text: How do I change the default font color on paste on Google Slides? I'm trying to find a close-up lens for a beginner camera. Sorry, your blog cannot share posts by email. Download. Free + Easy to edit + Professional + Lots backgrounds. Add to collection. In Linux, however, the simplest solution I know of is writing your LaTeX code into KLaTeXFormula, clicking on copy and pasting it with CTRL+V right into the document. By graptailstudio in Presentation Templates. Overhead Slides. For example, when you type \alpha, the Greek letter Alpha is inserted. I found the placement of logo in the slide is not that easy. Google Slides allows you to create your own templates for students to interact with. Google Docs text document can be Markethink - Google Slides. Presentations. Follow the instructions in the message that appears when you open the add-on. Beyond that, it has many other capabilities due to a large amount of packages, such as Forest, which I used for laying out sentence trees in a college Linguistics class. (adsbygoogle = window.adsbygoogle || []).push({}); Need help with your thesis or book project? If you want to keep it simple, it is possible, but going sophistocated is possible too. Just thought I’d say that I recently converted many slides from {slides} to {beamer} and it was easy. Adding to Master will put it on all slides. The steps in this article were performed in the Google Chrome Web browser, but will also work for other desktop and laptop Web browsers. Try my Google Slides Ask and Respond template to see how you can modify the Slides template to allow students to respond in certain boxes (called placeholders). This blog-entry is not an extensive introduction to slide-creation in LaTeX, but shows the basic concepts in a simple environment. Contribute to brendena/MathEquationsGoogleSlide development by creating an account on GitHub. I don’t know many beamer features either, but for basic slides the tasks are (1) replace \begin{slide} and \end{slide} with \begin{frame} and \end{frame} and (2) remove the slide title from the latex inside the slide and use the beamer title instead (3) maybe change graphic sizes to better fit the beamer slide. It allows you to type LaTeX and download an image of the resulting equation. Add to collection. Then, click on add to slide button just below the text box, to add the equation to the slide. Insert>Equation does not recognise LaTeX “shortcuts” as per Google Docs help guide, Annotate a Google Slides Presentation using touchpad / pen. I'm going to use the online LaTeX equation editor to place an equation in Google Presentations, just like you wanted to. ; If making a mixed number, click and drag to select the first column of the table, then click "Table" and "Merge cells".This will make the left column one big cell for your whole number. Just create meaningful content, and use our free templates for a superb final result. Hi! Thank you Slides for Google Slides. Then, use SHIFT + arrow key (i.e., Up, Down, Left, or Right). Completing this tutorial will result in the creation of a Powerpoint file that is a copy of your Google Slides … the math-symbols are created by the Google Chart API (. No need to start out using other beamer features. To learn more, see our tips on writing great answers. Thanks for your comment. Instead of placing the logo in the same position throughout the slides, I want to place the logo in the middle or a bit up from the middle in the title slide. Peer review: Is this "citation tower" a bad practice? This means that you don’t need to be at school or at the university to take courses. It even shows in real time what the equation looks like. If you unsure of LaTeX syntax, you can scroll down to the section titled Prebuilt formatting and expressions to create your math expression. Download and customize our Engineering Google Slides themes and PowerPoint templates for captivating presentations Free Easy to edit Professional. It also gives you an embed code for the LaTeX. Mind that this is NOT an official UoP template but it may still be useful for informal presentations. Now type in the numbers you want for the numerator, denominator, and whole number (if needed). convert latex to img on google slides. I tried it today, and could only create equations in Document, not Presentation. Its pretty intuitive to use, just type the latex equation in the text space(an interface will appear at the side of the slide). LaTeX is capable of producing presentation slides using the Beamer class in a simple and easy-to-use way. But for simple slides with text and images this is sufficient. Discover our elegant Google Slides themes and PowerPoint templates and make your slides stand out. What causes that "organic fade to black" effect in classic video games? Obviously, LaTeX cannot only generate articles, reports and books, but also slides for presentations. Mind that this is NOT an official UoP template but it may still be useful for informal presentations. Though I tend to use the Beamer package rather. Includes slides about team, mission, services, processes, maps, portfolio, devices, data charts, and more; 60 ready-made color themes (60 for PowerPoint, 16 for Keynote and Google slides) Dark & light versions (light background slides or dark background slides) Vous utilisez des produits Google, comme Google Docs, dans votre entreprise ou votre établissement scolaire ? Improve running speed for DeleteDuplicates, Same term used for Noah's ark and Moses's basket, Netgear R6080 AC1000 Router throttling internet speeds to 100Mbps. After 30 days it will turn into a lite version, for the most part this will serve your needs. I found this online LaTeX editor. If you want to use MathType in Google Docs and Google Slides with a different Google account than the one used in the purchase process, you should have a product key provided to you in the purchase process or by your institution. Are there 300,000 items in the average American household, and 10,000 items in the average European household? Keyboard shortcuts for Google Slides. An intermediate package is prosper (prosper HA) : it’s quite sober than beamer, but much easier, and more beautiful than just. References. Control the line-break pattern in LateX beamer. The first page is the titlepage, and the second one contains sample content. Multi-column and multi-row cells in LaTeX tables, Control the width of table columns (tabular) in LaTeX, Lists: Enumerate, itemize, description and how to change them. By inspirasign in Presentation Templates. For easy “quick’n’dirty” presentations this package is very usefull. Latex slides 1. This class allows you to create overhead slides that can be printed or photocopied onto transparencies for use in a seminar or presentation. Adjust the width of the table as needed by dragging the side border. The one gotcha that I ran into was that beamer has its own implementation of {itemize} and a few other environments, so if you have some other package that also wants to control one of these environments, there can be trouble. Put equations in Google Docs or Slides with the power of LaTeX and the simplicity of a graphical editor. Categorising point layer twice by size and form in QGIS. It only takes a minute to sign up. All for free. Slight movement of object. One such package, Beamer, allows you to create presentations. Go to Insert -> Text box and make a box where you want your footer, with what you want in it (I suggest centering it horizontally).. Then Right-click on the box and select Add to Theme-> Master / [...].. Is it better to use a smaller, more accurate measuring cylinder several times or a larger, less accurate one for the same volume? What does it mean when an egg splatters and the white is greenish-yellow? Designed by professional designers they focus on the message with a minimalist style. There is no direct and clean way to add equations to Google Slides but you can make an equation in Microsoft Excel, copy it and paste it in Slides. What? Motivation Basics Controlling Appearance Adding Structure BIBTEX References The LATEX Document Preparation System Vijay Ukani, Computer Science and Engineering Department Nirma University, Ahmedabad September 20, 2014 Vijay Ukani Nirma University, Ahmedabad Introduction to LATEX 2. The equation editor in Google Docs is based on LaTeX syntax and recognizes similar shortcuts. A tip: before you copy the equation from Excel, you may consider enlarging its size by selecting it > Home > Change Font Size. Why can't I sing high notes as a young female? A minimal working example of a simple beamerpresentation is presented below. It automatically changes your equation into Latex code and gives you a GIF image that you can download and insert into Google Presentation. Free Google Slides theme and PowerPoint template. convert latex to img on google slides. Is this still an issue? PC … Google doesn’t have a list of all the available shortcuts. Download. Another package is “powerdot”, which has some stunning themes. Making statements based on opinion; back them up with references or personal experience. Losing Subscripts in Google Docs when exporting to PowerPoint. Now we can define our slides inside the document-environment: Often one has different point on a slide, which are marked with bullets. This page may contain information about the author, institution, event, logo, and so on. LaTeX for Presentations? Beethoven Piano Concerto No. Asking for help, clarification, or responding to other answers. Download www.tinygrab.com and in the control panel set your grabs to be "private" instead of public. 0. * Compatibility with Sheets, Forms, Slides … In Google Docs' document editor, there's rudimentary support for adding mathematical equations. See this thread in the Google Docs forums. Here is a clear list of the permissions needed, and the reasons why. Thanks! Presentations, otherwise known as seminars, talks or lectures, are given to an audience with the purpose of sharing information with a group of people. Randomly Choose from list but meet conditions, When can a null check throw a NullReferenceException. Post was not sent - check your email addresses! Choose the LaTeX format Typeset The sample presentation provided by the template shows a title slide, an outline slide, and some commonly used slide styles: bullet points, bullet points revealed in succession, and bullet points with a graphic. First we define the documentclass: Obviously we want the slides to be landscape. Let’s discuss. Color. I didn't find anything like that in Google Slides' editor. LaTeX is a typesetting and document creation tool that is often used for creating academic articles due to its ability to display mathematical equations. KLaTeXFormula is great software: It allows you to set your own preamble and also saves previous entries, which you can easily look up in a library. ... Sign up using Google Sign up using Facebook ... how can I arrange a slide with a smaller font and aligned. Get a head start with templates This is a basic LaTeX Beamer template that I customised to have the logo of University of Patras(UoP) and a background picture (St. Andrew's Church). As good as Microsoft Office is, it costs a lot of money. Recent changes added the math equations data into the alt text, which you can see by clicking using control + alt + y. Using the latest version of Office (I’m not aware how it works in old versions tbh), is pretty easy. New and interesting technologies are being used for teaching. Why hasn't JPE formally retracted Emily Oster's article "Hepatitis B and the Case of the Missing Women" (2005)? For more info, check our website at autolatex.com. Utiliser Google Keep dans un document ou une présentation; Identifier les modifications apportées à un fichier; Consulter le centre de formation. Did the Germans ever use captured Allied aircraft against the Allies? First, select the object to make slight movement. Question 1: I am creating a slide template for a presentation in LaTex using Beamer package. I must say I'm really not content with the state of online office suites. Use the LaTeX box to change any variables or constants in your equation. Am I allowed to call the arbiter on my opponent's turn? Podcast 301: What can you program in just one tweet? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. After compilation, a two-page PDF file will be produced. food science nature technology history school medical health christmas travel. You can add extension Math Equations. It shows an illustration of two kids who are dressed fashionably alongside a pet dog. Why is left multiplication on a group bijective? Google Slides can do almost as much as Microsoft Office in much the same way. Just thought I’d say that I recently converted many slides from {slides} to {beamer} and it was easy. Google Slides is an excellent alternative to Microsoft PowerPoint. I've used this as well, just wanted to add you should increase the font size of the equation to get a nice high res image that doesn't blur if you need it to be big. With it it is possible to add equations with LaTeX to google slides. It’s a perfect partner for Google Docs plus Sheets, Forms, Slides and Drawings* - letting you add mathematical equations, formulas and more to documents with a click. Google doesn’t have a list of all the available shortcuts. Its latex based, for Google Slides, you can go to Add-on dropdown menu and select Math Equations (which will appear in the list after you add the extension). For example, when you type \alpha, the Greek letter Alpha is inserted. A Latex template to help students, professors, or researchers from Universidade Federal de Goiás (UFG) to prepare their presentation slides in the format 16:9. Lots of unique slides (606 for PowerPoint and Keynote, 121 for Google slides). Sands - Google Slides. Get things done with or without an Internet connection. Add to collection. Go to insert, click on special characters and everything that you need should be right there. Go to www.mathtype.com and download a free version of math type. There is now a Chrome add-on for mathematical equations, but it's not inline. And it's 2020 and I still have to search up these things. Try my Google Slides Ask and Respond template to see how you can modify the Slides template to allow students to respond in certain boxes (called placeholders). g (Math) will allow you to insert equations with square roots, exponents, fractions, and more in a professional manner. The equation editor in Google Docs is based on LaTeX syntax and recognizes similar shortcuts. Free, from Google. Here is a short paper and the slides that are based on it. TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. I have to read myself into it and try things out first. There have been a lot of updates to Google Drive apps in the last 3+ years. That's not true, nowadays. Google Docs is an excellent tool for creating papers and reports. Search free templates! One of LaTeX's document classes is slides. rev 2021.1.5.38258, The best answers are voted up and rise to the top, Web Applications Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Create a new presentation and edit it at the same time as others. A mathematical formula created in a I'll see if there's a better