(May be this is very basic question for MO)  Let $f\in L^{2} (\mathbb R)$ with $\lim_{t\to \pm \infty} f(t)=0.$ Put  $$F_{n} (x)= \frac{1}{2\pi} \int_{-n}^{n}e^{itx} f(t) dt \ (n=1,2,...)$$  Fix $\alpha \in (0, \infty)$ and we define $H_{n}(x)$ as follows: $$\frac{1}{2\pi}\int_{-n}^{n} e^{itx} (f(t+\alpha) -f(t-\alpha))dt = (e^{-i\alpha x}- e^{i\alpha x})F_{n}(x) + H_{n}(x)$$     My Question: Can we expect to prove: $H_{n}(x) \to 0$ as $n\to \infty$ in $L^{2}(\mathbb R)$ ?   I guess some where we need to use ; but I am bit confused, how to use it.  Thanks

Let $f\in L^{2} (\mathbb R)$ with $\lim_{t\to \pm \infty} f(t)=0.$  Put, $F_{n} (x)= \frac{1}{2\pi} \int_{-n}^{n}e^{itx} f(t) dt, \ (n=1,2,...).$ Fix $\alpha \in (0, \infty)$ and we define $H_{n}(x)$ as follows:  $$\frac{1}{2\pi}\int_{-n}^{n} e^{itx} (f(t+\alpha) -f(t-\alpha))dt = (e^{-i\alpha x}- e^{i\alpha x})F_{n}(x) + H_{n}(x).$$     My Question: How to show $H_{n}(x) \to 0$ as $n\to \infty$ in $L^{2}(\mathbb R)$ ?   (I guess some where we need to use ; but I am bit confused, how to use it.)   Edit: @, pointed out below, and in MO, for the same,  I have tried little in that direction:  $$H_{n}(x)= \frac{1}{2\pi}\int_{-n}^{n} e^{itx} (f(t+\alpha) -f(t-\alpha))dt -(e^{-i\alpha x}- e^{i\alpha x}) \frac{1}{2\pi} \int_{-n}^{n}e^{itx} f(t) dt$$ we may write, $H_{n}(x)= \frac{1}{2\pi} e^{-i\alpha x} \int_{-n+\alpha}^{n+\alpha}e^{itx} f(t) dt- \frac{1}{2\pi} e^{i\alpha x} \int_{-n-\alpha}^{n-\alpha} e^{itx} f(t) dt-(e^{-i\alpha x}- e^{i\alpha x}) \frac{1}{2\pi} \int_{-n}^{n}e^{itx} f(t) dt;$ Or, we may write,  $H_{n}(x)= \frac{1}{2\pi} e^{-i\alpha x} \int_{-n+\alpha}^{n+\alpha}e^{itx} f(t) dt- \frac{1}{2\pi} e^{i\alpha x} \int_{-n-\alpha}^{n-\alpha} e^{itx} f(t) dt- \frac{1}{2\pi}\int_{-n-\alpha}^{n+\alpha} e^{itx} f(t+\alpha) dt + \int_{-n+\alpha}^{n+\alpha} e^{itx} f(t-\alpha) dt= I_{1}-I_{2}-I_{3}+I_{4};$  But then,(using one of the above form), we need to show:  $\lim_{n\to \infty}\int_{\mathbb R} |H_{n}(x)|^{2} dx=0.$  Now If I interchange the limit and integral (this may not be possible, here, I am doing without rigours), and then I can take limit inside the square, and then after taking limit, each integrals, $I_{i}, (i=1,2,3,4)$, will be becomes over $\mathbb R$; then I think, it will cancels each other;      Is this o.k or am I missing something, still, I don't see, where we need to use asymptotic behaviours of $f$ (and what does it mean ?, here is $f$ is arbitrary member of $L^{2}$) ? I am wondering, is it possible to get solution without, Plancherel or parsevel somewhere ?


There is a small problem  I need to compare two objects, and based on the same keys in these objects pass values from second object to the original object.  Original object  {    content: "Old Value",    height: 200,    id: "15a2d286-d123-1cf0-4e40-b043b055a49f",    type: "location",    units: "some unit value",    width: 200, }   Second object  {    units: "some unit value",     content: "New Value" }   Keys is not necessary to check for compliance  The output will be something like that  {    content: "New Value", // changed value    height: 200,    id: "15a2d286-d123-1cf0-4e40-b043b055a49f",    type: "location",    units: "some unit value", // changed value    width: 200, }   Is there any elegant solution to this problem with Lodash or Underscore?

I need to be able to merge two (very simple) JavaScript objects at runtime.  For example I'd like to:  var obj1 = { food: 'pizza', car: 'ford' } var obj2 = { animal: 'dog' }  obj1.merge(obj2);  //obj1 now has three properties: food, car, and animal   Does anyone have a script for this or know of a built in way to do this?  I do not need recursion, and I do not need to merge functions, just methods on flat objects.


The interface NavigableSet<E> extends interface SortedSet<E> which declares the method SortedSet<E>   subSet(E fromElement, E toElement) .  However, when I look at , I see that it has declared the same method (with exactly the same signature). I also see that it says it inherits some methods (first, last, comparable) from .  Since by definition, interfaces only contain method signatures, why would any child interface redeclare the same method that the parent interface has already declared (and there's no difference in semantics, in the API javadoc)?  Edit: Came across a relevant and nice discussion here -

I've been looking at the JMS API from J2EE and found a strange behavior where certain methods that are declared in an interface (e.g., createQueue in Session) are declared again in the subinterfaces such as QueueSession, and with identical documentation.  Since an subinterface "inherits" all the method declarations of the interface it inherits, and since the JavaDoc tool has no problem sorting out the JavaDocs of the subinterface and creating an "inherited operations" list, I can't figure out what this achieves.  The only think of is that initially the call was in Session, and then moved to QueueSession when the specific subclass was created, though then I would have expected to see something in the documentation of the upperclass. But this is just conjecture.  So the question is: Is there a convincing reason to redeclare a method in a subinterface?


