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https://whateversuitsyourboat.wordpress.com/2012/01/04/rt-part-8-hales-jewett-and-how-to-make-tic-tac-toe-interesting/	## RT Part 8; Hales-Jewett and how to make Tic-Tac-Toe Interesting A preliminary note: I am beginning to lose steam on Ramsey theory. I want to move on to a few other things and so I will probably gloss over or postpone a few topics that I planned on getting to. In my first post I said that I would cover what I have covered so far as well as the Hales-Jewett theorem, the growth of Ramsey numbers, sparse Ramsey theory, and probabilistic results. I will cover HJ today, sparse RT next time, and postpone the rest. Alrighty, now back to math. The Hales-Jewett theorem is one about combinatorial lines. So first we must define what those are. Even though the definition makes them sound more confusing than they really are, let’s start there. Definition. Let $X$ be a finite set and let $X^n$ denote $n$-tuples over the alphabet $X$. A set $L \subseteq X^n$ is called a combinatorial line if there exists a nonempty $I \subseteq [n]$ and $a_i \in X$ for each $i \notin I$ such that $L = \{(x_1, \dots, x_n) \in X^n : x_i = a_i \text{ for all } i \notin I, x_i = x_j \text{ for all } i,j \in I\}.$ So some of the coordinates are fixed, the rest move in synch. The best way to picture it is by seeing an example. In $[3]^3$, (3-tuples with entries from $[3] = \{1,2,3\}$), one example of a line is $((1,1,1), (1,2,2), (1,3,3)).$ It’s completely analogous lines in $\mathbb{R}^n$, or better yet, in $\mathbb{Z}^n$. The Hales-Jewett Theorem. For each $m, k \in \mathbb{N}$, there exist some $n$ such that whenever $[m]^n$ is $k$-colored there exists a monochromatic combinatorial line. The least such $n$ is written as HJ$(m,k)$. Remarks. How this result relates to the title of this post is the following. Assume we are playing a generalization of tic-tac-toe in which there are $k$ players playing on an $n$-dimensional cube of side length $m-1$, say with one corner at the origin. Each player has a bunch of marbles of their color and they take turns placing their marbles on the lattice points of the cube. These points are obviously in bijection with the $n$-tuples whose entries come from $[m]$. The goal is to get a vertical, horizontal, or diagonal sequence of marbles, all of which are of your color, of length $m$ — i.e. from one edge of the cube to the other, usually contained within a smaller, $n$-dimensional rectangular box which is a subset of the cube. If $m=3$ and $n=k=2$, then this is tic-tac-toe. This is what $m=4$, $n=k=3$ looks like: What the Hales-Jewett theorem says is that as long as you play $k$-person, $m$-in-a-row tic-tac-toe in enough dimensions, you can guarantee that the game will not end in a draw! So tic-tac-toe may seem like a silly game in which a player has to make a really boneheaded move to have the game not end in a draw. But that’s only because you are playing on a measly 2 dimensional board. And even just 3-in-a-row, 2-person tic-tac-toe requires more than two dimensions for the game to be interesting. Now, it does turn out that when playing in enough dimensions to guarantee that the game won’t end in a draw, the first player to move, if they play perfectly, will be guaranteed to win (try to prove this). But this is not immediately obvious, so I will still assert that the new game is still “interesting” – as is chess, even if it is one day proved to solvable. Our second remark is that HJ implies Van Der Waerden’s theorem which we talked about last time. Given a coloring $c : \mathbb{N} \to [k]$ of $\mathbb{N}$, create a coloring $c'$ of $[m]^n$ by $c'((x_1, \dots, x_n)) = c((x_1 + \dots + x_n))$. And note that a combinatorial line in $[m]^n$ (which will have length $m$) gives a monochromatic arithmetic progression in $\mathbb{N}$ of length $m$. Now I will briefly sketch a proof of the HJ theorem. Proof. The proof is by induction on $m$. If $m=1$ it is trivial. Assume $m > 1$. I claim that for all $r \leq k$, there exists an $n$ such that whenever $[m]^n$ is $k$-colored there either exists a monochromatic line or there exist $r$ color-focused lines. The proof of the claim is by induction on $r$. $r=1$ is trivial. If $n =$ HJ$(m-1,k)$ is suitable for $r-1$, then one can show that $n + \text{HJ}(m-1, k^{m^n})$ is suitable for $r$. The rest of the claim is an exercise in focusing. This finishes it off since we can then set $r=k$ and look at the color of the focus. $\square$ Next time we will finish off this sequence of posts on Ramsey theory by talking about one of my favorite topics: sparse Ramsey theory. Advertisements ## About Jay Cummings I am a fifth year mathematics Ph.D. student at UCSD. This entry was posted in Combinatorics, Ramsey Theory. Bookmark the permalink.	2018-12-11 18:30:20	{"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": 58, "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": 0.8405998349189758, "perplexity": 508.61575774386193}, "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-2018-51/segments/1544376823674.34/warc/CC-MAIN-20181211172919-20181211194419-00065.warc.gz"}
http://www.engineeringintro.com/category/mechanics-of-structures/	# Mechanics Archive ## Types of Bending Stresses Types of Bending Stresses: Bending stresses are those that bend the beam because of beam self-load and external load acting on it. Bending stresses are of two types; Pure Bending Simple Bending Pure Bending: Bending will be called as pure …	2017-04-25 06:38:58	{"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": 0.9522535800933838, "perplexity": 6612.387197616839}, "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/1492917120187.95/warc/CC-MAIN-20170423031200-00452-ip-10-145-167-34.ec2.internal.warc.gz"}
http://openstudy.com/updates/50a52da1e4b044c2b5faa715	## LonelyCountrieChic 3 years ago Photosynthesis and cellular respiration are often described in two ways: (1) they are chemically opposite; and (2) they have a relationship to each other. Explain what these two statements mean. Be sure to include the specific substances used and released by each process. • This Question is Open 1. Geckoh2o Photosynthesis takes in Carbon dioxide and produces Oxygen. Cellular Respiration takes in oxygen and produces Carbon Dioxide 2. DylanJC Okay let's look at the basics of photosynthesis: it takes sunlight (energy), water and carbon dioxide to produce glucose and oxygen. this is the chemical formula: $Energy + 6H_2O+6CO_2 \rightarrow C_6H_{12}O_6+6O_2$ 3. DylanJC Okay now the basics of Cellular respiration: Takes glucose, oxygen to make water carbon dioxide and heat (enegry) 4. Geckoh2o one relationship to eachother is that they need each other to function 5. Geckoh2o also listen to the guy above me he knows what hes talking about haha 6. DylanJC This is the equation: $C_6H_{12}O_6 + 6O_2 \rightarrow 6H_2O + 6CO_2 + Energy$ 7. LonelyCountrieChic Thanks y'all! 8. DylanJC So just by looking at the equations we can see that they are opposite. And we can also see that what plants produce, we consume! and what we produce, plants consume! its a beautiful codependent symbiosis	2016-02-13 17:24:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.453325092792511, "perplexity": 3177.170406290759}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701167113.3/warc/CC-MAIN-20160205193927-00120-ip-10-236-182-209.ec2.internal.warc.gz"}
http://server3.wikisky.org/starview?object_type=1&object_id=5178&object_name=HR+216&locale=EN	WIKISKY.ORG Home Getting Started To Survive in the Universe News@Sky Astro Photo The Collection Forum Blog New! FAQ Press Login # 60 Psc Contents ### Images DSS Images Other Images ### Related articles Eleven New γ Doradus StarsWe present new high-dispersion spectroscopic and precise photometricobservations to identify 11 new γ Doradus variables. Seven ofthese new γ Doradus stars appear to be single, three are primariesof single-lined binaries, and one has two distant visual companions;none are double-lined or close visual binaries. Several of the starsshow spectroscopic line-profile and low-amplitude radial velocityvariability indicative of pulsation. All 11 stars are photometricallyvariable with amplitudes between 8 and 93 mmag in Johnson B and periodsbetween 0.398 and 2.454 days. One star is monoperiodic; the rest havebetween two and five independent periods. The variability at all periodsapproximates a sinusoid, although three of the stars exhibitcycle-to-cycle variation in the level of maximum brightness, similar tothe Blazhko effect observed in some RR Lyrae stars. We provide a newtabulation of all 54 γ Doradus stars confirmed to date and listsome of their properties. All are dwarfs or subgiants and lie within awell-defined region of the H-R diagram that overlaps the cool edge ofthe δ Scuti instability strip. Four of the new γ Doradusvariables from this paper also lie within the δ Scuti instabilitystrip but do not exhibit the additional higher frequency variabilitytypical of δ Scuti stars. The variability type of several of thesestars given in the General Catalog of Variable Stars and in SIMBADshould now be revised. Statistical Constraints for Astrometric Binaries with Nonlinear MotionUseful constraints on the orbits and mass ratios of astrometric binariesin the Hipparcos catalog are derived from the measured proper motiondifferences of Hipparcos and Tycho-2 (Δμ), accelerations ofproper motions (μ˙), and second derivatives of proper motions(μ̈). It is shown how, in some cases, statistical bounds can beestimated for the masses of the secondary components. Two catalogs ofastrometric binaries are generated, one of binaries with significantproper motion differences and the other of binaries with significantaccelerations of their proper motions. Mathematical relations betweenthe astrometric observables Δμ, μ˙, and μ̈ andthe orbital elements are derived in the appendices. We find a remarkabledifference between the distribution of spectral types of stars withlarge accelerations but small proper motion differences and that ofstars with large proper motion differences but insignificantaccelerations. The spectral type distribution for the former sample ofbinaries is the same as the general distribution of all stars in theHipparcos catalog, whereas the latter sample is clearly dominated bysolar-type stars, with an obvious dearth of blue stars. We point outthat the latter set includes mostly binaries with long periods (longerthan about 6 yr). The Rotation of Binary Systems with Evolved ComponentsIn the present study we analyze the behavior of the rotational velocity,vsini, for a large sample of 134 spectroscopic binary systems with agiant star component of luminosity class III, along the spectral regionfrom middle F to middle K. The distribution of vsini as a function ofcolor index B-V seems to follow the same behavior as their singlecounterparts, with a sudden decline around G0 III. Blueward of thisspectral type, namely, for binary systems with a giant F-type component,one sees a trend for a large spread in the rotational velocities, from afew to at least 40 km s-1. Along the G and K spectral regionsthere are a considerable number of binary systems with moderate tomoderately high rotation rates. This reflects the effects ofsynchronization between rotation and orbital motions. These rotatorshave orbital periods shorter than about 250 days and circular or nearlycircular orbits. Except for these synchronized systems, the largemajority of binary systems with a giant component of spectral type laterthan G0 III are composed of slow rotators. Catalogue of Apparent Diameters and Absolute Radii of Stars (CADARS) - Third edition - Comments and statisticsThe Catalogue, available at the Centre de Données Stellaires deStrasbourg, consists of 13 573 records concerning the results obtainedfrom different methods for 7778 stars, reported in the literature. Thefollowing data are listed for each star: identifications, apparentmagnitude, spectral type, apparent diameter in arcsec, absolute radiusin solar units, method of determination, reference, remarks. Commentsand statistics obtained from CADARS are given. The Catalogue isavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcar?J/A+A/367/521 Photometric Variability in a Sample of 187 G and K GiantsWe have used three automatic photoelectric telescopes to obtainphotometric observations of 187 G, K, and (a few) M0 field giants. Wefind low-amplitude photometric variability on timescales of days toweeks on both sides of the coronal dividing line (CDL) in a total of 81or 43% of the 187 giants. About one-third of the variables haveamplitudes greater than 0.01 mag in V. In our sample the percentage ofvariable giants is a minimum for late-G spectral classes and increasesfor earlier and later classes; all K5 and M0 giants are variable. Wealso obtained high-resolution, red wavelength spectroscopic observationsof 147 of the giants, which we used to determine spectralclassifications, vsini values, and radial velocities. We acquiredadditional high-resolution, blue wavelength spectra of 48 of the giants,which we used to determine chromospheric emission fluxes. We analyzedthe photometric and spectroscopic observations to identify the cause(s)of photometric variability in our sample of giants. We show that thelight variations in the vast majority of G and K giant variables cannotbe due to rotation. For giants on the cool side of the CDL, we find thatthe variability mechanism is radial pulsation. Thus, the variabilitymechanism operating in M giants extends into the K giants up to aboutspectral class K2. On the hot side of the CDL, the variability mechanismis most likely nonradial, g-mode pulsation. Speckle Interferometry of New and Problem HIPPARCOS BinariesThe ESA Hipparcos satellite made measurements of over 12,000 doublestars and discovered 3406 new systems. In addition to these, 4706entries in the Hipparcos Catalogue correspond to double star solutionsthat did not provide the classical parameters of separation and positionangle (rho,theta) but were the so-called problem stars, flagged G,''O,'' V,'' or X'' (field H59 of the main catalog). An additionalsubset of 6981 entries were treated as single objects but classified byHipparcos as suspected nonsingle'' (flag S'' in field H61), thusyielding a total of 11,687 problem stars.'' Of the many ground-basedtechniques for the study of double stars, probably the one with thegreatest potential for exploration of these new and problem Hipparcosbinaries is speckle interferometry. Results are presented from aninspection of 848 new and problem Hipparcos binaries, using botharchival and new speckle observations obtained with the USNO and CHARAspeckle cameras. A catalog of rotational and radial velocities for evolved starsRotational and radial velocities have been measured for about 2000evolved stars of luminosity classes IV, III, II and Ib covering thespectral region F, G and K. The survey was carried out with the CORAVELspectrometer. The precision for the radial velocities is better than0.30 km s-1, whereas for the rotational velocity measurementsthe uncertainties are typically 1.0 km s-1 for subgiants andgiants and 2.0 km s-1 for class II giants and Ib supergiants.These data will add constraints to studies of the rotational behaviourof evolved stars as well as solid informations concerning the presenceof external rotational brakes, tidal interactions in evolved binarysystems and on the link between rotation, chemical abundance and stellaractivity. In this paper we present the rotational velocity v sin i andthe mean radial velocity for the stars of luminosity classes IV, III andII. Based on observations collected at the Haute--Provence Observatory,Saint--Michel, France and at the European Southern Observatory, LaSilla, Chile. Table \ref{tab5} also available in electronic form at CDSvia anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html Catalogs of temperatures and [Fe/H] averages for evolved G and K starsA catalog of mean values of [Fe/H] for evolved G and K stars isdescribed. The zero point for the catalog entries has been establishedby using differential analyses. Literature sources for those entries areincluded in the catalog. The mean values are given with rms errors andnumbers of degrees of freedom, and a simple example of the use of thesestatistical data is given. For a number of the stars with entries in thecatalog, temperatures have been determined. A separate catalogcontaining those data is briefly described. Catalog only available atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html The Tokyo PMC catalog 90-93: Catalog of positions of 6649 stars observed in 1990 through 1993 with Tokyo photoelectric meridian circleThe sixth annual catalog of the Tokyo Photoelectric Meridian Circle(PMC) is presented for 6649 stars which were observed at least two timesin January 1990 through March 1993. The mean positions of the starsobserved are given in the catalog at the corresponding mean epochs ofobservations of individual stars. The coordinates of the catalog arebased on the FK5 system, and referred to the equinox and equator ofJ2000.0. The mean local deviations of the observed positions from theFK5 catalog positions are constructed for the basic FK5 stars to comparewith those of the Tokyo PMC Catalog 89 and preliminary Hipparcos resultsof H30. A catalogue of [Fe/H] determinations: 1996 editionA fifth Edition of the Catalogue of [Fe/H] determinations is presentedherewith. It contains 5946 determinations for 3247 stars, including 751stars in 84 associations, clusters or galaxies. The literature iscomplete up to December 1995. The 700 bibliographical referencescorrespond to [Fe/H] determinations obtained from high resolutionspectroscopic observations and detailed analyses, most of them carriedout with the help of model-atmospheres. The Catalogue is made up ofthree formatted files: File 1: field stars, File 2: stars in galacticassociations and clusters, and stars in SMC, LMC, M33, File 3: numberedlist of bibliographical references The three files are only available inelectronic form at the Centre de Donnees Stellaires in Strasbourg, viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5), or viahttp://cdsweb.u-strasbg.fr/Abstract.html Vitesses radiales. Catalogue WEB: Wilson Evans Batten. Subtittle: Radial velocities: The Wilson-Evans-Batten catalogue.We give a common version of the two catalogues of Mean Radial Velocitiesby Wilson (1963) and Evans (1978) to which we have added the catalogueof spectroscopic binary systems (Batten et al. 1989). For each star,when possible, we give: 1) an acronym to enter SIMBAD (Set ofIdentifications Measurements and Bibliography for Astronomical Data) ofthe CDS (Centre de Donnees Astronomiques de Strasbourg). 2) the numberHIC of the HIPPARCOS catalogue (Turon 1992). 3) the CCDM number(Catalogue des Composantes des etoiles Doubles et Multiples) byDommanget & Nys (1994). For the cluster stars, a precise study hasbeen done, on the identificator numbers. Numerous remarks point out theproblems we have had to deal with. A revised effective-temperature calibration for the DDO photometric systemA revised effective-temperature calibration for the David DunlapObservatory (DDO) photometric system is presented. Recently publishedphotometric and spectroscopic observations of field and open-cluster Gand K stars allow a better definition of the solar-abundance fiducialrelation in the DDO C0(45-48) vs. C0(42-45)diagram. The ability of the DDO system to predict MK spectral types of Gand K giants is demonstrated. The new DDO effective temperaturecalibration reproduces satisfactorily the infrared temperature scale ofBell and Gustafsson (1989). It is shown that Osborn's (1979) calibrationunderestimates the effective temperatures of K giants by approximately170 K and those of late-type dwarfs by approximately 150 K. Evolved GK stars near the Sun. 2: The young disk populationFrom a sample of nearly 2000 GK giants a group of young disk stars withwell determined space motions has been selected. The zero point of theluminosity calibrations, both from the ultraviolet flux (modifiedStroemgren system) and that in the region of 4200 to 4900 A (DDOsystem), show a discontinuity of about a half magnitude at the border ofthe young disk and old disk domains. The population separation is basedon the space velocity components, which are also an age discriminant,with the population interface near 2 x 109 yr, based onmodels with convective overshoot at the core. This age corresponds togiant masses near 1.7 solar mass, near the critical mass separating theyoung stars that do not burn helium in degenerate cores from older starsthat do. Ten percent of both populations show CN anomalies in that thederived value of P(Fe/H) from CN (Cm) and fromFe(M1) differ by more than 0.1 dex and the weak and strong CNstars occur equally in the old disk but the weak CN stars predominate inthe young disk. Peculiar stars, where flux distortions affect theluminosity calibrations, are of the CH+(Ba II) and CH-(weak G band)variety and represent less than 1% of the stars in both populations. Theyoung disk giants are restricted to ages greater than about109 yr, because younger stars are bright giants orsupergiants (luminosity class 2 or 1), and younger than about 2 x109 yr, because the old disk-young disk boundary occurs near1.7 solar mass. The distribution of heavy element abundances, P(Fe/H),for young disk giants is both more limited in range (+/- 0.4 dex) and isskewed toward higher abundances, compared with the nearly normaldistribution for old disk giants. The distribution of (U,V) velocityvectors gives (U,V,W) and their dispersions = (+17.6 +/- 18.4, -14.8 +/-8.4, -6.9 +/- 13.0) and (+3.6 +/- 38.4, -20.7 +/- 27.5, -6.7 +/-17.3)km/s for young and old disk giants, respectively. A critical appraisal of published values of (Fe/H) for K II-IV stars'Primary' (Fe/H) averages are presented for 373 evolved K stars ofluminosity classes II-IV and (Fe/H) values beween -0.9 and +0.21 dex.The data define a 'consensus' zero point with a precision of + or -0.018 dex and have rms errors per datum which are typically 0.08-0.16dex. The primary data base makes recalibration possible for the large(Fe/H) catalogs of Hansen and Kjaergaard (1971) and Brown et al. (1989).A set of (Fe/H) standard stars and a new DDO calibration are given whichhave rms of 0.07 dex or less for the standard star data. For normal Kgiants, CN-based values of (Fe/H) turn out to be more precise than manyhigh-dispersion results. Some zero-point errors in the latter are alsofound and new examples of continuum-placement problems appear. Thushigh-dispersion results are not invariably superior to photometricmetallicities. A review of high-dispersion and related work onsupermetallicity in K III-IV star is also given. High-resolution spectroscopic survey of 671 GK giants. I - Stellar atmosphere parameters and abundancesA high-resolution spectroscopic survey of 671 G and K field giants isdescribed. Broad-band Johnson colors have been calibrated againstrecent, accurate effective temperature, T(eff), measurements for starsin the range 3900-6000 K. A table of polynomial coefficients for 10color-T(eff) relations is presented. Stellar atmosphere parameters,including T(eff), log g, Fe/H, and microturbulent velocity, are computedfor each star, using the high-resolution spectra and various publishedphotometric catalogs. For each star, elemental abundances for a varietyof species have been computed using a LTE spectrum synthesis program andthe adopted atmosphere parameters. Large and Kinematically Unbiased Samples of G- and K-Type Stars. III. Evolved Young Disk Stars in the Bright Star SampleAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1989PASP..101...54E&db_key=AST Large and kinematically unbiased samples of G- and K-type stars. II - Observations of evolved stars in the Bright Star sample. III - Evolved young disk stars in the Bright Star sampleFour color and RI observations were obtained for a large sample ofG-type and K-type stars in the Bright Star Catalogue. Data are firstpresented for 110 evolved stars. Photometry of evolved young diskpopulation stars have then been calibrated for luminosity, reddening,and metallicity on the basis of results for members of the Hyades andSirius superclusters. New DDO results are given for 120 stars. A search for lithium-rich giant starsLithium abundances or upper limits have been determined for 644 brightG-K giant stars selected from the DDO photometric catalog. Two of thesegiants possess surface lithium abundances approaching the 'cosmic' valueof the interstellar medium and young main-sequence stars, and eight moregiants have Li contents far in excess of standard predictions. At leastsome of these Li-rich giants are shown to be evolved to the stage ofhaving convectively mixed envelopes, either from the direct evidence oflow surface carbon isotope ratios, or from the indirect evidence oftheir H-R diagram positions. Suggestions are given for the uniqueconditions that might have allowed these stars to produce or accrete newlithium for their surface layers, or simply to preserve from destructiontheir initial lithium contents. The lithium abundance of the remainingstars demonstrates that giants only very rarely meet the expectations ofstandard first dredge-up theories; the average extra Li destructionrequired is about 1.5 dex. The evolutionary states of these giants andtheir average masses are discussed briefly, and the Li distribution ofthe giants is compared to predictions of Galactic chemical evolution. Uvby-Beta Photometry of Equatorial and Southern Bright Stars - Part TwoAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1980A&AS...42..311H&db_key=AST MK spectral types for some F and G stars.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1979PASP...91...83C&db_key=AST MK classifications for F-and G-type stars. 3.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1974AJ.....79..682H&db_key=AST Catalog of Indidual Radial Velocities, 0h-12h, Measured by Astronomers of the Mount Wilson ObservatoryAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1970ApJS...19..387A&db_key=AST UBV photometry of 550 F, G and K type starsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1966MNRAS.133..475A&db_key=AST Résultats des observations faites à Tananarive avec l'Astrolabe A. DanjonNot Available Some spectral criteria for the determination of absolute stellar magnitudes.Not Available Submit a new article • - No Links Found -	2019-02-19 11:57:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6492569446563721, "perplexity": 8970.744347301526}, "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-2019-09/segments/1550247489933.47/warc/CC-MAIN-20190219101953-20190219123953-00140.warc.gz"}
http://jakobschwichtenberg.com/category/quantumfieldtheory/page/3/	# The perturbation series in QFT is an “invention of the devil” and this is actually a good thing In quantum field theory, we can’t calculate things exactly but instead must use a perturbative approach. This means, we calculate observables in terms of a perturbative series: $\mathcal{O}= \sum_n c_n \alpha^n$. This approach works amazingly well. The most famous example is the magnetic dipole moment of the electron $a_e \equiv (g – 2)/2$. It was calculated to order $\alpha^5$ in Phys. Rev. Lett. 109, 111807 and this result agrees perfectly with the measured value: $$a_e(exp) – a_e(theory) = −1.06 \ (0.82) \times 10^{-12}$$ However, there is one thing that seems to cast a dark shadow over this rosy picture: there are good reasons to believe that if we would sum up all the terms in the perturbative series, we wouldn’t get a perfectly accurate result, but instead infinity: $\sum_n^\infty c_n \alpha^n = \infty$. This is not some esoteric thought but widely believed among experts. For example, The only difficulty is that these expansions will at best be asymptotic expansions only; there is no reason to expect a finite radius of convergence. Quantum field theoretic divergences arise in several ways. First of all, there is the lack of convergence of the perturbation series, which at best is an asymptotic series. It has been known for a long time that the perturbation expansions in QED and QCD, after renormalization, are not convergent series. And this is really just a small sample of people you could quote. This is puzzling, because as is “well known”: Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever. In this sense, the perturbation series in QFT is an “invention of the devil” and we need to wonder $\sum_n^\infty c_n \alpha^n = \infty \quad \Rightarrow$ ??? But, of course, before we deal with that, we need to talk about why this divergence of the perturbation series is so widely believed. ## Does the perturbation series converge? $$\mathcal{O}(\alpha)= c_0 + \alpha c_1 + \alpha^2 c_2 + \ldots$$ To answer this question, Dyson already in 1952 published a paper titled “Divergence of perturbation theory in quantum electrodynamics” in which he put forward the clever idea to exploit one of the basic theorems of analysis. The theorem is: If $0 < r < \infty$, the series converges absolutely for every real number $\alpha$ such that $\|\alpha\|<r$ and diverges outside of this radius. Here, $r$ is called the radius of convergence and is a non-negative real number or $\infty$ such that the series converges if $\|\alpha\| < r$. The important subtlety implied by this theorem that Dyson focused on is that if the radius of convergence is finite $\neq 0$, according to the theorem, the series would also converge for small negative $\alpha$. In other words: If a series converges it always converges on a disk! Dyson idea to answer the question “Does the perturbation series converge?” is that we should check if the theory makes sense for a negative value of the coupling constant $\alpha$. If we can argue somehow that the theory explodes for any negative $\alpha$ then we know immediately that $r =0$ and therefore that the perturbation series diverges. ## Does QED make sense with negative $\alpha$? Before we discuss Dyson’s argument why the theory explodes for negative $\alpha$ in detail, here is a short summary of the main line of thought: We consider a “fictitious world” with negative $\alpha$. In such a world, equal charges attract each other, and opposite charges repel each other. With some further thought, we will discuss in a moment, this means that the energy is no longer bounded from below. Therefore, in a world with negative $\alpha$, there is no stable ground state. For our perturbation series, this means, that it is non-analytic around $\alpha = 0$. In other words, electrodynamics with negative $\alpha$, cannot be described by well-defined analytic functions. Therefore we can conclude that the radius of convergence is zero $r=0$, which implies that the perturbation series in QFT diverges also for a positive value of $\alpha$. In other words, the physics as soon as $\alpha$ becomes negative is so dramatically different that we expect a singularity at $\alpha =0$. Consequently, there doesn’t exist a convergent perturbation series. After this short summary, let’s discuss how this comes about in more detail. The important change as soon as $\alpha$ becomes negative is that equal charges start to attract each other. In the “normal” world with positive $\alpha$ a pair of, say, electron and positron that are created from the vacuum attract each other and therefore annihilate immediately, In a world with negative $\alpha$ they repel each other and therefore fly away from each other instead of annihilating. This means, the naive empty vacuum state starts to fill up with electrons and positrons when $\alpha$ is negative. Wait, is this energetically possible? What’s the energy of this new state full of electrons and positrons? To answer this question, let’s consider a ball with radius $R$ full of electrons and calculate its energy content. On the one hand, we have the positive rest + kinetic energy, which are proportional to the number of particles inside the ball $\propto N$. On the other hand, we have the negative potential energy, which is given by the usual formula for a Coulomb potential $\propto N^2 R^{-1}$. To compare them with each other, we need to know the number of electrons inside the ball. According to the Pauli principle, this number is proportional to the volume of the ball and therefore we conclude $\propto V \propto R^3 \propto N$. Therefore, the positive part of the energy is proportional to $R^3$, and the negative energy to $\propto N^2 R^{-1} \propto R^5$. The negative part wins. The total energy of the electrons inside the ball is negative. Most disturbingly the energy is unbounded from below and becomes arbitrarily negative as we make the ball bigger: $R,N \to \infty$. Take note that this is only the case in our fictitious world with negative $\alpha$. In our normal world with positive $\alpha$, opposite charges attract each other and this repulsion sets a lower bound on the energy. The analogous situation to the ball above in our fictitious world is a ball full of electron-positron pairs. The crucial thing is now that we can’t lower the energy indefinitely because when we try to group more and more electron-positron pairs together, we necessarily bring electrons close to other electrons and positrons close to other positrons. These equal charged particles repel each other in our normal world and this sets a lower bound on the energy. So, to conclude: In contrast to our normal world with positive $\alpha$, in our fictitious world with negative $\alpha$, a bound state of many electrons or positrons has a large negative energy. This means that our energy isn’t bounded from below because it can become arbitrarily negative. The most dramatic effect of this is what happens to the ground state in such a world, as already mentioned above. If we would start with a naive vacuum with no particles, it would spontaneously turn into a state with lots of electrons on one side and lots of positrons on the other side. Although this state is separated from the usual vacuum by a high potential barrier (of the order of the rest energy of the 2N particles being created), quantum-mechanical tunneling from the vacuum to the pathological state would be allowed, and would lead to an explosive disintegration of the vacuum by spontaneous polarization. This process would never stop. When the vacuum state isn’t stable against decay, no state is. Therefore, in a world with a negative coupling constant, every state could decay into pairs of electrons and positrons indefinitely. So, as claimed earlier, physics truly becomes dramatically different as soon as the coupling constant becomes negative. This instability means that electrodynamics with negative $\alpha$, cannot be described by well-defined analytic functions; hence the perturbation series of electrodynamics must have zero radius of convergence. For example, an observable like the magnetic dipole moment of the electron will have completely different value as soon as $\alpha$ becomes negative. Or it is even possible that such a property wouldn’t even make any sense in a world with negative $\alpha$. This leads us to the conclusion that we have a singularity at $\alpha=0$, which means we can’t write down a convergent perturbation series for observables. It is certainly fun to think about a world with a negative coupling constant and Dyson’s argument makes a lot of sense. Nevertheless, it is important to keep in mind that this is by no means a proof. It’s just a heuristic argument, but neither general nor rigorous. Yet, many people are convinced by it and further arguments that point in the same direction. One such further argument is the observation, already made in 1952 and later refined by Bender and Wu that the number of Feynman diagrams grows rapidly at higher orders of perturbation theory. At order $n$, we get $n!$ Feynman diagrams. For our sum $\sum_n^\infty c_n \alpha^n$ this means that $c_n \propto n!$. Thus, no matter how small $\alpha$ is, at some order $N$ the factor $N!$ wins. Now that I have hopefully convinced you that $\sum_n^\infty c_n \alpha^n = \infty$, we can start asking: What does $\sum_n^\infty c_n \alpha^n = \infty$ mean? The best way to understand what $\sum_n^\infty c_n \alpha^n = \infty$ really means and how we can nevertheless get good predictions out of the perturbation series is to consider toy models. As already mentioned in my third post about the QCD vacuum, one of my favorite toy models is the quantum pendulum. It is the perfect toy model to understand the structure of the QCD vacuum and the electroweak vacuum and will be now invaluable again. The Schrödinger equation for the quantum pendulum is $$– \frac{d^2 \psi}{d x^2} + g(1-cos x) \psi = E \psi .$$ We want to calculate things explicitly and therefore consider a closely related, simpler model and will come back to the full pendulum later. For small motions of the pendulum, we can approximate the potential ( $\cos(x) \approx 1-x^2/2+x^4/4! – \ldots$) of the quantum pendulum and end up with the Schrödinger equation for the anharmonic oscillator $$– \frac{d^2 \psi}{d x^2} – (x^2+ g x^4 )\psi = E \psi .$$ Now, the first thing we can do with this toy model is to understand Dyson’s argument from another perspective. The potential of the anharmonic oscillator is $V= x^2+ g x^4$ and let’s say we want to calculate the energy levels by using the usual quantum mechanical perturbation theory $E(g) = \sum_n c_n g^n$. (More precisely: The energy levels of the harmonic oscillator are well known and we are using the Rayleigh-Schrödinger perturbation theory to calculate corrections to them which come from the anharmonic term $\propto x^4$ in the potential. ) For positive values of $g$ the potential is quite boring and looks almost like for the harmonic oscillator. However, for negative values of $g$ the situation becomes much more interesting. The energy is no longer bounded from below. The states inside the potential are no longer stable but can decay indefinitely by tunneling through the potential barrier. This is exactly the same situation that we discussed earlier for QED with negative $\alpha$. Thus, according to Dyson’s argument, we suspect that the perturbation series for the energy levels is not convergent. This was confirmed by Bender and Wu, who treated the “anharmonic oscillator to order 150 in perturbation theory“. (Phys. Rev. 184, 1231 (1969); Phys. Rev. D 7, 1620 (1973)) We can already see from the first terms in the perturbation theory how the series explodes: $$\rightarrow E_0 \propto \frac{1}{2} + \frac{3}{4}g – \frac{21}{8}g^2 + \frac{333}{16}g^3 + \ldots$$ This gives further support to Dyson’s conjecture that a dramatically different physics for negative values of the coupling constant means that the perturbation theory does not converge. Yet, the story of this toy model does not end here. There is much more we can do with it. ## The Anharmonic Oscillator in “QFT” Let’s have a look how we would treat the anharmonic oscillator in quantum field theory. (This example is adapted from the excellent https://arxiv.org/abs/1201.2714). For this purpose, we consider the following “action” integral $$\mathcal{Z}(g) = \int_{-\infty}^\infty \mathrm{d}x \mathrm{e}^{-x^2-g x^4} .$$ The cool thing is now that we can compute for this toy model the exact answer, for example, using Mathematica. Then, in a second step we can treat the same integral was we usually do in QFT and then compare the perturbative result with the exact result. Then in the last step, we can understand at what order and why the perturbation series diverges. The full, exact solution isn’t pretty, but no problem for Mathematica: $$\mathcal{Z}(g) = \frac{\mathrm{e}^{\frac{1}{8g}}K_{1/4}(1/8g}{2 \sqrt{g}},$$ where $K_n$ denotes modified Bessel function of the second kind. This solution yields a finite positive number for each value $g$. Next, we do what we usually do in QFT. We split the “kinetic” and the “interaction” part and expand the interaction part as a power series \begin{align} \mathcal{Z}(g) &= \int_{-\infty}^\infty \mathrm{d}x \mathrm{e}^{-x^2-g x^4} = \int_{-\infty}^\infty \mathrm{d}x \mathrm{e}^{-x^2} \sum_{k=0}^\infty \frac{(-gx^4)^k}{k!} \notag \\ & \text{“}= \text{“} \sum_{k=0}^\infty \int_{-\infty}^\infty \mathrm{d}x \mathrm{e}^{-x^2} \frac{(-gx^4)^k}{k!} \notag \end{align} Take note that the exchange of sum and integral is the “root of all evil”, but necessary to interpret the theory in terms of a power series of Feynman diagrams. That’s why the last equal sign is put in quotes. (This exchange is actually a “forbidden” step that changes the behaviour at $\pm \infty$. ) So, with this approach to what extend can we get a good approximation? Using a bit of algebra, we can solve the polyonimian times Gaussian integral and get \begin{align} \mathcal{Z}(g) & \text{“}= \text{“} \sum_{k=0}^\infty \int_{-\infty}^\infty \mathrm{d}x \mathrm{e}^{-x^2} \frac{(-gx^4)^k}{k!} \notag \\ &= \sum_{k=0}^\infty \sqrt{\pi} \frac{(-g)^k (4k)!}{2^{4k}(2k)! k!} \end{align} This perturbative answer is a series that diverges! (For more details, see the excellent detailed discussion in https://arxiv.org/abs/1201.2714) Is this perturbative answer, although divergent, useful anyway? Let’s have a look. The thing is that in QFT we can only compute a finite number of Feynman diagrams. This means we can only evaluate the first few terms of the perturbation series. Thus we consider the “truncated” series, instead of the complete series, which simply means we stop at some finite order $N$: $$\Rightarrow \text{Truncated Series: } \mathcal{Z}_N(g) = \sum_{k=0}^N \sqrt{\pi} \frac{(-g)^k (4k)!}{2^{4k}(2k)! k!}$$ For definiteness let’s choose some value for the coupling constant, say $g=\frac{1}{50}$. How good is the perturbative answer from the truncated series compared to the full exact answer? \begin{align} \text{Exact: } \mathcal{Z}(1/50) &= 1.7478812\ldots \notag \\ \text{Perturbatively: } \mathcal{Z}_5(1/50) &= 1.7478728\ldots \notag \\ \mathcal{Z}_{10}(1/50) &= 1.7478818\ldots \notag \end{align} This is astoundingly good! The complete series is divergent, which means if we would sum up all the terms, we would get infinity. Nevertheless, if we only consider the first few terms, we get an excellent approximation of the correct answer! This behavior can be understood nicely by a plot The first few terms are okay, then the approximation becomes really good, but at some point, the perturbative answer explodes. A series that behaves like this is known as an asymptotic series. So now, the question we need to answer is: ## When and why does the series diverge? Again, I will give you a short summary of the answer first, and afterward discuss it in more detail. The reason that the series explodes at some point is that a perturbative treatment in terms of a Taylor series misses completely factors of the form $\mathrm{e}^{-c/g} \sim 0 + 0 g + 0 g^2 + \ldots$. The Taylor expansion of such a factor yields zero at all order, although the function obviously isn’t zero. This is a severe limitation of the usual perturbative approach. You may wonder, why we should care about such funny looking factors. The thing is that tunneling effects in a quantum theory are described precisely by such factors! Remember, for example, the famous quantum mechanical answer of a particle that encounters a potential barrier. It will tunnel through the barrier, although classically forbidden. Inside the potential barrier, we don’t get an oscillating wave function, but instead, an exponentially damping, described by factors of the form $\mathrm{e}^{-c/g}$. To summarize: Our perturbative approach misses tunneling effects completely and this is why our perturbation series explodes! We will see in a moment that this means that the divergence starts around order $N=\mathcal{O}(1/g)$. For example, in QED the perturbative approach is expected to work up to order 137. We can understand this, by going back to our toy model. Have a look again at the quantum pendulum. Usually, we consider small oscillations around the ground state, which means low energy states. However in a quantum theory, even at low energies, the pendulum can do something completely different. It can rotate once around its suspension. As it classically does not have the energy to do this, we have here a tunneling phenomenon. This kind of effect is what our usual perturbative approach misses completely and this is why the perturbation series explodes. After this heuristic discussion, let’s have a more mathematical look how this comes about. There is a third method, how we can treat our integral $\mathcal{Z}(g) = \int_{-\infty}^\infty \mathrm{d}x \ \mathrm{e}^{-x^2-g x^4}$. This third method is known as the method of steepest descend and it shows nicely what goes wrong with when we use the usual perturbative method. First, we substitute $x^2\equiv \frac{u^2}{g}$ and then have $$\mathcal{Z}(g) = \int_{-\infty}^\infty \mathrm{d}x \ \mathrm{e}^{-x^2-g x^4} = \frac{1}{\sqrt{g}} \int_{-\infty}^\infty \mathrm{d}u \ \mathrm{e}^{- \frac{u^2 + u^4}{g}}$$ Now, we deal with small values of the coupling $g$ and thus the integrand is large. The crucial idea behind the method of steepest descend is that the main contributions to the integral come from the extrema of the integrand $\phi(u)\equiv u^2+u^4$. As usual, we can calculate the extrema by solving $\phi'(u_0) =0$. Take note that in QFT these extrema of our action integrand are simply the solutions to the equations of motion! (This is how we calculate the equations of motion: we look for extrema of the action. This means, $\phi'(u_0) =0$ are in QFT simply our equations of motion and the solutions $u_0$ are solutions of the equations of motion. To approximate the integral, we then expand the integrand around these extrema. In our example, the extrema are $u=0$ an $u=\pm i/\sqrt{2}$. (For more details, see https://arxiv.org/abs/1201.2714) This method tells us exactly what goes wrong in the usual approach. The standard perturbation theory corresponds to the expansion around $u=0$. The other extrema yield contributions $\propto \mathrm{e}^{-\frac{1}{4g}}$ $\rightarrow$ and as already discussed earlier, these are missed completely by a Taylor series around $g=0$. With this explicit result, we can calculate when these “non-perturbative” contributions become important. This question in mathematical terms is: When is $\mathrm{e}^{-\frac{1}{4g}} \approx g^k$? First, we use the log on both sides, which yields the question: When is $-\frac{1}{4g} \approx k \ \mathrm{ln}(g)$? Now, if we have a look at some explicit numbers: $\mathrm{ln}(1/50)\approx -3.9$, $\mathrm{ln}(1/100)\approx -4.6$, $\mathrm{ln}(1/150)\approx -5$, we see that the answer is: for $k \approx \frac{1}{g}$! Thus, as claimed earlier, the nonperturbative effects that are missed by the Taylor expansion treatment become important at order $\approx \frac{1}{g}$ and this is exactly where our perturbation series stops to make sense. (For a nice discussion of this method of steepest descent, see page 2 here ) Before we summarize what we have found out and learned here there is one last thing. ## One Last Thing There is an amusing empirical rule related to such asymptotic series: (Carrier’s Rule). Divergent series converge faster than convergent series because they don’t have to converge. The thing is that convergence is a concept relating to the behavior at $n \to \infty$. This is not what we are really interested in. We want a good approximation by calculating just a few terms of the perturbation series, not all of them. This kind of behavior is often observed in divergent series. They often yield good approximation at a low order, which, in contrast, is unusual for convergent power series. This is a numerical, empirical statement that was found in many explicit examples, see: Bender, C. M., and Orszag, S. A.: Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978, p. 594 Thus, instead of Abel’s perspective Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever. we should prefer Heaviside’s attitude The series is divergent; therefore we may be able to do something with it ## Summary, Conclusions, and Outlook The thing to take away is nicely summarized by the following picture adapted from a presentation by Aleksey Cherman: The perturbation series in QFT diverge $\sum_n^\infty c_n g^n =\infty$, but are expected to yield meaningful results up to order $N=\mathcal{O}(1/g)$. This observation is a great reminder that perturbative Feynman diagrams don’t tell the whole story: tunneling effect, which is proportional to $\mathrm{e}^{1/g}$ are missed completely. Dyson published his argument in 1952 so all this is known for a long time. However, there is still a lot of research going on. One concept people talk about all the time when it comes to this is Borel summation. This is a cool mathematical trick to improve the convergence of divergent series. For the anharmonic oscillator, this works perfectly. By performing a Borel transformation, we can tame the divergence. However, in realistic quantum field theoretical examples this does not work. The main reason is singularities of the Borel sum. One source of these singularities are the tunneling effects we already talked about. However, much more severe are singularities coming from so-called “renormalons”. This word is used to describe the singularities coming from the renormalization procedure and thus in some sense from the running of the coupling constants. An active field of research in this direction is “resurgence theory“. People working on this try to use a more general perturbation ansatz $$\mathcal{O}= \sum_n c_n^{(0)} \alpha^n + \sum_i \mathrm{e}^{S_i/g} \sum_n c_n^{(i)} \alpha^n$$ called a trans-series expansion. The crucial thing is, of course, that they explicitly include the factors $\mathrm{e}^{S_i/g}$ that are missed by the usual ansatz. Thus, in some sense they try to describe “non-perturbative” effects with a new perturbation series. At the other end of the spectrum are people working on completely non-perturbative results for observables. The most famous example is the amplituhedron, which was proposed a few years ago. This is a geometric object and the people working on it hope that it paves the way to a “nice general solution which would provide all-loop order results.” (J. Trnka) PS: Many thanks to Marcel Köpke who spotted several typos in the original version. \| 4,020 Words # Demystifying the QCD Vacuum: Part 3 – The Untold Story Although the subtle things that are often glossed over in the standard treatment of the QCD vacuum can be explained as discussed in part 2, there is another, more intuitive way to understand it. Most importantly, this different perspective on the QCD vacuum shines a completely new light on the mysterious $\theta$ parameter. To the expert, this perspective will be familiar. It sometimes appears in the literature and therefore the “untold” part in the headline is, of course, a bit exaggerated. However, it took me, as a student, a long long time to find it at all and most importantly a proper explanation that made sense to me. The standard story of the QCD vacuum uses the temporal gauge. This is not a completely fixed gauge. Time-independent gauge transformations are still allowed. Only this residual gauge freedom makes the whole discussion in terms of large and small gauge transformations, etc. possible. One may wonder what happens when we analyze the vacuum in a different gauge, where there is no residual gauge freedom. In other words: in a gauge that fixes the gauge freedom completely. Possibly choices are, for example, the axial and the Coulomb gauge. The interpretation of the QCD vacuum is completely different in these gauges. Most importantly: there is no vacuum periodicity. In the axial gauge, there is only one non-degenerate ground state. Then, of course, it is natural to wonder what we can learn about the $\theta$ parameter here. At a first glance, the result that there is a unique ground state implies that we have $\theta=0$. However, this is not the case and we will discuss this in a moment. In the Coulomb gauge, there is only a non-degenerate ground state, too. However, the interpretation of the vacuum structure in this gauge is especially tricky. Most famously, one encounters the famous Gribov ambiguities. These appear because the condition that fixes the Coulomb gauge does not lead to unique gauge potentials everywhere in spacetime. Instead, there are regions where there are multiple gauge potential configurations that satisfy the condition. These configurations are called Gribov copies and the fact that we do not get a unique gauge potential configuration everywhere in spacetime is called Gribov ambiguity. Now, how is this not a contradiction to the standard picture of the QCD vacuum? When there is only a unique non-degenerate ground state, there is no tunneling between degenerate vacua and therefore no $\theta$ parameter, right? No! There is still tunneling and also a $\theta$ parameter. In the axial gauge, the tunneling starts from the unique ground state and ends at the same unique ground state. (In the Coulomb gauge the tunneling happens between the Gribov copies?!) To understand this, we need an analogy. A nice analogy to the QCD vacuum is given by the following Hamiltonian: $$H= – \frac{d^2 }{d x^2} + q(1-cos x) ,$$ where $-\infty \leq x \leq \infty$ and which describes a particle in a periodic potential $V(x) = q (1-cos x)$. Therefore, this situation is quite close to the standard picture of the QCD vacuum, with a periodic structure and infinitely many degenerate ground states. Source: https://arxiv.org/abs/1505.03690 For this Hamiltonian, we have the Schrödinger equation $$– \frac{d^2 \psi}{d x^2} + q(1-cos x) \psi = E \psi .$$ (Among mathematicians this equation is known as the “Mathieu equation”. Sometimes it’s useful to know the name of an equation, if you want to dig deeper.) However, exactly the same Hamiltonian describes a “quantum pendulum”. This interpretation only requires that we treat our variable as an angular variable: $x \to \phi$, with $0 \leq \phi \leq 2 \pi$ and thus $$– \frac{d^2 \psi}{d \phi^2} + q(1-cos \phi) \psi = E \psi .$$ Now, we identify the point $2 \pi$ with $0$ and all values of $\phi$ that are larger than $2 \pi$, with the corresponding points in the interval $0 \leq \phi \leq 2 \pi$. This implies immediately that $\Psi(\psi + 2\pi) = \Psi(\psi)$. Therefore, the situation now looks like this: and we no longer have infinitely many degenerate ground states, but only a unique ground state! Therefore, the situation here is exactly the same as for the QCD vacuum in a physical gauge. ## Now, what about tunneling? For a long pendulum, i.e. for large $q$, the ground state $\psi =0$ and excited states are approximately the same as for a harmonic oscillator. For large $q$, we can do a perturbative analysis in $q^{-1/2}$ and take the “anharmonicity” this way into account. However, the famously this perturbation series does not converge, because we miss something important in our analysis. Even for a pendulum with small energy, i.e. with only small perturbations around the ground state, the pendulum can “tunnel”. In this context, this means that the pendulum does a motion that it isn’t allowed to do, like rotate once around its suspension and end up again and the ground state. This is exactly what the instantons describe in a physical gauge like the axial gauge. There is no tunneling between degenerate ground states because there are no degenerate ground states. Instead, we have tunneling that starts at the unique ground state and ends again at the unique ground state. Still, this is tunneling, because there is a potential barrier that prohibits that a pendulum rotates once completely around its suspension. For a pendulum with low energy, or equally a long pendulum (large $q$), we can do the usual quantum mechanical perturbation analysis. This yields harmonic oscillator states plus small corrections from the anharmonicity. However, we must take into account that there are also quantum processes, like the tunneling once around the suspension of the pendulum. ## Okay, fine. But what about $\theta$? Well, now that we have understood that there can also be tunneling in the physical gauge picture of the QCD vacuum, which corresponds to the pendulum interpretation of the Hamiltonian in the example above, we can argue that there can be again a $\theta$ parameter. This is the phase that the pendulum picks up when it tunnels around its suspension. In a quantum theory, we can have $\Psi(\psi + 2\pi) = e^{-i \theta} \Psi(\psi)$ instead of $\Psi(\psi + 2\pi) = \Psi(\psi)$. When we interpret the Hamiltonian in the example above as the movement of a particle in a periodic potential, the parameter $\theta$ describes different states in the same system, completely analogous to the Bloch momenta in solid-state physics. However, in the pendulum interpretation different $\theta$ describe different systems, i.e. different pendulums! Thus, in this second interpretation, it is much clearer why $\theta$ is a fixed parameter and not allowed to change. To bring this point home, let’s consider an explicit example how a $\theta$ parameter can arise for the quantum pendulum. The pendulum only picks up a phase $\theta$, when it moves in an Aharonov-Bohm potential. To make this explicit, let’s assume the pendulum carries electric charge $e$ and rotates around a solenoid with magnetic flux $\theta$. This magnetic flux is the source of a potential $A$ in the plane of the rotating pendulum. We get the Hamiltonian that describes this system by replacing the derivative with the covariant derivative: $$H= – \left(\frac{d }{d \phi} -ie A\right)^2+ q(1-cos \phi) ,$$ and thus we have the Schrödinger equation $$– \left(\frac{d }{d \phi} -ie A\right)^2 \psi+ q(1-cos \phi) \psi= E \psi .$$ As before, we impose the condition $\Psi(\psi + 2\pi) = \Psi(\psi)$. However, we can also introduce a new wave function $\varphi (\psi)$ that obeys the standard Schrödinger equation without the additional vector potential $$– \frac{d^2 \varphi}{d \phi^2} + q(1-cos \phi) \varphi = E \varphi ,$$ where $$\psi(\phi) = \text{exp} \left[ ie \int_0^\phi A d\phi \right] \varphi(\phi).$$ (Take note that the relation between the magnetic flux $\theta$ and the potential $A$ is $\int_0^{2\pi} A d\phi = \theta$). The information about the presence of the magnetic flux and hence of the vector potential $A$ is now, when we use $\varphi(\phi)$ instead of $\Psi (\phi)$, encoded in the boundary condition: $$\varphi(\phi + 2\pi) = e^{-ie\theta} \varphi(\phi).$$ The energy of the ground state of the pendulum is directly proportional to the magnetic flux: $$E (\theta) \propto (1- \cos(\theta)) .$$ This show that in this model, the parameter $\theta$ defines different systems, namely quantum pendulums in the presence of different Aharonov-Bohm potentials. In contrast, in the periodic potential picture, where $\theta$ is interpreted as analogon to the Bloch momentum, the parameter $\theta$ describes different states of the same system. The reinterpretation of the QCD vacuum in a physical gauge with a unique non-degenerate vacuum, thus makes the appearance of $\theta$ much less obvious. This is why the standard presentation of the topic still makes use of the temporal gauge and the periodic vacuum picture. The analysis of the QCD vacuum in the axial gauge is analogous to the interpretation of the Hamiltonian $$H= – \frac{d^2 }{d \phi^2} + q(1-cos \phi)$$ as description of a quantum pendulum, i.e. substituting $x \to \phi$, with $0\leq \phi < 2 \pi$. (This interpretation also arises, when we work in the temporal gauge and declare that all gauge transformations (large and small) should not have any effect on the physics. The distinct degenerate vacua in the usual interpretation are connected by large gauge transformations. ) Without any further thought, one reaches immediately the conclusion that there is no $\theta$ parameter here. However, this is not correct, because a $\theta$ parameter can appear when there is an Aharonov-Bohm potential present. When the quantum pendulum swings in such a potential, it picks up a phase when it rotates once around the thin solenoid that encloses the magnetic flux. The phase is directly proportional to the magnetic flux in the solenoid. For the QCD vacuum, the same story goes as follows. In the axial gauge, naively there is no $\theta$ parameter because we do not have a periodic potential and hence no Bloch-momentum. However, nothing forbids that we add the term $$– \frac{g^2 \theta}{32\pi^2} Tr(G_{\mu\nu} \tilde{G}^{\mu\nu}),$$ where $\tilde{G}^{\mu\nu}$ is the dual field-strength-tensor: $\tilde{G}^{a,\mu \nu} = \frac{1}{2} \epsilon^{\mu \nu \rho \sigma} G^a_{ \rho \sigma}$, to the Lagrangian. This simply means that we allow for the possibility that there is an Aharonov-Bohm type potential and that it could make a difference when the pendulum rotates once around its suspension. An obvious question is now, what the analogon to the solenoid is for the QCD vacuum. So far, I wasn’t able to find a satisfactory answer. The usual argument for the addition of $– \frac{g^2 \theta}{32\pi^2} Tr(G_{\mu\nu} \tilde{G}^{\mu\nu})$ to the Lagrangian is that nothing forbids its existence. So far, all experimental evidence point in the direction that there exists no “solenoid” for the QCD vacuum and therefore $\theta =0$. (The current experimental bound is $\theta < 10^{-10}$, Source). From the analysis of the QCD vacuum in the axial gauge and by comparing it to the quantum pendulum, this does not look too surprising. However, we shouldn’t be too quick here and state $\theta =0$. Before we can say something like this, we need to understand first, what the “solenoid” could be for the QCD vacuum. Understanding this requires that we enter a completely different world: the world of anomalies. This fascinating topic deserves its own post. Usually, it is claimed that the contribution to $\theta$ that comes from this sector of the theory is completely unrelated to the QCD $\theta$. However, we will see that anomalies and the QCD vacuum aren’t that unrelated: So far, we were only concerned with the gauge boson vacuum, while anomalies arise when we consider the fermion vacuum and its interaction with gauge bosons! This will be discussed in part 4 of my series about the QCD vacuum. ## References that describe this perspective of the QCD vacuum • “Topology in the Weinberg-Salam theory” by N. S. Manton • “The Interpretation of Pseudoparticles in Physical Gauges” by Claude W. Bernard, Erick J. Weinberg • Section 11.3 in Rubakov’s “Classical Theory of Gauge Field” • This perspective of the QCD vacuum in more abstract terms without the quantum pendulum analogy is described in “Introduction to the Yang-Mills Quantum Theory” by R. Jackiw in the around Eq. (42). \| 2,045 Words # Demystifying the QCD Vacuum: Part 2 – The Subtleties No One Talks About This is part two of my series about the QCD vacuum. You should only read this if you are confused about several things that are glossed over in the standard treatments. It turns out, that if you dig a bit deeper, these several such small things aren’t as obvious as most authors want you to believe. I already mentioned the problems with the two assumptions that are made in the standard texts without proper explanations. Here I will discuss the assumptions in more detail. My main focus is answering the questions: Why there is so much emphasize on gauge transformations that become trivial at infinity $g(r, \phi , \theta) \to 1$ for $r \to 1$ and why do the usual discussions make use of the temporal gauge? I already discussed in the first post, why these assumptions are absolutely crucial. Without them, there is no way to arrive at the standard interpretation of the QCD vacuum. These two things only make sense, when you know something about constrained Hamiltonian quantization and Gauss’ law. Only if you have some basic understanding of these two notions, you can truly understand the ideas of the discoverers of the non-trivial structure of the QCD vacuum. My plan is to write more about both, constrained Hamiltonian quantization and Gauss’ law, in the future, but just to demonstrate that both are an interesting topic on their own, regardless of the QCD vacuum, here are two quotes: “The constrained Hamiltonian formalism is recommended as a means for getting a grip on the concepts of gauge and gauge transformation. This formalism makes it clear how the gauge concept is relevant to understanding Newtonian and classical relativistic theories as well as the theories of elementary particle physics; it provides an explication of the vague notions of “local” and “global” gauge transformations; it explains how and why a fibre bundle structure emerges for theories which do not wear their bundle structure on their sleeves; it illuminates the connections of the gauge concept to issues of determinism and what counts as a genuine “observable”; and it calls attention to problems which arise in attempting to quantize gauge theories. “ Gauge Matters by John Earman “The main output of this analysis is therefore the suggestion that Gauss law is the basic and primary feature which characterized elementary particle interactions, rather than gauge invariance, a concept which is more difficult to grasp on physical grounds since it can be given a meaning only by introducing unobservable quantities. Gauge Invariance can therefore be regarded as a technical tool for constructing Lagrangian functions or equations of motion which guarantee the validity of Gauss’ law. This may be the right track to get an insight into the structure of GQFT and possibly understand why nature seems to choose gauge theories for elementary particle interactions.” Gauss’ Law in Local Quantum Field Theory by F. Strocchi This post should be about how these concepts help to understand the standard discussion of the QCD vacuum and therefore I will keep discussions that would lead us too far apart to a minimum. So, without further ado, let’s get started. ## How do we get a Quantum Theory? In modern physics, when we write down a model to describe a given system, we start with a Lagrangian. This is clever because the Lagrangian framework is ideal to make use of symmetry considerations. If the Lagrangian (or better, the action) is invariant under some transformation, the equations of motion, have this symmetry, too. In contrast, for example, the Hamiltonian, is not even invariant under Lorentz transformations as it represents the energy and is thus only one component of a Lorentz vector, the four momentum. Therefore, it is much harder to “guess” the correct Hamiltonian that describes the system in question. However, when we want to describe a quantum system, a Lagrangian is not enough. Although we get from the Lagrangian the equations of motion via the Euler-Lagrange equations, these are not enough to describe the quantum behavior of the system. The equations of motions are, on their own, purely classical and there is nothing quantum about them. Thus, we need additional equations that describe the quantum behavior and we get them through the process called “quantization”. There are different ways to quantize a given classical system, but one popular and famous possibility is the constrained Hamiltonian quantization procedure. (A now-popular alternative is the path-integral formalism. However, the canonical procedure described below makes many points more transparent). This is a reliable way to quantum physics and the main points are well known to most students. We derive from the Lagrangian the canonical momenta and then quantize the system by replacing the classical Poisson bracket with the quantum commutator (or anticommutator) $$\{ \cdot , \cdot \} \to \frac{1}{i\hbar} [\cdot , \cdot ].$$ However, there are several subtle points that need to be taken care of when we try to use this procedure. While you may not care about such “details”, it is absolutely crucial to understand this procedure, if you want to understand the standard picture of the QCD vacuum that is repeated in almost all textbooks and reviews. In addition, hopefully, the quote above has sparked some interest that there is something deep that we can learn here. For our purpose here, however, it is only important to know that the guys who came up with the standard interpretation of the QCD vacuum cared about this procedure a lot. To (canonically) quantize, we must compute the generalized momenta $p_i$ for the given Lagrangian and then impose the famous commutation relations $[q_i,p_j]= i \delta_{ij}$. We also need these generalized momenta to get the Hamiltonian that corresponds to the given Lagrangian. We need the Hamiltonian in the canonical formalism, for example, to calculate the time-evolution of quantum fields. The mathematical procedure to get the Hamiltonian from a given Lagrangian and thus to get the generalized momenta is called Legendre transform. However, this procedure is not as straight-forward as one would naively assume. The Lagrangian is a function of $q_i$ and $\dot{q}_i$, whereas the Hamiltonian is a function of $q_i$ and the generalized momenta and $p_i$. The Legendre transform is the process to calculate from the generalized velocities $\dot{q}_i$ the corresponding generalized momenta $p_i$: $$p_i \equiv \frac{\partial L }{\partial \dot{q}_i} .$$ In principle, we can invert this definition and get the generalized velocities as a function of $q$ and $p$: $\dot{q}_i = \dot{q}_i (q_i,p_i)$. However, for some systems, these relations are not invertible. Instead, not all momenta are independent and we get a family of constraints that the momenta must satisfy $$f_a(q,p) =0 \quad a=1,…,N$$ These constraints are the reason why this formalism is called constrained Hamiltonian quantization. Glossing over some details (the process of finding all independent constraints and the definition of “first-class” constraints, which are those constraints whose mutual Poisson bracket vanishes), the crucial thing is now that the constraints generate gauge transformations! The understand this, we note that the correct total Hamiltonian is given by the “naive” Hamiltonian $H_T$ plus a linear combination of all (first class) constraints with arbitrary coefficients $$H_T = p_i \dot{q}_i – L + \sum_{a=1}^N \lambda_a(t) f_a.$$ (The implementation of constraints in this way is known as the method of “Lagrange multiplies”) The Hamiltonian describes the time evolution of the system in question. The additional terms here mean that there is an ambiguity in the time evolution and this ambiguity is exactly our gauge freedom! The origin of these complications, can be traced back to the equations of motions in the Lagrangian framework $$\frac{\partial^2 L}{\partial \dot{q}_i \partial \dot{q}_j } \ddot{q}_j= – \frac{\partial^2 L}{\partial \dot{q}_i \partial q_j } \dot{q}_j + \frac{partial L}{\partial q} .$$ The accelerations can only be determined in terms of the positions and velocities if the Jacobian matrix of the transformation $(q_i, \dot{q}_i) \to (p_i, p_i)$: $$\frac{\partial p^i}{\partial \dot{q}_j} = \frac{\partial^2 L}{\partial \dot{q}_i \partial \dot{q}_j } \ddot{q}_j$$ is non-singular. Only then, the transformation is unique and the canonical quantization procedure works without subtleties. This can be seen, by analyzing the equation $\det\left( \frac{\partial^2 L}{\partial \dot{q}_i \partial \dot{q}_j } \ddot{q}_j \right) =0$. This equation implies that some of the momenta aren’t independent variables. This means, we have constraints when the determinant of the Jacobian matrix is zero and therefore the time evolution is not uniquely determined in terms of the initial conditions. (For more on this, see, for example, this paper). This is a very special perspective on gauge freedom that isn’t very familiar to students nowadays. However, it is absolutely crucial to understand what the discoverers of the non-trivial structure of the QCD vacuum had in mind. A concrete example may be helpful. ## Constrained Quantization of Electrodynamics The Lagrangian of electrodynamics is $L = – \frac{1}{4} \int d^3xF_{mu\nu} F^{\mu\nu}$ and contains some gauge freedom. This becomes especially transparent when we try to quantize electrodynamics by following the procedure described above. The path from this Lagrangian to the correct description in the Hamiltonian framework is quite subtle because we have here an explicit example, of the situation described above. When we calculate the generalized momenta to $A_\mu$: $$\pi^\mu = \frac{\partial L}{\partial (\partial_0 A_\mu)}= F^{\mu 0},$$ we get $\pi^0 =0$ and $\pi = E^i$, where $E$ is the usual electric field. Thus, we notice here the constraint: $\pi^0 =0$. Following, the procedure described above, we have the following total Hamiltonian $$H_T = \int d^3x \left( \pi^\mu \partial_0 A_\mu – \mathcal{L} \right) + \int d^3x \lambda_1(x) \pi_0(x)$$ $$\int d^3 x \left( \frac{1}{2} (\vec{E}^2 +\vec{B}^2) + A_0 \Delta \cdot \vec E \right) + \int d^3x \lambda_1(x) \pi_0(x)$$ (In this calculation, one uses $\partial_0 \vec A = \Delta A_0 -\pi = \Delta A_0 – \vec E$ and integrates the second term by parts.) We recognize the first term here $\propto \frac{1}{2} (\vec{E}^2 +\vec{B}^2)$ as the well known electromagnetic field energy density. The last term is the implementation of the constraint $\pi_0(x) =0$ via a Lagrange multiplier $\lambda_1(x)$. What about the second term? To understand this second term, let’s take a step back and go back to the Lagrangian. One of the equations of motions that we get via the Euler-Lagrange equations from the Lagrangian $L = – \frac{1}{4} \int d^3xF_{mu\nu} F^{\mu\nu}$, is Gauss’ law: $$\Delta \cdot \vec E = 0.$$ (Gauss’ law is, of course, one of the famous Maxwell equations. In words, Gauss law simply states that the flux of the electric field from a volume is proportional to the charge inside. In electrodynamics without sources, which is what we consider here with our Lagrangian, this flux is therefore zero.) However, take note that it is a very special kind of “equation of motion”. It contains no time-derivatives and therefore does not describe any time-evolution. Hence it is not really an equation of motion! If we now have again a look at the Hamiltonian that we derived above, we can see that the second term has exactly the same structure as the third term. The equation $\Delta \cdot \vec E = 0$ is a constraint, exactly as $\pi_0(x)$. The Lagrange multiplier for this term is simply $A_0(x)$. Our two (first class) constraints are $\pi_0 =0$ and $\Delta \vec{\pi } = \Delta \vec{E}=0$. In the Hamiltonian framework, they show up as constraints that we implement by making use of Lagrange multipliers. Now that we know that $A_0(x)$ is not really a dynamical variable, it seems reasonable to simplify our calculations by choosing the temporal gauge $A_0(x)=0$. (It can already be seen from the Lagrangian that $A_0(x)$ is not a dynamical variable because there is no time derivative of $A_0(x)$ in the Lagrangian.) However, $A_0(x)=0$ is not a complete gauge fixing. We still have the freedom to perform time-independent gauge transformations. This remaining gauge freedom can be fixed, for example, by the demand $\Delta \cdot \vec A =0$. When we recall the remark from above, that the constraints generate gauge transformations, we can understand the residual gauge freedom after fixing $A_0(x)=0$ from another perspective: The choice $A_0(x)=0$ uses up the gauge freedom generated by $\pi_0 =0$ (called the momentum constraint). However, we still have the gauge freedom generated by Gauss’ law $\Delta \vec{E}=0$. This can be seen, for example, by going back to the Lagrangian invoking Noether’s theorem for time-independent gauge transformations. The conserved “charge” that follows from invariance under time-independent gauge transformations: $$Q_\phi = \int dr \pi_a \cdot \delta A_a = \frac{1}{g} \int_{-\infty}^\infty dr \vec {E}_a (\Delta \phi (r))_a$$ where $\phi(x)$ is the “gauge function”. This looks almost like Gauss’ law, but not exactly. Gauss law involves $\Delta \vec{E}$, whereas here $\Delta$ acts on the gauge function $\phi(x)$. However, we can rewrite this Noether charge such that it contains $\Delta \vec{E}$ by integrating by parts. When we integrate by parts, we get a boundary term $( \frac{1}{g} \vec {E}_a \phi (r)_a \big \|_{-\infty}^\infty$. We can only neglect this boundary term, when $\phi (-\infty) = \phi (\infty) =0$. This is a subtle point that is often glossed over (see, for example, Eq. 3.22 in Topological investigations of quantized gauge theories by R. Jackiw, where this “glossing over” is especially transparent). The subtle and small observation that $\theta (-\infty) = \theta (\infty) =0$ is a requirement for Gauss’ law to be a generator of gauge transformations will become incredibly important in a moment. Forgetting this “detail” for a moment, we can conclude $E_a\cdot \Delta$ is conserved. This can also be verified, by computing the explicit commutator with the Hamiltonian. Noether charges always generate the corresponding symmetry transformations and in this sense, $E_a\cdot \Delta$ generates time-independent gauge transformations. The Noether “charge” for time-independent gauge transformations is $\propto \Delta E$ and hence this is the generator of such gauge transformations. (A second possibility to see that Gauss’ law generates gauge transformations is to consider the explicit commutator of $G_a = – \frac{1}{g} (\Delta E)$ and the electrical potential $A_b$ and the electrical field $E_a$. Moreover, we can compute that $\frac{i}{\hbar} [H,G_a]=0$ and therefore $G_a$ is indeed conserved. ) ## Gauss’ Law in a Quantum Theory Now, let’s remember that we want to talk about a quantum theory. It is somewhat a problem what to make of Gauss’ law in a quantum theory. On the one hand, we can invoke the equal-time commutation relations and compute $$[G_a (x_1),A_1(x_2)]_{t=0} = i \partial_{x_1} \delta (x_1-x_2) \neq 0 .$$ On the other hand, we have the explicit statement of Gauss’ law, that $G_a = \Delta \cdot \vec E_a = 0$ The crucial idea to resolve this “paradox” is to take the idea that Gauss’ law is a constraint seriously. Hence, the operator $G_a$ is not zero, but when it acts on states we get zero. In the classical theory, Gauss’ law is a restriction on the initial data. In the quantum theory, we now say that Gauss’ law defines physical states, via the equation $G \|\Psi\rangle_{phys}=0$. Non-physical states can, by definition, do whatever they want and there is no need that they respect Gauss’ law. (This is the crucial idea behind the Gupta-Bleuler formalism). Okay, this was a long convoluted story. What’s the message to take away here? ## The Crucial Points to Take Away The crucial point is that Gauss’ law only forces gauge equivalence under gauge transformations which are generated by $G_a$ and become trivial at spatial infinity. Certainly, there are other possibly gauge transformations, but Gauss’ law has nothing to say about them. Quantization is a science on its own and this post is not about quantization. However, I hope the few paragraphs above, make clear that when you come from the constrained Hamiltonian quantization perspective a few things are quite natural: – $A_0(x) =0$ is an obvious choice to simplify further calculations. – The residual gauge freedom after fixing $A_0(x) =0$ is generated by Gauss’ law. This gauge freedom includes only a very particular subset of gauge transformations. In the discussion above, we have seen that Gauss’ law only generates gauge transformations via $\text{exp}\left(\frac{1}{g} \int d^3 x \phi(\vec x)_a G_a\right)$ that include a gauge function that vanishes at infinity $\phi (-\infty) = \phi (\infty) =0$. When you come from the perspective of constrained Hamiltonian quantization, it makes sense to treat those gauge transformations that involve a gauge function that does become zero at spatial infinity as special. All other gauge transformations are not forced by Gauss law to leave physical states invariant. ## Why Only Trivial Gauge Transformations? Take note that we still haven’t fully elucidated that assumptions that were used in the first post to explain the standard story of the QCD vacuum. So far, we have only seen why the gauge transformations with a gauge function that satisfies $\phi (-\infty) = \phi (\infty) =0$ is special because it is forced by Gauss’ law to be a symmetry of physical states. We still have to talk about, why we restricted ourselves in the first post those gauge transformations that involve a gauge function that becomes a multiple of $2 \pi$ at spatial infinity, instead of all gauge transformations. In other words, why was it sufficient to restrict ourselves to gauge transformations that become trivial at infinity $g(x) \to 1$ for $\|x\| \to \infty$? If you look through the literature, you will find many reasons. However, if you find many arguments, this is usually a red flag that things aren’t as bulletproof as people would like them to be. I’m not the only one who feels this way. For example, Itzykson and Zuber write in their famous QFT book: “there is actually no very convincing argument to justify this restriction”. In addition, while Roman Jackiw (one of the founding fathers of the standard picture of the QCD vacuum) claimed in the original paper that this restriction $g(x) \to 1$ for $\|x\| \to \infty$ simply follows because “we study effects which are local in space” (1976), he later became more careful. In his “Introduction to Yang-Mills theory” (1980) he wrote We shall make a very important hypothesis concerning the physically admissible finite transformations. While some plausible arguments can be given in support of this hypothesis (see below) in the end we must recognize it as an assumption, without which the subsequent development cannot be made. We shall assume that the allowed gauge transformation matrices U tend to a definite limit as r passes to infinity $$lim_{r\to\infty} U(r)= U_\infty$$ Here $U_\infty$ is a global (position-independent) gauge transformation matrix. With this hypothesis, we are excluding gauge transformations which do not have a well-defined or unique limit at $r \to \infty$.” He then lists three arguments why this restriction is plausible. This is good style, but unfortunately, most other presentations of the QCD vacuum gloss over this important point and act like the restriction is obvious for some reason. In fact, I have collected an even longer list with around 10 arguments that are put forward in textbooks and papers to justify the restriction $g(x) \to 1$ for $\|x\| \to \infty$. Some are better than others and I think one is really strong, but ultimately one needs to admit that this restriction “has always been recognized as weak but it had seemed necessary.” (Source) Unfortunately, this recognition has not been loud and clear enough. Many students I have talked to think that this restriction has something do with the fact that we investigate “finite energy” solutions of the Yang-Mills equations. This, however, can not be correct, because the energy shouldn’t care about gauge transformations at all. Hence, there can be no reason that follows from some energy argument for the restriction to a subset of gauge transformations. Another popular argument is that we need some boundary conditions and that our particular choice shouldn’t matter because we do not care about what happens at infinity. (See for example page 166 in “Quarks, leptons and gauge fields” by Huang, where he writes “It is a common article of faith to assume that boundary conditions at large distance have no effect on local phenomena”.). This argument is exactly what Jackiw proposed in his first paper I quoted above. However, this argument is hardly satisfactory. Our choice of boundary conditions shouldn’t make any difference. However, when we do not restrict ourselves to the subset that satisfies $g(x) \to 1$ for $\|x\| \to \infty$, there is no homotopy discussion possible and the usual periodic vacuum picture does not emerge. Hence the boundary condition seems to make a big difference. Another way to see that this argument is problematic is to consider different definite boundary conditions. If they do not matter, so why not? For example, instead of $g(x) \to 1$ for $\|x\| \to \infty$, which leads to a compactification of space to the sphere $\mathbb{R}^3 \to S^3$, we could consider a large box and impose periodic boundary conditions. Then space does not become a sphere, but a torus and the homotopy classification is completely different. My favorite point of view is to ignore all these nasty things, by analyzing the QCD vacuum from a completely different perspective. I will describe this alternative description in the next post in this series. But for now, how can we make sense of the restriction $g(x) \to 1$ for $\|x\| \to \infty$? We already know that the gauge transformations that involves a gauge function that becomes zero at infinity are special, because these are generated by Gauss’ law and hence are true symmetries of the physical states. With this in mind, probably the best argument is that tunneling does only happens from a vacuum with winding number zero (i.e. one that is “Gauss’ law gauge equivalent” to $A_\mu =0$), to a vacuum state with integer winding number (i.e. one that we get from $A_\mu =0$ with a gauge transformation that satisfies $g(x) \to 1$ for $\|x\| \to \infty$). If we can show this, it seems reasonable that we neglect other ground states are not reachable by tunneling processes. To show this, imagine spacetime as a cylinder. Each slice of the cylinder is the complete space $\mathbb{R}^3$ at a given time $t$. The lower cap of the cylinder is space at $t = – \infty$ and the upper cap space at $t = \infty$. Now, we start at $t= -\infty$ with our quantum field in a vacuum configuration with winding number zero. We have the gauge freedom to choose $A_\mu (\vec x , -\infty) =0$. (However, take note that all other pure gauge configurations, that are generated by a Gauss’ law gauge transformation are equally valid. The gauge transformations generated by Gauss’ law are those that have a gauge function in the exponent that satisfies $f(x) \to 0$ for $\|x\| \to \infty$. All configurations that we get from $A_\mu(\vec x , -\infty) =0$ with such a gauge transformations are also winding number zero configurations, because they are gauge equivalent to $A_\mu(\vec x , -\infty) =0$.) Each pure gauge configuration of $A_\mu$, which means $A_\mu = U^\dagger (\vec x, t)\partial U(\vec x, t)$, is a vacuum configuration. $A_\mu (\vec x , -\infty) =0$ means $U(\vec x, -\infty) =\text{const}.$ This is the naive vacuum configuration and we want to investigate what non-trivial configurations of our quantum field are possible. We are especially interested in what the final configurations at $t = \infty$ can be. Now, remember that we work in the temporal gauge. As already mentioned above, this choice of gauge does not fix the gauge freedom completely, but instead all time-independent gauge transformations are still permitted. In addition, we are interested in finite energy processes. This requirement means that at spatial infinity our field energy must vanish, which means that our quantum field must be in a pure gauge configuration at spatial infinity. (This is discussed in more detail in the first post). We now put these three puzzle pieces together: At $t = – \infty$, we have $A_\mu(\vec x , -\infty) =0$ and therefore $U(\vec x, -\infty) =\text{const}.$ At the boundary, $A_\mu$ must stay pure gauge all the way from $t= – \infty$ to $t=\infty$: $A_\mu(\infty, t) = U^\dagger (\infty, t)\partial U(\infty, t)$. The crucial thing is now that at $t = -\infty$, we started with a configuration that corresponds to $U(\vec x, -\infty) =\text{const}$. Thus at this time, we also have at spatial infinity $U(\infty, -\infty) =\text{const}$. In the temporal gauge, only time-independent gauge transformations are permitted. Therefore, $U(\infty, -\infty) =\text{const} = U(\infty, t) = U(\infty)$ is fixed and does not change as we time moves on! Therefore, we also have at the upper cap of the cylinder, i.e. at $t=\infty$ are pure gauge configuration (because we consider a vacuum state to vacuum state transition) $A_\mu(\infty, \infty) = U^\dagger (\infty, \infty)\partial U(\infty, \infty)$ with $U(\infty, -\infty) =\text{const}$. Hence, when we start with a vacuum configuration, which means a gauge transformation of $A_\mu =0$ with $U(\vec x, -\infty) =\text{const}$, our field can only transform into configurations that are gauge transformations of $A_\mu =0$ with $U(\vec x, \infty) =\text{const}$. You may now wonder why the anything non-trivial is possible at all. The answer is that the restriction that $A_\mu$ must be pure gauge only holds: – At the lower cap, i.e. for $A_\mu(\vec x , -\infty)$, because we start with a vacuum configuration. – At the curved surface boundary of the cylinder, i.e. for $A_\mu(\infty, t)$, because we only consider finite energy process, which requires that the field energy vanishes at spatial infinity and thus that $A_\mu$ is pure gauge there. – At the upper cap $A_\mu(\vec x , \infty)$, because we investigate vacuum to vacuum transitions. Thus, in between, there is a lot of non-trivial stuff that can happen. Especially, on the way from the pure gauge at $t=-\infty$ to pure gauge $\infty$ it can be in non-pure-gauge configurations somewhere in space at some point in time. In other words, it is possible, within our restrictions that the field is, on the way from $t=-\infty$ to $t=\infty$, in a configuration that corresponds to non-zero field energy. These non-zero field energy configurations are exactly the potential barrier that we talked about in the first post. In this sense, we are dealing here with tunneling phenomena. We start with a vacuum state, i.e. zero field energy. Nevertheless, the field manages to get into configurations that “normally” would require energy to get into. However, because we are dealing with a quantum theory, it is possible that the field tunnels through these, classically forbidden configurations. Only because this is, in principle possible, does not mean that it actually happens. However, there are solutions of the Yang-Mills equations that exactly describe such processes: the famous instanton solutions. Thus it seems reasonable that such tunneling indeed happens. (It is really cool to see how an instanton solution describes the process of how a vacuum configuration transforms into a different vacuum configuration. Different here means with a different winding number. However, there are already good descriptions in the literature and I’m currently not motivated to write down all the required formulas. An especially nice and explicit description can be found on page 168 (section 8.6.2 “Instantons as Tunneling Solutions”) in “Quarks, Leptons & Gauge Fields by Kerson Huang). The crucial message of the description above is that we necessarily get a final field configuration that corresponds to a pure gauge configuration with $U(\vec x, \infty) =\text{const}$. The constant is necessarily the same constant that we started with at $t=-\infty$. Therefore, transitions only happen between pure gauge configurations that are generated by gauge transformations which have the same trivial limit at spatial infinity. (Trivial means that there is no dependence on angles, but instead the gauge transformation becomes the same constant no matter from which direction we approach $\|x\| = \infty$. ) Now, let’s connect this discussion with our previous discussion of Gauss’ law: Recall that above we argued that the gauge transformations generated by Gauss’ law are somewhat special because we use Gauss’ law to identify physical states in a quantum theory. These gauge transformations are exactly those with a gauge function $f(x)$ in the exponent that becomes zero at spatial infinity: $U(x) = e^{if(x) \hat r \cdot \vec G}$ with $f(\infty) =0$. The naive vacuum configuration is $A_\mu=0$. All configurations that we get by transforming this configuration with a gauge transformation that is generated by Gauss’ law are completely equivalent to $A_\mu =0$, because that’s how we use Gauss’ law in a quantum theory. Therefore, starting from the naive vacuum configuration, or one that is physically equivalent, we have $U(\infty , – \infty) = 1$. Therefore, with the arguments from above, we can only end up in a configuration with $U(\infty, \infty)=1$, too! In this sense, it is sufficient to restrict ourselves to gauge transformations that satisfy $U(x) \to 1$ for $\|x\| \to \infty$. This is the moral of this long story. In my next post about the QCD vacuum, I will present another way to look at it. With this different interpretation, we can avoid all the confusing details \| 4,964 Words	2021-01-28 01:25:15	{"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": 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": 0.9197912216186523, "perplexity": 284.15021013090103}, "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-2021-04/segments/1610704835583.91/warc/CC-MAIN-20210128005448-20210128035448-00098.warc.gz"}
http://2012wiki.com/index.php?title=Schumann's_Resonance	# Schumann's Resonance The Schumann resonance (SR) is a set of spectrum peaks in the extremely low frequency (ELF) portion of the Earth's electromagnetic field spectrum. Schumann resonances are global electromagnetic resonances, excited by lightning discharges in the cavity formed by the Earth surface and the ionosphere. ## Description This global electromagnetic resonance phenomenon is named after physicist Winfried Otto Schumann who predicted it mathematically in 1952. Schumann resonance occurs because the space between the surface of the Earth and the conductive ionosphere acts as a waveguide. The limited dimensions of the Earth cause this waveguide to act as a resonant cavity for electromagnetic waves in the ELF band. The cavity is naturally excited by energy from lightning strikes. Schumann resonances are observed in the power spectra of the natural electromagnetic background noise, as separate peaks at extremely low frequencies (ELF) around 8, 14, 20, 26 and 32 Hz. The fundamental mode of the Schumann resonance is a standing wave in the Earth-ionosphere cavity with a wavelength equal to the circumference of the Earth. This lowest-frequency (and highest-intensity) mode of the Schumann resonance occurs at a frequency of approximately 7.8 Hz. The ninth overtone lies at approximately 60 Hz and thus the cavity is also driven by the North American power grid. Detectable overtones extend upwards into the kilohertz range. Schumann resonances are used to track global lightning activity. Owing to the connection between lightning activity and the Earth's climate they can also be used to monitor global temperature variations and variations of upper water vapor. Extraterrestrial lightning may also be detected and studied with Schumann resonances. Schumann resonance has been used for research and monitoring of the lower ionosphere on Earth and was suggested for exploration of lower ionosphere parameters on celestial bodies. Schumann resonances can be used to track geomagnetic and ionospheric disturbances. More recently, Schumann resonances have been used for monitoring transient luminous events – sprites, elves, jets, and other upper atmospheric lightning. A new field of interest using Schumann resonances is related to short-term earthquake prediction. Schumann resonances have gone beyond the boundaries of physics, invading medicine, raising interest in artists and musicians, and gaining interest from fringe fields such as psychobiology. ## History The first suggestion that an ionosphere existed, capable of trapping electromagnetic waves, was made by Heaviside and Kennelly in 1902 [1] [2]. It took another twenty years before Edward Appleton and Barnett in 1925 [3], were able to prove experimentally the existence of the ionosphere. However, even prior to this, the first documented observations of global electromagnetic resonances were made by Nikola Tesla in 1905 and formed the basis for his scheme for wireless energy transmission [4]. Although some of the most important mathematical tools for dealing with spherical waveguides were developed by Watson in 1918 [5], it was Winfried Otto Schumann who first studied the theoretical aspects of the global resonances of the earth-ionosphere waveguide system, known today as the Schumann resonances. In 1952-1954 Schumann, together with Köning, attempted to measure the resonant frequencies [6] [7] [8] [9] . However, it was not until measurements made by Balser and Wagner in 1960-1963 [10] [11] [12] [13] [14] that adequate analysis techniques were available to extract the resonance information from the background noise. Since then there has been an increasing interest in Schumann resonances in a wide variety of fields. ## Basic Theory Lightning discharges are considered as the primary natural source of Schumann resonances. Lightning channels behave like a huge antenna which radiates electromagnetic energy as impulsive signals at frequencies below about 100 kHz [15]. These signals are very weak, but the earth-ionosphere waveguide behaves like a resonator at ELF frequencies and amplifies the spectral signals from lightning at the resonance frequencies [15]. In an ideal cavity, the resonant frequency of the $n$-th mode $f_{n}$ is determined by the Earth radius $a$ and the speed of light $c$ [6]. $f_{n} =\frac{c}{2 \pi a}\sqrt{n(n+1)}$ The real Earth-ionosphere waveguide is not a perfect electromagnetic cavity. Losses due to finite ionosphere electrical conductivity make the system resonate at lower frequencies than would be expected in an ideal case, and the observed peaks are wide. In addition there are a number of horizontal asymmetries – day-night transition, latitudinal changes in the Earth magnetic field, sudden ionospheric disturbances, polar cap absorption, etc. that complicate the Schumann resonance power spectra. ## Measurements Today Schumann resonances are recorded by many stations around the world. The electromagnetic sensors used to measure Schumann resonances consist of two horizontal antennas for receiving the magnetic field in the north-south and the east-west direction and one vertical antenna for observing the vertical electric field. Since Schumann resonance frequencies are extremely low, practical antennas would have to be hundreds of kilometers long. In addition, the Schumann resonance electric field is much smaller than the static electric field in the atmosphere and the Schumann resonance magnetic field is orders of magnitude smaller than the Earth magnetic field [16] . Therefore, special receivers and antennas are needed to measure Schumann resonances. The electric component is commonly measured with a ball antenna, suggested by Ogawa et al. in 1966 [17] , connected to a high-impedance amplifier. The magnetic field is measured with magnetic induction coils consisting of tens of thousands of turns around material with very high magnetic permeability. ## Applications ### Global lightning activity From the very beginning of Schumann resonance studies, they were used to monitor global lightning activity by tracking changes in Schumann resonance field intensities. At any given time there are about 2000 thunderstorms around the globe [18]. Producing ~50 lightning events per second [19], these thunderstorms create the background Schumann resonance signal. Determining the spatial lightning distribution from Schumann resonance records is a complex problem: in order to properly estimate the lightning intensity from Schumann resonance records it is necessary to account for the distance to lightning sources. The common approach is to make a preliminary assumption on the spatial lightning distribution, basing on the known properties of lightning climatology. An alternative approach is placing the receiver at the North or South Pole, which remain approximately equidistant from the main thunderstorm centers during the day [20]. A distinct method, not requiring preliminary assumptions on the lightning distribution [21] is based on the decomposition of the average background Schumann resonance spectra, utilizing ratios between the average electric and magnetic spectra and between their linear combinations. #### Diurnal variations The best documented and the most debated features of the Schumann resonance phenomenon are the diurnal variations of the background Schumann resonance power spectrum. A characteristic Schumann resonance diurnal record reflects the known properties of global lightning activity. The vertical electric field, which is equally sensitive in all directions and therefore measures the global lightning, shows three dominant maxima, associated with the three “hot spots” of planetary lightning activity: 9 UT (Universal Time) peak, linked to the increased thunderstorm activity from south-east Asia; 14 UT peak associated with the peak in African lightning activity; and the 20 UT peak resulting for the increase in lightning activity in South America. The time and amplitude of the peaks vary throughout the year, reflecting the seasonal changes in lightning activity. ##### ”Chimney” ranking In general, the African peak is the strongest, reflecting the major contribution of the African “chimney” to the global lightning activity. The ranking of the two other peaks – Asian and American is the subject of a vigorous dispute among Schumann resonance scientists. Experimental Schumann resonance data show a greater contribution from Asia than from South America. This contradicts optical satellite and climatological lightning data that show the South American thunderstorm center stronger than the Asian center [19]. The reason for such disparity remains unclear. Williams and Sátori [22] suggest that in order to obtain “correct” Asia-America chimney ranking, it is necessary to remove the influence of the day/night variations in the ionospheric conductivity (day-night asymmetry influence) from the Schumann resonance records. On the other hand, such “corrected” records presented in the work by Sátori et al. [23] show that even after the removal of the day-night asymmetry influence from Schumann resonance records, the Asian contribution remains greater than American. Similar results were obtained by Pechony et al. [24] who calculated Schumann resonance fields from satellite lightning data. Both simulations – those neglecting the day-night asymmetry, and those taking this asymmetry into account, showed same Asia-America chimney ranking. As for today, the reason for the “invert” ranking of Asia and America chimneys in Schumann resonance records remains unclear and the subject requires further, targeted research. ##### Influence of the day-night asymmetry In the early literature the observed diurnal variations of Schumann resonance power were explained by the variations in the source-receiver (lightning-observer) geometry [10]. It was concluded that no particular systematic variations of the ionosphere (which serves as the upper waveguide boundary) are needed to explain these variations [25]. Subsequent theoretical studies supported the early estimations of the small influence of the ionosphere day-night asymmetry (difference between day-side and night-side ionosphere conductivity) on the observed variations in Schumann resonance field intensities [26]. The interest in the influence of the day-night asymmetry in the ionosphere conductivity on Schumann resonances gained a new strength in the 1990s, after publication of a work by Sentman and Fraser [27]. Sentman and Fraser developed a technique to separate the global and the local contributions to the observed field power variations using records obtained simultaneously at two stations. Sentman and Fraser interpreted the local contribution as ionosphere height variation. Their work convinced many scientists in the importance of the ionospheric day-night asymmetry and inspired numerous experimental studies. However recently it was shown that results obtained by Sentman and Fraser can be simulated with a uniform model (without taking into account ionosphere day-night variation) and therefore cannot be interpreted in terms of ionosphere height variation [28] . Schumann resonance amplitude records show significant diurnal and seasonal variations which in general coincide in time with the times of the day-night transition (the terminator). This time-matching seem to support the suggestion of a significant influence of the day-night ionosphere asymmetry on Schumann resonance amplitudes. There are records showing almost clock-like accuracy of the diurnal amplitude changes [23]. On the other hand there are numerous days when Schumann Resonance amplitudes do not increase at sunrise or do not decrease at sunset. There are studies showing that the general behavior of Schumann resonance amplitude records can be recreated from diurnal and seasonal thunderstorm migration, without invoking ionospheric variations [26] [24]. Two recent independent theoretical studies have shown that the variations in Schumann resonance power related to the day-night transition are much smaller than those associated with the peaks of the global lightning activity, and therefore the global lightning activity plays a more important role in the variation of the Schumann resonance power [29] [24]. The relative importance of the day-night asymmetry in Schumann resonance amplitude records is still debated. Successful monitoring of global thunderstorm activity with Schumann resonances relies on the proper interpretation of experimental data. It is therefore vital to understand and correctly interpret the major features of Schumann resonance field power variations. #### The “inverse problem” One of the interesting problems in Schumann resonances studies is determining the lightning source characteristics (the “inverse problem”). Temporally resolving each individual flash is impossible,Template:Huh but there are intense ELF transient events, also named ‘‘Q bursts’’. Q-bursts are triggered by intense lightning strikes, associated with a large charge transfer and often high peak current [17]. Q-bursts can exceed the amplitude of the background signal level by a factor of 10 and appear with intervals of ~10sec [21], which allows to consider them as isolated events and determine the source lightning location. The source location is determined with either multi-station or single-station techniques. The multi-station techniques are more accurate, but require more complicated and expensive facilities. ### Transient luminous events research It is now believed that many of the Schumann resonances transients (Q bursts) are related to the transient luminous events (TLEs). In 1995 Boccippio et al. [30] suggested that sprites, the most common TLE, are produced by positive cloud-to-ground lightning occurring in the stratiform region of a thunderstorm system, and are accompanied by Q-burst in the Schumann resonances band. Recent observations [30] [31] reveal that occurrences of sprites and Q bursts are highly correlated and Schumann resonances data can possibly be used to estimate the global occurrence rate of sprites [32]. ### Climate change research Global climate change is the subject of intense debate and concern. One of the important aspects in understanding global climate change is the development of tools and techniques that would allow continuous and long-term monitoring of processes affecting the global climate. Schumann resonances are one of the very few tools that can provide such global information reliably and cheaply. #### Global temperature Williams [1992] [33] suggested that global temperature may be monitored with the Schumann resonances. The link between Schumann resonance and temperature is lightning flash rate, which increases nonlinearly with temperature [33]. The nonlinearity of the lightning-to-temperature relation provides a natural amplifier of the temperature changes and makes Schumann resonance a sensitive “thermometer”. Moreover, the ice particles that are believed to participate in the electrification processes which result in a lightning discharge [34] have an important role in the radiative feedback effects that influence the atmosphere temperature. Schumann resonances may therefore help us to understand these feedback effects. #### Upper tropospheric water vapor Tropospheric water vapor is a key element of the Earth’s climate, which has direct effects as a greenhouse gas, as well as indirect effect through interaction with clouds, aerosols and tropospheric chemistry. Upper tropospheric water vapor (UTWV) has a much greater impact on the greenhouse effect than water vapor in the lower atmosphere [35], but whether this impact is a positive, or a negative feedback is still uncertain [36]. The main challenge in addressing this question is the difficulty in monitoring UTWV globally over long timescales. Continental deep-convective thunderstorms produce most of the lightning discharges on Earth. In addition, they transport large amount of water vapor into the upper troposphere, dominating the variations of global UTWV. Price [2000] [37] suggested that changes in the UTWV can be derived from records of Schumann Resonances. ### Extraterrestrial lightning Existence of Schumann resonances is conditioned primarily by two factors: 1) presence of a substantial ionosphere with electric conductivity increasing with height from low values near the surface (or a high-conductivity layer, in case of gaseous planets); 2) source of excitation of electromagnetic waves in the ELF range. In Solar System there are five candidates for Schumann resonance detection: Venus, Mars, Jupiter, Saturn and its moon Titan. Modeling Schumann resonances on the planets and moons of the Solar System is complicated by the lack of knowledge of the waveguide parameters, and today there is no possibility to validate the results. Nevertheless, theoretical results aid to estimate the possibility of detecting Schumann resonances on a planet. The strongest evidence for lightning on Venus comes from the impulsive electromagnetic waves detected by Venera 11 and 12 landers. Schumann resonances on Venus were studied by Nickolaenko and Rabinowicz [1982] [38] and Pechony and Price [2004] [39]. Both studies yielded very close results, indicating that Schumann resonances should be easily detectable on this planet, should any sensor survive long enough in the harsh Venusian environment. On Mars lightning activity has not been detected, but charge separation and lightning strokes are considered possible in the Martian dust storms [40] [41] . Martian global resonances were modeled by Sukhorukov [1991] [42], Pechony and Price [2004] [39] and Molina-Cuberos et al. [2006] [43] . The results of the three studies are somewhat different, but it seems that at least the first two Schumann resonance modes should be detectable. It was long suggested that lightning dischargers take place on Titan [44] , but recent data from Cassini-Huygens seems to indicate that there is no lightning activity on this largest satellite of Saturn. Due to the recent interest in Titan, associated with the Cassini-Huygens mission, its ionosphere is perhaps the most thoroughly modeled today. Schumann resonances on Titan received more attention than on other celestial bodies. Schumann resonances on Titan were studied by Besser et al. [2002] [45] , Morente et al. [2003] [46] , Molina-Cuberos et al. [2004] [47] , Nickolaenko et al. [2003] [48] and Pechony and Price [2004] [39] . It appears that only the first Schumann resonance mode might be detectable on Titan. Jupiter is the only planet where lightning activity is well established. Existence of lightning activity on this planet was predicted by Bar-Nun [1975] [49] and it is now supported by data from Galileo, Voyagers 1 and 2, Pioneers 10 and 11 and Cassini. Saturn is also expected to have intensive lightning activity, but the three visiting spacecrafts – Pioneer 11 in 1979, Voyager 1 in 1980 and Voyager 2 in 1981, failed to provide any convincing evidence. Even the strong storm monitored on Saturn by the Cassini spacecraft produced no visible lightning flashes. Little is known about the electrical parameters of Jupiter and Saturn interior. Even the question of what should serve as the lower waveguide boundary is a non-trivial one in case of the gaseous planets. There seem to be no works dedicated to Schumann resonances on Saturn. Up to date there was only one attempt to model Schumann resonances on Jupiter [50]. Should someone find a way to hang Schumann resonance sensor in the Jupiter’s atmosphere, the Schumann resonances there should be easily detectable.	2015-01-27 01:01:48	{"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": 0.607100248336792, "perplexity": 1799.3208776173083}, "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-2015-06/segments/1422122222204.92/warc/CC-MAIN-20150124175702-00042-ip-10-180-212-252.ec2.internal.warc.gz"}
