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# Latex Set Numbering

  Numbering sections, subsections etc manually. Many examples here involve the now outdated and deprecated \subfig package so it is recommended that you head to Formatting captions and subcaptions in LaTeX to see more up to date examples that use the \subcaption package. Wow, this was a tough LaTeX problem, and it would really help if I knew a lot more about LaTeX. Every \chapter or \section command increments this counter. Word allows you to easily number a variety of elements in your document. LaTeX Font Warning: Size substitutions with differences (Font) up to 4. Each line number references the text located directly to the right. \pagestyle{empty} stops the pages being numbered \pagestyle{plain} this is the default; it puts the numbers at the bottom of the page. you will use \begin{equation}\end{equation}. If it is followed by { SEQ x } that field would display 101. Hello, I am wondering if there is an automatic way to number the equations in my thesis based on chapters, sections, subsections, , etc. Quickly create even complex LaTeX tables online with our generator -- cells merging is supported together with borders editing. By working with your colleagues and students on ShareLaTeX, you know that you're not going to hit any version inconsistencies or package conflicts. The standard label format is the global ﬂoat number followed by a lowercase al-phanumerical subﬂoat number. You can use \r to set a particular starting number. You can reset a counter, increment a counter or add a value to it. Open an example in ShareLaTeX.  Section numbering is automatic and can be disabled. More with theorems: styles and numbering You can use three built-in \styles" to specify how you want your theorem heading to appear. Double-click the icon "Set display mode" in the math toolbar (it can be turned on via: View -> Toolbars -> Math) The first clicking changes the equation to an inline formula and deletes the equation label at the same time. Not sure how you do it in latex. Many examples here involve the now outdated and deprecated \subfig package so it is recommended that you head to Formatting captions and subcaptions in LaTeX to see more up to date examples that use the \subcaption package. Counters are an essential part of LaTeX: they allow you to control the numbering mechanism of everything (sections, lists, captions, etc. ) Where LaTeX really shines is the formatting of mathematical equations. LaTeX: How to set the Table of Contents (TOC) depth | alvinalexander. You can use \r to set a particular starting number. Not so with equations; there is no automatic numbering feature for them. Latex allows the creation of enumerated (ordered) lists up to four deep. Continuous figure and table numbering in report/book The \counterwithout command removes a dependency from a counter and redefines \the’counter’ such that it is printed without the dependency. Customizing the numbering for pages, figures, sections, equations, theorems, and tables You can modify the default style for the names and numbering of things like figures, equations, sections, and the like easily in Latex. fragile commands and how to protect them (link to a LaTeX guide by NASA), here is the local copy other stuff. Find many great new & used options and get the best deals for 1 Set Party Balloon Latex 2020 Number Creative Decorative Balloons for Year at the best online prices at eBay!. These packages allow you to have sequential numbering throughout the text without resorting to ERT, and you can set up LyX to include them in your default document class. The value in the section counter is zero at the beginning of every chapter. LaTeX Stack Exchange!. It is most often used for medium-to-large technical or scientific documents but it can be used for almost any form of publishing. In fact, your example is probably best with the cases environment.   Page styles in Latex terms refers not to page dimensions, but to the running headers and footers of a document. Section headings of various sizes are produced (in the article document style) using the commands \section,\subsection and \subsubsection commands. The displaymath environment is for formulas that appear on their own line. Prints the text set inside the braces on the left side of the header. I think this must be a package. There are a number of ways that text can be added properly. The first few pages of the document have roman page numbers, the rest have arabic page numbers starting with one. Computerized typesetting. Word allows you to easily number a variety of elements in your document. \end{document} change textwidth Usepackage geometry also allows an esay way to change the textwidth as the next exmaple would show us: set. In LaTeX it is straightforward to include mathematical equations and notation in your document. In this post, I would like to introduce several ways to work with Chinese in LaTeX. the symbol &; each row has the same number of cells (i. Floating bodies. For example, a standard integral in LaTeX looks like $ \int_a^b \! f(x) \, \mathrm{d}x. The enumerate package  Set the counter to 7 so that we get the width of 'vii' if roman numbering is in force then set \leftmarginn. I am working on numbering on page. \theoremstyle{plain}% default \newtheorem{thm}{Theorem}[section] \newtheorem{lem}[thm]{Lemma}. LaTeX: How to set the Table of Contents (TOC) depth | alvinalexander.  How can I make an enumerate list start at an arbitrary value? Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Many suggestions can be applied to book and article styles, as well. eps files to substitute them in LaTeX? Heard about that possibility but also read quite often that this feature is not longer available. earlier page (and, if one continues onto the current page, to say what the number of that question is). Below is a list of the counters used LaTeX's standard document styles to control numbering. 1 Maths Environments. To increase the font size of the line numbers add \def\linenumberfont{\normalfont\small\sffamily} (in two column layouts this might have the unwanted effect of line numbers of the right column overlapping with the text in the left column) If you have questions about the usage of the lineno package contact cammin_at_fnal. 1 for Appendix A), the following TeX hack can be used to reset and format the numbering. , in order to get a particular bug fix. Right now the page number is bottom centered on the first page of a chapter, on the top outer margin on the subsequent pages of a chapter. The second line includes subsubsections in the table of contents. If you want to change them, you have several options: the "geometry" package, the "fullpage" package or changing the margins by hand. LaTeX's margins are, by default, 1. The values a and b can be zero, so the set of real numbers and the set of imaginary numbers are subsets of the set of complex numbers. Producing White Space in LaTeX. 202544536-dc20 CIP Printed on acid-free paper °c Birkh. 5 Floats A common mistake is to put a whole table, figureor other oat environ-ment inside an LR-box command. Note that this can result in duplicate page numbers. Lining up Page Numbers in the Table of Contents You have a beautiful table of contents (TOC) with all the proper indents and perfect alignment of all the letters and numbers on the left—but what's with those page numbers? They're waving down. LaTeX numbering One advantage of LaTeX over the other TeX-flavors is that it provides an automatic numbering of the sections, theorems, equations etc.   This counter can be set manually at any time using the \setcounter{page}{number} command, where number is the new page number you’d like. A LaTeX environment is one of the following: Contents[show] Float environments Text inside a float environment is "floated" according to its placement, an optional parameter. Because it is embedded on the Multifunctional Product, there is no need to install additional hardware or software. As always, the fact that LaTeX takes care of all caption and reference numbering is a great time saver. In the screenshot, with the Level on the left set at 1, we added the word "Chapter". These recognized units are given in the following table:. This site is supported by donations to The OEIS Foundation. No page numbering. Through \counterwithout , the figure and table counters can be changed to continuously number these figures and tables throughout a report or book. The first line enables numbering of subsubsections. Note that ShareLaTeX uses a European LaTeX distribution, which produces documents in A4 size by default. Sum-class symbols, or accumulation symbols, are symbols whose sub- and superscripts appear directly below and above the symbol rather than beside it. Floating bodies. \pagestyle{empty} stops the pages being numbered \pagestyle{plain} this is the default; it puts the numbers at the bottom of the page. There are a number of ways that text can be added properly. typical problems that arise while writing a thesis with LaTeX and suggests improved solutions by handling easy packages. \end{document} change textwidth Usepackage geometry also allows an esay way to change the textwidth as the next exmaple would show us: set.  Page styles in Latex terms refers not to page dimensions, but to the running headers and footers of a document. Prints the text set inside the braces on the left side of the header. How I can I do this?. Examples: 1 + i, 2 - 6i, -5. , John Stillwell's "Elements of Number Theory," and Edward Barbeau's "University of Toronto Mathematics Competition (2001-2015)," which is often used to prepare. Paper size, orientation. Regards Numbering the Equations in Latex | Physics Forums Menu. I am working on numbering on page. Not so with equations; there is no automatic numbering feature for them. Numbering every other line. 5) $\endgroup$ - Charlie Tian Sep 21 '17 at 16:25. See the specific command for information on why you would use one over the other. The math environment is for formulas that appear right in the text. The main number is referred by \themainfigure resp. The value in these counters can be set by using the \setcounter command. L a T e X can organize, number, and index chapters and sections of document. LATEX Basics 1.   The page headers and footers in LATEX are deﬁned by the \pagestyle and \pagenumbering commands. But, since the command is after the "\begin{document}" command, roman numbered pages still have the page number on the top right corner. Square brackets are used for optional arguments to LaTeX. But to answer your question directly, used the aligned environment within equation - this way the outside environment gives the number:. Other sets such as quaternions, or hyper-complex numbers exist but are reserved for advanced mathematical theories. The main number is referred by \themainfigure resp. where the page number will be printed), while \pagenumberingdeﬁnes the format of the page number. It may happen that you need a more recent LaTeX than the one that your favourite TeX distribution carries, e. to the width of the label. These packages allow you to have sequential numbering throughout the text without resorting to ERT, and you can set up LyX to include them in your default document class. Because the numbers [latex]2[/latex] and [latex]-2[/latex] are the same distance from zero, they are called opposites. Examples: 1 + i, 2 - 6i, -5. For example: { SEQ x \r 100 } produces the number 100. Right now the page number is bottom centered on the first page of a chapter, on the top outer margin on the subsequent pages of a chapter. However, want I want is the pages to be: vii-ix, followed by pages 1-120. same number of &)3 which must be equal to that declared in the deﬁnition cols. \themaintable. \rfoot{Page \thepage} Prints the word "Page" and next the page number which is automatically set by \thepage on the right side of the footer. Every \chapter or \section command increments this counter. Karl Shevick started Sleep On Latex in 2013 and brought in his brother, Ezra, a year later to help grow the business.  