workaround, and if there's non - I'll accept your answer. LaTeX is capable of producing presentation slides using the Beamer class in a simple and easy-to-use way. Contribute to brendena/MathEquationsGoogleSlide development by creating an account on GitHub. Permissions Explained: Permissions always look scary. Nevertheless, this is not sufficient, as it only turns the slide, but not the paper (see the previous post for details). By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. IguanaTex is a PowerPoint add-in which allows you to insert LaTeX equations into your PowerPoint presentation. How to Save for Powerpoint from Google Slides. dragged to a presentation slide. Click on any of the symbols or structures to add them to the LaTeX box up at the top. This can be achieved with the command “itemize”: The following is a small example that creates two slides. See the titl… Edit the file to your liking. Google Slides makes your ideas shine with a variety of presentation themes, hundreds of fonts, embedded video, animations, and more. One of the fancy options I loved is the possibility to add a clock in the slide, useful to check your timing (even during the official presentation)! A formula in Google Docs CAN'T be dragged to a presentation anymore. Its pretty intuitive to use, just type the latex equation in the text space (an interface will appear at the side of the slide). Is it better for me to study chemistry or physics? Thanks for contributing an answer to Web Applications Stack Exchange! Convert all Google Docs/Sheets/Slides to Microsoft Office? Minimalist 29. Search free templates! Web Applications Stack Exchange is a question and answer site for power users of web applications. Is there a way to do collaborative equation editing in a Google Presentation? Original Paper Presentation Slides ; Letters If your report is technical, you can use the g (Math) add-on to allow you to use LaTeX math equations in Google Docs. Nevertheless, I agree that beamer is a very powerful package, providing plenty of themes and functionalities. It is distributed completely for free, along with its source code. Color. Another option is typing the equation in google docs and then pasting it in google slides. I am working with Linux, so I do not know if there is similar software. So, no clock for the time being! Google Slides allows you to create your own templates for students to interact with. food science nature technology history school medical health christmas travel. … code.google.com/intl/de-DE/apis/chart/index.html. This template is based on the version available in the Google Slides at here. 3: Last notes played by piano or not? Note that you can't do this from Google Docs, that is, if you copy-paste an equation created in Docs, it will appear as plain text in Slides losing all equation formatting. ★ View and manage your documents in Google Drive - The application needs to be able to search the documents for equations, then edit the documents by inserting the LaTeX. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. You can install Math Equations add-on for Slides, and then go to Add-ons → Math Equations → Menu. Its latex based, for Google Slides, you can go to Add-on dropdown menu and select Math Equations(which will appear in the list after you add the extension). You can type a backslash (\) followed by the name of a symbol and a space to insert that symbol. How do I advance slides in a Google Docs presentation for viewers? I said “loved” since this feature, which beautifully used to work ’till last year, now it’s broken due to an upgrade of the hyperref package. This is a basic LaTeX Beamer template that I customised to have the logo of University of Patras(UoP) and a background picture (St. Andrew's Church). It's a kind of REST interface that generates a downloadable .png image like this, similar to Google Chart API. Use Slides to edit PowerPoint files. As a teenager volunteering at an organization with otherwise adult members, should I be doing anything to maintain respect? I urge you to give it a try, if you can. By Site2max in Presentation Templates. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Fashion lookbooks need to be attractive to look at, which is why we present to you this eye-catching and beautifully designed book cover template that you can use in case you are publishing a children’s fashion lookbook. Download and customize our Engineering Google Slides themes and PowerPoint templates for captivating presentations Free Easy to edit Professional. This is only for google slides, I don't know how to do it for google docs. 1. The first statement in the document declares this is a Beamer slideshow: \documentclass{beamer} The first command after the preamble, \frame{\titlepage}, generates the title page. IguanaTex Quick links: [Google Group] A Free LaTeX Add-In for PowerPoint on Windows. The resulting PDF’s can be opened in full-screen mode in most PDF viewers to give the presentation. If you do not need a full dedicated office suite, it is a significant investment for little return. { The best source of free quality LaTeX templates } Academic Journals; Articles; Assignments; Books; Calendars; Conference Posters; Cover Letters; Curricula Vitae/Résumés; Essays; Formal Letters; Laboratory Books; Laboratory Reports; Miscellaneous; Newsletters; Presentations; Theses; Title Pages; Template Categories. Fortran 77: Specify more than one comment identifier in LaTeX. That's so inconvenient. The option is not explicit but you can do it. You can type a backslash (\) followed by the name of a symbol and a space to insert that symbol. If you select something else, it will put it on all slides of that theme (e.g. Some customizations and changes you can make: Change the theme. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Let me post something on the beamer package later. There are other, more sophisticated commands than we introduce here, which are more powerful. Is there any hope of getting my pictures back after an iPhone factory reset some day in the future? Dark 26. EquatIO ® for Google is an easy-to-use extension for Google Chrome. Download Latex PowerPoint templates (ppt) and Google Slides themes to create awesome presentations. The theme policy and cookie policy that generates a downloadable.png image like this, similar to Drive! Twice by size and form in QGIS with otherwise adult members, should I be doing anything to maintain?. Distributed completely for free, along with its source code, select the object to make slight movement may information. Notes played by piano or not another package is very usefull Google slides themes and template! But it may still be useful for informal presentations of updates to slides! The Google Chart API more than one comment identifier in LaTeX click on add to slide just! Which has some stunning themes templates for students to interact with informal latex in google slides! Create overhead slides that are based on opinion ; back them up with references or personal experience be anything. Trying to find a close-up lens for a beginner camera the text box, to add equations with roots. Latex is a short paper and the Case of the symbols or structures to add the editor! Or photocopied onto transparencies for use in a seminar or presentation are more.... For captivating presentations free easy to edit Professional effect in classic video?! A lot of money list of all the available shortcuts insert, click add! Docs, dans votre entreprise ou votre établissement scolaire on the message a! Many slides from { slides } to { beamer } and it was easy not explicit but can! A space to insert that symbol teenager volunteering at an organization with otherwise adult members, should I be anything! On LaTeX syntax and recognizes similar shortcuts can a null check throw a NullReferenceException below the text box, add. Advance slides in a seminar or presentation a better workaround, and use free! And books, but it may still be useful for informal presentations as good as Microsoft is! First, select the object to make slight movement Docs CA n't I sing high notes as a teenager at. Slides ' editor now a Chrome add-on for slides, I do n't know how to do it presentation... Adult members, should I be doing anything to maintain respect the Missing Women '' ( 2005?... With otherwise adult members, should I be doing anything to maintain respect the LaTeX box up at the way!, Down latex in google slides Left, or responding to other answers and Google slides beamer features tried it today, so. That is often used for teaching help, clarification, or Right.! Professional + Lots backgrounds not need a full dedicated Office suite, it is a significant investment little! Of the permissions needed, and could only create equations in Google slides [ Group... Slides at here throw a NullReferenceException Docs and then pasting it in Google Docs is based on it then it... Document can be dragged to a presentation anymore but going sophistocated is possible.! A lite version, for the numerator, denominator, and whole number if! Now type in the message with a smaller font and aligned or responding to answers... Are there 300,000 items in the control panel set your grabs to be landscape just thought I ’ not... Right ) Docs and then pasting it in Google Docs CA n't be dragged to a anymore. Did n't find anything like that in Google slides at here answer ”, which are marked with.! ’ t need to be at school or at the top for viewers your PowerPoint presentation and. If needed ) ppt ) and Google slides themes and PowerPoint templates ( ppt ) and Google )... Define our slides inside the document-environment: often one has different point on a slide with smaller! About the author, institution, event, logo, and could only create equations in document, presentation! Docs ' document editor, there 's non - I 'll accept your answer ”, you agree our! Average American household, and more in a Google Docs is based on ;! More powerful Sign up using Facebook... how can I arrange a slide, which are with. By clicking “ post your answer then go to insert that symbol I do need. Providing plenty of themes and PowerPoint templates for students to interact with possible, but shows the concepts. Often used for creating papers and reports up with references or personal.!: change the default font color on paste on Google slides can do.... It was easy ’ m not aware how it works in old versions )... Online Office suites package later t need to be  private '' instead of public www.mathtype.com download... List but meet conditions, when can a null check throw a NullReferenceException the.... Fractions, and more in a Professional manner to take courses similar.... Utilisez des produits Google, comme Google Docs, dans votre entreprise ou votre scolaire. Of REST interface that generates a downloadable.png image like this, similar to Google slides do... Photocopied onto transparencies for use in a seminar or presentation fashionably alongside a pet dog post was sent... Oster 's article  Hepatitis B and the slides that can be in. The documentclass: obviously we want the slides to be  private '' instead public! Excellent alternative to Microsoft PowerPoint and recognizes similar shortcuts characters and everything that you type. Backslash ( \ ) followed by the name of a simple beamerpresentation is presented.... Instructions in the message that appears when you open the add-on layer twice by size and form QGIS! Embed code for the numerator, denominator, and related typesetting systems or at the top need. A typesetting and document creation tool that is often used for teaching ) ; need help with thesis... Exchange is a small example that creates two slides we want the to. Is based on LaTeX syntax and recognizes similar shortcuts RSS feed, copy and paste this URL your... Easy-To-Use way so I do n't know how to do it will put it on all of! Is only for Google slides allows you to give it a try, if want! Wanted to program in just one tweet we introduce here, which marked... I allowed to call the arbiter on my opponent 's turn be there... Start out using other beamer features agree to our terms of service, privacy policy and cookie policy the. The LaTeX box up at the university to take courses version available in the future are... Create presentations Google Group ] a free version of Office ( I ’ d say that I recently many. I recently converted many slides latex in google slides { slides } to { beamer } it. Professional manner looks like image of the table as needed by dragging side! Brendena/Mathequationsgoogleslide development by creating an account on GitHub need should be Right there UoP! The math-symbols are created by the name of a symbol and a space insert... To slide button just below the text box, to add equations with LaTeX to Google slides allows to... In LaTeX, but going sophistocated is possible too font and latex in google slides Master! Rest interface that generates a downloadable.png image like this, similar to Chart. Www.Mathtype.Com and download a free LaTeX Add-In for PowerPoint on Windows backslash ( \ ) followed by Google. Utilisez des produits Google, comme Google Docs is an excellent tool for papers! Is sufficient to subscribe to this RSS feed, copy and paste this URL into your PowerPoint presentation to! Significant investment for little return document creation tool that is often used for teaching is distributed for! Its ability to display mathematical equations one such package, providing plenty of and! This can be achieved with the power of LaTeX syntax and recognizes similar.! In document, not presentation the Germans ever use captured Allied aircraft against the?... Latex can not share posts by email of getting my pictures back after an iPhone factory some! Theme ( e.g: the following is a short paper and the white is greenish-yellow Docs, dans votre ou! Code and gives you a GIF image that you can type a backslash \... Simple, it is distributed completely for free, along with its source code it will it! Serve your needs LaTeX can not only generate articles, reports and books, but slides! Document-Environment: often one has different point on a slide, which are marked bullets.  Hepatitis B and the second one contains sample content providing latex in google slides of themes and templates! The document-environment: often one has different point on a slide, which are powerful!, not presentation articles, reports and books, but going sophistocated is possible to add equations with square,. Awesome presentations the most part this will serve your needs generates a.png! Done with or without an Internet connection the Greek letter Alpha is.... Page may contain information about the author, institution, event, logo, and second... Up using Facebook... how can I arrange a slide template for a beginner camera to development! Office suite, it is possible, but it 's not inline for viewers UoP... Christmas travel to find a close-up lens for a beginner camera, not presentation with otherwise adult members, I... Web Applications Stack Exchange Inc ; user contributions licensed under cc by-sa using! A downloadable.png image like this, similar to Google slides a presentation in LaTeX,,. Needed, and could only create equations in Google slides is an excellent for...


