I am trying to prove the following result:     If $R$ is a commutative ring with identity, $I$ is an ideal of $R$ such that $I^2=\{0\}$ and $a+I$ is an idempotent element in $R/I$ then there are some idempotent element of $R$ in the coset $a+I$.   What I tried to do?  Well, suppose that $a+I$ is idempotent in $R/I$, then $(a+I)(a+I)=a+I$, so, $a^2+I=a+I$ and then $a^2-a \in I$. We know also that $1-a+I$ is idempotent since $(1-a+I)(1-a+I)=1-2a+a^2+I = 1-2a+a+I=1-a+I$. And then, from this we know that $a(1-a)+I$ is idempotent.  We need to show that there exist some $m \in I$ such that $(a+m)^2=a+m$, but $(a+m)^2=a^2+2am+m^2=a^2+2am$ since $m^2=0$, so $m$ needs to satysfy $a^2+(2m-1)a-m=0.$  I dont know if this reasoning is right, neither if this is a way to go over it. Can someone give me a hint to finish it?

The problem is this:      Suppose $I \subseteq R$ is a nilpotent ideal and there is $r \in R$ with $r \equiv r^2 \pmod I$. Show $r \equiv e \pmod I$ for some $e \in R$ idempotent.   I have spent a few hours rolling around in abstracta with no destination. I believe that if I could write down a concrete example of this, the example could guide me through the abstract definitions and show me where to look for an idempotent in $R$. I have looked at 2x2 matrices and could not find any such examples. Might anybody have one?


I have created a custom email template and added image into the html version  <img src="https://c.ap2.content.force.com/servlet/servlet.FileDownload?file=01528000001HUDq" alt="Company Logo" height="64" width="750"/>   i can see image in preview but after sending an email ,image is not  getting display in mailbox/outlook. Please suggest

I am trying to send an email using a Visualforce template and I want that template to include an icon. Is this possible?


Can I map a 360° panorama as equirectangular image to a sphere, so that it resembles the original panorama inside out?

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


I just installed Debian and now I am trying to set up Steam.  I did the first 2 steps in the  and also installed ia32-libs.  But when I run the following:  apt-get install libgl1-nvidia-glx:i386   It tells me this:  Reading package lists... Done Building dependency tree       Reading state information... Done E: Unable to locate package libgl1-nvidia-glx   How can I have apt-get locate and install libgl1-nvidia-glx?

I have ran into some issues when it went down to install Steam on Debian. The console as well as Apper comes up with missing dependencies  and the package isn't going to install.


I´d seen the phrase "Reviewed by (someone)" and also the phrase "Communicated by (someone)" in published papers, what they refer to or the difference(s) between them?  Thanks

What does it mean when it says under a journal article that it has been communicated by "XYZ" where XYZ is not the author but some other scholar with a very strong reputation? What is the relationship to the actual author and/or the content? Is this some sort of seal of approval to get results out and known quickly? (I am specifically wondering in the context of mathematics and mathematical physics.)


I'm using the solution provided by lockstep in  to spread the TOC over two columns. However, this gives some strange balancing problem which looks like this:  1.) Bla      4.) Blabla  2.) Blabla     3.) bla      5.) Blabla   But I would like to have it like:  1.) Bla      4.) Blabla  2.) Blabla   5.) Blabla  3.) bla         Since lockstep's solution used the mutlicol package I tried to use the non-balancing enviroment multicols*. But this seems to fail. Are there any other possibilities?

In my LaTeX  presentation I have a long Table of Contents, which has been split across two columns by using the  package. The problem is that I have not found any way to control vertical alignment in the multicols environment. Right now the left column starts lower than the right column, which looks weird. Instead, I would like the left column, or both columns, to be vertically aligned to the top.  I've found some related questions but nothing that solves my problem.  Look at the MWE shown below. As you can see right before Section 3, I tried adding a \vfill along a manual column break, but it didn't help... (The manual column break was added in order to keep Section 3's subsections together with the section in ToC).  Do you have any tricks?  Screenshot of the ToC slide:    MWE:  % MWE showing problems with vertical spacing in multicol ToC \pagenumbering{arabic} \documentclass[compress,14pt,t]{beamer} \usepackage[latin1]{inputenc} \usepackage{multicol} \usepackage{charter} \frenchspacing  \begin{document}  \begin{frame}     \frametitle{Outline}     \begin{multicols}{2}         \tableofcontents     \end{multicols} \end{frame}  \section{Section 1} \begin{frame}Test\end{frame}     \subsection{Subsection 1}     \begin{frame}Test\end{frame}     \subsection{Subsection 2}     \begin{frame}Test\end{frame}     \subsection{Subsection 3}     \begin{frame}Test\end{frame}     \subsection{Subsection 4}     \begin{frame}Test\end{frame}  \section{Section 2} \begin{frame}Test\end{frame}     \subsection{Subsection 1}     \begin{frame}Test\end{frame}     \subsection{Subsection 2}     \begin{frame}Test\end{frame}     \subsection{Subsection 3}     \begin{frame}Test\end{frame}  \addtocontents{toc}{\newpage}           % Splits manually the ToC into 2 columns %\addtocontents{toc}{\vfill\newpage}    % No difference \section{Section 3} \begin{frame}Test\end{frame}     \subsection{Subsection 1}     \begin{frame}Test\end{frame}     \subsection{Subsection 2}     \begin{frame}Test\end{frame}     \subsection{Subsection 3}     \begin{frame}Test\end{frame}  \section{Section 4} \begin{frame}Test\end{frame}     \subsection{Subsection 1}     \begin{frame}Test\end{frame}     \subsection{Subsection 2}     \begin{frame}Test\end{frame}     \subsection{Subsection 3}     \begin{frame}Test\end{frame}     \subsection{Subsection 4}     \begin{frame}Test\end{frame}  \section{Section 5} \begin{frame}Test\end{frame}     \subsection{Subsection 1}     \begin{frame}Test\end{frame}     \subsection{Subsection 2}     \begin{frame}Test\end{frame}  \end{document}


In classical mechanics the coordinates of a particle are functions of time. That path is a solution of the equations of motion. In principle then it is just a parameter and can be eliminated giving a direct relation between the coordinates E.g. If you do this for a particle subject to uniform downward acceleration you obtain the upside down parabolic relation of x with y. No time.  So is time really necessary?

This is an attempt to gather together the various questions about time that have been asked on this site and provide a single set of hopefully authoritative answers. Specifically we attempt to address issues such as:   What do physicists mean by time? How does time flow? Why is there an arrow of time?


Excuse my not so concise code, but I wrote this method, and I get three errors. The first one is when I declare int k=0; it says expresion expected and points to int. Two later errors are that k is undeclared.  The question is: is this the problem with how I initialize k or is it the problem with the code itself?  bool checkSum(long cardNumber, int numberOfDigits){       char str[250];       sprintf(str, "%ld", cardNumber);       printf("%s\n", str);          switch(numberOfDigits)       {           case 13:               int k = 0;               int sum=0;               int sum1=0;               int finalsum;               int multiplied;               int sumOfPartition = 0;               for(int i = 0; i<13; i++)               {                   k++;                    if(k%2==0)                   {                       char digit = str[13-i];                       //converting char to int                       int number = digit - '0';                       multiplied = number*2;                       // if multiplied has two digits                       if(multiplied>9)                       {                            char partitioned[2];                           sprintf(partitioned, "%d", multiplied);                           int firstDigitOfPartition = partitioned[0]-'0';                           int secondDigitOfPartition = partitioned[1]-'0';                           sumOfPartition = firstDigitOfPartition+secondDigitOfPartition;                           multiplied = 0;                       }                   }                   else                   {                       char digit1 = str[13-i];                       int number1 = digit1-'0';                       sum1 = sum1 +number1;                     }                  sum =  sum + sumOfPartition+multiplied;                  sumOfPartition = 0;               }               finalsum = sum+sum1;               if(finalsum%10==0)               {                   return true;               } else{                   return false;               }            case 14:             case 15:            case 16:            default:               printf("heh");        }           return true;   }

I've always wondered this - why can't you declare variables after a case label in a switch statement?  In C++ you can declare variables pretty much anywhere (and declaring them close to first use is obviously a good thing) but the following still won't work:  switch (val)   {   case VAL:     // This won't work   int newVal = 42;     break; case ANOTHER_VAL:     ...   break; }     The above gives me the following error (MSC):     initialization of 'newVal' is skipped by 'case' label   This seems to be a limitation in other languages too.  Why is this such a problem?


The following is an excerpt from the Washington Post article, titled "When did the world turn against Justin Timberlake and embrace Britney Spears?":     They had a bad break-up three years later. While no one really knows what really happened, the tabloids had a pretty good idea. As Buzzfeed points out, magazines like Us Weekly were clearly Team Timberlake, intimating that Spears cheated on him. And Timberlake implied as much with a Spears doppelganger in his famous “Cry Me a River” video.      ()   I am having trouble understanding why the author wrote: "knows" instead of "knew". On a paragraph level, the main tense is set in the past mood; on a sentence level, it is supposed to be "knew" because what the writer meant was that people did not know when the tabloids had a good idea.   Later in the article, the writer wrote:     "In true Taylor Swiftian coy style, he’ll never confirm it’s about Spears. But everyone knows it’s Spears, and he’s referred to her in many interviews."   So there's no reasoning that the writer used "knows" because people still don't know.  I recently have been bothered by the mixing of tenses, especially on a sentence level. Can anyone please explain?

Generally, I've been told that I should maintain consistency of tenses in my writing. That is, if I begin a piece of writing in the past tense, I should ensure that all verbs agree with that through the document. But as I read more articles, books, and other such things, I get confused by the verb tenses used by these other authors.  For example, I copied a portion of an article below. I believe it started in the past tense, yet the second paragraph switched to the present tense (it sounds like the...) In the third paragraph, the past and present usage is mixed (the word gave is in past tense, yet remain is in the present tense). I understand that the writing in the article is most likely correct. But why can it switch verb tenses and be ok while I was told in school by my professor to keep my essays in a single tense? Is there a guideline I can adhere to?      REPRESSED for decades, the anger burst like a summer storm. Rioting   youths flooded city streets. The shaken regime granted hasty   concessions: freer speech; an end to one-party rule; real elections.   But when Islamists surged towards victory in the first free elections   the army stepped in, provoking a bloody struggle that lasted until the   people, exhausted, acquiesced to a government similar in outlook,   repression and even personnel to that which they had revolted against   in the first place.      It sounds like the recent history of several Arab countries: Bahrain,   Egypt, Libya, Syria, Tunisia and Yemen, the states of the 2011 Arab   spring, have seen some or all of the story unfold. But this is also,   and originally, Algeria, a quarter of a century earlier—the first   major political crisis in the age of modern Islamism.      A flurry of freedom in the late 1980s gave way to a vicious civil war   in the 1990s that left as many as 200,000 dead and Algeria’s Islamists   more or less defeated, but not eradicated. Today the country’s   citizens remain powerless spectators to a continued stand-off between   what they call le pouvoir—the entrenched oligarchy that controls the   state, the oil money and the army—and the now-marginalised Islamist   radicals, who serve more as a justification for ongoing repression   than as any sort of inspiration to ordinary people.