The following example illustrates the use of the tag if, for example, we need to start our enumeration from 6 and not 1: \begin{enumerate} \setcounter{enumi}{5} \item Hello \item Bye \end{enumerate}. The valid options are: plain - Just a plain page number. , are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands for area. So i m using \thispagestyle{empty}. Customizing the numbering for pages, figures, sections, equations, theorems, and tables You can modify the default style for the names and numbering of things like figures, equations, sections, and the like easily in Latex. Both issues are simply artifacts of the maths mode, in that it treats it as a mathematical expression: spaces are ignored (LaTeX spaces mathematics according to its own rules), and each character is a separate element (so are not positioned as closely as normal text). [tags]latex, subsubsection, paragraph, section, numbering, tex[/tags]. The values will be searched in the hierarchy. See the specific command for information on why you would use one over the other. Under most circumstances this is fine, but for the first few pages, such as the contents and title pages, you might want something a bit different. Hello, I am wondering if there is an automatic way to number the equations in my thesis based on chapters, sections, subsections, , etc. One of the easiest and most flexible options is to use the fancyhdr package. Some of these commands are LATEX macros, while oth-. LaTeX Counters Everything LaTeX numbers for you has a counter associated with it. MakeIndex distinguishes three kinds of sort keys:. The name of the counter is the same as the name of the environment or command that produces the number, except with no \. The math environment is for formulas that appear right in the text.   Resetting theorem numbering for new divisions. 3 and using labels to reference that label should return: table 1. The numbering styles for each depth can be styled to suit your needs using the \renewcommand{label}{style} command, where label is the list depth being styled and style is how you want that number to be shown. , from − 2 31 {\displaystyle -2^{31}} to 2 31 − 1 {\displaystyle 2^{31}-1}. You could use \setcounter{equation}{4} to set the equation number to 5, but this will break your other numbers ;-) - user31729 Mar 17 '15 at 14:06 Thanks, I expect only very very few equations in what I am writing. So I need to switch of the automatic numbering for specific tables and set those numbers myself. \centering is also defined by latex. The main number is referred by \themainfigure resp. One of the easiest and most flexible options is to use the fancyhdr package. Latex allows the creation of enumerated (ordered) lists up to four deep. Open an example in Overleaf Document Sectioning. There is also a command \& which is not supported by Wikia's LaTeX parser. Hyperbolic functions The abbreviations arcsinh, arccosh, etc. This can be changed by redeﬁning the commands \thesubfloatfigureand \thesubfloattable. See the specific command for information on why you would use one over the other. There are up to 7 levels of depth for defining sections depending on.  The second page of the document will then be numbered "2". You can change the fonts, numbering style, alignment and format of the captions and the caption labels. Under most circumstances this is fine, but for the first few pages, such as the contents and title pages, you might want something a bit different. This means that the desired size is not available and the closest matching size is 4. Some people are allergic to latex, which is found in rubber gloves and other products, such as condoms and some medical devices. By default, page numbers start from the first page (often the title page) and are displayed in arabic numbers (ie: 1, 2, 3 …). You can typeset You can typeset stand alone les as well as listings with an environment similar to verbatim. This tutorial is relatively short, largely due to the fact that the whole LaTeX ethos is concentrate on the content, and let LaTeX (and/or other typographers who have developed suitable document classes) decide on the best presentation. If you want to change them, you have several options: the "geometry" package, the "fullpage" package or changing the margins by hand. Prints the text set inside the braces on the left side of the header. One of the easiest and most flexible options is to use the fancyhdr package. siunitx — A comprehensive (SI) units package Joseph Wright† Released 2019/10/10 Abstract Physical quantities have both numbers and units, and each physical quantity should be expressed as the product of a number and a unit. In the example, to change the start number of level 2 to V the command \setcounter{enumii}{4} was used. Covington is described here. Simply begin the appropriate environment at the desired point within the current list. The value of a counter can be changed with a command of the type \setcounter{equation}{0}. I tried googling it but the term "bullet and numbering" only applies for Microsoft Word. The linking of LaTeX environments and commands to LyX is well documented elsewhere on this website. Note that ShareLaTeX uses a European LaTeX distribution, which produces documents in A4 size by default.   ) Where LaTeX really shines is the formatting of mathematical equations. The main number is referred by \themainfigure resp. In LaTeX, by default, tables are numbered Table 1, Table 2, Table 3 an so on (or Table 1. Instead, you should put everything that is. With ShareLaTeX you get the same LaTeX set-up wherever you go. \end{document} change textwidth Usepackage geometry also allows an esay way to change the textwidth as the next exmaple would show us: set. The next two steps merge the reference section with our LaTeX document and then assign successive numbers in the last step. the symbol &; each row has the same number of cells (i. Anything that LaTeX automatically numbers, such as section headers, figures, and itemised lists, there is a counter associated with it that controls the numbering. We will review advanced options and what they effect, numbering settings. However, want I want is the pages to be: vii-ix, followed by pages 1-120. A combination of a real and an imaginary number in the form a + bi, where a and b are real, and i is imaginary. LaTeX, which is pronounced «Lah-tech» or «Lay-tech» (to rhyme with «blech» or «Bertolt Brecht»), is a document preparation system for high-quality typesetting. (If you have some typesetting experience, however, you may have noticed how nicely LaTeX justifies lines and how clever LaTeX is about hyphenating words. It is found in nature, but synthetic latexes can be made by polymerizing a monomer such as styrene that has been emulsified with surfactants. \rfoot{Page \thepage} Prints the word "Page" and next the page number which is automatically set by \thepage on the right side of the footer. Both issues are simply artifacts of the maths mode, in that it treats it as a mathematical expression: spaces are ignored (LaTeX spaces mathematics according to its own rules), and each character is a separate element (so are not positioned as closely as normal text). You can also de ne your own if these aren't enough.  \pagenumbering{arabic} The page numbering is switched to Arabic, this will also restart the page counter. 4), we should only use equation (and no other environment) to produce a single equation. Continuous figure and table numbering in report/book The \counterwithout command removes a dependency from a counter and redefines \the’counter’ such that it is printed without the dependency. eps files to substitute them in LaTeX? Heard about that possibility but also read quite often that this feature is not longer available. So i m using \thispagestyle{empty}. The ability to make the Xtick labels and Ytick labels utilize the same font as TEXT objects with LaTeX as their interpreter is not available in MATLAB 8. If I set example numbers to include chapter, than in the table of contents the example number overlaps with the text (i. It is found in nature, but synthetic latexes can be made by polymerizing a monomer such as styrene that has been emulsified with surfactants. Note that this can result in duplicate page numbers. Through \counterwithout , the figure and table counters can be changed to continuously number these figures and tables throughout a report or book. \setcounter{page}{3} This will manually set the page counter to 3 in this page, subsequent pages are numbered starting the count from this one. Prints the text set inside the braces on the left side of the header. The linking of LaTeX environments and commands to LyX is well documented elsewhere on this website. Autogenerate footnotes in $\LaTeX$ using BibLaTeX The abilities of BibTeX are limited to basic styles as depicted in the examples shown above. Required for descriptions. Intro to LATEX Intro to Beamer Geometric Analysis A Proof A Guide to Presentations in LATEX-beamer with a detour to Geometric Analysis Eduardo Balreira Trinity University.   With ShareLaTeX you get the same LaTeX set-up wherever you go. To change the start number or letter you must use the \setcounter command. By default, page numbers start from the first page (often the title page) and are displayed in arabic numbers (ie: 1, 2, 3 …). A combination of a real and an imaginary number in the form a + bi, where a and b are real, and i is imaginary. The only problem that Separator must be some symbol; there isn't an option "space". T his page shows how to customize the captions for figures, tables, subfigures and subtables in LaTeX. default albatross beaver beetle crane dolphin dove fly lily orchid rose seagull seahorse whale wolverine; default: AnnArbor: Antibes: Bergen: Berkeley: Berlin: Boadilla: CambridgeUS. Lists: Enumerate, itemize, description and how to change them. No extra packages are required to use these symbols. Doctors don't know what causes it. If you want to set each margin to 1. LaTeX Counters Everything LaTeX numbers for you has a counter associated with it. T he captions for figures, tables, subfigures and subtables in LaTeX can be customized in various ways using the caption and subcaption packages. Later on we will see how to create a label for an equation so that we can refer to the equation in the paper without having to know which number will be. The document style specifies what goes in the. LaTeX Math Formulas There are three environments that put LaTeX in math mode: math, displaymath, and equation. Btw, if you need to break down your document even more you can switch 3 to 4 in these lines to enable numbering for paragraphs. I tried googling it but the term "bullet and numbering" only applies for Microsoft Word. Paper size, orientation.  For example: { SEQ x \r 100 } produces the number 100. 4), we should only use equation (and no other environment) to produce a single equation. Quickly create even complex LaTeX tables online with our generator -- cells merging is supported together with borders editing. The syntax is \sqrt{x} which produces the square root of x, like so: n Roots. Note that this can result in duplicate page numbers. These recognized units are given in the following table:. 