text: In the All history panel, you can click on the history "slice" you need, and Download a project at this version if you need to retrieve a previous version. They are different in terms of ILD and density level. The LaTeX macros are at a high level. Most complete selection of mathematical and special symbols. Stanford Earth scientists work to gain a better understanding of our planet's energy & resource base that supports society, See the section on Builder Settings for details. local site, the macros give the same result regardless of the system, and the If no such directive is specified, pdflatex is the default. LaTeX allows commands to be freely intermixed with text in free-format. CoCalc’s support for multi-file documents is now available. Thus, commands names tend to be more verbose but self-explanatory. The dictionary paths must be compatible with those used by Sublime Text's spell-checker. Combine other materials of the known fetish scene to generate an edgier look. Indentation may be used to show the structure of the commands. My question is, which Latex features aren't supported by Mathjax? Other formats include ConTeXt, used primarily for desktop publishing and written mostly by Hans Hagen at Pragma. Read on to know more. Latexes are found in nature, but synthetic latexes are common as well.. Latex as found in nature is a milky fluid found in 10% of all flowering plants (angiosperms). When a large number of authors are commenting on the writing of one file, this can be very useful. Most usual is about 0.5 mm though. Authorea is a wonderful online LaTeX editor. Also, for compatibility with TeXshop, you can use TS-program instead of program. From OeisWiki. * Using the corresponding output_directory and aux_directory settings detailed in the settings section. 3. Visit Website. It is a complex emulsion consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums that coagulate on exposure to air. There is a well-written book for LaTeX containing both tutorial and reference Features of Trendy Latex Clothing. Here’s a summary of features: The user interface is initially identical to the current single-file interface. Typesetting of complex mathematical formulas. LaTeX Multi-File Support ¶. How it is run See the documentation on Preview Settings. It also lets you collaborate in real-time. Without the erotic part that is normally shown, it’s a challenge to create stunning photographs. master) file. There are several key features with regards to a latex mattress. That is, they make most of the formatting Equations can be entered via point-and-click interface or via keyboard with LaTeX commands (optionally via auto-completion). * Using a TEX directive, such as %!TEX output_directory = near the top of the file. Contents. Also, the master file na… Other extensions such as .Rnw and .tikz are supported, but, for now they will be treated as standard LaTeX documents (patches are always welcome!). Latex clothing is by and large prepared from beautiful sheets of latex. You can preview images included via the \includegraphics command. There are two different processes that mattress companies use. Latex foams are crafted from vulcanized rubber tree sap. Because LaTeX is an extension to the TeX typesetting system, it has TeX’s ability to typeset technical documents that contain complex mathematical equations. Latex Foam Mattresses is made up of visco elastic foams. There are no approved revisions of this page, so it may not have been reviewed. The name of the program used to To exit the History mode and return to normal editing mode, just click on Historyagain. Automatic generation of bibliographies and indexes. Click on the History tab above the preview panel. Latex is logically semi-transparent. Read more, 397 Panama Mall, CA 94305-2210 Mitchell Building 101. LyX is among the most popular LaTeX editors right now with support for many modern and unique features. Note: the --aux-directory flag is only implemented by MiKTeX, so the corresponding settings will only be valid if you are using MiKTeX, as indicated by your distro setting. Examples: Footnotes and marginal notes are automatically located on the page. The --output-directory and --aux-directory flags can be set in several ways: You get all the basic features you’d expect in a LaTeX editor. LaTeX includes a rich set of built-in commands. Note: the only file that gets saved automatically is the current one. The rubber material that latex beds are made of is mixed up into foam. See the documentation on Preview Settings for details. Now, it is possible to get the perfect sleep, all thanks to Natural latex mattress. Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home ; Questions ; Tags ; Users ; Unanswered ; Jobs; About the features of LaTeX3. In addition to that, you can access it offline or choose to sync files via Dropbox and GitHub. This relies on your system's texdoc command. Also, the master file name must have a valid tex extension (i.e., one configured in the tex_file_exts settings), or it won't be recognized. The basic programs are available free or at low cost and can be put on systems This is then referred to as AMS-LaTeX. Snippet completions are provided for every entry type supported by either BibTeX or BibLaTeX, as are completions for field names. Overleaf Enterprise - Features & Benefits. Simply type [[and Obsidian will auto-complete the link.. With connections in place, you can navigate your notes and get inspiration with backlinks and graph view. If you explicitly input other files, then build, there is a new menu on the top of a … One is to use a %!TEX options = ... line at the top of your file. Tucci MG(1), Mattioli Belmonte M, Toschi E, Pelliccioni GA, Checchi L, Castaldini C, Biagini G, Piana G. Author information: (1)Dermatological Department, University of Ancona, Italy. You should consult the subsection on project-specific settings for further details. The first is the process through which a latex bed is made. Also note that if you are using latexmk and you set the $pdflatex variable, the TeX options facility will not function, as latexmk does not support this. If you are using an alternate viewer, please see the relevant section under Available Viewers for any caveats or other instructions. If you have additional dictionaries, you can add them using the tex_spellcheck_paths setting, which is a mapping from the locales to the dictionary paths. Natural latex mattress, organic latex mattress, and Latex Mattress come with 7 interesting features. Our goal is to make writing LaTeX as easy and comfortable as possible. If LaTeX's default layout is not what you want, you can change the traditional builder on MiKTeX) or the simple builder, the jobname setting wil be ignored. As with many products, it is up to you which production style you choose. There are three special values that can be used, <> <> and <>. The beauty of LaTeX is that it allows you to define styles for individual elements. These are temperature-sensitive foams that can conform to the contours of your body. LaTeX was created to make it easier to produce general-purpose books and articles within TeX. of 3 – 5FT Latex . Command Demonstration of LaTeX features, using example input and output files This demonstration LaTeX file shows both the marked up input text, and the corresponding typeset output. Note that while the extension detection is used by features of LaTeXTools, including, other features---especially the completions---depend on the syntax of the file being set to LaTeX as well. the traditional builder on MiKTeX) or the simple builder, the output_directory and aux_directory settings will be ignored. The other process is known as the Talalay … Since the dictionary package is no longer available via Package Control, you can follow these steps to install it: LaTeXTools has some degree of support for LaTeX documents that are in files with an extension other than .tex. Clothing. It is possible to customize the command run by setting the command option under Builder Settings. Because it is taken from more natural … It was her expert who created printers capable of printing latex inks. Multi-file documents are supported as follows. From its appearance, the original latex mattress has a golden yellow color. LaTeXTools parses the %!TEX spellcheck directive to set the language for the spell-checker integrated in Sublime Text. You can consult the documentation for any LaTeX package by invoking the View Package Documentation command via the Command Palette (for now). That’s because the application of the latex purification process that the end result is yellow. If the first line in the current file consists of the text %!TEX root = , then tex & friends are invoked on the specified master file, instead of the current one. For example, in Latex I can write$\today$and it will return the current date. LaTeX is the de facto standard for the communication and publication of scientific documents. This behaviour is controlled through two settings, tex_file_exts and latextools_set_syntax. Full programming language features allow complicated macros to be easily defined. All the predefined mathematical symbols from the T e X package are listed below. If you are using texify (i.e. This behaviour is controlled by a single setting, use_biblatex (default: false), which indicates whether LaTeXTools should use the BibTeX versions of the auto-completions (this is the default behavior) or the BibLaTeX versions of the auto-completions (if use_biblatex is set to true). * Using a TEX directive, such as %!TEX jobname = near the top of the file. for documentation on using the script builder, Now you can install it as any other package: First select. The other is to use the options builder setting in your settings file. Control over large documents containing sectioning, cross-references, tables and figures. Structural features of latex gloves in dental practice. More symbols are available from extra packages. and to set paragraph entries in columns. If you are using texify (i.e. layout problems. sections, plus a good index. names may be any length. Latex is logically semi-transparent. For more on these settings, see the documentation on General Settings. This will run pdflatex / xelatex / lualatex with the --output-directory flag and then copy the resulting PDF to the same directory as your main TeX document. TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. 2. For more on Sublime Text support for spell checking, see the relevant online documentation. Thera-Band¨ Professional Resistance Bands help users rehabilitate injuries, improve functional living and enhance athletic performance. Platforms Supported: Windows. By default, LaTeXTools supports the following viewers, depending on platform: However, it is possible to use other programs to view PDF files. List of LaTeX mathematical symbols. You can also then click the Label this version button (visible in Single version view) to give a label to a specific "slice", so that you can find it easily later. If the default builder doesn't meet your needs for any reason, please see the page on available builders. printers or graphics terminals. You also have the ability to check document history to see what’s been removed and added. 7. invoke LaTeX may differ among systems, however. Mathematical formula editor which is easily best of breed. The default builder (called the traditional builder) supports several additional features. * Using the TeX Options feature to set --output-directory and / or --aux-directory. The original Latex has the following characteristics: 1. Both of these functions rely on Ghostscript and ImageMagick being installed and available on your texpath. Wow people like never before. Although it is stitched, … When the mattress is whitish yellow, it means the mattress uses synthetic latex. For example {"en-us": "Packages/Language - English/en_US.dic"} would be a valid value. Springy; Dense; Simple and energy-efficient production process; Suitable for a wider audience; Durable; Comparing Talalay And Dunlop Latex. The original latex mattress usually has large holes that function smoothly and ensure the elasticity of … format. Choose between our Cloud and Server options. Word and Writer have very good comments/annotations and edit-tracking features. Features Of Latex Gloves - Aug 21, 2020-Latex gloves are suitable for automobile manufacturing, battery manufacturing; glass fiber reinforced plastic industry, aircraft assembly; aerospace field; environmental cleaning and cleaning. Hygiene. As an alternative, to using the %!TEX root = syntax, if you use a Sublime project, you can set the TEXroot option (under settings): Note that if you specify a relative path as the TEXroot in the project file, the path is determined relative to the location of the project file itself. With the massive use of latex Heavy Rubber is special to every model. In addition, LaTeXTools provides smart completions for name fields (such as author, editor, etc.) Note that the output images shown here are low resolution JPEG files made from capturing screen images. LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. Key Features: Integrated LaTeX environment for Windows apps, Auto-completion, Complete UTF-8 support, Document navigator, Library of LaTeX snippets, Syntax Highlighting, Spell Checking and more. Standard colors are Black, White, and Red, but catsuits are accessible in any color including metallic shades or white. LaTeX creates a device-independent (DVI) output file in a standard, well-documented Formulas are immediately visually rendered on screen. See, in particular, the section on builder settings. TeXstudio is open source and is available for all major operating systems. Their meaning is the same as that found in the settings section and they are described there. and crossrefs. Typesetting journal articles, technical reports, books, and slide presentations. Preview functions are only available in Sublime Text Build 3118 and newer. In KaTeX, a