I keep reading the phrase 10 times lighter than..... or similar. This quote is current: "Plastic containers are cheaper to make and 15 times lighter than glass ones, says Dairy Crest". This can not be correct usage surely?  I can take 'glass ones being 15 times heavier than plastic ones' or, though unwieldy, plastic ones are 1/15th the weight of plastic (ones), but 15 times lighter?  It seems popular.

Lately I've been hearing and reading statistics that are communicated in wording that, frankly, confuses me.  Forgive me for not citing specific instances, but I can give a hypothetical statistic that exemplifies the kind I'm referring to:     Comparing the number of tax returns the IRS audited in 2002 and 2010, the number of unlucky folks who had their returns audited in 2002 was ten times fewer than the number in 2012.    There is something about that wording that bothers me, and I'm not sure why.    After a fruitless search on the internet using numerous combinations/permutations of words and phrases such as "X times fewer," "X times less," "mathematical expressions of 'times fewer' as opposed to 'a fraction fewer,' or 'a fraction less,'" and more, I came up empty. Perhaps this question is more appropriate on a math website, but in the off-chance members of EL&U might give their imprimatur to this question, here goes:  Here's a second hypothetical example.  Is it grammatical—not to mention mathematical—to say the following?:     There are ten times fewer pollinating honeybees worldwide today than there were in 1912.  [Though this is a made-up statistic, there has been a dramatic reduction in the number honey bees in America of late!]   Should not the expression be:     There are one-tenth fewer honeybees worldwide today than there were in 1912.     On the surface, the "ten times fewer" locution seems to me to be a contradiction in terms.  How can something less be 10 times fewer?    I can understand readily how, for example, 2012's bee population of, say, 90 million can be one-tenth (point one) less than 1912's population of 100 million, but ten times fewer?   I'm confused.  Which expression is "more" correct?


Let $f(x)=2021x^{2021}+x+1$, and compute the following limit: $$\lim_{x\to \infty} \frac{f^{-1}(2021x)-f^{-1}(x)}{\sqrt[2021] x}$$  My attempt: i want to use mean value theorem to $f^{-1}(x)$ then we have: $ \frac{2020x}{((2021)^2 (η_y)^{2021}+1)(\sqrt[2021] x)}$. And $f(η_y)=η_x$, $η_x∈(x,2021x) $. We know $η_x$ tend to 0 as x tend to $\infty$ so from the expression of $f$ we know $η_y$ is also.but we  don't know  the quotient of $η_y$ and $x$, so i think this way is fail. But i can't do it in other way.

If $f(x) = 8x^3+3x$ then, $$\lim_{x \to \infty} \frac{f^{-1}(8x)-f^{-1}(x)}{x^{1/3}}$$ is?  My attempt: It is clear that the function cannot be easily inverted. So, there must be something in the limit given itself that may simplify the problem. Honestly, I have no clue what to do here. There are a few things which I could see is that the function has only $1$ root(i.e $0$) and is bijective on $x \in \mathbb R$. But that gave no benefit except showing that the inverse of the function exists. Any help would be appreciated.


I have been using Ubuntu for the past few years and I've finally caved and decided to try to dual-boot Windows 7 with Ubuntu 16.04. But, everything says to install Windows first then Ubuntu with it.   I don't want to wipe it and put on Windows the Ubuntu, as I do have some stuff on it. It's all easily replaceable, but I just want to take as little time as possible.   I don't know if it will help, but I have a second storage drive formatted as NTFS.

I have Ubuntu on my laptop. Now I want install Windows 7 in a dual-boot. How can I do this? I can't lose my Ubuntu files, and I'm afraid that I might break . Go  for UEFI only!


I have a folder called HUD and it needs to go to c:/.../Steam/.  Can't find how I need to do it.  This is my script:  @echo off title[*] Yannick's Gui's installer :a: echo [*] Yannick's Gui's installer echo [*] Welcome %username% echo [*] %username% Je Kan kiezen uit deeze optie's  ECHO -------------------------------- ECHO 1.Install HUD ECHO 2.Delete HUD Echo 2.Close ECHO --------------------------------   CHOICE /C 123 /M "Optie?:"  IF ERRORLEVEL 5 GOTO ins IF ERRORLEVEL 4 GOTO del IF ERRORLEVEL 4 GOTO exit  xcopy "%~d0%~p0hud" C:\Program Files (x86)\Steam\SteamApps\common\Counter-Strike Source\cstrike\custom\ /c /d /e /h /i /k /q /r /s /x /y  :ins xcopy "%~d0%~p0hud" C:\Program Files (x86)\Steam\SteamApps\common\Counter-Strike Source\cstrike\custom\ /e pause  :del del C:\Program Files (x86)\Steam\SteamApps\common\Counter-Strike Source\cstrike\custom\hud GOTO End  :exit close

I am making a batch file in Windows XP to copy my folders I need to another folder on my PC. I am getting an error.  I get the error "Invalid number of parameters".  xcopy /s/z D:\Documents and Settings\%username%\Desktop C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Favorites C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Start Menu C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\My Documents C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\PrintHood C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\NetHood C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Templates C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Searches C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Local Settings\Application Data\Microsoft\Outlook C:\SomeRandomFolder\ pause   Then I changed the batch and get this error: "File not found - Desktop"   xcopy /s/z D:\...\%username%\Desktop C:\SomeRandomFolder\ pause   How do I fix these errors?


