you a cop)
Code
Paste in a new section above Main!
Ruby:
Prizes = [
[:POKEBALL,:REPEATBALL,:FASTBALL,:LEVELBALL,:NESTBALL,:DUSKBALL,:DIVEBALL,:HEAVYBALL,:GREATBALL,:MASTERBALL],
[:CHARMANDER,:CYNDAQUIL,:EEVEE,:PIKACHU,:CHIKORITA,:BULBASAUR,:SQUIRTLE,:TOTODILE,:MARILL,:RATTATA],
["100","200","300","400","500","600","700","800","900","1000"],
[:POKEBALL,"100",:CHARMANDER,:POKEBALL,"100",:CHARMANDER,:POKEBALL,"100",:CHARMANDER,:POKEBALL,"100",:CHARMANDER,],
["100","2500","100","7500","100","10000","100","5000","100","15000"],
]
WheelStyles = [
#bg graphic, wheel graphic, radius, minimum spins,
#spin SFX, volume, pitch
#winning sfx, volume, pitch
["hatchbg","prizewheel",110,3,"battle ball shake",80,150,"mining reveal full",100,100],
["hatchbg","prizewheel2",110,3,"battle ball shake",80,150,"mining reveal full",100,100]
]
def Wheel(prizelist,cost,style=0,costcoins=false,prizecoins=false)
PrizeWheel.new(prizelist,cost,style,costcoins,prizecoins)
end
class PrizeWheel
def pbUpdate
end
def initialize(prizelist,cost,style=0,costcoins=false,prizecoins=false)
@viewport = Viewport.new(0, 0, Graphics.width, Graphics.height)
@prizes=Prizes[prizelist]
@costcoins = costcoins
@prizecoins = prizecoins
@sprites = {}
@cost=cost
@style=WheelStyles[style]
@bg=@style[0]
@wheel=@style[1]
@minspins=@style[3]
@prizespin=0
@angle=[72,36,0,313,287,251,216,180,144,108]
@xyangle=[198,234,270,306,340,16,52,90,126,162]
@sprites["bg"] = Sprite.new(@viewport)
@sprites["bg"].bitmap = Bitmap.new("Graphics/Pictures/#{@bg}")
@sprites["downarrow"] = AnimatedSprite.new("Graphics/Pictures/downarrow",8,28,40,2,@viewport)
@sprites["downarrow"].x = (Graphics.width/2)-15
@sprites["downarrow"].y = 10
@sprites["downarrow"].z = 5
@sprites["downarrow"].play
@sprites["wheel"] = Sprite.new(@viewport)
@sprites["wheel"].bitmap = Bitmap.new("Graphics/Pictures/#{@wheel}")
@sprites["wheel"].center_origins
@sprites["wheel"].x=Graphics.width/2
@sprites["wheel"].y=Graphics.height/2
for i in 0...10
if GameData::Item.try_get(@prizes[i])
@sprites["prize#{i}"]=ItemIconSprite.new(0,0,0,@viewport)
@sprites["prize#{i}"].item = @prizes[i]
@sprites["prize#{i}"].ox=24
@sprites["prize#{i}"].oy=24
elsif GameData::Species.try_get(@prizes[i])
@sprites["prize#{i}"]=PokemonSpeciesIconSprite.new(@prizes[i],@viewport)
@sprites["prize#{i}"].shiny = false
@sprites["prize#{i}"].ox=32
@sprites["prize#{i}"].oy=32
else
@sprites["prize#{i}"] = Sprite.new(@viewport)
if @prizecoins == true
@sprites["prize#{i}"].bitmap = Bitmap.new("Graphics/Items/COINCASE")
else
@sprites["prize#{i}"].bitmap = Bitmap.new("Graphics/Pictures/Money")
end
@sprites["prize#{i}"].center_origins
end
@sprites["prize#{i}"].angle = @angle[i]
@sprites["prize#{i}"].x=(Graphics.width/2) + Math.cos(@xyangle[i].degrees)*@style[2]
@sprites["prize#{i}"].y=(Graphics.height/2) + Math.sin(@xyangle[i].degrees)*@style[2]
end
main
end
def main
loop do
Graphics.update
Input.update
pbUpdate
if Input.trigger?(Input::C)
if @cost>0
if @costcoins == true
confirmtext="Spin the wheel for #{@cost} coins?"
else
confirmtext="Spin the wheel for $#{@cost}?" end else confirmtext="Spin the wheel?" end if pbConfirmMessage("#{confirmtext}") if @costcoins == true if$Trainer.coins>=@cost
$Trainer.coins-=@cost else pbMessage(_INTL("You don't have enough coins...")) break end else if$Trainer.money>=@cost
$Trainer.money-=@cost else pbMessage(_INTL("You don't have enough money...")) break end end spins=rand(360) spins+=360*(@minspins) spun=0 click=true loop do pbUpdate @sprites["wheel"].angle -= 5 @prizespin+=5 for i in 0...10 @sprites["prize#{i}"].angle -= 5 @sprites["prize#{i}"].x= (Graphics.width/2) + Math.cos((@xyangle[i]+@prizespin).degrees)*@style[2] @sprites["prize#{i}"].y= (Graphics.height/2) + Math.sin((@xyangle[i]+@prizespin).degrees)*@style[2] end spun+=5 Graphics.update if click=true pbSEPlay(@style[4],@style[5],@style[6]) click=false else click=true end if spun>=spins prize=0 prizey=[] for i in 0...10 prizey[i]=@sprites["prize#{i}"].y end winner=prizey.min for i in 0...10 if @sprites["prize#{i}"].y==winner prize=i end end prize=@prizes[prize] pbSEPlay(@style[7],@style[8],@style[9]) if GameData::Item.try_get(prize) pbUpdate pbReceiveItem(prize) elsif GameData::Species.try_get(prize) pbUpdate pbAddPokemon(prize,20) else if @prizecoins == true pbMessage("You won #{prize} coins!") prize = prize.to_i$Trainer.coins+=prize
else
pbMessage("You won $#{prize}!") prize = prize.to_i$Trainer.money+=prize
end
end
break
end
end
end
end
if Input.trigger?(Input::B)
break
end
end
dispose
end
def dispose
pbDisposeSpriteHash(@sprites)
@viewport.dispose
end
end
#center_origins command from Marin's Scripting Utilities.
#If you have that script, you can delete this section
class Sprite
def center_origins
return if !self.bitmap
self.ox = self.bitmap.width / 2
self.oy = self.bitmap.height / 2
end
end
#.degrees command, to convert degrees to radians
class Numeric
def degrees
self * Math::PI / 180
end
end
If you're using this in a version before v19, there's a couple last steps you need to do.
Find this section:
Ruby:
if GameData::Item.try_get(@prizes[i])
@sprites["prize#{i}"]=ItemIconSprite.new(0,0,0,@viewport)
@sprites["prize#{i}"].item = @prizes[i]
elsif GameData::Species.try_get(@prizes[i])
@sprites["prize#{i}"]=PokemonSpeciesIconSprite.new(@prizes[i],@viewport)
@sprites["prize#{i}"].ox=32
@sprites["prize#{i}"].oy=32
Replace it with:
Ruby:
if getID(PBItems,@prizes[i])>0
@sprites["prize#{i}"]=ItemIconSprite.new(0,0,0,@viewport)
@sprites["prize#{i}"].item=getID(PBItems,@prizes[i])
@sprites["prize#{i}"].center_origins
elsif getID(PBSpecies,@prizes[i])>0
@sprites["prize#{i}"]=PokemonSpeciesIconSprite.new(getID(PBSpecies,@prizes[i]),@viewport)
@sprites["prize#{i}"].ox=32
@sprites["prize#{i}"].oy=32
Near the bottom, find this section:
Ruby:
if GameData::Item.try_get(prize)
pbUpdate
elsif GameData::Species.try_get(prize)
pbUpdate
pbAddPokemon(prize,20)
Replace it with:
Ruby:
if getID(PBItems,prize)>0
pbUpdate
elsif
getID(PBSpecies,prize)>0
pbUpdate
pbAddPokemon(prize,20)
Graphics
• Put "money.png" and "prizewheel.png" in Graphics/Pictures
• prizewheel2.png is an edit of the original wheel (also made by AiurJordan) to display some coin values on it! These correspond with the fourth prize array!
• If you're using the vanilla Game Corner tileset, put Game Corner interior.png in Graphics/Tilesets, overwriting the file already there. Otherwise, use an image editing program to put the wheeltile image into whatever tileset you're using.
• Old wheel is just there if anyone has any reason to need it. I really recommend you use AiurJordan's, though!
Using the script
There's a few things to do before putting your wheels in place!
We've got two arrays-of-arrays defined at the top of our script: Prizes and Wheel Styles.
Ruby:
Prizes = [
[:POKEBALL,:REPEATBALL,:FASTBALL,:LEVELBALL,:NESTBALL,:DUSKBALL,:DIVEBALL,:HEAVYBALL,:GREATBALL,:MASTERBALL],
[:CHARMANDER,:CYNDAQUIL,:EEVEE,:PIKACHU,:CHIKORITA,:BULBASAUR,:SQUIRTLE,:TOTODILE,:MARILL,:RATTATA],
["100","200","300","400","500","600","700","800","900","1000"],
[:POKEBALL,"100",:CHARMANDER,:POKEBALL,"100",:CHARMANDER,:POKEBALL,"100",:CHARMANDER,:POKEBALL,"100",:CHARMANDER,],
]
The arrays in Prizes are your prize pool! Items and Pokemon should be put in as :NAME, while money amounts should just be "X" (quotes included). It has to be exactly ten prizes- any less and it'll crash, any above ten won't display.
You probably won't use the WheelStyles array as much, but it's there to allow to easily save multiple graphic/audio changes!
Ruby:
WheelStyles = [
#bg graphic, wheel graphic, radius, minimum spins,
#spin SFX, volume, pitch
#winning sfx, volume, pitch
["hatchbg","prizewheel",110,3,"battle ball shake",80,150,"mining reveal full",100,100]
]
• bg graphic- filename of the background image in Graphics/Images, in quotes
• wheel graphic- filename of the background image in Graphics/Images, in quotes
• radius- the radius of the icons on the wheel. (Not necessarily the radius of the wheel itself, unless you want the icons to be on the edges)
• Minimum spins- the minimum number of times the wheel will make a full loop before landing. (It can make up to one final loop after that)
• Spin SFX, volume, pitch- The file in Audio/SFX that plays repeatedly as the wheel spins, to create the feel of the wheel clacking. Volume is 0 to 100, pitch is 0 to 150, just like if you called it via event.
• Winning SFX- same thing, except it's what plays when the wheel lands on a prize.
Now that that's all set up, all you have to is call it in an event, with Wheel(prizepool,cost,style=#)
• prizepool- The array in Prizes that are on the wheel (remember that it starts at 0!)
• cost- The cost to spin the wheel. (Set to 0 for a free wheel)
• style=# - The settings set up in WheelStyles (with # being the array it pulls from), if you want something different from the default.
• If you want to make the player spend coins instead of money, add costcoins=true into the command. (It'd look like Wheel(prizepoolcost,style=#,costcoins=true)
• If you want to make the player win coins instead of money, do the same thing, but with prizecoins=true. (I believe you still need to define costcoins in this, so be sure to do that as well, even if you want it to cost money- Wheel(prizepoolcost,style=#,costcoins=false,prizecoins=true) )
Future Goals
• Display the name of the prize on its slot. (Right now, the size of the text and getting rotation to work has been causing issues for me)
• Slots that let you win an item from an array- for example, landing a "Random Poké Ball" slot would pick a Poke Ball out of an array
• Allow for more customization of prizes- Shiny Pokémon, Pokémon with special moves, unique effects for your Pokémon, etc.
• Allow money and coins on the same wheel
• Allow for customization of how many prizes are in a wheel
• Allow devs to set specific probabilities for different slots
• Maybe make a pretty animation for the prize
• I might try to make this a plugin file rather than making it a new script section.
Credits
• Marin, for his scripting utilities
• Krom Stern from stackexchange for the circular movement
• Flylib.com for the conversion from radians into degrees
• AiurJordan for the tile and high-quality prize wheels, as well as the code relating to coin usage
• Ganz/Webkinz for the Wheel of Wow graphic this wheel was based on
• And me, TechSkylander1518!
Author
TechSkylander1518
433
Views
3,209
First release
Last update
Rating
7 ratings
1. ### Fixing shiny bug
Not sure why this is working this way, but it was defaulting to shiny menu sprites for Pokemon...
2. ### Graphic update and coins
Some beautiful new graphics made by AiurJordan! Also, coin functionality!
3. ### v19 Update
Now compatible with v19!
### Latest reviews
Really fun and unique, but a few pokemon I've tried (Treeko, Rowlett, Grookey) Appear as money symbols in the wheel and upon landing them, the game crashes.
TechSkylander1518
Hm, can you share what your prize array looks like?
One of my favorite plugins to use! It's a nice way to add random rewards, and fun all at the same time. 11/10!
TechSkylander1518
That's really kind of you to say! I'm glad you're having so much fun with it!
Oh yes, this looks so much fun. I can't wait to play with it.
TechSkylander1518
Thank you! I'm looking forward to seeing what you do with it!
Excellent Script. One of the best thing I can imagine to have in fangame. Too Creative.
TechSkylander1518
Thank you, that's really nice of you to say!
That's a great addition for the fangame development community and I'll be definitely using this in my future game projects, this'll look beautiful in the casino!
TechSkylander1518
Thank you! Looking forward to seeing what you do with it! | 2022-05-17 20:43:47 | {"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": 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": 0.3847232162952423, "perplexity": 7830.3038616124795}, "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-2022-21/segments/1652662520817.27/warc/CC-MAIN-20220517194243-20220517224243-00564.warc.gz"} |
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Please see edit below. So, let $A,A'/K$ be abelian varieties where $K$ is a $p$-adic local field with residue field $k$. Suppose further that they have good reduction with models ... | 2016-04-30 17:12:06 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8114662170410156, "perplexity": 472.61246545075056}, "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-2016-18/segments/1461860112228.39/warc/CC-MAIN-20160428161512-00104-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://mathoverflow.net/questions/366111/closed-form-solution-for-xaxt-b | # Closed form solution for $XAX^{T}=B$
Let $$d \times d$$ matrices $$A, B$$ be positive definite. Is there a closed form solution for the following quadratic equation in $$X$$?
$$X A X^{T} = B$$
Thank you.
• Just for completeness: this is usually called a Ricatti equation, sometimes also a Lyapunov equation. This might help to lookup references if needed. – leo monsaingeon Jul 20 at 17:10
• Related: mathoverflow.net/q/78106 – Rodrigo de Azevedo Jul 20 at 17:28
• Does this answer your question? Solving a quadratic matrix equation – vidyarthi Jul 20 at 17:59
• Thank you for the answers, I think Federico's answer is very neat, at least for the type of problem I specified. – Fabio Jul 20 at 20:29
$$B^{-1/2}XAX^TB^{-1/2}=I$$, so $$B^{-1/2}XA^{1/2}=Q$$ must be orthogonal. On the other hand, for any orthogonal $$Q$$, it is simple to verify that $$X = B^{1/2}QA^{-1/2}$$ solves the equation, so this is a complete parametrization of the solutions.
Here $$A^{1/2}$$ is the symmetric square root of $$A$$ (if you prefer you can work with the Cholesky factor and obtain similar results). | 2020-12-05 18:36:00 | {"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": 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": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8739062547683716, "perplexity": 347.9015400619409}, "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-2020-50/segments/1606141748276.94/warc/CC-MAIN-20201205165649-20201205195649-00209.warc.gz"} |
http://koasas.kaist.ac.kr/handle/10203/27295 | #### Fusion and fragmentation of phospholipid vesicles by apohemoglobin at low ph = 사람의 apohemoglobin 과 인지질막과의 상호작용에 관한 연구
Human apohemoglobin was found to induce fusion of various vesicles containing phosphatidylserine at low pH. The fusion of vesicles by apoHb was monitored by intermixing of internal aqueous contents, the resonance energy transfer assay which follows the mixing of membrane components and size increase from the electron microscopy and light scattering measurement. The fusion-pH profiles were similar to the binding profiles of apoHb to the same vesicles. Proteolytic digestion after hydrophobic labeling of PS and PS/PE vesicle-protein complex with dansyl chloride showed that a segment with a molecular weight of approximately 2500 penetrates the bilayer. It was also found that PS/PC(1:1) vesicles not only induces fusion of PS/PC(1:1) vesicles at low protein concentration but also frament the same vesicles to form micellar complex at high protein concentration. The micellization of PS/PC(1:1) vesicles was confirmed by light scattering, gel filtration and electron microscopy. The [125I] TID-labeling of the apohemoglobin in the vesicle-protein complex followed by CNBr cleavage of apohemoglobin showed that an N-terminal segment of $\beta$ subunit with a molecular weight of approximately 6000 seems to be mainly involved in the fusion process but the whole sequences of both a and $\beta$ chains participate in the micellization process. These results suggest thatn apoHb assumes differet topologies in the vesicle-protein complex depending on the L/P ratio causing either fusion or fragmentation of vesicles.
Kim, Hyoung-Manresearcher김형만researcher
Publisher
한국과학기술원
Issue Date
1991
Identifier
61657/325007 / 000855803
Language
eng
Description
학위논문(박사) - 한국과학기술원 : 생물공학과, 1991.8, [ viii, 128 p. ]
URI
http://hdl.handle.net/10203/27295
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=61657&flag=t
Appears in Collection
BS-Theses_Ph.D.(박사논문)
Files in This Item
There are no files associated with this item.
• Hit : 61 | 2017-08-22 15:03:43 | {"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": 0.6015439033508301, "perplexity": 8748.59063348029}, "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-2017-34/segments/1502886110792.29/warc/CC-MAIN-20170822143101-20170822163101-00484.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/112231-proof-probability-formula-involving-aub.html | # Thread: Proof of probability formula involving AuB
1. ## Proof of probability formula involving AuB
I am stuck in proving that if two events A and B are independent then :
P(AuB)=P(A)+P(A')P(B)
I am stuck with this question i know that if two events are independent then P(AnB)= P(A)P(B)
thanks
2. P(AUB)=P(A)+P(B)-P(AB)
use indep....
=P(A)+P(B)-P(A)P(B)
=P(A)+P(B)[1-P(A)]
=P(A)+P(B)P(A').
3. OK i think i have got the answer
P(AuB)=P(A)+P(B)-P(A)P(B)
P(AuB)=P(A)+P(B)(1-P(A)
P(AuB)=P(A)+P(B)P(A') | 2016-10-22 02:23:12 | {"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": 0.9835211038589478, "perplexity": 762.6280495926769}, "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-2016-44/segments/1476988718423.28/warc/CC-MAIN-20161020183838-00334-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://www.ask.com/math/0-5-fraction-6af48c152b1a1cdd | Q:
What is 0.5 as a fraction?
A:
The decimal 0.5 is expressed as the fraction one-half. This is found by evaluating the decimal over 1, multiplying the fraction by 10 and then simplifying.
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To change a decimal into a fraction, the decimal is placed over 1. Then, both the numerator and denominator are multiplied by a factor of 10 depending on how many digits are after the decimal point.
In the case of 0.5, there is one digit after the decimal, so it is only necessary to multiply by 10. When the numerator and denominator of the fraction 0.5/1 are multiplied by 10, it gives the fraction 5/10, which can be simplified. The number 5 goes into 10 twice. Dividing the numerator and denominator by 5 gives one-half.
The same result is given by reading 0.5 as 5/10, since the five is in the 10's place. This is written as 5/10, which simplifies to one-half.
Sources:
Related Questions
• A:
Two-thirds expressed as a decimal is 0.6, with a line over or under the six, indicating that the six repeats indefinitely, or as 0.666, which is accurate to three decimals. To convert a fraction to a decimal, divide the numerator, the top number, by the denominator, the bottom number.
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• A:
To calculate percentage, divide the number that is to be expressed as a percentage by the total or whole. The resulting number is then multiplied by 100 to obtain the percentage.
