Solve the Sturm-Louiville boundary value Problem $u_t(x,t)=u_{xx}(x,t)-bu(x,t)+q(t)$, where $b$ is a constant. Boundary conditions are $u(x,0)=0$ and $u(0,t)=0=u(\pi,t)$, with $0<x<\pi$ and $t>0$.  Following the only example in the textbook, I get:  Assume $u(x,t)$ is of the form $u(x,t)=\sum\limits_{n=1}^\infty B_ne^{-n^2t}\sin(nx)$. But that's for a heat equation: $u_t(x,t)=ku_{xx}(x,t)+q(t)$, boundary conditions $u(x,0)=f(x)$, $u(0,t)=0=u(\pi,t)$.  I don't know what I'm doing and the book and professor are incomprehensible. I really need help.

I have the example pde $u_t(x,t)=u_{xx}(x,t)-b(t)u(x,t)+q_0$, where $b(t)$ is a function of only $t$ and $q_0$ is a constant, $0<x<\pi$, $t>0$. The subscripts denote derivatives. I also have some boundary conditions: $u(x,0)=0$ and $u(0,t)=0=u(\pi,t)$. The problem solution using variation of parameters is $$u(x,t)=\frac{4q_0}{\pi a(t)}\sum\limits_{n=1}^\infty \frac{\sin((2n-1)x)}{2n-1}\int\limits_0^t e^{-(2n-1)^2(t-\tau)}a(\tau)d\tau$$ where $$a(t)=e^{\int\limits_0^t b(\sigma)d\sigma}.$$  The problem I'm working on is slightly different. It gives the pde $u_t(x,t)=u_{xx}(x,t)-bu(x,t)+q(t)$ where $b$ is a constant and $q(t)$ is a function of only $t$, $0<x<\pi$, $t>0$. The solution should be very similar to that of the example.  I don't know where to start. I'm using the textbook "Fourier Series and Boundary Value Problems" by Churchill and Brown, 7th edition, if anyone's interested. The "example" is problem 10 page 117 of that book.  Any help/hints would be greatly appreciated. Thanks!


I have this code: $conn = new mysqli($servername, $username, $password, $dbname);  if ($conn->connect_error) {   die("Connection failed: " . $conn->connect_error); }  mysqli_set_charset($conn,'latin1_swedish_ci');  echo mysqli_character_set_name($conn);  $sql = "SELECT * FROM ggg";  $result = $conn->query($sql);  if ($result->num_rows > 0) {    while($row = $result->fetch_assoc()) {      echo "keyword: " . $row["keyword"]. " - Name: " . $row["firstname"]. " " . $row["lastname"] . $row["info"] . "<br>";        } } else {   echo "0 results"; }  The $row["info"]-parts in the echoed result are full of questionmarks inside a rectangle instead of the swedish signs "å, ä, ö". Although the charset is correctly set to "latin1_swedish_ci" which is exactly the same as in the database (which I checked from phpMyAdmin). What to try next, anyone have any ideas?

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I'm getting swamped with outbound udp requests and it's blocking my internet connection.  While I figure out what's going on I'd like to block all outbound and inbound udp. I'm connecting via pppoe dial up but want to block on all ports and all connections. Is there a way to do this that won't interrupt my pppoe connection?  I've tried updating iptables but this seems to only block one port at a time if I understand correctly.  Though I have rules in my firewall to block the ports it seems to be too late.   For newbies like me it is difficult to get the pieces together and I couldn't find the answer on searching because didn't know to search for iptables and that doesn't cover the udp component. I have my question answered by think this should remain open for others as I believe it might be helpful.

Is there a "best practice" or standard to make a few iptables rules permanent? I mean: automatically applied upon a system reboot?  I am using a VPS with Ubuntu Server 10.04 LTS (Lucid Lynx).  Thank you.  BIG EDIT: I don't want ANY rule to be persisted (like iptables-persistent package does). I want only my own specific set to be reloaded... if other rules are eventually added by running iptables, these should be discarded...


I have multiple questions that I want to put in one sentence. Is this punctuation correct?  Is there anyone who can read it? Understand it? Translate it?  or  Is there anyone who can read it? understand it? translate it?  Alternate would be:  Is there anyone who can read it? Is there anyone who can understand it? Is there anyone who can translate it?

May I use a question mark in the middle of a sentence? Examples:  Would you like the drapes to be white? or perhaps something off-white? Would you like the logo to be centered? at the bottom? left off entirely?


I'm learning how to use selenium by using java. I got a problem. Having html code:
Laptop Dell XPS 13 2015 13.3inch Touch (Xám) - Hàng nhập khẩu
   And this is my code to get text:  By productName = By.className("cart-popup-product__title"); public String ProductName(){     String pn = driver.findElement(productName).getText();     return pn; }   Eclipse display error message: NullPointerException. I have tried to use xpath, cssSelector but it's not working.  *Update: I've solved my problem. I just add this.driver = driver; to constructor. I forgot to add when initialize constructor.  Thanks all for helping me improve.

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I thought this question when I learn about the superconductor which has no resistance.  If I made the round wire with the superconductor, I think it is possible for the current to flow through the wire that power consumption is zero. But I don't know that it is possible to flow permanently.   It is right that the round wire made with superconductor has no resistance. But I think the electron that flows through the wire does an acceleration exercise(circle motion), so it releases the electromagnetic waves.   But I don't know the exact answer. Is it possible to maintain the electric current permanently using the superconductor?   (I find it, but I think it is not clear answer)

I know that you can use induction to create a current in a superconducting loop, but this only works as long as the coil that induces the field has a current flowing through it. And obviously, this cannot work for the really big magnets that are used in MRI scanners or NMR machines.  How does it work?


I have character strings like   str1 <- "Hello {can you please} {extract this}"   I need to extract "can you please" and "extract" this as a list with regex.  How can I do it?

I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them?


I have a AMD 32-bit operating system, should i use the 32 bit or 64 bit download? (the reason i ask is because the 64 bit download is labeled AMD, and the 32 bit is labeled Intel. But mine is both AMD and 32 bit, so im a bit confused on which one to use.) Thanks!

I was told that computers with more than 2 gig's memory need a 64 bit operating system to utilize all RAM.  Is the 64bit Ubuntu download really JUST for AMD processors? I am asking because the disk image I downloaded says AMD64.  So will my new Intel 2.3Ghz Core i3 Dual Core processor work with 64 bit Ubuntu?  It runs the 64bit version of Windows without any qualm.


This the array...  $rt = array(     '0' => array(     'nombre'=>'Jojo',     'fecah'=> '195',     'fch'=>'12'     ),     '1' => array(         'nombre'=>'Tito',         'fecah'=> '197',         'fch'=>'13'     ),     '2' => array(         'nombre'=>'Jojo',         'fecah'=> '195',         'fch'=>'12'     ),     '3' => array(         'nombre'=>'Joji',         'fecah'=> '195',         'fch'=>'12'     ), );   and this is my code:  $a = array(); foreach ($rt as $k=>$v) {     if (in_array($v['nombre'], $a) && in_array($v['fecah'], $a) && in_array($v['fch'], $a) ) {         $a[]=$k;         echo 'The name ' . $v['nombre'] .' is in the array
';     } else {         echo 'The name is not in the array
';     } }   so as you can see  in the array index [2] the information also exist in the index [0], so I don't need it again, so I need a away to see if the data get repeated or not... if the data is "unique" then build the new array with the "unique" data if the data already exist then jump to next, but I need to compare the 3 keys not just the name... so how do I do that?

How can I remove duplicate values from a multi-dimensional array in PHP?  Example array:  Array (     [0] => Array     (         [0] => abc         [1] => def     )      [1] => Array     (         [0] => ghi         [1] => jkl     )      [2] => Array     (         [0] => mno         [1] => pql     )      [3] => Array     (         [0] => abc         [1] => def     )      [4] => Array     (         [0] => ghi         [1] => jkl     )      [5] => Array     (         [0] => mno         [1] => pql     )  )


Is age a hindrance of getting acceptance in a PhD program?  For instance, what if a student applies at the age of 45 for an admission?

I am 33. I live in the US. I am a neither a US citizen, nor a green card holder. I have worked in various jobs as a research assistant (physics, biology, economics) usually involving programming, mathematics or statistics.  As a newly minted undergraduate, I didn't really have much confidence in myself and I completely ruled out graduate school as pointless.  I didn't think of myself as smart enough.  I drifted into working in labs, because those are some of the easiest ones for which one can get a work permit in the US as a non-American.  Having worked in academia for a while now, I've had a chance to leap into various fields and help build solutions to complex problems.  I think I have literally gone as far as I can go researching in academia with no higher degree.  I work at one of the top universities in the world.  (If you looked at US News rankings or the Academic Ranking of World Universities, it's in the top 5.)  Lately, I've been thinking about applying for graduate school.  I do have a few papers in various fields.  I'm thinking of a PhD in either pure mathematics, applied mathematics, statistics or computer science.   I see two big minuses to applying to graduate school:   Most people applying are more than a decade younger than I am.  (Alas, more than a few gray hairs have made an appearance in recent years.) Perhaps my achievements would look good for someone younger, but partially my achievements are the result of a long career rather than any special brilliance. So, I wonder how my record will be perceived.  I did take GRE and I scored 800 quantitative, 800 verbal and a 5 on the essay.  (I would most likely have to do a GRE subject test depending on what field I ultimately decided.)   Please advise on how accomplished, but older candidates, are viewed in the graduate school application process.


I vividly remember a scene from a short story (?) I read back in the sixties or seventies, and am trying to remember the publication and title. If it sounds familiar to you, please post.   The scene is set in the distant future after mankind has slowly spread all the way to the far side of the galaxy, the core zones being too hostile to life (energetically). In all that time, we have never encountered another star-faring race. We have been modified slowly by the course of evolution over the millenia.   As the scene opens, it appears we have finally had a first encounter with another civilization. There is a meeting set and gradually dialog is established. The twist comes when it emerges that these creatures are, in fact, also the descendants of Earth modified in different ways during their slow passage the other way around the galaxy. We have proven that we are, indeed alone.   The story ached with pathos at the loneliness of being the only intelligent species in existence. (In terms of evolutionary theory, this would likely make us a ring species.)

I'm looking for a plot line (it should be a short story) that depicts Earth population (or their close descendants) establishing contact with another intelligent life form deep into space.   After careful studying of DNA samples and language / communication symbols they then realize that the civilization in question is also from Earth but that they departed very long ago and travelled throughout the galaxy in the completely opposite direction so that they are now meeting practically at the point of the circle opposite to Earth. There might have been some anatomical differences as well.  As far as I can remember, the story concludes shortly after that.  This should be a work of a well-known SF author, so I'm hoping for a quick response (if time didn't corrupt my memory too much).  I don't think it was part of an anthology, but it's entirely possible it was in a magazine.  As for the timeline, I've read it about 2-3 years ago, but since I have a passion for older SF works it might not be of much use.  Edit: Not sure if this could help but for what it's worth, it might be contained in .


I have a Nikon camera.  I received a Tamron 16-300 mm f/3.5-6.3 lens and a AF-S Nikkor 50 mm f/1.8G for Christmas. Do I need both? How do they differ in picture taking?

I have the Nikon kit lens that came with a D5100 — the kit lens is  . I was thinking of getting a fast lens and I am looking to buy the .  Should I consider 35mm or instead buy a 55-200mm for better range?


For any dimension $n \ge 1$ and any real number $a \ge 0$  $$S(a)=\{x\in \mathbb{R}^n \mid 0 \le x_i \text{ for all } i \text{ and}\, x_1+...+x_n\le a\}$$  Find the volume of the set S(a).  I tried writing it as a multiple integral but it got pretty complicated.

It's rather tedious to show using Fubini's Theorem and induction on $n$ that the volume of the region $x_1+x_2+...+x_n \leq 1$ with $x_1,...,x_n$ nonnegative is $\frac{1}{n!}$.  Is there an easier way to see this?


So here's the deal, I gave a couple of my friends the password to my WIFI, but since then the internet has been going too slow for long periods of time.  I suspect that one of them is using a torrent application to download movies or something, I want to know who that person is by knowing which pc is downloading through torrent.  I have the admin privileges on my network adapter, and would also like to know if there is away to see who is torrenting though my network using only my laptop by any means. so please help me.

My internet connection is very slow. I suspect someone in the network is using a BitTorrent client which takes huge amount of bandwidth.  Is there a way to detect who is using my bandwidth (network sniffing tools etc)?  I should have pointed out that I have no access to the router, what I am looking for is a way of detecting someone's MAC/IP if she uses Bittorrent.


Fridges were especially useful for storing perishable substances such   as milk, which had previously been the cause of thousands of   deaths every year in the big cities of the world.   In the above sentence, would the antecedent of the relative pronoun which be "milk" or "perishable substances such as milk". I get confused whenever I try to identify the antecedents of relative pronouns with two or more NPs joined together.

I am always confused with multiple attribute clauses. For example:   ... a complete virtual system composed of virtualized hardware components onto which an unmodified operating system can be installed.  For the "onto which an unmodified operating system call be installed." clause, does the which point to hardware components or a complete virtual system?  Does the attribute clause always modify the nearest noun?


I wanted to ask if anybody knows how I can check in a string if there is at least a character (either small or big) and if there is at least a number in Java.  Any ideas? Thanks!

I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them?


The cone has it's tip going up the Z axis.  The goal is to have the cone hv it's Z axis up facing the same way the selected face's normal do.  When i run the script, the orientation was a bit off.    Code here:  import bpy import bmesh import mathutils  # Get the active mesh (assumes starting in edit mode) obj = bpy.context.edit_object mw = obj.matrix_world.copy() bm = bmesh.from_edit_mesh(obj.data) # for this example jmake a face active face = bm.select_history.active o = face.calc_center_median() # calculate the axis dif in local coords  axis_src = face.normal # local z-axis axis_dst = mathutils.Vector((0, 0, 1))  matrix_rotate = mw.to_3x3()  matrix_rotate = matrix_rotate @ axis_src.rotation_difference(axis_dst).to_matrix() matrix_translation = mathutils.Matrix.Translation(mw @ o)  obj2 = bpy.context.view_layer.objects.get("Cone") obj2.matrix_world = matrix_translation @ matrix_rotate.to_4x4()

Blender 2.8 produces the following error  whilst multiplying a combination of matrices and vectors  >>> M = Matrix() >>> v = Vector() >>> M * v Traceback (most recent call last):   File "<blender_console>", line 1, in <module> TypeError: Element-wise multiplication: not supported between 'Matrix' and 'Vector' types  >>> v * v Traceback (most recent call last):   File "<blender_console>", line 1, in <module> TypeError: Element-wise multiplication: not supported between 'Vector' and 'Vector' types  >>> M * M Traceback (most recent call last):   File "<blender_console>", line 1, in <module> TypeError: Element-wise multiplication: not supported between 'Matrix' and 'Matrix' types


I'm trying to match a regex in a text which contains line breaks and whitespaces on JavaScript. Here is my code:    $(document).ready(function(){   var text = $('.main').text();   var output = $('.output');     var regex = /\*\*\*.*?\*\*\*.*?\*\-\*\*.*?\*\*\*/g;   var matches = regex.exec(text);   var i = 0;      while (result = regex.exec(text)) {     console.log(result);   }    });

***{{1}}:Meaning***
   ***{{2}}:Yep***
   ***{{2}}:True***

   Lorem ipsum dolor sit amet

   *-**{{2}}:True***
   *-**{{2}}:Yep***
   *-**{{1}}:Meaning***

     aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
     But with the 'g' flag it doesn't return the matches. I can get the matches with 's' because of line breaks.   I'm trying to get the expression between ***{{1}}:Meaning*** and *-**{{1}}:Meaning***. Firstly I used match() function, but it return only first match which is between ***{{1}}:Meaning*** and *-**{{2}}:True***. Then searched for it and find the exec() function which iterates.  I don't know how can I get the appropriate match. Here is the .  EDIT  I'm editing, because it's hard and takes time to understrand the codes above.  My regex is:  /qqq.*?qqq.*?qwq.*?qqq/s   And text is:  qqqLOREMqqq     Lorem ipsum dolor sit amet epictetus     qqqANOTHERLOREMqqq         Something something something     qwqANOTHERLOREMqqq     consectetur epilis qwqLOREMqqq Etiam ut felis molestie, tempor leo sit amet, pellentesque lorem. Sed consequat ut dui et mollis. Nulla sagittis vel felis id viverra.    I want to get the text between qqqLOREMqqq and qwqLOREMqqq, but it takes qqqLOREMqqq and qwqANOTHERLOREMqqq.

For example, this regex  (.*)<FooBar>   will match:  abcde<FooBar>   But how do I get it to match across multiple lines?  abcde fghij<FooBar>


Where is the equivalent of Blender 2.79's Toggle Fullscreen Area (Alt+F10)  in Blender v2.8?  Note: I apologize that my original question contained erroneous information. I do NOT need to know how to Toggle Window Fullscreen as that is located in the Window menu. Sorry for the confusion.

I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program.


Ubuntu 14 came with perl v5.18.2, but I would like to test my program with perl v5.22.0 which is installed through perlbrew and then perlbrew switch perl-5.22.0 to use the version I want.  After switch to perl v5.22.0, I have tried to test my program with sudo but why it is executed in default perl v5.18.2?      perl -v: result         sudo perl -v : result

This is the PATH variable without sudo:  $ echo 'echo $PATH' | sh  /opt/local/ruby/bin:/usr/bin:/bin   This is the PATH variable with sudo:  $ echo 'echo $PATH' | sudo sh /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/X11R6/bin   As far as I can tell, sudo is supposed to leave PATH untouched. What's going on? How do I change this? (This is on Ubuntu 8.04).  UPDATE: as far as I can see, none of the scripts started as root change PATH in any way.  From man sudo:      To prevent command spoofing, sudo   checks ``.'' and ``'' (both denoting   current directory) last when searching   for a command in the user's PATH (if   one or both are in the PATH). Note,   however, that the actual PATH   environment variable is not modified   and is passed unchanged to the program   that sudo executes.


Which formula can be used to calculate the sum:  $$\sum\limits_{i=1}^{12} \left(1 + \frac{i^2 -i}{2}\right)~~?$$  Is there any formula that can be applied instead of manually adding the 12 numbers?

I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals:  $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$  I really have no idea why this statement is true. Can someone please explain why this is true and if possible show how to arrive at one given the other?


I'm making two api calls and result of one should be merged with second api call i need to write these two like below  @RequestMapping("/greeting") public Greeting greeting() {     for(RTM rtm: callAPIFuncA()) {         try {          }       catch(Exception e) {           log(e);           }   }      for(NonRTM nRTM: callAPIFuncB()) {        try {          }       catch(Exception e) {            log(e);          }      }  return new Greeting(responseMap);  }   But the problem i am running into is first api returns data but second one gets an exception , i wanted to return the response even if any one of the api call fails. please tell me what i need to change in my code to make it work. rightnow the api calls return data but in next for loop when i make a second api call it gives exception and never return the data eve from the first successful api call

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I'm trying to understand why pianos "can't be tuned" and am looking for a proof of a corollary of the rational roots theorem found here (looking for proof not by contradiction):   It's stated:  For any integers $a, b$ and $n$ with $n > 1$ then $\big(\frac{a}{b}\big)^n \neq 2$

Video states that a corollary of the Rational Root Theorem is that $\left(\frac{a}{b}\right)^n != 2$ for integers $a,b,n$, where $n \gt 1$.  I'm simply looking for a proof by contradiction of this.  I started of by assuming $\left(\frac{a}{b}\right)^n = 2$, but couldn't arrive at a contradiction.  (I'm probably very close).  Any ideas?  I got to: $n(\log a - \log b) = \log 2 = 0.30102..$


Generally, when I want to change a page, I'll use a href to do so, or I'll use the header function.  For my current project, I need to use jquery to receive and modify the information that the client has entered, and I need to then use the post method to have php be able to access said information.  Upon receiving the information, I want a separate php file in an includes folder to do something with it, and then redirect the user away from the original page.  When working on the project, the page does not change, so I am wondering if the information is even reaches the includes folder.  Below you will find a miniature example of code that replicates the issue described above.  After the save button is pressed, I want the jquery to create $_POST['message'], check if it is set, send it to the changePage.inc.php page, check again if it is set, then redirect the user to the secondPage.php page which should display "Hello World".  File named index.php  <?php     session_start(); ?>  <!DOCTYPE html> <html> <script src="https://code.jquery.com/jquery-3.2.1.min.js"     integrity="sha256-hwg4gsxgFZhOsEEamdOYGBf13FyQuiTwlAQgxVSNgt4="     crossorigin="anonymous"> </script> <script>     $(document).ready(function(){         $('#saveForm').submit(function(event){             event.preventDefault();             var message = "";              var changeText = function(){                 message = "You wrote: " + $('#text').val();             };              var send = function(){                 if(message !== ""){                     $.post("includes/changePage.inc.php", {message: message});                     $.post("index.php", {message: message});                 }             };              changeText();             send();         });     }); </script> <?php     if(isset($_POST['message'])){         header("Location: includes.changePage.inc.php");     } ?> <body> <textArea id="text"></textArea> <form id="saveForm" action="includes/saveEssay.inc.php" method="POST">   <button type="submit" id="saveButton">Save!</button>     </form> </body> </html>   File named changeDirectory.inc.php (within a folder named includes)  <?php  session_start();  if(isset($_POST['message'])){     header("Location: ../secondPage.php"); }  exit();   File named secondPage.php  echo 'Hello World';   The first comment actually does not solve my problem!  I need to change the page from the php file within the includes folder, so I do not want to use jquery to redirect!  jquery is necessary here to format the text and have it be accessible as a post variable, and, once it is accessible as a post variable, I want the changePage file to be run.  I cannot stress this enough! The redirect must be done within the changePage.inc.php file

How can I redirect the user from one page to another using jQuery or pure JavaScript?


I'm running Ubuntu 14.04, and when I am watching a movie, after 10-20 minutes the NUC stop casting picture to my tv, and I need to wiggle the mouse to get the screen back on. I disabled the screen suspend to never, but it won`t work.  How can I fix it? :)

I would like to be able to keep the computer awake during certain activities and longer running tasks, such as downloading larger files and watching full screen videos.  I like using Caffeine to keep the computer from sleeping by preventing the display from sleeping. This worked well for me on my mac, but this does not work in Ubuntu.  How can I do this?


I'm a Statistics undergraduate student and, this semester, I took a Physics 1 (Mechanics) class. The physics in this class is really just high-school physics but with basic Calculus and some Linear Algebra. You get to ignore things like friction, air resistance, assume objects to be particles, all this kind of stuff that makes things simpler.  The textbook we're using in this class is Young & Freedman's University Physics. The problem I have with this book is that it's very slow because it's made for very young people, who are often fresh out of high school, and the authors don't assume previous knowledge of linear algebra, and only assume trivially basic knowledge of calculus.   As a consequence, the discussions and examples are unecessarily long and detailed. So what I'm looking for here is some material that covers Physics 1 mechanics but is focused on people who have already taken the standard calculus and linear algebra classes. And by material I mean anything really, lecture notes avaiable online, YouTube playlists, etc.

I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through . What books would be good for a beginner?


I am a ESL learner, has been recently started doing some practice test of IESLTS. Here is a question I am confused about within a reading passage.      There had, of course, been dictionaries in the past, the first of these being a little book of some 120 pages, compiled by a certain Robert Cawdray, published in 1604 under the title A Table Alphabeticall 'of hard usuall English wordes'.   I am struggling with the words "certain" that author used here, I will be really grateful if someone help me figure out the question, or any of the ideas would give a lot of help.

Consider the following sentences:     I had my identity stolen by Mr. Ripley.   and     I had my identity stolen by a Mr. Ripley.   and     I had my identity stolen by a certain Mr. Ripley.   In what sense do these 3 sentences differ from one another?  How do a and certain modify the middle and last sentences?


If "jumbo shrimp" is an oxymoron is there another term to describe phrases like "small shrimp" "bad wreck" "tough problem" and "most favorite"?

What's the opposite of oxymoron? That is, two words put together that seem identical?


Using \div gives me divergence sign instead of division (÷), for sure inside of math mode. \documentclass[conference]{IEEEtran} \usepackage{amsmath,amssymb}  \usepackage{physics}  \begin{document}  $ 1 \div 2 $  \end{document}  returns back ;  As far as I know the problem is physics package and without it everything is ok, but I need it.

I usually use \div to generate a divide-by symbol, but when using the physics package, \div gives a nabla followed by a dot ("period") instead.


I posted  question on Stack Overflow, and noticed the following behavior. The following quote does somehow cut the rest of the sentence:     'DoSomeList' cannot be used as type parameter 'TImplementation' in the generic type or method 'ServiceCollectionServiceExtensions.AddTransient(IServiceCollection)'. There is no implicit reference conversion from 'DoSomeList' to 'IDo>'.   'IDo>' should be IDo<System.Collections.Generic.List<SomeType>>. Check it out in the edit view.

I've posted a lot to StackOverflow, and I've noticed something kind of irritating with the formatting in writing questions and comments. If I need to put something inside a < and a >, without spaces in the middle (like right there), it will think it's code and not show up, like this   (obviously it won't come up what I wrote there, or else this wouldn't be an issue, but if you open up the question to edit you can see what's written there.)  If I want it to show up, right now I have to add an extra set of brackets inside of the originals with a junk variable, like right <here> (again, open in edit window to see).  This is really annoying when trying to show variables like lists that require those brackets, and I feel like the junk variables could confuse people looking at the edits. Is there a way to get around this formatting? Thanks!


$ sudo apt-get install cedarview-drm libva-cedarview-vaapi-driver cedarview-graphics-drivers  Reading package lists... Done Building dependency tree        Reading state information... Done  E: Unable to locate package cedarview-drm E: Unable to locate package libva-cedarview-vaapi-driver E: Unable to locate package cedarview-graphics-drivers   .  $ uname -m i686    Why can't I find these "cedarview-drm packages"?

I am looking for instructions on how to install cedarview graphics drivers on Ubuntu 13.04 32bit.  My graphics hardware is a GMA3600 aka Power VR SGX545.  EDIT: It seems that they are not in Raring yet, but only Precise:   EDIT2: they seem to be closed source.


\begin{center} \small \setlength\extrarowheight{0.01pt} \captionof{table}{Nomenclature} \renewcommand{\arraystretch}{1.3} \setlength\doublerulesep{.1pt} \begin{tabular}{ |p{2cm}|p{5cm}|} \hline  \hline  \textbf{\small Symbol}    & \textbf{\small Description} \\  \hline  $E_{c , TL}$&  Total energy consumption in a day \\  $R_{a}$ & ----------------\\  $S_{a}$ & S--------------- \\  $E_{a}$ & -----------\\ \end{tabular} \end{center}   And I want to make the font size small whatever written in the table, however, I have used \small but it doesn't work in a tabular environment. Kindly help me out.

What's the recommend way of changing the font size in a particular table? Is there a better way than enclosing all values with, for example, the \tiny function.


I calculated voltage at Vx. How to know the input impedance? V- is at virtual gnd. Will it be Ra+(Rb||R1).  My question of input impedance seeing from node Vs is right or should we consider only from node Vx. I’m trying to intuitively understand opamps.

What is the input impedance? I have tried to solve it, let me know whether it is right or not? Thanks in advance.


I have a friend who always says "Thank" instead of "Thanks" or "Thank you". For example, when I ask: " Do you like to come?", his answer is: "Thank. I am busy".  Can you explain why "Thank" cannot be alone?  Surely it must be “Thanks”, or “Thanks to you” or “Thank you”.

While looking at the part of speech of the noun "thanks" in an online dictionary I noticed that it was a plural noun and wondered if it could be used in singular form. Glancing at the origin it appears that the old English word "thanc" was once used as the singular form of this noun. I assume it would be appropriate at that time period to say "I have a thank!" if you felt thankful for a single thing instead of being limited to always say "I have thanks!" as we do in modern English.   Nowadays, I believe we only use the plural form "thanks" as the noun in all cases. We can never have a single "thank". Instead we can only have "thanks"! I find this odd! It would make sense to have kept the singular form of the noun. Often we are grateful for a single action or event and it seems more accurate to have a single "thank" rather than many "thanks".   Is there any known specific background history as to why this is?


This is my issue: I was robbed and my passport was stolen with my ATM cards. I went to the nearest police station to make a police report and an affidavit as I was advised to get a new passport before proceeding to the consular office. Which I did within a few days. A day after I got the new passport, I got a call from the police that my passport has been recovered along with the other stolen items.  So I went to the immigration office and told them that my passport had been recovered and asked if I need to go to the embassy again. I was told that I don’t need to go the embassy as all they will need to do is to cancel my old passport without tampering with my US valid visa on it, since I got a new passport and was told that I will need to hold both my new passport and old passport while traveling.  So I want to ask if this is right and won’t give me a problem at the US port of entry? Thanks.

I had lost my Indian passport with a US visa and later filed an FIR and got a new indian passport but before reporting to the US embassy i found my lost passport, can I travel with both my passports to the US as the US visa in my lost and found passport is still in force? note: I did not report my lost visa to the embassy as I found it before reporting. @ Patricia Shanahan, there was no such information given to me regarding returning it back.  @ Newton, thanks man, that information was for expired passport and not for lost and found passport, I have to feel that the found passport will be expired and I can travel with the valid visa only. @DumbCoder 3, that is when you reported it to the Embassy but I found the passport before informing them.


Is this grammatically and syntactically correct?     … by a) studying and b) helping   – or should it be:     … a) by studying and b) by helping

When one wants to list various cases/classes/categories/types of objects in a string of conjunctions, is it preferable (or even mandatory) to keep on using (the same) preposition in front of each one them?  Moreover, does singular or plural form of the word "case", "class", "category" make any difference in the previous question?  Examples:   In the present article, we study the case of X, of Y and of Z objects. (in this example, as in most of the ones I have in mind, it is the preposition "of" which is relevant to my question). We study the cases/classes of X and of Y objects. vs. We study the cases/classes of X and Y objects.   Although it is rather clear that, in the singular case, the absence of "of" in later conjuncts may lead to a logical confusion (e.g., mistakenly taken as the one class/case of objects which are both X and Y), when it comes to plural of the words "case", "class", etc., this might not be an issue. Still, there might anyway be a rule in the plural setting as well.


I inherited a database server with SQL Server 2012 Enterprise Edition. All the databases (except for the system databases) are at the 90 compatibility level.    How do I justify updating them to 110 compatibility level?  Let me rephrase my question:  The server is upgraded to SQL 2012 but user databases' compatibility levels were not updated to 110.  So tempdb etc system dbs are 110 but user databases are still 90.  I would like to update them all to compatibility level 110.  I wish it's as simple as ALTER database compatibility level. :) But I need to  justify use of resources to thoroughly test the applications out.   Am I right to say that even though the system databases were in compatibility level 110 but the user databases are not reaping the benefit of SQL Server 2012?  Which means the databases were not really upgraded?  Thanks!

Could somebody provide me with a better insight about the compatibility mode feature? It is behaving different than I expected.  As far as I understand compatibility modes, it is about the availability and support of certain language structures between the various versions of SQL Server.  It does not affect the inner workings of the database engine version. It would try to prevent use of features and constructs that were not yet available in earlier versions.  I just created a new database with compat level 80 in SQL Server 2008 R2. Created a table with a single int column and populated it with a few rows.  Then executed a select statement with a row_number() function.  My thought was, since the row_number function was only introduced in 2005, this would throw an error in compat 80 mode.  But to my surprise this worked fine. Then, surely, the compat rules are only evaluated once you 'save something'. So I created a stored proc for my row_number statement.  The stored proc creation went fine and I can perfectly execute it and obtain results.  Could someone help me to better understand the working of compatibility mode? My understanding is obviously flawed.


I answered a question on Science Fiction & Fantasy Stack Exchange, which I noticed had gotten a relatively large amount of votes. I figured it had probably gone HNQ, and went to check the  (spoilers for Harry Potter and the Half-Blood Prince, BTW). I found out that boy yeah it had gone HNQ:  All in all, there were 26 entries for "Became Hot Network Question" in the post revision history. Which... seems odd, since I'm pretty sure there's only supposed to be . This seems like a bug; there probably shouldn't be 26 different entries for a question hitting HNQ.

The Boardgames Stack Exchange question  became a Hot Network Question three times, according to its :  All three events have the exact timestamp (19:14:39 UTC - shown when you click the 'toggle format' link or upon hovering) so it's probably a race condition or something. It's not a unique case;  finds instances on a single site, and  lists all occurrences in the network (currently 448). The current record holders, with 44 HNQ entry events, are   on Retrocomputing  on Worldbuilding


An ETF is a collection of shares packaged into a single tradeable equity. But since the marketvalue of an ETF unit is determined by market forces, what impact does the change in value of an individual shares apart of ETF have.  e.g A Tech ETF holds shares of Apple, Google, and Amazon, if the share price of Google goes up, how is that reflected in the price of the ETF

I hold a position in , an ETF tied to the S&P 500 traded on the LSE. The closing price of CSPX was 262.68USD at a gain of 0.2%. The S&P 500 itself closed higher at at 1.6%. There are a couple of reasons I can think of as to why they are not equal:   The S&P 500, or rather the underlying assets, continued to be traded for several hours after the LSE ceased trading. If this is the case should I expect the value of the fund to rise on Monday morning? The fund manager for CSPX has elected to place more funds in some companies than others. In this case perhaps a higher tranche has gone into a company which has done poorly compared to the rest of the stocks in the index.   Generally speaking if a stock is bought a lot, the price goes up. Does the same ring true for ETFs? If a lot of people buy into the ETF will that affect the price at all or does the value of the ETF depend absolutely on the NAV of the underlying assets?


I want to know how much space (in gigabytes) will a clean installation of windows 7 32 bit version take after installation.

I have a Macbook Air and would like to install Windows 7 on it via Boot Camp. How much hard drive space should I make sure to have free before doing this?


Please help me, this is my last year at university, and all my files and projects are on my device.  I had two sections 399 gigs for the Mac system and 100 gaps on which I installed Linux .. After a while I deleted the Linux and upon restart I couldn't log in and some solutions worked out but the problem still exists.     Update:    Thanks, the answer worked, but I have this problem: When I start my compute, it goes to EFI boot, I think it's for windows 10. I don't need it. I want to delete it and put my priority macOS. How i can do that? I'm soooo scare to do any things.  And, I can't see the 100 GB partition.

Yesterday, I have tried to delete an Ubuntu partition. Since, my Mac (13", MBPro mid-2014) doesn't boot. Now, I boot on Mac OS copy with an USB. i follow different subject of this forum (like this : ), and my volume partition change from FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF to 48465300-0000-11AA-AA11-00306543ECAC. But I still can't boot to it...    Thank you very much !


I have to find the closed form for   $$T(n) = \begin{cases}  2 , &\text{ if } n=0 \\ 9T(n-1) - 56n + 63, &\text{ if } n > 1 \end{cases}$$  I used the repeated substitution method and I found that the pattern for the coefficient of n is equal to the following: $$f(1) = -56$$ $$f(n) = 9^{n-1} \times (-56) + f(n-1)$$  I tried to find the closed form of $f(n) = 9^{n-1} \times (-56) + f(n-1)$, but it just got more and more confusing. I believe it may be a series of some sort. Is there a way to find a closed form for this?  Thank you!

$T(n) = 2$ if $n=0$  $T(n) = 9T(n-1)-56n +63$ if $n>=1$  Repeated substitution  $k=1$  $T(n) = 9T(n-1)-56n+63 $  $k =2$  $T(n) = 81T(n-2) -560n + 1134$   $k =3$  $T(n) = 729T(n-3) -5096n + 15309$  I cant find the pattern for the n term and the integer  For now i just have  T(n) = $9^k(n-k)$


I've used TikZ Editor for some time to make my TikZ drawings. I've really appreciated the live-rendering features. Now, I'm wanting to make some graphics using the pst-optexp package, and I'm having a hard time finding an application that does what TikZ Editor does for pstricks. Theoretically, TikZ editor should do the trick... it allows me to change everything in the preamble, etc... except for allowing me to change the \begin{tikzpicture}.   Does anyone know of a way to:   Install software that allows live-reload of pspicture environment? Modify the code in TikZ Editor such that I can compile pspicture in this application?   For the record, I'm running OS X El Capitan. I'm thankful for the link to the other stack exchange question with a list of apps that people use for editing. However, most of those are either click-and-drag, or are for windows/linux. I'm not interested in a click-and-drag application. I'm more interested in something very similar to TikZ Editor. Is there any such editor that allows live preview of PSTricks on Mac?

I found  to be a useful tool to help generate code for graphs. I suppose there must be other tools to help draw diagrams such as Sets/Venn Diagrams or Electrical Circuits (Logic Gates). Which ones would you suggest?


Let  $p$ be a prime  number. The order of a $p$-Sylow subgroup of the group $GL_{50}(\mathbb{F}_p)$ of invertible $50×50$ matrices with entries from finite field $\mathbb{F}_p$ equals: $p^{50}$ $p^{125}$ $p^{1250}$ $p^{1225}$    I am completely stuck on it.can anyone help me please.

Let $p$ be a prime number . The order of a $p$-Sylow subgroup of the group $GL_{50}(F_p)$ of invertible $50\times50$ matrices with entries from the finite field $F_p$,equals which of the following    1.$p^{50}$ 2.$p^{125}$ 3.$p^{1250}$ 4.$p^{1225}$    I think order of this  group is $p^{2500}$  .A  sylow p-subgroup of order $P^k$ divides  order of the group but $p^{k+1}$  does not. I confused here how to apply these things .


Assume $G = \{1, a,b,c\}$ is a group of order $4$ with identity $1.$ Assume also that $G$ has no elements of order $4$. Show that there is a unique group table for $G$. Also show that $G$ is abelian.   If $G$ is abelian, then the group table matrix must be symmetric. How can I introduce a binary function and show it? I am new in this field, so I am not so familiar. I have proved many other exercises, but it is a little tough (for me).   Can you please help?  Edit: I know every element has order $\leq 3$ , but I do not understand how I will proceed.

Not sure how to make tables, but:  For a binary operation $*$, and set $\{e,a,b,c\}$, in the Cayley table, $a*a$ can be filled with either the identity or an element different from both $e$ and $a$. If in the table the place for $a*a$ is filled with $e$, then the rest of the table can be filled out in two different ways.  What are the two different ways?  Thanks


I have compiled a huge document with LuaLaTeX - I've tried stripping it down to a MWE but cannot get the behaviour to repeat.  The issue is that the document contains un-embedded fonts, and to submit my PhD thesis to my university I need all fonts to be embedded.  I have tried doing embedding fonts after compiling in Acrobat Pro, but lots of characters break when you do this.  So I have to do it in LaTeX - but I can't work out how to solve this. I've heard rumour of editing pdftex.map in some folder like /users//library/texlive etc etc but I can't find it, and don't know what to edit.  Any help would be much appreciated.  Cheers.  EDIT: I solved the problem through a lot of trial and error and wanted to describe how here in case someone else stumbles on this question. In short, I had pdf figures generated in R that did not contain embedded fonts. I started an Adobe Acrobat trial (free) so I could use the pro features. I then saved all figures as pdf/a. This embedded the fonts without any degradation or significant alterations (I tried other methods that stopped the graphs being lossless - but this method worked a treat).   One wrinkle was a few figures for which Adobe broke when trying to save as pdf/a. For these, I used the embedFonts() function in R - embedFonts(filename, new_filename) - this took the original pdf graphs and embedded the fonts. I still had to do the conversion to pdf/a for some reason in Adobe, but the combination of steps for the problem graphs.  The combination of these two approaches allowed me to upload my thesis to the online directory. Hope this helps someone else who runs into this issue.

I am writing a book using times font. It has MATLAB codes. I have used the listing package for generating matlab code in latex. For the remaining text I am using times package. But while trying to publish the book I am getting the error helvetica package not embedded. I do not want to use helvetica font as the publisher has a problem with that font. Can someone explain what is font embedding and how can I remove the Helvetica font.


I'm using Ubuntu for the first time and Python as well.  There are 2 versions of Python installed by default  $ python3 --version Python 3.5.2  $ python --version Python 2.7.12   I don't understand why two versions of the same software are installed.

I type python in a terminal window. I get Python 2.7 and not Python 3.5. According to the docs, Python 3.5 should come preloaded.


I remember reading a series of three books that started in some sort of slum with the female protagonist. At a certain point every kid, no matter the status, is tested for their ability to use magic. This is because magic can be extremely problematic when left alone. Mages normally explode quite violently when they die and their remaining magical energy gets out of control. Therefore everyone with an aptitude for magic gets recruited and trained in a special school to learn how to use magic.  The school also has a room where mages are supposed to die without hurting anyone. But strangely for most people, there is also some sort of old graveyard and nobody understands why - after all there is no body to bury if a mage dies.   The protagonist learns a lot of simple magic - little shields to be safe from physical attacks and methods to raise the core temperature when it's cold outside. Raising the core temperature was mentioned as something students starting in winter would learn really fast - they were only allowed certain clothes in the school.   The problem comes later in the books. The reader learns that there are other kinds of mages who were banned a long time ago and lived in the desert. They still knew how to raise their magical energy, which normal mages of the current time forgot. By cutting someone and touching their blood a mage could siphon their energy and increase their own pool of energy. The normal process was that there was one master and one student. The master taught the student and in turn got to take their magical energy. This also allowed to take all of the energy of a mage in their last moments, which means there was no energy to go wild after death and therefore no explosion.   By constantly increasing their magical energy their spells were extremely powerful. Once these people learned that others forgot about extracting magical energy from others they decided to start a war. They could easily kill most of the normal mages. Those were extremely weak compared with the bad guys and didn't expect such power.   Luckily the protagonist and one of her teachers(?) were different. He knew about this kind of magic and taught her about it. So they started fighting back and I think in the end they were able to defend themselves against the invaders by showing them, that the old knowledge was not lost and killing a handful of the enemies. Their numbers were really low and explosions from mage deaths were extremely devastating after all.   The magic system was really fascinating and I would love to read them again, but I only borrowed them from a friend around 2010 or so. I've read the books in German and each one had the female protagonists name in the title.   Can you help me remember what the name of the series was

I read a young adult novel around the turn of the century. This story features a young female protagonist that is very naturally gifted in magic. She is attending a  to learn mastery and control over her gifts.  A lot of her school revolves around magic dueling. The participants are taught to extend their inner aura like a second magical skin, possibly referred to as creating a shield, or . The user can increase the strength of the shield by focusing harder on it, but doing so means you have less ability to be offensive. The amount of energy needed to create a shield was half the energy a foe would need to focus at you to break it.  Ex: Mage A and B are equally matched. Mage A focuses half his power into a shield. Mage B would then need to focus 100% of his power to break A’s shield.  Another aspect I remember is that when dueling, a school master would extend a personal shield on to one of the combatants as a sort of secondary shield that goes underneath the combatants. When one mage broke the others mages personal shield, the school masters shield protects the losers life from harm, and the breaker of the shield is declared the winner.  I distinctly remember one match in which the protagonist is having a duel with another strong student. She creates a wind storm around herself that picks up the sand from the arena floor and makes her impossible to see and thus makes it hard for her opponent to focus on her shield to break it. She then lashes out at her opponent with incredibly powerful strikes with the final strike being so hard it shatters the opponents shield and then breaks the school masters shield as well and stops just shy of killing her dueling partner.  Any assistance on this one? I think my daughter would love to read it.


In this program below:  public class medianTemp { public static void main(String[] args){     int length = args.length;     int[] n = new int[length];     n[0] = Integer.parseInt(args[0]);       System.out.print(n[0] + " ");      for (int i = 1; i < length; i++ ){         String c = args[i];         if (c.equals(".")){             n[i] = n[i-1] + 0;             System.out.print(n[i] + " ");             }         if (c.equals("+")){             n[i] = n[i-1] + 1;             System.out.print(n[i] + " ");             }         if (c.equals("-")){             n[i] = n[i-1] - 1;             System.out.print(n[i] + " ");             }   Inside the for loop and inside the if statements. If I use for example args[i] == "." (instead of converting args[i] to string), the code above doesn't work and only the initial integer is displayed. Can someone please tell me why this happens?

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I am trying to write a shell script for the first time.  My aim is to check the login prompt for any device when I run the shell script through telnet.I need to give only the ip address as input.Username and passwords are same for all routers.  So once i give ./scriptname "ip address",it should automatically login with username and password which will be defined in script.  I tried a piece of code but didn't work well.  Can someone kindly help me on this?  Code:  #!/usr/bin/expect   read -s "Enter the ip address" ip  spawn telnet "$ip"  set timeout 20  expect -re "OS10 login:"  send "admin\n"  expect -re "Password:"  send "admin\n"  interact   Error:  wrong # args: should be "read channelId ?numChars?" or "read ?-nonewline? channelId"     while executing "read -s "Enter the ip address" ip"     (file "./telnet" line 3)

I have an expect script that connects to a few routers through ssh.  All these routers have the same password (I know, it's wrong), and the script needs to know that password in order to be able to connect to the routers.  Currently, the password is passed to my script as an argument on the command line, but this means that there's a trace of that password in my .bash_history file as well as in the running processes.  So instead I would like the user to be prompted for a password, if possible silently.  Do you know whether or not it's possible to prompt the user for a password with expect?  Thank you.  Edit: if I was connecting to servers instead of routers, I would probably use ssh keys instead of passwords.  But the routers I'm using just support passwords.


I dont know my user password and have tried many suggestions to add user ,change password etc without avail,ls home produces no such file or something ,although I can open Home on the desktop.Can I reinstall over the existing installation without losing data links etc and change the user password then Brian

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


I have read the definition of the opposite category in the abstract, but I don't understand it's interpretation, and the internet didn't help me.  If $C$ is a category where very morphism has an inverse (a groupoid), then I can imagine an interpretation of the opposite category $C^{op}$: We simply swap each function with its inverse.   But what if we have say, a category $C$ consisting of two objects $0$ and $1$, namely $0$ is the empty set, and $1$ is a set containing one element. Then there is one function from $0$ to $1$, and no functions from $1$ to $0$. Apart from the identity functions there are no other morphisms in this category.  What is the opposite category $C^{op}$ here? It is a category with a morphism from $1$ to $0$, but this morphism cannot be a set-theoretic function, so what does this morphism represent?   How do we interpret this opposite category? Is there necessarily a fixed interpretation?

The opposite category of C is defined by setting hom(x,y)=hom(y,x) for all objects x,y of C. However in a concrete category, morphisms do not always have inverses (because functions don't always have inverses). So I am wondering how it is possible to always construct a reversed arrow for a given arrow and whether or not it is always possible to construct the opposite category.  Edit: Thank you for the responses and references I think I understand the main part of the question. As I understand it, when you construct the opposite category you forget all the meaning that the objects and morphisms have and reverse the arrows only in terms of classes of objects and sets of morphisms. One question I have is this. When you say a statement about a category you get the dual statement for "free" because the proof also applies in the opposite category. Do you only get things for free when your are talking about types of categories and not specific categories. For example in the category of groups, products always exist but coproduction do not.


Any prime greater than 5 shall have 1,3,7 or 9 as last digit. Are the primes  equally distributed among the above four last digits or any  bias for  any particular last digit say  up to 10 to the power  12 or higher. I have recently read an article in Scientific American that adjacent primes are unlikely to share the same last digit. Is it possible to predict the distribution among the last digits as we go higher?

Let $n\geq 2$ and let $k$ be "considerably larger" than $n$ (like some large multiple of $n$). Then for each $i$ such that $0<i<n$ and $\gcd(i,n)=1$ let's define $$c_i=\left|\{p_j\;|\; p_j\equiv i \mod n,\;\mbox{where $p_j$ is the $j$-th prime, $1\leq j\leq k$}\}\right|$$ so $c_i$ represents how many of the first $k$ primes are congruent to $i$ modulo $n$.  What can we say about $c_i$s, that is about the distribution of the first $k$ primes modulo $n$?  I thought the distribution will be seemingly random, and that is mostly true - for example $c_i$s are always very close together. But there are observable non-random patterns. For example for $n=3$, for various $k$s I've tried  (up to $10^6$) I always got $c_2>c_1$. If this were just some kind of random discrepancy due to distribution of small primes, it would eventually vanish for large $k$s, which I don't observe.


The code is shown as follows:  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{pst-circ}  \begin{document}   \begin{center}     \begin{pspicture}[showgrid=true](3,2)       \pnodes(0,1){A}(3,1){B}       \resistor(A)(B){$R$}     \end{pspicture}   \end{center} \end{document} \usepackage{pst-circ}   and it shows "Undefined control sequence" at line 9 and 10.  How can I solve this?

\documentclass[12pt]{article} \usepackage[paperheight=9in,paperwidth=13.24in,margin=0in]{geometry} \usepackage{pstricks} \usepackage{graphicx} \begin{document} \thispagestyle{empty} \psset{unit=1in} \begin{pspicture}(13.24in,9in) \psframe[fillstyle=solid,fillcolor=Maroon](0,0)(13.24,9)  \end{pspicture}  \end{document}   I am following a tutorial outlined here:   I am following the Robbers book.  Everything seems fine until I paste the \psframe[fillstyle=solid,fillcolor=Maroon](0,0)(13.24,9)  What could be the problem?


I suspect there were multiple flags on the  and my flag was declined with the response to a different flag:    I was flagging in hopes of getting a bounty question closed, not in response to downvotes.

Sometimes a post has both valid flags and invalid flags. As far as I can tell, all the flags on the same post have to be dismissed with the same validity.  The scenario I encountered (on ):   A low-quality question is closed. The asker improves the question and flags for reopening. A moderator reopens the question, but doesn't dismiss the flag yet. Someone else flags the question as “off topic”.   Since I agree with the reopening, and I don't consider the question off-topic, I would like to dismiss the first flag as valid and the second flag as invalid. But there's only one set of buttons for both flags.  And just now, two flags on a closed question: one that says “delete it”, the other one that says “reopen it”. The correct course of action is neither (the ideal outcome would be for the question to be edited then reopened). I should provide different feedback to the two flaggers, but I can't.  Unless I've missed something, please allow multiple flags on the same post to be dismissed separately.


I bought a new dell laptop a couple of months ago that's running Windows 10. I did not install a password. I had heard about the secure boot and disabled it through the UEFI (F12 on startup).   I wanted an app (Microsoft now has an app store) but they make you get a Microsoft account. A few days later I shut down the machine and upon restart, it asked me for a password.   I knew that I could get into the machine and see the files (my passwords are in a text file on my windows desktop) if I installed Ubuntu.   I tried to see the files from the "Try Ubuntu" but  they weren't accessible, so I made a small partition and installed Ubuntu. That's when I first heard about fast boot. Ubuntu installed OK. I have the grub menu that shows both Ubuntu and Win 10.   When I try to boot to Windows 10 I get a pixelated screen and it will not boot.  I also can't access UEFI by hitting F12. My guess is I needed to disable the fast boot in Windows before I installed Ubuntu, but it's too late now.   Is there a way I can turn off grub or disable that feature from within Ubuntu?    I can't access the UEFI to get to the boot menu and it's stuck on booting from the HDD so I can't boot from a CD or USB.   I only need to get into Windows one time to turn off the hibernation/fast boot but can't find a way.   Any help you can give will be greatly appreciated!

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


Why does time dilation happens when the object moves, is it just because the physical processes, in the moving objects, happens slower? (this video suggests this: )  If yes, does this means if a person moves fast, this might alter his brain activity and his thinking process be altered?  Does this means there is no time dilation at all, but just that the physical processes happens slower when moving? This might explain why two atomic clocks are different, when on is taken to space and back.

Please will someone explain what time dilation really is and how it occurs? There are lots of questions and answers going into how to calculate time dilation, but none that give an intuitive feel for how it happens.


I cant find the solution for a regex that looks for a pattern but only in a specific range of the string  I want to find $ $ but only if it is in the 5-7 position of the string and it doesnt matter which character is between those two  Example  xxxx$x$xxxxx would match xx$x$xxxxxxx would not

I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them?


I have few questions regarding the Reputation thing. According to the site, reputation is the sign of trust.  I have noticed that I highly trust the answers given by high rep users moreso than the low rep users.  Even though I didn't understand fully sometimes what their answer was, but I am 100% sure that whatever he has written is right.  Now consider this case; suppose I have 40K rep and I usually answer the c++ or java questions.  Now I started answering questions of python or linux for which I am a newbie. Although I have 40k rep up till now, but for python questions I will be like a newbie since I have just started that. It happened with me that I used the high rep answer and it was wrong. I only relaized it later. Then I saw on the summary page that he is new to this area  Now when I give the answer for python question then its quality will be lower than other person with 5k rep who is regularly using python.  There is chance the OP uses the answer of 40k user by just looking at the rep, now that may contain some hidden problems, although the other community members can point that out but there are chances.  I was thinking is there any way we can give an indication along with rep that 40k rep is in c++ or java, but for python he is new.

When viewing a question, I was wondering if it would be possible on the nameplates of the members who asked the question and the members who provided answers and comments, that their nameplates only display the reputation points earned in relation to the tags which are attached to that question?  I'm not sure if I'm explaining this the way I intend to but what I would like is for the reputation points you see on a member's nameplate to only reflect the reputation earned for the tags on that question and off course still see the total rep in smaller font at the bottom of the nameplate.  This should be dynamic, and be derived on the fly, depending on the tags.  I would find this good as it would not give a false impression of someone. Say for example someone with 20k rep (all earned from c# questions/answers) is asking his first jQuery question. Seeing 20k rep on the nameplate could be miss-interpreted and influence how people may treat that question. Will there still be down-votes if it is a bad question? Maybe..but maybe not.  Same goes for answering off course. If I'm answering my first question under the Java tag and I never done that before, my rep should probably be 1 in relation to the tags on that post, still showing my full rep as well off course.  By no means has that any additional effect on privileges and the like as the total rep is still used for that off course.  We already have the number of answer or questions associated to tags on the profile page I was just wondering if something similar could be done to the reputation displayed on the name-plates (not on profile pages).  I don't know if I explained this right but if not let me know and I try to clarify.


Let's say that we have a function $f:\mathbb{M} \rightarrow \mathbb{M}$ where $\mathbb{M}$  is an arbitrary set. And let's say that the function f is injective.Does that mean that the function is surjective too? More generally: If a function's domain and codomain coincide and the function is injective does that imply that the function is surjective?My way of thinking this: Suppose that f is not surjective $\Rightarrow \exists y \in \mathbb{M}$ such that $f(x) \neq y, \forall x \in \mathbb{M}$ And since the domain and the codomain coincide this mean that two elements from domain must go in the exact element from the codomain which implies that f is not injective, which is a contradiction. Therefore f is surjective. Am I right? Thanks

Is it true that for each set $M$ a given injective function $f: M \rightarrow M$ is surjective, too?  Can someone explain why it is true or not and give an example?


In the “community selection” drop down menu, my reputation on a particular meta site has been displayed 100 points smaller than the true amount for at least a week or so. The behaviour is consistent across different browsers on several devices, and independent of which SE site I use to view the drop-down. Note that this is not just a case of changes of reputation from the main site being out of sync with the meta site, as the reputation is displayed correctly in other places (e.g., in my profile on the meta site).

While using the top bar to navigate across communities, I noticed that the reputation displayed on meta sites on that list does not match the one of their corresponding main sites:    I have noticed on past situations that reputation gained takes a bit to "update" on the display on Meta sites (that is, if you gain rep on SO, for example, it will take some time for you to see your updated rep on MSO).  However, I have never noticed this behavior here, on the Sites List of the top bar. Furthermore, the "delay" here seems to be more severe, as the "outdated" rep showed is of several days ago (for example, I turned 3k on SO almost exactly a week ago, but the rep shown on MSO is still <3k).  Any idea what could be causing this behavior?    Update: 2 months later this persists: my main site rep updates correctly but their corresponding meta rep remains the same as in the image above.     Update: As per Catija's  I removed the site (MSO) and put it back in, but it didn't update the rep.   However, after removing one site (TWP Meta), waiting at least a day, and then adding it back I see that although the reputations still don't match, the number displayed did changed a bit (previously 29,924 but now 33,112):


Let $A$ and $B$ be $n\times n$ matrices with integer entries. Show that if $B=A^{-1}$ then $A$ and $B$ are permutation matrices (matrix obtained by permuting rows of the identity matrix).  If the entries are non negative integers then it is quite easy to show, but if the entries also involve negative integers then I couldn't show it.

How to prove that if $A$ and $B$ are two $n×n$ matrices with non negative integer entries such that $AB=I$ then $A$ and $B$ are permutation matrices?  Permutation matrices are matrices with the columns just a permutation of the identity matrix. How do I proceed. Can somebody give hint?


When will Ubuntu 20.04 update available through Software updater?

I'm following the , but on launching the upgrade tool I get this response:  Checking for a new ubuntu release No new release found   Am I doing something wrong? Is there a workaround?


I have two users with home directories:  /home/user1/ /home/user2/   I would like to share a folder between the two users:  /home/user1/some/path/to/folder   but would only like user2 to have access to /home/user1/some/path/to/folder and not any of the parent directories.  I tried to chmod 777 /home/user1/some/path/to/folder, but that didn't work.

In my CMS, I noticed that directories need the executable bit (+x) set for the user to open them. Why is the execute permission required to read a directory, and how do directory permissions in Linux work?


I am trying to create a set from a list which I need it to be in order.      someList = ['from', 'from', 'who', 'are', 'are', 'frost', 'fire', 'are']  someSet = set(list)   Doing that yields a random ordered sets.  I need it to always be in order like  someSet >> {'from', 'who', 'are', 'frost', 'fire', 'are'}

Is there a built-in that removes duplicates from list in Python, whilst preserving order? I know that I can use a set to remove duplicates, but that destroys the original order. I also know that I can roll my own like this:  def uniq(input):   output = []   for x in input:     if x not in output:       output.append(x)   return output   (Thanks to  for that .)  But I'd like to avail myself of a built-in or a more Pythonic idiom if possible.  Related question:


I have my HSA that is currently in savings or checking account. The Insurance company provides option to keep the money in Investment account.  What are the pros and cons of parking HSA fund in Investment ?

I have an HSA that allows me to invest the money in the account in the stock market. Any money not invested is available to be used for health expenses. I currently have ~50% of the total balance of the HSA invested, with the other ~50% on hand for expenses.  I've run into a situation where the ~50% on hand for expenses does not cover all of my current expenses. To cover the remaining costs, should I sell off my the HSA investments or should I leave those as is and use money from my savings account?  I'm trying to determine if the tax advantages of the HSA combined with the returns the invested money is seeing is worth me leaving that money alone - and instead, take the money from my savings account to cover the costs.


This is the message it gives me:  W:Failed to fetch http://ppa.launchpad.net/sevenmachines/flash/ubuntu/dists/quantal/main/source/Sources  404  Not Found W:Failed to fetch http://ppa.launchpad.net/sevenmachines/flash/ubuntu/dists/quantal/main/binary-i386/Packages  404  Not Found E:Some index files failed to download. They have been ignored, or old ones used instead.

PPA seems to be constantly offline. Whenever I use sudo apt-get update, this error is shown:  W: Failed to fetch http://ppa.launchpad.net/ 404  Not Found   How do I fix these errors?


Lets take a class A. class A{     public getAbsoluteLocation(){         ....   } }  How can this class know in which directory it is located?

Does anyone know how to programmaticly find out where the java classloader actually loads the class from?    I often work on large projects where the classpath gets very long and manual searching is not really an option.  I recently had a  where the classloader was loading an incorrect version of a class because it was on the classpath in two different places.  So how can I get the classloader to tell me where on disk the actual class file is coming from?  Edit: What about if the classloader actually fails to load the class due to a version mismatch (or something else),  is there anyway we could find out what file its trying to read before it reads it?


I've got this particular problem that I receive a NullPointerException whenever I try copying a HashMap Object into another HashMap Object. Here my code snippet public void printCountNotAlreadyKeys(){   HashMap<String,String> count = new HashMap<>();   count.putAll(responder.getResponseMap());  } The method getResponseMap looks like this    public HashMap<String, String> getResponseMap(){       return responseMap;    }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


After doing a t-test that showed a significant difference, I did an ANCOVA with 3 covariates. The ANCOVA showed no significant effect of the variable that did show a significant difference in the t-test. However, one covariate showed a significant effect. This confused me a bit, so I have a few questions:     What does it mean dat the significant difference found in the t-test is no longer significant when doing an ANCOVA? How to interpret the significant covariate in my ANCOVA?

The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other explanatory variables.  How I have viewed it so far:  While each coefficient is being calculated, the other variables are not taken into account, so I consider them to be ignored.   So am I right when I think that the terms 'controlled' and 'ignored' can be used interchangeably?


EDIT: The question  does not answer my question. It does not address the TIME required for an umpire required to reach national level from local level.  Specifically, after officiating local matches, how much time does a state association take to send one's name to BCCI for level 1 exam?  Adding to the question, also how much time does it take for one to reach Ranji level from club level?

In cricket how does someone become an umpire at international level? Is there some procedure for this? How are they selected and what is the criteria for this?


"We got him," Belgian migration minister Theo Francken tweeted following the culmination of a four-month manhunt across Europe.   Why there isn't definite article in front of Europe? For me it would feel logical to say      manhunt across the Europe.   Is this wrong and if so why?  Another example:      The market is a gap which separates producer and consumer.    Why there isn't an article before producer and consumer. For me it would feel logical to say:      The market is a gap which separates a producer and a consumer.    Is this wrong and if so why?

I have been taught that it's grammatically proper to use the before countries like "Sudan and Yemen" but I was never given a reason (if there exists any, of course) when I asked why, except for "it is one of those ambiguous parts of English language that we – as non-native speakers – should just accept without trying to look for a reason". Now, I'd like to know if there is any answer to this "why" or I should keep on believing that there are no hard and fast rules when it comes to questions like these.


Yesterday I watched  and saw this scene.   Its around 1:15:25  So is  happened before Captain America: The Winter Soldier?? And when did Doctor Strange exactly took place?

The films from the Marvel Cinematic Universe (MCU) are usually set roughly around the time they are released (barring flashbacks) or at least in a chronological order congruent to their release order. They often reference events from past MCU films or foreshadow future films (e.g. in post-credits scenes). However, with  there seem to be some discrepancies with this approach.   At first, it seemed a reasonable assumption. There even seems to be a reference to Rhodie's accident in , when his assistent presents Dr. Strange with some potential patients and mentions something similar to (quoting from memory)     an Air Force Colonel paralyzed from the spine in a special protective suit.   And then there's also the post-credits scene with Thor, which seems to be a foreshadowing of the upcoming . However, someone pointed out, that the reference to the paralyzed Colonel might as well refer to the guy we see in Justin Hammer's failed attempt at copying the Iron Man suit in . Besides that, we don't exactly know how much time actually passes in Doctor Strange, considering how he seems to go through significant rehab treatment and spends his fortune trying various healing methods before getting involved with sorcery (let alone the time he actually spends studying at Kamar-Taj). And then I noticed something really interesting in , where Sitwell is interrogated about HYDRA's plans and says:     Zola's algorithm is a program for choosing Insight's targets...You! A TV anchor in Cairo, the Under Secretary of Defense, a high school Valedictorian   in Iowa City, Bruce Banner, Stephen Strange, anyone who's a threat to HYDRA.   And I wondered if Dr. Strange actually already had his magic powers at the time of The Winter Soldier. Or why else would he be a threat to HYDRA, as much as we know he's just a really good neurosurgeon. Then there's also the tidbit that for a Phase 3 movie the film seems a quite traditional origin story, resulting from the possibility that Dr. Strange's inclusion in the MCU might have been decided much later than the other plans for the MCU, based on its overall success and the motivation to take higher risks with less mainstream-famous characters. This might either point to an earlier setting of the film. Or it might as well render the above statement in The Winter Soldier somewhat of a premature blabbing which is now being retconned.   So is there any secured information about the setting of Doctor Strange within the MCU's timeline or at least more conclusive hints from this or other MCU movies? If not or if we are to assume it's released roughly chronologically, then what explains the above statement from The Winter Soldier about Stephen Strange being a threat to HYDRA before his involvement with magic? Or was this really just a throwaway comic reference without much thought or significance put into it?


Question:     How does one set the tags numbering according to the related section or subsection? E.g. If it is the section 3.4 I would like to be able to label an equation as    \documentclass{article} \usepackage{amsmath, amsfonts, amssymb}  \begin{document} $$(s_1 \circ \varphi^{-1}_1)^*\boldsymbol \omega =\mathrm{Im} \left(\frac{\bar q}{1+|q|^2}dq\right) \tag{3.4.1} $$ \end{document}   Unfortunately I haven't been able to do so yet, and I would like to know if it is possible. If so, could anyone show how?

Some document elements (e.g., figures in the book class) are numbered per chapter (figure 1.1, 1.2, 2.1, ...). How can I achieve continuous numbering (figure 1, 2, 3, ...)?  And vice versa: Some document elements (e.g., figures in the article class) are numbered continuously. How can I achieve per-section numbering?  \documentclass{book}% for "vice versa" variant, replace `book` with `article`  \begin{document}  \chapter{foo}% for "vice versa" variant, replace `\chapter` with `\section`  \begin{figure} \centering \rule{1cm}{1cm}% placeholder for graphic \caption{A figure} \end{figure}  \end{document}   Bonus question: Is it possible to adjust the numbering of the sectioning headings themselves? Can I, e.g., switch from per-chapter to continuous numbering of sections in the book class?


I was reading about AngularJS and came across the following statement on a newsgroup:     I have to say, though, that the more I use Angular, the less interest   I have in  creating classes.  Classes are not where javascript is at!    You can do pretty  much everything you need with pure functions and   closures and then you don't  have to worry about the troublesome   "this" and "that".   Can someone explain what is meant by "closures".

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


How can I detect this part: /table/LEKPOOZZZCV/LSK1633923 from string variable: '
<span class="table_names__name" data-v-fc63c1b6="" title="W............ using regex expression?

In .Net, I found this great library,  that allows you  to easily parse non-well-formed HTML using XPath.  I've used this for a couple years in my .Net sites, but I've had to settle for more painful libraries for my Python, Ruby and other projects.  Is anyone aware of similar libraries for other languages?


I've been trying for hours to be able to be able to give a label a picture if it has a blank image ('blank.jpg') and every time i'm coming up with either an out of bounds error or a null pointer error (currently). Can anyone help me out and check my code for the problem:  public class HomeController extends JFrame {    public HomeController()   {     JFrame main = new JFrame();     main.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);     main.setTitle("Smart Home Control Panel");             //PANEL CONTAINING THE PICTURES     JPanel labelPanel = new JPanel();      labelPanel.setLayout(new GridLayout(3,3));     labelPanel.setBorder(BorderFactory.createLineBorder(Color.BLACK));      ImageIcon blank = new ImageIcon("blank.jpg");     ImageIcon lamp = new ImageIcon("lamp.jpg");     ImageIcon clock = new ImageIcon("clock.jpg");     ImageIcon television = new ImageIcon("television.jpg");      JLabel pictures[]=new JLabel[9];     for (int i=0;i<=pictures.length; i++)     {         pictures[i].setBorder(BorderFactory.createLineBorder(Color.BLACK));         pictures[i].setIcon(blank);         labelPanel.add(pictures[i]);     }       main.add(labelPanel, BorderLayout.CENTER);     //----------------------------------------------------------       //PANEL CONTAINING BUTTONS     JPanel buttonPanel = new JPanel();      JButton but1 = new JButton("ADD APPLIANCE");     JButton but2 = new JButton("CLEAR SCREEN");     JButton but3 = new JButton("LOAD FILE");     JButton but4 = new JButton("SAVE FILE");      buttonPanel.add(but1);     buttonPanel.add(but2);     buttonPanel.add(but3);     buttonPanel.add(but4);       main.add(buttonPanel, BorderLayout.PAGE_END);     //-------------------------------------------      //EVENT HANDLER FOR BUTTONS     but1.addActionListener(new ActionListener()     {         public void actionPerformed(ActionEvent e)         {              Object[] options = {"Clock",                     "Lamp",                     "Television"};             int n = JOptionPane.showOptionDialog(main,             "Which type of appliance?  "             + "",             "",             JOptionPane.YES_NO_CANCEL_OPTION,             JOptionPane.QUESTION_MESSAGE,             null,             options,             options[2]);             if (n == JOptionPane.YES_OPTION)             {                 setAvailable(clock);             }           }           public void setAvailable(ImageIcon clock)          {             for (int i=0; i<=pictures.length; i++)             {                 if(pictures[i].getIcon().toString() == "blank.jpg")                 {                     pictures[i].setIcon(clock);                 }             }           }      }      //-------------------------  }       }


What does @ represent when dealing with Windows registry keys?  Examples:

When I navigate to "HKEY_LOCAL_MACHINE\SOFTWARE\Classes\WMP.PlayCD\Shell\Play" in The Windows  Registry, I find one REG_EXPAND_SE named MUIVerb on my Windows 7 system. However in its contents it's carrying "@%windir%\system32\wmploc.dll,-6503"  Now my question is: What does this @ character mean or do? I am an MS-DOS grown up and I haven't seen such a notation before. Should I interprete it as the @ like in an e-mail address? What is the final result. Does it become "C:\%windir%\system32\wmploc.dll,-6503" eventually ?


Is there any way to install Ubuntu 18.04 on Dell Alienware Aurora R11 (fitted with Nvidia 2080Ti GPU). Whenever I try to install 18.04 in it I end up getting a black screen (which I think is because of the graphics driver). . I am not able to really figure out what the problem is. I was able to flawlessly install Ubuntu 20.04 in it, but failed while installing 18.04. Any source of information/work around would be of great help to me. Thanks in advance.

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I'm getting this screen every time I post a question on the iOS app and try to view it.     For example:     Can this be fixed please?

I just now  from the Android app (the first I've actually published using it).  After telling me it was successfully submitted (which it was), I was taken to a screen in which I was presumably going to get to view my question. But on that very screen, I got a message saying: 'Loading the question failed.'  (The retry button didn't do anything.)    I'm using app version 1.0.11 on a HTC One running Android 4.3.  Here's what I did exactly:   Added tags to the question: , , then , then . (then removed ) Filled out the title Filled out the body Hit submit, without a preview.


It always puzzles me whenever I work on Lagrangian equations. It is easy to see that $L=T-V$  yields the correct equations of motion, but the question is, how do you get to that formula? Is it trial and error(making guesses and seeing if they actually give the correct equations), or does it have a deeper, more logical reasoning and thought behind it? Same is for all Lagrangians, from Hilbert action to the special relativistic one-how do you "derive" the lagrangian to get the correct equations. I hope you understand what I mean.

I have always been puzzled by how do you arrive at Lagrangians?  That is, how do you know that the functional you need to get Newton's equations is  $$L  =  T-V(x)~?$$ Do you derive the Lagrangian first somehow or do you just guess the one which would satisfy the action to give equation's of motion? (because then you would need to know the equations of motion first.) Also, is the Lagrangian always equivalent to something resembling $T-V$, or there are other ways to determine it? More generally, is the action known before you know the equations of motion, or vice versa?  What I really wish to know is, was the Einstein Hilbert action discovered before field equations were? If so, how? My major doubt is how do you come across the Lagrangian if you don't know the equations of motion, and you can't guess $L$ then?


I've a list of error in a XML file and I'm looking for a solution to get informations for one error. My file Looks like this.  <?xml version="1.0" encoding="utf-8"?> <List>   <ListingCodeErreur>     <Erreur ID="1100" ><Definition classe="0" Plage="Général" Text="Parameters    inside"/></Erreur>     <Erreur ID="1101" ><Definition classe="1" Plage="Général" Text="Parameters outside"/></Erreur>     <Erreur ID="1102" ><Definition classe="2" Plage="Général" Text="Unknow parameters"/></Erreur>   </ListingCodeErreur>   <ClasseErreur>     <Classe ID="0" ><Definition Text="Avertissement" Couleur='#145A14'/>/Classe>     <Classe ID="1" ><Definition Text="Stop" Couleur='#145A14'/></Classe>   </ClasseErreur> </List>   I've made a class   public class ListErreur {     public string ID { get; set; }     public Definition definition; }  public class Definition {     [XmlAttribute("Classe")]     public int Classe { get; set; }      [XmlAttribute("Plage")]     public int Plage { get; set; }      [XmlAttribute("Texte")]     public int Texte { get; set; } }   but I don't know how to create a function that receive the number in parameters and send informations back  Thanks you for your helps

How do I Deserialize this XML document:  <?xml version="1.0" encoding="utf-8"?> <Cars>   <Car>     <StockNumber>1020</StockNumber>     <Make>Nissan</Make>     <Model>Sentra</Model>   </Car>   <Car>     <StockNumber>1010</StockNumber>     <Make>Toyota</Make>     <Model>Corolla</Model>   </Car>   <Car>     <StockNumber>1111</StockNumber>     <Make>Honda</Make>     <Model>Accord</Model>   </Car> </Cars>   I have this:  [Serializable()] public class Car {     [System.Xml.Serialization.XmlElementAttribute("StockNumber")]     public string StockNumber{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Make")]     public string Make{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Model")]     public string Model{ get; set; } }   .  [System.Xml.Serialization.XmlRootAttribute("Cars", Namespace = "", IsNullable = false)] public class Cars {     [XmlArrayItem(typeof(Car))]     public Car[] Car { get; set; }  }   .  public class CarSerializer {     public Cars Deserialize()     {         Cars[] cars = null;         string path = HttpContext.Current.ApplicationInstance.Server.MapPath("~/App_Data/") + "cars.xml";          XmlSerializer serializer = new XmlSerializer(typeof(Cars[]));          StreamReader reader = new StreamReader(path);         reader.ReadToEnd();         cars = (Cars[])serializer.Deserialize(reader);         reader.Close();          return cars;     } }   that don't seem to work :-(


in blender 2.8 I pressed a button unintentionally, and as a consequence the mesh specifically only for this object had this change in which many edges do not appear even when I select the face that is still there for some reason does not appear

I have append a mesh (rex) from this .blend .  In edit Mode I see different vertices from objcet mode (see pictures). The vertices of belt are missing!  OBJECT MODE:   EDIT MODE:   How can I edit vertices of belt? Is It a bug?  This is my .blend  maybe can help.


If you want to map an equirectangular image texture to a sphere - like a map of the earth to a sphere - is there any necessity to use an UV map ? Or can I simply use the generated texture coordinates ? In general, when do you choose for UV unwrapping and when to use generated texture coordinates ?  I don't think this question is a duplicate with  question because these answers all start with the uv unwrapping method and I want to know if UV unwrapping or generated texture coordinates works best for my specific question. And I also would like to learn some general guidelines when choosing uv unwrapped vs generated texture coordinates

After reading  It seems that there is no perfect solution for getting rid of the stretch at the poles of UV spheres.  According to , icospheres can be used for stretch-less UV mapping:     All faces have the same area, which may be useful for certain types of UV mapping containing non-organic textures. An example that comes to mind is an isocahedral die or billiard balls where stretch must be minimized near the point where the number is printed onto the ball.   Incidentally, a lowish-poly billiard ball is exactly what I'm attempting to create.  However, my attempts at neatly unwrapping an icosphere have mostly failed (smart UV unwrap works perfectly for using baked textures, however I was hoping for something more like the example in the 6th post of , with a nice clean rectangular map).  How can an icosphere (I assumed the term "geosphere" in the thread was referring to a (geodesic) sphere made of triangles, like an icosphere) be cleanly unwrapped? Or if it's not possible, is there another way to do this which I'm missing?    I'm planning on using the resulting sphere in the BGE.


In c# when I always heard that is a good practice when creating a property for a class to include the get e set functions. For example:  public int Id { get; set; }   I think the reason to be a good practice is that if I want to change the behaviour I do not need to change the public interface of my class. Example:  public int Id  {     get;     set    {       if (value < 0)          value = 0;    } }   My question is, if I declare my property without the get and set methods I will not get the same effect? If I declare my property like this:  public int Count;   Can I change is behaviour without change the public interface? If I get the same effect then what’s the point of creating the get and set methods by default if in 90% of the time we don’t need them?

In C#, what makes a field different from a property, and when should a field be used instead of a property?


I know that the ring  $R=\mathbb{C}[x,y,z]/(xy-z^2)$ is not a field but an integral domain as you can easily show with Eisenstein criterion that $(xy-z^2)$ is an irreducible polynomial. Now I don't understand, why the irreducibility does not imply that $R$ is a field, because in other quotient rings I've seen before it was enough to show that " $I$ is irreducible then $R/I$ is a field ". Why here not? How can I show that $R$ is not a field here? Do I have to find a bigger Ideal than $(xy-z^2)$ in order to show that $(xy-z^2)$ is not maximal? I don't see any simpler way.

Given the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$, I've to check whether it's a field or an integral domain.   I'd say that $R$ is a field and an integral domain because $(xy-z^²)$ is irreducible in $\mathbb{C}[x,y,z]$ (Eisenstein with $x \in \mathbb{C}[x,y][z]$). However, I know that $R$ is not a field. I don't know what I've done wrong. Is my application of Eisenstein criteria false? How can I show that $R$ is not a field, but an integral domain?


Before anything, I'd like to clarify that I have no background in calculus (I'm still in school). I only try to learn calculus as a hobby. Please be gentle.  I'm trying to evaluate the aforementioned integral but the answer I got doesn't seem to match with 3 sources different sources that I found online. My process was to substitute in $x = \sec u, \ dx = \tan u\sec u\, du$. This led me to the answer $\tan (\mathrm{arcsec}\ x) - \mathrm{arcsec}\ x$. However after trying to check my answer I saw that  says it's $\arctan \left(\frac 1{\sqrt{x^2-1}}\right) + \sqrt{x^2-1}$,  says it's $-\arctan (\sqrt{x^2-1}) +  \sqrt{x^2-1}$, and this  says it's $-\mathrm{arcsec} \,x + \sqrt{x^2-1}$.  I plotted all four results on a . Symbolab and WolframAlpha only differ by a constant so I assume that both of them have the correct result whereas the video and I have the wrong ones. Also it can be seen that all the results are the same on the positive side of the x axis but things break down on the negative side.  My final questions are:    Where did the video creator and I go wrong? What is happening on the negative x axis?   EDIT: It seems this post might be a duplicate of . I hope this post doesn't get removed because I believe what I asked is a bit different from what was asked there. EDIT 2: Upon further inspection, I guess it's reasonable for this post to be removed.

My try, using $x = \sec(u)$ substitution:  $$ \begin{eqnarray} \int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x &=& \int \frac{\sqrt{\sec^2(u) - 1}}{\sec(u)}\tan(u)\sec(u) \mathrm{d}u \\ &=& \int \tan^2(u) \mathrm{d}u \\ &=& \tan(u) - u + C \\ &=& \tan(arcsec(x)) - arcsec(x) + C \end{eqnarray} $$  However, according to , the answer should be: $$ \int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x = \sqrt{x^2-1}+\arctan \left( \frac{1}{\sqrt{x^2-1}} \right)+C $$ When I derive this last answer I don't get back the integrand, but rather: $$ \frac{\mathrm d}{\mathrm d x}\left(\sqrt{x^2-1}+\arctan \left( \frac{1}{\sqrt{x^2-1}} \right)+C\right) = \frac{x}{\sqrt{x^2-1}}- \frac{x}{(x^2-1)^{3/2}\left(1+\frac{1}{x^2-1}\right)} $$  I don't know how to simplify this expression more. Also, I am unable to check whether my answer is correct because I don't know how to find the derivative of $arcsec(x)$.  Can someone check my calculations and tell me where I've done something wrong and how one can simplify the last expression to get back the integrand?