I recently bought a Lenovo 100s as a lightweight, portable, cheap pc. First step was to clean it and install Ubuntu but I've run into some problems. Firstly they have installed 32 bit Windows and a 32 bit EFI on the machine even though it has 64 bit architecture. The EFI also has no legacy support, so I need a 32 bit ubuntu with EFI support (although I want 64 bit since the hardware supports it). PC has no dvd drive or LAN port, so those boot options are not possible. Anyone have any ideas? I'm a bit of a linux scrub so a step by step would be much appreciated if possible. Thanks!

I recently purchased a Dell Venue 8 Pro.  I have read online about what it needs in order to boot into Ubuntu or any other Linux distro.  From what I have gathered, what really needs to happen is 32-bit UEFI support.  I got information from several sites, but where it was really summed up was in this previous post:    "Ubuntu has no 32-Bit Uefi installer, ask them to add support, they may listen."  That thread was specifically about getting the Dell Venue 8/11 Pro to boot Linux.  However, there are a slew of new tablets coming out running 32-bit UEFI, and I think this is a trend that is going to continue to grow:  mjg59.dreamwidth.org/26734.html  "UEFI on IA32 isn't going away. It will show up on more embedded systems as time goes on."  Others have tried this before with mixed success, but haven't gotten things to work quite right:    "It doesn’t really work. But it’s interestingly close."  I'm trying to start a thread dedicated thread on 32-Bit UEFI support, because that is the piece that is missing (from what I understand).  I don't really know how to work with this stuff, but I'm hoping that some people who do will read this and either contact canonical or somehow patch Ubuntu (or any other distro, really) to work this way.  Again, I don't really know how to do any of this...I'm just hoping someone can help!  Dell Venue 8, 11 Pro, Toshiba Encore, Acer w3, w4, Lenovo miix, and the asus transformer a100 are all tablets that will be affected by this...I think these are going to be incredibly popular tablets once their prices go down, and I think people are really going to get interested in putting linux on these.  Any help is appreciated, and thank you all so much!  EDIT 4/1/14:  Just booted into Ubuntu on my DV8Pro!  All you have to do is follow the instructions here:    To summarize, what you need to do is download the latest Ubuntu 14 daily build (AMD 64 is what worked for me) and put that on a USB drive via Rufus.  'For “Partition scheme and target system type”, choose “GPT partition scheme for UEFI computer.”' You can get the latest daily build here:   You will need to put the file found below into your EFI/Boot directory:   Disable Secureboot and such--follow the original instructions link if you don't know how.  Then set the USB to boot first in BIOS.  This should get you to GRUB.  The rest I'll quote the original author, it's real straightforward:  In the GRUB menu, highlight “Try Ubuntu”, and press “e” to edit it. In the editing screen, scroll down to the command line options, where it says “quiet splash”. Delete “splash” and replace it with: video=VGA-1:1368x768e reboot=pci,force [EDIT: For those of us using the Dell Venue 8 Pro, you need to use this line instead: video=VGA-1:800x1280e reboot=pci,force That accounts for the different resolution of screen.]  Then press F10 to boot. You should get all the way to the Desktop.  There you have it!  This got me to the Unity Desktop.  Problems:  Wifi is not working, but I used an Ethernet adapter and that seems to work.  I tried rotating the screen, but it throws your touch input off to one side, so I left it.    Make sure to read the tutorial mentioned earlier, it is more comprehensive, even though it is made for the ASUS T100.  If nothing else, the instructions I have provided should be enough just to get you to the Unity Desktop, which for me was amazing!  Hope you too can have the same success and keep building on it!  For what it's worth, someone else did this and posted a youtube video here:


I'm taking  on technical writing. It  that you can omit "on" from     The meeting happened on Monday   to turn it to     The meeting happened Monday   The second one seems wrong to me, and I haven't seen it being commonly used either.

When watching US television news or reading US news articles there is this affectation where instead of saying:     "Spotify music-streaming service to launch in U.S. on Thursday" ()   or      "Leading credit rating agency Moody's said on Wednesday that the U.S. government's impeccable credit..." ()   The on preposition is missed out.  Is this just a peculiar US journalistic "news speak" shortcut or do American non-journalist writers write this way too?


Quote:     $$\begin{aligned}3a+10b+5c&=0\\4a+6b+2c&=0\end{aligned}$$ solves to $$\frac{a}{30-20}=\frac{b}{6-20}=\frac{c}{-18+40}$$ so that $$\frac{a}{5}=\frac{b}{-7}=\frac{c}{11}$$   Can someone explain in deep how this equations are solved in this way?  First I thought it to do with using Cramer's rule but we are all aware that Cramer's rule work only for square matrix. And we can see this are only 2 equations with will not make matrix square.   So in my last question I was tempted to do only using Cramer's rule and now it has nothing to do with previous question!  I wish someone will find helping more important

I have 2 equation in terms of $a,b$ and $c$ .  $3a + 10b + 5c =0$ and $4a + 6b + 2c =0$  I need to find a:b:c and answer is $\dfrac a5 = \dfrac {b}{-7} = \dfrac {c}{11}$  I want to know how to get that?  My attempt:  Given equations can be written in form   $$\left ( \begin{matrix}           3 & 10 & 5 \\           4 & 6 &  2 \\           \end{matrix} \right )  \left ( \begin{matrix}           a\\         b\\         c\\         \end{matrix} \right ) =  \left ( \begin{matrix}            0 \\          0\\         \end{matrix} \right ) $$  But here I don't have any idea how to proceed. I can do for 3×3 matrix and I thought it can be done in same way.  Thanks.