Mathjax alternative, there seem to be more troublesome limitations such as \overrightarrow{AB} not working. Currently, there are viewers available for Preview.app, Okular and Zathura. If you thought that one cannot buy a good nights' sleep, then think again! It is also possible to show all images at once via phantoms. Play videos and movies continuously across slides, without the need to start and stop, find where you left off, or edit them into clips. These viewers can be chosen by changing the "viewer" setting. If you do, you will not get this functionality. Note: Jobname can only be set when using latexmk (i.e., the traditional builder on OS X and Linux), the basic builder or the script builder (see below for documentation on using the script builder). Finally, if you use project files, the program builder setting can also be customized there, under settings. Thanks to its antibacterial, germicidal and fungicidal properties, latex is extremely hygienic and non-allergic. See the Viewer Settings section for details. Let’s have a look at some of the unique features of LaTeX and how its a blessing to the academic research community: 1. You don't have to pay for using LaTeX, i.e., there are no license fees, etc. Latex gloves have abrasion resistance, puncture resistance; resistance to acids and alkalis, grease, fuel and various solvents, etc. ranging from PCs to Unix to VMS to IBM mainframes. Filter programs then convert this file to the format needed by various Copy/paste to and from LaTeX source code. LaTeXTools uses a cache to store relevant information about your document and improve the performance of commands. Labelled versions can be accessed quickly via the History > Labelspanel. Sign up to join this community. It only takes a minute to sign up. It may be less ambiguous to specify an absolute path to the TEXroot if possible. Latex clothing is by and large prepared from beautiful sheets of latex. * Using the TeX Options feature to set --jobname Note: for this to work, you must not customize the command option in LaTeXTools.sublime-settings. TeX/LaTeX uses only integer arithmetic, so it processes quickly. Only customize the compilation command if you know what you're doing. So go ahead. The higher the ILD and density, the firmer the mattress gets. If LaTeX's default layout is not what you … That is, they make most of the formatting decisions for you, which is good if you don't want to bother with typographical layout problems. decisions for you, which is good if you don't want to bother with typographical The first is known as the Dunlop process. Therefore TeXstudio has numerous features like syntax-highlighting, integrated viewer, reference checking and various assistants. The foam is then poured into a mold and heated to set the texture. Links are provided to open the image itself or the folder containing the image. Get in Touch to Request a Demo. Similarly, when auto-completions are triggered in a crossref field, a list of all current entry keys will be provided. The LaTeX macros are at a high level. Multi-file documents are supported: the directive must be in the root (i.e. Features available with Keynote. Math/science features . Memory foam beds are not the same. By default, we try to keep them invisible, so they are stored in the Sublime cache path. Combine latex as the second element to an elegance and creative fashion outfit and make it the icing on the cake. Showcase videos like never before. The --jobname flag can be set in several ways: LaTeX works the same way on all systems. The typeset output is a series of graphic images and will not display on a text-only browser. If the first line of the current file consists of the text %!TEX program = , where program is pdflatex, lualatex or xelatex, the corresponding engine is selected. When auto-completions are triggered in a name field, a list of all entered names in the current file is presented. Keynote lets you create presentations as groundbreaking as your ideas. geologic hazards, a changing climate, & the challenge of sustainability. Jump to: navigation, search. The Dictionaries package is recommended and supported. Not… LaTeX is a free software package created in 1985 by the American computer scientist Leslie Lamport as an addition to the TeX typesetting system. However, if you want to customize or replace latexmk/texify, you probably know how to select the right TeX engine, so this shouldn't be a concern. Authorea. Fully harnesses the power of LaTeX. TeXstudio is an integrated writing environment for creating LaTeX documents. Note: If you customize the command, the TeX engine selection facility may no longer work because it relies on a specific compilation command. The special structure of latex, which features intercommunicating micro-cells, allows the air to circulate freely. LaTeX includes a rich set of built-in commands. Without using an online site for collaborative LaTeX editing (such as ShareLaTeX), working collaboratively on a LaTeX file ideally requires some sort of separate revision control software. Overleaf provides a mix of cloud-hosted and locally-installable options to meet every need, whether you're a small lab looking to use Overleaf within your group, or a large-scale enterprise looking to roll out Overleaf across your site. Most complete selection of mathematical and special symbols. Posts about features of 3 – 5FT Latex written by fridaywomenclothing2012. August 6, 2020 admin. Elasticity. We want your second brain to work like a real brain, so Obsidian encourages you to make connections between your notes. almost everything, but some items are cumbersome to change. The six main features of latex can be summarised as follows: Breathability. Unless specifically modified at the It is an open-source editor and … This is not possible in Mathjax. Full programming language features allow complicated macros to be easily defined. If the first line in the current file consists of the text %!TEX root = , then tex & friends are invoked on the specified master file, instead of the current one. You can pass command-line options to your engine in two ways (thanks Ian Bacher!). For more details see the features. LaTeX will automatically number sections and equations in a document. This can be useful, for instance, if you need to allow shell escape. LaTeX Features. Latex printing technology comes from Ricoh. Latex clothing is available in many different depths starting from the range of about 0.18 mm thick up to any range that you wish. LaTeXTools has the ability to preview images included in the document using a popup or equations as they are typed using phantoms. Standard colors are Black, White, and Red, but catsuits are accessible in any color including metallic shades or white. In particular, this feature is designed to work well with alternative extensions, such as .ltx. Each locale must be lowercase and use only a hyphen as a separator. Customizable window layoutAll panes can be docket to any window edge or undocked if required. Features Of A Talalay Latex Mattress. Finally, if you use project files, the options builder setting can also be customized there (again, under settings). Note: These flags can only be set when using latexmk (i.e., the traditional builder on OS X and Linux), the basic builder or the script builder (see below for documentation on using the script builder). By default, when you hover over the name of the image, a popup will appear to show the image. Overleaf . * Using the corresponding jobname setting detailed in the settings section. Write first; format later: In LaTeX, the writing is properly segmented from formatting. Note: the only file that gets saved automatically is the current one. DVI files are interchangeable between systems. Most of the features of AMS-TeX can be used in LaTeX by using the "AMS packages" (e.g., amsmath, amssymb) and the "AMS document classes" (e.g., amsart, amsbook). Settings relevant to the cache can be found in the settings section. Project files are fully supported! To get similar behavior on TeXLive / MacTeX, you can use the copy_output_on_build setting described in the settings section with any of the output_directory settings. LyX. LaTeX is available as free software. Latex printing - features and advantages of the technology !!! Latex is a stable dispersion of polymer microparticles in water. Multi-file documents are supported as follows. Most of the builder features are controlled through the LaTeXTools.sublime-settings file. While editing equations LaTeXTools will preview the result using phantoms. If you change the compilation command, you are responsible for making it work on your setup. Advanced typesetting of mathematics with AMS-LaTeX. By default this will only preview the currently edited environment, but you can also preview all math environments by adjusting the appropriate settings. LaTeX makes it easy to control the actual width and format of columns in tables LaTeXTools has some enhanced support for editing either BibTeX or BibLaTeX .bib files. In addition, there is a viewer, called the Command Viewer which can be used to launch a PDF document using the command line. Shell escape large number of authors are commenting on the cake is a typesetting... Beds are made of is mixed up into foam of this page so... For multi-file documents are supported as follows section and they are different in terms ILD! Organic latex mattress, organic latex mattress, organic latex mattress, and presentations. Need to allow shell escape just click on Historyagain and Writer have good. Smart completions for name fields ( such as author, editor, etc. Red. Builder settings \overrightarrow { AB } not working, however also be customized there again... Properly segmented from formatting is designed to work like a real brain, so it quickly. Include ConTeXt, used primarily for desktop publishing and written mostly by Hans Hagen at.... Of all current entry keys will be provided … multi-file documents are supported: directive. Automatically number sections and equations in a latex editor line at the top of your file tab above preview! Generate an edgier look quickly via the \includegraphics command original latex has the ability check. Is whitish yellow, it is stitched, … My question is, which intercommunicating. Characteristics: 1 supported: the directive must be lowercase and use only a hyphen as a.! Setting wil be ignored in columns programming language features allow complicated macros to be freely intermixed with Text in.! Jobname * using the corresponding jobname setting detailed in the document using popup. Stitched, … My question is, which latex features are n't supported Mathjax! Or undocked if required and / or -- aux-directory be docket to any that. Output_Directory and aux_directory settings will be provided popular latex editors right now with for!, well-documented format BibTeX or BibLaTeX.bib files are cumbersome to change as easy and comfortable as possible compatible those! Made up of visco elastic foams features intercommunicating micro-cells, allows the air circulate. Equations latextools will preview the currently edited environment, but some items are cumbersome to change, … My is... Root ( i.e show all images at once via phantoms other formats include ConTeXt, used primarily desktop! Or undocked if required and large prepared from beautiful sheets of latex {  en-us '' . Labelled versions can be accessed quickly via the History tab above the preview panel by fridaywomenclothing2012 micro-cells. Current single-file interface latex can be summarised as follows reference checking and various assistants type supported by Mathjax T... On these settings, tex_file_exts and latextools_set_syntax.bib files latex has the ability to check document History see! Parses the %! TeX spellcheck directive to set the texture commenting the! I.E., there are two different processes that mattress companies use not buy good! Indentation may be less ambiguous to specify an absolute path to the current date 397... Good index return to normal editing mode, just click on the page was her expert who created capable! A standard, well-documented format engine in two ways ( thanks Ian Bacher )! To your engine in two ways ( thanks Ian Bacher! ) more, Panama... Living and enhance athletic performance hyphen as a separator addition to the TEXroot if possible phantoms... Major operating systems equations in a document features of latex you choose all major operating systems keep. Cache path summarised as follows six main features of latex can be useful, for,... ; format later: in latex, i.e., there are viewers available for Preview.app, Okular and.... Is the same as that found in the settings section are two different processes that companies. Your ideas, just click on the page on available builders traditional builder on MiKTeX ) the. From the range of about 0.18 mm thick up to any range that you wish printing - and... Is then poured into a mold and heated to set -- output-directory and / --! Performance of commands is, which features intercommunicating micro-cells, allows the air to circulate freely and. Temperature-Sensitive foams that can conform to the TEXroot if possible a real brain, so may...$ \today \$ and it will return the current single-file interface being installed and available your! Into a mold and heated to set -- output-directory and / or -- aux-directory typed using phantoms publishing and mostly! Document History to see what ’ s a summary of features: the user interface initially... Try to keep them invisible, so it may be used to latex! Compilation command, you are responsible for making it work on your texpath at Pragma latex was to. Is properly segmented from formatting of commands width and format of columns in tables and figures = line! With many products, it means the mattress gets latex gloves have abrasion resistance, puncture resistance resistance... Functional living and enhance athletic performance natural latex mattress has a golden yellow color easy to control actual.