4, Massimiliano Do-. It is most often used for medium-to-large technical or scientific documents but it can be used for almost any form of publishing. You can also combine several numbering styles in a single document, this. If you want to change them, you have several options: the "geometry" package, the "fullpage" package or changing the margins by hand. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The keyboard combination to display the current line number whilst you are using nano is CTRL+C. LaTeX Counters Everything LaTeX numbers for you has a counter associated with it. Not sure how you do it in latex. The length of the skip should be expressed in a unit recognized by LaTeX. Open an example in Overleaf Document Sectioning.   Section headings of various sizes are produced (in the article document style) using the commands \section,\subsection and \subsubsection commands. I already got reply for my previous question. The next step to achieve greater control of page layout is to set about designing your own class. Customizing the numbering for pages, figures, sections, equations, theorems, and tables You can modify the default style for the names and numbering of things like figures, equations, sections, and the like easily in Latex. Some of these commands are LATEX macros, while oth-. a The number of angels per unit area, see equation (1), page 1 m The mass of one angel, page 1 N The number of angels per needle point, see equation (1) Figure 4: Output with references Before we describe the usage of hpreﬁxi, we have to explain how MakeIn-dex sorts entries, see [2]. Now, two options. headings - Puts running headings on each page. You can also combine several numbering styles in a single document, this. Hats, bars, and accents Edit. For this to work, you must have \usepackage{amsmath} in the preamble. Page numbering in LATEX uses Arabic numbers by default, but this can be changed to use Roman numerals and/or letters. Sum-class symbols, or accumulation symbols, are symbols whose sub- and superscripts appear directly below and above the symbol rather than beside it. Simply begin the appropriate environment at the desired point within the current list. T he captions for figures, tables, subfigures and subtables in LaTeX can be customized in various ways using the caption and subcaption packages. (If you have some typesetting experience, however, you may have noticed how nicely LaTeX justifies lines and how clever LaTeX is about hyphenating words. Page breaks in math environments [].  \hline can be placed in the ﬁrst row or at the end of a row \\ and it draws an horizontal line as wide as the entire table. The enumerate package  Set the counter to 7 so that we get the width of 'vii' if roman numbering is in force then set \leftmarginn. Set the counter value explicitly \setcounter{CounterName}{number} Create a new counter (is automatically set to zero) \newcounter{NewCounterName} If you want the NewCounterName counter to be reset to zero every time that another OtherCounterName counter is increased, use: \newcounter{NewCounterName}[OtherCounterName] Return the value of the. Updating field numbering. They can also be produced with two commands, the \footnotemark and the \footnotetext commands. How can I alter the position of page numbers so that they become visible? I had a hard time finding an easy and clear solution on the internet. In the example, to change the start number of level 2 to V the command \setcounter{enumii}{4} was used. Does anybody know how I can get exactly that symbol for the set of real numbers in LaTeX? Additional image: In this picture you have the symbol for the set of integers, real numbers and complex numbers. List Hello World The following manually implements a very simple list. Not so with equations; there is no automatic numbering feature for them. The file actually contains six LaTeX examples, and in each step I add one more LaTeX feature that is a little. You can change the fonts, numbering style, alignment and format of the captions and the caption labels. Macros are also de ned so that the headers and footers can vary depending on whether a question is complete on the current page or continues on to the next page (and, if one continues, to say what the number of that question is) (see. Intro to LATEX Intro to Beamer Geometric Analysis A Proof A Guide to Presentations in LATEX-beamer with a detour to Geometric Analysis Eduardo Balreira Trinity University. Using the keyboard, press Ctrl+Shift+M twice. The most popular approaches to indicate a reference appearing in the text can be classified as "numeric" and "author-year". The document style specifies what goes in the. \pagestyle{empty} stops the pages being numbered \pagestyle{plain} this is the default; it puts the numbers at the bottom of the page.   Below is a list of the counters used LaTeX's standard document styles to control numbering. The name of the counter is the same as the name of the environment or command that produces the number, except with no \. How can I alter the position of page numbers so that they become visible? I had a hard time finding an easy and clear solution on the internet. By default, page numbers start from the first page (often the title page) and are displayed in arabic numbers (ie: 1, 2, 3 …). The most popular approaches to indicate a reference appearing in the text can be classified as "numeric" and "author-year". The default font style/size used is:. fancyhdr is a massive package with a crazy number of tweaks and modifications available for your document's header and footer styles. These packages allow you to have sequential numbering throughout the text without resorting to ERT, and you can set up LyX to include them in your default document class. The only problem that Separator must be some symbol; there isn't an option "space". The value in these counters can be set by using the \setcounter command. For a related list organized by mathematical topic, see List of mathematical symbols by subject. A basic article class document has figure and subfigure captions that look like this:. where the page number will be printed), while \pagenumberingdeﬁnes the format of the page number. It doesn’t mean that LaTeX doesn’t know those sets, or more importantly their symbols… There are two packages which provide the same set of symbols. The parameters passed to the command determine the layout. The package extends the syntax of the lists to allow an optional argument where a set of parameters in the form key=value are available.  If I set example numbers to include chapter, than in the table of contents the example number overlaps with the text (i. To change the start number or letter you must use the \setcounter command. The pdfpages package makes it easy to insert pages of external PDF documents without worrying about the print space. LATEX has four standard pagestyles:. Memberships and donations are tax-deductible in the US. a The number of angels per unit area, see equation (1), page 1 m The mass of one angel, page 1 N The number of angels per needle point, see equation (1) Figure 4: Output with references Before we describe the usage of hpreﬁxi, we have to explain how MakeIn-dex sorts entries, see [2]. A quick code example showing how to set the depth of the table of contents (toc) in a LaTeX document using tocdepth and setcounter. The package extends the syntax of the lists to allow an optional argument where a set of parameters in the form key=value are available. In this ﬁle you type both the text of your document and the LATEX commands to format it. Simply begin the appropriate environment at the desired point within the current list. The On-Line Encyclopedia of Integer Sequences® (OEIS®) Enter a sequence, word, or sequence number: Hints Welcome Video. 5) $\endgroup\$ - Charlie Tian Sep 21 '17 at 16:25. Double-click the icon "Set display mode" in the math toolbar (it can be turned on via: View -> Toolbars -> Math) The first clicking changes the equation to an inline formula and deletes the equation label at the same time. Instead of using the modulo option, it is possible to number every nth line (e. Just as with \pagebreak, \displaybreak can take an optional argument between 0 and 4 denoting the level of desirability of a page break. If the page numbering still shows "iii", then repeat the steps and set page.   4A65G69 1995 95-36881 688. Sum-class symbols, or accumulation symbols, are symbols whose sub- and superscripts appear directly below and above the symbol rather than beside it. LaTeX keeps track of numbering by means of counters. I just want to label equations in a post I could make in the next hours if I knew. So i m using \thispagestyle{empty}. In this video we will look at where you can find the different settings that affect your piece marks in Tekla Structures. Double-click the icon "Set display mode" in the math toolbar (it can be turned on via: View -> Toolbars -> Math) The first clicking changes the equation to an inline formula and deletes the equation label at the same time. 3 Single Equations that are Too Long: multline If an equation is too long, we have to wrap it somehow. To change the start number or letter you must use the \setcounter command. Integral expressions are formed from the use of sub- and superscript, the judicious use of spacing, and simply writing out the differential. Regards Numbering the Equations in Latex | Physics Forums Menu. So, a specific chapter or section number can be specified by manipulating the value inside this counter. LaTeX will happily allow you to insert a list environment into an existing one (up to a depth of four, more levels are available using packages). Page numbering in LATEX uses Arabic numbers by default, but this can be changed to use Roman numerals and/or letters. Then we set fancyhdr to display Page n of All" on the down right corner of the page, where n is the current page and All is the last page or total number of pages.  \item[x]text Use x instead of normal bullet or number. A LaTeX environment is one of the following: Contents[show] Float environments Text inside a float environment is "floated" according to its placement, an optional parameter. These packages allow you to have sequential numbering throughout the text without resorting to ERT, and you can set up LyX to include them in your default document class. We will review advanced options and what they effect, numbering settings. E First table in chapter 2 should be numbered: 1. [tags]latex, subsubsection, paragraph, section, numbering, tex[/tags]. I have a document with narrow margins (geometry: margin=1. Latex will sort out the layout and any numbering for you. No extra packages are required to use these symbols. Read More ->. LaTeX, which is pronounced «Lah-tech» or «Lay-tech» (to rhyme with «blech» or «Bertolt Brecht»), is a document preparation system for high-quality typesetting. LaTeX forum ⇒ Math & Science ⇒ How to number equations in cases. If the second section is not correctly numbered (because it doesn't start with the number you want), go to a header/footer containing a page number in the second section and activate it. There are five base classes included with LATEX: article, book, report, slides, and setting head or foot information, but most will set the page number formatting. This command sets the page numbers to lowercase Roman numerals. To change the start number or letter you must use the \setcounter command. Up to this point we've been using LaTeX's default page numbering. 202544536-dc20 CIP Printed on acid-free paper °c Birkh. The name of the counter is the same as the name of the environment or command that produces the number, except with no \.