Well, it's one particular name from One-Punch Man, Genos.  Sometimes i see it's written as Geno's arm/body parts or something along the line, but not the Genos's arm/body parts. Where did second s go?

Is it "The case' closure" or "The case's closure"? How exactly do I pronounce it?


Let $n=3^{100}+2$ and assume that $X^2-53$ does not have zeroes in $\mathbb{Z}/ n\mathbb{Z}$. Show that $n$ is not a prime.  I tried solving this problem by assuming that $n$ is a prime (in order to reach a contradiction). Then, using the law of quadratic reciprocity for Legendre symbols, we get $-1=\left(\frac{53}{3^{100}+2}\right)=\left(\frac{3^{100}+2}{53}\right)$. However, I do not know how to proceed from here.

So I have to prove that $n = 3^{100} + 2$ is not a prime number while we assume that $X^2 - 53$ has no zeroes in $\mathbb{Z}/n\mathbb{Z}$.   Because we are working with quadratic reciprocity in this chapter, I assumed that $\big(\frac{53}{n}\big) = -1$ and by the law of quadratic reciprocity, we know that $\big(\frac{n}{53}\big) = -1$. However, I have no clue how I could use this to prove that $n$ is not prime.


I wrote a simple code to provide a mini system for a game ticket reservation and while running my project i got some errors in the following function as shown below in the code   Code:   public void reverseTicket(int seatNum,int gameCode,int categ,int price)  {     checkseat(seatNum);     for(int i=0;i<=seat.counter;i++)     {     if(set[seat.counter].available==true)     {       gameCode=gameCode;      set[seat.counter].number=seatNum;      set[seat.counter].category=categ;      set[seat.counter].price=price;         seat.counter++;         break;      }     else     {         System.out.println("is seat number is full");        }       }  }     public void checkseat(int num){  for(int i=0;i< set.length;i++)  {      if(set[i].number==num)      {          System.out.println("Seat is reserved");          set[i].available=false;          break;      }      }  }   the errors appeared:   Exception in thread "main" java.lang.NullPointerException at sports.game.tickt.fans.checkseat(SportsGameTickt.java:199) at sports.game.tickt.fans.reverseTicket(SportsGameTickt.java:170)   How can I fix that please?

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


I have a small confusion. If a static instance (example" singleton instance) access static method. Does the class lock is acquired or instance lock? Class C{  public static cInstance = new C(); // suppose this.Kindle ignore the singleton pattern here private c(){}  public static synchronized m1(){ }  public static synchronized m2(){ }  public synchronized m3(){ //nonstatic }   }  Thread1 -> C.cInstance.m1() Thread2--> C.cInstance.m2() Thread3 --> C.cInstance.m3()  As I understand, m1 and m2 both should acquire class lock. Thread2 will wait for Thread1 to release the class lock. Thread3 will happily run since have acquired the instance lock. Kindly let me know if this holds true.

The Java documentation says:      It is not possible for two invocations of synchronized methods on the   same object to interleave.   What does this mean for a static method?  Since a static method has no associated object, will the synchronized keyword lock on the class, instead of the object?


I am aware that this may seem like a basic question or may have a duplicate (although I checked for both, and if this case I would happily remove the question) but I am curious about how many attacks and at what BAB those attacks are made if a character has if they go down the Two Weapon Fighting feat tree. Below are the feat descriptions of Two-Weapon Fighting, Improved Two-Weapon Fighting and Greater Two-Weapon Fighting.  Improved Two-Weapon Fighting: In addition to the standard single extra attack you get with an off-hand weapon, you get a second attack with it, albeit at a - 5 penalty (see Table 8-10, page 160). Greater Two-Weapon Fighting: You get a third attack with your off-hand weapon, albeit at a -10 penalty.  The Player's Handbook is fairly clear that if the off-hand weapon is light then the penalties are -2/-2.  So... Assuming a 11 level fighter with BAB of +11/+6/+1, a strength bonus of +1(for the sake of simplicity), wielding a shortsword(1d6) in his mainhand and a kukri(1d4) in the off-hand. How many and can he have and at what BAB if he has TWF, and ITWF? What weapons are used for each attack? How many and can he have and at what BAB if he only has TWF, ITWF and GTWF? What weapons are used for each attack?

Does the additional off-hand attack penalty from Improved Two Weapon Fighting stack with that of the off-hand penalty from Two Weapon Fighting?  I ask because I am unsure if the -5 penalty for the additional attack granted by Improved Two Weapon Fighting stacks with the -4 offhand penalty for Two Weapon Fighting for a total of -9 or if the -5 replaces that penalty.


If I have       public class Base{           public void method(){             System.out.println("I am base");         }      }      public class Derived extends Base{           public void method(){             System.out.println("I am derived");         }       }    is there a difference between  Base b = new Derived();   and   Derived d = new Derived();   ? And, would  b.method(); d.method();   print the same?

I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this?   I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly.   Is it just so if you were to do:  IInterface classRef = new ObjectWhatever()   You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that.   Also, how could you write a method that takes in an object that implements an interface? Is that possible?