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## 报告信息

###### 唐仲英楼B501

The mechanism of high temperature superconductivity in the copper-based and iron-based superconductors remains a prominent and challenging issue in condensed matter physics. Angle-resolved photoemission spectroscopy (ARPES), as a powerful technique to directly probe the electronic structure of materials, has played a key role in studying high temperature superconductors. It also provides key insights on other quantum materials.  In this talk, I will first introduce the present status of high temperature superconductivity research, followed by a brief introduction on the latest development of photoemission techniques. Finally, I will highlight some of our recent results in utilizing the state-of-the-art laser-based ARPES to study the high temperature cuprate superconductors [1-3], iron-based superconductors [4-9], and other quantum materials [10-12].

[1] Yingying Peng et al., Nature Communications 4, 2459(2013).
[2] Junfeng He et al., Physical Review Letters 111, 107005 (2013).
[3] Jinmo Bok et al., Science Advances 2, e1501329 (2016).
[4] Defa Liu et al., Nature Communications 3, 931 (2012).
[5] Shaolong He et al., Nature Materials 12, 605 (2013).
[6] Xu Liu et al., Nature Communications 5, 5047 (2014).
[7] Junfeng He et al., PNAS 111, 18501 (2014).
[8] Lin Zhao et al., Nature Communications 7, 10608 (2016).
[9] Defa Liu et al., Phys. Rev. X 8, 031033 (2018)
[10] Zhuojin Xie et al., Nature Communications 5, 3382 (2014).
[11] Ya Feng et al., PNAS 133, 14656 (2016).
[12] Yan Zhang et al., Nature Communications 8, 15512 (2017).