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# Mathematical Sciences Research Institute

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# One Stabilization is Not Enough for Contractible 4-Manifolds

## [HYBRID WORKSHOP] Floer Homotopical Methods in Low Dimensional and Symplectic Topology November 14, 2022 - November 18, 2022

November 17, 2022 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Sungkyung Kang (Institute for basic science)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
• corks

• stabilization

• involutive Heegaard Floer homology

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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#### One Stabilization Is Not Enough For Contractible 4-Manifolds

Abstract

We construct an example of a cork that remains exotic after taking a connected sum with $S^2 \times S^2$. Combined with a work of Akbulut-Ruberman, this implies the existence of an exotic pair of contractible 4-manifolds which remains absolutely exotic after taking a connected sum with $S^2 \times S^2$.

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#### One Stabilization Is Not Enough For Contractible 4-Manifolds

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# cirq.block_diag¶

cirq.block_diag(*blocks) → numpy.ndarray[source]

Concatenates blocks into a block diagonal matrix.

Parameters: *blocks – Square matrices to place along the diagonal of the result. A block diagonal matrix with the given blocks along its diagonal. ValueError – A block isn’t square.


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1. ## Lagrange Equation

$
y=xy'+\sqrt{b^{2}+a^{2}(y')^{2}}
$

2. Originally Posted by sinichko

$
y=xy'+\sqrt{b^{2}+a^{2}(y')^{2}}
$
If you differentiate both sides you get

$
y' = y' + x y'' + \frac{a^2 y' y''}{\sqrt{b^{2}+a^{2}(y')^{2}}}
$

or

$
\left(\frac{a^2 y'}{\sqrt{b^{2}+a^{2}(y')^{2}}} + x\right) y'' = 0
$
.

You now have two cases which can be solved. Remember, sub in your answer into the original ODE to make sure both (if any) are actual solutions.


text:
# Math Help - Simple groups that are maximal subgroups of G.

1. ## Simple groups that are maximal subgroups of G.

Hi:
I'll make a straightforward question: Let $G$ be group and $S \leq T \leq G$, these groups satisfying the following conditions:

(a) $T \unlhd G$.
(b) $T$ is simple.
(c) $T$ is a maximal subgroup of $G$.

Is there any other piece of information that can be deduced from these three facts? In particular, can I infer $S \unlhd G$?

2. ## Re: Simple groups that are maximal subgroups of G.

Originally Posted by ENRIQUESTEFANINI
Hi:
I'll make a straightforward question: Let $G$ be group and $S \leq T \leq G$, these groups satisfying the following conditions:

(a) $T \unlhd G$.
(b) $T$ is simple.
(c) $T$ is a maximal subgroup of $G$.

Is there any other piece of information that can be deduced from these three facts? In particular, can I infer $S \unlhd G$?
Well, no, because $T$ is simple. If $S\leq T\leq G$ and $S\lhd G$ then $S\lhd T$...

3. ## Re: Simple groups that are maximal subgroups of G.

That's a pity, because I'm in the process of solving a problem, half of which, it seems, I have already solved, and I thought I could extract aditional info from those facts. About the problem it would be unfair to speak because I've already posted in MHF stating its hypothesis (and the propositions I have arrived at up to now). Thanks for your reply.


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# Relation between reflection group and coxeter group

Reflection group is defined see https://en.wikipedia.org/wiki/Reflection_group. An abstract Coxter group is defined to have generators $s_1$, $s_2$, ..., $s_n$ and relations $s^2_i=e$, $(s_is_j)^{m_{ij}}=e$ for some $2\leq m_{ij}\leq \infty$.

I don't know why viewed as an abstract group, every reflection group is a Coxeter group? Can somebody give me an example to explain this? Thanks in advance.

• It says on the Wikipedia page there that every reflection group is a specific example of a Coxeter group. – Nick Mar 21 '16 at 21:07
• @Nick Please you tell me why every reflection group is a specific example of a Coxeter group. Can you give me an example? Thanks in advance. – bing Mar 22 '16 at 1:34

We have $(s_i)^2 = e$ because if we repeat the same reflection twice in a row we end up back where we started.
Since $s_i s_j$ is an element of a group, it has an order (possibly infinity), which we denote by $m_{ij}$.


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# Figure 5

 The left and right panels show the \pt dependence for the inclusive \psitwos production cross section in \pp collisions at $\s = 5.02$~TeV. The results are compared with the theory predictions based on NRQCD~ (left) and CEM~ (right) models. The calculation of the non-prompt contribution from FONLL calculations~ are also shown separately. See text for details


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# What is 7+6i divided by 10+i?

Sep 8, 2017

$\frac{7 + 6 i}{10 + i} = \frac{76}{101} + \frac{53}{101} i$

#### Explanation:

We can make the denominator real by multiplying the denominator with its complex conjugate, thus:

$\frac{7 + 6 i}{10 + i} = \frac{7 + 6 i}{10 + i} \cdot \frac{10 - i}{10 - i}$

$\text{ } = \frac{\left(7 + 6 i\right) \left(10 - i\right)}{\left(10 + i\right) \left(10 - i\right)}$

$\text{ } = \frac{70 - 7 i + 60 i - 6 {i}^{2}}{100 - 10 i + 10 i - {i}^{2}}$

$\text{ } = \frac{70 + 53 i + 6}{100 + 1}$

$\text{ } = \frac{76 + 53 i}{101}$

$\text{ } = \frac{76}{101} + \frac{53}{101} i$

Sep 8, 2017

$\frac{76}{101} + \frac{53}{101} i$

#### Explanation:

$\frac{7 + 6 i}{10 + i}$
First we have to rationalize the denominator by multiplying the complex number in the denominator and the numerator by the denominator's conjugate.

$\frac{\left(7 + 6 i\right) \left(10 - i\right)}{\left(10 + i\right) \left(10 - i\right)} = \frac{7 \left(10\right) + 6 i \left(10\right) - 7 \left(i\right) - 6 i \left(i\right)}{{10}^{2} - {i}^{2}}$ (using the difference of squares rule in the denominator)
$= \frac{70 + 60 i - 7 i - 6 \left({i}^{2}\right)}{100 - {i}^{2}} = \frac{70 + 53 i - 6 \left(- 1\right)}{100 - \left(- 1\right)}$**(since ${i}^{2} = - 1$)

$\frac{70 + 53 i - 6 \left(- 1\right)}{100 - \left(- 1\right)} = \frac{70 + 6 + 53 i}{100 + 1} = \frac{76 + 53 i}{101}$

$= \frac{76}{101} + \frac{53}{101} i$

I hope that this helps.


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# Difference between Soap and Detergent

In most articles and texts that I've read, soaps and detergents seem to be talked about collectively. I know that they are both surfactants and that soaps are usually natural, in comparison to detergent which is artificial. However, what are the differences in terms of chemical structure and properties (between soap and detergent)?

NOTE: not the same as Is there an important difference between soap and detergent?, as I'm asking about chemical structure and properties rather than the effects in everyday life.

There is no restriction that soap be natural or unnatural. Soap are salts and detergents are not necessarily salts. The latter is a very broad term. Soap has a narrow meaning.

IUPAC clearly defines soap as

"A salt of a fatty acid, saturated or unsaturated, containing at least eight carbon atoms or a mixture of such salts."

Just note that not all soaps are used for cleaning nor there is any condition that they should be soluble in water. Insoluble soaps of metallic salts serve as lubricants.

Similarly,

IUPAC defines a detergent as

"A surfactant (or a mixture containing one or more surfactants) having cleaning properties in dilute solutions (soaps are surfactants and detergents)"

Just like banana is a fruit but not all fruits are bananas, in the same way, all water soluble soaps are detergents and surfactants. Not all detergents are soaps.

Visit the IUPAC Gold Book and search the entries detergents and soap.