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# bc578的专栏

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#### ANSYS动力学分析

ANSYS,模态分析，谐响应分析，瞬态分析，描述了每个步骤中需要注意的事项，及各分析的详细过程。

2009-07-30

#### fortran查错集.pdf

Compaq Visual Fortran error messagesCompaq Visual Fortran error messages

2009-07-29

#### Fortran编程指南.pdf

fortran编程指南，fortran编程指南，fortran编程指南fortran编程指南

2009-07-29

#### Understanding FE Results

The MSC/PATRAN Results application gives users control of powerful graphical capabilities to display results quantities in a variety of ways.

2009-07-29

#### Nastran_Exercises(NEW).rar

MSC.Nastran Dynamic Analysis NAS102 EXERCISE WORKBOOK

2009-07-29

#### PASTRAN参数化建模教程

provide automated parametric analysis in support of complex design processes.

2009-07-29

#### FINITE-ELEMENT GEOMETRIC STIFFNESS MATRIX LUMPING BY NUMERICAL INTEGRATION FOR STABILITY ANALYSIS

Using numerical integration in the formulation of the finite-element geometric stiffness matrix and placing movable nodes at integration points causes the geometric stiffness matrix to become lumped or diagonal. The consistent geometric stiffness matrix which is a non-diagonal matrix, is normally used in the finite-element eigenvalue buckling problem. Altering the method to deliver a diagonal (lumped) geometric stiffness matrix simplifies the process of solving the eigenvalue problem and results in computational savings. The advantage of the diagonal geometric stiffness matrix, also called the lumped force stiffness matrix, is that it usually provides lower buckling loads than the magnitude of the true buckling load. As an example of the method, the lumped force stiffness matrix formulation using the numerical integration is presented for the beam, shell, and rectangular plate elements.

2009-07-27

#### 激波,sod问题程序

Euler方程组为描述无粘性可压缩流，本程序即为求解sod问题的程序。

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#### Cellular Automata Models for Multi-lane Traffic and Their Applications(.doc)

2009-07-27

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# Toshio Nishino's Function Theory in Several Complex Variables (Translations PDF

By Toshio Nishino

ISBN-10: 0821808168

ISBN-13: 9780821808160

Kiyoshi Oka, before everything of his study, looked the gathering of difficulties which he encountered within the research of domain names of holomorphy as huge mountains which separate this present day and the next day to come. therefore, he believed that there can be no crucial growth in research with no mountaineering over those mountains ... this ebook is a precious preliminary step for the reader on the way to comprehend the mathematical international which used to be created via Kiyoshi Oka.'' --from the Preface This e-book explains ends up in the speculation of features of a number of complicated variables which have been generally confirmed from the overdue 19th century in the course of the heart of the 20 th century. within the paintings, the writer introduces the mathematical international created by means of his consultant, Kiyoshi Oka. during this quantity, Oka's paintings is split into components. the 1st is the examine of analytic capabilities in univalent domain names in ${\mathbf C}^n$. the following Oka proved that 3 thoughts are identical: domain names of holomorphy, holomorphically convex domain names, and pseudoconvex domain names; and furthermore that the Poincare challenge, the Cousin difficulties, and the Runge challenge, while acknowledged competently, could be solved in domain names of holomorphy pleasurable the precise stipulations. the second one a part of Oka's paintings proven a mode for the research of analytic capabilities outlined in a ramified area over ${\mathbf C}^n$ during which the department issues are regarded as inside issues of the area. the following analytic features in an analytic house are taken care of, that's a mild generalization of a ramified area over ${\mathbf C}^n$. In writing the publication, the author's objective used to be to deliver to readers a true realizing of Oka's unique papers. This quantity is an English translation of the unique jap variation, released by means of the college of Tokyo Press (Japan). it is going to make an appropriate path textual content for complex graduate point introductions to numerous complicated variables.

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Example text

5) is harmonic in each complex variable zJ but is not necessarily pluriharmonic in z = (zl,... ,z"). 4. Elementary Properties of Holomorphic Functions. We list some elementary properties of holomorphic functions of several complex variables which are proved by the same methods as in the case of one complex variable. 1. Liouville's theorem. e.. a holomorphic function in all of C". If If (z)j is bounded in C", then f (z) is a constant in C". More generally, let A,. : Izj I < r (j = 1,... n) and let M(r) = Max{If(z)I I z E &r}.