When calling an app via cmd.exe to  for apps that need to run with elevated privileges, I find that the momentary popup of the cmd.exe is distracting / bothersome for some users. I'd like to eliminate that and it seems that start /b can do this, however I'm not readily seeing how to run start without initially executing cmd.exe as per the linked page above. For example, the /c start /b ... here doesn't really help at all since CMD is already creating a momentary blip up on the screen:  So I'm left with the thought: how can I run start without cmd.exe first? Or is there an even better way to handle this to prevent the momentary flash on the screen?

When I start SQL Server Management Studio 2008, I get an error that's been around forever and is documented .  One of the suggestions to fix it that actually worked was to start SSMS with Run as Administrator. So I modified the properties of the shortcut to always run it as the administrator.  The only annoyance is that I get a prompt every single time asking whether I really want to do it. Is there a way to tell just this one program (SSMS) to not pop up the prompt, while keeping this behavior for other apps?


I am using JabRef and for some bibliography entries, it is reporting a clash  Use of \blx@bbl@verbadd@i doesn't match its definition. \verb   I have already studied this answer , but I could not figure out how to implement it with JabRef.  The entry in the .bbl file is like that   \entry{book:464554}{book}{} \name{author}{1}{}{%   {{hash=TSJ}{%      family={Taylor},      family_i={T\bibinitperiod},      given={Stephen\bibnamedelima J.},      given_i={S\bibinitperiod\bibinitdelim J\bibinitperiod},   }}% } \strng{namehash}{TSJ1} \strng{fullhash}{TSJ1} \field{labelnamesource}{author} \field{labeltitlesource}{title} \field{sortinit}{2} \field{sortinithash}{2} \field{edition}{2nd} \field{isbn}{9812770844,9789812770844,9789812770851} \field{title}{Modelling Financial Times Series} \verb{url} \verb  http://gen.lib.rus.ec/book/index.php?md5=E14E3D6D5388324EF252FBB2008797 \verb 83 \endverb \field{year}{2007} \endentry   And when I comment the lines "verb", the problem disappears. However I have to do it manually every time I change the JabRef file (.bib) and it updates the .bbl file.  \entry{book:464554}{book}{} \name{author}{1}{}{%   {{hash=TSJ}{%      family={Taylor},      family_i={T\bibinitperiod},      given={Stephen\bibnamedelima J.},      given_i={S\bibinitperiod\bibinitdelim J\bibinitperiod},   }}% } \strng{namehash}{TSJ1} \strng{fullhash}{TSJ1} \field{labelnamesource}{author} \field{labeltitlesource}{title} \field{sortinit}{2} \field{sortinithash}{2} \field{edition}{2nd} \field{isbn}{9812770844,9789812770844,9789812770851} \field{title}{Modelling Financial Times Series} %\verb{url} %\verb % http://gen.lib.rus.ec/book/index.php?md5=E14E3D6D5388324EF252FBB2008797 %\verb 83 %\endverb \field{year}{2007} \endentry   I am using  \usepackage[ backend=bibtex, style=alphabetic, sorting=ynt, style=numeric-comp ]{biblatex} \usepackage[nottoc,numbib]{tocbibind} \bibliography{motivacao.bib}   My guess would be the problem is associated with the      @Book entry in the .bib file, because maybe the field "url" should not be there?   As soon as I comment or remove the field from there (JabRef) it works perfectly.  Does anybody have a proper workaround besides deleting or commenting the fault lines?  Thanks!

Currently having problems with compiling my Master's thesis after downloading the newest version of TeXStudio and MiKTeX. The error message is as follows:  Use of \blx@bbl@verbadd@i doesn't match its definition. \verb   The only other place I found a similar question regarding this error message was found here:   I am not sure how this applies to my problem, but from what I understand this is due to some problem in an external file. If you need the bibliography-entry, I can provide you with that on short notice, though it is rather long (which is why I didn't include it here in the first place).  I am using Mendeley Desktop v1.16.1 to automatically generate my BibTeX database.   I am using biblatex as follows:  \usepackage[backend = bibtex,         style = numeric-comp,         sorting = none,         natbib = true,         doi = false,         isbn = true,         hyperref = true]{biblatex}   I also have some code to change how the bibliography output, but I doubt it is causing the problem, as commenting it out did not help.  Hope anyone knows what causes my problem and how to fix it.  Thanks.


I have strange issue, df shows rootfs is 100% full but du shows it's 25% used. So I check on the unlinked files from the rootfs using lsof +aL1 / and it does not show me any deleted/unlinked files from rootfs. I tried find /proc/*/fd -ls | grep  '(deleted)' too and it does not show any unlinked file from rootfs!  Inode usage is only at 9%

When I sum up the sizes of my files, I get one figure. If I run du, I get another figure. If I run du on all the files on my partition, it doesn't match what df claims is used. Why are there so many different figures for the total size of my files? Can't computers add?  Speaking of adding: when I add the “Used” and “Available” columns of df, I don't get the total figure. And that total figure is smaller than the size of my partition. And if I add up my partition sizes I don't get my disk size! What gives?


There are many examples exist for validating full number but Could anybody help me how can I start for pre-guessing Credit Card validation while typing the number itself digit by digit (at least after entering 4 digit), not a full complete number in Java?  PS: Question is not duplicate, Full number validation answers exist but my requirement is after entering 4 digits. Thanks

I'm trying to figure out how to detect the type of credit card based purely on its number. Does anyone know of a definitive, reliable way to find this?


I would like to know how to find out the sum of this series:  $$1 - \frac{1}{2^2} + \frac{1}{3^2} - \frac{1}{4^2} + \frac{1}{5^2} - \frac{1}{6^2} + \cdots$$  The answer is that it converges to a sum between $\frac 34$ and $1$, but how should we go about estimating this sum?   Thanks!