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The mixed number 66 and two-thirds is 200 over 3, or 200/3, as a fraction. To convert a mixed number into a fraction, manipulate the whole number so that it shares a common denominator with the fractional component, and then add the two together. | 2014-12-19 06:34:49 | {"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": 0.9161038398742676, "perplexity": 523.3837762012922}, "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-2014-52/segments/1418802768276.101/warc/CC-MAIN-20141217075248-00068-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://smlnj-gforge.cs.uchicago.edu/scm/viewvc.php/sml/trunk/HISTORY?annotate=1878&root=smlnj&sortby=date&pathrev=1878 | Home My Page Projects Code Snippets Project Openings SML/NJ
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[smlnj] Annotation of /sml/trunk/HISTORY
[smlnj] / sml / trunk / HISTORY
# Annotation of /sml/trunk/HISTORY
1 : dbm 570 This is the HISTORY file for the Yale SML/NJ CVS repository. 2 : 3 : An entry should be made for _every_ commit to the repository. 4 : The entries in this file will be used when creating the README 5 : for new versions, so keep that in mind when writing the 6 : description. 7 : 8 : The form of an entry should be: 9 : 10 : mblume 1615 Name: 11 : mblume 1480 Date: yyyy/mm/dd 12 : Tag: 13 : Description: 14 : 15 : ---------------------------------------------------------------------- 16 : mblume 1863 Name: Matthias Blume (http://www.tti-c.org/blume/) 17 : mblume 1878 Date: 2005/11/21 14:00:00 CST 18 : Tag: blume-20051121-html-lib 19 : Description: 20 : 21 : Enabling $/html-lib.cm in config/preloads did not work. This is fixed 22 : now. (Since the anchor mapping for html-lib.cm is not yet in effect 23 : at the time when config/preloads is processed, the library has to 24 : be referred to by another name. In 110.57 this would be 25 :$SMLNJ-LIB/HTML/html-lib.cm. I arranged for $smlnj/smlnj-lib/html-lib.cm 26 : to be valid as well.) 27 : 28 : Thanks to Todd Wilson (Fresno) for alerting me to this issue. 29 : 30 : ---------------------------------------------------------------------- 31 : Name: Matthias Blume (http://www.tti-c.org/blume/) 32 : mblume 1874 Date: 2005/11/19 13:45:00 CST 33 : Tag: Release_110_57 34 : Description: 35 : 36 : Moved release tag for 110.57. 37 : 38 : ---------------------------------------------------------------------- 39 : Name: Matthias Blume (http://www.tti-c.org/blume/) 40 : mblume 1873 Date: 2005/11/19 23:35:00 CST 41 : Tag: blume-20051119-fish 42 : Description: 43 : 44 : Fixed a problem in config/install.sh where it tries to "fish" the 45 : name of the CM metadata directory from the wrong place (because 46 : the physical location of basis.cm has changed). Also, corrected the 47 : path anchor for$/html-lib.cm. (Thanks to M. Fluet for pointing out 48 : these problems.) 49 : 50 : ---------------------------------------------------------------------- 51 : Name: Matthias Blume (http://www.tti-c.org/blume/) 52 : mblume 1867 Date: 2005/11/16 14:30:00 CST 53 : mblume 1874 Tag: blume-orig-110_57 54 : mblume 1867 Description: 55 : 56 : New working version (110.57). NEW BOOTFILES! 57 : 58 : mblume 1874 UPDATE: The release tag has been moved to include a fix for a brown-paper- 59 : bag glitch (see above). 60 : 61 : mblume 1867 ---------------------------------------------------------------------- 62 : Name: Matthias Blume (http://www.tti-c.org/blume/) 63 : mblume 1866 Date: 2005/11/16 10:25:00 CST 64 : Tag: blume-22051116-btrace 65 : Description: 66 : 67 : Fixed problem with bogus exception message when using back-trace 68 : facility. 69 : 70 : ---------------------------------------------------------------------- 71 : Name: Matthias Blume (http://www.tti-c.org/blume/) 72 : mblume 1865 Date: 2005/11/15 22:35:00 CST 73 : Tag: blume-22051115-array2copy 74 : Description: 75 : 76 : Added simple implementation of Array2.copy. (Warning: mostly untested.) 77 : 78 : ---------------------------------------------------------------------- 79 : Name: Matthias Blume (http://www.tti-c.org/blume/) 80 : mblume 1864 Date: 2005/11/15 21:35:00 CST 81 : Tag: blume-22051115-versiontool 82 : Description: 83 : 84 : Reversed change to src/system/smlnj/internals/versiontool.cm. This 85 : file gets loaded as a tool -- by the equivalent of CM.make during the 86 : run of CMB.make. Thus, CMB's path configuration is meaningless for 87 : it. Instead, it has the status of "user code", so it should use 88 : $/basis.cm to refer to the Basis library. (At least that's true for 89 : the purpose of bootstrapping the previous change. In the future it 90 : might make sense to have versiontool.cm refer to 91 :$smlnj/basis/basis.cm, i.e., the version of the Basis that the 92 : compiler itself uses.) 93 : 94 : Also patched src/system/testml to have it activate those extra anchor 95 : bindings in config/extrapathconfig. 96 : 97 : ---------------------------------------------------------------------- 98 : Name: Matthias Blume (http://www.tti-c.org/blume/) 99 : mblume 1863 Date: 2005/11/15 16:35:00 CST 100 : Tag: blume-22051115-libraries 101 : Description: 102 : 103 : This change affects the way the following libraries are tied into 104 : the system: 105 : 106 : $/basis.cm 107 :$/smlnj-lib.cm 108 : $/pp-lib.cm 109 :$/controls-lib.cm 110 : $/html-lib.cm 111 :$/ml-yacc-lib.cm 112 : 113 : These libraries are now internally (as seen from the source code 114 : of the implementation itself) known by the following names: 115 : 116 : $smlnj/basis/basis.cm 117 :$smlnj/smlnj-lib/smlnj-lib.cm 118 : $smlnj/smlnj-lib/pp-lib.cm 119 :$smlnj/smlnj-lib/controls-lib.cm 120 : $smlnj/smlnj-lib/html-lib.cm 121 :$smlnj/ml-yacc/ml-yacc-lib.cm 122 : 123 : This makes it possible to work with code that requires different 124 : versions of these libraries, and which refers to these libraries using 125 : their "default" names (i.e., the first set of names above). In other 126 : words, one can un-define or re-define those default names without 127 : compromising the proper functioning of the compiler itself. 128 : 129 : A similar procedure had already been performed for several of the 130 : MLRISC libraries that are linked into the compiler. I did some 131 : cleanup on this code. 132 : 133 : A new file in the config directory (named extrapathconfig) is 134 : responsible for setting up path anchors that the compiler itself does 135 : not need, but that are typically required by user code. 136 : 137 : ---------------------------------------------------------------------- 138 : mblume 1862 Name: Matthias Blume 139 : Date: 2005/11/07 17:05:00 CST 140 : Tag: blume-20051107-slice 141 : Description: 142 : 143 : Fixed erroneous out-of-bounds test in the "update" function of 144 : various *ArraySlice modules. (Thanks to Vesa A. Norrman for pointing 145 : out the problem.) 146 : 147 : Pushed some Basis changes through ML-Lex, CML, and eXene. 148 : 149 : ---------------------------------------------------------------------- 150 : jhr 1858 Name: John Reppy (http://www.cs.uchicago.edu/~jhr) 151 : jhr 1861 Date: 2005/11/07 152 : Description: 153 : Fixed a Basis incompatibility: The depreciated function Substring.all 154 : was removed (use Substring.full instead). 155 : 156 : ---------------------------------------------------------------------- 157 : Name: John Reppy (http://www.cs.uchicago.edu/~jhr) 158 : jhr 1858 Date: 2005/11/05 159 : Description: 160 : Tweaked interval set API in SML/NJ library; see the CHANGES file for details. 161 : 162 : ---------------------------------------------------------------------- 163 : mblume 1856 Name: Matthias Blume (http://www.tti-c.org/blume/) 164 : Date: 2005/11/02 16:25:00 CST 165 : Tag: blume-20051102-hex 166 : Description: 167 : 168 : * Runtime system bootstrap code now accepts hex digits in BOOTLIST 169 : in either upper case or lower case format. 170 : * Pushed changes to names of Pack{Big,Little} structures through 171 : CML and eXene. 172 : 173 : ---------------------------------------------------------------------- 174 : jhr 1852 Name: John Reppy (http://www.cs.uchicago.edu/~jhr) 175 : jhr 1855 Date: 2005/11/02 176 : Description: 177 : Fixed a Basis incompatibility: Pack{Big,Little} structures should 178 : be called PackWord{Big,Little}. 179 : 180 : ---------------------------------------------------------------------- 181 : Name: John Reppy (http://www.cs.uchicago.edu/~jhr) 182 : jhr 1852 Date: 2005/10/28 183 : Description: 184 : Fixed a minor Basis incompatibility: hex digits should be upper case. 185 : 186 : ---------------------------------------------------------------------- 187 : mblume 1846 Name: Matthias Blume (blume (at) tti - c (dot) org) 188 : Date: 2005/10/25 16:00:00 CDT 189 : Tag: Release_110_56 190 : Description: 191 : 192 : New working version (110.56). NEW BOOTFILES! 193 : 194 : ---------------------------------------------------------------------- 195 : jhr 1838 Name: John Reppy (http://www.cs.uchicago.edu/~jhr) 196 : jhr 1840 Date: 2005/10/25 197 : Description: 198 : Added interval sets to utility library (signatures INTERVAL_DOMAIN 199 : and INTERVAL_SET, and functor IntervalSetFn). 200 : 201 : ---------------------------------------------------------------------- 202 : Name: John Reppy (http://www.cs.uchicago.edu/~jhr) 203 : jhr 1838 Date: 2005/10/14 204 : Description: 205 : Add Zhong Shao's fix for datatype equality functions. 206 : 207 : ---------------------------------------------------------------------- 208 : allenleung 1836 Name: Allen Leung (leunga (at) reservoir (dot) com) 209 : allenleung 1837 Date: 2005/10/14 12:30:00 EST 210 : Tag: leunga-20051014-x86-spill 211 : Description: 212 : 213 : Bug fix a bug found by Carl Hauser. 214 : There was a typo in the reload code for FCMP in x86SpillInstr.sml. 215 : 216 : ---------------------------------------------------------------------- 217 : Name: Allen Leung (leunga (at) reservoir (dot) com) 218 : allenleung 1836 Date: 2005/10/14 11:15:00 EST 219 : Tag: leunga-20051014-x86-asm 220 : Description: 221 : 222 : Removed some debugging code in file x86Asm.sml. 223 : The function emit_operand was printing out debugging output. 224 : 225 : ---------------------------------------------------------------------- 226 : jhr 1813 Name: John Reppy 227 : jhr 1831 Date: 2005/07/27 228 : Tag: 229 : Description: 230 : 231 : jhr 1832 Fixed ml-lex to recognize "\r" as representing carriage return. 232 : 233 : ---------------------------------------------------------------------- 234 : Name: John Reppy 235 : Date: 2005/07/27 236 : Tag: 237 : Description: 238 : 239 : jhr 1831 Fixed ml-yacc to work on files with non-native end-of-line 240 : encodings (e.g., Windows text file on a Unix system). 241 : 242 : ---------------------------------------------------------------------- 243 : Name: John Reppy 244 : jhr 1824 Date: 2005/07/20 245 : Tag: 246 : Description: 247 : 248 : Added changes from Dominic Evans (oldmanuk (at) gmail (dot) com) 249 : to support HPUX 11. 250 : 251 : ---------------------------------------------------------------------- 252 : Name: John Reppy 253 : jhr 1813 Date: 2005/07/06 254 : Tag: 255 : Description: 256 : 257 : Changes to the SML/NJ library. See smlnj-lib/CHANGES for details. 258 : 259 : ---------------------------------------------------------------------- 260 : mblume 1808 Name: Matthias Blume (blume (at) tti - c (dot) org) 261 : Date: 2005/07/06 00:45:00 CDT 262 : Tag: blume-20050706-slice-copy 263 : Description: 264 : 265 : Fixed reversed logic for deciding whether to "copy up" or "copy down" 266 : in *-array-slice.sml. 267 : 268 : ---------------------------------------------------------------------- 269 : allenleung 1806 Name: Allen Leung (leunga (at) reservoir (dot) com) 270 : allenleung 1807 Date: 2005/05/31 17:00:00 EST 271 : Tag: leunga-20050531-cygwin-fault-2 272 : Description: 273 : 274 : A typo in the cygwin code fixed. 275 : 276 : ---------------------------------------------------------------------- 277 : Name: Allen Leung (leunga (at) reservoir (dot) com) 278 : allenleung 1806 Date: 2005/05/31 16:47:00 EST 279 : Tag: leunga-20050531-cygwin-fault 280 : Description: 281 : 282 : Updated Cygwin's fault/signal handling to match the Windows version. 283 : Updated the export list. 284 : 285 : ---------------------------------------------------------------------- 286 : mblume 1791 Name: Matthias Blume (blume (at) tti - c (dot) org) 287 : mblume 1795 Date: 2005/05/18 13:35:00 CDT 288 : Tag: Release_110_54 289 : Description: 290 : 291 : New working version (110.54). NEW BOOTFILES! 292 : 293 : ---------------------------------------------------------------------- 294 : Name: Matthias Blume (blume (at) tti - c (dot) org) 295 : mblume 1794 Date: 2005/05/18 11:58:00 CDT 296 : Tag: blume-20050518-installer 297 : Description: 298 : 299 : Added support scripts for Mac OS X PackageMaker and modified 300 : config/install.sh so that it supports re-dumping a heap image 301 : after customization. 302 : 303 : ---------------------------------------------------------------------- 304 : Name: Matthias Blume (blume (at) tti - c (dot) org) 305 : mblume 1793 Date: 2005/05/18 10:55:00 CDT 306 : Tag: blume-20050518-realdiv-noovld 307 : Description: 308 : 309 : Un-overloaded / to work around bug in overloading resolution code. 310 : 311 : ---------------------------------------------------------------------- 312 : Name: Matthias Blume (blume (at) tti - c (dot) org) 313 : mblume 1792 Date: 2005/05/16 23:50:00 CDT 314 : Tag: blume-20050516-redump-heap 315 : Description: 316 : 317 : Added mechanism for re-creating a heap file for the interactive system 318 : after configuration variables have been changed. 319 : 320 : CM.redump_heap : string -> unit 321 : 322 : This is much like SMLofNJ.exportML, but starting from the resulting 323 : heap does not return to the caller of CM.redump_heap but 324 : restarts the interactive system from scratch. The original call of 325 : CM.redump_heap does not return but ends the interactive session. 326 : Thus, CM.redump_heap is a lot like SMLofNJ.exportFn. 327 : 328 : Internally, redump_heap winds the dynamic execution context back to 329 : the point where the original heap image was created and re-executes 330 : the heap image generation code in the boot code. 331 : 332 : ---------------------------------------------------------------------- 333 : Name: Matthias Blume (blume (at) tti - c (dot) org) 334 : mblume 1791 Date: 2005/05/09 21:55:00 CDT 335 : Tag: blume-20050509-word64 336 : Description: 337 : 338 : Added a hack to the existing hack known as Word64 to make fromString 339 : behave correctly. I am still not sure whether Word64.scan will work 340 : as specified with respect to the interaction of radix and prefix. 341 : 342 : ---------------------------------------------------------------------- 343 : allenleung 1785 Name: Allen Leung (leunga (at) reservoir (dot) com) 344 : Date: 2005/05/04 11:50:00 EST 345 : Tag: leunga-20050504-checkgc 346 : Description: 347 : 348 : Added a gc protocol checking phase. This phase is enabled with 349 : the flag "check-gc". "debug-check-gc" turns on the verbose mode. 350 : 351 : ---------------------------------------------------------------------- 352 : mblume 1741 Name: Matthias Blume (blume (at) tti - c (dot) org) 353 : mblume 1784 Date: 2005/05/04 10:45:00 CDT 354 : Tag: blume-20050504-intinf 355 : Description: 356 : 357 : Fixed a bug in the implementation of div and mod for IntInf. 358 : Thanks to Neophytos Michael for reporting the problem. 359 : 360 : ---------------------------------------------------------------------- 361 : Name: Matthias Blume (blume (at) tti - c (dot) org) 362 : mblume 1783 Date: 2005/05/04 10:35:00 CDT 363 : Tag: blume-20050504-join 364 : Description: 365 : 366 : Added a "join" combinator to the ParserComb module in smlnj-lib.cm. 367 : 368 : ---------------------------------------------------------------------- 369 : Name: Matthias Blume (blume (at) tti - c (dot) org) 370 : mblume 1770 Date: 2005/02/28 23:40:00 CST 371 : Tag: blume-20050228-mVar 372 : Description: 373 : 374 : Fixed serious bug (brown paper bag variety) in new implementation of 375 : structure Atom in CML. (I had accidentally used a mailbox instead of 376 : an mvar, leaving the door open for races.) 377 : 378 : ---------------------------------------------------------------------- 379 : Name: Matthias Blume (blume (at) tti - c (dot) org) 380 : mblume 1761 Date: 2005/02/25 15:00:00 CST 381 : Tag: Release_110_53 382 : Description: 383 : 384 : New working version (110.53). NEW BOOTFILES! 385 : 386 : ---------------------------------------------------------------------- 387 : Name: Matthias Blume (blume (at) tti - c (dot) org) 388 : mblume 1760 Date: 2005/02/25 14:50:00 CST 389 : Tag: blume-20050225-susp 390 : Description: 391 : 392 : Brought back SMLofNJ.Susp. The underlying suspension type is the one 393 : implemented in Core -- which means that it is the same as the one used 394 : by the lazy extension. 395 : 396 : ---------------------------------------------------------------------- 397 : Name: Matthias Blume (blume (at) tti - c (dot) org) 398 : mblume 1759 Date: 2005/02/24 16:50:00 CST 399 : Tag: blume-20050224-cml-atom 400 : Description: 401 : 402 : Simpler and at the same time more general implementation of structure 403 : Atom in CML. 404 : 405 : ---------------------------------------------------------------------- 406 : Name: Matthias Blume (blume (at) tti - c (dot) org) 407 : mblume 1758 Date: 2005/02/15 17:35:00 CST 408 : Tag: blume-20050215-tools 409 : Description: 410 : 411 : Created new "tools" directory under "src" and moved "TraceDebugProf" 412 : there. 413 : 414 : ---------------------------------------------------------------------- 415 : Name: Matthias Blume (blume (at) tti - c (dot) org) 416 : mblume 1755 Date: 2005/02/10 17:55:00 CST 417 : Tag: blume-20050210-longlong 418 : Description: 419 : 420 : Implemented "long long" arguments and results for NLFFI. (Only the 421 : PPC/MacOS implementation is complete, the other backends still need to 422 : be updated.) 423 : 424 : ---------------------------------------------------------------------- 425 : Name: Matthias Blume (blume (at) tti - c (dot) org) 426 : mblume 1751 Date: 2005/01/24 17:40:00 CST 427 : Tag: blume-20050124-mlyacc 428 : Description: 429 : 430 : Minor cleanup in ML-Yacc rule printing mechanism. This should fix a 431 : problem with certain "as" patterns which previously got rendered 432 : using incorrect syntax. 433 : 434 : ---------------------------------------------------------------------- 435 : Name: Matthias Blume (blume (at) tti - c (dot) org) 436 : mblume 1750 Date: 2005/01/18 12:00:00 CST 437 : Tag: blume-20050118-profile 438 : Description: 439 : 440 : Made time profiling code (interrupt handler) in runtime system aware 441 : of new array representation. 442 : 443 : ---------------------------------------------------------------------- 444 : Name: Matthias Blume (blume (at) tti - c (dot) org) 445 : mblume 1747 Date: 2005/01/14 18:00:00 CST 446 : Tag: blume-20050114-heap2exec 447 : Description: 448 : 449 : Implemented new (but still experimental) heap2exec facility. This is 450 : tested under Mac OS X and should work under Linux (will test shortly). 451 : It will probably also work on the Sparc (will test some time later). 452 : 453 : - removed old "HACKED_STANDALONE" hack from runtime 454 : 455 : To be able to test this, uncomment the request for "heap2asm" in 456 : config/targets prior to installation. (Notice that this is different 457 : from "heap2exec" mentioned below. Not a typo.) 458 : 459 : To perform an actual test, run the command 460 : 461 : $bin/heap2exec heapfile execfile 462 : 463 : (You can put heap2exec on your shell's path.) 464 : 465 : For example, run 466 : 467 :$ bin/heap2exec bin/.heap/ml-yacc.ppc-darwin mly 468 : 469 : This will create a standalone executable called "mly" which you can 470 : then invoke directly as a command. 471 : 472 : ---------------------------------------------------------------------- 473 : Name: Matthias Blume (blume (at) tti - c (dot) org) 474 : mblume 1746 Date: 2005/01/07 11:44:00 CST 475 : Tag: blume-20050107-mlstring 476 : Description: 477 : 478 : fixed off-by-one error in ML_STRING macro (globals.c) 479 : 480 : ---------------------------------------------------------------------- 481 : Name: Matthias Blume (blume (at) tti - c (dot) org) 482 : mblume 1744 Date: 2004/12/23 18:00:00 CST 483 : Tag: blume-20041223-santa 484 : Description: 485 : 486 : Made ml-build script "smarter" (but only very little). 487 : 488 : ---------------------------------------------------------------------- 489 : Name: Matthias Blume (blume (at) tti - c (dot) org) 490 : mblume 1742 Date: 2004/12/21 15:05:00 CST 491 : Tag: blume-20041221-longlong 492 : Description: 493 : 494 : * Implemented access to signed and unsigned long long data in NLFFI. 495 : (The parameter-passing part of the picture has not complete. But 496 : data structure access seems to work.) 497 : 498 : * Fixed CM's incorrect assumption that the PPC is little-endian. 499 : (On the Mac, it is big-endian. And that's currently our only 500 : PPC platform.) 501 : 502 : ---------------------------------------------------------------------- 503 : Name: Matthias Blume (blume (at) tti - c (dot) org) 504 : mblume 1741 Date: 2004/12/21 12:50:00 CST 505 : Tag: blume-20041221-memory 506 : Description: 507 : 508 : Some cleanup in the $c/memory.cm library: separated some concerns by 509 : moving allocation code and memory access code each into their own 510 : files. 511 : 512 : ---------------------------------------------------------------------- 513 : allenleung 1740 Name: Allen Leung (leunga (at) reservoir (dot) com) 514 : Date: 2004/12/17 16:12:00 EST 515 : Tag: leunga-20041217-cygwin-smlnj-home 516 : Description: 517 : 518 : The Unix I/O library of SML/NJ on cygwin does not understand 519 : Windows style pathname, so problems arise when SMLNJ_HOME is set 520 : to a Windows style pathname. _run-sml now converts SMLNJ_HOME 521 : to a POSIX pathname on cygwin. 522 : 523 : ---------------------------------------------------------------------- 524 : mblume 1737 Name: Matthias Blume (blume (at) tti - c (dot) org) 525 : mblume 1736 Date: 2004/12/16 13:35:00 CST 526 : Tag: Release_110_52 527 : Description: 528 : 529 : Last-minute changes incorporated into 110.52. Release tag moved. 530 : 531 : The changes: 532 : - HashString.hashString' -> HashString.hashSubstring 533 : - bug fix in UnivariateStats 534 : 535 : ---------------------------------------------------------------------- 536 : mblume 1702 Name: Matthias Blume (blume (at) tti - c (dot) org) 537 : mblume 1733 Date: 2004/12/15 23:40:00 CST 538 : Tag: blume-20041215-hashSubstring 539 : Description: 540 : 541 : - HashString.hashString' -> HashString.hashSubstring 542 : - corresponding changes in atom.sml 543 : - "de-compressed" (aka. un-obfuscated) code for UnivariateStats and 544 : added some comments 545 : 546 : ---------------------------------------------------------------------- 547 : Name: Matthias Blume (blume (at) tti - c (dot) org) 548 : mblume 1728 Date: 2004/12/15 15:30:00 CST 549 : mblume 1736 Tag: (Release_110_52) 550 : mblume 1728 Description: 551 : 552 : New working version (110.52). NEW BOOTFILES! 553 : 554 : ---------------------------------------------------------------------- 555 : Name: Matthias Blume (blume (at) tti - c (dot) org) 556 : mblume 1727 Date: 2004/12/15 12:45:00 CST 557 : Tag: blume-20041215-spaces 558 : Description: 559 : 560 : More on the space problem (this time for Win32). 561 : 562 : ---------------------------------------------------------------------- 563 : Name: Matthias Blume (blume (at) tti - c (dot) org) 564 : mblume 1725 Date: 2004/12/14 17:30:00 CST 565 : Tag: blume-20041214-spaces 566 : Description: 567 : 568 : Hacked some of the scripts (in particular: the installer) to cope with 569 : spaces in filenames a bit better. But beware: the current "solution" 570 : is likely still full of bugs and inherently incomplete. (We need to 571 : do away with those shell scripts for a comprehensive solution.) 572 : 573 : ---------------------------------------------------------------------- 574 : Name: Matthias Blume (blume (at) tti - c (dot) org) 575 : mblume 1724 Date: 2004/12/13 14:45:00 CST 576 : Tag: blume-20041213-ml-makedepend 577 : Description: 578 : 579 : Fixed bug in code for ml-makedepend. 580 : 581 : ---------------------------------------------------------------------- 582 : Name: Matthias Blume (blume (at) tti - c (dot) org) 583 : mblume 1720 Date: 2004/12/09 16:30:00 CST 584 : Tag: blume-20041209-statistics 585 : Description: 586 : 587 : Added two simple but potentially useful statistics modules to SML/NJ Library. 588 : (See CHANGES file there.) 589 : 590 : ---------------------------------------------------------------------- 591 : Name: Matthias Blume (blume (at) tti - c (dot) org) 592 : mblume 1718 Date: 2004/12/01 16:50:00 CST 593 : Tag: blume-20041201-atom 594 : Description: 595 : 596 : smlnj-lib: 597 : 598 : Added function HashString.hashString' for substrings. 599 : Hand-inlined CharVector.foldl into HashString (for speed). 600 : Modified implementation of structure Atom to avoid extracting 601 : strings from substrings unless necessary. 602 : (Also see CHANGES file for smlnj-lib.) 603 : 604 : ---------------------------------------------------------------------- 605 : Name: Matthias Blume (blume (at) tti - c (dot) org) 606 : mblume 1717 Date: 2004/11/24 22:15:00 CST 607 : Tag: blume-20041124-cml 608 : Description: 609 : 610 : Made sure CML compiles when Position = Int64. 611 : 612 : ---------------------------------------------------------------------- 613 : Name: Matthias Blume (blume (at) tti - c (dot) org) 614 : mblume 1715 Date: 2004/11/24 14:30:00 CST 615 : Tag: blume-20041124-position 616 : Description: 617 : 618 : The compiler can now be compiled in a mode that makes structure Position 619 : equal to Int64. The default, however, is unchanged (Position = Int31) 620 : for the time being. 621 : 622 : To enable 64-bit positions, use the following procedure: 623 : 624 : 1. Start sml 625 : 2. Autoload$smlnj/cmb.cm (if not already autoloaded) 626 : 3. Type 627 : #set (CMB.symval "USE_64_BIT_POSITIONS") (SOME 1); 628 : 4. Run CMB.make() as usual. 629 : 630 : This is barely tested. The only test so far was a little SML program 631 : counting the number of characters in an 8-gigabyte file by 632 : reading it character-by-character. That test was successful. 633 : 634 : In support of 64-bit positions, a number of new functions have been 635 : added to the runtime system. 636 : 637 : ---------------------------------------------------------------------- 638 : Name: Matthias Blume (blume (at) tti - c (dot) org) 639 : mblume 1716 Date: 2004/11/23 14:45:00 CST 640 : Tag: blume-20041123-useFile 641 : mblume 1712 Description: 642 : 643 : Fixed a problem with unhelpful error messages related to problems with 644 : .cm- or .sml files that appear as part of the sml command line. 645 : 646 : ---------------------------------------------------------------------- 647 : Name: Matthias Blume (blume (at) tti - c (dot) org) 648 : mblume 1703 Date: 2004/11/18 15:40:00 CST 649 : Tag: Release_110_51 650 : Description: 651 : 652 : New working version (110.51). NEW BOOTFILES! 653 : 654 : ---------------------------------------------------------------------- 655 : Name: Matthias Blume (blume (at) tti - c (dot) org) 656 : mblume 1702 Date: 2004/11/18 15:35:00 CST 657 : Tag: 658 : Description: 659 : 660 : Enabled dlopen and friends for FreeBSD (as recommended by Johannes 5 661 : Joemann). 662 : 663 : ---------------------------------------------------------------------- 664 : allenleung 1701 Name: Allen Leung (leunga (at) reservoir (dot) com) 665 : Date: 2004/11/17 16:05:21 EST 2004 666 : Tag: leunga-20041117-mlrisc-live-kill 667 : Description: 668 : 669 : Added support for MLTree constructs LIVE and KILL 670 : to all the architectures. 671 : 672 : ---------------------------------------------------------------------- 673 : mblume 1687 Name: Matthias Blume (blume (at) tti - c (dot) org) 674 : mblume 1689 Date: 2004/11/13 00:20:00 CST 675 : Tag: blume-20041113-versiontool 676 : Description: 677 : 678 : - Stripped down the versiontool: It now only handles the version number. 679 : The date string is generated at bootstrap time (during makeml). 680 : 681 : - In a previous commit, fixed a minor issue with how polyequal is being 682 : translated. In particular, the code now "looks through" abstractions. 683 : This results in slightly fewer polyEqual warnings and hopefully slightly 684 : more efficient code. Important examples for where this matters are 685 : the new int64 and word64 types. 686 : 687 : ---------------------------------------------------------------------- 688 : Name: Matthias Blume (blume (at) tti - c (dot) org) 689 : mblume 1687 Date: 2004/11/12 00:30:00 CST 690 : Tag: blume-20041112-int64 691 : Description: 692 : 693 : Structure Int64 fully hooked in. (The implementation is not very 694 : efficient, though.) 695 : 696 : ---------------------------------------------------------------------- 697 : Name: Matthias Blume (blume (at) tti - c (dot) org) 698 : mblume 1686 Date: 2004/11/11 17:30:00 CST 699 : Tag: blume-20041111-more64 700 : Description: 701 : 702 : All the pieces of Word64 are now there, with the exception of the 703 : conversions from and to LargeWord. (Eventually these need to be identities, 704 : but for the time being they don't even make sense because LargeWord is 705 : 32-bit wide.) 706 : 707 : Also started to add similar support for Int64, but major pieces of that 708 : are still missing. 709 : 710 : ---------------------------------------------------------------------- 711 : mblume 1668 Name: Matthias Blume (blume (at) tti - c (dot) org) 712 : mblume 1684 Date: 2004/11/11 00:15:00 CST 713 : Tag: blume-20041111-word64 714 : Description: 715 : 716 : Structure Word64 is now (almost) complete, word literals and patterns 717 : seem to work. There are a few odd pieces missing. In particular, 718 : I didn't do the {from,to}LargeWord parts because LargeWord is still Word32 719 : at the moment. 720 : 721 : Making Word64 official would mean that LargeWord becomes Word64. But 722 : this requires extreme care because most word-word conversions have to 723 : go through LargeWord, so making a mistake means loss of efficiency or 724 : worse. Eventually there will be a solution similar to (but actually 725 : simpler than) what I did with IntInf. 