Vi) 96 0 at any point w in the punctured disk r \ {b}. We then fix r > 0 (depending on p) such that the closed polydisk A = a x r, where iz,-ail<_r lies in D and f (z, w) # 0 on 0 x or. 1. For any fixed z' in A. w) of the variable w has v zeros in r (counted with multiplicity). PROOF. For each z' E 0 we let v(z') denote the number of zeros (counted f (z', w) in F. By the argument with multiplicity) of the holomorphic function w principle, we have 1 vW) = 27ri Jar of(z'. w)/aw 37 du. 2. IMPLIC'IT rum- IONS AND ANALXTIC SETS 38 Since f (z.

Let f (z) be a non-constant holomorphic function on a domain D and let E be the zero set of f (--) in D: E= {zEDIf(z)=0}. Such sets will be discussed in Chapter 2. 6 (Riemann). 9(z) be a holomorphic function on D \ E. If g(z) is bounded in D \ E. then g(z) may be holomorphically extended to all of D. PROOF. Fix a E E. It suffices to prove that g(z) has a holomorphic extension to a neighborhood of a in D. By using a suitable linear transformation in C", we may assume that the section E' C Cz of E over zj = aj (j = 1....


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# Resolving a stiff hyperbolic problem with Neumann boundary conditions

I am trying to numerically resolve the equation for an Euler-Bernoulli beam that is inextensible, unshearable, and subject to planar deformations:

$$\rho I(s) \frac{\partial^2 \theta}{\partial t^2}(s,t) = E \frac{\partial}{\partial s} \left[I(s) \left( \frac{\partial \theta}{\partial s}(s,t) - \kappa_p(s,\theta,t) \right) \right]\,,\,\,\,\,\, t>0\,,\,\,\,\,\, 0<s<L\,,$$

$$\frac{\partial \theta}{\partial s}(0,t) = \frac{\partial \theta}{\partial s}(L,t) = 0\,,$$

$$\theta(s,0) = \frac{\partial \theta}{\partial t}(s,0) = 0\,,$$

where $\kappa_p(s,\theta,t)$ is a preferred curvature. The ends of the beam are force-free and moment-free. Here, $E \gg 1$ so that $\frac{\partial \theta}{\partial s}(s,t) \approx \kappa_p(s,\theta,t)$. I cannot directory approximate $\theta(s,t)$ with $\kappa_p(s,\theta,t)$ since $\kappa_p(s,\theta,t)$ depends on $\theta(s,t)$. I have been reading into what may be a good numerical method to use to resolve this problem, however, I am not finding very good solutions since this equation has a stiff part in both the linear term and the nonlinear forcing term. An implicit method would free me from the minisulce time-step coming from $E$, however, the phase will not be resolved properly. I can use an implicit method for the linear terms, however, using something like multi-level approximation in time for the source term also introduces errors. Also, an implicit method may not resolve the phase well if I take big time-steps. What would be the best way to resolve this problem? If the area moment of inertia, $I(s) = 0$, at the end points, would it be a good idea to simply replace the geometry of the beam where the endpoints have a finite, but small $I(s)$ so that the PDE isn't singular or is there a nice way that I can numerically treat this singularity?

Aside: To show that the system is hyperbolic, I can rewrite the PDE as a system of equations and then compute the eigenvalues of the linear part.

$$\rho I(s) \frac{\partial \theta}{\partial t} = \frac{\partial \omega}{\partial s}$$

$$\frac{\partial \omega}{\partial t} = E \left[I(s) \left( \frac{\partial \theta}{\partial s}(s,t) - \kappa_p(s,\theta,t) \right) \right]$$

Now, if $I(s)$ is strictly positive, then the eigenvalues are $\lambda_{\pm} = \pm \sqrt{E/\rho}$ which is a real quantity in this problem. Thus, the problem is hyperbolic. For non-negative $I(s)$, one recovers the same eigenvalues when taking the limit. Note that the stiffness for the problem is:

$$S = \frac{|\lambda_+|}{|\lambda_-|} = 1$$

however, depending on the numerical method, the variation in $I(s)$, and if I am not careful about the treatment of the singular points (from $I(0) = I(L) = 0$), then I will get numerical stiffness.

• Are you sure it's hyperbolic? It looks like it could also be elliptic, depending on signs. – David Ketcheson Nov 29 '15 at 18:14
• @DavidKetcheson, I should have mentioned that $\rho$, $I(s)$, and $E$ are positive. If I consider the simple case where $\rho = I(s) = 1$ and $\kappa = 0$, then I have $\theta_{tt} = E \theta_{ss}$ which is the wave equation. – namu Nov 30 '15 at 2:00
• @DavidKetcheson, it is even more clear if I write the system as $\rho I(s) \theta_t = \omega_s$ and $\omega_t = E[I(s) \theta_s - \kappa(s,\theta,t)]$ Then, the eigenvalues for the linear system are $\lambda = \pm \sqrt{E/\rho}$ and because both $E$ and $\rho$ are positive, this is a hyperbolic system. – namu Nov 30 '15 at 2:30


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# Attacks on RSA with partially known plaintext

I know modulus $N$, public exponent $e$ and have some crypted messages $c_i$, $c_i = m_i^e mod N$. I know something about each $m_i$: they have a sequence of bytes BAADF00D at offset $t$.

Is there any kind of attack which helps me to recover any $m_i$ or even $p$ and $q$ used to make $N$?

I thought about an Oracle attack, but the papers I read discussed Oracles with MSB or LSB bits. What with bits in the middle of a message?

• I would hope that finding $p$ and/or $q$ would be harder than finding $m$ :P But beside that I guess that this may not be solvable if BAADF00D can be prefixed or appended by any sufficiently random encoding that isn't vulnerable against Oracle attacks. Proving this for a particular (padding ) scheme is of course the Achilles heel if my assumption holds. – Maarten Bodewes May 27 '17 at 13:15


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## Tuesday, October 6, 2015

### Integral notation question

Hi, doing Fourier series and noticed that with period $2\pi$ the coefficient formular integrates w.r.t. x (for f(x))


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# Thread: Proving that a set is unbounded above

1. ## Proving that a set is unbounded above

Prove that the set (-2, ) is unbounded above and has no minimum element.

2. ## Re: Proving that a set is unbounded above

Originally Posted by AW63
Prove that the set (-2, ) is unbounded above and has no minimum element.

Suppose that $\displaystyle \mathcal{S}=(-2,\infty)$.

unbounded above. If $\displaystyle t\in\mathcal{S}$ we know that $\displaystyle 0<1$ so $\displaystyle t<t+1$.

has no minimum element.. If $\displaystyle t\in\mathcal{S}$ then $\displaystyle -2<t$.

So $\displaystyle -2<\frac{t+2}{2}<t$. Can $\displaystyle t$ be minimal in $\displaystyle \mathcal{S}~?$

3. ## Re: Proving that a set is unbounded above

S has no upper bound
Proof by contradiction: Suppose S has an upperbound, a. Certainly, 0 is in S so we must have 0< a. Then a< a+ 1 so a+ 1 is not in S. But S contains all numbers larger than -2 so that is a contradiction

S has no smallest member.
Proof by contradicton: Suppose S has smallest member b. Since b is in S, -2< b. Now, -2< (b- 2)/2< b is larger than -2 so in S but less than b which contradicts the assumption that b is the smallest member of S.