• Anything chemical structure wise? Like are there differences in the chemical structure of the molecules – An0n1m1ty Jun 20 '20 at 5:36
• @M.Farooq I suppose you are trying to quote IUPAC's web version of "Gold Book". Keep in mind you can include an URL in a format [<text>](<link>), and use > for quoting third-party sources. Currently the quoted definitions are not referenced. – andselisk Jun 20 '20 at 8:49
• @andselisk, You might have noticed that I do not provide links to papers but write the textual form form of the reference. The intention is to promote students to search themselves. In my humble opinion, they should be curious enough to search the quote and land at the right website within a few seconds. You are right, I should provide the main page link to IUPAC Gold book so that they at least scroll down and look up the relevant entry. – M. Farooq Jun 20 '20 at 12:45
• @An0n1m1ty, I have given you enough description to begin the journey of search. Now it is your duty as future curious scientist to search the web. Search what how do fatty acids salts look like. Also read the Wikipedia entry on detergents and start from there. – M. Farooq Jun 20 '20 at 12:48
• @M.Farooq While I can clearly see you mean well, the problem is that SE sites are not exactly educational in a sense there is little to no dialogue in Q&A section, and, as a consequence, all answers must be complete and self-contained. Hints, unfinished posts and general recommendations are not answers. Yours, however, is, but it lacks referencing, which if good in a pedagogical sense for one person (OP), but drastically lowers the quality of your answer for all other users. – andselisk Jun 20 '20 at 14:04

The main difference between soap and detergent is the effects they produce when dissolved into pure water or tap water. Usually, tap water contains calcium carbonate, or at least calcium ions. When dissolved into tap water, soap reacts with these calcium ions, producing an insoluble substance which could be called "calcium soap". This substance stays usually in emulsion in water, making it cloudy or turbid. In the rotating washing machines, this deposit remains in the clothes, which become rough when dry. This does not happen with detergents, which do not react with calcium ions, and wash without producing this turbidity.


text:
# turicreate.sound_classifier.get_deep_features¶

turicreate.sound_classifier.get_deep_features(audio_data, verbose=True)

Calculates the deep features used by the Sound Classifier.

Internally the Sound Classifier calculates deep features for both model creation and predictions. If the same data will be used multiple times, calculating the deep features just once will result in a significant speed up.

Parameters: audio_data : SArray Audio data is represented as dicts with key ‘data’ and ‘sample_rate’, see turicreate.load_audio(…).

Examples

>>> my_audio_data['deep_features'] = get_deep_features(my_audio_data['audio'])
>>> train, test = my_audio_data.random_split(.8)
>>> model = tc.sound_classifier.create(train, 'label', 'deep_features')
>>> predictions = model.predict(test)


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# The law of Aboav--Weaire and extensions

 Workshop on Topology: Identifying Order in Complex Systems Topic: The law of Aboav--Weaire and extensions Speaker: Richard Ehrenborg Affiliation: University of Kentucky and Princeton University Date: Wednesday, December 10 Time/Room: 5:00pm - 6:00pm/S-101 Video Link: http://video.ias.edu/topology/2014/1210-RichardEhrenborg

In two-dimensional grain structure, one observes that grains with a small number of sides tend to be surrounded by grains with a large number of sides, and vice-versa. The Law of Aboav--Weaire gives this observation a mathematical formulation, that is, the average number of sides of the neighbors of an $n$-sided grain should be roughly $5 + 6/n$. By introducing the correct error term we prove this law of Material Science. We extend this law to three-dimensional grain structures. We also discuss the average number of sides of grains neighboring to two adjacent grains and three adjacent grains. This is joint work with Menachem Lazar and Jeremy Mason.


text:
Why is a LALR parser the correct choice for parsing mathematical content? (a question about Approach0)

This questions is about the work A novel similarity-search method for mathematical content in LaTeX markup and its implementation.

The parser used by Wei Zhong is LALR.

Now, supose I have to parse a function $$func(foo)=bar$$.

How is the parser able to understand the "$$func$$" as a whole string representing the name of a funciton and not several constants/variables $$f,u$$ and $$n$$ multiplying the function $$c(foo)=bar$$?

The grammar rules are found on pages 54/55:

• Splitting the text into tokens is the lexer’s job (usually), so check how it’s implemented in this case. Feb 3 at 12:43
• Some functions like $arccos$ or $max$ will be correctly handled by the lexer. Others are potentially problematic, like the above function, where there is a option to omit the dot sign ($.$) for the operation of multiplication. I mean, $func(x)$ might represent a single function or the constants $f$,$u$ and $n$ multiplying the function $c(x)$: $f.u.n.c(x)$. Do you understand my question? Feb 3 at 13:24

As @Dmitry said in a comment, the input is partitioned into tokens by the lexical analyser (or "scanner"), normally generated with (f)lex, and this stream of tokens becomes the input to the parser. The parser does not see the individual characters from the input.

Having said that, I don't believe that the parser can distinguish between different syntactic uses of juxtaposition. n(\pi/2) ($$n(\pi/2)$$) could be the product of $$n$$ with $$\pi/2$$, or it could be the application of the function $$n$$ to the argument $$\pi/2$$. Only semantic context could help the reader distinguish the two uses. (Was $$n$$ previously used as a variable or was it textually defined as a function or predicate?). [Note 1]

Since the goal of the cited thesis is to search a corpus of text for instances of mathematical equations similar to a given query, the precise parse is not required (and perhaps not even useful), so that resolving that ambiguity is not a goal of the project. Consequently, it's probably not a great witness for the question "What is the best parsing framework for parsing mathematical content?" In general, mathematicians tend to tolerate highly ambiguous syntaxes in presentations, relying on the common sense and semantic knowledge of the reader to disambiguate. (Much the same as our approach to human language in general.) But when logic and algebra are analysed theoretically, unambiguous syntaxes are required, and those are normally defined in such a way that they can be parsed with an LALR(1) parser. (Indeed, the usual syntactic definitions are defined recursively leading to the possibility of parsing with a recursive descent parser, which is not as powerful as LALR. But LALR might still be an appropriate pragmatic choice.)

The case of user-defined functions whose names contain more than one character is, perhaps, slightly interesting. LaTeX will always typeset juxtaposed letters in a manner consistent with the juxtaposition being a multiplication. Hence, $$find(\pi/2)$$ (find(\pi/2)) looks quite different from the use of predefined operator like \sin ($$\sin(\pi/2)$$). Note that the latter is written with a backslash; \sin is the keyword, not sin.

In LaTeX, you can define your own math operators with the DeclareMathOperator macro. That lets you write:

\DeclareMathOperator{\find}{find}

after which, you can use \find in your equations, producing $$\DeclareMathOperator{\find}{find}\find(\pi/2)$$. However, this feature is not handled by Wei Zhong's work, presumably because it was not useful for his problem (which does not require accurate parsing). Wei's parser only recognises specific LaTeX macros which have mathematical semantics. (These are listed in Appendix B of the thesis.) It ignores many other macros, more related to typography, as well as any user-defined macros. (Quote from page 37 of the thesis.)

Our lexer omits all LATEX control sequences not matching any pattern of our defined tokens, most of them are considered unrelated to math formula semantics.

Notes:

1. There is no universal convention to chose between $$\textrm{foo}(\pi/2)$$ and $$\textit{foo}(\pi/2)$$ (\textrm{foo} and \textit{foo}, respectively) to represent the application of a function named foo. But, at least in my opinion, $$foo(\pi/2)$$ (foo(\pi/2)) should never be used; the kerning is awful.

Apparently, there is an applicable ISO standard (ISO 80000-2:2019, in case you care) which seems to recommend the use of $$\textrm{foo}(\pi/2)$$ for cases where foo has been defined with a specific meaning. According to that document, cursive text ($$f(x)$$) should be used only for generic functions and variables.

I got the above information from this blog post by Nick Higham, which I found while I was writing this answer. Higham's post references the 2009 version of the standard, and includes a link to a more detailed summary by Claudio Becarri, written in 1997 and referencing a predecessor standard. Those resources are free, unlike the ISO standard, which costs CHF 166, or about five dollars per page.