726 : 727 : ---------------------------------------------------------------------- 728 : Name: Matthias Blume (blume (at) tti - c (dot) org) 729 : mblume 1683 Date: 2004/11/10 18:12:00 CST 730 : Tag: blume-20041110-64bit 731 : Description: 732 : 733 : More 64-bit hacking (but still not even half-way there yet). 734 : Also, some assorted improvements to the handling of 8-bit words. 735 : 736 : ---------------------------------------------------------------------- 737 : Name: Matthias Blume (blume (at) tti - c (dot) org) 738 : mblume 1682 Date: 2004/11/09 17:50:00 CST 739 : mblume 1683 Tag: 740 : mblume 1682 Description: 741 : 742 : Started adding some infrastructure for supporting 64-bit int- and 743 : word-types. (Still in its very early stages.) 744 : 745 : ---------------------------------------------------------------------- 746 : Name: Matthias Blume (blume (at) tti - c (dot) org) 747 : mblume 1672 Date: 2004/10/28 10:45:00 CDT 748 : Tag: Release_110_50 749 : Description: 750 : 751 : New working version (110.50). NEW BOOTFILES! 752 : 753 : ===================== 754 : 755 : Also: 756 : 757 : - Changend config/srcarchiveurl from a file just 758 : containing the URL string into a file containing 759 : shell script code. The code has access to the $VERSION variable. 760 : - Made corresponding changes to config/install.sh and config/unpack. 761 : - Default contents of config/srcarchiveurl uses$VERSION and 762 : normally does not have to be edited to reflect a version change. 763 : 764 : (As a result, a version change can be done by just editing 765 : config/version, the rest is now automatic.) 766 : 767 : ---------------------------------------------------------------------- 768 : Name: Matthias Blume (blume (at) tti - c (dot) org) 769 : mblume 1669 Date: 2004/10/27 17:50:00 CDT 770 : Tag: blume-20041027-btrace-msg 771 : Description: 772 : 773 : BackTrace.monitor now also reports the source of the exception that 774 : triggered the trace. 775 : 776 : ---------------------------------------------------------------------- 777 : Name: Matthias Blume (blume (at) tti - c (dot) org) 778 : mblume 1668 Date: 2004/10/27 17:20:00 CDT 779 : Tag: blume-20041027-x86-c-calls 780 : Description: 781 : 782 : This is the HISTORY entry for two earlier commits, both concerning 783 : the x86 c-calls code in MLRISC: 784 : 785 : - added a missing LOAD in the code that deals with struct arguments 786 : - made sure the caller does not add the wrong number of bytes to the 787 : stack pointer after a call of a function returning a struct 788 : (the callee already pops the implicit argument which points to 789 : the space reserved for the result) 790 : 791 : ---------------------------------------------------------------------- 792 : allenleung 1662 Name: Allen Leung (leunga (at) reservoir (dot) com) 793 : Date: 2004/10/24 14:00:00 EST 794 : Tag: leunga-20041024-x86-gas-fucomip 795 : Description: 796 : 797 : John discovered a bug in the syntax of fucomip. 798 : The opcodes FU?COMIP? have been changed to 799 : 800 : fu?comip? %st(i), %st 801 : 802 : ---------------------------------------------------------------------- 803 : mblume 1622 Name: Matthias Blume (blume (at) tti - c (dot) org) 804 : mblume 1656 Date: 2004/10/20 15:06:00 CDT 805 : Tag: blume-20041020-standalone-backtrace 806 : Description: 807 : 808 : Added a mechanism for getting back-trace information from standalone 809 : programs. Here is how it works: 810 : 811 : 1. The part of the program from which you want to get backtrace 812 : information (usually the whole program) should be wrapped with 813 : BackTrace.monitor. This is a (unit->'a)->'a function, and your 814 : main program could be modified from something like 815 : 816 : fun main (pgm, args) = ... 817 : 818 : to 819 : 820 : fun main (pgm, args) = BackTrace.monitor (fn () => ...) 821 : 822 : 2. To be able to access BackTrace.monitor, you have to add 823 : library $smlnj-tdp/plugins.cm to the .cm file that contains your 824 : main function. 825 : 826 : 3. Remove all compiled code (i.e., all the .cm/ subdirectories that 827 : CM might have created in the past for your project). 828 : 829 : 4. Build the system using this command line: 830 : 831 : ml-build -Ctdp.instrument=true \$smlnj-tdp/back-trace.cm \ 832 : myprog.cm MyProg.main myprog 833 : 834 : instead of the usual 835 : 836 : ml-build myprog.cm MyProg.main myprog 837 : 838 : I changed a library name: 839 : 840 : $/trace-debug-profile.cm -->$smlnj-tdp/plugins.cm 841 : 842 : New libraries: 843 : 844 : $smlnj-tdp/back-trace.cm 845 : -- when loaded causes the back-trace plugin to be installed 846 :$smlnj-tdp/coverage.cm 847 : -- when loaded causes the coverage plugin to be installed 848 : 849 : ---------------------------------------------------------------------- 850 : Name: Matthias Blume (blume (at) tti - c (dot) org) 851 : mblume 1655 Date: 2004/10/18 16:45:00 CDT 852 : Tag: blume-20041018-groupowner 853 : Description: 854 : 855 : Added an "obsolete" warning for the "group owner" syntax to CM's parser. 856 : 857 : Eliminated group owner specs from .cm files throughout the source tree. 858 : 859 : ---------------------------------------------------------------------- 860 : Name: Matthias Blume (blume (at) tti - c (dot) org) 861 : mblume 1653 Date: 2004/10/15 15:45:00 CDT 862 : Tag: blume-20041015-coverage 863 : Description: 864 : 865 : * Test coverage tool added! 866 : * Further reorganization of tracing-, debugging-, and profiling support: 867 : 868 : - moved original BTImp -- now called BackTrace -- into a separate 869 : library called $/trace-debug-profile.cm 870 : - eliminated all mentions of BTrace from SMLofNJ.Internals 871 : - only the instrumentation mechanism is now left in the compiler proper 872 : - BackTrace module is a plugin which is NOT plugged in by default 873 : - Coverage module is another such plugin 874 : 875 : To get the benefits of any of these plugin modules, the code in 876 : question must be compiled with tdp instrumentation turned on. This 877 : can be done by setting SMLofNJ.Internals.TDP.mode to true. 878 : (The ref cell is also controlled via the -Ctdp.instrument=... switch.) 879 : 880 : Plugins are selected at link time. (Pre-compiled instrumented code 881 : can be re-loaded with different plugins in effect.) When an 882 : instrumented module is linked, whatever plugins are at that time 883 : enabled will come into effect for that module. 884 : 885 : To enable the back-trace plugin, load library$/trace-debug-profile.cm 886 : and invoke BackTrace.install() (e.g., from the interactive prompt). 887 : To enable the coverage plugin, load the same library and invoke 888 : Coverage.install(). 889 : 890 : Back-traces are generated automatically on uncaught exceptions and 891 : when the code in question explicitly invokes BackTrace.trigger(). 892 : 893 : Coverage (and execution frequency-) information must be queried 894 : explicitly by calling Coverage.not_covered and Coverage.hot_spots. 895 : 896 : ---------------------------------------------------------------------- 897 : Name: Matthias Blume (blume (at) tti - c (dot) org) 898 : mblume 1652 Date: 2004/10/14 17:40:00 CDT 899 : Tag: blume-20041014-tdp-core 900 : Description: 901 : 902 : Snapshot of a significant overhaul of how the trace/debug/profile support 903 : is hooked into the system (specifically: Core and SMLofNJ.Internals). 904 : 905 : ---------------------------------------------------------------------- 906 : Name: Matthias Blume (blume (at) tti - c (dot) org) 907 : mblume 1650 Date: 2004/10/13 16:34:00 CDT 908 : Tag: blume-20041013-tdp 909 : Description: 910 : 911 : Some rationalization of names: 912 : 913 : structure BTrace -> structure TDPInstrument 914 : etc. 915 : 916 : This is is preparation of using the original back-trace 917 : instrumentation for other purposes. "TDP" stands for 918 : Trace/Debug/Profile. 919 : 920 : The control flag controlling whether instrumentation is on or off is now 921 : registered under a different name, so instead of running sml as 922 : 923 : sml -Cinstrument.btrace-mode=true 924 : 925 : one has to say 926 : 927 : sml -Ctdp.instrument=true 928 : 929 : ---------------------------------------------------------------------- 930 : Name: Matthias Blume (blume (at) tti - c (dot) org) 931 : mblume 1645 Date: 2004/10/11 16:37:00 CDT 932 : Tag: blume-20041011-regions 933 : Description: 934 : 935 : Made some minor modifications to elabcore.sml to have source regions 936 : be propagated more tightly -- resulting in better (i.e., smaller) 937 : regions being reported in error- and debug messages. 938 : 939 : ---------------------------------------------------------------------- 940 : Name: Matthias Blume (blume (at) tti - c (dot) org) 941 : mblume 1644 Date: 2004/10/08 22:50:00 CDT 942 : Tag: blume-20041008-cmkw 943 : Description: 944 : 945 : Fixed handling of keywords in .cm files: After seeing "is" the lexer 946 : treats subsequent occurrences of "group", "library", "source", "is", 947 : "*", and "-" as ordinary identifiers rather than keywords. 948 : 949 : Most seriously, this fixes a problem with CM's "shell" tool. The tool 950 : is supposed to accept a tool argument called "source", but this did 951 : not work because of the clash with the keyword. 952 : 953 : ---------------------------------------------------------------------- 954 : Name: Matthias Blume (blume (at) tti - c (dot) org) 955 : mblume 1642 Date: 2004/10/07 16:00:00 CDT 956 : Tag: blume-20041007-cleanup 957 : Description: 958 : 959 : Assorted cleanup work: 960 : 961 : - got rid of intstrmap in favor of using the library's 962 : hash table implementation 963 : - threw out most of the pathnames stuff, as it was not used anyway 964 : - simplified tokentable implementation 965 : - fixed some minor spelling errors 966 : 967 : ---------------------------------------------------------------------- 968 : Name: Matthias Blume (blume (at) tti - c (dot) org) 969 : mblume 1641 Date: 2004/10/06 15:15:15 CDT 970 : Tag: blume-20041006-handler 971 : Description: 972 : 973 : Cleaned up the absyn to reflect the invariant that HANDLE always 974 : carries a FNexp as part of the type definition. This eliminates some 975 : superfluous sanity checks at runtime down the road. 976 : 977 : Some minor cleanup of the btrace code. 978 : 979 : ---------------------------------------------------------------------- 980 : Name: Matthias Blume (blume (at) tti - c (dot) org) 981 : mblume 1640 Date: 2004/10/01 10:20:30 CDT 982 : Tag: blume-20041001-slave 983 : Description: 984 : 985 : Added hack to make slave mode work in the presence of the version 986 : tool. (Still, since the master does two passes over the code for 987 : CMB.make, the release number gets bumped twice when slaves are 988 : attached. I don't know if this is worth fixing...) 989 : 990 : ---------------------------------------------------------------------- 991 : Name: Matthias Blume (blume (at) tti - c (dot) org) 992 : mblume 1639 Date: 2004/09/30 10:55:00 CDT 993 : Tag: blume-20040930-version 994 : Description: 995 : 996 : * Moved the "version" magic into its own little library under 997 : mblume 1672 src/system/smlnj/internal. This avoids expensive reconstruction of 998 : a stable src/compiler/core.cm. 999 : mblume 1639 1000 : mblume 1672 * At the same time, structure CompilerVersion is now known as 1001 : structure SMLNJVersion. 1002 : mblume 1639 1003 : * Arranged for the version tool to NOT kick in when rebuilding the system 1004 : (makeml -rebuild, fixpt). Otherwise one would never reach a fixpoint. 1005 : Also, loading the versiontool does not work when rebuilding the system 1006 : because CM is not properly initialized at that time. 1007 : 1008 : ---------------------------------------------------------------------- 1009 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1010 : mblume 1638 Date: 2004/09/29 14:00:00 CDT 1011 : Tag: blume-20040929-autoversion 1012 : Description: 1013 : 1014 : Implemented some CM magic to have 1015 : file src/compiler/TopLevel/main/version.sml 1016 : generated automagically. 1017 : The version is taken from two files: config/version and config/release. 1018 : The first is expected to contain a two-part version number such as 110.49. 1019 : The second should contain a single number, but it may be missing. 1020 : 1021 : If the environment variable VERSIONTOOL_BUMP_RELEASE is defined at the 1022 : time the version tool is loaded (which is the first time you say CMB.make), 1023 : then the tool will increment the value stored in config/release every 1024 : time CMB.make is invoked. 1025 : 1026 : The binfile format is now insensitive to anything beyond the first 1027 : two components of a version number, so bumping the release does not render 1028 : binfiles incompatible. Auto-bumping can be used to keep track of versions 1029 : during development without invalidating existing binfiles. 1030 : 1031 : In any case, every CMB.make updates the date information in version.sml. 1032 : (This is the date that is printed in the banner.) 1033 : 1034 : ---------------------------------------------------------------------- 1035 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1036 : mblume 1634 Date: 2004/09/28 10:53:00 CDT 1037 : Tag: blume-20040928-controls 1038 : Description: 1039 : 1040 : Some cleanup of the controls code. 1041 : 1042 : ---------------------------------------------------------------------- 1043 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1044 : mblume 1633 Date: 2004/09/27 22:08:00 CDT 1045 : Tag: blume-20040927-controls 1046 : Description: 1047 : 1048 : Added two pieces of functionality to the Controls interface: 1049 : 1050 : 1. val save'restore: 'a control -> unit -> unit 1051 : 1052 : grabs the current value of the control in stage 1 and restores it 1053 : in stage 2. 1054 : 1055 : 2. val set' : 'a control * 'a -> unit -> unit 1056 : 1057 : stores the given value into the control in stage 2 (i.e., delayed) 1058 : but does all error checking in stage 1. 1059 : (This is for string controls that need to do parse their argument -- 1060 : something that might fail. In some cases, notably in CM, one 1061 : already knows the intended argument but wants to delay the actual 1062 : assignment until a time when error recovery would be more difficult.) 1063 : 1064 : Changed the handling of controls in tool arguments to classes "sml" and 1065 : "lazysml": 1066 : - use Controls.save'restore as a more robust way of restoring the 1067 : old value (in particular: without having to re-parse the string) 1068 : - use controls to handle the "overload" keyword in the init group 1069 : (I believe this change actually fixes a long-standing obscure bug.) 1070 : 1071 : ---------------------------------------------------------------------- 1072 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1073 : mblume 1632 Date: 2004/09/27 17:00:00 CDT 1074 : Tag: blume-20040927-lazysml 1075 : Description: 1076 : 1077 : Added a new tool class called "lazysml" to CM's tool chest. The only 1078 : difference to "sml" is that compilation is done with Control.lazysml 1079 : set to true. A source of class "lazysml" is automatically recognized 1080 : by a file name suffix of ".lml". 1081 : 1082 : In addition to the above feature, the original class "sml" now also 1083 : supports a tool argument "lazy" which has the same effect. As a 1084 : result, the following three lines are equivalent: 1085 : 1086 : foo.sml : lazysml 1087 : foo.sml : sml (lazy) 1088 : foo.sml (lazy) 1089 : 1090 : The setting goes into effect both during parsing and during 1091 : compilation. The original setting is restored right after parsing and 1092 : after compilation, respectively. 1093 : 1094 : In addition to all the above, there is also a general mechanism to set 1095 : ANY of the "controls" that are available at the command line via 1096 : "-C..." on a per-sml-file basis. The same rules that apply for "lazy" 1097 : apply as well. (In fact, "lazy" is implemented as a special case of 1098 : the general mechanism.) 1099 : 1100 : The .cm file syntax uses a new keyword tool argument called "with". 1101 : There are several ways of indicating the desired settings: 1102 : 1103 : foo.sml (with:parser.quotations=true) 1104 : foo.sml (with:(name:parser.quotations value:true)) 1105 : foo.sml (with:(name:name1 value:value1 name:name2 value:value2 ...)) 1106 : foo.sml (with:(name1=value1 name2=value2 ...)) 1107 : foo.sml (with:(name1=value1 name:name2 value:value2 name3=value3 ...)) 1108 : 1109 : etc. 1110 : 1111 : Another possible abbreviation is to leave out the =v or value:v part 1112 : if the name refers to a boolean control (in which case the value is 1113 : taken to be true). Thus, one could get lazy sml also by saying: 1114 : 1115 : foo.sml (with:parser.lazy-keyword=true) 1116 : foo.sml (with:parser.lazy-keyword) 1117 : foo.sml (with:(name:parser.lazy-keyword value:true)) 1118 : foo.sml (with:(name:parser.lazy-keyword)) 1119 : 1120 : ---------------------------------------------------------------------- 1121 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1122 : mblume 1631 Date: 2004/09/24 16:22:00 CDT 1123 : Tag: blume-20040924-ppc-long-branch 1124 : Description: 1125 : 1126 : Turned message about "emiting long form of branch" off by default. 1127 : Added a control flag to turn it back on when desired. 1128 : 1129 : ---------------------------------------------------------------------- 1130 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1131 : mblume 1630 Date: 2004/09/24 16:05:00 CDT 1132 : Tag: blume-20040924-rounding 1133 : Description: 1134 : 1135 : Applied patch for setting rounding modes under Mac OS X. Thanks to 1136 : Melissa O'Neill for providing the code! 1137 : 1138 : ---------------------------------------------------------------------- 1139 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1140 : mblume 1629 Date: 2004/09/23 17:30:00 CDT 1141 : Tag: blume-20040923-envvars 1142 : Description: 1143 : 1144 : 1. Changed definition of type ControlRegistry.registry_tree to 1145 : include control_info (i.e., the name of the controlling environment 1146 : variable). 1147 : 1148 : 2. Added command-line flags -e and -E to print the names of environment 1149 : variables that can be used to control internal settings. 1150 : (This uses the new API mentioned in 1.) 1151 : 1152 : ---------------------------------------------------------------------- 1153 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1154 : mblume 1622 Date: 2004/09/13 16:50:00 CDT 1155 : Tag: Release_110_49 1156 : Description: 1157 : 1158 : New working version (110.49). NEW BOOTFILES! 1159 : 1160 : ---------------------------------------------------------------------- 1161 : mblume 1621 Name: Matthias Blume 1162 : Date: 2004/09/13 16:20:00 CDT 1163 : Tag: blume-20040913-config-mlrisc 1164 : Description: 1165 : 1166 : Put target "mlrisc" back into the default list. 1167 : (There is no harm in having it, and some users have expressed their 1168 : wish to have "mlrisc" included by default.) 1169 : 1170 : ---------------------------------------------------------------------- 1171 : jhr 1620 Name: John Reppy 1172 : Date: 2004/09/13 1173 : Tag: jhr-20040913-signals 1174 : Description: 1175 : 1176 : Fixed the signal masking code to properly nest mask/unmask operations 1177 : on a per-signal basis. 1178 : 1179 : ---------------------------------------------------------------------- 1180 : mblume 1619 Name: Matthias Blume (blume (at) tti - c (dot) org) 1181 : Date: 2004/09/08 13:20:00 CDT 1182 : Tag: blume-20040908-heap-magic 1183 : Description: 1184 : 1185 : Bumped the heap macig number to 0x09082004 to account for the changed 1186 : layout of the ML frame under MacOS X. 1187 : 1188 : ---------------------------------------------------------------------- 1189 : allenleung 1618 Name: Allen Leung (leunga (at) reservoir (dot) com) 1190 : Date: 2004/09/03 11:26:00 EST 1191 : Tag: leunga-20040903-cygwin-install 1192 : Description: 1193 : 1194 : Added a patch to _arch-n-opsys to enable the Cygwin runtime. 1195 : The Cygwin runtime is turned on by setting the environment 1196 : variable SMLNJ_CYGWIN_RUNTIME to 1. 1197 : 1198 : ---------------------------------------------------------------------- 1199 : mblume 1615 Name: Matthias Blume (blume (at) tti - c (dot) org) 1200 : mblume 1617 Date: 2004/08/31 17:15:00 CDT 1201 : Tag: blume-20040831-core 1202 : Description: 1203 : 1204 : Added some exports to src/compiler/core.cm upon request by J. Joemann. 1205 : 1206 : ---------------------------------------------------------------------- 1207 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1208 : mblume 1616 Date: 2004/08/30 17:55:00 CDT 1209 : Tag: blume-20040830-installer 1210 : Description: 1211 : 1212 : Upon request by Johannes Joemann: 1213 : 1214 : - improved ML code of installer to fall back to coping when renaming 1215 : fails (i.e., when source and target are on different file systems); 1216 : the code compiles but has yet to be tested in anger 1217 : - removed mlrisc from list of default targets (config/targets) 1218 : 1219 : ---------------------------------------------------------------------- 1220 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1221 : mblume 1615 Date: 2004/08/27 17:20:00 CDT 1222 : Tag: blume-20040827-ptreql 1223 : Description: 1224 : 1225 : Added ptreql primop to structure InlineT (upon request from Larry 1226 : Paulson). 1227 : 1228 : ---------------------------------------------------------------------- 1229 : allenleung 1613 Name: Allen Leung (leunga (at) reservoir (dot) com) 1230 : allenleung 1614 Date: 2004/08/15 21:21:00 EST 1231 : Tag: leunga-110_48-udgraph 1232 : Description: 1233 : 1234 : Another bug fix from Carl Hauser: 1235 : 1236 : diff /net/niflab/smlnj48/src/MLRISC/graphs/udgraph.sml udgraph.sml 1237 : > 48c48 1238 : > < | rmv((e as (k,_))::es,L) = rmv(es,if k = i then es else 1239 : > e::L) 1240 : > --- 1241 : > > | rmv((e as (k,_))::es,L) = rmv(es,if k = i then L else e::L) 1242 : > Without this, any deletion of an edge in an undirected graph does severe 1243 : > violence to the graph. 1244 : 1245 : ---------------------------------------------------------------------- 1246 : Name: Allen Leung (leunga (at) reservoir (dot) com) 1247 : allenleung 1613 Date: 2004/08/10 23:35:00 EST 1248 : Tag: leunga-110_48-ppc 1249 : Description: 1250 : 1251 : The IBM/MacOS syntax switch on PPC was incorrectly swapped. 1252 : 1253 : ---------------------------------------------------------------------- 1254 : mblume 1602 Name: Matthias Blume (blume (at) tti - c (dot) org) 1255 : mblume 1615 Date: 2004/08/10 12:00:00 CDT 1256 : mblume 1602 Tag: Release_110_48 1257 : Description: 1258 : 1259 : New working version (110.48). NEW BOOTFILES! 1260 : 1261 : ---------------------------------------------------------------------- 1262 : allenleung 1599 Name: Allen Leung (leunga (at) reservoir (dot) com) 1263 : Date: 2004/08/09 12:21:00 EST 1264 : Tag: leunga-110_47-dijsktra 1265 : Description: 1266 : 1267 : Bug fix from Carl Hauser: 1268 : 1269 : single_source_shortest_paths in dijkstra.sml was observed to get wrong 1270 : answers (by comparing to single_source_shortest_paths in bellman-ford.sml). 1271 : 1272 : The problem is that following the expression A.update(dist,s,Num.zero) 1273 : it is necessary to update the priority queue using Q.decreaseWeight(Q,s). 1274 : 1275 : ---------------------------------------------------------------------- 1276 : mblume 1595 Name: Matthias Blume (blume (at) tti - c (dot) org) 1277 : Date: 2004/08/06 18:10:00 CDT 1278 : Tag: blume-20040806-cmdline 1279 : Description: 1280 : 1281 : Fiddled with handling of command-line options: 1282 : 1283 : * sml now quits after processing the command line 1284 : if -H, -S, -h, or -s appears as the last 1285 : command-line argument 1286 : * a new option -q terminates the session when encountered on 1287 : the command line; subsequent arguments will be ignored 1288 : * bug fixes: short (erroneous) arguments are no longer ignored 1289 : completely 1290 : 1291 : ---------------------------------------------------------------------- 1292 : allenleung 1593 Name: Allen Leung (leunga (at) reservoir (dot) com) 1293 : Date: 2004/08/04 18:17:00 EST 1294 : Tag: leunga-110_47-ppc-ibm-asm 1295 : Description: 1296 : 1297 : - Added minimal IBM assembly syntax support for PowerPC. 1298 : 1299 : - Cygwin: manually changed the file cygwin.def. Some exported symbols have 1300 : been altered in the runtime. We need an automatic way to keep the file 1301 : in sync. 1302 : 1303 : ---------------------------------------------------------------------- 1304 : mblume 1548 Name: Matthias Blume (blume (at) tti - c (dot) org) 1305 : mblume 1581 Date: 2004/08/04 14:00:00 CDT 1306 : Tag: Release_110_47 1307 : Description: 1308 : 1309 : New working version (110.47). NEW BOOTFILES! 1310 : 1311 : ---------------------------------------------------------------------- 1312 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1313 : mblume 1580 Date: 2004/08/03 14:25:00 CDT 1314 : Tag: blume-20040803-callingconv 1315 : Description: 1316 : 1317 : Added low-level support for choosing C calling conventions by 1318 : twiddling the type of rawccall. (See 1319 : src/compiler/Semant/types/cproto.sml for details.) 1320 : 1321 : ---------------------------------------------------------------------- 1322 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1323 : mblume 1579 Date: 2004/08/02 15:55:00 CDT 1324 : Tag: blume-20040802-backout 1325 : Description: 1326 : 1327 : Backed out of change to win32-filesys.c. The earlier patch to 1328 : get_file_time caused CM to produce files with the wrong time stamp. 1329 : 1330 : ---------------------------------------------------------------------- 1331 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1332 : mblume 1573 Date: 2004/08/02 14:45:00 CDT 1333 : Tag: blume-20040802-nlffi-win32 1334 : Description: 1335 : 1336 : Added NLFFI support for Win32, adapted from a patch provided by David 1337 : Hansel. This is currently completely untested. Also, the issue 1338 : concerning stdcall vs. ccall is still unresolved. 1339 : 1340 : ---------------------------------------------------------------------- 1341 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1342 : mblume 1572 Date: 2004/07/30 17:55:00 CDT 1343 : Tag: blume-20040730-various 1344 : Description: 1345 : 1346 : Gearing up towards 110.47... 1347 : 1348 : - various minor bugfixes to ml-nlffigen 1349 : - a beginning of a manual for nlffi 1350 : 1351 : - eliminated 'export name=value' in config/install.sh as this does 1352 : not work with certain versions of /bin/sh 1353 : (Thanks to David King at Motorola for catching this.) 1354 : 1355 : - several bugfixes provided or suggested by David Hansel at Reactive Systems: 1356 : - added a test for tm==NULL to gmtime.c and localtime.c 1357 : - applied patch for incorrect GetFileTime under win32 1358 : - toSeconds -> toMilliseconds in Win32/win32-process.sml 1359 : 1360 : ---------------------------------------------------------------------- 1361 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1362 : mblume 1557 Date: 2004/07/21 18:20:00 CDT 1363 : Tag: blume-20040721-nlffigen 1364 : Description: 1365 : 1366 : - Fixed minor issue in ml-nlffigen: Now generate structure T_foo 1367 : for a typedef to an incomplete type, but leave out the "typ" member. 1368 : (This is just for consistency.) 1369 : - Started to produce what is supposed to become better (i.e., comprehensive) 1370 : documentation of what ml-nlffigen does and produces. 1371 : 1372 : ---------------------------------------------------------------------- 1373 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1374 : mblume 1548 Date: 2004/07/14 16:25:00 CDT 1375 : Tag: blume-20040714-union 1376 : Description: 1377 : 1378 : Added C_UNION to c-calls/c-types.sml and updated the machinery 1379 : (ml-nlffigen, cproto.sml) that conveys C function interface 1380 : information to the code generator. 1381 : 1382 : However, the actual architecture-specific implementation of function 1383 : arguments and results that are C unions is still not implemented. 1384 : 1385 : ---------------------------------------------------------------------- 1386 : allenleung 1539 Name: Allen Leung (leunga (at) reservoir (dot) com) 1387 : allenleung 1546 Date: 2004/07/14 14:38:00 EST 1388 : Tag: leunga-110_46_1-ppc-lwzu 1389 : Description: 1390 : 1391 : Added these instructions to the PowerPC architecture: 1392 : LBZU(X), LHZU(X), LWZU(X), 1393 : STWU(X), STFDU, STFSU 1394 : 1395 : etc... 1396 : 1397 : Note: I haven't added their instruction encoding into the description. 1398 : 1399 : ---------------------------------------------------------------------- 1400 : Name: Allen Leung (leunga (at) reservoir (dot) com) 1401 : allenleung 1539 Date: 2004/07/13 15:04:00 EST 1402 : Tag: leunga-110_46_1-ppc-lwarx 1403 : Description: 1404 : 1405 : Added the two instructions LWARX and STWCX to the PowerPC 1406 : instruction set. 1407 : 1408 : A (untested) rewrite of loop-structure.sml. The old version 1409 : is completely broken. 1410 : 1411 : ---------------------------------------------------------------------- 1412 : mblume 1479 Name: Matthias Blume (blume (at) tti - c (dot) org) 1413 : mblume 1537 Date: 2004/07/13 13:50:00 CDT 1414 : Tag: blume-20040713-nlffi 1415 : Description: 1416 : 1417 : - use paramAlloc to report c-calls with too many arguments 1418 : (for PPC version where parameter area is pre-allocated) 1419 : - added ccall_maxargspace to machspec (to implement the above) 1420 : - made "make" commend in CM's "make" tool configurable 1421 : - added option (default: on) for passing the name of the SML/NJ's "bin" 1422 : directory to "make"; the call looks like this: 1423 : 1424 : make SMLNJ_BINDIR= 1425 : 1426 : This can be used by the Makefile to, e.g., pick the "right" version 1427 : of ml-nlffigen. 1428 : - minor code tweaks 1429 : 1430 : ---------------------------------------------------------------------- 1431 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1432 : mblume 1532 Date: 2004/07/12 22:50:00 CDT 1433 : Tag: blume-110_46_1-macosx-nlffi 1434 : Description: 1435 : 1436 : NLFFI under Mac OS X now working (sort of). This is largely untested, 1437 : though. 1438 : 1439 : Note: 1. You have to make a new, clean build of the runtime system. 1440 : 2. There are new BOOTFILES, you have to use them! 1441 : (Doing the bootstrap process yourself would be *very* painful! 1442 : If you absolutely have to do it, build the system under 1443 : a different architecture and then cross-compile.) 1444 : 1445 : Version bumped to 110.46.1 to account for runtime data format changes. 