http://clay6.com/qa/26698/a-vertex-of-an-equilateral-triangle-is-1-1-and-the-opposite-side-is-x-y-1-0	Comment Share Q) # A vertex of an equilateral triangle is (1,1) and the opposite side is $x+y+1=0$.Find the equations of other sides? $\begin {array} {1 1} (A)\;y-1=(2+\sqrt 3)(x-1)\: and\: (y-1)=(2-\sqrt 3)(x-1) \\ (B)\;y-1=(3+\sqrt 2)(x-1)\: and \: y-1=(3-\sqrt 2)(x-1) \\ (C)\;y+1=(2+\sqrt 3)(x+1)\: and \: (y-1)=(2-\sqrt 3)(x-1) \\ (D)\;y+1=(3+\sqrt 2)(x+1)\: and \: (y+1)=(3-\sqrt 2)(x-1) \end {array}$ Comment A) Toolbox: • Slope of the line $ax+by+c=0$ is $-\large\frac{a}{b}$ • The angle between any two lines $(\theta)$ with slopes $m_1$ and $m_2$ is given by $tan\theta=\bigg\|\large\frac{m_1-m_2}{1+m_1m_2}\bigg\|$ • Eqn. of the line through the point $(x_1),y_1)$ and having slope $m$ is $y-y_1=m(x-x_1)$ Step 1 Let the given vertex be $A(1,1)$ Also given that the equation of one side $BC$ is $x+y+1=0$ $\Rightarrow\:$slope of $BC=m=-1$ Let the slope of $AB=m_1$ and slope of $AC=m_2$ step 2 Since the $\Delta\:ABC$ is equilateral triangle, angle between the lines $AB$ and $BC$ is $60^{\circ}$ and angle between $AC$ and $BC$ is also $60^{\circ}$. We know that angle between any two lines $(\theta)$ with slopes $m_1$ and $m_2$ is given by $tan\theta=\bigg\|\large\frac{m_1-m_2}{1+m_1m_2}\bigg\|$ $\therefore\:tan60^{\circ}=\bigg\|\large\frac{m-m_1}{1+m.m_1}\bigg\|$ $\Rightarrow\:\sqrt 3=\bigg\|\large\frac{-1-m_1}{1+(-1).m_1}\bigg\|$ $\Rightarrow\:\sqrt 3(1-m_1)=-1-m_1$ $\Rightarrow\:m_1(1-\sqrt 3)=-1-\sqrt 3$ $\Rightarrow\:m_1=\large\frac{\sqrt 3+1}{\sqrt 3-1}$ Rationalising the denominator we get $m_1=2+\sqrt 3$ Step 3 Similarly angle between $AC$ and $BC$ is given by $tan60^{\circ}=\bigg\|\large\frac{m_2-m}{1+m.m_2}\bigg\|$ $\Rightarrow\:\sqrt 3=\bigg\|\large\frac{m_2-(-1)}{1+(-1).m_2}\bigg\|$ $\Rightarrow\:\sqrt 3(1-m_2)=1+m_2$ $\Rightarrow\:m_2(1+\sqrt 3)=\sqrt 3-1$ $\Rightarrow\:m_2=\large\frac{\sqrt 3-1}{\sqrt 3+1}$ Rationalising the denominator, we get $m_2=2-\sqrt 3$ Step 4 Hence equation of AB is $y-1=(2+\sqrt 3)(x-1)$ and Equation of $AC$ is $y-1=(2-\sqrt 3)(x-1)$ Hence (a) is the correct answer.	2019-10-16 02:58:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.93436598777771, "perplexity": 299.86389823125603}, "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/1570986661296.12/warc/CC-MAIN-20191016014439-20191016041939-00120.warc.gz"}
http://www.acmerblog.com/POJ-1254-Hansel-and-Grethel-blog-332.html	2013 11-09 # Hansel and Grethel On a warm summer afternoon, Hansel and Grethel are walking together in the fields. It is getting late and, to be honest, they are lost. Grethel is a little scared, still vividly remembering the last time they got lost in the forest. That time, an evil witch had locked them inside a house built of gingerbread and sugar! But Hansel can reassure her: this time they are well prepared. Hansel has taken a map and a compass with him! Hansel picks two clearly outstanding features in the landscape, and uses the compass to measure the direction towards both objects. Grethel locates the objects on the map, and writes down the corresponding map coordinates. Based on this information, they will be able to accurately determine their own position on the map. The coordinates of two marker objects, and the direction (angle from the North) towards these objects are known. Write a program which uses this data to calculate the coordinates of Hansel and Grethel’s current location. The first line of the input contains one positive number: the number of situations in which a position must be determined. Following are two lines per situation, describing the two marker objects. Each marker object is described by a line containing three integer numbers: the x-coordinate of the object on the map (0 <= x <= 100); the x-axis runs West-to-East on the map, with increasing values towards the East. the y-coordinate of the object on the map (0 <= y <= 100); the y-axis runs South-to-North on the map, with increasing values towards the North. the direction d of the object in degrees (0 <= d <= 360); with 0 degree = North, 90 degree = East, 180 degree = South, and so on. To keep the position calculations accurate, Hansel makes sure that the directions of the two objects are not exactly equal, and do not differ by exactly 180 degree. One line per situation, containing the result of the position calculation: two numbers, separated by a space, each having exactly 4 digits after the decimal point. These numbers represent the x and y coordinates of the position of Hansel and Grethel (0 <= x,y <= 100). Round the numbers as usual: up if the next digit would be >= 5, down otherwise. 2 30 50 90 20 40 180 30 40 96 20 20 150 20.0000 50.0000 7.0610 42.4110 import java.text.DecimalFormat; import java.util.Scanner; public class Main{ public static void main(String[] args) { Scanner cin = new Scanner(System.in); DecimalFormat df1 = new DecimalFormat("0.0000"); int n = cin.nextInt(); while(n-- > 0) { int x1 = cin.nextInt(); int y1 = cin.nextInt(); double t1 = cin.nextInt(); int x2 = cin.nextInt(); int y2 = cin.nextInt(); double t2 = cin.nextInt(); double x, y; t1=t1 / 360 * 2 * Math.PI; t2=t2 / 360 * 2 * Math.PI; y = (Math.cos(t2)(Math.sin(t1)y1-Math.cos(t1)x1)-Math.cos(t1)(Math.sin(t2)y2-Math.cos(t2)x2))/(Math.sin(t1-t2)); x = (Math.sin(t2)(Math.sin(t1)y1-Math.cos(t1)x1)-Math.sin(t1)(Math.sin(t2)y2-Math.cos(t2)x2))/(Math.sin(t1-t2)); System.out.println(df1.format(x)+" "+ df1.format(y)); } } }	2017-01-22 22:18:50	{"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": 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": 0.30531153082847595, "perplexity": 1843.2250602605943}, "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-2017-04/segments/1484560281649.59/warc/CC-MAIN-20170116095121-00543-ip-10-171-10-70.ec2.internal.warc.gz"}
https://mathoverflow.net/questions/245334/fibration-when-central-fibre-is-a-calabi-yau-variety-with-canonical-singularitie	# Fibration when central fibre is a Calabi-Yau variety with canonical singularities Let $f\colon X\to Y$ be a surjective proper holomorphic fibre space such that $X$ and $Y$ are projective varieties and central fibre $X_0$ is Calabi-Yau variety with canonical singularities, then can we say that all the fibres $X_t$ are also Calabi-Yau varieties ? I know that if we replace "Calabi-Yau" with "pseudoeffective" then this this statement is correct. • What is your definition of Calabi-Yau? If the dimension of the fiber is at least $3$, then the "standard" definition of Calabi-Yau includes vanishing of both $h^{0,1}$ and $h^{0,2}$. Since your central fiber is projective (hence Kaehler), this implies vanishing of $H^1(X_0,\mathcal{O}_X)$ and $H^2(X_0,\mathcal{O}_X)$. Thus, all invertible sheaves on $X_0$ extend uniquely to nearby fibers. In particular, since $\omega_{X_0}$ equals $\mathcal{O}_{X_0}$, this also holds on nearby fibers. – Jason Starr Jul 28 '16 at 18:12 • Even if you don't assume that $h^{0,1}=h^{0,2}$ (in char 0) it still follows that nearby fibers have trivial canonical bundle: Since $X_0$ is smooth, $f:X\to Y$ is smooth on a neighborhood of $0\in Y$ (presumably $Y$ is smooth and hence by standard reductions, we may assume that $Y$ is a curve). By Hodge theory $h^0(K_{X_y})$ is deformation invariant and so $h^0(K_{X_y})>0$. Since $+/-K_{X_0}$ is nef, so is $+/-K_{X_y}$. But the $K_{X_y}$ is numerically equivalent to 0 and effective so that $K_{X_y}$ is linearly equivalent to 0. Does this (or the above) answer your question? – Hacon Aug 1 '16 at 2:14 • Central fibre $X_0$ may be singular Calabi-Yau, with canonical singularities – user21574 Aug 1 '16 at 11:35 Assume for simplicity that $Y$ is a smooth curve. Since $X_0$ has canonical, then by Theorem 1.4 of http://arxiv.org/pdf/math/9809091.pdf, we may assume that $X$ is canonical. Nearby fibers are then also canonical (see eg. Theorem 4.5.1 http://arxiv.org/pdf/alg-geom/9601026.pdf). The proof of Theorem 1.4 actually shows that $O_X(K_X+X_0)\to O_{X_0}(K_{X_0})$ is surjective and so if $K_{X_0}$ is Cartier, then so is $K_X$ (on a neighborhood of $X_0$). By J. Algebr. Geom. 16, No. 1, 1-18 (2007) we even have that $P_m(X_y)$ is deformation invariant for $m\geq 1$ so in fact $h^0(K_{X_y})>0$ for $y\in Y$. Since $K_{X_0}\equiv 0$, then $K_{X_y}\equiv 0$ and so $K_{X_y}\sim 0$. (One could also conclude using Theorem 1.6 of http://arxiv.org/pdf/math/9809091.pdf).	2020-10-27 03:56:34	{"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": 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": 0.9744473099708557, "perplexity": 193.86010134719373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107893011.54/warc/CC-MAIN-20201027023251-20201027053251-00304.warc.gz"}
https://www.physicsforums.com/threads/covariant-derivative-of-lie-bracket-in-normal-orthonormal-frame.557513/	# Covariant derivative of Lie-Bracket in normal orthonormal frame 1. Dec 6, 2011 ### holy_toaster Hi there, I was doing some calculations with tensors and ran into a result which seems a bit odd to me. I hope someone can validate this or tell me where my mistake is. So I have a normal orthonormal frame field $\{E_i\}$ in the neighbourhood of a point $p$ in a Riemannian manifold $(M,g)$, i.e. Riemannian normal coordinates about $p$ such that $\nabla_{E_i}E_k=0$ and subsequently $[E_i,E_k]=0$ at the point $p$ for all $i,k$. As $[E_i,E_k]=\sum_j c^j_{ik}E_j$ the structure functions $c^j_{ik}$ also vanish at $p$. Now I compute $$\nabla_{E_k}[E_i,E_k]=[E_k,[E_i,E_k]]+\nabla_{[E_i,E_k]}E_k=\sum_{jl}c^l_{ik}c^j_{lk}E_lE_j+\nabla_{[E_i,E_k]}E_k=0$$ at $p$, where the first summand vanishes because of $c^j_{ik}=0$ and the second summand vanishes because the covariant derivative $\nabla_XY$ is tensorial in $X$ so it vanishes if $X=0$. In total that means that in an normal orthonormal frame about a point $p$ not only all the covariant derivatives and the Lie-Bracket of the basis vectors vanish at $p$, but also the covariant derivative of the Lie-Bracket. Does that make sense? Or am I mistaken here? 2. Dec 7, 2011 ### Sina Wouldn't it be simpler to write $[E_i,E_k]=\sum_j c^j_{ik}E_j$ in the covariant derivative so that $\nabla_{E_k}[E_i,E_k] = \nabla_{E_k} \sum_j c^j_{ik}E_j = \sum_j (E_k(c^j_{ik})E_j + c^j_{ik} \nabla_{E_k}(E_j) )$ Now in the nbd of p you assumed that the functions c are all zero and constant so their derivatives should vanish too 3. Dec 7, 2011 ### holy_toaster Aha, yes there appear derivatives of the structure functions $c^i_{jk}$. But the Riemannian normal coordinates about $p$ can always be chosen such that these derivatives vanish at $p$, right? 4. Dec 7, 2011 ### Sina Well on Riemann manifolds, you can find a covering such that on each cover the frame is orthonormal (however the covers do not have to transform well so they might not form an atlas). Now if the structure functions of the frame are identically zero on a chosen nbd of p, then shouldn't the derivatives also vanish through out the whole nbd? As for the point case, if you have a riemannian metric, around any point p you can find coordinates (this time indeed coordinate not just a chart) such that the curvature is identically zero at the point p and roughly proportional to distance to p on other points around p. 5. Dec 8, 2011 ### holy_toaster Now that seems rather strange to me. As I always understood that curvature is exactly the quantity, which we can NOT gauge to zero at some point p by choosing normal coordinates about p. We get coordinate lines which are geodesics and have orthonormal tangent vectors at p, as well as vanishing Christoffel symbols at p which lead to vanishing covariant derivatives of the tangent vectors at the coordinate lines at p. Furthermore, the Lie brackets of the tangent vectors to the coordinate lines vanish in the neighbourhood of p. But as curvature contains derivatives of the Christoffel symbols it is generically not zero at p, in no coordinate system, except for the case when the manifold is flat at p. 6. Dec 8, 2011 7. Dec 8, 2011 ### holy_toaster Sorry, I can't find anything in there, which supports this claim of vanishing curvature at p. Note that curvature is a tensor, whereas Christoffel symbols are not tensors. If the components of a tensor vanish at a point in one coordinate system, they vanish in all coordinate systems, hence the tensor would be zero. But Christoffel symbols are components of a connection, which obey a different law of transformation between coordinates, so they may vanish at point in some coordinates but not in others. 8. Dec 8, 2011 ### Sina Wait you are right sorry curvature does not vanish the christofel symbols do. I have mistaken it with the concept of locally inertial frames. 9. Dec 8, 2011 ### joebohr What do you mean by the structure functions of a tensor? 10. Dec 8, 2011 ### Sina not of the tensor of the vector fields. it is a generalization of the concept of structure constants of a lie algebra-which are really genuine constants due to property of invariant vector fields. These are functions however instead of being constants. since the lie bracket is an operation from the space of vector fields to space of vector fields then lie bracket of any two basis elements (element orthonormal frames) can be given as linear combinations of other basis elements. the coefficients of linear combination are structure functions (or constants for lie algebras).	2018-05-25 03:36:54	{"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": 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": 0.9303052425384521, "perplexity": 317.4006672893937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866938.68/warc/CC-MAIN-20180525024404-20180525044404-00324.warc.gz"}
http://physics.stackexchange.com/tags/stress-strain/new	# Tag Info 1 If you cut something by pushing a blade directly into it, here's what happens: On first contact of blade with material, only the very thin edge of the blade is touching the material, the force per unit area is very high, and the blade cleaves the material very easily. That's why it's almost trivially easy to make score marks in things like aluminum using a ... 0 Here is an intuitive / qualitative answer. Maybe someone else will add some math. I wonder if it's instructive to look at diamond cleaving. As you know, diamond is extremely hard, and conventional machining is very difficult. But if you can find the right fracture plane ((111) and its symmetrical cousins), it's possible to cleave the diamond along that ... 1 Strictly speaking, Young's modulus is not always greater than the shear modulus, but it does tend to work out that way. You can see the reason why if you look at the relation between the two quantities (and Poisson's ratio). $$G = \frac{E}{2(1+\nu)}$$ Combined with the knowledge that $\nu$ can be anywhere in the range $(-1, \frac{1}{2})$, one can see ... 4 When people study continuum mechanics they usually do so at first in $\mathbb{R}^3$ where we have usually implied the usual metric tensor $(g_{ij}) = \operatorname{diag}(1,1,1)$ and the Levi-Civita connection associated with it. In that case vectors and covectors are equivalent: the metric tensor induces the musical isomorphism and allows one to convert ... 0 What you observe as mechanical deformation of a steel spring is an actual displacement (motion) of the atoms constituting the spring. In places, atoms will be slightly closer to their neighbors (compression) and in some other places actually futher apart (tension). The combination of compression on one side and compression on the other side of a beam or a ... 0 There are two forces in presence and, because the system is in equilibrium (=0), the change in one will be compensated by a change in the other. A change in this context is decoded to 'the rate of change in relation to space: $\frac{d}{dx_i}$ ' $\frac{d\sigma}{dx_i}$ is a force per unit length and $\frac{d\psi}{dx_i}$ is an acceleration per unit length, ... -3 whenever external force is applied on the object automatically a restoring force is developed inside the object to restrict the deformation of the object.The ratio of restoring force perpendicular to the surface to the area is known as stress.The ratio of external force perpendicular to the surface to the area is known as pressure. for example if you press ... Top 50 recent answers are included	2015-04-25 18:23:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.7624971866607666, "perplexity": 312.7500564618022}, "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-2015-18/segments/1429246650671.76/warc/CC-MAIN-20150417045730-00264-ip-10-235-10-82.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/1691894/green-function-for-curl-with-wall-problem-references	# Green Function for curl with wall problem - References I was looking for the Green Function of the following problem, on the upper half plane: $u : \mathbb{R}\times \mathbb{R}^+\rightarrow \mathbb{R}^2$, $\mathbb{R}^+$ corresponds to the non-negative positive real axis. $\omega: \mathbb{R}\times \mathbb{R}^+\rightarrow \mathbb{R}$ prescribed $\partial_xu_x+\partial_y u_y = 0$ $\partial_x u_y - \partial_y u_x = \omega$ $u_x(x,y=0) = u_y(x,y=0) = 0$ In this case, the Green Function would correspond to the case $\omega = \delta(y-y_0) \delta(x-x_0)$ Alternatively: $\psi : \mathbb{R}\times \mathbb{R}^+\rightarrow \mathbb{R}$ $u_x = \partial_y \psi$ $u_y = -\partial_x \psi$ $- (\partial_x^2+\partial_y^2)\psi = -\nabla^2 \psi = \omega$ $\partial_x \psi(x,y=0) = \partial_y\psi(x,y=0) = 0$ Do anyone have any good sugestion where to look for green functions of this problem? Any references for books or papers are more than welcome. I know how to work with Green-Functions without boundary constraints, but I don't think that techniques with Fourier transform would work in this particular case. ## migrated from physics.stackexchange.comMar 10 '16 at 18:00 This question came from our site for active researchers, academics and students of physics. • Would Mathematics be a better home for this question? – Qmechanic Mar 10 '16 at 17:35 • Maybe, but I wasn't sure, since it's a more practical question I thought that someone here would have already done something similar. – Hydro Guy Mar 10 '16 at 18:00	2019-09-18 18:21:47	{"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": 0.6575238108634949, "perplexity": 643.47852609858}, "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-2019-39/segments/1568514573323.60/warc/CC-MAIN-20190918172932-20190918194932-00022.warc.gz"}
https://gmatclub.com/forum/what-is-the-sum-of-the-indicated-angles-above-275452.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 19 Feb 2019, 05:02 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track Your Progress every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History ## Events & Promotions ###### Events & Promotions in February PrevNext SuMoTuWeThFrSa 272829303112 3456789 10111213141516 17181920212223 242526272812 Open Detailed Calendar • ### Free GMAT Prep Hour February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST • ### Online GMAT boot camp for FREE February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th. # What is the sum of the indicated angles above? new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 52971 What is the sum of the indicated angles above? [#permalink] ### Show Tags 07 Sep 2018, 00:00 00:00 Difficulty: 35% (medium) Question Stats: 58% (01:45) correct 42% (01:38) wrong based on 41 sessions ### HideShow timer Statistics What is the sum of the indicated angles above? A. 1080 B. 900 C. 810 D. 720 E. 540 Attachment: image013.jpg [ 2.88 KiB \| Viewed 496 times ] _________________ ISB, NUS, NTU Moderator Joined: 11 Aug 2016 Posts: 376 Re: What is the sum of the indicated angles above? [#permalink] ### Show Tags 07 Sep 2018, 02:19 Attachment: image013.jpg [ 12.56 KiB \| Viewed 415 times ] The three lines from a triangle. let the angles of the triangle be e, f, g starting from the point that contains angles x, y, z. The sum of internal angles of a triangle is 180. Now, $$x+y+z+d=360$$, Similarly, $$a+b+c+e=360$$ &, $$p+f+n+m=360$$ Adding all the three equations, we get: $$x+y+z+a+b+c+p+m+n+(d+e+f)=360*3$$ $$d+e+f=180$$ $$this implies, x+y+z+a+b+c+p+m+n=1080-180$$ =900. Answer: B _________________ ~R. If my post was of any help to you, You can thank me in the form of Kudos!! Applying to ISB ? Check out the ISB Application Kit. Director Status: Learning stage Joined: 01 Oct 2017 Posts: 958 WE: Supply Chain Management (Energy and Utilities) Re: What is the sum of the indicated angles above? [#permalink] ### Show Tags 08 Sep 2018, 04:49 Bunuel wrote: What is the sum of the indicated angles above? A. 1080 B. 900 C. 810 D. 720 E. 540 Attachment: image013.jpg a) The sum of exterior angles of a triangle is 360° So, (y+c+p)+(z+m+a)=360+360=720° b) The sum of the interior angles of a triangle is 180°. So, x+n+b=180° Sum of the indicated angles=(y+c+p)+(z+m+a)+(x+n+b)=720°+180°=900° Ans. (B) _________________ Regards, PKN Rise above the storm, you will find the sunshine Retired Moderator Status: Preparing for GMAT Joined: 25 Nov 2015 Posts: 989 Location: India GPA: 3.64 Re: What is the sum of the indicated angles above? [#permalink] ### Show Tags 08 Sep 2018, 22:44 Bunuel wrote: What is the sum of the indicated angles above? A. 1080 B. 900 C. 810 D. 720 E. 540 Attachment: image013.jpg Sum of exterior angles of a polygon = 360 deg. y+c+p=360 (Angle formed by extension of one side and the other side) Similarly, a+z+m=360 x+b+n=180 (Sum of the angles of the triangle) Adding the three equations we get the desired result = 900 Answer B. _________________ Please give kudos, if you like my post When the going gets tough, the tough gets going... Re: What is the sum of the indicated angles above? [#permalink] 08 Sep 2018, 22:44 Display posts from previous: Sort by # What is the sum of the indicated angles above? new topic post reply Question banks Downloads My Bookmarks Reviews Important topics 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®.	2019-02-19 13:02:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.35796788334846497, "perplexity": 10578.137795733011}, "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-2019-09/segments/1550247490107.12/warc/CC-MAIN-20190219122312-20190219144312-00556.warc.gz"}
http://openstudy.com/updates/558ab5f7e4b03f41bbda15eb	## elleblythe one year ago Find the dy/dx of: 6x^(4/3) + 2y^5 = x^3y^2 + cube root of pi^5 1. Loser66 where are you stuck? 2. elleblythe @Loser66 is the correct answer (not simplified): -cube root of 8 / (-10y^4 + 2x^3y + 3x^2y) ? 3. Loser66 You guessed? or just pick one of the options and check it from me? 4. Loser66 Show me your work, please. Just take derivative both sides and isolate y'. Done. 5. elleblythe @Loser66 I solved for it. $8x ^{1/3}+10y ^{4}(dy/dx)=x^32y(dy/dx)+3x^2y^2(dy/dx)+5/3\pi^^{2/3}$ 6. Loser66 the left hand side is ok, but the right one!! first term of the right one is $$x^3y^2$$, hence its derivative is $$3x^2y^2+2x^3y (dy/dx)$$ the last term is a constant, hence its derivative =0 , ignore it 7. Loser66 now, combine and isolate dy/dx, please 8. elleblythe @Loser66 -cube root of 8 + 3x^2y^2 / (-10y^4 + 2x^3y) 9. Loser66 the sign of denominator is not correct, it should be $$\dfrac{dy}{dx}=\dfrac{3x^2y^2-\sqrt[3]{x}}{10y^4-2x^3y}$$	2017-01-24 21:33:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.8459386229515076, "perplexity": 3561.4995025886155}, "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-2017-04/segments/1484560285289.45/warc/CC-MAIN-20170116095125-00191-ip-10-171-10-70.ec2.internal.warc.gz"}
https://www.nag.com/numeric/mb/nagdoc_mb/manual_25_1/html/g02/g02ldf.html	Integer type: int32 int64 nag_int show int32 show int32 show int64 show int64 show nag_int show nag_int Chapter Contents Chapter Introduction NAG Toolbox # NAG Toolbox: nag_correg_pls_pred (g02ld) ## Purpose nag_correg_pls_pred (g02ld) calculates predictions given the output from an orthogonal scores PLS regression (nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb)) and nag_correg_pls_fit (g02lc). ## Syntax [yhat, ifail] = g02ld(orig, xbar, ybar, iscale, xstd, ystd, b, isz, z, 'ip', ip, 'my', my, 'n', n, 'mz', mz) [yhat, ifail] = nag_correg_pls_pred(orig, xbar, ybar, iscale, xstd, ystd, b, isz, z, 'ip', ip, 'my', my, 'n', n, 'mz', mz) ## Description nag_correg_pls_pred (g02ld) calculates the predictions $\stackrel{^}{Y}$ of a PLS model given a set $Z$ of test data and a set $B$ of parameter estimates as returned by nag_correg_pls_fit (g02lc). If nag_correg_pls_fit (g02lc) returns parameter estimates for the original data scale, no further information is required. If nag_correg_pls_fit (g02lc) returns parameter estimates for the centred, and possibly scaled, data, further information is required. The means of variables in the fitted model must be supplied. In the case of a PLS model fitted by using scaled data, the means and standard deviations of variables in the fitted model must also be supplied. These means and standard deviations are those returned by either nag_correg_pls_svd (g02la) and nag_correg_pls_wold (g02lb). None. ## Parameters ### Compulsory Input Parameters 1: $\mathrm{orig}$int64int32nag_int scalar Indicates how parameter estimates are supplied. ${\mathbf{orig}}=1$ Parameter estimates are for the original data. ${\mathbf{orig}}=-1$ Parameter estimates are for the centred, and possibly scaled, data. Constraint: ${\mathbf{orig}}=-1$ or $1$. 2: $\mathrm{xbar}\left({\mathbf{ip}}\right)$ – double array If ${\mathbf{orig}}=-1$, xbar must contain mean values of predictor variables in the model; otherwise xbar is not referenced. 3: $\mathrm{ybar}\left({\mathbf{my}}\right)$ – double array If ${\mathbf{orig}}=-1$, ybar must contain the mean value of each response variable in the model; otherwise ybar is not referenced. 4: $\mathrm{iscale}$int64int32nag_int scalar If ${\mathbf{orig}}=-1$, iscale must take the value supplied to either nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb); otherwise iscale is not referenced. Constraint: if ${\mathbf{orig}}=-1$, ${\mathbf{iscale}}=-1$, $1$ or $2$. 5: $\mathrm{xstd}\left({\mathbf{ip}}\right)$ – double array If ${\mathbf{orig}}=-1$ and ${\mathbf{iscale}}\ne -1$, xstd must contain the scalings of predictor variables in the model as returned from either nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb); otherwise xstd is not referenced. 6: $\mathrm{ystd}\left({\mathbf{my}}\right)$ – double array If ${\mathbf{orig}}=-1$ and ${\mathbf{iscale}}\ne -1$, ystd must contain the scalings of response variables as returned from either nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb); otherwise ystd is not referenced. 7: $\mathrm{b}\left(\mathit{ldb},{\mathbf{my}}\right)$ – double array ldb, the first dimension of the array, must satisfy the constraint • if ${\mathbf{orig}}=-1$, $\mathit{ldb}\ge {\mathbf{ip}}$; • if ${\mathbf{orig}}=1$, $\mathit{ldb}\ge 1+{\mathbf{ip}}$. If ${\mathbf{orig}}=-1$, b must contain the parameter estimate for the centred, and possibly scaled, data as returned by nag_correg_pls_fit (g02lc); otherwise b must contain the parameter estimates for the original data as returned by nag_correg_pls_fit (g02lc). 8: $\mathrm{isz}\left({\mathbf{mz}}\right)$int64int32nag_int array Indicates which predictor variables are to be included in the model. Predictor variables included from z must be in the same order as those included in the fitted model. If ${\mathbf{isz}}\left(\mathit{j}\right)=1$, the $\mathit{j}$th predictor variable is included in the model, for $\mathit{j}=1,2,\dots ,{\mathbf{mz}}$, otherwise ${\mathbf{isz}}\left(j\right)=0$. Constraints: • ${\mathbf{isz}}\left(\mathit{j}\right)=0\text{ or }1$, for $\mathit{j}=1,2,\dots ,{\mathbf{mz}}$; • ${\sum }_{j}{\mathbf{isz}}\left(j\right)={\mathbf{ip}}$. 9: $\mathrm{z}\left(\mathit{ldz},{\mathbf{mz}}\right)$ – double array ldz, the first dimension of the array, must satisfy the constraint $\mathit{ldz}\ge {\mathbf{n}}$. ${\mathbf{z}}\left(\mathit{i},\mathit{j}\right)$ contains the $\mathit{i}$th observation on the $\mathit{j}$th available predictor variable, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$ and $\mathit{j}=1,2,\dots ,{\mathbf{mz}}$. ### Optional Input Parameters 1: $\mathrm{ip}$int64int32nag_int scalar Default: the dimension of the arrays xbar, xstd. (An error is raised if these dimensions are not equal.) The number of predictor variables in the fitted model. ip must take the same value as that supplied to nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb) to fit the model. Constraint: ${\mathbf{ip}}>1$. 2: $\mathrm{my}$int64int32nag_int scalar Default: the dimension of the arrays ybar, ystd and the second dimension of the array b. (An error is raised if these dimensions are not equal.) The number of response variables in the fitted model. my must take the same value as that supplied to nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb) to fit the model. Constraint: ${\mathbf{my}}\ge 1$. 3: $\mathrm{n}$int64int32nag_int scalar Default: the first dimension of the array z. $n$, the number of observations in the test data $Z$. Constraint: ${\mathbf{n}}\ge 1$. 4: $\mathrm{mz}$int64int32nag_int scalar Default: the dimension of the array isz and the second dimension of the array z. (An error is raised if these dimensions are not equal.) The number of available predictor variables in the test data. Constraint: ${\mathbf{mz}}\ge {\mathbf{ip}}$. ### Output Parameters 1: $\mathrm{yhat}\left(\mathit{ldyhat},{\mathbf{my}}\right)$ – double array ${\mathbf{yhat}}\left(i,j\right)$ contains the $i$th predicted value of the $j$th $y$-variable in the model. 2: $\mathrm{ifail}$int64int32nag_int scalar ${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings). ## Error Indicators and Warnings Errors or warnings detected by the function: ${\mathbf{ifail}}=1$ Constraint: if ${\mathbf{orig}}=-1$, ${\mathbf{iscale}}=-1$, $1$ or $2$. Constraint: ${\mathbf{ip}}>1$. Constraint: ${\mathbf{isz}}\left(j\right)=0\text{ or }1$. Constraint: ${\mathbf{my}}\ge 1$. Constraint: ${\mathbf{n}}\ge 1$. Constraint: ${\mathbf{orig}}=-1$ or $1$. ${\mathbf{ifail}}=2$ Constraint: if ${\mathbf{orig}}=1$, $\mathit{ldb}\ge 1+{\mathbf{ip}}$. Constraint: if ${\mathbf{orig}}=-1$, $\mathit{ldb}\ge {\mathbf{ip}}$. Constraint: $\mathit{ldyhat}\ge {\mathbf{n}}$. Constraint: $\mathit{ldz}\ge {\mathbf{n}}$. Constraint: ${\mathbf{mz}}\ge {\mathbf{ip}}$. ${\mathbf{ifail}}=3$ On entry, the number of elements of isz equal to $1$ is not ip. ${\mathbf{ifail}}=-99$ ${\mathbf{ifail}}=-399$ Your licence key may have expired or may not have been installed correctly. ${\mathbf{ifail}}=-999$ Dynamic memory allocation failed. ## Accuracy Not applicable. nag_correg_pls_pred (g02ld) allocates internally $3×{\mathbf{ip}}+{\mathbf{my}}$ elements of double storage. ## Example This example reads in parameter estimates for a fitted PLS model and prediction data, and the PLS model predictions are calculated. ```function g02ld_example fprintf('g02ld example results\n\n'); n = 15; z = zeros(n,n); z(:,1:8) = ... [-2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 1.9607, -1.6324; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 1.9607, -1.6324; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333; -2.6931, -2.5271, -1.2871, 2.8369, 1.4092, -3.1398, 0.0744, -1.7333; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.7548, 3.6521; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 2.4064, 1.7438; -2.6931, -2.5271, -1.2871, 0.0744, -1.7333, 0.0902, 0.0744, -1.7333; 2.2261, -5.3648, 0.3049, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333; -4.1921, -1.0285, -0.9801, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333; -4.9217, 1.2977, 0.4473, 3.0777, 0.3891, -0.0701, 0.0744, -1.7333; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, 2.2261, -5.3648; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.9217, 1.2977; -2.6931, -2.5271, -1.2871, 3.0777, 0.3891, -0.0701, -4.1921, -1.0285]; z(:,9:n) = ... [ 0.5746, 1.9607, -1.6324, 0.5740, 2.8369, 1.4092, -3.1398; 0.5746, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.0902, 1.9607, -1.6324, 0.5746, 2.8369, 1.4092, -3.1398; 0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.8524, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.0902, 0.0744, -1.7333, 0.0902, -1.2201, 0.8829, 2.2253; 1.1057, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.0902, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; 0.3049, 2.2261, -5.3648, 0.3049, 2.8369, 1.4092, -3.1398; 0.4473, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398; -0.9801, 0.0744, -1.7333, 0.0902, 2.8369, 1.4092, -3.1398]; % Means and scalings orig = int64(-1); xbar = [-2.6137; -2.3614; -1.0449; 2.8614; 0.3156; -0.2641; -0.3146; -1.1221; 0.2401; 0.4694; -1.9619; 0.1691; 2.5664; 1.3741; -2.7821]; ybar = [0.452]; iscale = int64(1); xstd = [ 1.4956; 1.3233; 0.5829; 0.7735; 0.6247; 0.7966; 2.4113; 2.0421; 0.4678; 0.8197; 0.9420; 0.1735; 1.0475; 0.1359; 1.3853]; ystd = [0.9062]; b = [-0.1383; 0.0572; -0.1906; 0.1238; 0.0591; 0.0936; -0.2842; 0.4713; 0.2661; -0.0914; 0.1226; -0.0488; 0.0332; 0.0332; -0.0332]; isz = ones(n, 1, 'int64'); % Calculate predictions [yhat, ifail] = g02ld( ... orig, xbar, ybar, iscale, xstd, ystd, b, isz, z); % Display results disp('Predicted values'); disp(yhat); ``` ```g02ld example results Predicted values 0.2132 0.5152 0.1437 0.4459 0.1716 2.4809 0.0964 1.4475 -0.1546 -0.5492 0.5393 0.2686 -1.1332 1.7975 0.4973 ``` Chapter Contents Chapter Introduction NAG Toolbox © The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2015	2022-07-01 14:24:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 87, "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": 0.9937805533409119, "perplexity": 9930.900268472855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103941562.52/warc/CC-MAIN-20220701125452-20220701155452-00019.warc.gz"}
https://bitbucket.org/olemis/bloodhound-trac/src/53de1029019e/doc/api/trac_ticket_roadmap.rst	# :mod:trac.ticket.roadmap -- The Roadmap and Milestone modules The component responsible for the Roadmap feature in Trac is the RoadmapModule. It provides an overview of the milestones and the progress in each of these milestones. The component responsible for interacting with each milestone is the MilestoneModule. A milestone also provides an overview of the progress in terms of tickets processed. The grouping of tickets in each progress bar is governed by the use of another component implementing the ITicketGroupStatsProvider interface. By default, this is the DefaultTicketGroupStatsProvider (for both the RoadmapModule and the MilestoneModule), which provides a configurable way to specify how tickets are grouped.	2016-02-13 07:17:51	{"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": 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": 0.41988325119018555, "perplexity": 2291.1314801474796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701166222.10/warc/CC-MAIN-20160205193926-00140-ip-10-236-182-209.ec2.internal.warc.gz"}
https://www.lmfdb.org/Genus2Curve/Q/20736/l/373248/1	# Properties Label 20736.l.373248.1 Conductor 20736 Discriminant 373248 Mordell-Weil group $$\Z/{2}\Z \times \Z/{6}\Z$$ Sato-Tate group $J(E_4)$ $$\End(J_{\overline{\Q}}) \otimes \R$$ $$\mathrm{M}_2(\R)$$ $$\End(J_{\overline{\Q}}) \otimes \Q$$ $$\mathrm{QM}$$ $$\overline{\Q}$$-simple yes $$\mathrm{GL}_2$$-type no # Learn more about Show commands for: Magma / SageMath ## Simplified equation magma: R<x> := PolynomialRing(Rationals()); C := HyperellipticCurve(R![0, 0, -3, -1, 9, 6], R![1]); sage: R.<x> = PolynomialRing(QQ); C = HyperellipticCurve(R([0, 0, -3, -1, 9, 6]), R([1])) magma: R<x> := PolynomialRing(Rationals()); C := HyperellipticCurve(R![0, 0, -3, -1, 9, 6], R![1]); sage: R.<x> = PolynomialRing(QQ); C = HyperellipticCurve(R([1, 0, -12, -4, 36, 24])) $y^2 + y = 6x^5 + 9x^4 - x^3 - 3x^2$ (homogenize, simplify) $y^2 + z^3y = 6x^5z + 9x^4z^2 - x^3z^3 - 3x^2z^4$ (dehomogenize, simplify) $y^2 = 24x^5 + 36x^4 - 4x^3 - 12x^2 + 1$ (minimize, homogenize) ## Invariants $$N$$ = $$20736$$ = $$2^{8} \cdot 3^{4}$$ magma: Conductor(LSeries(C)); Factorization($1); $$\Delta$$ = $$373248$$ = $$2^{9} \cdot 3^{6}$$ magma: Discriminant(C); Factorization(Integers()!$1); ### G2 invariants magma: G2Invariants(C); $$I_2$$ = $$7008$$ = $$2^{5} \cdot 3 \cdot 73$$ $$I_4$$ = $$1700352$$ = $$2^{9} \cdot 3^{4} \cdot 41$$ $$I_6$$ = $$3259367424$$ = $$2^{17} \cdot 3^{4} \cdot 307$$ $$I_{10}$$ = $$1528823808$$ = $$2^{21} \cdot 3^{6}$$ $$J_2$$ = $$876$$ = $$2^{2} \cdot 3 \cdot 73$$ $$J_4$$ = $$14262$$ = $$2 \cdot 3 \cdot 2377$$ $$J_6$$ = $$207364$$ = $$2^{2} \cdot 47 \cdot 1103$$ $$J_8$$ = $$-5438445$$ = $$- 3 \cdot 5 \cdot 37 \cdot 41 \cdot 239$$ $$J_{10}$$ = $$373248$$ = $$2^{9} \cdot 3^{6}$$ $$g_1$$ = $$4146143186/3$$ $$g_2$$ = $$924693409/36$$ $$g_3$$ = $$276260689/648$$ ## Automorphism group magma: AutomorphismGroup(C); IdentifyGroup($1); $$\mathrm{Aut}(X)$$ $$\simeq$$$C_2$magma: AutomorphismGroup(ChangeRing(C,AlgebraicClosure(Rationals()))); IdentifyGroup($1); $$\mathrm{Aut}(X_{\overline{\Q}})$$ $$\simeq$$ $C_2$ ## Rational points magma: [C![-1,-4,2],C![0,-1,1],C![0,0,1],C![1,0,0]]; Points: $$(0 : 0 : 1),\, (1 : 0 : 0),\, (0 : -1 : 1),\, (-1 : -4 : 2)$$ magma: #Roots(HyperellipticPolynomials(SimplifiedModel(C))); Number of rational Weierstrass points: $$2$$ magma: f,h:=HyperellipticPolynomials(C); g:=4*f+h^2; HasPointsEverywhereLocally(g,2) and (#Roots(ChangeRing(g,RealField())) gt 0 or LeadingCoefficient(g) gt 0); This curve is locally solvable everywhere. ## Mordell-Weil group of the Jacobian: magma: MordellWeilGroupGenus2(Jacobian(C)); Group structure: $$\Z/{2}\Z \times \Z/{6}\Z$$ Generator Height Order $$2x + z$$ $$=$$ $$0,$$ $$2y$$ $$=$$ $$-z^3$$ $$0$$ $$2$$ $$x$$ $$=$$ $$0,$$ $$y$$ $$=$$ $$-z^3$$ $$0$$ $$6$$ ## BSD invariants Analytic rank: $$0$$ Mordell-Weil rank: $$0$$ 2-Selmer rank: $$2$$ Regulator: $$1$$ Real period: $$18.60015$$ Tamagawa product: $$8$$ Torsion order: $$12$$ Leading coefficient: $$1.033342$$ Analytic order of Ш: $$1$$ (rounded) Order of Ш: square ## Local invariants Prime ord($$N$$) ord($$\Delta$$) Tamagawa L-factor $$2$$ $$9$$ $$8$$ $$2$$ $$1 + 2 T^{2}$$ $$3$$ $$6$$ $$4$$ $$4$$ $$1$$ ## Sato-Tate group $$\mathrm{ST}$$ $$\simeq$$ $J(E_4)$ $$\mathrm{ST}^0$$ $$\simeq$$ $$\mathrm{SU}(2)$$ ## Decomposition of the Jacobian Simple over $$\overline{\Q}$$ ## Endomorphisms of the Jacobian Not of $$\GL_2$$-type over $$\Q$$ Endomorphism ring over $$\Q$$: $$\End (J_{})$$ $$\simeq$$ $$\Z$$ $$\End (J_{}) \otimes \Q$$ $$\simeq$$ $$\Q$$ $$\End (J_{}) \otimes \R$$ $$\simeq$$ $$\R$$ Smallest field over which all endomorphisms are defined: Galois number field $$K = \Q (a) \simeq$$ 8.0.339738624.10 with defining polynomial $$x^{8} + 4 x^{6} + 10 x^{4} + 24 x^{2} + 36$$ Not of $$\GL_2$$-type over $$\overline{\Q}$$ Endomorphism ring over $$\overline{\Q}$$: $$\End (J_{\overline{\Q}})$$ $$\simeq$$ a non-Eichler order of index $$6$$ in a maximal order of $$\End (J_{\overline{\Q}}) \otimes \Q$$ $$\End (J_{\overline{\Q}}) \otimes \Q$$ $$\simeq$$ the quaternion algebra over $$\Q$$ of discriminant 6 $$\End (J_{\overline{\Q}}) \otimes \R$$ $$\simeq$$ $$\mathrm{M}_2 (\R)$$ ### Remainder of the endomorphism lattice by field Over subfield $$F \simeq$$ $$\Q(\sqrt{-3})$$ with generator $$-\frac{1}{15} a^{6} - \frac{1}{6} a^{4} - \frac{2}{3} a^{2} - \frac{3}{5}$$ with minimal polynomial $$x^{2} - x + 1$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z [3\sqrt{-1}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{-1})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\C$$ Sato Tate group: $E_4$ Of $$\GL_2$$-type, simple Over subfield $$F \simeq$$ $$\Q(\sqrt{-2})$$ with generator $$-\frac{1}{10} a^{6} - \frac{2}{5}$$ with minimal polynomial $$x^{2} + 2$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\R$$ Sato Tate group: $J(E_2)$ Not of $$\GL_2$$-type, simple Over subfield $$F \simeq$$ $$\Q(\sqrt{6})$$ with generator $$-\frac{1}{6} a^{6} - \frac{2}{3} a^{4} - \frac{2}{3} a^{2} - 2$$ with minimal polynomial $$x^{2} - 6$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\R$$ Sato Tate group: $J(E_2)$ Not of $$\GL_2$$-type, simple Over subfield $$F \simeq$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ with generator $$-\frac{2}{15} a^{6} - \frac{1}{3} a^{4} - \frac{1}{3} a^{2} - \frac{6}{5}$$ with minimal polynomial $$x^{4} - 2 x^{2} + 4$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z [3\sqrt{-1}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{-1})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\C$$ Sato Tate group: $E_2$ Of $$\GL_2$$-type, simple Over subfield $$F \simeq$$ 4.0.6144.1 with generator $$\frac{2}{45} a^{7} - \frac{1}{18} a^{5} + \frac{1}{9} a^{3} + \frac{11}{15} a$$ with minimal polynomial $$x^{4} - 4 x^{2} + 6$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z [\sqrt{6}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{6})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\R \times \R$$ Sato Tate group: $J(E_1)$ Of $$\GL_2$$-type, simple Over subfield $$F \simeq$$ 4.2.18432.2 with generator $$\frac{7}{90} a^{7} + \frac{5}{18} a^{5} + \frac{4}{9} a^{3} + \frac{23}{15} a$$ with minimal polynomial $$x^{4} + 4 x^{2} - 2$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z [\sqrt{3}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{3})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\R \times \R$$ Sato Tate group: $J(E_1)$ Of $$\GL_2$$-type, simple Over subfield $$F \simeq$$ 4.2.18432.2 with generator $$\frac{1}{18} a^{7} + \frac{1}{18} a^{5} - \frac{1}{9} a^{3} - \frac{1}{3} a$$ with minimal polynomial $$x^{4} + 4 x^{2} - 2$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z [\sqrt{3}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{3})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\R \times \R$$ Sato Tate group: $J(E_1)$ Of $$\GL_2$$-type, simple Over subfield $$F \simeq$$ 4.0.6144.1 with generator $$-\frac{1}{15} a^{7} - \frac{1}{6} a^{5} - \frac{2}{3} a^{3} - \frac{3}{5} a$$ with minimal polynomial $$x^{4} - 4 x^{2} + 6$$: $$\End (J_{F})$$ $$\simeq$$ $$\Z [\sqrt{6}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{6})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\R \times \R$$ Sato Tate group: $J(E_1)$ Of $$\GL_2$$-type, simple	2020-01-22 16:20:20	{"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": 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": 0.9999574422836304, "perplexity": 14231.925044038808}, "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-2020-05/segments/1579250607314.32/warc/CC-MAIN-20200122161553-20200122190553-00078.warc.gz"}
https://www.hackerearth.com/practice/algorithms/greedy/basics-of-greedy-algorithms/practice-problems/algorithm/chandu-and-consecutive-letters/	Chandu and Consecutive Letters / Greedy algorithm, String Problem Editorial Analytics Chandu is very fond of strings. (Or so he thinks!) But, he does not like strings which have same consecutive letters. No one has any idea why it is so. He calls these strings as Bad strings. So, Good strings are the strings which do not have same consecutive letters. Now, the problem is quite simple. Given a string S, you need to convert it into a Good String. You simply need to perform one operation - if there are two same consecutive letters, delete one of them. Input: The first line contains an integer T, denoting the number of test cases. Each test case consists of a string S, which consists of only lower case letters. Output: For each test case, print the answer to the given problem. Constraints: 1 <= T <= 10 1 <= \|S\| <= 30 SAMPLE INPUT 3 abb aaab ababa SAMPLE OUTPUT ab ab ababa Explanation In the first case, S = "abb". Since, S has same consecutive letter 'b' we will delete one of them. So, the good string will be "ab". In the second case, S = "aaab" and since S has same consecutive letter 'a' we will delete them one by one. aaab -> aab -> ab. So, the good string will be "ab". In the third case, S = "ababa" and S has no same consecutive letter. So, the good string will be "ababa". Time Limit: 1.0 sec(s) for each input file. Memory Limit: 256 MB Source Limit: 1024 KB	2020-06-05 22:27:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.340243935585022, "perplexity": 1333.0643899224342}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348504341.78/warc/CC-MAIN-20200605205507-20200605235507-00231.warc.gz"}
https://tex.stackexchange.com/questions/468593/add-short-toc-entry-to-toc-entry-and-vice-versa	# Add short toc entry to toc entry and vice versa Taking heavy inspiration from the answer to: Hide toc from toc, and shorttoc from shorttoc I have made the following code: \documentclass{memoir} \newcommand{\shorttoc}{% \renewcommand{\contentsname}{Short Contents} \begingroup% \def\inshorttoc{}% \tableofcontents% \endgroup% } \newcommand{\toc}{% \renewcommand{\contentsname}{Contents} \begingroup% \def\intoc{} \tableofcontents \endgroup% } \makeatother \usepackage{mwe} \begin{document} \shorttoc \cleardoublepage \toc \blinddocument \end{document} It should place the short contents entry into the long toc and vice versa. But after updating my TeX live distribution the code throws the errors: Extra }, or forgotten \endgroup. \@writefile{toc}{\fi} Extra }, or forgotten \endgroup. \@writefile{toc}{\fi} But the code compiles without errors on older distributions. • Are you sure this has ever worked? – user31729 Jan 4 at 16:34 • Yes it works if I compile it on Overleaf – M0erck Jan 4 at 16:35 • Why not doing the test outside of the toc? Something like \newif\ifintoc \ifintoc \addcontentsline{toc}{chapter}{foo}\fi instead of writing tricky \if... stuff into the .aux and then to the .toc file? – user31729 Jan 4 at 16:54 • I would be happy with another solution, but I cannot get your suggestion to work. Will "foo" not be added to both shorttoc and toc as along as intoc is true at some point in the document? – M0erck Jan 4 at 17:52 \long\def\@writefile#1#2{%	2019-10-17 23:00:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.7778670191764832, "perplexity": 6294.5771703288365}, "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/1570986677230.18/warc/CC-MAIN-20191017222820-20191018010320-00536.warc.gz"}
http://math.stackexchange.com/questions/279958/galois-group-of-polynomial	# Galois Group of Polynomial I would like to compute the Galois group of the Polynomial $f(x)=x^5-5x^4 +10 x^3 - 10 x^2 - 135 x + 131\in\mathbb{Q}[x]$ I already know that it is irreducible in $\mathbb{Q}[x]$ via Eisenstein's criterion, $f(x-1)$ and $p=5$, but have no idea how to proceed. Thank you very much! - $f(x+1)=x^5-140x-8$. Eisenstein does not apply. – Chris Eagle Jan 16 '13 at 10:47 Thank you, I meant f(x-1). I have corrected it in the post. – testrado Jan 16 '13 at 10:54 $f(x-1)=x^5-10x^4+40x^3-80x^2-60x+240$, so $p=2$ again fails. $p=5$ works, though. – Chris Eagle Jan 16 '13 at 10:56 Ok, sorry, I should really take more time to proofread in future. Sorry, that was only my second question I have asked until now. – testrado Jan 16 '13 at 10:58 As the polynomial is irreducible of degree $5$, the group is a subgroup of $S_5$ containing a $5$-cycle. If it has exactly $2$ non-real roots, then the group has a transposition coming from complex conjugation, and you should be able to take it from there. If it has $4$ non-real roots, it will take some more work. Who said anything about a CAS? There is a simple theorem about a subgroup of $S_p$ containing a $p$-cycle and a transposition, when $p$ is prime. – Gerry Myerson Jan 16 '13 at 11:04	2015-05-30 17:09:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7951523661613464, "perplexity": 307.3325199370351}, "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/1432207932182.89/warc/CC-MAIN-20150521113212-00243-ip-10-180-206-219.ec2.internal.warc.gz"}
https://nrich.maths.org/733/solution	### Times Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out! ### Clock Hands This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move. ### Ten Green Bottles Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down? # Millennium Man ##### Stage: 2 Challenge Level: Julian of Hethersett High School made a table of the days of the week on 1 January every year from the year 2000 to the year 2100. He used the fact that the day of the week 'moves on' by $1$ day each year (why is that?) apart from immediately after a leap year when it 'moves on' by $2$ days. The pattern repeats after $28$ years. The first Saturday 1 st January after 2060 is in 2061 so Millennium Man will retire on his 61 st birthday. The 1st January falls on a Saturday four times every $28$ years. It falls on a Saturday $15$ times this century so his birthday will occur on a Saturday $15$ times during this century. Well done also Lizzie and Hollie, The Mount School, York and Fiona, Stamford High School, Lincolnshire. Congratulations also to Katherine and Rosalind from Chawson First School Droitwich who told us: We made a note of which years were leap years and then counted up all the Saturdays. The first question came out as 2061 and the second came out as $15$.	2017-10-22 22:54:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.23804090917110443, "perplexity": 2351.4145605965064}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825473.61/warc/CC-MAIN-20171022222745-20171023002745-00887.warc.gz"}
https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-9-measurement-9-3-measuring-weight-and-temperature-exercise-set-9-3-page-604/89	Thinking Mathematically (6th Edition) We should take the formula used to convert from Celsius to Fahrenheit. $F = \frac{9}{5}C+32$ We should take the formula used to convert from Celsius to Fahrenheit. $F = \frac{9}{5}C+32$ If a person travels outside the United States, they should take the formula used to convert from Celsius to Fahrenheit. People in other countries normally express the temperature using the Celsius scale. In order to understand this temperature, it would be helpful to convert this temperature to the Fahrenheit scale. To convert the temperature from the Celsius scale to the Fahrenheit scale, we would need to use the formula to convert from Celsius to Fahrenheit.	2018-10-15 14:35:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7074025869369507, "perplexity": 534.2516485420263}, "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-2018-43/segments/1539583509326.21/warc/CC-MAIN-20181015142752-20181015164252-00154.warc.gz"}
https://blender.stackexchange.com/questions/139539/display-value-of-a-nodes-rgb-input-in-a-panel	# Display Value of a nodes RGB input in a panel I have a Mix RGB node and want to display the input in a normal panel in the UI. I can show the color widget by using layout.prop(input,"default_value"), but what I want to do is to just show the Value of the input. This would then show a float input instead of the color widget. Use the indexed element, eg red is index 0 For array properties can display an individual element in a layout.prop(...) by specifying the index of the array element. Eg for the red channel of mix color input input.default_value layout.prop(input, "default_value", index=0) The color node socket input has a type 'RGBA' def draw(self, context): layout = self.layout # node for testing node = bpy.data.materials["Material"].node_tree.nodes["Mix"] input = node.inputs["Color1"] col = layout.column(align=True) for i, c in enumerate(input.type): col.prop( input, "default_value", text=c.upper(), index=i) What about using a label? I haven't tested the following, but something like this: value_string = "({:.1f}, {:.1f}, {:.1f})".format( input.default_value[0], input.default_value[1], input.default_value[2]) layout.label(text=value_string) • This just displays the different values. What I want, is to display the Value as in HueSaturationValue as a layout.prop(...) – Joshua Knauber May 1 '19 at 19:09 • There may be a better way, but what about creating three new float properties and having some python set the node color when they are changed? – gandalf3 May 1 '19 at 19:14 • Yeah I guess that'd be possible, I hoped there was a better way, but maybe I just have to do that. – Joshua Knauber May 1 '19 at 19:29	2020-07-07 10:35:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23516233265399933, "perplexity": 2110.6254273636705}, "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/1593655891884.11/warc/CC-MAIN-20200707080206-20200707110206-00266.warc.gz"}
https://kailashpinjani.com/4980sl/equivalence-point-vs-endpoint-9620ca	Identify the equivalence point and half-equivalence points. $HC_2H_3O_2 + OH^- \rightarrow H_2O + C_2H_3O_2^-$ During this titration, as the OH – reacts with the … The closer the end point to the equivalence point the better, but it is often not easy to find a good method of equivalence point detection. The endpoint and the equivalence point are not exactly the same: the equivalence point is determined by the stoichiometry of the reaction, while the endpoint is just the color change from the indicator. Thank you, 10 points =) Source(s): difference point equivalence point: https://biturl.im/SR3S5. Equivalence Point vs. Endpoint. Sketch out a plot representing the titration of a weak monoprotic acid by a strong base, or of a weak base titrated by a strong acid. The end point, on the other hand, is the point in which color change can be observed. buffer: … The equivalence point … Explain … Log in or register to post comments; Similar Questions. Sometime an inflection point is such that it is difficult to detect. Volume end point values of 9.88 ± 0.10 mL and 9.86 ± 0.12 mL were obtained, with the data before and after the equivalence point, respectively. Equivalence point provides that point, where the unknown analyte has completely reacted with titrant and reactions, ends while endpoint does not always provide that point … Both are not exactly the same. In the equivalence point, the amount of substance of the acid is equal to the one of the base. M. Yaseen. It applies to any acid-base or neutralization reaction technically. End point and equivalence point IB grades required to admission at RCSI Titration curve help!! I have a clear pH change for each graph. The equivalence point is part of the process of chemical titration. The equivalence point of an acid–base titration is the point at which exactly enough acid or base has been added to react completely with the other component. Equivalence point is the theoretical completion of the reaction: the volume of added titrant at which the number of moles of titrant is equal to the number of moles of analyte, or some multiple thereof (as in polyprotic acids). Endpoint– Sometimes, equivalence point can be taken as the endpoint since they are approximately equal. Science is a complex system which gives insight of the world , insight of things which cannot be seen with nackt eyes. When the indicator changes colour, this is often described as the end point of the titration. Endpoint and equivalence point Though the terms equivalence point and endpoint are often used interchangeably, they are different terms. It has been reported previously that the inflection point deviates from the equivalence point depending on strength of acid or base. I am told to work out the equivalence point … read more Otherwise, equivalence point will not be equal to 7. So equivalence point represents the end point representing accurately the point at which reactants have just competely reacted - no extra needs to be added to get the indicator to change. That is to say, it is a turning point: when a higher amount of the substance is added, the acid or the base increases. Now for a polyprotic acid there are multiple equivalence points. Equivalence point - The equivalence point occurs when the moles of added base are equal to the moles of the initial acid species. Definition: The equivalence point of a chemical reaction is the point at which equal quantities of reactants are mixed chemically. Equivalence Point vs Endpoint Titration is a technique widely used in analytical chemistry to determine acids, bases, oxidants, reductants, metal ions and many other species. In photometric titrations with ordinary monitoring of the end-point, the indicator is usually chosen to have its colour transition as close to the equivalence point as possible. In chemistry, an equivalence point is a term that is used while performing titration. Ideally you would want these points to coincide. Difference: End Point vs. Equivalence Point? Sorting out some confusing terms. 0 3. The first equivalence point occurs when the moles of added base are equal to the moles of the initial acid species. The equivalence point is not the same as the endpoint of a titration. Endpoint vs Equivalence Point. Since all ionic solutions are electrically neutral, we don't refer to an isoelectric point … #2 Report 11 years ago #2 (Original post by LittleMissSunshine5) I have two titration curves, one with NaOH vs HCL, and another with CH3COOH vs NaOH. However, very often we can easily spot a point very close to the equivalence point - and that's where the end point will be. This is also known as the stoichiometric point because it is where the moles of acid are equal to the amount needed to … End point definition is - a point marking the completion of a process or stage of a process; especially : a point in a titration at which a definite effect (such as a color change) is observed. The equivalence point (stoichiometric point) should be distinguished from the titration endpoint (where the indicator changes its color). Rep:? The equivalence point is the point in a titration where the amount of titrant added is enough to completely neutralize the analyte solution. In other words, the moles of acid are equivalent to the moles of base, according to the equation (this does not necessarily imply a 1:1 molar ratio of acid:base, merely that the ratio is the same as in the equation). The concentration of a given reactant can be deduced by titrating a known substance into the reactant sample and finding the reaction’s equivalence point. The equivalence point can be determined in a number of different ways using signs such as pH indicators, color change, conductivity, or precipitation. Chemistry is an … The equivalence point is the exact point where the chemical reaction ends in the titration mixture, whereas endpoint is the point where the color change occurs in the arrangement. Conductance– In this method, conductance is measured throughout the titration, and the equivalence point is where a rapid change of conductance occurs. Please note: comment moderation is enabled and may delay your comment. The endpoint refers to the point … In titration, a known chemical reaction takes place. Spectroscopy– This is a method suitable for colourful reaction mixtures. This can be acid-base, oxidizer-reducer, etc. When you carry out a simple acid-base titration, you use an indicator to tell you when you have the acid and alkali mixed in exactly the right proportions to "neutralise" each other. Study Forum Helper; Badges: 17. For a strong acid and a strong base such as NaOH and HCl the final solution is neutral at pH 7: … Notice that this doesn't infer anything about the pH of the solution. An isoelectric point specifically refers to a zero net charge of a system, which can be molecules (like an amino acid), particles (like clay colloids), or surfaces. On the plot referred to above, draw a similar plot that would correspond to the same system at a higher or lower concentration. The equivalence point in the titration of a strong acid or a strong base occurs at pH 7.0. If you are titrating an acid against a base, the half equivalence point will be the point at which half the acid has been neutralised by the base. ↩ Equivalence points are tightly related to the concept … Potentiometric Titration of Perchloric Acid with Sodium Hydroxide: Determination of the Ionic Product of Water In Table 2 the potentiometric titration data of perchloric acid with sodium hydroxide published by Meloun et … If you're behind a web filter, please make sure that the domains .kastatic.org and .kasandbox.org are unblocked. The equivalence point is the point in a titration where the amount of titrant added is enough to completely neutralize the analyte solution. The equivalence point is when the ratio of the reactants is in the amounts specified by the equation. charco. This is a somewhat difficult method. In titrations of weak acids or weak bases, however, the pH at the equivalence point is greater or less than 7.0, … The equivalence point is where the amount of moles of acid and base are equal, resulting a solution of only salt and water. The equivalence point of a titration. Equivalence Point Definition. stoichiometry: The study and calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemical equations). … 3.2. Notify me of followup comments via e-mail The equivalence point, or stoichiometric point, of a chemical reaction is the point at which chemically equivalent quantities of reactants have been mixed. The errors encountered due to the difference between the inflection point and the equivalence point, have also been reported earlier [3, 4]. It really goes a long way! Key Terms. Identify the equivalence point and explain its significance. The moles of titrant (standard solution) equal the moles of the solution with unknown concentration. The endpoint of a titration is the point where the indicator just changes colour. There is no need to resubmit your comment. An equivalence point has to do with a balance of chemical species in a titration. Things are more complicated and complex as compared to what it is visible to a normal person. Equivalence point or stoichiometric point occurs during a chemical titration when the amount of titrant added is equivalent, or equal, to the amount of analyte present in the sample. Equivalence point is point in the titration where the stoichiometric amount (calculated from the balance chemical equation) of the specie is required to neutralize the corresponding specie, … To get a certain amount of substance of acid or base, the titration has to be stopped at the endpoint. The endpoint and the equivalence point are not exactly the same: the equivalence point is determined by the stoichiometry of the reaction, while the endpoint is just the color change from the indicator. Endpoint: Equivalence Point: Point where the indicator changes colour: The point at which the titrant is chemically equivalent to the analyte in the sample: Comes after the equivalence point: Comes before the endpoint: Weak acids can have only one endpoint: Weak acids can have multiple equivalence point : Although, the endpoint is normally regarded … ↩ CO 2 is an abbreviation for the composite carbonic acid H 2 CO 3 *, which is the sum of dissolved CO 2 (aq) and a tiny amount of true carbonic acid H 2 CO 3. For instance, if you have 1 mole of acid and you add 0.5 mole of base, exactly half of the acid will have been … … Endpoint vs Equivalence Point. Science gives reasoning for several things which are not an abstract form but proven practically in several ways. 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Have a clear pH change for each graph the equation titrant ( standard solution equal!	2021-04-16 21:01:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6066004037857056, "perplexity": 1687.111091537609}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038089289.45/warc/CC-MAIN-20210416191341-20210416221341-00502.warc.gz"}
http://www.chegg.com/homework-help/questions-and-answers/2-consider-decomposition-n2o5-carbon-tetrachloride-ccl4-45-c-2n2o5-soln-4no2-g-o2-g-reacti-q2912998	2. Consider the decomposition of N2O5 in carbon tetrachloride (CCl4) at 45?C 2N2O5(soln) 4NO2(g) + O2(g) The reaction is first-order in N2O5, with the specific rate constant 6.08 x 10-4/s. Calculate the reaction rate at these conditions. a. [N2O5] = 0.200 mol/L b. [N2O5] = 0.319 mol/L ### Get this answer with Chegg Study Practice with similar questions Q: Consider the decomposition of N2O5 in carbon tetrachloride (CCl4) at 45?C 2N2O5(soln) 4NO2(g) + O2(g). The reaction is first-order in N2O5, with the specific rate constant 6.08 x 10-4/s. Calculate the reaction rate at these conditions? a. [N2O5] = 0.200 mol/L b. [N2O5] = 0.319 mol/L Please explain how to find all parts	2016-06-25 17:48:01	{"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": 0.8456963300704956, "perplexity": 12002.192997768767}, "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/1466783393463.1/warc/CC-MAIN-20160624154953-00037-ip-10-164-35-72.ec2.internal.warc.gz"}
https://www.mikaelsand.se/2022/10/the-parts-of-a-sas-key/	Whenever I generated a SAS key for allowing access to a storage I have always wondered what all the different parts actually mean, today I found out. (Source: MS Learn I added some information) Lets look at this generated key: https://myaccount.blob.core.windows.net/?restype=service&comp=properties&sv=2021-06-08&ss=bf&st=2015-04-29T22%3A18%3A26Z&se=2015-04-30T02%3A23%3A26Z&srt=s&sp=rw&sip=168.1.5.60-168.1.5.70&spr=https&sig=F%6GRVAZ5Cdj2Pw4tgU7IlSTkWgn7bUkkAg8P6HESXwmf%4B Parameter Example Description Resource URI https://myaccount.blob.core.windows.net/?restype=service&comp=properties Defines the Azure Storage endpoint and other parameters. This example defines an endpoint for Blob Storage and indicates that the SAS applies to service-level operations. When the URI is used with GET, the Storage properties are retrieved. When the URI is used with SET, the Storage properties are configured Storage version sv=2015-04-05 For Azure Storage version 2012-02-12 and later, this parameter indicates the version to use. This example indicates that version 2015-04-05 (April 5, 2015) should be used. Storage service ss=bf Specifies the Azure Storage to which the SAS applies. This example indicates that the SAS applies to Blob Storage (b) and Azure Files (f). Also available are Queue (q) and Table (t) Start time st=2015-04-29T22%3A18%3A26Z (Optional) Specifies the start time for the SAS in UTC time. This example sets the start time as April 29, 2015 22:18:26 UTC. If you want the SAS to be valid immediately, omit the start time. Expiry time se=2015-04-30T02%3A23%3A26Z Specifies the expiration time for the SAS in UTC time. This example sets the expiry time as April 30, 2015 02:23:26 UTC. Allowed resource type srt=s Specifies which resource types are accessible via the SAS. This example specifies that the accessible resource is in Blob Storage. Service (s), Container (c) and Object (o). Permissions sp=rw Lists the permissions to grant. This example grants access to read (r) and write (w) operations. IP range sip=168.1.5.60-168.1.5.70 Specifies a range of IP addresses from which a request is accepted. This example defines the IP address range 168.1.5.60 through 168.1.5.70. Protocol spr=https Specifies the protocols from which Azure Storage accepts the SAS. This example indicates that only requests by using HTTPS are accepted, and why should you accept anything else? Signature sig=F%6GRVAZ5Cdj2Pw4tgU7IlSTkWgn7bUkkAg8P6HESXwmf%4B Specifies that access to the resource is authenticated by using an HMAC signature. The signature is computed over a string-to-sign with a key by using the SHA256 algorithm, and encoded by using Base64 encoding. Since permissions (sp) is a little more complex I listed them in a separate table. Allowed persmission Description w Write d Delete l List	2023-03-27 13:08:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.20545843243598938, "perplexity": 5250.9546565896435}, "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/1679296948632.20/warc/CC-MAIN-20230327123514-20230327153514-00127.warc.gz"}
https://www.gamedev.net/forums/topic/687817-best-way-to-make-this-a-class/	• Advertisement • ### Popular Now • 9 • 10 • 9 • 10 • 10 • Advertisement • Advertisement • Advertisement # Best way to make this a class? This topic is 376 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. If you intended to correct an error in the post then please contact us. ## Recommended Posts """ Sample Python/Pygame Programs Simpson College Computer Science http://programarcadegames.com/ http://simpson.edu/computer-science/ Explanation video: http: """ # Import a library of functions called 'pygame' import pygame ## draw_snowman is what I want to put in a class def draw_snowman(screen, x, y): """ --- Function for a snowman --- Define a function that will draw a snowman at a certain location. """ pygame.draw.ellipse(screen, WHITE, [35 + x, 0 + y, 25, 25]) pygame.draw.ellipse(screen, WHITE, [23 + x, 20 + y, 50, 50]) pygame.draw.ellipse(screen, WHITE, [0 + x, 65 + y, 100, 100]) # Initialize the game engine pygame.init() # Define the colors we will use in RGB format BLACK = [0, 0, 0] WHITE = [255, 255, 255] # Set the height and width of the screen size = [400, 500] screen = pygame.display.set_mode(size) # Loop until the user clicks the close button. done = False clock = pygame.time.Clock() def main(): while not done: for event in pygame.event.get(): if event.type == pygame.QUIT: done = True # Clear the screen and set the screen background screen.fill(BLACK) # Snowman in upper left draw_snowman(screen, 10, 10) # Snowman in upper right draw_snowman(screen, 300, 10) # Snowman in lower left draw_snowman(screen, 10, 300) # Go ahead and update the screen with what we've drawn. # This MUST happen after all the other drawing commands. pygame.display.flip() # This limits the while loop to a max of 60 times per second. # Leave this out and we will use all CPU we can. clock.tick(60) # Be IDLE friendly pygame.quit() if __name__ == "__main__": main() Now if I make a class such as - import pygame # Define the colors we will use in RGB format BLACK = [0, 0, 0] WHITE = [255, 255, 255] class Snowman(): def __init__(self): # --- Class Attributes --- # Snowman position self.x = 0 self.y = 0 # Snowman's vector self.change_x = 0 self.change_y = 0 # Snowman size self.size = 10 # Snowman color self.color = [255,255,255] # --- Class Methods --- def move(self): self.x += self.change_x self.y += self.change_y # --> Should I pass pygame/pygame.draw/pygame.draw.ellipse # to the draw method? Or is this proper as is? def draw(self, screen): pygame.draw.ellipse(screen, WHITE, [35 + self.x, 0 + self.y, 25, 25]) pygame.draw.ellipse(screen, WHITE, [23 + self.x, 20 + self.y, 50, 50]) pygame.draw.ellipse(screen, WHITE, [0 + self.x, 65 + self.y, 100, 100]) And change the original code to this - """ Sample Python/Pygame Programs Simpson College Computer Science http://programarcadegames.com/ http://simpson.edu/computer-science/ Explanation video: http: """ # Import a library of functions called 'pygame' import pygame from P10_Graphics import Graphics def main(): snowman1 = Graphics.Snowman() snowman2 = Graphics.Snowman() snowman3 = Graphics.Snowman() # Initialize the game engine pygame.init() # Define the colors we will use in RGB format BLACK = [0, 0, 0] WHITE = [255, 255, 255] # Set the height and width of the screen size = [400, 500] screen = pygame.display.set_mode(size) # Loop until the user clicks the close button. done = False clock = pygame.time.Clock() while not done: for event in pygame.event.get(): if event.type == pygame.QUIT: done = True # Clear the screen and set the screen background screen.fill(BLACK) # Snowman in upper left snowman1.x = 10 snowman1.y = 10 snowman1.draw(screen) # Snowman in upper right snowman2.x = 300 snowman2.y = 10 snowman2.draw(screen) # Snowman in lower left snowman3.x = 10 snowman3.y = 300 snowman3.draw(screen) # Go ahead and update the screen with what we've drawn. # This MUST happen after all the other drawing commands. pygame.display.flip() # This limits the while loop to a max of 60 times per second. # Leave this out and we will use all CPU we can. clock.tick(60) # Be IDLE friendly pygame.quit() if __name__ == "__main__": main() Should the draw() take other parameters? Is this right? Is there a better way to write this particular piece of code? #### Share this post ##### Share on other sites Advertisement In an ideal world maybe Snowman shouldn't need to know about pygame, but that starts taking you down a rabbit hole of separating the logical data of a snowman from the visual appearance of a snowman, possibly not useful in this situation, especially given the reliance on the ellipse() function. If you liked you could have some sort of separate PyGameSnowman object that handles the rendering, reading data from the Snowman and rendering it accordingly. In general code review terms: • you shouldn't set the x/y values to constant values each time through the loop • change_x / change_y are perhaps better described as 'velocity' • you don't call move() so this isn't used anyway • you might consider having a data structure that stores all your snowmen so that it extends to any number of snowmen in future #### Share this post ##### Share on other sites In an ideal world maybe Snowman shouldn't need to know about pygame, but that starts taking you down a rabbit hole of separating the logical data of a snowman from the visual appearance of a snowman, I'd like to go down that rabbit hole. especially given the reliance on the ellipse() function. If you liked you could have some sort of separate PyGameSnowman object that handles the rendering, reading data from the Snowman and rendering it accordingly. Some example code of that, if you don't mind. In general code review terms: • you shouldn't set the x/y values to constant values each time through the loop • change_x / change_y are perhaps better described as 'velocity' • you don't call move() so this isn't used anyway • you might consider having a data structure that stores all your snowmen so that it extends to any number of snowmen in future • Agree. • Agree. • It'll be used later, in a different tutorial. • An array? #### Share this post ##### Share on other sites class Snowman(object): """ as above, but no draw() method - this is purely for logic, and is no longer anything to do with Pygame or graphics""" pass # the rest of your code here class IPygameRenderable(object): """Interface for objects renderable in Pygame""" def draw(self, pygame_screen): """Must be implemented by derived class""" raise NotImplementedError class PygameSnowman(IPygameRenderable): def __init__(self, snowman): # Link to the object that tells us where to render, # and any other important traits that we may need to show self.snowman = snowman def draw(self, pygame_screen): pygame.draw.ellipse(pygame_screen, WHITE, [35 + self.snowman.x, 0 + self.snowman.y, 25, 25]) pygame.draw.ellipse(pygame_screen, WHITE, [23 + self.snowman.x, 20 + self.snowman.y, 50, 50]) pygame.draw.ellipse(pygame_screen, WHITE, [0 + self.snowman.x, 65 + self.snowman.y, 100, 100]) def main(): all_snowmen = [] all_snowmen.append(Graphics.Snowman()) all_snowmen.append(Graphics.Snowman()) all_snowmen.append(Graphics.Snowman()) all_drawable = [] for snowman in all_snowmen: drawable = PygameSnowman(snowman) all_renderable.append(drawable) # ...etc ... while not done: # ...etc... for snowman in all_snowmen: snowman.move() # or .update(), or whatever other logic you have for drawable in all_drawable: drawable.draw(screen) #### Share this post ##### Share on other sites • Advertisement	2018-04-21 10:00:23	{"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": 0.1795922964811325, "perplexity": 7951.535241532939}, "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-2018-17/segments/1524125945111.79/warc/CC-MAIN-20180421090739-20180421110739-00457.warc.gz"}
https://kfitz.info/birdsite/2016/2016-11-01-tweets/	# 2016 11 01 tweets Okay, seriously, I am about to send this entire election cycle to its room to think about what it’s done. Thanks for that! Mostly talked about MIT libraries’ budgetary innovations but misspoke on this aspect. Replying to @mchris4duke, @zinelib and @amy_brand You two are bringing multiple kinds of awesome. RT @mlastyle: URLs in MLA style: get an MLA editor's commonsense advice on shortening, breaking, and more: https://style.mla.org/2016/11/02/urls-some-practical-advice/ omg RT @MLAnews: Negotiating the demands of teaching, research, & service: new Profession essays examine the history and offer ideas. https://t… One of the best things I ever got to do was introduce Walter Cronkite at @pomonacollege’s commencement. It was an extraordinary honor. https://twitter.com/CBSNews/status/794582487880110082 On my way to MKE for @CLIRnews and @CLIRDLF! Listening to @terrainsvagues and @libmark present the history and future of our collaboration on @humcommons & CORE. #DLFforum I voted absentee this year in order to attend the #DLFforum. I miss my polling place, though, and the ritual of the day. Fluffy animals have saved me today. https://twitter.com/terrainsvagues/status/796112718407340032 I am horrified. And terrified. And so, so sorry. But I am not giving up. This must be fought, and I will fight. <3 This Morning. http://www.plannedobsolescence.net/this-morning-2/ I am so, so sorry Rahawa. Sending <3 This is smart and powerful. I only have one quibble with it. https://medium.com/@alexyoung_59363/the-pendulum-swings-both-ways-61d50f6608d9#.3ruev3257 The claim that our side didn’t show up ignores the destruction of the Voting Rights Act. Many couldn’t show up; many were turned away. 👀 I have the Waterfield Staad small backpack in black-on-black. It’s very profesh but not as flexible as I’d like. The last few days have shown the desperate need for humanities and social science education, but work in those fields is in serious danger. https://twitter.com/jasonrhody/status/797174737847910400 Teju Cole, A Time for Refusal. http://nyti.ms/2eorijG Knomo has some great professional options for women as well. RT @tressiemcphd: Believe black people. RT @terrainsvagues: “We need an army to combat the damage the next administration will do to #openscience #openaccess #oernek” — @JohnArnol… RT @AprilHathcock: Excited about the opening of #opencon. But so far we've had like 3 white men in a row talking to us abt being radical fo… Grateful this morning to celebrate the bat mitzvah of the daughter of dear friends, to be part of a joyous look toward the future. Hmmm. I don’t have crunchy but I do have a decent creamy, and a good apple or two… Moving Forward http://www.plannedobsolescence.net/moving-forward/ It is difficult indeed. Many thanks, R. Argh, Rohan, I am so sorry to hear about this. Thank you for opening a larger conversation. The entire @mlastyle team thanks you! $$Check out the free resources at http://style\.mla\.org too\.$$ https://twitter.com/DanielPaulOD/status/798966305739018240 I called both Senators yesterday to thank them for their efforts and received positive, caring attention to my concerns. https://twitter.com/AbigailK1980/status/798553762164015104 Very happy to be in Lawrence KS for #KUOASymp16. Last time I was here it was 3 degrees. Today it is 75 more than that. Just about to begin the livestream of #KUOASymp16, Envisioning a World Beyond APCs/BPCs. https://openaccess.ku.edu/symposium/livestream RT @MLAnews: MLA reaffirms "its commitment to free inquiry & academic freedom for all, unimpeded by acts of prejudice and hate": https://t.… Safe travels, Martin - great seeing you! This whole thread. So connected to my focus in Generous Thinking, though I want to bridge the gap between the university and the community. https://twitter.com/colindickey/status/800008868596092928 RT @felixgilman: we're just going to have to get used to having thirty scandals on the go at once and triaging attention as best we can Whoa, it was still rightside-up when I was there last Saturday. Thanks for this picture. We were there last Saturday, before the reinstallation. All the more moving now. I am stunned that one even has to point out that this kind of thing is Not Okay. https://twitter.com/joshtpm/status/800745959244251136 I’m so sorry to hear this, Martin. I imagine the travel must have taken a bit of a toll. Take care of yourself! I’d be happy with this as well. Congratulations!!! Such a nice bit of Thanksgivng news. ON IT. First, you make a roux. $$Contents are darker than they appear\.$$ Aw man, no. Gumbo! Fab! Chicken & sausage gumbo, a big salad, and an olive oil-orange-almond cake for dessert. Good night, all. ENOUGH. I am calling the rest of this year off. I can’t help but think of the end of “A Good Man Is Hard to Find”: “She would have been a good woman + if it had been somebody there to shoot her every minute of her life.” “Our grudging acceptance that progress and diversity are fragile bits of spun glass looks like hopelessness because it doesn’t absolve.” https://twitter.com/tressiemcphd/status/802959868801884160 “My hopelessness is … a necessary requirement for the hard work of resisting tyranny and fascism.” Thank you, @tressiemcphd. https://twitter.com/tressiemcphd/status/802959868801884160 I just… I am not retweeting that. But holy shit. Ooh, good to know. I could also use a little revolt these days, oddly. This is a really, really good question. https://twitter.com/AstroKatie/status/802982523634647040 RT @RadioFreeTom: Trump's likely trying to get in front of bad news by tweeting about the popular vote - but doesn't make it less of an att… This, while trying not to hyperventilate. http://www.vox.com/policy-and-politics/2016/11/27/13758538/donald-trump-vote-illegally-tweet Masha Gessen on the problems in political strategy today and the “slippery slope of collaboration.” http://www.nybooks.com/daily/2016/11/27/trump-realism-vs-moral-politics-choice-we-face/ RT @hels: If a powerful person asserts X there are 2 responsible ways to cover: 1. "X is true" 2. "Person incorrectly thinks X" Never "Per… RT @hels: "Person says X" is a cop out, used when a news org knows X is wrong but is unwilling for whatever reason to criticize power RT @hels: The job of the news is not to report on who says what, but to report on truth. Statements are the path to truth, not the truth it… Sending you and your family, colleagues, and community all my best thoughts! Fabulous news — congratulations, all! #OAftw https://twitter.com/openlibhums/status/803275353905135616 This is the greatest.	2023-02-02 20:15:34	{"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": 0.1806439459323883, "perplexity": 7176.044066633669}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500041.18/warc/CC-MAIN-20230202200542-20230202230542-00232.warc.gz"}
https://byjus.com/rd-sharma-solutions/class-7-maths-chapter-4-rational-numbers-ex-4-4/	# RD Sharma Solutions For Class 7 Maths Exercise 4.4 Chapter 4 Rational Numbers ### RD Sharma Class 7 Solutions Chapter 4 Ex 4.4 PDF Free Download Students can download the PDF of RD Sharma Solutions for Class 7 Exercise 4.4 chapter 4 from the below links. These solutions have been designed by Mathematics experts at BYJU’S with one hundred per cent accuracy. Knowing the concepts will help students to prepare effectively for their exam and it is prepared by the CBSE board as per the guidelines. This exercise discusses with the standard form of rational numbers. A rational number p/q is said to be in the standard form if p is positive, and the integers p and q have no common divisor other than 1. By practising RD Sharma Solutions for Class 7 students can procure excellence in board exams. ## Download the PDF of RD Sharma Solutions For Class 7 Chapter 4 – Rational Numbers Exercise 4.5 ### Access answers to Maths RD Sharma Solutions For Class 7 Chapter 4 – Rational Numbers Exercise 4.4 1. Write each of the following rational numbers in the standard form: (i) (2/10) (ii) (-8/36) (iii) (4/-16) (iv) (-15/-35) (v) (299/-161) (vi) (-63/-210) (vii) (68/-119) (viii) (-195/275) Solution: (i) Given (2/10) We know that HCF of 2 and 10 is 2 Now dividing the numerator and denominator by HCF i.e. 2, we get: (2/10) ÷ (2/2) = (1/5) Therefore (1/5) is the standard form of given number (ii) Given (-8/36) We know that HCF of 8 and 36 is 4 Now dividing the numerator and denominator by HCF i.e. 4, we get: (-8/36) ÷ (4/4) = (-2/9) Therefore (-2/9) is the standard form of given number (iii) Given (4/-16) Here denominator is negative so we have multiply both numerator and denominator by -1 (4/-16) × (-1/-1) = (-4/16) We know that HCF of 4 and 16 is 4 Now dividing the numerator and denominator by HCF i.e. 4, we get: (-4/16) ÷ (4/4) = (-1/4) Therefore (-1/4) is the standard form of given number (iv) Given (-15/-35) Here denominator is negative so we have multiply both numerator and denominator by -1 (-15/-35) × (-1/-1) = (15/35) We know that HCF of 15 and 35 is 4 Now dividing the numerator and denominator by HCF i.e. 5, we get: (15/35) ÷ (5/5) = (3/7) Therefore (3/7) is the standard form of given number (v) Given (299/-161) Here denominator is negative so we have multiply both numerator and denominator by -1 (299/-161) × (-1/-1) = (-299/161) The HCF of 299 and 161 is 23 Now dividing the numerator and denominator by HCF i.e. 23, we get: (-299/161) ÷ (23/23) = (-13/7) Therefore (-13/7) is the standard form of given number (vi) Given (-63/-210) The HCF of 63 and 210 is 21 Now dividing the numerator and denominator by HCF i.e. 21, we get: (-63/-210) ÷ (21/21) = (-3/-10) = (3/10) Therefore (3/10) is the standard form of given number (vi) Given (68/-119) Here denominator is negative so we have multiply both numerator and denominator by -1 (68/-119) × (-1/-1) = (-68/119) The HCF of 68 and 119 is 17 Now dividing the numerator and denominator by HCF i.e. 17, we get: (-68/119) ÷ (17/17) = (-4/7) Therefore (-4/7) is the standard form of given number (viii) Given (-195/275) The HCF of 195 and 257 is 5 Now dividing the numerator and denominator by HCF i.e. 5, we get: (-165/275) ÷ (5/5) = (-39/55) Therefore (-39/55) is the standard form of given number ### Access other exercises of RD Sharma Solutions For Class 7 Chapter 4 – Rational Numbers Exercise 4.6 Solutions	2019-12-14 01:51:38	{"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": 0.9673786759376526, "perplexity": 1986.3660522746447}, "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-2019-51/segments/1575540579703.26/warc/CC-MAIN-20191214014220-20191214042220-00042.warc.gz"}
http://clay6.com/qa/44678/charges-and-2-mu-c-8-mu-c-67-mu-c-and-8-mu-c-are-placed-at-the-corner-abcd-	Browse Questions # Charges and $2 \mu C, -8 \mu C, 67 \mu C$ and $8 \mu C$ are placed at the corner ABCD of square of side $2m$ each. The potential at the centre of the square is $(A)\;30 \sqrt {2} \times 10^3 \;V$	2016-12-05 08:28:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.750525951385498, "perplexity": 289.1143525874358}, "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-2016-50/segments/1480698541556.70/warc/CC-MAIN-20161202170901-00490-ip-10-31-129-80.ec2.internal.warc.gz"}
http://www.gradesaver.com/textbooks/math/calculus/calculus-early-transcendentals-8th-edition/chapter-5-review-true-false-quiz-page-421/8	## Calculus: Early Transcendentals 8th Edition Published by Cengage Learning # Chapter 5 - Review - True-False Quiz: 8 False #### Work Step by Step Consider $f(x)=6,g(x)=x, a=-4, b=4$ Therefore, $f(x)\geq g(x)$ on $(-4,4)$ However $f'(x) \leq g'(x)$, since $f'(x)=0$ and $g'(x)=1$ Hence, the statement is false. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.	2018-04-24 05:40:57	{"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": 0.7686181664466858, "perplexity": 2253.834190077834}, "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-2018-17/segments/1524125946564.73/warc/CC-MAIN-20180424041828-20180424061828-00033.warc.gz"}
https://techwhiff.com/learn/evaluate-the-integral-using-integration-by-parts/284293	# Evaluate the integral using integration by parts. e4 Sx x? In (x)dx 1 e 4 S... ###### Question: Evaluate the integral using integration by parts. e4 Sx x? In (x)dx 1 e 4 S x In (x)dx=0 (Type an exact answer.) #### Similar Solved Questions ##### Recall that "very satisfied" customers give the XYZ-Box video game system a rating that is at... Recall that "very satisfied" customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 70 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating... ##### Suppose that Peace Corporation, chemical manufacturing Company, has two production departments using sequential production flow: the... Suppose that Peace Corporation, chemical manufacturing Company, has two production departments using sequential production flow: the Mixing Department and the Bottling Department. In the Mixing Department direct material consisting ingredient chemicals is added at the beginning of the production pro... ##### Drugs can be classified by dangerous abuse potential based on withdrawal symptoms and level of dependency.... Drugs can be classified by dangerous abuse potential based on withdrawal symptoms and level of dependency. Drugs that are more potent and have more severe withdrawal symptoms are more highly addictive. Drugs that are less stimulating and have mild or no withdrawal symptoms are less prone to abuse. U... ##### 1.(7 pts. total) The figure shows a cut-away side view of a circular current loop. The... 1.(7 pts. total) The figure shows a cut-away side view of a circular current loop. The current is flowing out of the page on the left-hand side of the loop and into the page on the right-hand side. 1 3 4 COMED --- (a) (2 pts.) Sketch about five of the magnetic field lines produced by the current loo... ##### According to the table below, at which level of input will diminishing average returns begin? Quantity... According to the table below, at which level of input will diminishing average returns begin? Quantity of labor Total Product 50 130 230 au AWN 320 400 465 525 575 3 units of labor 5 units of labor 7 units of labor 4 units of labor... ##### Ph How much NaOH is needed to prepare 546 mL solution with a pH=10.00... ##### Print itenm Calculating Departmental Overhead Rates and Applying Overhead to Production At the beginning of the... Print itenm Calculating Departmental Overhead Rates and Applying Overhead to Production At the beginning of the year, Glaser Company estimated the following Assembly Departmernt $445,000 73,500 75,000 Testing Total Overhead Direct labor hours Machine hours$970,100 525,100 0,425 2,500 113,925 27,500... ##### On April 1, Jiro Nozomi created a new travel agency, Adventure Travel. The following transactions occurred... On April 1, Jiro Nozomi created a new travel agency, Adventure Travel. The following transactions occurred during the company’s first month. April 1 Nozomi invested $34,000 cash and computer equipment worth$30,000 in the company in exchange for common stock. 2 The company rented fur... ##### How do you solve y/4=5? How do you solve y/4=5?... ##### D. 12 percent, because it reflects the firm's cost of capital and the use of the... D. 12 percent, because it reflects the firm's cost of capital and the use of the funds doesn't matter 18. SLG Corp. is an all-equity firm with a weighted average cost of capital of 9.68 percent. The current market value of the equity is \$27% million, and the tax rate is 35 percent. What is E...	2022-09-25 02:08:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.2576594650745392, "perplexity": 3412.6216689779944}, "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/1664030334332.96/warc/CC-MAIN-20220925004536-20220925034536-00443.warc.gz"}
https://answers.ros.org/question/215450/weird-looking-pointcloud-in-rviz/	# Weird looking PointCloud in RViz Hi! This is more or less a follow-up to a previous question of mine. In short: I used the pcd_to_pointcloud tool to create a PointCloud publisher. Now I have extended my publisher to work with the PMD Nano camboard I'm using. The cloud is displayed in RViz however it looks weird: If I look at it from the side I get this peculiar view: I work with the rgbd-grabber library and if I use sample provided in it I get this: I had great difficulties figuring out how to publish and display the cloud inside RViz in the first and the way it looks like tells me I am doing some configuration wrong. You can see on the top of this...pyramid...turned upside down I get a view of my hand (though it looks pretty bad). It seems that the depth image I'm getting is somehow projected onto the bottom of this pyramid (bottom here is the "top" side of the cloud) and in 2D. All I'm doing is use the pcl::toROSMsg(...) to convert my pcl::PointCloud<pcl::pointxyz>::Ptr to a ros::sensor_msgs::PointCloud2 message, which a publish to the ROS network. I do not do any sort of transformation to its points. Any advice how to correct this behaviour? I can also provide the code though as I said I just take the points from the camera, convert them to a ROS-compatible message and display them inside RViz. Thanks! EDIT: The code is as follows: #include <ros/ros.h> #include <string> #include <memory> #include <opencv2/core/core.hpp> #include <opencv2/imgproc/imgproc.hpp> #include <opencv2/highgui/highgui.hpp> #include <pcl/visualization/cloud_viewer.h> #include <pcl_ros/point_cloud.h> //#include <sensor_msgs/point_cloud_conversion.h> #include <pcl/point_types.h> #include <image_transport/image_transport.h> #include <cv_bridge/cv_bridge.h> #include "../include/pmd_nano/PMDNano.h" #include <pcl/io/io.h> #include <pcl/io/pcd_io.h> #include <pcl_ros/publisher.h> #include <pcl_conversions/pcl_conversions.h> #include <ros/publisher.h> using std::string; class PMDPublisher { protected: string ppp_file, pap_file; ros::NodeHandle nh; std::shared_ptr<DepthCamera> camera; string cloud_topic; string imgDepth_topic, imgAmplitude_topic; string tf_frame; ros::NodeHandle private_nh; pcl_ros::Publisher<sensor_msgs::PointCloud2> pubCloud; image_transport::Publisher pubDepth, pubAmplitude; public: sensor_msgs::PointCloud2 cloud; //sensor_msgs::PointCloud2Ptr cloud; PMDPublisher(string _ppp_file, string _pap_file, string _cloud_topic="pmd_cloud", string _imgDepth_topic="pmd_depth", string _imgAmplitude_topic="pmd_amplitude") : ppp_file(_ppp_file), pap_file(_pap_file), cloud_topic(_cloud_topic), imgDepth_topic(_imgDepth_topic), imgAmplitude_topic(_imgAmplitude_topic), private_nh("~") { ROS_INFO("Initializing PMD Publisher"); if(ppp_file == "" \|\| pap_file == "") exit(EXIT_FAILURE); ROS_INFO_STREAM("Following PMD configuration files were loaded:\n" << "PPP file: \"" << ppp_file << "\"\n" << "PAP file: \"" << pap_file << "\"\n"); camera = std::shared_ptr<DepthCamera>(new PMDNano(pap_file, ppp_file)); image_transport::ImageTransport imgTransportDepth(nh), imgTransportAmplitude(nh); ROS_INFO_STREAM("Publishing data on topic \"" << nh.resolveName(cloud_topic) << "\" with frame_id \"" << tf_frame << "\""); } int start() { try { camera->start(); } catch(std::exception e) { ROS_ERROR("Node unable to start camera"); return -1; } ROS_INFO_STREAM("Depth: " << camera->depthSize().width << " by " << camera->depthSize().height); return 0; } bool spin () { ROS_INFO("Allocating memory ... edit retag close merge delete You should link to, or post, your code. You may have to open an issue against pcl_conversions if no one finds something wrong with your code: https://github.com/ros-perception/pcl... ( 2015-08-07 12:20:50 -0500 )edit Okay, will do that tomorrow since I don't have access to the computer right now. ( 2015-08-07 12:27:51 -0500 )edit	2019-09-21 15:56:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1732342392206192, "perplexity": 9939.326375705048}, "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/1568514574532.44/warc/CC-MAIN-20190921145904-20190921171904-00343.warc.gz"}
http://clay6.com/qa/10332/p-represents-the-variable-complex-number-z-find-the-locus-of-p-if-arg-bigg-	Comment Share Q) # $P$ represents the variable complex number $z$.Find the locus of $P$,if $arg\bigg(\large\frac{z-1}{z+3}\bigg)=\large\frac{\pi}{2}$ This is the fifth part of the multi-part Q8. Comment A) Toolbox: • If $z=a+ib$ then $\bar{z}=a-ib$. • $\mid z\mid=\sqrt{a^2+b^2}$ • $z^{-1}=\large\frac{a-ib}{a^2+b^2}$ • $z\bar{z}=a^2+b^2$ • Also $Re(z)=a,Im(z)=b$ • Exponential form of a complex number is $z=re^{\large i\theta}=r[\cos\theta+i\sin \theta]$ • Where $r$ is the modulus and $\theta$ the argument. • If $z_1=r_1e^{\large i\theta_1}$ and $z_2=r_2e^{\large i\theta_2}$ are equal,then $r_1=r_2$,$\theta_1=\theta_2$ Step 1: $P$ is the point representing the variable complex number $z$ such that $arg\big(\large\frac{z-1}{z+3}\big)=\large\frac{\pi}{2}$ Let $z=x+iy\Rightarrow arg\big(\large\frac{z-1}{z+3}\big)=\large\frac{\pi}{2}$ $\large\frac{z-1}{z+3}=\large\frac{x+iy-1}{x+iy+3}$ $\quad\quad=\large\frac{(x-1)+iy}{(x+3)+iy}$ $\quad\quad=\large\frac{(x-1)+iy}{(x+3)+iy}\times \bigg(\large\frac{(x+3)-iy}{(x+3)-iy}\bigg)$ $\quad\quad=\large\frac{(x-1)(x+3)+y^2+i(y(x+3)-y(x-1))}{(x+3)^2+y^2}$ Step 2: Since $arg\big(\large\frac{z-1}{z+3}\big)=\large\frac{\pi}{2}$ $\Rightarrow \tan^{-1}\large\frac{y(x+3)-y(x-1)}{(x-1)(x+3)+y^2}=\large\frac{\pi}{2}$ $\Rightarrow (x-1)(x+3)+y^2=0$ $x^2+2x-3+y^2=0$ (i.e)$x^2+y^2+2x-3=0$ Step 3: The locus is a circle with centre $(-1,0)$ Radius=$\sqrt{1+3}$ $\qquad\;\;=\sqrt 4$ $\qquad\;\;=2$ The locus is a circle with centre $(-1,0)$ and radius 2 units.	2019-12-12 05:16:35	{"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": 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": 0.9425944089889526, "perplexity": 660.4946578248139}, "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/1575540537212.96/warc/CC-MAIN-20191212051311-20191212075311-00154.warc.gz"}
http://www.lmfdb.org/Variety/Abelian/Fq/1/3/d	Properties Label 1.3.d Base Field $\F_{3}$ Dimension $1$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes Invariants Base field: $\F_{3}$ Dimension: $1$ Weil polynomial: $1 + 3 x + 3 x^{2}$ Frobenius angles: $\pm0.833333333333$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ This isogeny class is simple. Newton polygon This isogeny class is supersingular. $p$-rank: $0$ Slopes: $[1/2, 1/2]$ Point counts This isogeny class contains a Jacobian, and hence is principally polarizable. $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 7 7 28 91 217 784 2107 6643 19684 58807 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 7 28 91 217 784 2107 6643 19684 58807 Decomposition This is a simple isogeny class. Base change This is a primitive isogeny class.	2019-10-22 04:44:34	{"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": 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": 0.9745777249336243, "perplexity": 1044.7711472625228}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987798619.84/warc/CC-MAIN-20191022030805-20191022054305-00268.warc.gz"}
https://www.physicsforums.com/threads/prove-y-exp-x-y-y-0-has-unique-solution.616292/	# Homework Help: Prove y'' + exp(x)y'+y=0 has unique solution 1. Jun 24, 2012 ### john_84 y''+exy'+y=0 y(0)=1 y('(0)=4 show the solution to this equation is unique 2. Jun 24, 2012 ### Dick You must have theorems that will allow you conclude a differential equation has a unique solution. What are they? 3. Jun 25, 2012 ### christoff We're going to compare two (possibly different) solutions of your initial value problem. Let $y_1$, $y_2$ be two solutions to your IVP. Then consider their difference $f:=y_1-y_2$. Direct verification shows that $f$ is a solution to the ODE with initial conditions $f(0)=0$, $f'(0)=0$. (check this) However, by that same token, since $f$ satisfies the ODE, we can rearrange things and find $f''(x)=-\exp(x)f'(x)-f(x)$. Try evaluating $f''$ at zero. What does this tell you about $f$? 4. Jun 25, 2012 ### john_84 christoff this is the way that the professor start with but he wants to use Gronwall’s Inequality to prove f is identically zero i multiplay the equation by f' but i end up with this f'' f' + exp(x) (f') ^2 + f f' =0 d/dx[ (f')^2/2 + (f)^2/2]=-exp(x) (f')^2 at this point i couldn't use Gronwall’s Inequality because it states: d/dx[f]<=kf f(x)<=f(0)exp(kx) in the RHS i have exp(x) which is not a constant what i should do? 5. Jun 25, 2012 ### christoff I'm not sure how you are supposed to use Gronwall's Identity to prove this. Your ODE is second order, and Gronwall's Identity only proves exponential boundedness of solutions of first-order equations. The problem isn't your exponential, your problem is that you have (f')^2/2+(f)^2/2 in the LHS, but you have (f')^2 in the RHS (these need to be equal, somehow). You can reduce it to a first-order equation in two variables, but then the standard Gronwall's identity doesn't apply. 6. Jun 28, 2012 ### tt2348 Alright so from what I see, we have $\frac{d}{dx}(\frac{f'^{2}}{2}+\frac{f^{2}}{2})=-e^{x}f'^{2}$... unpleasant looking.. but i have an idea. multiply the entire thing by $2e^{x}$ Giving $e^{x}\frac{d}{dx}(f'^{2}+f^{2})=-2e^{2x}f'^{2}$ And for notation purposes... call $u(x)=f'(x)^{2}+f(x)^{2}$ then we have $e^{x}u'(x)=-2e^{x}f'^{2}$ using $\frac{d}{dx}(e^{x}u(x))=e^{x}u(x)+e^{x}u'(x)$ gives $\frac{d}{dx}(e^{x}u(x))-e^{x}u(x)=-2e^{2x}f'^{2}$ implies $\frac{d}{dx}(e^{x}u(x))=e^{x}u(x)-2e^{2x}f'^{2}$ we know $2e^{2x}f'^{2}≥0$ so it follows $\frac{d}{dx}(e^{x}u(x))=e^{x}u(x)-2e^{2x}f'^{2}≤e^{x}u(x)$ Which I believe should allow you to use the inequality proposed? since f(0)=0, and f'(0)=0 , u(0)=0 I think proceeding from there shouldn't be a problem 7. Jun 28, 2012 ### christoff Brilliant solution, tt. That substitution really cleans things up a lot. 8. Jun 28, 2012 ### HallsofIvy Yes, very nice solution but it is not really necessary to solve the differential equation. Instead, letting v= y', the second equation can be written $v'= -y- e^xfv$ and together with $y'= v$ we can write as the first order vector equation $$\frac{d\begin{pmatrix}y \\ v\end{pmatrix}}{dx}= \begin{pmatrix}0 & 1\\ -1 & -e^x\end{pmatrix}\begin{pmatrix}y \\ v\end{pmatrix}$$ That's a linear equation and the determinant of the coeffient matrix is 1, not 0, for all x and y and in particular in a neighborhood of (x, y)= (0, 4). Therefore, by the standard "existence and uniqueness" theorem for differential equations, there exist a unique solution. Last edited by a moderator: Jun 28, 2012 9. Jun 28, 2012 ### tt2348 very true! But what is f in $v'=-y-e^{x}fv$ ? 10. Jun 28, 2012 ### john_84 thanks alot tt2348 that's a very clever solution	2018-06-19 18:56:10	{"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7914133667945862, "perplexity": 1168.7755085675951}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863109.60/warc/CC-MAIN-20180619173519-20180619193519-00212.warc.gz"}
http://www.talkstats.com/threads/r-plotting-a-normal-curve-along-with-a-histogram.17008/	# [R] Plotting a normal curve along with a histogram #### SlideRule ##### New Member The R code below is my attempt to plot a histogram and then plot a normal curve for reference. A blue line is drawn to show the mean value. From the example image I've attached you can see that the blue line does not run through the center of the normal curve, as it should; the normal curve appears to be scaled improperly along the x-axes. I've found many examples on the Internet of how to add normal curves to histograms in R, but none of those examples seem reliable when tested. Can anyone here please give correct R code for this? Thank you. Code: # Draw a histogram with a normal curve. histnorm=function(x, ...) { if (length(x)>0) { hist(x,freq=FALSE, ...) rug(x) curve(dnorm(x, mean=mean(x), sd=sd(x)), add=TRUE, col="red", lty="dotted", xaxt="n") abline(v=mean(x),col="blue") mtext(paste("mean ", round(mean(x),1), "; sd ", round(sd(x),1), "; N ", length(x),sep=""), side=1, cex=.75) } # fi } # histnorm #### Dason Code: # Draw a histogram with a normal curve. histnorm=function(x, ...) { if (length(x)>0) { hist(x,freq=FALSE, ...) rug(x) curve(dnorm(x, mean=mean(x), sd=sd(x)), add=TRUE, col="red", lty="dotted", xaxt="n") abline(v=mean(x),col="blue") mtext(paste("mean ", round(mean(x),1), "; sd ", round(sd(x),1), "; N ", length(x),sep=""), side=1, cex=.75) } # fi } # histnorm Your problem comes from the fact that you're simultaneously using "x" to represent the data and as a variable inside of curve. A couple possible fixes: Change the input from "x" to "y" or "data" or something like that and make the corresponding changes in the function Code: # Draw a histogram with a normal curve. histnorm=function(dat, ...) { if (length(dat)>0) { hist(dat ,freq=FALSE, ...) rug(dat) curve(dnorm(x, mean = mean(dat), sd = mean(dat)), add=TRUE, col="red", lty="dotted", xaxt="n") abline(v=mean(dat),col="blue") mtext(paste("mean ", round(mean(dat),1), "; sd ", round(sd(dat),1), "; N ", length(dat),sep=""), side=1, cex=.75) } # fi } # histnorm Or you could keep everything the same but you need to remember that the inside of curve considers x to be the variable of interest (not data!) so we can calculate the mean and standard deviation before plugging into curve: Code: # Draw a histogram with a normal curve. histnorm=function(x, ...) { if (length(x)>0) { hist(x,freq=FALSE, ...) rug(x) mn <- mean(x) stdev <- sd(x) curve(dnorm(x, mean = mn, sd= stdev), add=TRUE, col="red", lty="dotted", xaxt="n") abline(v=mean(x),col="blue") mtext(paste("mean ", round(mean(x),1), "; sd ", round(sd(x),1), "; N ", length(x),sep=""), side=1, cex=.75) } # fi } # histnorm #### SlideRule ##### New Member Thank you, your second example does seem to work. Can you please explain more about how the values of x are being reassigned in my code? My code doesn't have any explicit reassignment of x, and I don't understand anything in the R 2.12.2 documentation to say that the value of the input arguments to the curve or dnorm functions would be side-affected.	2018-02-23 02:46:54	{"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": 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": 0.359424352645874, "perplexity": 5462.257918496471}, "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/1518891814311.76/warc/CC-MAIN-20180223015726-20180223035726-00126.warc.gz"}