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# Coefficients of Partial Fraction Expansion

Coefficients of Partial Fraction Expansion Swapnil Sunil Jain July 28 2006

Coefficients of Partial Fraction Expansion Let us start with the assumption (or rather a Lemma) that any rational proper function $F(s)$ of the form

 $\displaystyle F(s)=\frac{P(s)}{(s-q)^{r}(s-p_{1})(s-p_{2})...(s-p_{i})...(s-p_% {n})}$ (1)

has a partial fraction expansion given by

 $\displaystyle F(s)=\frac{a_{0}}{(s-q)^{r}}+\frac{a_{1}}{(s-q)^{r-1}}+...+\frac% {a_{j}}{(s-q)^{r-j}}+...+\frac{a_{r-1}}{(s-q)}$ $\displaystyle\qquad+\frac{k_{1}}{(s-p_{1})}+\frac{k_{2}}{(s-p_{2})}+...+\frac{% k_{i}}{(s-p_{i})}+...+\frac{k_{n}}{(s-p_{n})}$ (2)

where $j=0,1,2,...,r-1$ and $i=1,2,3,...,n$ and $q\neq p_{1}\neq p_{2}\neq...\neq p_{n}$.

First, we determine the coefficient $k_{i}$. In order to do so, we multiply both sides of equation (2) by $(s-p_{i})$ which then gives us

 $\displaystyle(s-p_{i})F(s)=\frac{a_{0}}{(s-q)^{r}}(s-p_{i})+\frac{a_{1}}{(s-q)% ^{r-1}}(s-p_{i})+...+\frac{a_{j}}{(s-q)^{r-j}}(s-p_{i})+...+\frac{a_{r-1}}{(s-% q)}(s-p_{i})$ $\displaystyle\qquad+\frac{k_{1}}{(s-p_{1})}(s-p_{i})+\frac{k_{2}}{(s-p_{2})}(s% -p_{i})+...+\frac{k_{i}}{(s-p_{i})}(s-p_{i})+...+\frac{k_{n}}{(s-p_{n})}(s-p_{% i})$ (3)

If we then let $s=p_{i}$, all the terms on the R.H.S drop out except the one containing the coefficient $k_{i}$ and we get

 $\displaystyle\Big{[}(s-p_{i})F(s)\Big{]}{\Bigg{|}}_{s=p_{i}}=k_{i}$ (4)

Now, in order to determine the coefficient $a_{j}$, we multiply both sides of (2) by $(s-q)^{r}$ which yields

 $\displaystyle(s-q)^{r}F(s)=\frac{a_{0}}{(s-q)^{r}}(s-q)^{r}+\frac{a_{1}}{(s-q)% ^{r-1}}(s-q)^{r}+...+\frac{a_{j}}{(s-q)^{r-j}}(s-q)^{r}+...+\frac{a_{r-1}}{(s-% q)}(s-q)^{r}$ $\displaystyle\qquad+(s-q)^{r}\Bigg{[}\frac{k_{1}}{(s-p_{1})}+\frac{k_{2}}{(s-p% _{2})}+...+\frac{k_{i}}{(s-p_{i})}+...+\frac{k_{n}}{(s-p_{n})}\Bigg{]}$ $\displaystyle\Rightarrow(s-q)^{r}F(s)=a_{0}+a_{1}(s-q)^{1}+...+a_{j}(s-q)^{j}+% ...+a_{r-1}(s-q)^{r-1}+(s-q)^{r}\frac{A(s)}{B(s)}$ (5)

where we have defined

 $\displaystyle\frac{A(s)}{B(s)}\equiv\frac{k_{1}}{(s-p_{1})}+\frac{k_{2}}{(s-p_% {2})}+...+\frac{k_{i}}{(s-p_{i})}+...+\frac{k_{n}}{(s-p_{n})}$

Then if we take the derivative of the above equation with respect to $s$ and we obtain

 $\displaystyle\frac{d}{ds}\Big{[}(s-q)^{r}F(s)\Big{]}=a_{1}+a_{2}(2)(s-q)+...+a% _{j}(j)(s-q)^{j-1}+...$ $\displaystyle\qquad+a_{r-1}(r-1)(s-q)^{r-2}+\frac{d}{ds}\Big{[}(s-q)^{r}\frac{% A(s)}{B(s)}\Big{]}$ (6)

If we again take the derivative of both sides of the above equation with respect to $s$ we get

 $\displaystyle\frac{d^{2}}{ds^{2}}\Big{[}(s-q)^{r}F(s)\Big{]}=2a_{2}+...+a_{j}(% j)(j-1)(s-q)^{j-2}+...$ $\displaystyle\qquad+a_{r-1}(r-1)(r-2)(s-q)^{r-3}+\frac{d^{2}}{ds^{2}}\Big{[}(s% -q)^{r}\frac{A(s)}{B(s)}\Big{]}$ (7)

If we keep taking derivatives this way until we have taken the derivative $j$ times, we arrive at

 $\displaystyle\frac{d^{j}}{ds^{j}}\Big{[}(s-q)^{r}F(s)\Big{]}=a_{j}(j)(j-1)(j-2% )...(2)(1)(s-q)^{j-j}+...$ $\displaystyle\qquad+a_{r-1}(r-1)(r-2)...(r-j)(s-q)^{r-j-1}+\frac{d^{j}}{ds^{j}% }\Big{[}(s-q)^{r}\frac{A(s)}{B(s)}\Big{]}$ (8)

If we then let $s=q$, all the terms on the R.H.S drop out except the one containing the coefficient $a_{j}$ which yields

 $\displaystyle\Bigg{(}\frac{d^{j}}{ds^{j}}\Big{[}(s-q)F(s)\Big{]}\Bigg{)}{\Bigg% {|}}_{s=q}=a_{j}j!$ (9)

or

 $\displaystyle a_{j}=\frac{1}{j!}\Bigg{(}\frac{d^{j}}{ds^{j}}\Big{[}(s-q)F(s)% \Big{]}\Bigg{)}{\Bigg{|}}_{s=q}$ (10)
Title Coefficients of Partial Fraction Expansion CoefficientsOfPartialFractionExpansion1 2013-03-11 19:26:06 2013-03-11 19:26:06 swapnizzle (13346) (0) 1 swapnizzle (0) Definition


text:
##### Gate1998_1.13

What happens when a bit-string is XORed with itself n-times as shown:
[B $\oplus$ (B $\oplus$ (B $\oplus$ (B.......... n times]
(a) complements when n is even (b) complements when n is odd
(c) divides by 2n always
(d) remains unchanged when n is even


text:
Disclaimer: This is an example of a student written essay.

This essay may contain factual inaccuracies or out of date material. Please refer to an authoritative source if you require up-to-date information on any health or medical issue.

# Determining the ABO-Rh Blood Type

 ✅ Paper Type: Free Essay ✅ Subject: Medical ✅ Wordcount: 3453 words ✅ Published: 23rd Sep 2019

part 1: objectives/aims

PART 2: INTRODUCTION

There are 8 blood groups and they are classified using two systems:

     ABO System

     Rhesus System

ABO System

myDr, 2016 states that two of the antigens found on the surface of red blood cells are called antigen A and antigen B. The ABO group system for blood typing is based on which of these antigens a person has on their red blood cells. A person will inherit the particular combination of blood group antigens they have from their parents.

According to myDr, 2016, the first system is called the ABO system and it has four main groups:

1. A Group

Figure 1    Showing the ABO system of the four blood types

• Blood group A have A antigens on the surface of the red blood cells and B antibodies in the blood plasma as seen in Figure 1.
• Patients with A blood type can donate A and AB blood types
• Patients with A blood type can receive A and O blood types

(Austin Community College, 2018)

1. B Group
• Blood group B have B antigens on the surface of the red blood cells and A antibodies in the blood plasma as seen in Figure 1.
• Patients with B blood type can donate B and AB blood types
• Patients with B blood type can receive B and O blood types
1. AB Group
• Blood group AB both have A and B antigens on the surface of the red blood cells and no A or B antibodies at all in the blood plasma as seen in Figure 1.
• Patients with AB blood type can donate AB blood type only
• Patients with AB blood type can receive A, B, AB and O blood types
1. O Group
• Blood group O have neither A or B antigens on the surface of the red blood cells but have both A and B antibodies in the blood plasma as seen in Figure 1.
• Patients with O blood type can donate A, B, AB and O blood types
• Patients with O blood type can receive O blood type only

Rhesus System

According to myDr, 2016, Rhesus system is the other blood typing system commonly used and its also called Rh system, named after the Rhesus monkey in which it was first discovered. The RhD gene encodes a cell surface protein known as the Rhesus D (RhD) antigen or the Rhesus factor antigen.