1446 : 1447 : ---------------------------------------------------------------------- 1448 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1449 : mblume 1515 Date: 2004/06/18 14:30:00 CDT 1450 : Tag: blume-20040618-unix 1451 : Description: 1452 : 1453 : Changed the implementation of structure Unix so that the same stream 1454 : is returned every time one of the {text,bin}{In,Out}streamOf functions 1455 : is invoked on the same proc. This is not what the spec currently 1456 : says -- although IMO it arguably should. (See discussion below.) 1457 : 1458 : ---------------------------------------------------------------------- 1459 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1460 : mblume 1507 Date: 2004/06/17 18:15:00 CDT 1461 : Tag: Release_110_46 1462 : Description: 1463 : 1464 : New working version (110.46). NEW BOOTFILES! 1465 : 1466 : ---------------------------------------------------------------------- 1467 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1468 : mblume 1506 Date: 2004/06/17 17:20:00 CDT 1469 : Tag: blume-20040617-timer-unix 1470 : Description: 1471 : 1472 : Changed the interface of structures Timer and Unix to match the most 1473 : recent Basis spec. 1474 : 1475 : In the case of Unix there still seems to be an open/weird issue: 1476 : 1477 : The {text,bin}{In,Out}streamOf functions are supposed to create 1478 : fresh streams whenever they are called -- as opposed to have them 1479 : return the same stream every time. This design is supposed to 1480 : prevent space leaks caused by proc values hanging on to streams. 1481 : 1482 : The reap function, on the other hand, is supposed to close the 1483 : streams. This cannot be done without having a handle on the 1484 : stream in proc after all... 1485 : 1486 : I took the liberty to implement the following stopgap solution: 1487 : 1488 : The proc value hangs on to the most recently created stream(s). 1489 : Reap closes those. If either or both of the two streams hadn't 1490 : been created at all yet, then reap will close the corresponding 1491 : file descriptors directly. 1492 : 1493 : PS: I don't understand the original space leak argument anymore. If 1494 : a proc hangs on to the imperative stream, then I/O operations on those 1495 : will advance the state of the cached stream and avoid the space leak. 1496 : 1497 : ---------------------------------------------------------------------- 1498 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1499 : mblume 1500 Date: 2004/05/28 16:45:00 CDT 1500 : Tag: blume-20040528-basis 1501 : Description: 1502 : 1503 : Added signature PACK_REAL and exported functor PrimIO. 1504 : 1505 : ---------------------------------------------------------------------- 1506 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1507 : mblume 1498 Date: 2004/05/25 16:00:00 CDT 1508 : Tag: blume-20040525-group-owner 1509 : Description: 1510 : 1511 : CM now ignores (but still accepts) the "owner" information in group 1512 : descriptions. The owner of a group is its next enclosing 1513 : library. Each group must have a unique owner. (There is a virtual 1514 : mblume 1505 "toplevel" library that owns groups which are not nested within a real 1515 : mblume 1498 library.) Previously, each group had to explicitly declare its owner, 1516 : and CM would check that such a declaration is correct. The new scheme 1517 : is to have CM check that for each group there is precisely one owning 1518 : library. 1519 : 1520 : The advantage of the new scheme is that the programmer no longer needs 1521 : to maintain the somewhat annoying owner information. The downside is 1522 : that CM cannot enforce the ownership rule across multiple runs of 1523 : CM.make. Fortunately, enclosing the same group in two different 1524 : libraries A and B which are not part of the same program does not 1525 : cause real problems. 1526 : 1527 : ---------------------------------------------------------------------- 1528 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1529 : mblume 1496 Date: 2004/05/20 16:00:00 CDT 1530 : Tag: blume-20040520-win32 1531 : Description: 1532 : 1533 : Made the win32 version work again. (Strangely, a misplaced comma had 1534 : slipped into win32-process.c which prevented the runtime from being 1535 : compiled correctly.) 1536 : 1537 : Also, included a minor addition to ml-build.bat analogous to what was 1538 : done in blume-20040519-ml-build. 1539 : 1540 : ---------------------------------------------------------------------- 1541 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1542 : mblume 1494 Date: 2004/05/19 22:10:00 CDT 1543 : Tag: blume-20040519-ml-build 1544 : Description: 1545 : 1546 : Arranged for ml-build to clean up after itself a little bit better. 1547 : The script generates a temporary SML source file and compiles it using 1548 : CM, so CM generates metadata (GUID, SKEL, objectfile) for it. It now 1549 : gets rid of those at the end, so they don't accumulate under .cm. 1550 : 1551 : This required a minor change to install.sh because the name of the 1552 : metadata directory (default: .cm) is actually configurable at 1553 : installation time. 1554 : 1555 : ---------------------------------------------------------------------- 1556 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1557 : mblume 1491 Date: 2004/05/18 15:50:00 CDT 1558 : Tag: blume-20040518-mkreader 1559 : Description: 1560 : 1561 : Added Posix.IO.mk{Bin,Text}{Reader,Writer} by lifting their respective 1562 : implementations from internal modules PosixBinPrimIO and PosixTextPrimIO. 1563 : 1564 : ---------------------------------------------------------------------- 1565 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1566 : mblume 1489 Date: 2004/05/11 14:35:00 CDT 1567 : Tag: blume-20040511-win32sock 1568 : Description: 1569 : 1570 : Added previously missing support for many socket-related functions 1571 : under win32. Thanks to David Hansel 1572 : for the voluminous patch! 1573 : 1574 : (I have not tested this patch under win32 yet.) 1575 : 1576 : mblume 1490 Here is David's e-mail: 1577 : 1578 : Hi, 1579 : 1580 : Attached to this email you find a diff against sml/nj 110.45 1581 : that will enable socket support under Windows. 1582 : 1583 : To apply the patch (using unix or cygwin) 1584 : 1) gunzip runtime.diff.gz 1585 : 2) "cd" into "src/runtime" in the source tree of a fresh 1586 : 110.45 installation. 1587 : 3) patch -p 1 < [your/path/to]runtime.diff 1588 : 1589 : The code compiles fine but has NOT yet been extensively tested. 1590 : I only ran a few tests for basic socket client functionality 1591 : (which worked fine). Especially the functions that use ioctl 1592 : are not tested at all and might not work (see below). 1593 : 1594 : I implemented this since we want to move to a newer version of sml/nj 1595 : but need socket support in order to use it. This is the first time I 1596 : even had a look at the sml/nj source, so please review my changes 1597 : before making this part of the distribution! Here are a few issues 1598 : that I think might be better for someone to solve who is more 1599 : familiar with the sml/nj source (and socket programming): 1600 : 1601 : - getnetbyaddr.c and getnetbyname.c will raise a "not implemented" 1602 : exception since I could not figure out what the windows equivalent 1603 : of these functions is 1604 : 1605 : - In sockets-osdep.h there are a some #include statements that are 1606 : only used in a few files that include sockets-osdep.h 1607 : 1608 : - In smlnj-sock-lib.c, function init_fn() calls WSAStartup() but 1609 : does not process its return value since I don't know how to 1610 : report an error upwards. 1611 : 1612 : - It would probably be good to have a call to WSACleanup() when 1613 : the library is unloaded (if there is such a possibility). 1614 : Otherwise I think Windows will take care of this automatically 1615 : when the process finishes. 1616 : 1617 : - I used ioctlsocket() as a replacement for ioctl() but I have 1618 : no idea if that is actually the proper replacement on Windows. 1619 : 1620 : - All these issues are marked in the code by "FIXME" comments. 1621 : 1622 : We use sml/nj extensively in our products and are quite happy 1623 : with it. I hope this contribution will help you. 1624 : 1625 : Keep up the good work! 1626 : 1627 : David 1628 : 1629 : mblume 1489 ---------------------------------------------------------------------- 1630 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1631 : mblume 1488 Date: 2004/05/11 14:20:00 CDT 1632 : Tag: blume-20040511-installml 1633 : Description: 1634 : 1635 : Fixed two bugs in installml script. (Thanks to Vesa A. Norrman for 1636 : the patch.) 1637 : 1638 : ---------------------------------------------------------------------- 1639 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1640 : mblume 1487 Date: 2004/05/11 14:05:00 CDT 1641 : Tag: blume-20040511-nlffi-netbsd 1642 : Description: 1643 : 1644 : Added support for nlffi under netbsd. (Thanks to Vesa A. Norrman for 1645 : the patch.) 1646 : 1647 : ---------------------------------------------------------------------- 1648 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1649 : mblume 1486 Date: 2004/05/11 12:05:00 CDT 1650 : Tag: blume-20040511-exports 1651 : Description: 1652 : 1653 : As per request by Adam Chlipala , extended various 1654 : export lists in compiler-related .cm-files. 1655 : 1656 : ---------------------------------------------------------------------- 1657 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1658 : mblume 1485 Date: 2004/05/11 11:35:00 CDT 1659 : Tag: blume-20040511-allsource 1660 : Description: 1661 : 1662 : The installer now honors the "src-smlnj" target again, although its meaning 1663 : has changed from "all sources required for the compiler" to "all sources 1664 : the installer knows about". In other words, if you enable "src-smlnj" 1665 : in the "targets" file, then the installer will pull in sources for 1666 : everything. (Notice that this refers to source code only. Compiled 1667 : code is still only installed for modules that were requested explicitly 1668 : or which are required for other modules that were requested explicitly.) 1669 : 1670 : ---------------------------------------------------------------------- 1671 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1672 : mblume 1482 Date: 2004/04/23 17:40:00 CDT 1673 : Tag: blume-20040423-ieee-scan 1674 : Description: 1675 : 1676 : Fixed IEEEReal.scan (and .fromString) so that if there is an overflow 1677 : in the exponent calculation we get INF or ZERO (depending on the mantissa 1678 : and the sign of the exponent). 1679 : 1680 : ---------------------------------------------------------------------- 1681 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1682 : mblume 1480 Date: 2004/04/23 10:40:00 CDT 1683 : Tag: blume-20040423-ml-build 1684 : Description: 1685 : 1686 : The ml-build script now terminates with a non-0 status when something 1687 : goes wrong. 1688 : 1689 : ---------------------------------------------------------------------- 1690 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1691 : mblume 1479 Date: 2004/04/22 16:35:00 CDT 1692 : Tag: blume-20040422-Option 1693 : Description: 1694 : 1695 : Made exception Option to be the same as exception Option.Option 1696 : (as it should be). 1697 : 1698 : ---------------------------------------------------------------------- 1699 : allenleung 1468 Name: Allen Leung (leunga (at) reservoir (dot) com) 1700 : Date: 2004/03/19 14:40:00 EST 1701 : Tag: leunga-20040319-cygwin-nlffi 1702 : Description: 1703 : 1704 : Fixed the runtime so that ml-nlffi-lib runs on the cygwin version 1705 : of SML/NJ. The problem is that 1706 : 1707 : lib = dlopen(NULL, ...) 1708 : f = dlsym(lib, "malloc"); 1709 : 1710 : does not work on Windows unless we explicitly export symbols 1711 : such as 'malloc' during linking. We fixed this by explicitly 1712 : exporting the required symbols with the magic gcc incantation: 1713 : 1714 : -Wl,--export-all cygwin.def 1715 : 1716 : where cygwin.def is a file containing all the symbols that 1717 : we wish to export. 1718 : 1719 : I suspect this is a Windows problem and we'll have to 1720 : do the same (somehow with windows compilers) when 1721 : we build the native win32 version with the system 1722 : calls LoadLibrary/GetProcAddress. 1723 : 1724 : ---------------------------------------------------------------------- 1725 : mblume 1384 Name: Matthias Blume (blume (at) tti - c (dot) org) 1726 : mblume 1465 Date: 2004/03/04 16:35:00 CST 1727 : Tag: blume-20040304-intinf-fmt 1728 : Description: 1729 : 1730 : Fixed problem with IntInf.fmt (sign would show up on the right instead 1731 : of on the left for BIN, OCT, and HEX). 1732 : 1733 : ---------------------------------------------------------------------- 1734 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1735 : mblume 1464 Date: 2004/03/04 11:25:00 CST 1736 : Tag: blume-20040304-symlinks 1737 : Description: 1738 : 1739 : Fixed problem with installer script (unix only) where bin/ml-yacc and 1740 : friends pointed (via symlinks) to absolute locations instead of just 1741 : .run-sml. This was reported by Vesa A Norrman. 1742 : 1743 : ---------------------------------------------------------------------- 1744 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1745 : mblume 1455 Date: 2004/02/13 14:50:00 CST 1746 : Tag: Release_110_45 1747 : Description: 1748 : 1749 : New working version (110.45). New bootfiles. 1750 : 1751 : ---------------------------------------------------------------------- 1752 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1753 : mblume 1448 Date: 2004/01/26 15:15:15 CST 1754 : Tag: blume-20040126-toplevel 1755 : Description: 1756 : 1757 : Improved handling of exceptions at the interactive toplevel. 1758 : 1759 : ---------------------------------------------------------------------- 1760 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1761 : Date: 2004/01/26 11:25:00 1762 : mblume 1446 Tag: blume-20040126-app 1763 : Description: 1764 : 1765 : Type of top-level "app" corrected. 1766 : mblume 1447 Added code for setting vp_limitPtrMask to Win32-specific runtime. 1767 : mblume 1446 1768 : ---------------------------------------------------------------------- 1769 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1770 : mblume 1427 Date: 2003/11/18 17:10 CST 1771 : Tag: blume-20031118-basis-fiddle 1772 : Description: 1773 : 1774 : - changed Timer interface to what might become the spec 1775 : - POSIX_FLAGS -> BIT_FLAGS according to spec 1776 : - some other minor discrepancies wrt. spec eliminated 1777 : 1778 : ---------------------------------------------------------------------- 1779 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1780 : mblume 1414 Date: 2003/11/06 12:00:00 CST 1781 : Tag: Release_110_44 1782 : Description: 1783 : 1784 : New working version (110.44). New bootfiles. 1785 : 1786 : ---------------------------------------------------------------------- 1787 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1788 : mblume 1411 Date: 2003/11/04 11:50:00 CST 1789 : Tag: blume-20031104-move-libraries 1790 : Description: 1791 : 1792 : Eliminated the "dont_move_libraries" directive in config/targets. 1793 : (The mechanism was broken and could not be fixed easily. Moreover, 1794 : there does not seem to be any reason not to move all libraries into 1795 : lib during installation. I originally implemented this directive as a 1796 : backward-compatibility feature when I first introduced the new CM. 1797 : Now that things have been stable for a long time and going back to the 1798 : old CM is not an option, there is no reason to keep it around.) 1799 : 1800 : ---------------------------------------------------------------------- 1801 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1802 : mblume 1409 Date: 2003/11/03 16:00:00 CST 1803 : Tag: blume-20031103-installdir 1804 : Description: 1805 : 1806 : Made installer honor INSTALLDIR variable again. (Thanks to Chris 1807 : Richards for pointing out the problem and providing the solution.) 1808 : 1809 : ---------------------------------------------------------------------- 1810 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1811 : mblume 1400 Date: 2003/10/01 17:05:00 CDT 1812 : Tag: blume-20031001-lal-mlrisc 1813 : Description: 1814 : 1815 : MLRISC bug fix from Lal. 1816 : 1817 : ---------------------------------------------------------------------- 1818 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1819 : mblume 1399 Date: 2003/09/30 16:10:00 CDT 1820 : Tag: blume-20030930-primio-bat 1821 : mblume 1398 Description: 1822 : 1823 : 1. Added openVector, nullRd, and nullWr to PRIM_IO. 1824 : 2. Improved .bat files (for Win32 port) to make things work under Win95. 1825 : (thanks to Aaron S. Hawley for this one) 1826 : 1827 : ---------------------------------------------------------------------- 1828 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1829 : mblume 1395 Date: 2003/09/26 16:05:00 CDT 1830 : Tag: blume-20030926-wrappriv 1831 : Description: 1832 : 1833 : Added missing wrapper for privilege "primitive" in $smlnj/viscomp/core.cm. 1834 : 1835 : ---------------------------------------------------------------------- 1836 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1837 : mblume 1394 Date: 2003/09/26 15:00:00 CDT 1838 : Tag: blume-20030926-110_43_3 1839 : Description: 1840 : 1841 : - additional cleanup 1842 : - version number bump, NEW BOOTFILES 1843 : 1844 : ---------------------------------------------------------------------- 1845 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1846 : mblume 1393 Date: 2003/09/26 12:00:00 CDT 1847 : Tag: blume-20030926-ppautoload 1848 : Description: 1849 : 1850 : I modified the read-eval-print loop so that the autoloader gets 1851 : invoked whenever the prettyprinter tries to look up a symbol that 1852 : is not currently defined in the toplevel environment but which 1853 : appears in CM's autoload registry. As a result, we see far fewer of 1854 : those ?.Foo.Bar.xxx names in the prettyprinter's output. 1855 : 1856 : In addition to this I tried to clean up some pieces of the Basis 1857 : implementation (e.g., Socket, Word8Array) in order to prevent other 1858 : instances of these ?.Foo.Bar.xxx names from being printed. 1859 : 1860 : The mechanism that picks names for types still needs some work, though. 1861 : (Right now it seems that if there is a type A.t which is defined to 1862 : mblume 1394 be B.u, but B is unavailable at toplevel, then A.t gets printed as 1863 : "?.B.u" although the perhaps more sensible solution would be to use 1864 : mblume 1393 "A.t" in this case. In other words, the prettyprinter should follow 1865 : a chain of DEFtycs not farther than there are corresponding toplevel 1866 : names in the current environment.) 1867 : 1868 : ---------------------------------------------------------------------- 1869 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1870 : mblume 1391 Date: 2003/09/24 16:31:00 CDT 1871 : Tag: blume-20030924-installer 1872 : Description: 1873 : 1874 : Another installer tweak: All the ML code for the installer is now 1875 : compiled during CMB.make and put into a little library called 1876 :$smlnj/installer.cm. The installation then simply invokes 1877 : 1878 : sml -m $smlnj/installer.cm 1879 : 1880 : and everything happens automagically. 1881 : 1882 : Win32: ML code senses value of environment variable SMLNJ_HOME. 1883 : Unix: ML code senses values of environment variables ROOT, CONFIGDIR, 1884 : and BINDIR. 1885 : 1886 : The new scheme guarantees that the ML code responsible for the installation 1887 : is in sync with the APIs of the main system. Also, the installer is 1888 : somewhat faster because the installer script is precompiled. 1889 : 1890 : ---------------------------------------------------------------------- 1891 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1892 : mblume 1390 Date: 2003/09/24 15:35:00 CDT 1893 : Tag: blume-20030924-synsock 1894 : Description: 1895 : 1896 : Added a signature SYNCHRONOUS_SOCKET to basis.cm. This is like SOCKET 1897 : but excludes all non-blocking operations. Defined SOCKET (in Basis) 1898 : and CML_SOCKET in terms of SYNCHRONOUS_SOCKET. Removed superfluous 1899 : implementations of non-blocking operations from CML's Socket 1900 : structure. 1901 : 1902 : ---------------------------------------------------------------------- 1903 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1904 : mblume 1389 Date: 2003/09/24 15:10:05 CDT 1905 : Tag: blume-20030924-sockets 1906 : Description: 1907 : 1908 : 1. Fixed SOCKET API and implementation to match Basis spec. 1909 : This required changing the internal representation of sockets to one 1910 : that remembers (for each socket file descriptor) whether it is currently 1911 : blocking or non-blocking. This state is maintained lazily (i.e., a system 1912 : call is made only if the state actually needs to change). 1913 : 1914 : 2. OS-specific details of sockets were moved into separate files, thus 1915 : making it possible to unify the bulk of the socket implementations 1916 : between Unix and Win32. 1917 : 1918 : 3. CML's socket API changed accordingly. 1919 : (Note that we need to remove non-blocking functions from this API 1920 : since they are redundant in the case of CML!) 1921 : 1922 : 4. CML's socket implementation now makes use of non-blocking functions 1923 : provided by Basis, thus removing all OS-dependent code from this part 1924 : of CML. 1925 : 1926 : 5. Changed Real64.precision from 52 to 53. Minor cleanup in Real64 code. 1927 : 1928 : ---------------------------------------------------------------------- 1929 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1930 : mblume 1387 Date: 2003/09/22 12:10:00 CDT 1931 : mblume 1388 Tag: blume-20030922-110_43_2 1932 : mblume 1387 Description: 1933 : 1934 : Made a new interim version and bootfiles for developer's bootstrapping 1935 : convenience. 1936 : 1937 : 110.43.2 -- NEW BOOTFILES 1938 : 1939 : ---------------------------------------------------------------------- 1940 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1941 : mblume 1385 Date: 2003/09/19 15:55:00 CDT 1942 : Tag: blume-20030919-cmdir 1943 : Description: 1944 : 1945 : 1. new-install.sh -> install.sh 1946 : 2. changed default CM "metadata" directory name to ".cm" (instead of "CM") 1947 : 3. tweaked installer so that another name instead of .cm can be chosen 1948 : at install time (by setting the CM_DIR_ARC environment variable 1949 : during installation); once installation is complete, the name is 1950 : fixed 1951 : 1952 : ---------------------------------------------------------------------- 1953 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1954 : mblume 1384 Date: 2003/09/18 16:00:00 CDT 1955 : Tag: blume-20030918-110_43_1 1956 : Description: 1957 : 1958 : Made a new interim version and bootfiles for developer's bootstrapping 1959 : convenience. 1960 : 1961 : 110.43.1 -- NEW BOOTFILES 1962 : 1963 : ---------------------------------------------------------------------- 1964 : Name: Matthias Blume (blume (at) tti - c (dot) org) 1965 : mblume 1383 Date: 2003/09/18 15:20:00 CDT 1966 : Tag: blume-20030918-misc 1967 : Description: 1968 : 1969 : 1. Exported fractionsPerSecond etc. from TimeImp (but not from Time as 1970 : this seems to be controversial at the moment) and used those in 1971 : Posix.ProcEnv.times. 1972 : 1973 : 2. Added Time.{from,to}Nanoseconds to Time. 1974 : 1975 : 3. Improved Real.{from,to}LargeInt by avoiding needless calculations. 1976 : For example, fromLargeInt never needs to look at more than 3 "big 1977 : digits" to get its 53 bits of precision. 1978 : 1979 : ---------------------------------------------------------------------- 1980 : mblume 1384 Name: Matthias Blume (blume (at) tti - c (dot) org) 1981 : mblume 1381 Date: 2003/09/17 16:30:00 CDT 1982 : Tag: blume-20030917-real32-slices 1983 : Description: 1984 : 1985 : Added an entry to the primitive environment 1986 : (compiler/Semant/statenv/prim.sml) for int32->real64 conversion and 1987 : added code to compiler/CodeGen/main/mlriscGen.sml to implement it. 1988 : 1989 : Removed some of the "magic" constants in real64.sml and replaced them 1990 : with code that generates these values from their corresponding 1991 : integer counterparts. 1992 : 1993 : Made all(?) the slice-related changes to the Basis and made everything 1994 : compile again... 1995 : 1996 : ---------------------------------------------------------------------- 1997 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 1998 : mblume 1375 Date: 2003/09/15 17:45:00 CDT 1999 : Tag: blume-20030915-rbase 2000 : Description: 2001 : 2002 : Fixed bug in Real.fromLargeInt. 2003 : 2004 : ---------------------------------------------------------------------- 2005 : Name: Matthias Blume (blume (at) tti - c (dot) org) 2006 : mblume 1369 Date: 2003/09/13 18:11:00 CDT 2007 : Tag: blume-20030913-libinstall 2008 : Description: 2009 : 2010 : Minor bugfix in config/libinstall (set anchor with path to 2011 : standalone tool after installing it, otherwise libraries that 2012 : need ml-lex or ml-yacc won't compile the first time the installer 2013 : runs). 2014 : 2015 : ---------------------------------------------------------------------- 2016 : Name: Matthias Blume (blume (at) tti - c (dot) org) 2017 : mblume 1368 Date: 2003/09/12 11:45:00 CDT 2018 : Tag: blume-20030912-various 2019 : Description: 2020 : 2021 : - fixed bug in Real.toLargeInt 2022 : - fixed bug in Posix.ProcEnv.times 2023 : - changed inputLine functions to return an option 2024 : - minor installer improvements / bugfixes 2025 : - changed default @SMLalloc parameter for x86/celeron to 64k 2026 : 2027 : ---------------------------------------------------------------------- 2028 : Name: Matthias Blume (blume (at) tti - c (dot) org) 2029 : mblume 1356 Date: 2003/09/09 22:00:00 CDT 2030 : Tag: Release_110_43 2031 : Description: 2032 : 2033 : New working release 110.43. New bootfiles. 2034 : 2035 : ---------------------------------------------------------------------- 2036 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2037 : mblume 1354 Date: 2003/09/09 19:20:00 CDT 2038 : Tag: blume-20030909-installer 2039 : Description: 2040 : 2041 : Rewrote large parts of config/install.sh in SML (config/libinstall.sml). 2042 : Modified config/install.bat to take advantage of it. Also modified 2043 : config/install.sh (and called it config/new-install.sh) to take advantage 2044 : of it on Unix systems. (The SML code is (supposed to be) platform- 2045 : independent.) 2046 : 2047 : The installer can now install everything under Win32 2048 : as well as under *nix as long as it compiles. 2049 : 2050 : Other changes: 2051 : 2052 : - made CML compile again under Win32 2053 : - made eXene compile under Win32 (by providing a fake structure UnixSock 2054 : and by using OS.Process.getEnv instead of Posix.ProcEnv.getenv) 2055 : - fixed a bug in nowhere: it assumed that type OS.Process.status is the 2056 : same as type int; under Win32 it isn't 2057 : - fixed some slice-related problems in the win32-specific parts of CML 2058 : - added a functor argument "sameVol" to os-path-fn.sml in the Basis 2059 : (under Win32, the volume name is case-insensitive, and the 2060 : OS.Path code compares volume names for equality) 2061 : 2062 : ---------------------------------------------------------------------- 2063 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2064 : mblume 1353 Date: 2003/09/08 11:55:00 CDT 2065 : Tag: blume-20030908-fullpath 2066 : Description: 2067 : 2068 : Made Win32 version of OS.FileSys.fullPath return current directory 2069 : when given an empty string. This is what the spec says, and incidentally, 2070 : CM depends on it. (CM otherwise goes into an infinite loop in certain 2071 : cases when presented with the name of a non-existing .cm file.) 2072 : 2073 : ---------------------------------------------------------------------- 2074 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2075 : mblume 1350 Date: 2003/09/04 16:30:00 CDT 2076 : mblume 1352 Tag: blume-20030905-slices-etc 2077 : mblume 1350 Description: 2078 : 2079 : 1. Changed interface to vectors and arrays in Basis to match 2080 : (draft) Basis spec. 2081 : 2. Added signatures and implementations of slices according to 2082 : Basis spec. 2083 : 3. Edited source code throughout the system to make it compile again 2084 : under 1. and 2. (In some cases code had to be added to have it 2085 : match the new signatures.) 2086 : 4. MLRISC should be backward-compatible: the copies of the originals 2087 : of files that needed to change under 3. were retained, the .cm files 2088 : check the compiler version number and use old versions when 2089 : appropriate. 2090 : 5. Changed type of OS.FileSys.readDir and Posix.FileSys.readdir to 2091 : dirstream -> string option (in accordance with Basis spec). 2092 : 6. When generating code that counts lines, ml-lex used function 2093 : CharVector.foldli, taking advantage of its old interface. 2094 : This has been replaced with the corresponding code from 2095 : CharVectorSlice. (html-lex must be re-lexed!) 2096 : 7. BitArray in smlnj-lib/Util has been extended/modified to match the 2097 : new MONO_ARRAY signature. (Do we need BitArraySlice?) 2098 : 8. Removed temporary additions (fromInternal, toInternal) from the 2099 : (now obsolete) IntInf in smlnj-lib/Util. 2100 : 9. Cleaned up structure Byte. 2101 : 10. Added localOffset, scan, and fromString to Date (according to spec). 2102 : Cleaned/corrected implementation of Date. 2103 : (Still need to check for correctness; implement better canonicalizeDate.) 2104 : 11. Added "scan" to signature IEEE_REAL. 2105 : 12. Some improvements to IntInf [in particular: efficiency-hack for 2106 : mod and rem when second operand is 2 (for parity checks).] 2107 : 13. Changed representation of type Time.time, using a single IntInf.int 2108 : value counting microseconds. This considerably simplified the 2109 : implementation of structure Time. We now support negative time 2110 : values; scan and fromString handle signs. 2111 : 14. Functor PrimIO now takes two additional arguments (VectorSlice and 2112 : ArraySlice). 2113 : 2114 : ---------------------------------------------------------------------- 2115 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2116 : mblume 1347 Date: 2003/08/28 17:00:00 CDT 2117 : Tag: blume-20030828-intinf 2118 : Description: 2119 : 2120 : This is a major update which comes with a version number bump 2121 : (110.42.99 -- yes, we are really close to 110.43 :-), NEW BOOTFILES, 2122 : and an implementation of IntInf in the Basis. 2123 : 2124 : There are a fairly large number of related changes and updates throughout 2125 : the system: 2126 : 2127 : Basis: 2128 : - Implemented IntInf. 