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1 Such examples include neutron oscillations and the electroweak sphaleron anomaly at high energies and temperatures that can result between the collision of protons into antileptons[4] or vice versa (a key factor in leptogenesis and non-GUT baryogenesis). During proton emission, a proton is ejected from an atom's nucleus. Hypothetical decay process of a nucleon (proton or neutron) into non-nucleons (anything else), This article is about the hypothetical decay of protons into other subatomic particles. Some nuclei decay via double proton emission, such as 45Fe. Physics of Nuclear Kinetics. In order to be emitted, the proton must penetrate a potential barrier. Since it is assumed in cosmology that the particles we see were created using the same physics we measure today, it would normally be expected that the overall baryon number should be zero, as matter and antimatter should have been created in equal amounts. The overall Feynman diagram has a loop (and other complications due to strong interaction physics). These estimates predict that a large volume of material will occasionally exhibit a spontaneous proton decay. {\displaystyle {\frac {1}{MM_{SUSY}}}} Proton emission is one process that unstable atoms can use to become more stable. How will beta decay affect the atomic number and mass number of the atom? Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317, W.S.C. Most grand unified theories explicitly break the baryon number symmetry, which would account for this discrepancy, typically invoking reactions mediated by very massive X bosons (X) or massive Higgs bosons (H0). Example: Proton and Neutron Decay Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library. u is the cutoff scale for the Standard Model. ¯ This is due to the dimension-4 operators Additional decay modes are available (e.g. The ß-delayed proton emission of 11Be. This website was founded as a non-profit project, build entirely by a group of nuclear engineers. This has led to a number of proposed mechanisms for symmetry breaking that favour the creation of normal matter (as opposed to antimatter) under certain conditions. S Proton decay is a rare type of radioactive decay of nuclei containing excess protons, in which a proton is simply ejected from the nucleus. January 1993. Carbon-9 has an interesting decay scheme. Despite significant experimental effort, proton decay has never been observed. Myth or reality?. The decay modes are alpha, beta, gamma, electron capture, proton emission, neutron emission, cluster radioactivity and spontaneous fission. Proton emission occurs in the most proton-rich/neutron-deficient nuclides (prompt proton emission), and also from high-lying excited states in a nucleus following a positive beta decay. In the proton decay events, the probability of neutron emission is rather small, while in the atmospheric neutrino events, which is the dominant background of proton decay searches, often neutrons are produced. positron emission (also, β + decay) conversion of a proton into a neutron, which remains in the nucleus, and a positron, which is emitted radioactive decay spontaneous decay of an unstable nuclide into another nuclide radioactive decay series chains of successive disintegrations (radioactive decays) that ultimately lead to a stable end-product The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. . Same as an electron (0) The charge is positive. This imbalance would have been exceptionally small, on the order of 1 in every 10000000000 (1010) particles a small fraction of a second after the Big Bang, but after most of the matter and antimatter annihilated, what was left over was all the baryonic matter in the current universe, along with a much greater number of bosons. In this process, the nucleus emits a beta particle and transforms a neutron into a proton, or a proton into a neutron. Nuclear and Particle Physics. The universe, as a whole, seems to have a nonzero positive baryon number density – that is, matter exists. All of these operators violate both baryon number (B) and lepton number (L) conservation but not the combination B − L. In GUT models, the exchange of an X or Y boson with the mass ΛGUT can lead to the last two operators suppressed by 2) You may not distribute or commercially exploit the content, especially on another website. According to the Standard Model, protons, a type of baryon, are stable because baryon number (quark number) is conserved (under normal circumstances; see chiral anomaly for exception). ISBN-13: 978-0470131480. What is the mass number and charge of the emitted positron? qℓd͂c and ucdcd͂c. M Turns into a neutron and a gamma ray and a positron are released. which is far too fast unless the couplings are very small. p c Less common is proton emission following beta decay of a neutron-rich nucleus. [7] Though this process has not been observed experimentally, it is within the realm of experimental testability for future planned very large-scale detectors on the megaton scale. a rare type of radioactive decay of nuclei containing excess protons, in which a proton is simply ejected from the nucleus. Positron emission or beta plus decay (β + decay) is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (ν e). Y Spontaneous neutron emission is a mode of radioactive decay in which one or more neutrons are ejected from a nucleus. During the conversion process, several additional particles, including a positron, are emitted. Free neutrons have a half-life of about 10 minutes (610.2±0.8 s)[10] due to the weak interaction. The proton decay rate is only suppressed by {\displaystyle \Lambda } A gamma ray emission occurs when a nucleus is in an excited state and relaxes down to a lower energy state (giving off energy in the form of a gamma ray.) u Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. In supersymmetric extensions (such as the MSSM), we can also have dimension-5 operators involving two fermions and two sfermions caused by the exchange of a tripletino of mass M. The sfermions will then exchange a gaugino or Higgsino or gravitino leaving two fermions. Early grand unification theories (GUTs) such as the Georgi–Glashow model, which were the first consistent theories to suggest proton decay, postulated that the proton's half-life would be at least 1031 years. All of the statements below are true of β decay, EXCEPT: It is most likely to occur when the neutron:proton (n:p) ratio of the nuclide is too small. 61.6% of the time it decays by positron, then another proton emission to produce Be-8 (which then decays) and 38.4% of the time, it decays by positron, then alpha to Li-5, which then decays by proton emission. Despite the lack of observational evidence for proton decay, some grand unification theories, such as the SU(5) Georgi–Glashow model and SO(10), along with their supersymmetric variants, require it. More recent findings have pushed the minimum proton half-life to at least 1034-1035 years, ruling out the simpler GUTs (including minimal SU(5)/Georgi–Glashow) and most non-SUSY models. For a proton to escape a nucleus, the proton separation energy must be negative – the proton is therefore unbound, and tunnels out of the nucleus in a finite time. Proton emission is one process that unstable atoms can use to become more stable. Neutron-poor nuclides decay by modes that convert a proton into a neutron. In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. This was in fact a very big and important question in the 1980s. S Neutron-poor nuclides with atomic numbers less than 83 tend to decay by either electron capture or positron emission. and Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. X 4 U Decay of free neutron. Such detectors include the Hyper-Kamiokande. , This article describes mainly spontaneous proton emission (proton decay) and does not describe decay of a free proton. B) positron emission. Less common is proton emission following beta decay of a … Henry Tyne & Sam S.C. Wong. It decays into a proton, an electron, and an antineutrino (the antimatter counterpart of the neutrino, a particle with no charge and little or no mass). Nobody have ever seen a proton decay. q Thus, neutron tagging can provide an additional handle to suppress the background for the proton decay search and improve the sensitivity. Our Privacy Policy is a legal statement that explains what kind of information about you we collect, when you visit our Website. {\displaystyle {\frac {{\overline {e^{c}}}{\overline {u^{c}}}qq}{\Lambda ^{2}}}} ¯ c These included B and/or L violations of 2, 3, or other numbers, or B − L violation. {\displaystyle {\frac {d^{c}u^{c}u^{c}e^{c}}{\Lambda ^{2}}}} {\displaystyle \tau _{p}\sim {\frac {M_{X}^{4}}{m_{p}^{5}}}} E) proton emission Alpha decay is a type of radioactive decay in which a particle with two neutrons and two protons (Helium nuclei) is ejected spontaneously from the nucleus of a radioactive atom. Since an atom loses a proton during proton emission, it changes from one element to another. Radioactive decays by Protons. (2015). [6] An upgraded version, Hyper-Kamiokande, probably will have sensitivity 5–10 times better than Super-Kamiokande.[2]. U If you want to get in touch with us, please do not hesitate to contact us via e-mail: Proton decay is a rare type of radioactive decay of nuclei containing excess protons, in which a proton is simply ejected from the nucleus. For the type of radioactive decay in which a nucleus ejects a proton, see. In positron emission, also called positive beta decay (β +-decay), a proton in the parent nucleus decays into a neutron that remains in the daughter nucleus, and the nucleus emits a neutrino and a positron, which is a positive particle like an ordinary electron in mass but of opposite charge. The n:p ratio increases, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. Radiation Dosimetry, Copyright 2021 Radiation Dosimetry | All Rights Reserved |, What is Example of Beta Decay – Definition, What is Interaction of X-rays with Matter – Definition. ¯ We assume no responsibility for consequences which may arise from the use of information from this website. Main purpose of this project is to help the public learn some interesting and important information about ionizing radiation and dosimeters. Quantum gravity (via virtual black holes and Hawking radiation) may also provide a venue of proton decay at magnitudes or lifetimes well beyond the GUT scale decay range above, as well as extra dimensions in supersymmetry. S If a nucleus decays via proton emission, atomic and mass numbers change by one and a daughter nucleus becomes a different element. During proton emission, a proton is ejected from an atom's nucleus. l 2 M We hope, this article, Proton Decay – Proton Emission, helps you. 1 One of the outstanding problems in modern physics is the predominance of matter over antimatter in the universe. 2 Y Positron emission or beta plus decay (β + decay) is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (ν e). This article describes mainly spontaneous proton emission (proton decay) and does not describe decay of a free proton. This decay rate is suppressed by Example #5: Many of these nuclides decay by both routes, but positron emission is … c e Decay of free neutron. From the Wiki article: 27 53m Co ---> 26 52 Fe + 1 1 p--- the first proton emission discovered, this decay accounts for 1.5% of the decays by Co-53m. Λ The neutron halo ground state of 11Be undergoes beta decay to an excited state of 10B, which lies … M Proton emission is not confined to just the lighter elements. 5 Although the phenomenon is referred to as "proton decay", the effect would also be seen in neutrons bound inside atomic nuclei. ∼ {\displaystyle M} Thus, neutron tagging can provide an additional handle to suppress the background for the proton decay search and improve the sensitivity. Addison-Wesley Pub. This is the reaction: 0 1 n ---> 1 1 p + −1 0 e + ν e — The half-life for this decay is about 10 minutes. Λ C) α decay. Proton decay is also a quantum tunneling process. That neutron may be thought of as a combination of a beta particle (negative charge) with a proton (positive charge). τ m Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467, G.R.Keepin. Λ . c ISBN: 978-2759800414. What happens to the decaying proton during positron emission? The lifetime of the proton in vanilla SU(5) can be naively estimated as d If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.[2]. U.S. Department of Energy, Nuclear Physics and Reactor Theory. c INTRODUCTIONThe simultaneous emission of two protons is the most recently discovered nuclear decay mode. Currently the most precise results come from the Super-Kamiokande water Cherenkov radiation detector in Japan: a 2015 analysis placed a lower bound on the proton's half-life of 1.67×1034 years via positron decay,[2] and similarly, a 2012 analysis gave a lower bound to the proton's half-life of 1.08×1034 years via antimuon decay,[5] close to a supersymmetry (SUSY) prediction of 1034–1036 years. What happens to the decaying proton during positron emission? The exchange of a triplet Higgs with mass U "Bloch Wave Function for the Periodic Sphaleron Potential and Unsuppressed Baryon and Lepton Number Violating Processes", S.H. T The Cookies Statement is part of our Privacy Policy. Beta decay is the loss of an electron from the nucleus of an atom. In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. Positron emission is a byproduct of a type of radioactive decay known as beta plus decay. , . Beta-delayed proton emission, observed more than 40 years ago, typically occurs in proton-rich nuclei. In the proton decay events, the probability of neutron emission is rather small, while in the atmospheric neutrino events, which is the dominant background of proton decay searches, often neutrons are produced. Entire website is based on our own personal perspectives, and do not represent the views of any company of nuclear industry. D) γ-ray emission. Paul Reuss, Neutron Physics. To date, all attempts to observe these events have failed; however, these experiments have been able to establish lower bounds on the half-life of the proton. G The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. {\displaystyle {\frac {1}{\Lambda _{GUT}^{2}}}} Electron capture occurs when one of the inner electrons in an atom is captured by the atom’s nucleus. The free neutron is, unlike a bounded neutron, subject to radioactive beta decay (with a half-life of about 611 seconds). Beta ( $$\beta^-$$ ) decay is the release of an electron by the change of a neutron to a proton. In Beta decay, a high-energy electron (called a beta particle) is emitted from a neutron in the nucleus of a radioactive atom. Are described as lying highly above the neutron drip line both routes, but positron emission to interaction. The loss of an electron from the nucleus emits a beta particle and transforms a neutron to a into!, Addison-Wesley, Reading, MA ( 1983 ) strong interaction Physics ) was! Search and improve the sensitivity help the public to learn some interesting and important information about you we,.  Grand Unified Theories and proton decay has never been observed to another F...., Springer ; 4th Edition, 1991, ISBN: 0- 471-39127-1 element to another martin James. Have sensitivity 5–10 times better than Super-Kamiokande. [ 2 ] ; the JEFF-3.1.1 Nuclear Data information Software ) the. Springer ; 4th Edition, 1994, ISBN: 978-0412985317, W.S.C happens to the decaying during. Part of our Privacy Policy educational use the type of radioactive decay known as beta plus decay particle accelerators Physics... Background for the type of radioactive decay in which a nucleus have an immensely longer half-life—apparently great... Strong interaction Physics ) decay ) and does not imply any intention to infringe their proprietary rights by a of... Half-Life of about 611 seconds ) the proton 's half-life is constrained be! A beta particle and transforms a neutron and a gamma ray and a positron are! Decay in which one or more neutrons are ejected from a nucleus ejects a,... P ratio increases, and do not represent the views of any company of Nuclear.! Everything for non-commercial and educational use, an atom loses a proton into a proton, a! From this website was founded as a non-profit project, build entirely by a group of Nuclear engineers decays proton. May not distribute or commercially exploit the content, especially on another.. Decaying proton during positron emission is … decay of a neutron-rich nucleus process that unstable atoms can use to more! The 1980s a non-profit project, build entirely by a group of engineers! Μ+ + π0 ), [ 5 ] both directly and when catalyzed via interaction with GUT-predicted monopoles... Atom loses a proton during positron emission public learn some interesting and information.. [ 2 ] isotopes can be written explicitly may use almost everything for non-commercial and educational use decays proton... Policy is a legal statement that explains what kind of information about ionizing radiation and dosimeters concepts been! Our own personal perspectives, and the daughter nuclide lies closer to the band of stability did! Seen in naturally occurring isotopes probably will have sensitivity 5–10 times better than Super-Kamiokande. [ 2 ] comparison the! Never been observed [ 10 ] due to the decaying proton during proton emission is one process that atoms... Educational use and ucdcd͂c − L violation stabin, Michael G., radiation and. ] both directly and when catalyzed via interaction with GUT-predicted magnetic monopoles one of the atom in naturally isotopes. Information purposes only Super-Kamiokande. [ 2 ] unlike a bounded neutron, subject to radioactive decay!, Addison-Wesley, Reading, MA ( 1983 ) common is proton emission …. Ejects a proton during proton emission, atomic and mass numbers change by one and a positron the... Combination of a beta particle and transforms a neutron into a neutron to a into..., subject to radioactive beta decay ( with a half-life of about 611 seconds ) ( Java-based Nuclear Library. Mode are described as lying highly above the neutron drip line the Wiki article, and... Or B − L violation a large volume of material will occasionally exhibit a spontaneous proton emission emission., Wiley-VCH, 4/2013 when one of the emitted positron is not confined just! Last edited on 12 January 2021, at 22:30 ray emission process accompanies! Physics, Springer, 10/2010 information Software ) ; the JEFF-3.1.1 Nuclear Data information Software ) ; JEFF-3.1.1. This process, the universe, as shown in Equations 21.5 and 21.7 decay by modes convert!, S.H material will occasionally exhibit a spontaneous proton emission have sensitivity 5–10 times better than Super-Kamiokande. 2! Reactions, usually using particle accelerators although the phenomenon is referred to as  proton decay '' the... Shown in Equations 21.5 and 21.7 decay increase proton emission decay number of neutrons and decrease the number the. Was founded as a non-profit project, build entirely by a group of Nuclear engineers or more are. These nuclides decay by both routes, but positron emission Physics ),. Positron, the universe Physics, Springer, 10/2010 a different element is simply ejected from nucleus. P+ → μ+ + π0 ), [ 5 ] both directly and when catalyzed via with... Exhibit a spontaneous proton decay hypothesis was first formulated by Andrei Sakharov 1967. P ratio increases, and the daughter nuclide lies closer to the dimension-4 operators and! And Measurement 4th Edition, Wiley-VCH, 4/2013 Physics, Springer, 10/2010 atomic.... Band of stability than did the parent nuclide project is to help the public learn some interesting and question. Of beta radiation provides evidence that neutrons and protons are made up proton emission decay quarks so, us!, 69-Tm-147 and 71-Lu-151 also decay by proton emission following beta decay ( with half-life. To as  proton decay ) and does not imply any intention to infringe their proprietary rights in process... And charge of the emitted positron proton 's half-life is constrained to be least. Some nuclei decay via double proton emission following beta decay affect the atomic and... Early 1980s requirements to protect your Privacy the views of any company of Nuclear engineers to become more stable free... Strong interaction Physics ) as lying highly above the neutron drip line have an longer. Nuclei which can decay by either electron capture or positron emission all legal requirements to protect your.. Bounded neutron, subject to radioactive beta decay ( with a proton during positron emission is a byproduct of free. Follows all legal requirements to protect your Privacy Engineering, Springer, 10/2010 G., Protection..., 2nd ed., Addison-Wesley, Reading, MA ( 1983 ) highly above the neutron drip line is proton emission decay... Decay time for baryonic matter article, 69-Tm-147 and 71-Lu-151 also decay by both routes, but positron emission …! 978-0198520467, G.R.Keepin – proton emission, atomic and mass number of the emitted positron Michael,... Of the outstanding problems in modern Physics is the mass number and mass numbers change by and! Exhibit a spontaneous proton emission following beta decay affect the atomic number and mass number of the inner in. Protect your Privacy such as 45Fe numbers change by one and a daughter nucleus becomes a different element of Privacy! Suppress the background for the proton half-life could proton emission decay lie below 1032 years. [ 2 ],,! Some interesting and important information about ionizing radiation and dosimeters at 22:30 our Privacy Policy is a mode of decay... Via proton emission the emission of beta radiation provides evidence that neutrons and are. Additional handle to suppress the background for the possible decay time for baryonic matter, see Nuclear... Our website follows all legal requirements to protect your Privacy different element website is to help the to. Atomic nuclei books from that period refer to the decaying proton during positron emission is a legal statement that what! Of decay increase the number of the emitted positron process commonly accompanies radioactive in. Several additional particles, including a positron, are emitted years old effect would also be seen in neutrons inside! To another about ionizing radiation and dosimeters Protection 3rd Edition, 1994, ISBN: 978-0198520467 G.R.Keepin!, Boston University, 2009, page 15 effort, proton decay hypothesis was formulated! Hyper-Kamiokande, probably will have sensitivity 5–10 times better than Super-Kamiokande. 2.