• It's ISO 80000-2 section 3. Feb 4 at 1:29
• @Pseud: OK, added the document ID, and even a link for readers who have money to burn. Looking at the publicly-available excerpt, it seems like the relevant specifications are in section 4 of the current version.
– rici
Feb 4 at 2:46


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24 s   128 MB

## Description

### Sample Output

1
8 9 3
1 2 1
2 3 2
3 4 3
4 5 12
5 8 7
1 6 8
6 4 9
1 7 5
7 4 4
1 4 2
1 4 3
1 4 1

17
6
-1

## Source

2013 ACPC (Arab Collegiate Programming Contest)


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Concentration in mol/dm 3 = amount in mol ÷ volume in dm 3 This equation can be rearranged to find the amount of solute or volume of solution. How Do I Use Study.com's Assign Lesson Feature? A dilute solution is a solution that has very little solute in the solvent. © copyright 2003-2020 Study.com. Physicists and chemists typically use this parameter to express concentrations of various substances. We can also work this backwards. The molecular weight of hydrogen is about 1 g/mol. A solution that is filled to capacity is called a saturated solution. In this chapter, we will learn about what is meant by the concentration of a solution; we will also see how to find the concentration of a solution and the different methods of expressing concentration of solution. For example, we might say: ''a 1 M solution of hydrochloric acid. We also look at solution concentration levels and how to calculate the concentration of a solution. just create an account. 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Get the unbiased info you need to find the right school. A solution is a combination of two or more compounds. A solvent is the material used to dissolve another material into it. Log in here for access. We could just as easily refer to a dozen hydrochloric acid molecules if we only wanted to talk about 12 molecules of hydrochloric acid. Create your account. Question 1) 2ml of water is added to 4g of a powdered drug. A minor disturbance of the solution or introduction of a "seed" or tiny crystal of solute will force crystallization of excess solute. In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. In this example, the solvent is the water and the solute is the sugar. Part A) What is the percent by mass of sulfuric acid in this solution? Normality (N) = $\frac{\text{Weight of solute in grams}}{\text{Equivalent mass\times Volume in litre}}$. 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Thinking back to a dozen, this would be just like if we took the weight of 12 atoms of hydrogen and recorded it, then recorded the weight of 12 atoms of carbon, and so on; then we would know the weight in 1 dozen of each element. Dilution is the addition of solvent, which decreases the concentration of the solute in the solution. Sorry!, This page is not available for now to bookmark. The concentration of a solution is most of the time expressed as the number of moles of solute present in 1 Liter of the solution (also called molarity) (There are also other ways to express concentration. Find the mass of Na3PO4 needed to make 2.0L of the solution? A solute is what is being dissolved into the solvent. #m_(solution) = m_(solvent) + m_(solute)# There are two ways to change a solution's concentration by mass. Saturated Or first two years of college and save thousands off your degree. The vinegar label will report that the solution is 5% by weight acetic acid. 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What is Meant by Concentration of a Solution, How to find the Concentration of a Solution using Different Methods, Question 2) Many people use a solution of Na, to clean walls before putting up wallpaper. The recommended concentration is 1.7%(m/v). We can determine the concentration of a solution in molarity, or moles of solvent per liter, by determining the number of moles of solute in a liter of solution. Dilution means to reduce the concentration of a solution. Answer 1) The answer to this question depends on how we define concentration. Anyone can earn Therefore, in a 1000 mL solution ethanol = 73 mL. Meaning of concentration. If we talk about molarity, then yes it does change. the act or process of concentrating. So what does that mean and how do we know that there is 1 mole in the liter of solution? Cor S = $\frac{\text{Weight of solute in grams}}{\text{Volume in litres}}$. You can test out of the In biology, the "%" symbol is sometimes incorrectly used to denote mass concentration, also called "mass/volume percentage." Let's say we wanted to make a 1 M solution of hydrochloric acid. Solutions can be concentrated (lots of solute) or dilute (little solute) depending on our needs. A concentrated solution is a solution where the solvent has a lot of solute in the solution. Depending upon the proportion of solute, a solution can be: 1. All other trademarks and copyrights are the property of their respective owners. One way to describe the concentration of a solution is by the percent of the solution that is composed of the solute. - Definition & Examples, Solute Concentration: Definition & Overview, Molar Volume: Using Avogadro's Law to Calculate the Quantity or Volume of a Gas, Limiting Reactant: Definition, Formula & Examples, Volcanic Hazards & Prevention: Landslides, Lahars & Tsunamis, Aqueous Solution: Definition, Reaction & Example, Solubility Lesson for Kids: Definition & Rules, Basic Solutions in Chemistry: Properties & Examples, GACE Geography (536): Practice & Study Guide, Praxis PLT - Grades K-6 (5622): Practice & Study Guide, FTCE Professional Education Test (083): Practice & Study Guide, Praxis Special Education (5354): Practice & Study Guide, MTEL English (07): Practice & Study Guide, MTTC Elementary Education (103): Practice & Study Guide, GACE Early Childhood Education (501): Practice & Study Guide, MTEL Communication & Literacy Skills (01): Practice & Study Guide, TExES Core Subjects EC-6 - Social Studies (803): Practice & Study Guide, ILTS TAP - Test of Academic Proficiency (400): Practice & Study Guide, Praxis Family & Consumer Sciences (5122): Practice & Study Guide, NYSTCE Social Studies (115): Practice & Study Guide, Praxis Middle School Social Studies (5089): Practice & Study Guide, Praxis Health Education (5551): Practice & Study Guide, Praxis Reading Specialist (5301): Practice & Study Guide, Instructional Strategies for Learner-Centered Teaching. The standard formula is C = m/V, where C is the concentration, m is the mass of the solute dissolved, and V is the total volume of the solution. A solution can be diluted by adding more solvent to the solution, then (i) volume of solution … All rights reserved. The molecular weight of chlorine is about 35.5 g/mol. credit by exam that is accepted by over 1,500 colleges and universities. However, instead of a dozen (which is way too small), we've calculated moles. So we end up with needing to use 36.5 g of hydrochloric acid to make 1 liter of a 1 M solution of hydrochloric acid. flashcard set{{course.flashcardSetCoun > 1 ? The additional solute will not dissolve in a saturated solution. Plus, get practice tests, quizzes, and personalized coaching to help you Question 2) A 28.00%-by-mass solution of nitric acid, A gas contains 55.0 wt% methane, 10.00 wt% ethane, 30.0 wt% ethylene, and the balance water. The molar concentration has … We will also see other methods on how to calculate concentration of a solution based on the different methods of expressing concentrations. In chemistry, the concentration of a solution is the quantity of a solute that is contained in a particular quantity of solvent or solution. Concentration is the removal of solvent, which increases the concentration of the solute in the solution. Everyone talks about the concentration of solutions. Learn more. Whereas when the solution has more solvent in it, we call it a dilute solution. Try refreshing the page, or contact customer support. A solution with 1 g of solute dissolved in a final volume of 100 mL of solution would be labeled as "1%" or "1% m/v" (mass/volume). Information and translations of concentration in the most comprehensive dictionary definitions resource on the web. In an aqueous solution, two parts exist, namely solute and solvent. Finally, multiply it by 100% to convert it to percentage. imaginable degree, area of A concentrated solution is a solution where the solvent has a lot of solute in the solution. concentration definition: 1. the ability to think carefully about something you are doing and nothing else: 2. a large…. A solution can be dilute or concentrated. Percentage weight in volume expresses the number of grams of solute in 100 ml of product. We end up with 1 liter of a 1.2 M hydrochloric acid solution. credit-by-exam regardless of age or education level. The recommended concentration is 1.7%(m/v). Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. 'This means that there is 1 mole of hydrochloric acid per liter of solution. Select a subject to preview related courses: The nice thing about a mole is that we have determined the weight of every element in 1 mole of that element. There are various methods of expressing concentration of a solution. Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science. and career path that can help you find the school that's right for you. Decisions Revisited: Why Did You Choose a Public or Private College? 2.the ratio of the mass or volume of a solute to the mass or volume of the solution or solvent. The image shows a solution from the most dilute solution to the most concentrated solution. Determine: a. the molarity of the solution. A solute is what is being dissolved into the solvent. Often, a worker will need to change the concentration of a solution by changing the amount of solvent. In everyday life we refer to a solution as a way to solve a problem, but in science, solution can mean something else. The concentration of the solution tells you how much solute has been dissolved in the solvent. 3.intense mental focus. mass/volume can be abbreviated as m/v 340 lessons Maybe we want to only slightly dilute a compound. Solubilities are sometimes given in units of grams of solute per 100 mL of water, that is, as a weight/volume percentage concentration. The formula for normality is given as follows. The degree of concentration is measured in moles. As a member, you'll also get unlimited access to over 83,000 Create an account to start this course today. Its dilute form makes it much easier to work with. Percent concentration by mass is defined as the mass of solute divided by the total mass of the solution and multiplied by 100%. The amount of solute that is dissolved in a solvent is the concentration. to form a new equilibrium constant, K water (K w). In chemistry, we define concentration of solution as the amount of solute in a solvent. How much hydrochloric acid would we need to put into 1 liter of water? Another definition is that concentration is the ratio of solute in a solution to either solvent or total solution. Based on our needs, we can have a solution on a continuum between dilute and concentrated. But, if both the solute and solvent are either increasing or decreasing in volume/mass/moles in an equal ratio, the concentration and molarity will remain the same. The amount of solute that can be dissolved in a solvent to form a saturated solution depends on a variety of factors. Typically, we refer to these compounds as the solvent or the solute. by evaporation of the solvent, diffusion, or purification. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons mass concentration the mass of a constituent substance divided by the volume of the mixture, as milligrams per liter (mg/l). Weight / Weight % 2% w / w solution means grams of solute is dissolved in 100 grams of solution. Concentration of a solution - definition The amount of solute dissolved in an unit amount of solvent. Calculate the molar composition of this gas on both a wet and a dry basis and the ratio (mol H_2O/mol dry g, In a mixture of three gases (A, B, and C), the number of moles of each gas is known (nA, nB, and nC). The vinegar label will report that the solution is 5% by weight acetic acid. b. the molality of the solution. Of these, a pH of 4 is the lowest. Percentage by Mass - formula The amount of solute in the solvent is what is called the concentration of a solution. Diluted 2. It is expressed in terms of volume percentage of solute to the solvent. b) 500 g of 5.0% aqueous FeCl3 solution from FeCl3?6H20(s). Let's look at a solution of hydrochloric acid. A concentration can be any kind of chemical mixture, but most frequently solutes and solvents in solutions. For example, if you add one teaspoon to two cups of water, the concentration could be reported as 1 t salt per 2 c water. Volume percentage of A = $\frac{\text{Volume of component A}}{\text{Total volume of solution}}\times 100$. flashcard sets, {{courseNav.course.topics.length}} chapters | Pro Lite, Vedantu The formula for mass percentage is given as follows. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol⋅dm −3 in SI unit. Visit the GACE Middle Grades Science (014): Practice & Study Guide page to learn more. Question 1) Does Solution Concentration Change when Solution Volume Changes? It is a commonly used method for expressing concentrations. The chemical formula for hydrochloric acid is HCl, so there is 1 hydrogen atom and 1 chlorine atom in each molecule of hydrochloric acid. Suppose we have a solution containing As a solute and B as the solvent. Hydrochloric acid can be very dangerous, but if it is dilute then it is not as dangerous to use. Enrolling in a course lets you earn progress by passing quizzes and exams. To learn more, visit our Earning Credit Page. We always need to keep an account of the amount of solute in the solution. Now that you understand the concept of what is concentration of solution let's move on to the different methods of expressing concentration. Chemists working with the number of molecules the stoichiometry of reactants for solution reactions Convert from molarity to a Course! Or more compounds and what makes up a solution forms when a solution that filled. Is that concentration is the material used to denote mass concentration, and personalized coaching to you. To multiply the molarity by the total mass of the solute in the solution is ratio... Regardless of age or education level there 7.3 mL most frequently solutes and in... Page to learn more basic solution concentration terms that you understand the concept of is. W / w solution means grams of hydrochloric acid ), we might say:  a 1 concentration of solution meaning of. Quizzes and exams the solvent is concentration of solution this page is not as dangerous to use concentration. By chemical means, e.g another definition is that concentration is the water and the solute less potent such. Case, the solvent is the removal of solvent molarity, then yes it does.... Depends on a variety of factors and 5 a ( XA ) calculated! Be very dangerous, but if it concentration of solution meaning not available for now to bookmark powers of concentration, and 98.0... Concentration can also refer to these compounds as the solvent or total solution ( solution ) ) * %... Of expressing concentration concentration of solution meaning the First two years of college and save thousands off your degree it is based the!, molar concentration has … a concentrated solution is produced when a solution where the solvent the. And ( 1000-73 ) = 927 mL of a solute to the solution has more solvent solutions. Access risk-free for 30 days, just create an account is, as a weight/volume percentage.. Keep track of the mass of the First two years of college and save thousands off your degree Practiced... Continuum between dilute and concentrated, when an aqueous solution is one in which there a... Molarity by the total mass of the solution grams of solute per 100 mL solution ethanol = 73.... Called  mass/volume percentage. unless the substance is with an undefined density s ) the of. Long as you know the moles of solvent a large amount of solvent, decreases... Change with its volume, and volume concentration at a solution is 5 % by weight acetic acid quantitative... Parts per million is given as follows and 1:10000 refers to the amount of in. To only slightly dilute a compound expressed as the number of grams of solute present in solvent! Solid ( FW = 329.25 ) is simply defined as the amount of per. Or solvent 1 g/mol be measured by chemical means, e.g this lesson, we also... Ph of 4 and 5 solubilities are sometimes given in units of grams of contained. % aqueous FeCl3 solution from FeCl3? 6H20 ( s ) coaching to help you succeed ). That concentration is 1.7 % ( m/v ) personalized coaching to help you succeed a concentrated.. 'S Assign lesson Feature 1. the ability to think carefully about something you are doing and nothing:! Abbreviated as m/v 1.increase in strength by evaporation of the solvent is what is being dissolved the. Definitions resource on the matter at hand multiply the molarity by the concentration of solutions that the solution 1 1000,000! 6.02 x 10^23 molecules of atoms from molarity to a weight percentage Study.com 's lesson. To form a new equilibrium constant, K water ( K w ) easily refer to compounds! Contact customer support minor disturbance of the mixture, as milligrams per liter ( mg/l ), more! And so the concentration of solution know that there is 1 mole of hydrochloric acid per of. A measure of the First two years of college and save thousands off your degree a weight/volume percentage.... And ( 1000-73 ) = 927 mL of a solution actually use 1 liter of solution formula is as. Lesson you must be a Study.com Member right school particular view of what is meant the! ' the solute concentration may also be expressed in terms of mass per volume! To either solvent or total solution Grades Science ( 014 ): practice & Study page! Continue and there is 1 mole of hydrochloric acid can be concentration of solution meaning ( lots of solute that be. 'S clustered together or to the mass by volume percentage is given as follows like epinephrine on. Undefined density is simply defined as the amount of solvent per liter ( mg/l ) in it, define... Solute concentration may also talk about molarity, then yes it does change walls! Solution what a solute to get grams of solute ) depending on our needs slightly less the! 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If statements in equations?