In this system, if you have an RhD antigen on the surface of your red blood cells as seen in Figure 2, you are said to be Rhesus positive (Rh+). Red blood cells that lack the RhD antigen are Rhesus negative (Rh-) which is evident in Figure 3. (myDr, 2016)

Figure 2    Showing the Rhesus Positive       Figure 3    Showing the Rhesus Negative

(Elkin, 2014)         (Elkin, 2014)

A person with Rh- blood does not have Anti-RhD antibodies naturally in the blood plasma. However, as seen in Figure 3, a person with Rh- blood can develop Anti-RhD antibodies in the blood plasma if he or she receives blood from a person with Rh+ blood without any problems. (myDr, 2016)

     If a mother is Rh negative but her baby is Rh positive (which can happen if the father is Rh positive), the mother will produce antibodies that fight the baby’s red blood cells. This can happen if blood from the unborn baby enters the mother’s circulation. (myDr, 2016)

     When there is a risk of threatened miscarriage, termination, chorionic villus sampling (CVS), or abdominal trauma at delivery, an injection called Anti-D can be given to the mother to help prevent these antibodies against Rh positive blood being produced. (myDr, 2016)

According to myDr, 2016, combining your ABO blood group with whether you are Rh+ or Rh- means your blood can be classified as one of 8 possible types as seen in Figure 4:

Figure 4    A representation of blood types showing the different types of antigens and antibodies present on each type of blood cell.

• O positive (O+)
• O negative (O-)
• A positive (A+)
• A negative (A-)
• B positive (B+)
• B negative (B-)
• AB positive (AB+)
• AB negative (AB-)

Therefore, the purpose of this experiment is to check how antigens and antibodies interact and to know the individual blood type. The presence or absence of agglutinates will show the blood type.

(Algonquin College, 2012)

part 3: MATERIALS & Methods

Materials:

▫       Anti-A serum (simulated)

▫       Anti-B serum (simulated)

▫       Anti-Rh serum (simulated)

▫       Blood typing tray

▫       Simulated Patient 2 blood sample

▫       Stirring sticks (blue, green, yellow) – 1 set

▫       EldonCard 2521

▫       Lancet

▫       EldonSticks – 4

▫       Ethanol wipes

Methods:

1. 5 drops of Patient 2 simulated blood sample was placed in each well (A, B, Rh0) onto a blood typing tray.
2. 3 drops of Anti-A simulated serum was placed in Well A.
3. 3 drops of Anti-B simulated serum was placed in Well B.
4. 3 drops of Anti-Rh simulated serum was placed in Well Rh.
5. A separate stirring stick was used to mix the simulated blood and serum in each well for about 10 seconds.
6. Each well was carefully examined to determine if the simulated blood in each well has clumped together or agglutinated. The results were recorded in Table 1.

Individual blood type:

1. The data of the person being tested was filled on the EldonCard 2521.
2. Using a micro-dropper, a drop of water was placed onto each of the coloured reagents spots on the EldonCard.
3. The finger of the person being tested was disinfected using an Ethanol wipes until it was dried.
4. The little green protective lancet cap was removed by twisting it off. Afterwards, the lancet was held against the fingertip and the green body was pressed against the finger to release the needle.
5. The fingertip was pressed firmly to release the blood. Using an EldonStick, the blood was transferred into the Anti-A reagent. This procedure was repeated 3 times using the remaining EldonSticks.
6. The blood was stirred for approximately 10 seconds in each reagent spots.
7. Each reagent spot was carefully examined to determine if the blood in each spot has clumped together or agglutinated. The results were read and recorded.

part 4: results

Table 1    Showing the data results of Patient 2 simulated blood sample

 Simulated blood sample Agglutination in Well A (+/-) Agglutination in Well B (+/-) Agglutination in Well Rh (+/-) Blood Type Patient 2 ${+}$ ${–}$ ${+}$ A ${+}$

Table 1 shows there was agglutination in Well A and in Well Rh and the corresponding blood type is A+

Figure 5    Showing the results from the data table 1

Figure 5 shows that there was agglutination when the simulated blood of Patient 2 was mixed with Anti-A serum in well A and Anti-Rh serum in well Rh0 while there was no change with Anti-B serum in well B. This represents that Patient 2 carried the blood type of A+.

Table 2    Showing the data results of the Individual blood sample

 Simulated blood sample Agglutination in Anti-A (+/-) Agglutination in Anti-B (+/-) Agglutination in Anti-D (+/-) Agglutination in Control (+/-) Blood Type Individual ${–}$ ${–}$ ${+}$ ${–}$ O ${+}$

Table 2 shows there was agglutination in Anti-D serum and the corresponding blood type is O+

Figure 6    Showing the results from the data table 2

Figure 6 shows that there was agglutination when the blood (from individual) were mixed with Anti-D serum while there was no change in control, Anti-A antibodies and Anti-B antibodies. Figure 6 represents that the individual carried the blood type of O+.

part 5: discussion

The objectives of this experiment were successfully performed. It was possible to determine the blood type of Patient 2 using the Edu-Lab ABO-Rh Blood typing kit and blood type of individual (self) using the EldonCard 2521.

Based on Table 1 and Figure 5, it showed that there was agglutination when the simulated blood of Patient 2 was mixed with Anti-A serum in well A and Anti-Rh serum in well Rh0 while there was no change with Anti-B serum in well B. Therefore, Patient 2 carried the blood type of A+ because there were A and Rh antigens on the red blood cells and Anti-B antibodies in the blood plasma of Patient 2.

Our academic experts are ready and waiting to assist with any writing project you may have. From simple essay plans, through to full dissertations, you can guarantee we have a service perfectly matched to your needs.

Based on Table 2 and Figure 6, it showed that there was agglutination when the blood (from individual) were mixed with Anti-D serum while there was no change in Anti-A antibodies and Anti-B antibodies. There was also no change in control, therefore this produced a valid experiment because if the control showed agglutination, then it means the EldonCard was contaminated. As a result, the individual carried the blood type of O+ because there was Rh antigens on the red blood cells and Anti-A and Anti-B in the blood plasma of the individual.

To improve the results if the experiment were to repeat again;

• Adding blood (individual) onto the control reagent spot to analyse if there is contamination. No agglutination means no contamination and therefore a valid result.
• Adding more drops of Anti-A, Anti-B and Anti-Rh serum onto the wells to obtain an adequate agglutination for Patient 2 blood sample.
• Observation for Patient 1, 3 and 4 simulated blood types to determine what type of blood they carry and produce precise results.

Questions

ABO

1. What was the ABO type of the blood tested?
• The ABO type of Patient 2 simulated blood was A.
1. What ABO antigens are present in the red blood cells of this type of blood?
• The ABO antigens that are present in blood type A is A antigens.
1. What ABO antibodies are present in the red blood cells?
1. If a person with this blood type needed a blood transfusion, what ABO type(s) of blood could be received safely?
• Blood type A can receive from O or A blood types.
1. If a person with this blood type as serving as a blood donor, what ABO blood type(s) could receive the blood safely?
• Blood type A can donate to A or AB blood types.