2129 : - Made LargeInt a projection of IntInf (by filtering through INTEGER). 2130 : mblume 1348 - Added some missing Real64 operations, most notably Real.toLargeInt. 2131 : mblume 1347 - Added FixedInt as a synonym for Int32. 2132 : 2133 : compiler: 2134 : * Added support for a built-in intinf type. 2135 : - literals 2136 : - pattern matching 2137 : - conversion shortcuts (Int32.fromLarge o Int.toLarge etc.) 2138 : - overloading on literals and operations 2139 : 2140 : This required adding a primitive type intinf, some additional 2141 : primops, and implementations for several non-trivial intinf 2142 : operations in Core. (The intinf type is completely abstract 2143 : to the compiler; all operations get delegated back to the Core.) 2144 : 2145 : * Intinf equality is handled by polyequal. However, the compiler 2146 : does not print its usual warning in this case (since polyequal 2147 : is the right thing to do there). 2148 : 2149 : * Improved the organization of structure InlineT. 2150 : 2151 : * A word about conversion primops: 2152 : If conversions involving intinf do not cancel out during 2153 : mblume 1348 CPS contract, then the compiler must insert calls to Core functions. 2154 : mblume 1347 Since all core access must be resolved already during the FLINT 2155 : translate phase, it would be too late a the time of CPS contract 2156 : mblume 1348 to add new Core calls. For this reason, conversion primops 2157 : mblume 1347 for intinf carry two arguments: 1. the numeric argument that 2158 : they are supposed to convert, and 2. the Core function that 2159 : can help with this conversion if necessary. If CPS contract 2160 : mblume 1348 eliminates a primop, then the associated Core function becomes 2161 : dead and goes away. Intinf conversion primops that do not get 2162 : eliminated by CPS contract get rewritten into calls of their 2163 : core functions by a separate, new phase. 2164 : mblume 1347 2165 : interactive system: 2166 : - Control.Print.intinfDepth controls max length of intinf constants 2167 : being printed. (Analogous to Control.Print.stringDepth.) 2168 : - Cleanup in printutil and pputil: got rid of unused stuff and 2169 : duplicates; replaced some of the code with code that makes better 2170 : use of library functionality. 2171 : 2172 : CM: 2173 : Bugfix: parse-errors in init group (system/smlnj/init/init.cmi) 2174 : are no longer silent. 2175 : 2176 : CKIT: 2177 : Fixed mismatched uses of Int32 and LargeInt. I always decided 2178 : in favor of LargeInt -- which is now the same as IntInf. 2179 : CKIT-knowledgable people should check whether this is what's 2180 : intended and otherwise change things back to using Int32 or 2181 : FixedInt. 2182 : 2183 : Throughout the code: 2184 : mblume 1348 Started using IntInf.int literals and built-in operations 2185 : mblume 1347 (e.g., comparison with 0) where this seems appropriate. 2186 : 2187 : 2188 : ---------------------------------------------------------------------- 2189 : macqueen 1343 Name: Dave MacQueen (dbm@cs.uchicago.edu) 2190 : Date: 2003/08/13 11:36:00 CDT 2191 : Tag: dbm-20030813-mcz-merge1 2192 : Description: 2193 : 2194 : Merging changes from the mcz-branch development branch into trunk. 2195 : These changes involve replacement of the emulated old prettyprinter 2196 : interface with direct use of the SML/NJ Lib PP library, and fixing 2197 : of a couple of bugs (895, 1186) relating to error messages. A new 2198 : prettyprinter for ast datatypes (Elaborator/print/ppast.{sig,sml}) 2199 : has been added. 2200 : 2201 : ---------------------------------------------------------------------- 2202 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2203 : mblume 1342 Date: 2003/08/11 15:45:00 CDT 2204 : Tag: blume-20030811-windows 2205 : Description: 2206 : 2207 : Version number bumped to 110.42.9. NEW BOOTFILES!!! 2208 : 2209 : http://smlnj.cs.uchicago.edu/dist/working/110.42.9/ 2210 : 2211 : This patch restores SML/NJ's ability to run under win32. There are a 2212 : number of changes, including fixes for several bugs that had gone 2213 : unnoticed until now: 2214 : 2215 : - uname "CYGWIN_NT*" is recognized as win32 (This is relevant only when 2216 : trying to run the win32 version from within cygwin.) 2217 : 2218 : - There are a number of simple .bat scripts that substitute for their 2219 : corresponding Unix shell-scripts. (See below.) 2220 : 2221 : - The internals of ml-build have been modified slightly. The main 2222 : difference is that instead of calling ".link-sml" (or link-sml.bat) 2223 : using OS.Process.system, the ML process delegates this task back 2224 : to the script. Otherwise problems arise in mixed environments such 2225 : as Cygwin where scripts look and work like Unix scripts, but 2226 : where OS.Process.system cannot run them. 2227 : 2228 : - In CM, the srcpath pickler used native pathname syntax -- which 2229 : is incorrect in the case of cross-compilation. The new pickle format 2230 : is independent of platform-specific naming conventions. 2231 : 2232 : - Path configuration files (such as lib/pathconfig) can now choose 2233 : between native and standard syntax. Placing a line of the form 2234 : 2235 : standard! 2236 : 2237 : into the file causes all subsequent paths to be interpreted using 2238 : CM standard pathname syntax (= Unix conventions); a line 2239 : 2240 : native! 2241 : 2242 : switches back to native style. This was needed so that 2243 : path config files can be written portably, see src/system/pathconfig. 2244 : 2245 : - Runtime system: 2246 : 2247 : - win32-filesys.c: get_file_time and set_file_time now 2248 : access modification time, not creation time. 2249 : 2250 : - I/O code made aware of new array representation. 2251 : 2252 : - Bug fixes in X86.prim.masm. 2253 : 2254 : - src/system/makeml made aware of win32. (For use under cygwin 2255 : and other Unix-environments for windows.) 2256 : 2257 : - In Basis, fixed off-by-one error in win32-io.sml (function vecF) 2258 : which caused BinIO.inputAll to fail consistently. 2259 : 2260 : .bat scripts: 2261 : 2262 : Windows .bat scripts assume that SMLNJ_HOME is defined. 2263 : 2264 : - sml.bat, ml-yacc.bat, ml-lex.bat: Driver scripts for standalone 2265 : applications (sml, ml-yacc, ml-lex). 2266 : - ml-build.bat: analogous to ml-build. 2267 : - config\install.bat: Analogous to config/install.sh. This requires 2268 : that SMLNJ_HOME is set and that Microsoft Visual C is ready to use. 2269 : (nmake etc. must be on the path, and vcvars32 must have been run.) 2270 : Moreover, sources for ml-lex and ml-yacc need to exist under src, 2271 : and the bootfile hierarchy must have been unpacked under 2272 : sml.boot.x86-win32. 2273 : The script is very primitive and does a poor job at error checking. 2274 : It only installs the base system, ml-lex, and ml-yacc. No other 2275 : libraries are being installed (i.e., you get only those that 2276 : are part of the compiler.) 2277 : - link-sml.bat: analogous to .link-sml, but not currently used 2278 : 2279 : Unrelated bug fixes: 2280 : 2281 : - ml-nlffigen now exports structures ST_* corresponding to incomplete 2282 : types. 2283 : - Added getDevice to PP/src/pp-debug-fn.sml. (Would not compile 2284 : otherwise.) 2285 : 2286 : ---------------------------------------------------------------------- 2287 : macqueen 1337 Name: Dave MacQueen (macqueen@cs.uchicago.edu) 2288 : Date: 2003/06/17 2289 : Tag: macqueen-20030617-bug895 2290 : Description: 2291 : 2292 : Modified compiler/Elaborator/print/pptype.sml to fix bug 895. 2293 : Tag will be used for new development branch (mcz-branch) for 2294 : use by MacQueen, (Lucasz) Zairek, and (George) Cao at uchicago. 2295 : 2296 : ---------------------------------------------------------------------- 2297 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2298 : mblume 1335 Date: 2003/05/27 16:55:00 CDT 2299 : Tag: blume-20030527-polyeq 2300 : Description: 2301 : 2302 : Tried to eliminated most cases of polymorphic equality. 2303 : 2304 : ---------------------------------------------------------------------- 2305 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2306 : mblume 1334 Date: 2003/05/21 17:45:00 CDT 2307 : Tag: blume-20030517-complete 2308 : Description: 2309 : 2310 : Two changes: 2311 : 2312 : 1. Added a flag for controlling whether non-exhaustive bindings will 2313 : be treated as errors (default is false). 2314 : 2. Cleaned up the *entire* source tree so that CMB.make goes through 2315 : without a single non-exhaustive match- or bind warning. 2316 : 2317 : ---------------------------------------------------------------------- 2318 : mblume 1368 Name: Matthias Blume (blume (at) tti - c (dot) org) 2319 : mblume 1332 Date: 2003/05/17 10:20:00 CDT 2320 : Tag: blume-20030517-absyn 2321 : Description: 2322 : 2323 : 1. Added cases for IF, WHILE, ANDALSO, and ORELSE to Absyn. 2324 : 2325 : This mainly affects the quality of error messages. However, some 2326 : of the code is now more straightforward than before. (Treatment of 2327 : the above four constructs in translate.sml is much simpler than 2328 : the "macro-expansion" that was going on before. Plus, the mach- 2329 : compiler no longer gets invoked just to be able to compile an 2330 : if-expression.) 2331 : 2332 : 2. The ErrorMsg.Error exception is now caught and absorbed by the 2333 : interactive loop. 2334 : 2335 : ---------------------------------------------------------------------- 2336 : allenleung 1327 Name: Allen Leung 2337 : Date: 2003/05/16 13:05:00 CDT 2338 : Tag: leunga-20030516-cygwin-runtime 2339 : Description: 2340 : 2341 : Ported the runtime system to cygwin, which uses the unix 2342 : x86-unix bin files. Missing/buggy features: 2343 : 2344 : o getnetbyname, getnetbyaddr: these functions seem to be missing in 2345 : the Cygwin library. 2346 : o Ctrl-C handling may be flaky. 2347 : o Windows system calls and Windows I/O are not supported. 2348 : 2349 : A new set of binfiles is located at: 2350 : 2351 : http://www.dorsai.org/~leunga/boot.x86-unix.tgz 2352 : 2353 : This is only needed for bootstrapping the cygwin version of smlnj. 2354 : Other x86 versions can use the existing binfiles. 2355 : 2356 : ---------------------------------------------------------------------- 2357 : mblume 1317 Name: Matthias Blume 2358 : Date: 2003/04/08 15:42:00 CDT 2359 : Tag: blume-20030408-listpair 2360 : Description: 2361 : 2362 : 1. Added a target 'mlrisc' to installer. 2363 : 2364 : 2. Added missing elements to structure ListPair. 2365 : 2366 : ---------------------------------------------------------------------- 2367 : leunga 1296 Name: Allen Leung 2368 : Date: 2003/01/07 10:40:00 EST 2369 : Tag: leunga-20030107-int-rem 2370 : Description: 2371 : 2372 : Fixed a bug in Int.rem(x,y) where y is a power of 2 on x86. 2373 : The arguments to the SUBL instruction were swapped. 2374 : 2375 : ---------------------------------------------------------------------- 2376 : blume 1229 Name: Matthias Blume 2377 : blume 1294 Date: 2002/12/12 16:25:00 EST 2378 : Tag: blume-20021212-risc-ra 2379 : Description: 2380 : 2381 : Fixed a serious bug in the rewrite code for FP spilling/reloading that 2382 : sent the RA into an infinite loop when floating point registers get 2383 : spilled. (Because of this bug, e.g., nucleic stopped compiling between 2384 : 110.37 and 110.38.) 2385 : There was another set of potential problems related to the handling of 2386 : MLRISC annotations (but those did not yet cause real problems, apparently). 2387 : 2388 : ---------------------------------------------------------------------- 2389 : Name: Matthias Blume 2390 : blume 1291 Date: 2002/12/06 22:40:00 EST 2391 : Tag: blume-20021206-cm-fileid 2392 : Description: 2393 : 2394 : Added a call of SrcPath.sync at the beginning of Parse.parse (in CM). 2395 : This fixes the problem of CM getting confused by files that suddenly 2396 : change their identity (e.g., by getting unlinked and recreated by some 2397 : text editor such as vi). There might be a better/cheaper/cleaner way 2398 : of doing this, but for now this will have to do. 2399 : 2400 : ---------------------------------------------------------------------- 2401 : Name: Matthias Blume 2402 : blume 1288 Date: 2002/10/28 09:50:00 EST 2403 : Tag: blume-20021028-typecheck 2404 : Description: 2405 : 2406 : Exported structure Typecheck from$smlnj/viscomp/core.cm. 2407 : 2408 : ---------------------------------------------------------------------- 2409 : Name: Matthias Blume 2410 : blume 1282 Date: 2002/10/17 09:10:00 EDT 2411 : blume 1279 Tag: Release_110_42 2412 : Description: 2413 : 2414 : blume 1282 In good old tradition, there has been a slight hiccup so that we have 2415 : to patch 110.42 after the fact. The old release tag has been replaced 2416 : (see below). 2417 : 2418 : The change solves a problem with two competing approaches the 2419 : configuration problem regarding MacOS 10.1 vs. MacOS 10.2 which got in 2420 : each other's way. 2421 : 2422 : This change only affects the runtime system code and the installer script. 2423 : (No new bootfiles.) 2424 : 2425 : ---------------------------------------------------------------------- 2426 : Name: Matthias Blume 2427 : Date: 2002/10/16 12:00:00 EDT 2428 : Tag: Release_110_42_removed 2429 : Description: 2430 : 2431 : blume 1279 New working release. New bootfiles. 2432 : 2433 : ---------------------------------------------------------------------- 2434 : Name: Matthias Blume 2435 : blume 1273 Date: 2002/10/10 13:10:00 EDT 2436 : Tag: blume-20021010-ppc-divs 2437 : Description: 2438 : 2439 : The mltree operator DIVS must be implemented with an overflow check on 2440 : the PPC because the hardware indicates divide-by-zero using "overflow" as 2441 : well. 2442 : 2443 : ---------------------------------------------------------------------- 2444 : Name: Matthias Blume 2445 : blume 1261 Date: 2002/07/23 11:45:00 2446 : Tag: blume-20020723-smlnj-home 2447 : Description: 2448 : 2449 : Sml now senses the SMLNJ_HOME environment variable. If this is set, 2450 : then the bin dir is assumed to be in $SMLNJ_HOME/bin and (unless 2451 : CM_PATHCONFIG is also set), the path configuration file is assumed 2452 : to be in$SMLNJ_HOME/lib/pathconfig. This way one can easily move 2453 : the entire tree to some other place and everything will "just work". 2454 : 2455 : (Companion commands such as ml-build and ml-makedepend also sense this 2456 : variable.) 2457 : 2458 : ---------------------------------------------------------------------- 2459 : Name: Matthias Blume 2460 : blume 1259 Date: 2002/07/12 21:19:00 EDT 2461 : Tag: blume-20020712-liveness 2462 : Description: 2463 : 2464 : Exported two useful "step" functions from liveness module (MLRISC). 2465 : 2466 : ---------------------------------------------------------------------- 2467 : Name: Matthias Blume 2468 : blume 1253 Date: 2002/07/05 16:00 EDT 2469 : Tag: Release_110_41 2470 : Description: 2471 : 2472 : New working release. New bootfiles. 2473 : 2474 : ---------------------------------------------------------------------- 2475 : Name: Matthias Blume 2476 : blume 1250 Date: 2002/07/05 10:25:00 EDT 2477 : Tag: blume-20020705-btimp 2478 : Description: 2479 : 2480 : Exported structure BTImp from $smlnj/viscomp/debugprof.cm so that 2481 : other clients can set up backtracing support. 2482 : 2483 : ---------------------------------------------------------------------- 2484 : Name: Matthias Blume 2485 : blume 1249 Date: 2002/06/25 17:23:00 EDT 2486 : Tag: blume-20020625-fpmax 2487 : Description: 2488 : 2489 : Fixed a bug in translation of INLMAX (and INLMIN) for the floating-point 2490 : case. (The sense of the isNaN test was reversed -- which made min and 2491 : max always return their first argument.) 2492 : 2493 : ---------------------------------------------------------------------- 2494 : Name: Matthias Blume 2495 : blume 1240 Date: 2002/06/11 2496 : Tag: blume-20020611-unixpath 2497 : Description: 2498 : 2499 : Back-ported OS.Path.{from,to}UnixPath from idlbasis-devel branch. 2500 : 2501 : ---------------------------------------------------------------------- 2502 : Name: Matthias Blume 2503 : blume 1238 Date: 2002/06/10 16:35:00 EDT 2504 : Tag: blume-20020610-ieeereal 2505 : Description: 2506 : 2507 : I back-ported my implementation of IEEEReal.fromString from the 2508 : idlbasis-devel branch so that we can test it. 2509 : 2510 : Another small change is that ppDec tries to give more information 2511 : than just "" in the case of functors. However, this code is 2512 : broken in some mysterious way if the functor's body's signature 2513 : has not been declared by ascription but gets inferred from the 2514 : implementation. This needs fixing... 2515 : 2516 : ---------------------------------------------------------------------- 2517 : Name: Matthias Blume 2518 : blume 1229 Date: 2002/05/31 2519 : Tag: blume-20020531-btrace-mode 2520 : Description: 2521 : 2522 : Resurrected SMLofNJ.Internals.BTrace.mode. (It accidentally fell by 2523 : the wayside when I switched over to using Controls everywhere.) 2524 : 2525 : ---------------------------------------------------------------------- 2526 : george 1222 Name: Lal George 2527 : Date: 2002/05/23 12:21:40 EDT 2528 : Tag: george-20020523-visual-labels 2529 : Description: 2530 : 2531 : Labels are now displayed in the graphical output to make 2532 : the fall-through and target blocks obvious. 2533 : 2534 : ---------------------------------------------------------------------- 2535 : blume 1204 Name: Matthias Blume 2536 : blume 1220 Date: 2002/05/22 11:03:00 EDT 2537 : Tag: blume-20020522-shrink 2538 : Description: 2539 : 2540 : John tweaked yesterday's fix for 1131 to handle an out-of-memory 2541 : situation that comes up when allocating huge arrays. 2542 : 2543 : ---------------------------------------------------------------------- 2544 : Name: Matthias Blume 2545 : blume 1215 Date: 2002/05/21 16:00:00 EDT 2546 : Tag: Release_110_40 2547 : Description: 2548 : 2549 : New working release (110.40). New bootfiles. 2550 : 2551 : [Also: John Reppy fixed GC bug 1131.] 2552 : 2553 : ---------------------------------------------------------------------- 2554 : Name: Matthias Blume 2555 : blume 1212 Date: 2002/05/21 12:35:00 EDT 2556 : Tag: blume-20020521-cmdoc 2557 : Description: 2558 : 2559 : CM documentation update. 2560 : 2561 : ---------------------------------------------------------------------- 2562 : Name: Matthias Blume 2563 : blume 1211 Date: 2002/05/21 10:55:00 EDT 2564 : Tag: blume-20020521-misc 2565 : Description: 2566 : 2567 : - John tweaked runtime to be silent on heap export (except when 2568 : GC messages are on). 2569 : - I added a few more things (cross-compiling versions of CMB) to 2570 : config/preloads (as suggestions). 2571 : 2572 : ---------------------------------------------------------------------- 2573 : Name: Matthias Blume 2574 : blume 1208 Date: 2002/05/20 22:25:00 EDT 2575 : Tag: blume-20020520-controls 2576 : Description: 2577 : 2578 : - Added ControlUtil structure to control-lib.cm. 2579 : - Use it throughout. 2580 : - Used Controls facility to define MLRISC controls (as opposed to 2581 : registering MLRISC control ref cells with Controls after the fact) 2582 : - Fixed messed-up controls priorities. 2583 : 2584 : * Removed again all the stuff from config/preloads that one wouldn't 2585 : be able to preload at the time the initial heap image is built. 2586 : (Many libraries, e.g., CML, do not exist yet at this time. The 2587 : only libraries that can be preloaded via config/preloads are those 2588 : that come bundled with the bootfiles.) 2589 : 2590 : ---------------------------------------------------------------------- 2591 : Name: Matthias Blume 2592 : blume 1204 Date: 2002/05/20 10:59:00 EDT 2593 : Tag: blume-20020520-preloads 2594 : Description: 2595 : 2596 : Added a lot of commented-out suggestions for things to be included 2597 : in config/preloads. 2598 : 2599 : ---------------------------------------------------------------------- 2600 : leunga 1203 Name: Allen Leung 2601 : Date: 2002/05/18 14:20:00 EDT 2602 : Tag: leunga-20020518-mdl 2603 : Description: 2604 : 2605 : o Made the mdl tool stuff compile and run again. 2606 : o I've disabled all the stuff that depends on RTL specifications; they 2607 : are all badly broken anyway. 2608 : 2609 : ---------------------------------------------------------------------- 2610 : blume 1201 Name: Matthias Blume 2611 : Date: 2002/05/17 16:49:00 EDT 2612 : Tag: blume-20020517-controls 2613 : Description: 2614 : 2615 : 0. John Reppy made several modifications to the SML/NJ library. 2616 : In particular, there is a shiny new controls-lib.cm. 2617 : 2618 : 1. Pushed new controls interface through compiler so that everything 2619 : compiles again. 2620 : 2621 : 2. Added FormatComb and FORMAT_COMB to the CML version of the 2622 : SML/NJ library (so that CML compiles again). 2623 : 2624 : 3. Modified init scripts because XXX_DEFAULT environment variables 2625 : are no longer with us. (Boot-time initialization is now done 2626 : using the same environment variables that are also used for 2627 : startup-time initialization of controls.) 2628 : 2629 : ---------------------------------------------------------------------- 2630 : george 1192 Name: Lal George 2631 : Date: 2002/05/15 09:20:10 EDT 2632 : Tag: george-20020515-pseudo-op-decls 2633 : Description: 2634 : 2635 : All pseudo-ops emitted before the first segment declaration 2636 : such as TEXT, DATA, and BSS directives are assumed to be global 2637 : declarations and are emitted first in the assembly file. This is 2638 : useful in a number of situations where one has pseudo-ops that are not 2639 : specific to any segment, and also works around the constraint that one 2640 : cannot have client pseudo-ops in the TEXT segment. 2641 : 2642 : Because no segment is associated with these declarations it is 2643 : an error to allocate any space or objects before the first segment 2644 : directive and an exception will be raised. However, we cannot make 2645 : this check for client pseudo-ops. 2646 : 2647 : These top level declarations are a field in the CFG graph_info. 2648 : In theory you can continue to add to this field after the CFG has been 2649 : built -- provided you know what you are doing;-) 2650 : 2651 : ---------------------------------------------------------------------- 2652 : blume 1175 Name: Matthias Blume 2653 : blume 1190 Date: 2002/05/13 16:40:00 EDT 2654 : Tag: blume-20020513-pp-etc 2655 : Description: 2656 : 2657 : A few minor bugfixes: 2658 : 2659 : - Stopgap measure for bug recently reported by Elsa Gunter (ppDec). 2660 : (Bogus printouts for redefined bindings still occur. Compiler 2661 : bug should no longer occur now. We need to redo the prettyprinter 2662 : from scratch.) 2663 : 2664 : - CM pathname printer now also adds escape sequences for ( and ) 2665 : 2666 : - commend and docu fixes for ml-nlffi 2667 : 2668 : ---------------------------------------------------------------------- 2669 : Name: Matthias Blume 2670 : blume 1189 Date: 2002/05/10 16:40:00 EDT 2671 : Tag: blume-20020510-erg-textio 2672 : Description: 2673 : 2674 : Applied the following bugfix provided by Emden Gansner: 2675 : 2676 : Output is corrupted when outputSubstr is used rather than output. 2677 : 2678 : The problem occurs when a substring 2679 : 2680 : ss = (s, dataStart, dataLen) 2681 : 2682 : where dataStart > 0, fills a stream buffer with avail bytes left. 2683 : avail bytes of s, starting at index dataStart, are copied into the 2684 : buffer, the buffer is flushed, and then the remaining dataLen-avail 2685 : bytes of ss are copied into the beginning of the buffer. Instead of 2686 : starting this copy at index dataStart+avail in s, the current code 2687 : starts the copy at index avail. 2688 : 2689 : Fix: 2690 : In text-io-fn.sml, change line 695 from 2691 : val needsFlush = copyVec(v, avail, dataLen-avail, buf, 0) 2692 : to 2693 : val needsFlush = copyVec(v, dataStart+avail, dataLen-avail, buf, 0) 2694 : 2695 : ---------------------------------------------------------------------- 2696 : Name: Matthias Blume 2697 : blume 1186 Date: 2002/04/12 13:55:00 EDT 2698 : Tag: blume-20020412-assyntax 2699 : Description: 2700 : 2701 : 1. Grabbed newer assyntax.h from the XFree86 project. 2702 : 2. Fiddled with how to compile X86.prim.asm without warnings. 2703 : 3. (Very) Minor cleanup in CM. 2704 : 2705 : ---------------------------------------------------------------------- 2706 : Name: Matthias Blume 2707 : blume 1185 Date: 2002/04/01 (no joke!) 17:07:00 EST 2708 : Tag: blume-20020401-x86div 2709 : Description: 2710 : 2711 : Added full support for div/mod/rem/quot on the x86, using the machine 2712 : instruction's two results (without clumsily recomputing the remainder) 2713 : directly where appropriate. 2714 : 2715 : Some more extensive power-of-two support was added to the x86 instruction 2716 : selector (avoiding expensive divs, mods, and muls where they can be 2717 : replaced with cheaper shifts and masks). However, this sort of thing 2718 : ought to be done earlier, e.g., within the CPS optimizer so that 2719 : all architectures benefit from it. 2720 : 2721 : The compiler compiles to a fixed point, but changes might be somewhat 2722 : fragile nevertheless. Please, report any strange things that you might 2723 : see wrt. div/mod/quot/rem... 2724 : 2725 : ---------------------------------------------------------------------- 2726 : Name: Matthias Blume 2727 : blume 1184 Date: 2002/03/29 17:22:00 2728 : Tag: blume-20020329-div 2729 : Description: 2730 : 2731 : Fixed my broken div/mod logic. Unfortunately, this means that the 2732 : inline code for div/mod now has one more comparison than before. 2733 : Fast paths (quotient > 0 or remainder = 0) are not affected, though. 2734 : The problem was with quotient = 0, because that alone does not tell 2735 : us which way the rounding went. One then has to look at whether 2736 : remainder and divisor have the same sign... :( 2737 : 2738 : Anyway, I replaced the bootfiles with fresh ones... 2739 : 2740 : ---------------------------------------------------------------------- 2741 : Name: Matthias Blume 2742 : blume 1183 Date: 2002/03/29 14:10:00 EST 2743 : Tag: blume-20020329-inlprims 2744 : Description: 2745 : 2746 : NEW BOOTFILES!!! Version number bumped to 110.39.3. 2747 : 2748 : Primops have changed. This means that the bin/boot-file formats have 2749 : changed as well. 2750 : 2751 : To make sure that there is no confusion, I made a new version. 2752 : 2753 : 2754 : CHANGES: 2755 : 2756 : * removed REMT from mltree (remainder should never overflow). 2757 : 2758 : * added primops to deal with divisions of all flavors to the frontend 2759 : 2760 : * handled these primops all the way through so they map to their respective 2761 : MLRISC support 2762 : 2763 : * used these primops in the implementation of Int, Int32, Word, Word32 2764 : 2765 : * removed INLDIV, INLMOD, and INLREM as they are no longer necessary 2766 : 2767 : * parameterized INLMIN, INLMAX, and INLABS by a numkind 2768 : 2769 : * translate.sml now deals with all flavors of INL{MIN,MAX,ABS}, including 2770 : floating point 2771 : 2772 : * used INL{MIN,MAX,ABS} in the implementation of Int, Int32, Word, Word32, 2773 : and Real (but Real.abs maps to a separate floating-point-only primop) 2774 : 2775 : 2776 : TODO items: 2777 : 2778 : * Hacked Alpha32 instruction selection, disabling the selection of REMx 2779 : instructions because the machine instruction encoder cannot handle 2780 : them. (Hppa, PPC, and Sparc instruction selection did not handle 2781 : REM in the first place, and REM is supported by the x86 machine coder.) 2782 : 2783 : * Handle DIV and MOD with DIV_TO_NEGINF directly in the x86 instruction 2784 : selection phase. (The two can be streamlined because the hardware 2785 : delivers both quotient and remainder at the same time anyway.) 2786 : 2787 : * Think about what to do with "valOf(Int32.minInt) div ~1" and friends. 2788 : (Currently the behavior is inconsistent both across architectures and 2789 : wrt. the draft Basis spec.) 2790 : 2791 : * Word8 should eventually be handled natively, too. 2792 : 2793 : * There seems to be one serious bug in mltree-gen.sml. It appears, though, 2794 : as if there currently is no execution path that could trigger it in 2795 : SML/NJ. (The assumptions underlying functions arith and promotable do not 2796 : hold for things like multiplication and division.) 2797 : 2798 : ---------------------------------------------------------------------- 2799 : Name: Matthias Blume 2800 : blume 1181 Date: 2002/03/27 16:27:00 EST 2801 : Tag: blume-20020327-mlrisc-divisions 2802 : Description: 2803 : 2804 : Added support for all four division operations (ML's div, mod, quot, 2805 : and rem) to MLRISC. In the course of doing so, I also rationalized 2806 : the naming (no more annoying switch-around of DIV and QUOT), by 2807 : parameterizing the operation by div_rounding_mode (which can be either 2808 : DIV_TO_ZERO or DIV_TO_NEGINF). 2809 : 2810 : The generic MLTreeGen functor takes care of compiling all four 2811 : operations down to only round-to-zero div. 2812 : 2813 : Missing pieces: 2814 : 2815 : * Doing something smarter than relying on MLTreeGen on architectures 2816 : like, e.g., the x86 where hardware division delivers both quotient and 2817 : remainder at the same time. With this, the implementation of the 2818 : round-to-neginf operations could be further streamlined. 2819 : 2820 : * Remove inlining support for div/mod/rem from the frontend and replace it 2821 : with primops that get carried through to the backend. Do this for all 2822 : int and word types. 2823 : 2824 : ---------------------------------------------------------------------- 2825 : Name: Matthias Blume 2826 : blume 1180 Date: 2002/03/25 17:25:00 EST 2827 : Tag: blume-20020325-divmod 2828 : Description: 2829 : 2830 : I improved (hopefully without breaking them) the implementation of Int.div, 2831 : Int.mod, and Int.rem. For this, the code in translate.sml now takes 2832 : advantage of the following observations: 2833 : 2834 : Let q = x quot y r = x rem y 2835 : d = x div y m = x mod y 2836 : 2837 : where "quot" is the round-to-zero version of integer division that 2838 : hardware usually provides. Then we have: 2839 : 2840 : r = x - q * y where neither the * nor the - will overflow 2841 : d = if q >= 0 orelse x = q * y then q else q - 1 2842 : where neither the * nor the - will overflow 2843 : m = if q >= 0 orelse r = 0 then r else r + y 2844 : where the + will not overflow 2845 : 2846 : This results in substantial simplification of the generated code. 2847 : The following table shows the number of CFG nodes and edges generated 2848 : for 2849 : fun f (x, y) = x OPER y 2850 : (* with OPER \in div, mod, quot, rem *) 2851 : 2852 : 2853 : OPER | nodes(old) | edges(old) | nodes(new) | edges(new) 2854 : -------------------------------------------------------- 2855 : div | 24 | 39 | 12 | 16 2856 : mod | 41 | 71 | 12 | 16 2857 : quot | 8 | 10 | 8 | 10 2858 : rem | 10 | 14 | 8 | 10 2859 : 2860 : 2861 : ---------------------------------------------------------------------- 2862 : Name: Matthias Blume 2863 : blume 1179 Date: 2002/03/25 22:06:00 EST 2864 : Tag: blume-20020325-cprotobug 2865 : Description: 2866 : 2867 : Fixed a bug in cproto (c prototype decoder). 