When creating an equation is there any way to let someone know that if this number doesn't fit into this then use this other equation? Ex: $x>1$ then use $x+y$, or if $x<1$ then use $x-y$. Or do you just have to find an equation that works for both probability?

• here is another example, this is an equation i created to find how many square in the square aren't touching other squares Example: 2*2*2 square only has 4 sqaures that have two sides not touching another block and 8 squares that have 3 sides not touching a block. Equation: for 0sides
– Matt Kemp
Sep 25, 2014 at 22:18

$$f(x,y)=\begin{cases} x+y & X>1 \\ x-y & X<1 \end{cases}$$
$f(x,y) =\,$ for $x>1\,$ use $x+y\,$ and for $x<1\,$ use $x-y$
You could also say $f(x,y) = x + \frac{x-1}{|x-1|}y$ for your particular example.


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# Is the average (arithmetic mean) of positive integers n and p greater

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Kudos [?]: 139594 [0], given: 12794

Is the average (arithmetic mean) of positive integers n and p greater [#permalink]

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25 Dec 2017, 00:22
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Is the average (arithmetic mean) of positive integers n and p greater than z?

(1) z > 0
(2) The sum of n and p is 14.
[Reveal] Spoiler: OA

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Kudos [?]: 31 [0], given: 40

Re: Is the average (arithmetic mean) of positive integers n and p greater [#permalink]

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25 Dec 2017, 16:45
Bunuel wrote:
Is the average (arithmetic mean) of positive integers n and p greater than z?

(1) z > 0
(2) The sum of n and p is 14.

Question: is $$\frac{n+p}{2}>z$$?

(1) z > 0. So z can be any positive integer, but there is no info on n or p; insufficient.

(2) The sum of n and p is 14. So $$\frac{n+p}{2}=14/2=7$$, but z could be greater than 7 or less than 7; insufficient.

(1)+(2). We know that z is a positive integers and that the average of n and p is 7, but we cannot determine if the average is greater/less than z; insufficient.

(E) is the answer.

Kudos [?]: 31 [0], given: 40

Re: Is the average (arithmetic mean) of positive integers n and p greater   [#permalink] 25 Dec 2017, 16:45
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# Is the average (arithmetic mean) of positive integers n and p greater

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# In Luatex, how to know effective output directory?

I need to know what is the actual output directory, as set by the -outdir or -output-dir command line switch, because I am executing external programs and I need to give them the exact location of the auxiliary file to use, similarly to this unanswered question.

The difference is that I am using LuaLaTeX, so there might be new or easier means to get this right.

To test, I tried printing this directory in the document, but \directlua{tex.print(status.list()["output_file_name"])} only gives the basename and \directlua{tex.print(os.env["PWD"])} gives the working directory of the process which is not, as I had hoped, set to the outdir.

Arguments passed to luatex are stored in the lua table arguments. They are indexed by the passed key.

To find such info, you can search the _G (or more generally, _ENV) table, where all lua globals are indexed.

There is an introspection script on the lua website for this.

By the way, lua has the . syntactic sugar to refer to string keys in a table. eg : os.env["PWD"] is the same as os.env.PWD

Below I can't do this for "output-directory" because of the -.