I am given the following series:  $$\sum_{n=1}^\infty \frac{(-1)^n}{n^2}$$   I have used the alternating series test to show that the series converges.   However, how do I go about showing what it converges to?


So I've installed the Add Mesh: Extra Objects add-on because I want to make a mesh from a mathematical function.  However, the tutorial I'm following seems to use an old menu that I cannot find in the latest version. It looks like this :    How can I find this menu in the latest version of Blender. I'm new to Blender so any help would be appreciated.

hello everyone I have a little problem, how do I bring up the menu in the circle? when I select another object the menu becomes non-existent


I'm on Catalina 10.15.6 on a MacBook 2019 (16-inch) and one hour ago after startup my mac started  with an extremely loud fan and overheating. As Im writing this even the typing is lagging behind. Does anyone know why this is happening and how to fix it? I closed all apps running already and restarted several times, but nothing seems to work.

Why are the accountsd and securityd processes using so much CPU on OS X 10.10.3? I am on a Early 2011 Macbook Pro.  What are these processes for? Is it safe to kill them? The machine has only been up 4 hours so has been rebooted recently.


We recently had a harddisk failure on our mail server (debian/postfix/courier) so I'm researching a way to build redundancy.  The first way I found was to setup multiple mx Records in the DNS Server so that the second Mailserver jumps in when the first fails. While this is easy to build it's not what I have in mind for redundancy.  The second one is to use a third box which provides a NFS share where the Mailboxes are stored. This isn't really an option, because it provides a single point of failure like a standalone Mailserver.  I would like to have a way to synchronize the two servers, so that, if the first Mailserver fails, the enduser doesn't notice there had been a failure. (Mails still in the IMAP Mailbox etc.)  Any chance?

I'm needing to set up a remote mirror for a postfix server (where the content of both mail servers should be the same at any time).  The idea is that if the main server comes down at some point the mirror server will take its place, manage the new incoming mails, and when the e-mail server comes up again, it will update it with the new e-mails and return it the control to manage the new incoming mails.  The mail servers will be hosted in different places (i.e. maindomain.com, themirrorsite.com).  Getting a simple back-up server doesn't seem too difficult:        But the problem is that this configuration wouldn't make the back-up site a complete mirror of the main mail server (it will hold only the e-mails received while the main server is down).  Is there a way to achieve the required configuration?


At the beginning of a Hearthstone match, you can choose to either keep or discard your starting hand. If you discard cards, are they placed at the back of the deck or are they shuffled before the game begins allowing them to (possibly) come out in early draws.

When you discard cards at the beginning of the game, where do they go? The appearance is that they get shuffled back into the deck. However, after discarding key cards and not receiving them the whole game, I am now wondering if they get put in the bottom of the deck. Where do they go after being discarded?


how can I create a cpio archive by ignoring the modification times of the files (or imposing them at a known value)?  The context is as follows: in the build process of an embedded project some "intermediate" files are stored in a cpio archive. They will be used by the FW of a microcontroller, so neither uid/gid nor modification time is involved. My constraint is that I must be able to rebuild a certain version at any time, ensuring that I always get the exact same binary (bit by bit). But if the modification time is also stored in the cpio this constraint is no longer met.

I would like my initramfs to have the same hash no matter when or where I build it if the contents of the files are the same (and are owned by root and have same permissions).  I don't see any options in GNU cpio to strip or set timestamps of files in the archive.  Is there a relatively standard way to massage the input to cpio and other archive programs so you can get reproducible products?  Going along with this, is there a conventional "We aren't giving this a date" timestamp?  Something most software won't wig out about? For example 0 epoch-seconds?  For example, if I did a find pass on an input directory for an initramfs and manually set all the timestamps to 0, could I build that archive, extract it on another system, repeat the process, and build it again and get bit-identical files?


When I am reading answers to a question with many answers, the further down the list of questions I go, the more blank space at the end of each answer is there.  After about 5 answers, you start getting about a  screen full of nothing but white space at the end of the answer.  I'm on a Motorola razr maxx, running cyanogenmod This screenshot is from the latest example I've seen, on rpg.se, but it occurred on Stack overflow also.    Top of the example answer:   Bottom of the example answer:   Here's the question from the screenshots

Noticed that sometimes when there are 10+ answers to a question - some answers look like they have \n\n...\n line breaks in the end, so the body of the answer has incorrect height.  It probably has something to do with ViewHolder or adapter not setting correct row height. Although as far as I know, it should do this according to text amount/length.


I'm writing my thesis in philosophy using Lyx and found out that most of them are written with this particular typewriter-like font. Could someone tell me where i could find this font? Does Lyx already provide a similar font?   Thanks to everybody

Is it possible to identify the font used in a specific document/picture?  Answers to this question should identify:   Possible methods to do this (perhaps one answer per method) and adequately describe how to use it (as opposed to merely stating it); Ways of finding the identified fonts, if possible (free or not); and Any prerequisites associated with the method used, if required (for example, "In order to use method X, your document has to be in format Y").   This question is meant as an FAQ, based on an . Its aim is to facilitate the community with the general procedures involved in font identification. Similar cases are solved on a per-usage basis on 's  tag.