Is there any difference in meaning between the following terms? Can they be used interchangeably?   terminal console shell command line interface   If any, what are the differences?

I think these terms almost refer to the same thing, when used loosely:   terminal shell tty console   What exactly does each of these terms refer to?


Think about: If the cube is held in a particular orientation, there are 6! ways to paint the six faces. However, if you rotate the cube around, some of these colorings are equivalent. How many colorings are in each equivalence class?  So from what I understand, two colorings are equivalent provided that if the cube is rotated, they have the same coloring.  How can I tackle this problem? I know the strategy for anagrams, but maybe the context of this one is goofing me up. How can I find how many colorings are in each equivalence class?

How to find the number of ways in which six digits $1,2,..,6$ can be assigned to six faces of a cube (without repetition of digits) so that one arrangement cannot be obtained from another by a rotation of the cube?  I tried to find the number of unique $4-$adjacencies of the faces of the cube. I drew a simple undirected graph $A,B,...,F$ having $6$ vertices with each of them having degrees equal to $4$. There were $12$ edges. Considering the choice between the top and the bottom of the cube, I found the result to be $12 \times 2=24.$  Am I correct? Please suggest better approach approach or bijections(if there are any).


I'm working with NeoPixel led strip and a microcrontroller which run at 3.3V. As you can read in the  using a micro with 3.3V out on pin require the DATA signal to be shifted up from 3.3V to 5V to avoid unexpected behaviour. On the Adafruit page they suggest to use a 74AHCT125 converter IC.  Is it possible to achieve same result avoiding IC? (eg. with mosfet or similar).  NeoPixel data protocol is very strict about timing (800 KHz signal), so I think solution needs fast ON/OFF switching time.

Is there any IC that interfaces any 3.3V Input/Output to 5V Output/Input? I need it primarily for an Arduino Due but if there any bidirectional IC that works like that it would be great.  Some people advised me to use the SN74AHC125 and CD4050 ICs, but I don't understand how they work or how to interface with them.


Inspired by Greta Thunberg's handwriting, a new font named "GretaGrotesk" has just been published. When will it be available for TeX/LaTeX?   Font characteristics are here:

One of the annoying aspects of LaTeX is the limited number of fonts that come by default, and the pain involved in making new fonts 'LaTeX' ready. I have a collection of truetype fonts that I'd like to prepare for use, and I definitely want to make sure I have vector versions of these fonts (i.e not type 3/bitmapped versions). Is there a relatively painless way to do this ?


Generally, "you've" is used in conjunction with another verb, such as "I see you've arrived" or "She asked if you've seen this".  Is it also acceptable to use "you've" without a second verb, using the "have" as possessive? ex: "I see you've a new car".

I feel uncomfortable saying sentences like the following:    "I've a car" instead of "I have a car" "They've a great time" instead of "They have a great time" "He's a pen" instead of "He has a pen" etc   I ask this because I read this sort of thing in a book.  Are they correct? And what is the rule? Can you use such forms in a formal setting?


Jaynes wrote a paper called information theory and statistical mechanics (1957). I tried to read this but found it somewhat hard to follow, and I suspect it's because it's one of the earlier works, and that a modern text might be more refined since we've had time to work it out. On the other hand, what I've read from physics textbooks don't explicitly talk about information theoretic concepts like shannon entropy.  Is there a good modern introduction to the information theoretic view of entropy?

I am interested in knowing if some one here knows book/notes for statistical mechanics from the information theoretic viewpoint.  Additional Request from user83014  "Jaynes wrote a paper called Information theory and statistical mechanics (1957). I tried to read this but found it somewhat hard to follow, and I suspect it's because it's one of the earlier works, and that a modern text might be more refined since we've had time to work it out. On the other hand, what I've read from physics textbooks don't explicitly talk about information theoretic concepts like shannon entropy.  "Is there a good modern introduction to the information theoretic view of entropy?"


I started learning about binomial theorem where my teacher told me that for binomial coefficient $ n \choose r$ to be defined - $n$ $\in$ $ \mathbb{N}$ , $r$ $\in$ $ \mathbb{W}$, $n$ $\ge$ $r$ but out of some curiosity I looked whether  $0 \choose 0$ is defined or not and I found out from this site only that it is defined , therefore $n$ must  $\in$ $ \mathbb{W}$?

I am thinking what values can n and r take in the following notation, $\binom{n}{r} = {n!\over r!(n-r)!}$ ? I mean which one among the following is correct and why?  $0≤r≤n$ where $r,n\in Z_0^+---------(1)$ $0≤r≤n$ where $r,n\in Z^+---------(2)$ $0<r≤n$ where $r,n\in Z_0^+---------(3)$ $0<r≤n$ where $r,n\in Z^+---------(4)$  Furthermore, can you kindly say if $\binom{0}{0}$ exists. If it does exist, I can not find it holding a physical meaning even though we can obtain 1 by simplifying. I would like to know which is correct for nPr from the above 4 connections I have written. 1, 2, 3 or 4 and why? Thanks in advance.


i will create file sh (bash script)  #!/bin/bash su - username -c XXXXXXXX   xxxxxx= command  where i put my password?( but NOT ask me password in terminal..how?)

The purpose is to restart the machine if it doesn't get an abort command from the user. The problem is that the way the terminals are set up, user must supply SU password for shutdown, init, reboot, etc. commands. We are wondering if it's possible to supply password in bash script itself, maybe using stdin. i.e.:  #!/bin/bash # (script) echo "Terminal will restart in 60s, Ctrl+C to cancel." sleep 60 su - root -c "init 6" < "password"   We are going to try putting the password in a file and stdin that.  Edit: sudo and expect are out as solutions as getting them installed will be impossible due to a massive amount of paperwork for permission and a limited timeframe. Also we would like to use init 6 or shutdown -r rather than reboot.


I've defined a function in a class like this. In this class, a value is either looked up or calculated if not found among a list of already calculate values.  If calculated anew, the result is stored in a list so that I can look it up in subsequent calls.  The problem is that the compiler doesn't like the way I do it and tells me   An object reference is required for the non-static field, method or property App.GetGoodFontSize(string, Size).   I don't understand what the compiler suggests. Which object reference does it mean?  Thank you.  public class App : Application {     private List<udt> _list = new List<udt>();      private class udt     {         public int iLen { get; set; }         public Size nSize { get; set; }         public double FontSize { get; set; }     }      public double GetGoodFontSize(string uText, Xamarin.Forms.Size uTextRect)     {         for (int i = 0; i < _list.Count; i++)         {             if ((_list[i].iLen == uText.Length) && (_list[i].nSize == uTextRect))             {                 return _list[i].FontSize;             }         }          int iBest = 100;          for (int i = 100; i > 6; i--)         {             Size nSize = GetTextSize(uText, i);              if (nSize.Width <= uTextRect.Width)             {                 if (nSize.Height <= uTextRect.Height)                 {                     iBest = i;                     break;                 }             }         }          udt n = new udt();         n.iLen = uText.Length;         n.nSize = uTextRect;         n.FontSize = iBest;         _list.Add(n);          return iBest;     }

Consider:  namespace WindowsApplication1 {     public partial class Form1 : Form     {         public Form1()         {             InitializeComponent();         }          private void button1_Click(object sender, EventArgs e)         {             //int[] val = { 0, 0};             int val;             if (textBox1.Text == "")             {                 MessageBox.Show("Input any no");             }             else             {                 val = Convert.ToInt32(textBox1.Text);                 Thread ot1 = new Thread(new ParameterizedThreadStart(SumData));                 ot1.Start(val);             }         }          private static void ReadData(object state)         {             System.Windows.Forms.Application.Run();         }          void setTextboxText(int result)         {             if (this.InvokeRequired)             {                 this.Invoke(new IntDelegate(SetTextboxTextSafe), new object[] { result });             }             else             {                 SetTextboxTextSafe(result);             }         }          void SetTextboxTextSafe(int result)         {             label1.Text = result.ToString();         }          private static void SumData(object state)         {             int result;             //int[] icount = (int[])state;             int icount = (int)state;              for (int i = icount; i > 0; i--)             {                 result += i;                 System.Threading.Thread.Sleep(1000);             }             setTextboxText(result);         }          delegate void IntDelegate(int result);          private void button2_Click(object sender, EventArgs e)         {             Application.Exit();         }     } }   Why is this error occurring?     An object reference is required for the nonstatic field, method, or property 'WindowsApplication1.Form1.setTextboxText(int)


I have a Minecraft Realm, but I cannot give others access to the configuration page, please help!

I'm considering buying a subscription to Minecraft Realms (on PC) as a gift for somebody I know. Mojang doesn't have a gift option, and I don't want to spoil the surprise, so I was thinking I'd just buy it myself and give them access.   If I do this, will the recipient be able to turn around and invite their own friends? Can I grant them "admin" access to the server?


Is there a way to do an accent/diacritic insensitive search in sqlite?  Googling, I've found , but I sincerely don't know how to create my "collation function" in C#. I'm trying create the pt-br collation for Sqlite...

Sqlite3 by default sorts only by ascii letters. I tried to look in google, but the only thing I found were informations about collations. Sqlite3 has only NOCASE, RTRIM and BIARY collations. How to add support for a specific locale? (I'm using it in Rails application)


I am having a bit of difficulties with expanding perturbation series. I need to find a first and second order perturbative approximation to the root of $1+(x^2+\epsilon)^{1/2}=e^x$.  I first tried the following: $$1+(x^2+\epsilon)^{1/2}=e^x$$ Set $\epsilon = 0$ $$1+(x^2)^{1/2}=e^x$$ $$1+x=e^x$$ $$x=0$$  But the derivative of $1+x-e^x$ evaluated at $x=0$ is $1-e^0=0$, so it is singular, and we can't use Taylor expansion.  So, I tried,  $$1+(x^2+\epsilon)^{1/2}=e^x$$ $$(x^2+\epsilon)^{1/2}=e^x-1$$ $$x^2+\epsilon=(e^x-1)^2$$ $$x^2=(e^x-1)^2-\epsilon$$ Let $y=e^x-1$ $$e^x=y+1$$ So, $x=ln(y+1)$  Plugging it back to the above equation, $$(ln(y+1))^2=y^2-\epsilon$$  Then I think I need to use the method of dominant balance and then go back to the very first equation written in terms of $x$ and $\epsilon$, but I am not quite sure how or if this is correct. Can someone please help? Thanks!

I am trying to find a two term expansion for the root of $$1+\sqrt{(x^2+\epsilon)}=e^x$$. Since $$\epsilon << 1$$, I can tell that this equation behaves like $$1+x=e^x$$ which has a root close to zero. That gave me the idea that the root might look like $$x \approx x_0 + \epsilon^{\alpha} x_1 + \dots  $$. I used Taylor expansion for both functions $\sqrt{(x^2+\epsilon)}$ and $e^x$ and then plugged my guess into the Taylor expanded equation and balance of O(1) terms gave me $$x_0=0$$ as expected. My problem begins now. For the higher orders of $\epsilon$. Long story short this expansion ends up with some inconsistencies. So I thought maybe $x \approx x_0+\mu(\epsilon)$. But then again I get nowhere. I am getting frustrated and I would really appreciate some help.  Thank you in advance.


I need to pass some parameters in the url and they can have special characters like ", spanish Ñ or ñ, : spaces and accents.  What is the propper way to encode them before adding to the url or in case I got in the html like that, read them?  I tried this:   arrayData[i] = pair[1].replace('+', " ").replace('%22', "\"");   But just get working with + or spaces, not both at the same time or in 2 lines:      arrayData[i] = pair[1].replace('+', " ");     arrayData[i] = pair[i].replace('%22', "\"");

How do you safely encode a URL using JavaScript such that it can be put into a GET string?  var myUrl = "http://example.com/index.html?param=1&anotherParam=2"; var myOtherUrl = "http://example.com/index.html?url=" + myUrl;   I assume that you need to encode the myUrl variable on that second line?


I'm sure a lot of people is having the same problem as mine because I've tried to make this work in two completely different computers and nothing happens.  I'm trying to use "Jump to the line" on my texmaker and it's not working. I'm trying on my notebook running Linux and on my PC desktop Running Windows. I will leave the information of my two operational systems here (maybe one is easier to fix than another).       Notebook:       Linux Mint 17 KDE 64-bit version of Texmaker: 4.1-1 (I downloaded it   from software manager)        PC desktop      Windows 8 PRO (64 bit)      Version of Texmaker 4.4.1 (I suppose it's the latest because I   downloaded it from the official site some weeks ago)     If someone could help me I would be very grateful not only because of me, but because this would help a lot of people having the same problem which goes here using search engines.  If you need ANY information of my PC, my Texmaker or my operational system, just ask and I will answer very quickly.

I am compiling LaTeX files with Texmaker on Ubuntu 12.04 system.   When I run pdflatex and then view the pdf file (internal), it does not show me the exact place where I am editing on Texmaker i.e. the generated pdf file does not show me the position of the cursor.   But some days before it was working fine. I don't know what causes this problem.  I already tried uninstalling and then reinstalling, I did update and upgrade too. But the problem still persists.


I'm asking this because of my paranoia. I already know about this question: , but I want someone to confirm that this is working on 16.04 too.  I want to buy 2 Xbox 360 Controllers, and they come with a Wireless adapter from a site like eBay. The problem is that I want to use them on my Ubuntu 16.04 Laptop, and I want to be sure that this configuration will work. What do I need to install and do?

I have a Microsoft XBOX 360 gamepad with the wireless adapter and I was wondering what I would have to install to use them with Ubuntu I do know that when using this on Windows I have to manually install the drivers for the wireless receiver (if that is relevant.)


I'm taking a intro to mathematical analysis course and I'm having trouble understanding this definition.   They are talking about how it can be interesting to see what happens if you take the derivative of a function multiple times (this is discussed in the intro to Taylor polynomials). They throw this definition at us, which they call $C^kfunctions$:  A function $f: I \rightarrow \mathbb{R} $ belongs to $C^k(I)$ if it is possible to take the derivative of the function k times on $I$ and if $f^{(k)}(x)$ is continuous on $I$  I'm a little confused by this. Aren't all functions $C^\infty$ then? Can't you just keep taking the derivative of a function even if it becomes $0$? Specifically I'm on a chapter now where they are discussing curve integrals and they keep mentioning that it is a $C^2$ function. What does this mean? Can you only take the derivative 2 times?  I'm confused and can't wrap my mind around it. I would love if anyone was able to explain it in such a way that I could understand and apply it. Thanks in advance.

Is there an example of function that is differentiable at $a$, but the second derivative is not defined at $a$? I bet that this is not possible, because if the function is differentiable then it is smooth and the slope is not vertical, so the only way the second derivative to be not defined is if the slope of the first derivative is vertical. That means that the rate of change is ambiguous at $a$, since there are at least two points almost equal for the same $x$, so I bet that such function doesn't stand a chance not even in the real world, but also in the wonderword of math. Prove me wrong!


I had a problem with WPF events which I managed me to solve. But I'm not sure why my solution works and why the problem existed in the first place.  The following code runs as expected:  void Test () {      TextBox tbOne = new TextBox();     TextBox tbTwo = new TextBox();      tbOne.TextChanged += (sender, e) => Change(sender, e, 1);     tbTwo.TextChanged += (sender, e) => Change(sender, e, 2);      tbOne.Text = "asdf";     tbTwo.Text = "asdf"; }  public void Change (object sender, TextChangedEventArgs e, int i) {     MessageBox.Show("Changed " + i); }   As the two Message Boxes are displayed: "Changed 1" and "Changed 2"   I would have expected the result of the following code to be the same:  void Test () {      TextBox tbOne = new TextBox();     TextBox tbTwo = new TextBox();      int i = 1;     tbOne.TextChanged += (sender, e) => Change(sender, e, i);     i = 2;     tbTwo.TextChanged += (sender, e) => Change(sender, e, i);      tbOne.Text = "asdf";     tbTwo.Text = "asdf"; }  public void Change (object sender, TextChangedEventArgs e, int i) {     MessageBox.Show("Changed " + i); }   But this displays "Changed 2" and "Changed 2"  In my situation (this code is massively simplified) I had to put the integer into a class of its own in order to "remember" it correctly.  void Test () {      TextBox tbOne = new TextBox();     TextBox tbTwo = new TextBox();      int i = 1;     IntClass icOne = new IntClass(i);     tbOne.TextChanged += (sender, e) => Change(sender, e, icOne);     i = 2;     IntClass icTwo = new IntClass(i);     tbTwo.TextChanged += (sender, e) => Change(sender, e, icTwo);      tbOne.Text = "asdf";     tbTwo.Text = "asdf"; }  public void Change (object sender, TextChangedEventArgs e, IntClass i) {     MessageBox.Show("Changed " + i.i); }   Where the class IntClass is defined by:  public class IntClass {     public int i;     public IntClass (int j)     {         i = j;     } }   And this works correctly giving "Changed 1" and "Changed 2".  My Question is, why does it work with instances of classes and objects which are stored as references (or with the integer typed directly) and not with an int variable? I understand that an int isn't stored using a reference but by the value itself, but I don't understand why it should make any difference.  Thanks in advance!

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?


So I tried converting a USB flash drive (16 gb) to live usb for a Linux distribution, Not going into details, it ended with me deleting those files and trying to format the USB drive and this happened to the USB drive.  I tried formatting it, and it showed "There is no disk in drive E: Insert a disk, and then try again." Then I tried using disk management, changing the letter and so on, and it showed this  I also tried using deskpart, but it still didn't worked. It showed: Disk ###  Status         Size     Free     Dyn  Gpt --------  -------------  -------  -------  ---  --- Disk 1    No Media           0 B      0 B  What should I do to make the usb drive workable again? I am fine if all the data is lost because it wasn't important, but I would like the USB drive to work again.

When I plug in my USB flash drive, it shows up on my computer as write-protected or read-only. I am unable to transfer data to it, nor can I modify or delete any files already stored on it. I also cannot repartition or reformat the drive using Windows Disk Management, DiskPart, GParted, or other tools. The drive does not have a write-protect switch.  Why did this happen and what can I do about it? Is there a way to remove the write protection?  (Note that this can happen with some memory cards, too, as they often use controllers similar to those used in flash drives. In some cases, the system may report that the drive or card was formatted successfully even though it was never actually formatted; the original data reappears when the device is reinserted.)     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details.


Will the water pressures at the base of two different sized cylinders be the same if they are filled to the same height? Sorry for crappy drawing

The question asks, For which design will the water pressure at the base of the dam wall be the greatest?  The answer is all are equal.    This doesn't make sense to me.  Using the formula: P (pressure) = p (atmospheric pressure) + rho (density) * g (gravity) * y (depth below water surface)    What is confusing me is the y value, the depth below the surface. Yes both red points are the same depth below the water surface. But doesn't the red point in dam III only "see" a smaller column of water above it and so shouldn't it have less pressure on it than the red point in dam II?    Also, I know the formula would give the points at the base of dam I and dam II equal. But why doesn't the extra water in dam II (shaded in black) cause it to have a higher pressure at the base?


How to know the Employees.class is null or not using Java Relection?  Example Class: Employees.class  Problem:   employees.getName(); value getName is Mikel employees is null if employess != null is TRUE. this class already 'new Employees()'   Employees.Class  public class Employees{  private Long id;
 private String kodStuff;
 private String Name;
  //Getter and Setter
 }   Example Process Method:  public void check(){     Employees employees = new Empoyees;     employees.setName("Mikel");     employees.setKodStuff("KL370");     //employees not save yet and process redirect check value of Name wuth return boolean     Boolean empty = checkName(employees);  }  public boolean checkName(Employees employees){     boolean notNull = false;     if(employees !=null && StringUtils.isNotBlank(employees.getName())){ // this is line 11         notNull = true;     }     return notNull; }   Throws exception at line no '11':  java.lang.NullPointerException   How can i check null exception during process on line no.11?

I use object != null a lot to avoid . What is an alternative to: if (someobject != null) {     someobject.doCalc(); }


If a character was killed and then a druid attempted to resurrect them, would the character know which resurrection spell was used? I'm primarily asking because I have a character who was killed and would want to be revived but the only character in our party for that game was a druid who was not a fan of my race (tiefling). She would want to come back but not if the druid attempted to do so with  as she would not want the 97% chance to not come back as a tiefling.  Note for any potential "ask your DM" answerers: I'm asking about a campaign that has already ended so instead of answers like that please say what you would do as the DM in this situation.

Specifically, would a soul know that the body they're being invited into was created via Reincarnate? After all, for some souls, changing species might be a big deal, possibly of the 'rather stay dead' kind.


Consider a rigid body performing a rotational motion around a vertical fixed axis $z$ with constant angular velocity $\vec{\Omega}$.  The angular momentum vector $\vec{L}$ is not parallel to $z$ (and so to $\vec{\Omega}$) and follows a uniform precession motion.   Supposing to take as pivot point for the calculation of momenta any point $P$ on the $z$ axis. Then the axial component of $\vec{L}$ (called $L_z$) does not depend on the choose of the pivot point $P$ on the axis, while the component of $\vec{L}$ perpendicular to $z$ (called $L_n$) does depend on the choice of $P$.  Since $\vec{L}$ is not constant there must be an external torque $\vec{\tau}$ acting on the system. In particolar, since $\vec{L}$ follows a uniform precession motion  $\vec{\tau}=\frac{d\vec{L}}{dt}=\vec{\Omega} \wedge \vec{L} \implies \tau=L_n \Omega$  Does this mean that $\vec{\tau}$ depends on the choice of the pivot point $P$? And is the $\vec{\tau}$ calculated with this formula the torque with respect to the same point $P$ used for calculation of $\vec{L}$?  Example Take the following dumbell rotating around a vertical axis $z$ not passing through its center with constant angular velocity $\omega$.    If the pivot point (here I called it $O$ instead of $P$) is on the dumbell (situation (A)) then the resulting angular momentum is axial, and that means no external torque on the system. If the pivot point $O$ is somewhere else on the $z$ axis (situation (B)) then the angular momentum is not axial anymore and the external torque must be different from zero.  Does this mean that if I calculate the torque on the dumbell about the point $O$ (on the $z$ axis) I necessarily find:   zero if $O$ is at the intersection between the dumbell and the $z$ axis  not zero if $O$ is somewhere on the $z$ axis?

I have difficulties in understanding, in the rotation of a rigid body, the properties of the component of the angular momentum vector $ \vec {L} $ which is perpendicular to the fixed axis of rotation $ z $. I will call this component $ \vec {L_n } $. Suppose that the angular velocity  $ \Omega $ is constant in direction but can vary in magnitude.    $ | \vec {L_ {n, i}} | = m_i r_i R_i \Omega cos \theta_i \implies | \vec {L_n} | = \Omega \sum m_i r_i R_i cos \theta_i$  Can I therefore say that $ | \vec {L_n} | \propto | \vec {\Omega} | $ (1)?  If so, suppose to apply a torque perpendicular to the $z$ axis and parallel to $ \vec {L_n} $, so that the magnitude of this vector increases. Follows from (1) that there should be an angular acceleration $ \vec {\alpha} $, although we are in the absence of a torque with an axial component.  This would go against the fact that $ I_z \vec {\alpha} = \vec { M_z}$ (Where $I_z $ is the moment of inertia with respect to the $z$ axis and $ M_z $ is the axial component of the exerted torque).


I am creating an ubuntu based distro, and I want to add an ubuntu app to it so it is available for use straight away when the user installs the iso. I was just wondering how to go about this. Any help is greatly appreciated.

I would like to customize Ubuntu live CD by installing some additional packages. I have followed   but it doesn't seems to work. Can anyone provide clear instructions?   Note: I do not prefer Remastersys, manual way will be appreciated.  Customization  Packages that I want to install:   Thunderbird    Samba    SSH       Changes that I need:   Remove Games menu from the Application menu Firefox shortcut on Desktop Radiance as the default Theme Different default Ubuntu Wallpaper   Configuration file changes   I want the panel to be placed at the bottom I want to paste my Samba configuration file instead of default Samba configuration I have few Firefox shortcuts and folders I would like to show that in Desktop Also it will be nice if you say me how to change the icon sets   Recent Updates   I have customized Ubuntu 10.10 with Firefox shortcuts and few folders on desktops. Everything went smooth. But the installer gets crashes after choosing the timezone. How do i fix this issue? Also setting wallpaper affects the login screen. The wallpaper which i set is displayed on the login screen also. I just want the default one for the login screen.


I see leaves rustling all around me (I'm at 14th Street/Union Square)!! Do I have to do some thing to make the pokemon spawn, or is it just random? I've tried walking above them with no success.

After catching my starter Pokémon I've not encountered any more Pokémon, is it entirely random when Pokémon pop up or is there some kind of indicator for me to be on the lookout for?


The frictional force in a motion of a rolling body is along the direction of motion. Then what stops the motion of a rolling body?

Rolling friction is the resistance to motion experienced by a body when it rolls upon another. It is much less than sliding friction for same pair of bodies. When one body rolls upon another, there is theoretically no sliding or slip between them. And if both are perfectly rigid, there is no surface of contact.   Then the book writes:     Different causes are present depending on the nature of the wheel and the road. For a hard wheel on a soft dirty road, as the road is slightly depressed at the point of contact and a ridge is formed in front of the wheel. Thus, the wheel is being continuously pulled up in a minute hill which causes rolling friction.   Now, my questions are: - How does the ridge provide rolling friction in the opposite direction of rolling? - There is not always soft road. What happens in the hard road? - Why is rolling friction less than sliding friction??  Please help.


New to everything web-programming wise.  I'm trying to vertically align the two wrapper divs so that they are in the middle of the page, irrespective of the browser.   The website can be found here:   I've looked up dozens of tutorials on this very question, and cannot get anything to work.  Any ideas?

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


I'm trying to use the function strtok to tokenize an input from the user and then print out the result with new lines between each word. However, this error pops up.  #include <iostream> #include <stdio.h> #include <string.h>  using namespace std;  int main() {     string str;     char *tokenPtr;      cout << "Enter a sentence : " << endl;     getline(cin, str);      tokenPtr = strtok( str, " " ); // ERROR: No matching function for call to 'strtok'     while( tokenPtr != NULL ) {         cout << tokenPtr << endl;         tokenPtr = strtok( NULL, " " );     }      return 0; }

I have a string that I would like to tokenize. But the C strtok() function requires my string to be a char*. How can I do this simply?  I tried:  token = strtok(str.c_str(), " ");    which fails because it turns it into a const char*, not a char*


In this example:  import java.util.*;  public class Example {     static void doesntCompile(Map<Integer, List<? extends Number>> map) {}     static <T extends Number> void compiles(Map<Integer, List<T>> map) {}      static void function(List<? extends Number> outer)     {         doesntCompile(new HashMap<Integer, List<Integer>>());         compiles(new HashMap<Integer, List<Integer>>());     } }   doesntCompile() fails to compile with:  Example.java:9: error: incompatible types: HashMap<Integer,List<Integer>> cannot be converted to Map<Integer,List<? extends Number>>         doesntCompile(new HashMap<Integer, List<Integer>>());                       ^   while compiles() is accepted by the compiler.   explains that the only difference is that unlike <? ...>, <T ...> lets you reference the type later, which doesn't seem to be the case.  What is the difference between <? extends Number> and <T extends Number> in this case and why doesn't the first compile?

I have a couple of questions about generic wildcards in Java:   What is the difference between List<? extends T> and List<? super T>? What is a bounded wildcard and what is an unbounded wildcard?


I am asking if, hypothetically, The death star jumps to Yavin through hyperspace, but it lands with the super laser facing the other way, why? I mean wouldn't it have been easier for the empire to jump facing the planet. I mean i know it would ruin the story because the Rebels wouldn't have a chance to save the day but the empire doesn't want that. So why not jump with the super laser facing the planet? please help me make sense of this plan. Thank you.

We are talking about battle station with a hyperdrive. And there we have to wait till it orbits around Yavin to get a shot at the moon.   .  But why didn't they navigate DS1 so that it had a clear shot at the rebel moon in the first place?  And why couldn't it orbit faster?    (Source: )


Google says that ${(-1)}^{2/3}$ is $-0.5+\frac{\sqrt{3}}{2}i$ but on  it says that it is 1. Which one is it?

Following from  question, I came up with another interesting question: What is  $(-1)^{\frac{2}{3}}$?  Wolfram alpha  it equals to some weird complex number (-0.5 +0.866... i), but when I try I do this: $(-1)^{\frac{2}{3}}={((-1)^2)}^{\frac{1}{3}}=1^{\frac{1}{3}}=1$.If it has multiple "answers", should we even call it a "number"? Because if we don't, it would be a bit different from what we were taught in elementary school. I actually thought if it doesn't have a variable in it, it should be a number.  I'm a bit confused. Which one is correct and why? I would appreciate any help.


I know that the vector of the intensity of the electric field has the opposite direction of the gradient of the electric potential. But what baffles me is that the magnitude of the intensity and the electric potential both get smaller with distance.  Is that because we consider the charge creating the field to be positive? If so, if it's negative charge creating the field the potential should get bigger with distance and the intensity gets smaller?  P.S. sorry if my question doesn't use the right terminology. also for not being styled right.

E = electric field V = electrostatic potential r = distance ' = derivative   E = - (V)'   therefore if E increases V decreases Also if r increases E decreases                                                      because  E=kq/r^2 From 1 & 2, if r increases then V increases But V=kq/r, so if r increases V decreases   Why does the 3rd point contradict with the 4th ?


I'm running Ubuntu 12.04 LTS on a Samsung Chronos 7 laptop. The computer was running fine, until recently after a required reboot, the screen was black showing:  "error: hd0 out of disk grub rescue>"  I have absolutely NO IDEA what's going on here AT ALL. I've read that it has to do with conflicting partitions, but I'm 99% sure that I deleted the entire hard drive of any existing partition when first installing Ubuntu. Does anybody have a clue?

I installed Ubuntu via usb with no problems, but when I restart, I get an error message:   error out of disk" 'grub rescue.   How can I fix this?


Is there a way for a web developer to turn off Chrome/Safari/WebKit's spellchecking on particular input or textarea elements? I mean either by special tag attribute or a proprietary CSS instruction.  There is a CSS instruction for turning off outlining of inputs so I thought that might also exist. I know how a user can do it.  Or, as a user, can I disable it for some particular domain?

Can I somehow disable spell-checking on HTML textfields (as seen in e.g. Safari)?


I have an Ubuntu 16.04 system without GUI (only command line) with a very limited root partition (20GB) and 1 storage partition (1000GB) as below  sudo parted -l  Model: QEMU QEMU HARDDISK (scsi) Disk /dev/sda: 21.5GB Sector size (logical/physical): 512B/512B Partition Table: msdos Disk Flags:   Number  Start   End     Size    Type     File system  Flags  1      1049kB  21.5GB  21.5GB  primary  ext4         boot   Model: QEMU QEMU HARDDISK (scsi) Disk /dev/sdb: 1074GB Sector size (logical/physical): 512B/512B Partition Table: msdos Disk Flags:   Number  Start   End     Size    Type     File system  Flags  1      1049kB  1074GB  1074GB  primary  ext4   The current status of these disk are:  df -hP Filesystem      Size  Used Avail Use% Mounted on udev             27G     0   27G   0% /dev tmpfs           5.4G  530M  4.9G  10% /run /dev/sda1        20G   19G  194M  99% /    (almost full!!!!!) tmpfs            27G  112K   27G   1% /dev/shm tmpfs           5.0M     0  5.0M   0% /run/lock tmpfs            27G     0   27G   0% /sys/fs/cgroup /dev/sdb1       985G  602G  333G  65% /rasv1 (more space!!!!!) tmpfs           5.4G   20K  5.4G   1% /run/user/121 tmpfs           5.4G     0  5.4G   0% /run/user/1001   How can I increase the size of root partition for /dev/sda1 (e.g: 20GB -> 100 GB) from /dev/sdb2 (1000GB -> 900GB) online (no liveCD, USB boot, reboot)?

Is there anyway to resize a virtual machine's disk? Say increasing the disk size from 32GB to 64GB. I am running KVM/Qemu on Ubuntu server 11.10 64bit. Thanks.


Plugging in a power adaptor with mismatched voltage will damage an electronic device. However, plugging in a power adaptor with mismatched current rating will not. Why is this do?

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.


According to articles by multiple respected technology bloggers, Microsoft's KB3185330 patch for Windows, entitled "Security Monthly Quality Rollup" actually contains both security and non-security updates.  See:         There is widespread concern that this update could contain patches that force telemetry onto customers' Windows computers.  What non-security updates are included in this particular "Security Monthly Quality Rollup"?

For Windows 7, what, specifically, is included in the May 2017 Security Monthly Quality Rollup that is not included in the May 2017 Security Only Quality Update?


As a follow-up question from , let $f : [a, b] \to \mathbb{R}$ be continuous and let $X = \{x \in [a, b] : f(x) = 0\}$. Clearly $f$ is uniformly continuous, the set $X$ is bounded, and $a \leq \sup X \leq b$. From the linked question, is it very possible for $X$ to be a closed nowhere dense set such as . But, nevertheless,  Is it true that $\sup X \in X$?  My intuition was challenged many times during my studies of real analysis. But if this one is false, it will be by far the biggest challenge to my intuition, ever!

Prove: the set of zeros of a continuous function is closed.  And should the function on a closed interval?


Where do you place punctuation when quoting a question? Also in general. I’m not sure whether to place the quotation mark before or after the punctuation mark.  -“How can a young man cleanse his ways”?  Or   -“How can a young man cleanse his ways?”

I am very well aware of punctuation usage difference between American and British usage, but this part confuses me a little.  Example:     A. Why did he ask, "Who are you?"   B. Why did he ask, "Who are you?"?   C. Why did he ask, "Who are you"?   The reason I am confused is because a question is enclosed in a question. Now I know when to put a question mark inside and outside quotation mark:     He asked, "Will you go and jump in the pond?" [a question within a statement]      He really said, "Go jump in the pond"? [a statement within a question]   So, which one of the three options is correct? Same goes for use of the period. Should it be placed inside or outside:     D. He said, "Pluck that flower."   E. He said, "Pluck that flower".   F. He said, "Pluck that flower.".   If I pick the D option, would it also mean that my sentence ended with the enclosed sentence? If I pick the E option, would it mean that my sentence ended while the enclosed sentence was incomplete?  B. and F. seems awkward. Please help!


If an electron taken alone by oscillating produce an electromagnetic wave. Can a collection of atoms, i.e., in my case a stone produce an electromagnetic wave/ electromagnetic radiation if we oscillate it?   Any stone is composed of atoms. Any atoms is composed of electrons , protons and neutrons, so according to classical theory that any accelerating charge produces an electromagnetic wave then a stone can also produce one as it is oscillating the electric field produced by itself? Wouldn't it? Please help  How it is different from the existing question:  The previous question defines itself as electrically neutral. Here, I don't fully understand the idea behind the term electrically neutral. I agree in fact that the AMOUNT of positive charge is equal to the negative charge. But I don't understand how it stops from oscillating the electric field that itself produced.  The point is if this is true we should have this effect when Faraday experimented with a stone instead of a bar magnet or if I'm missing something in my understanding, please help.

For example an electron radiates when accelerated. So does a positron. But is the radiation emitted by accelerated positronium the sum of the radiation emitted by each separately? If not, why not? If so, does this provide a way of testing whether a given neutral particle is composite? For example, does a neutron bremsstrahlung when decelerated?


I'm interested in buying a mountain bike. Recently, I was at a Decathlon and checked out their mountain bikes. They only had 3 fullies and I really liked the 700 Eur one. I didn't buy it outright because the dampening locking mechanism seemed to be broken as I was still able to push the handle down even after locking. Maybe you can tell me whether that's normal for any dampening locking mechanism / normal for cheap ones / definitely broken. Here's a short video of me pushing the handle with various amounts of force but generally the same amount of force before and after locking:                                  I'm not sure whether the one I found on their website that one because it looks different (maybe because it's a different color) but  is the only 700 Eur fully they list.  I didn't only check out bikes at Decathlon but I also looked around bike shops when I was touring around or just cycling in town and came by one. I don't think I ever saw a fully that cheap, and anything that I'd figure comparable would've cost at least triple that.  Now I know very little about bikes. I never bought a new bike and never ever bought a mountain bike. I used the very old mountain bike my father bought some 20 or more years ago and didn't need anymore. But it broke down recently and is in disrepair, so I'm looking for a new one. It did not have fancy things like a dampening locking mechanism, so I have no experience with that.  What potential improvement is there when spending double the money? I don't wanna spend triple to money but double would be okay. I've got a feeling that I'm really missing something here but even after weeks of thinking about it, I still can't put my finger on it.

I am not experienced with bicycles, although I have been using them for years to get to work, as well as to go out in the countryside (dirt trails) to take nature photos.  I have used affordable B'twin bikes and I was generally happy, but after my last bicycle was stolen I am looking to step up a bit. There are countless articles on the internet suggesting not to spend too little. But I find it very difficult to find anything tangible or easy to understand about what precisely one would really get by paying more.  Take for example the Rockrider ,  and . (I am linking the English Decathlon site so people here can read it, but I do not live in the UK.) I am looking at these: all of them are better than what I had. The price more than doubles when going from the 520 to the 560. I look at the specs, but I am unable to translate them into what I could do with the 560 that is not possible with the 520, or how the experience would be different.  I am looking for help with this, especially advice that I could translate to other models as well, although it is these three that I am looking at now.  All of these are marked as:     Not suitable for XC, All Mountain, Enduro and BMX.   This restriction seems to cover all forms of mountain biking (which is puzzling) and some websites suggest to dismiss all of these bicycles from the start because of this note. However,  is 50% more expensive, way more than what I can afford (where I live, it's actually 2x the price of the discounted 560).  To sum up:  For any bicycle I pick, it is easy to find another one that is two or four times as expensive. How can I better understand what one gets in practice for paying more? The specs often just mention components of a certain brand, but it is hard to even see which component is better, not to mention how having a better component translates into riding experience (please see the specification lists I linked).  When looking at the three choices above, my spouse asked me "Even the cheapest one is better than what you had. What would you gain by paying more than that?". And I could not answer. What I really wanted (bigger wheel, better gear range and theoretically better brakes) is indeed present in the 520 already.  As to the question "why a mountain bike", I would like to be able to go on rougher trails (rocks, roots) without too much worry. I would like to learn how to do that safely and efficiently. However, I am not young and sporty or physically skilful person. I also keep thinking that my own physical limits may be reached much before that of an expensive (for me) bicycle.


Is there a way to list all files that have been downloaded in the past 12 hours (or 10 days, or 2 months) without knowing the exact location?  For example, let's say that the system downloaded automatically 1200 files, which are likely in 1 or 2 folders (same hard drive, SDA1), however in this folder there are already 5000 files.  Is there a way from the command line to find out which files where downloaded eg. today and put their names in a txt file? Note that while the files were being downloaded i was working on other files in the same directory, so I am not interested to find out which file(s) was last modified, but more specifically which files where downloaded today.

I have an email account that has passed 60GB of emails, and currently I'm having a lot of trouble using an email client to archive emails of last year (2011).  Via terminal, I am trying to use  to locate the files between 2011-01-01 and 2011-12-31, but no avail.  How can I find files between two dates?  If relevant, the end goal will be a batch that will move each file found, matching the date interval, to a folder.


Let $f$ be a twice differentiable function on the open interval $(-1,1)$ such that $f(0)=1$. Suppose $f$ also satisfies $f(x)\geq 0$,  $f'(x)\leq 0$, $f''(x)\leq f(x)$  for all $x\geq0$     Show that $f′(0)\geq−{\sqrt[]{2}}$.   All I am to see in this question is that $f(x)$ is decreasing in $(0,1)$ but I don't  know how  to prove this inequality  can somebody give me a hint on how to proceed with it.

Let $f$ be a twice differentiable function on the open interval $(-1,1) $such that $f(0)=1$. Suppose $f$ also satisfies $f(x) \ge 0, f'(x) \le 0 $and $f''(x) \le f(x)$, for all $ x\ge 0$. Show that $f'(0) \ge -\sqrt2.$  My attempt $ \rightarrow$  From Taylor's we see that $0 \leq f(x)=f(0)+f'(0)x+\frac{f''(\zeta)x^2}{2} $ for some $\zeta \in (0,x) .$  $f'(x)\leq 0$ and $  f'(x) \le 0 \implies$  $  f''(\zeta) \leq f(\zeta)\leq 1$  Thus $1+f'(0)x+\frac{x^2}{2} \geq 0 $.  I'm stuck upto this,I can see that if the discriminant of the quadratic is less than $ 0$ we're done but how do I conclude that the discriminant would be $0$ ?


I am quite new to topics in linear algebra and try to verify my claim that there does not exist a non-zero matrix $B$ such that $AB=0$ given that $A$ is non-singular.   I browsed the forum for related question but could not find a convincing answer so far. The forum only investigated cases when $A$ it self has not full rank and then found that there indeed exists such a matrix $B$ that is non zero.   Can anybody help me to construct such a proof or provide me counter example that my claim is false?

$A$ is defined as an $m\times m$ matrix which is not invertible. How can i show that there is an $m\times m$ matrix $B$ where $AB = 0$ but $B$ is not equal to $0$?   For the solution of this question I think giving an example is not enough because it is too easy to solve this by giving an example, so how can I show that $B$ is not the $0$ matrix?


I  have come  across  to  the following question :   Let  $\mathscr{T}_\alpha$  be a family  of  topologies    on  $ X$ .  Show  that   there  is   a  unique  smallest   topology   on  $X$    containing   all   the  collections   $\mathscr{T}_\alpha$ , and  a  unique    largest   topology   contained   in  all  $\mathscr{T}_\alpha$.   I think  that  the unique smallest  topology  equals  the union  of  all  the $\mathscr{T}_\alpha's$, and the unique largest  topology  contained  in  all  $\mathscr{T}_\alpha$  equals  the  intersection of all  the $\mathscr{T}_\alpha's$ .

I'm doing this exercise:     Let $\{T_\alpha\}$ be a family of topologies on $X$. Show that there   is a unique smallest topology on $X$ containing all the collections   $T_\alpha$, and a unique largest topology contained in all $T_\alpha$.   I have proved everything except the unique part.. I just can't get my head around what is meant with unique here. Which may sounds silly.   I have proved that the intersection is a topology. And if you are a topology that is also contained in every $T_\alpha$, than you surely are contained in the intersection, so you are not larger.  But I don't see from what it follows that this intersection is the unique largest topology contained in all $T_\alpha$. One part of my head say it is trivial, the other part gets confused. Like it is redundant to talk about unique in this context.  The same for proving the uniqueness of the smallest topology.   Edit Should I read topology $A$ larger than topology $B$ as, $A$ has more elements than $B$ ? I thought that, because the author uses the word finer for $A \supset B$.


I've often wondered if it is possible to search the Stack Exchange sites using a single tag and in the run up to asking this question, I have managed to burrow down into the depths of Meta and find out that it is possible:  [xml] closed:0   For me though, writing this every time seems like a bit too much work. Surely there must be a more accessible operator to search by rather than including closed:0 every time?  EDIT: It seems the query above does not produce the desired results, so I guess this question is even more pertinent now.

I can search question with target using [target] but the result questions also include question tagged with other tags.   How to get the question with only one specific tag?


Well I'm working on a government website that needs a lot of security insurances! the security thingy guys keep saying that there are couple of Drupal name in the source that shouldn't be there!   So far I changed Drupal Meta Generator but still there are some javascript files and Drupal. Settings that still shows up in the source code. Here's what I'm referring to:  jQuery.extend(Drupal.settings, {"basePath":"\/","pathPrefix":"","ajaxPageState":{"theme":"stme","theme_token":"tytMMj0EavWD-6KgUbjQYEmSyk35cF3mwLTcqBKhO5U","js":{"misc\/jquery.js":1,"misc\/jquery.once.js":1,"misc\/drupal.js":1,"misc\/ui\/jquery.ui.core.min.js":1,"misc\/ui\/jquery.ui.widget.min.js":1,"misc\/ui\/jquery.ui.button.min.js":1,    this is just a part of the code between  tag, What I need is to change jQuery.extend(Drupal.settings to something else and also change the name of drupal.js .  I have no idea that could it have any side effects if I manage to make it? and before all how am I be able to do these changes?

Is there anything I can do to prevent somebody from knowing my site is using Drupal by looking at the source code of the front page? I am referring to people who scan sites using software that detects the software used to run the website to be able to attack it using any known weak point.  If it is not possible to completely hide the fact that the site is using Drupal, is it at least possible to confuse them (e.g., by aliasing the node pages with URLs like http://example.com/servlets/<node-id>.jsp)?


What branch(es) of math are used in Quantum Field Theory?  Or the question, by way of analogy:  Tensor Calculus is to General Relativity as What is to Quantum Field Theory?

I am curious about which areas of mathematics one should be comfortable with before learning QFT.  I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to know how to avoid that in learning QFT.  Naming of specific textbooks is appreciated.  (For the sake of this discussion, "learning QFT" can be taken to mean "learning at the level of/from Peskin and Schroeder's text.")  In particular, I would like to know what, in addition to the material in Rudin's Real and Complex Analysis, one should know.  Would this be sufficient?  How about Folland's Real Analysis?


Is there any well known basis (Hamel basis) for the vector space $\ell^p$? And what about the cardinality of such basis? Is it countable?

I am looking for an explicit example for a Hamel basis for  $\ell^{p}$?. As we know that for a Banach space a Hamel basis has either finite or uncountably infinite cardinality and for such a basis one can express any element of the vector space as a finite linear combination of these. After some trying I could not write one explicitly. A quick google search did not reveal anything useful except for the proof of uncountability of a an infinite Hamel basis. Maybe I am being a bit silly but I don't think the answer is as obvious as for a Schauder basis for the same case.  So, what is an explicit example for a Hamel basis for $\ell^{p}$??


Suppose A is some arbitrary hash function, for example BCrypt or MD5. And B be some other arbitrary hash function, maybe SHA256 or SCrypt. Let passwordHashedWithA = A(password) and  passwordHashedWithB = B(password). If an attacker is given just passwordHashedWithA and finds a pA such that: passwordHashedWithA == A(pA) Then the attacker has performed a successful preimage attack on A. I want to know if it is theoretically possible to construct a hash function C out of two arbitrary hash functions A and B, such that for any A and B, performing a successful preimage attack on C would require performing a preimage attack on both A and B. The question can be extended to build C from N arbitrary hash functions. I strongly suspect that this is theoretically impossible; it seems like a free lunch. But I cannot begin to think how to prove it. If such a thing does exist then it would be incredibly useful: we could combine old, proven hashes like BCrypt with slightly newer and fancier hashes like SCrypt, such that we have the best of both worlds. Like I said - sounds too much like a free lunch. I am asking this from a theoretical perspective, I'm aware that BCrypt or SCrypt are probably good enough for most production systems. I'm looking for a proof that this is impossible, or a construction of C that provides these properties. Examples of C that don't work Suppose we try C(password) = A(password) + B(password) where + is just concatenation of the hashes. The result of this is obviously a weaker hash: we can preimage C by finding the original password by cracking  A or B. If we try C(password) = A(B(password)), this initially looks stronger but you really can't say much about C without looking at the specifics of A and B. For example if A was a completely useless hash that always returned a constant string, the strengths in B would be irrelevant, and any string would be a preimage of C.

Assume I want to design a protocol (or data format or similar) including some cryptographic hash, and want it to be as future-proof as possible, i.e. I want to avoid that breakthroughs in cryptography make my old data insecure.  If I use only one hash algorithm, I can have bad luck to pick just the one which will be broken after some years.  For example,  (published 1990) had first collision attacks in 1995, and as of 2007 these are even cheaper than calculating the hash itself.  So, the idea would be to combine multiple such algorithms in a way that breaking just one (or some) of them does not compromise the security of the combined construct - breaking all of them would be necessary.  I do not care about efficiency loss from calculating multiple hashes instead of one, I just want to be sure against better cryptanalysis.  So, if I have hash functions $H_1$, $H_2$, ..., $H_n$. How to combine them to form a hash function which is as secure as any of them?  Two basic ideas, which do not work as intended:   simple concatenate the outputs:  $H_1(m) || H_2(m) || ... || H_n(m)$.  This should be quite secure against collision attacks, but is only as secure to preimage attacks as the weakest of them (and the other ones then can be used to check if I found the right preimage). chaining the functions: $H_1(H_2(...(H_n(m)...))$  For preimage attacks, you would now need to break all of them. But a collision in Hn trivially leads to a collision in the result, too. (Collisions in the others are less easy to exploit, as you then need to have to get preimages in the previous ones.)   Any better ways of combining them? Or is this a stupid idea at all?    To clarify: I do not really need more security than the hardest of the component functions, but I want at least that much. (And using more space is not really a problem here.)  And for preimages, I'm now mainly concerned about someone finding the original preimage (which is around the size of the hashes output),  and it looks like this will be at most as difficult as for the weakest hash, in the case of simple concatenation. I'm not so much concerned about someone constructing a new one - this sounds quite difficult, but is not so much, if the size of the message can grow as needed (one block per bit of hash or such) and we have collision attacks on the compression function, as Joux shows.


The question is: Suppose that T is a self-adjoint operator on a finie-dimensional inner product space and that 2 and 3 are the only eigenvalues of T. Prove that $T^2-5T+6I = 0$.   To prove this question, can I take the inner product of $(T^2-5T+6I)v$ and $Tv$, where $Tv = 2v$ and $v \neq 0$, and then show that the inner product of those two vectors is equal to $0$? Since $v \neq 0$, would that imply that $T^2-5T+6I = 0$? Or am I coming at this question completely wrong?   Thanks.

Let $T$ be a self adjoint operator on a finite dimensional inner product space. And let $4$ and $5$ be the only eigenvalues of $T$. Show $T^2-9T + 20I = 0$ .  proof:Let $T$ be a self adjoint. And let $4 , 5$ be the only eigenvalues of $T$. Then $Tv = 4v, Tv = 5v$ for some $v \neq 0$. Then $Tv = 4v, Tv = 5v$ if and only if $(T-4I)v = 0, (T-5I)v=0$.  Then $ (T-4I) (T-5I)v=0$ implies $(T^2 -5T -4T + 20I^2)v = 0$, implies   $(T^2 -9T + 20I)v = 0$, so we have  $T^2 -9T + 20I = 0  $. Can someone please check this? if it's not correct, could I please have some help on it? Thank you


Numerous exceptions r there in English grammar ,why it is so? Like I m still confused between  India HAS/HAVE won the match?

I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved?


I ran updates from the update manager today on my ASUS notebook and when it asked for reboot, it hung at the splash screen.  Every time I try to reboot, it hangs at the splash screen.    I tried running recovery mode from GRUB boot but that did not help, I get a repeating message:  udevd [360] timeout killing /sbn/modprobe -bv pci: longstringnumbers [597]   I can boot into previous version 3.2.0-92 from GRUB.  Is there a way to delete this update and revert to previous?  Or should I consider saving my data and restore to factory?

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


I've used both hyperref and url to enable href and url, but heard that they're redundant. Also I realized that ordering \usepackages matters. For example,  \usepackage{hyperref} \usepackage[doublespacing]{setspace}   applies doublespacing to footnotes, while  \usepackage[doublespacing]{setspace} \usepackage{hyperref}   doesn't. So I'm trying to review all the preamble I've used to detect any unnecessary repetition or improper arrangement. Here's the code.  \usepackage[margin=1in]{geometry}      % Give 1 inch margins \usepackage[doublespacing]{setspace}   % Use doublespacing and enable SPACING \usepackage[pdfpagemode=UseNone,       % Suppress bookmarks in Acrobat     pdfstartview=]{hyperref}           % Use a default zoom \usepackage[round]{natbib}             % Alter brackets by parentheses \usepackage[font=footnotesize,         % Make captions smaller     labelsep=period,                   % Alter Table 1: by Table 1.     skip=0pt]{caption}                 % Tune the gap between captions and tables \usepackage[input-decimal-markers={.}, % Use decimal alignment     group-separator={,},               % Give thousand separators     parse-numbers=false]{siunitx}      % Use a math mode for S columns \ExplSyntaxOn                          % Make SIUNITX be compatible with TABU     \cs_new_eq:NN     \siunitx_table_collect_begin:Nn     \__siunitx_table_collect_begin:Nn \ExplSyntaxOff \usepackage{pdflscape,                 % Use a landscape mode with rotation     xcolor,                            % Enable COLORBOX     amsmath,                           % Use usual math syntax     amssymb,                           % Use some math symbols     amsthm,                            % Use theorem-like environments     textcomp,                          % Enable TEXTMINUS     cancel,                            % Enable CANCEL     tabu,                              % Enable TABU and the X columns     booktabs,                          % Enable TOPRULE, MIDRULE, BOTTOMRULE     multirow,                          % Enable MULTIROW     graphicx}                          % Enable INCLUDEGRAPHICS \setlength{\fboxsep}{0pt}              % Tune the padding setting of COLORBOXs \theoremstyle{plain}                   % Apply PLAIN to these NEWTHEOREMs \newtheorem{definition}{Definition}    % Enable DEFINITION \newtheorem{proposition}{Proposition}  % Enable PROPOSITION \newtheorem{hypothesis}{Hypothesis}    % Enable HYPOTHESIS   I'd appreciate any single comment in advance.

This isn't a real question, so I'm marking it community wiki.  When I was new to LaTeX, I thought that the \usepackage command worked much like the #include command of the C language: just put whatever you need in the preamble, in whatever order you like.  But then bugs began to bite me and I realised, with growing horror, that commutative packages seem to be the exception rather than the rule.    so  that I think it would be useful to have a list here of problematic interactions between pairs of packages, and their correct order.  Also, a question for amusement:   I want to know if there exists three packages A, B and C, such that A has to be included before B and B needs to be included before C, but C needs to be included before A.


Sometimes One does not wish to post a problem/solution directly as a ques/ans at stackexchange sites, but posts indirectly (share the link, and that link contains the ques/ans in math(latex ) format). what are those latex writing and sharing pad?

I have heard rumors that you can compile documents online, and more specifically that Google has a free online compiler, but I have never been able to find any. Is there a way to compile documents online, so that I can write and compile documents even if I don't have a TeX distribution installed on my computer?


So I created a list within a list and printed it:  a = [] b = [] for i in range(3):     a.append(0) for i in range(3):     b.append(a) print(b)   and the result was: [[0, 0, 0], [0, 0, 0], [0, 0, 0]] as expected  but when I try assigning the first value of the first list within b with  b[0][0] = 1 print(b)   the result comes out as: [[1, 0, 0], [1, 0, 0], [1, 0, 0]]  How do I assign 1 to only the first value so I get: [[1, 0, 0], [0, 0, 0], [0, 0, 0]]?

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


How i solve this?  I have not idea how to approach this differential equation.  y′−∫x0y(t)dt=2   I get the probably familiar DE: y′′−y=0.   please someone can solve this exercise

I have not idea how to approach this differential equation.   $$y'-\int_0^xy(t)dt=2$$.  Basically, I did,  $$F''(t)-F(x)+F(0)=2 \;\;\;\;\;\;\; F'=y$$  I am stuck.  Thank You.


Out of the blue, I'm getting this error for all my .tex files with citations (even those which ran smoothly just a couple of days ago). I typeset them on another MacBook with the same distribution and all updates and they work just fine. I've tried uninstalling and reinstalling my TeX Distribution but I keep getting the same error.  INFO - This is Biber 1.9 INFO - Logfile is 'siÌlabo_lyta_1.blg' read_file '/var/folders/g9/qcll94p57w985k2gtngk3dcr0000gn/T/par-687966616e7465/cache-a3cdad92316c60c9c5179d80d6bb51a7a024393c//inc/lib/Biber/LaTeX/recode_data.xml' - sysopen: No such file or directory at /var/folders/g9/qcll94p57w985k2gtngk3dcr0000gn/T/par-687966616e7465/cache-a3cdad92316c60c9c5179d80d6bb51a7a024393c/bda77484.pm line 112. Latexmk: Failed to find one or more biber source files:   NONE Latexmk: Errors, so I did not complete making targets Collected error summary (may duplicate other messages):   biber sílabo_lyta_1: Could not find all biber source files for 'sílabo_lyta_1' Latexmk: Use the -f option to force complete processing,  unless error was exceeding maximum runs of latex/pdflatex.

I'm trying to use biblatex and when I compile my document I get an error like the following:  Windows  data source C:\Users\<username>\AppData\Local\Temp\par-5061756c\ cache-890efc00b3ca6b775c7d44a325c1349fb2a3a3bd\inc\lib/Biber/LaTeX/recode_data.xml not found in .   Mac  data source /var/folders/v2/rld0ls7d2935gkvqv5hfr1x00000gn/T/par-616c616e/ cache-cdd483146f82a9655ce063f848d5139480fbf872/inc/lib/Biber/LaTeX/recode_data.xml not found in .   Linux  data source /tmp/par-6963617269756d/cache-f37ab610b7d79b2720a8ee3732849c6821705520 /inc/lib/Biber/LaTeX/recode_data.xml not found in .


I am reading a paper and they write that Fermat derived his little theorem from this observation: If $p$ is a prime, and $a$ is any number not divisible by $p$, then the order of a modulo $p$ divides $p−1$. In terms of divisiblity and this is the theorem that Fermat found the theorem looks like this: If $p$ is prime and $a$ is coprime to p, then $p$ divides $a^{p−1}−1\implies p \mid a^{p-1}-1$ The multiplicative order in terms of divisibility looks like this: the order of $a$ mod $p$ is the smallest $e > 0$ so that $p$ divides $a^e−1\implies p \mid a^{e}-1$ I am trying to obtain Fermat's theorem by having a look on his observation: So I want to show that: "If $p$ is a prime, and $a$ is any number not divisible by $p$, then the order of a modulo $p$ divides $p−1$" leads to "If $p$ is prime and $a$ is coprime to p, then $p$ divides $a^{p−1}−1$". My approach is, taking the definition of order: p | $a^e-1$ and using the observation $=>$p | $a^{e|p-1}-1$. This already looks pretty similar to  $ p $ | $a^{p-1}-1$, but not quite and I am not sure if I am on the right track. Thanks for your help

I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two:   $13^{100} \bmod 7$ $7^{100} \bmod 13$   I've also heard of this formula:  $$a \equiv b\pmod n \Rightarrow a^k \equiv b^k \pmod n $$  But I don't see how exactly to use that here, because from $13^1 \bmod 7$ I get 6, and $13^2 \bmod 7$ is 1. I'm unclear as to which one to raise to the kth power here (I'm assuming k = 100?)  Any hints or pointers in the right direction would be great.


Could anyone tell me what energy really is? I searched for it, and some people said that energy doesn't exist physically and it is not fundamental, but it is a relationship between other fundamental things, and there is not energy by itself, so it should be related to something else.  So could anyone help me understand it?

The simplistic undergrad explanation aside, I've never really understood what energy really is. I've been told that it's something when converted from one kind of something to another kind, or does some "work", as defined by us, but what is that something?  Moreover, if the total amount of energy in the universe is finite and we cannot create energy. Then, where did it come from? I've learned from thermodynamics where it goes, but where does it come from?  I know this sounds like something trivially simple, but there is so much going on in the physical universe and I just can't grasp what it is. Maybe it is because I lack the mathematical understanding that I can't grasp the subtle things the universe is doing. Still, I want to understand what it is doing.  How do I get to the point of understanding what it's doing?  (Note: What prompted me to ask this was . I'm afraid that it just puzzled me further and I sat there staring at the screen for a good 10 minutes.)


There are lots of txt files in a directory.  If I do time wc -l *.txt | head it takes   real    0m0.032s user    0m0.020s sys     0m0.008s   If I do time wc -l *.txt | tail it takes  real    0m0.156s user    0m0.076s sys     0m0.088s   Does this mean that wc will know beforehand that it is piping to head and will only count for first 10 files and save time? In other words, is it aware of the pipe? And is this somethign special about wc or does it apply to all standard/built-in commands?

I was just running a few commands in a terminal and I started wondering, does Unix/Linux take shortcuts when running piped commands?  For example, let's say I have a file with one million lines, the first 10 of which contain hello world. If you run the command grep "hello world" file | head does the first command stop as soon as it finds 10 lines, or does it continue to search the entire file first?


I am trying to light up 12V LED from 32V comes from another board. I have used voltage regulator (LM7812), but the problem is the regulator heats up very quickly even when I use 12V as input rather than 32!  Is there any special type of regulators that fit my application?   Thanks

I'm using a 5 V / 2 A voltage regulator () without a heatsink. I'm testing the circuit with a microcontroller (PIC18FXXXX), a few LEDs and a 1 mA piezzo buzzer. The input voltage is aprox. 24 VDC. After running for a minute, the voltage regulator starts to overheat, meaning it burns my finger if I keep it there for more than a second. Within a few minutes it starts to smell like it's burnt. Is this a normal behavior for this regulator? What could cause it to heat that much?    Other components used in this circuit:  L1:   R2:   F1:


I want to show that for all $n\ge 2$, it holds that $$ \int \cos^n x\ dx = \frac{1}{n} \cos^{n-1} x \sin x + \frac{n-1}{n}\int \cos^{n-2} x\ dx. $$ I'm not even getting the result for the induction base $(n=2)$: Using integration by parts, I only get $$ \int \cos^2 x\ dx = \cos x \sin x + \int \sin^2 x\ dx. $$ I'm suspecting that I need to use some trigonometric identity here.

I am trying to prove  $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$  This problem is a classic, but I seem to be missing one step or the understanding of two steps which I will outline below.   $$I_n := \int\cos^n x \ dx = \int\cos^{n-1} x \cos x \ dx \tag{1}$$  First question: why rewrite the original instead of immediately integrating by parts of $\int \cos^n x \ dx$?  Integrate by parts with $$u = \cos^{n-1} x, dv = \cos x \ dx \implies du = (n-1)\cos^{n-2} x \cdot -\sin x, v = \sin x$$  which leads to  $$I_n = \sin x \ \cos^{n-1} x +\int\sin^2 x (n-1) \ \cos^{n-2} x \ dx \tag{2}$$  Since $(n-1)$ is a constant, we can throw it out front of the integral:  $$I_n = \sin x \ \cos^{n-1} x +(n-1)\int\sin^2 x \ \cos^{n-2} x \ dx\tag{3}$$  I can transform the integral a bit because $\sin^2 x + cos^2 x = 1 \implies \sin^2 x = 1-\cos^2 x$  $$I_n = \sin x \ \cos^{n-1} x + (n-1)\int(1-\cos^2 x) \ \cos^{n-2} x \ dx \tag{4}$$  According to Wikipedia as noted , this simplifies to:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) \int \cos^{n-2} x \ dx - (n-1)\int(\cos^n x) \ dx \tag{5}$$  Question 2: How did they simplify the integral of $\int(1-\cos^2 x) \ dx$ to $\int(\cos^n x) \ dx$?  Assuming knowledge of equation 5, I see how to rewrite it as  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x  - (n-1) I_{n} \tag{6}$$  and solve for $I_n$. I had tried exploiting the fact that  $$\cos^2 x = \frac{1}{2} \cos(2x) + \frac{1}{2} $$  and trying to deal with $\int 1 \ dx - \int \frac{1}{2} \cos (2x) + \frac{1}{2} \ dx$  which left me with $\frac{x}{2} - \frac{1}{4} \sin(2x)$ after integrating those pieces. Putting it all together I have:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x \left(-(n-1) (\frac{x}{2} - \frac{1}{4} \sin 2x) \right) \tag{7}$$  but I'm unsure how to write the last few terms as an expression of $I_{something}$ to get it to match the usual reduction formula of   $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$


I am stuck with the following question from my homework:  $\lim_{n \to \infty} \left ( \sqrt{n + \sqrt{n}} - \sqrt{n - \sqrt{n}} \right )$  Using  gives me 1 for the solution. However, I would like to know how you come up with this result. I hope someone can explain this to me.

How can I evaluate  $\lim_{x \to \infty}\left(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}\right)$?


I am trying to do matrix factorization.  $ \frac{1}{2} \vert\vert X - WZ ^T \vert\vert ^2_F $  How do I find the derivative wrt W ?  I am just told that it is $  W^T = (Z^TZ + \lambda I_K)^{-1}Z^TX^T $  I come from a lousy school please help show me the way.

Whats a quick way to work the below (and problems similar) out?   For me to take this derivative it involves a lot of time and boring calculation, there has to be a better way.    This is taken from the solutions to Chris Bishop's Pattern Recognition and Machine learning:


My phone is an Android Evo, and it keeps telling me I have low storage. I have removed everything - facebook, email, messages, text messages, and pictures, but it's still low.

If you're not used to seeing the 'low on internal storage' notification, what is it that you're doing to keep your phone's internal memory from filling up so quickly?   The 'SD Card and Phone Storage' menu in the settings doesn't really tell me much other than how much is free. And, I don't really have that many applications installed. The top 5 storage hogging apps on my phone are Gmail (18.6 MB), Twitter (17.5 MB), Facebook (12.55 MB), Maps (9.63 MB), and Swype (6.06 MB).  So, are there apps out there (besides your normal file manager ones, like Astro) that will help monitor internal phone storage? Is there something I should be doing to keep my phone storage use to a minimum?


I have a problem in removing a div without its content. I have this html structure:

Menu 1

Menu 2

Menu 3

Menu 4

   I need to remove the div containing the class "wrap". I desire a structure like this, only without "wrap":

Menu 1

Menu 2

Menu 3

Menu 4

   I tried with this jquery:  $("button").click(function () { $(".test").not().siblings().unwrap(); });   and with this:  var content = $(".wrap").html(); $(".wrap").remove(); $("body").append(content);   with the second one I reach my target but I lost the DOM order. How can I fix it?

Let's say:
   pre text

child foo

child bar
     nested text
   post text
   to this:
   pre text
child foo

child bar
   nested text   post text
   I've been figuring out using Mootools, jQuery and even (raw) JavaScript, but couldn't get the idea how to do this.


I have a custom keyboard and I try to convert input value like a double. For example, input 1 is 0.01. My main goal is to  show only two elements after a dot, always, but if the input is 80 then result is 0.8 ,but I want it to be 0.80 Here is my source    userEntered = userEntered + pressedString;  Double dd = Double.parseDouble(userEntered);  dd = dd / 100;  amountText.setText(dd.toString());   I clearing input value like this in a button click  if (userEntered.length() > 0) {     userEntered = userEntered.substring(0, userEntered.length() - 1);     Double dd = Double.parseDouble(userEntered);     dd = dd / 100;     amountText.setText(dd.toString()); }   How I can solve a problem? Thanks everyone

What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -> 0.91239 0.912300 -> 0.9123   What is the best way to achieve this in Java?


How can i solve this problem?  The following packages have unmet dependencies: libgl1-mesa-dri : Depends: libdrm-amdgpu1 (>= 2.4.85-0~x~padoka0) but 2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1 is to be installed  libgl1-mesa-dri:i386 : Depends: libdrm-amdgpu1:i386 (>= 2.4.85-0~x~padoka0) but 2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1 is to be installed  libgl1-mesa-glx : Depends: libdrm-amdgpu1 (>= 2.4.85-0~x~padoka0) but 2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1 is to be installed  libgl1-mesa-glx:i386 : Depends: libdrm-amdgpu1:i386 (>= 2.4.85-0~x~padoka0) but 2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1 is to be installed  mesa-vdpau-drivers : Depends: libdrm-amdgpu1 (>= 2.4.85-0~x~padoka0) but 2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1 is to be installed E: Unmet dependencies. Try 'apt-get -f install' with no packages (or specify a solution).   sudo apt-get install -f Does not help  after run this comand  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages were automatically installed and are no longer required:   libcuda1-375 libdrm-common nvidia-opencl-icd-375 Use 'sudo apt autoremove' to remove them. The following additional packages will be installed:   libdrm-amdgpu1 libdrm-amdgpu1:i386 The following packages will be upgraded:   libdrm-amdgpu1 libdrm-amdgpu1:i386 2 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 44 not fully installed or removed. Need to get 0 B/59,7 kB of archives. After this operation, 14,3 kB of additional disk space will be used. Do you want to continue? [Y/n]  (Reading database ... 271931 files and directories currently installed.) Preparing to unpack .../libdrm-amdgpu1_2.4.85-0~x~padoka0_i386.deb ... De-configuring libdrm-amdgpu1:amd64 (2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1) ... Unpacking libdrm-amdgpu1:i386 (2.4.85-0~x~padoka0) over (2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1) ... dpkg: error processing archive /var/cache/apt/archives/libdrm-amdgpu1_2.4.85-0~x~padoka0_i386.deb (--unpack):  trying to overwrite '/usr/share/libdrm/amdgpu.ids', which is also in package libdrm-common 2.4.85~git20171023.e580be90-0ubuntu0ricotz~16.04.1 Preparing to unpack .../libdrm-amdgpu1_2.4.85-0~x~padoka0_amd64.deb ... De-configuring libdrm-amdgpu1:i386 (2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1) ... Unpacking libdrm-amdgpu1:amd64 (2.4.85-0~x~padoka0) over (2.4.84+git20171019.511c71c8-0ubuntu0ricotz~16.04.1) ... dpkg: error processing archive /var/cache/apt/archives/libdrm-amdgpu1_2.4.85-0~x~padoka0_amd64.deb (--unpack):  trying to overwrite '/usr/share/libdrm/amdgpu.ids', which is also in package libdrm-common 2.4.85~git20171023.e580be90-0ubuntu0ricotz~16.04.1 Processing triggers for libc-bin (2.23-0ubuntu9) ... /sbin/ldconfig.real: /usr/lib/nvidia-384/libEGL.so.1 is not a symbolic link  /sbin/ldconfig.real: /usr/lib32/nvidia-384/libEGL.so.1 is not a symbolic link  Errors were encountered while processing:  /var/cache/apt/archives/libdrm-amdgpu1_2.4.85-0~x~padoka0_i386.deb  /var/cache/apt/archives/libdrm-amdgpu1_2.4.85-0~x~padoka0_amd64.deb E: Sub-process /usr/bin/dpkg returned an error code (1)

Occasionally, when I'm installing stuff, I get an error like the following:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  package1 : Depends: package2 (>= 1.8) but 1.7.5-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.   How can I resolve this?