2868 : 2869 : ---------------------------------------------------------------------- 2870 : Name: Matthias Blume 2871 : blume 1178 Date: 2002/03/25 16:00:00 EST 2872 : Tag: blume-20020325-raw-primops 2873 : Description: 2874 : 2875 : I did some cleanup to Allen's new primop code and 2876 : replaced yesterday's bootfiles with new ones. 2877 : (But they are stored in the same place.) 2878 : 2879 : ---------------------------------------------------------------------- 2880 : Name: Matthias Blume 2881 : blume 1175 Date: 2002/03/24 22:40:00 EST 2882 : Tag: blume-20020324-bootfiles 2883 : Description: 2884 : 2885 : Made the bootfiles that Allen asked for. 2886 : 2887 : ---------------------------------------------------------------------- 2888 : leunga 1174 Name: Allen Leung 2889 : Date: 2002/03/23 15:50:00 EST 2890 : Tag: leunga-20020323-flint-cps-rcc-primops 2891 : Description: 2892 : 2893 : 1. Changes to FLINT primops: 2894 : 2895 : (* make a call to a C-function; 2896 : * The primop carries C function prototype information and specifies 2897 : * which of its (ML-) arguments are floating point. C prototype 2898 : * information is for use by the backend, ML information is for 2899 : * use by the CPS converter. *) 2900 : | RAW_CCALL of { c_proto: CTypes.c_proto, 2901 : ml_args: ccall_type list, 2902 : ml_res_opt: ccall_type option, 2903 : reentrant : bool 2904 : } option 2905 : (* Allocate uninitialized storage on the heap. 2906 : * The record is meant to hold short-lived C objects, i.e., they 2907 : * are not ML pointers. With the tag, the representation is 2908 : * the same as RECORD with tag tag_raw32 (sz=4), or tag_fblock (sz=8) 2909 : *) 2910 : | RAW_RECORD of {tag:bool,sz:int} 2911 : and ccall_type = CCALL_INT32 | CCALL_REAL64 | CCALL_ML_PTR 2912 : 2913 : 2. These CPS primops are now overloaded: 2914 : 2915 : rawload of {kind:numkind} 2916 : rawstore of {kind:numkind} 2917 : 2918 : The one argument form is: 2919 : 2920 : rawload {kind} address 2921 : 2922 : The two argument form is: 2923 : 2924 : rawload {kind} [ml object, byte-offset] 2925 : 2926 : 3. RAW_CCALL/RCC now takes two extra arguments: 2927 : 2928 : a. The first is whether the C call is reentrant, i.e., whether 2929 : ML state should be saved and restored. 2930 : b. The second argument is a string argument specifying the name of 2931 : library and the C function. 2932 : 2933 : These things are currently not handled in the code generator, yet. 2934 : 2935 : 4. In CProto, 2936 : 2937 : An encoding type of "bool" means "ml object" and is mapped into 2938 : C prototype of PTR. Note that "bool" is different than "string", 2939 : even though "string" is also mapped into PTR, because "bool" 2940 : is assigned an CPS type of BOGt, while "string" is assigned INT32t. 2941 : 2942 : 5. Pickler/unpicker 2943 : 2944 : Changed to handle RAW_RECORD and newest RAW_CCALL 2945 : 2946 : 6. MLRiscGen, 2947 : 2948 : 1. Changed to handle the new rawload/rawstore/rawrecord operators. 2949 : 2. Code for handling C Calls has been moved to a new module CPSCCalls, 2950 : in the file CodeGen/cpscompile/cps-c-calls.sml 2951 : 2952 : 7. Added the conditional move operator 2953 : 2954 : condmove of branch 2955 : 2956 : to cps. Generation of this is still buggy so it is currently 2957 : disabled. 2958 : 2959 : ---------------------------------------------------------------------- 2960 : george 1168 Name: Lal George 2961 : Date: 2002/03/22 14:18:25 EST 2962 : george 1171 Tag: george-20020322-cps-branch-prob 2963 : george 1168 Description: 2964 : 2965 : george 1171 Implemented the Ball-Larus branch prediction-heuristics, and 2966 : george 1168 incorporated graphical viewers for control flow graphs. 2967 : 2968 : george 1171 Ball-Larus Heuristics: 2969 : george 1168 --------------------- 2970 : See the file compiler/CodeGen/cpscompile/cpsBranchProb.sml. 2971 : 2972 : By design it uses the Dempster-Shafer theory for combining 2973 : probabilities. For example, in the function: 2974 : 2975 : fun f(n,acc) = if n = 0 then acc else f(n-1, n*acc) 2976 : 2977 : the ball-larus heuristics predicts that the n=0 is unlikely 2978 : (OH-heuristic), and the 'then' branch is unlikely because of the 2979 : RH-heuristic -- giving the 'then' branch an even lower combined 2980 : george 1171 probability using the Dempster-Shafer theory. 2981 : george 1168 2982 : Finally, John Reppy's loop analysis in MLRISC, further lowers the 2983 : probability of the 'then' branch because of the loop in the else 2984 : branch. 2985 : 2986 : 2987 : Graphical Viewing: 2988 : ------------------ 2989 : I merely plugged in Allen's graphical viewers into the compiler. The 2990 : additional code is not much. At the top level, saying: 2991 : 2992 : Control.MLRISC.getFlag "cfg-graphical-view" := true; 2993 : 2994 : will display the graphical view of the control flow graph just before 2995 : back-patching. daVinci must be in your path for this to work. If 2996 : daVinci is not available, then the default viewer can be changed 2997 : using: 2998 : 2999 : Control.MLRISC.getString "viewer" 3000 : 3001 : which can be set to "dot" or "vcg" for the corresponding viewers. Of 3002 : course, these viewers must be in your path. 3003 : 3004 : The above will display the compilation unit at the level of clusters, 3005 : many of which are small, boring, and un-interesting. Also setting: 3006 : 3007 : Control.MLRISC.getInt "cfg-graphical-view_size" 3008 : 3009 : will display clusters that are larger than the value set by the above. 3010 : 3011 : 3012 : ---------------------------------------------------------------------- 3013 : blume 1159 Name: Matthias Blume 3014 : Date: 2002/03/21 22:20:00 EST 3015 : Tag: blume-20020321-kmp-bugfix 3016 : Description: 3017 : 3018 : Changed the interface to the KMP routine in PreString and fixed 3019 : a minor bug in one place where it was used. 3020 : 3021 : ---------------------------------------------------------------------- 3022 : leunga 1156 Name: Allen Leung 3023 : leunga 1158 Date: 2002/03/21 20:30:00 EST 3024 : Tag: leunga-20020321-cfg 3025 : Description: 3026 : 3027 : Fixed a potential problem in cfg edge splitting. 3028 : 3029 : ---------------------------------------------------------------------- 3030 : Name: Allen Leung 3031 : leunga 1156 Date: 2002/03/21 17:15:00 EST 3032 : Tag: leunga-20020321-x86-fp-cfg 3033 : Description: 3034 : 3035 : 1. Recoded the buggy parts of x86-fp. 3036 : 3037 : a. All the block reordering code has been removed. 3038 : We now depend on the block placement phases to do this work. 3039 : 3040 : b. Critical edge splitting code has been simplified and moved into the 3041 : CFG modules, as where they belong. 3042 : 3043 : Both of these were quite buggy and complex. The code is now much, much 3044 : simpler. 3045 : 3046 : 2. X86 backend. 3047 : 3048 : a. Added instructions for 64-bit support. Instruction selection for 3049 : 64-bit has not been committed, however, since that 3050 : requires changes to MLTREE which haven't been approved by 3051 : Lal and John. 3052 : 3053 : b. Added support for FUCOMI and FUCOMIP when generating code for 3054 : PentiumPro and above. We only generate these instructions in 3055 : the fast-fp mode. 3056 : 3057 : c. Added cases for JP and JNP in X86FreqProps. 3058 : 3059 : 3. CFG 3060 : 3061 : CFG now has a bunch of methods for edge splitting and merging. 3062 : 3063 : 4. Machine description. 3064 : 3065 : John's simplification of MLTREE_BASIS.fcond broke a few machine 3066 : description things: 3067 : 3068 : rtl-build.{sig,sml} and hppa.mdl fixed. 3069 : 3070 : NOTE: the machine description stuff in the repository is still broken. 3071 : Again, I can't put my fixes in because that involves 3072 : changes to MLTREE. 3073 : 3074 : ---------------------------------------------------------------------- 3075 : blume 1145 Name: Matthias Blume 3076 : blume 1155 Date: 2002/03/20 15:55:00 EST 3077 : Tag: blume-20020320-kmp 3078 : Description: 3079 : 3080 : Implemented Knuth-Morris-Pratt string matching in PreString and used 3081 : it for String.isSubstring, Substring.isSubstring, and 3082 : Substring.position. 3083 : 3084 : (Might need some stress-testing. Simple examples worked fine.) 3085 : 3086 : ---------------------------------------------------------------------- 3087 : Name: Matthias Blume 3088 : blume 1152 Date: 2002/03/19 16:37:00 EST 3089 : Tag: blume-20020319-witnesses 3090 : Description: 3091 : 3092 : Added a structure C.W and functions convert/Ptr.convert to ml-nlffi-lib. 3093 : 3094 : This implements a generic mechanism for changing constness qualifiers 3095 : anywhere within big C types without resorting to outright "casts". 3096 : (So far, functions such as C.rw/C.ro or C.Ptr.rw/C.Ptr.ro only let you 3097 : modify the constness at the outermost level.) 3098 : The implementation of "convert" is based on the idea of "witness" 3099 : values -- values that are not used by the operation but whose types 3100 : "testify" to their applicability. On the implementation side, "convert" 3101 : is simply a projection (returning its second curried argument). With 3102 : cross-module inlining, it should not result in any machine code being 3103 : generated. 3104 : 3105 : ---------------------------------------------------------------------- 3106 : Name: Matthias Blume 3107 : blume 1148 Date: 2002/03/15 16:40:00 EST 3108 : Tag: blume-20020315-basis 3109 : Description: 3110 : 3111 : Provided (preliminary?) implementations for 3112 : 3113 : {String,Substring}.{concatWith,isSuffix,isSubstring} 3114 : 3115 : and 3116 : 3117 : Substring.full 3118 : 3119 : Those are in the Basis spec but they were missing in SML/NJ. 3120 : 3121 : ---------------------------------------------------------------------- 3122 : Name: Matthias Blume 3123 : blume 1145 Date: 2002/03/14 21:30:00 EST 3124 : Tag: blume-20020314-controls 3125 : Description: 3126 : 3127 : Controls: 3128 : --------- 3129 : 3130 : 1. Factored out the recently-added Controls : CONTROLS stuff and put 3131 : it into its own library$/controls-lib.cm. The source tree for 3132 : this is under src/smlnj-lib/Controls. 3133 : 3134 : 2. Changed the names of types and functions in this interface, so they 3135 : make a bit more "sense": 3136 : 3137 : module -> registry 3138 : 'a registry -> 'a group 3139 : 3140 : 3. The interface now deals in ref cells only. The getter/setter interface 3141 : is (mostly) gone. 3142 : 3143 : 4. Added a function that lets one register an already-existing ref cell. 3144 : 3145 : 5. Made the corresponding modifications to the rest of the code so that 3146 : everything compiles again. 3147 : 3148 : 6. Changed the implementation of Controls.MLRISC back to something closer 3149 : to the original. In particular, this module (and therefore MLRISC) 3150 : does not depend on Controls. There now is some link-time code in 3151 : int-sys.sml that registers the MLRISC controls with the Controls 3152 : module. 3153 : 3154 : CM: 3155 : --- 3156 : 3157 : * One can now specify the lambda-split aggressiveness in init.cmi. 3158 : 3159 : ---------------------------------------------------------------------- 3160 : leunga 1142 Name: Allen Leung 3161 : Date: 2002/03/13 17:30:00 EST 3162 : Tag: leunga-20020313-x86-fp-unary 3163 : Description: 3164 : 3165 : Bug fix for: 3166 : 3167 : > leunga@weaselbane:~/Yale/tmp/sml-dist{21} bin/sml 3168 : > Standard ML of New Jersey v110.39.1 [FLINT v1.5], March 08, 2002 3169 : > - fun f(x,(y,z)) = Real.~ y; 3170 : > [autoloading] 3171 : > [autoloading done] 3172 : > fchsl (%eax), 184(%esp) 3173 : > Error: MLRisc bug: X86MCEmitter.emitInstr 3174 : > 3175 : > uncaught exception Error 3176 : > raised at: ../MLRISC/control/mlriscErrormsg.sml:16.14-16.19 3177 : 3178 : The problem was that the code generator did not generate any fp registers 3179 : in this case, and the ra didn't know that it needed to run the X86FP phase to 3180 : translate the pseudo fp instruction. This only happened with unary fp 3181 : operators in certain situations. 3182 : 3183 : ---------------------------------------------------------------------- 3184 : blume 1137 Name: Matthias Blume 3185 : blume 1140 Date: 2002/03/13 14:00:00 EST 3186 : Tag: blume-20020313-overload-etc 3187 : Description: 3188 : 3189 : 1. Added _overload as a synonym for overload for backward compatibility. 3190 : (Control.overloadKW must be true for either version to be accepted.) 3191 : 3192 : 2. Fixed bug in install script that caused more things to be installed 3193 : than what was requested in config/targets. 3194 : 3195 : 3. Made CM aware of the (_)overload construct so that autoloading 3196 : works. 3197 : 3198 : ---------------------------------------------------------------------- 3199 : Name: Matthias Blume 3200 : blume 1138 Date: 2002/03/12 22:03:00 EST 3201 : Tag: blume-20020312-url 3202 : Description: 3203 : 3204 : Forgot to update BOOT and srcarchiveurl. 3205 : 3206 : ---------------------------------------------------------------------- 3207 : Name: Matthias Blume 3208 : blume 1137 Date: 2002/03/12 17:30:00 EST 3209 : Tag: blume-20020312-version110392 3210 : Description: 3211 : 3212 : Yet another version number bump (because of small changes to the 3213 : binfile format). Version number is now 110.39.2. NEW BOOTFILES! 3214 : 3215 : Changes: 3216 : 3217 : The new pid generation scheme described a few weeks ago was overly 3218 : complicated. I implemented a new mechanism that is simpler and 3219 : provides a bit more "stability": Once CM has seen a compilation 3220 : unit, it keeps its identity constant (as long as you do not delete 3221 : those crucial CM/GUID/* files). This means that when you change 3222 : blume 1145 an interface, compile, then go back to the old interface, and 3223 : blume 1137 compile again, you arrive at the original pid. 3224 : 3225 : There now also is a mechanism that instructs CM to use the plain 3226 : environment hash as a module's pid (effectively making its GUID 3227 : the empty string). For this, "noguid" must be specified as an 3228 : option to the .sml file in question within its .cm file. 3229 : This is most useful for code that is being generated by tools such 3230 : as ml-nlffigen (because during development programmers tend to 3231 : erase the tool's entire output directory tree including CM's cached 3232 : GUIDs). "noguid" is somewhat dangerous (since it can be used to locally 3233 : revert to the old, broken behavior of SML/NJ, but in specific cases 3234 : where there is no danger of interface confusion, its use is ok 3235 : (I think). 3236 : 3237 : ml-nlffigen by default generates "noguid" annotations. They can be 3238 : turned off by specifying -guid in its command line. 3239 : 3240 : ---------------------------------------------------------------------- 3241 : george 1136 Name: Lal George 3242 : Date: 2002/03/12 12 14:42:36 EST 3243 : Tag: george-20020312-frequency-computation 3244 : Description: 3245 : 3246 : Integrated jump chaining and static block frequency into the 3247 : compiler. More details and numbers later. 3248 : leunga 1025 3249 : george 1003 ---------------------------------------------------------------------- 3250 : george 1133 Name: Lal George 3251 : Date: 2002/03/11 11 22:38:53 EST 3252 : Tag: george-20020311-jump-chain-elim 3253 : Description: 3254 : 3255 : Tested the jump chain elimination on all architectures (except the 3256 : hppa). This is on by default right now and is profitable for the 3257 : alpha and x86, however, it may not be profitable for the sparc and ppc 3258 : when compiling the compiler. 3259 : 3260 : The gc test will typically jump to a label at the end of the cluster, 3261 : where there is another jump to an external cluster containing the actual 3262 : code to invoke gc. This is to allow factoring of common gc invocation 3263 : sequences. That is to say, we generate: 3264 : 3265 : f: 3266 : testgc 3267 : ja L1 % jump if above to L1 3268 : 3269 : L1: 3270 : jmp L2 3271 : 3272 : 3273 : After jump chain elimination the 'ja L1' instructions is converted to 3274 : 'ja L2'. On the sparc and ppc, many of the 'ja L2' instructions may end 3275 : up being implemented in their long form (if L2 is far away) using: 3276 : 3277 : jbe L3 % jump if below or equal to L3 3278 : jmp L2 3279 : L3: 3280 : ... 3281 : 3282 : 3283 : For large compilation units L2 may be far away. 3284 : 3285 : 3286 : ---------------------------------------------------------------------- 3287 : blume 1132 Name: Matthias Blume 3288 : Date: 2002/03/11 13:30:00 EST 3289 : Tag: blume-20020311-mltreeeval 3290 : Description: 3291 : 3292 : A functor parameter was missing. 3293 : 3294 : ---------------------------------------------------------------------- 3295 : leunga 1130 Name: Allen Leung 3296 : leunga 1131 Date: 2002/03/11 10:30:00 EST 3297 : leunga 1142 Tag: leunga-20020311-runtime-string0 3298 : leunga 1131 Description: 3299 : 3300 : The representation of the empty string now points to a 3301 : legal null terminated C string instead of unit. It is now possible 3302 : to convert an ML string into C string with InlineT.CharVector.getData. 3303 : This compiles into one single machine instruction. 3304 : 3305 : ---------------------------------------------------------------------- 3306 : Name: Allen Leung 3307 : leunga 1130 Date: 2002/03/10 23:55:00 EST 3308 : Tag: leunga-20020310-x86-call 3309 : Description: 3310 : 3311 : Added machine generation for CALL instruction (relative displacement mode) 3312 : 3313 : ---------------------------------------------------------------------- 3314 : blume 1128 Name: Matthias Blume 3315 : Date: 2002/03/08 16:05:00 3316 : Tag: blume-20020308-entrypoints 3317 : Description: 3318 : 3319 : Version number bumped to 110.39.1. NEW BOOTFILES! 3320 : 3321 : Entrypoints: non-zero offset into a code object where execution should begin. 3322 : 3323 : - Added the notion of an entrypoint to CodeObj. 3324 : - Added reading/writing of entrypoint info to Binfile. 3325 : - Made runtime system bootloader aware of entrypoints. 3326 : - Use the address of the label of the first function given to mlriscGen 3327 : as the entrypoint. This address is currently always 0, but it will 3328 : not be 0 once we turn on block placement. 3329 : - Removed the linkage cluster code (which was The Other Way(tm) of dealing 3330 : with entry points) from mlriscGen. 3331 : 3332 : ---------------------------------------------------------------------- 3333 : leunga 1127 Name: Allen Leung 3334 : Date: 2002/03/07 20:45:00 EST 3335 : Tag: leunga-20020307-x86-cmov 3336 : Description: 3337 : 3338 : Bug fixes for CMOVcc on x86. 3339 : 3340 : 1. Added machine code generation for CMOVcc 3341 : 2. CMOVcc is now generated in preference over SETcc on PentiumPro or above. 3342 : 3. CMOVcc cannot have an immediate operand as argument. 3343 : 3344 : ---------------------------------------------------------------------- 3345 : blume 1126 Name: Matthias Blume 3346 : Date: 2002/03/07 16:15:00 EST 3347 : Tag: blume-20020307-controls 3348 : Description: 3349 : 3350 : This is a very large but mostly boring patch which makes (almost) 3351 : every tuneable compiler knob (i.e., pretty much everything under 3352 : Control.* plus a few other things) configurable via both the command 3353 : line and environment variables in the style CM did its configuration 3354 : until now. 3355 : 3356 : Try starting sml with '-h' (or, if you are brave, '-H') 3357 : 3358 : To this end, I added a structure Controls : CONTROLS to smlnj-lib.cm which 3359 : implements the underlying generic mechanism. 3360 : 3361 : The interface to some of the existing such facilities has changed somewhat. 3362 : For example, the MLRiscControl module now provides mkFoo instead of getFoo. 3363 : (The getFoo interface is still there for backward-compatibility, but its 3364 : use is deprecated.) 3365 : 3366 : The ml-build script passes -Cxxx=yyy command-line arguments through so 3367 : that one can now twiddle the compiler settings when using this "batch" 3368 : compiler. 3369 : 3370 : TODO items: 3371 : 3372 : We should go through and throw out all controls that are no longer 3373 : connected to anything. Moreover, we should go through and provide 3374 : meaningful (and correct!) documentation strings for those controls 3375 : that still are connected. 3376 : 3377 : Currently, multiple calls to Controls.new are accepted (only the first 3378 : has any effect). Eventually we should make sure that every control 3379 : is being made (via Controls.new) exactly once. Future access can then 3380 : be done using Controls.acc. 3381 : 3382 : Finally, it would probably be a good idea to use the getter-setter 3383 : interface to controls rather than ref cells. For the time being, both 3384 : styles are provided by the Controls module, but getter-setter pairs are 3385 : better if thread-safety is of any concern because they can be wrapped. 3386 : 3387 : ***************************************** 3388 : 3389 : One bug fix: The function blockPlacement in three of the MLRISC 3390 : backpatch files used to be hard-wired to one of two possibilities at 3391 : link time (according to the value of the placementFlag). But (I 3392 : think) it should rather sense the flag every time. 3393 : 3394 : ***************************************** 3395 : 3396 : Other assorted changes (by other people who did not supply a HISTORY entry): 3397 : 3398 : 1. the cross-module inliner now works much better (Monnier) 3399 : 2. representation of weights, frequencies, and probabilities in MLRISC 3400 : changed in preparation of using those for weighted block placement 3401 : (Reppy, George) 3402 : 3403 : ---------------------------------------------------------------------- 3404 : george 1116 Name: Lal George 3405 : george 1124 Date: 2002/03/07 14:44:24 EST 2002 3406 : Tag: george-20020307-weighted-block-placement 3407 : 3408 : Tested the weighted block placement optimization on all architectures 3409 : (except the hppa) using AMPL to generate the block and edge frequencies. 3410 : Changes were required in the machine properties to correctly 3411 : categorize trap instructions. There is an MLRISC flag 3412 : "weighted-block-placement" that can be used to enable weighted block 3413 : placement, but this will be ineffective without block/edge 3414 : frequencies (coming soon). 3415 : 3416 : 3417 : ---------------------------------------------------------------------- 3418 : Name: Lal George 3419 : george 1116 Date: 2002/03/05 17:24:48 EST 3420 : Tag: george-20020305-linkage-cluster 3421 : 3422 : george 1124 In order to support the block placement optimization, a new cluster 3423 : is generated as the very first cluster (called the linkage cluster). 3424 : It contains a single jump to the 'real' entry point for the compilation 3425 : unit. Block placement has no effect on the linkage cluster itself, but 3426 : all the other clusters have full freedom in the manner in which they 3427 : reorder blocks or functions. 3428 : george 1116 3429 : On the x86 the typical linkage code that is generated is: 3430 : ---------------------- 3431 : .align 2 3432 : L0: 3433 : addl L1-L0, 72(%esp) 3434 : george 1124 jmp L1 3435 : george 1116 3436 : 3437 : .align 2 3438 : L1: 3439 : ---------------------- 3440 : 3441 : 72(%esp) is the memory location for the stdlink register. This 3442 : must contain the address of the CPS function being called. In the 3443 : george 1124 above example, it contains the address of L0; before 3444 : george 1116 calling L1 (the real entry point for the compilation unit), it 3445 : must contain the address for L1, and hence 3446 : 3447 : addlL1-L0, 72(%esp) 3448 : 3449 : george 1124 I have tested this on all architectures except the hppa.The increase 3450 : in code size is of course negligible 3451 : george 1116 3452 : ---------------------------------------------------------------------- 3453 : leunga 1115 Name: Allen Leung 3454 : Date: 2002/03/03 13:20:00 EST 3455 : Tag: leunga-20020303-mlrisc-tools 3456 : 3457 : Added #[ ... ] expressions to mlrisc tools 3458 : 3459 : ---------------------------------------------------------------------- 3460 : blume 1096 Name: Matthias Blume 3461 : blume 1098 Date: 2002/02/27 12:29:00 EST 3462 : Tag: blume-20020227-cdebug 3463 : Description: 3464 : 3465 : - made types in structure C and C_Debug to be equal 3466 : - got rid of code duplication (c-int.sml vs. c-int-debug.sml) 3467 : - there no longer is a C_Int_Debug (C_Debug is directly derived from C) 3468 : 3469 : ---------------------------------------------------------------------- 3470 : Name: Matthias Blume 3471 : blume 1096 Date: 2002/02/26 12:00:00 EST 3472 : Tag: blume-20020226-ffi 3473 : Description: 3474 : 3475 : 1. Fixed a minor bug in CM's "noweb" tool: 3476 : If numbering is turned off, then truly don't number (i.e., do not 3477 : supply the -L option to noweb). The previous behavior was to supply 3478 : -L'' -- which caused noweb to use the "default" line numbering scheme. 3479 : Thanks to Chris Richards for pointing this out (and supplying the fix). 3480 : 3481 : 2. Once again, I reworked some aspects of the FFI: 3482 : 3483 : A. The incomplete/complete type business: 3484 : 3485 : - Signatures POINTER_TO_INCOMPLETE_TYPE and accompanying functors are 3486 : gone! 3487 : - ML types representing an incomplete type are now *equal* to 3488 : ML types representing their corresponding complete types (just like 3489 : in C). This is still safe because ml-nlffigen will not generate 3490 : RTTI for incomplete types, nor will it generate functions that 3491 : require access to such RTTI. But when ML code generated from both 3492 : incomplete and complete versions of the C type meet, the ML types 3493 : are trivially interoperable. 3494 : 3495 : NOTE: These changes restore the full generality of the translation 3496 : (which was previously lost when I eliminated functorization)! 3497 : 3498 : B. Enum types: 3499 : 3500 : - Structure C now has a type constructor "enum" that is similar to 3501 : how the "su" constructor works. However, "enum" is not a phantom 3502 : type because each "T enum" has values (and is isomorphic to 3503 : MLRep.Signed.int). 3504 : - There are generic access operations for enum objects (using 3505 : MLRep.Signed.int). 3506 : - ml-nlffigen will generate a structure E_foo for each "enum foo". 3507 : * The structure contains the definition of type "mlrep" (the ML-side 3508 : representation type of the enum). Normally, mlrep is the same 3509 : as "MLRep.Signed.int", but if ml-nlffigen was invoked with "-ec", 3510 : then mlrep will be defined as a datatype -- thus facilitating 3511 : pattern matching on mlrep values. 3512 : ("-ec" will be suppressed if there are duplicate values in an 3513 : enumeration.) 3514 : * Constructors ("-ec") or values (no "-ec") e_xxx of type mlrep 3515 : will be generated for each C enum constant xxx. 3516 : * Conversion functions m2i and i2m convert between mlrep and 3517 : MLRep.Signed.int. (Without "-ec", these functions are identities.) 3518 : * Coversion functions c and ml convert between mlrep and "tag enum". 3519 : * Access functions (get/set) fetch and store mlrep values. 3520 : - By default (unless ml-nlffigen was invoked with "-nocollect"), unnamed 3521 : enumerations are merged into one single enumeration represented by 3522 : structure E_'. 3523 : 3524 : ---------------------------------------------------------------------- 3525 : leunga 1080 Name: Allen Leung 3526 : leunga 1094 Date: 2002/02/25 04:45:00 EST 3527 : Tag: leunga-20020225-cps-spill 3528 : 3529 : This is a new implementation of the CPS spill phase. 3530 : The new phase is in the new file compiler/CodeGen/cpscompile/spill-new.sml 3531 : In case of problems, replace it with the old file spill.sml 3532 : 3533 : The current compiler runs into some serious performance problems when 3534 : constructing a large record. This can happen when we try to compile a 3535 : structure with many items. Even a very simple structure like the following 3536 : makes the compiler slow down. 3537 : 3538 : structure Foo = struct 3539 : val x_1 = 0w1 : Word32.int 3540 : val x_2 = 0w2 : Word32.int 3541 : val x_3 = 0w3 : Word32.int 3542 : ... 3543 : val x_N = 0wN : Word32.int 3544 : end 3545 : 3546 : The following table shows the compile time, from N=1000 to N=4000, 3547 : with the old compiler: 3548 : 3549 : N 3550 : 1000 CPS 100 spill 0.04u 0.00s 0.00g 3551 : MLRISC ra 0.06u 0.00s 0.05g 3552 : (spills = 0 reloads = 0) 3553 : TOTAL 0.63u 0.07s 0.21g 3554 : 3555 : 1100 CPS 100 spill 8.25u 0.32s 0.64g 3556 : MLRISC ra 5.68u 0.59s 3.93g 3557 : (spills = 0 reloads = 0) 3558 : TOTAL 14.71u 0.99s 4.81g 3559 : 3560 : 1500 CPS 100 spill 58.55u 2.34s 1.74g 3561 : MLRISC ra 5.54u 0.65s 3.91g 3562 : (spills = 543 reloads = 1082) 3563 : TOTAL 65.40u 3.13s 6.00g 3564 : 3565 : 2000 CPS 100 spill 126.69u 4.84s 3.08g 3566 : MLRISC ra 0.80u 0.10s 0.55g 3567 : (spills = 42 reloads = 84) 3568 : TOTAL 129.42u 5.10s 4.13g 3569 : 3570 : 3000 CPS 100 spill 675.59u 19.03s 11.64g 3571 : MLRISC ra 2.69u 0.27s 1.38g 3572 : (spills = 62 reloads = 124) 3573 : TOTAL 682.48u 19.61s 13.99g 3574 : 3575 : 4000 CPS 100 spill 2362.82u 56.28s 43.60g 3576 : MLRISC ra 4.96u 0.27s 2.72g 3577 : (spills = 85 reloads = 170) 3578 : TOTAL 2375.26u 57.21s 48.00g 3579 : 3580 : As you can see the old cps spill module suffers from some serious 3581 : leunga 1115 performance problem. But since I cannot decipher the old code fully, 3582 : instead of patching the problems up, I'm reimplementing it 3583 : leunga 1094 with a different algorithm. The new code is more modular, 3584 : smaller when compiled, and substantially faster 3585 : (O(n log n) time and O(n) space). Timing of the new spill module: 3586 : 3587 : 4000 CPS 100 spill 0.02u 0.00s 0.00g 3588 : MLRISC ra 0.25u 0.02s 0.15g 3589 : (spills=1 reloads=3) 3590 : TOTAL 7.74u 0.34s 1.62g 3591 : 3592 : Implementation details: 3593 : 3594 : As far as I can tell, the purpose of the CPS spill module is to make sure the 3595 : number of live variables at any program point (the bandwidth) 3596 : does not exceed a certain limit, which is determined by the 3597 : size of the spill area. 3598 : 3599 : When the bandwidth is too large, we decrease the register pressure by 3600 : packing live variables into spill records. How we achieve this is 3601 : completely different than what we did in the old code. 3602 : 3603 : First, there is something about the MLRiscGen code generator 3604 : that we should be aware of: 3605 : 3606 : o MLRiscGen performs code motion! 3607 : 3608 : In particular, it will move floating point computations and 3609 : address computations involving only the heap pointer to 3610 : their use sites (if there is only a single use). 3611 : What this means is that if we have a CPS record construction 3612 : statement 3613 : 3614 : RECORD(k,vl,w,e) 3615 : 3616 : we should never count the new record address w as live if w 3617 : has only one use (which is often the case). 3618 : 3619 : We should do something similar to floating point, but the transformation 3620 : there is much more complex, so I won't deal with that. 3621 : 3622 : Secondly, there are now two new cps primops at our disposal: 3623 : 3624 : 1. rawrecord of record_kind option 3625 : This pure operator allocates some uninitialized storage from the heap. 3626 : There are two forms: 3627 : 3628 : rawrecord NONE [INT n] allocates a tagless record of length n 3629 : rawrecord (SOME rk) [INT n] allocates a tagged record of length n 3630 : and initializes the tag. 3631 : 3632 : 2. rawupdate of cty 3633 : rawupdate cty (v,i,x) 3634 : Assigns to x to the ith component of record v. 3635 : The storelist is not updated. 3636 : 3637 : We use these new primops for both spilling and increment record construction. 3638 : 3639 : 1. Spilling. 3640 : 3641 : This is implemented with a linear scan algorithm (but generalized 3642 : to trees). The algorithm will create a single spill record at the 3643 : beginning of the cps function and use rawupdate to spill to it, 3644 : and SELECT or SELp to reload from it. So both spills and reloads 3645 : are fine-grain operations. In contrast, in the old algorithm 3646 : "spills" have to be bundled together in records. 3647 : 3648 : Ideally, we should sink the spill record construction to where 3649 : it is needed. We can even split the spill record into multiple ones 3650 : at the places where they are needed. But CPS is not a good 3651 : representation for global code motion, so I'll keep it simple and 3652 : am not attempting this. 3653 : 3654 : 2. Incremental record construction (aka record splitting). 3655 : 3656 : Long records with many component values which are simulatenously live 3657 : (recall that single use record addresses are not considered to 3658 : be live) are constructed with rawrecord and rawupdate. 3659 : We allocate space on the heap with rawrecord first, then gradually 3660 : fill it in with rawupdate. This is the technique suggested to me 3661 : by Matthias. 3662 : 3663 : Some restrictions on when this is applicable: 3664 : 1. It is not a VECTOR record. The code generator currently does not handle 3665 : this case. VECTOR record uses double indirection like arrays. 3666 : 2. All the record component values are defined in the same "basic block" 3667 : as the record constructor. This is to prevent speculative 3668 : record construction. 3669 : 3670 : ---------------------------------------------------------------------- 3671 : Name: Allen Leung 3672 : leunga 1086 Date: 2002/02/22 01:02:00 EST 3673 : Tag: leunga-20020222-mlrisc-tools 3674 : 3675 : Minor bug fixes in the parser and rewriter 3676 : 3677 : ---------------------------------------------------------------------- 3678 : Name: Allen Leung 3679 : leunga 1085 Date: 2002/02/21 20:20:00 EST 3680 : Tag: leunga-20020221-peephole 3681 : 3682 : Regenerated the peephole files. Some contained typos in the specification 3683 : and some didn't compile because of pretty printing bugs in the old version 3684 : of 'nowhere'. 3685 : 3686 : ---------------------------------------------------------------------- 3687 : Name: Allen Leung 3688 : leunga 1079 Date: 2002/02/19 20:20:00 EST 3689 : Tag: leunga-20020219-mlrisc-tools 3690 : Description: 3691 : 3692 : Minor bug fixes to the mlrisc-tools library: 3693 : 3694 : 1. Fixed up parsing colon suffixed keywords 3695 : 2. Added the ability to shut the error messages up 3696 : 3. Reimplemented the pretty printer and fixed up/improved 3697 : the pretty printing of handle and -> types. 3698 : 4. Fixed up generation of literal symbols in the nowhere tool. 3699 : 5. Added some SML keywords to to sml.sty 3700 : 3701 : ---------------------------------------------------------------------- 3702 : Name: Matthias Blume 3703 : blume 1078 Date: 2002/02/19 16:20:00 EST 3704 : Tag: blume-20020219-cmffi 3705 : Description: 3706 : 3707 : A wild mix of changes, some minor, some major: 3708 : 3709 : * All C FFI-related libraries are now anchored under $c: 3710 :$/c.cm --> $c/c.cm 3711 :$/c-int.cm --> $c/internals/c-int.cm 3712 :$/memory.cm --> $c/memory/memory.cm 3713 : 3714 : * "make" tool (in CM) now treats its argument pathname slightly 3715 : differently: 3716 : 1. If the native expansion is an absolute name, then before invoking 3717 : the "make" command on it, CM will apply OS.Path.mkRelative 3718 : (with relativeTo = OS.FileSys.getDir()) to it. 3719 : 2. The argument will be passed through to subsequent phases of CM 3720 : processing without "going native". In particular, if the argument 3721 : was an anchored path, then "make" will not lose track of that anchor. 3722 : 3723 : * Compiler backends now "know" their respective C calling conventions 3724 : instead of having to be told about it by ml-nlffigen. This relieves 3725 : ml-nlffigen from one of its burdens. 3726 : 3727 : * The X86Backend has been split into X86CCallBackend and X86StdCallBackend. 3728 : 3729 : * Export C_DEBUG and C_Debug from$c/c.cm. 3730 : 3731 : * C type encoding in ml-nlffi-lib has been improved to model the conceptual 3732 : subtyping relationship between incomplete pointers and their complete 3733 : counterparts. For this, ('t, 'c) ptr has been changed to 'o ptr -- 3734 : with the convention of instantiating 'o with ('t, 'c) obj whenever 3735 : the pointer target type is complete. In the incomplete case, 'o 3736 : will be instantiated with some "'c iobj" -- a type obtained by 3737 : using one of the functors PointerToIncompleteType or PointerToCompleteType. 3738 : 3739 : Operations that work on both incomplete and complete pointer types are 3740 : typed as taking an 'o ptr while operations that require the target to 3741 : be known are typed as taking some ('t, 'c) obj ptr. 3742 : 3743 : voidptr is now a bit "more concrete", namely "type voidptr = void ptr'" 3744 : where void is an eqtype without any values. This makes it possible 3745 : to work on voidptr values using functions meant to operate on light 3746 : incomplete pointers. 3747 : 3748 : * As a result of the above, signature POINTER_TO_INCOMPLETE_TYPE has 3749 : been vastly simplified. 3750 : 3751 : ---------------------------------------------------------------------- 3752 : Name: Matthias Blume 3753 : blume 1076 Date: 2002/02/19 10:48:00 EST 3754 : Tag: blume-20020219-pqfix 3755 : Description: 3756 : 3757 : Applied Chris Okasaki's bug fix for priority queues. 3758 : 3759 : ---------------------------------------------------------------------- 3760 : Name: Matthias Blume 3761 : blume 1073 Date: 2002/02/15 17:05:00 3762 : blume 1069 Tag: Release_110_39 3763 : Description: 3764 : 3765 : blume 1073 Last-minute retagging is becoming a tradition... :-( 3766 : 3767 : This is the working release 110.39. 3768 : 3769 : ---------------------------------------------------------------------- 3770 : Name: Matthias Blume 3771 : Date: 2002/02/15 16:00:00 EST 3772 : Tag: Release_110_39-orig 3773 : Description: 3774 : 3775 : blume 1069 Working release 110.39. New bootfiles. 3776 : 3777 : blume 1073 (Update: There was a small bug in the installer so it wouldn't work 3778 : with all shells. So I retagged. -Matthias) 3779 : 3780 : blume 1069 ---------------------------------------------------------------------- 3781 : Name: Matthias Blume 3782 : blume 1068 Date: 2002/02/15 14:17:00 EST 3783 : Tag: blume-20020215-showbindings 3784 : Description: 3785 : 3786 : Added EnvRef.listBoundSymbols and CM.State.showBindings. Especially 3787 : the latter can be useful for exploring what bindings are available at 3788 : the interactive prompt. (The first function returns only the list 3789 : of symbols that are really bound, the second prints those but also the 3790 : ones that CM's autoloading mechanism knows about.) 3791 : 3792 : ---------------------------------------------------------------------- 3793 : Name: Matthias Blume 3794 : blume 1067 Date: 2002/02/15 12:08:00 EST 3795 : Tag: blume-20020215-iptrs 3796 : Description: 3797 : 3798 : Two improvements to ml-nlffigen: 3799 : 3800 : 1. Write files only if they do not exist or if their current contents 3801 : do not coincide with what's being written. (That is, avoid messing 3802 : with the time stamps unless absolutely necessary.) 3803 : 3804 : 2. Implement a "repository" mechanism for generated files related 3805 : to "incomplete pointer types". See the README file for details. 3806 : 3807 : ---------------------------------------------------------------------- 3808 : Name: Matthias Blume 3809 : blume 1066 Date: 2002/02/14 11:50:00 EST 3810 : Tag: blume-20020214-quote 3811 : Description: 3812 : 3813 : Added a type 't t_' to tag.sml (in ml-nlffi-lib.cm). This is required 3814 : because of the new and improved tag generation scheme. (Thanks to Allen 3815 : Leung for pointing it out.) 3816 : 3817 : ---------------------------------------------------------------------- 3818 : george 1065 Name: Lal George 3819 : Date: 2002/02/14 09:55:27 EST 2002 3820 : Tag: george-20020214-isabelle-bug 3821 : Description: 3822 : 3823 : Fixed the MLRISC bug sent by Markus Wenzel regarding the compilation 3824 : of Isabelle on the x86. 3825 : 3826 : From Allen: 3827 : ----------- 3828 : I've found the problem: 3829 : 3830 : in ra-core.sml, I use the counter "blocked" to keep track of the 3831 : true number of elements in the freeze queue. When the counter goes 3832 : to zero, I skip examining the queue. But I've messed up the 3833 : bookkeeping in combine(): 3834 : 3835 : else (); 3836 : case !ucol of 3837 : PSEUDO => (if !cntv > 0 then 3838 : (if !cntu > 0 then blocked := !blocked - 1 else (); 3839 : ^^^^^^^^^^^^^^^^^^^^^^^ 3840 : moveu := mergeMoveList(!movev, !moveu) 3841 : ) 3842 : else (); 3843 : 3844 : combine() is called to coalesce two nodes u and v. 3845 : I think I was thinking that if the move counts of u and v are both 3846 : greater than zero then after they are coalesced then one node is 3847 : removed from the freeze queue. Apparently I was thinking that 3848 : both u and v are of low degree, but that's clearly not necessarily true. 3849 : 3850 : 3851 : 02/12/2002: 3852 : Here's the patch. HOL now compiles. 3853 : 3854 : I don't know how this impact on performance (compile 3855 : time or runtime). This bug caused the RA (especially on the x86) 3856 : to go thru the potential spill phase when there are still nodes on the 3857 : freeze queue. 3858 : 3859 : 3860 : 3861 : 3862 : ---------------------------------------------------------------------- 3863 : blume 1058 Name: Matthias Blume 3864 : blume 1064 Date: 2002/02/13 22:40:00 EST 3865 : Tag: blume-20020213-fptr-rtti 3866 : Description: 3867 : 3868 : Fixed a bug in ml-nlffigen that was introduced with one of the previous 3869 : updates. 3870 : 3871 : ---------------------------------------------------------------------- 3872 : Name: Matthias Blume 3873 : blume 1063 Date: 2002/02/13 16:41:00 EST 3874 : Tag: blume-20020213-cmlpq 3875 : Description: 3876 : 3877 : Added new priority queue export symbols (which have just been added to 3878 : smlnj-lib.cm) to CML's version of smlnj-lib.cm. (Otherwise CML would 3879 : not compile and the installer would choke.) 3880 : 3881 : ---------------------------------------------------------------------- 3882 : Name: Matthias Blume 3883 : blume 1062 Date: 2002/02/13 16:15:00 EST 3884 : Tag: blume-20020213-various 3885 : Description: 3886 : 3887 : 1. More tweaks to ml-nlffigen: 3888 : 3889 : - better internal datastructures (resulting in slight speedup) 3890 : - "-match" option requires exact match 3891 : - "localized" gensym counters (untagged structs/unions nested within 3892 : other structs/unions or within typedefs get a fresh counter; their 3893 : tag will be prefixed by a concatenation of their parents' tags) 3894 : - bug fixes (related to calculation of transitive closure of types 3895 : to be included in the output) 3896 : 3897 : 2. Minor Basis updates: 3898 : 3899 : - added implementations for List.collate and Option.app 3900 : 3901 : ---------------------------------------------------------------------- 3902 : Name: Matthias Blume 3903 : blume 1060 Date: 2002/02/11 15:55:00 EST 3904 : Tag: blume-20020211-gensym 3905 : Description: 3906 : 3907 : Added a "-gensym" option to command line of ml-nlffigen. This can be 3908 : used to specify a "stem" -- a string that is inserted in all "gensym'd" 3909 : names (ML structure names that correspond to unnamed C structs, unions, 3910 : and enums), so that separate runs of ml-nlffigen do not clash. 3911 : 3912 : ---------------------------------------------------------------------- 3913 : Name: Matthias Blume 3914 : blume 1059 Date: 2002/02/11 12:05:00 EST 3915 : Tag: blume-20020211-gensml 3916 : Description: 3917 : 3918 : A quick fix for a problem with GenSML (in the pgraph-util library): 3919 : Make generation of toplevel "local" optional. (Strictly speaking, 3920 : signature definitions within "local" are not legal SML.) 3921 : 3922 : Other than that: updates to INSTALL and cm/TODO. 3923 : 3924 : ---------------------------------------------------------------------- 3925 : Name: Matthias Blume 3926 : blume 1058 Date: 2002/02/08 15:00:00 EST 3927 : Tag: blume-20020208-uniquepid 3928 : Description: 3929 : 3930 : 0. Version number has been bumped to 110.38.1. NEW BOOTFILES!!! 3931 : 3932 : 1. The installer (config/install.sh) has gotten smarter: 3933 : 3934 : - Configuration options are a bit easier to specify now 3935 : (in config/targets). 3936 : - Bug in recognizing .tar.bz2 files fixed. 3937 : - Installer automatically resolves dependencies between 3938 : configuration options (e.g., if you ask for eXene, you will 3939 : also get cml -- regardless whether you asked for it or not). 3940 : - Installer can run in "quieter mode" by setting the environment 3941 : variable INSTALL_QUIETLY to "true". "Quieter" does not mean 3942 : "completely silent", though. 3943 : - Build HashCons library as part of smlnj-lib. 3944 : 3945 : 2. A new scheme for assigning persistent identifiers to compilation 3946 : units (and, by extension, to types etc.) has been put into place. 3947 : This fixes a long-standing bug where types and even dynamic values 3948 : can get internally confused, thereby compromising type safety 3949 : (abstraction) and dynamic correctness. See 3950 : 3951 : http://cm.bell-labs.com/cm/cs/who/blume/pid-confusion.tgz 3952 : 3953 : for an example of how things could go wrong until now. 3954 : 3955 : The downside of the new scheme is that pids are not quite as 3956 : persistent as they used to be: CM will generate a fresh pid 3957 : for every compilation unit that it thinks it sees for the first 3958 : time. That means that if you compile starting from a clean, fresh 3959 : source tree at two different times, you end up with different 3960 : binaries. 3961 : 3962 : Cutoff recompilation, however, has not been compromised because 3963 : CM keeps pid information in special caches between runs. 3964 : 3965 : ---------------------------------------------------------------------- 3966 : george 1053 Name: Lal George 3967 : george 1055 Date: 2002/02/07 15:34:13 EST 2002 3968 : Tag: 3969 : Description: 3970 : 3971 : Compilers that generate assembly code may produce global labels 3972 : whose value is resolved at link time. The various peephole optimization 3973 : modules did not take this in account. 3974 : 3975 : TODO. The Labels.addrOf function should really return an option 3976 : type so that clients are forced to deal with this issue, rather 3977 : than an exception being raised. 3978 : 3979 : ---------------------------------------------------------------------- 3980 : Name: Lal George 3981 : george 1053 Date: 2002/02/06 13:55:02 EST 3982 : Tag: george-20020206-ra-breakup 3983 : Description: 3984 : 3985 : 1. A bug fix from Allen. 3986 : 3987 : A typo causes extra fstp %st(0)'s to be generated at compensation 3988 : edges, which might cause stack underflow traps at runtime. This 3989 : occurs in fft where there are extraneous fstps right before the 'into' 3990 : trap instruction (in this case they are harmless since none of the 3991 : integers overflow.) 3992 : 3993 : george 1054 2. Pulled out various utility modules that were embedded in the modules 3994 : george 1053 of the register allocator. I need these modules for other purposes, but 3995 : george 1054 they are not complete enough to put into a library (just yet). 3996 : george 1053 ---------------------------------------------------------------------- 3997 : blume 1049 Name: Matthias Blume 3998 : Date: 2002/01/31 16:05:00 EST 3999 : Tag: blume-20020131-sparc-ccalls 4000 : Description: 4001 : 4002 : 1. C-calls on Sparc needlessly allocated a huge chunk (96 bytes) 4003 : of extra stack space by mistake. Fixed. 4004 : 4005 : 2. Bug in logic of handling of command-line options in ml-nlffigen fixed. 4006 : 4007 : ---------------------------------------------------------------------- 4008 : leunga 1048 Name: Allen Leung 4009 : Date: 2002/01/30 4010 : Tag: leunga-20020130-nowhere-bug-fix 4011 : Description: 4012 : 4013 : MLRISC bug fixes: 4014 : 1. Fixed a bindings computation bug in the 'nowhere' program generator tool. 4015 : 2. MachineInt.fromString was negating its value. 4016 : 4017 : ---------------------------------------------------------------------- 4018 : blume 1039 Name: Matthias Blume 4019 : blume 1047 Date: 2002/01/29 4020 : Tag: blume-20020129-INSTALL 4021 : Description: 4022 : 4023 : - Added somewhat detailed installation instructions (file INSTALL). 4024 : - Fixed curl-detection bug in config/install.sh. 4025 : - It is now possible to select the URL getter using the URLGETTER 4026 : environment variable: 4027 : 4028 : not set / "unknown" --> automatic detection (script tries wget, 4029 : curl, and lynx) 4030 : "wget" / "curl" / "lynx" --> use the specified program (script "knows" 4031 : how to properly invoke them) 4032 : other --> use \$URLGETTER directly, it must take 4033 : precisely two command-line arguments 4034 : (source URL and destination file name) 4035 : 4036 : ---------------------------------------------------------------------- 4037 : Name: Matthias Blume 4038 : blume 1044 Date: 2002/01/28 4039 : blume 1045 Tag: blume-20020128-sparc-ccalls 4040 : Description: 4041 : 4042 : - Fixed problem with calculation of "used" registers in sparc-c-calls. 4043 : - Make use of the allocParam argument in sparc-c-calls. 4044 : 4045 : ---------------------------------------------------------------------- 4046 : Name: Matthias Blume 4047 : Date: 2002/01/28 4048 : blume 1044 Tag: blume-20020128-allocParam 4049 : Description: 4050 : 4051 : John Reppy: Changes c-calls API to accept client-callback for 4052 : allocating extra stack space. 4053 : me: Corresponding changes to mlriscGen (using a dummy argument that 4054 : does not change the current behavior). 4055 : 4056 : ---------------------------------------------------------------------- 4057 : Name: Matthias Blume 4058 : blume 1040 Date: 2002/01/28 12:00:00 4059 : Tag: Release_110_38 4060 : Description: 4061 : 4062 : This time for real!!! 4063 : 4064 : ---------------------------------------------------------------------- 4065 : Name: Matthias Blume 4066 : blume 1039 Date: 2002/01/28 10:56:00 EST 4067 : Tag: blume-20020128-retraction 4068 : Description: 4069 : 4070 : 0. Retracted earlier 110.38. (The Release_110_38 tag has been replaced 4071 : with blume-Release_110_38-retracted.) 4072 : 4073 : 1. Fixed a problem with incorrect rounding modes in real64.sml. 4074 : (Thanks to Andrew Mccreight .) 4075 : 4076 : 2. A bug in ml-nlffigen related to the handling of unnamed structs, unions, 4077 : and enums fixed. The naming of corresponding ML identifiers should 4078 : now be consistent again. 4079 : 4080 : ---------------------------------------------------------------------- 4081 : leunga 1038 Name: Allen Leung 4082 : Date: 2002/01/27 4083 : Tag: leunga-20020127-nowhere 4084 : Description: 4085 : 4086 : Added a target called nowhere in the configuration scripts. 4087 : Enabling this will build the MLRISC 'nowhere' tool (for translating 4088 : programs with where-clauses into legal SML code) during installation. 4089 : 4090 : ---------------------------------------------------------------------- 4091 : blume 1036 Name: Matthias Blume 4092 : leunga 1038 Date: 2002/01/25 21:27:00 EST 4093 : blume 1039 Tag: blume-Release_110_38-retracted 4094 : blume 1037 Description: 4095 : 4096 : Call it a (working) release! Version is 110.38. Bootfiles are ready. 4097 : 4098 : README will be added later. 4099 : 4100 : blume 1039 !!! NOTE: Re-tagged as blume-Release_110_38-retracted. Original tag 4101 : (Release_110_38) removed. Reason: Last-minute bug fixes. 4102 : 4103 : blume 1037 ---------------------------------------------------------------------- 4104 : Name: Matthias Blume 4105 : blume 1036 Date: 2002/01/25 4106 : Tag: blume-20020125-ffi 4107 : Description: 4108 : 4109 : A large number of tweaks and improvements to ml-nlffi-lib and 4110 : ml-nlffigen: 4111 : 4112 : - ML represenation types have been streamlined 4113 : - getter and setter functions work with concrete values, not abstract 4114 : ones where possible 4115 : - ml-nlffigen command line more flexible (see README file there) 4116 : - some bugs have been fixed (hopefully) 4117 : 4118 : ---------------------------------------------------------------------- 4119 : george 1034 Name: Lal George 4120 : Date: 2002/01/24 4121 : Tag: george-20020124-risc-ra-interface 4122 : Description: 4123 : 4124 : There is a dramatic simplification in the interface to the 4125 : register allocator for RISC architectures as a result of making 4126 : parallel copy instructions explicit. 4127 : 4128 : ---------------------------------------------------------------------- 4129 : blume 1028 Name: Matthias Blume 4130 : blume 1032 Date: 2002/01/22 4131 : Tag: blume-20020122-x86-ccalls 4132 : Description: 4133 : 4134 : Bug fix for c-calls on x86 (having to do with how char- and 4135 : short-arguments are being handled). 4136 : 4137 : ---------------------------------------------------------------------- 4138 : Name: Matthias Blume 4139 : blume 1031 Date: 2002/01/21 4140 : Tag: blume-20020121-ff 4141 : Description: 4142 : 4143 : Another day of fiddling with the FFI... 4144 : 4145 : 1. Bug fix/workaround: CKIT does not complain about negative array 4146 : dimensions, so ml-nlffigen has to guard itself against this possibility. 4147 : (Otherwise a negative dimension would send it into an infinite loop.) 4148 : 4149 : 2. Some of the abstract types (light objects, light pointers, most "base" 4150 : types) in structure C are now eqtypes. 4151 : 4152 : 3. Added constructors and test functions for NULL function pointers. 4153 : 4154 : ---------------------------------------------------------------------- 4155 : Name: Matthias Blume 4156 : blume 1028 Date: 2002/01/18 4157 : blume 1030 Tag: blume-20020118-ready-for-new-release 4158 : Description: 4159 : 4160 : Made config/srcarchiveurl point to a new place. (Will provide boot 4161 : files shortly.) 4162 : 4163 : Maybe we christen this to be 110.38? 4164 : 4165 : ---------------------------------------------------------------------- 4166 : Name: Matthias Blume 4167 : Date: 2002/01/18 4168 : blume 1029 Tag: blume-20020118-more-ffifiddle 4169 : Description: 4170 : 4171 : Today's FFI fiddling: 4172 : 4173 : - Provided a structure CGetSet with "convenient" versions of C.Get.* and 4174 : C.Set.* that use concrete (MLRep.*) arguments and results instead 4175 : of abstract ones. 4176 : 4177 : - Provided word-style bit operations etc. for "int" representation 4178 : types in MLRep.SBitops where ranges over Char, Int, Short, 4179 : and Long. 4180 : 4181 : ---------------------------------------------------------------------- 4182 : Name: Matthias Blume 4183 : Date: 2002/01/18 4184 : blume 1028 Tag: blume-20020118-use-x86-fp 4185 : Description: 4186 : 4187 : Now that x86-fast-fp seems to be working, I turned it back on again 4188 : by default. (Seems to work fine now, even with the FFI.) 4189 : 4190 : Other than that, I added some documentation about the FFI to 4191 : src/ml-nlffigen/README and updated the FFI test examples in 4192 : src/ml-nlffi-lib/Tests/*. 4193 : 4194 : ---------------------------------------------------------------------- 4195 : leunga 1025 Name: Allen Leung 4196 : Date: 2002/01/17 4197 : Tag: leunga-20020117-x86-fast-fp-call 4198 : Description: 4199 : 4200 : 1. Fixed a problem with handling return fp values when x86's fast fp 4201 : mode is turned on. 4202 : 4203 : 2. Minor pretty printing fix for cellset. Print %st(0) as %st(0) instead 4204 : of %f32. 4205 : 4206 : 3. Added a constructor INT32lit to the ast of MLRISC tools. 4207 : 4208 : ---------------------------------------------------------------------- 4209 : blume 1021 Name: Matthias Blume 4210 : Date: 2002/01/16 4211 : Tag: blume-20020116-ffifiddle 4212 : Description: 4213 : 4214 : More fiddling with the FFI interface: 4215 : 4216 : - Make constness 'c instead of rw wherever possible. This eliminates 4217 : the need for certain explicit coercions. (However, due to ML's 4218 : value polymorphism, there will still be many cases where explicit 4219 : coercions are necessary. Phantom types are not the whole answer 4220 : to modeling a subtyping relationship in ML.) 4221 : 4222 : - ro/rw coersions for pointers added. (Avoids the detour through */&.) 4223 : 4224 : - "printf" test example added to src/ml-nlffi-lib/Tests. (Demonstrates 4225 : clumsy workaround for varargs problem.) 4226 : 4227 : ---------------------------------------------------------------------- 4228 : george 1016 Name: Lal George 4229 : Date: 2002/01/15 4230 : Tag: 4231 : Description: 4232 : 4233 : 1. Since COPY instructions are no longer native to the architecture, 4234 : a generic functor can be used to implement the expandCopies function. 4235 : 4236 : 2. Allowed EXPORT and IMPORT pseudo-op declarations to appear inside a 4237 : TEXT segment. 4238 : 4239 : ---------------------------------------------------------------------- 4240 : blume 1011 Name: Matthias Blume 4241 : blume 1015 Date: 2002/01/15 4242 : Tag: blume-20020115-ffiupdates 4243 : Description: 4244 : 4245 : 1. Fix for bug resulting in single-precision float values being returned 4246 : incorrectly from FFI calls. 4247 : 4248 : 2. Small modifications to C FFI API: 4249 : 4250 : - memory-allocation routines return straight objects (no options) 4251 : and raise an exception in out-of-memory situations 4252 : - unsafe extensions to cast between function pointers and pointers 4253 : from/to ints 4254 : - added structure C_Debug as an alternative to structure C where 4255 : pointer-dereferencing (|*| and |*!) always check for null-pointers 4256 : - added open_lib' to DynLinkage; open_lib' works like open_lib 4257 : but also takes a (possibly empty) list of existing library handles 4258 : that the current library depends on 4259 : 4260 : ---------------------------------------------------------------------- 4261 : Name: Matthias Blume 4262 : blume 1011 Date: 2002/01/10 4263 : Tag: blume-20020110-newffigen 4264 : Description: 4265 : 4266 : 1. Updates to portable graph code. 4267 : 4268 : 2. Major update to ml-nlffigen and ml-nlffi-lib. Things are much 4269 : more scalable now so that even huge interfaces such as the one 4270 : for GTK compile in finite time and space. :-) 4271 : See src/ml-nlffigen/README for details on what's new. 4272 : 4273 : ---------------------------------------------------------------------- 4274 : george 1003 Name: Lal George 4275 : george 1009 Date: 2001/01/09 14:31:35 EST 2002 4276 : Tag: george-20011206-rm-native-copy 4277 : Description: 4278 : 4279 : Removed the native COPY and FCOPY instructions 4280 : from all the architectures and replaced it with the 4281 : explicit COPY instruction from the previous commit. 4282 : 4283 : It is now possible to simplify many of the optimizations 4284 : modules that manipulate copies. This has not been 4285 : done in this change. 4286 : 4287 : ---------------------------------------------------------------------- 4288 : Name: Lal George 4289 : george 1003 Date: 2001/12/06 16:50:13 EST 2001 4290 : Tag: george-20011206-mlrisc-instruction 4291 : Description: 4292 : george 824 4293 : george 1003 Changed the representation of instructions from being fully abstract 4294 : to being partially concrete. That is to say: 4295 : 4296 : from 4297 : type instruction 4298 : 4299 : to 4300 : type instr (* machine instruction *) 4301 : 4302 : datatype instruction = 4303 : LIVE of {regs: C.cellset, spilled: C.cellset} 4304 : | KILL of {regs: C.cellset, spilled: C.cellset} 4305 : | COPYXXX of {k: CB.cellkind, dst: CB.cell list, src: CB.cell list} 4306 : | ANNOTATION of {i: instruction, a: Annotations.annotation} 4307 : | 2021-05-19 00:49:38 | {"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": 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": 0.3424099385738373, "perplexity": 10192.295056895167}, "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/1620243989874.84/warc/CC-MAIN-20210518222121-20210519012121-00492.warc.gz"} |
http://hal.in2p3.fr/view_by_stamp.php?label=LPC-CAEN&action_todo=view&langue=en&id=in2p3-00675640&version=1 | 236 articles – 1783 references [version française]
HAL: in2p3-00675640, version 1
Nuclear Physics in Astrophysics V, Eilat : Israël (2011)
Direct radiative proton capture 23Al(p,$\alpha$)24Si studied via one-proton nuclear breakup of 24Si
(2012)
We present the results of an experimental work that studied the direct component of the radiative proton capture reaction 23Al(p,$\gamma$)24Si for its relevance in X-ray burst nucleosynthesis. The experiment was performed at GANIL using one-proton nuclear breakup reaction at intermediate energies to determine the Asymptotic Normalization Coefficient (ANC) of the system 24Si $\rightarrow$ 23Al + p. Using the ANC, we evaluated the corresponding astrophysical S factor and reaction rate.
Research team: Structure nucléaire
Subject(s) : Physics/Nuclear Experiment
in2p3-00675640, version 1 http://hal.in2p3.fr/in2p3-00675640 oai:hal.in2p3.fr:in2p3-00675640 From: Michel Lion <> Submitted on: Thursday, 1 March 2012 16:15:44 Updated on: Thursday, 24 July 2014 10:04:12 | 2014-09-19 12:06:29 | {"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": 0.5112425684928894, "perplexity": 9359.337295423396}, "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-2014-41/segments/1410657131304.74/warc/CC-MAIN-20140914011211-00062-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://solvedlib.com/n/ouneton-7cowumr-ucjn-doxalucrpfedar-grin-j277t-deina-ueas,4762745 | # Ouneton 7cowumr Ucjn DoxAlucRpfedar-Grin J277T Deina=Ueas
###### Question:
Ouneton 7 cowumr Ucjn DoxAluc Rpfedar-Grin J 277T Deina= Ueas
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https://docs.litespeedtech.com/lscache/lscjoomla/settings/ | Settings¶
You can configure LSCJoomla to work according to your site's particular needs.
LiteSpeed Cache Configuration¶
From the Joomla! Administration area, navigate to System > Global Configuration > LiteSpeed Cache. There you will find the following tabs of settings that you may adjust as needed:
Basic Tab¶
On this tab, you can turn caching on and off, determine the length of time to cache the site, define purging behavior on updates, and turn logging on and off.
Enable LiteSpeed Cache¶
By default, caching is already enabled once you install and enable the plugin. If you need to stop caching your site for whatever reason, you can press Disable to turn it off. Simply press Enable to get it back up and running again.
Public Cache TTL¶
"TTL" stands for "Time to Live," and it refers to the length of time a web page is valid within the cache. The default is 2000 minutes, but if you have a site that updates frequently, you might want to make that number smaller. Similarly, if you have a site that is fairly static and rarely changes, you can make that number much larger.
Note
LSCache’s "smart purge" technology allows you to confidently set a high TTL, knowing that if content changes during that time, the cache will automatically be purged for any pages that are relevant to that change.
Purge All on Plugin Update¶
If you are concerned that plugin updates are going to change some of the pages of your site (thereby causing the cached copies to become outdated), then you should enable this setting. It’s disabled by default, because usually plugin updates have minimal effect (if any) on the displayed content.
Purge All on Language Update¶
This is similar to the previous setting, except it refers to language updates, and it is enabled by default.
Logging Level¶
You can leave logging off in most cases. It’s handy to turn on logging when you are trying to diagnose a problem. If you’ve contacted our support team for help with an issue, chances are we’ll ask you to turn on logging and we’ll also tell you which level would be appropriate.
Tip
If you are turning on LSCJoomla's logging, you might also want to enable Joomla's own debug log. Visit Extensions > Plugins, find the System - Debug plugin, visit the Logging tab, and set Log Almost Everything to Yes. Now you should be able to see Joomla logs in /home/YOUR_ACCOUNT/public_html/administrator/logs, or another folder defined in System > Global Configuration > System > Path to Log Folder.
Any time you turn on logging, it should be temporary, as logs can eat up disk space pretty quickly.
Exclude Rules Tab¶
Your site may have pages that should not be cached. This tab allows you to specify exceptions. Any pages covered by the following rules will not be cached.
Exclude Components¶
If you have site components that behave oddly when cached, you can exclude them here. Put your cursor in the box, and a list of available components will appear. Select any component(s) you wish to add to the exclude list. By default the "Users" component is not cached.
This field works similarly to the previous one. Put your cursor inside the box, and select any menus to exclude. When you choose a menu, every page that is a part of that menu is excluded from the cache.
Exclude URLs¶
Use this box to enter individual paths that should not be cached. Enter the paths one per line. You may use regular expressions.
Verify a Page is Not Being Cached¶
If you have configured LSCache to exclude certain content, you can use this method to verify that it works as expected:
1. From a non-logged-in browser, navigate to the page, open the Network tab in the developer tools, refresh the page, and click the first listed resource. This should be the URI of the page, as described above.
2. Look for the X-LiteSpeed-Cache-Control: no-cache header. If you find it, then the page has successfully not been served via LSCache.
It's also a good idea to make sure that the browser is not caching the page. For that to be true, you need to look for two headings: - cache-control: no-cache, must-revalidate, max-age=0 - expires: Wed, 11 Jan 1984 05:00:00 GMT
Tip
The date in the expires header can be any date that is prior to the current date.
If either of those headers is not present, or has a different value, the browser is likely caching your page. This can lead to serving outdated or stale content. Typically, browser caching is accidentally enabled via bad optimization rules that add the cache control header to dynamic requests. Check your .htaccess file to fix this
You can set up ESI here (a must if you are trying to cache an ecommerce site), give yourself the ability to clear the cache from a secure link outside of Admin, set a different TTL for the homepage, and set up LSCache to save separate views for mobile and desktop.
ESI Feature Enabled¶
LiteSpeed's implementation of ESI (Edge Side Includes) brings caching to the next level by allowing you to mix public and private content on a single page, and still serve that page from cache. ESI is an important aspect of any eCommerce caching strategy.
ESI must be enabled both in the plugin and at the server level. ESI is enabled by default in the plugin (but you can turn it off, if you don't need it). The ESI feature is disabled by default at the server level. You will need to enable ESI in LiteSpeed Enterprise before using ESI-related features in the plugin.
Warning
OpenLiteSpeed does not support ESI, so you cannot use this feature with OpenLiteSpeed.
Want to learn more about ESI? This blog post explains it in some depth.
Render Login Module as ESI¶
This setting is enabled by default. It allows you to "punch a hole" for the login module on any page where it appears, so that those pages may continue to be cached publicly, while the login module itself is cached privately.
Without ESI, every page that contains a login module would need to be cached privately or not at all after a user logs in.
Note
If you have already configured the login module separately in the LiteSpeed Cache Settings (ESI Module Settings) screen, this setting will not override your previous configuration.
Homepage Public Cache TTL¶
Use this setting to choose a different TTL than the other pages on your site. This is useful if you have a static home page (set the TTL very high) or a home page that changes much more frequently than the rest of the site (set the TTL very low). The default is 2000 minutes, which is the same as the default main TTL setting.
Separate View for Mobile Device¶
This option enables users to display a separate HTML for mobile and desktop views. This is primarily used for non-responsive themes, but can also be used in situations where different modules are loaded depending on browser type.
Display Purge Message¶
This setting controls whether you see a message each time the cache is purged. It's enabled by default, but if you don't need to see a notification, you can disable the settings.
Clean Cache Secure Words¶
Sometimes you don't want to go to the bother of logging in to the Administration area in order to purge the cache. With this setting you don't have to. Specify a secure string to attach to the end of a special URL, and you may clear the cache at any time by visiting that URL from your browser.
For example, if your Clean Cache Secure Words is set to abracadabra, then you could clear the cache by visiting the following URL:
http://example.com/joomlapath/index.php?option=com_lscache&cleancache=abracadabra
We do recommend you choose something more secure than abracadabra, though.
If the cache was successfully cleared, you will see the confirmation message, All LiteSpeed Cache Purged!.
Web interface to purge all LiteSpeed Cache¶
To manually purge all LiteSpeed Cache from the web interface, click the Web interface to purge all LiteSpeed Cache URL. You can bookmark this URL to avoid logging into the Joomla backend in the future.
Web interface to rebuild all LiteSpeed Cache¶
To manually start the crawler to rebuild all LiteSpeed Cache, click the Web interface to rebuild all LiteSpeed Cache URL. You can also set up a cron job to do this periodically.
To run the above crawler, your curl_exec cannot be disabled in your php.ini settings. Also you will need to enable the crawler feature at the server level, which is most likely disabled by default, if you are on shared hosting. You may need to contact your hosting provider.
If curl_exec was disabled from php.ini, you may see an error similar to:
Warning: curl_exec() has been disabled for security reasons in /home/joomla/public_html/plugins/system/lscache/lscache.php on line 1564
If the crawler feature is not enabled at the server level, you may see an error like the following:
Run Crawler Once Manually¶
You can click the Web interface to rebuild all LiteSpeed Cache link to run the crawler manually. It will only run once until completion.
Run Crawler as Cron Job¶
To set up the crawler as a cron job, you can simply use curl to retrieve the cachelink URL (please replace the URL with your own value):
curl -N https://yourdomain.com/index.php?option=com_lscache&recache=1234567890abcdef1234567890abcdef
Example
Set up the above cron job daily to run at 0:00, in crontab -e user:
0 0 * * * curl -N https://yourdomain.com/index.php?option=com_lscache&recache=1234567890abcdef1234567890abcdef
Tip
If your website blocks requests from empty user agents, and returns either a 443 or 406 error, you can use this curl command instead:
curl -N --user-agent "Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1)" "https://yourdomain.com/index.php?option=com_lscache&recache=1234567890abcdef1234567890abcdef"
How to Keep the Page Cached More Often¶
The Homepage Public Cache TTL (minutes) setting defines how long before the cache will be expired. The default setting is 2000 minutes, which is around 33 hours.
To keep the page cached most of the time, you can either set a longer Time to Live (TTL) to make the cache valid for a longer time, or run the crawler periodically before the TTL is up and the cache expires. For example, for a 2000 minute TTL, running the crawler cron job daily will keep the pages cached all the time.
Logged-in Users Tab¶
These settings pertain to caching for users who are logged in. By default caching for logged-in users is disabled.
Override ESI Feature¶
This setting determines whether the global ESI setting should be honored for logged-in users. You may wish to have ESI enabled for logged-in users at all times, regardless of whether it's enabled for guests. In that case, select Always Enabled.
By default Do Not Override is selected, which means that logged-in users will have ESI enabled or disabled according to the global settings.
Show Cache Content for Logged-in Users¶
When this setting is enabled, logged-in users are served cached content. It's disabled by default, which means that once a user logs in, they are no longer served from cache at all.
Separate Cache Copy for Logged-in Users¶
LiteSpeed Cache can store multiple cached copies of the same page. This setting configures whether to do this for logged-in users, and if so, how many copies should be saved.
1. Disabled: logged-in users and logged-out users are both served from public cache and only one cache copy is stored. This is the default behavior.
2. for All Users: there will be two copies of the page stored in public cache: one for all logged-out users to share, and one for all logged-in users to share.
3. by User Group: one copy is stored for all logged-out users, but then there are multiple copies stored for logged-in users based on their user group. So, if you have three user groups, there would be three logged-in cache copies: one customized to each group.
Note
This setting is dependent on Show Cache Content for Logged-in Users. If that setting is disabled, then this one is ignored.
This setting is the same as the Exclude Menus setting on the Exclude Rules tab, however it only applies to logged-in users.
If you have already excluded menus from public cache, there is no need to repeat the exclusions here. Any menus added here will be excluded in addition to those.
Exclude URLs¶
Similar to the above setting, this one is the same as the Exclude URLs setting on the Exclude Rules tab, and it, too, only applies to logged-in users.
If you have already excluded URLs from public cache, there is no need to repeat the exclusions here. Any URLs added here will be excluded in addition to those.
Recache Tab¶
Usually, when a page is purged from the cache, it remains uncached until a visitor comes along and requests the page. These settings change that behavior.
Auto Recache¶
With Auto Recache enabled, LiteSpeed will automatically re-cache purged pages, which means that your site’s visitors will have a lower chance of ever encountering uncached content. It's a good thing to keep your cache warm in this manner, however it has the potential to impact server performance.
If you have plenty of resources, and server performance isn't at risk, choose Aggressive. The aggressive option is very thorough about recaching all of the pages that are related to a particular purge. If you prefer to use fewer resources, select Moderate, which recaches most of the related pages, but may miss some of them.
Note
Auto Recache doesn't kick in after an automatic Purge All command. If you wish to re-populate the cache in that event, you will need to do so manually from the LiteSpeed Cache Settings (ESI Module Settings) screen, located in the Components menu.
Auto Recache Max Duration¶
Another way to control server impact is by setting a maximum recaching duration. For example, you can specify that the server should spend at most 10 seconds recaching content. After that, it should stop, even if all of the recaching is not complete. The default value here is 5 seconds, but you can adjust that based on what your server can handle.
Recache Component Generated URLs¶
This option allows you to recache URLs that are generated by a component but are not part of the menu system.
Permissions Tab¶
This is a standard Joomla! permissions page, and every setting defaults to Inherited. There should be no need to change anything here.
Support Tab¶
Technically, this screen doesn't contain settings at all, but simply links to places where you can get support.
Slack¶
Join our Slack community, then join the #joomla-cache channel.
Wiki¶
The LSCJoomla wiki has been deprecated in favor of this new documentation, which you are reading right now. If you need it, the permalink is: https://docs.litespeedtech.com/lscache/lscjoomla/
Github¶
Check out the extension's open source code in our GitHub repository.
ESI Settings¶
ESI allows you to cache certain blocks on your site differently than the rest of the page. This is useful for eCommerce, for example, as you could cache a shopping cart module in private cache, while the rest of the page remained in public cache.
LiteSpeed Cache for Joomla allows you to set up any module as an ESI block. ESI module cache is independent from page cache, and may be shared by multiple pages with different cache settings.
ESI Module Cache Types¶
There are three ways to cache an ESI module:
• Public: ESI module will be cached, and the cache will be shared by all visitors
• Private: ESI module will be cached with a separate individualized copy for each visitor
• None: ESI module will not be cached (not recommend)
ESI module cache settings work independently of the page cache. It doesn't matter whether the page they appear on is in public cache, private cache, or is not cached at all (though, there is no real benefit to using ESI on an uncached page).
Where to Set¶
Navigate to Components > LiteSpeed Cache. You should see a list of Normal Modules.
How to Set¶
Select the listed module you want to be rendered as ESI, and click the Render Modules as ESI button. In the above screenshot, the Search module has been selected. You will see that once you press the button, the screen will change, and will display only the ESI modules.
Tip
You can get back to the Normal Modules view via the drop-down box where ESI Modules is currently displayed.
From the ESI Modules view, you can click on the module name to bring up the options for that module.
ESI Module Cache Type¶
Public is the default ESI Module Cache Type option. You may want to choose Private for modules with personalized information, such as Login and Shopping Cart modules. Only select None when the module is absolutely not cache compatible. Having any uncached content on a page will slow that page down dramatically, so if you can avoid having uncached ESI modules, we recommend that you do avoid it.
ESI Module Cache Timeout¶
Set the time (in minutes) that the content of this module can be considered valid.
ESI Module Type¶
Your ESI modules may be Normal or Advanced. The normal ESI modules are rendered quickly, but do not support plugins. If a plugin is important to the content of your ESI block, select Advanced. The rendering will be slower, but the plugin will be supported.
Revert Back to Normal Module¶
In the ESI Modules view, select the module you want to revert, and click the Render Module As Normal button. The module will no longer be rendered as an ESI module.
Last update: January 26, 2021 | 2021-03-02 13:47:27 | {"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": 0.17308759689331055, "perplexity": 3127.9879184035913}, "config": {"markdown_headings": false, "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-2021-10/segments/1614178364008.55/warc/CC-MAIN-20210302125936-20210302155936-00013.warc.gz"} |
http://meetings.aps.org/Meeting/GEC06/SessionIndex3/?SessionEventID=50799 | ### Session BT1: Plasma Sources I
Chair: A.R. Ellingboe, Dublin City University, Ireland
Room: Holiday Inn Salon CD
Tuesday, October 10, 2006 8:00AM - 8:15AM BT1.00001: Electron beam-generated ion-ion plasmas: Etching and diagnostics S.G. Walton , D. Leonhardt , R.F. Fernsler Positive ion-negative ion (ion-ion) plasmas are those where negative ions are the primary negative charge carrier and in the absence of any significant electron density, these negative ions are not confined to the bulk plasma. Thus, a nearly equal and anisotropic flux of positive and negative ions can be delivered to surfaces located adjacent to the plasma and eliminate electron-induced damage to substrates in etching applications. A requirement for the formation of ion-ion plasmas in low pressure, halogen-based gas backgrounds is a low electron energy so that the attachment rate is comparable to the ionization rate and the plasma electrons can be rapidly converted to negative ions. Electron beam-generated plasmas provide an opportunity to investigate ion-ion plasmas and their potential applications because of their uniquely low electron temperature compared to conventional discharges. In this presentation, we discuss recent investigations of ion-ion plasmas formed in pulsed, electron beam-generated plasmas produced in mixtures of SF$_{6 }$and their use in silicon etching. In this system, positive and negative ions were extracted using a low frequency (10-50 kHz), low voltage (0-300 V) bias. The results of Si etching experiments and plasma diagnostics will be presented with the goal of understanding the optimum system configuration and operating conditions. Tuesday, October 10, 2006 8:15AM - 8:30AM BT1.00002: Automated method for creating arbitrary substrate voltage wave forms for manipulating energy distribution of bombarding ions during plasma processing Amy Wendt , Marlann Patterson , Hsuan-Yih Chu Accurate and reproducible control of ion bombardment energy during plasma processing is a means to better understand the nature of plasma-surface interaction and to control process outcomes. Ion energy distribution (IED) control can be achieved by tailoring the wave form shape of an rf bias applied to the substrate during processing, through the use of a programmable wave form generator in combination with a power amplifier. Due to the frequency dependence of the amplifier gain and the impedance of the plasma in contact with the substrate, however, it is not practical to predict the shape of wave form needed at the generator to produce a desired result at the substrate. Introduced here is a systematic approach using feedback control in the frequency domain to produce arbitrary wave form shapes at the substrate. Specifically, a fast Fourier Transform (FFT) of the substrate wave form is compared, one frequency at a time, with the FFT of a desired “target” wave form, to determine adjustments needed at the generator. This iterative procedure, which is fully automated and tested for several target wave form shapes, is repeated until the substrate wave form converges to the targeted shape, providing a quick systematic method for producing an arbitrary IED at the substrate. Tuesday, October 10, 2006 8:30AM - 8:45AM BT1.00003: Scaling laws in dc micro discharges Marija Radmilovic-Radjenovic , Zoran Petrovic , Branislav Radjenovic , Paule Maguire , Charles Mahony In order to establish the operation regime of micro discharges we should start from the low pressure discharges and employ the standard scaling laws. Discharges should scale according to the reduced electric field $E/N$ and $p$d - product proportional to the number of collisions. Finally, the scaling should be made in accordance with the $jd^2$ - describing the space charge effects [1]. We have calculated the Paschen curves and Volt- Ampere characteristic by using a PIC code and appropriate data for argon in order to establish whether the standard micro discharges operate in Townsend regime or in Glow Regime. \newline [1] A.V.Phelps, Z.Lj.Petrovi\'{c} and B.M.Jelenkovi\'{c}, Phys. Rev. E \textbf{47} 2825 (1993) Tuesday, October 10, 2006 8:45AM - 9:00AM BT1.00004: Hydrodynamic models for the positive column with neutral gas depletion. Jean-Luc Raimbault , Laurent Liard , Pascal Chabert In the classical low-temperature plasma equilibrium, the ionization degree is sufficiently small that neutral density is considered constant. However, in many contemporary plasma reactors, such as helicons, the ionized fraction can be significant. This fraction may even reach 100\% in plasma thrusters. In such circumstances, neutral dynamics has to be included in order to solve the plasma equilibrium. We have revisited the plasma equilibrium models, from low-pressure (Tonks-Langmuir) to high pressure (ambipolar diffusion) regime, including the neutral dynamics. The results show that neutrals are pushed towards the wall by the electronic pressure, creating a neutral depletion at the center of the discharge. The effect is significant when the electronic pressure becomes comparable to the neutral pressure. The electron temperature becomes a function of the electron density, so that particle and power balance are not decoupled. Finally, we derived a new expression for the edge-to-center electron density ratio which accounts for neutral density depletion. Tuesday, October 10, 2006 9:00AM - 9:15AM BT1.00005: Numerical Simulation of the DC Discharge Using CFD-ACE+ Ning Zhou , Peng Zhang A low pressure DC discharge is simulated using the CFD-ACE+. The electron kinetics is obtained from the kinetic module. The local and non-local approaches are used separately for solving the kinetic equation. The results are compared at different locations in the discharge. It is shown that although the local approximation gives a good description of the electron energy distribution function (EEDF) in the bulk plasma, it fails to give accurate information of the EEDF near the wall, which is highly non-Maxwellian. As a result, the non-local approach is more appropriate for the kinetic treatment of plasma electrons in a low pressure DC discharge. The ion number density and momentum are obtained from a fluid model. For comparison, the electron continuity equations are also included. Based on the simulation model, the species' density profile, the power balance and the influence of the electron-electron coulomb collisions on the EEDF and discharge physics are investigated. The simulation results are also compared with results from pure fluid model without kinetic description. Tuesday, October 10, 2006 9:15AM - 9:30AM BT1.00006: Simulation of moving striations in rare gas plasmas Vladimir Kolobov , Robert Arslanbekov Ionization waves (moving striations) have been observed in classical DC discharges of rare gases in a wide range of gas pressures and discharge currents. Recently, striations have been also observed in plasma display cells and other micro-discharges. We have obtained moving striations in computer experiments using self-consistent discharge model. The model includes Boltzmann solver for electron kinetics, fluid model for ion transport, Poisson equation for the electric field and (optionally) an external circuit model. Simulations are performed from cathode to anode in 1d or 2d settings. Striations appear initially near the cathode and propagate towards the anode as observed in experiments. The model allows studies of nonlinear waves and effects of external circuit on the wave properties. We will discuss the mechanism of striations for different operating conditions and present results of simulations for a DC discharge in Argon gas for a typical pressure of 1 Torr, tube radius R=1 cm, for different discharge currents. High sensitivity of striations to the state of electron gas and ionization kinetics makes them an ideal tool for testing discharge models and advanced plasma diagnostics. | 2013-05-20 14:02:10 | {"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": 0.5103516578674316, "perplexity": 1882.8866564762782}, "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-2013-20/segments/1368699036375/warc/CC-MAIN-20130516101036-00091-ip-10-60-113-184.ec2.internal.warc.gz"} |