My problem is that  pointOnMap() runs before xmlPreparer() despite on order. I think it has something to do with using AJAX. parseXML creates object i need . So when i use pointOnMap() it already should be initialized.  On page is first that i see from pointOnMap - 0 and after that from parse ..So it is not in right order . Thank you for your advices.  var mesta= new Array();   function init() {     xmlPreparer();     pointOnMap();    }  //add source function xmlPreparer() {        $.ajax({     type: "GET",     url: "./mesta.xml",     dataType: "xml",     success: parseXml   }); }  function parseXml(xml) {      var type;     var name;     var latitude;     var longitude;    $(xml).find("city").each(function()   {     type=$(this).find("type").text();     name=$(this).find("name").text();     latitude= $(this).find("latitude").text();     longitude=$(this).find("longitude").text();     var mesto = {type:type, name:name, latitude:latitude, longtitude:longitude};     mesta.push(mesto);   });     alert(mesta.length);//this prints right size }  //add source function pointOnMap() { alert(mesta.length);//for no reason prints 0 and runs before xmlparser? $('#dot').css('top', YLatToPixel(0,$('#jpMapa'))) $('#dot').css('left', XLngToPixel(0,$('#jpMapa'))+'px'); }  function YLatToPixel(lat,elem){ var containerHeight=$(elem).height(); lat+=90; var calculatedHeight=((lat*containerHeight)/180); return $(elem).offset().top+($(elem).height()-calculatedHeight); }   function XLngToPixel(lng,elem){ var containerWidth=($(elem).width()); lng=lng+180; return $(elem).offset().left+((lng*containerWidth)/360); }

I have a JavaScript widget which provides standard extension points. One of them is the beforecreate function. It should return false to prevent an item from being created.   I've added an Ajax call into this function using jQuery:  beforecreate: function (node, targetNode, type, to) {   jQuery.get('http://example.com/catalog/create/' + targetNode.id + '?name=' + encode(to.inp[0].value),    function (result) {     if (result.isOk == false)          alert(result.message);   }); }   But I want to prevent my widget from creating the item, so I should return false in the mother-function, not in the callback. Is there a way to perform a synchronous AJAX request using jQuery or any other in-browser API?


I am a junior developer and visit Stack Overflow multiple times a day to get answers on all sorts of development topics; however I do not have enough reputation to say if comments are helpful or not. I would like to give feedback sometimes that the answers are worthless and need to be downvoted but most are exactly what I needed.   What is the fastest way to get enough reputation to up-/down-vote and is it even worth it to try to build up the reputation to give back to the community?

I have been on Stack Overflow for some time.  It is an AMAZING resource and don't know if I would've got through the past 18 months without it.  I love it!  Problem is that I have "1" reputation.  All of my questions have already been asked and answered.  My "new user restrictions" mean: - I can't vote up answers that were helpful. - I can't comment on answers.  I sometimes have a question to ask one of the users that answered someone else's question but I can't.  This is hard!  How do I get a break?  Do I have to troll for a couple of days/weeks/months to answer enough questions in the hope someone votes some of them up just so I can do some basic functions?  Perhaps the number of site visits and length of membership could count for something?


I have the following problem: when calculating the cost for delivery of an order, I noticed that in some cases (-1.4210854715202E-14 in my case) a floating point error shows up. You can find the function I am using below, the error shows up when $orderTotal has the same value as $totalPackagePrice.  public function getPaidPackages() {     $orderTotal = doubleval($this->total_price); //price the customer paid for     $totalPackagePrice = doubleval($this->getTotalOrderPrice()); //price of all the orderitems within all the packages combined      //error shows up when substracting the same values (e.g. 68.55 in my case)     $packagingCosts = $orderTotal - $totalPackagePrice; //shows a negative value when debugging      ... }   Any help to tackle this problem is appreciated, so far I've tried to cast both input values to a float or a double to no avail.

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


Is it possible to only show the launcher on a specific workspace? I would like the launcher for my top left workspace, but none of the others.  I seem to remember seeing an option or setting for this, but now I can't find it now that I need it.

I want to keep launcher active only in main workspace. E.g. I like to keep Citrix window in full display mode without launcher (in workspace II).


I would like to add an operator to a class.  I currently have a GetValue() method that I would like to replace with an [] operator.  class A {     private List<int> values = new List<int>();      public int GetValue(int index) => values[index]; }

DataGridView, for example, lets you do this:  DataGridView dgv = ...; DataGridViewCell cell = dgv[1,5];   but for the life of me I can't find the documentation on the index/square-bracket operator.  What do they call it?  Where is it implemented?  Can it throw?  How can I do the same thing in my own classes?  ETA: Thanks for all the quick answers.  Briefly: the relevant documentation is under the "Item" property; the way to overload is by declaring a property like public object this[int x, int y]{ get{...}; set{...} }; the indexer for DataGridView does not throw, at least according to the documentation.  It doesn't mention what happens if you supply invalid coordinates.  ETA Again: OK, even though the documentation makes no mention of it (naughty Microsoft!), it turns out that the indexer for DataGridView will in fact throw an ArgumentOutOfRangeException if you supply it with invalid coordinates.  Fair warning.


Historically our branch offices have had their own servers to do DNS, Active Directory and a few other services. But the number of people working out of our branch office has shrunk to about 4 people.  From head office we provide VPN access to all our remote users. I am proposing that instead of providing a server (and maintaining it) each user in this office instead uses VPN.  Email, File and Database access will be provided by head office in either configuration.  My question is how many users can work in the branch office before it becomes unworkable and I would need a server with site to site VPN?

This is a  about  Related:      I have a question regarding capacity planning. Can the Server Fault community please help with the following:   What kind of server do I need to handle some number of users? How many users can a server with some specifications handle? Will some server configuration be fast enough for my use case? I'm building a social networking site: what kind of hardware do I need? How much bandwidth do I need for some project? How much bandwidth will some number of users use in some application?