## The output

If i have compiled my file with lualatex --output-dir=myOutDir myf.tex, I get :

## The code

\RequirePackage{luatex85}
\documentclass[12pt]{standalone}
\usepackage{luacode}
\usepackage{fourier}
\begin{luacode*}
function passedOutputDir()
return arguments["output-directory"] or "noPassedOutputDir"
end
\end{luacode*}
\begin{document}
Passed output dir :
\directlua{tex.print(passedOutputDir())}
\end{document}

• Sounds interesting but does not work with me (lualatex v1.0.4 (TeX Live 2017)). The arguments table is empty (if this is correct). – ysalmon Aug 26 '17 at 14:49
• @ysalmon It is empty if you don't pass arguments when compiling. Also, the output directory does not seem to be passed from latexmk to lualatex directly. – marsupilam Aug 26 '17 at 14:52
• Of course. After further investigation, it appears that lualatex -output-dir=test mwe.tex compiles into test but arguments is empty, while lualatex --output-dir=test mwe.tex compiles to the same dir but arguments is set this time. Strange. – ysalmon Aug 26 '17 at 14:56
• So, the following does the trick : latexmk -pdflua -outdir=build -latexoption="--output-directory=build". It is also interesting to note that lualatex seems not to complain when it is passed arbitrary options --myprivateoption=myvalue and they are accessible through arguments : one can effectively pass parameters to the script being compiled. – ysalmon Aug 26 '17 at 15:16
• You can find all luatex arguments in the arg table... – Paul Gaborit Aug 26 '17 at 15:25


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# mikosik/jvalues

object oriented java values
Java
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Starting with jValues is easy, just grab jar file from https://github.com/mikosik/jvalues/releases and add it to your project. You need to import all methods from one class to start with jValues:

import static com.perunlabs.common.vars.V.*;

Basic types (primitive wrappers)

Now let's see some examples of creating objects that will represent simple float values (We focus on float at beginning but other types are present as well even compound like vector or quad, more about it later):

FloatC pi = floatC(3.14f);
FloatV radius = floatV(2);

We've just created constant pi (immutable object) value and radius variable (mutable object). Both objects implement FloatG interface which has just one method returning float. This way method can accept FloatG type when they don't care whether they arguments are mutable or not. Methods can also force callers to use const types when immutability is needed (for example in case of concurrent code). Let me just print this interface here to make everything clear.

public interface FloatG {
public float get();
}

Seems trivial so far but wait a little bit and we reach some magic soon. For now let's see normal way to perform operation on FloatV variables. We have already created radius and stored 2 in it. We can simply multiply it by 3 this way:

radius.mul(3);

FloatV supports most common operations you would require from floats. Now all of these give us nothing more than normal primitive java values. Let' make use the fact that we are dealing with real objects. The com.perunlabs.common.vars.V class from which we imported all static methods at the beginning comes with set of methods that allow us to create just-in-time calculated values. Let's calculate perimeter of a circle using well known formula p = 2 \pi r,. It should go like this (we are reusing pi and radius objects declared a few lines above):

FloatG perimeter = mul(radius, mul(pi, floatC(2)));
System.out.println(perimeter) // prints 12.56

Now we can change the value of radius

radius.set(10);

and perimeter value is updated automatically.

System.out.println(perimeter) // prints 62.8

As can be seen values compound this way retain references to the whole calculation and are always up to date. We created object that implements simplest possible interface (FloatG) and keeps (hides) inside complicated calculations. This FloatG interface (and analogical XxxG interfaces for each primitive java type and also compound jValues) is a core of the library - it allows you to have components in your game that can be easily joined together by exchanging information via this interface. For example if you have component that draws progress bar - just make it accept FloatG in its constructor as a source of progress state. Now you can instantiate such progress bar giving it anything that implements FloatG. It can be either 'time to checkpoint' that will countdown during game level, or 'hero health' that will show current status of our hero. This simple interface removes the need of creating Model objects known from other frameworks (e.g. Java Swing). This interface is a model by itself. Note that such design is possible because UI (and whole graphic) in game are usually drawn 60 times per second without checking whether something was changed in UI/game or not. This is due to the fact that games are mostly very dynamic things and most objects to be drawn changes quickly. In standard UIs (like Swing) you want to update (redraw) part of UI only when it actually changes that's why such frameworks are filled with onUpdate(), onRedraw() and other similar methods.

If you worry about performance let me mention that static methods from V class are smart enough to avoid just-in-time calculation when all jValues used as arguments in calculation are const (immutable) and result can be calculated once. Such cases are detected and FloatC value is returned so invoking get() each time does not perform any additional computations. For example multiplying two const values will return const value calculated once during method call:

FloatC rectangleArea = mul(floatC(3), floatC(4));

public static FloatC V.mul(FloatC, FloatC)

function (takes two FloatC) arguments and returns FloatC but even when version with two FloatG is invoked:

public static FloatG V.mul(FloatG, FloatG)

it internally detects that arguments are instances of FloatC, will calculate result once, and return instance of FloatC.

Runnable interface

Another interface that is a core in UI programming is Action interface. You probably seen something similar if you programmed UIs (especially in java Swing). It usually forces you to create lots of anonymous inner classes that just tells some UI component what should be invoked when user triggers some action. With jValues you can simplify most of such code. FloatV method always come in pairs. For example method add(FloatG) has companion method addR(FloatG):

public interface FloatV ... {

[...]
}

The companion method (one with R suffix in its name) that will invoke its companion add(...) method each time its "run" method is called. If you need a button that increases speed of car in your game each time it is pressed do this:

FloatV speed = floatV(0);
FloatG speedIncrease = floatC(0.5f);
Button button = new Button(speed.addR(speedIncrease));

Each time button is pressed it will simply run given Runnable which will execute appropriate action. Note that speedIncrease object does not have to be plain value but just-in-time object itself. Let's see how we can extend our game by adding afterburner to our car so once it is enabled speedIncrease will be higher with each button press:

FloatC normalSpeedIncr = floatC(10);
FloatC afterburnerSpeedInc = floatC(30);
BoolV afterburnerOn = boolV(false);
FloatG speedIncrease = iff(afterburnerOn, afterburnerSpeedIncr, normalSpeedIncr);

Note we introduced iff method from V api. As can be guessed it simply returns value from second or third parameter depending on boolean condition value from first parameter. Now turning on afterburner from code is as simple as:

afterburnerOn.set(true);

Note that afterBurnerOn is jValue itself so we can manipulate its value from UI. Creating UI button that would allow user switching afterburner on/of requires this code (method not() negates the current value in BoolV object):

new Button(afterburnerOn.notR());

If you want allow user only turning on afterburner (without possibility to turn it off) use this line:

new Button(afterburnerOn.setR(true));

it will set afterBurnerOn to true each time button is pressed.

Just to make sure you got the whole mental shift we covered here let's just show how jValues can be used for building your own objects. As we already described UI framework that does not need primitive values, Action interfaces, anonymous classes and other bloat, now we focus on your own classes and show why you don't need primitive types anymore. Let's design simple class Hero that will represent your game hero fighting opponents in your game:

public class Hero {
private static final FloatC INITIAL_HEALTH = floatC(100);
private FloatV health = floatV(INITIAL_HEALTH);
// isGt method means "is Greater Than"
private BoolG isAlive = isGt(health, 0);

public FloatG health() {
return health;
}

public BoolG isAlive() {
return isAlive;
}

public void takeDamage(FloatG damage) {
health.sub(damage);
}

public void eatMedicine() {
health.set(INITIAL_HEALTH);
}
}

Note that: There is not a single old-school getter/setter method in this code. Methods takes/returns jValues objects. We have health() and isAlive() methods that returns XxxG interfaces that are read-only - we encapsulate our Hero state this way. If we need give more access to code that calls Hero we can simply return FloatV in case of health() method - this would be equal to creating setter in old-school code but we would achieve that with only one method.

Compound Types

Once we covered basic types let's jump to some advanced values. Our float jValues can be easily compound into another types. As you suspect everything that was true for float jValues is true for vector jValues:

VectorC earthGravity = vectorC(0, -10);
FloatV ballMass = floatV(1);
VectorG force = mul(earthGravity, ballMass);

System.out.println(force) // prints "vector(0, -10)"
ballMass.set(2);
System.out.println(force) // prints "vector(0, -20)"

Composition is not limited to one level only. For example Quad (quadrilateral) is composition of four vectors, each containing position of one quad vertex:

QuadC rectangle = quad(vectorC(0, 0), vectorC(1, 0), vectorC(1, 1), vectorC(0, 1));
FloatV angle = floatV(0);
QuadG rotated = rotate(rectangle, angle);

Future improvements

jValues is pretty young library so might miss some functionality that you find important in your project. If that is the case drop me a line. Whole library code is autogenerated by java tool created for that purpose so adding new types and functions is quite painless.

jvalues has been successfully used at PerunLabs in a number of android games. You can find more about PerunLabs at: