Is it true that for a k-manifold with boundary $M \subset \mathbb{R}^n$, and subset $A \subset M$, and k-form $w$ on $M$,  $\int_M w = \int_{M - A}  w + \int_A w$? (Call this Equation 1) I'm not sure here, because on the one hand, the integral $\int_M w$ is defined to be  $\int_c w$ where $c:W \rightarrow \mathbb{R}^n$ is a k-cube which is also a coordinate system. The fact that $c$ is a coordinate system means that $c$ is injective. Injectivity leads me to believe that Equation 1 is correct, since the above equation makes sense if I think about it pulled back to $[0,1]^k$. On the other hand, if I let $A = \partial M$, then $\int_M w = \int_{M - \partial M}  w + \int_{\partial M} w$. But the last term $\int_{\partial M} w$ doesn't make sense to me, since $w$ is a $k$-form but $\partial M$ is a $k-1$ manifold. So I'm tempted to also say that Equation 1 doesn't hold Which understanding is correct?

I'm confused whether the following statement is true: Let $K$ be a compact, orientable manifold of dimension $n$ with boundary and $\omega$ be a smooth $n$-form on $K$. Say for example $K$ is the closed unit disc in $\mathbb{R}^2$ and $\omega$ is any $2$-form on $\mathbb{R}^2$ restricted to $K$. Is the following statement true?: $$  \int_{K} \omega = \int_{\overset{°}{K}} \omega $$ , where $\overset{°}{K}$ is the interior of $K$.  I.e. can the boundary of a set be ignored when integrating over the set ? I think it should be true, since the boundary should be a set of measure zero in $K$, but is there a flaw with this reasoning ? Thanks for your help.


looking for some help with this.  I have a custom object named Annual_Sales_Targets__c with a master detail relationship to Contracts.  When a contract is activated, a workflow will kick off and send an email to various people.  The template is a visualforce template that creates a pdf with the contract details. I'm good up to this point.  I need help with querying the custom object to pull the corresponding sales targets and them as a table to the pdf.

I'm diving into visualforce and the standard controller for the first time and having trouble iterating over a single opportunity's related records. The below code produces an error:  <apex:page standardController="Opportunity"> <apex:pageBlock title="{!Opportunity.name}">     <apex:pageBlockSection title="{!Opportunity.Id}">         <apex:repeat value="{!Opportunity.Custom_object__c}" var="c">             <apex:pageBlockSectionItem>                 {!c.Name}             </apex:pageBlockSectionItem>         </apex:repeat>     </apex:pageBlockSection> </apex:pageBlock></apex:page>   The error I'm receiving is as follows:  Error: Unknown property 'String.Name'   I take from this that the Visualforce is not interpreting the {!c.Name} as the array of objects I thought it was but instead as a string. I am able to save the file when I remove {!c.Name} which makes me think that  is correct but, on the other hand, when substituting value="{!Opportunity.Account}" the code correctly retrieves the related Account. My instinct is that I'm not referencing the related child-objects correctly. I've been banging my head for a bit of time and was wondering if someone could provide some insight as to what is going on?


There are two advertised positions at one department. The department is approx. 30 people. So it is not a large institution where my two applications would be "lost". I am sure if I apply for both positions it will end up at the same people/commitee. Both position are for scientific staff, not for postdoc. The two positions are quite similar but there are some differences. I think I match one position more than the second one. Should I apply only to one position or can I apply for both? The application has to be done through online submission system, i.e. it is not possible just write to the cover letter that I am eventually interested in both positions.

The following question is not a general question about , but rather about applying to several positions within the same institution (regardless of applying to multiple other institutions as well).  Starting questions are, as follows. What are the potential effects, following such strategy? Mostly negative, mostly positive, or neutral? A situation often occurs, such that an institution advertises several positions that I believe I would fit, however, among those, only one (usually) is the best fit (my preference), but others are also suitable (decent fit).  Therefore, my main question is twofold: 1) is it a good strategy to apply to all suitable positions within an institution; 2) if Yes, should I mention my preference, for example, in an application letter (if No, I assume that the optimal choice is to apply to the position with the best fit)?


I'm having two oracle databases. A is used for production, B is some kind of staging instance where people are preparing content that is brought to the production system over night. It is a fully working structural clone of A that will also give you a preview of the upcoming next release. While the overnight synchronization is completely automatized (by scripts), structural changes are first applied to B and are two days later applied to A. This depends on manual operations and is build up on sql and sh scripts.  I'm wondering if there are features that lead to better maintainability and can be utilized for manually triggered synchronization. What would be the a modern approach automatizing structural database changes brought from B to A with Oracle Database 11g?  Please excuse this vague question. Since I'm not experienced in this topic I'm looking more for a starting point on what to read than a full solution to my problem.

I am interested to know what methods other people are using to keep track of changes made to the database including table definition changes, new objects, packages changes, etc.  Do you use flat files with an external version control system?  Triggers? Other software?


If $G$ is a finite group with the property that every non-identity element has even order, what could be said about $G$? For example the most trivial property might be that $G$ is a group of even order. I was wondering if more could be said about the structure of $G$.  Thanks!

Let $G$ be a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$  I know G is abelian since $ab = (ab)^{-1} = b^{-1} a^{-1} = ba$ for all non-trivial $a,b \in G$ so I have several questions remaining:    How do I prove $|G| = 2^n$? I'd like to say we use induction to prove this but I'm at a loss as to where I would start. Why is $G \simeq C_2 \times C_2 \times\cdots\times C_2$?   I've read several answers to question similar to this yet unfortunately most of them involve Galois Fields and vector spaces, both concepts I'm unfamiliar with. I'd greatly appreciate an intuitive proof.


Suppose we want to reach the point on earth which in relative terms is exactly on the opposite end of the sphere we call earth (I know it is not an exact sphere).  We either dig vertically downwards, pass through the center of the earth and come out on the other end as it happens in the cartoon. But taking a more pragmatic approach means using air travel.  If we face North, we could either go East or West to get to the directly opposite point on earth which means traveling a distance of half the circumference of earth.  Now here is my question, since the earth is spinning, does it mean that if we fly in direction opposite to which the earth spins, we shall reach the other end quicker? why or why not?  If this is the case, the the opposite is true also i.e it will take longer for us to reach the other end if we travel in the direction of earth spin. Is this taken into consideration in actual flight routes?

Say I'm flying from Sydney, to Los Angeles (S2LA), back to Sydney (LA2S).  During S2LA, travelling with the rotation of the earth, would the flight time be longer than LA2S on account of Los Angeles turning/moving away from our position?  Or, in the opposite direction, would the flight to Sydney be faster since the Earth turns underneath us and moves Sydney closer?  ===   Please ignore jet stream effects and all other variables; this is a control case in an ideal environment. By "dramatically" I suppose I mean a delay of 1 hour or more.


I have an old Kodak printer dock for an Easyshare camera but I'm missing the power source for it. The dock requires 24V 1.8A power so I bought a power supply marked 24V (24.2 measured) and 70W but the printer only powers up and then shuts down after a few seconds. If the problem is the supply amperage is too high can I use a resistor inline somewhere to lower the amperage? As you may have guessed, I've done some research but I'm new to this kind of thing.

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


I was always taught that a plural of a word ending in y was slept ies instead of ys. So for example:  City => Cities Country => Countries Bakery => Bakeries  but with Array the plural is Arrays despite this rule, why?

Words like "sky" and "money" have "ies" as a plural suffix (i.e. "skies" and "monies") but other words like "monkey" and "Emmy" do not ("monkeys" and "Emmys"). Is there a rule dictating the use of "ies"?


In The Lord of the Rings, we know of the five Istari sent to Middle-earth to help resist Sauron. There was Saruman, the White; Gandalf, the Grey; Radagast, the Brown; and Alatar and Pallando, the Blue. As per , we know that the Blue wizards seemed to have traveled together to the East, and that their mission seemed to have been unsuccessful. The question is--why were they both blue? Saruman is white; Gandalf is grey; Radagast is brown. Why were the remaining two the same color? I'd be curious about answers both in-universe and out.

The 5 known  wizards all had different colors (Saruman the White, Gandalf the Gray, Radagast the Brown and two blue ones, with the later changes of Gandalf to white and Saruman to 'many colors').  Is there a (preferably in-universe) explanation for the reason/symbolism behind the specific colors? The Wikia article linked above doesn't list any.


I've been browsing some class files and many of them have a (commented) \CharacterTable at the begin. What is the purpose of this table?  Example of such a table from  :  %% \CharacterTable %%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z %%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z %%   Digits        \0\1\2\3\4\5\6\7\8\9 %%   Exclamation   \!     Double quote  \"     Hash (number) \# %%   Dollar        \$     Percent       \%     Ampersand     \& %%   Acute accent  \'     Left paren    \(     Right paren   \) %%   Asterisk      \*     Plus          \+     Comma         \, %%   Minus         \-     Point         \.     Solidus       \/ %%   Colon         \:     Semicolon     \;     Less than     \< %%   Equals        \=     Greater than  \>     Question mark \? %%   Commercial at \@     Left bracket  \[     Backslash     \\ %%   Right bracket \]     Circumflex    \^     Underscore    \_ %%   Grave accent  \`     Left brace    \{     Vertical bar  \| %%   Right brace   \}     Tilde         \~}

What is the reason to insert the code below at the beginning of a style file? For example, the code below can be found on lipsum.sty.   %% \CharacterTable %%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z %%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z %%   Digits        \0\1\2\3\4\5\6\7\8\9 %%   Exclamation   \!     Double quote  \"     Hash (number) \# %%   Dollar        \$     Percent       \%     Ampersand     \& %%   Acute accent  \'     Left paren    \(     Right paren   \) %%   Asterisk      \*     Plus          \+     Comma         \, %%   Minus         \-     Point         \.     Solidus       \/ %%   Colon         \:     Semicolon     \;     Less than     \< %%   Equals        \=     Greater than  \>     Question mark \? %%   Commercial at \@     Left bracket  \[     Backslash     \\ %%   Right bracket \]     Circumflex    \^     Underscore    \_ %%   Grave accent  \`     Left brace    \{     Vertical bar  \| %%   Right brace   \}     Tilde         \~} %%   What is it for?


How do I show that     Let $n\ge0$. Then,   $$I:=\int_{0}^{1}(1-x^2)^ndx={(2n)!!\over (2n+1)!!}$$   Here, $m!!$ denotes the product of all positive integers $i \in \left\{1,2,\ldots,m\right\}$ that have the same parity as $m$.   My try: Using Binomial theorem  $$(1-x^2)=1-nx^2+{n(n+1)\over2!}x^4-{n(n+1)(n+2)\over 3!}x^6+\cdots$$  $$\int_{0}^{1}\left(1-nx^2+{n(n+1)\over2!}x^4-{n(n+1)(n+2)\over 3!}x^6+\cdots\right)dx$$  $$I=x-n{x^3\over 3}+{n(n+1)\over 2!}{x^5\over 5}-{n(n+1)(n+2)\over 3!}{x^7\over 7}+\cdots|_{0}^{1}$$  $$I=1-{n\over 1\cdot 3}+{n(n+1)\over 2!\cdot 5}-{n(n+1)(n+2)\over 3!\cdot  7}+\cdots$$  I need help can't see how it will simplify to ${(2n)!!\over (2n+1)!!}$

The actual question was to find the area bounded by the curve $y=\int_{-1}^{1}(1-x^2)^ndx$ and coordinate axes. But I haven't came across these type of problems with power $n$.


Two people flip a coin $n$ times each. What is the probability that they both get the same number of heads? If I let $k$ be the number of heads, I can get $$\frac{{n\choose k}^2}{2^{2n}}$$ which is correct so far: but I kind of don't understand why this is correct. Why doesn't $\frac{1}{2}$ show up anywhere? I would've expected $$(\frac{1}{2})^k (\frac{1}{2})^{n-k}$$ to appear somewhere. What I initially proposed was $\frac{\left(\frac{1}{2}\right)^{k}\left(\frac{1}{2}\right)^{n-k} {n\choose k}}{\left(\frac{1}{2}\right)^{2n}}$, why is this wrong? Anyway, i could continue with the first equation to produce $$\frac{{2n\choose n}}{2^{2n}}$$ as the final probability. But I think there should be a logical argument that leads straight to the final answer in one line, given the equiprobability events. What could that be? Edit: perhaps, the equiprobability explains my flawed second argument? I don't need to consider $\frac{1}{2}$ because both events are equally likely, so choosing is sufficient?

Say we have Tom and John, each tosses a fair coin $n$ times. What is the probability that they get same number of heads?    I tried to do it this way: individually, the probability of getting $k$ heads for each is equal to $$\binom{n}{k} \Big(\frac12\Big)^n.$$ So, we can do $$\sum^{n}_{k=0} \left( \binom{n}{k} \Big(\frac12\Big)^n \cdot \binom{n}{k}\Big(\frac12\Big)^n \right)$$ which results into something very ugly. This ugly thing is equal to the 'simple' answer in the back of the book: $\binom{2n}{n}\left(\frac12\right)^{2n},$ but the equality was verified by WolframAlpha -- it's not obvious when you look at it. So I think there's a much easier way to solve this, can someone point it out? Thanks.


I have developed a staff record system for my company. The problem im facing is that the staff leaves their systems logged on and even forget to logout. I want the system to logout the user after leaving the system idle for 10 minutes. I have virtually no idea on how to go about it. I need your help

I need to keep a session alive for 30 minutes and then destroy it.


I am thinking of installing Ubuntu 16.04 in My Laptop (HP Probook 440 G1). It has 4GB RAM. SO my question is How much space should I allocate for swap area?  Note:  1. I read some articles about it but some said 1.5 times of RAM, some said 2 times of RAM. I'm really confused here.  2. Can actually swap area increase my PC speed? Because I know that hard drive is too slow then RAM. Thanks in Advance.

I read many places that the rule of thumb for swap space is to double the amount of physical RAM. However, 32 GB does seem a LOT. Do I need that much? Do I need it at all with this high amount of physical RAM?


I have recently dual-booted Ubuntu to run alongside Windows 8.1 and now both are pretty slow and laggy.  I have a 500 GB HDD and I gave equal amounts of space to both (250 GB each) and now I want to give Ubuntu more space. I want to do a clean reset of Ubuntu and give it more space. I am running Ubuntu 16.04 LTS.

I would like to see a full how-to guide on how to install Ubuntu.


I'm stuck on the 3rd question asking how many candies does the candiest person in the world possess?

I encountered The Squirrel at "A tree."              |   |                                                                         |   |                     "   Hello, I'm The                        |             |                        Squirrel. I can                        |             |                      provide you candies,                     |             |                      and lots of things.                                    |                      I know how much you                                    |        _.-'''-,      love candies. But I                                    |      .'        `\     feel alone in this                                    |     /           /          forest.       "                         |        |    /      .--^_^                                                   |        |    |     /  C ,,\                                                           |    |    |   \  _.)                           ___                            |     \   |   /  \                   ____.----'.-'                            |      '-, \./ \)\)               .-' --  __.-'                   |            \        `-/   );/           ___/  - _.-'                        |             \_________''--'-'________.-' --    /                            |              -   --        -  -     -     __.-'                                              -    --    -     --   --  /                                                 _________________________.-'                                 He asks you some questions. What are the correct answers, and what is the reward for getting them correct?


In Harry Potter and the Half Blood Prince, Horace Slughorn, the former potions master, returns to teach at Hogwarts. In his class, unlike that of Snape's, students follow the standard potions book, Advanced Potion-Making by Libatius Borage.  However, following the instructions from the book, even Hermione is unable to prepare a perfectly correct potion. Only Harry succeeds, and that is just because he follows the instructions given by Snape in his copy of the book.  Given that Slughorn had been the potions master for decades before Snape, and that the book by Libatius Borage was probably followed for a similarly long duration, how did any one in the current generation who worked in the field of potions do it correctly? Wouldn't they have learnt from these texts themselves? If this was not the case, why weren't the standard texts updated?  Or, did the arrival of Snape redefine what "correct" was? If so, and that experienced and respected potioneers like Slughorn could recognize it, why didn't everyone change their way of doing things?

They don't seem to be giving the correct instructions in concocting the potions- as seen when Hermione isn't able to make her draught in Slughorn's class.


I am a Canadian citizen and a permanent resident of the US.   Would I be allowed entry into Canada to visit my elderly and ailing father during COVID-19 border restrictions?

I am a Canadian citizen currently in the United States.  After calling CBSA at 1-204-983-3500, they indicated that returning to Canada right now would be considered "non-essential". Does that mean as a Canadian citizen, I would be denied entry to Canada? Wouldn't this be illegal/unconstitutional to deny a Canadian citizen entry to Canada?


If $p$ is a prime number, how can I prove by contradiction that this equation  $x^{n}=p$ doesn't admit solutions in $\mathbb {Q}$ where $n\ge2$

It is well known that $\sqrt{2}$ is irrational, and by modifying the proof (replacing 'even' with 'divisible by $3$'), one can prove that $\sqrt{3}$ is irrational, as well.  On the other hand, clearly $\sqrt{n^2} = n$ for any positive integer $n$.  It seems that any positive integer has a square root that is either an integer or irrational number.        How do we prove that if $a \in  \mathbb N$, then $\sqrt a$ is an integer or an irrational number?      I also notice that I can modify the proof that $\sqrt{2}$ is irrational to prove that $\sqrt[3]{2}, \sqrt[4]{2}, \cdots$ are all irrational.  This suggests we can extend the previous result to other radicals.        Can we extend 1? That is, can we show that for any $a, b \in \mathbb{N}$, $a^{1/b}$ is either an integer or irrational?


The range of values of a, so that all the roots of the equation $$2x^3-3x^2-12x+a=0$$ are real and distinct, belong to

Find the range of values of $a$ for which the equation $$2x^3-3x^2-12x+a=0$$ will have all roots real and distinct.   what i tried  I found the derivative and got the roots of $f'(x)$ as $-1,2$ but now i need another condition to find values of a but i don't know what that condition should be.  Thanks in advance !


Trying to compile:  Glider.h:  class Glider { public:  static int RuleNumber;  static void SetRuleNumber(const int RuleNmb); };   Glider.cpp:  #include "Glider.h"  void Glider::SetRuleNumber(const int RuleNmb) { Glider::RuleNumber=RuleNmb; return; };   Produces:  1>Glider.cpp 1>Glider.obj : error LNK2001: unresolved external symbol "public: static int Glider::RuleNumber" (?  RuleNumber@Glider@@2HA) fatal error LNK1120: 1 unresolved externals   What is wrong with this code? Can't figure it out. Using newest Visual Studio.

Very simply put:  I have a class that consists mostly of static public members, so I can group similar functions together that still have to be called from other classes/functions.  Anyway, I have defined two static unsigned char variables in my class public scope, when I try to modify these values in the same class' constructor, I am getting an "unresolved external symbol" error at compilation.  class test  { public:     static unsigned char X;     static unsigned char Y;      ...      test(); };  test::test()  {     X = 1;     Y = 2; }   I'm new to C++ so go easy on me. Why can't I do this?


I wanna regex which will allow the following samples  1) abcd 2) abcd123 3) abcd-123   which should not allow   1) 123abcd 2) 123 3) 123-123

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?


For example, there are 3 tags on Stack Overflow:        How can I merge all 3? It is not interesting to have different versions. I would like to keep xacml and have the others as synonyms. Is that possible?  EDIT - Version synonyms  I cannot follow the instructions in the answer to the duplicate question. See below...

What are tag synonyms? How can tag synonyms be distinguished from "real" tags? How are new tag synonyms created? Who can create tag synonyms? How can I delete/reverse/undo bad tag synonyms? What are merged tags?


I am searching for the right website where I can ask Mantis bug tracker related questions? Can anybody suggest the appropriate site? It is a bug tracker application related query.  This is a specific question related with Mantis bug tracker.

There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.


Even though I have gone through the questions similar being asked, I am not clear as to what is Live Server and how to use it. Based on few documentation I tried to install Live Server and I feel that it is same as Server Installation. So what is the difference and how to use true Live Server. Please guide me. Manish Chawda

Hi I want to try Ubuntu 20.04 without installing it due to some driver issues in my laptop. But I already have 2 OS ( Windows 10 and Ubuntu 20.04 [Dualboot] ), so will trying Ubuntu mess with the already installed Operating systems? And I know how to make live usb and booting from it but don't know how to exit it and then bring my laptop back to normal. Tried finding procedure on internet but reliable results are not found.


I am trying to create a table in a beamer class document which includes some entries in math mode. Below I provide a very minimal working example of what I am trying to accomplish: \documentclass{beamer}  \begin{document}  \begin{frame}  \begin{tabular}{cc} $n$ & $m$ \\  2 & 3 \\ \end{tabular}  \end{frame}  \end{document}  This code causes a fatal error to occur and no pdf file is produced. I am using texmaker with SumatraPDF. Why does this code produce a fatal error?

I have this problem where I can't built slide documents with beamer every time I include a math environment as simple as $\mu = A$. The log file posts this message at the end:  !pdfTeX error: miktex-pdftex.exe (file mathkerncmssi10): Font mathkerncmssi10 a t 657 not found  ==> Fatal error occurred, no output PDF file produced!   I understand that the file (mathkerncmssi10) that is apparently missing is part of the package sansmathaccent, but the package is already there and updated.  This is driving me crazy, I would appreciate any help.    Sure, I tried this with several examples. I can post this one  \documentclass{beamer} \usepackage[latin1]{inputenc} \usetheme{Warsaw} \title[Make a LaTeX presentation using Beamer]{Introduction  to Beamer\\How to make a presentation with LaTeX?} \author{Nadir Soualem -- Astozzia} \institute{Math-linux.com} \date{Jule 13, 2007} \begin{document} \begin{frame} \titlepage \end{frame} \begin{frame}{Introduction} This is a short introduction to Beamer class. $\mu=A$ \end{frame} \end{document}    By the way, it turns out that I just tried this one in another PC and works fine.


In this post I look rather for clarification than technical solution (the problem is already solved, see below).  I just upgraded from 14.04 to 16.04 and installed a fresh Firefox, which happened to be Quantum 57.0.3 (64 bit). Flash didn't work, thus I installed flashplugin-installer, which has in its description:     The Adobe Flash Player plugin will work with a range of web-browsers >including, limited to:    * Firefox   Unfortunately it didn't help. What helped was the installation of browser-plugin-freshplayer-pepperflash instead. The description of the latter package states:     The main goal of the project is to get PPAPI (Chrome) plugins   working in Firefox (and any other web-browser supporting NPAPI plugins   I wanted to understand why the former package didn't work, thus I started to read and found out  that Firefox since ver 52 does not support NPAPI plugins, except for Adobe Flash. Therefore, it seemed that having adobe-flashplugin installed should be enough and one does not need to deal with the NPAPI/PPAPI issues. Indeed, after I removed browser-plugin-freshplayer-pepperflash and sticked to adobe-flashplugin, everything worked fine. Thus, I suspect that the crux was in one of the packages required by browser-plugin-freshplayer-pepperflash, not that package itself.   Would the conclusion be that Firefox in 16.04 ships without Flash support, even when adobe-flashplugin is present (I wonder why)?  If so, some users might bump at this problem, just as I did.

What is the most straight forward way to downgrade Firefox 57 to Firefox 56?   This is to have more time to wait for working replacements for legacy extensions.


I am having a problem with lighting my room with the sun.  I don't think its a problem with my window but just in case I put the node group. No matter how much strength I put on it doesn't light up the room.As long as the room has a ceiling, even if I put the sun in the middle of the room, it will not light up. When I turn off cast shadow however the room lights but I know it is not the way lighting is intended. I am fairly new to blender .

Here's a sample scene:  A room with a window, a point light to project light into the room, an HDR environment outside the room and a nice Image by Rembrandt that should be somewhat reflected on the glass:    Using a standard glass shader on the window, the direct light from the lamp does not shine into the room, regardless of how bright that light is. So I can't recreate the impression of hard day light, with clearly defined areas of light and shadow.    Adding a transparent shader to the glass shader I get a very pleasing result. The light from the lamp illuminates into the room creating defined shadows, transparency seems unaffected, to see the HDR in the background, the refection seem correct to me (I also like how I get double reflections from the thick glass).    Even though I am quite happy with this solution, I've gotten a few comments on making a setup with light path nodes controlling the mix of transparent and glass. The biggest issue is that the reflections on the glass are brighter than what they should be.  So the question is: By using this approach am I messing up any of the qualities of glass? And if so, what would make a proper glass shader that is realistic, in terms of letting direct light through, while keeping reflections, refraction and transparency?  A file to play with:    The HDR image used was created by


An ideal parasite is a parasite which thrives within a host without harming it (according to my NCERT textbook).   Then, quite obviously, why hasn't that happened yet? I mean, natural selection can lead to such a species, which is beneficial to us and also, not at all detrimental to the parasite.

I have yet to understand why so many viruses or bacteria haven't evolved to be harmless (specifically, I don't know of any harmless virus). I think it would be greatly beneficial for a virus to control his population and use natural transfer channels that dont cause discomfort(like feces), since it would be allowed to stay in an organism indefinitely and would have a lifetime channel for transmission, hopefully getting to be the most common strain.  So, why have viruses not evolved to be harmless to their hosts?


I'm having some trouble converting a value from double to int. After my conversion of the number with value of 1 and 2 in the tenth position, the value being converted is actually deducted by one. Can someone help me fix this problem? #include <iostream> #include <cstring> #include <cmath>  typedef char* BookName;  using namespace std;  class DecimalBookInfo {     public:         DecimalBookInfo(char inName[], double number);      private:         BookName name;         double code;         bool verifyCode(double number);  };  int main() {     char name[] = "TestBook";     DecimalBookInfo testBook(name, 230.1); }  DecimalBookInfo::DecimalBookInfo(char inName[], double number) {     // initiate new cstring     name = new char[strlen(inName)];     strcpy(name, inName);          if (verifyCode(number))         code = number;     else     {         cout << "Wrong code...\n";         exit(1);     } }  bool DecimalBookInfo::verifyCode(double number) {     double areaCode = floor(number);     cout << areaCode << endl;     double subCode = ((number - areaCode) * 100.0);      cout << static_cast<int>(subCode) << endl;      if (areaCode > 999 || areaCode < 100 ||      ((subCode - 10) != 0))     {         return false;     }      return true; }  The result is: 230 9 Wrong code... so I'm not sure why this is so. The number after 230 is supposed to be 10. Thank you

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I'm making a website and after it's main content I want to have a nice footer at the bottom. My problem is, that due to dynamically loaded content, I can not predict how long it will be. So If I just put a div with my footer at the end of a body it could get awkwardly in the middle of page if the content is short. On the other hand I've tried using bootstrap's .fixed-bottom but it overlaps my content if it is long. I would not like having some script that checks how long my page is and dynamically alternating the position of my footer. Is there a nice simple solution to my problem? Preferably using bootstrap or simple custom css.

I have a simple 2-column layout with a footer that clears both the right and left div in my markup.  My problem is that I can't get the footer to stay at the bottom of the page in all browsers.  It works if the content pushes the footer down, but that's not always the case.


I recently fixed my old laptop and I was wondering if I can use it as a second monitor for my PC, even though my PC is using an ethernet cable, as my motherboard doesn't support wifi.

Is it possible to make my laptop's screen act as a second monitor for my desktop computer?


Let $A, B \in M_{2}(\mathbb{R})$ two matrices such that $(A-B)^2=O_2$.   Prove:      1) $\det(A^2-B^2)=(\det(A) - \det(B))^2$      2) $\det(AB-BA)=0$ iff $\det(A)=\det(B)$     My attempt  Using Cayley it follows $\det(A-B)=0$ and $tr(A-B)=0$ therefore $tr(A)=tr(B)=t$ and $A^2 = tA-\det(A)I_2, B^2 = tB-\det(B)I_2$.   From the last two equalities: $A^2-B^2=t(A-B) - (\det(A) - \det(B))I_2$  Here I've got stuck, because applying determinant to the last equality doesn't seem to lead somewhere.

Let $A,B \in M_2(\mathbb{R})$ be two matrices such that $(A-B)^2=O_2$.      Prove $\det(A^2 - B^2)=(\det(A) - \det(B))^2$.   OBS. $O_2$ is the zero matrix    Let $D=A-B$ then $D^2=O_2$ therefore, using Cayley Hamilton theorem, we get $tr(D)=\det(D)=0$. It follows $tr(A)=tr(B)=t$ and, from here, $A^2 -B^2=t(A-B) + (\det(A) - \det(B))I_2$  This is all I could get.  UPDATE  The matrices are from $M_2(\mathbb{R})$. Sorry for misleading you.


Does anyone remember a cartoon show from probably somewhere in 2000 to 2015? It involved magic cubes, a yellow robot sidekick, a big Mexican mechanic, and a girl who couldn't sing.

Can you please help me find this animated show? There is a four member team with two boys and two girls. The boys can summon, with their stones, a rock golem (black wearing summoner) and a robot (orange wearing summoner). The two girls can summon something like a dragonfly (green wearing summoner, little girl) and the blue girl, I don't remember what she can summon.  I don't know where the animated show comes from.  By throwing the stone, they activate the stone's power. Each stone has different characters on it. When you don't match them correctly, you get a rebound effect.


Please give me some hints or solution for this limit. I had it on my exam and I'm curious how to solve it. $$ \lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x} $$

I tried to evaluate $$\lim_{x\to0}\frac{(1+x)^{1/x}-e}x$$but all my efforts were in vain . L'Hospital rule becomes very complicated.


Can we have a set which is called by a small greek letter, e.g. a set $\alpha$?

If capital letters are supposed to be sets, why is $N$ used as a number? For example, in this definition of a Cauchy Sequence it says:      A sequence ${p_n}$ in a metric space $X$ is said to be a Cauchy sequence if for every $\epsilon\gt 0$ there is an integer $N$ such that $d(p_n,p_m)\lt \epsilon$ if $n\ge N$ and $m\ge N$.   Is this saying that for an arbitrarily large $n$ and $m$ this is true? I'm confused on why it uses $N$ when I've been told that capital letters are supposed to be sets.


I want to display a property in the viewport without using a modal operator. is it possible? I found , but I did not understand how I can use (I started with python).

At the moment, i draw ma text in viewport with this modal operator:  _handle = None  def modal(self, context, event):     context.area.tag_redraw()     if not context.window_manager.show_text.enabled:         return {'CANCELLED'}     return {'PASS_THROUGH'}  @staticmethod def handle_add(self, context):     VIEW3D_OT_ADH_display_text._handle = bpy.types.SpaceView3D.draw_handler_add(            draw_text_callback,             (self, context),            'WINDOW', 'POST_PIXEL')  @staticmethod def handle_remove(context):     _handle = VIEW3D_OT_ADH_display_text._handle     if _handle != None:         bpy.types.SpaceView3D.draw_handler_remove(_handle, 'WINDOW')     VIEW3D_OT_ADH_display_text._handle = None  def invoke(self, context, event):     if context.window_manager.show_text.enabled == False:         context.window_manager.show_text.enabled = True         VIEW3D_OT_ADH_display_text.handle_add(self, context)          return {'RUNNING_MODAL'}     else:         context.window_manager.show_text.enabled = False         VIEW3D_OT_ADH_display_text.handle_remove(context)          return {'CANCELLED'}      return {'CANCELLED'}   Is it possible to draw my text without modal operator and update it with:  bpy.app.handlers.scene_update_post   when my mesh is updated please ?


What is the correct way of getting the  (more or less what the now deprecated GetVersionEx does, but without lying).  Please don't tell me that I shouldn't use version checking, or that I should use . It's not for version checking but for generating a report. And it should also work in future versions of Windows (e.g Windows 11 or whatever)

I know I can call the GetVersionEx Win32 API function to retrieve Windows version. In most cases returned value reflects the version of my Windows, but sometimes that is not so.  If a user runs my application under the compatibility layer, then GetVersionEx won't be reporting the real version but the version enforced by the compatibility layer. For example, if I'm running Vista and execute my program in "Windows NT 4" compatibility mode, GetVersionEx won't return version 6.0 but 4.0.  Is there a way to bypass this behaviour and get true Windows version?


I'm install OpenJDK Java on my Ubuntu 12.04 desktop using the following command:  sudo apt-get install openjdk-7-jdk   But I keep having java not found:  The program 'java' can be found in the following packages:  * default-jre  * gcj-4.6-jre-headless  * openjdk-6-jre-headless  * gcj-4.5-jre-headless  * openjdk-7-jre-headless Try: sudo apt-get install <selected package>   What's the reason here? I tried reinstall, even deleting /usr/lib/jvm but it still doesn't work.  There is no java in /usr/lib/jvm/java-1.7.0-openjdk-amd64/bin, only javac and other things. Also when I run javac, this is the error:  javadoc: error while loading shared libraries: libjli.so: cannot open shared object file: No such file or directory

How do I install Java, including in my browser, so websites with Java work?


I see a lot of questions in various sites about why the 2 theories are or aren't  incompatible, I'm satisfied as to why that's the case.  However it has been mentioned that both theories make predictions about phenomena that contradict or are incompatible, and I've been unable to find any examples.  What are the conflicting/contrary/incompatible predictions made by General Relativity versus Quantum Mechanics? Or are the claims false?

It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?  E.g. relativity theory uses a space-time continuum, while quantum theory uses discrete states.  I am not merely looking for a solution or rebuttal of such opposites, more for a survey of the field out of interest.


I guess it has something to do with the precision but I don't understand it. I have this piece of code that should perform rounding to 2 places (value is the input):  Dim a As Double Dim b As Double Dim c As Double Dim result As Double  a = CDbl(value) * 100 b = a + 0.5 //because Int in the next line performs floor operation, 0.5 is added to ensure proper rounding, example for 123.5: Int(123.5) = 123 but we need Int(123.5 + 0.5) = 124 c = Int(b) result = c / 100   The thing is, it doesn't work properly for a value 134.605. While debugging I found out that a value is calculated incorrectly. In fact I have checked this:  ?13460.5 = (134.605*100) False ?(134.605*100) - 13460.5 -1,02318153949454E-12   And I'm stuck. I can either rewrite the rounding function differently, but I don't have an idea for it without *100 multiplication. Or I could find out how to make *100 operation work correctly for all the values. Could anyone try to explain me why it happens and suggest a solution?

I have trouble comparing 2 double in Excel VBA  suppose that I have the following code  Dim a as double Dim b as double a = 0.15 b = 0.01   After a few manipulations on b, b is now equal to 0.6  however the imprecision related to the double data type gives me headache because  if a = b then  //this will never trigger end if   Do you know how I can remove the trailing imprecision on the double type?


The  for my combined Stack Exchange profiles shows 7 sites:  But it doesn't show  or , and I have over 200 reputation on both of those sites.  According to the  on my network profile, the combined flair "is only updated once every 24-36 hours."  But if you look at my , I went over 200 rep on July 27 at 19:35, which was over 101 hours ago:  Also, my  shows that I went over 200 rep on July 28 at 17:14, which was over 79 hours ago:  I found  to a different flair issue that said "if you don't see it changing within 48-96 hours let us know", so I figured I'd let you know about this issue.

So, recently, perhaps out of sheer boredom, I have decided to go around and collect scores of > 200 on different SE websites. Some I have gotten reputation through answers, some through questions, and, in the case of skeptics, I got the last 20 points for editing out people's mistakes (because I'm just not that skeptical).  This does leave me wondering though, how many of these sites will give me icons on my flair?    And now, your obligatory .


I have a Mac mini that runs a Samba server through the "file sharing" option in settings.  I can create files on it and my clients can access it. However, creating files on the client end causes my Mac not to have access to those files.   There doesn't seem to be a way to change that on the client end. I tried going into properties and unchecking the "read only" option on the file but it gets checked again when I hit "apply." My clients are Android and Windows.

We just got a new iMac are using the /Users/Shared directory to store media assets (pictures, audio, video) that we want accessible to all users on the machine. After copying over all the files initially, we set the desired permissions and then applied the same permissions to all directory contents recursively. This is working fine, except then whenever someone creates a new file or directory, it does not have the same permissions and we have to repeat the whole permissions process before everyone can access it.  Is there a way that we can set permissions for all new files/directories created within that directory?


I've tried to follow many posts about this general issue but have not yet understood the problem or how to fix it.  In this example, the color overlaps the left border, or the left border does not display. After dvips. I am using dvips because of pstricks.  In other words, the border seems to look okay when zoomed in in xdvi, but not after converted to postscript. Before zooming in the border (left border of fist cell in first row) appears to be missing in xdvi as well.  How can I cause the border to display or not be overlapped?  \documentclass{article} \usepackage{colortbl} \begin{document} \begin{tabular}{|l|l|} \hline \multicolumn{2}{|l|}{\cellcolor{yellow}blarg blarg} \\ \hline & y \\ \hline \end{tabular} \end{document}

When I change the background color of a cell in a table, the color covers the borders, however I want the horizontal lines to remain.  I have a simple command \cellcolor[gray]{0.9} in my table. Can anybody help me with this problem?


Got a strange bug.  The output of following is:  RANGE: 100000 - 125000 RANGE: 100000 - 125000 RANGE: 100000 - 125000 RANGE: 100000 - 125000   And this is wrong! If I add an extra local var in the loop, the output is right!  int ax = i; var curtask = Task.Run(() =>Work(ax, blocksize, size));   Output:  RANGE: 75000 - 100000 RANGE: 0 - 25000 RANGE: 25000 - 50000 RANGE: 50000 - 75000   (it's ok that the order isn't kept)  So the i var is not given to the task on creation? I find this situation very dangerous. Normally I would have trust in the parallels!  private static void Work(int startIndex, int blocksize, int maxSize) {     int end = startIndex + blocksize;     Trace.WriteLine($"RANGE: {startIndex} - {end}");     Console.WriteLine($"RANGE: {startIndex} - {end}"); }  static void Main(string[] args) {     int i = 0;     int size = 100000;     int blocksize = size/4;     int taskcount = 0;     var tasks = new List<Task>();      while (i < size)     {         //THIS WORKS!!!         //int ax = i;         //var curtask = Task.Run(() =>Work(ax, blocksize, size));          var curtask = Task.Run(() => Work(i, blocksize, size));         taskcount++;         tasks.Add(curtask);          i = i + blocksize;     }     Task.WaitAll(tasks.ToArray());     Console.WriteLine("DONE");     Console.ReadKey(); }

I met an interesting issue about C#. I have code like below.  List<Func<int>> actions = new List<Func<int>>();  int variable = 0; while (variable < 5) {     actions.Add(() => variable * 2);     ++ variable; }  foreach (var act in actions) {     Console.WriteLine(act.Invoke()); }   I expect it to output 0, 2, 4, 6, 8. However, it actually outputs five 10s.  It seems that it is due to all actions referring to one captured variable. As a result, when they get invoked, they all have same output.  Is there a way to work round this limit to have each action instance have its own captured variable?


I installed Ubuntu 18.10 and windows 10 as dual OS but whenever i restart from one of the OS i will be given an option to choose the operating system to boot or Ubuntu boot automatically after some seconds. I will love to make the last OS used to boot automatically how can i do this?

says the following:     Saving an OS can be achieved by running sudo grub-set-default if   DEFAULT=saved is set in /etc/default/grub. It may also be saved if   GRUB_SAVEDEFAULT=true is also set in /etc/default/grub. In this case,   the default OS remains until a new OS is manually selected    from the   GRUB 2 menu or the grub-set-default command is executed.   I put the lines DEFAULT=saved AND GRUB_SAVEDEFAULT=true in /etc/default/grub, and ran sudo grub-set-default.  Here is the output:  $ sudo grub-set-default entry not specified. Usage: grub-set-default [OPTION] entry Set the default boot entry for GRUB.    -h, --help              print this message and exit   -v, --version           print the version information and exit   --boot-directory=DIR    expect GRUB images under the directory DIR/grub                           instead of the /boot/grub directory  ENTRY is a number or a menu item title.  Report bugs to <bug-grub@gnu.org>.   Am I not following the documentation correctly?  What's the correct way to do this?


I encountered a question that I really can't figure out:  Suppose your hypothesis class(H) consists of decision trees with 7 nodes that splits on only one feature. How to calculate the VC dimension of H?  I understand all the trees in the hypothesis class have 7 binary splits. But I really don't understand how to calculate the VC dimension of H?  Thank you!

What is the  of a decision tree with k splits in two dimensions? Let us say the model is CART and the only allowed splits are parallel to the axes.  So for one split we can  and then for any labeling of the points we could get perfect prediction (i.e.: shattered points)  But what about 2 splits, or any general k?


Five cards are numbered as the following $$5 , 5 , 5 , 4 ,4$$ Three cards are chosen randomly , whats the probability that the third card is numbered 4 ? Without replacement My turn Let the first two cards are numbered 5 and the third is4 So we get $$3C1 \times 2C1 \times 2C1$$ Let the first is 5 and the second and the third are 4 So  $$3C1 \times 2C1 \times 1$$  The same thing happens if the first and the third are 4 and the second is 5 so The probability is $$\frac{ the sum }{5P3}$$ Is the solution correct ?

We had this question arise in class today and I still don't understand the answer given. We were to assume that drawing cards are independent events. We were asked what the probability that the second card drawn is a queen if we take two from the deck. The answer given was 4/52, which seems counter-intuitive to me. How is the probability still 4/52 if there was a card drawn before it? What if the first card drawn was a queen?


Every few months I have moved data out of my mac computer onto a hard drive because of this problem. I now again have this alert in the Terminal: Your disk space is critically low. Older terminal scrollback contents may be automatically discarded to conserve VM backing store.:  And this one on the desktop: Your disk is almost full. Save space by optimising storage:  I click on Manage and see that system storage is taking 80 GB on a 128 GB SSD drive:  I cleared more files yesterday and had 6 GB of storage free. A few hours later, free space went down to 3 GB, all taken by system storage. I will soon have nothing left on the computer but system storage, and then have to reinstall it and go back to the . I have run this command to find files larger than 1 GB; it shows only the Spotlight file with 4 GB. $ sudo find /Volumes/Macintosh\ HD/ -size +1G  2>/dev/null Password: /Volumes/Macintosh HD//.Spotlight-V100/Store-V2/CA9AE856-FB94-4765-9028-38E04BEC9683/0.indexArrays  What Terminal commands could I run to identify the source of this runaway system storage and to clear it? Note: Similar to the unanswered  , except that I provided more textual details on the alert and that I am looking first to identify the issue with a Terminal command.

Every few days I get notices on my MacBook that it's running or run out of hard drive space. Curiously, restarting the computer will enable me to recover gigabytes of space (this past time, it was able to recover about 2.2GB). However, I can't identify anything in my personal activity that consumed that space.  It's possible that it's a rogue iTunes podcast or a huge software update that my Mac is automatically downloading - would either of these reclaim the space upon a restart?  One possibility that I can think of is that FileVault has some sort of disk leak, allocating but not freeing files. Does this make sense? Is there a tool that I can run to determine where this space is going? Assuming it is FileVault, should I try to disable it? What's the best way to turn of FileVault on a nearly full computer?


I want to sent files over a private network from Ubuntu 16.04 to a windows box.(Its an IOT box) I am able to scp into other linux devices but how do I send files to windows? I want to do this via terminal? As I am building a console application. I want to do this entirely from the Ubuntu ask the windows box is remote. Thanks.

I'm using Ubuntu 11.10, and am trying to mount a freenas server.  I have the server set to share in cifs and nfs with no luck.   I have tried smbmount //192.168.1.### /mnt/  I am not new to Ubuntu but am nowhere near a power user, so I'd prefer a GUI option if available.  How do I mount a cifs share in 11.10?


lets assume I am user(with no rights) and I need to change my shell as a default to /bin/bash by editing a file. So where I can find a file for a specific user where I can edit my default shell and set it permanently without involving an administrator.   And also, is there any command to change my own shell on top of that I can edit in the file directly.   I have tried to find something, but is only telling commands and files only if you have root access.  Thank you.

I am using my school's computers and would like to use zsh instead of bash. I'd like to make it the default shell, but I cannot run a command such as $ chsh -s $(which zsh) because I don't have admin privileges.   Is there a way I can put something in my .bashrc or something that automatically calls zsh when it opens as a workaround?   To clarify, zsh is already installed.


Let m be a positive integer greater than 1.  Prove that if r is a primitive root of m, then $r^{φ(m)/2} ≡ -1$ (mod m).

Let $p$ be an odd prime, and let $g$ be a primitive root modulo $p$. Prove that $g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$.  I've seen this solution on the math stack exchange but most of the solutions use quadratic reciprocity. Unfortunately, I skipped that section because it seemed very hard, but the proof that  $g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$ seems easy with it.  Is there another way to solve this This question is proposed in the chapter of Finite Abelian Groups.  DEF:In elementary number theory, an integer $g$ is called a primitive root for the modulus $n$ if $\mathbb{Z}_n^\times$ is a cyclic group and $[g]_n$, is a generator for $\mathbb{Z}_n^\times$.


How can I change my desktop background from command line?

I have a script that updates my desktop background every day with the NASA APOD. Since upgrading to 11.10, that script stopped working, presumably because I'm using gconftool-2 to actually update the desktop background. Is there a new way to do this under Unity?


A square plate of metal is expanding under the action of heat, and its side is increasing at the uniform rate of 0.1 cm per hour. What is the rate of increase of its area at the moment when the side is 16cm long?

.... At what rate is the perimeter changing when the side is 10cm long?  I am not very good at these related rate questions so if anyone could help me through it that would be great.   From what i know and if i am correct, this is what i have so far..  ds/dt = 5 A = s^2   Let A be area in cm, Let s be the length of the side, Let t be the time in seconds   So we are looking for dA/dt when s = 10? If i am correct?  If so then would this be the formula?  dA/dt = d/dt (s^2) = 2s(ds/dt)?    Now i am a little confused.


It is my first question on any stackoverflow site, so sorry if I have not researched the current available questions and answers enough (I tried), but I have thoroughly searched both the internet and the english stackoverflow site as well as I could (I was not sure as to what tag I should have searched to get the correct answer to my question).  That aside I am stuck as to whether I am using a possessive noun or a non possessive noun.  The question is pretty simple which sentence is correct.   Many other online IQ tests rely on knowledge orientated questions to test ones IQ.   Or   Many other online IQ tests rely on knowledge orientated questions to test one's IQ.   I understand one is correct and one is not, but it would be most helpful if someone could explain what the true difference between the two is, and when I should use one and not the other.  I am no English language expert, and I am sure this has been answered many times on this site but I could not find it, I am sure as I continue to use the stackoverflow websites I will become more efficient at finding answers to my questions. If anyone has any tips on how to do this I would be most grateful, maybe a little FAQ on how to search?

I've been confused about this as long as I can remember. Should it be:     One should do ones duty.   or     One should do one's duty.   I'm guessing it should be the latter. But that doesn't sit well with the possessive pronoun 'its'. For example:     It is its own purpose.   vs.     It is it's own purpose.   Here, the former seems clearly correct.


I was trying to think of a proof of the following proposition:     Let $K$ be a field. Then $R=K[x_1,...,x_n]$ is not a PID for $n>1$.   So here's what I've written so far:   Suppose $R$ is a PID and consider the ideal $I=\langle x_1,x_2 \rangle$. Then $I=\langle f \rangle$ for some $f \in R$. In particular, we have $$(1) \space x_1=gf$$ $$(2) \space x_2=hf,$$  for $g,h \in R$. But then, from (1), we must have $\deg_{x_2}(f)=0$ and $\deg_{x_1}(f) \in \{0,1\}$. Analogously, from (2) it follows that $\deg_{x_1}(f)=0$ and $\deg_{x_2}(f) \in \{0,1\}$. In conclusion, $\deg_{x_1}(f)=0=\deg_{x_2}(f)$.  So the polynomial $f$ must be a non zero constant in $K$ or it must be a polynomial which doesn't have $x_1$ or $x_2$ as one of its variables. For the first case, I know how to arrive to a contradiction, for if $f=k \in K \setminus \{0\}$, then $1 \in \langle x_1,x_2 \rangle$, so $$1=hx_1+hx_2$$  Evaluating at $(x_1,...,x_n)=(0,...,0)$, we conclude $1=0$, which is absurd.  I am not sure what to do in the other case, I don't even know a notation to express an arbitrary polynomial of several variables. I would appreciate some help to conclude the proof. Thanks in advance.

Let $R$ be a field. Show that the polynomial ring $R[x_{1},...,x_{n}]$ is not a PID if $n>1$.    How do I show this?   So far, I've shown that $(2)+(x)$ wouldn't be principal in $\mathbb{Z}[x]$ so I was thinking of showing that $(x_1)+(x_2)$ would not be principal.


when I try to join a Minecraft server running on 1.7.10, it just crashes when I join it. I'm trying to join invadedlands. The IP is right, but it crashes me after "Logging in..."  Crash log:  ---- Minecraft Crash Report ---- // My bad.  Time: 6/24/19 10:22 AM Description: Ticking screen  java.lang.IndexOutOfBoundsException     at java.nio.Buffer.checkIndex(Buffer.java:540)     at java.nio.DirectIntBufferU.get(DirectIntBufferU.java:253)     at bma.a(SourceFile:271)     at bma.a(SourceFile:220)     at bao.a(SourceFile:1694)     at bao.a(SourceFile:1652)     at bjb.a(SourceFile:125)     at hd.a(SourceFile:70)     at hd.a(SourceFile:13)     at ej.a(SourceFile:174)     at bcx.e(SourceFile:78)     at bao.p(SourceFile:1343)     at bao.ak(SourceFile:774)     at bao.f(SourceFile:728)     at net.minecraft.client.main.Main.main(SourceFile:148)   A detailed walkthrough of the error, its code path and all known details is as follows: ---------------------------------------------------------------------------------------  -- Head -- Stacktrace:     at java.nio.Buffer.checkIndex(Buffer.java:540)     at java.nio.DirectIntBufferU.get(DirectIntBufferU.java:253)     at bma.a(SourceFile:271)     at bma.a(SourceFile:220)     at bao.a(SourceFile:1694)     at bao.a(SourceFile:1652)     at bjb.a(SourceFile:125)     at hd.a(SourceFile:70)     at hd.a(SourceFile:13)     at ej.a(SourceFile:174)     at bcx.e(SourceFile:78)  -- Affected screen -- Details:     Screen name: bcx  -- Affected level -- Details:     Level name: MpServer     All players: 0 total; []     Chunk stats: MultiplayerChunkCache: 0, 0     Level seed: 0     Level generator: ID 00 - default, ver 1. Features enabled: false     Level generator options:      Level spawn location: World: (8,64,8), Chunk: (at 8,4,8 in 0,0; contains blocks 0,0,0 to 15,255,15), Region: (0,0; contains chunks 0,0 to 31,31, blocks 0,0,0 to 511,255,511)     Level time: 0 game time, 0 day time     Level dimension: 0     Level storage version: 0x00000 - Unknown?     Level weather: Rain time: 0 (now: false), thunder time: 0 (now: false)     Level game mode: Game mode: survival (ID 0). Hardcore: false. Cheats: false     Forced entities: 0 total; []     Retry entities: 0 total; []     Server brand: ~~ERROR~~ NullPointerException: null     Server type: Non-integrated multiplayer server Stacktrace:     at bjf.a(SourceFile:289)     at bao.b(SourceFile:1972)     at bao.f(SourceFile:737)     at net.minecraft.client.main.Main.main(SourceFile:148)  -- System Details -- Details:     Minecraft Version: 1.7.10     Operating System: Windows 10 (amd64) version 10.0     Java Version: 1.8.0_51, Oracle Corporation     Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Oracle Corporation     Memory: 104190592 bytes (99 MB) / 167772160 bytes (160 MB) up to 2147483648 bytes (2048 MB)     JVM Flags: 8 total; -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx2G -XX:+UnlockExperimentalVMOptions -XX:+UseG1GC -XX:G1NewSizePercent=20 -XX:G1ReservePercent=20 -XX:MaxGCPauseMillis=50 -XX:G1HeapRegionSize=32M     AABB Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used     IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0     Launched Version: 1.7.10     LWJGL: 2.9.1     OpenGL: GeForce GTX 1060/PCIe/SSE2 GL version 4.6.0 NVIDIA 388.16, NVIDIA Corporation     GL Caps: Using GL 1.3 multitexturing. Using framebuffer objects because OpenGL 3.0 is supported and separate blending is supported. Anisotropic filtering is supported and maximum anisotropy is 16. Shaders are available because OpenGL 2.1 is supported.      Is Modded: Probably not. Jar signature remains and client brand is untouched.     Type: Client (map_client.txt)     Resource Packs: [vanilla]     Current Language: English (US)     Profiler Position: N/A (disabled)     Vec3 Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used     Anisotropic Filtering: Off (1)

Whenever I try to run older versions of Vanilla Minecraft it won't allow me to create or load a world in Singleplayer. If I try, it will start to generate the world, then crash.  Error Message:  ---- Minecraft Crash Report ---- // Oh - I know what I did wrong!  Time: 2/1/16 10:14 PM Description: Unexpected error  java.lang.IndexOutOfBoundsException     at java.nio.Buffer.checkIndex(Buffer.java:540)     at java.nio.DirectIntBufferU.get(DirectIntBufferU.java:253)     at bls.a(SourceFile:270)     at bls.a(SourceFile:220)     at azd.a(SourceFile:1675)     at azd.a(SourceFile:1633)     at biv.a(SourceFile:113)     at gu.a(SourceFile:70)     at gu.a(SourceFile:13)     at ef.a(SourceFile:164)     at azd.o(SourceFile:1566)     at azd.ad(SourceFile:753)     at azd.e(SourceFile:704)     at net.minecraft.client.main.Main.main(SourceFile:103)   System Details:    -- System Details -- Details:     Minecraft Version: 1.7.2     Operating System: Mac OS X (x86_64) version 10.10.4     Java Version: 1.8.0_60, Oracle Corporation     Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Oracle Corporation     Memory: 148530064 bytes (141 MB) / 285257728 bytes (272 MB) up to 1048576000 bytes (1000 MB)     JVM Flags: 5 total; -Xmx1G -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn240M     AABB Pool Size: 18497 (1035832 bytes; 0 MB) allocated, 18497 (1035832 bytes; 0 MB) used     IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0     Launched Version: 1.7.2     LWJGL: 2.9.1     OpenGL: Intel(R) HD Graphics 6000 GL version 2.1 INTEL-10.6.31, Intel     Is Modded: Probably not. Jar signature remains and client brand is untouched.     Type: Client (map_client.txt)     Resource Packs: []     Current Language: English (US)     Profiler Position: N/A (disabled)     Vec3 Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used     Anisotropic Filtering: Off (1)   Is this a system problem, is there a problem with my system settings that would cause this error? If so, what steps can be done to correct it. If not, what could be the problem?


How can I create matrices in general in LaTeX? As well as the one below?   Are there packages that are preferred over others?

How do we add a matrix to a LaTeX document?


The following question was proposed by a student durante a lecture for a grad course in EM.  What happens to the energy of an EM wave during destructive interference in vacuum, in regards to the conservation of energy?  Interestingly, for some reason I've never gave the proper thought about it, and while we indeed arrived at a solution, I thought it would be interesting to share it here due to the conceptual importance to undertanding the nature of waves.  I'll post the answer later in the day, so in the meanwhile feel free to offer your answers or interpretations regarding this question (note that there's a similar question on the site but it only deals with material media, so please don't flag this)

What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be destructed. My guess is that the kinetic energy is transformed into potential energy. Or maybe it depends on the context of the waves where do the energy goes? Can someone elaborate on that or correct me if I'm wrong?


Apache proxy with one physical IP = 10.2.2.1 and a logical IP = 10.2.2.2  Configuration is similar to below  <VirtualHost *:80>    ServerName example.com    <Location />            ProxyPass http://server:8080/            ProxyPassReverse http://server:8080/    </Location> </VirtualHost>  <VirtualHost *:80>    ServerName example2.com    <Location />            ProxyPass http://server:8081/            ProxyPassReverse http://server:8081/    </Location> </VirtualHost>  <VirtualHost 10.2.2.2:443> ServerName example3.com SSLEngine on SSLCertificateFile /example3.com.cer SSLCertificateKeyFile /example3.com.key SSLCertificateChainFile /example3chain.com.cer                                               Redirect / https://example3.com <Location />         ProxyPass http://server:8082/         ProxyPassReverse http://server:8082/     </Location>  </VirtualHost>  <VirtualHost 10.2.2.1:443> ServerName example4.com SSLEngine on SSLCertificateFile /example4.com.cer SSLCertificateKeyFile /example4.com.key SSLCertificateChainFile /example4chain.com.cer                                               Redirect / https://example4.com <Location />         ProxyPass http://server:8083/         ProxyPassReverse http://server:8083/     </Location>  </VirtualHost>  <VirtualHost *:80>     ServerName example4.com     Redirect / https://example4.com </VirtualHost>   What is happening is the URL  site is not hitting the correct virtual host it is going to the non-SSL redirect and just staying there and serving an SSL error page. I have been assured the DNS and firewalls are correct.  Is there a restriction when using mixed IP and Name based vhosts that the SSL sites have to be on separate IP's from each other and the non-SSL sites? Need some help here.

My apache2 configuration is problematic: I've two website on a server:   domain1.tdl domain2.tdl   One of them (domain2.tdl) must be and is accessible on port 443 (with SSL). All domains must be and are accessible by port 80. But when we try to access to domain1.tdl on port 443 the domain2.tdl files are display. So, on port 443, domain2.tdl is accessible by domain1.tdl and domain2.tdl. I don't want it !  My configuration:  domain1.tdl:  <VirtualHost *:80>   DocumentRoot /home/sites/domain1.tdl/www   ServerName domain1.tdl   ServerAlias www.domain1.tdl   ServerAdmin xxx@mail.com   RewriteEngine on   <Directory "/home/sites/domain1.tdl/www">     AllowOverride All     allow from all     Options -Indexes   </Directory> </VirtualHost>  <VirtualHost *:443>   DocumentRoot /home/sites/domain1.tdl/www   ServerName domain1.tdl   ServerAlias www.domain1.tdl   ServerAdmin xxx@mail.com   RewriteEngine on   <Directory "/home/sites/domain1.tdl/www">     AllowOverride All     allow from all     Options -Indexes </Directory>   domain2.tdl:  <VirtualHost *:80>   DocumentRoot "/home/sites/domain2.tdl/web"   ServerName domain2.tdl   ErrorLog /var/log/apache2/site/error_domain2.tdl.log                 CustomLog /var/log/apache2/site/access_domain2.tdl.log combined   <Directory "/home/sites/domain2.tdl/web">     allow from all     Options -Indexes   </Directory>   ServerAlias www.domain2.tdl </VirtualHost>  <VirtualHost domain2.tdl:443>   DocumentRoot "/home/sites/domain2.tdl/web"   ServerName domain2.tdl   ErrorLog /var/log/apache2/site/error_domain2.tdl.log   CustomLog /var/log/apache2/site/access_domain2.tdl.log combined    SSLEngine on   SSLCertificateFile /etc/ssl/private/domain2.tdl/domain2.tdl.crt   SSLCertificateKeyFile /etc/ssl/private/domain2.tdl/domain2.tdl.key   SSLCACertificateFile /etc/ssl/private/domain2.tdl/GandiStandardSSLCA.pem   SSLVerifyClient None    <Directory "/home/sites/domain2.tdl/web">     allow from all     Options -Indexes   </Directory>   ServerAlias www.domain2.tdl </VirtualHost>


Find: $$\displaystyle\lim_{x\to\infty}x\Big(\big(1+\tfrac1x\big)^x-\mathrm{e}\Big) $$   EDIT: so we have here a $\infty\cdot0$ so I'll try LHR, Edit2: I don't think LHR will get me anywhere since it will always be zero in the denominator...   Maybe develop a Taylor series ?  Wrong try:  $\displaystyle\lim_{x\to\infty}(1+\frac1x)^x=\frac 1e$ is a well known limit so:  $\lim_{x\to\infty}x(\displaystyle\lim_{x\to\infty}(1+\frac1x)^x-e)=\lim_{x\to\infty}x(\frac 1e-e)=-\infty $

I am stuck on how to calculate the following limit: $$\lim_{x\to\infty}x\left(\left(1 + \frac{1}{x}\right)^x - e\right).$$  Definitely, it has to be through l'Hôpital's rule. We know that $\lim_{x\to\infty} (1+(1/x))^x = e$. So, I wrote the above expression as $$\lim_{x\to\infty}\frac{\left(1 + \frac{1}{x}\right)^x - e}{1/x}.$$Both numerator and denominator tend to zero as x tends to infinity. I applied l'Hôpital's rule twice, but I got the limit equal to infinity which is clearly wrong. In the book, it says that the limit should be $-e/2$.  Any help please? Also, in case someone managed to solve it, please tell me which numerator and denominator did you apply your l'Hôpital's rule to in both cases? Thanks a lot  Also, guys can you tell me how to write equations in this forum? Thanks.


For a finite group $G$ and its subgroup $H$. Show that there is a subset $T$ which is simultaneously a transversal for the left and right cosets of $H$.  Further ,if we consider any two partition of $G$,and the sets have the same cardinality.Can we find a transversal for both of them?  I get the answer as the comments tell me how to do it.Considerating the left cosets as point in left,and right cosets in right.Two points are adjacent when they are in different sides and have common elements.Then I realized that if there exists a complement match,then I can prove it.The condition of Hall's theorem is easy to be seen as it will lead to a controdiction of the cardinality as they are partitions with the sets of same cardinality.  However,when it comes to the sitiation of infinte cardinality of  G,what can we say about it?

Let $G$ be a group and $H$ a subgroup of $G$. If $G$ is finite, then according to Philip Hall's "marriage theorem" there is a left transversal $T$ of $H$ in $G$ (that is, $T$ contains precisely one element from each left coset of $H$) such that $T$ is also a right transversal of $H$.   Does this theorem generalize to infinite groups? The original theorem treats only the case where $|H| < \infty$ and $[G:H] < \infty$.  What can we say when $|H| = \infty$ and $[G:H] = \infty$? What about $|H| < \infty$ and $[G:H] = \infty$? Also $|H| = \infty$ and $[G:H] < \infty$?


I know ssh root@localhost is a bad idea...I get it.  But why doesn't ssh root@localhost work?  I even changed my root password just in case:  > sudo -s > passwd   But still when I do ssh root@localhost I get  root@localhost's password: [I enter the password]  Permission denied, please try again.    I tried ssh -v not sure what to look for here are the final few lines:  ... debug1: Offering RSA public key: /home/myName/.ssh/id_rsa debug1: Authentications that can continue: publickey,password debug1: Trying private key: /home/myName/.ssh/id_dsa debug1: Trying private key: /home/myName/.ssh/id_abcde debug1: Trying private key: /home/myName/.ssh/id_ed123456 debug1: Next authentication method: password root@localhost's password:  debug1: Authentications that can continue: publickey,password                                                                                Permission denied, please try again.                                                                                root@localhost's password:                                                                                debug1: Authentications that can continue: publickey,password                                                                                Permission denied, please try again.                                                                                root@localhost's password:                                                                                debug1: Authentications that can continue: publickey,password                                                                                debug1: No more authentication methods to try.                                                                                Permission denied (publickey,password).      /etc/ssh/sshd_config  ChallengeResponseAuthentication no PermitRootLogin without-password

What am I missing?  I change the root password on a unix machine, then try to log in with that password.  PasswordAuthentication is set to yes in sshd_config and the sshd daemon has been restarted.  This behavior happens whether I log in remotely or locally:  root@ip-10-0-0-155:~# passwd Enter new UNIX password:  Retype new UNIX password:  passwd: password updated successfully root@ip-10-0-0-155:~# ssh root@127.0.0.1 root@127.0.0.1's password:  Permission denied, please try again. root@127.0.0.1's password:


I thought maybe I can do a work around of this issue "Maximum view state size limit (135KB) exceeded" by having the user insert all the document into salesforce first then select the documents that they want and then Ill do a merge and insert it into Document. but I am still getting the same error "Maximum view state size limit (135KB) exceeded. Actual view state size for this page was 1,112.297KB  "   public with sharing class MultiDocController {       Blob b;   public MultiDocController() {           docNames = new List<SelectOption>();           for (Document d :documents = [SELECT Id, Name , Body                          from Document Where FolderId =: UserInfo.getUserId()  AND ContentType = 'application/pdf']){             docNames.add(new SelectOption(d.Id,d.Name));          }      }             String M =(String)JSON.deserializeStrict(responseBody,String.class);             b = EncodingUtil.base64Decode(M);             System.debug('Blob here' + b);          Document record = new Document( FolderId = UserInfo.getUserId() ,AuthorId=UserInfo.getUserId(); Name='Tes'+'.pdf', Body = b ,ContentType='application/pdf;charset=UTF-8');         System.debug('Record' + record);         insert record;         done();   I am using Component and I am not sure what else to share here. but I need to by pass that Error.  and by the way samething happens if I do attachment record instead of Document record  Component   <apex:component controller="MultiDocController" allowDML="true">     <apex:attribute name="objId" type="String" description="The id of the object to manage attachments for" required="true" assignTo="{!sobjId}"/> apex:form id="frm">              <apex:commandButton action="{!save}" value="Click" reRender="frm"/>         <!-- </apex:pageBlock> -->     </apex:form> </apex:component>

I have used simple code to upload File.   Now My page is giving me the following error:      Maximum view state size limit (135KB) exceeded. Actual view state size for this page was 838.719KB     I have tried making all variables Transient  Removed PageBlock   Instead of coming on this error page - I want to show an Error Message like "Too big File. Upload files having size less than 2 MB."    How can I achieve this. Any Help or Any other suggestions ?  Visualforce Code :       <apex:page standardController="Contact" showHeader="true" extensions="PhotoUploadController">   <apex:sectionHeader title="Upload photo of {!obj.name}"/>        <apex:form >     <apex:pagemessages />
         <apex:outputText >1. Select the photo</apex:outputText>

 &nbsp; &nbsp; &nbsp;         <apex:outputText > Click the "Choose File" to find the photo.</apex:outputText>

&nbsp; &nbsp; &nbsp;         <apex:inputFile title="Upload Photo" contentType="{!objAttach.ContentType}" value="{!objAttach.body}" fileName="{!objAttach.name}" id="file"></apex:inputFile>

         <apex:outputText>2. Upload Photo</apex:outputText>

&nbsp; &nbsp; &nbsp;         <apex:outputText >Click the "Upload Photo" button.</apex:outputText>

&nbsp; &nbsp; &nbsp;         <apex:commandButton value="Upload Photo" action="{!savePhoto}"/>

     </apex:form>    </apex:page>   Controller Code :   public with sharing class PhotoUploadController {     public Attachment objAttach{  get {                                         if(objAttach== null)                                           objAttach= new Attachment();                                         return objAttach;                                      }                                    set;                                  }      transient Public Contact obj{get;set;}       public PhotoUploadController(ApexPages.StandardController controller){         objAttach=new Attachment();         obj= (Contact)controller.getRecord();         if(obj.id!=null){             obj= [select id,name from Contact where id=:obj.id];         }      }       public pageReference savePhoto(){           try {                 transient String contentType=objAttach.ContentType;                  if(contentType == 'image/jpeg' || contentType== 'image/png' ){                      if(objAttach.body!=null && objAttach.name!=null){                         objAttach.parentId=obj.id;                                                try {                              upsert objAttach;                              obj.Image_URL__c=URL.getSalesforceBaseUrl().toExternalForm()+'/servlet/servlet.FileDownload?file='+objAttach.id;                              objAttach =null;                              upsert obj;                              obj=null;                         }catch (DMLException e) {                             ApexPages.addMessage(new ApexPages.message(ApexPages.severity.ERROR,'Error uploading attachment'));                             return null;                         }finally {                           objAttach.body = null;                         }                       }                   return new pagereference('/'+obj.id);                                   }else{                       ApexPages.addMessage(new ApexPages.Message(ApexPages.Severity.ERROR,'Please, Upload image file with extension .JPG or .PNG'));                       return null;                }            }            catch(Exception e){                  ApexPages.addMessages(e);                  return null;            }                     } }


Prove that quotient of a PID  by a prime ideal is PID.

Please help me prove that      the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain.   This was from Abstract Algebra


I received a couple of shapefiles made in France supposed to be projected in WGS84. When I upload them to QGIS3, it recognizes them as WGS84. However, their coordinates are displayed in a strange format with 6 digits. My shapefiles projected in WGS84 display well with the usual Lat/Lon degrees format. Anybody has any ideas of what might be going on? The CRS layer data in the shapefiles I received is exactly the same as that of my own: WGS 84 WKT GEODCRS["WGS 84", DATUM["World Geodetic System 1984", ELLIPSOID["WGS 84",6378137,298.257223563, LENGTHUNIT["metre",1]]], PRIMEM["Greenwich",0, ANGLEUNIT["degree",0.0174532925199433]], CS[ellipsoidal,2], AXIS["geodetic latitude (Lat)",north, ORDER[1], ANGLEUNIT["degree",0.0174532925199433]], AXIS["geodetic longitude (Lon)",east, ORDER[2], ANGLEUNIT["degree",0.0174532925199433]], AREA["World"], BBOX[-90,-180,90,180], ID["EPSG",4326]] Proj4 +proj=longlat +datum=WGS84 +no_defs Extensão -180.00, -90.00, 180.00, 90.00 I am baffled and stuck...

I put 4 different layers into my ArcMap document, but only one of them will show up on the map! I should be seeing the other 3 layers as well. When I do a Zoom to layer, I can see one layer, but I cannot figure out how to make the other 3 show up at once on top of each other.  Before I opened ArcMap, I used ArcCatalog where I right-clicked 3/4 of the shapefiles and  clicked Properties → Coordinate system → Import and then clicked on my Trees layer, which has the coordinate system I want the other 3 to have. But when I opened ArcMap the 4 layers did not overlap, nor could I move them above or below each other.


Say, I have two normally distributed random variables:  $X \sim \mathcal N(\mu_x, \sigma_x^2), Y \sim \mathcal N(\mu_y, \sigma_y^2)$.  I want to test if $\mu_x = \mu_y$. Further, I assume that these variables are independent of each other. Then, I believe the test statistic would be:  ${\mu_x - \mu_y}\over{\sqrt{\sigma_x^2 + \sigma_y^2)}}$  EDIT:  I want to be a bit more specific. In a journal article they test if two regression coefficients from two DIFFERENT regressions are equal.   So, I want to test if two estimated OLS coefficients from DIFFERENT regression models (the sample size is identical) are different from each other. I assume that the coefficients are independent.

This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this?   More formally, suppose I ran the following two regressions:  $$ y_1 = X_1\beta_1 + \epsilon_1 $$ and  $$ y_2 = X_2\beta_2 + \epsilon_2 $$ where $X_i$ refers to the design matrix of regression $i$, and $\beta_i$ to the vector of coefficients in regression $i$. Note that $X_1$ and $X_2$ are potentially very different, with different dimensions etc. I am interested in for instance whether or not $\hat\beta_{11} \neq \hat\beta_{21}$.   If these came from the same regression, this would be trivial. But since they come from different ones, I am not quite sure how to do it. Does anyone have an idea or can give me some pointers?   My problem in detail: My first intuition was to look at the confidence intervals, and if they overlap, then I would say they are essentially the same. This procedure does not come with the correct size of the test, though (i.e. each individual confidence interval has $\alpha=0.05$, say, but looking at them jointly will not have the same probability). My "second" intuition was to conduct a normal t-test. That is, take   $$ \frac{\beta_{11}-\beta_{21}}{sd(\beta_{11})} $$  where $\beta_{21}$ is taken as the value of my null hypothesis. This does not take into account the estimation uncertainty of $\beta_{21}$, though, and the answer may depend on the order of the regressions (which one I call 1 and 2).   My third idea was to do it as in a standard test for equality of two coefficients from the same regression, that is take  $$ \frac{\beta_{11}-\beta_{21}}{sd(\beta_{11}-\beta_{21})} $$   The complication arises due to the fact that both come from different regressions. Note that   $$ Var(\beta_{11}-\beta_{21}) = Var(\beta_{11}) + Var(\beta_{21}) -2 Cov(\beta_{11},\beta_{21}) $$ but since they are from different regressions, how would I get $Cov(\beta_{11},\beta_{21})$?  This led me to ask this question here. This must be a standard procedure / standard test, but I cound not find anything that was sufficiently similar to this problem. So, if anyone can point me to the correct procedure, I would be very grateful!


I want to pass JSON as request Body in rest API request call using the POST method.  JSON:-   {  "product": {     "title": "Burton Custom Freestyle 151",     "body_html": "Good snowboard!",     "vendor": "Burton",     "product_type": "Snowboard",     "tags": "Barnes & Noble, John's Fav, \"Big Air\"",     "images": [       {         "src": "http://example.com/rails_logo.gif"       }     ]   } }   How to do this?

I do not have any idea about this, but I am trying to create JSON using Apex class.  I think it can be done using serialize method.  But I need a simple example so that I can understand the procedure. Any example or easy to understand link would be really appreciated.


This is the bicycle that I own:     My problem is that the handlebars have become loose right right where that red bolt is located. There is an identical bolt on the other side. I have tried adjusting them but they won't budge.   Does anybody know what these kind of handlebars are called and how they can be adjusted?

I was trying to adjust the position of my handle bar...but might have turned the screw too hard in the wrong direction or perhaps it was like this earlier...not sure....    Thanks  Update 3 - Thank you All for the help !! This is now resolved, I was messing with the wrong screws...there was one underneath and that was the one I had to loosen to change the position of the handlebar -   and thx to the immediate response from Pacific Cycles (Schwinn) letting me know what had to be done !! Update 2 - I removed the other side screw and am attaching some photos, and a video which might give some more ideas.   Update 1 - thanks for all the great suggestions folks ! I will try out the options and report back !!  The Bad screw (you might see that it is almost gone round)   The Good screw on the other side


I am not sure about my answer. I think that the cup of tea cools down by the following modes:   Radiation between the surface of the tea and the air molecules. Conduction between the tea and the cup itself and between the cup and the table or whatever the surface is.   Do you think it is correct?

For a while now I've noticed that if I take a cup of hot tea and pour it into two cups and leave it then both cups will cool faster than the single cup.  How is it that nature cools two cups of tea in parallel more quickly? It's still the same amount of tea but it gets cooled quicker if I have two cups.


is my answer to a question, well, it used to be until the edit.   is the edit history for my answer. I just opened StackOverflow and I saw some users(Users -  and ) has edited my answer to a answer of their own while my answer is also a correct one.  When those users had an answer to the question, shouldn't they    post their answer as a different answer instead of overwriting mine??  have added their solutions as suggestions in comments to my answer?? have at least appended their answers to my answer instead of overwriting mine??   I just need my answer back there and their answers posted as a new one.

. When I took a look at it now, some guy edited my answer, which totally changed the answer and made it wrong. To my surprise, the edit was approved in review. To add to that, that same guy who edited my answer posted his own answer, which ended up being accepted.  Seems like peer review of the edit was taken lightly, and others just want others' answers wrong. From my end, it seems very unfair. What can be done to prevent such events?


I want to show that the slope coefficient for the jth regressor for $i = 1, \dots, 2$ and $j = 1, \dots, k$ is given as $$ b_j = \frac{Cov(y_j, u{_{ji}})}{Var(u_{ji})}$$ where $u_{ji}$ is the residual from a regression of $x_{ji}$ on all other covariates.

I've found for my econometrics exams that if I forget the scalar notation, I can often save myself by remembering the matrix notation and working backwards. However, the following confused me.  Given the simple estimation  $$\hat{y_i} = \hat{\beta_0} + \hat{\beta_1}x_{i1}$$  How do we get from  $$\boldsymbol{\hat{\beta}} = \boldsymbol{(X'X)}^{-1}\boldsymbol{X'y} $$  to  $$\hat{\beta}_1 = \frac{\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i=1}^n(x_i-\bar{x})^2} $$  I get stuck at  $$\hat{\beta}_1 = \frac{\sum_{i=1}^nx_iy_i}{\sum_{i=1}^nx_i^2}$$


After I upgraded from 17.10, right click behaves like left click.  I'm using Dell Vostro 14.  It's always getting this error when I install Ubuntu starting from 16.04 yesterday, the error is still the same... touchpad and click.   Here's the output when I type xinput in my terminal   $ xinput ⎡ Virtual core pointer                          id=2    [master pointer  (3)] ⎜   ↳ Virtual core XTEST pointer                id=4    [slave  pointer  (2)] ⎜   ↳ SynPS/2 Synaptics TouchPad                id=13   [slave  pointer  (2)] ⎣ Virtual core keyboard                         id=3    [master keyboard (2)]     ↳ Virtual core XTEST keyboard               id=5    [slave  keyboard (3)]     ↳ Power Button                              id=6    [slave  keyboard (3)]     ↳ Power Button                              id=7    [slave  keyboard (3)]     ↳ Sleep Button                              id=8    [slave  keyboard (3)]     ↳ Integrated_Webcam_HD: Integrate           id=9    [slave  keyboard (3)]     ↳ Intel HID events                          id=10   [slave  keyboard (3)]     ↳ Dell WMI hotkeys                          id=11   [slave  keyboard (3)]     ↳ AT Translated Set 2 keyboard              id=12   [slave  keyboard (3)]

I have installed Ubuntu 18.04 LTS on my HP Pavilion series laptop. After installing this version of Ubuntu, right click is not working of my touchpad. How can I solve this?  BTW:  does not have any solution which which is working for me. PS:- Problem remains after selection area in gnome-tweak-tool


We have 736  machines that sometimes access the central server via ssh. In the worst-case, all machines can be connected to the one server at the same time. Is there any restriction on how many ssh connections can be established at the same time? I can see that in sshd_config I have #MaxSessions 10 but this parameter is disabled, so what is the default setting?

I landed up in a situation wherein I had to access a Linux machine via puTTY.I made various attempts to SSH but failed to connect to the machine. I then realised my colleague was accessing the same Linux machine as root user,and I too wanted to access as a root user.I asked him to log out so that I can login as root. Is there a way we limit number of SSH login on a linux OS? Is this some kind of security feature that distinguishes a windows based OS with a linux based OS.


I have seen some articles and some claims on answers in SO questions that using new and constructor functions is wrong and should not be used.  They go against the prototype nature of JavaScript.  Could someone please enlighten me and show a situation where using new and constructor functions is so bad it should never be used?

In another , a user pointed out that the new keyword was dangerous to use and proposed a solution to object creation that did not use new. I didn't believe that was true, mostly because I've used Prototype, Scriptaculous and other excellent JavaScript libraries, and everyone of them used the new keyword.  In spite of that, yesterday I was watching Douglas Crockford's talk at YUI theater and he said the exactly same thing, that he didn't use the new keyword anymore in his code ().  Is it 'bad' to use the new keyword? What are the advantages and disadvantages of using it?


When reorder the "Your Sites" list on the Android app, the list doesn't get refreshed accordingly. Sites are shown in correct order on computer but not in Android app.  My phone model is HTC One, Android 4.2.2, app version 1.0.31  Steps to reproduce problem:   Pull the left panel. Click on "edit" next to the "Your sites" label. Reorder your sites. Press back button to go back. Check if the ordering of your sites on the left panel are updated.   In my experience, sites are always listed by the time of pinning. It doesn't change when I manually reorder them.  I believe the reason why no one could reproduce this problem is because the problem occurs only if you add more than 10 sites.  I first thought that the app does not refresh the list but later I found out that there could be a problem in the ordering algorithm because it adds the 11th, 12th, 13th, etc. item right after the first item. And if you add more than 20 sites, it puts 21st, 22nd, etc under the second item on the actual list.

In the Android app, left sidebar, there is an editable list of "Your Sites". In the editing pane, the sites are re-orderable (although awkwardly), and the order one places the sites in there is preserved, even after quitting the app and returning to this pane. One expects that order to be reflected in the "Your Sites" portion of the left sidebar when the editing pane is closed, but it is not.  I'm not sure what is determining the order of the sites in the left sidebar, it doesn't seem to be by date they were "pinned" into the list one wants to show, either.


I'm happy to get rid of Win 7 now, how do I do it and will it bring my files over?

I want to keep Ubuntu but remove Windows.


#!/bin/bash  for a in ./*.flac; do   ffmpeg -i "$a" -qscale:a 0 "${a[@]/%flac/mp3}" done   I found this script a few days ago to convert all FLAC files in the current directory into the MP3 format.  What I don't understand here is the "${a[@]/%flac/mp3}" part. I think it replaces the ending flac with mp3 for the current filename. But what eactly does the [@] part do? Is it a regular expression?

I'm quite confused about the following regular expressions I found in a shell script:  ${0##*/} ${0%/*}   How do they work?


I recently wrote a paper, and the examiner picked me up on using 'due to' when apparently I should have been using 'owing to'. I understand that there is some difference between them, as was discussed . My question is however, should I worry myself with using one in place of the other? Has their distinction fallen out of popular discourse?

"Due to" seems more common than "owing to" in modern English. Is "owing to" simply an old-fashioned way of saying the same thing, or is there a rule to using it?


I am not at all familiar with mathematical proof-writing and would like to learn how to create my own proofs. So, I was wondering whether it would be possible for you to recommend me to any book or site that would introduce me to proof-writing.  Additionally, I would like this source to not be of a very high mathematical level and not be about computer science based proofs.  Thank you :)

Lately I've gotten a friend of mine interested in mathematics. He has no college-level education to speak of, but is well employed as a software engineer. So I feel he's competent to learn this stuff on his own.  He asked me recently if there was a 'mathematical' version of .  The point being, if there was an "introduction to proofs" book which took a more hand-holding approach. He's also expressed fondness for the .  However, metamath's proofs are obviously a bit too low level to learn anything serious.  At one point in our conversation, I mentioned the dependently typed programming language , but I felt it's not quite as helpful until he at least gets some experience with  (for which the target audience of Agda is Haskell programmers, hence the similarity in syntax).  Anyone have any good suggestions on a book?