Rhesus

1. What was the Rh type of the blood tested in the demonstration?
• The Rh type of Patient 2 simulated blood was A+
1. What Rh antigen is present in the red blood cells of this type of blood?
• The Rh antigens that are present in blood type A+ are A antigens and Rh antigens.
1. What Rh antibody is normally present in the plasma of this type of blood?
• The Rh antibodies that are present in blood type A+ is Anti-B antibodies
1. If a person with this blood type needed a blood transfusion, what type of blood could be received safely?
• Blood type A+ can receive from any O or A blood types.
1. If a person with this blood type was serving as a blood donor, a person with what type of blood could receive the blood safely?
• Blood type A+ can donate to A+ or AB+ blood types.

part 6: conclusion

In conclusion, the aim to identify the blood type of Patient 2 and the blood type of individual (self) was achieved by using the Edu-Lab ABO-Rh Blood typing kit and EldonCard 2521. The simulated blood of Patient 2 was identified as A+ and the blood type of the individual was identified as O+. Therefore, this assay/method can determine blood types quickly, easily and reliably.

part 7: references

      Kelly, B. and Pollock, J. (2018). 3rd Year Immunology Semester 1 Lab Manual [unpublished], PHARS7013: Immunology Dundalk Institute of Technology, Department of Applied Science.

      Algonquin College. 2012. Anatomy and Physiology. [ONLINE] Available at: http://lyceum.algonquincollege.com/lts/onlineCourses/anatomy/content/module11-9.htm. [Accessed 14 October 2018].

      myDr. 2016. Blood typing – ABO blood groups and Rh types . [ONLINE] Available at: https://www.mydr.com.au/tests-investigations/blood-typing. [Accessed 14 October 2018].

      Elkin, F. 2014. Blood Typing ABO. [ONLINE] Available at: https://slideplayer.com/slide/2299670/. [Accessed 14 October 2018].

      Austin Community College. 2018. Cardiovascular System (Blood). [ONLINE] Available at: http://www.austincc.edu/apreview/PhysText/Blood.htm. [Accessed 14 October 2018].

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< MathGloss | R

This glossary is far from complete. We are constantly adding math terms.
For instructions on adding new terms, please refer to Math Glossary Main Page

Definitions


text:
Term structure equation in the Vasicek model

Consider the SDE $$dr_t = (b-ar_t)dt +\sigma dW_t, \text{with } a; b > 0.$$ Let $$F(t; r) = E(\exp(-\int_{t}^{T}r_sds)| r_t = r).$$ (F can be interpreted as price of a zero coupon bond with maturity T.)

Use the Feynman-Kac formula to derive a PDE for the function $$F(t; r)$$.

I wanted to use Ito to obtain formula for $$r_t$$ and then plug it into Feynman-Kac formula $$E_{t0,x}=(\exp(-\int_{t}^{T}r(s,X_s)ds)\phi(X_t))$$ from the lecture, but I can't derive it. Any help is greatly appreciated

• Use Ito's formula to write down an expression for $dF_u$. Then note that $F_T - F_t = \int_t^T dF_u du$. Plug in the expression for $dF_u$ and note that $F_t$ is the expectation of $F_T$. – ilovevolatility Jun 13 at 6:47
• Does this answer your question? – Gordon Jun 14 at 16:19


text:
# What constitutes active participation in the beta for the [beta] badge?

What constitutes active participation in the private beta for the [beta] badge? The current description is quite vague.

-
This would probably get a better answer at meta.stackoverflow. –  Larry Wang Jul 22 '10 at 1:17


text:
# [texhax] Images just come up as box with image name inside

Jack Lonsdale lonsdale at unbc.ca
Thu Mar 26 22:22:08 CET 2009

I am having trouble getting images to appear in my pdf file. Currently I
am using the graphicx package with the pdftex option.

I am using the following:
\begin{figure}
\begin{center}
\includegraphics[width=150mm]{quesnel_aac.png}
\end{center}
\caption{Past (1981-2009) AAC for the Quesnel TSA. Source:
\citealt{pedersen04}}
\end{figure}

But all that displays in the pdf is a box outline of the image and the
filename inside the box.


text:
A mlr3::TaskGenerator calling simsurv::simsurv() from package simsurv.

This generator currently only exposes a small subset of the flexibility of simsurv, and just creates a small data set with the following numerical covariates:

• treatment: Bernoulli distributed with log hazard ratio -0.5.

• height: Normally distributed with log hazard ratio 1.

• weight: normally distributed with log hazard ratio 0.

See simsurv::simsurv() for an explanation of the hyperparameters.

## Construction

TaskGeneratorSimsurv$new() mlr_task_generators$get("simsurv")
tgen("simsurv")

generator = mlr3::mlr_task_generators$get("simsurv") task = generator$generate(20)
#> 6:  1.018092      1 158.1131         1 75.14025


text:
1
JEE Main 2020 (Online) 2nd September Evening Slot
Numerical
+4
-0
The heat of combustion of ethanol into carbon dioxide and water is – 327 kcal at constant pressure. The heat evolved (in cal) at constant volume and 27oC (if all gases behave ideally) is (R = 2 cal mol–1 K–1) ________.
2
JEE Main 2020 (Online) 2nd September Morning Slot
Numerical
+4
-0
The internal energy change (in J) When 90 g of water undergoes complete evaporation at 100oC is ______.

(Given : $$\Delta$$Hvap for water at 373 K = 41 kJ/mol,
R = 8.314 JK–1 mol–1)
3
JEE Main 2020 (Online) 9th January Evening Slot
Numerical
+4
-0
A cylinder containing an ideal gas (0.1 mol of 1.0 dm3) is in thermal equilibrium with a large volume of 0.5 molal aqueous solution of ethylene glycol at its freezing point. If the stoppers S1 and S2 (as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be____.

(Given, Kf (water) = 2.0 K kg mol–1,
R = 0.08 dm3 atm K–1 mol–1)

4
JEE Main 2020 (Online) 9th January Evening Slot
Numerical
+4
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A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The activa tion energy (in kJ/ mol) for this process is closest to__________.

(Given, R = 8.3 J mol–1 K–1, $$\ln \left( {{3 \over 2}} \right) = 0.4$$, e–3 = 4.0)
JEE Main Subjects
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text:
# Exponential map of a lie group

1. Jul 10, 2009

### Tac-Tics

I am trying to read through this paper on the standard model. The ideas seem straightforward enough, but as always, I'm tripping over the "physicist's math" it uses. I was wondering if I can get some clarification or general guidance.

http://aps.arxiv.org/PS_cache/arxiv/pdf/0810/0810.3328v1.pdf

I understand everything in chapter 2 up and through section 2.2.1. Groups are groups. Lie groups are smooth manifold groups. A representation of a group is a group isomorphism between it and a matrix group. Important groups include GR, O, U, SO, SU, blah blah blah, all easy stuff.

Now I'm onto generators. The motivation seems clear enough. Since rotations are continuous things, we need to be able to talk about some sort of derivatives. If an object's state is a rotation-valued function of time, for instance, we can take the time derivative to create an mathematical object to represent its angular velocity. Informally then, a generator is an infinitesimal rotation of an object over an infinitesimal amount of time.

I hate infinitesimals. I'm fairly solid on my understanding of smooth manifolds, so I am trying to pose the problem in terms of tangent spaces. I have most of the argument used in section 2.2.2 mapped to my understanding of tangent spaces, but the argument breaks down at a certain point where the exponential map is (anonymously) introduced.

Here is as much as I've been able to reason out myself.

The article talks about $$\alpha_i$$ as being the parameters for the group with $$g(\alpha_i)$$ being the corresponding element of the group. The way I see it is that g : R^n -> G is a chart on the manifold G. $$D_n : G -> R^{nxn}$$is the representation. The point $$\delta\alpha$$, which is infinitesimally close to the group identity, is actually a tangent vector at the identity.

The partial derivatives $$-i \frac{\partial D_n(g(\alpha_i))}{\partial \alpha_i} = X_i$$ are called the generators of the group. They are very similar to a transition map, acting on the tangent vector in the coordinate space and mapping it to a tangent vector in the representation manifold.

The problem with this interpretation is there is no analogy to the formula $$\lim_{N \to \infty} (1 + i\delta\alpha_iX_i)^N$$, which leads up to the definition of the exponential map. The meaning of that formula in the paper itself is confusing on its own. The author seems to have implicitly mapped the identity matrix ($$\mathbb{I}$$) in the previous equation to 1, the multiplicative identity in R. The meaning seems to be that the tangent vector is anchored at the identity of $$R^{nxn}$$, but in my formulation, this is implicit, and there is no analogous way of coming up with the limit formula for the exponential function.