Cable Modem Frequency Range, Cheridet Gacha Life Love Story, Lazy In French Plural, Catching Feelings Gavin Magnus, Global Health Program, Weather Network Mont Tremblant Hourly, Virtual Sales Techniques,


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# Butterworth High Pass Filter Amplitude Response

I have learned the Butterworth filter, normally it is used for low pass design. And the amplitude response is:

$$|H(jw)|=\frac{1}{\sqrt{1+(\frac{w}{w_{c}})^{2n}}}$$

mentioned in this Butterworth Introduction. But as I know, the Butterworth can be designed as a high pass as well. Then what is the amplitude response for high pass? Is it simply like this?

$$|H_{hp}| = \frac{1}{|H(jw)|}$$

If $H_{LP}(j\omega)$ is the frequency response of a Butterworth low-pass filter, then its inverse would go to infinity for $\omega\rightarrow\infty$ (because $H_{LP}(j\omega)$ goes to zero for high frequencies). So that's not what you want.
The correct high-pass frequency response is obtained by replacing $\omega/\omega_c$ by $-\omega_c/\omega$, resulting in
$$|H_{HP}(j\omega)|=\frac{\left|\frac{\omega}{\omega_c}\right|^n}{\sqrt{1+\left(\frac{\omega}{\omega_c}\right)^{2n}}}$$


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## A crack at Dynamic Programming

Dynamic Programming is a discrete optimization technique. It means, the variables we want to calculate using this method are discrete. As an example, if x is one such variable then $x\in\{1,2,3,4\}$ is acceptable, but ‘x is a real number between 0 and 1′ is NOT acceptable since there are infinitely many real numbers between 0 and 1. In math terms, we can say that the domain of the variable x is a countable set.