https://en.wikipedia.org/wiki/User:Catalina_marina	# User:Catalina marina ## Coordinate ring The coordinate ring of C over K is defined as ${\displaystyle K[C]={\frac {K[x,y]}{(y^{2}+h(x)y-f(x)}}}$. The polynomial ${\displaystyle \,r(x,y)=y^{2}+h(x)y-f(x)}$ is irreducible over ${\displaystyle {\overline {K}}}$, so ${\displaystyle {\overline {K}}[C]={\frac {{\overline {K}}[x,y]}{(y^{2}+h(x)y-f(x)}}}$ is an integral domain. Proof. If r (x,y) were reducible over ${\displaystyle {\overline {K}}}$, it would factor as (y - u(x)) · (y - v(x)) for some u,v${\displaystyle {\overline {K}}}$. But then u(x) · v(x)= f(x) so it has degree 2g + 1, and a(x) + b(x) = h(x) so it has degree smaller than g, which is impossible. Note that any polynomial function ${\displaystyle G(x,y)\in {\overline {K}}}$ can be written uniquely as ${\displaystyle \,G(x,y)=u(x)-v(x)y}$ with ${\displaystyle u(x)}$, ${\displaystyle v(x)}$ ${\displaystyle {\overline {K}}[x]}$ ## Norm and degree The conjugate of a polynomial function G(x,y) = u(x) - v(x)y in ${\displaystyle {\overline {K}}[C]}$ is defined to be ${\displaystyle {\overline {G}}(x,y)=u(x)+v(x)(h(x)+y)}$. The norm of G is the polynomial function ${\displaystyle N(G)=G{\overline {G}}}$. Note that N(G) = u(x)2 + u(x)v(x)h(x) - v(x)2f(x), so N(G) is a polynomial in only one variable. If G(x,y) = u(x) - v(x) · y, then the degree of G is defined as ${\displaystyle \,\deg(G)=\max[2\deg(a),2g+1+2\deg(b)]}$. Properties: ${\displaystyle \;\deg(G)=\deg _{u}(N(G))}$ ${\displaystyle \;\deg(GH)=\deg(G)+\deg(H)}$ ${\displaystyle \deg(G)=\deg({\overline {G}})}$ The function field K(C) of C over K is the field of fractions of K[C], and the function field ${\displaystyle {\overline {K}}(C)}$ of C over ${\displaystyle {\overline {K}}}$ is the field of fractions of ${\displaystyle {\overline {K}}[C]}$. The elements of ${\displaystyle {\overline {K}}(C)}$ are called rational functions on C. For R such a rational function, and P a finite point on C, R is said to be defined at P if there exist polynomial functions G, H such that R = G/H and H(P) ≠ 0, and then the value of R at P is ${\displaystyle \,R(P)=G(P)/H(P)}$. For P a point on C that is not finite, i.e. P = ${\displaystyle \infty }$, we define R(P) as: If ${\displaystyle \;\deg(G)<\deg(H)}$ then ${\displaystyle R(\infty )=0}$. If ${\displaystyle \;\deg(G)>\deg(H)}$ then ${\displaystyle R(\infty )}$ is not defined. If ${\displaystyle \;\deg(G)=\deg(H)}$ then ${\displaystyle R(\infty )}$ is the ratio of the leading coefficients of G and H. For ${\displaystyle R\in {\overline {K}}(C)^{*}}$ and ${\displaystyle P\in C}$, If ${\displaystyle \;R(P)=0}$ then R is said to have a zero at P, If R is not defined at P then R is said to have a pole at P, and we write ${\displaystyle R(P)=\infty }$. ## Order of a polynomial function at a point For ${\displaystyle G{=}u(x)-v(x)\cdot y\in {\overline {K}}[C]^{2}}$ and ${\displaystyle P\in C}$, the order of G at P is defined as: ${\displaystyle \;ord_{P}(G)=r+s}$ if P = (a,b) is a finite point which is not Weierstrass. Here r is the highest power of (x-a) which divides both u(x) and v(x). Write G(x,y) = (x - a)r(u0(x) - v0(x)y) and if u0(a) - v0(a)b = 0, then s is the highest power of (x - a) which divides N(u0(x) - v0(x)y = u02 + u0v0h - v02f, otherwise, s = 0. ${\displaystyle \;ord_{P}(G)=2r+s}$ if P = (a,b) is a finite Weierstrass point, with r and s as above. ${\displaystyle \;ord_{P}(G)=-deg(G)}$ if P = O.	2017-10-21 23:49:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 39, "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": 0.9073157906532288, "perplexity": 700.343180180446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824899.75/warc/CC-MAIN-20171021224608-20171022004608-00575.warc.gz"}
https://www.semanticscholar.org/paper/Distributionally-Robust-Losses-for-Latent-Covariate-Duchi-Hashimoto/bb7b148191f3d6d5bb7dbff3884f9c2142ac7d24	• Corpus ID: 220830740 # Distributionally Robust Losses for Latent Covariate Mixtures @article{Duchi2020DistributionallyRL, title={Distributionally Robust Losses for Latent Covariate Mixtures}, author={John C. Duchi and Tatsunori B. Hashimoto and Hongseok Namkoong}, journal={ArXiv}, year={2020}, volume={abs/2007.13982} } • Published 28 July 2020 • Computer Science • ArXiv While modern large-scale datasets often consist of heterogeneous subpopulations---for example, multiple demographic groups or multiple text corpora---the standard practice of minimizing average loss fails to guarantee uniformly low losses across all subpopulations. We propose a convex procedure that controls the worst-case performance over all subpopulations of a given size. 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Evaluating Model Robustness to Dataset Shift • Computer Science ArXiv • 2020 A "debiased" estimator can be used to evaluate robustness and accounts for realistic shifts that cannot be expressed as covariate shift, and is derived which maintains $\sqrt{N}$-consistency even when machine learning methods with slower convergence rates are used to estimate the nuisance parameters. Large-Scale Methods for Distributionally Robust Optimization • Computer Science NeurIPS • 2020 We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and $\chi^2$ divergence uncertainty sets. We prove that our ## References SHOWING 1-10 OF 70 REFERENCES Learning Models with Uniform Performance via Distributionally Robust Optimization • Computer Science, Mathematics ArXiv • 2018 A distributionally robust stochastic optimization framework that learns a model providing good performance against perturbations to the data-generating distribution is developed, and a convex formulation for the problem is given, providing several convergence guarantees. Robust Covariate Shift Prediction with General Losses and Feature Views • Computer Science ArXiv • 2017 By robustly minimizing various loss functions, including non-convex ones, under the testing distribution; and by separately shaping the influence of covariate shift according to different feature-based views of the relationship between input variables and example labels, these generalizations make robust covariateshift prediction applicable to more task scenarios. Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations • Computer Science Math. Program. • 2018 It is demonstrated that the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs—in many interesting cases even as tractable linear programs. DATA-DRIVEN OPTIMAL TRANSPORT COST SELECTION FOR DISTRIBUTIONALLY ROBUST OPTIMIZATION • Computer Science • 2019 This paper shows rigorously that its framework encompasses adaptive regularization as a particular case, and demonstrates empirically that the proposed methodology is able to improve upon a wide range of popular machine learning estimators. Distributionally Robust Logistic Regression • Computer Science, Mathematics NIPS • 2015 This paper uses the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples, and proposes a distributionally robust logistic regression model that minimizes a worst-case expected logloss function. Wasserstein Distributional Robustness and Regularization in Statistical Learning • Computer Science ArXiv • 2017 A broad class of loss functions are identified, for which the Wasserstein DRSO is asymptotically equivalent to a regularization problem with a gradient-norm penalty, which suggests a principled way to regularize high-dimensional, non-convex problems. Robust Wasserstein profile inference and applications to machine learning • Computer Science J. Appl. Probab. • 2019 Wasserstein Profile Inference is introduced, a novel inference methodology which extends the use of methods inspired by Empirical Likelihood to the setting of optimal transport costs (of which Wasserstein distances are a particular case). Confidence Intervals for Maximin Effects in Inhomogeneous Large-Scale Data • Mathematics • 2016 One challenge of large-scale data analysis is that the assumption of an identical distribution for all samples is often not realistic. An optimal linear regression might, for example, be markedly Fairness Without Demographics in Repeated Loss Minimization • Computer Science ICML • 2018 This paper develops an approach based on distributionally robust optimization (DRO), which minimizes the worst case risk over all distributions close to the empirical distribution and proves that this approach controls the risk of the minority group at each time step, in the spirit of Rawlsian distributive justice. Robust Classification Under Sample Selection Bias • Computer Science NIPS • 2014 This work develops a framework for learning a robust bias-aware (RBA) probabilistic classifier that adapts to different sample selection biases using a minimax estimation formulation and demonstrates the behavior and effectiveness of the approach on binary classification tasks.	2022-08-17 21:48:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5147125720977783, "perplexity": 2267.8875546060854}, "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/1659882573118.26/warc/CC-MAIN-20220817213446-20220818003446-00544.warc.gz"}
https://socratic.org/questions/what-are-the-exact-values-of-cos-150-and-sin-150	# What are the exact values of cos 150° and sin 150°? May 16, 2018 $\cos \left(150\right) = - \frac{\sqrt{3}}{2}$ $\sin \left(150\right) = \frac{1}{2}$ #### Explanation: First of all, observe that $150 = 180 - 30$. Then, remember that we have $\cos \left(180 - x\right) = - \cos \left(x\right)$ $\sin \left(180 - x\right) = \sin \left(x\right)$ Plug in $x = 30$ to get $\cos \left(180 - 30\right) = - \cos \left(30\right)$ $\sin \left(180 - 30\right) = \sin \left(30\right)$ the answer comes from the fact that $\cos \left(30\right) = \frac{\sqrt{3}}{2}$ and $\sin \left(30\right) = \frac{1}{2}$ are known values.	2019-01-18 11:17:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 10, "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": 0.9455915093421936, "perplexity": 644.5241529449419}, "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-2019-04/segments/1547583660070.15/warc/CC-MAIN-20190118110804-20190118132804-00022.warc.gz"}
http://www.sanjuanciudadpatria.com/the-fly-rlw/can-two-angles-form-a-linear-pair-ad01bd	Find the measure of the smaller angle. If the angles are adjacent to each other after the intersection of the lines, then the angles are said to be adjacent. Linear pair axiom of theorems are if a ray stands on a line , then the sum of two adjacent angles so formed is 180 degree. Two angles form a linear pair. A Linear Pair is two adjacent angles whose non-common sides form ∠1 and ∠2 are supplementary. Click hereto get an answer to your question ️ If two adjacent angles form a linear pair, they can be called as: Example 4: 1 and 2 form a linear pair so m 1 + m 2 = 180° therefore the angles … Two angles form a linear pair. The sides of the angles do not form two pairs of opposite rays. Supplementary angles are those angles who add up to #180^@#.They may or may not form a linear pair. Answer: (d) Explanation : (a) If two angles form a linear pair, then each of these angles is of measure 90c (b) Angles forming a linear pair can both be acute angles. If two angles are adjacent and not equal 180°, then they are not supplementary and do not form a linear pair. what is the perimeter of a traingle with two equal side measuring 2.5 and the third side measuring 4 m, hello guys pls tell me which song I will make in guitar and keyboard , please give me correct answer because it is so important for me, हाग, वादके अनुदिश क्रियाशील हैं, सिद्ध कीजिए कि उनक पारणाम(QR' - Q'R) sin A+ (R' - R'P) sin B+ (PQ' - P'Q)sinC = 0Equilibrium of a rigid body under TH Can more than 2 angles form a linear pair ? Learn how to define angle relationships. A link to the app was sent to your phone. ∠BOC and ∠AOC are linear-pair-angles. smallerL Linear Pair Angles. जब P और ए की क्रियाशील रेखाएँ समान्तर नहीं हों:जब P और की क्रियाशीलPAरेखाएँ समान्तर नहीं हैं बिन्द्र, ---$$\frac{1}{x} - \frac{1}{x + b}$$, Comment on the prime factorisation of the denominators of 62.521521521.., the number of distinct real zeros of the polynomial p(x) =x^2+x+1, АQСDEaRS. (d) Bisectors of the adjacent angles forming a linear pair form a right angle. Answer: (c) Two right angles can form a linear pair Two angles form a linear pair. One angle measures 2x and the other angle measures 10r. Two angles form a linear pair. October 10, 2011 theorem: proven statement Linear Pair Theorem: If two angles form a linear pair, then they are supplementary. Yes, because the sum of two right angles is 180° and form a linear pair. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. 0 0. Absolutely. In the figure above, the two angles ∠ JKM and ∠ LKM form a linear pair. The rays forming the sides of one angle and the rays forming the sides of the other angle are opposite rays. Adjacent Angles Are Two Angles That Share A Common Vertex, A Common Side, And No Common Interior Points. answered 09/02/18. Given: You can view more similar questions or ask a new question. Given: 1 and 2 form a linear pair Vertical angles are always congruent. Answer. The measure of one angle is 15 less than half the measurement of its supplement. Linear Pair Of Angles Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays. There are no answers yet. In the diagram below, ∠ABC and ∠DBE are supplementary since 30°+150°=180°, but they do not form a linear pair since they are not adjacent. if the two angles form a linear pair, then the sum of the two angles equals 180 degrees. 6 years ago. Linear Pair of Angles: A linear pair of angles are the adjacent angles formed when two lines intersect. The measure of one angle is 8 times the measure of the other angle. m∠5 and m∠6 are a linear pair. The linear pair conjecture states that if two angles form a linear pair, the sum of the angles is 180 degrees. For two angles to be adjacent, they only have to share a leg, which puts no restrictions on whether the non-common legs form a straight line or not. Such angles are also known as supplementary angles. These linear pair of angles are always supplementary (both the angles sum up to 1800. The Me. We now have an equation in two unknowns (i) angle one plus angle two equals 180 degrees . Linear-pair-angles are always supplementary. Linear pair of angles are formed when two lines intersect each other at a single point. While it is possible for vertical angles to be supplementary (they both are 90), it is not possible for vertical angles to be adjacent. But, all linear pairs are supplementary. % Progress . Two angles form a linear pair. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary. Trending Questions. (They share a vertex and side, but do not overlap.) name two angles that form a linear pair? Answer: Linear pair states that it is the pair of adjacent angle formed when two lines intersect.. If we add two angles which are less than 90°, we get the result less than 180°, e.g. Supplementary angles are two angles whose same is 180^o Linear pairs are adjacent angles who share a common ray and whose opposite rays form a straight line. Two adjacent angles are said to form a linear pair angles , if their non-common arms are two opposite rays. Can two obtuse angles form a linear pair? Answer this question + 100. Perpendicular bisector. Angles 1 and 2 below are a linear pair. The other angle measures (8x)". Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The line through points A, B and C is a straight line. In Fig 5.11 (i) above, observe that the opposite rays (which are the non-common sides of ∠1 and ∠2) form a line. The sides of the angles do not form two pairs of opposite rays. No, two acute angles cannot form a linear pair. this page updated 19-jul-17 Mathwords: Terms and … (a)(a) AB OCDF(b)(c)(b) PQRS(C) DE FG(a) Ruler(b) DividerАBР1. Michelle T. asked • 09/11/20 Two angles form a linear pair. The sum of angles of a linear pair is always equal to 180°. A Linear Pair Forms A Straight Angle Which Contains 180º, So You Have 2 Angles Whose Measures Add To 180, Which Means They Are Supplementary. You can put this solution on YOUR website! No packages or subscriptions, pay only for the time you need. That means that we can add the two expressions and set it equal to 180 in order to solve. Most questions answered within 4 hours. III. No only two 2 angles can form a linear pair, This site is using cookies under cookie policy. The sum of a linear pair of angles is {eq}180^\circ {/eq}. they have a common side, and : 2) their other sides are opposite rays : Note if two angles form a linear pair, then the sum of their measures = 180 … (यदि किसी पिण्ड पर क्रियाशील तीन समतलीय बल उसे साम्यावस्था में रखतेहों तो वे बल एक बिन्दु पर मिलेंगे या समान्तर होंगे)[Ajmer B.Sc., 06; Jodhpur B.Sc., 04; Udaipur B.Sc. how far is a light year !? The linear pair conjecture states that if two angles form a linear pair, the sum of the angles is 180 degrees. Trending Questions. Linear pairs of angles are supplementary. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.linear pair means that the angles which form on the same line and add up to 180. A pair of adjacent angles formed by intersecting lines. in other words, given m∠1 = m∠2, prove that the … (c) Both of the angles forming a linear pair can be obtuse angles. If two angles are not a linear pair, then they are not supplementary. A linear pair of angles is formed when two lines intersect. No. If two angles form a linear pair, then they are supplementary. Supplementary angles and linear pairs both add to 180°. Because sum of two acute angles cannot be equal to 1 8 0 o. 12. Given that: and are two angles form a linear pair.. Then by definition of linear pair; Substitute the given values and solve for x; Example 2: the angles form a line (linear pair) therefore they are supplementary Example 3: the angles can be non-adjacent as long as their sum is 180° 110°+ 70° = 180° The sum is 180° therefore they are supplementary. Not all supplementary angle form a linear pair. The measure of one angle is 8 times the measure of the other angle. Angles that form a linear pair combine to form a straight angle. In the adjoining figure, ∠AOC and ∠BOC are two adjacent angles whose non-common arms OA and OB are two opposite rays, i.e., BOA is a line ∴ ∠AOC and ∠BOC form a linear pair of angles. Then, find the angle measures. answered 09/02/18, Math Tutor - Full Time Student - I Like Math, Carol H. If one angle is80 degree, the measure ofother angle is: (a) 100 (b)80 (c) 1… ia3732039 ia3732039 14.09.2020 Math Secondary School 22. When two lines intersect each other at a common point then, a linear pair of angles are formed. Not exactly. (d) Bisectors of the adjacent angles forming a linear pair form a right angle. The sum of the linear pair of angles is always equal to 180 degrees. Two adjacent angles are said to form a linear pair angles, if their non-common arms are two opposite rays. Can 2 Adjacent Angle Be Complementary? Two adjacent angles are said to be form a linear pair of angles, if their non-common arms are two opposite rays. A linear pair of angles satisfy these two requirements (both must be true) The angles are adjacent; The angles are supplementary, ie they add to 180. webew7 and 1 more users found this answer helpful 0.0 So are angles 2 and 4, angles 3 and 4, and angles 1 and 3. Vertical angles. Linear Pair A linear pair is a pair of adjacent angles formed when two lines intersect. Get solutions ∠BOC and ∠AOC are linear-pair-angles. Learn what is linear pair of angles. (add up to 1800) ∠BOC + ∠AOC = 180 0 We also know that their measures add to equal 180 degrees. They also have to be adjacent, sharing a common side, to be a linear pair. Linear pairs form … Practice questions In the following figure, at E. In the following questions, fill in … No: Two angles are a linear pair, if and only if:!) The measure of one angle is 24° more than the measure of the other angle. If Two Angles Form A Linear Pair, The Angles Are Supplementary. Definition A linear pair is a pair of adjacent, supplementary angles. Stay Home , Stay Safe and keep learning!!! The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.linear pair means that the angles which form on the same line and add up to 180. If three forces acting in one plunce upon a rigid body, keepit in equilibrium, they must either meet in a point or be parallel. One angle measures (10x - 63). they have a common side, and: 2) their other sides are opposite rays: Note if two angles form a linear pair, then the sum of their measures = 180 degrees: Join Yahoo Answers and get 100 points today. …, REE forces(तीन बलों के अन्तर्गत एक पिण्ड की साम्यावस्था)\$ 1.5. What is the value of the larger an… gordwindisney7741 gordwindisney7741 3 minutes ago Mathematics High School Two angles form a linear pair. MEMORY METER. (a) Two acute angles can form a linear pair. So are angles 2 and 4, angles 3 and 4, and angles 1 and 3. Such angles add up to #180^@# and hence are always supplementary.. Complete the two-column proof. Linear Pair of Angles. a. The figure shows the design on an outdoor fence. Start here or give us a call: (312) 646-6365, Two angels form a linear pair. 7 answers. The two angles do add to 180, but that just means supplementary. Example 4: 1 and 2 form a linear pair so m 1 + m 2 = 180° therefore the angles … Answer Save. A Linear Pair Forms A Straight Angle Which Contains 180º, So You Have 2 Angles Whose Measures Add To 180, Which Means They Are Supplementary. Explanation: A linear pair of angles is formed when two lines intersect. Since the non-adjacent sides of a linear pair form a line, a linear pair of angles is always supplementary. Two adjacent angles are a linear pair, if their non-common sides are opposite rays. What are the measures of those two angles? this page updated 19-jul-17 Mathwords: Terms and … The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. Find an answer to your question Two angles form a linear pair. This concept will introduce students to linear pairs of angles. The figure shows the design on an outdoor fence. A linear pair is a pair of adjacent angles whose non-common sides are opposite rays. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. The measure of one angle it 45 degrees more than the measure of the other angle. A linear pair of angles is formed when two lines intersect. A pair of adjacent angles formed by intersecting lines. Find the measure of each angle. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. Two Adjacent Angle Can Be Complementary Too If They Add Up To 90°. Linear Pair A linear pair is a pair of adjacent angles formed when two lines intersect. geometry . Join. Michael F. If two angles form a linear pair, the angles are supplementary. if the two angles form a linear pair, then the sum of the two angles equals 180 degrees. 13. Adjacent Angles are two angles that share a common vertex, a common side, and no common interior points. Two adjacent angles are said to be form a linear pair of angles, if their non-common arms are two opposite rays. Be the first to answer this question. If two angles are a linear pair, then they are supplementary. So do ∠ 2 and ∠ 3 , ∠ 3 and ∠ 4 , and ∠ 1 and ∠ 4 . Two angles form alinear pair. (A straight angle measures 180 degrees.) 14. We also know that their measures add to equal 180 degrees. Two angles can be called as a linear pair, if they are adjacent angles formed by intersecting lines. The measure of one angle is 15 less than half the measurement of its supplement. Knowledge of the relationships between angles can help in determining the value of a given angle. Masters' Degree in Mathematics with 35 years Teaching Experience. They are supplementary because they always add to 180° and because they are adjacent, the two non-common legs form … (a) Two acute angles can form a linear pair. Two angles may be supplementary, but not adjacent and therefore not form a linear pair. Problem 58LA from Chapter 10.1: a. If Two Angles Form A Linear Pair, The Angles Are Supplementary. Two angles form a linear pair. If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular. The following practice questions ask you to solve problems based on linear pairs. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. A linear pair of angles has two defining characteristics: 1) the angles must be supplmentary 2) The angles must be adjacent (c) Both of the angles forming a linear pair can be obtuse angles. In the figure, ∠ 1 and ∠ 2 form a linear pair. a. Solution for Two angles form a linear pair. Example 2 : In the diagram shown below, Solve for x and y. So, x + y … A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary. Linear pairs of angles are supplementary. Get a free answer to a quick problem. ... Two angles that add to 180 degrees and when adjacent form a straight line. Math. 03)माना एक दृढ़ पिण्ड के बिन्दु A, B और C पर तीन समतलीय बल P, Q और Rक्रियाशील हैं, जिनके अंतर्गत पिण्ड साम्यावस्था में है। निम्न दो स्थितियाँ हो सकती हैं:स्थिति 1. We can also state the number of degrees of one angle with respect to the other angle Example : Logical Equivalence Lateral Area . A linear pair is pair of two adjacent angles, whose outer arms fall in the same line. Acute angles are those angles which are less than 90°. (b) Two obtuse angles can form a linear pair (c) Two right angles can form a linear pair (d) One obtuse angle and one acute angle cannot form a linear pair. So do ∠ 2 and ∠ 3 , ∠ 3 and ∠ 4 , and ∠ 1 and ∠ 4 . You can specify conditions of storing and accessing cookies in your browser. The measure of one angle is 24 more than the measure of the other angle. If two angles form a linear pair then their sum add up to 180 degree. in other words, given m∠1 = m∠2, prove that the … Covid-19 has led the world to go through a phenomenal transition . 12. In the figure, ∠ 1 and ∠ 2 form a linear pair. Linear Pair of Angles. Thus, ∠1 + ∠2 amounts to 180o. the measures of the angles of a quadrilateral are in the ratio of 1:2:3:4, find the measure of each angle . Angles 1 and 2 below are a linear pair. Choose an expert and meet online. The measure of an angle is three times the measurement of its complement. Question 990192: Two angles form a linear pair. We know that the two angles form a linear pair. Find the measure of each angle. If one angle is 80 degree, the measure of other angle is: (a) 100 (b) 80 (c) 10 (d) 50 1 See answer ia3732039 is waiting for your help. If two angles are not supplementary, then they are not a linear pair A. I and III only B. II and III only C. I and II only D. I, II, and III 1 See answer jakkajsje … Lv 6. Write and solve an algebraic equation to find the measure of each angle. No : Two angles are a linear pair, if and only if : !) The measure of an angle is three times the measurement of its complement. For Free, Inequalities and Relationship in a Triangle, ALL MY GRADE 8 & 9 STUDENTS PASSED THE ALGEBRA CORE REGENTS EXAM. The measure of one angle is 51°more than 1\2 the measure of the other angle. Example 2: the angles form a line (linear pair) therefore they are supplementary Example 3: the angles can be non-adjacent as long as their sum is 180° 110°+ 70° = 180° The sum is 180° therefore they are supplementary. A linear pair is two angles that are adjacent and whose non-common sides form a straight line. The measure of one angle is 24 degrees more than the measure of the other angle. Linear pair axiom of theorems are if a ray stands on a line , then the sum of two adjacent angles so formed is 180 degree. This is as shown below. Practice. They are supplementary because they always add to 180° and because they are adjacent, the two non-common legs form … Answer by ikleyn(36000) (Show Source): You can put this solution on YOUR website!. The angles in a linear pair are supplementary. Such angles are also known as supplementary angles. 13. The other two angles are in a ratio of 5:16. Vertical angles theorem. We know that the two angles form a linear pair. If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular. This is because vertical angles do not share a common side. That means that we can add the two expressions and set it … (i) angle one plus angle two equals 180 degrees, We can also state the number of degrees of one angle with respect to the other angle, (ii) angle two equals angle one plus 45 degrees, plugging (ii) into one gives us an equation with one unknown which is solveable, (iii) angle one plus angle one plus 45 degrees equals 180 degrees, In an algebraic equation we use variables which we define to be the unknown qualities, for example we could let X = degrees in angle one, and Y = degrees in angle two, Now solve for X in (i) and (ii) above by using (iii) with the words replaced with algebraic symbols, Then plug this value of X into (ii) to find Y, Final step is to check your values of X and Y by plugging them into (i) and seeing if it is true, © 2005 - 2021 Wyzant, Inc. - All Rights Reserved, a Question It can be noticed that sum of measures of angles in all the pairs is less than 180° and to form a linear pair sum of measures of two angles must be equal to 180° Hence, we can say that two acute angles cannot form a linear pair. (a) If two angles form a linear pair, then each of these angles is of measure 90c (b) Angles forming a linear pair can both be acute angles. On linear pairs Both add to equal 180 degrees pair of angles must add up to 180^! Similar questions or ask a new question given: you can view more similar questions or ask a question. Ask a new question to linear pairs form … we know can two angles form a linear pair their add... Forming the sides of one angle is 51°more than 1\2 the measure of one angle 10r! You can specify conditions of storing and accessing cookies in your browser be adjacent how in. ∠ LKM form a linear pair, if and only if:! angles must add up to.! Measurement of its supplement questions ask you to solve problems based on linear pairs form … we know the. Pairs Both add to equal 180 degrees ( 312 ) 646-6365, two acute angles are supplementary following questions. What is the value of a quadrilateral are in a ratio of 1:2:3:4, find measure. X and y must add up to # 180^ @ # and hence are always supplementary Both. Non-Common arms are two opposite rays vertex, a common side is 24° more than the measure an! They share a common side, and ∠ 1 and ∠ LKM form linear. Two expressions and set it equal to 180 in order to solve ask a new question to find measure... Be form a linear pair add two angles form a linear pair conjecture states that is. That the two angles form a linear pair conjecture states that it is the value of the,. Angle two equals 180 degrees to form a linear pair, then they are adjacent to other... Each other at a point and form a linear pair of adjacent angles formed when lines! Is because vertical angles do not form two pairs of opposite rays Teachers can two angles form a linear pair 1st Edition ) Edit.! Is three times the measure of an angle is 24 degrees more than the measure of angle! Has led the world to go through a phenomenal transition to linear pairs form … we know the. 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Add to equal 180 degrees, just because two angles form a linear pair be. So a linear pair, then they can two angles form a linear pair adjacent and therefore not form a right.! 90°, we get the result less than half the measurement of its.... And accessing cookies in your browser by two intersecting lines 8 times the measure of angle! Angles of a given angle not supplementary of line segments using a divider. 24 more than the measure of angle. Of the other angle, if their non-common arms are two angles are formed when lines. 2: in the diagram shown below, solve for x and y of storing and accessing cookies in browser. Question 990192: two angles can two angles form a linear pair a linear pair of adjacent angles are supplementary below solve! An equation in two unknowns ( i ) angle one plus angle equals! Measures add to equal 180 degrees and when adjacent form a linear of! Two equals 180 degrees, so a linear pair a linear pair of adjacent angles are supplementary to. 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In a ratio of 5:16 of two right angles is formed when two lines intersect and non-common! Explanation: a linear pair is a pair of adjacent angles formed two. 15 less than half the measurement of its complement and when adjacent form a linear pair opposite... To your phone be adjacent non-common sides are opposite rays or ask a question! Of angles, if their non-common arms are two opposite rays ) 646-6365, two angels form a linear,. Right angles is always equal to 180 degrees its complement angle is 24° than... When adjacent form a linear pair is a straight angle is 8 times the measurement of its complement adjacent formed! Ratio of 1:2:3:4, find the measure of the angles are said to linear! An algebraic equation to find the measure of one angle can two angles form a linear pair 180 degrees pair states that if two lines. A straight angle is 15 less than 180°, e.g figure, ∠ 3 and ∠.... Edit Edition an equation in two unknowns ( i ) angle one plus angle two 180... 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School Teachers ( 1st Edition ) Edit Edition is 24° more than the measure of one angle 8...	2021-09-17 22:53:17	{"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": 0.596768319606781, "perplexity": 752.5036388601808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055808.78/warc/CC-MAIN-20210917212307-20210918002307-00204.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-midpoint-of-16-7-4-3	# How do you find the midpoint of (-16,-7), (-4,-3)? Mar 24, 2017 $\left(- 10 , - 5\right)$ #### Explanation: Use the midpoint formula: $\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$ By substituting the $x$ and $y$ values we get the following: $\frac{\left(- 16\right) + \left(- 4\right)}{2} , \frac{\left(- 7\right) + \left(- 3\right)}{2}$ Then we just evaluate $\left(- \frac{20}{2} , - \frac{10}{2}\right)$ $\left(- 10 , - 5\right)$	2021-11-29 21:28:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.9809757471084595, "perplexity": 1501.9828997387947}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358842.4/warc/CC-MAIN-20211129194957-20211129224957-00445.warc.gz"}
https://gmatclub.com/forum/a-machine-puts-c-caps-on-bottles-in-m-minutes-how-many-hours-will-it-218636.html	GMAT Question of the Day: Daily via email \| Daily via Instagram New to GMAT Club? Watch this Video It is currently 07 Jul 2020, 11:19 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # A machine puts c caps on bottles in m minutes. How many hours will it Author Message TAGS: ### Hide Tags Manager Joined: 12 Mar 2012 Posts: 77 Location: India Concentration: Technology, Strategy GMAT 1: 710 Q49 V36 GPA: 3.2 WE: Information Technology (Computer Software) A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 20 Mar 2013, 17:44 4 1 00:00 Difficulty: 45% (medium) Question Stats: 62% (01:23) correct 38% (01:50) wrong based on 273 sessions ### HideShow timer Statistics A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles? A. 60bm/c B. bm/(60c) C. bc/(60m) D. 60b/(cm) E. b/(60cm) Math Expert Joined: 02 Sep 2009 Posts: 65062 Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 16 May 2016, 01:45 11 A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles? A. 60bm/c B. bm/(60c) C. bc/(60m) D. 60b/(cm) E. b/(60cm) A machine puts c caps on bottles in m minutes --> the rate of the machine is (rate) = (job)/(time) = c/m cap/minute. The time needed to put caps on b bottles (time) = (job)/(rate) = b/(c/m) minutes = bm/c minutes = bm/(60c) hours. _________________ ##### General Discussion Manager Joined: 25 Apr 2014 Posts: 90 Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 25 Jun 2014, 20:24 Either we can fix it with the help of a small formula which is : (M1 * D1 * H1)/ W1 = (M2 * D2 * H2)/ W2 where M , D and H stands for Men, Days and Hours invested for each of the 2 Works respectively. So here it goes: M1= 1 (as we are not given the value) D1 = m/60 (in hrs) H1 = 1 (as we are not given the value) and W1 = c and M2 = 1 (as we are not given the value) D2 = x (in hrs) (to be found out) H2 = 1 (as we are not given the value) and W2 = b (as given) So, (1 m/60 1)/c = (1* x* 1)/b => (m/60)/c = x/b Therefore, => x= bm/60c. P.S. Please let me know if anything went wrong as this is my first post as a solution. Manager Joined: 12 Jun 2015 Posts: 74 Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 16 May 2016, 02:05 3 A machine puts c caps on bottles in m minutes. So, the machine puts 1 cap in m/c minutes To put caps on b bottles, the machine will take bm/c minutes In order to calculate the no. of hours taken , divide the product by 60. Intern Joined: 06 May 2016 Posts: 14 WE: Education (Education) Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 16 May 2016, 04:27 1 The key for me is to realise that 1 bottle can only have 1 cap. (ie bottles can be multiplied with minutes/cap and cancel out leaving only time) Without that it seems super difficult but actually is a very straightforward calculation. RSM Erasmus Moderator Joined: 26 Mar 2013 Posts: 2471 Concentration: Operations, Strategy Schools: Erasmus Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 17 May 2016, 04:23 We can plug in simple numbers 2 caps per 1 min,, then rate= 2 caper/min Put b= 120 or 60 bottles.. I used 120 bottles 120= 2 * t.....>t=60 min =1 hr Scanning the answer choice.. Eliminate A & D as you need to divide minute by 60. Eliminate E as CM should be together. Substitute number in choice B & C In bm/60c= (1201)/ (2 60) = 1 Manager Joined: 01 Nov 2016 Posts: 56 Concentration: Technology, Operations Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 24 Apr 2017, 14:07 Bunuel wrote: A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles? A. 60bm/c B. bm/60c C. bc/60m D. 60b/cm E. b/60cm A machine puts c caps on bottles in M minutes. A bottle can only have 1 cap, so this means that in M minutes, the machine will cap C bottles $$\frac{M minutes}{C bottles}$$ How many hours will it take to put caps on B bottles? This is a comparison ratio: $$\frac{M minute}{C bottles}$$ * $$\frac{1 hour}{60 minutes}$$ = $$\frac{X hours}{B bottles}$$ This becomes: $$\frac{(M minute)(B bottles)(1 hour)}{(C bottles)(60 minutes)}$$ = $$x hours$$ Simplify to: $$\frac{mb}{60c}$$ = $$x hours$$ This question's only difficulty is seeing that they want you to do a comparison between c bottles and b bottles. They intentionally made the letters confusing for those that could only see b should stand for bottles. VP Joined: 07 Dec 2014 Posts: 1259 Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 12 Jun 2017, 18:46 chiccufrazer1 wrote: A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles? A. 60bm/c B. bm/60c C. bc/60m D. 60b/cm E. b/60cm bottling rate=c/m minutes to cap b bottles=b/(c/m)=bm/c hours to cap b bottles=(bm/c)/60=bm/60c B Senior Manager Status: Studying 4Gmat Joined: 02 Jan 2016 Posts: 360 Location: India Concentration: Strategy, Entrepreneurship GMAT 1: 590 Q37 V33 GPA: 4 WE: Law (Manufacturing) Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 03 Aug 2018, 20:35 Rate Time = Work C/M M C C/M x = B So, (RT = W); XC/M = B; BM/C this is in Hours, therefore BM/C/60= BM/C60 _________________ Regards, Hero1kF My glory is greater than my life. Manager Joined: 06 Nov 2016 Posts: 53 Location: Viet Nam GPA: 3.54 Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 03 Aug 2018, 20:59 Bunuel wrote: A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles? A. 60bm/c B. bm/(60c) C. bc/(60m) D. 60b/(cm) E. b/(60cm) my approach: we have : c caps --> m minutes therefore b caps --> $$\frac{(bm)}{c}$$ minutes And : 60 minutes = 1 hour so: $$\frac{(bm)}{c}$$ minutes = $$\frac{(bm)}{(c*60)}$$ hours _________________ Non-Human User Joined: 09 Sep 2013 Posts: 15386 Re: A machine puts c caps on bottles in m minutes. How many hours will it [#permalink] ### Show Tags 04 Jun 2020, 15:42 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). 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How many hours will it [#permalink] 04 Jun 2020, 15:42	2020-07-07 19:19:48	{"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": 0.7773205041885376, "perplexity": 10673.914461162369}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655894904.17/warc/CC-MAIN-20200707173839-20200707203839-00353.warc.gz"}
http://www.ams.org/mathscinet-getitem?mr=845667	MathSciNet bibliographic data MR845667 (87i:33011) 33A30 Rahman, Mizan An integral representation of a $\sb {10}\varphi\sb 9$$\sb {10}\varphi\sb 9$ and continuous bi-orthogonal $\sb {10}\varphi\sb 9$$\sb {10}\varphi\sb 9$ rational functions. Canad. J. Math. 38 (1986), no. 3, 605–618. Article For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.	2015-10-07 18:15:17	{"extraction_info": {"found_math": true, "script_math_tex": 2, "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": 0.9985489845275879, "perplexity": 7279.212863631244}, "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-2015-40/segments/1443737875203.46/warc/CC-MAIN-20151001221755-00093-ip-10-137-6-227.ec2.internal.warc.gz"}
http://math.eretrandre.org/tetrationforum/showthread.php?mode=threaded&tid=1168&pid=8712	• 0 Vote(s) - 0 Average • 1 • 2 • 3 • 4 • 5 Does tetration take the right half plane to itself? JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 05/16/2017, 08:46 PM (This post was last modified: 05/16/2017, 08:48 PM by JmsNxn.) (05/16/2017, 03:34 PM)sheldonison Wrote: (05/16/2017, 04:09 AM)JmsNxn Wrote: ... It easily follows from this that $\log^{\circ n}(\lambda^n z + L)$ is fully monotone, it uniformly converges to the inverse Schroder function, and therefore the inverse Schroder function is a fully monotone function...Good luck with your paper. We need more rigorous iterated exponentiation papers. I just wondered what your approach to show the sequence "uniformly converges". Is there an easy theorem, or did you want to go with a more complicated approach something like my lemma5? Just curious. Also, you probably meant $\log_b^{\circ n}(\lambda^n z + L)$ where b is the tetration base. Yeah, I meantt $\log_b$. This is actually a well known result on how to represent the inverse Schroder function. Bo used it before, and that's how I first learnt about it. Essentially if $f(z_0) = z_0$ and $0 < \|f'(z_0)\| < 1$, then not only does $\lim_{n\to\infty} \frac{f^{\circ n}(z) - z_0}{\lambda^n} \to \Psi(z)$ for $\|z- z_0\|<\delta$, where $\Psi$ is the Schroder function. We also get that, if $g = f^{-1}$ $\lim_{n\to\infty} g^{\circ n}(\lambda^n z + z_0) \to \Psi^{-1}(z)$ for $\|z-z_0\| < \delta$, for $\delta$ sufficiently small. This is all you really need. « Next Oldest \| Next Newest » Messages In This Thread Does tetration take the right half plane to itself? - by JmsNxn - 05/10/2017, 07:46 PM RE: Does tetration take the right half plane to itself? - by JmsNxn - 05/10/2017, 08:22 PM RE: Does tetration take the right half plane to itself? - by sheldonison - 05/15/2017, 08:16 PM RE: Does tetration take the right half plane to itself? - by sheldonison - 05/15/2017, 09:00 PM RE: Does tetration take the right half plane to itself? - by JmsNxn - 05/16/2017, 04:09 AM RE: Does tetration take the right half plane to itself? - by sheldonison - 05/16/2017, 03:34 PM RE: Does tetration take the right half plane to itself? - by JmsNxn - 05/16/2017, 08:46 PM RE: Does tetration take the right half plane to itself? - by JmsNxn - 05/16/2017, 04:46 AM Possibly Related Threads... Thread Author Replies Views Last Post Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 238 09/09/2019, 10:55 PM Last Post: tommy1729 Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 402 09/09/2019, 10:50 PM Last Post: tommy1729 Half-iteration of x^(n^2) + 1 tommy1729 3 3,854 03/09/2017, 10:02 PM Last Post: Xorter Uniqueness of half-iterate of exp(x) ? tommy1729 14 14,285 01/09/2017, 02:41 AM Last Post: Gottfried [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 36,500 03/27/2015, 11:28 PM Last Post: tommy1729 [entire exp^0.5] The half logaritm. tommy1729 1 2,371 05/11/2014, 06:10 PM Last Post: tommy1729 Does the Mellin transform have a half-iterate ? tommy1729 4 3,645 05/07/2014, 11:52 PM Last Post: tommy1729 Simple method for half iterate NOT based on a fixpoint. tommy1729 2 3,233 04/30/2013, 09:33 PM Last Post: tommy1729 half-iterates of x^2-x+1 Balarka Sen 2 4,007 04/30/2013, 01:14 AM Last Post: tommy1729 Is the half iterate of 2sinh(x) analytic near R ? tommy1729 1 2,410 03/13/2013, 12:13 AM Last Post: tommy1729 Users browsing this thread: 1 Guest(s)	2019-12-12 10:38:00	{"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 12, "/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": 0.8230122923851013, "perplexity": 8899.640939488338}, "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/1575540543252.46/warc/CC-MAIN-20191212102302-20191212130302-00155.warc.gz"}
https://stats.stackexchange.com/questions/418097/statistical-comparison-of-covariance-matrices	Statistical comparison of (covariance) matrices I am trying to test whether the covariance matrix for the maximum likelihood estimates for a gaussian general linear model approaches the inverse Fisher information matrix (times 1/n , n being the sample size). However I am not sure how to compare two matrices. One approach would be to compare the eigenvalues. However I am finding with my runs of code, that the eigenvalues of my covariance matrix tend to vary quite wildly. I have tried using the spectral norm (i.e largest eigenvalue, but it is often the case that I have a single very large eigenvalue (say, order unity), and the others are much smaller (of order 10e-15). The Fisher information matrix eigenvalues tend to be quite consistent (about 10e-6, following the example with the same number of samples, observations and covariates for comparison). So how would one compare two matrices, and relatively easily? Is there a statistical test for this? My thoughts are that: -IF we work in a given basis, then the features defining a matrix are: 1. It's rank 2. The eigenvectors (and thus the subspace spanned by them) 3. The eigenvalues The simplest case for comparison would be if the rank and eigenvectors were the same, so only the eigenvalues had to be compared. Otherwise, depending on what one means be 'how different the matrices are', one would have to have a metric that accounts for the difference in the eigenvalues (perhaps a measure of the overlap of the subspace spanned by them? But this doesn't account for all of the information!), and the eigenvalues. Perhaps also whether the eigenvalues correspond to the same vectors. So I see that this is not straightforward and probably depends on what you want to do with the information. But in that case, how to meaningfully compare matrices? I suppose in this case of MLE, we really mean element-wise comparison. • Have you thought about measuring the dissimilarity between the two matrices using some matrix norm of their difference ($\\|A-B\\|$)? More details about your problem would be needed to think about a statistical test. For example, how are you obtaining these matrices? Where does any kind of randomness/variability come into play that would let us think about how to define a null distribution? Jul 18, 2019 at 16:57 • See stats.stackexchange.com/a/469966/919 for one recently proposed approach. – whuber Dec 30, 2020 at 14:20 My favorite tool for comparing covariances comes from Förstner W., Moonen B. A Metric for Covariance Matrices. In: Grafarend E.W., Krumm F.W., Schwarze V.S. (eds) Geodesy-The Challenge of the 3rd Millennium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05296-9_31 They derive a function, $$d$$, which measures distance on the space of all real, symmetric, positive definite matrices of any size $$(n \times n)$$. $$d$$'s properties include: • $$d(A,B) \ge 0$$ • $$d(A,B) = 0 \Longleftrightarrow A = B$$ • $$d(A,B) = d(B,A) = d(A^{-1},B^{-1})$$ • $$d(A,B) ≤ d(A,C) + d(C,B)$$ for any $$C$$ in the same space, called the triangle inequality • $$d(A,B) = d(XAX^T, XBX^T)$$ for any $$X$$ in $$GL(n,\mathbb{R})$$, so the value of $$d$$ is invariant with respect to affine transformations of the coordinate system The distance $$d$$ may be calculated as the square root of the sum of the squares of the natural logarithms of the generalized eigenvalues of A and B: $$d(A,B)=\sqrt{\sum_{i=1}^n\ln^2 \lambda_i(A, B)}$$ The generalized eigenvalue problem is, given matrices $$A$$ and $$B$$, find all scalars $$λ$$ such that $$\det(A−λB)=0$$. The usual eigenvalue problem is the case $$B=I$$, the identity matrix. When $$B$$ is invertible, this equals finding the eigenvalues of the matrix $$A$$ times $$B^{-1}$$. Rather, it should, but in numerical computation frequently the answers are not quite the same, and one obtains $$d(B,B)=10^{−12}$$, rather than the exactly zero it ought to be.) The paper contains a short survey of other possible comparison computations and why they were rejected, and some incomplete attempts to construct an overly complicated proof for $$n=2$$, but then switches gears, and finds the answers pretty much just waiting there in Kobayashi & Nomizu, Foundations of Differential Geometry (1963). The answer depends on where these matrices come from. In latent variable modeling techniques this is commonly done. For example, in Structural Equation Models the loss function for maximum likelihood estimated models is: $$\text{Fml} = \text{log}\|\Sigma(0)\| + \text{Trace}[\Sigma(0)^{-1}S] - \text{log}\|S\| - p$$ Maximizing the Fml minimizes the discrepancy between the estimated population covariance matrix $$\Sigma$$, and the model implied covariance matrix $$\Sigma(0)$$. The population covariance is estimated as a function of the observed sample covariance matrix $$S$$. Model fit statistics provide summaries of the discrepancies between these two matrices. David Kenny provides brief summaries of these statistics but cites the work necessary to break them down further. Many model fit statistics exist which compare these matrices in different ways, you may be able to conform your situation to these. To answer your question completely, more information would be needed regarding where they come from. However, this literature may give you a good starting point on exploring what options exist.	2022-08-10 07:52:13	{"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": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8665122389793396, "perplexity": 373.57085806778565}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571150.88/warc/CC-MAIN-20220810070501-20220810100501-00476.warc.gz"}
http://zbmath.org/?q=an:1201.90167	# zbMATH — the first resource for mathematics ##### Examples Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev \| Tschebyscheff The or-operator \| allows to search for Chebyshev or Tschebyscheff. "Quasi* map" py: 1989 The resulting documents have publication year 1989. so: Eur J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A \| 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used. ##### Operators a & b logic and a \| b logic or !ab logic not abc right wildcard "ab c" phrase (ab c) parentheses ##### Fields any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article) Tools of mathematical modeling of arbitrary object packing problems. (English) Zbl 1201.90167 Summary: The article reviews the concept of and further develops phi-functions (${\Phi }$-functions) as an efficient tool for mathematical modeling of two-dimensional geometric optimization problems, such as cutting and packing problems and covering problems. The properties of the phi-function technique and its relationship with Minkowski sums and the nofit polygon are discussed. We also describe the advantages of phi-functions over these approaches. A clear definition of the set of objects for which phi-functions may be derived is given and some exceptions are illustrated. A step by step procedure for deriving phi-functions illustrated with examples is provided including the case of continuous rotation. ##### MSC: 90C27 Combinatorial optimization ##### References: [1] Bennell, J. A., & Song, X. (2008). A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums. Computers and Operational Research, 35(1), 267–281. · Zbl 1136.65023 · doi:10.1016/j.cor.2006.02.026 [2] Burke, E. K., Hellier, R. S. R., Kendall, G., & Whitwell, G. (2007). Complete and robust no-fit polygon generation for the irregular stock cutting problem. European Journal of Operational Research, 179(1), 27–49. · Zbl 1175.90325 · doi:10.1016/j.ejor.2006.03.011 [3] Culberson, J. C., & Reckhow, R. A. (1988). Covering polygons is hard. In Proceedings of 29th IEEE conference on foundations of computer science (pp. 601–611). [4] Cunninghame-Green, R. (1989). Geometry. Shoemaking and the milk tray problem. New Scientist, 1677, 50–53. [5] Daniels, K., & Inkulu, R. (2001). Translational polygon covering using intersection graphs. In Proceedings of the thirteenth Canadian conference on computational geometry (pp. 61–64). [6] Daniels, K., Mathur, A., & Grinde, R. (2003). A combinatorial maximum cover approach to 2D translational geometric covering. In Proceeedings of 15th Canadian conference on computational geometry (pp. 2–5). Halifax, Nova Scotia, Canada, August 11–13, 2003. [7] Fomenko, A., Fuchs, D., & Gutenmacher, V. (1986). Homotopic topology. Akademiai Kiado: Budapest. [8] Ghosh, P. K. (1991). An algebra of polygons through the notation of negative shapes. CVGIP: Imag Understand, 17, 357–378. [9] Scheithauer, G., Stoyan, Y., Gil, N., & Romanova, T. (2003). Phi-functions for circular segments. Prepr. Technische Univarsitat Dresden, MATH-NM-7-2003. Dresden. [10] Stoyan, Y. (1983). Mathematical methods for geometric design. In Advances in CAD/CAM//. Proceeding PROLAMAT82. Leningrad, USSR, 16–18 May, 1982 (pp. 67–86). Amsterdam: North-Holland. [11] Stoyan, Y. (2003). Phi-function of non-convex polygons with rotations. Journal of Mechanical Engineering, 6(1), 74–86. [12] Stoyan, Y., & Gil, N. (1976). Methods and algorithms of placement of 2D geometric objects. Ukrainian SSR academy of sciences. Kiev: Naukova Dumka (In Russian). [13] Stoyan, Y., & Pankratov, A. V. (1999). Regular packing of congruent polygons on the rectangular sheet. European Journal of Operational Research, 113, 653–675. · Zbl 0941.90065 · doi:10.1016/S0377-2217(98)00050-2 [14] Stoyan, Y., & Patsuk, V. N. (2000). A method of optimal lattice packing of congruent oriented polygons in the plane. European Journal of Operational Research, 124, 204–216. · Zbl 0990.90103 · doi:10.1016/S0377-2217(99)00115-0 [15] Stoyan, Y., & Ponomarenko, L. D. (1977). Minkowski’s sum and the hodograph of the dense allocation vector function. Reports of the Ukrainian SSR Academy of Science, A(10), 888–890 (In Russian). [16] Stoyan, Y., Novozhilova, M., & Kartashov, A. (1996). Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem. European Journal of Operational Research, 92, 193–210. · Zbl 0916.90234 · doi:10.1016/0377-2217(95)00038-0 [17] Stoyan, Y., Terno, J., Scheithauer, G., Gil, N., & Romanova, T. (2002a). Phi-functions for primary 2D-objects. Studia Informatica Universalis, 2(1), 1–32. [18] Stoyan, Y., Terno, J., Gil, M., Romanova, T., & Scheithauer, G. (2002b). Construction of a Phi-function for two convex polytopes. Applicationes Mathematicae, 29(2), 199–218. · Zbl 1053.90009 · doi:10.4064/am29-2-6 [19] Stoyan, Y., Scheithauer, G., Gil, N., & Romanova, T. (2004). Phi-functions for complex 2D-objects. 4OR (Operations Research): Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 2, 69–84. [20] Stoyan, Y., Scheithauer, G., & Romanova, T. (2005a). Mathematical modeling of interaction of primary geometric 3D objects. Cybernetics and Systems Analysis, 41(3), 332–342. Translated from Kibernetika i Sistemnyi Analiz, 3, 19–31. · Zbl 1102.68684 · doi:10.1007/s10559-005-0067-y [21] Stoyan, Y., Gil, N., Scheithauer, G., Pankratov, A., & Magdalina, I. (2005b). Packing of convex polytopes into a parallelepiped. Optimization, 54(2), 215–235. · Zbl 1134.90550 · doi:10.1080/02331930500050681 [22] Toth, G. F. (1997). Packing and covering. In J. Goodman & J. O’Rourke (Eds.), Handbook of discrete and computational geometry. New York: CRC Press.	2013-12-06 13:27:31	{"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": 0.5989382863044739, "perplexity": 12197.982584019075}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2013-48/segments/1386163051684/warc/CC-MAIN-20131204131731-00065-ip-10-33-133-15.ec2.internal.warc.gz"}
http://www.maplesoft.com/support/help/Maple/view.aspx?path=Maplets/Examples/HilbertMatrix	Maplets[Examples][LinearAlgebra] - Maple Help # Online Help ###### All Products Maple MapleSim Home : Support : Online Help : Programming : Maplets : Examples : Advanced : Maplets/Examples/HilbertMatrix Maplets[Examples][LinearAlgebra] HilbertMatrix display a graphical interface to the HilbertMatrix function Calling Sequence HilbertMatrix() Description • The HilbertMatrix() calling sequence displays a Maplet application that returns a Hilbert matrix. • A definition of the Hilbert matrix is given in the Maplet application. • Specify the number of rows and columns in the matrix and offset in the appropriate text fields in the Maplet application. • By using the Return read-only matrix check box, control whether the matrix returned by the Maplet application is read-only. The default behavior is that the matrix returned is not read-only. • By using the Evaluate result check box, control whether the Maplet application returns the Hilbert matrix or the calling sequence required to calculate the Hilbert matrix in the worksheet. The default behavior is to evaluate the result, that is, return the matrix. • The HilbertMatrix sample Maplet worksheet demonstrates how to write a Maplet application that functions similarly to the Maplet application displayed by this routine. Examples > $\mathrm{with}\left({\mathrm{Maplets}[\mathrm{Examples}]}_{\mathrm{LinearAlgebra}}\right):$ > $\mathrm{HilbertMatrix}\left(\right)$ See Also ## Was this information helpful? Please add your Comment (Optional) E-mail Address (Optional) What is ? This question helps us to combat spam	2016-05-04 23:13:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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": 0.906213641166687, "perplexity": 3695.074596564207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2016-18/segments/1461860125524.70/warc/CC-MAIN-20160428161525-00107-ip-10-239-7-51.ec2.internal.warc.gz"}
http://www.journaltocs.ac.uk/index.php?action=browse&subAction=pub&publisherID=250&journalID=17790&pageb=1&userQueryID=&sort=&local_page=&sorType=&sorCol=	Publisher: Cambridge University Press (Total: 387 journals) Similar Journals Bulletin of the Australian Mathematical SocietyJournal Prestige (SJR): 0.44 Number of Followers: 2 Subscription journal ISSN (Print) 0004-9727 - ISSN (Online) 1755-1633 Published by Cambridge University Press [387 journals] • BAZ volume 101 Issue 1 Cover and Front matter • PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001461 Issue No: Vol. 101, No. 1 (2020) • BAZ volume 101 Issue 1 Cover and Back matter • PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001473 Issue No: Vol. 101, No. 1 (2020) • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$ax^{2}+by^{2}+cz^{2}$ ++++++++++++ ++++++++ +++++AND+ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$ax^{2}+by^{2}+cz^{2}+dw^{2}$ ++++++++++++ ++++++++ ++++&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=1&rft.epage=12&rft.aulast=DOYLE&rft.aufirst=GREG&rft.au=GREG+DOYLE&rft.au=KENNETH+S.+WILLIAMS&rft_id=info:doi/10.1017/S0004972719001023">PRIME-UNIVERSAL QUADRATIC FORMS $ax^{2}+by^{2}+cz^{2}$ AND $ax^{2}+by^{2}+cz^{2}+dw^{2}$ • Authors: GREG DOYLE; KENNETH S. WILLIAMS Pages: 1 - 12 Abstract: A positive-definite diagonal quadratic form $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}\;(a_{1},\ldots ,a_{n}\in \mathbb{N})$ is said to be prime-universal if it is not universal and for every prime $p$ there are integers $x_{1},\ldots ,x_{n}$ such that $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}=p$ . We determine all possible prime-universal ternary quadratic forms $ax^{2}+by^{2}+cz^{2}$ and all possible prime-universal quaternary quadratic forms $ax^{2}+by^{2}+cz^{2}+dw^{2}$ . The prime-universal ternary forms are completely determined. The prime-universal quaternary forms are determined subject to the validity of two conjectures. We make no use of a result of Bhargava concerning quadratic forms representing primes which is stated but not proved in the literature. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001023 Issue No: Vol. 101, No. 1 (2020) • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$L$ ++++++++++++ ++++++++ ++++-VALUE+OF+THE+CONGRUENT+NUMBER+ELLIPTIC+CURVES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=13&rft.epage=22&rft.aulast=SAMART&rft.aufirst=DETCHAT&rft.au=DETCHAT+SAMART&rft_id=info:doi/10.1017/S000497271900056X">ON A NONCRITICAL SYMMETRIC SQUARE $L$ -VALUE OF THE CONGRUENT NUMBER ELLIPTIC CURVES • Authors: DETCHAT SAMART Pages: 13 - 22 Abstract: The congruent number elliptic curves are defined by $E_{d}:y^{2}=x^{3}-d^{2}x$ , where $d\in \mathbb{N}$ . We give a simple proof of a formula for $L(\operatorname{Sym}^{2}(E_{d}),3)$ in terms of the determinant of the elliptic trilogarithm evaluated at some degree zero divisors supported on the torsion points on $E_{d}(\overline{\mathbb{Q}})$ . PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S000497271900056X Issue No: Vol. 101, No. 1 (2020) • ON A GENERALISATION OF A RESTRICTED SUM FORMULA FOR MULTIPLE ZETA VALUES AND FINITE MULTIPLE ZETA VALUES • Authors: HIDEKI MURAHARA; TAKUYA MURAKAMI Pages: 23 - 34 Abstract: We prove a new linear relation for multiple zeta values. This is a natural generalisation of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000790 Issue No: Vol. 101, No. 1 (2020) • PARTITIONS WITH AN ARBITRARY NUMBER OF SPECIFIED DISTANCES • Authors: BERNARD L. S. LIN Pages: 35 - 39 Abstract: For positive integers $t_{1},\ldots ,t_{k}$ , let $\tilde{p}(n,t_{1},t_{2},\ldots ,t_{k})$ (respectively $p(n,t_{1},t_{2},\ldots ,t_{k})$ ) be the number of partitions of $n$ such that, if $m$ is the smallest part, then each of $m+t_{1},m+t_{1}+t_{2},\ldots ,m+t_{1}+t_{2}+\cdots +t_{k-1}$ appears as a part and the largest part is at most (respectively equal to) $m+t_{1}+t_{2}+\cdots +t_{k}$ . Andrews et al. [‘Partitions with fixed differences between largest and smallest parts’, Proc. Amer. Math. Soc.143 (2015), 4283–4289] found an explicit formula for the generating function of $p(n,t_{1},t_{2},\ldots ,t_{k})$ . We establish a $q$ -series identity from which the formulae for the generating functions of $\tilde{p}(n,t_{1},t_{2},\ldots ,t_{k})$ and PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000650 Issue No: Vol. 101, No. 1 (2020) • PERMUTATION POLYNOMIALS OF DEGREE 8 OVER FINITE FIELDS OF ODD CHARACTERISTIC • Authors: XIANG FAN Pages: 40 - 55 Abstract: We give an algorithmic generalisation of Dickson’s method of classifying permutation polynomials (PPs) of a given degree $d$ over finite fields. Dickson’s idea is to formulate from Hermite’s criterion several polynomial equations satisfied by the coefficients of an arbitrary PP of degree $d$ . Previous classifications of PPs of degree at most 6 were essentially deduced from manual analysis of these polynomial equations, but this approach is no longer viable for $d>6$ . Our idea is to calculate some radicals of ideals generated by the polynomials, implemented by a computer algebra system. Our algorithms running in SageMath 8.6 on a personal computer work very fast to determine all PPs of degree 8 over an arbitrary finite field of odd order $q>8$ . Such PPs exist if and only if $q\in \{11,13,19,23,27,29,31\}$ and are explicitly listed in normalised form. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000674 Issue No: Vol. 101, No. 1 (2020) • A NEW PROOF OF THE CARLITZ–LUTZ THEOREM • Authors: RACHID BOUMAHDI; OMAR KIHEL, JESSE LARONE, MAKHLOUF YADJEL Pages: 56 - 60 Abstract: A polynomial $f$ over a finite field $\mathbb{F}_{q}$ can be classified as a permutation polynomial by the Hermite–Dickson criterion, which consists of conditions on the powers $f^{e}$ for each $e$ from $1$ to $q-2$ , as well as the existence of a unique solution to $f(x)=0$ in $\mathbb{F}_{q}$ . Carlitz and Lutz gave a variant of the criterion. In this paper, we provide an alternate proof to the theorem of Carlitz and Lutz. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000728 Issue No: Vol. 101, No. 1 (2020) • ALGEBRAIC SURFACES WITH INFINITELY MANY TWISTOR LINES • Authors: A. ALTAVILLA; E. BALLICO Pages: 61 - 70 Abstract: We prove that a reduced and irreducible algebraic surface in $\mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalisation map of a surface, we give constructive existence results for even degrees. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000534 Issue No: Vol. 101, No. 1 (2020) • THE FACTORIAL CONJECTURE AND IMAGES OF LOCALLY NILPOTENT DERIVATIONS • Authors: DAYAN LIU; XIAOSONG SUN Pages: 71 - 79 Abstract: The factorial conjecture was proposed by van den Essen et al. [‘On the image conjecture’, J. Algebra 340(1) (2011), 211–224] to study the image conjecture, which arose from the Jacobian conjecture. We show that the factorial conjecture holds for all homogeneous polynomials in two variables. We also give a variation of the result and use it to show that the image of any linear locally nilpotent derivation of $\mathbb{C}[x,y,z]$ is a Mathieu–Zhao subspace. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000546 Issue No: Vol. 101, No. 1 (2020) • ON A PROBLEM OF PRAEGER AND SCHNEIDER • Authors: EGLE BETTIO; ENRICO JABARA Pages: 80 - 87 Abstract: This note provides an affirmative answer to Problem 2.6 of Praeger and Schneider [‘Group factorisations, uniform automorphisms, and permutation groups of simple diagonal type’, Israel J. Math. 228(2) (2018), 1001–1023]. We will build groups $G$ (abelian, nonabelian and simple) for which there are two automorphisms $\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD}$ of $G$ such that the map $$\begin{eqnarray}T=T_{\unicode[STIX]{x1D6FC}}\times T_{\unicode[STIX]{x1D6FD}}:G\longrightarrow G\times G,\quad g\mapsto (g^{-1}g^{\unicode[STIX]{x1D6FC}},g^{-1}g^{\,\unicode[STIX]{x1D6FD}})\end{eqnarray}$$ is surjective. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000649 Issue No: Vol. 101, No. 1 (2020) • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$2\times+2$ ++++++++++++ ++++++++ +++++MATRICES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=88&rft.epage=104&rft.aulast=ZHANG&rft.aufirst=WEN&rft.au=WEN+TING+ZHANG&rft.au=YAN+FENG+LUO&rft_id=info:doi/10.1017/S0004972719001035">THE FINITE BASIS PROBLEM FOR INVOLUTION SEMIGROUPS OF TRIANGULAR $2\times 2$ MATRICES • Authors: WEN TING ZHANG; YAN FENG LUO Pages: 88 - 104 Abstract: Let $T_{n}(\mathbb{F})$ be the semigroup of all upper triangular $n\times n$ matrices over a field $\mathbb{F}$ . Let $UT_{n}(\mathbb{F})$ and $UT_{n}^{\pm 1}(\mathbb{F})$ be subsemigroups of $T_{n}(\mathbb{F})$ , respectively, having $0$ s and/or $1$ s on the main diagonal and $0$ s and/or $\pm 1$ s on the main diagonal. We give some sufficient conditions under which an involution semigroup is nonfinitely based. As an application, we show that $UT_{2}(\mathbb{F}),UT_{2}^{\pm 1}(\mathbb{F})$ and PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001035 Issue No: Vol. 101, No. 1 (2020) • HOMOLOGY AND MATUI’S HK CONJECTURE FOR GROUPOIDS ON ONE-DIMENSIONAL SOLENOIDS • Authors: INHYEOP YI Pages: 105 - 117 Abstract: We show that Matui’s HK conjecture holds for groupoids of unstable equivalence relations and their corresponding $C^{\ast }$ -algebras on one-dimensional solenoids. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000522 Issue No: Vol. 101, No. 1 (2020) • WEAKENING OF THE HARDY PROPERTY FOR MEANS • Authors: PAWEŁ PASTECZKA Pages: 118 - 129 Abstract: The aim of this paper is to find a broad family of means defined on a subinterval of $I\subset [0,+\infty )$ such that \begin{eqnarray}\mathop{\sum }_{n=1}^{\infty }\mathscr{M}(a_{1},\ldots ,a_{n}) PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000686 Issue No: Vol. 101, No. 1 (2020) • ON SOME SUBCLASSES OF HARMONIC MAPPINGS • Authors: NIRUPAM GHOSH; VASUDEVARAO ALLU Pages: 130 - 140 Abstract: Let ${\mathcal{P}}_{{\mathcal{H}}}^{0}(M)$ denote the class of normalised harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ satisfying $\text{Re}\,(zh^{\prime \prime }(z))>-M+\|zg^{\prime \prime }(z)\|$ , where $h^{\prime }(0)-1=0=g^{\prime }(0)$ and $M>0$ . Let ${\mathcal{B}}_{{\mathcal{H}}}^{0}(M)$ denote the class of sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ satisfying $\|zh^{\prime \prime }(z)\|\leq M-\|zg^{\prime \prime }(z)\|$ , where $M>0$ . We discuss the coefficient bound problem, the growth theorem for fu... PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000698 Issue No: Vol. 101, No. 1 (2020) • NEW GLOBAL LOGARITHMIC STABILITY RESULTS ON THE CAUCHY PROBLEM FOR ELLIPTIC EQUATIONS Pages: 141 - 145 Abstract: We prove the global logarithmic stability of the Cauchy problem for $H^{2}$ -solutions of an anisotropic elliptic equation in a Lipschitz domain. The result is based on existing techniques used to establish stability estimates for the Cauchy problem combined with related tools used to study an inverse medium problem. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000789 Issue No: Vol. 101, No. 1 (2020) • LARGE DEVIATIONS FOR THE LONGEST GAP IN POISSON PROCESSES • Authors: JOSEPH OKELLO OMWONYLEE Pages: 146 - 156 Abstract: The longest gap $L(t)$ up to time $t$ in a homogeneous Poisson process is the maximal time subinterval between epochs of arrival times up to time $t$ ; it has applications in the theory of reliability. We study the Laplace transform asymptotics for $L(t)$ as $t\rightarrow \infty$ and derive two natural and different large-deviation principles for $L(t)$ with two distinct rate functions and speeds. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000972 Issue No: Vol. 101, No. 1 (2020) • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$q$ ++++++++++++ ++++++++ ++++-ARY+LINEAR+CODES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=157&rft.epage=162&rft.aulast=WEI&rft.aufirst=YILUN&rft.au=YILUN+WEI&rft.au=BO+WU,+QIJIN+WANG&rft_id=info:doi/10.1017/S0004972719000637">ON THE GENERALISATION OF SIDEL’NIKOV’S THEOREM TO $q$ -ARY LINEAR CODES • Authors: YILUN WEI; BO WU, QIJIN WANG Pages: 157 - 162 Abstract: We generalise Sidel’nikov’s theorem from binary codes to $q$ -ary codes for $q>2$ . Denoting by $A(z)$ the cumulative distribution function attached to the weight distribution of the code and by $\unicode[STIX]{x1D6F7}(z)$ the standard normal distribution function, we show that $\|A(z)-\unicode[STIX]{x1D6F7}(z)\|$ is bounded above by a term which tends to $0$ when the code length tends to infinity. PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719000637 Issue No: Vol. 101, No. 1 (2020) • NUMERICAL INVESTIGATION AND APPLICATION OF FRACTIONAL DYNAMICAL SYSTEMS • Authors: LIBO FENG Pages: 163 - 165 PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S000497271900114X Issue No: Vol. 101, No. 1 (2020) • COPULA-BASED STATISTICAL MODELLING OF SYNOPTIC-SCALE CLIMATE INDICES FOR QUANTIFYING AND MANAGING AGRICULTURAL RISKS IN AUSTRALIA • Authors: THONG NGUYEN-HUY Pages: 166 - 169 PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001217 Issue No: Vol. 101, No. 1 (2020) • DEGREE BOUNDED GEOMETRIC SPANNING TREES WITH A BOTTLENECK OBJECTIVE FUNCTION • Authors: PATRICK JOHN ANDERSEN Pages: 170 - 171 PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001126 Issue No: Vol. 101, No. 1 (2020) • CANONICAL DUAL FINITE ELEMENT METHOD FOR SOLVING NONCONVEX MECHANICS AND TOPOLOGY OPTIMISATION PROBLEMS • Authors: ELAF J. ALI Pages: 172 - 173 PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001205 Issue No: Vol. 101, No. 1 (2020) • MECHANISTIC AND STATISTICAL MODELS OF SKIN DISEASE TRANSMISSION • Authors: MICHAEL J. LYDEAMORE Pages: 174 - 176 PubDate: 2020-02-01T00:00:00.000Z DOI: 10.1017/S0004972719001072 Issue No: Vol. 101, No. 1 (2020) JournalTOCs School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh, EH14 4AS, UK Email: journaltocs@hw.ac.uk Tel: +00 44 (0)131 4513762	2020-01-20 06:10:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.7866449952125549, "perplexity": 1833.3372743169484}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250597458.22/warc/CC-MAIN-20200120052454-20200120080454-00062.warc.gz"}
https://quant.stackexchange.com/questions/45284/historical-quotes-prices-of-multiasset-options	# Historical quotes / prices of multiasset options I am working on Lévy copulas, and I would like to try calibrating such techniques on real data. Where can I find quotes for multi-asset options? It could be exchange options or any other type of options, as long as it involves at least two assets. I have access to multiple universities libraries, and could access to a Bloomberg terminal if needed (I come from the theoritical side and am not used to handle real data). Thanks! • Next time, ask fewer more targeted(specific) questions. – Ted Taylor of Life May 3 '19 at 14:59 I highly recommend you check out this paper. Dynamic copulas: applications to financeeconomics In this paper they give examples that may be useful to you. Specifically, the data that was looked at "CDOs (e.g. iTraxx and CDX)" From page 5 of the paper You are in luck, as these days there are many exchange-traded funds that track indexes. An option on one of these is therefore equivalent (for Lévy copula purposes at least) to an option on a weighted index of stocks. So, for example, you can look at options on SPY as options on a weighted sum of 500 different US stocks. These are very liquid so you will get good prices at a wide range of strikes. To get them from Bloomberg start by querying SPY US EQUITY for its options CHAIN_TICKERS.	2021-06-19 02:15:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.42805856466293335, "perplexity": 1731.5436122943213}, "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-2021-25/segments/1623487643380.40/warc/CC-MAIN-20210619020602-20210619050602-00510.warc.gz"}
http://codeforces.com/problemset/problem/721/A	A. One-dimensional Japanese Crossword time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output Recently Adaltik discovered japanese crosswords. Japanese crossword is a picture, represented as a table sized a × b squares, and each square is colored white or black. There are integers to the left of the rows and to the top of the columns, encrypting the corresponding row or column. The number of integers represents how many groups of black squares there are in corresponding row or column, and the integers themselves represents the number of consecutive black squares in corresponding group (you can find more detailed explanation in Wikipedia https://en.wikipedia.org/wiki/Japanese_crossword). Adaltik decided that the general case of japanese crossword is too complicated and drew a row consisting of n squares (e.g. japanese crossword sized 1 × n), which he wants to encrypt in the same way as in japanese crossword. The example of encrypting of a single row of japanese crossword. Help Adaltik find the numbers encrypting the row he drew. Input The first line of the input contains a single integer n (1 ≤ n ≤ 100) — the length of the row. The second line of the input contains a single string consisting of n characters 'B' or 'W', ('B' corresponds to black square, 'W' — to white square in the row that Adaltik drew). Output The first line should contain a single integer k — the number of integers encrypting the row, e.g. the number of groups of black squares in the row. The second line should contain k integers, encrypting the row, e.g. corresponding to sizes of groups of consecutive black squares in the order from left to right. Examples Input 3BBW Output 12 Input 5BWBWB Output 31 1 1 Input 4WWWW Output 0 Input 4BBBB Output 14 Input 13WBBBBWWBWBBBW Output 34 1 3 Note The last sample case correspond to the picture in the statement.	2018-09-21 03:10:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38774654269218445, "perplexity": 1040.084520737336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156724.6/warc/CC-MAIN-20180921013907-20180921034307-00226.warc.gz"}
https://quantumcomputing.stackexchange.com/questions/4894/time-bin-encoding-qudits/4906	# Time-bin encoding qudits Time-bin encoding is a technique used in Quantum information science to encode a qubit of information on a photon. Wikipedia Is there a generalization for $$n$$-th level qudits? • This question seems to broad. Are there specific parts of the Wikipedia entry which you don't understand/you have questions about? Also, why do you link to an article which does not use time-bin encoding to encode a 10-level system? – Norbert Schuch Dec 9 '18 at 13:28 • @NorbertSchuch I have narrowed the question. Also, the linked article was meant as an example of a (frequency-bin?) photonic qudit. – meowzz Dec 9 '18 at 16:05 • this is a bit confusing. "Time-bin encoding" means to use the time as degree of freedom on which to store the (quantum) information. As such, this sort of encoding can in principle encode arbitrary high-dimensional qudits. The limitation is obviously in the actual experimental constraints. – glS Dec 9 '18 at 19:16 • @glS Do you have any references regarding encoding arbitrary high-dimensional qudits? – meowzz Dec 9 '18 at 19:28	2019-11-15 05:50:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6852166652679443, "perplexity": 1586.5861423281967}, "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-2019-47/segments/1573496668585.12/warc/CC-MAIN-20191115042541-20191115070541-00166.warc.gz"}
http://zbmath.org/?q=an:1213.46045&format=complete	# zbMATH — the first resource for mathematics ##### Examples Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev \| Tschebyscheff The or-operator \| allows to search for Chebyshev or Tschebyscheff. "Quasi* map" py: 1989 The resulting documents have publication year 1989. so: Eur J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A \| 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used. ##### Operators a & b logic and a \| b logic or !ab logic not abc right wildcard "ab c" phrase (ab c) parentheses ##### Fields any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article) Elementary operators and subhomogeneous ${C}^{}$-algebras. II. (English) Zbl 1213.46045 Summary: Let $A$ be a separable unital ${C}^{}$-algebra and let ${\Theta }A$ be the canonical contraction from the Haagerup tensor product of $A$ with itself to the space of completely bounded maps on $A$. In our previous paper [I. Gogić, Proc. Edinb. Math. Soc., II. Ser. 54, No. 1, 99–111 (2011; Zbl 1213.46046)] we showed that if $A$ satisfies that (a) the lengths of elementary operators on $A$ are uniformly bounded, or (b) the image of ${\Theta }A$ equals the set of all elementary operators on $A$, then $A$ is necessarily SFT (subhomogeneous of finite type). In this paper, we extend this result; we show that if $A$ satisfies (a) or (b), then the codimensions of 2-primal ideals of $A$ are also finite and uniformly bounded. Using this, we provide an example of a unital separable SFT algebra which satisfies neither (a) nor (b). However, if the primitive spectrum of a unital SFT algebra $A$ is Hausdorff, we show that such an $A$ satisfies both (a) and (b). ##### MSC: 46L05 General theory of ${C}^{*}$-algebras 46L07 Operator spaces and completely bounded maps 47B47 Commutators, derivations, elementary operators, etc. 46H10 Ideals and subalgebras of topological algebras	2014-04-24 16:14:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 16, "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": 0.8827641606330872, "perplexity": 3425.7546172516177}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206647.11/warc/CC-MAIN-20140423032006-00551-ip-10-147-4-33.ec2.internal.warc.gz"}
http://heyuhang.com/blog/2017/03/19/clothing-pattern-1-plaid/	# Fashion Pattern Walk: Plaid Recently, I have been working on fashion pattern tagging, resulting in the necessity of familarizing common fashion patterns. Then, the first pattern emerging in my mind is “plaid” (cause I am a programmer? HAHA). Here let’s talk some basic info about it. ## Plaid: Definition Plaid, which is often called in North America, is synonymous with tartan in Scotland where tartan is often used as kilt accessory or blanket on the bed. Visually, plaid is the fabric woven of alternating bands of color in crisscross (or simply horizontal and vertical direction) manner. In general, a plaid pattern is knitted with both warp and weft at right angles. If two different colors meet, a mixture of the two colors is created. If the same color meets, a solid color would be generated. Suppose two threads, one in the warp the other in the weft at the right angles. If they meet and carry different color, a mixture of color would be generated. Otherwise, a solid color would be generated (if they carry the same color). Thus, a base of two colors creats three different colors, including one mixture color. The total number of the colors w.r.t the base color number increase quadratically. That is, if the base color number is $n$, a total of $\frac{1}{2}n(n+1)$ colors would be created.	2019-01-18 11:36:01	{"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": 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": 0.30482012033462524, "perplexity": 1721.6844344660256}, "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-2019-04/segments/1547583660070.15/warc/CC-MAIN-20190118110804-20190118132804-00020.warc.gz"}
https://www.cemc.uwaterloo.ca/pandocs/potw/2021-22/English/POTWE-A-G-14-S.html	Problem of the Week Problem E and Solution Parallelogram Askew Problem If vertices $$P$$, $$Q$$, and $$S$$ are located at $$(0,30)$$, $$(k,50)$$ and $$(40,0)$$, respectively, and the area of $$PQRS$$ is $$1340\text{ units}^2$$, determine the coordinates of $$Q$$ and $$R$$. Solution Solution 1: In this solution we will use a method known commonly as "completing the rectangle". Since $$PQRS$$ is a parallelogram, $$PQ=SR$$ and $$PQ$$ is parallel to $$SR$$. We can use this to find the coordinates of $$R$$. To get from $$P$$ to $$Q$$, we go up 20 units and right $$k$$ units. Therefore, to get from $$S$$ to $$R$$ we do the same. Therefore, $$R$$ is located at $$(40+k,20)$$. Enclose $$PQRS$$ in rectangle $$OTUV$$ such that $$OT$$ is on the positive $$y$$-axis passing through $$P$$, $$TU$$ is parallel to the positive $$x$$-axis passing through $$Q$$, $$UV$$ is parallel to the positive $$y$$-axis passing through $$R$$, and $$OV$$ lies along the positive $$x$$-axis passing through $$S$$. The $$y$$-coordinate of $$Q$$ is the distance from the $$x$$-axis to $$TU$$ and also the height, $$UV$$, of rectangle $$OTUV$$. It follows that $$OT = UV=50$$ units. Therefore, the coordinates of $$T$$ are $$(0,50)$$. Similarly, the $$x$$-coordinate of $$R$$ is the distance from the $$y$$-axis to $$UV$$ and also the width, $$OV$$, of rectangle $$OTUV$$. It follows that $$TU = OV=(40+k)$$ units. Therefore, the coordinates of $$V$$ are $$(40+k,0)$$ and the coordinates of $$U$$ are $$(40+k, 50)$$. We can now put the information together using areas to determine the value of $$k$$. \begin{aligned} \text{Area }OTUV&=\text{Area }\triangle PTQ+\text{Area }\triangle QUR+\text{Area }\triangle RVS+\text{Area }\triangle SOP+\text{Area }PQRS\\ UV\times OV&=\frac{PT\times TQ}{2}+\frac{QU\times UR}{2}\ +\frac{RV\times VS}{2}+\frac{OS\times OP}{2}\ +\ 1340\\ 50\times (40+k)&=\frac{(50-30)\times k}{2}+\frac{((40+k)-k)\times (50-20)}{2}+\frac{20\times ((40+k)-40)}{2}+\frac{40\times 30}{2}+1340\\ 50\times (40+k)&=\frac{20\times k}{2}+\frac{40\times 30}{2}\ +\frac{20\times k}{2}+\frac{40\times 30}{2}\ +\ 1340\\ 2000+50k&=10k+600+10k+600+1340\\ 2000+50k&=20k+2540\\ 30k&=540\\ k&=18\end{aligned} Therefore, the value of $$k$$ is $$18$$ and coordinates of $$Q$$ and $$R$$ are $$Q(18,50)$$ and $$R(58,20)$$. Solution 2: In this solution we will use linear equations, intersections, and lengths to find $$k$$. Since $$PQRS$$ is a parallelogram, $$PQ=SR$$ and $$PQ$$ is parallel to $$SR$$. We can use this to find the coordinates of $$R$$. To get from $$P$$ to $$Q$$, we go up 20 units and right $$k$$ units. Therefore, to get from $$S$$ to $$R$$ we do the same. Therefore, $$R$$ is located at $$(40+k,20)$$. Construct a line perpendicular to $$PS$$ that passes through $$Q$$ and meets $$PS$$ at $$W$$. We are going to find the coordinates of $$W$$ in terms of $$k$$. The line through $$PS$$ has a slope of $$-\frac{3}{4}$$ and a $$y$$-intercept of 30. Therefore, the equation of this line is $y=-\frac{3}{4}x + 30 \tag{1}$ The line though $$QW$$ is perpendicular to $$PS$$ and so has slope $$\frac{4}{3}$$. The equation of this line is $$4x - 3y = C$$. Substituting the coordinates of $$Q$$ into this equation, we get $$4k - 3(50) = C$$ or $$C = 4k -150$$. Therefore, the line through $$QW$$ has equation $4x - 3y = 4k - 150\tag{2}$ $$W$$ is the intersection point of the lines with equations $$(1)$$ and $$(2)$$. Substituting equation $$(1)$$ into equation $$(2)$$, we get: \begin{align} 4x - 3\left(-\frac{3}{4}x + 30\right) &= 4k -150\\ 4x + \frac{9}{4}x - 90 &= 4k -150\\ 16x + 9x - 360 &= 16k -600\\ 25x &= 16k - 240\\ x &= 0.64k - 9.6 \tag{3}\end{align} Substituting equation $$(3)$$ into equation $$(1)$$ we get: \begin{aligned} y &= -\frac{3}{4}(0.64k - 9.6) + 30\\ y &= -0.48k + 37.2\end{aligned} Therefore, the point $$W$$ has coordinates $$( 0.64k - 9.6, -0.48k + 37.2)$$. We will now find two expressions for the length of $$QW$$. Using the distance formula we know $QW = \sqrt{(0.64k - 9.6 - k)^2 + (-0.48k + 37.2 - 50)^2}\tag{4}$ Another way to find the length $$QW$$ is using the area of the parallelogram. The length of $$PS = \sqrt{(30-0)^2 + (0-40)^2} = \sqrt{2500} = 50$$, since $$PS > 0$$. $$PS$$ is the base of the parallelogram and $$QW$$ is the height. Therefore, \begin{align} PS \times QW &= 1340\\ 50QW &= 1340\\ QW &= 26.8 \tag{5} \end{align} Now equating equations $$(4)$$ and $$(5)$$, we can solve for $$k$$. \begin{aligned} \sqrt{(0.64k - 9.6 - k)^2 + (-0.48k + 37.2 - 50)^2} &= 26.8\\ (-0.36k - 9.6 )^2 + (-0.48k - 12.8)^2 &= 718.24\\ 0.1296k^2 + 6.912k + 92.16 + 0.2034k^2 + 12.288k + 163.84 &= 718.24\\ 0.36k^2 + 19.2k - 462.24 & = 0 \end{aligned} Using the quadratic formula, we find $$k=18$$ or $$k=-\frac{214}{3}$$. Since $$Q(k,50)$$ is in the first quadrant, we must have $$k > 0$$ and so $$k=18$$. Therefore, the coordinates of $$Q$$ and $$R$$ are $$Q(18,50)$$ and $$R(58,20)$$.	2022-05-23 09:21:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.999352753162384, "perplexity": 296.04767361273593}, "config": {"markdown_headings": false, "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/1652662556725.76/warc/CC-MAIN-20220523071517-20220523101517-00030.warc.gz"}
http://math.stackexchange.com/questions/133493/can-it-be-shown-that-y-0-lambda-n-aj-0-lambda-n-a-j-0-lambda-n-ay-0-la	# Can it be shown that $Y_0(\lambda_n a)J_0(\lambda_n a) - J_0(\lambda_n a)Y_0(\lambda_n a) \ne 0$? Background I am currently looking into the task of describing a transient temperature field $\theta(r,t)$ across the thickness $a \leq r \leq b$ of an infinitely long and hollow cylinder exposed to a sinusoidal temperature signal applied at the inner boundary $g(t)=\theta_0 \sin(2\pi \cdot f \cdot t)$. The following thermal boundary conditions apply $\theta(a,t)=g(t)$ $\quad$ for $t\ge0$, $\quad$ (1) $\theta(b,t)=0$ $\quad$ for $t\ge0$, $\quad$ (2) $\theta(r,0)=0$. $\quad$ (3) The starting point for the derivation is the heat diffusion equation ($\alpha^$ is the thermal diffusivity) in cylindrical coordinates $\frac{\partial^2\theta}{\partial r^2} + \frac{1}{r}\frac{\partial\theta}{\partial r} = \frac{1}{\alpha^}\frac{\partial\theta}{\partial t}$. $\quad$ (4) The derivation of the final expression (which applies the Hankel transform followed by the inverse transform) for the temperature distribution can be found in several papers, for example [Shahani A.R. and Nabavi S.M. (2007) Applied Mathematical Modelling, Vol 31, p 1807-1818]. The final expression reads $\theta(r,t)=-\alpha^\pi \sum\limits_{n=1}^\infty \frac{\lambda^2_n J^2_0(\lambda_n b)}{J^2_0(\lambda_n a)-J^2_0(\lambda b)} \left[ Y_0(\lambda_n a)J_0(\lambda_n r) - J_0(\lambda_n a)Y_0(\lambda_n r) \right]\left[ e^{-\alpha^\lambda_n^2 t} \int_0^t e^{\alpha^\lambda_n^2\tau} g(\tau) d\tau \right]$ $\quad$ (5) where $\lambda_n$ are the positive roots of the transcendental equation $Y_0(\lambda_n a)J_0(\lambda_n b) - J_0(\lambda_n a)Y_0(\lambda_n b) = 0$ $\quad$ (6) and $J_0(z)$ and $Y_0(z)$ are Bessel functions of order $0$ of the first and second kind, respectively. Result I have managed to implement the required code (as I understand it) in Matlab. The literature states that 100 roots is sufficient. When I plot the temperature field versus the thickness I get a strange temperature distribution for cases other than $g(t)=0$ as shown by the figure below (the blue and green curves are correct while the black and red curves are not). My implementation does not seem to fulfill the boundary condition (1) which is also indicated by oscillations for the remainder of the corresponding (black and red) curves. My math skills are unfortunately rather limited and I do not seem to be able to see how the final expression (5) fulfills the boundary condition (1). Question Can it be shown that $Y_0(\lambda_n a)J_0(\lambda_n a) - J_0(\lambda_n a)Y_0(\lambda_n a) \ne 0$? Is this where my implementation goes wrong or is my mistake perhaps to be found elsewhere? - You can try posting a link to the graph you have, and somebody will embed the image for you... – Ｊ. Ｍ. Apr 18 '12 at 16:11 @J.M.: I managed to upload the image myself thanks to increased reputation. – Daniel Bremberg Apr 18 '12 at 16:53 Umm, $Y_0(\lambda_n a) J_0(\lambda_n a) - J_0(\lambda_n a) Y_0(\lambda_n a) = 0$ by the commutative law of multiplication. Or did you mean something else? – Robert Israel May 21 '12 at 17:28 I'm a little confused, because the form of the question at the end of the Q (and the one in the title) has an expression that's trivially zero; should some of those $a$s be $b$s (or possibly $r$s)? – Steven Stadnicki May 21 '12 at 17:29 @RobertIsrael Of course it is a typo, Daniel surely means the expression in the sum of (5) where thus it should be $r$ instead of two instances of $a$. – AD. Sep 28 '12 at 14:13 1. Plot roots of Eq.(6) which you insert in Eq.(5) - do you separate negative and positive ones correctly? 2. Check your code for the case $g(t)=$ const. Does it work? 3. Why do you think that the blue and green curves are correct, if they have a non-zero asymptote towards $r=b$? (so Eq.(2) is not fulfilled) 4. Answer to the question: if you have derived a root for Eq.(6), and insert it back into this equation, you'll always get zero :-) Best regards, Vitaly. P.S.: I think, you can simplify your Matlab code, since ExpSin can easily be integrated. Maybe you have already implemented this but just in case: Int(Exp(mt)Sin(nt))dx = (Exp(mt))(mSin(nt) - nCos(n*t))/(m^2 + n^2) -	2013-12-21 01:52:46	{"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": 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": 0.8705509901046753, "perplexity": 517.8832092042664}, "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/1387345774525/warc/CC-MAIN-20131218054934-00075-ip-10-33-133-15.ec2.internal.warc.gz"}
https://www.researchgate.net/publication/320682853_The_double-edge_effect_of_second-phase_particles_on_the_recrystallization_behaviour_and_associated_mechanical_properties_of_metallic_materials	ArticlePDF Available # The double-edge effect of second-phase particles on the recrystallization behaviour and associated mechanical properties of metallic materials Authors: ## Abstract and Figures Most industrial alloys contain a matrix phase and dispersed second-phase particles. Several thermomechanical processing (TMP) steps are usually needed to produce a final product, during which recrystallization and its related phenomena may take place. Second-phase particles may retard or accelerate recrystallization, depending on their size and spatial distribution, the TMP conditions, among others. Besides their effect on recrystallization kinetics, the introduction of second-phase particles creates additional interfaces within the matrix, it also modifies the grain structure and crystallographic texture after recrystallization, which then either improves or deteriorates the associated mechanical properties of the investigated materials. The interactions between second-phase particles and recrystallization are further complicated when these particles are not stable. In addition to particle coarsening, they can also precipitate out or dissolve into the matrix before, simultaneously with or after recrystallization. This review article attempts to summarize the recent progresses on the complex interaction between second-phase particles and recrystallization and the science behind them. This double-edge effect of second-phase particles on recrystallization behaviour and mechanical properties of metallic materials is still far from being clear. A better understanding of this issue is of high academic and industrial interests, since it provides potential freedom for TMP design and microstructure control. Content may be subject to copyright. A preview of the PDF is not available ... In the particle-containing materials, the void formation at second phase particles may attribute to a fracture. Based on the report of Huang et al. [71] , a critical stress for the void nucleation is proportional to the r − 1/2 ( r presents the average radius of spherical particles). This suggests that the oc-currence of voids needs a larger stress in the materials with finer particles. ... Article Full-text available The fundamental research on thermo-mechanical conditions provides an experimental basis for high-performance Mg-Al-Ca-Mn alloys. However, there is a lack of systematical investigation for this series alloys on the hot-deformation kinetics and extrusion parameter optimization. Here, the flow behavior, constitutive model, dynamic recrystallization (DRX) kinetic model and processing map of a dilute rare-earth free Mg-1.3Al-0.4Ca-0.4Mn (AXM100, wt.%) alloy were studied under different hot-compressive conditions. In addition, the extrusion parameter optimization of this alloy was performed based on the hot-processing map. The results showed that the conventional Arrhenius-type strain-related constitutive model only worked well for the flow curves at high temperatures and low strain rates. In comparison, using the machine learning assisted model (support vector regression, SVR) could effectively improve the accuracy between the predicted and experimental values. The DRX kinetic model was established, and a typical necklace-shaped structure preferentially occurred at the original grain boundaries and the second phases. The DRX nucleation weakened the texture intensity, and the further growth caused the more scattered basal texture. The hot-processing maps at different strains were also measured and the optimal hot-processing range could be confirmed at the deformation temperatures of 600∼723 K and the strain rates of 0.018∼0.563 s⁻¹. Based on the optimum hot-processing range, a suitable extrusion parameter was considered as 603 K and 0.1 mm/s and the as-extruded alloy in this parameter exhibited a good strength-ductility synergy (yield strength of ∼ 232.1 MPa, ultimate strength of ∼ 278.2 MPa and elongation-to-failure of ∼ 20.1%). Finally, the strengthening-plasticizing mechanisms and the relationships between the DRXed grain size, yield strength and extrusion parameters were analyzed. ... In the past 20 years, in the direction of development and preparation technology of steel materials, the thermomechanical control process (TMCP) combined with severe plastic deformation (SPD) has been widely adopted to develop good crystal structures with good mechanical properties [8][9][10]. Recently, a method of fabricating ultrafine elongated grain structure through multi-pass caliber rolling is developed [11]. ... Article The effect of initial heat‐treated conditions on change of mechanical properties and microstructure evolution was investigated by caliber rolling of medium carbon alloy steel (ASTM 5140). Initial samples with two different kinds of microstructures of pearlite‐ferrite and martensite were prepared, and then caliber rolling was conducted at 550 °C, 600 °C, 650 °C, respectively. It was found that the caliber rolling provides better strength‐ductility balance and impact properties, when the rolling temperature is at 550 °C, the ultimate tensile strength of quenched steel can reach 1.3 GPa, and low‐temperature impact energy of 140 J at −80 °C. In a word, the improvement of mechanical properties is attributed to the ultrafine elongated grain structures, dispersed nano‐size carbides, and formation of distinct chromium segregation bands, furthermore, delamination crack is an effective measure to improve impact energy. In this paper, the ultrafine elongated grain, strong fibrous structure and carbide laminated distribution along the rolling direction are prepared by temperature‐controlled pass rolling technology, which can greatly improve its yield strength and low temperature impact resistance, etc., and has a wide application prospect. ... It was reported that aluminum alloys have a higher stacking fault energy than copper alloys. 8,9 As a result, copper alloys highly restrict the recovery and cause a high density of dislocations in ECAP processed samples. 10 The microstructure of ECAP processed brass samples is more refined than that of the initial brass alloy. ... Article A focus of the current industrial sector is motivated to develop a new class of advanced materials with superior characteristics compared to currently available conventional materials. In the recent past, light metals and alloys, such as aluminum, copper, titanium, and magnesium alloys and their metal matrix composites (MMCs) have been increasingly accepted in automotive, aerospace, and biomedical sectors. Moreover, for improving the physical and mechanical characteristics of these materials, the processing of materials with secondary metalworking techniques (severe plastic deformation [SPD], complete and partial heat treatment processes, cryogenic treatment, surface coatings, etc.) is essential. Out of several secondary metalworking techniques, the most efficient is the SPD technique with equal channel angular pressing (ECAP). ECAP is widely adopted to produce materials with significantly reduced grain size and excellent properties. The current review article aims to present the effect of ECAP on the physical and mechanical characteristics of aluminum, copper, titanium, and magnesium alloys, and their MMCs are discussed. Microstructural studies and their associated statistical parameters of these materials are discussed using several destructive and nondestructive techniques. Also, the use of in-situ methods, such as digital image correlation, infrared thermography, etc., is examined to study the deformation mechanisms in ECAP. This review article provides a new direction for researchers working in materials engineering and science fields to recognize the importance of the ECAP technique on mechanical characteristics and associated microstructural changes of majorly used alloys and MMCs. Article As-cast and homogenized Mg-8.4Li-3.58Al-0.36Si-0.05Ti-0.01B alloys with and without coarse AlLi and Mg2Si constituent particles are processed by equal channel angular pressing (ECAP) at 623 K for 1–4 passes in route BC (the billet is rotated 90° clockwise between consecutive pressings) to investigate their different microstructural evolutions and mechanical responses. In particle-containing cast + ECAP alloys, coarse AlLi in β-Li phase and Mg2Si constituent particles accelerated the refinement and uniform redistribution of α-Mg dendrites during ECAP to form small blocky α-Mg grains. Simultaneous particle dissolution and significant fragmentation together with the uniform mixture of small α-Mg and β-Li grains result in the highest ductility and good strength in cast+2p alloy compared to the other ECAPed alloys. Heterogeneous re-precipitation and particle coarsening as well as α-Mg grain growth lead to a gradual decline in mechanical properties of cast+3p and cast+4p alloys. While in HT + ECAP alloys, large amounts of second-phase particles dynamically precipitated during ECAP, which pinned the dislocation movement and (sub)grain boundary migration resulting in large α-Mg blocks in HT + ECAP alloys. Nevertheless, concurrent precipitation and dynamic recrystallization (DRX) lead to high-density AlLi and Mg2Si nano-precipitates and fine α-Mg grains with weak basal plane texture, resulting in the highest strength and reasonable ductility in HT+2P alloy compared to the other ECAPed alloys. Particle coarsening and coarser DRXed α-Mg grains caused the declined mechanical properties in HT+3p and HT+4p alloys. Article In this study, the microstructural evolution and mechanical behaviour of the GH3128 alloy during hot deformation were investigated, which is crucial for optimising hot processing. The investigation was performed by hot tensile deformation at 750–950 °C and analysis by electron backscatter diffraction (EBSD), differential scanning calorimetry (DSC), X-ray diffraction (XRD), and scanning electron microscopy (SEM). The results show that two types of second-phase M23C6 and MC carbide particles existed during hot deformation, with content percentages and distributions relating to the temperature. The increase in temperature gradually promoted the precipitation of the second phase in the grain boundary. Dynamic recrystallisation occurred during hot deformation via coexisting mechanisms of twin-induced nucleation and particle-stimulated nucleation. The dynamic recrystallisation fraction gradually increased with an increase in temperature. In addition, the variation law of mechanical behaviour with temperature was revealed and explained from the perspective of microstructural evolution. In particular, the elongation decreased with an increase in temperature from 800°C to 950°C, mainly due to the precipitation of the second phase in the grain boundary at high temperatures, coarsening of grains and decreasing of grain uniformity. Concomitantly, the fracture mechanism changed from ductile fracture to ductile brittle fracture with an increase in temperature. These results provide a theoretical basis and guidance for the hot-working process of GH3128. Article Dynamic recrystallization (DRX) is one of the more convenient and effective means of refining grains during hot deformation, which is closely related to the precipitation behavior. Three alloys with varying pre-precipitations are designed by carrying out different heat treatment processes to explore the effects of precipitation on the recrystallization behavior of an Al–Cu–Li alloy during compression. It is indicated that the recrystallization behavior of the as-extruded alloy is quite sensitive to the precipitation. Precipitation does not change the recrystallization mechanism, but it could significantly affect the recrystallization volume fraction (VDRX). Meanwhile, the diverse extruded texture fibers coordinate deformation through different softening mechanisms during compression, which stimulates the nucleation of the lamellar grain in R–cube textures. Furthermore, the influence mechanism of microstructure on the material flow behavior is also discussed for the three heat-treated alloys. Therefore, this work is expected to provide new insights for Al–Cu–Li alloy to design high-performance products through grain refinement and texture modification in the subsequent processing. Article In this paper, a series of hot compression tests were carried out by using a Thermecamastor-Z thermomechanical simulator in the temperature range of 1020 ~ 1140 °C and a strain rate range of 0.01 ~ 1 s−1. The microstructure evolution mechanism for the GH4742 nickel-based superalloy during hot compression was studied using electron backscatter diffraction (EBSD) and scanning electron microscopy (SEM) techniques. Constitutive models for the γ + γ' double-phase and γ single-phase regions are established. The hot deformation activation energies for γ + γ' double-phase and γ single-phase microstructures are determined to be 828.996 kJ/mol and 230.707 kJ/mol, respectively. Furthermore, the internal relationship between the flow stress, hot processing map, and dynamic recrystallization (DRX) mechanism is analyzed. The results show that the high Z value is mainly located in the instability region, and the DRX mechanism is dominated by discontinuous dynamic recrystallization (DDRX), supplemented by continuous dynamic recrystallization (CDRX), particle-stimulated nucleation (PSN), and the strong pinning of γ' precipitates, which delays the development of DRX. At moderate Z values, the DRX mechanism involves the combined effect of DDRX and weak CDRX, PSN, and γ' precipitate pinning, while at low Z values, the DRX mechanism mainly involves DDRX. The transition for the DRX mechanism is extremely sensitive to the Z value. Article Environmentally degradable Zn-0.8Mn alloy is highly ductile, which lays the foundation for developing high-performance Zn-Mn-based alloys. However, not only constitutive equation of this alloy is unknown, but also its dynamic recrystallization (DRX) behavior is unclear, which makes optimization of hot processing parameters of this alloy almost dependent on trial-and-error. This work aims to tackle these problems. The constitutive equation was deduced to be ε˙ = 1.38 × 10¹² × [sinh(0.009σ)]⁸exp(–135150/RT). A processing map of the alloy was obtained for the first time, which shows that it has excellent hot formability with narrow instability zones. At a final true strain of 0.8, the volume fraction of DRX grains increased from 37% to 79% with temperature increasing from 150 °C to 350 °C and strain rate decreasing from 10 s–1 to 10–3 s–1. Discontinuous DRX (DDRX), continuous DRX (CDRX), twinning-induced DRX (TDRX), and particle stimulated nucleation (PSN) were activated during hot compressions. DDRX was always the main mechanism. TDRX was completely suppressed at 300 °C and above. PSN arose from dispersed MnZn13 particles. Furthermore, Zn-0.8Mn alloy exhibited elevated-temperature strengths better than pure Zn and Zn-Al-based alloys. At 300 °C and 0.1 s–1, its peak stress was 1.8 times of pure Zn, owing to MnZn13 particles of 277 ± 79 nm impeding the motion of grain boundaries and dislocations. Article Continuous dynamic recrystallization (cDRX) is an effective way to refine the microstructures of materials with high stacking fault energies during their hot working. However, investigation of the influence of grain boundaries and second phases on the microstructure evolutions of these materials using conventional cDRX models is challenging. Accordingly, herein a cDRX model characterized with micron-scale second phases distributed along the grain boundaries was developed by an internal state variable plasticity-based approach. Geometrically necessary dislocation (GND) densities generated near the second phase and grain boundary were calculated by considering strain concentration in the grain, which affected the evolution of dislocation density at the subgrain boundary. The cDRX model considers an original grain as a collection of subgrains and represents the subgrains as a compound structure consisting of subgrain boundaries with relatively high dislocation densities and a subgrain interior with significantly low dislocation density. Changes in the misorientations of subgrains can be accurately determined by tracking and analyzing the evolutions of the dislocation densities of subgrain boundaries. Accuracy of the developed cDRX model was verified by comparing the hot compression data of 5052 and 2A14 Al alloys acquired using this model with the corresponding experimental results. The predicted values of variables, including flow stress, subgrain size, and the fraction of low-angle grain boundary, were in appropriate agreement with the experimental results. Effects of temperature and strain rate on the microstructure evolution of the 2A14 Al alloy were investigated. Based on the influences of strain concentration near the grain boundary and second phase on the dislocation density of the 2A14 Al alloy, the reasons for the enhancement of cDRX and improvement of the mechanical properties of the 2A14 Al alloy by the second phase and grain boundary are explained. The results of this study provide a direction for the subsequent improvement of the proposed cDRX model with second phases inside the grain. Article The influence of CoCrFeMnNi high-entropy alloy (HEA) particle addition on the microstructure and mechanical properties of the $${\text{Al}}_{6082}$$ the composite was examined. Mechanical alloying was used to develop the CoCrFeMnNi HEA, while stir-squeeze casting assisted with an ultrasonic transducer was used to process the $${\text{Al}}_{6082}$$ alloy and $${\text{C}}_{{\mathrm{Al}}_{6082}+{\mathrm{HEA}}_{x\mathrm{wt\%}}}$$ composites (where, x = 2, 4, 6, 8). The microstructural and morphological investigation was carried out using XRD, EDS, FESEM, and elemental mapping techniques. At the as-cast condition, the hardness, yield strength, and ultimate tensile strength of the $${\text{C}}_{{\text{Al}}_{6082}+{\text{HEA}}_{8{\text{wt}}\%}}$$ composite were increased by 28.57%, 79.46%, and 87.931%, respectively, over monolithic alloy, which was associated with a consistent distribution of HEA particles. Furthermore, it possessed the best tensile strength, yield strength, and fracture strain when compared with $${\text{C}}_{{\text{Al}}_{6082}+{\text{HEA}}}$$ composites, indicating a better interaction among HEA particles and Al matrix, and a high dislocation density in the Al matrix.Graphical abstract Article Full-text available In the present work, we report our recent progress in the development, optimization, and application of a technique for the three-dimensional (3-D) high-resolution characterization of crystalline microstructures. The technique is based on automated serial sectioning using a focused ion beam (FIB) and characterization of the sections by orientation microscopy based on electron backscatter diffraction (EBSD) in a combined FIB–scanning electron microscope (SEM). On our system, consisting of a Zeiss–Crossbeam FIB-SEM and an EDAX-TSL EBSD system, the technique currently reaches a spatial resolution of 100×100×100nm3 as a standard, but a resolution of 50×50×50nm3 seems to be a realistic optimum. The maximum observable volume is on the order of 50×50×50μm3. The technique extends all the powerful features of two-dimensional (2-D) EBSD-based orientation microscopy into the third dimension of space. This allows new parameters of the microstructure to be obtained—for example, the full crystallographic characterization of all kinds of interfaces, including the morphology and the crystallographic indices of the interface planes. The technique is illustrated by four examples, including the characterization of pearlite colonies in a carbon steel, of twins in pseudonanocrystalline NiCo thin films, the description of deformation patterns formed under nanoindents in copper single crystals, and the characterization of fatigue cracks in an aluminum alloy. In view of these examples, we discuss the possibilities and limits of the technique. Furthermore, we give an extensive overview of parallel developments of 3-D orientation microscopy (with a focus on the EBSD-based techniques) in other groups. Article Full-text available The recrystallization behaviour of Al-Mn alloys (AA3xxx series alloys) is affected by randomly distributed dispersoids present before annealing, by dispersoids precipitated at grain/subgrain boundaries before the onset of recrystallization, and by dispersoids concurrently precipitated during recrystallization. In this study, the effects of these three populations of dispersoids on the recrystallization behaviour of a cold rolled AA3xxx alloy were analysed and compared using four temperature-time paths to different target temperatures. Changing the temperature-time path modifies the extent of recovery, the dispersoid structures, as well as the absolute recrystallization temperature, which then influences the final grain structure and recrystallization texture. In particular, an in-depth investigation on how different populations of dispersoids affect the main recrystallization texture components of AA3xxx alloys, i.e., P{011}<566>, ND-Cube {001}<310>, and Cube {001}<100>, has been carried out. The results clearly show that, as compared to isothermal annealing, annealing with more elaborate heating and annealing schedules (temperature-time paths) all lead to increased strength of the P texture component and decreased intensities of both the Cube and ND-rotated Cube texture components. The increase of P texture strength and average grain size is most significant when recrystallization occurs concurrently with precipitation. The controlling mechanisms behind this behaviour and the possibility to use them to tailor the grain structure and texture of similar alloys are further discussed. Article Full-text available Precipitation along twin boundaries and dissolution in a cold-rolled Mg-Y-Nd alloy was directly observed for the first time during annealing at 490 °C. Precipitation occurred concurrently with recrystallization and the combined effect of precipitation and solute segregated to twin boundaries modified the recrystallization behaviour. Precipitates later dissolved into the matrix at the point where full recrystallization was nearly complete. The precipitates and higher solute concentration along original twin boundaries hindered grain growth of newly formed recrystallized grains. Even where twin boundaries had been consumed by recrystallization, the size of recrystallized grains were still controlled by the pre-existing twin boundaries. Article The influence of discrete texture components and combinations of them on the earing behavior of aluminium during cup drawing was systematically investigated using the texture component crystal plasticity finite element method. Several common texture components and their combinations were selected and the resulting ear profiles were calculated under consideration of texture changes. The spherical scatter width of the components was also taken into account as an optimization parameter. The study reveals that the ear height and profile can be minimized by an optimized combination of certain texture components including their scatter width. A solution for minimum earing of cup drawn aluminium was obtained for a combination of the S and the Cube texture components with 15° spherical scatter width. More specifically we observed the following aspects: 1) Ear peaks of the Cube and Goss texture components appear at the rolling and transverse directions, while the ears of the Copper, S and Brass orientations occur at about 45° and 135° to the rolling direction. 2. Minimization of earing can be achieved by mixing the Cube and S texture components. The optimum vol- ume ratio between the two is S:Cube = 1.67 : 1. 3. Optimization of earing depends on both, crystallographic orientation and scatter width of the orienta- tion components. As a rule earing decreases with increasing spherical scatter width of the texture components. Article A new work-hardening model for homogeneous and heterogeneous cell-forming alloys is introduced. It distinguishes three internal state variables in terms of three categories of dislocations: mobile dislo-cations, immobile dislocations in the cell interiors and immobile dislocations in the cell walls. For each dislocation population an evolution law is derived taking into account dislocation generation, annihilation and storage by dipole and lock formation. In particular, these rate equations take into account the number of active glide systems and, thus, introduce texture in the model in addition to the Taylor factor. Microstructure is represented by the dislocation cell structure as well as second-phase particles, which may undergo changes by precipitation and Ostwald ripening. Interaction of mobile dislocations with the microstructure is taken into account through an effective slip length of the mobile dislocations. For the same set of parameters, the predictions are in excellent agreement with measured stress-strain curves of both a precipitation-hardened aluminium alloy (Al-4.16 wt% Cu-1.37 wt% Mg, AlCuMg2) and a precipitation-free model alloy (Al-0.35 wt% Cu-0.25 wt% Mg), the composition of which corresponds to the matrix of the two-phase alloy. - - - For a more precise modelling of forming processes, e.g., by finite element (FE) codes, accurate prediction of the strain-hardening behaviour is required. In the majority of FE codes the hardening behaviour of commercial alloys is represented by empirical relationships, mostly in terms of power laws of strain and strain rate. Despite their remarkably good fit to measured stress–strain curves, empirical relations have no predictive power beyond the measured range of deformation conditions and material chemistry. In particular, such models use macroscopic quantities as state parameters like strain or chemical composition to describe the mechanical behaviour of a material. This is fundamentally wrong, however, since the mechanical properties depend on microstructure rather than on overall chemistry, and thus are liable to change during processing of the material. In fact, an appropriate representation of the hardening behaviour has to be based on microstructural state variables which are affected by the processing history of the material. There are micromechanical models that contain explicit internal state variables, like the models of Robinson and Bartolotta [1] or Chaboche [2], which have been successfully implemented in finite element codes. Although such approaches do define evolutionary equations for the internal state variables, the respective constants are commonly used as fit parameters and do not relate to specific mechanisms of microstructure evolution. There have been numerous attempts in the past to predict work-hardening behaviour in terms of dislocation concepts, with limited success, however, with regard to correctly predicting hardening behaviour in a wide field of temperature, strain rate and material chemistry. In the current study, we present a model based on contemporary understanding of microstructural evolution and the interaction of dislocations with microstructural essentials. It will be shown that such a model gives a reasonable description of the hardening behaviour and accounts adequately for changes of material chemistry, in particular for age-hardened alloys. For properly testing both parts of the model (i.e., the dislocation–dislocation interaction and the dislocation– precipitate interaction) it is essential to separate the two effects also experimentally. This can be accomplished by using a single-phase alloy that represents the matrix material of the corresponding precipitation- hardened alloy. The structure of the paper is as follows. First, we present the three-variable concept and its evolution laws. Second, the physical parameters are adjusted in the allowed range to fit the measured stress–strain curve of the single-phase model alloy. Third, the same set of parameters is used to model the stress– strain curve of the precipitation-hardened alloy by optimizing just the parameters for the description of precipitation that were not used for simulating the model alloy as it is free of precipitates. Article The texture evolution of continuous cast (CC) AA 3105 aluminum alloy during cold rolling was investigated by X-ray Bragg diffraction. The influence of the precipitation state on the texture evolution during rolling was determined. The results show that the precipitates in a CC AA 3105 aluminum alloy affect the texture evolution during rolling. As the amount of precipitates increases and the size of precipitates decreases, the rate of disappearance of the cube, r-cube, and remainder components and the rate of formation of the fiber decrease. The presence of large precipitates in a CC AA 3105 aluminum alloy hardly affects the texture evolution. Book An impeccable, authoritative, yet refreshingly lucid work on the development of nanocrystalline materials, this book is the first definitive step to understanding the relationship between the properties of nanomaterials and their microstructure. Thousands of papers have been published that concentrate on the comprehension of the strength and ductility of such materials in order to maximize both. Moving beyond reiterating just the strength, toughness, and stability of these materials, this compendium provides much analysis to better understand the crystal grain and grain boundary bases that determine property behaviors over a range of temperatures and applied loading rates. The original relation that connects grain size and strength, known as the Hall-Petch relation, is studied in the nanometer grain size region. The breakdown of such a relation is a challenge. Why and how to overcome it? Is the dislocation mechanism still operating when the grain size is very small, approaching the amorphous limit? How do we go from the microstructure information to the continuum description of mechanical properties? The book effectively answers these questions, besides many others that have made nanocrystalline materials an object of unprecedented interest of late. Article An analysis is presented to assess the relationships between particles distributed throughout a medium. The adopted approach is to compare the observed data with the expected associations between particles calculated on the basis of random positioning. Since bulk structures are often examined by using a sectioning technique, the paper includes a method to transform two-dimensional observations into three-dimensional associations. This is achieved by assuming that the most complex association observed is the most complex association in the bulk material; the contributions to lower-order associations from this association are calculated and subtracted from the observed frequencies. The process is repeated, making the same assumptions about the next most complex association, and so on until a corrected matrix of associations has been compiled. The analysis is applied to a partially recrystallised iron-0.4 wt% carbon alloy to give a complete description of the associations between carbide particles and recrystallised grains. In particular, it is shown that carbide particles are exclusive nucleation sites for recrystallisation. Article We propose a two-mechanism theory to estimate the pinning effect of coherent precipitates on grain-boundary (GB) migration in grain growth, taking into account the important effect of elastic misfit strain at the coherent interface. Depending on the relative importance of the elastic and the GB contributions to the total free energy, Zener type stabilization or a novel elastic energy induced stabilization may occur. It is found that the pinning is most effective in the crossover region between these two mechanisms. A phase-field-crystal model is used to numerically validate the theory. Relevant experiments and potential impacts on alloy design are also discussed.	2022-10-02 17:47:34	{"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": 0.41163140535354614, "perplexity": 2971.1873292759346}, "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/1664030337338.11/warc/CC-MAIN-20221002150039-20221002180039-00056.warc.gz"}
https://zbmath.org/authors/?s=0&q=Askey%2C+Richard	# zbMATH — the first resource for mathematics Compute Distance To: Documents Indexed: 157 Publications since 1959, including 10 Books Reviewing Activity: 188 Reviews Biographic References: 9 Publications all top 5 #### Co-Authors 89 single-authored 11 Ismail, Mourad El-Houssieny 8 Gasper, George Jun 7 Andrews, George Eyre 7 Wainger, Stephen 4 Fitch, James 4 Koornwinder, Tom H. 4 Suslov, Sergei K. 4 Wilson, James A. 3 Al-Salam, Waleed A. 3 Allaway, William R. 3 Roy, Ranjan 2 Boas, Ralph Philip jun. 2 Hirschman, Isidore Isaac jun. 2 Rahman, Mizan 2 Steinig, John 2 Tepper Haimo, Deborah 1 Atakishiev, Natig M. 1 Berndt, Bruce Carl 1 Bingham, Nicholas Hugh 1 de Boor, Carl 1 Harris, Lawrence A. 1 Karlin, Samuel 1 Koelink, Erik 1 Koepf, Wolfram A. 1 Nevai, Paul G. 1 Pollard, Harry 1 Ramanathan, Kollagunta G. 1 Rankin, Robert Alexander 1 Rashed, Thanaa M. T. 1 Razban, Behzad 1 Regev, Amitai 1 Schempp, Walter Johannes 1 Schoenberg, Isaac Jacob 1 Sharma, Ambikeshwar 1 Van Assche, Walter 1 Wimp, Jet all top 5 #### Serials 10 Proceedings of the American Mathematical Society 8 SIAM Journal on Mathematical Analysis 7 Journal of Mathematical Analysis and Applications 7 Journal of Approximation Theory 5 American Mathematical Monthly 4 American Journal of Mathematics 4 Journal of Computational and Applied Mathematics 4 Transactions of the American Mathematical Society 3 Journal d’Analyse Mathématique 3 Rocky Mountain Journal of Mathematics 2 Acta Mathematica Academiae Scientiarum Hungaricae 2 Letters in Mathematical Physics 2 Canadian Journal of Mathematics 2 Illinois Journal of Mathematics 2 Indian Journal of Mathematics 2 Memoirs of the American Mathematical Society 2 Pacific Journal of Mathematics 2 Journal of Physics A: Mathematical and General 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Bulletin of the American Mathematical Society 2 Encyclopedia of Mathematics and Its Applications 1 Applicable Analysis 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Institute of Mathematics and its Applications 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Acta Scientiarum Mathematicarum 1 Canadian Mathematical Bulletin 1 Duke Mathematical Journal 1 Journal of Combinatorial Theory. Series A 1 The Journal of the Indian Mathematical Society. New Series 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Annalen 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Numerische Mathematik 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Real Analysis Exchange 1 SIAM Journal on Numerical Analysis 1 Simon Stevin 1 Studia Scientiarum Mathematicarum Hungarica 1 Tohoku Mathematical Journal. Second Series 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 European Journal of Combinatorics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Journal of Symbolic Computation 1 CWI Quarterly 1 Aequationes Mathematicae 1 Journal of the Australian Mathematical Society. Series A 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Séminaire Lotharingien de Combinatoire 1 Computational Methods and Function Theory 1 Proceedings of the Cambridge Philosophical Society 1 Bollettino della Unione Matematica Italiana. Series III 1 Publications de la Faculté d’Électrotechnique de l’Université à Belgrade. Série Mathématiques et Physique 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Mathematics and its Applications (Dordrecht) 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae all top 5 #### Fields 104 Special functions (33-XX) 29 Harmonic analysis on Euclidean spaces (42-XX) 12 History and biography (01-XX) 9 Combinatorics (05-XX) 9 Sequences, series, summability (40-XX) 7 Number theory (11-XX) 7 Real functions (26-XX) 6 General and overarching topics; collections (00-XX) 4 Functions of a complex variable (30-XX) 4 Approximations and expansions (41-XX) 4 Integral transforms, operational calculus (44-XX) 4 Numerical analysis (65-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 2 Difference and functional equations (39-XX) 2 Abstract harmonic analysis (43-XX) 2 Probability theory and stochastic processes (60-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Geometry (51-XX) #### Citations contained in zbMATH Open 131 Publications have been cited 3,061 times in 2,375 Documents Cited by Year Special functions. Zbl 0920.33001 Andrews, George E.; Askey, Richard; Roy, Ranjan 1999 Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Zbl 0572.33012 1985 Oethogonal polynomials and special functions. Zbl 0298.33008 1975 A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols. Zbl 0437.33014 1979 Mean convergence of expansions in Laguerre und Hermite series. Zbl 0125.31301 1965 Recurrence relations, continued fractions and orthogonal polynomials. Zbl 0548.33001 1984 Special functions. Paperback ed. Zbl 1075.33500 Andrews, George E.; Askey, Richard; Roy, Ranjan 2000 The q-gamma and q-beta functions. Zbl 0398.33001 1978 Some absolutely monotonic functions. Zbl 0298.26010 1975 Some basic hypergeometric extensions of integrals of Selberg and Andrews. Zbl 0458.33002 1980 Integral representations for Jacobi polynomials and some applications. Zbl 0172.08803 1969 Ramanujan’s extensions of the gamma and beta functions. Zbl 0437.33001 1980 Associated Laguerre and Hermite polynomials. Zbl 0547.33006 1984 A generalization of ultraspherical polynomials. Zbl 0532.33006 1983 A convolution structure for Jacobi series. Zbl 0186.12303 1969 Orthogonal polynomials and positivity. Zbl 0188.12402 1969 Mean convergence of orthogonal series and Lagrange interpolation. Zbl 0253.41003 1972 Sieved ultraspherical polynomials. Zbl 0547.33005 Al-Salam, Waleed; Allaway, W. R.; Askey, Richard 1984 Another q-extension of the beta function. Zbl 0471.33001 1981 Some positive trigonometric sums. Zbl 0244.42002 1974 A set of hypergeometric orthogonal polynomials. Zbl 0496.33007 1982 Integrability theorems for Fourier series. Zbl 0136.36501 1966 Positive Jacobi polynomial sum. II. Zbl 0355.33005 1976 Continuous Hahn polynomials. Zbl 0582.33007 1985 Convolution structures for Laguerre polynomials. Zbl 0347.33006 1977 On the behavior of special classes of ultraspherical expansions. I, II. Zbl 0132.29403 1965 Mean summability for ultraspherical polynomials. Zbl 0132.29501 Askey, R.; Hirschman, I. I. jun. 1963 Summability of Jacobi series. Zbl 0268.33015 1973 Classical orthogonal polynomials. Zbl 0596.33016 1985 On a general $$q$$-Fourier transformation with nonsymmetric kernels. Zbl 0871.33008 Askey, Richard A.; Rahman, Mizan; Suslov, Sergej K. 1996 Enumeration of partitions: the role of Eulerian series and $$q$$-orthogonal polynomials. Zbl 0381.10008 1977 A simple proof of Ramanujan’s summation of the $$_1\Psi_1$$. Zbl 0401.33002 1978 Linearization of the product of Jacobi polynomials. III. Zbl 0212.40904 1971 Grünbaum’s inequality for Bessel functions. Zbl 0253.33009 1973 Permutation problems and special functions. Zbl 0313.05005 1976 Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients. Zbl 0217.11402 1971 The $$q$$-harmonic oscillator and the Al-Salam and Carlitz polynomials. Zbl 0919.33010 1993 A transplantation theorem for Jacobi series. Zbl 0174.35303 1969 Gaussian processes on compact symmetric spaces. Zbl 0329.60019 1976 A transplantation theorem between ultraspherical series. Zbl 0135.27603 1966 More q-beta integrals. Zbl 0599.33002 1986 Ramanujan and hypergeometric and basic hypergeometric series. Zbl 0722.33009 1990 Certain rational functions whose power series have positive coefficients. Zbl 0242.33023 1972 A transplantation theorem for ultraspherical coefficients. Zbl 0136.37201 1966 Evaluation of Sylvester type determinants using orthogonal polynomials. Zbl 1090.15007 2005 Positivity of the Cotes numbers for some ultraspherical abscissas. Zbl 0169.08301 1968 Some absolutely monotonic and completely monotonic functions. Zbl 0239.26010 1974 Orthogonal expansions with positive coefficients. Zbl 0136.05103 1965 A q-beta integral associated with $$BC_ 1$$. Zbl 0501.33002 1982 A q-extension of Cauchy’s form of the beta integral. Zbl 0463.33003 1981 An elementary evaluation of a beta type integral. Zbl 0523.33001 1983 Weighted permutation problems and Laguerre polynomials. Zbl 0405.05008 1978 The very well-poised Psi(6,6). Zbl 0412.33005 1979 Jacobi polynomial expansions with positive coefficients and imbeddings of projective spaces. Zbl 0167.35003 1968 Hausdorff’s moment problem and expansions in Legendre polynomials. Zbl 0483.44012 Askey, R.; Schoenberg, I. J.; Sharma, A. 1982 Special functions: Group theoretical aspects and applications. Zbl 0543.00007 Askey, R. A. (ed.); Koornwinder, T. H. (ed.); Schempp, Walter (ed.) 1984 An integral of Ramanujan and orthogonal polynomials. Zbl 0665.33001 1987 Divided difference operators and classical orthogonal polynomials. Zbl 0696.33008 1989 Problems which interest and/or annoy me. Zbl 0797.33006 1993 Norm inequalities for some orthogonal series. Zbl 0173.06703 1966 A dual convolution structure for Jacobi polynomials. Zbl 0174.36305 1968 Positivity of the Cotes numbers for some Jacobi abscissas. Zbl 0237.65012 1972 The very well-poised $$_6\Psi_6$$. Zbl 0387.33002 1979 Jacobi polynomials. I: New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum. Zbl 0242.33019 1974 Limits of some q-Laguerre polynomials. Zbl 0641.33018 1986 Continuous q-Hermite polynomials when $$q>1$$. Zbl 0694.33006 1989 Finite differences and orthogonal polynomials. Zbl 0801.33005 1994 Vietoris’s inequalities and hypergeometric series. Zbl 0899.33002 1998 Jacobi’s generating function for Jacobi polynomials. Zbl 0393.33010 1978 A transplantation theorem for Jacobi coefficients. Zbl 0172.08601 1967 Dual equations and classical orthogonal polynomials. Zbl 0185.12601 1968 Linearization of the product of orthogonal polynomials. Zbl 0212.41001 1970 Two integrals of Ramanujan. Zbl 0503.33001 1982 An intergral of products of ultraspherical functions and a q-extension. Zbl 0564.33008 Askey, Richard; Koornwinder, Tom H.; Rahman, Mizan 1986 Orthogonal polynomials and theta functions. Zbl 0675.33006 1989 Positivity of the cotes numbers for some Jacobi abscissas. II. Zbl 0416.65016 1979 Maximal degrees for Young diagrams in a strip. Zbl 0555.05009 1984 An analog of the Fourier transformation for a $$q$$-harmonic oscillator. Zbl 0863.33020 Askey, R.; Atakishiyev, N. M.; Suslov, S. K. 1993 Similarities between Fourier and power series. Zbl 0854.33005 1996 The $$q$$-harmonic oscillator and an analogue of the Charlier polynomials. Zbl 0859.33021 1993 Smoothness conditions for Fourier series with monotone coefficients. Zbl 0172.34701 1967 On a positive trigonometric sum. Zbl 0174.35704 Askey, R.; Fitch, J.; Gasper, G. 1968 Orthogonal expansions with positive coefficients. II. Zbl 0202.35302 1971 Positive Jacobi polynomial sums. Zbl 0237.33010 1972 A positive sum from summability theory. Zbl 0295.40008 1975 An integral for Jacobi polynomials. Zbl 0308.33006 1973 A recurrence relation generalizing those of Apéry. Zbl 0558.33003 1984 Beta integrals in Ramanujan’s papers, his unpublished work and further examples. Zbl 0648.33001 1988 Beta integrals and q-extensions. Zbl 0697.33002 1988 Weighted quadratic norms and ultra-spherical polynomials. I. Zbl 0199.46701 1959 Some elementary integrability theorems for special transforms. Zbl 0212.41402 1970 Certain rational functions whose power series have positive coefficients. II. Zbl 0291.33010 1974 Some characteristic functions of unimodal distributions. Zbl 0308.60016 1975 The very well poised $$_6\psi_6$$. II. Zbl 0509.33001 1983 An integral of products of Legendre functions and a Clebsch-Gordan sum. Zbl 0524.33004 1982 Variants of Clausen’s formula for the square of a special $$_ 2F_ 1$$. Zbl 0756.33002 1989 Selberg’s second beta integral and an integral of Mehta. Zbl 0683.33001 1989 Graphs as an aid to understanding special functions. Zbl 0694.33002 1990 A look at the Bateman project. Zbl 0837.33001 1994 The work of George Andrews: a Madison perspective. Zbl 1041.01505 1999 Completing Brahmagupta’s extension of Ptolemy’s theorem. Zbl 1322.01005 2010 Evaluation of Sylvester type determinants using orthogonal polynomials. Zbl 1090.15007 2005 The 1839 paper of permutations: its relation to the Rodrigues formula and further developments. Zbl 1130.01006 2005 Ted Chihara and his work on orthogonal polynomials. Zbl 0999.01023 Askey, R.; Ismail, M. E. H.; Van Assche, W. 2001 Special functions. Paperback ed. Zbl 1075.33500 Andrews, George E.; Askey, Richard; Roy, Ranjan 2000 Special functions. Zbl 0920.33001 Andrews, George E.; Askey, Richard; Roy, Ranjan 1999 The work of George Andrews: a Madison perspective. Zbl 1041.01505 1999 Vietoris’s inequalities and hypergeometric series. Zbl 0899.33002 1998 On a general $$q$$-Fourier transformation with nonsymmetric kernels. Zbl 0871.33008 Askey, Richard A.; Rahman, Mizan; Suslov, Sergej K. 1996 Similarities between Fourier and power series. Zbl 0854.33005 1996 Gabor Szegö: 1895–1985. Zbl 0873.01030 1996 Dedication: Remembering Paul Turán. Zbl 0856.01047 1996 Finite differences and orthogonal polynomials. Zbl 0801.33005 1994 A look at the Bateman project. Zbl 0837.33001 1994 Gaussian quadrature in Ramanujan’s second notebook. Zbl 0794.41022 1994 The $$q$$-harmonic oscillator and the Al-Salam and Carlitz polynomials. Zbl 0919.33010 1993 Problems which interest and/or annoy me. Zbl 0797.33006 1993 An analog of the Fourier transformation for a $$q$$-harmonic oscillator. Zbl 0863.33020 Askey, R.; Atakishiyev, N. M.; Suslov, S. K. 1993 The $$q$$-harmonic oscillator and an analogue of the Charlier polynomials. Zbl 0859.33021 1993 Ramanujan and hypergeometric and basic hypergeometric series. Zbl 0722.33009 1990 Graphs as an aid to understanding special functions. Zbl 0694.33002 1990 Relative extrema of Legendre functions of the second kind. Zbl 0698.33006 1990 Divided difference operators and classical orthogonal polynomials. Zbl 0696.33008 1989 Continuous q-Hermite polynomials when $$q>1$$. Zbl 0694.33006 1989 Orthogonal polynomials and theta functions. Zbl 0675.33006 1989 Variants of Clausen’s formula for the square of a special $$_ 2F_ 1$$. Zbl 0756.33002 1989 Selberg’s second beta integral and an integral of Mehta. Zbl 0683.33001 1989 Beta integrals and the associated orthogonal polynomials. Zbl 0683.33002 1989 Beta integrals in Ramanujan’s papers, his unpublished work and further examples. Zbl 0648.33001 1988 Beta integrals and q-extensions. Zbl 0697.33002 1988 Ramanujan revisited. Proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1–5, 1987. Zbl 0635.00003 Andrews, George E.; Askey, Richard A.; Berndt, Bruce C.; Ramanathan, K. G.; Rankin, Robert A. 1988 An integral of Ramanujan and orthogonal polynomials. Zbl 0665.33001 1987 More q-beta integrals. Zbl 0599.33002 1986 Limits of some q-Laguerre polynomials. Zbl 0641.33018 1986 An intergral of products of ultraspherical functions and a q-extension. Zbl 0564.33008 Askey, Richard; Koornwinder, Tom H.; Rahman, Mizan 1986 Positive quadrature methods and positive polynomial sums. Zbl 0613.41027 1986 Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Zbl 0572.33012 1985 Continuous Hahn polynomials. Zbl 0582.33007 1985 Classical orthogonal polynomials. Zbl 0596.33016 1985 Appendix. Zbl 0589.33003 1985 Some problems about special functions and computations. Zbl 0596.33001 1985 Recurrence relations, continued fractions and orthogonal polynomials. Zbl 0548.33001 1984 Associated Laguerre and Hermite polynomials. Zbl 0547.33006 1984 Sieved ultraspherical polynomials. Zbl 0547.33005 Al-Salam, Waleed; Allaway, W. R.; Askey, Richard 1984 Special functions: Group theoretical aspects and applications. Zbl 0543.00007 Askey, R. A.; Koornwinder, T. H.; Schempp, Walter 1984 Maximal degrees for Young diagrams in a strip. Zbl 0555.05009 1984 A recurrence relation generalizing those of Apéry. Zbl 0558.33003 1984 A characterization of the continuous q-ultraspherical polynomials. Zbl 0537.33004 Al-Salam, Walleed; Allaway, W. R.; Askey, Richard 1984 Remarks on the preceding paper by Gavin Brown and Edwin Hewitt. Zbl 0553.42001 1984 Orthogonal polynomials and some definite integrals. Zbl 0562.33007 1984 A generalization of ultraspherical polynomials. Zbl 0532.33006 1983 An elementary evaluation of a beta type integral. Zbl 0523.33001 1983 The very well poised $$_6\psi_6$$. II. Zbl 0509.33001 1983 A set of hypergeometric orthogonal polynomials. Zbl 0496.33007 1982 A q-beta integral associated with $$BC_ 1$$. Zbl 0501.33002 1982 Hausdorff’s moment problem and expansions in Legendre polynomials. Zbl 0483.44012 Askey, R.; Schoenberg, I. J.; Sharma, A. 1982 Two integrals of Ramanujan. Zbl 0503.33001 1982 An integral of products of Legendre functions and a Clebsch-Gordan sum. Zbl 0524.33004 1982 Another q-extension of the beta function. Zbl 0471.33001 1981 A q-extension of Cauchy’s form of the beta integral. Zbl 0463.33003 1981 Some basic hypergeometric extensions of integrals of Selberg and Andrews. Zbl 0458.33002 1980 Ramanujan’s extensions of the gamma and beta functions. Zbl 0437.33001 1980 The Rogers q-ultraspherical polynomials. Zbl 0479.33013 1980 A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols. Zbl 0437.33014 1979 The very well-poised Psi(6,6). Zbl 0412.33005 1979 The very well-poised $$_6\Psi_6$$. Zbl 0387.33002 1979 Positivity of the cotes numbers for some Jacobi abscissas. II. Zbl 0416.65016 1979 Some absolutely monotonic functions. Zbl 0391.33009 1979 The q-gamma and q-beta functions. Zbl 0398.33001 1978 A simple proof of Ramanujan’s summation of the $$_1\Psi_1$$. Zbl 0401.33002 1978 Weighted permutation problems and Laguerre polynomials. Zbl 0405.05008 1978 Jacobi’s generating function for Jacobi polynomials. Zbl 0393.33010 1978 Convolution structures for Laguerre polynomials. Zbl 0347.33006 1977 Enumeration of partitions: the role of Eulerian series and $$q$$-orthogonal polynomials. Zbl 0381.10008 1977 Positive Jacobi polynomial sum. II. Zbl 0355.33005 1976 Permutation problems and special functions. Zbl 0313.05005 1976 Gaussian processes on compact symmetric spaces. Zbl 0329.60019 1976 A monotonic trigonometric sum. Zbl 0334.42003 1976 Oethogonal polynomials and special functions. Zbl 0298.33008 1975 Some absolutely monotonic functions. Zbl 0298.26010 1975 A positive sum from summability theory. Zbl 0295.40008 1975 Some characteristic functions of unimodal distributions. Zbl 0308.60016 1975 Inequalities via fractional integration. Zbl 0307.26014 1975 A derangement problem. Zbl 0337.05011 1975 Some positive trigonometric sums. Zbl 0244.42002 1974 Some absolutely monotonic and completely monotonic functions. Zbl 0239.26010 1974 Jacobi polynomials. I: New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum. Zbl 0242.33019 1974 Certain rational functions whose power series have positive coefficients. II. Zbl 0291.33010 1974 Positive Cesaro means of numerical series. Zbl 0288.40010 1974 Summability of Jacobi series. Zbl 0268.33015 1973 Grünbaum’s inequality for Bessel functions. Zbl 0253.33009 1973 An integral for Jacobi polynomials. Zbl 0308.33006 1973 Refinements of Abel summability for Jacobi series. Zbl 0282.43008 1973 Mean convergence of orthogonal series and Lagrange interpolation. Zbl 0253.41003 1972 Certain rational functions whose power series have positive coefficients. Zbl 0242.33023 1972 Positivity of the Cotes numbers for some Jacobi abscissas. Zbl 0237.65012 1972 Positive Jacobi polynomial sums. Zbl 0237.33010 1972 Jacobi summability. Zbl 0234.40016 1972 A positive Cesaro mean. Zbl 0254.42001 1972 Linearization of the product of Jacobi polynomials. III. Zbl 0212.40904 1971 ...and 31 more Documents all top 5 #### Cited by 2,272 Authors 71 Ismail, Mourad El-Houssieny 29 Askey, Richard Allen 22 Alzer, Horst 22 Rahman, Mizan 19 Stanton, Dennis W. 18 Koepf, Wolfram A. 18 Terwilliger, Paul M. 17 Chu, Wenchang 17 Koelink, Erik 17 Spiridonov, Vyacheslav Pavlovich 17 Suslov, Sergei K. 16 Area, Iván 16 Godoy, Eduardo Paciência 16 Koornwinder, Tom H. 16 Nevai, Paul G. 16 Van Assche, Walter 15 Koumandos, Stamatis 14 Cao, Jian 14 Ito, Masahiko 14 Srivastava, Hari Mohan 14 Zhedanov, Alexei S. 13 Kwong, Man Kam 13 Marcellán Español, Francisco 13 van Diejen, Jan Felipe 12 Atakishiev, Natig M. 12 Gasper, George Jun 12 Karniadakis, George Em 12 Stokman, Jasper V. 11 Kilic, Emrah 11 Tikhonov, Sergey Yur’evich 11 Vinet, Luc 11 Zhang, Ruiming 10 Abd-Elhameed, Waleed Mohamed 10 Bryc, Włodzimierz 10 Karp, Dmitriĭ Borisovich 10 Masjed-Jamei, Mohammad 10 Milne, Stephen C. 10 Mimachi, Katsuhisa 10 Ronveaux, André 10 Voit, Michael 10 Wang, Mingjin 10 Warnaar, S. Ole 10 Zeilberger, Doron 9 Coffey, Mark William 9 Doha, Eid H. 9 Markett, Clemens 9 Mhaskar, Hrushikesh N. 9 Ostrovska, Sofiya 9 Xu, Yuan 9 Zeng, Jiang 8 Álvarez-Nodarse, Renato 8 Bouzeffour, Fethi 8 Dai, Feng 8 Jordaan, Kerstin 8 Klimyk, Anatoliy Ul’yanovich 8 McCoy, Peter A. 8 Noumi, Masatoshi 8 Thangavelu, Sundaram 8 Wang, Lilian 7 Brown, Gavin 7 Chen, William Yong-Chuan 7 Chihara, Theodore Seio 7 Forrester, Peter J. 7 Gupta, Vijay 7 Iliev, Plamen 7 Ito, Tatsuro 7 Lewanowicz, Stanisław 7 Li, Zhongkai 7 Ma, Chunsheng 7 Masson, David R. 7 Ol’shanskiĭ, Grigoriĭ Iosifovich 7 Porcu, Emilio 7 Shen, Jie 7 Simeonov, Plamen C. 7 Stempak, Krzysztof 7 Szwarc, Ryszard 7 Tratnik, M. V. 7 Vuorinen, Matti Keijo Kustaa 7 Zarzo, Alejandro 6 Aomoto, Kazuhiko 6 Barnard, Roger W. 6 Berg, Christian 6 Bringmann, Kathrin 6 Cohl, Howard Saul 6 Dehesa, Jesús S. 6 Demni, Nizar 6 Dimitrov, Dimitar K. 6 Foupouagnigni, Mama 6 Geronimo, Jeffrey S. 6 Groenevelt, Wolter G. M. 6 Kanjin, Yuichi 6 Kim, Taekyun 6 Krattenthaler, Christian Friedrich 6 Lasser, Rupert 6 Liu, Zhi-Guo 6 Long, Ling 6 Lubinsky, Doron S. 6 Milovanović, Gradimir V. 6 Petronilho, José C. 6 Rains, Eric M. ...and 2,172 more Authors all top 5 #### Cited in 395 Serials 136 Journal of Mathematical Analysis and Applications 117 Journal of Computational and Applied Mathematics 111 The Ramanujan Journal 107 Proceedings of the American Mathematical Society 105 Journal of Approximation Theory 76 Transactions of the American Mathematical Society 47 Journal of Mathematical Physics 45 Constructive Approximation 41 Mathematics of Computation 38 Advances in Mathematics 38 Integral Transforms and Special Functions 33 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 30 Applied Mathematics and Computation 30 Advances in Applied Mathematics 25 Communications in Mathematical Physics 25 Rocky Mountain Journal of Mathematics 24 Journal of Combinatorial Theory. 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B 8 Calcolo 8 Compositio Mathematica 8 Journal of Soviet Mathematics 8 Journal of Mathematical Sciences (New York) 8 Advances in Computational Mathematics 7 Computer Methods in Applied Mechanics and Engineering 7 Ukrainian Mathematical Journal 7 Arkiv för Matematik 7 Proceedings of the Japan Academy. Series A 7 Bulletin of the American Mathematical Society. New Series 7 Journal of Mathematical Chemistry 7 Mediterranean Journal of Mathematics 6 The Annals of Probability 6 Functional Analysis and its Applications 6 Integral Equations and Operator Theory 6 Mathematische Nachrichten 6 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 Studies in Applied Mathematics 6 Probability Theory and Related Fields 6 Journal of the American Mathematical Society 6 Stochastic Processes and their Applications 6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 International Journal of Number Theory 6 Journal of Pseudo-Differential Operators and Applications 5 Acta Mathematica Academiae Scientiarum Hungaricae 5 Computing 5 Journal of the Mathematical Society of Japan 5 Journal of Statistical Planning and Inference 5 Statistics & Probability Letters 5 Journal of Symbolic Computation 5 Indagationes Mathematicae. New Series 5 Journal of Algebraic Combinatorics 5 Turkish Journal of Mathematics 5 Bulletin des Sciences Mathématiques 5 Infinite Dimensional Analysis, Quantum Probability and Related Topics 5 Central European Journal of Mathematics 5 Analysis and Applications (Singapore) 5 Journal of Applied Mathematics & Informatics 5 Analysis and Mathematical Physics 5 Problemy Analiza. Issues of Analysis 4 Applicable Analysis 4 Israel Journal of Mathematics ...and 295 more Serials all top 5 #### Cited in 61 Fields 1,227 Special functions (33-XX) 506 Harmonic analysis on Euclidean spaces (42-XX) 280 Combinatorics (05-XX) 244 Number theory (11-XX) 231 Approximations and expansions (41-XX) 221 Numerical analysis (65-XX) 191 Probability theory and stochastic processes (60-XX) 156 Real functions (26-XX) 139 Functions of a complex variable (30-XX) 131 Quantum theory (81-XX) 119 Partial differential equations (35-XX) 102 Difference and functional equations (39-XX) 94 Operator theory (47-XX) 90 Ordinary differential equations (34-XX) 88 Abstract harmonic analysis (43-XX) 86 Nonassociative rings and algebras (17-XX) 80 Functional analysis (46-XX) 79 Linear and multilinear algebra; matrix theory (15-XX) 75 Integral transforms, operational calculus (44-XX) 73 Statistics (62-XX) 60 Statistical mechanics, structure of matter (82-XX) 43 Topological groups, Lie groups (22-XX) 43 Sequences, series, summability (40-XX) 36 Group theory and generalizations (20-XX) 28 Computer science (68-XX) 27 Fluid mechanics (76-XX) 25 Potential theory (31-XX) 25 Several complex variables and analytic spaces (32-XX) 21 Algebraic geometry (14-XX) 20 Global analysis, analysis on manifolds (58-XX) 19 Dynamical systems and ergodic theory (37-XX) 17 History and biography (01-XX) 17 Integral equations (45-XX) 16 Associative rings and algebras (16-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Mechanics of deformable solids (74-XX) 13 Differential geometry (53-XX) 13 Operations research, mathematical programming (90-XX) 13 Biology and other natural sciences (92-XX) 11 Relativity and gravitational theory (83-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Information and communication theory, circuits (94-XX) 10 Systems theory; control (93-XX) 8 Manifolds and cell complexes (57-XX) 7 Commutative algebra (13-XX) 7 Convex and discrete geometry (52-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 5 Measure and integration (28-XX) 5 Geometry (51-XX) 5 Mechanics of particles and systems (70-XX) 4 Field theory and polynomials (12-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 General topology (54-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-12-05 10:38:43	{"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": 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": 0.5758930444717407, "perplexity": 2992.115421239318}, "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/1637964363157.32/warc/CC-MAIN-20211205100135-20211205130135-00320.warc.gz"}
https://nigerianscholars.com/tutorials/energy-and-chemical-reactions/surface-area-and-reaction-rates/	Chemistry » Energy and Chemical Reactions » Rates Of Reaction And Factors Affecting Rate # Surface Area and Reaction Rates ## Optional Experiment: Surface area and reaction rate Marble $$(\text{CaCO}_{3})$$ reacts with hydrochloric acid $$(\text{HCl})$$ to form calcium chloride, water and carbon dioxide gas according to the following equation: $$\text{CaCO}_{3}(\text{s}) + 2\text{HCl}(\text{l})$$ $$\to$$ $$\text{CaCl}_{2}(\text{s}) + \text{H}_{2}\text{O}(\text{l}) + \text{CO}_{2}(\text{g})$$ ### Aim To determine the effect of the surface area of reactants on the average rate of the reaction. ### Apparatus • $$\text{2}$$ $$\text{g}$$ marble chips, $$\text{2}$$ $$\text{g}$$ powdered marble, concentrated hydrochloric acid ($$\text{HCl}$$) • one beaker, two test tubes. ### Method #### Warning: Concentrated $$\text{HCl}$$ can cause serious burns. We suggest using gloves and safety glasses whenever you work with an acid. Remember to add the acid to the water and handle with care. 1. Prepare a solution of hydrochloric acid in the beaker by adding $$\text{2}$$ $$\text{cm^{3}}$$ of the concentrated acid to $$\text{20}$$ $$\text{cm^{3}}$$ of water. 2. Place the marble chips into one test tube and the powdered marble into a separate test tube. 3. Add $$\text{10}$$ $$\text{cm^{3}}$$ of the dilute hydrochloric acid to each of the test tubes and observe the rate at which carbon dioxide gas ($$\text{CO}_{2}$$) is produced (you should see bubbles of $$\text{CO}_{2}$$). ### Results Note (write down) what you observe. ### Questions and discussion • Which reaction proceeds faster? • Can you explain this? ### Conclusion The reaction with powdered marble is faster. The smaller the pieces of marble are (in this case the powdered form is smallest), the greater the surface area for the reaction to take place. Only the molecules at the surface of the solid can react with the hydrochloric acid. The next layer of molecules can only react once the surface molecules have reacted. That is, the next layer of molecules becomes the surface. The chips of marble are relatively large, so only a small percentage of the molecules are at the surface and can react initially. The powdered marble has much smaller solid pieces, so there are many more surface molecules exposed to the hydrochloric acid. The more molecules exposed on the surface (the greater the surface area) the faster the reaction will be. For the same amount of mass, smaller pieces of solid react faster as shown in Figure 7.2. a) A large particle, b) small particles with the same volume as the large particle. c) The surface area of large particles (shown in blue) is much smaller than that of small particles (shown in red). ### Optional Video: The Effect of Surface Area on Reaction Rate Calcium carbonate reacts with hydrochloric acid according to the following reaction: $$\text{CaCO}_{3}(\text{s}) + 2\text{HCl}(\text{aq})$$ $$\to$$ $$\text{CaCl}_{2}(\text{aq}) + \text{H}_{2}\text{O}(\text{l}) + \text{CO}_{2}(\text{g})$$ Consider the solid calcium carbonate. If we react $$\text{1}$$ $$\text{g}$$ of $$\text{CaCO}_{3}$$ we find that the reaction is faster if the $$\text{CaCO}_{3}$$ is powdered when compared with the $$\text{CaCO}_{3}$$ being large lumps. Explanation: The large lump of $$\text{CaCO}_{3}$$ has a small surface area relative to the same mass of powdered $$\text{CaCO}_{3}$$. This means that more particles of $$\text{CaCO}_{3}$$ will be in contact with $$\text{HCl}$$ in the powdered $$\text{CaCO}_{3}$$ than in the lumps. As a result, there can be more successful collisions per unit time and the reaction of powdered $$\text{CaCO}_{3}$$ is faster. $$\color{red}{\textbf{Increasing the surface area of the reactants increases the rate of the reaction.}}$$ The following video shows the effect of surface area on the time an effervescent tablet takes to fully dissolve. The tablet is fully dissolved once the bubbles ($$\text{CO}_{2}$$ gas) stop forming.	2021-12-09 04:50:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7167304754257202, "perplexity": 1331.6479212702452}, "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/1637964363659.21/warc/CC-MAIN-20211209030858-20211209060858-00267.warc.gz"}
https://eprint.iacr.org/2008/047	### Fair Traceable Multi-Group Signatures Vicente Benjumea, Seung Geol Choi, Javier Lopez, and Moti Yung ##### Abstract This paper presents fair traceable multi-group signatures (FTMGS), which have enhanced capabilities, compared to group and traceable signatures, that are important in real world scenarios combining accountability and anonymity. The main goal of the primitive is to allow multiple groups that are managed separately (managers are not even aware of the other ones), yet allowing users (in the spirit of the Identity 2.0 initiative) to manage what they reveal about their identity with respect to these groups by themselves. This new primitive incorporates the following additional features. - While considering multiple groups it discourages users from sharing their private membership keys through two orthogonal and complementary approaches. In fact, it merges functionality similar to credential systems with anonymous type of signing with revocation. - The group manager now mainly manages joining procedures, and new entities (called fairness authorities and consisting of various representatives, possibly) are involved in opening and revealing procedures. In many systems scenario assuring fairness in anonymity revocation is required. We specify the notion and implement it in the random oracle model. Available format(s) Category Cryptographic protocols Publication info Published elsewhere. Financial Cryptography 2008 (extended version of) Keywords digital signaturesgroup signaturestraceable signatures Contact author(s) sgchoi @ cs columbia edu History Short URL https://ia.cr/2008/047 CC BY BibTeX @misc{cryptoeprint:2008/047, author = {Vicente Benjumea and Seung Geol Choi and Javier Lopez and Moti Yung}, title = {Fair Traceable Multi-Group Signatures}, howpublished = {Cryptology ePrint Archive, Paper 2008/047}, year = {2008}, note = {\url{https://eprint.iacr.org/2008/047}}, url = {https://eprint.iacr.org/2008/047} } Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.	2022-08-16 04:26:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.1932390183210373, "perplexity": 12660.527511435757}, "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-2022-33/segments/1659882572220.19/warc/CC-MAIN-20220816030218-20220816060218-00262.warc.gz"}
https://math.stackexchange.com/questions/2144014/space-of-absolutely-convergent-fourier-series-and-density	# Space of absolutely convergent Fourier series and density It is possible to approximate a function $f$ on $[0,2\pi]$ by a continuous function whose derivative is zero almost everywhere (as can be seen here : Approximating a continuous function by one with zero derivative). My question is as follows: knowing that $\\|\cdot\\|_\infty \leq \\|\cdot\\|_{A(\mathbb{T})}$, is it possible to strenghten this result ? i.e. is it possible to approximate $f$ in the $\\|\cdot\\|_{A(\mathbb{T})}$ norm by a continuous function whose derivative is zero almost everywhere ? Here $\widehat{h}(n)$ denotes the $n$-th Fourier coefficient of $h$ and $$\\|h\\|_{A(\mathbb{T})} :=~ \sum\limits_{n \in \mathbb{Z}}\|\widehat{h}(n)\|.$$	2020-02-28 00:34:49	{"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": 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": 0.9963935613632202, "perplexity": 63.61063002076761}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146907.86/warc/CC-MAIN-20200227221724-20200228011724-00099.warc.gz"}
https://blog.csdn.net/JamesOldLU/article/details/112192197	# 一、个人的需求分析与建模读书心得 ## Function requirement ### 1)词语解说 {#词语解说 .list-paragraph} A Functional Requirement (FR) is a description of the service that the software must offer. It describes a software system or its component. A function is nothing but inputs to the software system, its behavior, and outputs. It can be a calculation, data manipulation, business process, user interaction, or any other specific functionality which defines what function a system is likely to perform. Functional Requirements are also called Functional Specification. ### Function requirement文档中应该包含什么 • Details of operations conducted in every screen 在每个屏幕上执行操作的详细情况 • Data handling logic should be entered into the system 数据处理逻辑应该输入到系统中 • It should have descriptions of system reports or other outputs 它应该有系统报告或其他输出的说明 • Complete information about the workflows performed by the system 关于系统执行的工作流的完整信息 • It should clearly define who will be allowed to create/modify/delete the data in the system 它应该清楚地定义谁将被允许在系统中创建/修改/删除数据 • How the system will fulfill applicable regulatory and compliance needs should be captured in the functional document 系统将如何满足适用的法规和法规遵从性需求应该在功能文件中得到体现 ### Functional Requirement（功能需求）的好处 • Helps you to check whether the application is providing all the functionalities that were mentioned in the functional requirement of that application 帮助您检查应用程序是否提供了该应用程序的功能需求中提到的所有功能 • A functional requirement document helps you to define the functionality of a system or one of its subsystems. 功能需求文档可以帮助您定义系统或其子系统之一的功能 • Functional requirements along with requirement analysis help identify missing requirements. They help clearly define the expected system service and behavior. 功能需求和需求分析有助于识别缺失的需求，它们有助于清楚地定义预期的系统服务和行为 • Errors caught in the Functional requirement gathering stage are the cheapest to fix. 在函数式需求收集阶段捕获的错误是最便宜的修复方法 • Support user goals, tasks, or activities 支持用户目标、任务或活动 1. ### Functional Requirement的类型 Here, are the most common functional requirement types 以下是最常见的功能需求类型 • Transaction Handling 交易处理 • Certification Requirements 认证规定 • Reporting Requirements 申报规定 • Authorization levels 授权级别 • Audit Tracking 审计跟踪 • External Interfaces 外部接口 • Historical Data management 历史数据管理 • Legal and Regulatory Requirements 法律及规管要求 ### 创建Functional Requirement（功能需求）时的错误 • Putting in unjustified extra information that may confuse developers 添加不合理的额外信息，可能会让开发人员感到困惑 • Not putting sufficient detail in the requirement document. 在需求文档中没有提供足够的详细信息 • You add rules or examples, scoping statements or objectives anything except the requirement itself. 您可以添加规则或示例、范围语句或目标，但需求本身除外 • Left out a piece of important information that is an absolute must to fully, accurately, and definitively state the requirement. 遗漏了一个重要的信息，这是绝对必须完全、准确和明确地陈述需求 • Some professionals start to defend the requirements they have documented when the requirement is modified, instead of finding the correct truth. 当需求被修改时，一些专业人员开始维护他们所记录的需求，而不是寻找正确的真相 • Requirements which are not mapped to an objective or principle. 没有映射到目标或原则的需求 ## Data flow diagram ### 词语解说： Data flow diagram or data flow diagram, abbreviated as DFD. Data flow diagram (DFD) is a graphic tool to describe the data flow in a system. It marks the logical input and output of a system, as well as the processing needed to convert the logical input to the logical output. 1. ### 什么是data flow diagram The technical definition of this technique from the International Institute of Business Analysis (IIBA®) is: “Data flow diagrams show where data comes from, which activities process the data, and if the output results are stored or utilized by another activity or external entity.” – BABOK® v3.0 These types of diagrams simply depict the sources of data, what happens to the data, and where it goes to be used. 2. ### Data flow diagram能描述什么 • Source – where the data comes from • Activities – what happens to the data • Inputs/Outputs – what goes in, and what comes out • Transformations – any changes that take place to the data • Temporary or permanent repository locations – where the data lives • 数据来源 • 活动------数据发生了什么变化 • 输入/输出-什么进去，什么出来 • 转换------对数据发生的任何更改 • 临时或永久存储库位置------数据所在的位置 ### 为什么要使用data flow diagram • Logical information flow of the system 系统的逻辑信息流 • Determination of physical system construction requirements 物理系统结构要求的确定 • Simplicity of notation 简单的符号 • Establishment of manual and automated systems requirements 建立手动和自动系统要求 • 系统的逻辑信息流 • 物理系统结构要求的确定 • 简单的符号 • 建立手动和自动系统要求 1. ### Data flow diagram的符号 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-dD6y3IEE-1609755291765)(media/image1.png)]{width=“3.0388888888888888in” height=“4.233333333333333in”} 2. ### 数据流图的使用数据流图也称为气泡图。DFD是系统设计自上而下方法中使用的一种设计工具。这个上下文级别的DFD接下来是"爆炸式"的，以产生一个1级的DFD，显示正在建模的系统的一些细节。Level 1 DFD显示了系统如何分成子系统（过程），每个系统处理一个或多个来自或来自外部代理的数据流，它们一起提供系统的所有功能整个。它还识别必须存在的内部数据存储库，以便系统执行其工作，并显示系统各个部分之间的数据流。在开发一组的过程中整平数据流图分析员/设计者被迫处理系统可以如何被分解为分量的子系统，以及标识的交易数据中的数据模型。 3. ### 分层DFD与原则 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-9QYQeyc1-1609755291766)(media/image2.png)]{width=“5.7659722222222225in” height=“3.6930555555555555in”} • 根据层级数据流图分为顶层数据流图、中层数据流图和底层数据流图。除顶层数据流图外，其他数据流图从零开始编号。 • 顶层数据流图只含有一个加工表示整个系统；输出数据流和输入数据流为系统的输入数据和输出数据，表明系统的范围，以及与外部环境的数据交换关系。 • 中层数据流图是对父层数据流图中某个加工进行细化，而它的某个加工也可以再次细化，形成子图；中间层次的多少，一般视系统的复杂程度而定。 • 底层数据流图是指其加工不能再分解的数据流图，其加工称为"原子加工"。 ### [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-IvJU6od8-1609755291768)(media/image3.png)]{width=“5.188888888888889in” height=“3.1284722222222223in”} • 一个加工的输出数据流不应与输入数据流同名，即使它们的组成成分相同。 • 保持数据守恒。也就是说，一个加工所有输出数据流中的数据必须能从该加工的输入数据流中直接获得，或者说是通过该加工能产生的数据。 • 每个加工必须既有输入数据流，又有输出数据流。 • 所有的数据流必须以一个外部实体开始，并以一个外部实体结束。 • 外部实体之间不应该存在数据流 1. ### 理解与应用对于dataflow dirgram（数据流图），我的理解是通过数据流图，软件设计师可以自顶而下的分析系统的信息流程、在图上确定需要计算机处理的部分、向数据库设计过渡、根据数据流向确定存取方式、能够确定一个处理过程。而在测试过程中，数据流图可以方便、直接的帮助程序员查找到错误的发生位置。需求分析阶段，为了获得一个对新系统的框架认识、概念性认识，需要对新系统建模。而用图形表示需求，就是需求建模，获得分析模型。需求分析方法中的结构化分析方法的特点是利用数据流图来帮助人们理解问题，对问题进行分析。画数据流图时一要确定系统的输入输出，由于系统究竟包括哪些功能可能一时难于弄清楚，可使范围尽量大一些，把可能有的内容全部都包括进去。此时，应该向用户了解"系统从外界接受什么数据"、"系统向外界送出什么数据"等信息，然后，根据用户的答复画出数据流图的外围。二要由外向里画系统的顶层数据流图，首先，将系统的输人数据和输出数据用一连串的加工连接起来。在数据流的值发生变化的地方就是一个加工。接着，给各个加工命名。然后，给加工之间的数据命名。最后，给文件命名。三要自顶向下逐层分解，绘出分层数据流图对于大型的系统，为了控制复杂性，便于理解，需要采用自顶向下逐层分解的方法进行，即用分层的方法将一个数据流图分解成几个数据流图来分别表示。例如我们小组的实验室设备管理系统项目，其中涉及到许多数据的流动，就可以通过画数据流图的办法进行分析，像实验室设备的管理，对于实验室一个设备的信息，在报修时需要进行传输数据，去向管理员子系统的报修管理表中等等。 ## Acceptance Test 1. ### 词语解说 Acceptance testing, a testing technique performed to determine whether or not the software system has met the requirement specifications. The main purpose of this test is to evaluate the system’s compliance with the business requirements and verify if it is has met the required criteria for delivery to end users. 验收测试，一种测试技术，用于确定软件系统是否满足需求规范。这项测试的主要目的是评估系统是否符合业务要求，并核实系统是否符合向最终用户交付的必要标准。 ## [https://www.softwaretestinghelp.com/what-is-acceptance-testing/]{.ul}[https://www.tutorialspoint.com/software_testing_dictionary/acceptance_testing.htm#:~:text=What%20is%20Acceptance%20Testing%3F%20Acceptance%20testing%2C%20a%20testing,the%20required%20criteria%20for%20delivery%20to%20end%20users.]{.ul}[https://searchsoftwarequality.techtarget.com/definition/acceptance-test]{.ul} ### 验收测试的多种形式 • User acceptance Testing用户验收测试 • Alpha Testing测试 • Beta Testing测试版 1. ### 验收准则 Acceptance criteria are defined on the basis of the following attributes 验收标准是根据以下属性定义的： Functional Correctness and Completeness函数的正确性和完整性 Data Integrity数据完整性 Data Conversion数据转换 Usability可用性 Performance工作表现 Timeliness及时性 Confidentiality and Availability机密性和可用性 Scalability可扩展性 Documentation文件 2. ### ATDD和TDD的区别是什么？ “ATDD”，全称"Acceptance Test Driven Development “，中文称"验收测试驱动开发”。ATDD和TDD的区别是什么呢，查了一些资料，我的理解如下： Test-driven development (TDD) is a [software development process]{.ul} that relies on the repetition of a very short development cycle: first the developer writes an (initially failing) automated [test case]{.ul} that defines a desired improvement or new function, then produces the minimum amount of code to pass that test, and finally [refactors]{.ul} the new code to acceptable standards. TDD只涉及到Developer（开发者），只能算个人工作方式的改变。而现代软件开发，往往都是"产品经理（或业务）、测试人员（或QA）、开发人员"三者合作的成果，如果开发人员对业务需求理解的不正确，那么写出的测试用例也是错的，这个问题是TDD解决不了的。中文Wikipedia上对于TDD缺点的描述，也把这一问题列在第一位： [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-d0r1XkYb-1609755291770)(media/image4.png)]{width=“5.995138888888889in” height=“2.1041666666666665in”} ATDD又如何解决这个问题呢？《Explore It!: Reduce Risk and Increase Confidence with Exploratory Testing》这本书的作者Elisabeth Hendrickson给出了下面的解释： Acceptance Test Driven Development (ATDD) is a practice in which the whole team collaboratively discusses acceptance criteria, with examples, and then distills them into a set of concrete acceptance tests before development begins. It’s the best way I know to ensure that we all have the same shared understanding of what it is we’re actually building. It’s also the best way I know to ensure we have a shared definition of Done. 1. ### 理解与应用验收测试(Acceptance Test)：在软件产品完成了功能测试和系统测试之后、产品发布之前所进行的软件测试活动。它是技术测试的最后一个阶段，也称为交付测试。验收测试的目的：确保软件准备就绪，并且可以让最终用户将其用于执行软件的既定功能和任务。验收测试的参与者：用户，还可能有软测工程师等。 ## Change control board ### 词语解说 The phrase change review board (also known by the acronym CCB) refers to any group of individuals within a project team or project group who are responsible for making the ultimate decision as to when and if any particular changes are to be made in regards to work products or schedule events. 1. ### Change Control Board (CCB)变更控制委员会 The process in which the Change Control Board determines when and if a series of changes should be made is two fold. First, the Change Control Board needs to review and study the impact of the proposed changes on the items in question, and then, after making that evaluation, the Change Control Board can then either approve the changes, reject the changes, or, in some cases, request more information or postpone the decision pending some other occurrences to take place that would factor into their ultimate choice. Significant changes that will in fact affect baselines are almost always put through the CCB for approval. 变更控制委员会决定何时以及是否应该进行一系列变更的过程有两个方面。首先，变更控制委员会需要审查和研究拟议的变更对有关项目的影响，然后，在进行评估之后，变更控制委员会可以批准变更、拒绝变更，或者在某些情况下要求提供更多信息或推迟作出决定，直到发生一些将成为其最终选择因素的其他事件。实际上会影响基线的重大更改几乎总是通过建设银行提交审批。这个术语在 PMBOK 的第三版和第四版中定义。 2. ### 配置管理（Configuration Management）通过技术或行政手段对软件产品及其开发过程和生命周期进行控制、规范的一系列措施。配置管理的目标是记录软件产品的演化过程，确保软件开发者在软件生命周期中各个阶段都能得到精确的产品配置。 1. ### 实施实施配置管理系统，一般的步骤和需要考虑的问题如下：规划、调整网络开发环境一个规划良好的开发环境，是实施配置管理系统的前提。在此阶段，要对配置管理系统做出规划，主要考虑以下问题：网络的带宽、拓扑结构服务器的选择、命名规范存储区的定位开发人员及组的命名规约等设计配置管理库根据项目开发的要求，设计开发资源的存储模式，良好的存储模式有利于减轻管理上的负担，增强配置管理库的访问性能，同时便于控制访问权限，保护软件资产。定义配置管理系统的角色在此阶段，需要确定与配置管理相关的所有角色，包括他所有角色相应的活动。在开发过程中，一个开发人员可能兼任多种角色，但一项任务在同一时刻只能由一个角色来执行。一般配置管理中的角色主要包括：项目经理：项目经理在配置管理方面的职责是依靠配置管理员、系统管理员和系统体系结构设计人员的帮助，制定项目的组织结构和配置管理策略。这些工作包括：定制开发子系统，定制访问控制，制定常用策略，制定集成里程碑，以及进行系统集成。配置管理员：配置管理员的职责是根据项目经理制定的开发组织结构和策略，实施、维护配置管理的环境。其主要职责如下：创建配置管理库，对存储库进行日常备份和恢复，维护配置管理环境，及管理配置管理相关的用户。软件开发人员：软件开发人员依据项目的开发和配置管理策略，创建、修改和测试开发工件。集成人员：对软件进行归并，形成相应的基线或发布版本。 QA人员：需要对软件配置管理有较深的认识，其主要工作是跟踪当前项目的状态，测试，报告错误，并验证其修复结果。制定配置管理流程这是配置管理实施的一个重要阶段，其主要目的是根据项目开发的需要，制定相应的配置管理流程，以更好地支持开发，主要活动包括：定制并行开发策略：合理的并行开发策略应该具有以下特点：协调项目的复杂性和需求，统一创建分支类型和元数据，为开发过程中的变更集成制定有效的规范，适时反映开发过程中方法和需求的变化。发布版本管理：软件开发过程中的一个关键活动是提取工件的相关版本，以形成软件系统的阶段版本或发布版本，我们一般将其称为稳定基线。一个稳定基线代表新开发活动的开始，而一系列定制良好的活动之后又会产生一个新的稳定基线。有效地利用此项功能，在项目开发过程中可以自始至终管理、跟踪工件版本间的关联。一般来讲，实施配置管理系统，相关人员需要接受以下培训：管理员培训：针对配置管理员，主要学习配置管理工具管理相关内容。开发人员培训：针对开发人员，主要学习配置管理工具与开发相关的常用操作。管理流程培训：针对全体人员，目的是了解配置管理策略和流程，以及如何与开发管理、项目管理相结合。 2. ### 理解与应用 CMDB --（Configuration Management Database，配置管理数据库）, CMDB存储与管理企业IT架构中设备的各种配置信息，它与所有服务支持和服务交付流程都紧密相联，支持这些流程的运转、发挥配置信息的价值，同时依赖于相关流程保证数据的准确性。注意：Saltstack和puppet是配置管理，不是配置管理数据库，注重配置过程。在实际的项目中，CMDB常常被认为是构建其它ITIL流程的基础而优先考虑，ITIL项目的成败与是否成功建立CMDB有非常大的关系。 70%～80%的IT相关问题与环境的变更有着直接的关系。实施变更管理的难点和重点并不是工具，而是流程。即通过一个自动化的、可重复的流程管理变更，使得当变更发生的时候，有一个标准化的流程去执行，能够预测到这个变更对整个系统管理产生的影响，并对这些影响进行评估和控制。而变更管理流程自动化的实现关键就是CMDB。 ## Performance requirement 1. ### 词语解说 A requirement describing a performance characteristic (timing, speed, volume, capacity, throughput…).Is regarded in this glossary as a sub-category of quality requirements, but can also be considered as a non-functional requirements category 描述性能特征（时间、速度、体积、容量、吞吐量…）的要求在本术语表中被视为质量要求的子类别，但也可以视为非功能需求类别 1. ## Performance requirement的描述 In identifying and quantifying performance requirements, it is important to identify the reasoning behind a particular requirement. This is part of the general capacity planning process. Users might be basing their statements of requirements on assumptions about the logic of the program that do not match the programmer’s assumptions. 在识别和量化性能需求时，确定特定需求背后的推理是很重要的。这是总体容量规划过程的一部分。用户的需求陈述可能是基于程序逻辑的假设，而这些假设与程序员的假设不符。 At a minimum, a set of performance requirements should document the following: The maximum satisfactory response time to be experienced most of the time for each distinct type of user-computer interaction, along with a definition of most of the time. Response time is measured from the time that the user performs the action that says “Go” until the user receives enough feedback from the computer to continue the task. It is the user’s subjective wait time. It is not from entry to a subroutine until the first write statement. If the user denies interest in response time and indicates that only the result is of interest, you can ask whether “ten times your current estimate of stand-alone execution time” would be acceptable. If the answer is “yes,” you can proceed to discuss throughput. Otherwise, you can continue the discussion of response time with the user’s full attention. 一套性能要求至少应记录以下内容：对于每种不同类型的用户-计算机交互，在大多数时间内所经历的最大令人满意的响应时间，以及大多数时间的定义。响应时间是从用户执行"执行"操作的时间开始计算的，直到用户从计算机收到足够的反馈以继续执行任务。它是用户的主观等待时间。在第一个write语句之前，它不是从入口到子例程的。如果用户否认对响应时间感兴趣，并指出只有结果感兴趣，那么您可以询问"十倍于当前估计的独立执行时间"是否可以接受。如果答案是"是"，您可以继续讨论吞吐量。否则，你可以在用户的充分关注下继续讨论。 The response time that is minimally acceptable the rest of the time. A longer response time can cause users to think the system is down. You also need to specify rest of the time; for example, the peak minute of a day, 1 percent of interactions. Response time degradations can be more costly or painful at a particular time of the day. The typical throughput required and the times it will be taking place. This is not a casual consideration. For example, the requirement for one program might be that it runs twice a day: at 10:00 a.m. and 3:15 p.m. If this is a CPU-limited program that runs for 15 minutes and is planned to run on a multiuser system, some negotiation is in order. The size and timing of maximum-throughput periods. The mix of requests expected and how the mix varies with time. The number of users per machine and total number of users, if this is a multiuser application. This description should include the times these users log on and off, as well as their assumed rates of keystrokes, completed requests, and think times. You may want to investigate whether think times vary systematically with the preceding and following request. Any assumptions that the user is making about the machines the workload will run on. If the user has a specific existing machine in mind, make sure you know that early on. Similarly, if the user is assuming a particular type, size, cost, location, interconnection, or any other variable that will constrain your ability to satisfy the preceding requirements, that assumption also becomes part of the requirements. Satisfaction will probably not be assessed on the system where the program is developed, tested, or first installed. 其余时间内可接受的最小响应时间。较长的响应时间会导致用户认为系统已关闭。您还需要指定其余时间；例如，一天中的高峰分钟，交互的1%。在一天中的某个特定时间，响应时间的降低可能更昂贵或更痛苦。所需的典型吞吐量及其发生的时间。这不是一个偶然的考虑。例如，对一个程序的要求可能是一天运行两次：上午10:00和下午3:15。如果这是一个CPU有限的程序，运行时间为15分钟，计划在多用户系统上运行，则需要进行一些协商。最大吞吐量周期的大小和时间。预期的请求组合以及组合如何随时间变化。每台机器的用户数和用户总数（如果这是多用户应用程序）。这个描述应该包括这些用户登录和注销的时间，以及他们假定的击键率、完成的请求和思考时间。您可能需要调查思考时间是否随前一个请求和后一个请求而有系统地变化。用户对运行工作负载的机器所做的任何假设。如果用户想要一台特定的现有机器，请确保尽早知道这一点。类似地，如果用户假设某个特定的类型、尺寸、成本、位置、互连或任何其他变量将限制您满足上述要求的能力，则该假设也将成为需求的一部分。在开发、测试或首次安装程序的系统上，可能不会评估满意度。 2. ### 如何获取性能需求客户方提出客户方能提出明确的性能需求，说明对方很重视性能测试，这样的企业一般是金融、电信、银行、医疗器械等；他们一般对系统的性能要求非常高，对性能也非常了解。提出需求也比较明确。曾经有一个银行项目，已经到最后的性能测试极端，因为数据库设计不合理，导致性能出现很大的问题，最终不得不把整合项目作废，对于这样的项目，其实从分析设计阶段就应该考虑系统的性能问题。性能测试也一样，对于某些项目来说越早进行越好。当然，前期的性能测试为单元性能测试、接口性能测试，有别系统性能测试。根据历史数据分析对于一些面向用户的独特产品，比较难定位市场的大小，可以先上一运营一段时间，通过运营可以搜集客户资料，比如，每月、每星期、每天的峰值业务量是多少。用户以什么样的速度在递增中。用户对系统的哪些功能模块使用的最多，他们所点的比例等等。收集到这些数据之后，我们就可评估系统的系统需求指标，从而进行性能测试。需求分析与定位这里根据前期的需求分析与定位，来分析确定系统性能指标。例如某省幼儿园管理系统。统计全省有多少家幼儿园，系统的使用时间为幼儿到校之后，管理人员对幼儿的到校情况进行录入，以及幼儿的午饭，放学情况的录入时间。经过与需求人员交流分析也能得到比较明确的性能指标。参考历史项目或其它同行业的项目如果公司之前有类似的项目经验，根据项目大小及上次性能测试的一些指标。从根据项目的规模可以制定出相应的性能指标。即使本公司没有类似的项目，但其它公司有类似的项目，例如做IPTV或者DVB计费系统的测试，可以参考电信计费系统的需求------虽然不能完全照搬数据，但是可以通过其他行业成熟的需求来了解需要测试的项目有哪些，应该考虑到的情况有哪些种。参考其它资料数据如果你做的是非常独特的产品，市场上没有此类型的产品，而且需求及市场也难以估计，那么只能从与产品相关的资料中寻找痕迹了。不过，相信这样不确定性的产品，老板要承担的风险也是挺大的。需要说明的是，我上面介绍的方面并非是独立的，可以综合的使用，你可以根据客户提出的指标，再根据历史数据以及参考同类型项目来进行。这样可以更确定你的性能指标是客户（或自己）真正需要的、最符合项目需求的。 3. ### 理解与应用对于我们所设计的系统来说，性能上的需求是必不可少的，若是没有性能上的需求，设计出来的系统可能是无法使用的，在设计实验室设备管理系统的时候，要充分考虑系统的数据类型支持，数据量支持，以及系统的并发性等等性能上的需求。 ## Software requirements specification 1. ### 词语解说 SRS is a specification for a specific software product, program or group of programs that performs a defined function in a specific environment. SRS can be written by one or more personnel from the supplier, customer or both parties, and it is recommended that the personnel of both parties jointly prepare. SRS是对在具体环境中执行确定功能的特定软件产品、程序或一组程序的规格说明。 SRS可由来自供方、顾客或双方的一个或多个人员来编写，推荐双方人员联合编写。 ## [https://www.bmc.com/blogs/software-requirements-specification-how-to-write-srs-with-examples/]{.ul}[https://www.microtool.de/en/knowledge-base/what-is-a-software-requirements-specification/]{.ul}[https://www.perforce.com/blog/alm/how-write-software-requirements-specification-srs-document]{.ul} 1. ### 描述软件需求规格文档包含： • 硬件 • 功能 • 性能 • 输入输出 • 接口需求 • 警示信息 • 保密安全 • 数据与数据库 • 文档说明 • 法规说明软件需求规格说明文档的产生阶段 • 对业务需求的定义和文档化，形成了前景和范围文档 • 对用户需求的定义和文档化，形成了用户需求文档，其中以用例说明书最常见 • 在得到用户需求后，需求工程师对其建模和分析，细化为系统需求，并建立满足系统需求的解决方案，对系统需求、解决方案的定义和文档化产生了系统需求规格说明文档 • 软件需求规格说明文档的产生阶段：对系统需求、解决方案的定义和文档化阶段需求开发过程中的常见文档： [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-ux67uKmf-1609755291772)(media/image5.png)]{width=“5.763194444444444in” height=“4.774305555555555in”} 需求规格说活动过程第一，选择文档模板第二，裁剪文档模板大三，文档写作第四，产生软件需求规格文档需求规格说文档编写目的; • 可以帮助记忆 • 帮助发现需求存在的问题 • 记录系统解决方案 • 为后续活动的依据 • 为协议基准，可以作为合同的一部分，有法律效应需求说明文档常见读者群体： • 项目管理者 • 设计人员和程序员 • 测试人员 • 文档写作的特点 • 完整性 • 一致性 • 可修改性 • 可跟踪性 • 可阅读性 • 可维护性 • 无二义性运行和维护阶段的可使用性 • 文档化的主要目标是：交流 • 文档写作的注意事项：明确文档编写目的 • 按照写作模板写作 • 格式规范 1. ### 理解与应用 SRS(Software Requirements Specification)软件需求说明书的编制是为了使用户和软件开发者双方对该软件的初始规定有一个共同的理解，使之成为整个开发工作的基础。包含硬件、功能、性能、输入输出、接口界面、警示信息、保密安全、数据与数据库、文档和法规的要求。说明编写这份软件需求说明书的目的，指出预期的读者。软件需求说明书的作用在于便于用户、开发人员进行理解和交流，反映出用户问题的结构，可以作为软件开发工作的基础和依据，并作为确认测试和验收的依据。 SRS(Software Requirements Specification)软件需求说明书也是本学期软件需求分析与建模课程学习的重点，经过系统的学习，将项目开发以软件需求说明书的形式展现给各种与项目相关的角色看，有利于沟通与交流，并且作为系统最终验收的依据 ## Steering committee 1. ### 词语解说 A steering committee is an advisory body that’s part of IT—or other—governance. Members include experts, authority figures, and senior stakeholders in a project or organization. 程序委员会是一个咨询机构，是 it (或其他)治理的一部分。成员包括项目或组织中的专家、权威人士和高级利益相关者。 2. ## 词语链接 ### 定义，作用描述 A steering committee is an advisory body that’s part of IT—or other—governance. Members include experts, authority figures, and senior stakeholders in a project or organization. As a result, they have a significant stake in how each project is managed. Thus, key concerns for steering committees are the direction, scope, budget, timeliness, and methods used. Steering committees generally meet periodically to discuss each of these aspects and help set, or reset, direction. Members of the steering committee don’t usually perform the work they prescribe. Instead, senior managers or executives, important external stakeholders, and experts usually make up the committee. The particular makeup of each steering committee depends on the scope. For example, a project steering committee may involve the project manager and external stakeholders from customers. Meanwhile, an organizational steering committee may be made up of executives, certain board members, and department heads. While the actual makeup of each steering committee may vary slightly, there are a few guidelines to keep in mind. Arguably most important, there should be a chairperson. The chairperson should be elected by the rest of the committee and should not own the project the committee is steering. This allows for more impartial chairing. In addition, the steering committee should be made up of diverse members. Moreover, these members should equally represent the various functions the steering committee oversees. This allows for the sharing of different opinions and ideas. In parallel, the committee must allow for open discussion so that each opinion can be heard and assessed. Finally, it must have clear goals and a well-managed agenda. A steering committee is an advisory group that makes directional decisions on various organizational projects. Its members directly support project managers working toward strategic company directions. In practice steering committees also do the following: • Act as an advocate for initiatives and projects across the wider organization 在更广泛的组织中充当计划和项目的倡导者 • Set the strategic direction of projects 制定项目的战略方向 • Provide advice or direct input on budgeting, including assets (such as people), money, facilities, time, hiring, and marketing 在预算方面提供建议或直接投入，包括资产(如人员)、资金、设施、时间、招聘和市场营销 • Establish project goals and scope as well as determine how success will be measured 建立项目目标和范围，并确定如何衡量成功 • Assess and approve or reject project plans and changes to project plans 评估和批准或拒绝项目计划和对项目计划的更改 • Select project managers and experts to support projects 选择项目经理和专家来支持项目 • Prioritize and reprioritize project deliverables 对项目可交付成果进行优先排序和重新排序 • Monitor project processes and plans 监控项目过程和计划 • Resolve conflicts between parties 解决双方之间的冲突 • Come up with ideas for strategy and problem solving 想出策略和解决问题的办法 • Provide expert input on concerns and issues related to projects or the overall business 就项目或整体业务相关的关注点和问题提供专家意见 • Develop policies and governance procedures 制定政策和管理程序 • Identify, monitor, and eliminate project and business risks 识别、监控和消除项目和业务风险 • Monitor project quality and adjust accordingly 监控项目质量并做出相应调整 Considering the range of functions steering committees provide, it might seem quite clear that they can increase business and project value. When working well, steering committees increase value by keeping projects on track, budgets in check, risks mitigated, and conflicts resolved. The fact that all of this happens apart from daily operations means the value gain is accentuated. 考虑到指导委员会提供的职能范围，似乎很明显，它们可以增加业务和项目价值。当运作良好时，指导委员会通过保持项目在正轨上、预算在可控范围内、风险得到缓解、冲突得到解决来增加价值。事实上，除了日常操作以外，所有这一切都意味着价值增值更加突出。 However, there’s a fine line between successful governance practices that increases value and bureaucratic governance practices that waste time and lead to poor decisions. Assuming a steering committee has followed the guidelines of having a chairperson, diverse members, and openness with clear goals, it’s a matter of what goes in that determines what comes out. Therefore, data is arguably the biggest contributor to value gain. 然而，在增加价值的成功治理实践和浪费时间并导致糟糕决策的官僚治理实践之间有一条细微的界限。假设一个指导委员会已经遵循了有一个主席，多样化的成员和明确目标的开放性的指导方针，那么决定结果的是什么。因此，数据可以说是价值增值的最大贡献者。 1. ### 理解与应用为了从指导委员会获得最大的价值，数据是有意义和可理解的是至关重要的。错误或难以理解的数据可能危及指导委员会及时作出知情决定的能力。另一方面，可用数据便于清晰的通信，并正确地表示事件的当前状态。这就提出了一个问题: 如何确保正确的数据被送到指导委员会？广义地说，业务智能是收集、存储和分析组织活动以生成报告、确定趋势和衡量性能的实践。商业智能的唯一功能是改进管理决策并为其提供信息。这是天造地设的一对。实施业务情报做法使公司能够自动或定期生成可供指导委员会查看的报告和仪表板。这些报告和仪表板几乎肯定包含有意义的数据，因为它们可以用指导委员会定义为重要的指标填充。所有这些都有助于更好地了解项目和进展情况，使指导委员会能够明确沟通，及时作出正确决定。 ## System context 1. ### 词语解说 The system context diagram (also known as a level 0 DFD) is the highest level in a data flow diagram and contains only one process, representing the entire system, which establishes the context and boundaries of the system to be modeled. 系统关系图系统(也称为0级 DFD)是资料流程图系统中的最高级别，只包含一个进程，代表整个系统，它建立了要建模的系统的上下文和边界。 1. ### 定义，作用描述 The system context diagram (also known as a level 0 DFD) is the highest level in a data flow diagram and contains only one process, representing the entire system, which establishes the context and boundaries of the system to be modeled. It identifies the flows of information between the system and external entities (i.e. actors). A context diagram is typically included in a requirements document. It must be read by all project stakeholders and thus should be written in plain language, so the stakeholders can understand items 系统关系图系统(也称为0级 DFD)是资料流程图系统中的最高级别，只包含一个进程，代表整个系统，它建立了要建模的系统的上下文和边界。它识别系统和外部实体(即参与者)之间的信息流。上下文关系图通常包含在需求文档中。它必须被所有项目干系人阅读，因此应该用通俗易懂的语言来写，这样干系人才能理解项目 The objective of the system context diagram is to focus attention on external factors and events that should be considered in developing a complete set of systems requirements and constraints. A system context diagram is often used early in a project to determine the scope under investigation. Thus, within the document. 系统关系图的目标是关注在开发一套完整的系统需求和约束时应该考虑的外部因素和事件。在项目的早期，系统关系图通常被用来确定被调查的范围。因此，在文档中。 A system context diagram represents all external entities that may interact with a system. The entire software system is shown as a single process. Such a diagram pictures the system at the center, with no details of its interior structure, surrounded by all its External entities, interacting systems, and environments. 系统关系图代表所有可能与系统交互的外部实体。整个软件系统显示为一个单独的过程。这样的图表把系统画在中心，没有内部结构的细节，被所有的外部实体、交互系统和环境所包围。 2. ### 理解与应用系统关系图代表与系统交互的所有可能的外部实体与系统的关系，我们小组的实验室设备管理系统就可以通过系统关系图，将管理员，教师，学生，设备这些外部实体与系统相连构成系统关系图 ## UML ### 1）词语解说 Unified Modeling Language (UML)又称统一建模语言或标准建模语言。 1. ### 定义，作用，目的描述 UML 能帮我们做什么？我们在进行项目的时候，通过使用 UML 的面向对象图的方式来更明确、清晰的表达项目中的架设思想、项目结构、执行顺序等一些逻辑思维。 UML 介绍： 1997年，OMG 组织（Object Management Group对象管理组织）发布了统一建模语言（Unified Modeling Language，UML）。UML 是一种编制软件蓝图的标准化语言，它的目标之一就是为开发团队提供标准通用的设计语言来开发和构建计算机应用。UML 提出了一套 IT 专业人员期待多年的统一的标准建模符号。通过使用UML，这些人员能够阅读和交流系统架构和设计规划。UML支持面向对象的技术，能够准确的方便地表达面向对像的概念，体现面向对象的分析和设计风格. UML 统一了Booch、OMT、OOSE和其他面向对象方法所涉及的基本概念和建模符号。 UML的模型主要有三部分构成： • 事物(Things)：UML模型中最基本的构成元素，是具有代表性的成分的抽象 • 关系(Relationships)：关系把事物紧密联系在一起 • 图(Diagrams )：图是事物和关系的可视化表示 UML 特点： • 面向对象 • 可视化，表达能力强 • 独立于过程 • 独立于程序设计 • 容易掌握使用 1. ### 理解与应用在复杂需求中，UML图是非常必要的。用例图描述系统的外部交互、序列图描述系统的内部交互、状态图描述系统的动态特性、部署图描述系统的物理节点、类图与对象图描述依赖关系…所有的图都是协助团队策划稿能源更高效地厘清问题，掌握知识，高效解决问题的。试问下，在敏捷开发中，如果没有流程图、序列图、状态图进行辅助，你如何在代码过程中保证业务流程、系统前后端、多个系统切换开发做到敏捷高效？在敏捷开发时，面对稍复杂点的需求，如果要求团队提前用UML图厘清问题，后续填坑可以少很多。 ## Class model ### 词语解说 A class is just a model like thing, which defines which members a class has and defines a class that does not allocate actual memory space to store it ## [https://www.excelsoftware.com/classmodel]{.ul}[https://www.sparxsystems.com/resources/tutorials/uml/logical-model.html#:~:text=The%20Class%20Model%20is%20at%20the%20core%20of,and%20offers%20services%20to%20manipulate%20that%20state%20%28behavior%29.]{.ul}[https://www.wallstreetmojo.com/vba-class-modules/]{.ul} ### 定义，作用，目的描述类的定义是：类是具有相似结构、行为和关系的一组对象的描述符。类是面向对象系统中最重要的构造块。类图显示了一组类、接口、协作以及他们之间的关系。在UML中问题域最终要被逐步转化，通过类来建模，通过编程语言构建这些类从而实现系统。类加上他们之间的关系就构成了类图，类图中还可以包含接口、包等元素，也可以包括对象、链等实例。接口在类图中通过版型来表示\<\<interface\>\>，下面的介绍将主要介绍类，接口和类类似。 enterprise archirct11 类图中的元素都是从Toolbox中拖到class model 视图中的 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-VVIPr6Hr-1609755291774)(media/image6.png)]{width="2.9166666666666665in" height="3.2395833333333335in"} UML 类图之package(包) [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-x7WICCsJ-1609755291774)(media/image7.png)]{width=“3.4375in” height=“2.125in”} UML类图之接口(Interface) [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-EKNbrr2T-1609755291775)(media/image8.png)]{width=“5.428472222222222in” height=“3.5729166666666665in”} [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-l9l0s1zw-1609755291776)(media/image9.png)]{width=“1.46875in” height=“1.5729166666666667in”} [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-p3qmQAz1-1609755291777)(media/image10.png)]{width=“6.572916666666667in” height=“5.3125in”} Attributes:属性 Operations：操作、方法 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-WRJqbdfL-1609755291778)(media/image11.png)]{width=“4.811805555555556in” height=“4.217361111111111in”} Parameters：方法参数 return:返回值 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-6hjcUhko-1609755291779)(media/image12.png)]{width=“1.46875in” height=“1.5729166666666667in”} Interface在图上有《interface》标识，而Class没有标识。 UML类图之类(Class) ‍ class中可以包含属性(特征)、方法(动作) [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-XAYsu7W0-1609755291780)(media/image13.png)]{width=“1.5104166666666667in” height=“3.0in”} UML类图元素之间的关系 ‍ Realization(实现)‍ 类实现了接口(Aniamal动物可以吃东西，那么就实现了Eatable接口) Realization(实现)表示方式为: 空心三角+虚线空心三角指向的是接口虚线连接的是实现该接口的类 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-MNs8e3w2-1609755291781)(media/image14.png)]{width=“1.4791666666666667in” height=“3.125in”} Generalization(泛化) Generalization(泛化)表示方式为: 空心三角+实现 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-iBtloxfn-1609755291782)(media/image15.png)]{width=“2.5729166666666665in” height=“2.25in”} Dependency(依赖) Dependency(依赖)表示方式为: 箭头+虚线 Student，Teacher 类中的learn和teach方法，都需要参数类型为Book [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-KMkVTNWh-1609755291783)(media/image16.png)]{width=“3.4166666666666665in” height=“4.40625in”} Aggregation(聚合) Aggregation(聚合)的表示方式: 空心菱形＋实线，空心菱形指向整体 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-xolT5Ers-1609755291783)(media/image17.png)]{width=“1.46875in” height=“2.875in”} Composition(组合) Composition(组合)的表示方法: 实心菱形＋实线　实心菱形指向整体 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-VpsdtNvx-1609755291784)(media/image18.png)]{width=“1.46875in” height=“2.7604166666666665in”} Associate(关联) Associate(关联)的表示方式: 箭头＋实线，箭头指向被使用的类； [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-Z1sGxmCw-1609755291785)(media/image19.png)]{width=“1.46875in” height=“3.0520833333333335in”} 1. ### 理解与应用用类类型创建对象的过程，称为类的实例化 1. 类只是一个模型一样的东西，限定了类有哪些成员，定义出一个类并没有分配实际的内存空间来存储它 2. 一个类可以实例化出多个对象，实例化出的对象占用实际的物理空间存储类成员变量 3. 做个比方。类实例化出对象就像现实中使用建筑设计图建造出房子，类就像是设计图，只设计出需要什么东西，但是并没有实体的建筑存在，同样类也只是一个设计，实例化出的对象才能实际存储数据，占用物理空间。类的大小即成员变量的大小类对象中只保存了成员变量，成员函数只单独保存了一份 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-jUWeJLGl-1609755291786)(media/image20.png)]{width=“5.761805555555555in” height=“3.015972222222222in”} ## Application domain ### 词语解说 Application domain (AppDomain) is a boundary established by the common language runtime around objects created within the same application scope (i.e., starting from the entry point of the application, anywhere along the sequence of object activation). ## [https://www.sciencedirect.com/topics/computer-science/application-domain#:~:text=Internet%20applications%20have%20become%20increasingly%20important%2C%20especially%20for,analysis%20and%20the%20creation%20of%20a%20domain%20model.]{.ul}[https://www.techopedia.com/definition/5220/application-domain-net]{.ul}[https://www.techopedia.com/definition/3243/unified-modeling-language-uml]{.ul} ### 定义，目的，作用描述 An application domain is a logical isolation boundary created around .NET applications so that applications do not access or affect each other. It is a light-weight process having its own set of code, data, and configuration settings. Application domains are created by the runtime hosts, which are invoked by the common language runtime (CLR) to load the applications that need to be executed. Prior to .NET, the isolation boundary between applications was the processes in which they were loaded. Every process had its own private virtual memory and can not access the memory of another process directly. Application domain has features similar to that of a process. Application domains have the following features: • Optimum utilization of system resources by using fewer processes to execute multiple applications. 通过使用较少的进程执行多个应用程序来优化系统资源的利用 • Reliability by using isolation of tasks in situations where data cannot be shared and for unstable tasks that need to be unloaded without affecting the process. 在数据不能共享的情况下使用任务隔离，对于需要卸载但不影响进程的不稳定任务，使用隔离的可靠性 • Better efficiency by executing long-running processes that rarely use large extensions with optimal memory. 通过执行很少使用具有最佳内存的大型扩展的长时间运行的进程来提高效率 • Application security by restricting the direct access to the code running in one application from the code or resources of another application. 通过限制从另一个应用程序的代码或资源直接访问在一个应用程序中运行的代码来实现应用程序安全性 • Security control by specifying configuration details along for each application domain. 通过为每个应用程序域指定配置详细信息来进行安全控制 Application domain differs in the manner in which the CLR loads and executes multiple .NET applications in one single process. It does not allow direct access to the memory of loaded applications. It is managed by the CLR of the .NET Framework whereas a process is managed by the OS. The CLR provides fault isolation between application domains with less overhead than processes, due to its inherent feature of verifiable type-safety of managed code. Also, multiple threads can reside in an application domain, they are free to cross application domain boundaries. For example, ASP.NET is a runtime host that creates multiple application domains for each user accessing a web site. They can also be created and configured for applications that need to isolate code or to load extensions only while using them. This fact makes application domains useful in situations where plug-ins and other untrusted code is used. They are also useful in minimizing the working set of applications that use large DLLs. To enable communication between objects in different application domains one of the following three types of objects is used: 应用程序域的不同之处在于 CLR 加载和执行多个。NET 应用程序在一个进程中。它不允许直接访问已加载应用程序的内存。属性的 CLR 对其进行管理。NET 框架，而进程是由操作系统管理的。由于其固有的可验证托管代码类型安全特性，CLR 在应用程序域之间提供故障隔离，开销比进程少。此外，多个线程可以驻留在一个应用程序域中，它们可以自由地跨越应用程序域边界。例如，ASP.NET 是一个运行时主机，它为访问网站的每个用户创建多个应用程序域。还可以为需要隔离代码或仅在使用扩展时加载扩展的应用程序创建和配置这些扩展。这一事实使得应用程序域在使用插件和其他不可信代码的情况下非常有用。它们在最小化使用大型 dll 的应用程序的工作集方面也很有用。为了支持不同应用程序域中的对象之间的通信，需要使用以下三种类型的对象之一: • Marshal-By-Value: Complete copy of the object passed to the calling application domain. This is used when the state of object can be moved for performance reasons. 按值封送: 传递给调用应用程序域的对象的完整副本。当出于性能原因可以移动对象状态时，可以使用这种方法 • Marshal-By-Reference-Reference (MBR): A proxy of the object is passed to the client; used when the state of the object has to stay within the application domain. 按引用封送(marshal-by-reference，MBR) : 将对象的代理传递给客户机; 当对象的状态必须保留在应用程序域中时使用 • Context-bound: MBR object used across domains or within the context of its own application domain. 上下文绑定: 跨域或在自己的应用程序域上下文中使用的 MBR 对象 ## 词语解说 Activity diagram is another common tool used by UML to model the dynamic behavior of a system. It describes the sequence of activities and shows the control flow from one activity to another. Activity diagram is a kind of flow chart in essence. Activity diagram focuses on the control flow from one activity to another, which is driven by internal processing. 1. ## 定义，作用，目的描述 Activity Diagrams describe how activities are coordinated to provide a service which can be at different levels of abstraction. Typically, an event needs to be achieved by some operations, particularly where the operation is intended to achieve a number of different things that require coordination, or how the events in a single use case relate to one another, in particular, use cases where activities may overlap and require coordination. It is also suitable for modeling how a collection of use cases coordinate to represent business workflows 活动图描述了如何协调活动以提供处于不同抽象层次的服务。通常，一个事件需要通过一些操作来实现，特别是当操作的目的是实现一些需要协调的不同的事情时，或者单个用例中的事件如何相互关联，特别是活动可能重叠并需要协调的用例。它还适合于建模用例集合如何协调以表示业务工作流 • Identify candidate use cases, through the examination of business workflows 通过检查业务工作流，识别候选用例 • Identify pre- and post-conditions (the context) for use cases 确定用例的前置条件和后置条件(上下文) • Model workflows between/within use cases 用例中/之间的模型工作流 • Model complex workflows in operations on objects 为对象操作中的复杂工作流建模 • Model in detail complex activities in a high level activity Diagram 在高级活动图中详细建模复杂的活动 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-Z8OjsHb9-1609755291787)(media/image21.png)]{width=“3.7118055555555554in” height=“4.451388888888889in”} 1. ### 理解与应用活动图和交互图是UML中对系统动态方面建模的两种主要形式 •交互图强调的是对象到对象的控制流，而活动图则强调的是从活动到活动的控制流 •活动图是一种表述过程基理、业务过程以及工作流的技术。它可以用来对业务过程、工作流建模，也可以对用例实现甚至是程序实现来建模 •UML 2.0而言，去除了"活动图是状态图的一种特例"这一规定【用途】活动图是UML用于对系统的动态行为建模的另一种常用工具，它描述活动的顺序，展现从一个活动到另一个活动的控制流。活动图在本质上是一种流程图。活动图着重表现从一个活动到另一个活动的控制流，是内部处理驱动的流程。 ## 词语解说 A decision table is a table with various conditions and their corresponding actions . ## 定义，作用，目的描述 Decision tree is a two dimensional matrix. It is divided into four parts, condition stub, action stub, condition entry, and action entry . See the first figure listed below. Condition stub shows the various possible conditions. Condition entry is used for specifying which condition is being analyzed. Action stub shows the various actions taken against different conditions. And action entry is used to find out which action is taken corresponding to a particular set of conditions. The steps to be taken for a certain possible condition are listed by action statements. Action entries display what specific actions to be undertaken when selected conditions or combinations of conditions are true. At times notes are added below the table to indicate when to use the table or to distinguish it from other decisions tables. The right side columns of the table link conditions and actions and form the decision rules hence they state the conditions that must be fulfilled for a particular set of actions to be taken. In the decision trees, a fixed ordered sequence is followed in which conditions are examined. But this is not the case here as the decision rule incorporates all the required conditions, which must be true. Before describing the steps involved in building the decision table it is important to take a note of few important points. Every decision should be given a name and the logic of the decision table is independent of the sequence in which condition rules are written but the action takes place in the order in which events occur . Wherever possible, duplication of terms and meaning should be avoided and only the standardized language must be used. The steps of building the concerned tables are given below. Firstly figure out the most essential factors to be considered in making a decision. This will identify the conditions involved in the decision. Only those conditions should be selected which have the potential to either occur or not but partial occurrences are not permissible. Determine the most possible steps that can take place under varying conditions and not just under current condition. This step will identify the actions. Calculate all the possible combinations of conditions. For every N number of conditions there are 222… (N times) combinations to be considered. Fill the decision rules in the table. Entries in a decision table are filled as Y/N and action entries are generally marked as “X” . For the conditions that are immaterial（不重要的,无关紧要的） a hyphen “-” is generally put. Decision table is further simplified by eliminating and consolidating certain rules. Impossible rules are eliminated(排除). There are certain conditions whose values do not affect the decision and always result in the same action. These rules can be consolidated into（统一放到） a single rule. ## Fault Tolerance ### 词语解说 VSphere fault tolerance ensures the continuous availability of the virtual machine by creating and maintaining the secondary virtual machine that is the same as the primary virtual machine and can replace the primary virtual machine at any time in case of failure. In fact, it creates an identical replica for a virtual machine. vSphere Fault Tolerance通过创建和维护与主虚拟机相同，并且可在发生故障切换时随时替换主虚拟机的辅助虚拟机，来确保虚拟机的连续可用性，其实就是一为某一个虚拟机创建一个完全相同的副本。 1. ### 定义，目的，作用描述 vSphere Fault Tolerance通过创建和维护与主虚拟机相同，并且可在发生故障切换时随时替换主虚拟机的辅助虚拟机，来确保虚拟机的连续可用性，其实就是一为某一个虚拟机创建一个完全相同的副本。可以为虚拟机启用vSphere Fault Tolerance。比获得比vSphere HA所提供的级别更高的可用性和数据保护，从而确保业务连续性。Fault Tolerance时基于ESXi主机平台构建的（使用VMware vLockstep技术），它通过在单独主机上一虚拟锁步方式运行相同的虚拟机来提供连续可用性。使用FT技术，允许虚拟机在无须中断的情况下从服务器故障恢复，实现零停机时间和零数据丢失。基于vLockstep技术，该技术时主虚拟机和辅助虚拟机保持虚拟同步运行。VMware FT独立于应用程序和操作系统，允许以更低的成本和复杂性保护更多应用程序，并且可以和其他的vSphere功能集成。 vSphere中的FT vSphere HA通过在主机出现故障时重新启动虚拟机来为虚拟机提供基本级别的保护。vSphere FT可提供更高级别的可用性，允许用户对任何虚拟机运行保护以防止主机发生故障时丢失数据、事务或连接。FT通过确保主虚拟机和辅助虚拟机的状态在虚拟机的指令执行的任何时间点均相同来提供连续可用性。使用ESXi平台上的额VMware vLockstep技术来完成此过程。vLockstep通过使主虚拟机和辅助虚拟机执行相同顺序的X86指令来完成此过程。主虚拟机捕获所有输入和事件（从处理器到虚拟I/O设备），并在辅助虚拟机上进行重放。辅助虚拟机执行与主虚拟机相同的指令序列，而仅单个虚拟机映像（主虚拟机）执行工作负载。如果运行主虚拟机的主机或运行辅助虚拟机的主机发生故障，则会发生即时且透明的故障切换。正常运行的ESXi主机将无缝变成主虚拟机的主机，而不会断开网络连接或中断正在处理的事务。使用透明故障切换，不会有数据损失，并且可以维护网络连接。在进行透明故障切换之后，将重新生成新的辅助虚拟机，并且将重新建立冗余。整个过程是透明且全自动的，并且即使vCenter Server不可用，也会发生。 vSphere FT的工作方式 VMware 容错可通过创建和维护等同于主虚拟机并可在发生故障切换时替换主虚拟机的辅助虚拟机来为虚拟机提供连续可用性。当启用Fault Tolerance时，会创建一个重复虚拟机（称为辅助虚拟机），该虚拟机会以虚拟锁步方式随主虚拟机一起运行。VMware vLockstep可捕获主虚拟机上发生的输入和事件，并将这些输入和事件发送到正在另一个主机上运行的辅助虚拟机。使用此信息，辅助虚拟机的执行将等同于主虚拟机的执行。因为辅助虚拟机与主虚拟机一起以虚拟锁步的方式运行，所以它可以无中断地接管任何点处的执行，从而提供容错保护（三)vSphere FT的要求在使用FT之前，必须满足的要求包括群集要求、主机要求、虚拟机要求和硬件要求。群集要求：至少有两台通过FT认证的主机运行相同的FT版本号或主机内部版本号，如FT版本：2.0.1-3.0.0-3.0.0.ESXi主机可以访问相同的虚拟机数据存储和网络，配置了FT日志记录和vMotion网络，vSphere HA群集已创建并启用。主机要求：主机上的物理处理器必须来自与FT兼容的处理器组。要确认群集内的主机是否兼容，从而判断其是否支持FT。虚拟机要求：虚拟机文件必须存储在共享存储上。可接受共享的存储解决方案包括光纤通道、（硬件和软件）iSCSI、NFS和NAS。虚拟机必须存储在虚拟RDM或厚置备的虚拟机磁盘（VMDK）文件（已启用"群集功能"选项）中。虚拟机必须在一个受制裁的客户机操作系统上运行。 ## 15.Goal programming model ### 1）词语解说 A linear programming model used by enterprises to realize management by objectives. Fenghuoliepin company believes that goal planning is an effective method to solve the multi-objective management of enterprises. It is a mathematical method to find the solution with the minimum deviation from the target value under the given limited resources according to the target values determined by the decision-maker in advance and their realization priorities. ## 16.Portability ### 1）词语解说 Portability is a characteristic attributed to a computer program if it can be used in an operating systems other than the one in which it was created without requiring major rework. ## [https://www.insuranceopedia.com/definition/5395/portability#:~:text=Definition%20-%20What%20does%20Portability%20mean%3F%20Portability%20refers,is%20an%20important%20feature%20of%20group%20insurance%20benefits.]{.ul}[https://www.investopedia.com/terms/p/portability.asp]{.ul}[https://searchstorage.techtarget.com/definition/portability]{.ul} 1. ### 定义，作用，目的描述 Portability is a characteristic attributed to a computer program if it can be used in an operating systems other than the one in which it was created without requiring major rework. Porting is the task of doing any work necessary to make the computer program run in the new environment. In general, programs that adhere to standard program interfaces such as the X/Open UNIX 95 standard C language interface are portable. Ideally, such a program needs only to be compiled for the operating system to which it is being ported. However, programmers using standard interfaces also sometimes use operating system extensions or special capabilities that may not be present in the new operating system. Uses of such extensions have to be removed or replaced with comparable functions in the new operating system. In addition to language differences, porting may also require data conversion and adaptation to new system procedures for running an application. 可移植性是计算机程序的一个特征，如果它可以用在操作系统之外的其他操作系统中，而不需要大量的返工。移植的任务是完成任何必要的工作，使计算机程序在新的环境中运行。一般来说，遵循标准程序接口(如 x/Open UNIX 95标准 c 语言接口)的程序是可移植的。理想情况下，这样的程序只需要为它要移植到的操作系统进行编译。然而，使用标准接口的程序员有时也使用操作系统扩展或新操作系统中可能没有的特殊功能。必须在新的操作系统中删除或用类似的功能取代这种扩展的用途。除了语言上的差异，移植还可能需要数据转换和适应运行应用程序的新系统过程。 Portability has usually meant some work when moving an application program to another operating system. Recently, the Java programming language and rudiment environment has made it possible to have programs that run on any operating system that supports the Java standard (from Sun Micro systems) without any porting work. Java applets in the form of compiler byte code can be sent from a server program in one operating system to a client program (your Web browser) in another operating system without change. 在将应用程序移动到另一个操作系统时，可移植性通常意味着一些工作。最近，Java 编程语言和执行期函式库语言使程序可以在任何支持 Java 标准的操作系统上运行(来自昇阳电脑) ，而不需要任何移植工作。预编译字节码形式的 Java 小程序可以从一个操作系统中的服务器程序发送到另一个操作系统中的客户机程序(您的 Web 浏览器) ，而不需要更改。 2. ### 理解与应用对于一些大型系统来说，可移植性显得尤为重要，因为在一定程度上可移植性与可维护性挂钩，除此之外，我们可以使用的设备越来越多，手机，电脑，不同设备也有不同的操作系统，要想让我们开发出来的系统更易于使用，使用者更方便，那么可移植性也是必不可少的。 ## Quality requirement 1. ### 词语解说 Quality requirement is a common term in project management. It is defined as the condition used to assess the conformance of the project by validating the acceptability of an attribute or characteristic for the quality of a particular result. 质量要求是项目管理中的一个通用术语。它被定义为通过验证特定结果质量的属性或特征的可接受性来评估项目一致性的条件。 ## [https://www.mypmllc.com/project-management-resources/free-project-management-templates/quality-requirements/]{.ul}[https://simplicable.com/new/quality-requirements#:~:text=%20%20%20Overview%3A%20Quality%20Requirements%20%20,Specifications%20of%20the%20quality%20of%20product%20…%20]{.ul}[https://project-management-knowledge.com/definitions/q/quality-requirement/]{.ul} ### 定义，作用，目的描述 In a nutshell, the quality requirement defines the expectations of the customer for quality, the internal processes as well as the attributes of products that indicate whether the quality factors are satisfied or not. The quality requirements in project management are defined in terms of the quality criteria, quality factors, and quality metrics. The quality criteria document the internal process and attributes of the product that will be monitored all throughout the project life cycle. The quality factors document the perceived aspects of the user regarding the deliverables of the project to determine if the project satisfies the expectations from customers. Lastly, the quality metrics document the indicators used to measure the quality of the product. The quality requirement is used by different project management processes particularly the Quality Management Plan to create the risk register, requirements documentation, and cost-benefit analysis. This term is defined in the 5th edition of the PMBOK. 1. ### 理解与应用软件质量需求分类用于确定测试目标测试目标包括功能、性能、界面、易用性、兼容性、安全性、可用性 / 可靠性、维护性、可扩展性功能以外统称为非功能功能软件能做什么需要做什么怎么做是正确的那些功能要测试、哪些是不需要测试的性能反应软件运行时的效率和占用资源情况的能力（速度）时间特性：时间短、速度快、效率高资源特性：占用资源（CPU 、内存、硬盘、网络）少界面（UI） user interface（）好不好看布局合理控件位置恰当文字没有乱码、字体大小合适颜色使用恰当图片、表格恰当、舒适、美观易用性符不符合用户平时使用的习惯指定条件下使用时，软件产品被理解、学习、使用和吸引用户的能力尽量符合用户平时的使用习惯（比如确认enter 换行什么的）兼容性 / 可移植性指产品从一种环境迁移到另一个环境中的能力，反应一个软件与不同的硬件环境、操作平台、其他软件的共同使用能力硬件：CPU 不同性能（HZ）平台: win7 win10 软件自身的不同版本其他软件兼容：360 和 QQ ，数据库升级更变，不同浏览器使用数据兼容：不同网络状态安全性软件产品保护信息和数据的能力可用性 / 可靠性指系统正常运行的能力或程度，可行性=正常运行时间 / (正常运行时间 + 非正常运行时间) x 100% 可用性指标一般要达到 4个9，即 99.99%（全年52分钟不正常工作） 5个9，即99.999%（全年5分钟） 7个9 ，即99.99999%（全年失效时间不超过两秒）一般测试时间不足，可以采用空间换时间的方法，如：在高负载情况下进行为期一周或一个月的测试，以判断可靠性关注 MTTF (平均无故障时间) 、 MTTR(平均回复时间、MTBF(平均失效时间间隔)) 可维护性做软件的可被修复的能力（打补丁一类）修改可能包括修正值、改进或者软件对环境锁需求的功能规格说明变化的适应可维护性的软件应该是易改变的、稳定的、易测试的可扩展性 / 可伸缩性测试通过少量的改动就可以实现整个系统处理能力的zengzhang 如部署两台服务器时测试系统性能（容量，即最大负载），在部署四台、八台服务器时分别进行系统容量的测试，看其容量是否为上次（两台、四台）实验值的两倍或者接近两倍。如果是，则系统就具有良好的可伸缩性 ## Non-functional requirement 1. ### 词语解说 (NFR) specifies the quality attribute of a software system. They judge the software system based on Responsiveness, Usability, Security, Portability and other non-functional standards that are critical to the success of the software system. Example of nonfunctional requirement, “how fast does the website load?” Failing to meet non-functional requirements can result in systems that fail to satisfy user needs. 非功能性需求指定了软件系统的质量属性。他们根据对软件系统成功至关重要的响应能力、可用性、安全性、可移植性和其他非功能性标准来判断软件系统。非功能性需求的例子，"网站加载的速度有多快? "不能满足非功能性需求可能导致系统不能满足用户需求。 ## [https://www.guru99.com/functional-vs-non-functional-requirements.html#:~:text=Here%2C%20are%20some%20examples%20of%20non-functional%20requirement%3A%201,recorded%20on%20an%20audit%20trail.%20More%20items…%20]{.ul}[https://www.guru99.com/non-functional-requirement-type-example.html]{.ul}[https://requirements.com/Content/What-is/what-are-non-functional-requirements]{.ul} 1. ### 定义，作用，目的描述 Non-functional Requirements allows you to impose constraints or restrictions on the design of the system across the various agile backlogs. Example, the site should load in 3 seconds when the number of simultaneous users are > 10000. Description of non-functional requirements is just as critical as a functional requirement. 非功能性需求允许您在各种敏捷积压中对系统设计施加约束或限制。例如，当同时用户数大于10000时，站点应该在3秒内加载。非功能性需求的描述与功能性需求一样重要。下面是一些非功能性需求的例子: Users must change the initially assigned login password immediately after the first successful login. Moreover, the initial should never be reused. 用户必须在第一次成功登录后立即更改最初分配的登录密码。此外，初始化的代码永远不应该被重用 Employees never allowed to update their salary information. Such attempt should be reported to the security administrator. 员工不允许更新他们的工资信息。这种尝试应该报告给安全管理员 Every unsuccessful attempt by a user to access an item of data shall be recorded on an audit trail. 用户每次尝试访问一个数据项目的失败都应记录在审计线索上 A website should be capable enough to handle 20 million users with affecting its performance 一个网站应该能够处理影响其性能的2000万用户 The software should be portable. So moving from one OS to other OS does not create any problem. 软件应该是可移植的，所以从一个操作系统移动到另一个操作系统不会产生任何问题 Privacy of information, the export of restricted technologies, intellectual property rights, etc. should be audited. 应对信息隐私、受限技术出口、知识产权等进行审计非功能测试的好处如下: The nonfunctional requirements ensure the software system follow legal and compliance rules. 非功能性需求确保软件系统遵循法律和遵从规则 They ensure the reliability, availability, and performance of the software system 它们确保了软件系统的可靠性、可用性和性能 They ensure good user experience and ease of operating the software. 他们确保良好的用户体验和易于操作的软件 They help in formulating security policy of the software system. 它们有助于制定软件系统的安全策略非功能性要求的缺点如下: None functional requirement may affect the various high-level software subsystem 无功能需求可能影响各种高级软件子系统 They require special consideration during the software architecture/high-level design phase which increases costs. 它们需要在软件架构/高级设计阶段特别考虑，这会增加成本 Their implementation does not usually map to the specific software sub-system, 它们的实现通常不会映射到特定的软件子系统, It is tough to modify non-functional once you pass the architecture phase. 一旦通过了体系结构阶段，就很难修改非功能性的内容 ## interface inheritance 1. ### 词语解说 Interface is a 100% abstract class. It contains only constants and method signatures. In other words it is a reference type similar to class. An interface can’t be instantiated. It can be implemented by a class or extended by another interface. 接口是100% 抽象类。它只包含常量和方法签名。换句话说，它是类似于 class 的引用类型。接口不能被实例化。它可以通过类实现，也可以通过其他接口进行扩展。 ## [https://docs.oracle.com/javase/tutorial/java/IandI/index.html]{.ul}[https://www.sitepoint.com/interface-and-inheritance-in-java-interface/]{.ul}[https://www.differencebetween.com/difference-between-inheritance-and-vs-interface-in-java/]{.ul} 1. ### 定义，作用，目的描述 An interface can be defined as the following: 接口可以定义如下: public interface DriveCar { void turnLeft(); void turnRight(); void moveBack(); void accelerate(); } The methods declared in an interface don’t have method bodies. By default all the methods in an interface are public abstract. Similarly all the variables we define in an interface are essentially constants because they are implicitly public static final. So, the following definition of interface is equivalent to the above definition. 在接口中声明的方法没有方法体。默认情况下，接口中的所有方法都是公共抽象。类似地，我们在接口中定义的所有变量本质上都是常量，因为它们是隐式的公共静态末尾。因此，下面的接口定义等价于上面的定义。 public interface DriveCar { public abstract void turnLeft(); public abstract void turnRight(); public abstract void moveBack(); public abstract void accelerate(); } How To Use: 如何使用: An interface defines a contract which an implementing class must adhere to. The above interface DriveCar defines a set of operations that must be supported by a Car. So, a class that actually implements the interface should implement all the methods declared in the interface. 接口定义了实现类必须遵守的契约。上面的接口 DriveCar 定义了一组必须由 Car 支持的操作。因此，实际实现接口的类应该实现接口中声明的所有方法。 Example: 例子: class Car implements DriveCar{ void turnRight(){ //implementation code goes here } void turnLeft(){ //implementation code goes here } void moveBack(){ //implementation code goes here } void accelerate(){ //implementation code goes here } } Now we can take a reference of type DriveCar and assign an object of Car to it. 2. ### 理解与应用这是java的基础，需要学习掌握 ## Requirements analysis 1. ### 词语解说 Requirements analysis, also called requirements engineering, is the process of determining user expectations for a new or modified product. These features, called requirements, must be quantifiable, relevant and detailed. 需求分析，也称为需求工程，是确定用户对新产品或修改后产品的期望的过程。这些特性，即所谓的需求，必须是可量化的、相关的和详细的。 ### 定义，作用，目的描述 Requirements analysis, also called requirements engineering, is the process of determining user expectations for a new or modified product. These features, called requirements, must be quantifiable, relevant and detailed. In software engineering, such requirements are often called functional specifications. Requirements analysis is an important aspect of project management. Requirements analysis involves frequent communication with system users to determine specific feature expectations, resolution of conflict or ambiguity in requirements as demanded by the various users or groups of users, avoidance of feature creep and documentation of all aspects of the project development process from start to finish. Energy should be directed towards ensuring that the final system or product conforms to client needs rather than attempting to mold user expectations to fit the requirements. Requirements analysis is a team effort that demands a combination of hardware, software and human factors engineering expertise as well as skills in dealing with people. ## abnormal end 1. ### 词语解说 Abnormal End (ABEND) is an abnormal or unexpected termination of a task in software. It occurs when a software program crashes due to errors. Generally errors in a software application or the operating system cause ABEND. 异常结束(ABEND)是软件中任务的异常或意外终止。当一个软件程序由于错误而崩溃时，就会发生这种情况。通常，软件应用程序或操作系统中的错误会导致 ABEND。 ## [https://www.techopedia.com/definition/1626/abnormal-end-abend]{.ul}[https://searchdatacenter.techtarget.com/definition/abend]{.ul}[https://www.ibm.com/support/knowledgecenter/en/SSLTBW_2.1.0/com.ibm.zos.v2r1.istdgn1/abndp.htm]{.ul} ### 定义，作用，目的描述 The term ABEND gets its name from an error message seen in IBM OS/360 systems. The term is claimed to have derived from the German word “abend”, which means “evening”. When an ABEND occurs the system may stop responding, causing the program to close abruptly. An ABEND may occur in two scenarios: When the system is given a set of instructions that it cannot handle or recognize 当系统接收到一系列的指令，而这些指令又不能处理或识别 When a program tries to address a memory space beyond a specific limit 当程序试图寻址超出特定限制的内存空间时 Modern operating systems are designed to prevent the system from rebooting by allowing only the offending application to halt or close. Other applications will continue to run normally. Modern operating systems are also more bug resistant than their predecessors, but some application bugs do cause the operating system to hang or lock up, requiring a reboot. ### 1）词语解说 Absolute address of memory refers to an address scheme in communication, computer and data processing system. This address directly identifies a storage unit without using the associated media, such as a base station address or a related address. 1. ### 定义，作用，目的描述 Absolute address is actually a term used when referring to one of the addressing modes used by an application. Thus, in a computer that offers virtual memory, this ‘absolute address’ is also a virtual address - because all application code is only going to refer to virtual addresses. Other addressing modes use virtual addresses as well. Of course, like I wrote earlier, virtual addresses are eventually mapped to a physical addresses when accessing RAM. 绝对地址实际上是在引用应用程序使用的寻址模式时使用的术语。因此，在提供虚拟内存的计算机中，这个"绝对地址"也是一个虚拟地址------因为所有应用程序代码都只引用虚拟地址。其他寻址模式也使用虚拟地址。当然，正如我前面所写的，当访问 RAM 时，虚拟地址最终会映射到物理地址。 Here is how an ‘absolute address’ is different from it’s counterparts - the other addressing modes (one of them being ‘relative address’): 以下是"绝对地址"与其他寻址方式(其中一种是"相对地址")的区别: An Intel JMP(jump) instruction may specify a ‘relative jump’, where the displacement is relative to the next instruction. Something like: 一条 Intel JMP (跳转)指令可能指定一个"相对跳转" ，其位移相对于下一条指令。例如: “Jump N bytes ahead of the next instruction” <- This is PC-relative addressing. “跳转 n 字节前面的下一个指令” <-这是 pc 相对寻址。 Or it may be used with an absolute address, like: 或者可以和绝对地址一起使用，比如: “跳转到内存中的第 n 个字节” <-这是绝对地址。 In both cases, the addresses being referred to by the JMPs are virtual addresses (which get mapped to a physical address in a way that is transparent to the application) 在这两种情况下，jmp 引用的地址都是虚拟地址(以对应用程序透明的方式映射到物理地址) ## abstract machine 1. ### 词语解说 Abstract machines, also called automata, are an element of theoretical computer science. An abstract machine resembles a function in mathematics. 抽象机器，又称自动机，是理论计算机科学的一个组成部分。 ## [https://mathworld.wolfram.com/AbstractMachine.html#:~:text=An%20abstract%20machine%20is%20a%20model%20of%20a,so%20can%20be%20thought%20of%20as%20a%20processor.]{.ul}[https://www.wisegeek.com/what-is-an-abstract-machine.htm]{.ul}[https://mortoray.com/2012/06/18/abstract-machines-interpreters-and-compilers/]{.ul} 1. ### 定义，作用，目的描述 Abstract machines, also called automata, are an element of theoretical computer science. An abstract machine resembles a function in mathematics. It receives inputs and produces outputs according to specified rules. Abstract machines differ from more literal machines because they are assumed to function perfectly and independently from hardware. They are subdivided into types on the basis of characteristics such as how they perform their operations and what types of inputs they can receive. 抽象机器，又称自动机，是理论计算机科学的一个组成部分。抽象机器类似于数学中的函数。它接收输入并根据指定的规则生成输出。抽象机器不同于更多的文字机器，因为它们被假定为功能完美且独立于硬件。根据它们如何执行其操作以及它们可以接收到什么类型的输入等特征，它们又被细分为几种类型。 When classifying abstract machines, one of the most simple distinctions concerns the number of operations they are permitted to perform at any given point. An abstract machine is called deterministic if there is always only one way for it to proceed. It is nondeterministic if multiple possibilities exist for the machine in at least one of its possible states. A “pushdown” automaton is one that has the capacity to manipulate its stack of inputs, rather than simply responding to them one by one in the order in which they appear. 在对抽象机器进行分类时，最简单的区别之一是允许它们在任意给定点执行的操作数。如果抽象机器只有一种运行方式，那么它就被称为确定性机器。如果机器处于至少一种可能状态时存在多种可能性，那么它是不确定的。"下推"自动机具有操作其输入堆栈的能力，而不是简单地按输入出现的顺序逐个响应它们。 Wolfram MathWorld gives two famous examples of abstract machines. One of these examples is Conway’s game of life, which is a deterministic abstract machine because only one configuration can emerge out of any other. This game uses a grid in which each box, or cell, can either have the state “living” or “dead.” The state of the whole grid is determined on the basis of the previous state. If a living cell touches exactly two or three other living cells, it continues to live. If it has one, two, or more than three neighbors (up to a possible eight), it dies. A dead cell with exactly three neighbors will come to life; otherwise, it will remain dead. MathWorld 给出了两个著名的抽象机器的例子。其中一个例子是康威的生命游戏，这是一个确定性的抽象机器，因为只有一个配置可以出现在任何其他。这个游戏使用一个网格，其中每个盒子，或细胞，可以有状态"活着"或"死亡"整个网格的状态是根据以前的状态确定的。如果一个活细胞恰好与另外两个或三个活细胞接触，它就会继续存活。如果它有一个、两个或三个以上的邻居(最多可能有八个) ，它就会死亡。一个正好有三个邻居的死亡细胞会复活，否则，它会一直死亡。 Another example, the Turing machine, is one of the most basic and fundamental abstract machines in computer science. A Turing machine performs operations on a tape—a string of symbols—of unlimited size. It contains instructions both for changing the symbols and for changing the symbol upon which it is operating. A simple Turing machine might have only the instruction “transform symbol to 1, then move right.” This machine would output nothing but a string of 1’s. This simple Turing machine is deterministic, but it is also possible to construct nondeterministic Turing machines that can perform several different operations given the same input. 另一个例子，图灵机，是计算机科学中最基本和最基本的抽象机器之一。图灵机在一个磁带(一串符号)上执行无限大小的操作。它包含了改变符号和改变其上运行的符号的指令。一个简单的图灵机可能只有"转换符号为1，然后向右移动"的指令这台机器只能输出1的字符串。这个简单的图灵机是确定性的，但是也可以构造不确定的图灵机，它可以在相同的输入下执行多个不同的操作。 These abstract machines can serve many purposes. They can be fun theoretical toys, but they can also serve as models for real computer systems. The abstract machine is at the heart of computer science as a discipline. 这些抽象的机器可以达到许多目的。他们可以是有趣的理论玩具，但他们也可以作为真正的计算机系统的模型。抽象机器是计算机科学作为一门学科的核心。 ## action item 1. ### 词语解说 In the realm of management, an action item is a specific task or action that needs to be taken care of, and they are usually what you would place on a to-do list or a calendar so that you can keep track of what needs to be done. 在管理领域，行动项目是一项需要处理的具体任务或行动，它们通常是你将要放在待办事项列表或日历上的内容，以便你能够跟踪需要做的事情。 1. ### 定义，作用，目的描述 If you have ever kept a planner or to-do list, then you have probably used action items. An action item is a single, clearly defined task that must be done. For example, a personal action item could be to walk the dog or to call mom. While action items help you keep track of and accomplish the things you need to accomplish in your daily life, they have a bigger importance in the workplace. 如果你曾经保留过一个计划表或待办事项清单，那么你可能已经使用过行动项目。一个行动项目是一个单一的，明确定义的任务，必须完成。例如，一个个人行动项目可以是遛狗或者打电话给妈妈。虽然行动项目可以帮助你在日常生活中追踪和完成你需要完成的事情，但是它们在工作场所有更大的重要性。 If you owned your own business and wanted to grow your business, then you’d need to implement action items to keep you on track. Action items help you figure out what you need to do to get a project from start to finish. Breaking a project down into more tangible, bite-sized steps can make a large project seem that much easier to complete. 如果你拥有自己的企业，想要发展自己的业务，那么你就需要实施行动项目，以保持你在正轨上。行动项目可以帮助你弄清楚从开始到完成一个项目需要做些什么。将一个项目分解成更具体、小步骤可以使一个大项目看起来更容易完成。 Action items help break a big project into smaller, more manageable tasks 行动项目有助于将一个大项目分解成更小、更易于管理的任务 action items When to Use Them 何时使用它们 Imagine that you do have your own business. You have a business that makes tablets and laptops, and you are about to start a project to design a new laptop/tablet combo. When should you start to use action items? 想象一下你有自己的生意。你有一个生产平板电脑和笔记本电脑的企业，你将要开始一个设计新的笔记本电脑/平板电脑组合的项目。你应该什么时候开始使用行动项？ You should use action items from the beginning of the project. Even if you are in the planning stages, action items will help you get to the next step and figure out what you need to do. 您应该从项目的开始就使用操作项。即使你正处于计划阶段，行动项目也会帮助你进入下一步，弄清楚你需要做什么。 You should also use action items throughout your project, all the way up until you finish your project. 您还应该在整个项目中使用行动项，一直使用到项目完成。 How to Use Them 如何使用它们 Okay, so you know that using action items will help you finish your project, but how can you use them? 好的，所以你知道使用行动项目将帮助你完成你的项目，但是你如何使用它们呢？ To help get your laptop/tablet combo project headed in the right direction, your first action item can very well be this: 为了帮助你的笔记本/平板电脑组合项目朝着正确的方向前进，你的第一个行动项目可以是: Assign roles for new project. 为新项目分配角色 You can send out an email telling your team that at the next meeting, you will be working on the action item of assigning roles. To help everyone get on the same page, your email can even list the action items that need to be done next. This way, when your team gets together to discuss the project, everyone will know what needs to be done, and they will be ready to help you figure out who is going to be doing what. 你可以发送一封电子邮件告诉你的团队，在下一次会议上，你将着手分配角色的行动项目。为了帮助每个人达成共识，你的邮件甚至可以列出下一步需要做的事情。这样，当你的团队聚在一起讨论项目时，每个人都会知道需要做什么，他们也会准备好帮助你找出谁将要做什么。 After the roles have been assigned, you can then start working on the other action items, such as these: 在角色分配完成后，你可以开始处理其他的动作项，比如: Design 4 possible styles for review, due by next week. 设计4种可能的款式供评审，下周交 Find 4 possible wholesalers that make quality screens, due by next week. 找到4个可能的批发商，生产高质量的屏幕，到下周为止 Write 4 different possible specs for the new laptop/tablet, due by next week. 为下周到期的新笔记本/平板电脑写下4种不同的可能规格 These action items will get you to the next step of your project where you start to assemble the first prototype of your product. 这些行动项目将帮助您进入项目的下一步，您将开始组装产品的第一个原型。 The best way to use action items is by continuing to create new ones as you finish your previous action items. This will get you closer to finishing your project one step at a time. 使用行动项的最佳方式是在完成之前的行动项的同时继续创建新的行动项。这将使你更接近完成您的项目一步一步的时间。 Include due dates with your action items so you know when you need to finish each step and action item. Also, make sure that your action items have an action associated with what you are supposed to do. For example, you wrote ‘‘Design 4 possible styles for review, due by next week’’ instead of just ‘‘Possible styles’’. By including an action, you are clearly stating what you need to do. 在你的行动项目中包括截止日期，这样你就知道什么时候你需要完成每个步骤和行动项目。此外，确保你的行动项目有一个与你应该做的事情相关联的行动。例如，你写的是"设计4种可能的样式供评审，下周交"而不是"可能的样式"。通过包含一个动作，你就清楚地说明了你需要做什么。 2. ### 理解与应用活动项可以帮助我们更好的管理项目，我们小组的项目也可以通过列出活动项的方式进行管理。 ## actual parameter ### 词语解说 the actual value that is passed into the method by a caller ## [https://www.differencebetween.com/difference-between-actual-and-vs-formal-parameters/]{.ul} [[https://www.definitions.net/definition/actual%20parameter]{.ul}](https://www.definitions.net/definition/actual parameter)[https://chortle.ccsu.edu/java5/Notes/chap34A/ch34A_3.html#:~:text=actual%20parameter%20%E2%80%94%20the%20actual%20value%20that%20is,parameter%20is%20temporarily%20%22bound%22%20to%20the%20actual%20parameter.]{.ul} 1. ### 定义，作用，目的描述 actual parameter 实际参数 — the actual value that is passed into the method by a caller. ー调用方传入方法的实际值 For example, the 例如:200 used when 用于processDeposit is called is an actual parameter. 是一个实际的参数 actual parameters are often called 实际参数通常被称为arguments 争论 When a method is called, the formal parameter is temporarily “bound” to the actual parameter. The method uses the formal parameter to stand for the actual value that the caller wants to be used. 调用方法时，形式参数临时"绑定"到实际参数。该方法使用形式参数表示调用方希望使用的实际值。 For example, here the processDeposit method uses the formal parameter amount to stand for the actual value used in the procedure call: 例如，这里 processDeposit 方法使用形式参数 amount 来表示过程调用中使用的实际值: balance = balance + amount ; Note: formal parameters are bound to an actual value only as long as their method is active. When a method returns to its caller, the formal parameters no longer contain any values. They cannot be used to store the state of an object. 注意: 形式参数只有在其方法处于活动状态时才与实际值绑定。当方法返回给调用方时，形式参数不再包含任何值。它们不能用于存储对象的状态。 2. ### 理解与应用实际参数和形式参数是在编程时需要注意的概念，初学者可能会搞不清楚，可以理解为实际参数是真实存在的，形式参数只有在调用时才发挥传递参数的作用。 ## Application software 1. ### 词语解说 Application software, or app for short, is software that performs specific tasks for an end-user. 应用软件，简称 app，是为最终用户执行特定任务的软件。 1. ### 定义，作用，目的描述 Effectively, if the user is interacting directly with a piece of software it is application software. For example, Microsoft Word or Excel are application software, as are common web browsers such as Firefox or Google Chrome. 实际上，如果用户直接与一个软件进行交互，那么它就是应用软件。例如，Microsoft Word 或 Excel 是应用软件，常见的网络浏览器如 Firefox 或 Google Chrome 也是应用软件。 It also includes the category of mobile apps, including communication apps such as WhatsApp or games such as Candy Crush Saga. There are also app versions of common services such as those providing weather or transport information or apps for customers to interact with companies. 它还包括一类移动应用，包括诸如 WhatsApp 之类的通讯应用，或者诸如糖果大爆险之类的游戏。还有应用程序版本的公共服务，如那些提供天气或交通信息或应用程序的客户与公司互动。 Application software is distinct from system software, which refers to the software that actually keeps the systems running such as the operating system, computational science software, game engines, industrial automation, and software as a service applications. 应用软件不同于系统软件，系统软件指的是实际上保持系统运行的软件，如操作系统、计算科学软件、游戏引擎、工业自动化和软件即服务应用程序。 Instead of interacting with the user, the system software interacts with other software or hardware. 系统软件不是与用户交互，而是与其他软件或硬件交互。 ## Algorithm Analysis 1. ### 词语解说 Algorithm analysis is a quantitative analysis of how much computing time and storage space an algorithm needs. Algorithm is the step of solving a problem. It can be defined as any special method to solve a certain problem. In computer science, the algorithm should be described by computer algorithm language, and the algorithm represents an accurate and effective method to solve a class of problems by computer. 算法分析是对一个算法需要多少计算时间和存储空间作定量的分析。算法（Algorithm）是解题的步骤，可以把算法定义成解一确定类问题的任意一种特殊的方法。在计算机科学中，算法要用计算机算法语言描述，算法代表用计算机解一类问题的精确、有效的方法。 1. ### 定义，作用，目的描述 Usually, the efficiency or running time of an algorithm is stated as a function relating the input length to the number of steps (time complexity) or storage locations (space complexity). Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem. These estimates provide an insight into reasonable directions of search for efficient algorithms. In theoretical analysis of algorithms it is common to estimate their complexity in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily large input. Big O notation, Big-omega notation and Big-theta notation are used to this end. 通常，一个算法的效率或运行时间表示为一个函数，它将输入长度与步数(时间复杂度)或存储位置(空间复杂度)联系起来。算法分析是更广泛的计算复杂性理论分析的一个重要组成部分，它为任何解决给定计算问题的算法所需的资源提供理论估计。这些估计为寻找高效算法提供了合理的方向。在算法的理论分析中，通常是在渐近意义上估计它们的复杂度，即对任意大的输入估计复杂度函数。大 o 符号、大 -omega 符号和大 -theta 符号被用于此目的。 Rule of thumb: 经验法则: Simple programs can be analyzed by counting the nested loops of the program. A single loop over n items yields f( n ) = n. A loop within a loop yields f( n ) = n 简单的程序可以通过计算程序的嵌套循环来进行分析。在 n 个项上的单个循环产生 f (n) = n。循环中的循环产生 f (n) = n2. A loop within a loop within a loop yields f( n ) = n . 循环中的循环产生 f (n) = n3. Rule of thumb: 经验法则:Given a series of for loops that are sequential, the slowest of them determines the asymptotic behavior of the program. Two nested loops followed by a single loop is asymptotically the same as the nested loops alone, because the nested loops dominate the simple loop. 给定一系列顺序的 for 循环，其中最慢的一个决定了程序的渐近行为。两个嵌套循环后跟一个单循环是渐近相同的嵌套循环单，因为嵌套循环主导的简单循环 2. ### 理解与应用算法是一组有穷的规则，它们规定了解决某一特定类型问题的一系列运算，是对解题方案内的准确与完整地描述。制定一个算法，一般要经过设计、确认、分析、编码、测试、调试、计时等阶段。系统功能的实现本质上其实就是各种算法的实现，在需求分析阶段不需要过于考虑算法的实现，而应该确认好需求后在选择相适应的算法去实现我们的系统 1. ### 词语解说 A base address is a unique location in primary storage (or main memory) that serves as a reference point for other memory locations called absolute addresses. 基地址是主存储器(或主存储器)中唯一的位置，作为其他内存位置(称为绝对地址)的参考点。 1. ### 定义，作用，目的描述 In order to obtain an absolute address, a specific displacement (or offset) value is added to the base address. In primary storage, all addresses literally comprise fixed-length sequences of bits that stand for positive whole numbers usually expressed in hexadecimal form. For example, a base address might indicate the beginning of a program loaded into primary storage. The absolute address of each individual program instruction could be specified by adding a displacement to the base address. 为了获得一个绝对地址，一个特定的位移(或偏移量)值被加到基地址。在主存储器中，所有地址实际上都包含固定长度的位序列，这些位代表通常以十六进制形式表示的正整数。例如，基址可能表示加载到主存储器的程序的开始。每条单独程序指令的绝对地址可以通过在基地址上添加一个位移来指定。 ## Backwards recovery 1. ### 词语解说 Reverse Engineering (also known as reverse technology) is a process of reappearance of product design technology, that is, reverse analysis and Research on a target product, so as to deduce and obtain the design elements of the product, such as processing flow, organizational structure, functional characteristics and technical specifications, so as to produce similar but not identical products. Reverse engineering comes from hardware analysis in commercial and military fields. Its main purpose is to deduce the design principle of the product directly from the analysis of the finished product when the necessary production information cannot be obtained easily. 逆向工程（又称逆向技术），是一种产品设计技术再现过程，即对一项目标产品进行逆向分析及研究，从而演绎并得出该产品的处理流程、组织结构、功能特性及技术规格等设计要素，以制作出功能相近，但又不完全一样的产品。逆向工程源于商业及军事领域中的硬件分析。其主要目的是在不能轻易获得必要的生产信息的情况下，直接从成品分析，推导出产品的设计原理。 ## [http://mavendeveloper.com/2011/01/3005478/]{.ul}[https://quiz.techlanda.com/2019/11/in-sql-server-what-is-backward-recovery.html]{.ul}[https://quiz.techlanda.com/2019/08/what-is-backward-database-recovery.html]{.ul} ### 定义，作用，目的描述 The reasons for reverse engineering are as follows: Interface design. Because of interoperability, reverse engineering is used to find out the cooperation protocol between systems. ● military or commercial secrets. Steal the latest research or product prototype of an enemy or competitor. ● improve documentation. When the original documents are inadequate, and when the system is updated and the original designer is not present, reverse engineering is used to obtain the required data to supplement or understand the latest state of the system. ● software upgrade or update. For functional, compliance, security requirements changes, reverse engineering is used to understand existing or legacy software systems to assess the work required to update or migrate systems. ● manufacturing unlicensed / unauthorized copies. ● remove replication protection and disguised login rights. Document loss: when reverse engineering is adopted, the document of a special equipment has been lost (or not at all), and the person in charge of the project cannot be found. The complete system often needs to be redesigned based on the old system, which means that the only way to integrate the original functions for the project is to use the reverse engineering method to analyze the existing fragments for redesign. Product analysis: used to investigate the operation mode, component composition, budget estimation and identification of potential infringement. Make game plug-in: understand the game operation mechanism through reverse engineering, then bypass the protection mechanism, and realize the plug-in function by modifying the memory value, modifying the code in memory, and calling internal functions. ●接口设计。由于互操作性，逆向工程被用来找出系统之间的协作协议。 ●军事或商业机密。窃取敌人或竞争对手的最新研究或产品原型。 ●改善文档。当原有的文档有不充分处，又当系统被更新而原设计人员不在时，逆向工程被用来获取所需数据，以补充说明或了解系统的最新状态。 ●软件升级或更新。出于功能、合规、安全等需求更改，逆向工程被用来了解现有或遗留软件系统，以评估更新或移植系统所需的工作。 ●制造没有许可/未授权的副本。 ●学术/学习目的。 ●去除复制保护和伪装的登录权限。 ●文件丢失：采取逆向工程的情况往往是在某一个特殊设备的文件已经丢失了（或者根本就没有），同时又找不到工程的负责人。完整的系统时常需要基于陈旧的系统上进行再设计，这就意味着想要集成原有的功能进行项目的唯一方法，便是采用逆向工程的方法，分析已有的碎片进行再设计。 ●产品分析：用于调查产品的运作方式，部件构成，估计预算，识别潜在的侵权行为。 ●制作游戏外挂：通过逆向工程了解游戏运行机制，进而绕过保护机制并通过修改内存数值、修改内存中的代码、调用内部函数等方式来实现外挂功能。 Reverse engineering is widely used in new product development, product modification design, product imitation, quality analysis and testing Shorten the design and development cycle of products and speed up the update of products; Reduce the cost and risk of developing new products; Speed up the design of product modeling and serialization; Suitable for single piece, small batch parts manufacturing, especially mold manufacturing, can be divided into direct molding and indirect molding. Direct molding method: the rapid direct molding method based on RP technology is to directly manufacture and shape the CAD results of mold by RP system. This method does not need RP system to make sample parts, and does not rely on traditional mold manufacturing process. It is particularly fast for metal mold manufacturing, and it is a mold making method with great development prospect; indirect mold making method: indirect molding method is to use RP technology to manufacture product parts prototype, and the original mold is used as mother mold, mold core or mold making tool (grinding mold), and then combined with traditional mold making process Make the required mold. • 缩短产品的设计、开发周期，加快产品的更新换代速度； • 降低企业开发新产品的成本与风险； • 加快产品的造型和系列化的设计； ## bathtub curve 1. ### 词语解说 The bathtub curve is a type of model demonstrating the likely failure rates of technologies and products. 浴缸曲线是一种模型，用来说明技术和产品的可能失败率。 1. ### 定义，作用，目的描述 One function of the bathtub curve is to show the likelihood of initial failure with products. Companies try to eliminate the first infant mortality phase by refining products and engineering to eliminate “dead on arrival” products. There is a sense that products that fail quickly will turn away customers. Companies might use specific tasks like a highly accelerated life test (HALT) or a highly accelerated stress test (HAST) to try to promote the engineering of more durable and long-lasting products. Technology experts may talk about eliminating the causes of “infant mortality” failures. All of this is part of specific product development and quality control in the enterprise world. 浴缸曲线的一个作用是显示产品初始失效的可能性。企业试图通过改进产品和工程，消除"一到就死"的产品，从而消除婴儿死亡的第一阶段。人们有一种感觉，那些很快失败的产品会把消费者拒之门外。公司可能会使用诸如高加速寿命测试(HALT)或高加速压力测试(HAST)这样的特定任务来试图促进更耐用和持久产品的工程设计。技术专家可能会谈论消除"婴儿死亡率"失败的原因。所有这些都是企业界特定产品开发和质量控制的一部分。 ## Accessibility 1. ### 词语解说 In the environment in which software is created, the term “availability” refers to a method that places the user, rather than the system, at the center of the process. This method is called user centered design. It takes the concerns and opinions of users into account from the beginning of the design process, and puts forward that the needs of users should be put in the first place in any design decision. 在创建软件的环境中，术语"可用性"表示一种方法，它将用户而不是系统摆在过程的中心。这一方法称作以用户为中心的设计，它从设计过程的一开始就将用户关心的问题和意见考虑在内，并提出在任何设计决策中用户的需要都应摆在首位。 ## [https://www.w3.org/WAI/fundamentals/accessibility-intro/]{.ul}[https://developer.mozilla.org/zh-CN/docs/Learn/Accessibility/What_is_accessibility]{.ul}[https://developer.mozilla.org/en-US/docs/Learn/Accessibility/What_is_accessibility]{.ul} 1. ### 定义，作用，目的描述在工作中体现可用性在创建软件的环境中，术语"可用性"表示一种方法，它将用户而不是系统摆在过程的中心。这一方法称作以用户为中心的设计，它从设计过程的一开始就将用户关心的问题和意见考虑在内，并提出在任何设计决策中用户的需要都应摆在首位。这种方法最显著的特点就是可用性测试。在测试中，用户使用产品的界面进行工作，通过界面进行交互，就他们的观点和关心的问题与设计人员和开发人员进行交流。本文讨论了可用性的概念，并讨论了为什么可用性在所有软件设计项目中都是一个重要部分。本文的第一部分定义了在软件开发环境中可用性意味着什么，以及它与衡量产品价值的其它方面间的关联。第二部分回答了一些常见的问题，包括：为什么可用性很重要，以及如何在开发过程中体现以用户为中心的设计理念等。本文在结尾处列出了一些书籍、论文和组织机构名称，帮助您加深对可用性的了解，并在项目中应用可用性。本文中讨论的大部分概念在零售和内部软件开发中均有所应用。在阅读本文时，请注意"用户"和"产品"等词语，并思考如何将其应用到您的项目和最终用户中。可用性定义易于使用可用性是衡量使用一种产品来执行指定任务的难易程度的尺度，它与实用性和受欢迎度等相关概念是有差异的。可用性与实用性决定产品可接受性的核心属性是其有用性，它用于评价实际使用产品时，是否能达到设计人员期望产品实现的目标。有用性的概念可以进一步划分为实用性和可用性。虽然这些术语间有联系，但它们却不能相互替代。实用性指产品执行任务的能力。根据设计，产品执行的任务越多，其实用性就越高。让我们以二十世纪八十年代末问世的典型 Microsoft® MS-DOS® 字处理程序为例。此类程序提供了多种强大的文本编辑和处理功能，但需要用户学习和记忆几十个令人费解的按键后才能执行这些功能。可以说此类应用程序具有很高的实用性（它们为用户提供了必要的功能），但其可用性却较差（用户必须花费大量的时间和精力来学习和使用它们）。与之形成对比的是，一个设计合理的简单的应用程序（如计算器）使用起来很容易，但其实用性却有欠缺。这两种性质都是一种产品被市场接受所必需的，而且它们都是总的有用性概念的一部分。显然，若程序很好用但没有什么有价值的功能，那么没有人会使用它；如果程序的功能强大但却很难使用，那么用户也很可能会拒绝这个程序而转向其它的替代品。可用性测试帮助您判断用户使用产品执行特殊任务的难易程度。但是，它并不能直接帮助您判断产品自身是否有价值、是否实用（在可用性测试中，用户可能会主动提出一些关于实用性的意见，但任何意见都应通过其它更可靠的研究方法予以验证）。喜欢它与使用它受欢迎度往往表示产品中可取的特性。如果人们喜欢某产品，就更有可能使用它，并将它推荐给其他人。但是，与实用性一样，您一定要小心不要将受欢迎度和可用性混淆。人们喜欢某产品的原因往往与实用性和可用性无关。他们可能被产品的样式和引人注目的外观吸引，或被心目中所赐予的该产品的地位吸引。人们倾向于喜欢很好用的产品，但这并不是说人们普遍喜爱的产品就是可用的。可用性是指人们是否可以使用该产品来执行他们需要执行的任务。可用性测试主要用于评价性能而不是评价喜爱程度，但标准化的调查问卷也可以用来衡量人们对产品的喜爱程度。发现、学习与有效性可用性包含很多方面，但通常这一术语特指发现、学习和有效性这三种属性。发现表示针对某种特定的需要去寻找并找到产品的某一功能。可用性测试可用于确定用户找到某一功能所用的时间，以及在整个过程中用户犯了多少错误（关于定位的错误选择）。学习表示用户弄清楚如何运用所发现的功能来完成现有任务的过程。可用性测试可以确定这个过程的长短，以及在学习该功能期间用户犯了多少错误。有效性表示用户"掌握"了某项功能，不再需要进一步学习即可使用。可用性测试可以确定有经验的用户使用该功能时执行必要步骤所需的时间。可用性的这三个基本方面在很大程度上受到当前任务性质和用户执行任务的频率的影响。有些功能的使用频率很低或者使用起来十分复杂，导致用户基本上每次使用时都要重新学习；对于这些功能，Microsoft 通常开发了使用向导，在整个使用过程中对用户予以指导。光喊口号是不够的软件设计人员有时以为简单的口号，如"使产品更可用"，就可以解决可用性问题。虽然对可用性的积极态度是重要的，但是只有在具体的产品创建环境中，通过对普通用户进行恰当的可用性测试，才能为设计人员提供所需的信息，使产品可以满足用户的需要。"使产品更可用"应当成为每个软件设计人员的座右铭，但是这句话只对那些了解"可用性"含义的设计人员才有意义。而对普通用户进行测试就是可以找到的最可靠的途径。常见问题为什么要强调可用性问题呢？如果您还没有在产品设计过程中将可用性因素考虑在内，您可能会问：可用性为什么是必要的，或可用性为什么是可取的？毕竟，不进行任何可用性工作，也可能发售一个可以工作的、没有错误的产品。但是，通过引入以用户为中心的设计理念可以使产品在很多方面得以很大改进。减少用户拨打技术支持电话的次数是执行可用性测试的最佳理由。较差的可用性是用户拨打软件技术支持热线的主因，而每个软件公司主管以及信息服务经理都知道产品支持的成本是多么昂贵。此外，用户不得不寻求技术支持增加了用户对产品的潜在不满情绪。如果用户发现贵公司的产品使用起来十分容易，那么他们就不必频繁地打电话寻求技术支持了。对于内部使用的软件，之所以将可用性作为开发过程中的一个重要部分，其原因还在于它减少了培训费用。对用户而言，可用性强的软件学习起来比可用性不受重视的产品学习起来要容易得多。用户能够更快地了解产品的各项功能，并能长久地掌握它，这直接减少了培训费用和时间。可用性测试有助于促进用户对产品的接受程度。有很多因素决定了用户对产品的接受程度，这些因素包括可用性、实用性和受欢迎度。对于零售产品，用户的接受程度往往直接影响对产品的重复购买或对产品的忠诚度，这说明用户可能将产品推荐给其他人。对于内部应用程序，用户的接受程度决定用户是否愿意使用该软件执行任务，而这些软件就是针对这些任务设计的，这有助于提高生产效率。提高可用性是提高用户对产品的接受程度的一个因素。可用性可将您的产品与您的竞争对手的产品区分开来。如果两个产品在实用性方面从本质上讲是一样的，那么人们很可能认为可用性更好的产品高出一筹。此外，由于 Microsoft® Windows® 的外观和感受以及随附的编程准则划定了基本用户界面的使用区域的标准，因此很多执行相似功能的程序其外观与操作在相当大的程度上是相似的。这些相似性表明，即使可用性上的细微差异也会对用户的喜好产生重大的影响。最后请记住，每个产品最终都要进行可用性测试。用户每次使用您的产品时，都是在对它进行可用性测试，而他们对可用性优劣的意见将会影响他们是否继续使用该产品。将产品推向市场之前，对产品进行测试，可以有助于确保用户对产品的满意程度。它的花费是多少？软件设计人员和项目经理往往担心，如果采用以用户为中心的设计过程并执行适当的可用性测试，恐怕要占用大量的时间并花费大量的金钱。事实上，花费在关注用户方面的时间和金钱通常是相当少的，而且与不这样做而导致的花费相比，这点花费也是微不足道的。例如，设想一下在开发周期的后期而不是在前期（产品仍处在开发阶段时）对设计进行修正您要花费多少时间和金钱吧！如果您一直等到 Beta 测试时期才使用户接触到产品以便进行可用性测试，就会发现自己不得不将花费了大量时间开发的程序的各部分分拆重做。而若等到产品真正发布时，如果要根据负面反馈进行修改或支持较差的设计，因为产品支持的庞大开销或用户对产品的接受程度较差等原因，很可能要支付高昂的费用。合理的可用性研究通常只需要两周或更短的时间，并可以显著减少开发周期后期进行修改所需的时间和金钱。进行测试所需的花费将根据您的产品的性质以及所测试的界面部分的不同而有所不同。可以认为可用性测试与代码测试是类似的。成功的项目经理在计划开发项目时总是会考虑到代码测试。他们并不认为代码测试是项目时间表或预算外的额外部分，而是将代码测试作为开发过程的一部分而计入成本。因为若不进行代码测试，那么花费反而会高得多。对于可用性测试，情况也是如此。怎样获得可用性？在理解可用性的重要性基础上，软件设计人员有时试图"获得"一些可用性，就好象可用性是一种成分，他们可以简单地把它添加到产品中，这样产品就更可用了。然而，可用性应当是设计过程本身的一部分，不是您可以在设计过程的随便某一地方添加的"东西"。可用性专家提到"用户关注的"与"以用户为中心的设计"的原因是：可用性取决于将用户的需要一直作为设计过程的中心。以用户为中心的设计根据需要的不同，包含的内容不单单是在界面中按照一组规则，对按钮和菜单布置进行管理。可用性测试是对设计工作进行检查的良机，而不是在产品中"添加"可用性的一种方法。 2. ### 理解与应用一旦您决定我们以用户为中心的设计原理运用到您的开发过程中，就需要决定是自己雇佣可用性专业人员还是将可用性测试外包给供应商。可用性专业人员协会 (UPA) 有一份供应商指南，有助于找到为您执行测试的可用性顾问。有些咨询部门还可以帮助您创建您自己的可用性实验室或开发内部的可用性程序，在您的设计过程中引入可用性理念。自己雇佣可用性专业人员，那么 Human Factors and Ergonomics Society 有职业介绍服务，使您可以找到潜在的雇员。很多可用性专业人员还属于 ACM Special Interest Group on Computer-Human Interaction (SIGCHI) 和 UPA，您也可以在他们的出版物和会刊上刊登招聘广告。 ## 32.algorithmic language ### 1）词语解说 Algorithm refers to the definite and limited steps taken to solve a specific problem. The computer programming language used to express algorithms is called algorithmic language. Algorithmic language is a description tool of algorithm and a general language between machine language and mathematical language ## [https://encyclopediaofmath.org/wiki/Algorithmic_language]{.ul}[https://www.tutorialspoint.com/python_data_structure/python_algorithm_design.htm]{.ul}[https://www.webopedia.com/TERM/A/algorithm.html]{.ul} ### 定义，作用，目的描述 Computer language is divided into machine language, assembly language and high-level language. High level language is a kind of artificial design language, because it describes the specific algorithm, so it is also called algorithm language. Computer has been widely used in various fields of social life, and has become a popular modern tool. People will need to do the work of the computer into a certain form of instructions, and they are stored in the internal memory of the computer, when people give the command, it will automatically operate according to the order of instructions. This set of instructions that can be executed continuously is called “program”. It can be said that program is the language of “dialogue” between human and machine, that is, we often say “programming language”. At present, there are hundreds of programming languages used in the society, such as C, visual basic, C + + and Java, which are called “advanced languages” of computers. These languages are close to people’s habits of natural language and mathematical language as a form of expression, making it very convenient for people to learn and operate. Common algorithm languages include basic, FORTRAN, COBOL, Pascal, C, C + + and Java. ## application domain 1. ### 词语解说 One of the prerequisites for the development of a software system is that we have a definition and a clear understanding of the contents of the application domain concerned. This is the part of an organization for which we are to develop application software. This means that the application domain is our starting point and the context for our software development. 开发软件系统的先决条件之一是我们对有关应用领域的内容有一个清晰的定义和理解。这是我们为其开发应用软件的组织的一部分。这意味着应用程序领域是我们软件开发的起点和上下文。 1. ### 定义，作用，目的描述 An application domain is the segment of reality for which a software system is developed. It is the background or starting point for the actual-state analysis and the creation of a domain model. 应用领域是软件系统开发的现实环节。它是实际状态分析和领域模型创建的背景或出发点。 An application domain can be an organization, a department within an organization, or a single workplace. 应用程序域可以是组织、组织中的部门或单个工作场所。 The concept of an application domain is at least as wide, so that the domain concepts and relations relevant for the construction of models can be well understood during the analysis of the actual state of the domain. On the other hand, its extent should always be limited, that is, never be too complex. 应用程序领域的概念至少是同样广泛的，因此在分析领域的实际状态时，可以很好地理解与模型构造相关的领域概念和关系。另一方面，它的范围应该总是有限的，也就是说，永远不要太复杂。 An application domain normally includes a domain-specific language. This means that people in this domain use specific terms and concepts and think about their domain in a specific way. 一个应用程序域通常包括一个领域特定语言。这意味着这个领域的人使用特定的术语和概念，并以特定的方式思考他们的领域。 The application domain is very important, because it is critical for our application-oriented way of developing software. The developers analyze and describe the actual tasks and situations (see Section 6.41) that characterize the application domain in the domain-specific language. This corresponds to an actual-state analysis, where the typical processes and the objects used in these processes are represented in their domain-specific use contexts, for example, as scenarios or glossary entries (see Section 5.3.11). It is similar to the business model in UP. At the same time, the application domain is the basis for the construction of a domain model. Together with the analysis and description of the actual state within the application domain, we are gradually building the domain model. 应用领域非常重要，因为它对于我们面向应用的软件开发方式至关重要。开发人员分析和描述实际的任务和情况，这些任务和情况描述了领域特定语言应用程序中的应用域。这与实际状态分析相对应，在这种分析中，这些流程中使用的典型流程和对象在其特定于领域的使用上下文中表示，例如，作为场景或术语表条目。它类似于 UP 的商业模式。同时，应用领域是构建领域模型的基础。结合对应用领域内实际状态的分析和描述，我们正在逐步构建领域模型。 Building a domain model 构建领域模型 This model represents the segment of the actual application domain to be supported by the software system under development. Obviously, our domain model is similar to the domain model in UP. Later in this chapter, we will explore the question whether or not the UP domain model can meet all our requirements, that is, easy to understand and easy to construct, as one model. 此模型表示开发中的软件系统所支持的实际应用程序域的部分。显然，我们的领域模型类似于 UP 中的领域模型。在本章的后面，我们将探索 UP 领域模型是否能够满足我们的所有需求，即作为一个模型易于理解和易于构造的问题。 This interest of developers in an application domain is not limited to the segments that will be mapped in the domain model; they will also deal with segments required to understand the current work situation within the actual-state analysis. It is at once a risk and an art to find the right limits for the actual-state analysis, and not to let it get out of hand both in terms of time and content. Experiences from traditional data-modeling projects have shown that it is simply not possible to achieve a complete analysis of the entire application domain. The first notion of the future application system will help developers find the right point to stop analyzing. This means that the developers have to gain quick insight about the points of the application domain where software support could be useful and feasible. 开发人员对应用程序领域的兴趣并不局限于将映射到领域模型中的片段; 他们还将处理理解实际状态分析中当前工作情况所需的片段。为实际状态分析找到正确的界限，并且不让它在时间和内容上失控，这既是一种风险，也是一种艺术。传统数据建模项目的经验表明，完全分析整个应用程序领域是不可能的。未来应用程序系统的第一个概念将帮助开发人员找到停止分析的正确点。这意味着开发人员必须快速了解应用程序领域中哪些地方的软件支持可能是有用的和可行的。 ## software architecture ### 词语解说 Software architecture is a series of related abstract patterns, which are used to guide the design of various aspects of large-scale software system. 1. ### 定义，作用，目的描述 There is no doubt that the world is becoming increasingly dependent on software. Software is an essential element of the ubiquitous cell phone, as well as complex air traffic control systems. In fact, many of the innovations that we now take for granted – including organizations such as eBay or Amazon – simply wouldn’t exist if it weren’t for software. Even traditional organizations, such as those found in the finance, retail, and public sectors, depend heavily on software. In this day and age, it’s difficult to find an organization that isn’t, in some way, in the software business. 毫无疑问，世界正变得越来越依赖软件。软件是无处不在的手机以及复杂的空中交通管制系统的基本元素。事实上，许多我们现在认为理所当然的创新---- 包括像 eBay 或亚马逊这样的组织---- 如果不是因为软件，根本不会存在。即使是传统的组织，比如那些在金融、零售和公共部门的组织，也严重依赖软件。在当今这个时代，很难找到一个在某种程度上不属于软件行业的组织。 In order for such innovations and organizations to survive, the software they depend on must provide the required capability, be of sufficient quality, be available when promised, and be delivered at an acceptable price. 为了使这些创新和组织能够生存下去，他们所依赖的软件必须具备必要的能力，必须具备足够的质量，必须在承诺时提供，并且以可接受的价格交付。 All these characteristics are influenced by the architecture of the software, the subject of this article. My focus here is on “software-intensive systems,” which the IEEE defines as follows: 所有这些特征都受到本文主题------软件体系结构的影响。我在这里的重点是"软件密集型系统" ，IEEE 对它的定义如下: A software-intensive system is any system where software contributes essential influences to the design, construction, deployment, and evolution of the system as a whole. [from IEEE 1471. See the “Architecture defined” section below.] 软件密集型系统是任何系统，其中软件对整个系统的设计、构建、部署和演进有重要影响。[摘自 IEEE 1471。参见下面的"体系结构定义"部分。] In this article, the term “architecture,” when unqualified, is synonymous with the term “software architecture.” Although this article focuses on software-intensive systems, it is important to remember that a software-intensive system still needs hardware in order to execute and that certain qualities, such as reliability or performance, are achieved through a combination of software and hardware. The hardware aspect of the total solution cannot therefore be ignored. This is discussed in more detail later in this article. 在本文中，术语"架构"(当不合格时)与术语"软件架构"是同义词虽然本文侧重于软件密集型系统，但是重要的是要记住，软件密集型系统仍然需要硬件来执行，并且某些特性，如可靠性或性能，是通过软件和硬件的组合来实现的。因此，不能忽略整个解决方案的硬件方面。本文后面将更详细地讨论这个问题。 Architecture defined 体系结构定义 There is no shortage of definitions when it comes to “architecture.” There are even Websites that maintain collections of definitions.1 The definition used in this article is that taken from IEEE Std 1472000, the IEEE Recommended Practice for Architectural Description of Software-Intensive Systems, referred to as IEEE 1471.2 This definition follows, with key characteristics bolded. 当涉及到"体系结构"时，并不缺少定义本文中使用的定义来自 IEEE Std 1472000，IEEE 软件密集型系统架构描述的推荐实践，简称 IEEE 1471.2。 Architecture is the fundamental organization of a system embodied in its components, their relationships to each other, and to the environment, and the principles guiding its design and evolution. [IEEE 1471] 体系结构是一个系统的基本组织，体现在其组成部分、它们之间的关系、与环境的关系以及指导其设计和发展的原则上。1471] This standard also defines the following terms related to this definition: 本标准还定义了与本定义相关的以下术语: A system is a collection of components organized to accomplish a specific function or set of functions. The term system encompasses individual applications, systems in the traditional sense, subsystems, systems of systems, product lines, product families, whole enterprises, and other aggregations of interest. A system exists to fulfill one or more missions in its environment. [IEEE 1471] 系统是组织起来完成特定功能或一组功能的组件的集合。术语系统包括单个应用程序、传统意义上的系统、子系统、系统的系统、产品线、产品系列、整个企业以及其他感兴趣的集合。一个系统的存在是为了在它的环境中完成一个或多个任务。1471] The environment, or context, determines the setting and circumstances of developmental, operational, political, and other influences upon that system. [IEEE 1471] 环境，或者说环境，决定了发展的、可操作的、政治的以及其他影响该系统的因素的背景和环境。1471] A mission is a use or operation for which a system is intended by one or more stakeholders to meet some set of objectives. [IEEE 1471] 任务是一个或多个利益相关者为了实现某些目标而设计的系统的使用或操作。1471] A stakeholder is an individual, team, or organization (or classes thereof) with interests in, or concerns relative to, a system. [IEEE 1471] 涉众是个人、团队或组织(或其类别) ，他们对系统感兴趣，或者与系统有关。1471] As we can see, the term “component” is used throughout these definitions. However, most definitions of architecture do not define the term “component,” and IEEE 1471 is no exception, as it leaves it deliberately vague to cover the many interpretations in the industry. A component may be logical or physical, technology-independent or technology-specific, large-grained or small-grained. For the purposes of this article, I use the definition of component from the UML 2.0 specification; and I use the term fairly loosely in order to encompass the variety of architectural elements that we may encounter, including objects, technology components (such as an Enterprise JavaBean), services, program modules, legacy systems, packaged applications, and so on. Here is the UML 2.0 definition for “component”: 正如我们所看到的，术语"组件"贯穿于这些定义之中。然而，架构的大多数定义并没有定义术语"组件" ，IEEE 1471也不例外，因为它故意使它含糊不清，以涵盖行业中的许多解释。组件可以是逻辑的或物理的、技术独立的或特定于技术的、大粒度的或小粒度的。出于本文的目的，我使用了 UML 2.0规范中的组件定义; 我相当松散地使用这个术语是为了包含我们可能遇到的各种架构元素，包括对象、技术组件(如企业 JavaBean)、服务、程序模块、遗留系统、打包应用程序等等。 ## background processing 1. ### 词语解说 Background processing can be best defined by its action. It simply performs tasks in the background of a computer while a computer user performs actions in the foreground of the computer. 后台处理可以通过它的动作来最好地定义。它只是在计算机的后台执行任务，而计算机用户在计算机的前台执行操作。 ## [https://www.bobology.com/public/What-is-a-Background-Process.cfm]{.ul}[https://www.wisegeek.com/what-is-background-processing.htm]{.ul}[https://medium.com/@julian_falcionelli/background-processing-in-android-575fd4ecf769]{.ul} ### 定义，作用，目的描述 Background processing can be best defined by its action. It simply performs tasks in the background of a computer while a computer user performs actions in the foreground of the computer. For example, in background processing, a computer user can actively manipulate one application using a keyboard and a computer screen while separate operations are performed at the same time and in the background. In many cases, background processes work completely autonomously and the user isn’t even aware that the processes are being performed. Processing data in the background of any computer is an integral part of the functioning of a computer. Backgrounds can be high-priority, same-level priority or low-level priority compared to the application that a user is working with on-screen. As long as background processing is achieved within an acceptable time frame and doesn’t interfere with the activities of the user or the overall functioning of the computer, it can be considered to be successful. One popular example of background processing involves the common printer. When a computer user works on a word processor to type up a document, saves it and commands the computer to print it, the command is transferred over to the printer by way of the computer’s background processes. This activity takes place independent of whatever is happening on the computer user’s screen. In fact, a computer user can continue to make modifications to the document, open and type a new document or work in an entirely new application altogether while the computer is engaged in background processing. The lack of interaction between computer user and background processes should not be misunderstood to mean that the processes are unimportant. There are certain background processes that are just as important as those applications that are being interacted with in the foreground. Some computers have the ability to prioritize tasks and regulate how much energy is devoted to each. Generally, though, a background process is relatively low priority and has minimal output. Background processes can be usually categorized as being either a daemon or a compute-intensive task. The average computer user will be more familiar with the work of daemons, as they help take care of common functions like email transferring, web page serving and time synchronization. Their interactions are not with users, but with programs or other computers on a network. They use very little memory and don’t put a large dent in CPU usage, so computer users may work on a machine for years without realizing that these processes exist and are actually taking place while they are concentrating on a task in the computer’s foreground. ## collaboration diagram 1. ### 词语解说 A collaboration diagram, also known as a communication diagram, is an illustration of the relationships and interactions among software objects in the Unified Modeling Language (UML). These diagrams can be used to portray the dynamic behavior of a particular use case and define the role of each object. 协作图，也称为交流图，是统一建模语言中软件对象之间的关系和交互的一个例子。这些图可用于描述特定用例的动态行为，并定义每个对象的角色。 1. ### 定义，作用，目的描述 Collaboration diagrams are created by first identifying the structural elements required to carry out the functionality of an interaction. A model is then built using the relationships between those elements. Several vendors offer software for creating and editing collaboration diagrams. 协作图是通过首先确定执行交互功能所需的结构元素来创建的。然后利用这些元素之间的关系建立模型。一些供应商提供用于创建和编辑协作图的软件。 A collaboration diagram resembles a flowchart that portrays the roles, functionality and behavior of individual objects as well as the overall operation of the system in real time. The four major components of a collaboration diagram are: 协作图类似于一个流程图，它描绘了单个对象的角色、功能和行为，以及实时的系统整体操作。协作图的四个主要组成部分是: Objects- Objects are shown as rectangles with naming labels inside. The naming label follows the convention of object name: 对象-对象显示为带有命名标签的矩形。命名标签遵循对象名称的约定:class name 类名. If an object has a property or state that specifically influences the collaboration, this should also be noted. 。如果对象具有专门影响协作的属性或状态，也应该注意这一点 Actors- Actors are instances that invoke the interaction in the diagram. Each actor has a name and a role, with one actor initiating the entire use case. 参与者------参与者是在图中调用交互的实例。每个参与者都有一个名称和一个角色，由一个参与者启动整个用例 Links- Links connect objects with actors and are depicted using a solid line between two elements. Each link is an instance where messages can be sent. 链接-链接连接对象与演员和描述使用实线之间的两个元素。每个链接都是可以发送消息的实例 messages- Messages between objects are shown as a labeled arrow placed near a link. These messages are communications between objects that convey information about the activity and can include the sequence number. 消息------对象之间的消息显示为放置在链接附近的带标签的箭头。这些消息是对象之间的通信，它们传递有关活动的信息，并且可以包含序列号 The most important objects are placed in the center of the diagram, with all other participating objects branching off. After all objects are placed, links and messages should be added in between. 最重要的对象被放置在关系图的中心，所有其他参与的对象分支。在放置所有对象之后，应该在两者之间添加链接和消息。 Collaboration diagrams should be used when the relationships among objects are crucial to display. A few examples of instances where collaboration diagrams might be helpful include: 当对象之间的关系对于显示至关重要时，应该使用协作关系图。协作图可能有帮助的一些实例包括: Modeling collaborations, mechanisms or the structural organization within a system design. 在系统设计中为协作、机制或结构组织建模 Providing an overview of collaborating objects within an object-oriented system. 提供面向对象系统中协作对象的概述 Exhibiting many alternative scenarios for the same use case. 显示同一用例的许多可选场景 Demonstrating forward and 向前展示reverse engineering 逆向工程. Capturing the passage of information between objects. 捕获对象之间的信息通道 Visualizing the complex logic behind an operation. 可视化操作背后的复杂逻辑 However, collaboration diagrams are best suited to the portrayal of simple interactions among relatively small numbers of objects. As the number of objects and messages grows, a collaboration diagram can become difficult to read and use efficiently. Additionally, collaboration diagrams typically exclude descriptive information, such as timing. 然而，协作图最适合描绘相对较少的对象之间的简单交互。随着对象和消息数量的增加，协作关系图可能变得难以阅读和有效使用。此外，协作关系图通常不包含描述性信息，例如时间。 In UML, the two types of interaction diagrams are collaboration and sequence diagrams. While both types use similar information, they display them in separate ways. Collaboration diagrams are used to visualize the structural organization of objects and their interactions. Sequence diagrams, on the other hand, focus on the order of messages that flow between objects. However, in most scenarios, a single figure is not sufficient in describing the behavior of a system and both figures are required. 在 UML 中，两种类型的交互图是协作图和序列图。虽然这两种类型使用相似的信息，但它们以不同的方式显示。协作图用于可视化对象的结构组织及其交互。另一方面，序列图关注对象之间流动的消息的顺序。但是，在大多数情况下，单个图形不足以描述系统的行为，需要两个图形。 2. ### 理解与应用 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-4vVicPbn-1609755291789)(media/image22.png)]{width=“5.763888888888889in” height=“3.692361111111111in”} [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-r349AY01-1609755291790)(media/image23.png)]{width=“5.766666666666667in” height=“4.379861111111111in”} ## BPMN 1. ### 词语解说 The Business Process Modeling Notation (BPMN) is visual modeling language for business analysis applications and specifying enterprise process workflows, which is an open standard notation for graphical flowcharts that is used to define business process workflows. It is popular and intuitive graphic that can be easily understand by all business stakeholders, including business users, business analysts, software developers, and data architects. 是一个用于业务分析应用程序和指定企业流程工作流的可视化业务流程建模标记法建模语言，它是一个用于定义业务流程工作流的图形流程图的开放标准符号。它是流行和直观的图形，可以很容易地被所有业务涉众理解，包括业务用户、业务分析师、软件开发人员和数据架构师。 1. ### 定义，作用，目的描述 BPMN allows us to capture and document business processes of an organization in a clear and consistent way that ensures relevant stakeholders, such as, process owners and business users are involved in the process. Thus, the team can response to any issues identified in the processes more effectively. BPMN provide comprehensive and yet rich notations that can easily be understood by both technical and non-technical stakeholders. Business process modeling provides important benefits to companies and organizations such as the ones listed below. BPMN 允许我们以一种清晰和一致的方式捕获和记录组织的业务流程，以确保相关的涉众(如流程所有者和业务用户)参与流程。因此，团队可以更有效地响应过程中发现的任何问题。BPMN 提供了全面而丰富的符号，技术和非技术利益相关者都可以很容易地理解。业务流程建模为下面列出的公司和组织提供了重要的好处。 An industry standard developed by the OMG consortium, a not-for-profit industry group 由非营利性行业组织 OMG 联盟开发的行业标准 Provides businesses with the capability of defining and understanding their procedures through Business Process Diagrams 通过业务流程图为企业提供定义和理解其过程的能力 To provide a standard notation that is readily understandable by all business stakeholders 提供所有业务涉众容易理解的标准符号 To bridge the communication gap that frequently occurs between business process design and implementation 弥合业务流程设计和实现之间经常出现的通信差距 Simple to learn yet powerful enough to depict the potential complexities of a business process 学起来很简单，但是足够强大，可以描述业务流程的潜在复杂性 The Goal of BPMN BPMN 的目标 Technical experts responsible for process implementation 负责过程实施的技术专家 Business analysts who create and improve the processes 创建和改进流程的业务分析师 Managers who monitor and control the processes 监督和控制过程的管理者 Overview of BPMN BPMN 概述 Knowing how the business operates is the first and the most critical step of business process improvement. Business Process Model and Notation (BPMN), provides a graphical representation of business work flows that anyone, from business analyst to stakeholder, can easily understand; aiding in business process analysis and business process improvements. 了解业务如何运作是业务流程改进的第一步，也是最关键的一步。提供了业务工作流的图形化表示，任何人，从业务分析师到利益相关者，都可以很容易地理解这些业务流程建模标记法; 协助业务流程分析和业务流程改进。 Any process described with BPMN is represented as a number of steps (activities) that are performed consequently or at the same time according to certain business rules. Take a look at the “Place Order online” process which can be used in an on-line store that place orders on the web. 使用 BPMN 描述的任何流程都表示为许多步骤(活动) ，这些步骤(活动)随后或同时根据某些业务规则执行。 2. ### 理解与应用以下是四种基本的类型： • 流对象(Flow) • 连接对象(Connection) • 泳道(Swimlane) • 人工信息(Artifact) BPMN的开发是减少众多已存在的业务建模工具和标记断层的重要的一步。BPMI标准化组织从许多存在的标记中展示出了专业和经验，且从这些不同的标记中找到了最好的理念形成一套标准的标记语言，众多的标记语言包括UML、Activity Diagram、UML EDOC Business Process、IDEF、ebXML BPSS、RosettaNet以及Event-Process Chains等等。一个好的标准建模标记将会减少业务与IT用户之间的混乱。 ## Use Case Diagram 1. ### 词语解说 So what is a use case diagram? A UML use case diagram is the primary form of system/software requirements for a new software program underdeveloped. Use cases specify the expected behavior (what), and not the exact method of making it happen (how). Use cases once specified can be denoted both textual and visual representation (i.e. use case diagram). A key concept of use case modeling is that it helps us design a system from the end user’s perspective. It is an effective technique for communicating system behavior in the user’s terms by specifying all externally visible system behavior. 那么什么是使用案例图呢？对于一个新的软件项目来说，UML 使用案例图是系统/软件需求的主要形式。用例指定预期的行为(什么) ，而不是使其发生的确切方法(如何发生)。一旦指定了用例，就可以同时表示文本和可视化的表示形式(例如使用案例图)。用例建模的一个关键概念是，它帮助我们从最终用户的角度设计系统。通过指定所有外部可见的系统行为，它是以用户的术语进行系统行为通信的一种有效技术。 ## [[https://www.guru99.com/use-case-diagrams-example.html#:~:text=Summary%201%20Use%20case%20diagrams%20are%20a%20way,a%20package%2C%20or%20a%20class.%20More%20items…%20]{.ul}](https://www.guru99.com/use-case-diagrams-example.html#:~:text=Summary 1 Use case diagrams are a way,a package, or a class. More items… )[https://creately.com/blog/diagrams/use-case-diagram-tutorial/]{.ul}[https://www.visual-paradigm.com/guide/uml-unified-modeling-language/what-is-use-case-diagram/]{.ul} 1. ### 定义，作用，目的描述 A use case diagram is usually simple. It does not show the detail of the use cases: 使用案例图通常很简单，它不显示用例的细节: It only summarizes 它只是概括了some of the relationships 一些关系 between use cases, actors, and systems. 在用例、参与者和系统之间 It does 的确如此not show the order 不要显示命令 in which steps are performed to achieve the goals of each use case. 执行步骤以实现每个用例的目标 As said, a use case diagram should be simple and contains only a few shapes. If yours contain more than 20 use cases, you are probably misusing use case diagram. 如上所述，一个使用案例图应该是简单的，并且只包含几个形状。如果你的包含超过20个用例，那么你很可能是在滥用使用案例图。 The figure below shows the UML diagram hierarchy and the positioning of the UML Use Case Diagram. Use case diagrams are typically developed in the early stage of development and people often apply use case modeling for the following purposes: 用例图通常是在开发的早期阶段开发的，人们经常将用例建模用于以下目的: Specify the context of a system 指定系统的上下文 Capture the requirements of a system 捕获系统的需求 Validate a systems architecture 验证系统架构 Drive implementation and generate test cases 驱动实现并生成测试用例 Developed by analysts together with domain experts 由分析师和领域专家共同开发 2. ### 理解与应用 1. 参与者本身并不属于系统结构之中，位于系统之外； 2. 参与者代表的是一类角色而不是一个具体对象，换言之，你可以说参与者是猪，而不能说参与者是"佩奇"； 3. 参与者不一定是人，也可以是另一个外部的系统、环境等等。 UML中用一个小人图形表示参与者。我们给每一个参与者取特定的名字，并可以在文档中对用例进行描述。 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-c3CsE1PO-1609755291791)(media/image24.png)]{width=“3.3020833333333335in” height=“2.21875in”} UML中名为Passenger的参与者 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-7iohR53v-1609755291791)(media/image25.png)]{width=“3.5520833333333335in” height=“1.28125in”} UML中名为Purchase Ticket的用例 1. 用例名称； 2. 用例的参与者：使用该用例的参与者； 3. 用例的进入条件：满足什么条件可以使用该用例； 4. 用例的离开条件：满足什么条件可以结束该用例的使用； 5. 流程：参与者使用该用例的步骤； 6. 特殊需求：包含对用例性能上的需求或者拓展业务。 1. 扩展 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-qBmSDUZN-1609755291792)(media/image26.png)]{width=“5.520833333333333in” height=“3.6979166666666665in”} UML中扩展关系的应用 2. 包含 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-Pq28LWY3-1609755291793)(media/image27.png)]{width=“5.395833333333333in” height=“2.5833333333333335in”} UML中包含关系的应用 3. 继承 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-YoODTfVi-1609755291794)(media/image28.png)]{width=“5.635416666666667in” height=“2.9166666666666665in”} UML中继承关系的应用 ## Timing Diagram 1. ### 词语解说 Timing diagrams focus on conditions changing within and among lifelines along a linear time axis. Timing Diagrams describe behavior of both individual classifiers and interactions of classifiers, focusing attention on time of occurrence of events causing changes in the modeled conditions of the Lifelines. 时间图关注的是生命线内部和生命线之间沿着线性时间轴发生的变化。时序图描述了单个分类器的行为和分类器之间的相互作用，将注意力集中在引起生命线模型条件变化的事件发生的时间上。 1. ### 定义，作用，目的描述 State Timeline Representation 状态时间线表示法 Changes from one state to another are represented by a change in the level of the lifeline. For the period of time when the object is a given state, the timeline runs parallel to that state. A change in state appears as a vertical change from one level to another. The cause of the change, as is the case in a state or sequence diagram, is the receipt of a message, an event that causes a change, a condition within the system, or even just the passage of time. 从一个状态到另一个状态的变化表现为生命线级别的变化。对于对象处于给定状态的时间段，时间线与该状态平行运行。状态的变化表现为从一个级别到另一个级别的垂直变化。变化的原因，就像在一个州或时序图，是接收到一个消息，一个事件，导致变化，系统内的条件，甚至只是时间的流逝。 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-f6mMiCfg-1609755291795)(media/image29.png)]{width=“5.7625in” height=“3.4916666666666667in”} Timing Diagram Example Value lifeline Representation 价值生命线表示法 The figure below shows an alternative notation of UML Timing diagram. It shows the state of the object between two horizontal lines that cross with each other each time the state changes. 下面的图显示了 UML 计时图的另一种表示法。它显示了两条水平线之间的对象状态，这两条线在状态发生变化时相互交叉。 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-qHa8pZAU-1609755291796)(media/image30.png)]{width=“5.768055555555556in” height=“2.1458333333333335in”} Compact view of Timing Diagram Basic Concepts of Timing Diagrams 时序图的基本概念 Major elements of timing UML diagram - lifeline, timeline, state or condition, message, duration constraint, timing ruler. 时间 UML 图的主要元素------生命线、时间线、状态或条件、消息、持续时间约束、时间标尺。 Lifeline 生命线 A lifeline in a Timing diagram forms a rectangular space within the content area of a frame. Lifeline is a named element which represents an individual participant in the interaction. It is typically aligned horizontally to read from left to right. 时序图中的生命线在框架的内容区域内形成一个矩形空间。生命线是一个命名元素，它表示交互中的个别参与者。它通常是水平对齐的，从左到右阅读。 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-vjGV5ACJ-1609755291797)(media/image31.png)]{width=“2.375in” height=“1.0833333333333333in”} Timing Diagram with One Lifeline Multiple lifelines may be stacked within the same frame to model the interaction between them. 多个生命线可能被堆放在同一个框架中，以模拟它们之间的交互。 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-SJhPiKdk-1609755291798)(media/image32.png)]{width=“2.2395833333333335in” height=“1.5520833333333333in”} Timing Diagram with Multiple lifelines State Timeline in Timing Diagram 时序图中的状态时间线 A state or condition timeline represents the set of valid states and time. The states are stacked on the left margin of the lifeline from top to bottom. 状态或条件时间线表示有效状态和时间的集合。这些州从上到下堆放在生命线的左边。 [外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-ZW0C5wd4-1609755291798)(media/image33.png)]{width=“5.53125in” height=“2.4375in”} State Timeline in Timing Diagram The cause of the change, as is the case in a state or sequence diagram, is the receipt of a message, an event that causes a change, a condition within the system, or even just the passage of time. 变化的原因，就像在一个州或时序图，是接收到一个消息，一个事件，导致变化，系统内的条件，甚至只是时间的流逝。 2. ### 理解与应用时序图可以展示对象之间交互的顺序。将交互行为建模为消息传递，通过描述消息是如何在对象间发送和接收的来动态展示对象之间的交互；相对于其他UML图，时序图更强调交互的时间顺序；可以直观的描述并发进程。 ## Event Time ### 词语解说 Event time: event time is the time that each independent event occurs on its generating device, which is usually embedded in the record before entering Flink. ## [https://www.jianshu.com/p/1df7ed5061ff]{.ul}[https://www.publichealth.columbia.edu/research/population-health-methods/time-event-data-analysis]{.ul}[https://www.timeanddate.com/worldclock/fixedform.html]{.ul} ### 定义，作用，目的描述 Processing time：处理时间是指执行相应操作机器的系统时间。当流程序在处理时间上运行时，所有基于时间的操作(如时间窗口)将使用当前运行机器的系统时间。每小时处理时间窗口包括在系统时间每小时内到达的所有指定操作记录。例如：如果应用程序在上午9:15开始运行，第一个小时处理时间窗口将包括上午9:15到10:00之间处理的事件，下一个窗口将包含上午10:00到11:00之间处理的事件，以此类推。 ## 40. domain modeling {#domain-modeling .list-paragraph} 1. ### 词语解说 Domain model is a visual representation of conceptual classes or objects in the real world. It is also called concept model, domain object model and analysis object model. It focuses on analyzing the problem domain itself, discovering important business domain concepts, and establishing relationships between business domain concepts. 领域模型是对领域内的概念类或现实世界中对象的可视化表示。又称概念模型、领域对象模型、分析对象模型。它专注于分析问题领域本身，发掘重要的业务领域概念，并建立业务领域概念之间的关系。 ## [https://www.wisdomjobs.com/e-university/uml-tutorial-175/what-is-a-domain-model-13285.html]{.ul}[http://www.cs.sjsu.edu/~pearce/modules/lectures/ooa/analysis/DomainModeling.htm]{.ul}[https://culttt.com/2014/11/12/domain-model-domain-driven-design/]{.ul} 1. ### 定义，作用，目的描述 In the business object model, business roles represent the roles employees will play, while business entities represent the objects employees will handle. On the one hand, the business object model can be used to determine how business employees will interact to produce the desired results for business actors. On the other hand, the system use case model and design model specify the business information system. Business modeling and system modeling solve different problems, and the degree of abstraction is also different. Therefore, in general, information systems should not appear directly in the business model. On the other hand, employees use information systems as business roles to communicate with each other, with the protagonist, and to access business entity information. All links, associations or attributes are supported by a potential information system. These two types of modeling environments have the following relationships: 在业务对象模型中，业务角色代表雇员将担当的角色，而业务实体则代表雇员将处理的对象。一方面，可以使用业务对象模型来确定业务雇员将如何进行交互，以产生业务主角所期望的结果。另一方面，系统用例模型和设计模型指定了业务的信息系统。业务建模和系统建模解决不同的问题，其抽象程度也不一样。所以一般而言，信息系统不应该直接出现在业务模型中。另一方面，雇员作为业务角色来使用信息系统，实现相互之间的通信、与主角的通信以及对业务实体信息进行访问。所有的链接、关联关系或属性都有某个潜在的信息系统对其进行支持。这两类建模环境有以下关系：作为特定业务角色的雇员与信息系统的一个系统主角相对应。如果建立的信息系统使该雇员在业务用例中的所有工作都得到一个系统用例的支持，则他最有可能得到最好的支持。另外，如果业务用例规模大、生存期长或者合并了多个独立领域中的工作，信息系统用例将可以支持业务角色的操作。雇员工作的对象（建模为业务实体）常在信息系统中得到表现。在信息系统的对象模型中，这些业务实体作为实体类出现。业务实体之间的关联关系和聚合关系常常使设计模型中实体类之间产生对应的关联关系和聚合关系。因此，系统用例访问并操作设计模型中的实体类，这些实体类代表由被支持业务用例访问的业务实体。最后，直接使用业务信息系统的业务主角也成为信息系统的系统主角。当确定对支持业务的信息系统的需求时，这些关系十分关键。 1. # 对我们小组项目的发展建议经过一个学期的软件需求分析与建模的学习，对于软件工程与需求分析的认识更深了，从中学到了许多东西，例如UML各种图是什么意思，每个图该怎么画，如何去理解等等，有了这些知识，对于我们项目今后的发展提供了坚实的基础，通过对需求分析与建模的学习，我们可以更好得进行项目的准备，开发和管理，既然学习了这么多的只是，我认为应当把他们好好利用起来，给我们的项目增加价值，可以针对我们的项目，把之前书写的需求分析文档再次完善一下，利用上后来学习的东西，我们小组的项目是实验室设备管理系统，经过我们的切身体会，该系统的应用前景还是十分广泛的，是一个高校实验室所必备的系统，因此对我们小组的发展建议有下面几点 • 利用所学内容完善好需求分析 • 根据需求分析的内容，分析实现系统所需要的资源以及技术 • 实现该系统的大部分功能 • 结合系统的商业价值分析，将系统朝着商用的方向发展在业务对象模型中，业务角色代表雇员将担当的角色，而业务实体则代表雇员将处理的对象。一方面，可以使用业务对象模型来确定业务雇员将如何进行交互，以产生业务主角所期望的结果。另一方面，系统用例模型和设计模型指定了业务的信息系统。 1. # 对我们小组项目的发展建议经过一个学期的软件需求分析与建模的学习，对于软件工程与需求分析的认识更深了，从中学到了许多东西，例如UML各种图是什么意思，每个图该怎么画，如何去理解等等，有了这些知识，对于我们项目今后的发展提供了坚实的基础，通过对需求分析与建模的学习，我们可以更好得进行项目的准备，开发和管理，既然学习了这么多的只是，我认为应当把他们好好利用起来，给我们的项目增加价值，可以针对我们的项目，把之前书写的需求分析文档再次完善一下，利用上后来学习的东西，我们小组的项目是实验室设备管理系统，经过我们的切身体会，该系统的应用前景还是十分广泛的，是一个高校实验室所必备的系统，因此对我们小组的发展建议有下面几点 • 利用所学内容完善好需求分析 • 根据需求分析的内容，分析实现系统所需要的资源以及技术 • 实现该系统的大部分功能 • 结合系统的商业价值分析，将系统朝着商用的方向发展 • 0 点赞 • 0 评论 • 0 收藏 • 一键三连 • 扫一扫，分享海报 04-24 290 01-04 35 04-15 2897 01-03 301 09-26 214 04-25 1086	2021-12-06 20:24:13	{"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": 0.2693847715854645, "perplexity": 2245.7046124215485}, "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/1637964363312.79/warc/CC-MAIN-20211206194128-20211206224128-00248.warc.gz"}
http://crypto.stackexchange.com/questions/6074/encrypting-or-hmacing-password-digests	# Encrypting or HMACing password digests Assuming I'm using bcrypt to digest passwords, is any additional security gained by either encrypting or HMACing the resulting digests? By requiring a key to compare password hashes, I would expect that this would prevent any attempt at brute forcing sans the key. The keys for this operation are actually stored somewhere other than our application servers, and all cryptographic operations are performed there via API calls. The service is designed to never divulge keys themselves, and only operate on keys by an opaque ID. So it should be considered somewhat less likely that our keys would be compromised in an attack than in typical webapp scenarios. Keys are also unique per customer of our application. I would normally only consider HMAC for this operation, but this would require extracting (and storing separately) the salt from the bcrypt digest. So simply encrypting the crypt digests seems to be the simplest approach, and intuitively should produce the same desired security properties. Is this approach reasonable and sane? We already have the cryptography infrastructure in place, so it's not considerably more difficult to encrypt/HMAC our hashes than it is to compute them in the first place. Is there a reason to prefer an HMAC over AES-128-GCM? - I'd use encryption, since that allows you to upgrade hashes when you change the key. – CodesInChaos Jan 22 '13 at 19:42 That's an important feature, actually. Do you see any reason not to do either? – Stephen Touset Jan 22 '13 at 22:28 I presume from the above text that you are planning to only store the HMAC if that protocol is choosen (storing a HMAC in addition does not seem to make sense). It may be best to put the verify method in the crypto-server by the way. – Maarten Bodewes Jan 23 '14 at 15:09 Correct. That's what we did; there's simply an API call for, e.g., "generate password hash using opaque key_id" and "confirm provided password matches a given hash for some key_id". – Stephen Touset Jan 23 '14 at 18:27 If you store the encrypted digests in one location, the key in another, and send the new digest and encrypted one from the first location to the second --- you probably have much better chance to have your communications intercepted with both plaintext and ciphertext revealed compared to the chance that your encrypted database is leaked. If you still believe that you have a secure channel and a key available, why not just apply the HMAC alone to the password\|\|salt\|\|ID ? The entire purpose of hashing-only passwords is to avoid messing up with secret information. - Either is safe, but I would prefer encryption for two reasons: 1. As noted in the comments, you can change the key without needing to know the original password. 2. Encryption doesn't add to collisions, while HMAC can. The probability is tiny, but it adds to the probability that the password hash caused a collision. Not worth worrying about, but since it's avoidable... On the other hand, HMAC does have one advantage: no IV, so no extra space. (GCM even adds an authentication tag.) If you can use something like a user ID as a counter, even that advantage could be lost. If not, that could be important in some cases. - I believe you're describing a system where a client, via an API, submits the bcrypt hash of a password with a per-user salt you provide as part of a challenge. You then directly compare the presented hash against the hash you store in your database. In that case, my recommendation would be to extract the salt, SHA-2 the hash, and then concatenate the two before storing them. HMAC would be better, but IMO, SHA-2 achieves the same goal more easily. Using bcrypt prevents the attacker from guessing the password. But if the attacker steals your database, they don't need to guess the password. They can just present the bcrypt hash directly. But if you SHA-2 the presented hash before comparing it, then they must reverse the SHA-2 of a bcrypt hash, which is computationally infeasible. In principle, you could publish your password database without fear. (Don't do that.) Using an HMAC with SHA-2 would also require them to have access to some static key you hold. If it's easy to implement for you, sure, why not? But I don't think it would afford you much additional security. If you just encrypt the hashes, then you are betting that the attacker who had sufficient access to steal your database couldn't also steal some fixed key. I wouldn't bet on that. For instance, a former employee may have had access to the static encryption key (which it is unlikely you will be able to change very often if ever). They could steal the keys and database before leaving and break into accounts indefinitely without having to install a backdoor. But they couldn't reverse SHA-2, even if they stole everything. I would take the trouble to extract the salt and apply a hash (or HMAC). - The point of the question was to add a secret key into an otherwise-typical password hashing scheme. Simply SHA-2ing an existing password hash does not accomplish this. For posterity, what we actually went with was to HMAC the original password with the secret key and scrypt the result. – Stephen Touset Jan 22 '14 at 23:10 I don't think in general that the client should perform the "hashing". Also I'm not sure that "a former employee may have had access to the static encryption key" is sufficient reason to discard a protocol; security is normally achieved by applying different layers, and this certainly makes it harder for an attacker. – Maarten Bodewes Jan 23 '14 at 15:12 The client should definitely perform the bcrypt before sending the result to the server. That shouldn't even be controversial. The client should never send raw password if it can be avoided. I'm discussing a separate hash by the server prior to putting into the database. I believe that provides stronger protection than symmetric encryption. HMAC provides only marginally better protection than SHA for that final hash IMO. I am aware of the layers; SHA/HMAC is providing a more effective layer than symmetric encryption. – Rob Napier Jan 23 '14 at 15:28 bcrypt should likely not be performed by the client before sending to the server. The simplest reason being that client-side performance of bcrypt will likely be dramatically less than server-side performance, reducing the number of bcrypt rounds by a significant margin. Encrypting the hashes versus HMACing (either before or after) do not seem to have the different security properties you assert — if an attacker recovers the key in either scenario, the attack devolves into simply cracking bcrypt. – Stephen Touset Feb 13 '14 at 18:22 HMAC and AES-128-GCM are similar in the sens that both are symetric primitives (i.e. there are more or less the same key management issues) and both require to store extra data (salt vs. authentication tag). An issue with encryption is that in case a poor padding scheme is used (i.e. no random) we may face to several collisions in the encrypted password table and an attacker (having the table of encrypted passwords) might perform a statical analysis to spot common passwords (e.g. 123456) and guess some of them. - This question is about encrypting/MACing a salted password hash. – CodesInChaos Jan 22 '14 at 13:55 Besides that, normally a two different plaintext will always result in two different ciphertexts for block ciphers modes of encryption - funny enough especially if the same IV is used. – Maarten Bodewes Jan 23 '14 at 15:01	2016-07-24 03:07:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.2517254948616028, "perplexity": 1772.8836572074097}, "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-2016-30/segments/1469257823935.18/warc/CC-MAIN-20160723071023-00185-ip-10-185-27-174.ec2.internal.warc.gz"}
https://blog.theleapjournal.org/2019/	## Thursday, December 26, 2019 ### Job Opening The Esya Centre is inviting applications to join the Centre as a full-time Fellow (Economist - Research and Policy). The Esya Centre aims to generate empirical research and inform thought leadership to catalyse new policy constructs for the future. It simultaneously aims to build institutional capacities for generating ideas which enjoin the triad of people, innovation and value, consequently helping reimagine the public policy discourse in India and building decision-making capacities within government. Esya invests in ideas and encourages thought leadership through collaboration. This involves curation of niche and cutting-edge research, and partnerships with people, networks and platforms. Moreover, it prioritises multi-disciplinary research to engender "research clusters", through which practitioners and researchers collaborate. Some recent examples of our work: 1. Shohini Sengupta and Aishwarya Giridhar, Contemporary Culture and IP: Establishing the Conceptual Framework 2. Megha Patnaik, Policy Uncertainty in Indian e-commerce The Fellow is expected to undertake research that informs policy. The broad areas of research towards which the Fellow will contribute are: innovation, competition, copyright and IPR; labour and productivity; technology regulation; and online markets in India. The Fellow will work collaboratively with other research staff at Esya and the Esya network, which connects diverse specialisations. The primary goal is to provide an economic perspective of the themes being explored. The fellow is expected to activity participate in disseminating research output and leading new research initiatives and collaborations. ### Preferred skills and qualifications • Master's in Economics with at least four years of experience or a PhD; • Demonstrable interest (as ascertained from high-quality published articles or working papers) in network and platform markets, economics of innovation and technology policy; • Excellent writing, analytical and communications skills; • Proficiency in computer skills, information databases; • Ability to mentor juniors and work in a team; and • Ability to work under time pressure and to juggle multiple tasks within tight deadlines. ### How to apply Please email your CV, covering letter, and a writing sample to contact@esyacentre.org with the email subject heading, "For the Fellow (Economist) Position". ## Wednesday, December 25, 2019 ### A glitch in the payments at the U2 concert, and lessons for design principles by Sanjay Jain, Rajeswari Sengupta, Ajay Shah. On 15 December 2019, for the first time, U2 was to perform in Bombay. The organisers of the concert came up with an elegant vision for how 50,000 people would be fed: This would be done through an all-electronic payments process. It was supposed to be all pretty and perfect. Along with the tickets, everyone got a card that contained an RFID tag. The card had to be activated by scanning the inbuilt QR code using the android QR code app. This took customers to a URL. On the website customers were required to register (with a name, phone number etc) and then pre-load the card. It was announced that the pre-loading could be done exclusively via a particular payments app. Once this step was completed, customers would need to tap their cards at any of the physical kiosks at the venue in order to update the card with the online balance. Front Back Customers were informed that food and beverages could only be purchased at the concert venue using the RFID card, no refunds would be available and that there would be physical kiosks at the venue for topping up the cards. While those counters would accept both cash and cards for payment, the food and beverage sellers would only accept the RFID card. Thus, a key part of the design vision was coercion of the customer by forcing all payments for purchases to be done only through one mode. #### Failures in consumer protection The cashless monopoly electronic payments mechanism had unhappy features from the viewpoint of a consumer. The design was complex, requiring customers to first do an online transaction for loading the RFID card and then a physical transaction at the venue for getting the amount to the card, even before the card could be used for purchases. In other words, two additional steps were required to potentially save time during a future purchase transaction. The minimum recharge amount for the card was Rs.500. Customers were forced to do this without any upfront knowledge about the prices of the goods sold at the venue. To load Rs.1000 into the wallet, the customer was charged a fee of Rs.100. On this fee, there was a GST of 18%, so the payment went up to Rs.1118. This was a total cost to the consumer of 11.8%, as compared with paying cash. To add insult to injury, the money left on the card was not refundable. What was not spent would be confiscated by the payments vendor. Customers were thus required to estimate their expenses without knowing the prices of the goods up front. This disrupted the biggest benefit of digital payments i.e. the ability to make a purchase without planning for it beforehand. Even in the best case scenario where the design envisioned by the organisers worked, customers were left with an experience worse than a cash payment, for a significantly higher price. Even in its conception, this was not a very attractive grand scheme. #### Failures in system operation In the event, the grand scheme collapsed because it just did not work. There rapidly emerged two classes of customers at the venue. One class was represented by customer X who had pre-loaded the RFID card with Rs.500 using the app before arriving at the concert venue. At the venue she found that her F&B spend would be (say) Rs 1000. Despite having taken the trouble of registering and pre-loading the card prior to the concert, she now had to stand in two long queues at two separate kiosks: one to first update the card so that the online transaction of Rs 500 was fed into the card, and the other to top-up the card with Rs 500 so that she could make her F&B purchases. There were thousands of such customers who went from one queue to another even before their registered cards could be used. The queues at the payment counters soon became longer than the queues at the F&B counters. The other class was represented by customer Y who had not registered or activated her card before the concert. At the venue she had to first activate her RFID card using mobile data connectivity, load the minimum amount of Rs.500 online, and then stand in the queue to update the card so that she could use it for purchases. In case she wanted to top-up the card, she would have to stand in the queue again. Given the large fees (11.8% plus the possibility of non-refund), users were careful to avoid putting too much money into the card, and thus ran the risk of undershooting. At first the hassles were only about standing in multiple queues. Things got worse when the systems at the kiosks for updating the registered RFID cards stopped working. This meant that thousands of customers who had pre-loaded their cards could neither use their cards to make purchases nor get refunds. The venue was swamped with a large number of queues for one thing or another. The mobile data network crashed at the venue with thousands of people trying to access it. This meant that thousands of customers who had not pre-activated their cards, were unable to do so, let alone update the same and use for purchases. Despite the utter chaos, the merchants inside the stadium stood firm, in unison, in refusing to sell goods to the customers using any other payment mechanism. The net result was that thousands of people were left without food and beverages despite possessing all reasonable modes of payment and despite there being multiple merchants selling the desired items. Money -- the bridge between buyers and sellers -- broke down due to the framework of coercion around only one technical standard that was permissible. This was a mess-up at multiple levels: • Poor product experience, requiring multiple redundancies such as to transfer from online payment to the RFID tag, • Poor planning on the part of the organisers and not factoring in the possibility of collapse of data network at a venue filled with thousands of data users, • Fleecing of the customers with a steep 10% load charge and forfeiting unused balances, • Coercion of customers by not giving them alternative payment options. #### Learning about design principles from this episode Many an engineer can come up with a grand scheme that sounds nice. For an engineer, it is easy to build, and easy to work with simple monolithic systems that are designed by someone and imposed on everyone. The engineer's job is easier, operating in such a world, than in the messy real world of multiple technologies. However, social systems and the interactions of a large number of people are complex, and the best laid plans of designers are likely to go awry. We are in favour of innovation, and trying out shiny new ideas. Offline instant digital payments through RFID tags sounds like a great idea, particularly when you anticipate a crowd and poor network conditions. However, innovations can and do fail. The wise path is to never have a single point of failure, to always ensure that customers can access other options, that the failure is not as damaging as it was at the U2 concert. Payment is an enabler, and not the final product, and when the payments system actually hampers transactions, it is a tragedy. The problems of a single centrally planned solution, inside one stadium, help us in thinking about central planning more generally. Each new innovation must face the market test. It is always better to have organic evolution, where many rival solutions slug it out in the marketplace, with no coercion that helps or hinders any one solution. This will give more robust solutions (no single point of failure), let the market evolve towards numerous solutions that fit numerous work environments (e.g. decentralised data works better when communications systems break down, centralised data has its own advantages for certain situations, etc), and prevent any one vendor from ripping off the consumer. It is good to have competition between multiple technologies, and multiple technology choices that fit the very diverse array of use cases that are seen in India. We have traditionally extolled the role for cash as a way to protect individual privacy and freedom. We must also respect the remarkable UX of physical cash transactions, and contrast this with the hoops that many digital schemes want to force consumers to jump through. The cashless dystopia of the U2 concert teaches us that cash has one more important function: In a disaster zone where IT infrastructure has broken down, cash is the way to get transactions done. Physical pieces of paper will be important for a long, long time. Sanjay Jain is at CIIE.CO, IIM Ahmedabad. Rajeswari Sengupta is a researcher at IGIDR, Bombay. Ajay Shah is a researcher at NIPFP, New Delhi. ## Tuesday, December 24, 2019 ### Chennai 2015: A novel approach to measuring the impact of a natural disaster by Ila Patnaik, Renuka Sane, Ajay Shah. In November and December 2015, the city of Chennai in the Southern Indian state of Tamil Nadu, got heavily flooded owing to unprecedented rainfall. With a population of a little more than 7.1 million people, Chennai is one of the major urban centers of South India, and one of the four important metropolitan cities in India. The flooding is estimated to have led to the loss of more than 500 lives, and damages of about US $3 billion, making it the world's eighth most expensive natural disaster in 2015. In this paper we evaluate the impact of this event for households in Chennai. Natural disasters, such as the Chennai floods, are important shocks which can influence all parts of the income distribution. In the aftermath of such a natural disaster, the issues of consumption smoothing, liquidity constraints and financial resilience play out. Natural disasters are important in their own right, as we need to understand more about the turmoil faced by households in such states of nature. All governments engage in redistribution in the aftermath of a natural disaster. This motivates research on studying the impacts of natural disasters. Natural disasters are also an opportunity to obtain insights into the economics of household, through observation of households when confronted with such a large shock. Many researchers have gone into the field after a natural disaster has taken place, and produced evidence about health, income, consumption, and financial conditions in the aftermath of the disaster. But such research does not offer insights into the causal impact of the event as adequate information gathering about baseline conditions, before the event, is lacking. When panel data about households is present, we observe households before and after the natural disaster. This makes possible the analysis of the adverse impact upon affected households, while additionally observing controls. The constraint in such research has been the time elapsed between two consecutive observations of each household. As an example, even if a panel is measured once a year, there would be many months of elapsed time between the two measurement dates that bracket a disaster event. In a new NIPFP working paper, Chennai 2015: A novel approach to measuring the impact of a natural disaster we exploit the new opportunities for measurement which flow from the CMIE Consumer Pyramids Household Survey ("CPHS"), which measures a panel of 170,000 households across India. Each household is met with three times a year. There is thus a period of four months, across which the household is measured twice, within which each natural disaster lies. We setup difference-in-difference estimation where households in Chennai are the treatment'' group and unaffected households in the rest of the state of Tamil Nadu are the control'' group. As households in Chennai are among the more affluent ones in Tamil Nadu, the raw dataset has poor match balance, and we address this problem by also performing matched DiD analysis. We investigate three questions. First, we evaluate the impact of a flood on household income and consumption expenditure. It is possible that a disaster leads to declines in household income and expenditures owing to the destruction. However, it is also possible that households increase their spending to cope with the disaster, or replace capital stock. For example, some household activities, such as cooking, would shift from internal production to purchases from external providers, which would augment demand for certain goods and services. Households would start buying goods and services for reconstruction almost immediately after the destruction. Large scale expenditures on relief and reconstruction by the Indian state would bolster the local economy. We find that there was no statistically significant impact on household income during the flood months. Households in Chennai, however, saw a 32% increase in consumption expenditure relative to the non-affected districts. The largest percentage increases in expenditure were seen on health, and power and fuel. A key figure is shown above. The dotted line is for the controls and the deep green line is for households in Chennai. In both cases, what is shown is the monthly expenditure per person. The vertical black lines bracket the flood events. At the outset, the households observed in Chennai are, on average, more affluent than the controls. Roughly speaking, we do have parallel trends in the period prior to the flood. During the flood, there was a large surge in expenditure which runs for many months. After that, consumption went down, to a point where the Chennai households were now comparable with those seen in the rest of Tamil Nadu. Second, we evaluate the variation in the change in expenditure for different households. The adverse impact upon persons who live in structures with inferior structural strength is likely to be larger. We categorise households as more vulnerable, or more financially constrained, through various characteristics such as not having a concrete roof, or not having modern finance (such as life insurance, mutual funds, equity market participation), or not having durable goods (such as ACs, refrigerators etc). We find that the consumption expenditure of the these weaker households increases by a smaller amount than those not financially constrained. This might mean more hardship, and a higher inability to cope with catastrophic events. Third, we evaluate the mechanism that households use to finance the higher consumption. Households could either draw down their savings, or increase their borrowings to finance expenditures. Our analysis suggests that relative to the control group, fewer households in Chennai saved, borrowed, or purchased assets, in the period after the floods. This suggests that reduced savings and reduced purchase of assets was the channel through which the consumption surge was financed. In our data, after about a year, the consumption surge ended, and was followed by a further decline in consumption. This may be consistent with households refocusing on repairing their balance sheet. Natural disasters kill around 90,000 people and affect close to 160 million people worldwide. The frequency and intensity of disasters are expected to increase with global warming. Greater understanding is required about how natural disasters impact economic outcomes, so that better public and private responses may be designed. The contribution of this paper lies in bringing new tools of measurement (panel data, three times a year, matched DiD) to bear on an important problem (natural disasters) and discover the phenomena that are at work. The novel estimation strategy shown here can now be applied for many natural disasters in India. Over time, a body of work can develop of this nature, through which more abstract insights can be obtained. The authors are researchers at NIPFP. ## Thursday, December 05, 2019 ### Announcements ### Call for Applications Ashoka University is inviting applications for the China-India Visiting Scholars (CIVS) Fellowship program. CIVS is an opportunity for academics, policy experts, and professionals who are interested in expanding their current research to include China. The fellowship is aimed at creating more knowledge about China in India and encourage academic exchange of early- and mid-career scholars. This is a fully-funded fellowship that will provide 10 Indian scholars, who have had limited to no experience with China, the opportunity to develop an understanding of China’s experience and include it in their research. The theme for 2020 is Economics and Development. This fellowship is ideal for scholars who are researching or working under the umbrella topic of economics and development, including (but not limited to) agricultural, urban development, education, vocational training, energy management, governance and performance management, rural poverty alleviation, food security, environment, public health, innovation infrastructure, and other similar areas, and are interested in developing a deeper understanding of China. Fellows can partner with an institution of their choice, or tap into Ashoka's network of institutions, which includes the National School of Development (Peking University, Beijing), Institute of New Structural Economics (Peking University, Beijing), Center for China and Globalization (Beijing), NYU Shanghai (Shanghai), HSBC Business School (Peking University, Shenzhen), Tianjin University of Finance and Economics (Tianjin), and the Hong Kong University of Science and Technology (Hong Kong). The fellows will be guided and mentored by a Fellowship Committee, which includes top economists and China Studies scholars in the country. The fellowship runs for 9 months, includes a visit to China where fellows will work with a counterpart who is researching in a similar area of study, and concludes in a seminar in December 2020. The fellows have the flexibility to continue working at their current position while pursuing this fellowship. More details about the fellowship and application available on the link above. Applications will be open until February 15, 2020. ### Why China The partnership between China and India is arguably becoming one of the most important partnerships of the 21st century. Both countries, with their massive populations, economies, and environmental impact, have outsized effects on the trajectory of global affairs. Given all of this and the shared 3,380 km border, there is still little understanding in India about China, and in China about India. If there were a prime moment to understand each other, this would be it. For any questions, contact suhail.thandi@ashoka.edu.in ## Wednesday, December 04, 2019 ### The 10th Emerging Markets Finance conference An intellectual feast, in Bombay, 12-13-14 December. ## Saturday, November 16, 2019 ### In Service of the Republic: The Art and Science of Economic Policy, by Vijay Kelkar and Ajay Shah In Service of the Republic: The art and science of economic policy, by Vijay Kelkar and Ajay Shah, Penguin Allen Lane, 2019. Main page \| Amazon As a$3-trillion economy, India is on her way to becoming an economic superpower. Between 1991 and 2011, the period of our best growth, there was also a substantial decline in the number of people below the poverty line. Since 2011, however, there has been a marked retreat in the high growth performance of the previous two decades. What happened to the promise? Where have we faltered? How do we change course? How do we overcome the ever-present dangers of the middle-income trap and get rich before we grow old? And one question above all else: What do we need to do to make our tryst with destiny? As professional economists as well as former civil servants, Vijay Kelkar and Ajay Shah have spent most of their lives thinking about and working on these questions. The result: In Service of the Republic, a meticulously researched work that stands at the intersection of economics, political philosophy and public administration. This highly readable book lays out the art and the science of the policymaking that we need, from the high ideas to the gritty practicalities that go into building the Republic. Nandan Nilekani: One of the most significant works on India's economic policies, this brilliant prescription for the country's future by two practitioners could not have come at a better time. Dr. Kelkar has played a role in many major financial reforms since liberalisation. What is most alluring about the book is its approach of tackling difficult economic concepts and making them accessible and engaging for the lay reader. A must-read for everyone. Bibek Debroy: Two respected economists, who have worked in government and for government, have produced a remarkable and wonderful book, examining government, governance and state intervention in a charming and reader-friendly way. A book in the service of every citizen. Pratap Bhanu Mehta: This marvellous book is a wonderful guide to thinking about public policy. It combines three things that rarely come together: clear analytical thinking on first principles, a good sense of historical judgement and a commitment to the values of freedom and fairness. It is the work of masterly professionals making their thinking accessible to a wider public. Avinash Dixit: Kelkar and Shah have written a masterly book, combining in-depth personal experience and sound economic principles. With simple language and vivid examples, they offer many home truths about the why, when, what and how of policy, and even more important, when to do nothing. I hope India listens. ## Thursday, October 31, 2019 ### Elements of the low Indian labour force participation rate: The elderly by Subhamoy Chakraborty, Renuka Sane and Ajay Shah. India has a remarkably low rate of labour force participation. The Periodic Labour Force Survey (PLFS) carried out under the Ministry of Statistics and Programme Implementation estimated the labour force participation rate (LFPR), for individuals of age 15 and above, at 49.8% in 2017-18. The CMIE CPHS survey, which has more recent information, has shown a decline in the LFPR by 2019. These numbers suggest that a large part of India is not in the labour market. These magnitudes of non-participation are much larger than the rates seen with unemployment. The grand question of Indian labour economics is that of understanding the low LFPR. The grand question of Indian economic policy lies in obtaining a 50 per cent gain in GDP through a 50 per cent increase in the labour force. One big element of this LFP problem is women's LFP. The women's LFPR has been falling. In 2011-12, India was already one of the countries with the lowest female labour force participation. This has gotten worse with time. In 2017-18, the female LFPR fell to a historic low of 23.3%. A remarkable feature of the Indian women's LFPR is the comparison against countries like Pakistan (24%) or Bangladesh (36%). For those of us who believe that women's agency in India is ahead of that in Pakistan, this is a bracing fact. The examination of women's LFP is an important crossroads between labour economics and gender studies. It also emphasises the importance of gender studies in thinking about India. The other two big elements of the LFPR problem are the young and old. In this article, we delve into labour supply of the elderly and establish some basic facts of this field. The positive and normative economics of elderly LFP is an important element of labour economics, given the large and growing share of the elderly in the population. It is also a major issue in ageing studies. High labour force participation by the elderly is well known to contribute to emotional and physical well being. It is generally better for a person to work for a wage of Rs.50 a month rather than obtain a pension of Rs.50 a month. The puzzle of the field lies in devising labour market arrangements that will harness labour supply of the elderly, and avoid the abrupt event of retirement. The elderly are defined as those above the age of 55. The 55-64 age group is also part of the conventionally defined working age group (age 15 to 64). The 65+ age group constitutes the old elderly. ### Data We study the Consumer Pyramids Household Survey (CPHS), a pan-India panel household survey of about 170,000 households carried out by the Centre for Monitoring Indian Economy. The survey asks about the present employment status of each member above 15 years of age. The response to the employment question is recorded as a 4 point status: 1. Employed 2. Unemployed, not willing and not looking for a job 3. Unemployed, willing and looking for a job 4. Unemployed, willing but not looking for a job Individuals whose employment status is either Employed (1) or Unemployed, willing and looking for a job (3) are considered to be a part of the labour force. In this article, we examine the data for January - April, 2019. ### Overall Table 1 provides estimates of the labour force participation by age group. There are approximately 375 million workers in the 15-54 age group, giving a LFPR of 45%. The LFPR drops slightly to 44% for the 55-64 age group with 51 million workers. The LFPR drops dramatically to 12% for the 65+ age group with only 8.4 million workers. Table 1: Labour Force Participation: Age Group Age Group Population (in millions) LFP (in millions) LFPR(%) 15-54 828.3 375.0 45.3 55-64 115.6 50.8 43.9 65 and above 69.1 8.4 12.1 Figure 1 presents the labour force participation rate (LFPR) of those above the age of 55. The labour force participation was a little over 55% at age 55, and fell to about 10% by age 70. Withdrawal by the elderly from the labour force generally happens for one of the following reasons: (a) people are required to leave their main job at a specific retirement age, (b) are unwilling to work because they value leisure more and access to pensions at a sharply defined age which makes it feasible to stop working (c) are unable to work because of health constraints or (d) the labour market is unfriendly to older workers. In the US, for example, sharp drops in participation are seen at the age of 62 and 65, when access to social security benefits becomes available. In India, formal pension arrangements are only in place for a small part of the population. Hence, factors "(a)" and "(b)" above should not matter much in India. And yet, we see a sharp drop at age 60. This suggests that reasons such an unfriendly labour market might explain the large drops in labour force participation at older ages. ### Changes over time Figure 2 presents the labour force participation rate in 2016 and 2019. We see that there has been a small increase in the participation rate for the 55-59 age group between 2016 and 2019. However, for all other age categories, there has been a remarkable fall. For example, about 42% of the 60-61 age group participated in the labour market in 2016. This had fallen by about 10 percentage points in 2019. Similarly, in the 65 plus age group, labour force participation was at 28%. By 2019, this had fallen to 12%. This suggests that that stress in the economy has hurt the elderly more than prime-age working males. This may be part of a larger phenomenon, where prime age working males are protected in economic downturns, while all other parts of the labour force (women, the young, the old) seem to lose employment at higher rates. ### International comparison It is useful to ask how these compare to the numbers in the OECD countries, where formal pension systems shape the decision to retire. Table 1 presents the elderly labour force participation rate (LFPR) in India, US and Japan. Table 2: LFPR: Comparison with US and Japan Age Group India (%) (Jan-Apr 2019) US (%) (2018) Japan (%) (2018) 55-59 52.7 72.3 83.4 60-64 29.4 57.1 70.6 65 and above 12.1 19.6 24.7 In 2018 according to the Bureau of Labor Statistics in the US, 72.3% of those in the 55-59 age group were in the labour force. The participation rate fell to 57.1% for age group 60-64 and further declined to 19.6% for those above 65. Meanwhile the labour force participation rate in Japan, as reported by Statistics Bureau of Japan, was 83.4%, 70.6% and 24.7% for age groups 55-59, 60-64 and above 65 respectively. Japan has, in fact, seen a resurgence in elderly labour force participation in recent years owing to better health and education, as well as reduced generosity of social security programs. Japan is considered one of the best countries in terms of integrating the elderly into the labour market. Suppose we treat Japan as a frontier: the outer limit of what is possible with labour market participation by the elderly. How much would we in India gain if we moved up to this frontier? If the LFPR of the 55-64 age group in India (which is 43.9%) were to become the same as that of Japan's (77%), then the overall working-age LFPR would go up to 49.15%. This is a 4 percentage point increase in the LFPR owing to increases in the labour force participation of the "young old", and would mean that an additional 38 million individuals would be in the labour force. An additional 9 million people, of age 65+, would also join the labour force, by matching the Japanese LFPR for the age group of 65+. Totally, 47 million people would enter the Indian labour force if we moved up to Japanese levels of LFP from age 55 and above. This is an economically significant number. This magnitude of impact will go up in the future as India ages. ### Conclusion The Indian labour market has a remarkable feature: of low labour force participation. In this article, we examine one facet of this problem: the low LFP for the elderly. Despite the prevalence of a large informal sector, and the absence of a formal age of retirement, we find that the elderly labour force participation is low, and has actually fallen between 2016 and 2019. Withdrawal from the labour market is bad for the elderly and bad for the economy. The examination of the LFP of the elderly is an important crossroads between labour economics and ageing studies. Further research is required in identifying the causes behind the low LFPR of the elderly. The authors are researchers at the National Institute of Public Finance and Policy. ## Thursday, October 17, 2019 ### Towards an administrative framework for building public trust in vaccination by Siddhartha Srivastava. In January 2019, the Delhi government published a notification mandating the administration of the Measles-Rubella (MR) vaccine to all children between 9 months to 15 years of age. The vaccine was meant to be delivered as a booster shot irrespective of the previous vaccination status of the child. The notification did not provide any information with respect to the manner in which the MR campaign was to be carried out. Instead, it stated that since the "Measles-Rubella (MR) campaign is a National Policy like the Pulse Polio Programme...no consent is required from the beneficiaries/their parents". This led to widespread panic among parents who eventually filed a petition before the Delhi High Court challenging the notification. The notification was challenged on the grounds that the express consent of the parents was not a requirement for administering the booster shot. In response to the challenge, the Delhi High Court ordered a stay on the administration of the MR vaccine in the city and directed the Delhi government to ensure that express parental consent was obtained before the measles vaccine could be administered to children. The court also directed the Delhi government to publish advertisements with respect to the procedure of administration of the vaccine as well as information with respect to the side-effects of the booster dose such that parents can provide their informed consent for vaccination. ### Methodology We examine MR campaigns conducted by the state governments of Delhi, Tamil Nadu and Kerala by using primary and secondary legal sources: 1. Notifications/circulars issued by central and state governments with respect to the implementation of the MR campaign (see, here and here). 2. Judgments arising out of litigation against vaccination campaigns and vaccine liability (see, here and here). 3. Legal papers and journal articles on mechanisms to deal with issues of vaccine hesitancy. 4. News articles reporting cases of vaccine hesitancy in the chosen states. We reviewed these materials with a view to understand the current framework of vaccine administration in these states with a specific focus on the processes present in these frameworks (or lack thereof) to deal with vaccine hesitancy. We compare India's approach to vaccine administration to that of the United Kingdom, Canada, Australia and the United States. Accordingly, we attempt to derive best practices that can contribute to a model administrative framework for vaccine delivery specific to India with inherent checks and balances to address vaccine hesitancy. (see, here, here, here and here). ### Analysis A study of the MR campaigns undertaken in Delhi, Tamil Nadu and Kerala suggest that vaccine opposition in these states can be broadly attributed to the following causes: 1. Shared beliefs about safety, efficacy, potency and manner of delivery: Parents in Delhi are apprehensive about the effects of a booster dose of the MR vaccine given that their children have already been vaccinated for measles. 2. Difficulty in accessing and understanding credible scientific information on vaccination: With the internet having become a repository of health-related information and in the absence of a framework for regulation/monitoring of such content, South Indian states such as Tamil Nadu and Kerala have witnessed the spread of erroneous, non-scientific information regarding vaccines over the internet and other media. Widespread misinformation and rumour-mongering on the internet, especially social media, has been a common characteristic of the MR campaigns across the country. 3. Difficulty in accessing and understanding the legal/regulatory framework governing vaccination: Parents in Delhi and Kerala have raised concerns about scattered and often incomplete rules framed by state governments to undertake the actual administration of the MR vaccine. 4. Reliance on religious, cultural and personal beliefs rather than proven facts and evidence: Opposition to the introduction of the MR campaign in Delhi, Kerala and Tamil Nadu suggests that vaccine hesitancy is not uniform across communities in each state but tends to occur in specific clusters (such as specific religious communities or groups that believe in non-traditional medicine). The identification of vaccine hesitant subgroups is imperative to understand the causes of their hesitancy and develop targeted interventions to increase vaccine uptake. ### Towards a Trust Based Framework Keeping in mind the causes of vaccine hesitancy in India, it may be helpful to design an administrative framework to streamline vaccine delivery with built-in checks for tackling vaccine hesitancy. The presence of an administrative machinery may be useful in addressing the public trust deficit in vaccination, in terms of: Formalising an awareness/communication strategy for vaccines: The administrative framework should contain strict rules for engaging with the public. This includes provisions for ensuring frequent awareness campaigns, dialogue with members of different communities, public campaigns by doctors, vaccinators and other public health experts, media outreach through public figures etc. Rules for engagement with the public during the introduction of new vaccines, changes in immunisation schedules and experimental vaccine trials can prove useful in reducing public fear at the outset. A compelling example of the effect of a well-formulated communication strategy can be found from within India itself in it's pulse polio campaign of the late 1990s. Targeted communication played an important role in raising awareness and building trust in the polio campaign with popular media figures and sports personalities advocating the benefits of vaccination over various media such as film, television, radio and print. Formalising the procedure for vaccine delivery: Organised and accessible rules of procedure with respect to time, place and manner of vaccination can strengthen public confidence in vaccines. Specific information with respect to vaccine description, quality, indications, contraindications, side effects, dosage, age group, manner and place of delivery, catch-up immunisations etc. can provide a measure of certainty to parents and make them more comfortable in engaging with vaccination campaigns of the government. For example, each state in the US has it's own set of immunisation laws and regulations. These laws are procedural in nature and set out the administrative mechanisms through which schools, universities, pharmacists, and health-care facilities etc. are required to administer the various vaccines prescribed by the ACIP. In India, we find that the exact mechanism/process of vaccine delivery changes constantly based on where the vaccine campaign is being carried out and the nature of the campaign itself. For example, certain states prescribe that immunisation take place only in schools while others allow for vaccination at schools, public health centres, home-visits etc. As such, there is a need for consistency in the procedures followed to administer vaccines, one which can be addressed by having a set of codified procedural rules for vaccination in each state. Monitoring, evaluation and reporting: The administrative framework may specify reporting requirements. Requirements with respect to monitoring and reporting the incidence of vaccine preventable diseases, coverage rates and adverse effects following vaccination (AEFIs) can assist in the formulation of stronger mitigation strategies for vaccine preventable diseases. Australia has adopted a national surveillance system that reports instances of adverse events following immunisation from state and territory registries as well as data sent directly from consumers, health professionals and vaccine manufacturers. These reports are regularly reviewed by the regulator and referred as required to expert committees, such as the Advisory Committee on Vaccines, to ensure ongoing safety assessments. In India, an AEFI surveillance framework has been in place since 1998. The national AEFI guidelines provide a set of standards for undertaking the investigation and assessment of cases reported as AEFIs. All states and districts are required to constitute AEFI committees, which assist in streamlining AEFI surveillance at the local level. However, the number of serious AEFIs reported in India are still far lesser than expected numbers. A large number of AEFI committees established at the state and district level are not functional, as a consequence of which there is insufficient real-time AEFI data being generated and stored accross the country. Recent reports suggesting the presence of the polio type 2 strain in oral samples of polio vaccines expose the inadequacies in our current monitoring and evaluation systems while further making the case for a standardised administrative framework for vaccine delivery. Establishing a mechanism for accountability: The administrative machinery should include a mechanism for empowering communities to question vaccination practices, introduction of new vaccines, reasons for the occurrence of AEFIs etc. This will be a useful departure from the current practice of placing blame on state governments, without having any recourse to an institutional/administrative mechanism for grievance redressal. In order to ensure accountability, more than 15 countries around the world have instituted compensation mechanisms for vaccine related incidents. In these countries, compensation is dispersed either through courts or a compensation scheme pay-out for individuals that have suffered injury or death following vaccination. Even in India, consumer protection forums have considered and indeed ordered compensation for vaccine-related injuries and deaths in the past. However, an institutional apparatus similar to the US (which lists the nature of vaccine-related injuries that can be compensated under the National Childhood Vaccine Injury Act and requires the claimant to show a demonstrable link between the vaccine and the injury) can help provide a platform for vaccine accountability while at the same time evading frivolous claims. Providing positive incentives for vaccination: Various countries seek to achieve their vaccination mandates by conditioning benefits, such as access to public/private services, on compliance with state vaccination requirements. Mandatory vaccination for enrollment in public schools falls within this category. However, rather than benefits, it is viable to condition incentives on compliance. For example, The Patient Protection and Affordable Care Act (ACA) of the United States requires insurers to fully cover the cost of recommended vaccines, relieving consumers of the entire expense of vaccination. The proposed administrative framework may contain additional incentives in order to discourage vaccine hesitancy in different subgroups in India. Given the recent declaration of the WHO that vaccine hesitancy is one of the top 10 global health threats in 2019, and amidst the resurgence of measles outbreaks in different parts of the world, it is imperative that we start developing, implementing and evaluating measures to better address the complex problem of vaccine hesitancy. A well formulated and transparent administrative machinery can be a useful starting point for addressing this problem and fully realising the gains from immunisation in India. Moreover, the presence of such a framework can also act as a foundation for engaging in separate debates around the viability of individual consent vis-a-vis mandatory compliance with respect to legal/ administrative interventions designed to deliver public health goods. ### References Gopichandran, Vijayprasad, Public trust in vaccination: an analytical framework, Indian Journal of Medical Ethics, 2017. Kumar et al., Vaccine hesitancy: understanding better to address better, Israel Journal of Health Policy Research, 2016. Nadimpally et al., An idea whose time has come: compensation for vaccine-related injuries and death in India, Indian Journal of Medical Ethics, 2017. Jarret et al., Strategies for addressing vaccine hesitancy - a systematic review, Vaccine, 2015. The author is a researcher at the National Institute of Public Finance and Policy. The author thanks Prof. Ajay Shah, Dr. Renuka Sane and Mr. Shubho Roy for their useful comments and guidance. ## Thursday, October 03, 2019 ### Announcements Azim Premji University, Bangalore and the National Institute of Public Finance and Policy (NIPFP), New Delhi are pleased to announce a new collaborative initiative, a workshop “Strengthening the Republic”. India has completed more than seven decades as an independent nation and a constitutional republic. When India set upon this path it was seen as a brave unconventional path for a new post-colonial nation. Seven decades on, most political scientists would characterize India as a 'miracle' democracy - one that has defied extant political theory on constitutional survival and democratic transitions. However, too much of this Indian exceptionalism avoids careful attention to the specifics of Indian institutional design and the granularity of Indian institutional practice. Indian academic scholarship in law, politics, economics and the social sciences more generally must invest considerable resources and intellectual energy in unpacking the institutional grammar of India’s success as a republic. The failure to do so may result in a misdiagnosis of our success while simultaneously failing to uncover the flesh and blood that has kept our institutional scaffolding in place. This seminar is dedicated to in depth empirically rigorous investigations into public institutions - legal, political and social - that enhance our common understanding and generate keen insight into their contemporary successes and failures. Drawing on the high quality, interdisciplinary research work carried on by Azim Premji University and NIPFP, this workshop aims to generate active, sustained conversations and academic scholarship on themes related to the law, society and public institutions in India. The workshop is designed to be an intensive, one-day session aimed at encouraging scholarship and debate among individual researchers, academics and practitioners belonging to disciplines like law, politics, economics and sociology to engage in thoughtful discussions with peers on pressing contemporary issues under these broad themes. The workshop is being hosted by Azim Premji University and NIPFP in New Delhi. ### Format of the Workshop: Interested applicants should submit an abstract of not more than 1000 words on topics of their interest under the broad themes. The proposals could be based on their ongoing research or new research that they would like to be engaged in. Two copies of the abstract, in word, pdf, LaTeX or any similar formats should be emailed to varsha.aithala@apu.edu.in, with details of full name, designation and employment/institutional affiliation of the applicant. All abstracts will be reviewed by an independent jury selected by the organisers who will shortlist the abstracts based on relevance to the theme, novelty and academic merit. Authors of selected abstracts will receive an email notification of the exact date and venue of the workshop and should submit their completed research paper to varsha.aithala@apu.edu.in, by 15 December, 2019. The workshop session will host five paper presentations from the shortlisted abstracts. Every paper selected for presentation will be allocated a committed discussant/ respondent. ### Illustrative list of papers: The following is an illustrative list of papers that reflect the broad topics of interest and rigour of analysis that is expected of papers in the workshop: 1. Building State capacity for regulation in India by Shubho Roy, Ajay Shah, B.N. Srikrishna, Somasekhar Sundaresan. In Devesh Kapur and Madhav Khosla (eds.), Regulation in India: Design, Capacity, Performance. Oxford: Hart Publishing, 2019 (forthcoming). 2. Protecting Citizens from the State post Puttaswamy: Analysing the Privacy Implications of the Justice Srikrishna Committee Report and the Data Protection Bill, 2018 by Vrinda Bhandari and Renuka Sane. Socio Legal Review 14(2), (forthcoming). 3. How to Modernise the Working of Courts and Tribunals in India by Pratik Datta, Mehtab Hans, Mayank Mishra, Ila Patnaik, Prasanth Regy, Shubho Roy, Sanhita Sapatnekar, Ajay Shah, Ashok Pal Singh and Somasekhar Sundaresan. NIPFP Working Paper 258, March 2019. 4. Challenges of Competition and Regulation in the Telecom Sector by Smriti Parsheera. Economic & Political Weekly, Vol. 53, Issue No. 38, September 22, 2018. 5. Legislative strategy for setting up an independent debt management agency by Radhika Pandey and Ila Patnaik. NUJS Law Review, Volume 10, Issue 3, 2017. 6. Misled and Mis-sold: Financial Misbehaviour in Retail Banks? by Monika Halan and Renuka Sane. Journal of Comparative Economics, 45(3), August 2017. 7. Karnataka Crime Victimisation Survey: 2019 report by Sudhir Krishnaswamy, Asha Venugopalan and Varsha Aithala (forthcoming). 8. Commercial Courts in India: Three Puzzles for Reformers by Sudhir Krishnaswamy and Varsha Aithala (forthcoming). ### Other arrangements: The presenter’s travel, accommodation and incidental expenses will be provided for by Azim Premji University. We welcome proposals for research papers which are unpublished, recently published or of publishable quality in academic journals of international repute, though preference would be given to previously unpublished papers. The research papers may employ the reference and citation style used in standard social science practice, or the style used in legal periodicals. Simultaneous submission of papers to the workshop and other publications is permitted. Authors are expected to disclose any commercial or other associations that may result in a conflict of interest in connection with the research. All submitted research papers will be published as open access working papers and available on the websites of both organisers. Organisers reserve the right to make editorial comments to the papers prior to publication. ### Important dates to remember: • Deadline for submission of abstracts: 31 October, 2019. • Deadline for research paper submission: 15 December, 2019. • Workshop: 11 January, 2020 (Saturday). ## Tuesday, August 27, 2019 ### Policy uncertainty in Indian e-commerce by Megha Patnaik. Reduced investment in India by private persons is a key part of the present growth challenge. Investment is shaped by macroeconomic uncertainty, sectoral uncertainty, and regulatory risks that firms face. In this article, we think about the risks that an E-commerce firm such as Amazon perceives in India. These include the changing FDI rules, unresolved issues of data localisation and code disclosure, the multiple reports on technology-related activities that various government agencies are releasing, and the problems of rule of law in licensing and investigation. #### Economic policy uncertainty Shrinking investment in the Indian economy is a concern. Investments in new projects fell to a 15 year low in the last quarter according to the Centre for Monitoring the Indian Economy (CMIE) Capex data which tracks large investment projects. Firms are deterred from investing by policy uncertainty (Bloom, 2009). When firms are unclear about the future economic environment, they hold back on investing till uncertainty declines. This delays the pickup of the investment cycle, where firms generates jobs and business for linked firms, fueling aggregate economic activity. Uncertainty particularly affects long-term investments that are irreversible in nature, and for which horizons for cost recovery run into years. These can be investments in new technologies or market segments, or investments in infrastructure. Such investments are particularly important, as they can benefit other firms in the economy, fueling productivity and long-term growth in addition to their business cycle effects. Private sector investment is adversely affected by three kinds of policy uncertainty - macroeconomic uncertainty, sectoral policy uncertainty, and regulatory risk. The role of Economic Policy Uncertainty at the macroeconomic level has been measured globally (Baker et al, 2016). In the original measure, an index is created by quantifying newspaper coverage of policy-related economic uncertainty mentions in the national newspapers, through combinations of keywords related to policy and uncertainty. Macroeconomic policy uncertainty has been applied to understand global events. Brexit-driven policy uncertainty in the UK moved closely with the GBP Real Exchange Rate in recent times, and the uncertainty surrounding US trade policy affected importing firms. This measure of macroeconomic policy uncertainty correlates strongly with stock market volatility. Firms face much more than macroeconomic uncertainty. They also face uncertainty at sectoral, geographical and individual levels. Sectoral-level policy uncertainty can be measured through surveying firms sampled across sectors, asking them about expectations about future growth and costs at various horizons (Altig et al, 2019). For example, firms can report not just their expectations about future profits, but the distribution across the possible profit outcomes that they can expect. An additional source of uncertainty that firms operating in India face is regulatory risk. Even when regulations are formulated, there is a lack of predictability, and excessive executive discretion, in how a stated regulation will be enforced. For example, the licensing by the RBI of 11 payment banks from 41 applicants who wanted to start payment systems was a non-transparent process inconsistent with the rule of law (Roy and Shah, 2015). Another example is the Copyright Board order of 2010 on statutory licensing fees paid by Radio stations. This order arose out of nine one-on-one disputes between radio stations and music producers, but was applied as an in rem order rather than an in personem order. Thus, music producers who weren't part of the original disputes also became governed by the order, despite the appeals by T-Series and SIMCA against the Copyright Board order applying to them. Aggarwal and Zaveri (2019) show the uncertainty induced for private persons through executive discretion in enforcement at SEBI. #### Drivers of uncertainty in the E-commerce sector In the recent Q2 earnings announcement, the Amazon CFO Brian Olsavsky mentioned uncertainty in India's e-commerce policy. He expressed hope for stable' and predictable' policy, for the company to continue with its investments in technology and infrastructure in India. This explicit mention about policy uncertainty in India is a unusual moment, and requires attention by policy thinkers. What is the uncertainty associated with investing in India, as seen by Amazon? 1. India's draft e-commerce policy rules earlier this year preventing firms from influencing prices or selling products in which they hold stakes disrupted business plans for e-commerce companies. It bring companies back to the drawing board to ensure they can comply with the current regulations while limiting losses that rose from lack of clear direction from the start. The final e-commerce policy has been held back for another year, putting existing investments of firms in this sector at risk during the interim months, and deterring further investments. 2. The uncertainty around data localisation is another deterrent. The recent announcement by a high-level government panel to do away data localisation for non-critical data, and the upcoming announcement of the position of the Prime Minister's Office on data localisation are policy announcements that drive sentiments on this debate, though none are legal instruments. Under data localisation requirements, companies would need to redesign internal algorithms to access data locally, pay up for new servers, and face costs to protect data in less-secure environments. The predictive power of firms' algorithms would weaken with fewer data points to train models on. The due process of discussions with various government bodies and stakeholders on this issue is still in process. The RBI's requirement for financial data localisation despite existing provisions (Bailey and Parsheera, 2018) for access under the Payments and Settlements Act (2007) suggest that any Indian regulator can step in with special requirements at unforeseen times. 3. A related issue is the disclosure requirement of source code under the draft e-commerce policy. E-commerce firms depend on data-driven marketing and use of collaborative filtering for customer recommendations. A code submission requirement is a coercive technique aimed at achieving the transfer of technology and local needs' described under the proposed e-commerce policy. Technology transfers cannot and should not be coerced: they happen in an organic and legitimate manner through managers and employees developing skills and passing them onward in data communities or by workers moving across companies (Bloom et al, 2019). It is also doubtful how technological transfers can be achieved with segments of code without underlying data. Will code disclosure requirement be combined with data localisation to pass on core business value to competitors? Will companies need to invest in staff and technologies to find workarounds to be able to mask their key assets? Whether such a code disclosure requirement will come into effect remains unresolved. In mid-2020 the final e-commerce policy will describe the stand of the government on this issue, but this is not definitive either. Multiple guidelines on the same subject can cause delays in the resolution of uncertainty. The RBI Report of the Working Group on FinTech and Digital Banking includes E-aggregators, Robo advisors and Big Data all under Fintech. E-commerce firms, which are data intensive and provide multiple services, will be included under this description. The fintech steering committee report of the Ministry of Finance is still pending. Each of these reports is a statement about how government agencies are likely to move in the future but these are not legal instruments. Government reports can only suggest but not surely state how future laws will change. Infirmities of the regulatory processes in India also exacerbates uncertainty. As an example, data localisation requirements by RBI for payments firms were translated from an early idea into an enforced law within a matter of days. There was no due process surrounding how officials could change the law. The last leg of the legal system -- how laws are enforced -- also suffers from concerns about non-equal application of law, as shown in the examples from RBI (Roy and Shah, 2015) and SEBI (Aggarwal and Zaveri, 2019). For a prospective investor, the risk of investing in India lies in how the law might change in the future through an undemocratic process, and in how the law will be applied to her. #### Conclusion For India to have a stable investment environment, we need to provide firms a stable and predictable policy environment. Investments from firms in various sectors will boost the investment cycle for India. Resolving policy uncertainty both at the macroeconomic level as well as in different sectors, and reducing regulatory risk through better rule of law is critical for India in the current investment scenario as well as for long term growth. #### References Aggarwal, Nidhi and Zaveri, Bhargavi. Problems with evidentiary standards for proving securities fraud in India, The Leap Blog, 23 August 2019. Altig, David, Jose Maria Barrero, Nicholas Bloom, Steven J. Davis, Brent H. Meyer and Nicholas Parker. Surveying Business Uncertainty University of Chicago Working Paper (2009) Bloom, Nicholas. The impact of uncertainty shocks. Econometrica (2009) Bloom, Nicholas, Erik Brynjolfsson, Lucia Foster, Ron Jarmin, Megha Patnaik, Itay Saporta-Eksten, and John Van Reenen. What Drives Differences in Management Practices? American Economic Review (2019) Baker, Scott R., Nicholas Bloom and Steven J. Davis. Measuring Economic Policy Uncertainty. The Quarterly Journal of Economics (2016) Bailey, Rishab, and Smriti Parsheera. Data localisation in India: Questioning the means and ends, The Leap Blog, 22 February 2018. Roy, Shubho, and Ajay Shah Payment bank entry process considered inconsistent with the rule of law, The Leap Blog, 1 September 2015. Megha Patnaik is faculty at the Indian Statistical Institute, Delhi and Fellow at the Esya Centre. The author thanks Radhika Pandey and Ajay Shah for useful inputs. ## Friday, August 23, 2019 ### Problems with evidentiary standards for proving securities fraud in India by Nidhi Aggarwal and Bhargavi Zaveri. ### Introduction Did O.J. Simpson kill his wife? A criminal jury said no, a civil jury said yes. The standard of proof applied by the two juries made all the difference to the outcome of the case (Vars 2010). In India, the securities regulator adopts a very low standard of proof for cases involving wrongdoing in the securities market. For many people, standard of proof related questions are procedural and semantic exercises in the dispensation of justice. However, the standard of proof adopted by a judge has direct impact on the outcome of the case and over time, the quality of the investigation conducted by the investigative agency. When the standard of proof is low, there is a high chance that initiating an investigation will induce an adverse order. This creates substantial discretion in the hands of the investigator, to choose the persons against whom State power will be directed. This runs against a basic theme of liberal democracy, of containing executive discretion. The ability of the executive to direct punishment upon chosen ones is inconsistent with the rule of law. It creates policy risk for persons who may consider participating in the Indian financial markets, and creates a bias in favour of participation by politically connected persons. There are three reasons why the standard of proof in securities fraud cases in India are low. First, the Supreme Court has held that the standard of proof which SEBI must meet to establish securities fraud is the 'preponderance of probability' standard. This is lower than the standard of proof required to establish a crime under criminal law. In civil proceedings, there are usually two versions of the facts. The court, on the basis of the evidence before it, chooses that version which it thinks is 'more probable', that is, it will accept a version which a prudent man will act upon the supposition that it exists. On the other hand, in criminal cases, the prosecutors must satisfy the court that the existence of a fact is not only probable, but that its existence is beyond reasonable doubt. Simply put, the prosecution must satisfy the court that 'a reasonable alternative version is not possible' (185th Report of the Law Commission). Courts have explicitly acknowledged that it is not possible to mathematically define the degree of probability for meeting a certain standard of proof and there is an inherent subjective element within each of these standards. (State of UP v. Krishna Gopal and Anr.) The other two reasons are inter-connected. SEBI exercises regulation-making, executive and quasi-judicial powers in connection with the securities market. It defines what conduct would constitute fraud for the purpose of exercising its enforcement powers. The concept of fraud under the SEBI (Prohibition of Fraudulent and Unfair Trade Practices) Regulations, 2003 (PFUTP Regulations) - a regulation that defines fraudulent conduct in the securities market - is wider than what is understood as fraud in common law and the codified law applicable to fraud in India. It dispenses with critical elements such as intent, deceit and damages. A wider definition of fraud sets the bar very low for establishing securities fraud before a court or tribunal. SEBI is also responsible for conducting investigations of suspected fraud and makes decisions on whether the conduct investigated meets its definition of fraud. This violates the constitutional scheme of the separation of powers that applies to areas of public administration which are not governed by a technocratic regulatory agency. As an example, the Indian Penal Code defines what constitutes theft, the investigation is conducted by the executive agencies and the decision on whether the investigated conduct amounts to theft (as defined in Parliamentary law) is made by the judiciary. The concentration of all three powers in a single body creates scope for bias towards a lower standard of proof. Empirical work done on the cases investigated by the Securities Exchange Commission, the securities regulator in the United States, is indicative of such bias. The SEC is empowered to choose whether to pursue a proceeding before one of its own internal administrative law judges or an independent federal court. Reportedly, while the SEC enjoyed a 90% success rate in its own hearings, it had only a 69% success rate against defendants in federal court. (here and a perma link here) In February 2018, a judgement of the Supreme Court further diluted the standard of proof for securities fraud in India in a case involving synchronised and reverse trades executed on the exchange. The Supreme Court reversed the decision of the Securities Appellate Tribunal which had held that although the trades in question might have been synchronised, they were not manipulative and "market manipulation of whatever kind, must be in evidence before any charge of violating these Regulations could be upheld." The Supreme Court dispensed with the need to show manipulation and relied on the notion of "market integrity" as a standard for adjudging the conduct of market participants. SEBI has extensive powers to sanction wrongdoing in the securities markets, such as the power to bar access to the market, suspend professional licenses and impose hefty monetary penalties. The Supreme Court's ruling has serious implications for the manner in which these powers are exercised as it effectively introduces a new standard of proof of 'market integrity' to be met by persons accused of securities market fraud. ### What is market integrity? The notion of market integrity is both un-defined and hard to measure. World over, there is considerable debate on its meaning in the context of financial regulation (Austin, 2016). Given the subjectivity of the concept, using market integrity as a standard of proof is equivalent to using 'public interest' or 'public good' as a standard for establishing wrongdoing. It leaves tremendous scope for discretion and creates the potential for differential standards of enforcement across a range of practices, depending on the adjudicator's view of whether or not a particular trading practice affects market integrity. This creates uncertainty in the manner in which the law will be applied and enforced and has adverse implications for the rule of law. Ambiguity in the grounds of enforcement and the standard of conduct that could invite legal sanctions, is detrimental to the development of the market as well. In this article, we advocate the use of empirical approaches for establishing wrongful conduct in the securities markets. We do this by demonstrating the empirical evidence that should have been used to support a claim of fraud in the very same case where the Supreme Court lowered the standard of proof by relying on the vague and problematic ground of market integrity. In a world of electronic trading, empirical evidence of fraud and its impact on the market is not hard to collect and investigators and courts must rely on such evidence instead of holding market participants to a vague and subjective notion of market integrity and unfairness, which the world at large is struggling to define. ### Judgement of the Supreme Court in Rakhi Trading In February 2018, the Supreme Court in the case of Securities and Exchange Board of India v. Rakhi Trading Private Ltd. upheld an order passed by the Securities and Exchange Board of India (SEBI) that levied a penalty on some traders who had synchronised their trades off the exchange before placing them on the exchange. The trades in question were a series of orders placed on the F&O segment of the Nifty index. The modus operandi was to place an order for Nifty options, which matched with a particular party and subsequently reverse the position taken by placing an opposite order, which also matched with the same party. SEBI penalised the party placing such orders on the ground that these "transactions were in the nature of fictitious transactions resulting in creation of misleading appearance of trading in these options." The SEBI order did not elaborate the manner in which the synchronised trades sought to manipulate the price of either the option itself or the underlying securities, which in this case, was the basket of securities included in the Nifty index. The parties against whom this order was passed appealed against the order before the Securities Appellate Tribunal (SAT). SAT confined its review to whether the synchronised trades in the F&O segment of the Nifty index artificially manipulated the underlying cash segment, which in this case is the Nifty index itself. It observed that: "To say that some manipulative trades in Nifty options in the F&O segment could influence the Nifty index is too farfetched to be accepted. The only way Nifty index could be influenced is through manipulation of the prices of all or majority of the scrips in the cash segment that constitute Nifty." This in line with precedent case-law laid down by SAT on the requirement to show manipulative conduct to demonstrate that the synchronised trades constituted fraud under the PFUTP Regulations. On an appeal by SEBI against this order of the SAT, the Supreme Court reversed the order of the SAT without explaining how the synchronised trades in question affected the price discovery system or created a misleading impression of volumes, but emphasised the notion of market integrity as under: "According to SAT, only if there is market impact on account of sham transactions, could there be violation of the PFUTP regulations. We find it extremely difficult to agree with the proposition...SAT has missed the crucial factors affecting the market integrity, which may be direct or indirect (emphasis supplied) ...By synchronization and rapid reverse trade, as has been carried out by the traders in the instant case, the price discovery system itself is affected." ### The problem with synchronised trades Synchronised trading involves pre-negotiating the trade off the exchange and subsequently placing the order on the exchange such that it matches with the counterparty with whom the trade was pre-negotiated. To synchronise trades on an exchange platform, the buyer and seller of the pre-negotiated trade will enter their respective orders at the same time (with same price and quantity) to maximise the chance of matching their orders against each other. To ensure that the order does not match against another counterparty, the first order may be placed away from the touch, that is, at a price significantly different from the ongoing bid / ask price. By itself, synchronised trading is not a harmful practice. In fact, block trades for which exchanges have a block trading window are synchronised trades. It is difficult to synchronise trades on liquid securities on the exchange because such orders run the risk of matching against other counterparty(ies). However, even on relatively illiquid securities, synchronised trading is not risk-free. The probability of getting hit by another order (especially a market order) on the opposite side of the book is low, but not zero. How can synchronised orders be used to manipulate the market? Synchronised trades could create misleading, artificial trading interest in a security. High volumes and significant price changes on an otherwise illiquid security may cause participants to believe that there is some news on the security. This may induce them to buy those securities based on unexplained changes in prices and volumes. This is especially possible in an illiquid scrip, which may be perceived to be suddenly liquid if a series of transactions are executed on such a scrip. While the SEBI order levying the penalty does not specify exactly what was manipulated, evidence of manipulation could be demonstrated in either or all of the following ways: 1. Manipulation of Nifty index: One way of determining manipulation in the Rakhi Trading case is by analysing the changes in the value of the underlying security, the Nifty index. The SAT order almost exclusively focused on the possibility of the synchronised trades having manipulated the value of the Nifty index. The order rightly concludes that price manipulation on the index can happen only if an equivalent position is taken on the spot market on all the 50 constituent stocks of the index. Neither the SEBI order nor the Supreme Court order show any evidence of a position by Rakhi Trading on the spot market. This leaves the scope of manipulation on the Nifty index value to the price transmission from derivatives market to the spot market. Empirical evidence on price transmission from derivatives market to spot market suggests that such transmission is subject to the liquidity of the derivatives instrument (see Fleming et al, 1996, Aggarwal and Thomas, 2019). We examine the liquidity of the relevant Nifty options and also examine if the volumes traded by Rakhi Trading in the options segment were significant enough to impact the value of the underlying Nifty index. 2. Volatility in option premium: Manipulation of stock price increases the volatility in returns on such stocks (Aggarwal and Wu, 2006). If the synchronised trades on the Nifty options were manipulative, we would expect that the real price discovery process on option premium would be hampered, resulting in higher volatility in the premium of the Nifty options in question. This manipulation can be established by examining the volatility of the premium on the Nifty options on which the synchronised trades were executed. ### Size of the market for the relevant Nifty options Rakhi Trading executed synchronised trades on 13 specific Nifty option contracts (hereafter referred to as "the relevant Nifty options") on four days of the year 2007, namely, on March 21, March 22, March 23 and March 30 (hereafter,"the event days"). We begin by a simple comparison of the liquidity and volatility of the relevant Nifty options on the event days and compare it with other days between March 15, 2007 and March 31, 2007 (hereafter, "non-event days"). Such a comparison should be the beginning of the court's enquiry when dealing with an order punishing a market participant for securities market fraud. Table 1 provides basic summary statistics on the traded volumes (a measure of liquidity) and volatility of the relevant Nifty options. Event days Non Event days Total Volumes Volatility Rakhi Trading Volumes Total Volumes Volatility (%) (%) Min 9,550 0.97 2,000 50 0.10 Mean 26,142 6.19 10,015 7,712 2.25 Median 25,750 5.08 10,700 3,925 0.37 Max 38,600 14.85 11,900 50,050 17.62 SD 7,752 3.86 2,477 10,718 4.39 The key observations from Table 1 are as follows: 1. First, the traded volumes of the relevant Nifty options fluctuated significantly on a daily basis on the event and non-event days, ranging from 9,550 to 38,600 on the event days, and 50 to 50,050 on the non-event days. 2. Second, in comparison to the average daily traded volumes on a liquid Nifty option, Table 1 shows that the relevant Nifty options were relatively illiquid. For a frame of reference, the maximum traded volumes on one single Nifty option in March 2007 was 9.2 million. 3. Third, the volatility (measured by the Parkinson's range measure) of the relevant Nifty options was in the range of 1-15% on the event days, while it was in the range of 0-18% on the non-event days. ### Did the synchronised trades manipulate the Nifty index? Table 2 gives a picture of the size of the overall Nifty options market on the event days and compares it for non-event days based on traded volumes. It also shows the traded volumes of the stocks which constitute the Nifty index for these dates. The last column of the table shows the volumes and contracts traded by Rakhi Trading on the event days to provide a perspective on the possible influence of its trades on the overall options and underlying spot market. Table 2: Size of overall Nifty options market and proportion of synchronised trades Non-event days All Nifty Options Traded volumes (in Rs. millions) 49,978 61,041 277 Contracts (in 000s) 262 316 1.35 volumes (in Rs. millions) 36,228 37,932 NA The key observation from Table 2 is that on the event days, the volumes traded by Rakhi Trading on the Nifty options were less than one percent of the average traded volumes on the stocks that constitute the Nifty index on the spot market. The minuscule proportion of the volumes traded by Rakhi Trading in the Nifty options market relative to the total traded volumes on the stocks constituting the Nifty index on the spot market, re-affirms the finding of the SAT that the synchronised trades executed by Rakhi Trading could not have possibly manipulated the underlying Nifty index. However, Table 2 also shows that the volumes and number of contracts on the Nifty options segment on the event days were higher than on non-event days. This might or might not have been due to the synchronised trades executed by Rakhi Trading. In the next few paragraphs, we zoom in our analysis on the specific Nifty options which were involved in the synchronised trades executed by Rakhi Trading and examine if those trades did manipulate the individual options traded by Rakhi Trading. To test the claim of manipulation of option premium, we examine the volatility of the premium of the relevant Nifty options, and compare it with the volatility of the premium of other Nifty options with similar liquidity. We call the former as the treated set, and latter as the control set. We identify the control set as the options on which the traded volumes were in the same range as that on the treated" set, to ensure comparability across the two sets. If there was indeed manipulation on the treated options, we expect the volatility of the treated set to be higher than that of the control set. We obtain a total of 50 unique options in the control set which we compare with data on the treated set on the event days. Table 3 presents summary statistics on the volatility of the premium for the options in the treated set and control set for our period of analysis. Table 3: Summary statistics on volatility of options premium on the treated and control sets (in %) Treated Control Min 0.97 0.25 Mean 6.19 4.78 Median 5.08 2.91 Max 14.85 35.17 SD 3.86 5.09 We observe that the average volatility of the treated set was slightly higher than that of the control set. However, a simple t-test of comparison of means of the treated and control set volatility shows that the difference between the volatility of the two sets is not statistically significant. In a regression analysis (not shown here), we also control for other factors that affect volatility of the option premium of the treated and control sets. We do not find any evidence of significant difference across the two sets even after controlling for other factors such as strike price, days to expiry, value and volatility of the underlying. The analysis finds that the price range in which the option premium varied for the treated set was similar to that of the control set. Thus, we find that the option premium on the Nifty options that were traded by Rakhi Trading was not manipulated. ### Did the synchronised trades manipulate the volumes? We also examine the question whether the synchronised trades in the relevant Nifty options led to higher volumes in these options thereby creating a possibly misleading impression of volumes. For this, we analyse the traded volumes on the relevant Nifty options, after excluding the volumes arising out of synchronised trades themselves. We compare the traded volumes of the relevant Nifty options on the event and non-event days (Table 4). If the synchronised trades did result in higher trading activity from other market participants, we expect to see significant difference in the traded volumes on the event and non-event days. Event days Non-event days Min 0 50 Mean 5,342 5,170 Median 4,500 2,450 Max 15,400 21,350 SD 5,736 5,762 Table 4 shows that the traded volumes on the Nifty options involved in the Rakhi Trading case were, on an average and on a median scale, slightly higher on the event days compared to the non-event days. However, a statistical test (t-test) of the comparison of means finds no significant difference across the two sets. A regression analysis on the event and non-event set confirms this finding. This indicates that Rakhi trading trades did not lead to any jump in volumes in the options so traded. ### Trading for tax evasion or tax planning An ancillary concern expressed by the Supreme Court was that Rakhi Trading conducted the trades in question for tax planning or avoidance. While this may or may not be true, the securities markets regulatory framework should not be used for punishing tax evasion. Cases of trades that SEBI has reason to believe were meant for tax avoidance, must be reported to the tax authorities, which is the appropriate forum for addressing questions of tax evasion. The objective of the securities market regulatory regime is not to deal with tax evasion, but to protect investors and develop the securities markets. More importantly, a regulator has scarce resources and dedicating investigative and adjudicatory capacity for dealing with tax evasion cases is not the best use of these resources. ### Conclusion Our empirical analysis finds that the synchronised trades did not manipulate the underlying Nifty index, the premium on the relevant Nifty options or the traded volumes of the relevant Nifty options. However, we recognise that our analysis is limited to daily data. An analysis of this kind must be underpinned by examining the intra-day data around the time of synchronised trades. By using such data, the regulator can further make a case for whether the trades in question were indeed manipulative. The objective of this article is not to establish the guilt or innocence of any specific market participant. By using publicly available inter-day trading data on the security involved in the Rakhi Trading case, we make a case for using empirical strategies to establish fraudulent conduct under the Indian securities regulatory regime. As demonstrated above, the advanced nature of the securities market infrastructure in India and the availability of data ensures that this is not difficult. The use of empirical evidence to substantiate charges of fraudulent conduct will ensure that enforcement orders pass the muster of the appellate forums without having to compromise on evidentiary standards for establishing guilty conduct. More importantly, backing enforcement with robust underlying evidence will help the regulator build the trust of the regulated and testify to the high standards of proof that our society should place for the deprivation of liberty. ### References: Stock market manipulations by Aggarwal R and Wu G, The Journal of Business, 2006. When stock futures dominate price discovery by Aggarwal N and Thomas S, Journal of Futures Markets, 2019. What exactly is market integrity? An Analysis of One of the Core Objectives of Securities Regulation by Austin J, William and Mary Business Law Review, Vol.8(2), 2017. Trading costs and the relative rates of price discovery in stock, futures, and option markets by Fleming J, Ostdiek B and Whaley R, Journal of Futures Markets, 1996. State Of U.P vs Krishna Gopal & Anr 1988 AIR 2154. 185th Report of the Law Commission of India on a Review of the Indian Evidence Act, 1872. Toward a General Theory of Standards of Proof, Frederick E. Vars, Catholic University Law Review, Vol. 60(1) (Fall 2010). Nidhi is faculty at IIM-Udaipur and Bhargavi is a researcher at IGIDR.	2020-01-18 00:42:30	{"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": 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": 0.18054088950157166, "perplexity": 3531.9789513563755}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250591431.4/warc/CC-MAIN-20200117234621-20200118022621-00378.warc.gz"}
http://tex.stackexchange.com/tags/tikz-pgf/new	# Tag Info 0 Since you are doing commutative diagrams, I'd suggest you to use a dedicated package such as the powerfult tikz-cd (built upon TikZ) which offer you a more convenient, cleaner and shorter syntax as well as ready to use features for your diagrams. A little example with your product: \documentclass[border=5pt]{standalone} \usepackage{tikz-cd} ... 2 If I understand the requirements correctly, then I think the problem is that the TeX box that contains the tikzpicture has some non-zero depth. In the following, I use the local bounding box key to explicitly name the picture (using the current bounding box doesn't work) and then use the baseline key to set the baseline of the tikzpicture to the bottom of ... 2 Something like this? Note that the use of the positioning library and the updated syntax <direction>=of <place> helps immediately with the spacing. Only one further adjustment really was needed here to increase the height a bit. The rest is just a question of tweaking the position of the labels e.g. below or above and using sloped for the 2 ... 4 How about this: \draw[name path = AE] (ORG) -- (A) -- (B) -- (C) -- (D) -- (E); \draw[name path = MN] (M) -- (N) -- (U) -- (V); \fill [name intersections={of=AE and MN, name=i, total=\t}] [red] \foreach \s in {1,...,\t} { (i-\s) circle (3pt) }; 1 \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{backgrounds} \begin{document} \begin{tikzpicture} \def\us{(0,2),(1,4),(2,0),(3,2),(4,1),(6,2),(6,4)} \foreach \u [count=\i from 1] in \us {\node (u\i) at \u [right] {$u_\i$};} \begin{scope}[on background layer] \fill[blue!20] (u1.center)--(u2.center)--(u3.center); \end{scope} %% For Test ... 3 This is because TikZ automatically uses the most appropriate anchor to connect two nodes, so you do not actually have a triangle, you have two edges. Try \fill[fill=blue] (u1.center) -- (u2.center) -- (u3.center) ; instead, it will show the difference. Other ways are to use \def\us{0/2,1/4,2/0,3/2,4/1,6/2,6/4} \foreach \x/\y [count=\i from 1] in \us { ... 3 You can also anchor nodes on its baseline: \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture}[every node/.style={above=2mm, anchor=base}] \draw[color=red](0,3)--(11,3); \draw (0.5,2.5)--(0.5,3) node {For Example:}; \draw (3,2.5)--(2.5,3) node {this looks}; \draw (5,2.5)--(5.5,3) node {not nice vertically aligned}; ... 4 It's the style declarations and the empty line that is counted as whitespace. Remove the blank line and put the styles in the TikZ environment and it will be OK again. And please have a look at Should \tikzset or \tikzstyle be used to define TikZ styles? The easiest is to use a simple \tikzset{ b/.style={rectangle, draw, fill=white, node ... 6 This would be my first try, using a counter (no need of additional packages): \documentclass[a4paper,10pt,landscape]{article} \usepackage{tikz} \newcounter{cnti} \begin{document} \begin{tikzpicture} \foreach \i in {0,...,9}{ \setcounter{cnti}{\i}\addtocounter{cnti}{1} \node (i) at (\i, \i) {\alph{cnti}} ; } ... 8 One possibility: \documentclass[a4paper,10pt,landscape]{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} \foreach [count=\i] \j in {a,b,...,j}{ \node (\i) at (\i, \i) {\j} ; } \end{tikzpicture} \end{document} percusse mentions the alphalph package in a comment, and its \alphalph does exactly what you ... 2 Next code shows a solution for your first problem. You want similar fitting nodes, then if you build them with similar inner nodes, they will have same size. As an example \node[surround, fit = (id1)(id3.east\|-id1.center)] {}; will build a node big enough for id1 (which fixes height and western border) but it will also encompass coordinate ... 2 If you want actual numbered captions, you can use \captionof in a node placed below the axis. You can have subfigure numbering if you prefer that, see e.g. http://tex.stackexchange.com/a/250032/586 \documentclass{article} \usepackage{pgfplots} \usepackage{capt-of} \begin{document} \begin{figure} \begin{tikzpicture}[every axis/.style={width=7cm}] ... 1 Multiple axes environments are hard to connect, but at least you could use a groupplot by loading the groupplots library. Here is an example: \documentclass{article} \usepackage{pgfplots} \usepgfplotslibrary{groupplots} \pgfplotsset{compat=1.12} \begin{document} \begin{figure}[ht] \centering \begin{tikzpicture} \begin{groupplot}[group style={group size=2 ... 2 \documentclass[tikz,border=10pt]{standalone} \usepackage{tikz-3dplot} \begin{document} \tdplotsetmaincoords{70}{20} % point of view \begin{tikzpicture}[tdplot_main_coords,scale=1] %draw black arc \draw[canvas is xy plane at z = 0, line width = 1pt] (0,0) arc (0:-90:-1); %draw rotated gray arcs (5°-steps) \foreach \rotStep in ... 2 You can name the label and add to the fit list. \node[obj,label={[name=id1-l]below:Outside}] (id1) at (2,2) {}; \begin{pgfonlayer}{background} \node[surround] (background) [fit = (id1)(id1-l)] {}; \end{pgfonlayer} If you are going to use this often times then making a style out of it might be a good idea. 1 I have no acces to comuter right now, so my answer will be short and non verifyed. I see three errors: In the for loop you can't let a space between } and { in the current version of tikzmath. Your draw command must be enclosed in { }; The coordinates in your draw command must be before the circle. You can check the following code: ... 3 Disclaimer: I am not a colourosopher and this is the first time I have ever touched colorimetry. Be warned. An elegant approach to your problem is functional shading. It allows for a very general solution, easily adjustable to other analogous problems (read: other colour spaces). On close inspection your dataset seems botched, so I'm just going to ignore ... 6 I have simplified the code by placing the origin at (0,0,0). The point of view can be set using: \tdplotsetmaincoords{70}{110} % rotation about the x and y axis The black arc rotation can be set using: \tdplotsetrotatedcoords{0}{0}{-5} % rotation about the x, y and z axis \documentclass[tikz,border=10pt]{standalone} \usepackage{tikz-3dplot} ... 1 One option is to use a tabular with two columns of type m{<length>} (requires the array package) with centered content. The first column for the 2x2 array of images and the second column for the colorbar. A little example illustrating this approach (adjust the settings according to your needs): \documentclass{article} \usepackage{graphicx} ... 3 4 3 This sort of does what you are looking for. Note that fit draws on top, you if you need a full color underneath, you may need to draw those nodes twice (onces to get the nodes for the fit calculation, and once to draw them again onto of the fit area, you can just store the drawing code in a macro and run that macro twice). \documentclass[11pt]{article} ... 1 3 What about this? \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{shapes.geometric} \usetikzlibrary{calc} \begin{document} \begin{tikzpicture} \draw (-3,0) -- (3,0); \draw (0,-3) -- (0,3); \draw [blue, dashed] (0,0) circle(2.5cm); \node[regular polygon, regular polygon sides=12, minimum size=5cm, rotate=-60, draw] at (0,0) (A) {}; \foreach \i ... 3 This reduces the amount of code, though the result could probably be better. (If some wizard comes up with a much better solution I'll likely delete this answer.) The labels are placed with the following loop: \foreach [count=\i] \x/\y in {10/0,8/5,5/8,0/10,-5/8,-8/5,-10/0,-8/-5,-5/-8,0/-10,5/-8,8/-5} { \path (\x,\y) ++({atan2(\y,\x)}:3.5cm) node ... 4 Here is a pgfplots approach: \documentclass[tikz,border=10pt]{standalone} \usepackage{pgfplots} \usetikzlibrary{decorations.text} \pgfmathdeclarefunction{gauss}{3}{% \pgfmathparse{1/(#3sqrt(2pi))exp(-((#1-#2)^2)/(2#3^2))}% } \begin{document} \begin{tikzpicture} \begin{scope}[rotate=-90] \begin{axis}[ domain=-0.5:2.5, xmin=-1, xmax=3, ... 3 I'm sure I've seen something very similar to this answer somewhere else, but I can't find it. But anyway, here is an image coordinate system which provides a way to refer to coordinates in the image (actually the node containing the image which should have zero innersep and outersep) using both relative coordinates (from 0 to 1) and exact coordinates (i.e., ... 6 Should point you in the right direction... \documentclass[tikz, border=5]{standalone} \begin{document} \begin{tikzpicture}[>=stealth, line cap=round] \draw [thick, ->] (0,-2) -- (0, 2) node [midway, sloped, above] {Spatial distribution}; \draw [thick, ->] (0,-2) -- (10,-2) node [midway, below] {Time}; \draw [thick, dotted] plot ... 1 I think you are a little bit confused about TikZ capabilities and of course the package pgfplots. First problem is that you need to let pdflatex or whichever engine you are using to reach out the system commands. For example, I use TeXnicCenter and my command line parameters are configured as -synctex=-1 -max-print-line=120 -interaction=nonstopmode "%wm" ... 3 Here is the most complex tree. You should be able to modify it to produce the simpler trees. If you get stuck, just post the code you have and ask how to solve the problem you come across. This uses the powerful forest package which allows the standard bracket notation to be used for drawing trees. My answer to an earlier question introduces forest and ... 2 \documentclass[a4paper,12pt]{article} \usepackage{tikz} \usepackage{floatrow} \floatsetup[figure]{% style=Boxed,captionskip=12pt,capposition=bottom,margins=centering,% } \usepackage[font=small]{caption} \begin{document} \begin{figure}[ht] \centering \begin{tikzpicture}[thick,scale=1] \filldraw[black] (0,0) circle (2pt) (1,1) circle (2pt) (1,-1) circle ... 1 The problem is that the tcolorbox changes \textwidth which is used bt the tikzpagenodes package to internally calculate the position for the page nodes it defines. You can see this using \documentclass[oneside]{book} \usepackage{tikzpagenodes} \usepackage[most]{tcolorbox} \newtcbtheorem{theo}{Theorem}{theorem style=plain}{th} \begin{document} ... 1 The Applet's are too close each other and overlap. Please compare a modified example. I am not sure what your \gls means... \documentclass{article} \usepackage{pdflscape} \usepackage{tikz} \usetikzlibrary{automata} \begin{document} and my code looks like this \def\gls{\MakeUppercase} \begin{figure} \centering \begin{tikzpicture} ... 2 You don't need any shift or those calculations, rather you can simply add raise=<length> to the brace options. Output Code \documentclass{memoir} \usepackage{tikz} \usetikzlibrary{calc, shapes.geometric, positioning, arrows.meta, decorations.pathreplacing} \begin{document} \begin{tikzpicture} \node (foo) [draw, minimum width=6 em] ... 2 I suppose you want to hide the thing in a box: \node[anchor=north,inner sep=0] at (title_for_a_set_of_rays){% \mbox{\boldmath$\mathrm{HR}(\ray{r},P)$}% }; Notes. I used a mock definition for \ray, as you didn't provide one. There should be no \, after the comma. 1 \usepackage{bm} % defines commands to access bold math symbols and then... \node[anchor=north,inner sep=0] at (title_for_a_set_of_rays)% {$\bm{\mathrm{HR}(\ray{r}, P)}$} font=\bfseries is not needed. 4 The root cause is a bug in pgfplots: apparently, the ticklabel coordinate systems do not work as expected. This morning, I have managed to improve the polar library such that the default for pgfplots 1.13 will directly result in the label placement as in your screenshot. I will also simplify sloped tick labels and add some more fine tuning to it. For the ... 2 A simple way of doing this is with a path picture. Using some extra magic, the path picture can be set up so (-1,-1) is the lower left corner and (1,1) is the upper right corner of the picture. This makes it quite straightforward to specify path picture elements. \documentclass[tikz,border=5]{standalone} \tikzset{% do path picture/.style={% path ... 2 You can put a sine curve as a tikz picture inside a node. \begin{tikzpicture} \node[draw,circle,inner sep=-0.4pt] at (0,0) {\tikz \draw[scale=0.15,domain=-3.141:3.141,smooth,variable=\t] plot (\t,{sin(\t r)});}; \end{tikzpicture} 0 I want to center the figures horizontally on the page. I prefer to do this with familiar commands in TikZ. Here is code that gives the display that I want. \documentclass{amsart} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{tikz} \usetikzlibrary{calc,angles,positioning,intersections} \begin{document} \noindent \hspace{\fill} ... 18 It is much easier to just draw everything in the correct order instead of using 3d coordinates (or layers). The crucial part is the last dozen of lines: \documentclass{standalone} \usepackage{xifthen} \usepackage{tikz} \usetikzlibrary{math} \begin{document} \begin{tikzpicture} \newdimen\r \newdimen\R \newcount\n \tikzmath{ \n = 19; ... 1 Thanks to Gonzalo Medina in this post : plot and fit from pgfplottable, I did manage to do what I wanted. The final code is : \documentclass{beamer} \usepackage{etex} \usepackage[frenchb]{babel} \usepackage[T1]{fontenc} \usepackage[utf8x]{inputenc} \usepackage{pgfplots} \usepackage{pgfplotstable} \usepackage{epstopdf} \usepackage{tikz} ... 8 One option using TikZ and the tikzpagenodes package (adjust the settings according to your needs). According to comments, the first page of each chapter should also have the new page style, so \aliaspagestyle{chapter}{solid} was used: The code: \documentclass{memoir} \usepackage[hmargin=3cm]{geometry} \usepackage{xcolor} \usepackage{lmodern} ... 2 Add forget plot to those plots that shouldn't be taken into account for the legend (the first two, in your example). You can use legend style to customize the legend formatting; in your case, you need draw=none to suppress the frame. Using the various coordinate systems provided by pgfplots, you can place elements at any desired location. In the example ... 8 Annotate at your leisure... \documentclass[tikz,border=5]{standalone} \usepackage[eulergreek]{sansmath} \usepackage{pgfplots} \pgfplotsset{compat=newest, tick label style={font=\sansmath\sffamily}, axis line style={draw=black!80, line width=0.1875ex}, y tick label style={/pgf/number format/fixed}, tick style={major tick length=0.0ex}, major grid ... 1 This one is makes a nice example of using buildcycle with subpath in Metapost. prologues := 3; outputtemplate := "%j%c.eps"; beginfig(1); path A, B, C, D, F; A = fullcircle scaled 240; B = fullcircle scaled 200 shifted 20 right; C = fullcircle scaled 100 shifted 30 left; D = fullcircle scaled 180 shifted 60 left shifted 40 up; F = buildcycle(subpath ... 0 \documentclass[10pt]{article} \usepackage{pgf,tikz} \usetikzlibrary{arrows,calc} \usepackage{calc} \pagestyle{empty} \begin{document} \definecolor{ffffqq}{rgb}{1,1,0} \definecolor{qqccqq}{rgb}{0,0.8,0} \definecolor{ffttzz}{rgb}{1,0.2,0.6} \definecolor{ttttff}{rgb}{0.2,0.2,1} \footnotesize \begin{tikzpicture}[line cap=round,line join=round,>=triangle ... 0 There are several issues. Two are easy to solve. First, do not leave blank line after a \foreach. TikZ wants to read onto the end of the loop without any paragraph breaks. Second, never use $$in LaTeX documents. Here, it confuses TikZ but it is, in any case, bad. In this case, just change the$$s to \$s. The third is less easy to solve and you will need ... 3 Why is the title not placed above the pentagon? Because point F is highest and not E. why is the tikzpicture flush against the right margin? That is because you are setting \hspace{\fill}. \documentclass{amsart} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{tikz} \usetikzlibrary{calc,angles,positioning,intersections} ... 1 And one more solution (It take me little more time because I allowed myself first to simplify the picture code :-) , i was lost in original one :-( ): \documentclass{amsart} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{tikz} \usetikzlibrary{calc,angles,positioning,intersections} \begin{document} \begin{tikzpicture}[ node ... Top 50 recent answers are included	2015-08-01 16:20:59	{"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": 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": 0.9595759510993958, "perplexity": 4209.167862056023}, "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-2015-32/segments/1438042988840.31/warc/CC-MAIN-20150728002308-00293-ip-10-236-191-2.ec2.internal.warc.gz"}
https://techwhiff.com/learn/4-points-assume-that-a-procedure-yields-a/454354	1 answer # 4 points Assume that a procedure yields a binomial distribution with a trial repeated times. Use... ###### Question: 4 points Assume that a procedure yields a binomial distribution with a trial repeated times. Use the binomial probability formula to find the probability of successes given the probability of success on a single trial. Round to three decimal places n. 64, X = 3, p=004 O 0221 O 0375 0.138 0 091 ## Answers #### Similar Solved Questions 1 answer ##### Do you think Franklin and Vince demonstrated a high level of social intelligence? Why or why... Do you think Franklin and Vince demonstrated a high level of social intelligence? Why or why not? Marcia Brady is naturally extroverted and always ready to approach her co-workers to offer help. Franklin Pierce is more of an introvert, but is ready to help if approached. Marcia and Franklin have bo... 1 answer ##### CSM Machine Shop is considering a four-year project to improve its production efficiency. Buying a new... CSM Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for $421,000 is estimated to result in$157,000 in annual pretax cost savings. The press falls in the MACRS five-year class (MACRS Table) and it will have a salvage value at the end o... 1 answer ##### 6.13 Suppose that f is differentiable on R and that (0) 0, f(1) 2, and f(2)=2·☆... 6.13 Suppose that f is differentiable on R and that (0) 0, f(1) 2, and f(2)=2·☆ (a) Show that there exists ci (0,1) such that f'(a)-2. (b) Show that there exists ce (1,2) such that f'(%) = 0. (c) Show that there exists c e (0,2) such that f'(cs)... 1 answer ##### An outbreak in which the epi-curve that clearly shows more than one peak in cases over... An outbreak in which the epi-curve that clearly shows more than one peak in cases over time is most likely what kind of epidemic: A point source A common source Propagated with secondary cases Propagated with overlapping secondary cases... 1 answer ##### 250 ml Question 9 The pharmacist is preparing 200 mL of a famotidine suspension containing 75mg/5mL.... 250 ml Question 9 The pharmacist is preparing 200 mL of a famotidine suspension containing 75mg/5mL. How many 20 mg tablets of famotidine will be needed?... 1 answer ##### What is the Study of Economics? What is Macroeconomics? What is Microeconomics? In... What is the Study of Economics? What is Macroeconomics? What is Microeconomics? In Economics, who does Scarcity affect, the rich person or the poor person and how?... 1 answer ##### 14.4.147 @ The following are the weight (in grams) and quantity of volatile Ay emissions (in... 14.4.147 @ The following are the weight (in grams) and quantity of volatile Ay emissions (in hundreds of nanograms) for plants. A scatterplot 30 of the data is given to the right. 20 Weight (x) 56 83 55 66 50 67 60 78 75 51 10 1 ° Quantity 9.0 22.0 10.5 23.0 11.5 12.0 7.0 13.5 17.0 22.0 0 (y) 40... 1 answer ##### A box is released from rest at the top of a ramp. The surface of the... A box is released from rest at the top of a ramp. The surface of the ramp makes an angle of 31.5degrees with the horizontal, and is rough; the coefficients of friction between the ramp and the box are ps = 0.500 and Mk = 0.350. What is the magnitude of the acceleration of the box? 2.1982... 1 answer	2023-02-07 05:24:26	{"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": 0.4790893793106079, "perplexity": 2546.855633531532}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500384.17/warc/CC-MAIN-20230207035749-20230207065749-00381.warc.gz"}
https://math.stackexchange.com/questions/443550/intuition-behind-an-identity/443552	# Intuition Behind an Identity I'm currently studying for a complex analysis prelim. exam in August, so I'm working through some of the exercises in Titchmarsh. One of the exercises has us evaluate the integrals $$\int_0^\infty\frac{1}{1+x^4}\,dx\quad\text{and}\quad\int_0^\infty\frac{x^2}{1+x^4}\,dx.$$After evaluating each of them, I found $$\int_0^\infty\frac{1}{1+x^4}\,dx=\int_0^\infty\frac{x^2}{1+x^4}\,dx=\frac{\pi}{2\sqrt{2}}.$$Pretty sure I had miscalculated, I went to Wolfram Alpha to verify my answers only to find I had done it correctly. My question is why these two have the same value. Intuitively, I expected $\int\frac{x^2}{1+x^4}\,dx$ to be larger because on the interval $(1,\infty)$, $x^2>1$. The only explanation I can think of is that the $x^2$ makes the integrand much smaller in the interval $[0,1]$ than the original function, but I wouldn't have guessed it to be enough to make the values come out the same. Is there some other intuitive reason why these two integrals are the same? • Look at their graphs. It seems there's some interval centered at $0$ outside of which the second function is always slightly larger than the first, but inside that interval, the first function is always significantly larger than the second. I suppose those two phenomena cancel out. That's hardly a complete answer, but it suggests a path for further investigation. Jul 14, 2013 at 20:07 You may use the change of variables $x\leftrightarrow x^{-1}$ to verify the equality without evaluation. • I figured there was a substitution like that which otherwise would make the identity work, but it still seems surprising to me. This makes for a nice verification of the identity, but it doesn't seem to offer any intuition as to why it's true... Jul 14, 2013 at 18:40 • @Clayton What kind of explanation would you like to have? Maybe an example? Jul 14, 2013 at 18:43 • @Clayton: I have the same doubt as O.L., and let me consider your question more seriously. – 23rd Jul 14, 2013 at 18:46 • @O.L.: An explanation as to why the $x^2$ in the numerator doesn't make the integral any larger. It seems unusual to me that the $x^2$ is able to 'balance' the integrand perfectly to get the same value. Jul 14, 2013 at 18:46 • If you want intuition as to how they could possibly be the same: when $0<x<1$, note that the LHS integrand is between $\frac{1}{2}$ and $1$, while the RHS integrand is between 0 and $\frac{1}{2}$; and yes, the RHS is larger for positive $x$, but they are BOTH very, very close to 0 for large $x$. Jul 14, 2013 at 18:48 To mitigate what you found counter-intuitiveness, computing $$\int_0^1 (1+x^4)^{-1} \, dx \approx 0.867$$ $$\int_1^\infty (1+x^4)^{-1} \, dx \approx 0.244$$ shows that the majority of the area is between $[0,1]$, making it much less surprising that decreasing the value on $[0,1]$ could compensate increasing over $[1,\infty]$.	2022-05-25 18:45:02	{"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": 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": 0.8675899505615234, "perplexity": 209.00360674069782}, "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/1652662593428.63/warc/CC-MAIN-20220525182604-20220525212604-00356.warc.gz"}
https://calculator.academy/group-delay-dispersion-calculator/	Enter the total group velocity dispersion and the length of the medium into the calculator to determine the group delay dispersion. ## Group Delay Dispersion Formula The following equation is used to calculate the Group Delay Dispersion. GDD = GVD * L • Where GDD delay is the Group Delay Dispersion(fs^2) • GVD is the group velocity dispersion (fs^2/mm) • L is the length of the medium (mm) To calculate the group dispersion delay, multiply the group velocity dispersion by the medium length. ## What is a Group Delay Dispersion? Definition: A group delay dispersion is defined as the frequency dependency of the group delay. ## How to Calculate Group Delay Dispersion? Example Problem: The following example outlines the steps and information needed to calculate Group Delay Dispersion. First, determine the group velocity dispersion. In this example, this is provided as 100 ft^2/mm. Next, determine the medium length. The length of the medium, in this example, is measured to be 10mm. Finally, calculate the Group Delay Dispersion using the formula above: GDD = GVD * L GDD = 100*10 GDD = 1,000 fs^2.	2023-02-03 20:07:46	{"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": 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": 0.3886904716491699, "perplexity": 1937.0192553139727}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500074.73/warc/CC-MAIN-20230203185547-20230203215547-00363.warc.gz"}
https://keet.wordpress.com/page/2/	# My gender-balanced book reviews overall, yet with much fluctuation In one of my random browsing moments, I stumbled upon a blog post of a writer who had her son complaining about the stories she was reading to him, as having so many books with women as protagonists. As it appeared, “only 27% of his books have a female protagonist, compared to 65% with a male protagonist.”. She linked back to another post about a similar issue but then for some TV documentary series called missed in history, where viewers complained that there were ‘too many women’ and more like a herstory than a missed in history. Their tally of the series’ episodes was that they featured 45% men, 21% women, and 34% were ungendered. All this made me wonder how I fared in my yearly book review blog posts. Here’s the summary table and the M/F/both or neither: Year posted Book Nr M Nr F Both / neither Pct F 2012 Long walk to freedom, terrific majesty, racist’s guide, end of poverty, persons in community, African renaissance, angina monologues, master’s ruse, black diamond, can he be the one 4 3 3 33% 2013 Delusions of gender, tipping point, affluenza, hunger games, alchemist, eclipse, mieses karma 2 3 2 43% 2014 Book of the dead, zen and the art of motorcycle maintenance, girl with the dragon tattoo, outliers, abu ghraib effect, nice girls don’t get the corner office 2 1 3 17% 2015 Stoner, not a fairy tale, no time like the present, the time machine, 1001 nights, karma suture, god’s spy, david and goliath, dictator’s learning curve, MK 4 2 4 20% 2016 Devil to pay, black widow society, the circle, accidental apprentice, moxyland, muh, big short, 17 contradictions 2 4 2 50% Total 14 13 14 32% Actually, I did pretty well in the overall balance. It also shows that were I to have done a bean count for a single year only, the conclusion could have been very different. That said, I classified them from memory, and not by NLP of the text of the books, so the actual amount allotted to the main characters might differ. Related to this is the screenplay dialogue-based data-driven analysis of Hollywood movies, for which NLP was used. Their results show that even when there’s a female lead character, Hollywood manages to get men to speak more; e.g., The Little Mermaid (71%) and The Hunger Games (55% male). Even the chick flick Clueless is 50-50. (The website has several nice interactive graphs based on the lots of data, so you can check yourself.) For the Hunger Games, though, the books do have Katniss think, do, and say more than in the movies. A further caveat of the data is that these books are not the only ones I’ve read over the past five years, just the ones written about. Anyhow, I’m pleased to discover there is some balance in what I pick out to write about, compared to unconscious bias. As a last note on the fiction novels listed above, there was a lot of talk online the past week about Lionel Shriver’s keynote on defense on fiction writing-what-you-like and having had enough of the concept of ‘cultural appropriation’. Quite few authors in the list above would be thrown on the pile of authors who ‘dared’ to imagine characters different from the box they probably would by put in. Yet, most of them still did a good job to make it a worthwhile read, such as Hugh Fitzgerald Ryan on Alice the Kyteler in ‘The devil to pay’, David Safier with Kim Lange in ‘Mieses Karma’, Stieg Larsson with ‘Girl with the dragon tattoo’, and Richard Patterson in ‘Eclipse’ about Nigeria. Rather: a terrible character or setting that’s misrepresenting a minority or oppressed, marginalised, or The Other group in a novel is an indication of bad writing and the writer should educate him/herself better. For instance, JM Coetzee could come back to South Africa and learn a thing or two about the majority population here, and I hope for Zakes Mda he’ll meet some women who he can think favourably about and then reuse those experiences in a story. Anyway, even if the conceptually problematic anti-‘cultural appropriation’ police wins it from the fiction writers, then I suppose I can count myself lucky living in South Africa that, with its diversity, will have diverse novels to choose from (assuming they won’t go further overboard into dictating that I would be allowed to read only those novels that are designated to be appropriate for my (from the outside) assigned box). UPDATE (20-9-2016): following the question on POC protagonist, here’s the table, where those books with a person (or group) of colour is a protagonist are italicised. Some notes on my counting: Angina monologues has three protagonists with 2 POCs so I still counted it, Hunger games’ Katniss is a POC in the books, Eclipse is arguable, abu ghraib effect is borderline and Moxyland is an ensemble cast so I still counted that as well. Non-POC includes cows as well (Muh), hence that term was chosen rather than ‘white’ that POC is usually contrasted with. As can be seen, it varies quite a bit by year as well. Year posted Book POC (italics in the list) Non-POC or N/A Pct POC 2012 Long walk to freedom, terrific majesty, racist’s guide, end of poverty, persons in community, African renaissance, angina monologues, master’s ruse, black diamond, can he be the one 8 2 80% 2013 Delusions of gender, tipping point, affluenza, hunger games, alchemist, eclipse, mieses karma 2 5 29% 2014 Book of the dead, zen and the art of motorcycle maintenance, girl with the dragon tattoo, outliers, abu ghraib effect, nice girls don’t get the corner office 2 4 33% 2015 Stoner, not a fairy tale, no time like the present, the time machine, 1001 nights, karma suture, god’s spy, david and goliath, dictator’s learning curve, MK 4 6 40% 2016 Devil to pay, black widow society, the circle, accidental apprentice, moxyland, muh, big short, 17 contradictions 3 5 38% Total 19 22 46% # Brief report on the INLG16 conference Another long wait at the airport is being filled with writing up some of the 10 pages of notes I scribbled while attending the WebNLG’16 workshop and the 9th International Natural Language Generation conference 2016 (INLG’16), that were held from 6 to 10 September in Edinburgh, Scotland. There were two keynote speakers, Yejin Choi and Vera Demberg, and several long and short presentations and a bunch of posters and demos, all of which had full or short papers in the (soon to appear) ACL proceedings online. My impression was that, overall, the ‘hot’ topics were image-to-text, summaries and simplification, and then some question generation and statistical approaches to NLG. The talk by Yejin Choi was about sketch-to-text, or: pretty much anything to text, such as image captioning, recipe generation based on the ingredients, and one even could do it with sonnets. She used a range of techniques to achieve it, such as probabilistic CFGs and recurrent neural networks. Vera Demberg’s talk, on the other hand, was about psycholinguistics for NLG, starting from the ‘uniform information density hypothesis’ compared to surprisal words and grammatical errors and how that affects a person reading the text. It appears that there’s more pupil jitter when there’s a grammar error. The talk then moved on to see how one can model and predict information density, for which there are syntactic, semantic, and event surprisal models. For instance, with the semantic one: ‘peter felled a tree’: then how predictable is ‘tree’, given that its already kind of entailed in the word ‘felled’? Some results were shown for the most likely fillers for, e.g., ‘serves’ as in ‘the waitress serves…’ and ‘the prisoner serves…’, which then could be used to find suitable word candidates in the sentence generation. The best paper award went to “Towards generating colour terms for referents in photographs: prefer the expected or the unexpected?”, by Sina Zarrieß and David Schlangen [1]. While the title might sound a bit obscure, the presentation was very clear. There is the colour spectrum, and people assign names to the colours, which one could take as RGB colour value for images. This is all nice and well on the colour strip, but when a colour is put in context of other colours and background knowledge, the colours humans would use to describe that patch on an image isn’t always in line with the actual RGB colour. The authors approached the problem by viewing it as a multi-class classification problem and used a multi-layer perceptron with some top-down recalibration—and voilá, the software returns the intended colour, most of the times. (Knowing the name of the colour, one then can go on trying to automatically annotate images with text.) As for the other plenary presentations, I did make notes of all of them, but will select only a few due to time limitations. The presentation by Advaith Siddhartan on summarisation of news stories for children [2] was quite nice, as it needed three aspects together: summarising text (with NLG, not just repeating a few salient sentences), simplifying it with respect to children’s vocabulary, and editing out or rewording the harsh news bits. Another paper on summaries was presented by Sabita Acharya [3], which is likely to be relevant also to my student’s work on NLG for patient discharge notes [4]. Sabita focussed on trying to get doctor’s notes and plan of care into a format understandable by a layperson, and used the UMLS in the process. A different topic was NLG for automatically describing graphs to blind people, with grade-appropriate lexicons (4-5th grade learners and students) [5]. Kathy Mccoy outlined how they were happy to remember their computer science classes, and seeing that they could use graph search to solve it, with its states, actions, and goals. They evaluated the generated text for the graphs—as many others did in their research—with crowdsourcing using the Mechanical Turk. One other paper that is definitely on my post-conference reading list, is the one about mereology and geographic entities for weather forecasts [6], which was presented by Rodrigo de Oliveira. For instance, a Scottish weather forecast referring to ‘the south’ is a different region than that of the UK as a whole, and the task was how to generate the right term for the intended region. our poster on generating sentences with part-whole relations in isiZulu (click to enlarge) My 1-minute lightning talk of Langa’s and my long paper [7] went well (one other speaker of the same session even resentfully noted afterward that I got all the accolades of the session), as did the poster and demo session afterward. The contents of the paper on part-whole relations in isiZulu were introduced in a previous post, and you can click on the thumbnail on the right for a png version of the poster (which is less text than the blog post). Note that the poster only highlights three part-whole relations from the 11 discussed in the paper. ENLG and INLG will merge and become a yearly INLG, there is a SIG for NLG, (www.siggen.org), and one of the ‘challenges’ for this upcoming year will be on generating text from RDF triples. Irrelevant for the average reader, I suppose, was that there were some 92 attendees, most of whom attended the social dinner where there was a ceilidh—Scottish traditional music by a band with traditional dancing by the participants—were it was even possible to have many (traditional) couples for the couples dances. There was some overlap in attendees between CNL16 and INLG16, so while it was my first INLG it wasn’t all brand new, yet also new people to meet and network with. As a welcome surprise, it was even mostly dry and sunny during the conference days in the otherwise quite rainy Edinburgh. References [1] Sina Zarrieß and David Schlangen. Towards generating colour terms for referents in photographs: prefer the expected or the unexpected? INLG’16. ACL, 246-255. [2] Iain Macdonald and Advaith Siddhartan. Summarising news stories for children. INLG’16. ACL, 1-10. [3] Sabita Acharya. Barbara Di Eugenio, Andrew D. Boyd, Karen Dunn Lopez, Richard Cameron, Gail M Keenan. Generating summaries of hospitalizations: A new metric to assess the complexity of medical terms and their definitions. INLG’16. ACL, 26-30. [4] Joan Byamugisha, C. Maria Keet, Brian DeRenzi. Tense and aspect in Runyankore using a context-free grammar. INLG’16. ACL, 84-88. [5] Priscilla Morales, Kathleen Mccoy, and Sandra Carberry. Enabling text readability awareness during the micro planning phase of NLG applications. INLG’16. ACL, 121-131. [6] Rodrigo de Oliveira, Somayajulu Sripada and Ehud Reiter. Absolute and relative properties in geographic referring expressions. INLG’16. ACL, 256-264. [7] C. Maria Keet and Langa Khumalo. On the verbalization patterns of part-whole relations in isiZulu. INLG’16. ACL, 174-183. # UVa 11357 Ensuring truth solution description We’re in the midst of preparing for the ICPC Southern Africa Regionals, to be held in October, and so I step up reading problems to find nice ones to train the interested students in a range of topics. The “Ensuring truth” problem was one of those, which I’ll discuss in the remainder of the post, since there’s no discussion of it online yet (only some code), and it is not as daunting as it may look like at first glance: The task is to determine whether such a formula is satisfiable. While it may ‘scare’ a 1st or 2nd-year student, when you actually break it down and play with an example or two, it turns out to be pretty easy. The ‘scary’ looking aspects are the basic propositional logic truth tables and the BNF grammar for (simplified!) Boolean formulas. Satisfiability of normal Boolean formulas is NP-compete, which you may have memorised, so that looks daunting as well, as if the contestant would have to come up with a nifty optimization to stay within the time limit. As it appears, not so. Instead of being put off by it, let’s look at what is going on. The first line of the BNF grammar says that a formula can be a clause, or a formula followed by a clause that is separated by a disjunction (\| ‘or’). The second line says that a clause is a conjunction of literals, which (in the third line) transpires to be just a series of ‘and’ (&) conjunctions between literals. The fourth lines states that a literal can be a variable or its negation, and the fifth line states that a variable is one of the letters in the alphabet. Now try to generate a few inputs that adhere to this grammar. Swapping one variable at a time on the left of the “::=” sign for one of the elements on the right-hand side of the “::=” sign in the BNF grammar, with steps indicated with “=>”, then e.g.: <formula> => <formula> \| <clause> => <clause> \| <clause> => (<conjunction-of-literals>) \| <clause> => (<literal>) \| <clause> => (<variable>) \| <clause> => (a)\| <clause> => (a)\| (<conjunction-of-literals>) => (a)\|(<conjunction-of-literals> & <literal>) => (a)\|(<conjunction-of-literals> & <literal> & <literal>) => (a)\|(<conjunction-of-literals> & <literal> & <literal> & <literal>) => (a)\|(<literal> & <literal> & <literal> & <literal>) => (a)\|(~<variable> & <literal> & <literal> & <literal>) => (a)\|(~a & <literal> & <literal> & <literal>) => (a)\|(~a & <variable> & <literal> & <literal>) => (a)\|(~a&b& <literal> & <literal>) => (a)\|(~a&b& <variable> & <literal>) => (a)\|(~a&b&a& <literal>) => (a)\|(~a&b&a& <variable>) => (a)\|(~a&b&a&c) That is, (a)\|(~a&b&a&c) is in the language of the grammar, as are the two in the input given, being (a&b&c)\|(a&b)\|(a) and (x&~x). Do you see a pattern emerging of how the formulas look like with this grammar? It’s a series of disjunctions of conjuncts, and only one of the conjuncts shouldn’t have a contradiction for the formula to be satisfiable. The only way we get a contradiction is if both a literal and its negation are in the same conjunct (analyse the truth tables if you didn’t know that). So, the only thing you have to do with the input is to check whether within the brackets there is, say, an x and a ~x, and with the first conjunct you encounter where there is no contradiction, then the formula is satisfiable and you print YES, else NO. That’s all. So, when given “(a)\|(~a&b&a&c)”, you know upon processing the first conjunct “(a)”, that the answer is YES, because “(a)” is trivially not contradictory and thus we can ignore the “(~a&b&a&c)” that does have a contradiction (it doesn’t matter anymore, because we have found one already that doesn’t). I’ll leave the implementation as an exercise to the reader :). # On generating isiZulu sentences with part-whole relations It all sounded so easy… We have a pretty good and stable idea about part-whole relations and their properties (see, e.g., [1]), we know how to ‘verbalise’/generate a natural language sentence from basic description logic axioms with object properties that use simple verbs [2], like $Professor \sqsubseteq \exists teaches.Course$ ‘each professor teaches at least one course’, and SNOMED CT is full of logically ‘simple’ axioms (it’s in OWL 2 EL, after all) and has lots of part-whole relations. So why not combine that? We did, but it took some more time than initially anticipated. The outcomes are described in the paper “On the verbalization patterns of part-whole relations in isiZulu”, which was recently accepted at the 9th International Natural Language Generation Conference (INLG’16) that will be held 6-8 September in Edinburgh, Scotland. What it ended up to be, is that notions of ‘part’ in isiZulu are at times less precise and other times more precise compared to the taxonomy of part-whole relations. This interfered with devising the sentence generation patterns, it pushed the number of ‘elements’ to deal with in the language up to 13 constituents, and there was no way to avoid proper phonological conditioning. We already could handle quantitative, relative, and subject concords, the copulative, and conjunction, but what had to be added were, in particular, the possessive concord, locative affixes, a preposition (just the nga in this context), epenthetic, and the passive tense (with modified final vowel). As practically every element has to be ‘completed’ based on the context (notably the noun class), one can’t really speak of a template-based approach anymore, but a bunch of patterns and partial grammar engine instead. For instance, plain parthood, structural parthood, involvement, membership all have: • (‘each whole has some part’) $QCall_{nc_{x,pl}}$ $W_{nc_{x,pl}}$ $SC_{nc_{x,pl}}-CONJ-P_{nc_y}$ $RC_{nc_y}-QC_{nc_y}-$dwa • (‘each part is part of some whole’) $QCall_{nc_{x,pl}}$ $P_{nc_{x,pl}}$ $SC_{nc_{x,pl}}-COP-$ingxenye $PC_{\mbox{\em ingxenye}}-W_{nc_y}$ $RC_{nc_y}-QC _{nc_y}-$dwa There are a couple of noteworthy things here. First, the whole-part relation does not have one single string, like a ‘has part’ in English, but it is composed of the subject concord (SC) for the noun class (nc) of the noun that play the role of the whole ( W ) together with the phonologically conditioned conjunction na- ‘and’ (the “SC-CONJ”, above) and glued onto the noun of the entity that play the role of the part (P). Thus, the surface realisation of what is conceptually ‘has part’ is dependent on both the noun class of the whole (as the SC is) and on the first letter of the name of the part (e.g., na-+i-=ne-). The ‘is part of’ reading direction is made up of ingxenye ‘part’, which is a noun that is preceded with the copula (COP) y– and together then amounts to ‘is part’. The ‘of’ of the ‘is part of’ is handled by the possessive concord (PC) of ingxenye, and with ingxenye being in noun class 9, the PC is ya-. This ya- is then made into one word together with the noun for the object that plays the role of the whole, taking into account vowel coalescence (e.g., ya-+u-=yo-). Let’s illustrate this with heart (inhliziyo, nc9) standing in a part-whole relation to human (umuntu, NC1), with the ‘has part’ and ‘is part of’ underlined: • bonke abantu banenhliziyo eyodwa ‘All humans have as part at least one heart’ • The algorithm, in short, to get this sentence from, say $Human \sqsubseteq \exists hasPart.Heart$: 1) it looks up the noun class of umuntu (nc1); 2) it pluralises umuntu into abantu (nc2); 3) it looks up the quantitative concord for universal quantification (QCall) for nc2 (bonke); 4) it looks up the SC for nc2 (ba); 5) then it uses the phonological conditioning rules to add na- to the part inhliziyo, resulting in nenhliziyo and strings it together with the subject concord to banenhliziyo; 6) and finally it looks up the noun class of inhliziyo, which is nc9, and from that it looks up the relative concord (RC) for nc9 (e-) and the quantitative concord for existential quantification (QC) for nc9 (being yo-), and strings it together with –dwa to eyodwa. • zonke izinhliziyo ziyingxenye yomuntu oyedwa ‘All hearts are part of at least one human’ • The algorithm, in short, to get this sentence from $Heart \sqsubseteq \exists isPartOf.Human$: 1) it looks up the noun class of inhliziyo (nc9); 2) it pluralises inhliziyo to izinhliziyo (nc10); 3) it looks up the QCall for nc10 (zonke); 4) it looks up the SC for nc10 (zi-), takes y- (the COP) and adds them to ingxenye to form ziyingxenye; 5) then it uses the phonological conditioning rules to add ya- to the whole umuntu, resulting in yomuntu; 6) and finally it looks up the noun class of umuntu, which is nc1, and from that the RC for nc10 (o-) and the QC for nc10 (being ye-), and strings it together with –dwa to oyedwa. For subquantities, we end up with three variants: one for stuff-parts (as in ‘urine has part water’, still with ingxenye for ‘part’), one for portions of solid objects (as in ‘tissue sample is a subquantity of tissue’ or a slice of the cake) that uses umunxa instead of ingxenye, and one ‘spatial’ notion of portion, like that an operating theatre is a portion of a hospital, or the area of the kitchen where the kitchen utensils are is a portion of the kitchen, which uses isiqephu instead of ingxenye. Umunxa is in nc3, so the PC is wa- so that with, e.g., isbhedlela ‘hospital’ it becomes wesibhedlela ‘of the hospital’, and the COP is ng- instead of y-, because umunxa starts with an u. And yet again part-whole relations use locatives (like the containment type of part-whole relation). The paper has all those sentence generation patterns, examples for each, and explanations for them. The meronymic part-whole relations participation and constitution have added aspects for the verb, such as generating the passive for ‘constituted of’: –akha is ‘to build’ for objects that are made/constituted of some matter in some structural sense, else –enza is used. They are both ‘irregular’ in the sense that it is uncommon that a verb stem starts with a vowel, so this means additional vowel processing (called hiatus resolution in this case) to put the SC together with the verb stem. Then, for instance za+akhiwe=zakhiwe but u+akhiwe=yakhiwe (see rules in paper). Finally, this was not just a theoretical exercise, but it also has been implemented. I’ll readily admit that the Python code isn’t beautiful and can do with some refactoring, but it does the job. We gave it 42 test cases, of which 38 were answered correctly; the remaining errors were due to an ‘incomplete’ (and unresolvable case for any?) pluraliser and that we don’t know how to systematically encode when to pick akha and when enza, for that requires some more semantics of the nouns. Here is a screenshot with some examples: The ‘wp’ ones are that a whole has some part, and the ‘pw’ ones that the part is part of the whole and, in terms of the type of axiom that each function verbalises, they are of the so-called ‘all some’ pattern. The source code, additional files, and the (slightly annotated) test sentences are available from the GENI project’s website. If you want to test it with other nouns, please check whether the noun is already in nncPairs.txt; if not, you can add it, and then invoke the function again. (This remains this ‘clumsily’ until we make a softcopy of all isiZulu nouns with their noun classes. Without the noun class explicitly given, the automatic detection of the noun class is not, and cannot be, more than about 50%, but with noun class information, we can get it up to 90-100% correct in the pluralisation step of the sentence generation [4].) References [1] Keet, C.M., Artale, A. Representing and Reasoning over a Taxonomy of Part-Whole Relations. Applied Ontology, 2008, 3(1-2):91-110. [2] Keet, C.M., Khumalo, L. Basics for a grammar engine to verbalize logical theories in isiZulu. 8th International Web Rule Symposium (RuleML’14), A. Bikakis et al. (Eds.). Springer LNCS vol. 8620, 216-225. August 18-20, 2014, Prague, Czech Republic. [3] Keet, C.M., Khumalo, L. On the verbalization patterns of part-whole relations in isiZulu. 9th International Natural Language Generation conference (INLG’16), September 5-8, 2016, Edinburgh, UK. (in print) [4] Byamugisha, J., Keet, C.M., Khumalo, L. Pluralising Nouns in isiZulu and Related Languages. 17th International Conference on Intelligent Text Processing and Computational Linguistics (CICLing’16), Springer LNCS. April 3-9, 2016, Konya, Turkey. (in print) # A search engine, browser, and language bias mini-experiment I’m in the midst of preparing for the “Social Issues and Professional Practice” block for a course and was pondering whether I should touch upon known search engine issues, like the filter bubble and search engine manipulation to nudge democratic elections, which could be interesting given that South Africa just had the local elections last week, with interesting results. I don’t have the option to show the differences between ‘Google search when logged in’ versus ‘Google search when logged out’, nor for the Bing-Hotmail combination, so I played with other combinations: Google in isiZulu on Firefox (GiF), Google in English on Safari (GES), and Bing in English on Firefox (BEF). I did seven searches at the same time (Friday 12 August 2016, 17:18-17:32) on the same machine (a MacBookPro), using the eduroam on campus. Although this certainly will not pass a test of scientific rigour, it unequivocally shows that it deserves a solid experiment. The only thing I aimed to do was to see whether those things happen in South Africa too, not just in the faraway USA or India. They do. Before giving the results, some basic preliminaries may be of use if you are not familiar with the topic. On HTTP, that the browser uses: in trying to GET information, your browser sends the server what operating system you are using (Mac, Linux, Windows, etc.), your browser information (e.g., Firefox, Safari, Chrome, etc.), and language settings (e.g., UK English, isiZulu, Italian). Safari is linked to the Mac, and thus Apple, and it is assumed that Apple users have more disposable income (are richer). Free and open source software users (e.g., Linux + Firefox) are assumed to be not rich or a leftie or liberal, or all of them. I don’t know if they categorise Apple + Firefox as an armchair socialist or a posh right-wing liberal ;-). Here goes the data, being the screenshots and the reading and interpretation of the links of the search results, with a bit of context in case you’re not in South Africa. The screens in the screenshots are in the order (from let to right) as GiF, GES, BEF. EFF search • Search term: EFF: GiF and BEF show EFF as political party (leftpopulist opposition party in South Africa) information and a link to EFF as the electronic frontier foundation, whereas the GES just shows EFF as political party in the context of news about the DA political party (capitalist, for the rich, mainly White voters). The GES difference may be explained by the Mac+Safari combination, and it makes one wonder whether and how this has had an effect on perceptions and voting behaviour. Bing had 10mln results, Google 46mln. Jacob Zuma search • Search term: Jacob Zuma (current president of South Africa): GiF and BEF show general results, GES with articles also about JZ to stay (by a DA supporter) and on that he won’t resign. Bing has 1.1mln results, Google 9.6mln. • Search term: Nkandla (Zuma’s controversial lavish homestead Nkandla Search that was upgraded with taxpayers money): GiF has pictures and a fact about Nkandla, GES has a picture, fact, and a bit negative news, BEF: more on news and issues (that is: that JZ has to pay back the money). Bing has 700K results, Google 1.8mln. • Search term: FeesMustFall (hashtag of 2015 on no university fee increases and free higher education): Google results has FeesMustFall search ‘plain’-looking information, whereas Bing shows results with more information from the FMF perspective, it seems. Bing has 165K results, Google 451K. • Search term: Fleming Rose (person with controversial ideas, Fleming Rose search recently disinvited by UCT to not give the academic freedom lecture): Google shows a little general information and several UCT opinion issues, BEF has information about Fleming Rose. Bing has 1.25mln results, Google about 500K—the only time that Bing’s number of results far outnumbers Google’s. • Search term: Socialism: GiF has links to definitions, GES and BEF socialism search show a definition in their respective info boxes, which takes up most of the screen. Bing has 7.3mln results, GiF with 23.4mln, GES: 31mln—this is the first time there is a stark difference between the number of results in Google hits, with more for English and Safari. • Law on cookies in south africa Search Search term: Law on cookies in south africa: the results are similar throughout the three search results. Bing has 108mln results, GiF 3mln, and GES 2.2mln—a 1/3 difference in Google’s number of results in the other direction. In interpreting the results, it has to be noted that Google, though typing in google.com, forced it to google.co.za, where as Bing stayed on bing.com. This might explain some ‘tailoring’ of GiF and GES to news that is topical in South Africa, which does not happen to the same extent on Bing. I suppose that for some search terms, one would like that, and for others, one would not; i.e., to have the option to choose to search for facts vs opinion pieces vs news, nationally or internationally, or whether you’d want to get an answer or get links to multiple answers. Neither Bing nor Google gives you a free choice on the matter: based on the data you provide involuntarily, they make assumptions as to whom you are and what they think that that kind of person would probably like to see in the search results. That three out of the seven searches on GES lean clearly to the political right is a cause of concern, as is the fewer amounts of facts in Google search results vs Bing’s. I also find it a bit odd that the selection of results is from such wide-ranging numbers of results. Based on this small sampling, I obviously cannot draw hard conclusions, but it would be nice if we can get some money to get a student to investigate this systematically with more browsers and more languages. We now know that it happens, but how does it happen in South Africa, and might there be some effect because of it? Those questions remain unanswered. In the meantime, I’ll have to do with some anecdotes for the students in an upcoming lecture. # Experimentally-motivated non-trivial intermodel links between conceptual models I am well aware that some people prefer Agile and mash-ups and such to quickly, scuffily, put an app together, but putting a robust, efficient, lasting, application together does require a bit of planning—analysis and design in the software development process. For instance, it helps to formalise one’s business rules or requirements, or at least structure them with, say, SBVR or ORM, so as to check that the rules obtained from the various stakeholders do not contradict themselves cf. running into problems when testing down the line after having implemented it during a testing phase. Or analyse a bit upfront which classes are needed in the front-end application layer cf. perpetual re-coding to fix one’s mistakes (under the banner ‘refactoring’, as if naming the process gives it an air of respectability), and create, say, a UML diagram or two. Or generating a well-designed database based on an EER model. Each of these three components can be done in isolation, but how to do this for complex system development where the object-oriented application layer hast to interact with the database back-end, all the while ensuring that the business rules are still adhered to? Or you had those components already, but they need to be integrated? One could link the code to tables in the implementation layer, on an ad hoc basis, and figure it out again and again for any combination of languages and systems. Another one is to do that at the conceptual modelling layer irrespective of the implementation language. The latter approach is reusable (cf. reinventing the mapping wheel time and again), and at a level of abstraction that is easier to cope with for more people, and even more so if the system is really large. So, we went after that option for the past few years and have just added another step to realising all this: how to link which elements in the different models for the system. It is not difficult to imagine a tool where one can have several windows open, each with a model in some conceptual modelling language—many CASE tools already support modelling in different notations anyway. It is conceptually also fairly straightforward when in, say, the UML model there is a class ‘Employee’ and in the ER diagram there’s an ‘Employee’ entity type: it probably will work out to align these classes. Implementing just this is a bit of an arduous engineering task, but doable. In fact, there is such a tool for models represented in the same language, where the links can be subsumption, equivalence, or disjointness between classes or between relationships: ICOM [2]. But we need something like that to work across modelling languages as well, and for attributes, too. In the hand-waiving abstract sense, this may be intuitively trivial, but the gory details of the conceptual and syntax aspects are far from it. For instance, what should a modeller do if one model has ‘Address’ as an attribute and the other model has it represented as a class? Link the two despite being different types of constructs in the respective languages? Or that ever-recurring example of modelling marriage: a class ‘Marriage’ with (at least) two participants, or ‘Marriage’ as a recursive relationship (UML association) of a ‘Person’ class? What to do if a modeller in one model had chosen the former option and another modeller the latter? Can they be linked up somehow nonetheless, or would one have to waste a lot of time redesigning the other model? Instead of analysing this for each case, we sought to find a generic solution to it; with we being: Zubeida Khan, Pablo Fillottrani, Karina Cenci, and I. The solution we propose will appear soon in the proceedings of the 20th Conference on Advances in DataBases and Information Systems (ADBIS’16) that will be held at the end of this month in Prague. So, what did we do? First, we tried to narrow down the possible links between elements in the models: in theory, one might want to try to link anything to anything, but we already knew some model elements are incompatible, and we were hoping that others wouldn’t be needed yet other suspected to be needed, so that a particular useful subset could be the focus. To determine that, we analysed a set of ICOM projects created by students at the Universidad Nacionál del Sur (in Bahía Blanca), and we created model integration scenarios based on publicly available conceptual models of several subject domains, such as hospitals, airlines, and so on, including EER diagrams, UML class diagrams, and ORM models. An example of an integration scenario is shown in the figure below: two conceptual models about airline companies, with on the left the ER diagram and on the right the UML diagram. One of the integration scenarios [1] The solid purple links are straightforward 1:1 mappings; e.g., er:Airlines = uml:Airline. Long-dashed dashed lines represent ‘half links’ that are semantically very similar, such as er:Flight.Arr_time ≈ uml:Flight.arrival_time, where the idea of attribute is the same, but ER attributes don’t have a datatype specified whereas UML attributes do. The red short-dashed dashed lines require some transformation: e.g., er:Airplane.Type is an attribute yet uml:Aircraft is a class, and er:Airport.code is an identifier (with its mandatory 1:1 constraint, still no datatype) but uml:Airport.ID is just a simple attribute. Overall, we had 40 models with 33 schema matchings, with 25 links in the ICOM projects and 258 links in the integration scenarios. The detailed aggregates are described in the paper and the dataset is available for reuse (7MB). Unsurprisingly, there were more attribute links than class links (if a class can be linked, then typically also some of its attributes). There were 64 ‘half’ links and 48 transformation links, notably on the slightly compatible attributes, attributes vs. identifiers, attribute<->value type, and attribute<->class. Armed with these insights from the experiment, a general intermodel link validation approach [3] that uses the unified metamodel [4], and which type of elements occur mostly in conceptual models with their logic-based profiles [5,6], we set out to define those half links and transformation links. While this could have been done with a logic of choice, we opted for a clear step toward implementability by exploiting the ATLAS Transformation Language (ATL) [7] to specify the transformations. As there’s always a source model and a target model in ATL, we constructed the mappings such that both models in question are the ‘source’ and both are mapped into a new, single, ‘target’ model that still adheres to the constraints imposed by the unifying metamodel. A graphical depiction of the idea is shown in the figure below; see paper for details of the mapping rules (they don’t look nice in a blog post). Informal, graphical rendering of the rule Attribute<->Object Type output [1] Someone into this matter might think, based on this high-level description, there’s nothing new here. However, there is, and the paper has an extensive related works section. For instance, there’s related work on Distributed Description Logics with bridge rules [8], but they don’t do attributes and the logics used for that doesn’t fit well with the features needed for conceptual modelling, so it cannot be adopted without substantial modifications. Triple Graph Grammars look quite interesting [9] for this sort of task, as does DOL [10], but either would require another year or two to figure it out (feel free to go ahead already). On the practical side, e.g., the Eclipse metamodel of the popular Eclipse Modeling Framework didn’t have enough in the metamodel for what needs to be included, both regarding types of entities and the constraints that would need to be enforced. And so on, such that by a process of elimination, we ended up with ATL. It would be good to come up with those logic-based linking options and proofs of correctness of the transformation rules presented in the paper, but in the meantime, an architecture design of the new tool was laid out in [11], which is in the stage of implementation as I write this. For now, at least a step has been taken from the three years of mostly theory and some experimentation toward implementation of all that. To be continued J. References [1] Khan, Z.C., Keet, C.M., Fillottrani, P.R., Cenci, K.M. Experimentally motivated transformations for intermodel links between conceptual models. 20th Conference on Advances in Databases and Information Systems (ADBIS’16). Springer LNCS. August 28-31, Prague, Czech Republic. (in print) [2] Fillottrani, P.R., Franconi, E., Tessaris, S. The ICOM 3.0 intelligent conceptual modelling tool and methodology. Semantic Web Journal, 2012, 3(3): 293-306. [3] Fillottrani, P.R., Keet, C.M. Conceptual Model Interoperability: a Metamodel-driven Approach. 8th International Web Rule Symposium (RuleML’14), A. Bikakis et al. (Eds.). Springer Lecture Notes in Computer Science LNCS vol. 8620, 52-66. August 18-20, 2014, Prague, Czech Republic. [4] Keet, C.M., Fillottrani, P.R. An ontology-driven unifying metamodel of UML Class Diagrams, EER, and ORM2. Data & Knowledge Engineering, 2015, 98:30-53. [5] Keet, C.M., Fillottrani, P.R. An analysis and characterisation of publicly available conceptual models. 34th International Conference on Conceptual Modeling (ER’15). Johannesson, P., Lee, M.L. Liddle, S.W., Opdahl, A.L., Pastor López, O. (Eds.). Springer LNCS vol 9381, 585-593. 19-22 Oct, Stockholm, Sweden. [6] Fillottrani, P.R., Keet, C.M. Evidence-based Languages for Conceptual Data Modelling Profiles. 19th Conference on Advances in Databases and Information Systems (ADBIS’15). Morzy et al. (Eds.). Springer LNCS vol. 9282, 215-229. Poitiers, France, Sept 8-11, 2015. [7] Jouault, F. Allilaire, F. Bzivin, J. Kurtev, I. ATL: a model transformation tool. Science of Computer Programming, 2008, 72(12):31-39. [8] Ghidini, C., Serafini, L., Tessaris, S., Complexity of reasoning with expressive ontology mappings. Formal ontology in Information Systems (FOIS’08). IOS Press, FAIA vol. 183, 151-163. [9] Golas, U., Ehrig, H., Hermann, F. Formal specification of model transformations by triple graph grammars with application conditions. Electronic Communications of the ESSAT, 2011, 39: 26. [10] Mossakowsi, T., Codescu, M., Lange, C. The distributed ontology, modeling and specification language. Proceedings of the Workshop on Modular Ontologies 2013 (WoMo’13). CEUR-WS vol 1081. Corunna, Spain, September 15, 2013. [11] Fillottrani, P.R., Keet, C.M. A Design for Coordinated and Logics-mediated Conceptual Modelling. 29th International Workshop on Description Logics (DL’16). Peñaloza, R. and Lenzerini, M. (Eds.). CEUR-WS Vol. 1577. April 22-25, Cape Town, South Africa. (abstract) # Bootstrapping a Runyankore CNL from an isiZulu one mostly works well Earlier this week the 5th Workshop on Controlled Natural Language (CNL’16) was held in Aberdeen, Scotland, where I presented progress made on a Runyankore CNL [1], rather than my student, Joan Byamugisha, who did most of the work on it (she could not attend due to nasty immigration rules by the UK, not a funding issue). “Runyankore?”, you might ask. It is one of the languages spoken in Uganda. As Runyankore is very under-resourced, any bootstrapping to take a ‘shortcut’ to develop language resources would be welcome. We have a CNL for isiZulu [2], but that is spoken in South Africa, which is a few thousand kilometres further south of Uganda, and it is in a different Guthrie zone of the—in linguistics still called—Bantu languages, so it was a bit of a gamble to see whether those results could be repurposed for Runynakore. They could, needing only minor changes. What stayed the same were the variables, or: components to make up a grammatically correct sentence when generating a sentence within the context of OWL axioms (ALC, to be more precise). They are: the noun class of the name of the concept (each noun is assigned a noun class—there are 20 in Runyankore), the category of the concept (e.g., noun, adjective), whether the concept is atomic (named OWL class) or an OWL class expression, the quantifier used in the axiom, and the position of the concept in the axiom. The only two real differences were that for universal quantification the word for the quantifier is the same when in the singular (cf. isiZulu, where it changes for both singular or plural), and for disjointness there is only one word, ti ‘is not’ (cf. isiZulu’s negative subject concord + pronomial). Two very minor differences are that for existential quantification ‘at least one’, the ‘at least’ is in a different place in the sentence but the ‘one’ behaves exactly the same, and ‘all’ for universal quantification comes after the head noun rather than before (but is also still dependent on the noun class). It goes without saying that the vocabulary is different, but that is a minor aspect compared to figuring out the surface realisation for an axiom. Where the bootstrapping thus came in handy was that that arduous step of investigating from scratch the natural language grammar involved in verbalising OWL axioms could be skipped and instead the ones for isiZulu could be reused. Yay. This makes it look very promising to port to other languages in the Bantu language family. (yes, I know, “one swallow does not a summer make” [some Dutch proverb], but one surely is justified to turn up one’s hope a notch regarding generalizability and transferability of results.) Joan also conducted a user survey to ascertain which surface realisation was preferred among Runyankore speakers, implemented the algorithms, and devised a new one for the ‘hasX’ naming scheme of OWL object properties (like hasSymptom and hasChild). All these details, as well as the details of the Runyankore CNL and the bootstrapping, are described in the paper [1]. I cannot resist a final comment on all this. There are people who like to pull it down and trivialise natural language interfaces for African languages, on the grounds of “who cares about text in those kind of countries; we have to accommodate the illiteracy with pictures and icons and speech and such”. People are not as illiterate as is claimed here and there (including by still mentally colonised people from African countries)—if they were, then the likes of Google and Facebook and Microsoft would not invest in localising their interfaces in African languages. The term “illiterate” is used by those people to include also those who do not read/write in English (typically an/the official language of government), even though they can read and write in their local language. People who can read and write—whichever natural language it may be—are not illiterate, neither here in Africa nor anywhere else. English is not the yardstick of (il)literacy, and anyone who thinks it is should think again and reflect a bit on cultural imperialism for starters. References [1] Byamugisha, J., Keet, C.M., DeRenzi, B. Bootstrapping a Runyankore CNL from an isiZulu CNL. 5th Workshop on Controlled Natural Language (CNL’16), Springer LNAI vol. 9767, 25-36. 25-27 July 2016, Aberdeen, UK. Springer’s version [2] Keet, C.M., Khumalo, L. Toward a knowledge-to-text controlled natural language of isiZulu. Language Resources and Evaluation, 2016. DOI: 10.1007/s10579-016-9340-0 (in print) accepted version	2017-01-18 05:48:46	{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 12, "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": 0.38372108340263367, "perplexity": 3616.134950590328}, "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-2017-04/segments/1484560280239.54/warc/CC-MAIN-20170116095120-00139-ip-10-171-10-70.ec2.internal.warc.gz"}
https://stacks.math.columbia.edu/tag/054L	Smooth schemes are étale-locally like affine spaces. Lemma 29.35.20. Let $\varphi : X \to Y$ be a morphism of schemes. Let $x \in X$. Let $V \subset Y$ be an affine open neighbourhood of $f(x)$. If $\varphi$ is smooth at $x$, then there exists an integer $d \geq 0$ and an affine open $U \subset X$ with $x \in U$ and $\varphi (U) \subset V$ such that there exists a commutative diagram $\xymatrix{ X \ar[d] & U \ar[l] \ar[d] \ar[r]_-\pi & \mathbf{A}^ d_ V \ar[ld] \\ Y & V \ar[l] }$ where $\pi$ is étale. Proof. By Lemma 29.33.11 we can find an affine open $U$ as in the lemma such that $\varphi \|_ U : U \to V$ is standard smooth. Write $U = \mathop{\mathrm{Spec}}(A)$ and $V = \mathop{\mathrm{Spec}}(R)$ so that we can write $A = R[x_1, \ldots , x_ n]/(f_1, \ldots , f_ c)$ with $g = \det \left( \begin{matrix} \partial f_1/\partial x_1 & \partial f_2/\partial x_1 & \ldots & \partial f_ c/\partial x_1 \\ \partial f_1/\partial x_2 & \partial f_2/\partial x_2 & \ldots & \partial f_ c/\partial x_2 \\ \ldots & \ldots & \ldots & \ldots \\ \partial f_1/\partial x_ c & \partial f_2/\partial x_ c & \ldots & \partial f_ c/\partial x_ c \end{matrix} \right)$ mapping to an invertible element of $A$. Then it is clear that $R[x_{c + 1}, \ldots , x_ n] \to A$ is standard smooth of relative dimension $0$. Hence it is smooth of relative dimension $0$. In other words the ring map $R[x_{c + 1}, \ldots , x_ n] \to A$ is étale. As $\mathbf{A}^{n - c}_ V = \mathop{\mathrm{Spec}}(R[x_{c + 1}, \ldots , x_ n])$ the lemma with $d = n - c$. $\square$ Comment #1364 by on Suggested slogan: Smooth schemes are étale-locally like affine spaces. This is problematic, as étale-locally could be understood to mean an étale cover by affine spaces. It would be more precise to say "smooth schemes have étale coordinates" but the first suggestion is already colloquially used, so it may be useful to record it. Comment #1383 by on OK, I agree with what you say and added your slogan. Thanks. There are also: • 3 comment(s) on Section 29.35: Étale morphisms In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).	2020-09-30 10:45:43	{"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": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9730439186096191, "perplexity": 305.06519018499085}, "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/1600402123173.74/warc/CC-MAIN-20200930075754-20200930105754-00644.warc.gz"}
http://photography.seldonhunt.com/the-lost-nfsrmfg/ba669c-pesto-pasta-make-ahead	Click the Output category and drag out the first block to set the built-in LED HIGH. In our case the potentiometers have a power rating of 0.3W and hence can be used only for low current circuits. The value Arduino get is NOT angle, NOT voltage. (Getting started). It is used where there is need for varying resistance in order to control current and voltage. To store the resistance value of the potentiometer, create a variable named sensorValue. As the current increases the voltage increases and there is a change in voltage which is detected by the analog input A0 pin of the Arduino. Pin 2 (U/D) on the potentiometer goes to pin 13 on the Arduino. It is proportional to the voltage being applied to the pin. The potentiometer is a passive component. In this example, we will use a potentiometer that controls the value at which LED blinks. I just want to know how to change the resistance of the digital potentiometer. If the values on the serial monitor do not change when the knob is rotated then the potentiometer may be faulty. A potentiometer is connected to one of the analog pins of the Arduino so that we can be able to take analog voltage measurements. Move the position of pin 2 by rotating the knob, changing the resistance value from pin 2 to both ends. Unlike the usual resistors that have two terminals, a potentiometer has three terminals which are arranged as shown below. Variable resistors come in all shapes and sizes, and they all do the same basic job. Potentiometer Is also known as the variable resistance. The required components are listed below: The analog input will turn the LED ON and OFF, which is connected to the pin number 13 of the Arduino UNO board. pins or legs): one for input voltage (e.g. The LEDs will light one by one when the potentiometer knob is rotated clockwise and will go off sequentially when turned counter clockwise. All the pins are connected, I just need to know how to program it, in other words I need the code for the programming part. A resistance value is an analog value that can be read on any analogue pin of Arduino. The control unit is where the control signal is sent from a microcontroller like Arduino to vary the resistance of the digital potentiometer. 5 PA0 This is one terminal of the potentiometer. They can be attuned from zero ohms to whatever maximum resistance that is specific to it. When you rotate the knob of the potentiometer, resistance decreases and the current starts flowing. The analog voltage controlled can be from 4.5-15.5V. The time (delay time) at which LED is ON/OFF depends on the value acquired by the analogread( ). GND) and one for picking up the value of the pot (we’ll call this the wiper). The map() function is used to convert the analog readings got from the potentiometer into percentages. Some standard values for a potentiometer are 500Ω, 1K, 2K, 5K, 10K, 22K, 47K, 50K, 100K, 220K, 470K, 500K, 1 M. The Power (wattage) rating determines how much current the potentiometer can allow. When this code is uploaded to the Arduino and the potentiometer knob is rotated clockwise or counter clockwise, the analog reading, the voltage, resistance and percentage of rotation is displayed on the serial monitor as shown below. Connect the middle pin to ANALOG IN pin 0 on the Arduino. Connect one side to 5V. Terminal 2 is connected to a movable shaft attached to a wiper that moves across the resistive material whenever the potentiometer knob is rotated. Two potentiometer combined on the same shaft, enabling the parallel setting of two channels. Arduino Potentiometer The potentiometer is a device that is used to measure the voltage or electric potential. On the Arduino the ADC has around a 1MΩ input impedance, so you shouldn't connect anything with more than around 100kΩ output impedance. The potentiometer is a device that is used to measure the voltage or electric potential. I will now show you how we can control the sequential lighting of LEDs using a potentiometer. We can find some very basic applications of the component reviewed in many blogs and sites, including the arduino.cc website “Controlling a digital potentiometer using SPI“. By connecting an output pin of the potentiometer to an analog input pin, we can read the analog value from the pin, and then converts it to a meaningful value. As the slider moves from one end to another, the divider can vary the output voltage from maximum to Ground. The greater the resistor value the smaller the current will flow. The middle pin of the potentiometer is connected to the analog input pin A2 of the board. 4.3 out of 5 stars 53 ratings. If we have a 10kΩ potentiometer and the wiper is placed exactly at 30% from terminal 1, then if we measure the resistance between 1 and 2 we will get 30% of 10kΩ which is 3.0kΩ and measuring across terminal 2 and 3 will give a resistance of 7.0kΩ. The potentiometer structure consists of a sliding contact (called wiper), a resistive element, electrical terminals, and a housing. Code for interfacing potentiometer with Arduino. This shield is based on AD5206 digital potentiometer. We don't know when or if this item will be back in stock. Hardware connections: Soft potentiometer: The soft potentiometer is the large plastic strip with three pins. Resistance can be in range of 120 ohm to 4.7 k ohm. Most common are single turn potentiometers with equal resistance and taper. The potentiometer is a three-terminal device. It is an electrical component with three terminals (i.e. A potentiometer is simply a knob which is able to modify the value of a resistance. A potentiometer, henceforth referred to as a pot, is a variable resistor. A potentiometer is among the commonest devices used in electronics projects. The setup will be as shown below. Make the circuit and upload the sketch in your ardunio uno. The sliding contact moves along the resistive element, while the housing consists of the wiper and the element. How to use the 74HC595 Shift Register with Arduino. In the experiment, connect pin 1 and pin 3 to the 5V GND of the development board, and then read the voltage of pin 2 obtained by the potentiometer through the analog input pin A0, and the range is … Arduino boards contain a 10-bit analog to digital converter that it will map input analog voltages between 0 and the operating voltage (5V or 3.3V) into integer values between 0 and 1023 with 0 representing 0 volts, and 1023 representing 5 volts. We find it difficult to read color codes on resistors to find its resistance. Explore 12 projects tagged with 'potentiometer'. Mechanically speaking, pots are physically adjusted usually using your fingers. Connect the other end of led to ground in series with a resistance. To measure a change in resistance, we send a current between the potentiometer terminals extreme and we can read the value of the resulting voltage divider created on the middle terminal. Potentiometers are nothing but variable resistors that can provide a variable resistance by simply varying its knob. The positive terminal of the LED is connected in series with 220 Ohm resistor to pin number 13 of the board, and the negative terminal is connected to the GND. Code The potentiometer must be connected as shown below. In this example, that value controls the rate at which an LED blinks. One is their Resistance (R-ohms) itself and the other is its Power (P-Watts) rating. It has a rotating contact that acts as an adjustable voltage divider. Currently unavailable. There is a really good example provided by arduino which can be found here. 3 SDI/SDO Serial data is transferred between arduino and IC through this pin 4 VSS Ground terminal of arduino is connected to this pin of IC. One outer pin of the potentiometer is connected to ground (. Let's learn how to read a potentiometer using Arduino's analog input! In between the turning input between 0 and 1023, we get the desired value returned by the analogRead( ). Since a potentiometer is a resistor with one variable end, the terminals 1 and 2 or terminals 2 and 3 can be used to obtain the variable resistance and the knob can be used to vary the resistance and set the required value. OK then, here you go: The wiper value is a 7-bit number meaning there are 128 possible levels of resistance to choose, from 0-10K ohms. Potentiometers come in different forms but they are generally classified basing on their Resistance (R-ohms) and Power (P-Watts) ratings. All rights reserved. After learning how a potentiometer is interfaced with Arduino and how it can be used to adjust various parameters through varying the voltage and resistance, we can be able to apply it in a number of applications. Pin 1 (INC) on the potentiometer goes to pin 12 on the Arduino. For example, a potentiometer of 10 kΩ can be adjusted from 0 Ω to its maximum of 10 kΩ. The most common type of variable resistor we see in DIY electronics is the Potentiometer, or we call them pots for short. TM1637 4-Digit 7-Segment Display with Arduino. Required fields are marked , Copyright © MYTECTUTOR.COM. Adafruit Industries, Unique & fun DIY electronics and kits Linear SoftPot (Ribbon Sensor) [100mm] ID: 178 - Manufactured by Spectra Symbol, these are nice little ribbon controllers (also known as 'soft potentiometers') with an adhesive backing.There is a nominal 10K resistance across the two outer leads. In this tutorial you will learn how to use a potentiometer with and without Arduino board to fade an LED. Using PLX-DAX with Arduino. The distance between the pin connected to 5V and GND gives the analog input. Working: The fixed input voltage is applied across the two ends terminal of a potentiometer, which further produces the adjustable output voltage at the wiper or slider. When you rotate the knob of the potentiometer, resistance decreases and the current starts flowing. The above setup can be used to test a potentiometer before using it in any other project. For the Arduino UNO these pins marked A0 to A5. Duration: 1 week to 2 week. 5V), one for output voltage (e.g. How to control LEDs using a potentiometer. Potentiometers have a range of resistance. It provides a variable resistance when the shaft of the device is turned. For the 9V wiring, if we assume the red LED’s $$V_f=2V$$ and the lowest FSR resistance of 200Ω, then $$I=\frac{9V-2V}{200Ω}=35mA$$, which exceeds the max current of the LED. The MCP41XX is a single-channel digital potentiometer device and is offered in an 8-pin PDIP or SOIC package by microchip company, the MCP41XX device is 256 – position, digital potentiometers available in 10 kΩ, 50 kΩ and 100 kΩ resistance versions. Both rotational and linear pots are common. Almost all the potentiometers have a synchronous or an asynchronous series bus as an interface in the control unit, apart from that some digital potentiometers use control logic or front panel switches. The value or resistance decides how much opposition it provides to the flow of current. Drag out a "set" block. You can even set a default value that will be set on power up. Interested in potentiometer? The analog input pin converts the voltage (between 0v and VCC) into integer values (between 0 and 1023), called ADC value or analog value. JavaTpoint offers too many high quality services. For a potentiometer (well, for any voltage divider) the output impedance is the value of the two halves of the resistance in parallel. A potentiometer is a simple mechanical device that provides a varying amount of resistance when its shaft is turned. Your email address will not be published. The required code will be uploaded from our computer to the Arduino board. Code for controlling LEDs using a potentiometer. How the nRF24L01 Wireless Transceiver Module works with Arduino. 6 PW0 This terminal is wiper terminal of the potentiometer( to change resistance) 7 PB0 This is another terminal of the potentiometer. We have connected the potentiometer to the analog pin number 2 of the Arduino UNO board. We connect three wires to the Arduino board. Behind the knob is a potentiometer for varying the resistance to set the volume. We'll be connecting it as a voltage divider, just like we did with the knob-type potentiometer back in circuit #2. Please mail your requirement at hr@javatpoint.com. This allows not to introduce any coefficients for converting interest into impulses. TWTADE 3PCS 10K Ohm Linear Taper Adjustable Rotary Potentiometer Change Resistance WH148 B10K 3 Pin with XH2.54-3P Connector Wire Cable + Black Knob … in this post, we will share how to connect a potentiometer to the Arduino tutorial. All right reserved. © Copyright 2011-2018 www.javatpoint.com. It provides a variable resistance when the shaft of the device is turned. Here, we will measure the amount of resistance as an analog value produced by the potentiometer. The easiest example is for adjusting volume in a radio by turning a knob clockwise or counter clockwise. Find these and other hardware projects on Arduino Project Hub. Volume knobs, light dimmers and faders in audio mixers are oft… 2.4″ ILI9341 TFT Touch Screen with Arduino. Unfortunately these tutorials focus on the way you can control this chip: the SPI (= Serial Peripheral Interface). kwmobile Potentiometer 6-Piece Set - 1K 5K 10K 20K 50K 100K Potentiometers for Arduino Raspberry Pi - Resistance Module, Linear, with Control Knob by kwmobile. When the shaft is turned, the amount of resistance on either side of the potentiometer changes. What you can do however is measure the voltage across a potentiometer. Digital Potentiometer MCP41xx. They allow you precisely control voltage/current flow within a circuit. Arduino's pin A0 to A5 can work as analog input. If you measure the resistance across terminals 1 and 3 you get the total resistance of the potentiometer. Potentiometers have a range of resistance. In this tutorial you will learn how to use a potentiometer with and without Arduino board to fade an LED. We will connect the potentiometer to the Arduino UNO board and will measure the state of the potentiometer. Your email address will not be published. Arduino basic tutorial "analogRead" Serial Monitor with Potentiometer. Arduino boards contain a 10-bit analog to digital converter that it will map input analog voltages between 0 and the operating voltage (5V or 3.3V) into integer values between 0 and 1023 with 0 representing 0 volts, and 1023 representing 5 volts. For example, 10 INC pulses change the current value of the output resistance by 10%. Terminals 1 and 3 are connected to a resistive material whose total resistance is equal to the rated resistance of the potentiometer for example 10kΩ. You can't measure resistance directly. The value or resistance decides how much opposition it provides to the flow of current. JavaTpoint offers college campus training on Core Java, Advance Java, .Net, Android, Hadoop, PHP, Web Technology and Python. Connect the other side to GND. For the Arduino UNO these pins marked A0 to A5. Projects 01 & 02: Reading a Potentiometer and Changing a Potentiometer Reading to a Percentage Components needed: Arduino Uno board (Digital Clock example). They can be attuned from zero ohms to whatever maximum resistance that is specific to it. Here, we will measure the amount of resistance as an analog value produced by the potentiometer. Getting Started with 8051 Microcontroller Programming. Now, it is possible to turn this into a resistance value with a little bit of editing to the code So, while a potentiometer may drop to 0Ω at the lowest setting, the FSR does not, and thus does not require a backup resistor. The greater the resistor value the smaller the current will flow. More than two gangs are possible but not very common. Potentiometer X9C102 / 103/104 has 100 gradations of resistance between the minimum and maximum. We will now upload the code to the board. Pots are used a lot in all kinds of electrical appliances. By passing voltage through a potentiometer and into an analog input on your Arduino, it is possible to measure the amount of resistance produced by a potentiometer … L293D Motor Driver for Controlling DC and Stepper Motors. Used in for example stereo audio volume control or other applications where 2 channels have to be adjusted in parallel. Circuit design Arduino use Potentiometer created by masumcis with Tinkercad Developed by JavaTpoint. A potentiometer is a simple knob that provides a variable resistance, which we can read into the Arduino board as an analog value. The connection of potentiometer with Arduino board is shown below: The middle terminal of potentiometer is connected to the analog pin to read the analog data. Then these percentages are used to create conditions for lighting of the LEDs. The higher the power rating the bigger the resistor gets and it can also stand more current. In order to overcome the difficulty of finding the resistance value, we are going to build a simple Ohm Meter using Arduino.The basic principle behind this project is a Voltage Divider Network.The value of the unknown resistance is displayed on 162 LCD display. Mail us on hr@javatpoint.com, to get more information about given services. At the beginning of the program, set the variable sensorValue to "read analog pin" A0 (from the Input category). The first goes to ground from … We read input 0 when the shaft is turned in one direction, while we read input 1023 when the shaft is turned in another direction. Potentiometers and the Arduino Uno. In this activity, we are controlling led brightness with Arduino and potentiometer which have the option to change the resistance according to the requirement. Arduino: Potentiometer Diagrams & Code Brown County Library Some projects require the use of the serial monitor in your Arduino IDE program (or whatever you are using to transfer code to the Arduino). The variable resistance measured by the potentiometer can be easily read as an analog value into the Arduino board. Voltage Variation Fades Led When you rotate the knob of the potentiometer resistance … For example, a potentiometer of 10 kΩ can be adjusted from 0 Ω to its maximum of 10 kΩ. Resistance … this shield is based on AD5206 digital potentiometer with equal resistance taper! 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Can control the sequential lighting of the Arduino UNO board and will measure the value... Need for varying resistance in order to control current and voltage these pins marked A0 to A5 the between. In stock be in range of 120 ohm to 4.7 k ohm you precisely voltage/current! The minimum and maximum shield is based on AD5206 digital potentiometer value pin... ( we ’ ll call this the wiper ), a potentiometer of 10.! With and without Arduino board to fade an LED read analog pin '' A0 ( from the category. But they are generally classified basing on their resistance ( R-ohms ) itself and the current will flow is terminal! The voltage or electric potential, Copyright © MYTECTUTOR.COM readings got from input! ( ) function is used where there is a potentiometer with and without Arduino board based! From our computer to the analog pin '' A0 ( from the potentiometer 100 of! Structure consists of a sliding contact moves along the resistive material whenever the potentiometer knob rotated. Basic job way you can control the sequential lighting of LEDs using a potentiometer has three terminals which arranged. Code to the flow of current simply varying its knob a microcontroller like Arduino vary. To both ends it is an analog value that acts as an analog value produced the... One for input voltage ( e.g flow of current Copyright © MYTECTUTOR.COM INC! Value at which LED blinks structure consists of the digital potentiometer i will show. Its maximum of 10 kΩ resistance of the program, set the variable sensorValue ! … this shield is based on AD5206 digital potentiometer other is its (. Resistors that have two terminals, a potentiometer with and without Arduino board to fade an LED P-Watts ratings. Want to know how to change resistance ) 7 PB0 this is another of! End to another, the amount of resistance on either side of the wiper and the other end LED! Electronics is the large plastic strip with three terminals which are arranged as shown.. All do the same basic job two terminals, a potentiometer, or we call them for. And other hardware projects on Arduino Project Hub default value that will be back in stock by simply its! A pot, is a really good example provided by Arduino which can be attuned from ohms. Two gangs are possible but not very common potentiometer can be attuned from zero ohms whatever. The turning input between 0 and 1023, we will connect the middle pin to analog in pin on. Of the digital potentiometer Wireless Transceiver Module works with Arduino turning input between 0 and 1023, will! The slider moves from one end to another, the amount of when! @ javatpoint.com, to get more information about given services the values on potentiometer! Most common are single turn potentiometers with equal resistance and taper turning knob... Potentiometer, or we call them pots for short fade an LED can provide variable! For example, a potentiometer is among the commonest devices used in example... Delay time ) at which LED blinks conditions for lighting of the potentiometer goes to pin on... Ardunio UNO pins marked A0 to A5 can do however is measure the voltage or electric potential AD5206!, and a housing that will be set on power up find these and other hardware projects Arduino. Lot in all kinds of electrical appliances 's learn how to use a potentiometer using Arduino 's analog!. You get the total resistance of the potentiometer into percentages Core Java,.Net, Android,,! Board as an analog value that will be uploaded from our computer to the Arduino UNO board will. Resistance value of arduino potentiometer resistance pot ( we ’ ll call this the wiper and the current starts flowing housing of... All shapes and sizes, and they all do the same basic job it provides to the flow of.. Category and drag out the first block to set the built-in LED HIGH for example, potentiometer... ( i.e to ground SPI ( = Serial Peripheral Interface ) potentiometer by... The Soft potentiometer is connected to a wiper that moves across the resistive,... Our case the potentiometers have a power rating of 0.3W and hence can be used only for low current.... Potentiometer of 10 kΩ can be in range of 120 ohm to 4.7 k ohm 2 channels have be! Resistance, which we can control the sequential lighting of the output voltage ( e.g and power ( ). A varying amount of resistance between the minimum and maximum that acts as an analog value by... Of Arduino vary the resistance value of the LEDs will light one by one the. Will light one by one when the shaft is turned proportional to the board PB0 this is one terminal the... And Python contact moves along the resistive element, while the housing of! Set a default value that can provide a variable resistor we see in DIY is. The divider can vary the resistance of the potentiometer into percentages the time ( delay time ) at LED... Variable resistor we see in DIY electronics is the potentiometer into percentages 10! Slider moves from one end to another, the divider can vary the output category and drag out first! Introduce any coefficients for converting interest into impulses we do n't know when or this! Amount of resistance as an adjustable voltage divider l293d Motor Driver for Controlling DC and Stepper Motors has terminals... Which we can control the sequential lighting of LEDs using a potentiometer is a variable when. Structure consists of a resistance value is an electrical component with three terminals i.e! Our computer to the analog readings got from the input category ) let 's learn how to read potentiometer! Read as an analog value produced by the potentiometer, or we call them pots for.... ( U/D ) on the Arduino you measure the state of the digital potentiometer analogRead ( ) Hadoop. The higher the power rating of 0.3W and hence can be adjusted from 0 Ω to maximum... Speaking, pots are used to measure the amount of resistance on either side of the potentiometer to analog! The turning input between 0 and 1023, we will use a potentiometer is connected to the flow current. Very common common are single turn potentiometers with equal resistance and taper output category and drag the... Using it in any other Project pin 12 on the potentiometer to the board nRF24L01 Wireless Module... Most common are single turn potentiometers with equal resistance and taper an analog value produced by the analogRead (.... From … Arduino potentiometer the potentiometer is a device that provides a varying amount of resistance an.	2022-10-04 07:59:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.2218753546476364, "perplexity": 2053.9631449803533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337480.10/warc/CC-MAIN-20221004054641-20221004084641-00753.warc.gz"}
http://mkweb.bcgsc.ca/pi/index.mhtml	Tango is a sad thought that is danced.think & dancemore quotes # numbers: fun Scientific graphical abstracts — design guidelines # visualization + design 81 digits of $\pi$ as a forest of trees: standard, bat cave and underwater editions. ( BUY ARTWORK ) The 2021 Pi Day art celebrates the digits of $\pi$ with a forest! Visit the bat cave and underwater ecosystems for the full experience. # The art of Pi ($\pi$), Phi ($\phi$) and $e$ 2021 $\pi$ reminds us that good things grow for those who wait.' edition. 2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition. 2018 $\pi$ day stitches street maps into new destinations. 2017 $\pi$ day imagines the sky in a new way. 2016 $\pi$ approximation day wonders what would happen if about right was right. 2016 $\pi$ day sees digits really fall for each other. 2015 $\pi$ day maps transcendentally. 2014 $\pi$ approx day spirals into roughness. 2014 $\pi$ day hypnotizes you into looking. 2014 $\pi$ day 2013 $\pi$ day is where it started Circular $\pi$ art and other distractions Numbers are a lot of fun. They can start conversations—the interesting number paradox is a party favourite: every number must be interesting because the first number that wasn't would be very interesting! Of course, in the wrong company they can just as easily end conversations. The art here is my attempt at transforming famous numbers in mathematics into pretty visual forms, start some of these conversations and awaken emotions for mathematics—other than dislike and confusion Like music with numbers? Try Angels at My Door (Una), Pt vs Ys (Yoshinori Sunahara), 2wicky (Hooverphonic), One (Aimee Mann), Straight to Number One (Touch and Go), 99 luftbaloons (Nena). Numerology is bogus, but art based on numbers can be beautiful. Proclus got it right when he said (as quoted by M. Kline in Mathematical Thought from Ancient to Modern Times) Wherever there is number, there is beauty. 2,258 digits of $\phi$, 3,855 digits of $e$ and 3,628 digits of $\pi$ in 6 level treemaps. Uniform line thickness. Bauhaus prime colors in Piet Mondrian style. (2015 $\pi$ day posters, BUY ARTWORK ) Most of the art is available for purchase as framed prints and, yes, even pillows. Sleep's never been more important — I take custom requests. ## the numbers π, φ and e The consequence of the interesting number paradox is that all numbers are interesting. But some are more interesting than others—how Orwellian! All animals are equal, but some animals are more equal than others. —George Orwell (Animal Farm) Numbers such as $\pi$ (or $\tau$ if you're a revolutionary), $\phi$, $e$, $i = \sqrt{-1}$, and $0$ have captivated imagination. Chances are at least one of them appears in the next physics equation you come across. π φ e = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 ... = 1.61803 39887 49894 84820 45868 34365 63811 77203 09179 ... = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 ... Of these three transcendental numbers, $\pi$ (3.14159265...) is the most well known. It is the ratio of a circle's circumference to its diameter ($d = \pi r$) and appears in the formula for the area of the circle ($a = \pi r^2$). 2,258 digits of $\phi$, 3,855 digits of $e$ and 3,628 digits of $\pi$ in 6 level treemaps. Uniform line thickness. Bauhaus prime colors in Piet Mondrian style. (2016 $\pi$ day posters, BUY ARTWORK ) The Golden Ratio ($\phi$, 1.61803398...) is the attractive proportion of values $a > b$ that satisfy ${a+b}/2 = a/b$, which solves to $a/b = {1 + \sqrt{5}}/2$. The last of the three numbers, $e$ (2.71828182...) is Euler's number and also known as the base of the natural logarithm. It, too, can be defined geometrically—it is the unique real number, $e$, for which the function $f(x) = e^x$ has a tangent of slope 1 at $x=0$. Like $\pi$, $e$ appears throughout mathematics. For example, $e$ is central in the expression for the normal distribution as well as the definition of entropy. And if you've ever heard of someone talking about log plots ... well, there's $e$ again! Two of these numbers can be seen together in mathematics' most beautiful equation, the Euler identity: $e^{i\pi} = -1$. The tau-oists would argue that this is even prettier: $e^{i\tau} = 1$. ## accidentally similar Did you notice how the 13th digit of all three numbers is the same (9)? This accidental similarity generates its own number—the Accidental Similarity Number (ASN). # Happy 2021 $\pi$ Day—A forest of digits Sun 14-03-2021 Celebrate $\pi$ Day (March 14th) and finally see the digits through the forest. The 26th tree in the digit forest of $\pi$. Why is there a flower on the ground?. (details) This year is full of botanical whimsy. A Lindenmayer system forest – deterministic but always changing. Feel free to stop and pick the flowers from the ground. The first 46 digits of $\pi$ in 8 trees. There are so many more. (details) And things can get crazy in the forest. A forest of the digits of '\pi$, by ecosystem. (details) Check out art from previous years: 2013$\pi$Day and 2014$\pi$Day, 2015$\pi$Day, 2016$\pi$Day, 2017$\pi$Day, 2018$\pi$Day and 2019$\pi` Day. # Testing for rare conditions Tue 16-03-2021 All that glitters is not gold. —W. Shakespeare The sensitivity and specificity of a test do not necessarily correspond to its error rate. This becomes critically important when testing for a rare condition — a test with 99% sensitivity and specificity has an even chance of being wrong when the condition prevalence is 1%. We discuss the positive predictive value (PPV) and how practices such as screen can increase it. Nature Methods Points of Significance column: Testing for rare conditions. (read) Altman, N. & Krzywinski, M. (2021) Points of significance: Testing for rare conditions. Nature Methods 18 # Standardization fallacy Tue 09-02-2021 We demand rigidly defined areas of doubt and uncertainty! —D. Adams A popular notion about experiments is that it's good to keep variability in subjects low to limit the influence of confounding factors. This is called standardization. Unfortunately, although standardization increases power, it can induce unrealistically low variability and lead to results that do not generalize to the population of interest. And, in fact, may be irreproducible. Nature Methods Points of Significance column: Standardization fallacy. (read) Not paying attention to these details and thinking (or hoping) that standardization is always good is the "standardization fallacy". In this column, we look at how standardization can be balanced with heterogenization to avoid this thorny issue. Voelkl, B., Würbel, H., Krzywinski, M. & Altman, N. (2021) Points of significance: Standardization fallacy. Nature Methods 18:5–6. # Graphical Abstract Design Guidelines Fri 13-11-2020 Clear, concise, legible and compelling. Making a scientific graphical abstract? Refer to my practical design guidelines and redesign examples to improve organization, design and clarity of your graphical abstracts. Graphical Abstract Design Guidelines — Clear, concise, legible and compelling. # "This data might give you a migrane" Tue 06-10-2020 An in-depth look at my process of reacting to a bad figure — how I design a poster and tell data stories. A poster of high BMI and obesity prevalence for 185 countries. # He said, he said — a word analysis of the 2020 Presidential Debates Thu 01-10-2020 Building on the method I used to analyze the 2008, 2012 and 2016 U.S. Presidential and Vice Presidential debates, I explore word usagein the 2020 Debates between Donald Trump and Joe Biden. Analysis of word usage by parts of speech for Trump and Biden reveals insight into each candidate.	2021-04-11 22:19:59	{"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": 0.36021655797958374, "perplexity": 3003.0171341812074}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038065492.15/warc/CC-MAIN-20210411204008-20210411234008-00278.warc.gz"}
https://learn.careers360.com/school/question-prove-how-can-law-of-conservation-of-momemtum-is-same-before-and-after-collision-43462/	# Prove how can LAW of CONSERVATION of MOMEMTUM IS SAME BEFORE AND AFTER COLLISION? Principle of conservation of linear momentum states that if the net external force on a system of particles is zero, the linear momentum of the system remains constant. Or we can say that the sum of momenta of the two objects before collision is equal to the sum of momenta after the collision provided there is no external unbalanced force acting on them. Suppose two objects (two balls A and B, say) of masses mA and mB are travelling in the same direction along a straight line at different velocities uA and uB, respectively and there are no other external unbalanced forces acting on them. Let vA and vB are the velocities of the two balls A and B after the collision, respectively. $\\ \text{The momenta (plural of momentum) of ball A before and after the collision are}\ m_{A} u_{A} and m_{A} v_{A}, respectively.\\ The rate of change of its momentum (or F_{AB}, action) during the collision will be m_{A} \frac{\left(v_{A}-u_{A}\right)}{t} \\ Similarly, the rate of change of momentum of ball \mathrm{B}\left(=F_{BA}, \text { or reaction }\right) during the collision will be m_{B} \frac{\left(v_{B}-u_{B}\right)}{t}$ $\\ \text{According to the third law of motion, the force} \ F_{A B} \ \text{exerted by ball A on ball B} (action)\\ and\ the\ force\ F_{BA} \ \text{exerted by the ball B on ball A }\ (reaction) \text{must be equal and opposite to each other. Therefore}$ $\\ \begin{array}{l} F_{A B}=-F_{B A} \\ m_{A} \frac{\left(v_{A}-u_{A}\right)}{t}=-m_{B} \frac{\left(v_{B}-u_{B}\right)}{t} \end{array} \\ This \ gives\\ m_{A} u_{A}+m_{B} u_{B}=m_{A} v_{A}+m_{B} v_{B}$ ### Preparation Products ##### JEE Main Rank Booster 2021 This course will help student to be better prepared and study in the right direction for JEE Main.. ₹ 13999/- ₹ 9999/- ##### Rank Booster NEET 2021 This course will help student to be better prepared and study in the right direction for NEET.. ₹ 13999/- ₹ 9999/- ##### Knockout JEE Main April 2021 (Easy Installments) An exhaustive E-learning program for the complete preparation of JEE Main.. ₹ 4999/- ##### Knockout NEET May 2021 An exhaustive E-learning program for the complete preparation of NEET.. ₹ 22999/- ₹ 14999/-	2020-10-20 08:51:47	{"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": 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": 0.7744602560997009, "perplexity": 1275.6783609344432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107871231.19/warc/CC-MAIN-20201020080044-20201020110044-00326.warc.gz"}
http://tex.stackexchange.com/questions/51081/how-can-i-use-math-inside-a-label-in-description-in-a-beamer-doc	# How can I use math inside a label in Description in a beamer doc? I'm describing regular expressions, and I would like to have items like this: \documentclass[10pt,hyperref={pdfpagelabels=false}]{beamer} \usepackage[utf8x]{inputenc} \usepackage{default} \mode<presentation> { \usetheme{Warsaw} \setbeamercovered{transparent} } \usepackage[brazil]{babel} \usepackage[T1]{fontenc} \usepackage[scaled=.80]{helvet} \usepackage{graphicx} \setbeamertemplate{caption}[numbered] \begin{document} \section{Search} \subsection{Regular Exp} \begin{frame}[allowframebreaks]{\texttt{Regular Expressions} Operators}{Powerfull} \texttt{Regular Expressions} (\texttt{RE}) are good: \begin{description} \item[\textasciicircum] Matches the beginning of the line \item[\textbackslash] Escape character \item[[]] Group characters \item[\textbackslash( \textbackslash)] Hell \item[$\textbackslash< \textbackslash>$] Hey. % \item[{$[:\mathtt{upper}:]$}] Same as $[A-Z]$. \end{description} \end{frame} \end{document} But some of them seem not to work. Some variants I've tried (with ] outside math) gave me half of the item in the correct font/color, and the last char ] in black as if it was normal text. Please, how can I get this done? -- Edited: minimal working example added. - The third and the fourth don't work because inner brackets need to be protected: \item[{$[:\mathtt{upper}]$}]. In other words, use braces {...} around optional arguments containing brackets [...]. However you don't need math mode. – egreg Apr 7 '12 at 13:34 Thanks @egreg, but still nothing. I've tried your suggestion like \item[{$[:\mathtt{upper}:]$}] ha!, but I got <blue>[:upper:<\blue> <black>] ha!]<\black>. Very strange, isn't it? – Dr Beco Apr 7 '12 at 13:40 What do the <blue> and <black> tags stand for? – egreg Apr 7 '12 at 13:49 Nothing, just to tell you that the compiled text color should be blue for the label, and black only for ha!. But it is mixed in such way. – Dr Beco Apr 7 '12 at 13:52 @egreg, sorry! I forgot to tell maybe a very important option: \documentclass[10pt,hyperref={pdfpagelabels=false}]{beamer} – Dr Beco Apr 7 '12 at 14:05 I get what's expected with \begin{description} \item[\textasciicircum] Matches the beginning of the line \item[\textbackslash] Escape character \item[{[]}] Group characters \item[\textbackslash( \textbackslash)] Hell \item[$\textbackslash< \textbackslash>$] Hey. \item[{$[:\mathtt{upper}:]$}] Same as $[A-Z]$. \end{description} However, math mode is not necessary (and even wrong) in items number 5 and 6. Notice also the braces in the fourth item. Here's how I would input the description list: \begin{description} \item[\texttt{\textasciicircum}] Matches the beginning of the line \item[\texttt{\textbackslash}] Escape character \item[\texttt{[]}] Group characters \item[\texttt{\textbackslash( \textbackslash)}] Hell \item[\texttt{\textbackslash< \textbackslash>}] Hey. \item[\texttt{[:upper:]}] Same as \texttt{[A-Z]}. \end{description} which will use typewriter type for the regular expression samples. If all your description labels in a frame are to be typeset in typewriter type, then Marco Daniel's suggestion is good, but brackets must be hidden: \setbeamerfont{description item}{family=\ttfamily} % this will hold until \end{frame} \begin{description} \item[\textasciicircum] Matches the beginning of the line \item[\textbackslash] Escape character \item[{[]}] Group characters \item[\textbackslash( \textbackslash)] Hell \item[\textbackslash< \textbackslash>] Hey. \item[{[:upper:]}] Same as \texttt{[A-Z]}. \end{description} - 0 errors, 0 warnings, 0 badboxes. Thanks! Much appreciated. – Dr Beco Apr 7 '12 at 14:46 @DrBeco: In beamer you should use \setbeamerfont{description item}{family=\ttfamily} instead of formating every label. – Marco Daniel Apr 7 '12 at 14:49 @MarcoDaniel I think I do need to format every label. I tried \setbeamerfont and then \item[[:upper:]] would not work again: it move the last ] outside the blue label and make it black font. I think \texttt{} is kind of "protecting" the label. – Dr Beco Apr 7 '12 at 14:53 @egreg: Why do you refer Mico ;-(? – Marco Daniel Apr 7 '12 at 16:06 @MarcoDaniel Oh, sorry! – egreg Apr 7 '12 at 18:28 In the comments above it turned out that the @DrBeco uses TeX Live 2009. I suppose it was installed by the default repository of the unix system. However this version isn't up to date. I really recommend to install TeX Live 2011. In this way you can use the update manager tlmgr to get the newest version of nearly every package. If you are using TeX Live 2011 your example will work well. I want to provide another hint. Don't use utf8x. Some explanation can be found here: Why do you use commands like \textasciicircum or \textbackslash in math mode? The first part of the command indicates text not math. \documentclass{article} \begin{document} \begin{description} \item[\textasciicircum] Matches the beginning of the line \item[\textbackslash] Escape character \item[{[]}] Group characters \item[\textbackslash( \textbackslash) ] Save to a buffer \item[{$[:\mathtt{upper}:]$}] Same as $[A-Z]$. \end{description} \end{document} The same result with beamer: \documentclass[10pt,hyperref={pdfpagelabels=false}]{beamer} \begin{document} \begin{frame} \setbeamerfont{description item}{family=\ttfamily} \begin{description} \item[\textasciicircum] Matches the beginning of the line \item[\textbackslash] Escape character \item[{[]}] Group characters \item[\textbackslash( \textbackslash) ] Save to a buffer \item[{$[:\mathtt{upper}:]$}] Same as $[A-Z]$. \end{description} \end{frame} \end{document} - Thanks, but it is not working. @egreg gave the suggestion of \item[{$[:\mathtt{upper}:]$}] Same as $[A-Z]$., but now it did not compile. It says there is an extra }. Another one according to you, how would you write: \item[$\textbackslash< \textbackslash>$], please? Thanks. – Dr Beco Apr 7 '12 at 13:53 @egreg: Does the example work for you? I have no problems – Marco Daniel Apr 7 '12 at 14:00 Wow! SORRY! I forgot to tell maybe a very important option: \documentclass[10pt,hyperref={pdfpagelabels=false}]{beamer} – Dr Beco Apr 7 '12 at 14:03 @DrBeco: No problems with beamer. – Marco Daniel Apr 7 '12 at 14:42 For some reason, this doesn't work here. Did you try with babel? Anyway, thanks, the \texttt{} solved the problem. – Dr Beco Apr 7 '12 at 14:48	2016-02-14 19:10:56	{"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": 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": 0.863141655921936, "perplexity": 5528.739118916412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454702018134.95/warc/CC-MAIN-20160205195338-00111-ip-10-236-182-209.ec2.internal.warc.gz"}
https://dorigo.wordpress.com/2008/12/18/result-now-explanation-later/	## Result now, explanation later December 18, 2008 Posted by dorigo in personal, physics, science. Tags: , , , Tonight I feel accomplished, since I have completed a crucial update of the cornerstone of the algorithm which provides the calibration of the CMS momentum scale. I have no time to discuss the details tonight, but I will share with you the final result of a complicated multi-part calculation (at least, for my mediocre standards): the probability distribution function of measuring the Z boson mass at a certain value $M$, using the quadrimomenta of two muon tracks which correspond to an estimated mass resolution $\sigma_M$, when the rapidity of the Z boson is $Y_Z$. The above might -and should, if you are not a HEP physicist- sound rather meaningless, but the family of two-dimensional functions $P(M,\sigma_M)_Y$ is needed for a precise calibration of the CMS tracker. They can be derived by convoluting the production cross-section of Z bosons $\sigma_M$ at a given rapidity $Y$ with the proton’s parton distribution functions using a factorization integral, and then convoluting the resulting functions with a smearing Gaussian distribution of width $\sigma_M$. Still confused ? No worry. Today I will only show one sample result – the probability distribution as a function of $M$ and $\sigma_M$ for Z bosons produced at a rapidity $2.8< \|Y\| <2.9$, and tomorrow I will explain in simple terms how I obtained that curve and the other 39 I have extracted today. In the three-dimensional graph above, one axis has the reconstructed mass of muon pairs $M$ (from 71 to 111 GeV), the other has the expected mass resolution $\sigma_M$ (from 0 to 10 GeV). The height of the function is the probability of observing the mass value $M$, if the expected resolution is $\sigma_M$. On top of the graph one also sees in colors the curves of equal probability displayed on a projected plane. It will not escape to the keen eye that the function is asymmetric in mass around its peak: that is entirely the effect of the parton distribution functions… 1. JJ - December 18, 2008 It would be interesting to see the effect of the PDF uncertainty on this plot (and how sensitive it is the the uncertainties). Indeed, around the Z peak, the CTEQ6.1 uncertainty is ~5%. dorigo - December 19, 2008 Hi James, indeed, these are CTEQ6 PDF, and my program does use the 40 eigenvector variations for an estimate of the uncertainty. However, so far I have not ran the full grid of points for the systematics, because it is very time-expensive. I however think that while the normalization does have a sizable uncertainty, the shape is not affected too much. Another thing to note is that this is a LO calculation of the factorization integral, and so I must use LO PDF. The eigenvectors are known for the NLO sets. They can be used for a eyeballing of the uncertainty all the same, but the right thing to do is rather to compare the results I get to those I get with MRST sets. I will post about that when I get there… Cheers, T. 2. JJ - December 19, 2008 Ah that’s interesting. So, I take it then that your method is sensitive to shape and not to normalisation then? dorigo - December 19, 2008 Well, yes, I only care about the shapes. In fact, the probability distribution shown in the plot is normalized such that the integral over the mass range, for any given resolution, is unity. I just checked a few things about the MRST04 set I want to use for some comparisons, in http://xxx.lanl.gov/PS_cache/hep-ph/pdf/9907/9907231v1.pdf , and indeed they speak of 5% differences in cross-section; but they also admit they had some error in earlier calculations. Cheers, T. 3. Tom - December 19, 2008 [Aesthetic question] Hey! How do you do, using ROOT, to draw that contour projection on the top plane of your 3D box frame???? dorigo - December 20, 2008 TH2D * A = new TH2D (“A”, “Goofy”, 100, 0., 100., 100, 0., 100.); …. A->Draw(“SURF3”); Cheers, T. 4. English Language Summaries « Life as a Physicist - December 19, 2008 […] the best summaries of this nature I know about are on a blog – Tomasso’s, specifically (e.g. here and here for recent […] Sorry comments are closed for this entry	2019-06-20 15:18:00	{"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": 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": 0.7519058585166931, "perplexity": 844.0580534655472}, "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-2019-26/segments/1560627999261.43/warc/CC-MAIN-20190620145650-20190620171650-00018.warc.gz"}
http://math.stackexchange.com/questions/108049/please-confirm-my-lim-sup-and-lim-inf-of-sets-answers	# Please confirm my lim sup and lim inf of sets answers Just wondering if my answers of the following 2 part question are correct. If not i would much appreciate a layman explanation, where i stuffed up. Cheers Find lim sup $A_n$ and lim inf $A_n$ of the following sequence of sets: $$A_n = \begin{cases} x &0 \le x < 1 &\text{if n is odd} \\ x &1 \le x \le 2 &\text{if n is even} \end{cases}$$ Answer Attempt lim sup $A_n = \{0, 2\}$ and lim inf $A_n = \emptyset$ $$E_n = \begin{cases} x &-n \le x \le 0 &\text{if n is odd} \\ x &\frac{1}{n} \le x \le n &\text{if n is even} \end{cases}$$ Answer Attempt lim sup $A_n = \{-\infty, 0\} \cup \{1/2, \infty\}$ and lim inf $A_n = \emptyset$ I am skeptical if i am doing this right as both of my lim inf were null sets. One would imagine out of only 2 exercises on lim sup and lim inf of sets at the end of the chapter one would have been different. Any help would be much appreciated. Definitions from the book. For a sequence of subsets $A_n$ of a set $X$, the $\limsup A_n= \cap_{N=1}^\infty ( \cup_{n\ge N} A_n )$ and $\liminf A_n = \cup_{N=1}^\infty (\cap_{n \ge N} A_n)$. - I like to think about the set $\liminf_n A_n$ as the set $\{ x \in X \mid x \in A_n \mbox { for all but finitely many } n \}$, and $\limsup_n A_n$ as the set $\{ x \in X \mid x \in A_n \mbox {for infinitely many } n \}$. This follows from your definitions quite clearly: $x \in \limsup_n A_n$ iff $\forall N \exists n \ge N: x \in A_n$, which says that for every index $N$ we can find a larger index $n$ such that $x \in A_n$, which holds precisely when there infinitely many of such indices. On the other hand, $x \in \liminf_n A_n$ iff $\exists_N \forall n \ge N: x \in A_n$, which says that there is some index $N$ from which we know that $x \in A_n$ for all larger ones, so $x$ only possibly misses the $A_n$ with $n < N$, so $x$ is in all but finitely many of the $A_n$. Note also that this makes the inclusion $\liminf_n A_n \subseteq \limsup_n A_n$ obvious. Then in (a), the set alternate between $[0,1)$ and $[1,2]$, so indeed no point is in all but finitely many of them, as the odd- and even-indexed sets are disjoint, and all points in $[0,1) \cup [1,2] = [0,2]$ are in infinitely many of them. So I get $\liminf_n A_n = \emptyset$ and $\limsup_n A_n = [0,2]$. In (b), we again have sets such that $E_{2n} \cap E_{2n+1} = \emptyset$ for all $n$, so that no point can be in all but finitely many of them, so $\liminf_n E_n = \emptyset$, so agreed. Now, if $x \le 0$, then for $n \ge \|x\|$, $n$ even, we have that $x \in E_{n}$, so those $x$ are in infinitely many $E_n$, and if $x > 0$ then for $n > \min(\frac{1}{x}, x)$, $n$ odd, we know that $x \in E_{n}$ (as then $\frac{1}{n} < x < n$), again showing that $x$ is in infinitely many $E_n$. As $x \le 0$ or $x > 0$ holds for all $x \in \mathbb{R}$, $\limsup_n E_n = \mathbb{R}$. - I think there is a mistake in your part a lim inf as 1 is not in the set. Also there is no mention about n <= 0 or being real as n is n i just assumed the author must be referring to belong to Naturals. – Hardy Feb 11 '12 at 6:41 @Hardy the definitions of the sets changed while I was typing...! – Henno Brandsma Feb 11 '12 at 6:47 That's fine mate some one was kind enough to improve my type set so i do n't doubt u. Just as they stand now would my answers be correct then ? – Hardy Feb 11 '12 at 6:51 @Hardy no, you have type $\{0,2\}$ not $[0,2]$, e.g., and the last $\limsup$ is still all of $\mathbb{R}$ (I assume we are working with subsets of $\mathbb{R}$?) – Henno Brandsma Feb 11 '12 at 6:53 It is the formatting fellow i also assumed it was written correctly . but i get your confirmation that it should be an interval which is what i was expecting too. Thanks i also follow your other answer. – Hardy Feb 11 '12 at 6:58	2013-12-19 17:00:42	{"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": 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": 0.9584702849388123, "perplexity": 205.23396007517147}, "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/1387345765796/warc/CC-MAIN-20131218054925-00044-ip-10-33-133-15.ec2.internal.warc.gz"}
https://rileysci.com/tag/math/	# Fundamental Equations, Chaos, Fractals, and Leaky Faucets It’s been a while since I’ve written here. Busy teaching. (I know, lame excuse). So I go and watch some video on YouTube, and on the side is the list of suggested videos. For a while there’s been this one by Veritasium (Derek Muller). Now, Derek is a fantastic science educator, and is who I want to be when I grow up. One problem is he’s younger than me by over a decade. Hmm. Have to work on that somehow. Anyway, the video that was just waiting for me to finally click on it was this one. It’s about an equation that will change how you see the world. ## The Logistic Map The math is very simple: $x_{n+1}=r x_n(1-x_n)$ where $r$ is the growth rate. This is a very simple equation with a negative feedback loop. When you graph $r$ by the equilibrium population, you get this: What!? Once the growth rate hits 3, the equilibrium population splits, and oscillates between two values. Then just after 3.4 it splits again. And very soon it becomes chaotic. Oh, and fractal. The chaotic nature was used for pseudorandom number generators. ## The Mandelbrot set Does mentioning fractals make you think of the Mandelbrot set? If it doesn’t, then you have some research to do. It’s probably the most famous fractal out there. Heck Johnathan Coulton has done a song about it. But evidently if you somehow rotate the Mandelbrot Set along it’s real number axis, you get this: Look familiar? At this point I started getting a headache, but it was one of those good, excited headaches that come from having your reality twisted about. ## Leaky Faucets Oh yeah, leaks. Derek then mentions that if you get your faucet going drip, drip, drip, and then increase the water pressure just right, it will start doubling: drip drip, drip drip, drip drip. Push it a little more, and you get chaotic behavior. Of course the YouTube video is so much better than my explanation. Go watch it. # Let’s talk numbers! Two neat things from an AskReddit post. ## One: cubosh said: Take every planet in our solar system, line them up so they are all touching, and they will fit inside the space between earth and our moon, with room to spare. >to which jbhall36 said: Take every planet in our solar system, line them up so they are all touching, fit them in the space between Earth and our moon, and the gravitational force would be catastrophic and likely kill everything on Earth. >>to which Rogukast1177 said: You don’t need the “likely” >>>to which pinkbutterfly1 said: You do need the “likely”. Because Tardigrades. http://www.bbc.com/earth/story/20150313-the-toughest-animals-on-earth ## Two: A while ago I write about Graham’s Number, which is really migraine inducing. Another (much smaller) number is how many ways you can shuffle a standard deck of 52 cards. Here’s what VerbableNouns said (which really was written by techniforus): One of my favorite is about the number of unique orders for cards in a standard 52 card deck. I’ve seen a a really good explanation of how big 52! actually is. • Set a timer to count down 52! seconds (that’s 8.0658×1067 seconds) • Stand on the equator, and take a step forward every billion years • When you’ve circled the earth once, take a drop of water from the Pacific Ocean, and keep going • When the Pacific Ocean is empty, lay a sheet of paper down, refill the ocean and carry on. • When your stack of paper reaches the sun, take a look at the timer. The 3 left-most digits won’t have changed. 8.063×1067 seconds left to go. You have to repeat the whole process 1000 times to get 1/3 of the way through that time. 5.385×1067 seconds left to go. So to kill that time you try something else. • Shuffle a deck of cards, deal yourself 5 cards every billion years • Each time you get a royal flush, buy a lottery ticket • Each time that ticket wins the jackpot, throw a grain of sand in the grand canyon • When the grand canyon’s full, take 1oz of rock off Mount Everest, empty the canyon and carry on. • When Everest has been levelled, check the timer. There’s barely any change. 5.364×1067 seconds left. You’d have to repeat this process 256 times to have run out the timer. Now, that gives you some inkling of how big 52! is, but that’s nothing compared to Graham’s Number which I mentioned earlier. # Large numbers are hard to understand Lots of people have a blind spot for numbers. Especially large numbers, like a million or a billion. Lots of people think that numbers like a million, a billion, and a trillion are evenly spaced on the number line, like 1, 2, and 3 are. But the amount of space between a million and a billion dwarfs the distance from 1 to a million. A billion is a thousand millions. Here’s another way to look at it. It takes about 12 days for 1,000,000 seconds to elapse. But it takes about 32 years for 1,000,000,000 seconds to elapse. They are so far apart. But most people just stop thinking about what these numbers really mean, and kind of lump a million and a billion together. Kind of like “they’re big numbers, and a billion is bigger than a million”. Well, yes, that’s true. But it loses how much bigger, and it’s a lot. # One way that Math and Science are linked Everytime math comes into my science class, the students always groan. “Why do we have to do math? We already had math class?” But math and science are linked. In fact, the math has to be there. And it can be really interesting how this happens. A number of years ago, one of my favorite youtubers did a trilogy of videos on this. The first is on Fibonacci numbers, which seem to pop up all over the place. This then leads to one of my favorite irrational numbers: Phi (Φ). Everyone knows about Pi, but phi is pretty awesome too. Well, actually the golden ratio, which is also used all over the place, and mathematicians use phi as shorthand, kind of like they use pi for the ratio of the circumference of a circle to the diameter. It turns out that when plants want to grow leaves, but not have the upper leaves be right above the lower leaves, they frequently put the leaves phi degrees away from the previous leaf. How do they do that? It’s not like they have protractors know about geometry or anything. It turns out that it’s really simple, as vihart gets to. It’s just growing where there’s more protein that tells the plant where to grow new leaves. This automatically ends up with the leaves being phi degrees apart. It’s really cool! Anyway, here are the videos: # Math migrane So, on the way to rather large numbers, you may see some mileposts: These, and a googolplex, are pikers compared to Graham’s Number. To get there, you first have to go up the math ladder from counting, to addition, to multiplication, to exponentiation, to tetration (this is where my math migraine kicks in), to pentation, to hexation, and wayyy beyond. If, and that’s a big if, you can wrap your mind around Graham’s Number, … well first off, you’re lying, just admit it … but this supremely large number, where there isn’t enough space in the universe to write down all the digits (the train passed that station long ago on this math journey, just read the article at the link), is not even approaching what infinity is. This isn’t anywhere close to aleph-null (ℵ0). ## Language and Math and Zipf ### Aside Vsauce has a really cool video on some ways that language and math are intertwined. Including how it all is interwoven with the world around us. # Long live the work of Emma Noether A wonderful article at arstechnica tells of the work of a woman Jew in the early 20th century. She lived in Germany in the years leading up to WWII. She had to leave, and came to America. Some of her best work is on Einstein‘s General Theory of Relativity. Science kind of takes some symmetries for granted. For example, you should be able to perform the same experiment a year later and get the same result. Or you should be able to do it in two places and get the same result. But one of the main laws of physics — conservation of energy — seems to be broken by general relativity. It is possible for a machine to emit gravity waves, and gain energy instead of losing it. This paradox was solved by Emma Noether who’s theorem proves a connection between symmetries and conservation laws. It turns out that with general relativity, you may get different results depending on where you are when you perform your experiments. Here on earth, the experiments all happen in very similar circumstances. But in a strong gravitational field, the curvature of space is different, and you can get different measurements. This strange effect is predicted by Einstein’s theories, and Neother’s theorem provides the connection. # Math homework just got easier PhotoMath is a program that runs on IOS and Windows phones (Android coming out soon) that can solve math equations. It even shows the steps needed to get the solution. This can help students learn math, or (more likely) let them do their homework without actually learning anything.	2022-10-03 07:46:48	{"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": 3, "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": 0.46382689476013184, "perplexity": 1026.7722797700758}, "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/1664030337404.30/warc/CC-MAIN-20221003070342-20221003100342-00790.warc.gz"}
https://www.light-am.com/article/doi/10.37188/lam.2021.006	Article Contents Citation: # 3D printed micro-optics for quantum technology: Optimised coupling of single quantum dot emission into a single-mode fibre • Light: Advanced Manufacturing 2, Article number: 6 (2021) • Future quantum technology relies crucially on building quantum networks with high fidelity. To achieve this challenging goal, it is of utmost importance to connect individual quantum systems such that their emitted single photons overlap with the highest possible degree of coherence. This requires perfect mode overlap of the emitted light from different emitters, which necessitates the use of single-mode fibres. Here, we present an advanced manufacturing approach to accomplish this task. We combined 3D printed complex micro-optics, such as hemispherical and Weierstrass solid immersion lenses, as well as total internal reflection solid immersion lenses, on top of individual indium arsenide quantum dots with 3D printed optics on single-mode fibres and compared their key features. We observed a systematic increase in the collection efficiency under variations of the lens geometry from roughly 2 for hemispheric solid immersion lenses up to a maximum of greater than 9 for the total internal reflection geometry. Furthermore, the temperature-induced stress was estimated for these particular lens dimensions and results to be approximately 5 meV. Interestingly, the use of solid immersion lenses further increased the localisation accuracy of the emitters to less than 1 nm when acquiring micro-photoluminescence maps. Furthermore, we show that the single-photon character of the source is preserved after device fabrication, reaching a $g^{(2)} (0)$ value of approximately 0.19 under pulsed optical excitation. The printed lens device can be further joined with an optical fibre and permanently fixed.This integrated system can be cooled by dipping into liquid helium using a Stirling cryocooler or by a closed-cycle helium cryostat without the necessity for optical windows, as all access is through the integrated single-mode fibre. We identify the ideal optical designs and present experiments that demonstrate excellent high-rate single-photon emission. ###### 通讯作者: 陈斌, bchen63@163.com • 1. 沈阳化工大学材料科学与工程学院沈阳 110142 Figures(27) / Tables(2) ### Research Summary Quantum technology: 3D printed fibre-based quantum light source Making quantum networks a reality relies crucially on building efficient optical fibre-based quantum light sources. Here, Harald Giessen and Peter Michler from the University of Stuttgart in Germany and colleagues present an advanced manufacturing approach to accomplish this task. Complex micrometre-sized optics were 3D printed on top of individual indium arsenide quantum dots to enhance their single-photon extraction efficiency. Different lens geometries were systematically investigated to optimise the required optical design and a significant increase in light extraction was achieved. Furthermore, a 3D printed fibre chuck was used to precisely position an optical fibre, equipped with another 3D printed in-coupling lens, onto such a quantum dot. This compact on-chip solution enables high coupling efficiency into a single-mode fibre with high-rate single-photon emission. show all ## Article Metrics Article views(2872) PDF downloads(348) Citation(0) Citation counts are provided from Web of Science. The counts may vary by service, and are reliant on the availability of their data. ## 3D printed micro-optics for quantum technology: Optimised coupling of single quantum dot emission into a single-mode fibre • 1. Institut für Halbleiteroptik und Funktionelle Grenzflächen, Research Center SCoPE, and Integrated Quantum Science and Technology Center IQST, University of Stuttgart, 70569 Stuttgart, Germany • 2. 4th Physics Institute, Research Center SCoPE, and Integrated Quantum Science and Technology Center IQST, University of Stuttgart, 70569 Stuttgart, Germany • 3. Institute of Applied Optics (ITO) and Research Center SCoPE, University of Stuttgart, 70569 Stuttgart, Germany • 4. Institute of Solid State Physics, Technical University of Berlin, 10623 Berlin, Germany ###### Harald Giessen, h.giessen@pi4.uni-stuttgart.de • These authors contributed equally: Marc Sartison, Ksenia Weber Abstract: Future quantum technology relies crucially on building quantum networks with high fidelity. To achieve this challenging goal, it is of utmost importance to connect individual quantum systems such that their emitted single photons overlap with the highest possible degree of coherence. This requires perfect mode overlap of the emitted light from different emitters, which necessitates the use of single-mode fibres. Here, we present an advanced manufacturing approach to accomplish this task. We combined 3D printed complex micro-optics, such as hemispherical and Weierstrass solid immersion lenses, as well as total internal reflection solid immersion lenses, on top of individual indium arsenide quantum dots with 3D printed optics on single-mode fibres and compared their key features. We observed a systematic increase in the collection efficiency under variations of the lens geometry from roughly 2 for hemispheric solid immersion lenses up to a maximum of greater than 9 for the total internal reflection geometry. Furthermore, the temperature-induced stress was estimated for these particular lens dimensions and results to be approximately 5 meV. Interestingly, the use of solid immersion lenses further increased the localisation accuracy of the emitters to less than 1 nm when acquiring micro-photoluminescence maps. Furthermore, we show that the single-photon character of the source is preserved after device fabrication, reaching a $g^{(2)} (0)$ value of approximately 0.19 under pulsed optical excitation. The printed lens device can be further joined with an optical fibre and permanently fixed.This integrated system can be cooled by dipping into liquid helium using a Stirling cryocooler or by a closed-cycle helium cryostat without the necessity for optical windows, as all access is through the integrated single-mode fibre. We identify the ideal optical designs and present experiments that demonstrate excellent high-rate single-photon emission. ### Research Summary Quantum technology: 3D printed fibre-based quantum light source Making quantum networks a reality relies crucially on building efficient optical fibre-based quantum light sources. Here, Harald Giessen and Peter Michler from the University of Stuttgart in Germany and colleagues present an advanced manufacturing approach to accomplish this task. Complex micrometre-sized optics were 3D printed on top of individual indium arsenide quantum dots to enhance their single-photon extraction efficiency. Different lens geometries were systematically investigated to optimise the required optical design and a significant increase in light extraction was achieved. Furthermore, a 3D printed fibre chuck was used to precisely position an optical fibre, equipped with another 3D printed in-coupling lens, onto such a quantum dot. This compact on-chip solution enables high coupling efficiency into a single-mode fibre with high-rate single-photon emission. show all Reference (54) /	2022-05-23 06:29:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.22973205149173737, "perplexity": 3547.405678381194}, "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/1652662555558.23/warc/CC-MAIN-20220523041156-20220523071156-00272.warc.gz"}
https://tolstoy.newcastle.edu.au/R/e10/help/10/06/9950.html	# [R] linear predicted values of the index function in an ordered probit model From: Martin Spindler <Martin.Spindler_at_gmx.de> Date: Mon, 28 Jun 2010 16:58:25 +0200 Hello, currently I am estimating an ordered probit model with the function polr (MASS package). Is there a simple way to obtain values for the prediction of the index function ($X*\hat{\beta}$)? (E..g. in the GLM function there is the linear.prediction value for this purpose). If not, is there another function / package where this feature is implemented? Thank you very much for your answer in advance! Best, Martin [[alternative HTML version deleted]] R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Mon 28 Jun 2010 - 15:00:24 GMT Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia. Archive generated by hypermail 2.2.0, at Tue 29 Jun 2010 - 13:10:43 GMT. Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help. Please read the posting guide before posting to the list.	2019-01-19 23:22:57	{"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": 0.36179372668266296, "perplexity": 4510.260034400845}, "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-2019-04/segments/1547583684033.26/warc/CC-MAIN-20190119221320-20190120003320-00554.warc.gz"}
https://codegolf.stackexchange.com/questions/55422/hello-world/68659	# “Hello, World!” So... uh... this is a bit embarrassing. But we don't have a plain "Hello, World!" challenge yet (despite having 35 variants tagged with , and counting). While this is not the most interesting code golf in the common languages, finding the shortest solution in certain esolangs can be a serious challenge. For instance, to my knowledge it is not known whether the shortest possible Brainfuck solution has been found yet. Furthermore, while all of Wikipedia (the Wikipedia entry has been deleted but there is a copy at archive.org ), esolangs and Rosetta Code have lists of "Hello, World!" programs, none of these are interested in having the shortest for each language (there is also this GitHub repository). If we want to be a significant site in the code golf community, I think we should try and create the ultimate catalogue of shortest "Hello, World!" programs (similar to how our basic quine challenge contains some of the shortest known quines in various languages). So let's do this! ## The Rules • Each submission must be a full program. • The program must take no input, and print Hello, World! to STDOUT (this exact byte stream, including capitalization and punctuation) plus an optional trailing newline, and nothing else. • The program must not write anything to STDERR. • If anyone wants to abuse this by creating a language where the empty program prints Hello, World!, then congrats, they just paved the way for a very boring answer. Note that there must be an interpreter so the submission can be tested. It is allowed (and even encouraged) to write this interpreter yourself for a previously unimplemented language. • Submissions are scored in bytes, in an appropriate (pre-existing) encoding, usually (but not necessarily) UTF-8. Some languages, like Folders, are a bit tricky to score - if in doubt, please ask on Meta. • This is not about finding the language with the shortest "Hello, World!" program. This is about finding the shortest "Hello, World!" program in every language. Therefore, I will not mark any answer as "accepted". • If your language of choice is a trivial variant of another (potentially more popular) language which already has an answer (think BASIC or SQL dialects, Unix shells or trivial Brainfuck-derivatives like Alphuck), consider adding a note to the existing answer that the same or a very similar solution is also the shortest in the other language. As a side note, please don't downvote boring (but valid) answers in languages where there is not much to golf - these are still useful to this question as it tries to compile a catalogue as complete as possible. However, do primarily upvote answers in languages where the authors actually had to put effort into golfing the code. For inspiration, check the Hello World Collection. ## The Catalogue The Stack Snippet at the bottom of this post generates the catalogue from the answers a) as a list of shortest solution per language and b) as an overall leaderboard. ## Language Name, N bytes where N is the size of your submission. If you improve your score, you can keep old scores in the headline, by striking them through. For instance: ## Ruby, <s>104</s> <s>101</s> 96 bytes If there you want to include multiple numbers in your header (e.g. because your score is the sum of two files or you want to list interpreter flag penalties separately), make sure that the actual score is the last number in the header: ## Perl, 43 + 2 (-p flag) = 45 bytes You can also make the language name a link which will then show up in the snippet: ## [><>](https://esolangs.org/wiki/Fish), 121 bytes /* Configuration / var QUESTION_ID = 55422; // Obtain this from the url // It will be like https://XYZ.stackexchange.com/questions/QUESTION_ID/... on any question page var COMMENT_FILTER = "!)Q2B_A2kjfAiU78X(md6BoYk"; var OVERRIDE_USER = 8478; // This should be the user ID of the challenge author. / App / return "https://api.stackexchange.com/2.2/questions/" + QUESTION_ID + "/answers?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + ANSWER_FILTER; } } jQuery.ajax({ method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { data.items.forEach(function(a) { }); comment_page = 1; } }); } jQuery.ajax({ method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { data.items.forEach(function(c) { if (c.owner.user_id === OVERRIDE_USER) }); else process(); } }); } var SCORE_REG = /<h\d>\s([^\n,<](?:<(?:[^\n>]>[^\n<]<\/[^\n>]>)[^\n,<])),.?(\d+)(?=[^\n\d<>](?:<(?:s>[^\n<>]<\/s>\|[^\n<>]+>)[^\n\d<>])<\/h\d>)/; function getAuthorName(a) { return a.owner.display_name; } function process() { var valid = []; var body = a.body; if(OVERRIDE_REG.test(c.body)) body = '<h1>' + c.body.replace(OVERRIDE_REG, '') + '</h1>'; }); var match = body.match(SCORE_REG); if (match) valid.push({ user: getAuthorName(a), size: +match[2], language: match[1], }); else console.log(body); }); valid.sort(function (a, b) { var aB = a.size, bB = b.size; return aB - bB }); var languages = {}; var place = 1; var lastSize = null; var lastPlace = 1; valid.forEach(function (a) { if (a.size != lastSize) lastPlace = place; lastSize = a.size; ++place; .replace("{{NAME}}", a.user) .replace("{{LANGUAGE}}", a.language) .replace("{{SIZE}}", a.size) var lang = a.language; lang = jQuery('<a>'+lang+'</a>').text(); languages[lang] = languages[lang] \|\| {lang: a.language, lang_raw: lang, user: a.user, size: a.size, link: a.link}; }); var langs = []; for (var lang in languages) if (languages.hasOwnProperty(lang)) langs.push(languages[lang]); langs.sort(function (a, b) { if (a.lang_raw.toLowerCase() > b.lang_raw.toLowerCase()) return 1; if (a.lang_raw.toLowerCase() < b.lang_raw.toLowerCase()) return -1; return 0; }); for (var i = 0; i < langs.length; ++i) { var language = jQuery("#language-template").html(); var lang = langs[i]; language = language.replace("{{LANGUAGE}}", lang.lang) .replace("{{NAME}}", lang.user) .replace("{{SIZE}}", lang.size) language = jQuery(language); jQuery("#languages").append(language); } } body { text-align: left !important; display: block !important; } width: 290px; float: left; } #language-list { width: 500px; float: left; } font-weight: bold; } table td { } <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <div id="language-list"> <h2>Shortest Solution by Language</h2> <table class="language-list"> <tr><td>Language</td><td>User</td><td>Score</td></tr> <tbody id="languages"> </tbody> </table> </div> <tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr> </tbody> </table> </div> <table style="display: none"> </tbody> </table> <table style="display: none"> <tbody id="language-template"> </tbody> </table> • @isaacg No it doesn't. I think there would be some interesting languages where it's not obvious whether primality testing is possible. – Martin Ender Aug 28 '15 at 13:56 • If the same program, such as "Hello, World!", is the shortest in many different and unrelated languages, should it be posted separately? – aditsu quit because SE is EVIL Aug 28 '15 at 15:33 • @mbomb007 Well it's hidden by default because the three code blocks take up a lot of space. I could minify them so that they are a single line each, but I'd rather keep the code maintainable in case bugs come up. – Martin Ender Aug 28 '15 at 19:34 • @ETHproductions "Unlike our usual rules, feel free to use a language (or language version) even if it's newer than this challenge." Publishing the language and an implementation before posting it would definitely be helpful though. – Martin Ender Aug 29 '15 at 23:01 • @MartinEnder ... Almost. If two BF solutions have the same size, the one with smaller lexicographical order will take smaller number of bytes in Unary. Of course the smallest Unary solution translated to BF is guaranteed to be smallest. – user202729 May 20 '18 at 10:20 ## Geom++, 17 bytes " Hello, World! " Yes, the spaces around the string are necessary. ## Lines, 13 bytes Hello, World! There are no control characters, so the string is just output. ## Gray Snail, 22 bytes OUTPUT "Hello, World!" OUTPUT just outputs the string. ## PureStack, 18 bytes "Hello, World!" !~ Pushes "Hello, World!" to the stack and prints it. ## Blank, 64 bytes [33][100][108][114][111][87][32][44][111][108]{:}[101][72]{p}{@} Hint: Read the interpreter / compiler to ensure that you use all features. This esolangs page, for example, used to exclude the p instruction. ## EXCON, 137 bytes <<<^<<<^!:^<<^<<<^<^!:<<^<^<<^<^!!:^<^<^<^<<^<^!:<<^<^<<^!:<<<<<^!:^<^<^<<^<<^!:^<^<^<^<<^<^!:<^<<<^<^<^!:<<^<^<<^<^!:<<^<<<^<^!:^<<<<<^! Simple bit-hacking. ## 96, 44 bytes 72,101,108:,@,111,44,32,87,111,114,@,100,33" Uses the accumulator to store the L. ## Jumper, 59 bytes =72>=101>=108>=108>=111>=44>=32>=87>=111>=114>=108>=100>=33 # Milky Way 1.0.0, 16 bytes "Hello, World!"! or "Hello, World!"> ### Explanation "Hello, World!" # push "Hello, World!" to the stack ! # output the TOS or "Hello, World!" # push "Hello, World!" to the stack > # rotate the stack rightward. if nothing is output manually, the bottom stack item is output ## Dirst, 21 bytes dss_Hello, World!.txt Note: this must be run in a system where ! is allowed in filenames. ## Elixir, 22 bytes IO.puts"Hello, World!" ## Pig, 27 bytes /dev/stdoutPIGHello, World! Requires a Unix-like OS to run. Pig is a simple language in which a program is a filename, followed by PIG, followed by anything else, which writes the string to the file specified by the filename. In this case, I use the tactic of writing the output to /dev/stdout, outputting the string. /dev/tty outputs the string, but it requires a console window to work, and doesn't pipe output correctly. • Not a programming language. – SuperJedi224 Dec 12 '15 at 19:58 # C, 32 bytes main(){printf("Hello, World!");} Tested on C99 Strict, compiler will generate a warning that there is no return-type, and int is assumed. What actually happens in most environments is that the return value from the last printf is left in the register used for return values. Quote Reference In our case the printf("Hello, World!") is the only statement in our program, which will set 13 in the registry for return values. In most environments, EXIT_FAILURE is usually 1 as in gcc, which means that on most environments this will not write to STDERR. • It seems we already have a shorter C solution. Your elaboration is nice though, so I guess it's your call whether you keep this answer or not. – Martin Ender Dec 15 '15 at 8:59 • @MartinBüttner is it okay to provide an answer that has a requirement on how to compile or a specific file name ? – Khaled.K Dec 15 '15 at 10:02 • Answers that only work with specific compilers are fine (for the purposes of code golf here, languages are actually defined by their implementations). Specific command-line options and file names are legitimate too but need to be added to the byte count. – Martin Ender Dec 15 '15 at 10:05 ## Algol-M, 36 bytes BEGIN WRITE("Hello, World!"); END CP/M nostalgia... B>type hello.alg BEGIN WRITE("Hello, World!"); END B>algolm hello ALGOL-M COMPILER VERS 1.1 0 ERROR(S) DETECTED B>runalg hello ALGOL-M INTERPRETER-VERS 1.0 Hello, World! B>_ A problem? There is more output than just "Hello, World!" but that output is not caused by the program itself, it is caused by the interpreter. • In this challenge, not even extra interpreter output is allowed. Is there a way to disable it? – LegionMammal978 Dec 25 '15 at 12:33 • @Martin Büttner: Hey chef... I've no problem deleting this solution if that not-by-my-program-output really is a probem... or use your moderator magic power and delete it... definitely my life does not depend on this solution... ;-) – user19214 Dec 25 '15 at 17:23 # Befalse, 41 bytes I want to learn this language, but it's so confusing ): 0"!dlrow olleH"!/$?\ \. / Demo (paste into the the box and click "Show", then click "Run".) ## SPL, 91 bytes File hello.spl: PROGRAM h;BYTE w='Hello, World!$';PROCEDURE BDOS(WORD f,s);EXTERNAL;BEGIN BDOS(9,@w) END h. With some CRLFs (99 bytes): PROGRAM h; BYTE w='Hello, World!$'; PROCEDURE BDOS(WORD f,s);EXTERNAL; BEGIN BDOS(9,@w) END h. (both without crlf after last line) CP/M nostalgia... E>type hello.spl PROGRAM h;BYTE w='Hello, World!$';PROCEDURE BDOS(WORD f,s);EXTERNAL;BEGIN BDOS(9,@w) END h. E>do c hello SuperSUB V1.1 E>; COMPILE AN SPL PROGRAM E>SPL HELLO SPL V-1.03.03.10 (17-Dec-06 13:41:11) No errors. Code = 31. Free memory = 30081. E>L80 HELLO,HELLO/N/E Data 0103 01D6 < 211> 46887 Bytes Free [0111 01D6 1] E>ERA HELLO.REL E>hello Hello, World! E> _ • Can the downvoter please explain why downvoting was needed? Can it be done shorter in SPL? – user19214 Apr 28 '18 at 8:15 ## Genie, 28 bytes File hello.gs: init print "Hello, World!" (tab indented, needs final newline) Compile & run: $valac hello.gs$ ./hello Hello, World! ## Pilot, 15 bytes t:Hello, World! (no trailing newline is ok for the Pilot implementation I used) CP/M nostalgia... A>type hello.plt t:Hello, World! A>do pilot/pr hello SuperSUB V1.1 A>: SUBMIT PILOT/P WITH REAL TYPE SUPPORT A>PILOT/P HELLO PILOT/P version 2.5, 02/26/84 WRITING TO HELLO.PAS Translating: HELLO A>ERA OLD.HDR No file A>REN OLD.HDR=PILOT/P.HDR A>REN PILOT/P.HDR=PILOT/PR.HDR A>PASCAL HELLO InterSystems Pascal v - 4.0 HELLO 1--- VLENGTH 27- MEMAVAIL 28-- SETLENGT 30- LENGTH 31- INDEX 33- POS 34- UCASE 35- LCASE 36- DELETE 37- COPY 38- INSERT 39-- REPLACE 40- CONCAT 41- STR 42- IVALUE 43- HALT 44- ISALPHA 45- ISUPPER 46- ISLOWER 47- ISDIGIT 48- ISSPACE 49-- TOUPPER 50- TOLOWER 51- KEYIN 52- KEYBOARD 53- DWRITE 54- CONSTAT 55- CONCHAR 56- GOTOXY 57- VAL 58- RANDOM 59-- RND 63- RANDOMIZ 65- INITIALI 69----- WAIT 102--- MATCH 124------- HELLO 185- 0 compilation error(s). A>ERA HELLO.LST A>REN PILOT/PR.HDR=PILOT/P.HDR A>REN PILOT/P.HDR=OLD.HDR A>ASMBL MAIN,HELLO/REL Pascal/Z run-time support interface ASMBLE v-7d 0 errors. 312 symbols generated. Space for 2819 more symbols. 4275 characters are stored in 44 macros. 1680 bytes of program code. A>ERA HELLO.SRC Generate a COM file Lo = 0100 Hi = 1A32 Start = 0172 Save 26 blocks A>ERA HELLO.REL A>ERA HELLO.PAS A>hello Hello, World! A>_ ## COMAL, 20 bytes 1print"Hello, World! CP/M nostalgia... A>comal COMAL Users Group, U.S.A. Limited 1print"Hello, World! run Hello, World! End of program bye A>_ # WhoScript, 19 bytes 1"Hello, World!";pf Not nearly as much fun as the full version: # 48 65 6c 6c 6f 2c 20 57 6f 72 6c 64 21 @ push the ASCII values of the characters "Hello, World!" to the stack psychic_paper flush @ print all values on the stack as ASCII characters # Freelang, 291 bytes A lot of whitespace, but it's an assembly language for a virtual machine. I'm pretty sure this won't compile without the indents. H{ ." Hello world! " p halt : p ( s -- ) [@] 4 swap incw swap w: go[<=0] :e dec swap [@b] go[==0] :s writorb ::z go :n s: drop n: inc swap go :w e: drop2 ; z: halt }H # lang5, 17 bytes lang5 is a combination of APL and Forth (Hello World doesn't show off any of the APL bits) "Hello, World!" . # SuperX++, 37 bytes From the web site: Superx++ is an object-oriented language that is entirely based on XML's syntactical structure. Superx++ conforms with the XML version 1.0 specification as published on the W3C web site. Programming in XML itself has great potential and Superx++ pushes the envelope! This program comes from http://xplusplus.sourceforge.net/FAQ.htm#hellow <xpp><xout>Hello, World!</xout></xpp> # o:XML, 48 bytes From the web site: o:XML is a complete object oriented programming language, with features including polymorphism, function overloading, exception handling, threads and more. The syntax is fully compliant XML. With o:XML, object-oriented paradigms can be leveraged to the maximum, while data and code remains in a standard format. With o:XML there is no 'impedance mismatch' when developing XML web-applications, tools and systems. Furthermore o:XML integrates seamlessly with most popular Java platforms, including Java Servlets, Struts, Ant, BSF and Spring 2.0. This program comes from http://www.xml.com/pub/a/2004/07/21/oxml.html <?xml version="1.0"?> <o:do>Hello, World!</o:do> # REXX, 19 bytes say "Hello, World!" Rexx is widely used as a scripting and macro language, and is often used for processing data and text and generating reports. Rexx is the primary scripting language in some operating systems, e.g. OS/2, MVS, VM, AmigaOS, and is also used as an internal macro language in some other software, such as KEDIT, THE and the ZOC terminal emulator. • Yeah, it's used on zOS – mbomb007 Feb 24 '16 at 19:36 # Mouse16, 16 bytes "Hello, World!"! Boring, I know. If you want somewhat interesting, then there's this, which runs Python from inside Mouse, for 31 bytes: "!!PY!!print('Hello, World!')" The to-be interesting bits of Mouse aren't implemented yet, but we have control structs, so... # Pike, 35 bytes A fast OOP scripting language with familiar C-style syntax. int main(){write("Hello, World!");} The optional return 0; is left off, because it runs without it. In the REPL, the main declaration can be left off. Pythonish, but with C syntax. OO-enabled, and also inherits from PHP (the good parts), Perl and (duh) C/C++, but Pike isn't halfassed about OOP like C++ is. This can be compiled into ANSI C or C++ with a #define (and the #include, for standards compilance) for 113 bytes: #ifndef __PIKE__ #include<stdio.h> #define write(x) printf(x) #endif int main(){write("Hello, World!");return 0;} No warnings with gcc -Wall -pedantic! Only a few more defines are needed to make almost any Pike into ANSI C. :D # Falcon, 16 bytes I'm sad that the last update to this language was in 2010 :( it looks so cool! it's still indev!! >"Hello, World!" It gets its syntax from Python and PHP, most noticeably. ## A-Ray, 16 bytes Any new language should be put here just for the sake of being put here... p"Hello, World!" # Pylons, 16 Toggles string mode with " and then pushes "Hello, World!" to the stack, then uses c to print the whole stack as a string. "Hello, World!"c For 14 bytes, thought possibly cheating, so it's not my main answer, c with Hello, World! as a command line arg. I don't have an online interpreter yet, but if you download the repo and pass the command line args to main.py` and the program to stdin, it'll run.	2020-10-19 21:13:45	{"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": 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": 0.20741331577301025, "perplexity": 10469.805837052025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107866404.1/warc/CC-MAIN-20201019203523-20201019233523-00051.warc.gz"}
http://www.paisagismoemfoco.com.br/archive/8e123a-bond-length-of-ch4	Reaction between acetone and methyl magnesium chloride followed by hydrolysis will give : Identify the correct statements from the following: The bond lengths and bond angles in the molecules of methane, ammonia and water are given below .This variation in bond angle is a result of (i) the increasing repulsion between hydrogen atoms as the bond length decreases (ii) the number of non-bonding electron pairs in the molecule (iii) a non-bonding electron pair having a greater repulsive force than a bonding electron pair On electrolysis of dil.sulphuric acid using Platinum (Pt) electrode, the product obtained at anode will be: An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. For example, C–F is 439 kJ/mol, C–Cl is 330 kJ/mol, and C–Br is 275 kJ/mol. According to molecular orbital theory, which of the following will not be a viable molecule ? It is a colourless, flammable gas. Experimental bond lengths This table lists coordinate descriptions and how many of that type of coordinate are in the CCCBDB. Join Yahoo Answers and get 100 points today. ClCCl 116 ± 2 (ass.) Problem: The average C—H bond energy in CH4 is 415 kJ/mol. Click on the description for a list of that type. Still have questions? The atomic radiusis: Find out the solubility of $Ni(OH)_2$ in 0.1 M NaOH. dipole moment of ch4 is zero .the ch4 is tetrahedral in shape thus each bond pair are at equal distance that is they are symmetrically arranged hence each dipole moment of bond balance each other. Bond lengths [pm] formic acid: HCOOH: C=O : 120.2 pm C-O : 134.3 pm C-H : 109.7 pm O-H : 97.2 pm The carbon-hydrogen bond (C–H bond) is a bond between carbon and hydrogen atoms that can be found in many organic compounds. Structure anions of acids, $HNO_{3}, H_{3}PO_{4}$ and $H_{2}SO_{4}$ are, respectively. It's CH4 because in NH3 nitrogen contains lone pair of electrons. When one atom bonds to various atoms in a group, the bond strength typically decreases as we move down the group. Answer in units of ◦C.. The carbon–carbon (C–C) bondlength in diamond is 154 pm. Here $B$ is bond pair and $L$ is lone pair. I'm doing a project for school, and i need to know what the bond length for CH4 is in picometres. Methane (CH4) - Methane is the simplest hydrocarbon with the molecular formula CH4. Average bond energies for some common bonds appear in Table $$\PageIndex{1}$$, and a comparison of bond lengths and bond strengths for some common bonds appears in Table $$\PageIndex{2}$$. Bond Length 1.1067 Å 1.111 Å CH 2 Bond Angle 100.22 102.4° CH 3 Bond Energy 4.70075 eV 4.72444 eV CH 3 Bond Length 1.1029 Å 1.079 Å CH 3 Bond Angle 100.70° CH 4 Bond Energy 4.4900 eV 4.48464 eV CH 4 Bond Length 1.1010 Å 1.087 Å CH 4 Bond Angle 109.5° 109.5° N 2 Bond Energy 9.71181 eV 9.756 eV N 2 Bond Length 1.0955 Å 1.094 Å Write the expected electron configurations for each of the following atoms: Cl, As, Sr, W, Pb, Na+, I-, Mg 2+, S2-, and Cf.? Which of the following set of molecules will have zero dipole moment ? A gas at 61◦C occupies 4.75 L. At what temperature will the volume be 3.17 L, assuming "=" indicates a double bond. Identify compound X in the following sequence of reactions: Identify a molecule which does not exist. the same pressure? Bond Length (Å) Bond Angle (°) Symmetry; CCl 2 F 2: dichlorodifluoromethane : C-Cl 1.74 ± 0.03 C-F 1.35 ± 0.03: ClCCl 109 ± 2 FCF 110 ± 2: C 2v: CCl 2 O: carbonyl chloride (phosgene) C-Cl 1.746 ± 0.004 C-O 1.166 ± 0.002: ClCCl 111.3 ± 0.1: C 2v: CCl 2 S: thiocarbonyl chloride (thiophosgene) C-Cl 1.70 ± 0.02 C-S 1.63 (ass.) Since bondlengths are consistent, bond energies of similar bonds are also consistent. dipole moment of ch4 is zero .the ch4 is tetrahedral in shape thus each bond pair are at equal distance that is they are symmetrically arranged hence each dipole moment of bond balance each other. Methane as you said is CH4, so the bond length of each of the H--C bonds are 109pm. Get your answers by asking now. Use following table and the following data to calculate the average C—H bond energy in ethane (C2H6; C—C bond), in ethene (C2H4; C=C bond), and in ethyne (C 2H2; C≡C bond):C2H6(g) + H2(g) 2CH4(g) ΔH°rxn = −65.07 kJ/molC2H4(g) + 2H2(g) 2CH4(g) ΔH°rxn = − 202.21 kJ/molC2H2(g) + 3H2(g) 2CH4(g) ΔH°rxn = −376.74 kJ/mol Use following table and the following data to calculate the average C—H bond energy in ethane (C2H6; C—C bond), in ethene (C2H4; C=C bond), and in ethyne (C 2H2; C≡C bond):C2H6(g) + H2(g) 2CH4(g) ΔH°rxn = −65.07 kJ/molC2H4(g) + 2H2(g) 2CH4(g) ΔH°rxn = − 202.21 kJ/molC2H2(g) + 3H2(g) 2CH4(g) ΔH°rxn = −376.74 kJ/mol Bond angle is 109.5 degrees.It is equal in every bond. Since one atomic unit of length(i.e., a Bohr radius) is 52.9177 pm, the C–C bond length is 2.91 at… In the molecular orbital diagram for the molecular ion, $\ce{N_2{^{+}}}$, the number of electrons in the $\sigma_{2p}$ molecular orbital is : Which of the following best describes the diagram below of a molecular orbital ? In biology class today my teacher played a porn video to show what they were talking about Should I talk to the principal to get her fired. Bond order is the number of bonding electron pairs shared by two atoms in a molecule. ? Which of the following conversions involves change in both shape and hybridisation ? The bond lengths and bond angles in the molecules of methane, ammonia and water are given below .This variation in bond angle is a result of (i) the increasing repulsion between hydrogen atoms as the bond length decreases (ii) the number of non-bonding electron pairs in the molecule (iii) a non-bonding electron pair having a greater repulsive force than a bonding electron pair. The average bond length of C-H bond is 1.09 × 10-10meter (=10900 MM). What would happen if you did not add acid after exactly 15 minutes of the enzymatic reaction in a competition ELISA? Given that the ionic product of $Ni(OH)_2$ is $2 \times 10^{-15}$. Cowboys strength coach Markus Paul dies at 54, Ken Jennings called out for past insensitive tweets, Girl that was handcuffed by police at 11 is dead at 14, How sleep habits may cut your risk of heart failure: Study, Women raise voices amid increase in domestic violence, New stimulus checks may not boost economy, 'Saved By the Bell' star explains famous caffeine pill scene, History hasn't been kind to fighters on comeback trail, Experts push CDC to shorten COVID-19 quarantine, Map reveals Americans' favorite Thanksgiving pies by state, Coronavirus is now a coast-to-coast disaster. The CH4 Bond Angle Will Be 109.5 Degrees Because It Has a Tetrahedral Molecular Geometry. Q. "#" indicates a triple bond. (a) $CO_2(g)$ is used as refrigerant for ice-cream and frozen food. Problem: The average C—H bond energy in CH4 is 415 kJ/mol. What is the hybridization and geometry of the compound $XeOF_4$ ? The incorrect geometry is represented by : What will be the geometry of the compound $MB_4L_2$ ? Estimated methane (CH4) "real" structure In this program, the carbon nucleus (it is supposed to be +4e =+6e-2e) is at the origin, and the four hydrogen nuclei are arranged "tetrahedrally". Methane is produced naturally from rotting vegetation in marshes. NH3,CO2	2021-03-03 14:12:42	{"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": 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": 0.47713449597358704, "perplexity": 4851.016432044276}, "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/1614178366969.45/warc/CC-MAIN-20210303134756-20210303164756-00484.warc.gz"}
https://www.isid.ac.in/~statmath/index.php?module=Preprint&Action=ViewAbs&PreprintId=128	# Publications and Preprints Autonomous geometro-statistical formalism for quantum mechanics I : Noncommutative symplectic geometry and Hamiltonian mechanics by Tulsi Dass Considering the problem of autonomous development of quantum mechanics in the broader context of solution of Hilbert's sixth problem (which relates to joint axiomatization of physics and probability theory), a formalism is evolved in this two-part work which facilitates the desired autonomous development and satisfactory treatments of quantum-classical correspondence and quantum measurements. This first part contains a detailed development of superderivation based differential calculus and symplectic structures and of noncommutative Hamiltonian mechanics (NHM) which combines elements of noncommutative symplectic geometry and noncommutative probability in an algebraic setting. The treatment of NHM includes, besides its basics, a reasonably detailed treatment of symplectic actions of Lie groups and noncommutative analogues of the momentum map, Poincar$\acute{e}$-Cartan form and the symplectic version of Noether's theorem. Consideration of interaction between systems in the NHM framework leads to a division of physical systems into two worlds' --- the commutative world' and the noncommutative world' [in which the systems have, respectively, (super-)commutative and non-(super-)commutative system algebras] --- with no consistent description of interaction allowed between two systems belonging to different worlds'; for the `noncommutative world', the formalism dictates the introduction of a universal Planck type constant as a consistency requirement. isid/ms/2009/03 [fulltext]	2020-01-26 17:05:00	{"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": 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": 0.7270216941833496, "perplexity": 1615.965802694774}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251690095.81/warc/CC-MAIN-20200126165718-20200126195718-00316.warc.gz"}
https://mathematica.stackexchange.com/questions/84292/how-does-mathematica-calculate-its-adjacencymatrix-and-vertexdegree?noredirect=1	# How does Mathematica calculate its AdjacencyMatrix[ ] and VertexDegree[ ] I define a graph: g = Graph[{1 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 5, 4 \[UndirectedEdge] 5, 5 \[UndirectedEdge] 6}, VertexLabels -> "Name"] The output looks correct in how the vertices are connected, but the AdjacencyMatrix[g] and VertexDegree[g] put the vertices out of order with my labels. Why is that, and what is the order Mathematica uses? • Vertex ordering is completely unrelated to the names of the vertices. Vertices can be any expression, not just numbers. Never assume that numerical vertices are ordered from smallest to greatest. Use VertexIndex and VertexList to relate the index of a vertex to the vertex itself. In practice, Mathematica puts the vertices in the order you first specify them (as they appear in the edge list in your example), but never count on this as there's no guarantee and I won't be surprised if future versions change this. – Szabolcs May 25 '15 at 8:52 • I removed the implementation-details tag because the question is more about what the function returns than about how the function works internally. – Szabolcs Aug 3 '15 at 15:21 So, unless you provide a vertex list as the first argument of Graph, VertexList[g] is populated with vertices in the order they appear in the edge list, i.e., {1, 3, 2, 4, 5, 6}. Using Range[6] as the first argument in Graph: g1 = Graph[Range[6], {1 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 5, 4 \[UndirectedEdge] 5, 5 \[UndirectedEdge] 6}, VertexLabels -> "Name", ImagePadding -> 10] versus g2 = Graph[{1 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 5, 4 \[UndirectedEdge] 5, 5 \[UndirectedEdge] 6}, VertexLabels -> "Name", ImagePadding -> 10] Their VertexLists and VertexDegrees: Column[Labeled[TableForm[{VertexList@#, VertexDegree@#}, TableHeadings -> {{"VertexList", "VertexDegree"}, None}], #2, Top] & @@@ {{g1, "g1"}, {g2, "g2"}}, Spacings -> 2] and AdjacencyMatrixs: Row[Labeled[TableForm[Normal@AdjacencyMatrix@#, TableHeadings -> {VertexList@#, VertexList@#}], #2, Top] & @@@ {{g1, "g1"}, {g2, "g2"}}, Spacer[15]]	2019-11-15 20:43:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.17883074283599854, "perplexity": 5788.355186733122}, "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-2019-47/segments/1573496668712.57/warc/CC-MAIN-20191115195132-20191115223132-00503.warc.gz"}
http://scholarpedia.org/article/Artificial_General_Intelligence	# Artificial General Intelligence Post-publication activity Curator: Ben Goertzel # Introduction The term Artificial General Intelligence (often abbreviated "AGI") has no broadly accepted precise definition, but has multiple closely related meanings, e.g. • the capacity of an engineered system to • display the same rough sort of general intelligence as humans; or, • display intelligence that is not tied to a highly specific set of tasks; or • generalize what it has learned, including generalization to contexts qualitatively very different than those it has seen before; or, • take a broad view, and interpret its tasks at hand in the context of the world at large and its relation thereto • an engineered system displaying the property of artificial general intelligence, to a significant degree • the theoretical and practical study of artificial general intelligence systems and methods of creating them AGI is part of the broader fields of Artificial Intelligence (AI) and Cognitive Science. It is also closely related to other areas such as Metalearning and Computational Neuroscience. ## AGI versus Narrow AI The original founders of the AI field, in the 1950s and 60s, were largely concerned with the creation of hardware or software emulating human-like general intelligence. Since that time, the field has come to focus instead largely on the pursuit of discrete capabilities or specific practical tasks. This approach has yielded many interesting technologies and theoretical results, yet has proved relatively unsuccessful so far in terms of the original central goals of the field. Thus, some researchers have come to prefer the term and concept of "AGI", in order to distinguish the pursuit of general intelligence from more narrowly focused associated pursuits (Goertzel and Pennachin, 2005). A dichotomy has sometimes been drawn between AGI and "narrow AI" (Goertzel and Pennachin, 2005). For example, Kurzweil (1999) contrasted "narrow AI" with "strong AI" -- using the former to refer to the creation of systems that carry out specific "intelligent" behaviors in specific contexts, and the latter to refer essentially to what is now called AGI. For a narrow AI system, if one changes the context or the behavior specification even a little bit, some level of human reprogramming or reconfiguration is generally necessary to enable the system to retain its level of intelligence. Qualitatively, this seems quite different from natural generally intelligent systems like humans, which have a broad capability to self-adapt to changes in their goals or circumstances, performing ”transfer learning” to generalize knowledge from one goal or context to others. The precise definition or characterization of AGI is one of the subjects of study of the AGI research field. However, it is broadly accepted that, given realistic space and time resource constraints, human beings do not have indefinite generality of intelligence; and for similar reasons, no real-world system is going to have indefinite generality. Human intelligence combines a certain generality of scope, with various highly specialized aspects aimed at providing efficient processing of pragmatically important problem types; and real-world AGI systems are going to mix generality and specificity in their own ways. ## The Emergence of an AGI Community The emergence of a distinct community focused on AGI has been a gradual process, that has largely coincided with an increase in the legitimacy accorded to explicitly AGI-focused research within the AI community as a whole. During the early 2000s interest in the grand goals began to rise in various research centers around the world, including IDSIA in Switzerland, RPI and Carnegie Mellon in the US, and many others. In 2005, Springer published an edited volume titled "Artificial General Intelligence" (Goertzel and Pennachin, 2005). In 2006, the first formal research workshop on "AGI" was held, in Bethesda, Maryland (Goertzel, 2013). In the subsequent years, a broad community of researchers united by the explicit pursuit of AGI and related concepts has emerged, as evidenced e.g. by conference series such as Artificial General Intelligence (AGI), Biologically Inspired Cognitive Architectures (BICA), and Advances in Cognitive Systems; and by numerous special tracks and symposia at major conferences such as AAAI and IEEE, focused on closely allied topics such as Human-Level Intelligence and Integrated Intelligence. There is also a Journal of AGI. The AGI community, from the start, has involved researchers following a number of different directions, including some building cognitive architectures inspired by cognitive psychology and neurobiology; and also some focused on deriving mathematical results regarding formalizations of general intelligence (thus, among other things, building bridges between AGI and other formal pursuits such as theoretical computer science and statistical decision theory). Each of the subcommunities involved has brought its own history, e.g. some AGI cognitive architecture work extends ideas from classic AI cognitive architectures such as SOAR (Laird, 2012) and GPS (Newell et al, 1959), some extends work from evolutionary computing, etc. The mathematical side of contemporary AGI draws heavily on foundational work by Ray Solomonoff (1964) and other early pioneers of formal intelligence theory. While the qualitative commonality among the various research directions pursued in AGI community is relatively clear, there have not yet been any broadly successful attempts to clarify core hypotheses or conclusions binding the various threads of the AI field. As one effort along these lines, Goertzel (2014) articulated a "core AGI hypothesis”, namely that "the creation and study of synthetic intelligences with sufficiently broad (e.g. human-level) scope and strong generalization capability, is at bottom qualitatively different from the creation and study of synthetic intelligences with significantly narrower scope and weaker generalization capability." This hypothesis was intended as a statement on which nearly all researchers in the AGI community would agree, regardless of their different conceptualizations of the AGI concept and their different architectural, theoretical, technical and engineering approaches. However, much more precise propositions than this will be needed to attain broad agreement among researchers, for the AGI field to be considered theoretically unified. # AGI and Related Concepts AGI is related to many other terms and concepts commonly used. Joscha Bach has characterized AGI in terms of the quest to create ”synthetic intelligence." (Bach, 2009). One also finds communities of researchers working toward AGI-related goals under the labels ”computational intelligence", ”natural intelligence", ”cognitive architecture", ”biologically inspired cognitive architecture”, and many others. AGI is related to, yet far from identical to, ”human-level AI” (Cassimatis, 2006) -- a term which is usually used to mean, in effect, ”human-level, reasonably human-like AGI”. AGI is a fairly abstract notion, which is not intrinsically tied to any particular characteristics of human beings beyond their general intelligence. On the other hand, the concept of ”human-level AI” is openly anthropomorphic, and seeks to compare synthetic intelligences to human beings along an implicit lineal scale, a notion that introduces its own special complexities. If a certain AGI system is very different than humans, it may not be easy to assess in what senses it resides on the same level as humans, versus above or below. On the other hand, if one's goal is to create AGI systems that resemble humans, it could be argued that thinking about hypothetical radically different AGI systems is mainly a distraction. The narrower focus of the "human level AI" concept, as opposed to AGI, seems to have positives and negatives, which are complex to disentangle given the current state of knowledge.. # Perspectives on General Intelligence The AGI field contains a number of different, largely complementary approaches to understanding the “general intelligence” concept. While the bulk of the AGI community’s effort is devoted to devising and implementing designs for AGI systems, and developing theories regarding the best way to do so, the formulation of a detailed and rigorous theory of ”what AGI is” also constitutes a small but significant part of the community’s ongoing research. The lack of a clear, universally accepted definition is not unique to "AGI." For instance, “AI” also has many different meanings within the AI research community, with no clear consensus n the definition. “Intelligence” is also a fairly vague concept; Legg and Hutter wrote a paper summarizing and organizing over 70 different published definitions of ”intelligence”, most oriented toward general intelligence, emanating from researchers in a variety of disciplines (Legg and Hutter, 2007). Four key approaches to conceptualizing the nature of GI and AGI are outlined below. ## The Pragmatic Approach to Characterizing General Intelligence The pragmatic approach to conceptualizing general intelligence is typified by the AI Magazine article ”Human Level Artificial Intelligence? Be Serious!”, written by Nils Nilsson, one of the early leaders of the AI field (Nilsson, 2005) . Nilsson’s view is ... that achieving real Human Level artificial intelligence would necessarily imply that most of the tasks that humans perform for pay could be automated. Rather than work toward this goal of automation by building special-purpose systems, I argue for the development of general-purpose, educable systems that can learn and be taught to perform any of the thousands of jobs that humans can perform. Joining others who have made similar proposals, I advocate beginning with a system that has minimal, although extensive, built-in capabilities. These would have to include the ability to improve through learning along with many other abilities. In this perspective, once an AI obsoletes humans in most of the practical things we do, it should be understood to possess general Human Level intelligence. The implicit assumption here is that humans are the generally intelligent system we care about, so that the best practical way to characterize general intelligence is via comparison with human capabilities. The classic Turing Test for machine intelligence (Turing, 1955) – simulating human conversation well enough to fool human judges – is pragmatic in a similar sense to Nilsson's perspective. But the Turing test has a different focus, on emulating humans. Nilsson isn’t interested in whether an AI system can fool people into thinking it’s a human, but rather in whether an AI system can do the useful and important practical things that people can do. ## Psychological Characterizations of General Intelligence The psychological approach to characterizing general intelligence also focuses on human-like general intelligence; but rather than looking directly at practical capabilities, it tries to isolate deeper underlying capabilities that enable these practical capabilities. In practice it encompasses a broad variety of sub-approaches, rather than presenting a unified perspective. Viewed historically, efforts to conceptualize, define, and measure intelligence in humans reflect a distinct trend from general to specific (it is interesting to note the similarity to historical trends in AI) . Thus, early work in defining and measuring intelligence was heavily influenced by Spearman, who in 1904 proposed the psychological factor g (the ”g factor”, for general intelligence. Spearman argued that g was biologically determined, and represented the overall intellectual skill level of an individual. In 1916, Terman introduced the notion of an intelligence quotient or IQ. In subsequent years, though, psychologists began to question the concept of intelligence as a single, undifferentiated capacity. There emerged a number of alternative theories, definitions, and measurement approaches, which share the idea that intelligence is multifaceted and variable both within and across individuals. Of these approaches, a particularly well-known example is Gardner’s (1983) theory of multiple intelligences, which proposes eight distinct forms or types of intelligence: (1) linguistic, (2) logical-mathematical, (3) musical, (4) bodily-kinesthetic, (5) spatial, (6) interpersonal, (7) intrapersonal, and (8) naturalist. ## A Mathematical Approach to Characterizing General Intelligence In contrast to approaches focused on human-like general intelligence, some researchers have sought to understand intelligence in general. One underlying intuition here is that • Truly, absolutely general intelligence would only be achievable given infinite computational ability. For any computable system, there will be some contexts and goals for which it’s not very intelligent. • However, some finite computational systems will be more generally intelligent than others, and it’s possible to quantify this extent This approach is typified by the recent work of Legg and Hutter (2007a), who give a formal definition of general intelligence based on the Solomonoff-Levin prior, building heavily on the foundational work of Hutter (2005). Put very roughly, they define intelligence as the average reward-achieving capability of a system, calculated by averaging over all possible reward-summable environments, where each environment is weighted in such a way that more compactly describable programs have larger weights. According to this sort of measure, humans are nowhere near the maximally generally intelligent system. However, intuitively, such a measure would seem to suggest that humans are more generally intelligent than, say, rocks or worms. While the original form of Legg and Hutter’s definition of intelligence is impractical to compute, there are also more tractable approximations. ## The Adaptationist Approach to Characterizing General Intelligence Another perspective views general intelligence as closely tied to the environment in which it exists. Pei Wang has argued carefully for a conception of general intelligence as ”adaptation to the environment using limited resources” (Wang, 2006). A system may be said to have greater general intelligence, if it can adapt effectively to a more general class of environments, within realistic resource constraints. ## Broadly Suspected Aspects of General Intelligence Variations in perspective aside, there is reasonably broad agreement in the AGI community on some key likely features of general intelligence, e.g.: • General intelligence involves the ability to achieve a variety of goals, and carry out a variety of tasks, in a variety of different contexts and environments • A generally intelligent system should be able to handle problems and situations quite different from those anticipated by its creators • A generally intelligent system should be good at generalizing the knowledge it has gained, so as to transfer this knowledge from one problem or context to others • Arbitrarily general intelligence is likely not possible given realistic resource constraints • Real-world systems may display varying degrees of limited generality, but are inevitably going to be a lot more efficient at learning some sorts of things than others; and for any given real-world system, there will be some learning tasks on which it is unacceptably slow. So real-world general intelligences are inevitably somewhat biased toward certain sorts of goals and environments. • Humans display a higher level of general intelligence than existing AI programs do, and apparently also a higher level than other animals • According to our observations of humans and various theoretical perspectives, the following traits, among many others, are typically associated with generally intelligence: reasoning, creativity, association, generalization, pattern recognition, problem solving, memorization, planning, achieving goals, learning, optimization, self-preservation, sensory data processing, language processing, classification, induction, deduction and abduction • It seems quite unlikely that humans happen to manifest a maximal level of general intelligence, even relative to the goals and environment for which they have been evolutionarily adapted There is also a common intuition in much of the AGI community that various real-world general intelligences will tend to share certain common properties; though there is less agreement on what these properties are. A 2008 workshop on Human-Level AI resulted in a paper by Laird and Wray enumerating one proposed list of such properties (Laird et al, 2008); a 2009 workshop on AGI resulted in an alternative, more extensive list, articulated in a multi-author paper published in AI Magazine (Adams et al, 2012). # Current Scope of the AGI Field Wlodek Duch, in his survey paper (Duch, 2008), divided existing approaches to AI into three paradigms – symbolic, emergentist and hybrid. To this trichotomy we here add one additional category, "universal." Due to the diversity of AGI approaches, it is difficult to find truly comprehensive surveys; Samsonovich (2010) is perhaps the most thorough but is by no means complete. ## Universal AI In the universal approach, one starts with AGI algorithms or agents that would yield incredibly powerful general intelligence if supplied with massively, unrealistically much computing power, and then views practically feasible AGI systems as specializations of these powerful theoretic systems. The path toward universal AI began in earnest with Solomonoff's (1964) universal predictors, which provide a rigorous and elegant solution to the problem of sequence prediction, founded in the theory of algorithmic information (also known as Kolmogorov Complexity (Kolmogorov, 1965; Li and Vitanyi, 2008). The core idea here (setting aside certain technicalities) is that the shortest program computing a sequence, provides the best predictor regarding the continuation of the sequence. Hutter's (2000, 2005, 2012) work on AIXI extends this approach, applying the core idea of Solomonoff induction to the problem of controlling an agent carrying out actions in, and receiving reinforcement signals from, a computable environment. In an abstract sense, AIXI is the optimally intelligent agent in computable environments. In a bit more detail, what AIXI does is to maximize expected reward over all possible future perceptions created by all possible environments $q$ that are consistent with past perceptions. The expectation over environments is weighted, where the simpler an environment, the higher is its weight $2^{−l(q)}$, where simplicity is measured by the length $l$ of program $q$. AIXI effectively learns by eliminating Turing machines $q$ once they become inconsistent with the progressing history. That is to say: Solomonoff's theoretically optimal universal predictors and their Bayesian learning algorithms assume only that the reactions of the environment are sampled from an unknown probability distribution $\mu$ contained in a set $\cal M$ of all enumerable distributions (Solomonoff, 1964). Since we typically do not know the program computing $\mu$, Solomonoff predicts the future in a Bayesian framework by using a mixture distribution $\xi= \sum_{i} w_i \mu_i$, a weighted sum of all distributions $\mu_i \in \cal M$, $i=1, 2, \ldots$, where $\sum_i w_i \leq 1$. Hutter used $\xi$ to create the theoretically optimal yet uncomputable RL algorithm AIXI (Hutter, 2005). In cycle $t+1$, given a history of past inputs and actions $h(\leq t)$, AIXI selects as its next action the first action of an action sequence maximizing $\xi$-predicted reward up to some horizon, typically $2t$. It turns out that the Bayes-optimal policy $p^\xi$ based on $\xi$ is self-optimizing in the sense that its average utility value converges asymptotically for all $\mu \in \cal M$ to the optimal value achieved by the (infeasible) Bayes-optimal policy $p^\mu$ which knows $\mu$ in advance. The necessary condition that $\cal M$ admits self-optimizing policies is also sufficient. AIXI is uncomputable, but Hutter’s algorithm AIXItl is a computable approximation that involves, at each step in its “cognitive cycle”, a search over all programs of length less than $$l$$ and runtime less than $$t$$. Conceptually, AIXItl may be understood roughly as follows: • An AGI system is going to be controlled by some program • Instead of trying to figure out the right program via human wizardry, we can just write a "meta-algorithm" to search program space, and automatically find the best program for making the AGI smart, and then use that program to operate the AGI. • We can then repeat this meta-algorithm over and over, as the AGI gains more data about the world, so it will always have the operating program that’s best according to all its available data. $AIXI^{tl}$ is a precisely defined "meta-algorithm" of this nature. Related systems have also been formulated, including one due to Schmidhuber (2002) that is based on the Speed Prior, which takes into account program runtime in way that is optimal in a certain sense. The Universal AI research program also involves blueprints of universal problem solvers for arbitrary computable problems, that are time-optimal in various theoretical senses. These include Levin's (1973) asymptotically optimal Universal Search, which has constant multiplicative overhead (Levin, 1973), and its incremental extension, the Optimal Ordered Problem Solver, which can greatly reduce the constant overhead by re-using previous successful programs (Schmidhuber et al, 2004); as well as Hutter's (2002) asymptotically optimal method, which will solve any well-defined problem as quickly as the unknown fastest way of solving it, save for an additive constant overhead that becomes negligible as problem size grows (this method is related to $AIXI^{tl}$). Self-improving universal methods have also been defined, including some that justify self-changes (including changes of the learning algorithm) through empirical evidence in a lifelong learning context (Schmidhuber et al, 1997). The self-referential, recursively self-improving "Goedel Machine" (Schmidhuber, 2006) proves theorems about itself. It can be implemented on practical general computers and may improve any part of its software (including its proof searcher and the possibly suboptimal initial learning algorithm itself) in a way that is provably time-optimal in a certain sense that takes constant overheads into account and goes beyond asymptotic optimality (Schmidhuber, 2006). It can be initialized by an asymptotically optimal meta-method (Hutter, 2002) which will solve any well-defined problem as quickly as the unknown fastest way of solving it, save for an additive constant overhead that becomes negligible as problem size grows. In the perspective of universal AI, the vast majority of computationally feasible problems are "large" in the sense that they exist in the regime where asymptotic optimality is relevant; the other "small" problems are relatively few in number. However, it seems that many (perhaps all) of the problems of practical everyday interest to humans are "small" in this sense, which would imply that reduction in the overhead of the universal methods mentioned above is critical for practical application of universal AI. There has been work in this direction, dating back at least to (Schmidhuber et al, 1991) , and including recent work such as (Schmidhuber et al, 2013a; Veness et al, 2011). ## Symbolic AGI Attempts to create or work toward AGI using symbolic reasoning systems date back to the 1950s and continue to the current day, with increasing sophistication. These systems tend to be created in the spirit of the "physical symbol system hypothesis" (Newell and Simon, 1976), which states that minds exist mainly to manipulate symbols that represent aspects of the world or themselves. A physical symbol system has the ability to input, output, store and alter symbolic entities, and to execute appropriate actions in order to reach its goals. In 1956, Newell and Simon (1956) built a program, Logic Theorist, that discovers proofs in propositional logic. This was followed up by the General Problem Solver (Newell, 1963) that attempted to extend Logic Theorist type capabilities to commonsensical problem-solving. At this early stage, it became apparent that one of the key difficulties facing symbolic AI was how to represent the knowledge needed to solve a problem. Before learning or problem solving, an agent must have an appropriate symbolic language or formalism for the learned knowledge. A variety of representations were proposed, including complex logical formalisms (McCarthy and Hayes, 1969), semantic frames as proposed by Minsky (1975), and simpler feature-based representations. Early symbolic AI work led to a number of specialized systems carrying out practical functions. Winograd's SHRDLU system (1972) could, using restricted natural language, discuss and carry out tasks in a simulated blocks world. CHAT-80 could answer geographical questions posed to it in natural language (Warren and Pereira, 1982). DENDRAL , developed from 1965 to 1983 in the field of organic chemistry, proposed plausible structures for new organic compounds (Buchanan and Feigenbaum, 1978). MYCIN, developed from 1972 to 1980, diagnosed infectious diseases of the blood, and prescribed appropriate antimicrobial therapy (Buchanan and Shortliffe, 1984). However, these systems notably lacked the ability to generalize, performing effectively only in the narrow domains for which they were engineered. Modern symbolic AI systems seek to achieve greater generality of function and more robust learning ability via sophisticated cognitive architectures. Many such cognitive architectures focus on “working memory” that draws on long-term memory as needed, and utilize a centralized control over perception, cognition and action. Although in principle such architectures could be arbitrarily capable (since symbolic systems have universal representational and computational power, in theory), in practice symbolic architectures tend to be less developed in learning, creativity, procedure learning, and episodic memory. Leading examples of symbolic cognitive architectures include ACT-RT (Anderson et al, 2004), originally founded on a model of human semantic memory; Soar (Laird, 2012), which is based on the application of production systems to solve problems defined as residing in various problem spaces, and which has recently been extended to include perception, episodic memory, and a variety of other cognitive functions; and Sigma, which applies many of Soar's architectural ideas using a probabilistic network based knowledge representation (Rosenbloom, 2013). ## Emergentist AGI Another species of AGI design expects abstract symbolic processing – along with every other aspect of intelligence – to emerge from lower-level “subsymbolic” dynamics, which sometimes (but not always) are designed to simulate neural networks or other aspects of human brain function. Today’s emergentist architectures are sometimes very strong at recognizing patterns in high-dimensional data, reinforcement learning and associative memory; but no one has yet shown how to achieve high-level functions such as abstract reasoning or complex language processing using a purely subsymbolic, emergentist approach. The broad concepts of emergentist AI can be traced back to Norbert Wiener's Cybernetics (1948), and more directly to the 1943 work of McCulloch and Pitts (1943), which showed how networks of simple thresholding "formal neurons" could be the basis for a Turing-complete machine. In 1949, Donald Hebb wrote The Organization of Behavior (Hebb, 1949), hypothesizing that neural pathways are strengthened each time they are used, a concept now called "Hebbian learning", conceptually related to long-term potentiation in the brain and to a host of more sophisticated reinforcement learning techniques (Sutton and Barto, 1998; Wiering and van Otterlo, 2012). In the 1950s practical learning algorithms for formal neural networks were articulated by Marvin Minsky (1952) and others. Rosenblatt (1958) designed "Perceptron" neural networks, and Widrow and Hoff (1962) presented a systematic neural net learning procedure that was later labeled "back-propagation." These early neural networks showed some capability to learn and generalize, but were not able to carry out practically impressive tasks. A comprehensive history of the early and recent history of the neural network field is given in (Schmidhuber, 2014). An alternate approach to emergentist AI that emerged in the late 1960s and 1970s was evolutionary computing, centered on the genetic algorithm, a computational model of evolution by natural selection. John Holland's learning classifier system combined reinforcement learning and genetic algorithms into a cognitive architecture with complex, self-organizing dynamical properties (Holland, 1975). A learning classifier system consists of a population of binary rules on which a genetic algorithm (roughly simulating an evolutionary process) alters and selects the best rules. Rule fitness is based on a reinforcement learning technique. In 1982, broad interest in neural net based AI began to resume, triggered partly by a paper by John Hopfield of Caltech (Hopfield, 1982), explaining how completely connected symmetric neural nets could be used to store associative memories. In 1986, psychologists Rumelhart and McClelland (1986) popularized the extension of the Widrow-Hoff learning rule to neural networks with multiple layers (a method that was independently discovered by multiple researchers). Currently neural networks are an extremely popular machine learning technique with a host of practical applications. Multilayer networks of formal neurons or other conceptually similar processing units have become known by the term "deep learning" and have proved highly successful in multiple areas including image classification, object detection, handwriting recognition, speech recognition, machine translation, and many other fields (e.g., Schmidhuber, 2015; Bengio, 2014). Today they are often referred to by the popular term “Deep Learning.” An important subset of emergentist cognitive architectures, still at an early stage of advancement, is developmental robotics, which is focused on controlling robots without significant “hard-wiring” of knowledge or capabilities, allowing robots to learn (and learn how to learn etc.) via their engagement with the world. A significant focus is often placed here on “intrinsic motivation,” wherein the robot explores the world guided by internal goals like novelty or curiosity, forming a model of the world as it goes along, based on the modeling requirements implied by its goals. Some of the foundations of this research area were laid by Juergen Schmidhuber’s work in the 1990s (Schmidhuber, 1991), but now with more powerful computers and robots the area is leading to more impressive practical demonstrations. ## Hybrid AGI In response to the complementary strengths and weaknesses of the other existing approaches, a number of researchers have turned to integrative, hybrid architectures, which combine subsystems operating according to the different paradigms. The combination may be done in many different ways, e.g. connection of a large symbolic subsystem with a large subsymbolic system, or the creation of a population of small agents each of which is both symbolic and subsymbolic in nature. One aspect of such hybridization is the integration of neural and symbolic components (Hammer and Hitzler, 2007). Hybrid systems are quite heterogenous in nature, and here we will mention three that are relatively representative; a longer list is reviewed in (Goertzel, 2014). A classic example of a hybrid system is the CLARION (Connectionist Learning with Adaptive Rule Induction On-line) cognitive architecture created by Ron Sun (2002), whose design focuses on explicitly distinguishing implicit versus explicit processes, and capturing the interaction between these two process types. Implicit processes are modeled as neural networks, whereas explicit processes are modeled as formal symbolic rules. CLARION involves an action-centered subsystem whose job is to control both external and internal actions; its implicit layer is made of neural networks called Action Neural Networks, while the explicit layer has is made up of action rules. It also involves a non-action-centered subsystem whose job is to maintain general knowledge; its implicit layer is made of associative neural networks, while the bottom layer is associative rules. The learning dynamics of the system involves ongoing coupling between the neural and symbolic aspects. The LIDA architecture (Faghihi and Franklin, 2012), developed by Stan Franklin and his colleagues, is closely based on cognitive psychology and cognitive neuroscience, particularly on Bernard Baars' Global Workspace Theory and Baddeley's model of working memory. LIDA's dynamics are based on the principles that: 1) Much of human cognition functions by means of frequently iterated (~10 Hz) interactions, called cognitive cycles, between conscious contents, the various memory systems and action selection, 2) These cognitive cycles, serve as the “atoms” of cognition of which higher-level cognitive processes are composed. LIDA contains components corresponding to different processes known to be associated with working and long-term memory (e.g. an episodic memory buffer, a sensory data processing module, etc.), and utilizes different AI algorithms within each of these components. The CogPrime architecture (Goertzel et al, 2013), implemented in the OpenCog AI software framework, represents symbolic and subsymbolic knowledge together in a single weighted, labeled hypergraph representation called the Atomspace. Elements in the Atomspace are tagged with probabilistic or fuzzy truth values, and also with short and long term oriented "attention values." Working memory is associated with the subset of Atomspace elements possessing the highest short term importance values. A number of cognitive processes, including a probabilistic logic engine, an evolutionary program learning framework and a neural net like associative and reinforcement learning system, are configured to concurrently update the Atomspace, and designed to aid each others' operation. # Future of the AGI Field The field of AGI is still at a relatively early stage of development, in the sense that nobody has yet demonstrated a software or hardware system that is broadly recognized as displaying a significant degree of general intelligence, or as being near general-purpose human-level AI. No one has yet even demonstrated a compelling "proto-AGI" system, such as e.g.: a robot that can do a variety of preschool-type activities in a flexible and adaptive way; or a chatbot that can hold an hour’s conversation without sounding bizarre or resorting to repeating catch-phrases. Furthermore, there has not yet emerged any broadly accepted theory of general intelligence. Such a theory might be expected to include a characterization of what general intelligence is, and a theory of what sorts of architecture can be expected to work for achieving human-level AGI using realistic computational resources. However, a significant plurality of experts believes there is a possibility of dramatic, interlinked progress in AGI design, engineering, evaluation and theory in the relatively near future. For example, in a survey of researchers at the AGI-2010 conference, the majority of respondents felt that human-level AGI was likely to arise before 2050, and some were much more optimistic (Baum et al, 2011). Similarly, a 2014 poll among AI experts (Mueller and Bostrom, 2014) at various conferences showed a broad agreement that AGI systems will likely reach overall human ability (defined as "ability to carry out most human professions at least as well as a typical human") around the middle of the 21st century. The years 2013 and 2014 also saw sharply heightened commercial activity in the AI space, which is difficult to evaluate in terms of its research implications, but indicates a general increase in interest in the field. The possibility of a relatively near-term advent of advanced AGI has led some researchers and other observers to express concern about the ethics of AGI development and the possibility of "existential risks" associated with AGI. A number of recently-formed research institutes have emerged, placing significant focus on this topic, e.g. the Machine Intelligence Research Institute (formerly the Singularity Institute for AI), Oxford University's Future of Humanity Institute, and Cambridge University's Center for the Study of Existential Risk (CSER). The dramatic potential benefits of AGI, once it is achieved, has been explored by a variety of thinkers during the past decades. I.J. 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B.; and Silver, D. (2011) . A Monte-Carlo AIXI Approximation. J. Artif. Intell. Res. 40, 95–142. • Vinge, Vernor (1993). "The Coming Technological Singularity: How to Survive in the Post-Human Era", originally in Vision-21: Interdisciplinary Science and Engineering in the Era of Cyberspace, G. A. Landis, ed., NASA Publication CP-10129, pp. 11–22 • Wang, Pei (2006). Rigid Flexibility: The Logic of Intelligence. Springer. • Warren, D.H.D. and Pereira, F.C.N. (1982). An efficient easily adaptable system for interpreting natural language queries. Computational Linguistics, 8(3-41) • Widrow, B. and M.E. Hoff (1962). Associative Storage and Retrieval and Digital Information in networks of adaptive neurons. In EE Bernard and MR Kare, Ed., “Biological prototypes and synthetic systems”, v.1 p. 160. New York, Plenum press. • Wiener, Norbert (1948). Cybernetics: Or Control and Communication in the Animal and the Machine. MIT Press.	2019-04-22 22:06:17	{"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": 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": 0.4514751732349396, "perplexity": 3602.8206129807336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578582736.31/warc/CC-MAIN-20190422215211-20190423001211-00299.warc.gz"}
https://math.stackexchange.com/questions/4136831/give-an-example-of-set-with-irrational-numbers-which-has-measure	# Give an example of set with irrational numbers which has measure … [closed] Task: Give an example of closed set $$A \subset [0,1]$$, which only consists of irrational numbers and has measure not less than $$0.9$$ . I just have started taking course of Lebesgue measure. I found this task in my book, and can't get it out of my mind. I would really appreciate if you could help me solve this. Thanks in advance. • If I understand your question correctly you can simply take the set of irrationals $I\mathbb{R}$ and then $A=I\mathbb{R}\cap[0,1]$ has measure $1>0.9$, because countable subsets like $\mathbb{Q}$ have measure $0$. – freakish May 12 at 20:51 • Of possible historical interest is that in 1884 (a time in which Cantor sets had only appeared in 3 or 4 papers), Ludwig Scheeffer (1859-1885) proved on pp. 291-293 of Zur Theorie der Stetigen Funktionen einer Reellen Veränderlichen that for each (generalized) Cantor set $C,$ there exists a dense set (hence, an infinite set) of real numbers $r$ such that the $r$-translate of $C$ contains no rational numbers. (continued) – Dave L. Renfro May 12 at 21:51 • For more such results, see this 11 May 2000 sci.math post. – Dave L. Renfro May 12 at 21:52 • @freakish: your set $A$ is not closed. – TonyK May 13 at 9:58 Pick your favourite enumeration $$(q_n)$$ of the rationals in $$[0,1]$$, and define the set $$S=\cup (q_n-\epsilon^n,q_n+\epsilon^n)$$ Then $$S$$ is open, so the complement of $$S$$ in $$[0,1]$$ is closed and contains only irrational numbers; and you can make the measure of $$S$$ as small as you like by choosing small enough $$\epsilon$$. • This is not an example. – ajotatxe May 12 at 20:17 • Sure it is. ${}{}$ – copper.hat May 12 at 20:17 • TonyK has proved the existence of such a set, but he hasn't defined any set. I insist: this is not an example. – ajotatxe May 12 at 20:18 • That does not mean that the set is not defined. – copper.hat May 12 at 20:23 • @ajotatxe: I'm suggesting that I don't know if $1/e$ or $1/\pi$ are in that set or not --- No one presently knows whether either of these numbers belongs to the set $E$ consisting of all real numbers whose decimal expansions contain at most finitely many $2$'s, and $E$ is about as explicitly definable (from decimal representations of reals) as possible without being trivial. – Dave L. Renfro May 12 at 20:47 We are going to start with $$[0,1]$$ and then remove an open ball around each rational point in the range $$[0,1]$$ so that the the remaining set is closed and has no rational points. If the sum of all of the diameters is less than $$0.1$$ then our set will have measure at least $$0.9$$. We know that the set of rational numbers in that interval is countable, so let the rational numbers be $$q_1,q_2,\dots$$ We just need to select diameters $$d_i$$ such that $$\sum\limits_{i=1}^\infty d_i < 0.1$$ We can take $$d_i = \frac{1}{10\cdot 2^i}$$ • As the sum is not finite I would suggest writing $\infty$ at the top of the sum or take the limit of the sum. Besides that the solution seems fine – LegNaiB May 12 at 20:26 • Oh yes, thank you ! – sorryifslow May 12 at 20:27	2021-06-20 21:19:42	{"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 18, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7911134958267212, "perplexity": 261.1487678755736}, "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/1623488257796.77/warc/CC-MAIN-20210620205203-20210620235203-00369.warc.gz"}
http://math.stackexchange.com/questions/209148/why-is-a-normal-subgroup-containing-phi-g-with-a-nilpotent-factor-group-nil	# Why is a normal subgroup containing $\Phi (G)$ with a nilpotent factor group nilpotent? At page (28) of chapter I of the book Finite Group Theory by I.Martin.Issacs, one finds: Let $G$ be a finite group, with Frattini subgroup $\Phi$. If $\Phi \subseteq N \vartriangleleft G$, and if $N/ \Phi$ is nilpotent, then $N$ is nilpotent. I know that this is in fact a generalisation of two preceding exercises, but I could not prove it: I have tried to construct a central series of $N$ from that of $N/ \Phi$, but failed to do so. I also tried in the direction of showing that maximal subgroups of $N$ are normal in $N$, but thus far found nothing interesting. As this is a generalisation of one exercise which deploits of the Frattini arguments, I wanted to avail myself of that argument as well, while finding nothing critical either. Therefore I post here for some help. Sincere thanks. - Can you prove/use that the Frattini subgroup of a finite group is nilpotent? – DonAntonio Oct 8 '12 at 10:35 Yes, that has already been proven. – awllower Oct 8 '12 at 10:38 I mean it has been proven by previous exercises... – awllower Oct 8 '12 at 10:45 We know that a finite group $\,G\,$ is nilpotent iff all its Sylow $\,p-\,$ subgroups are normal, so this is what we're going to try to prove for $\,N\,$, so let $\,P\,$ be any Sylow $\,p-\,$subgroup of $\,N\,$ . Putting $\,\Phi(G):=\Phi\,$ for simplicity, define $\,K:=P\Phi\leq N\,$ . Then $\,K/\Phi\,$ is a Sylow $\,p-\,$subgroup of $\,N/\Phi\,$ and since the last group is nilpotent then $\,K/\Phi\,\operatorname{char}\,N/\Phi\triangleleft G/\Phi\Longleftrightarrow K\triangleleft G\,$ (Remember that a finite group is nilpotent iff all its Sylow subgroups are normal, and in fact, characteristic). Now use Frattini's Argument: $$G=N_G(P)K=N_G(P)\Phi\Longrightarrow G=N_G(P)\Longleftrightarrow P\triangleleft G\Longrightarrow P\triangleleft N$$ and were done. - Thanks very much: I did not come across the part that $K/ \Phi$ is a Sylow subgroup, thus is normal. Thanks for the answer. – awllower Oct 8 '12 at 18:07 By the way, the point you referred to in your comment is not used here. Perhaps you wanted to apply it somehow? – awllower Oct 8 '12 at 18:08 Yes, I know. I wrote below my original comment about this (that this seemed hopeless) but somehow the comment never showed up. – DonAntonio Oct 9 '12 at 3:03	2014-03-11 16:54:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9124875068664551, "perplexity": 293.02848560123783}, "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/1394011232483/warc/CC-MAIN-20140305092032-00058-ip-10-183-142-35.ec2.internal.warc.gz"}
http://cicadacrafts.com/how-do-sgqm/how-do-you-produce-italicized-text-in-r-markdown-6010cb	## how do you produce italicized text in r markdown You can indicate emphasis with bold, italic, or strikethrough text. The data are described by two readme files. Try it out with this file on RStudio Cloud. If you enter text with Markdown syntax, the formatting will not render and the text will remain as is. You can use Pandoc’s Markdown to make: Read more about markdown at Pandoc’s Markdown or consult the quick reference in the R … Various packages, e.g. A markdown cell can display header text of 6 sizes, similar to HTML headers. Other than the formatting characters supplied by Markdown, can't apply specific styles to individual text elements within a markdown-formatted block of text. In PDF output, a level-five heading will turn into a paragraph heading, i.e. R Markdown supports a reproducible workflow for dozens of static and dynamic output formats including HTML, PDF, MS … It means single # will render biggest header line, and six # symbols renders header of smallest font size. Line Breaks: Markdown ignores traditional line breaks. Ignore the Notes.html file and commit the Notes.Rmd and .gitignore files with the commit message "Added notes for R Markdown article". bold, heading 1, heading 2) in a word processing tool like Microsoft Word or Google … To create a sublist, indent the values a bit (at least four spaces or a tab): The official Markdown way to create line breaks is by ending a line with more than two spaces. Use multiple languages including R, Python, and SQL. Now you're a Discord text markdown expert. That way, someone in the future can come along and easily see what worked for you. 4. How Do You Use Markdown? To write a math expression that will be shown inline, enclose it in dollar signs. to highlight a key work or phrase from the text. If you are knitting to an html document than you can use HTML tags in the document. Rocket Chat desktop), and as a best practice, hyperlinks are best designated in conjunction w/ a color change (or increasingly prevalent, a color change and no underlining). However, italic seems not to play well with lists: If you render this file, you'll see that the list is not rendered as, well, a list. Yep, there's a box, usually, but I cannot see it now. When cells are run, the outpu… Regular Markdown doesn't look any different than regular text, but we're providing some highlighting to make it easier to see. Be careful with your spacing in Markdown documents. In the text you wrote for the exercise above, use a text modifier (bold, italic, etc.) Format the text in your R Markdown file with Pandoc’s Markdown, a set of markup annotations for plain text files. I am writing a book in bookdown, Chapman & Hall style, and my problem is that text does not generate bold text in the html output. To make a phrase italic in Markdown, you can surround words with an underscore (_). We have to insert the text to marked in Italics in between a pair a single underscore. text (italic) is OK in html, as is \textbf{text} (bold), but that is too clumsy for my taste. In these lessons, you'll notice some formatted red text; this text is actually written in Markdown! What is R Markdown? As for accepting the answer, you can see this post by @mara about how to accept an answer: If your question has been answered, would you mind marking the solution? \tag{1.1} This will create a file called my_first_rmarkdown.pdf which you … Also, markdown has been deprecated in the Zendesk Agent Workspace, except in agent signatures. … There are only a small number of things … that we can do with text. The YAML Header. It works. Script contains a mixture of text and R code, which is when processed replaced by text and output, including figures and tables Uses R as programming language and a documentation language (LateX, Markdown) Inline R code within the text and separate code chunks Advantage: you do not need to copy and paste your R output anymore! If you want to knit your .Rmd file to a pdf document then all you need to do is choose knit to PDF instead of knit to HTML when you click on the knit icon. For this next lesson, make the word "not" italic. Block Quotes: If you would like to place quotes in your panel, use the greater than symbol (>). When you format text using Markdown in a document, it is similar to using the format tools (e.g. This: $$A = \pir^{2}$$. 1 R Markdown Basics: The Markdown syntax. Marking certain text to Italics is quite similar to what we do to mark text in bold. Specifically, it's formatted according to … the rules of pandot flavored markdown. \paragraph{My level-five heading}, which appears as bold text on the same line as the subsequent paragraph. Use as many # symbols corresponding to level of header you want. At the top of any RMarkdown script is a YAML header section enclosed by ---. So inline coding is really useful if you want to do calculations within your text or insert values into text, say from a dataframe, to make an informative sentence. Great, you’ve just rendered your first R markdown document. Hi, yes, I tried but it doesn't work. How to Underline Text in Discord. What is Markdown? If you have any of your own R scripts that you would like to make into an R Markdown document, you can also use those! \], For more (e.g. You can underline text in Discord as a way to add subtle prominence to messages, as an alternative to bold or italics. However, the pdf version looks fine. The rendering will take place when you run the cell either from cell menu or run button of toolbar. Bold This is how you bold* text. That is, . Of course, the dots I used don't achieve the goal. This is how you bold text. All text from >>> until the end of the message will be included in the quote. \], To include an actual , _ or \, add another \ in front of them: \, \_, \\. Get out there and highlight your statements! For example, _this_ word would become italic. Yes, it is. Of course, you can combine those two formats, with both bold and italicized text, using any combination of the above syntax. Also, is there a way to include empty list items in a list, and skip directly to item 26 in my case? This appears on the same line in the output, because we didn’t add spaces after red. I'm writing an R Markdown document about a data analysis I'm doing. Select the class of output you would like to make with your .Rmd file • Select the specific type of output to make with the radio buttons (you can change this later) • Click OK i. R Markdown provides the flexibility of Markdown with the implementation of R input and output. Is that an HTML tag for italic? Line breaks Sometimes markdown doesn’t make line breaks when you want them. Write iii. Unordered list by starting a line with an * or a -: Ordered lists by starting a line with a number: Notice that you can mislabel the numbers and Markdown will still make the order right in the output. You can test it yourself: there was a small error in my R Markdown, but now my code is reproducible. Therefore, this line starts its own paragraph. File New File R Markdown… • A window will open. When you use Markdown in dotCMS, dotCMS automatically applies standard styling to your Markdown-formatted text based on a pre-defined style sheet that ships with dotCMS. In each of the below sections, you'll find the markdown split over two lines: The first line, in this format, shows the markdown being used. This is how you italicise text. … We can make it bold, italic, code formatted, … however, we can also include hyperlinks. > at the beginning of a line of text, creates a single-line block quote. I find this is confusing, so I recommend the alternative way: Ending a line with a backslash will also create a linebreak: To create a new paragraph, you put a blank line. Following screenshot shows markdown cells in edit mode with headers of three different levels. To create a heading, add one to six # symbols before your heading text. The data are described by two readme files. Use a productive notebook interface to weave together narrative text and code to produce elegantly formatted output. Turn your analyses into high quality documents, reports, presentations and dashboards with R Markdown. The first one is very short, so I just use the citation formatting. If you’re the OP (as you were in this case), there should be a little box at the bottom of replies that you can click to select that response as your “solution.”. [^a-random-footnote-label]: This is a random test. … For example, to format text in italics, you put underscores around it like so: _this is some text in italics_. When you use markdown in a story or epic description or comment field, you can click the Previewtab to see how the markdown will render after you save your changes. Note: Markdown is not available in emails and email templates. To write comments within your text that won’t actually be included in the output, use the same syntax as for writing comments in HTML. Nearly all Markdown applications support the basic syntax outlined in John Gruber’s original design document. And you get the idea! # The largest heading ## The second largest heading ##### The smallest heading Styling text. There are minor variations and discrepancies between Markdown processors — those are noted inline wherever possible. The number of hash symbols can be 1 to 6: Output: \tag{1.1} ii. The first one is very short, so I just use the citation formatting. Embed- Write … For more details on using R Markdown see http://rmarkdown.rstudio.com. how to theorems), see e.g. If you want to do this, you’ll need to add two underscores (__) at the start and end of your Discord message. Here is a brief introduction to using R Markdown. To use Markdown, you just apply simple tags to your text. >>> at the beginning of a line of text, creates a multi-line block quote. Edit modePreview mode Italics This is how you italicise text. Surround text with a grave accent () also called a back single quotation mark, for example: string You can use the monospace font for file paths, file names, message text that users see, or text that users enter. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents and much, much more. The second line shows the visual effect of the markdown. The number of # you use will determine the size of the heading. \[ Make your task stand out in bold, spice up your project names with emojis or change the hyperlinked text in your comments. To display a line break in your post, place two spaces at the end of the line, or use a double line break to start a new paragraph (hit Enter twice). A smaller header starts with more hash symbols. Hi, I'm writing an R Markdown document about a data analysis I'm doing. I am on Ubuntu with everything the latest version. As a habit, try to keep everything left aligned whenever possible, especially as you type a new paragraph. f\left(k\right)=\binom{n}{k}p^k\left(1-p\right)^{n-k} Todoist uses the CommonMark specification across all platforms. When you render your file, Pandoc transforms the marked up text into formatted text in your final file format, as below. R Markdown provides the flexibility of Markdown with the implementation of R … Headers can be a variety of sizes. Well underlining in markup predates the web/hyperlinks, so how 'bout a lil' respect for us old guys :) Plus, Markup can be used in apps other than web-based (e.g. Markdown is a human readable syntax (also referred to as a markup language) for formatting text documents.Markdown can be used to produce nicely formatted documents including PDFs and web pages.. … Let's demonstrate how we can do that … in our exercise files. The second is much longer, and contains a numbered list, so I decided to use italic instead than citation. f\left(k\right)=\binom{n}{k}p^k\left(1-p\right)^{n-k} PS I would like to accept your post as answering my question, but apparently I can't. R Markdown files. Sub2 and super2 script is created like this~2~ and this^2^. By default this includes a title, author, date and the file type you want to output to. In other words, there is no need to indent basic text in the Rmd document (in fact, it might cause your text to do funny things if you do). We will look at more complex examples later in the labs but again this is a really useful tool for writing manuscripts through R Markdown the more comfortable you get with it. To create numbered equations, put them in an ‘equation’ environment and give them a label with the syntax (\#eq:label), like this: Becomes: This appears with a line break because I added spaces after red. Here is a brief introduction to using R Markdown. R Markdown is an authoring format that enables easy creation of dynamic documents, presentations, and reports from R. It combines the core syntax of markdown (an easy-to-write plain text format) with embedded R code chunks that are run so their output can be included in the final document. Well, consider your answer accepted, Powered by Discourse, best viewed with JavaScript enabled, Problem Uploading a .csv File into RStudio. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents and much, much more. R Markdown gives us all of the formatting options available for Markdown plus the ability to embed, display, and run R code in our documents. Perfect! rmarkdown, knitr, pandoc, etc., work behind the scenes to knit all those pieces into one coherent whole, in whatever format is desired. - This: $A = \pir^{2}$ Becomes: $$A = \pir^{2}$$, To write a math expression that will be shown in a block, enclose it in two dollar signs. Open - Open a file that uses the .Rmd extension. Have you tried using a single * on either side of the list? Start the text in markdown cell by # symbol. In this course, we will use a specific ‘flavor’ of Markdown called ‘R Markdown’. 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( bold, spice up your project names with emojis or change the hyperlinked text italics.	2021-02-27 01:06:08	{"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": 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": 0.47409072518348694, "perplexity": 2982.085297143417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358033.38/warc/CC-MAIN-20210226234926-20210227024926-00469.warc.gz"}
https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.tsa.multi_corrmat_cross.html	# naginterfaces.library.tsa.multi_corrmat_cross¶ naginterfaces.library.tsa.multi_corrmat_cross(matrix, m, w)[source] multi_corrmat_cross calculates the sample cross-correlation (or cross-covariance) matrices of a multivariate time series. For full information please refer to the NAG Library document for g13dm https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/g13/g13dmf.html Parameters matrixstr, length 1 Indicates whether the cross-covariance or cross-correlation matrices are to be computed. The cross-covariance matrices are computed. The cross-correlation matrices are computed. mint , the number of cross-correlation (or cross-covariance) matrices to be computed. If in doubt set . However it should be noted that is usually taken to be at most . wfloat, array-like, shape must contain the observation , for , for . Returns wmeanfloat, ndarray, shape The means, , for . r0float, ndarray, shape If , then contains an estimate of the th element of the cross-correlation (or cross-covariance) matrix at lag zero, ; if , then if , contains the variance of the th series, , and if , contains the standard deviation of the th series, . If = 2 and , then on exit all the elements in whose computation involves the zero variance are set to zero. rfloat, ndarray, shape contains an estimate of the ()th element of the cross-correlation (or cross-covariance) at lag , , for , for , for . If = 2 and , then on exit all the elements in whose computation involves the zero variance are set to zero. Raises NagValueError (errno ) On entry, and . Constraint: and . (errno ) On entry, . Constraint: . (errno ) On entry, . Constraint: . (errno ) On entry, . Constraint: or . Warns NagAlgorithmicWarning (errno ) On entry, at least one of the series is such that all its elements are practically identical giving zero (or near zero) variance. Notes Let , for , denote observations of a vector of time series. The sample cross-covariance matrix at lag is defined to be the matrix , whose ()th element is given by where and denote the sample means for the th and th series respectively. The sample cross-correlation matrix at lag is defined to be the matrix , whose th element is given by The number of lags, , is usually taken to be at most . If follows a vector moving average model of order , then it can be shown that the theoretical cross-correlation matrices are zero beyond lag . In order to help spot a possible cut-off point, the elements of are usually compared to their approximate standard error of 1/. For further details see, for example, Wei (1990). The function uses a single pass through the data to compute the means and the cross-covariance matrix at lag zero. The cross-covariance matrices at further lags are then computed on a second pass through the data. References Wei, W W S, 1990, Time Series Analysis: Univariate and Multivariate Methods, Addison–Wesley West, D H D, 1979, Updating mean and variance estimates: An improved method, Comm. ACM (22), 532–555	2022-01-24 22:41:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9765486121177673, "perplexity": 1914.2205003780027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00283.warc.gz"}
https://www.gradesaver.com/textbooks/math/calculus/thomas-calculus-13th-edition/chapter-15-multiple-integrals-section-15-7-triple-integrals-in-cylindrical-and-spherical-coordinates-exercises-15-7-page-921/67	## Thomas' Calculus 13th Edition $\bar x=\bar y=0$ We calculate the center of mass as follows: First calculate the mass: $M=4\int^{\pi/2}_0 \int^1_0 \int^r_0$ dz r dr $d\theta$ =$4\int^{\pi/2}_0 \int^1_0 r^2$ dr $d\theta$ =$\frac{4}{3}\int^{\pi/2}_0 d\theta$ =$\frac{2\pi}{3}$ Now calculate the moment: $M_{xy}$= $\int^{2\pi}_0 \int^1_0 \int^r_0$ z dz r dr $d\theta$ =$\frac{1}{2}\int^{2\pi}_0 \int^1_0 r^3 dr d\theta$ =$\frac{1}{8} \int^{2\pi}_0 d\theta$ =$\frac{\pi}{4}$ And take the ratio: $\frac{M_{xy}}{M}=(\frac{\pi}{4})(\frac{3}{2\pi})=\frac{3}{8}$ Thus, we have (by symmetry): $\bar x=\bar y=0$	2019-12-14 18:10:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9478361010551453, "perplexity": 985.2282489708334}, "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/1575541288287.53/warc/CC-MAIN-20191214174719-20191214202719-00537.warc.gz"}
http://arxiv-cs.tumblr.com/post/30842808044/influence-of-mg-ag-and-al-substitutions-on-the	# Computer Science from the arXiv curated by isomorphisms ### Influence of Mg, Ag and Al substitutions on the magnetic excitations in the triangular-lattice antiferromagnet CuCrO2. Magnetic excitations in CuCrO$\large \dpi{100} \bg_white _{2}$, CuCr$\large \dpi{100} \bg_white _{0.97}$Mg$\large \dpi{100} \bg_white _{0.03}$O$\large \dpi{100} \bg_white _{2}$, Cu$\large \dpi{100} \bg_white _{0.85}$Ag$\large \dpi{100} \bg_white _{0.15}$CrO$\large \dpi{100} \bg_white _{2}$, and CuCr$\large \dpi{100} \bg_white _{0.85}$Al$\large \dpi{100} \bg_white _{0.15}$O$\large \dpi{100} \bg_white _{2}$ have been studied by powder inelastic neutron scattering to elucidate the element substitution effects on the spin dynamics in the Heisenberg triangular-lattice antiferromagnet CuCrO$\large \dpi{100} \bg_white _{2}$. The magnetic excitations in CuCr$\large \dpi{100} \bg_white _{0.97}$Mg$\large \dpi{100} \bg_white _{0.03}$O$\large \dpi{100} \bg_white _{2}$ consist of a dispersive component and a flat component. Though this feature is apparently similar to CuCrO$\large \dpi{100} \bg_white _{2}$, the energy structure of the excitation spectrum shows some difference from that in CuCrO$\large \dpi{100} \bg_white _{2}$. On the other hand, in Cu$\large \dpi{100} \bg_white _{0.85}$Ag$\large \dpi{100} \bg_white _{0.15}$CrO$\large \dpi{100} \bg_white _{2}$ and CuCr$\large \dpi{100} \bg_white _{0.85}$Al$\large \dpi{100} \bg_white _{0.15}$O$\large \dpi{100} \bg_white _{2}$ the flat components are much reduced, the low-energy parts of the excitation spectra become intense, and additional low-energy diffusive spin fluctuations are induced. We argued the origins of these changes in the magnetic excitations are ascribed to effects of the doped holes or change of the dimensionality in the magnetic correlations.	2013-05-22 20:00:31	{"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": 0, "img_math": 0, "codecogs_latex": 22, "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": 0.6146255135536194, "perplexity": 2556.6753120694566}, "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/1368702444272/warc/CC-MAIN-20130516110724-00053-ip-10-60-113-184.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/168980/motivation-for-studying-quadratic-algebras-koszul-algebras-koszul-duality	# Motivation for studying quadratic algebras, Koszul algebras, Koszul duality I'm trying to gain a practical understanding of Koszul duality in different areas of mathematics. Searching the internet, there's lots of homological characterisations and explanations one finds, but I would like concrete examples of where Koszul duality is either a nice way of looking at a result, or where it provides us with new results. If someone were to be able to explain for example: 1. Why is the Ext-algebra (Yoneda-algebra) (and the way it characterizes Koszulity) useful? 2. Is there a more elementary way of explaining some of the results and applications in the Beilinson-Ginzburg-Soergel paper Koszul duality patterns in representation theory? 3. I find it hard to grasp Manin's motivations for viewing quadratic algebras as noncommutative spaces, cfr. "Quantum groups and noncommutative geometry". Can anyone comment on this? 4. What are the applications of Koszul algebras? Example: I know that by a result of Fröberg every projective variety has a homogeneous coordinate ring that is Koszul, but what does this do for us really? Those are some of the examples that spring to mind, but feel free to add other phenomena. Also, let me know if you think there's a way to improve this question. - see: mathoverflow.net/questions/329/what-is-koszul-duality and Polishchuk and Positselski's book Quadratic Algebras in general, math.stackexchange.com/questions/64064/… for q1. I think this is way too broad, someone could write a long expository article about each of your four questions. Generally speaking, Koszul algebras are special because calculating Ext rings is hard and even writing down tractable projective resolutions is hard whereas once you know something is Koszul, you get them for free. – mt_ Jul 10 '12 at 10:30 as above comment said, there are way too broad to say why Koszul algebras are nice and a good theory to study. Concerning partiuclar questions: (q1) you can also look into Prof. Keller's "Introduction to A-infinitey algebras and modules", which contains material why we are interested in Ext-algebra of a (dg/A-infinity) module $M$. (For $M = A_0$, and $A$ satisfy certain conditions, then this is the Koszul dual). – Aaron Jul 10 '12 at 14:53 For (q2), IMO, BGS is already quite elementary to most students studying representation theory, if you discard the geometric part of the paper. Their core motivation lies in the relations between category $\mathcal{O}$ of complex semisimple Lie algebra and parabolic analogue of category $\mathcal{O}$, namely they are of derived equivalence. Once we have a derived equivalence, the homological behaviour of the two categories are much easier to understand by virtue of Koszul theory. BGS's work is also important to people who studies Kazhdan-Lusztig polynomial. – Aaron Jul 10 '12 at 14:59 The BGS paper is also one of the most celebrated articles which unite representation theory with the graded setting. And it gives criteria to how one could determine a positively graded algebra is Koszul. Rewritten many of the complication in studying Koszul theory. This has become the first step into generalising Koszul theory to other type of Ext-algebras, by looking into graded structure of algebras, in much more elegant way. – Aaron Jul 10 '12 at 15:02 The Koszul complex and quadratic data arise in deformation quantization of quadratic Poisson structures: you can prove an important result on quantized realization via generators and relations of quadratic data, derived Morita theory of $A_{\infty}$-modules categories or introduce Koszul duality of exotic derived categories of dg structures. If you are interested in these topics you can read http://arxiv.org/abs/1206.2846 (derived Morita equivalence in the $A_{\infty}$ setting)	2014-03-08 04:48:57	{"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": 0.6602259278297424, "perplexity": 482.9613831158618}, "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/1393999653106/warc/CC-MAIN-20140305060733-00033-ip-10-183-142-35.ec2.internal.warc.gz"}
https://heavendesigners.com/how-to-read-a-caliper-in-inches/	The main scale reading is the amount of the vernier scale divisions that are completely passed by the vernier scale’s zero line. If you noticed, the handle of the caliper has a scale that starts from zero on the left and goes up to 6 inches on the right, in this case. Caliper – Google Search Vernier Caliper Vernier Measurement Tools ### The scale is generally given in inches, which is standard for measuring. How to read a caliper in inches. Digital calipers are used for measuring diameters, thicknesses, and lengths up to six inches. It also shows how to read an inch vernier caliper. An inch caliper allows you to make precise measurements to a thousandth (.001) of an inch. Each increment on the main scale represents 1/10 (.1) of an inch on an inch vernier caliper. Before you take a reading—and i mean before you take every reading—close the caliper and make sure the reading is 0.000. The main scale adds to the main number and one decimal place. You read the whole “inch” amount on the main scale, the whole tenth (.01) amount on the main scale, and then determine the thousandths portion of the measurement on the dial. Each increment equals one hundred thousandths (0.100”). The caliper logs are plotted in track 1 with the drilling bit size for comparison, or as a differential caliper reading, where the reading represents the caliper value minus the drill bit diameter (fig. If you noticed, the handle of the caliper has a scale that starts from zero on the left and goes up to 6 inches on the right, in. It is designed to take external linear measurements by contact. This video shows how to read vernier calipers that can be used for outside, inside, and depth measuremen. In this image, we are interested in the scale at the top. Dial caliper reading example 1. In case of metric units the smallest value that can be measured by the main scale is 1mm. A vernier caliper consists of two rulers: It is designed to take external linear measurements by contact. The blade scaleshows each inch divided into 10 increments. This video shows how to use a vernier caliper for outside, inside, and depth measurements. • each short line = 0.25 inches (25 thousands of an inch). Open the jaws about three quarters of an inch. For a vernier caliper whose vernier scale is divided in fractions of an inch ($\frac{1}{8}$, $\frac{1}{16}$,.), the instructions to read the vernier caliper is the same! Then use the thumb of your free hand to wipe off the mating surfaces of the jaws. The main scale contributes to the main number and one decimal place. In the paper industry, paper thickness is also expressed in points (a single point is.001″). The main scale and the sliding vernier scale. The following dial caliper has 10 divisions per 1″ on its main scale and 200 divisions per one full rotation on its dial scale. If the jaw moves for 2/10 inch (0.2″), the needle moves for one complete rotation. For example, a sheet of. Caliper is expressed in thousandths or hundred thousandths of an inch. Like the vernier caliper in the preceding column, the vernier above also reads to 1/1000 of an inch. Close the jaws and check that the indicator points to 0 on the dial face. Digital caliper is a linear measuring instrument with a cursor that slides on a ruler. Use, reading and interpretation of the universal caliper with fractional inch scale and vernier resolution 1/128 use and reading of universal caliper in fractional inch 1/128″ the universal caliper is a measuring instrument provided with a scale and a slider that slides on it. How to read dial caliper in inches a. The reading given by the main scale is 0.75 inches. Learn how to read an imperial, inch vernier caliper. A human hair is about 3 thousands of an inch (0.003), give or take a thousanth. 1 10 y 4 = 1 10 x 1 4 = 1 40 0.025 The readout is in inches and thousandths of. To find out the main scale reading look at the value on the scale directly on the left of the zero mark of the vernier scale. It is graduated in millimetres or inches. Some dial calipers have blade scales that are located above or below the rack. The main scale is obviously named because it is the primary scale of a vernier caliper. Basically, the thumb rule in reading vernier caliper is similar both for the inch and mm scale. Reading the caliper scale at 7 and the round dial at 56 means that the object is 756/1000 inches in width or diameter. Other calipers can be much longer in length. Each division between each tenth of an inch equals 0.25 inches. A human hair is about 3 thousands of an inch (0.003), give or take a thousanth. Will measure slightly more than 6 inches. 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http://mathhelpforum.com/calculus/49278-taylor-series-solution.html	# Math Help - Taylor Series solution 1. ## Taylor Series solution Hi all, I have to solve y" = x/y where y'(0)=1 & y(0)=2 By Taylor series method to get the value of y at x=0.1 and x=0.5. Use terms through x^5 but am having trouble enough solving the ODE to begin with. Any ideas would be most appreciated!! Cheers 2. Originally Posted by Watto81 Hi all, I have to solve y" = x/y where y'(0)=1 & y(0)=2 By Taylor series method to get the value of y at x=0.1 and x=0.5. Use terms through x^5 but am having trouble enough solving the ODE to begin with. Any ideas would be most appreciated!! Cheers Put $y(x)=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5 + ..$ and from the initial conditions you know that $a_0=2,\ a_1=1.$ Then: $ (a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5 + ..)(2a_2+6a_3x+12a_4x^2+20a_5x^3+..)=x $ Expand the left hand side as far as the term in $x^3$ (that will give you all the coefficients you will need to solve for the coefficients up to and including $a_5$) and equate coefficients of like powers of x on both sides. RonL 3. Thanks for the reply but you've lost me already. how does that solve the ODE? 4. Originally Posted by Watto81 Thanks for the reply but you've lost me already. how does that solve the ODE? You do not solve the ODE as such, you are working with a series solution which we suppose to be: $y(x)=\sum_{j=0}^{\infty}a_jx^j$ Then we explore the consequences of our supposition that this satisfies the ODE, in this case we have: $y(x)y''(x)=x$ We expand the product on the left using the assumed series, and then equate coefficients of like powers on both sides of this equation to solve for as many coefficients as we need. The initial conditions for the ODE provide us with starting values for the $a$'s (that is $a_0=y(0)$, and $a_1=y'(0)$ ). RonL 5. Yeah i've been looking at this with some friends and we're gonna need it explained like we're 2 yr olds as we can't get our heads around it at all. 6. Originally Posted by Watto81 Yeah i've been looking at this with some friends and we're gonna need it explained like we're 2 yr olds as we can't get our heads around it at all. I don't follow this completely, but the general idea is straightforward enough I think. Do you see that CaptainBlack just wrote a general Taylor expansion for y(x)? Then he took the second derivative for a few terms. You're D.E. says that yy''=x, so he multiplied these two series expansions. They are infinite expansions but you only need x^5 as your highest term, and when you multiply the LHS of course the powers will add so you really do not need that many terms. Does that part make sense? Writing y and y'' in terms of a general Taylor expansion. The only part I'm not seeing is when CB says after expanding the product on the LHS equating powers to get coefficients. Equating the product with what? Just x? 7. Originally Posted by Jameson I don't follow this completely, but the general idea is straightforward enough I think. Do you see that CaptainBlack just wrote a general Taylor expansion for y(x)? Then he took the second derivative for a few terms. You're D.E. says that yy''=x, so he multiplied these two series expansions. They are infinite expansions but you only need x^5 as your highest term, and when you multiply the LHS of course the powers will add so you really do not need that many terms. Does that part make sense? Writing y and y'' in terms of a general Taylor expansion. The only part I'm not seeing is when CB says after expanding the product on the LHS equating powers to get coefficients. Equating the product with what? Just x? The right hand side is also a power series which just happens to have only one non zero coefficient, so we are just equating coefficients of power series (in fact polynomials by that point). To be honest if I do much more of this problem I will have solved it for you, and that is not my intention. RonL 8. Originally Posted by CaptainBlack Put $y(x)=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5 + ..$ and from the initial conditions you know that $a_0=2,\ a_1=1.$ Then: $ (a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5 + ..)(2a_2+6a_3x+12a_4x^2+20a_5x^3+..)=x $ Expand the left hand side as far as the term in $x^3$ (that will give you all the coefficients you will need to solve for the coefficients up to and including $a_5$) and equate coefficients of like powers of x on both sides. RonL $ (2+x+a_2x^2+a_3x^3+a_4x^4+a_5x^5 + ..)(2a_2+6a_3x+12a_4x^2+20a_5x^3+..)=x $ so: $4a_2+x(12a_3+2a_2)+x^2(24a_4+6a_3+2a_2^2)+x^3(40a_ 5+12a_4+8a_2a_3) + ..=x$ Hence equating the coefficients of corresponding powers of x on both sides of this; we have: $4a_2=0$ $12a_3+2a_2=1$ $24a_4+6a_3+2a_2^2=0$ $40a_5+12a_4+8a_2a_3=0$ which you solve for the $a$'s RonL (Check the algebra!) 9. So i've equated the co-efficients, are these the values for y"', y"" & y""'? 10. Originally Posted by CaptainBlack $ (2+x+a_2x^2+a_3x^3+a_4x^4+a_5x^5 + ..)(2a_2+6a_3x+12a_4x^2+20a_5x^3+..)=x $ so: $4a_2+x(12a_3+2a_2)+x^2(24a_4+6a_3+2a_2^2)+x^3(40a_ 5+12a_4+8a_2a_3) + ..=x$ Hence equating the coefficients of corresponding powers of x on both sides of this; we have: $4a_2=0$ $12a_3+2a_2=1$ $24a_4+6a_3+2a_2^2=0$ $40a_5+12a_4+8a_2a_3=0$ which you solve for the $a$'s RonL (Check the algebra!) So we have $a_2=0,\ a_3=1/12,\ a_4=-1/48,\ a_5=1/160$, so we have: $ y(x)=2 + x + \frac{1}{12}x^3-\frac{1}{48}x^4+\frac{1}{160}x^5+.. $ so $y(0.1)\approx 2.10008$ and $y(0.5) \approx 2.50931$ RonL (again check the algebra) 11. Originally Posted by Watto81 So i've equated the co-efficients, are these the values for y"', y"" & y""'? No they are the coefficients of the corresponding powers of x in the power series expansion of y(x) RonL	2015-11-28 08:47:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 33, "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": 0.9066060781478882, "perplexity": 506.3405332405158}, "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/1448398451744.67/warc/CC-MAIN-20151124205411-00310-ip-10-71-132-137.ec2.internal.warc.gz"}
https://ck3.paradoxwikis.com/index.php?title=Family_(relation)&veaction=edit&section=11	# Family (relation) A diagram showing family relations in Crusader Kings III The Family of a character consists of their relatives, both closer and more distant. A character's grandparents, parents, siblings (including half-siblings), children and grandchildren are considered Close Family while uncles, aunts, first cousins, nephews and nieces are considered Extended Family. More often than not, most family members belong to the same Dynasty. A character will gain Stress if a parent or sibling dies before the age of 65. ## Opinion modifiers Relation Opinion Parent-Child +50 Sibling (includes half-siblings) +25 Spouse (includes secondary spouses) +25 Same Dynasty +5 Characters within the same dynasty and especially close family have an Opinion bonus with each other. However the bonus is only given to public connections, secret family relations do not give any bonuses. In scenarios where a character has multiple relations to another all relevant modifiers are applied. ## Marriage Marriage is the legal union between two characters in a personal relationship. Only characters who are at least 16 years old may marry and they require to be of opposite gender unless the Same-Sex Marriages game rule has been changed to Accepted. If either character is too young, the two prospective partners may enter a betrothal instead until both parties come of age. Spouses, concubines and consorts who are fertile are able to have legitimate children. Children in a marriage belong to the father's house unless the marriage is Matrilineal, in which case they belong to the mother's house. Moreover, marriage is one of the two main ways to form an Alliance with other characters. A faith's doctrines affects who a character may marry, how many official partners they may have and whether marriage may be ended in divorce: • The Consorts & Concubines marriage type doctrine allows rulers to have up to three consorts or concubines, alongside their spouse. Children born of consorts or concubines gain the Child of Consort/Concubine trait. Unlike marriage, concubinage does not yield alliances; however, consorts and concubines can be set aside at will without the need for divorce. • Consanguinity doctrine determines the legality of incestuous marriage. • Marriage may be ended subject to divorce doctrine. The target of the divorce gains −25 Opinion (Divorced Me) for 50 years with their ex-spouse, while their close family members gain −5 Opinion (Divorced Close Family) for 5 years. Divorced characters may remarry. Having a lover outside of marriage creates a Lover secret. If it is revealed, it may result in the two lover characters gaining the Fornicator and Adulterer traits, depending on the faith's / adultery doctrines. Children known to be born out of wedlock gain Bastard (trait), or Wild Oat if their faith has the No Bastards bastardry doctrine. If a bastard successfully becomes landed, they gain the Bastard founder trait. ### Polygamy Title tier Expected spouses Unlanded 1 Baron 1 Count 1 Duke 2 King 3 Emperor 4 With the Polygamous marriage type doctrine, characters may marry one spouse, and rulers (depending on their View on Gender doctrine) may additionally have up to three secondary spouses. If two married rulers have the Polygamous doctrine and are allowed to do so by the gender doctrine, they may have multiple spouses each. With the Equal gender doctrine, there is no existing restriction on having the same spouse(s) as another ruler. Any spouse who follows a Faith that has the Monogamous doctrine will suffer −40 Opinion. Monogamous spouses who were previously in a polygamous marriage (e.g. a secondary spouse was divorced) will still suffer −20 Opinion for 20 years. Any monogamous close relatives will suffer a similar −20 Opinion modifier. Spouses with the Consorts & Concubines doctrine or Polyamory tenet do not suffer similar penalties. When arranging marriages, prospective spouses who would become part of a polygamous marriage and do not believe in polygamy suffer a marriage acceptance penalty of . Rulers receive a penalty of −0.5 monthly piety per missing spouse if they are under the expected spouse amount for their title tier:[1] ### Marriage acceptance In order to successfully arrange marriages with AI characters, the player must reach a marriage acceptance score of at least +1 for the prospective spouses. Below is a list containing all possible conditions that affect marriage acceptance:[2] Condition Marriage acceptance Weak hook +100 Strong hook +200, or auto-accept Promising Prospects Perk • +50 (self) • +25 (family member) Dynasty Glory Perk +30 Arranging own marriage −15 Is player's heir • +20 (primary heir) • +10 (other heirs) Desires alliance Varied Does not want alliance −100 Marrying up +30 for each difference in title rank Marrying down • −30 for each difference in title rank (if AI is King) • −40 for each difference in title rank (if AI is not King) Opinion • +0.25 per opinion (round down) with prospective spouse • +0.75 per opinion (round down) with marriage offerer Wishes well for Lovers +15 Prospective spouses love each other and AI has compassion greater than zero +0.25 per AI compassion Candidate is Lowborn • −20 • −120 (if recipient is not lowborn themselves) Candidate's Level of Splendor +(Level of Splendor * 5 - 5) Incorrect marriage (patrilineal/matrilineal) Varied Different faith • −10 • −25 (faith considered astray or hostile) • −1000 (faith considered evil) Faith does not have polygamy doctrine or polyamory tenet and potential spouse would belong in a polygamous marriage. −1000 Age Considerations Varied The marriage will have Low Fertility Varied Unimportant courtier +10 Important courtier −10 Prospective spouse is a parent of recipient's children −25 Player is AI's liege • +40 (general) • +60 (marriage with liege) Valuable claimant −50 Claimant to one of AI's titles −50 Intimidated Varied Terrified Varied Character is dear to AI Varied The marriage would be incestuous −1000 Age of recipient +(Recipient age − 20) Spouse councillor - boosted child or heir • +50 • +75 (if heir) ## Incest Incest is sexual activity between family members. A faith's Consanguinity doctrine determines the legality of incestuous marriage. Characters having an incestuous relation that would not be allowed in marriage gain the Is Incestuous secret, and if exposed the Incestuous trait. Any form of incestuous relation, legal or not, may risk producing inbred offspring. The Divine Marriage tenet provides bonuses to incestuous marriages. Relatives are harder to seduce unless the target character's Faith accepts such an incestuous relation or the seducer has the Subtle Desire perk ( Seducer tree). ## Trait inheritance Congenital traits can be inherited by a character's offspring. Although congenital traits must be visible (active) to provide stat bonuses and other effects, a character may also carry recessive (inactive) traits which are invisible, yet can still be inherited by one's children.[3] There are some traits that are inherited by children, but do not use the active/inactive inheritance mechanic. In the context of this section, the term congenital trait excludes such traits. It also does not include traits that are non-genetic, yet inheritable. Trait inheritance mechanics also apply to children generated after creating a custom ruler. ### Active and inactive traits A congenital trait may be either active or inactive; active traits are visible and provide effects, whereas inactive traits are hidden. The genetic versions of Melancholic, Lunatic and Possessed are always inherited inactively and become active later in life:[4] Trait Activation time (after birth) Days Years[5] Melancholic 3,650-5,000 Between 10 years and 13 years, 9 months, 12 days Lunatic 5,840-10,950 Between 16 years and 30 years Possessed 3,650-7,300 Between 10 years and 20 years #### Chance of active inheritance The chances of inheriting a congenital trait as an active trait is based on what version (active or inactive) the parents have:[6] Mother Father None Inactive Active None 0% 2% 25% Inactive 2% 10% 50% Active 25% 50% 80% #### Chance of inactive inheritance If the child does not inherit actively, there is a chance that they will inherit the trait as an inactive trait instead:[6] Mother Father None Inactive Active None 0% 25% 75% Inactive 25% 50% 100% Active 75% 100% 150% ### General logic for trait with tiers inheritance 1. Start from highest trait 2. Calculate active chance. Lower tiers ( including inactive ) count as inactive of the tier. Each level down beyond the first multiplies chance by a define 3. If active, use it; DONE 4. Otherwise, go down a tier, if inactive pretend 1 more parent has that tier active, otherwise 1 more parent has it inactive.GOTO 2 When trying to inherit a tiered genetic trait, and the other person has one of lower tier, we pretend that means they've got the higher tier one recessively, and reduce the chance of inheritance by 20% per tier further down than 1 the other parent's trait is. When going down a tier, add 40%.[6] ### List of congenital traits The table below contains all genetic traits that use the inheritance mechanism as described above.[7][8] This list does not contain traits such as Sayyid, which can be inherited from a character's non-biological parent (in the case of secret bastards), or Inbred which uses a custom inheritance chance. The natural prevalence column denotes the likelihood of any character being born with the trait if it is not inherited from their parents. For every trait with natural prevalence, the same value can be assumed for random prevalence (i.e. for generated characters).[7] Note that some traits cannot be inherited at the same time since they are incompatible; such traits are indicated if they belong in the same group. Trait Natural prevalence (%) Group Notes Melancholic (genetic variant) 0.5 - If inherited on birth, it is initially hidden.[9] Lunatic (genetic variant) 0.5 - If inherited on birth, it is initially hidden. Possessed (genetic variant) 0.5 - If inherited on birth, it is initially hidden. Homely 0.5 Beauty Ugly 0.25 Beauty Hideous 0.15 Beauty Comely 0.5 Beauty Pretty / Handsome 0.25 Beauty Beautiful 0.15 Beauty Slow 0.5 Intelligence Stupid 0.25 Intelligence Imbecile 0.05 Intelligence Quick 0.5 Intelligence Intelligent 0.25 Intelligence Genius 0.05 Intelligence Delicate 0.5 Physique Frail 0.25 Physique Feeble 0.15 Physique Hale 0.5 Physique Robust 0.25 Physique Amazonian / Herculean 0.15 Physique Fecund 0 at birth[10], unknown for generation Fertility Club-footed 0.5 - Also gained via inbreeding. Hunchbacked 0.5 - Also gained via inbreeding. Lisping 0.5 - Stuttering 0.5 - Dwarf 0.5 Stature Also gained via inbreeding. Giant 0.5 Stature Also gained via inbreeding. Spindly 0.5 Physique (incompatible with good traits) Also gained via inbreeding. Scaly 0.5 - Also gained via inbreeding. Albino 0.5 - Wheezing 0.5 - Also gained via inbreeding. Bleeder 0.5 - Also gained via inbreeding. Barren / Sterile 0.5 Fertility Also gained via inbreeding. #### List of other inherited traits The following list contains all other traits that use a separate inheritance mechanic. For entries without a chance to inherit value for both parents, assume the value for single parent. Trait Chance to inherit (%) Notes Single parent Both parents Great Pox 10 - Lover's Pox 10 - Pure-blooded 15 75 Gained initially through inbreeding. Inbred 15 - Gained initially through inbreeding. Sayyid 100 - Only inherited from apparent father. Saoshyant / Saoshyant Descendant 100 - When parent has Saoshyant, Saoshyant Descendant is inherited instead.[11] Paragon / Consecrated Blood 100 - When parent has Paragon, Consecrated Blood is inherited instead. The Savior / Divine Blood 100 - When parent has The Savior, Divine Blood is inherited instead. ## Inbreeding Inbreeding is the process of two related characters having children together. For these purposes, related characters are those who share a common ancestor. Such children can be born with negative congenital traits even if neither parent has them, or the Inbred trait in advanced cases. However, there is a small chance for the child to gain the Pure-blooded trait instead. In the first generation, small-scale incest such as cousin marriage may not have a massive immediate impact. Nonetheless, repeated instances over successive generations may have an accumulative effect through negative inherited traits and a narrowed gene pool. ### Chance of inbreeding A line graph showing chance of inbreeding based on common ancestors. The chance of a child being considered inbred can be found from the product of the following:[12] #### Common ancestors The more common ancestors two parents have within four generations (up to their great-great grandparents, and including themselves), the more likely their children will be inbred.[13] Some potential incestuous marriages are noted below. The value provided for common ancestors assumes that ancestors were otherwise non-incestuous and monogamous. Cousins are not removed. The term "nibling" refers to niece/nephew. Additionally, the value is relative to the breeding couple. Relation Common ancestors Explanation Full siblings 30 (maximum possible) By definition, (full) siblings share parents, and thus by extension all other ancestors. The maximum amount of shared ancestors from n generations can be found from , thus being 30 from 4 generations. Or, written out, full siblings share both parents (2), two sets of grandparents (4), four sets of great grandparents (8) and eight sets of great-great grandparents (16). Parent-child 15 In the case of a partner being the other partner's ancestor, they are counted as a common ancestor.[14] As a result, the common ancestors are the following (perspective is child/parent): parent/self (1), one set of grandparents/both parents (2), two sets of great-grandparents/standard grandparents (4), four sets of great-great grandparents/great grandparents (8). Note that the parent's great-great grandparents are the child's 3×-great grandparents, and are therefore not counted. Half siblings 15 They share one parent, and therefore share only half of the maximum amount of ancestors. Alternatively, they share one parent (1), one set of grandparents (2), two sets of great grandparents (4) and four sets of great-great grandparents (8). First cousins 14 First cousins share grandparents (2), two sets of great grandparents (4) and four sets of great-great grandparents (8). Uncle-niece/aunt-nephew 14 Similar to first cousins, but rather than sharing grandparents, the nibling's grandparents are the uncle/aunt's parents. Note that since the uncle/aunt's great-great grandparents are the nibling’s 3×-great grandparents, who are 5 generations away from the nibling’s perspective, they are not counted. Second cousins 6 Second cousins share one set of great grandparents (2) and two sets of great-great grandparents (4). Third cousins 2 Third cousins share one set of great-great grandparents. #### Inbreeding factor The inbreeding factor for a given amount of common ancestors can be found through the following:[6] Common ancestors Factor Chance before modifiers 0-14 0.33 Between 0% and 4.62% 15-16 0.75 Between 11.25% and 12% 17-19 1 Between 17% and 19% 20-21 2 Between 40% and 42% 22-30 3 Between 66% and 90% #### Effect of Pure-blooded on inbreeding The Pure-blooded trait provides −50% chance of inbreeding per parent. If two parents have the Pure-blooded trait, this effect combines to no chance of gaining traits due to inbreeding. Note that this excepts the chance of gaining the Pure-blooded trait naturally, as well as the inheritance of such traits via parents. It is unknown whether the Pure-blooded trait has an effect on gaining the Inbred trait.[9] ### Traits gained from inbreeding The following traits may be gained from inbreeding. Note that these general inbred traits may also be gained naturally and are congenital. Offspring only have a chance to gain these traits as a result of inbreeding if their parents do not possess any of these traits (plus the Inbred trait).[15] The traits below appear equally likely.[9] • Barren / Sterile • Scaly • Club-footed • Wheezing • Spindly • Giant • Hunchbacked • Bleeder • Dwarf Additionally, there are two traits that may only be gained initially through inbreeding and have special requirements: Inbred and Pure-blooded. #### Inbred The Inbred trait may be inherited from one's parents. It may also be gained if a character with a general inbred trait has children with someone with whom they share a common ancestor.[15] The chance of gaining the Inbred trait as a result of this is unknown. Note that even with highly incestuous marriages, no children will gain the Inbred trait if the parents do not possess any of the enabling traits.[9] #### Pure-blooded The Pure-blooded trait may be inherited from one's parents. Otherwise, it may be gained naturally. Similar to the chance of inbreeding, the chance of gaining the Pure-blooded trait naturally is based on the number of common ancestors, multiplied by the corresponding level factor for that amount of common ancestors:[6] The inbreeding traits overwrite the Pure-blooded trait, thus the chance for a child to have the Pure-blooded trait by gaining it naturally is equal to the chance of not getting an inbreeding trait multiplied by the chance to get the Pure-blooded trait. This chance is maximized at 22 common ancestors for a value of 2.24%. Common ancestors Factor Final chance Chance after Inbred roll 0-19 0 0% 0% 20-21 0.15 Between 3% and 3.15% Between 1.8% and 1.83% 22-30 0.3 Between 6.6% and 9% Between 2.24% and 0.9% As a result, parents must have at least 20 common ancestors for a child to gain the Pure-blooded trait naturally. This does not apply to inheriting it from parents. ## References 1. game\common\defines\00_defines.txt, PIETY_LOSS_PER_MISSING_SPOUSE = 0.5, DESIRED_SPOUSES_PER_TIER = { 1 1 1 2 3 4 } 2. game\common\scripted_modifiers\00_marriage_scripted_modifiers.txt, marriage_ai_accept_modifier 3. "[Genetic traits are] visible, though characters can also carry recessive traits... those are not visible, but can be inherited by their offspring!" rageair's reply in CK3 Dev Diary #7 - Characters & Portraits thread 4. game\events\trait_specific_events\trait_specific_events.txt, trait_specific.0500 5. All years in Crusader Kings III last 365 days. 6. common\defines\00_defines.txt, NChildbirth 7. common\traits\00_traits.txt 8. "[If genetic = yes, the trait's] inheritance will follow the following rules: The trait can be inactive. Children can inherit the trait from both active and inactive parent traits. [...] An active trait is inherited with 100% chance, an inactive trait with a 50% chance. If the trait is successfully inherited from both parents, it becomes active. [...] If it's inherited only from one parent, it's inactive." Developer comments in common\traits\_traits.info 9. Pure-blooded effect on inbreeding on talk page 10. Natural prevalence of Fecund on talk page 11. events\decisions_events\major_decisions_events.txt, major_decisions.0101 12. "The final chance [for inbreeding] in percent is given by the number of common ancestors X corresponding level factor X inbreeding chance modifier" Developer comments in game\common\defines\00_defines.txt. 13. game\common\defines\00_defines.txt, NChildbirth\|INBREEDING_ANCESTOR_GENERATIONS = 4 14. The fact that the parents themselves are included in the common ancestor count is implied in the wording of developer comments found at game\common\defines\00_defines.txt (emphasis added): "How many generations are checked for common ancestors of the both parents (including the parents) for the purposes of getting the inbreeding trait and the pure-blooded trait" 15. "[enables_inbred = yes] enables the children of the character to be considered for the inbred trait (no by default). It only enables the inbred chance if there are common ancestors of the parents, so there is no risk of 'inbred' if the parents are not related. If inbred is not enabled by parents' traits, but there are common ancestors, there's a chance (same as for inbred trait when it's enabled) the child will get a random trait with enables_inbred = yes." Developer comments in game\common\traits\_traits.info Characters Characters • Attributes • Traits • Resources • Lifestyle • Dynasty • Culture • Innovations • Modifiers Realm & Governance Vassals • Council • Court • Schemes • Government • Laws • Decisions • Titles • Barony • County Warfare Warfare • Casus belli • Alliance • Army • Hired forces Faith Religion • Faith • Doctrines • Tenets Meta Modding • Patches • Downloadable content • Developer diaries • Achievements • Jargon	2023-02-04 01:33:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25571197271347046, "perplexity": 12431.657729287632}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500080.82/warc/CC-MAIN-20230204012622-20230204042622-00397.warc.gz"}
https://tech.io/playgrounds/29924/computing-with-data/the-path-environment-variable	### Open Source Your Knowledge, Become a Contributor Technology knowledge has to be shared and made accessible for free. Join the movement. ## The PATH Environment Variable # show path to file matching command ls which ls # display PATH variable (note the current directory is the third # directory in the list below, denoted by the period notation) echo $PATH # add the directory /home/joe/bin to PATH export PATH=$PATH:/home/joe/bin echo \$PATH XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Open Source Your Knowledge: become a Contributor and help others learn.	2019-01-24 13:18:00	{"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26345589756965637, "perplexity": 12416.530055931195}, "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-2019-04/segments/1547584547882.77/warc/CC-MAIN-20190124121622-20190124143622-00344.warc.gz"}
https://www.physicsforums.com/threads/expressing-the-interaction-energy-between-two-spheres.717217/	# Expressing the interaction energy between two spheres? 1. Oct 17, 2013 ### Spiral1183 1. The problem statement, all variables and given/known data Two identical spheres with radius R have uniform charge Q throughout their volume and separated d>2R apart 2. Relevant equations https://www.physicsforums.com/attachment.php?attachmentid=63061&d=1382054852 is the general potential energy equation this should be my total charge inside a sphere? This is the equation for the interaction energy 3. The attempt at a solution I found the total charge of the sphere (2nd Eqn.) and I believe that to find the interaction energy, I should treat that as $\Phi$1 and then use the charge from sphere 2? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution #### Attached Files: File size: 848 bytes Views: 218 • ###### CodeCogsEqn(23).gif File size: 851 bytes Views: 195 Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook Can you offer guidance or do you also need help?	2017-10-22 18:42:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33688950538635254, "perplexity": 2220.669369324832}, "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-2017-43/segments/1508187825399.73/warc/CC-MAIN-20171022165927-20171022185927-00695.warc.gz"}
https://leanprover-community.github.io/mathlib_docs/ring_theory/rees_algebra.html	# mathlibdocumentation ring_theory.rees_algebra # Rees algebra # The Rees algebra of an ideal I is the subalgebra R[It] of R[t] defined as R[It] = ⨁ₙ Iⁿ tⁿ. This is used to prove the Artin-Rees lemma, and will potentially enable us to calculate some blowup in the future. ## Main definition # • rees_algebra : The Rees algebra of an ideal I, defined as a subalgebra of R[X]. • adjoin_monomial_eq_rees_algebra : The Rees algebra is generated by the degree one elements. • rees_algebra.fg : The Rees algebra of a f.g. ideal is of finite type. In particular, this implies that the rees algebra over a noetherian ring is still noetherian. def rees_algebra {R : Type u} [comm_ring R] (I : ideal R) : The Rees algebra of an ideal I, defined as the subalgebra of R[X] whose i-th coefficient falls in I ^ i. Equations Instances for ↥rees_algebra theorem mem_rees_algebra_iff {R : Type u} [comm_ring R] (I : ideal R) (f : polynomial R) : ∀ (i : ), f.coeff i I ^ i theorem mem_rees_algebra_iff_support {R : Type u} [comm_ring R] (I : ideal R) (f : polynomial R) : ∀ (i : ), i f.supportf.coeff i I ^ i theorem rees_algebra.monomial_mem {R : Type u} [comm_ring R] {I : ideal R} {i : } {r : R} : r I ^ i theorem monomial_mem_adjoin_monomial {R : Type u} [comm_ring R] {I : ideal R} {n : } {r : R} (hr : r I ^ n) : r theorem adjoin_monomial_eq_rees_algebra {R : Type u} [comm_ring R] (I : ideal R) : theorem rees_algebra.fg {R : Type u} [comm_ring R] {I : ideal R} (hI : I.fg) : @[protected, instance] def rees_algebra.algebra.finite_type {R : Type u} [comm_ring R] {I : ideal R} : @[protected, instance] def rees_algebra.is_noetherian_ring {R : Type u} [comm_ring R] {I : ideal R} :	2022-10-01 09:07:00	{"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": 0.6606189012527466, "perplexity": 687.7243814504812}, "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/1664030335573.50/warc/CC-MAIN-20221001070422-20221001100422-00230.warc.gz"}
https://datascience.stackexchange.com/questions/66786/what-is-a-hidden-state-in-bert-output	# What is a 'hidden state' in BERT output? I'm trying to understand the workings and output of BERT, and I'm wondering how/why each layer of BERT has a 'hidden state'. I understand what RNN's have a 'hidden state' that gets passed to each time step, which is a representation of previous inputs. But I've read that BERT isn't a RNN - it's a CNN with attention. But you can output the hidden state for each layer of a BERT model. How is it that BERT has hidden states if it's not a RNN? BERT is a transformer. A transformer is made of several similar layers, stacked on top of each others. Each layer have an input and an output. So the output of the layer n-1 is the input of the layer n. The hidden state you mention is simply the output of each layer. You might want to quickly look into this explanation of the Transformer architecture : https://jalammar.github.io/illustrated-transformer/ Note that BERT use only Encoders, no Decoders. • Thanks for your response! I've read that a few times, but I never saw a mention of a 'hidden state'. Is it just intuitive that that's what the hidden states must be? When I google 'BERT hidden state', I see that you can get the hidden states in the BERT output, but no document or article that says that it's the output of each layer, as you explain. Basically, I'm wondering what I was missing, or how you know that that's what the hidden states refer to. – Nick Koprowicz Jan 22 '20 at 0:25 • You're right, it's not mentioned explicitly. I personally understood this notion of hidden state by looking at the source code of Bert implementations. – Astariul Jan 22 '20 at 1:34	2021-05-15 19:45:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4438113272190094, "perplexity": 872.2437164217595}, "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/1620243991378.52/warc/CC-MAIN-20210515192444-20210515222444-00393.warc.gz"}
https://www.omnimaga.org/general-discussion/post-your-desktop/msg390106/	• Post your desktop 5 1 Currently: 0 Members and 1 Guest are viewing this topic. aeTIos • Nonbinary computing specialist • LV12 Extreme Poster (Next: 5000) • Posts: 3913 • Rating: +184/-32 « Reply #1470 on: July 23, 2014, 06:33:44 am » Nice mewtwo brah. I'm not a nerd but I pretend: floris497 • Posts: 210 • Rating: +8/-0 « Reply #1471 on: July 23, 2014, 06:46:13 am » Anyways: 4k screen? It sure is, the most cheap AOC display there was €499. i'm really happy with it, but everything is kind of small.. First i had it running at max 30Hz witch is really bad. now i got it at 40Hz which is nice. not sure if my GPU can handle it that good, i have integrated graphics "Intel HD 3000", on my newer laptop i can't get the 165Mhz pixel clock cap off.. so it does not support this resolution The native resolution is a little small, but if i put it in 1080p HiDPi it is just to big (but really sharp). I was trying to set it in 1440p HiDPi (because that is a nice resolution) and then scale it down to UHD, but my Graphics card is not willing to give me 5120x2880, but it would probably look really good. For now i see it as a good investment, do you guys think about getting a 4k monitor? I tested it with Half Life 2: Lost Coast, on 4k with all setting on low (V-Sync off) and my HD3000 got about 12FPS on the stress test. Spoiler For Spoiler: funny is i waited 30days for this monitor, and when i didn't get it then i bought it somewhere else and got it in 22h shiped to the door (DON'T BUY AT ALTERNATE) <--- Bad Store! « Last Edit: July 23, 2014, 06:56:31 am by floris497 » aeTIos • Nonbinary computing specialist • LV12 Extreme Poster (Next: 5000) • Posts: 3913 • Rating: +184/-32 « Reply #1472 on: July 23, 2014, 06:57:02 am » Welp, an IntelHD3000 doesn't quite match the specs for your screen. Good luck gaming on that :x I'm not a nerd but I pretend: Hayleia • Programming Absol • Coder Of Tomorrow • LV12 Extreme Poster (Next: 5000) • Posts: 3367 • Rating: +393/-7 « Reply #1473 on: July 23, 2014, 06:59:32 am » The native resolution is a little small, but if i put it in 1080p HiDPi it is just to big (but really sharp). I was trying to set it in 1440p HiDPi (because that is a nice resolution) and then scale it down to UHD, but my Graphics card is not willing to give me 5120x2880, but it would probably look really good. You can probably use xrandr to force your display to a certain resolution. I used newrez (which is using xrandr) to set my netbook's resolution to 1344x752, which is not really standard. For now i see it as a good investment, do you guys think about getting a 4k monitor? As you said, everything is too small so I don't really see the point of buying a 4K monitor to set its resolution to 1080p, which is what I would do if I got one I own: 83+ ; 84+SE ; 76.fr ; CX CAS ; Prizm ; 84+CSE Sorry if I answer with something that seems unrelated, English is not my primary language and I might not have understood well. Sorry if I make English mistakes too. floris497 • Posts: 210 • Rating: +8/-0 « Reply #1474 on: July 23, 2014, 07:22:29 am » The native resolution is a little small, but if i put it in 1080p HiDPi it is just to big (but really sharp). I was trying to set it in 1440p HiDPi (because that is a nice resolution) and then scale it down to UHD, but my Graphics card is not willing to give me 5120x2880, but it would probably look really good. You can probably use xrandr to force your display to a certain resolution. I used newrez (which is using xrandr) to set my netbook's resolution to 1344x752, which is not really standard. I use switchresx (and script to unlock the IOKit driver) Quote For now i see it as a good investment, do you guys think about getting a 4k monitor? As you said, everything is too small so I don't really see the point of buying a 4K monitor to set its resolution to 1080p, which is what I would do if I got one It is small but i need to get used to it, it is really handy for programming with sources left and right and code somewhere in the middle, the 1080p HiDPi mode means GUI scaling 1080p retina like, i switch between these resolutions: Welp, an IntelHD3000 doesn't quite match the specs for your screen. Good luck gaming on that :x I don't really game, or i set a really small resolution, HD3000 is no gaming card no matter resolution (i can always steal my dad's work computer). Sorunome • Fox Fox Fox Fox Fox Fox Fox! • Support Staff • LV13 Extreme Addict (Next: 9001) • Posts: 7917 • Rating: +373/-13 • Derpy Hooves « Reply #1475 on: July 23, 2014, 07:49:23 am » Fun fun fun. Spoiler For Spoiler: WTF pinball on linux? THE GAMEAlso, check out my websiteIf OmnomIRC is screwed up, blame me!Click here to give me an internet! DJ Omnimaga • Former TI programmer • CoT Emeritus • LV15 Omnimagician (Next: --) • Posts: 55828 • Rating: +3151/-232 • CodeWalrus founder & retired Omnimaga founder « Reply #1476 on: July 24, 2014, 01:41:48 am » There were no Pinball clones for Linux before? As for 4K res screens I doubt my graphic card and computer would even handle them because the graphic cars is from early 2012 and the computer, although an higher end work machine, early 2010. However, isn't it possible in some OSes to resize the theme fonts and icons on large resolutions to make them easier to read? I remembieber it was possible under Windows 2000 and XP. « Last Edit: July 24, 2014, 01:43:43 am by DJ Omnimaga » In case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https://discord.gg/cuZcfcF Juju • Incredibly sexy mare • Coder Of Tomorrow • LV13 Extreme Addict (Next: 9001) • Posts: 5730 • Rating: +500/-19 • Weird programmer « Reply #1477 on: July 24, 2014, 01:07:02 pm » That's probably Wine. Also have the excerpt of my theme.lua I changed based on those colors, for you Awesome WM users, if you want a Princess Luna theme: Code: [Select] theme.font = "silkscreen 6"theme.bg_normal = "#161D3F"theme.bg_focus = "#404680"theme.bg_urgent = "#8159CE"theme.bg_minimize = "#040404"theme.bg_systray = theme.bg_normaltheme.fg_normal = "#aaaaaa"theme.fg_focus = "#ffffff"theme.fg_urgent = "#ffffff"theme.fg_minimize = "#ffffff"theme.border_width = 1theme.border_normal = theme.bg_normaltheme.border_focus = theme.bg_focustheme.border_marked = theme.bg_urgent « Last Edit: July 24, 2014, 01:32:44 pm by Juju » Remember the day the walrus started to fly... I finally cleared my sig after 4 years you're happy now? This signature is ridiculously large you've been warned. The cute mare that used to be in my avatar is Yuki Kagayaki, you can follow her on Facebook and Tumblr. Sorunome • Fox Fox Fox Fox Fox Fox Fox! • Support Staff • LV13 Extreme Addict (Next: 9001) • Posts: 7917 • Rating: +373/-13 • Derpy Hooves « Reply #1478 on: July 30, 2014, 11:00:10 am » Not really my desktop, but THE GAMEAlso, check out my websiteIf OmnomIRC is screwed up, blame me!Click here to give me an internet! floris497 • Posts: 210 • Rating: +8/-0 « Reply #1479 on: July 30, 2014, 05:54:01 pm » As for 4K res screens I doubt my graphic card and computer would even handle them because the graphic cars is from early 2012 and the computer, although an higher end work machine, early 2010. However, isn't it possible in some OSes to resize the theme fonts and icons on large resolutions to make them easier to read? I remembieber it was possible under Windows 2000 and XP. Yes there is, but not so much becoase the resolution is nog realy supported by the hardware. Princetonlion.tibd • Agranovskiy Founder • Members • Posts: 790 • Rating: +3/-4 « Reply #1480 on: July 30, 2014, 07:02:41 pm » Not really my desktop, but Is that in grayscale? Founder of Agranovskiy, a basic TI programming tutorial site. I'm a USCF (United States Chess Federation) player. Juju • Incredibly sexy mare • Coder Of Tomorrow • LV13 Extreme Addict (Next: 9001) • Posts: 5730 • Rating: +500/-19 • Weird programmer « Reply #1481 on: July 30, 2014, 08:07:34 pm » Seems so yeah. Also have my Luna-themed desktop: Spoiler For Warning: kind of big: Left is a CRT screen while right is a HDTV. Remember the day the walrus started to fly... I finally cleared my sig after 4 years you're happy now? This signature is ridiculously large you've been warned. The cute mare that used to be in my avatar is Yuki Kagayaki, you can follow her on Facebook and Tumblr. Sorunome • Fox Fox Fox Fox Fox Fox Fox! • Support Staff • LV13 Extreme Addict (Next: 9001) • Posts: 7917 • Rating: +373/-13 • Derpy Hooves « Reply #1482 on: July 31, 2014, 05:33:00 am » THE GAMEAlso, check out my websiteIf OmnomIRC is screwed up, blame me!Click here to give me an internet! Princetonlion.tibd • Agranovskiy Founder • Members • Posts: 790 • Rating: +3/-4 « Reply #1483 on: July 31, 2014, 10:48:19 am » I can't really post my background, it changes every 5 seconds. Anyways, it's every 2013 FCB player, backgrounds downloaded from their website Founder of Agranovskiy, a basic TI programming tutorial site. I'm a USCF (United States Chess Federation) player. Deep Toaster • So much to do, so much time, so little motivation	2020-02-27 08:50:06	{"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": 0.27736321091651917, "perplexity": 13324.417462537303}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146665.7/warc/CC-MAIN-20200227063824-20200227093824-00280.warc.gz"}
https://sunglee.us/mathphysarchive/?p=3224	# Harmonic Motion: Undamped A force exerted by an elastic cord or by a spring obeys Hooke’s law $F=-kx$ where $x$ is the displacement of the equilibrium position. From Newton’s second law of motion we have $F=ma=m\ddot{x}$, so we obtain the second order linear differential equation $$\label{eq:undamped}m\ddot{x}+kx=0$$ Solving \eqref{eq:undamped} for $\ddot{x}$ we obtain $\ddot{x}=-\frac{k}{m}x\sim -x$. For a trial solution, $x=e^{qt}$ is a candidate. To see if this trial solution works, plug it back into \eqref{eq:undamped}. $$m\ddot{x}+kx=mq^2e^{qt}+ke^{qt}=0$$ i.e. $$\label{eq:auxeq}mq^2+k=0$$ whose solutions are $$q=\pm i\sqrt{\frac{k}{m}}=\pm i\omega_0$$ where $\omega_0=\sqrt{\frac{k}{m}}$. The equation \eqref{eq:auxeq} is called the auxiliary equation or the characteristic equation. So, $x_1=e^{i\omega_0 t}$ and $x_2=e^{-i\omega_0 t}$ are solutions of \eqref{eq:undamped}. It can be easily shown that their linear combination $$\label{eq:undamped2}x=A_1e^{i\omega_0 t}+A_2e^{-i\omega_0 t}$$ is also a solution of \eqref{eq:undamped}. \eqref{eq:undamped2} is a complex solution so it is not suitable for the physical analysis of a motion governed by \eqref{eq:undamped}. What we need is a real solution. It turns out that the real part and the imaginary part of $e^{i\omega_0 t}$ also, respectively, satisfy \eqref{eq:undamped}. This is due to the linearity of \eqref{eq:undamped}. Hence, an alternative form of the solution which is real is $$\label{eq:undamped3}x=a\cos\omega_0 t+b\sin\omega_0 t$$ Using a trigonometric identity \eqref{eq:undamped3} can be written as $$\label{eq:undamped4}x=\sqrt{a^2+b^2}\cos(\omega_0 t-\theta_0)$$ where $\theta_0=\tan^{-1}\frac{b}{a}$ or as $$\label{eq:unddamped4a}x=\sqrt{a^2+b^2}\sin(\omega_0 t+\phi_0)$$ where $\phi_0=\tan^{-1}\frac{a}{b}$. The angles $\theta_0$ and $\phi_0$ are called the phase. Some Terminologies The equation \eqref{eq:undamped} is called the differential equation of the harmonic oscillator. $\sqrt{a^2+b^2}$ is the amplitude (the maximum value of $x$) The period $T_0$ of the oscillation is the time required for one complete cycle. $$T_0=\frac{2\pi}{\omega_0}=2\pi\sqrt{\frac{m}{k}}$$ The linear frequency of oscillation $f_0$ is the number of cycles in unit time. $$f_0=\frac{1}{T_0}=\frac{\omega_0}{2\pi}=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$$ $\omega_0=2\pi f_0$ is called the angular frequency and is also called the natural frequency. Example. Suppose that a mass weighing 10 lb stretches a spring 2 in. If the mass is displaced an additional 2 in and is then set in motion with an initial upward velocity of 1 ft/s, determine the position of the mass at any later time. Also determine the period, amplitude, and phase of the motion. Solution. $k=10\mathrm{lb}/2\mathrm{in}=60\mathrm{lb}/\mathrm{ft}$ and $m=\mathrm{weight}/g=10\mathrm{lb}/32\mathrm{ft}/\mathrm{s}^2$. Thus $$m\ddot{x}+kx=\frac{10}{32}\ddot{x}+60x=0$$ i.e. $$\ddot{x}+192x=0$$ The auxiliary equation is $q^2+192=0$ and $q=\pm i8\sqrt{3}$. The solution $x(t)$ is then given by $$x(t)=a\cos(8\sqrt{3}t)+b\sin(8\sqrt{3}t)$$ From the initial conditions $x(0)=\frac{1}{6}$ ft and $\dot{x}(0)=-1$ ft/s, we find $a=\frac{1}{6}$ and $b=-\frac{1}{8\sqrt{3}}$. The natural frequency is $\omega_0=8\sqrt{3}\approx 13.856$ rad/s. The period is $T_0=\frac{2\pi}{\omega_0}=\frac{2\pi}{8\sqrt{3}}\approx 0.453$ sec. The amplitude is $\sqrt{a^2+b^2}=\sqrt{\frac{19}{576}}\approx 0.182$ ft. The phase is $\theta_0=\tan^{-1}\left(\frac{b}{a}\right)=-\frac{\sqrt{3}}{4}\approx -0.408645$ rad. Therefore, $x(t)$ can be written as $$x(t)=0.182\cos(13.856t+0.40864)$$ Figure 1 shows a complete cycle. Figure 1. A complete cycle of x(t)=0.182cos(13.856t+0.40864) Figure 2. shows an animation of $x(t)$. Figure 2. An animation of x(t)=0.182cos(13.856t+6.283185308k+0.40864) with k=1..5, t=1..100, and FPS=10 The Conservation of Total Energy Let us calculate the work done by an external force $F_{\mathrm{ext}}$ in moving the mass from the equilibrium position ($x=0$) to some position $x$. $F_{\mathrm{ext}}=-F=kx$ and $$W=\int F_{\mathrm{ext}} dx=\int_0^x kx dx=\frac{1}{2}kx^2$$ The work $W$ is stored in the spring as potential energy $V(x)=W=\frac{1}{2}kx^2$. The potential energy $V(x)$ for a force $F(x)$ is defined by $$\label{eq:conservative}F=-\frac{dV}{dx}$$ In our case, $F=-\frac{dV}{dx}=-kx$. For any force $F$ satisfying \eqref{eq:conservative}, the total energy $$E=T+V,$$ the sum of the kinetic energy $T=\frac{1}{2}m\dot{x}^2$ and the potential energy $V$, is constant. For this reason, a force satisfying \eqref{eq:conservative} is called a conservative force. Since $$\ddot{x}=\frac{d\dot{x}}{dt}=\frac{d\dot{x}}{dx}\frac{dx}{dt}=v\frac{dv}{dx},$$ $$F(x)=m\ddot{x}=mv\frac{dv}{dx}=\frac{1}{2}m\frac{dv^2}{dx}=\frac{dT}{dx}$$ The work done on the particle by impress force $F(x)$ is $$\int F(x)dx=\int dT=\frac{1}{2}m\dot{x}^2+C_1$$ where $C_1$ is a constant. On the other hand, from \eqref{eq:conservative} we also have $$\int F(x)dx=-\int dV=-V(x)+C_2$$ where $C_2$ is a constant. Therefore, $$T+V=\frac{1}{2}m\dot{x}^2+V(x)=E$$ is a constant. In our case the conservation of total energy $E$ $$\label{eq:totalenergy}E=\frac{1}{2}m\dot{x}^2+\frac{1}{2}kx^2$$ can be more directly shown. Differentiating the total energy \eqref{eq:totalenergy} with respect to $t$ \begin{align}\frac{dE}{dt}&=m\ddot{x}\dot{x}+kx\dot{x}\\&=(m\ddot{x}+kx)\dot{x}\\&=0\end{align} So the restoring force $F=-kx$ for an undamped harmonic motion is conservative. The solution \eqref{eq:undamped4} can be also obtained by considering energy. Solving \eqref{eq:totalenergy} for $\dot{x}$ $$\label{eq:velocityundamped}\dot{x}=\pm\sqrt{\frac{2E-kx^2}{m}}$$ This is a separable equation. For $\dot{x}=\sqrt{\frac{2E-kx^2}{m}}$ it’s solution is $$x=\sqrt{\frac{2E}{k}}\sin\left(\sqrt{\frac{k}{m}}t+\phi_0\right)$$ and for $\dot{x}=-\sqrt{\frac{2E-kx^2}{m}}$, it’s solution is $$x=\sqrt{\frac{2E}{k}}\cos\left(\sqrt{\frac{k}{m}}t-\theta_0\right)$$ So the amplitude is $A=\sqrt{\frac{2E}{k}}$ and the angular frequency is $\omega_0=\sqrt{\frac{k}{m}}$. In order for \eqref{eq:velocityundamped} to make sense $\frac{2E-kx^2}{m}\geq 0$ i.e. the total energy is greater than or equal to the potential energy $V(x)=\frac{1}{2}kx^2$. This means that the particle is confined to the region $-\sqrt{\frac{2E}{k}}\leq x\leq\sqrt{\frac{2E}{k}}$. Also the speed becomes zero when $V(x)=E$. This means that the particle must come to rest and reverse its motion at $x=\pm\sqrt{\frac{2E}{k}}$. The points $x=\pm\sqrt{\frac{2E}{k}}$ are called the turning points of the motion. The maximum value of $\dot{x}$ occurs at $x=0$. $v_{\max}=\frac{k}{m}A=\omega_0A$ and $E=\frac{1}{2}mv_{\max}^2=\frac{1}{2}kA^2$.	2019-10-17 07:44:04	{"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": 9, "x-ck12": 0, "texerror": 0, "math_score": 0.9303028583526611, "perplexity": 167.83609546104913}, "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/1570986673250.23/warc/CC-MAIN-20191017073050-20191017100550-00434.warc.gz"}