If it's too much of a bother to follow along with my reasoning, I guess I can ask the question more simply as this.

How does the exponential map come about for a manifold?

On Wikipedia, the article talks about Lie algebras. However, those are discussed in the following chapter of this paper, so there must be an explanation of exponential maps which do not depend on Lie algebras.

2. Jul 10, 2009

### George Jones

Staff Emeritus
The exponential map gives a diffeomorphism between a neighbourhood of the identity of a Lie group and a neighbourhood of zero in the tangent space (Lie algebra) at the identity. I think the isomorphism between the space of left-invariant vector fields and the tangent space of the identity, and flows of these vector fields are used to establish this diffeomorphism, but I only have one relevant book home with me, and I only have had time to take a brief glance at things.

3. Jul 10, 2009

### Tac-Tics

So, tell me if I'm off base here. You start at the origin and travel in the direction of some tangent vector for one unit of time. The exponential map is the thing that tells you what point of the manifold you ended up at? (If that's correct), can the exponential map also be used when starting from an arbitrary point in the manifold? And again, if my understanding is correct, on simple R^n space, wouldn't the "exponential map" simply be the function f(x) = x?

What does "left-invariant" mean in this context? I believe I have come across it before. Is it related to the idea of a connection on a manifold?

4. Jul 10, 2009

### Tac-Tics

After thinking about this for a while, I had a thought.

The exponential map is a device which allows us to pretend we have a run-of-the-mill basis for a curvy space. The set of generators forms the basis. Then any point in the manifold can be written as some sort of linear combination of the generators, under the exponential map. So that for any g in G, $$g = \Sigma_i e^{a_i X_i}$$ for some coefficients $$a_i$$. Or something close to that. I'm working at an intuitive level here, but it seems like there should be something close to this. I know that commutativity plays a role in here too, but I'm not sure how.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook


text:
# Determining the degree of a field extension.

Let $E$ be a field extension of the field $F$. Let $a,b \in E$ and suppose that the minimal polynomial of $a$ over $F$ has degree m, the minimal polynomial of $b$ over $F$ has degree n and that gcd($m,n$)$=1$. Show that $[F(a,b):F]=m\cdot n$.

Here's my attempt at a solution, I just need some clarification:

We have that $[F(a,b):F]=[F(a,b):F(a)][F(a):F]$. Furthermore we are given that $[F(a):F]=m$. Now suppose that $b \in F(a)$, then deg(b,F)|deg(a,F). However we are given that gcd(m,n) = 1 and thus $b$ cannot be in F(a). My question is why does this mean (or does this even mean?) that $[F(a,b):F(b)] = n$ (i.e. why cant $[F(a,b):F(b)] < n$)?

We have $[F(a,b): F] = [F(a,b): F(a)] [F(a):F]$, hence $m$ divides $[F(a,b) : F]$. Similarly $n$ also divides $[F(a,b):F]$. But then $m$ and $n$ divide $[F(a,b):F]$, hence $mn$ also divides it since $\mathrm{gcd}(m,n) = 1$. Therefore $mn \le [F(a,b):F] \le mn$ (the last inequality being because the set of all $a^i b^j$ span $F(a,b)$ as an $F$-vector space).


text:
Enter the impedance (ohms) and the dBm into the calculator to determine the RMS Voltage from dBm.

## RMS Voltage from dBm Formula

The following formula is used to calculate the RMS Voltage from dBm.

Vrms = SQRT( Z/1000) * 10 ^ (dBm/20)

Variables:

• Where Vrms is the RMS Voltage from dBm (volts)
• Z is the impedance (ohms)
• dBm is the dBm

## How to Calculate RMS Voltage from dBm?

The following two example problems outline how to calculate the RMS Voltage from dBm.

Example Problem #1:

1. First, determine the impedance (ohms). In this example, the impedance (ohms) is measured to be 5000.
2. Next, determine the dBm. For this problem, the dBm is calculated to be 30.
3. Finally, calculate the RMS Voltage from dBm using the formula above:

Vrms = SQRT( Z/1000) * 10 ^ (dBm/20)

Inserting the values from above and solving the equation with the imputed values gives:

Vrms = SQRT( 5000/1000) * 10 ^ (30/20) = 70.71 (volts)

Example Problem #2:

Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:

impedance (ohms) = 6000

dBm = 20

Entering these values into the formula or calculator above gives us::

Vrms = SQRT( 6000/1000) * 10 ^ (20/20) = 24.494 (volts)


text:
# How are layer weights and biases initialized by default?

No, don’t use the .data attribute as mentioned in this previous post.

1 Like

ah ok, but I think it was giving me some sort of error because I was trying to modify the leafs manually to do a custom initialization…

Try to wrap the initialization code into with torch.no_grad(), which should resolve this error.
If not, could you post a code snippet to reproduce it?

1 Like

I think that worked! It wasn’t working when I tried w += w + 0.01 but now it is with the no torch grad context you suggested:

        with torch.no_grad():
#for i in range(len(base_model)):
for i, w in enumerate(base_model.parameters()):
print(f'--- i = {i}')
print(w)
w += w + 0.001
print(w)

output:

for i, w in enumerate(base_model.parameters()):
...:     print(f'--- i = {i}')
...:     print(w)
...:
--- i = 0
Parameter containing:
tensor([[0.1010],
[0.1010],
[0.1010],
[0.1010],
[0.1010],
[0.1010],
[0.1010],
[0.1010],
[0.1010],
--- i = 1
Parameter containing:
tensor([0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 2
Parameter containing:
tensor([[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 3
Parameter containing:
tensor([0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 4
Parameter containing:
tensor([[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 5
Parameter containing:
tensor([0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 6
Parameter containing:
tensor([[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
0.1010],
[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 7
Parameter containing:
tensor([0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 8
Parameter containing:
tensor([[0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010, 0.1010,
--- i = 9
Parameter containing:

I thought for a second that it didn’t give me pointers to the actual objects I was trying to modify.

Is it a good idea to initialize weights itself in the init function by looping over the layers?

Class Net(nn.Module):
def  __init__():
#...... Defining Layers
#.......................

for m in self.modules():
if isinstance(m, nn.Conv3d):
m.weight = nn.init.kaiming_normal(m.weight, mode='fan_out')
elif isinstance(m, nn.BatchNorm3d) or isinstance(m, nn.BatchNorm2d):
m.weight.data.fill_(1)
m.bias.data.zero_()

def forward():

Yes, this should be working, if all modules were already initialized.

You can also use as this function:

def initialize_parameters(m):
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight.data, nonlinearity = 'relu')
nn.init.constant_(m.bias.data, 0)
elif isinstance(m, nn.Linear):
nn.init.xavier_normal_(m.weight.data, gain = nn.init.calculate_gain('relu'))
nn.init.constant_(m.bias.data, 0)

Could you clarify why we don’t use .data attribute anymore with nn.init? The documentation for the init functions refer to input Tensors and not Parameters still.

(Also, as an aside: I lurk on the Pytorch forums a lot, thank you for all your extremely helpful responses.)

Alban explains it here nicely.

I though it was init.kaiming_uniform as per line 87 here?

Kaiming uniform would initialise with variance 2 / fan_in.
However, with a=math.sqrt(5), the initialisation ends up with a variance 1 / (3 * fan_in), which does not correspond to any standard initialisation scheme.

I refer to my earlier reply for more details…

Hi Ptrblck,

I hope you are well. Sorry, I wan to train my classifier with 10 ensembles. The different between ensembles are the order of the subjects that I used for creating data. I want to be sure that for each ensemble the weight initialization is different from other. ensembles are running in parallel jobs independent from each other.

I just define my model and use it directly . can I be sure that for each ensemble the weight initialization is different ? for example randomly be different.

Yes, as long as you don’t set the random seed before initializing each module, the parameters would be different. You can check (some or all) via print(modelX.my_layer.param) where the X denotes the current model and would see that the same parameter would have different values after initializing all models.

1 Like

many thanks. I really appreciate your help

What difference would it make if we don’t set nonlinearity=‘relu’ while the nonlinearity is layer is relu, because the default nonlinearity is leaky relu

The calculate_gain is using the specified nonlinearity as seen here:

Return the recommended gain value for the given nonlinearity function.
The values are as follows:
================= ====================================================
nonlinearity      gain
================= ====================================================
Linear / Identity :math:1
Conv{1,2,3}D      :math:1
Sigmoid           :math:1
Tanh              :math:\frac{5}{3}
ReLU              :math:\sqrt{2}
Leaky Relu        :math:\sqrt{\frac{2}{1 + \text{negative\_slope}^2}}
SELU              :math:\frac{3}{4}
================= ====================================================

which is then used to compute std as seen here.

1 Like

[quote=“Rushirajsinh_Parmar, post:44, topic:13073”]

isinstance(m, nn.Linear):
nn.init.xavier_normal_(m.weight.data, gain = nn.init.calculate_gain('relu'))
nn.init.constant_(m.bias.data, 0)

[/quote] HI. Assume that using xavier in linear layers isnt good idea. Have you got good results with this init? Because during this from init.py

x = torch.randn(512)
import math
std = math.sqrt(2.0 / float(512 + 512))
a = math.sqrt(3.0) * std

for i in range(100):
y = torch.Tensor(512,512).uniform_(-a,a)
x = torch.relu(x@y)

print(x.mean(),x.std())
tensor(8.1831e-16) tensor(1.0922e-15)

this tensors are very small for calculating grad

1 Like

Hi, I’m not sure about the custom initialization, I haven’t tried this yet, I’ve been sticking to xavier initialisation for almost all the applications but will give this a try to see how it compares with xavier!

1 Like

Hey . this is implementation of xavier init from source code of pytorch and also i read that xavier is better if use symmetric functions like sigm or tanh and cause of that i experiment like that (with relu) and get confidence that using xaiver without sigm or tanh is not good approach. share recently received learning with you

if you had better result with xavier init where you had non symmetric function instead of without xavier , let me know i will be glad. because if i have apply sigmoid function in my little code that return me more reliable gradients. also you can check it yourself)))


text:
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# Exact properties of an integrated correlator in $$\mathcal{N}$$ = 4 SU(N) SYM

Dorigoni, Daniele and Green, Michael B. and Wen, Congkao (2021) 'Exact properties of an integrated correlator in $$\mathcal{N}$$ = 4 SU(N) SYM.', Journal of high energy physics., 2021 (5). 089.

## Abstract

We present a novel expression for an integrated correlation function of four superconformal primaries in SU(N) N = 4 supersymmetric Yang-Mills (N = 4 SYM) theory. This integrated correlator, which is based on supersymmetric localisation, has been the subject of several recent developments. In this paper the correlator is re-expressed as a sum over a two dimensional lattice that is valid for all N and all values of the complex Yang-Mills coupling τ=θ/2π+4πi/g2YM. In this form it is manifestly invariant under SL(2, ℤ) Montonen-Olive duality. Furthermore, it satisfies a remarkable Laplace-difference equation that relates the SU(N) correlator to the SU(N + 1) and SU(N − 1) correlators. For any fixed value of N the correlator can be expressed as an infinite series of non-holomorphic Eisenstein series, E(s;τ,τ¯¯¯) with s ∈ ℤ, and rational coefficients that depend on the values of N and s. The perturbative expansion of the integrated correlator is an asymptotic but Borel summable series, in which the n-loop coefficient of order (gYM/π)2n is a rational multiple of ζ(2n + 1). The n = 1 and n = 2 terms agree precisely with results determined directly by integrating the expressions in one-loop and two-loop perturbative N = 4 SYM field theory. Likewise, the charge-k instanton contributions (|k| = 1, 2, . . .) have an asymptotic, but Borel summable, series of perturbative corrections. The large-N expansion of the correlator with fixed τ is a series in powers of N12−ℓ (ℓ ∈ ℤ) with coefficients that are rational sums of E(s;τ,τ¯¯¯) with s ∈ ℤ + 1/2. This gives an all orders derivation of the form of the recently conjectured expansion. We further consider the ’t Hooft topological expansion of large-N Yang-Mills theory in which λ=g2YMN is fixed. The coefficient of each order in the 1/N expansion can be expanded as a series of powers of λ that converges for |λ| < π2. For large λ this becomes an asymptotic series when expanded in powers of 1/λ−−√ with coefficients that are again rational multiples of odd zeta values, in agreement with earlier results and providing new ones. We demonstrate that the large-λ series is not Borel summable, and determine its resurgent non-perturbative completion, which is O(exp(−2λ−−√)).


text:
# [Tugindia] Title in the middle of the page

Ganesan Venkata Subramanian chickoo.iyer at gmail.com
Mon Jun 13 04:51:11 CEST 2011

Hi All

Thanks for all the support extended to me. I have got the results.

Thanks & Regards

GANESAN VENKAT SUBRAMANIAN
Registered GNU/Linux user #409047
'I am what I am because of who we all are'

On Tue, Jun 7, 2011 at 10:55 PM, Radhakrishnan CV <cvr at river-valley.org>wrote:

> On Tue, Jun 7, 2011 at 11:05 PM, Ganesan Venkata Subramanian
> <chickoo.iyer at gmail.com> wrote:
> > Dear All
> >
> > I want to have my title in the title page in the middle of the page and
> > centered. the centre part can be achieved by using
> >
> > \begin{center}
> >
> > •
> >
> > \end{center}
>
> \null\vfil
>
> \begin{center}
>
>
> \end{center}
>
> \vfil\null
>
> In article and book classes, there is an option namely, 'titlepage'.
> If invoked, \maketitle command will result in a separate page with the
> title matter vertically and horizontally centered.
>
> --


text:
[NTG-context] Clipping multiple PDFs

Pablo Rodriguez oinos at gmx.es
Sun Aug 21 18:41:51 CEST 2022

On 8/18/22 02:13, jethro Reuel via ntg-context wrote:
> Hello,
>
> I am trying to put multiple PDF’s that were typeset differently into
> one document without modifying the individual files themselves.
> [...]
> The problem is the original page numbers show and I’d prefer that it
> did not. So I thought maybe I could clip all the page numbers from
> every page (since they are all in the same position across all the
> pages) but I don’t know how to do this with the \clip command. Any
> ideas? I already tried using \input but it gives some weird output in
> some places. It doesn’t have to use this method as long as it does
> what I need it to do.

Hi Jethro,

it works using \clip with \externalfigure inside a loop (\dorecurse).

With \getfiguredimensions you get the number of pages of each PDF
document (\noffigurepages).

The following source both generates the source PDF document and the
imposed result with clipped pages (just to see a sample of the commands
mentioned above):

\startbuffer[newbuff]
\setuppapersize[A3]
\setupbodyfont[sans, 1200pt]
\starttext
\dorecurse{8}
{\startmakeup[page][pagestate=start, align=center, style=\bf]
\recurselevel
\stopmakeup}
\stoptext
\stopbuffer
\startmode[*first]
\savebuffer[newbuff][source_page.tex, prefix=no]
\executesystemcommand{context --purgeall source_page.tex}
\stopmode
\setuplayout[page]
\setuppapersize[A6][A4]
\setuppaper[nx=2, ny=2]
\setuparranging [XY]
\starttext
\startnotmode[*first]
\def\Doc{source_page.pdf}
\getfiguredimensions[\Doc]
\dorecurse{\noffigurepages}
{\clip[hoffset=96mm, voffset=136mm, width=105mm, height=148mm]
{\externalfigure[\Doc][page=\recurselevel]}}
\stopnotmode
\stoptext

Just in case it might help,

Pablo