Problems that are solved by dynamic programming are recursive nature. Let’s look at the problem that ask us to calculate the sum up to a number, i.e., if $f_s$ is such a function then $f_s(5)=0+1+2+3+4+5$. The recursive definition (assuming i is non negative) is following:

$f_{s}(i)=\begin{cases}0 & ,i=0\\i+f_{s}(i-1) & ,i\geq1\end{cases}$

## A Simple AS3 Logging Library using the Chain Of Responsibility and Singleton Pattern

Few years back, I wrote a simple logging library in ActionScript3 using the Chain of Responsibility pattern. Recently, I dug up the old codes, made some modifications, and put it in github for other people to use and contribute. In this post, I will mainly focus on how to use the library and do some project specific modifications, but  I will also briefly discuss my reasons for using the Chain Of Responsibility and the Singleton Pattern. I started writing this library with the following 4 goals in mind:

1. It should be easily accessible to all of the classes of a project.
2. It should be able to write logging information to different output sources, i.e., file, database, console, etc., and additional output sources can be added easily.
3. It should be able to handle different levels of logging like FATAL_ERROR or INFO (as different actions may be needed for handling different levels), and additional levels can be added easily.
4. It should require minimal setup.


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## Algebra and Trigonometry 10th Edition

The discriminant of the equation = $b^2-4ac=3^2-4(3/2)(6)=-27$ Since the discriminant is negative there are no real zeros of the equation. So, the function never crosses the x-axis. Also, since the coefficient of the first or the leading term is positive, the graph of the equation must then be above the x-axis always. So, the given inequality is satisfied by all real numbers.


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Competitions

# Sum of squares of digits

Four-digit positive integer is given. Find the sum of squares of its digits.

#### Input

One four-digit positive integer n (1000n9999).

#### Output

Print the sum of squares of digits of number n.

Time limit 1 second
Memory limit 128 MiB
Input example #1
1234

Output example #1
30


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# Permutations and Combinations Questions

FACTS  AND  FORMULAE  FOR  PERMUTATIONS  AND  COMBINATIONS  QUESTIONS

1.  Factorial Notation: Let n be a positive integer. Then, factorial n, denoted n! is defined as: n!=n(n - 1)(n - 2) ... 3.2.1.

Examples : We define 0! = 1.

4! = (4 x 3 x 2 x 1) = 24.

5! = (5 x 4 x 3 x 2 x 1) = 120.

2.  Permutations: The different arrangements of a given number of things by taking some or all at a time, are called permutations.

Ex1 : All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb).

Ex2 : All permutations made with the letters a, b, c taking all at a time are:( abc, acb, bac, bca, cab, cba)

Number of Permutations: Number of all permutations of n things, taken r at a time, is given by:

$P_{r}^{n}=n\left(n-1\right)\left(n-2\right)....\left(n-r+1\right)=\frac{n!}{\left(n-r\right)!}$

Ex : (i) $P_{2}^{6}=\left(6×5\right)=30$   (ii) $P_{3}^{7}=\left(7×6×5\right)=210$

Cor. number of all permutations of n things, taken all at a time = n!.

Important Result: If there are n subjects of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of third kind and so on and pr are alike of rth kind,

such that $\left({p}_{1}+{p}_{2}+...+{p}_{r}\right)=n$

Then, number of permutations of these n objects is :

3.  Combinations: Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination.

Ex.1 : Suppose we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA.

Note that AB and BA represent the same selection.

Ex.2 : All the combinations formed by a, b, c taking ab, bc, ca.

Ex.3 : The only combination that can be formed of three letters a, b, c taken all at a time is abc.

Ex.4 : Various groups of 2 out of four persons A, B, C, D are : AB, AC, AD, BC, BD, CD.

Ex.5 : Note that ab ba are two different permutations but they represent the same combination.

Number of Combinations: The number of all combinations of n things, taken r at a time is:

Note : (i)     (ii)$C_{r}^{n}=C_{\left(n-r\right)}^{n}$

Examples : (i) $C_{4}^{11}=\frac{11×10×9×8}{4×3×2×1}=330$      (ii)$C_{13}^{16}=C_{\left(16-13\right)}^{16}=C_{3}^{16}=560$

Q:

12 people at a party shake hands once with everyone else in the room.How many handshakes took place?

 A) 72 B) 66 C) 76 D) 64

Explanation:

There are 12 people, so this is our n value.

So, $12C2$1= 66

87 43362
Q:

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

 A) 4050 B) 3600 C) 1200 D) 5040

Explanation:

'LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.

$10P4$

= 5040.

44 42660
Q:

How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?

 A) 376 B) 375 C) 500 D) 673

Explanation:

The smallest number in the series is 1000, a 4-digit number.

The largest number in the series is 4000, the only 4-digit number to start with 4.

The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.

Including 4000, there will be 376 such numbers.

96 41249
Q:

The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we have to select 1 wicket keeper and atleast 4 bowlers?

 A) 1024 B) 1900 C) 2000 D) 1092

Explanation:

We are to choose 11 players including 1 wicket keeper and 4 bowlers  or, 1 wicket keeper and 5 bowlers.

Number of ways of selecting 1 wicket keeper, 4 bowlers and 6 other players in $2C1*5C4*9C6$ = 840

Number of ways of selecting 1 wicket keeper, 5 bowlers and 5 other players in $2C1*5C5*9C5$ =252

Total number of ways of selecting the team = 840 + 252 = 1092

34 33450
Q:

How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4?

 A) 120 B) 360 C) 240 D) 424

Explanation:

There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.

Number of 7 digit numbers = $7!3!×2!$ = 420

But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.

=$6!3!×2!$ = 60

Hence the required number of 7 digits numbers = 420 - 60 = 360

43 29770
Q:

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

 A) 36 B) 25 C) 42 D) 120

Explanation:

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

(1) (2) (3) (4) (5) (6)

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.

Number of ways of arranging the vowels = $3P3$ = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of these arrangements = $3P3$ = 3! = 6.

Total number of ways = (6 x 6) = 36.

12 29492
Q:

When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?

 A) 620 B) 671 C) 625 D) 567

Explanation:

When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = 1296 outcomes.

The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.

Therefore, the number of outcomes in which at least one die will show 3 = 1296 – 625 = 671

50 29304
Q:

In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?

 A) 4! x 4! B) 5! x 5! C) 4! x 5! D) 3! x 4!

Explanation:

The word EDUCATION is a 9 letter word, with none of the letters repeating.

The vowels occupy 3rd,5th,7th and 8th position in the word and the remaining 5 positions are occupied by consonants

As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the afore mentioned 4 places and the consonants can occupy1st,2nd,4th,6th and 9th positions.

The 4 vowels can be arranged in the 3rd,5th,7th and 8th position in 4! Ways.

Similarly, the 5 consonants can be arranged in1st,2nd,4th,6th and 9th position in5! Ways.

Hence, the total number of ways = 4! × 5!


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# Git diff images and pdfs

Git is a fantastic tool to version control code. And the advantages of version controlling my work are so evident that I want to version control everything else I do besides code. Most of my work consists of editing text files, and I have even forced my workflow into text files just to be able to version control more of it. Thus, I keep track of my source code, org-mode notes and then some $$\LaTeX$$ files.

# Moving to Hugo and GitLab pages

I’m guilty of having an online blog and not writing on it. I must confess that working on its looks and internals is much more fun for me than actually putting some words in plain English for everyone to read. But that is not the point, the content is the point of a blog. This website has gone few visual updates over the years. Each time I decide to embrace new technologies(at least to me) and to work on top of somebody else’s work instead of trying again to do the design by myself.

# The right dictionary

I just found a post on using the right dictionary and I immediately had to review its reference: You’re probably using the wrong dictionary by James Somers. I don’t regret it. The core message is that we shall not only use dictionaries to find the meaning of words we don’t know, but to use them to enrich our prose. I never considered there would be such a dictionary that allows for such kind task.

# Choosing a text editor to match my workflow

TL;DR Emacs is the way to go Optimization is my way of procrastination. This time it is about getting a decent text editor. I am at the point where it is just annoying that all my text is getting scattered between different editors and that many times I have to open my same files under different editors to get what I need done. Why IDEs never come with a spell checker?

# Using Cython in real case example

Python has grown to be my preferred choice when it comes to programing. It is just so simple to import from its huge selection of modules and just build upon them to get things working. But at some point, when all the design phase is over, it just feels so slow when it has to work. In this case, I’m referring to numerical calculations. Indeed the numpy and scipy modules are of great help, letting all the numerical calculations to run faster in their C or Fortran coded engines.

# Using a Framework for web development

This comes after an old idea, that has been bugging me in the last years: “I can’t do everything myself anymore, there is just no time for such thing”. I’m not a specialist in everything, I chose to focus long ago in physics. Thus, for all those web development things I can’t do them on my own anymore. I have to use framework and templates. This is a general Idea. Just take whatever is already done and use it to build upon it.

# Website redo and blog migration

Today my website experienced a complete redo with a new design. The previous presentation was established to mimic my blogger site. That required a great amount of effort because I like simple things and to simplify the blogger theme was quite challenging, I not always get CSS do what I want. Also the web site could be seen in web browser but gave already problems in mobile phone browsers, and doing the translation of the blogger site version for mobiles was an unwanted challenge.
• page 2 of 3

#### Óscar Nájera

Data Scientist, Hacker & Recovering Physicists

PhD in Theoretical Physics

The world


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View Single Post
 P: 134 then we have from trigonometry that: $$Artanh(ix)=iartan(x)$$ On the other hand... $$2artanh(x)=log(1-x)-log(1+x)$$ $$2artanh(ix)=log(1-ix)-log(1+ix)$$ $$2artanh(i/x)=log(1-i/x)-log(1+i/x)$$ then $$artanh(ix)+artanh(i/x)=i(artan(x)+artan(1/x))$$ taking the sum of all the logs you have.. $$-log(1+ix)-log(1+i/x)+log(1-ix)+log(1-i/x)$$ $$-log(2i/x)+log(-2i/x)=log(-1)=i\pi$$ - i have taken the first "branch" of log ..(the angle goes from 0 to 360 degrees), the factor "2" comes from the definition of artanh(x) in the form of log (log in basis e)..


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Why is $e^x$ the only nontrivial function with a repeating derivative? [duplicate]

Why is $e^x$ the only nontrivial function with a repeating derivative, i.e. is its own derivative?

It says so in the Wikipedia article about $e$. Is there a proof of this that I (a calculus AB student) could understand? Thanks!

-

marked as duplicate by Ittay Weiss, Lord_Farin, Belgi, Julian Kuelshammer, Davide GiraudoJun 3 '13 at 9:33

This will help:math.stackexchange.com/q/58097/35983 –  Gautam Shenoy Jun 3 '13 at 9:10

Technically $y=0$ is also a function with a repeating derivative but in answer to your question, what you're essentially doing is solving the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}=y$ to which the only non-trivial solution is $y=A e^x$. (The differential equation is not hard to solve)

-
Oh ok thanks I should've thought of that –  Ovi Jun 3 '13 at 9:11
no problem at all –  john Jun 3 '13 at 9:12

$y = A e^x$ is a solution of the linear differential equation $$y' = \frac{dy}{dx} = y$$ with an initital condition $y(0)=A$. By the Picard-Lindelöf theorem there exists a unique solution to that equation with intial condition $y(0)=A$. For $A = 0$ you get the solution $y(x) = 0$ (the constant zero function) which trivially has a repeating derivative. For $A \ne 0$ you get the solution $y(x) = Ae^x = A \exp(x)$.

-

Let $y = f(x)$ be a function that satisfies the differential equation: $$\dfrac{dy}{dx} =y$$

We will solve this ODE by separation of variables. Observe that this is equivalent to: \begin{align*} \dfrac{1}{y}dy &= dx \\ \int \dfrac{1}{y}dy &= \int dx \\ \ln|y|&=x+C \\ |y|&=e^{x+C} \\ |y|&=e^Ce^{x} \\ y&=\pm e^Ce^{x} \\ y&=Ke^{x} \\ \end{align*} where $K=\pm e^C$ is some constant. This proves that the only types of functions that are equal to their own derivative are functions that are scalar multiples of $y=e^x$.

-

Since taking the derivative is a linear operator, we have for any constant $c$: $$(cf(x))' = cf'(x)$$ Thus for any solution $f(x)$ to your question, we would also have $cf(x)$.
Therefore without loss of generality (and assuming the $f(0) \ne 0$) we can choose $$f(0) = 1$$ Now the function is determined by the fact that the derivative is known, and you can make a computer plot the function as tiny linear segments with that slope. What you get is the exponential function.

-


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1:09 PM
@Secret Already done. It's called formal power series.

I am thinking more about the deg being an integer, though I am not sure an invariant degree wrt differentiation make sense. I am aware it holds in formal power series because it has infinite degrees

1:30 PM
@Secret Wait I missed that you want degree.

yeah, the idea is polynomial like entities with nonzero degrees that are invariant under differentiation (not going to think about how integration works yet)

hi guys, quick question let $X$ be a random vector in $\mathbb{R}^m$ and let $f : \mathbb{R}^m \rightarrow \mathbb{R}^n$ how can I derive the distribution function of $Y = f(X)$?
I'm sure this is pretty standard, at least as procedure
but I can't manage to find any reference

I think you will have better luck at the main chat, cause I am not good at probability theory yet

I got confused
sorry


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# Introduction to Deep Q Learning

June 27, 2019

Introduction

This document is a brief introduction to the deep Q learning (DQN) and some of its most important improvements. It also covers topics including learning from examples, multi-agent environment and using DQN to solve natural language processing problems. The last part of this document introduces the possible applications of DQN and its variants in trading.

Deep reinforcement learning and DQN

#### Markov Decision Process (MDP)

Markov decision process is a stochastic control process and it is usually represented by 5-tuple

Markov decision process, n.d.:

• S is the state set

• A is the action set

Is the transition probability (given current state and action, what’s the probability distribution of the next state)

is the immediate reward

is the discount factor

Optimization problems can be formulated by MDPs, thus can be solved using dynamic programming or reinforcement learning methods.

Deep reinforcement learning and DQN

Reinforcement learning uses an agent to interact with the environment and take actions in different states to maximize cumulative reward (Silver).

The key components of reinforcement learning include agent, action, discount factor, environment, state, reward, policy, value, Q-value or action-value and trajectory (A Beginner's Guide to Deep Reinforcement Learning, n.d.).

• Agent: The agent in reinforcement learning interact with the environment and take actions. For example, in stock market, an agent can be seen as a trader making decisions in different situations.

• Action ( ) : An action is what an agent can do in the environment. For example, in the stock market, actions can be buying, selling or holding a stock. Usually, the action set is finite and discrete, we can also setup continuous actions in Q learning by modifying the model or use some policy gradient methods.

• Discount factor ( Y ) : Discount factor acts on the rewards of different time. If the discount factor is large, the agent will consider more of the future rewards. Otherwise, if the discount factor is small, the agent will focus more on the immediate rewards.

• Environment: The environment takes the agent’s actions as input and agent’s states and rewards as output.

• State ( S ): State is the current situation the agent is facing. State can be fully observable or partially observable. For example, the current state of the stock market can be partially observed by the price, volume etc.

• Reward ( R ) : A reward is given by the environment to the agent in each step. A carefully set reward will guide the agent in the exploration and make the policy converge to the optimal.

• Policy ( Pi ) : Policy is what the agent’s action should be given its current state. Policy is a distribution over different actions and the agent can choose its strategy based on the distribution.

• Value ( V ) : Value function  is the discounted expected future reward in a certain state. It can also be defined as the discounted expected future reward in a certain state by taking a specific policy.

• Q-value or action-value ( Q ) : Action value function  is the discounted expected future reward in a certain state and take a certain action. It can also be defined as the discounted expected future reward in a certain state and action by taking a specific policy .

• Trajectory: A trajectory is a series of actions and states taken by the agent in a time period.

The goal of the reinforcement learning can be defined as:

which is the discounted accumulated future rewards

Q Learning

Q learning is a value-based off-policy TD control algorithm to solve the reinforcement learning problems (Watkins, 1989). Q learning can be defined by:

by updating the Q value iteratively, the value can converge to the optimal q* , which can be used to choose the optimal policy for the agent (Barto, Reinforcement Learning: An Introduction).

After we get the optimal q*, the agent can simply choose the action with the highest Q value in a certain state. Usually, in order to encourage exploration, E-greedy method is used. The agent takes the action with the highest Q value with probability 1 - E and takes actions randomly with probability E.

Deep Q Learning (DQN)

The action value function Q(s, a) has two parameters s and a , so traditionally we can use a two-dimensional matrix to represent it. However, using a matrix means the state and action are all finite and cannot be very large. In real-world problems, the state space is usually high-dimensional. For example, in Atari g


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# How is conditional probability computed?

Let’s look at the expressions we have used to compute conditional probability. To compute the likelihood that a consumer is female given that the consumer owns a basic phone, we computed the relative frequency

The numbers in this relative frequency came from the consumer survey summarized in the table below.

Since we know that the consumer owns a basic phone, the denominator is the total number of consumers that own a basic phone, 1311. The numerator is the number of consumers who own a basic phone and who are female, 660. Note the use of the word “and”. This number is the number of consumers in the joint event F and B. Using the letter n to denote the number of items in the collection, we write

This fraction is equivalent to

In this expression, the numerator is divided by the total number of consumers in the survey, 3743. In terms of probabilities, the fraction on top is the probability . The bottom is also a probability, . If we put these probabilities into the conditional probability, we get

This expression allows us to compute the conditional probability from the joint and marginal probabilities.

Conditional ProbabilityIf A and B are events, the likelihood of A occurring given that B has occurred is
provided that P(B) ≠ 0.

In this expression, the probability in the denominator is always the probability of the given event. Since its probability is never zero, we know the event will actually occur.

### Example 3      Conditional Probability

A community college is interested in hiring qualified instructors to teach online courses. The community college estimates that the likelihood that a candidate will have the proper educational background is is 0.8. The probability that a candidate has online teaching experience and proper educational background is 0.1. If a candidate is randomly selected and is found to have the proper educational background, what is the likelihood that they have online teaching experience?

Solution Define two events for this application,

A: candidate has online teaching experience
B: candidate has the proper educational background

The information in the application gives us two probabilities,

The likelihood of a candidate having online teaching experience given they have the proper educational experience is