I am trying to solve the following problem in ZF: "Show that the collection $\{\kappa \ | \ \kappa=\aleph_\kappa\}$ is a proper class. My thinking is that in the construction any element of this collection, one takes an arbitrary ordinal $\alpha$, and that therefore one might be able to show it is a proper class by showing that there is a bijection between the class of all ordinals and the class given above, since the class of all ordinals is a proper class.  However, I'm not sure how to fully make sense of the concept of a function between proper classes, since a function is normally defined as being between sets. Is this a valid line of reasoning, and if so, how does one formalise this using the axioms of ZF?

In some set theories such as ZF+, in which GAC is global axiom of choice, the Von Neumann universe $V$ bijects to $Ord$, the class of ordinals. It suggests us that proper classes may also have cardinality，in the example is $|V|=|Ord|$. In addition, if we are in ZF+GAC+, it seems $|V|$ is the only cardinality which is not a cardinal number. Moreover, it seems some properties such as Cantor–Bernstein–Schroeder theorem also holds for cardinality of proper classes, but I'm not sure if it is well-defined and won't cause any paradox...


Question: Prove that the sum of the binomial coefficients for the nth power of $(x + y)$ is $2^n$.   i.e. the sum of the numbers in the $(n + 1)^{st}$ row of Pascal’s Triangle is $2^n$ i.e. prove $$\sum_{k=0}^n \binom nk = 2^n.$$ Hint: use induction and use Pascal's identity  What I have so far: $$p(n)= \sum^{n}_{k=0}{n\choose k} = 2^n$$ $$P(0)=\sum^{0}_{k=0}{0\choose k} = 2^0$$ LHS: ${0\choose k}=1$ RHS $2^0=1$  now of for the inductive step I am getting all tangled up in my terms. It seems like a silly thing to get confused on but every inductive proof I've done I do $P(n) =$ something to $P(1)$ then my inductive step is $P(k)$ and $P(k+1)$ but I don't think can use that terminology because those variables are in the problem. Also the two (i.e) are throwing me off, am i even setting it up right to begin with or am I missing something. How does $(x+y)^n$ even fit in to here, I know how it connects to pascals because I googled it but I don't understand how it fits into my inductive proof.  I need help getting on track form here. PS my professor is a stickler for set up so making sure I write it properly is a big part of it.

Prove by induction that for all $n \ge 0$:  $${n \choose 0} + {n \choose 1} + ... + {n \choose n} = 2^n.$$  In the inductive step, use Pascal’s identity, which is:  $${n+1 \choose k} = {n \choose k-1} + {n \choose k}.$$  I can only prove it using the binomial theorem, not induction.


There is setLocale method in MainActivity.class.  public void setLocale(String selected) {     Locale locale = new Locale( selected );     Locale.setDefault( locale );     Configuration config = new Configuration(  );     config.setLocale( locale );     getBaseContext().getResources().updateConfiguration( config, getBaseContext().getResources().getDisplayMetrics() );      SharedPreferences.Editor editor = getSharedPreferences( "LanguageSetting", MODE_PRIVATE ).edit();     editor.putString( "MyLanguage", selected );     editor.apply();  }   I want to call this method above in a Fragment below.  @Override     public void onItemClick(AdapterView<?> parent, View view, int position, long id) {         final String[] languageItems = {"English", "Polish"};         mainActivity = new MainActivity();         switch (parent.getItemAtPosition( position ).toString()){             case "Language":                 new AlertDialog.Builder( getContext() ).setTitle( R.string.nav_bottom_dialog )                         .setSingleChoiceItems( languageItems, -1, new DialogInterface.OnClickListener() {                             @Override                             public void onClick(DialogInterface dialog, int which) {                                 switch (languageItems[which]){                                     case "English" :                                         mainActivity.setLocale( "en" );                                         mainActivity.recreate();                                         break;                                     case "Polish" :                                         mainActivity.setLocale( "pl" );                                         mainActivity.recreate();                                         break;                                 }                                  dialog.dismiss();                             }                         } ).show();   It works when I have setLocale method and run it in MainActivity. I don't know why it doesn't work when I call the method in a Fragment showing NullPointerException Error like below.  There is no any error shown in Android Studio, does anyone know why??  E/AndroidRuntime: FATAL EXCEPTION: main     Process: org.language.languageapp, PID: 16894     java.lang.NullPointerException: Attempt to invoke virtual method 'android.content.Context android.content.Context.getApplicationContext()' on a null object reference         at android.content.ContextWrapper.getApplicationContext(ContextWrapper.java:118)         at org.techtown.techApp.MainActivity.setLocale(MainActivity.java:134)         at org.techtown.techApp.ui.fragment.Fragment01$1.onClick(Fragment01.java:74)   MainActivity.java:134 =>  getBaseContext().getResources().updateConfiguration( config, getBaseContext().getResources().getDisplayMetrics() );  Fragment01.java:74 => mainActivity.setLocale( "en" );

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


This question is from Wayne Patty's Topology Section 5.2.  Consider $A$ be a compact subset of a regular space and let $U$ be an open set such that $A\subseteq U$. Prove that there is an open set $V$ such that $A \subseteq  V \subseteq \overline{V} \subseteq U$.  Let $p \in A$ which implies $p \in U$. Then a result is given in   the book (Theorem 5.11): A $T_1$-space $(X, \mathcal T)$ is regular if and only if for each member $p$ of $X$ and each neighbourhood $U$ of $p$, there is a neighbourhood $V$ of $p$ such that $\overline{V}\subseteq U$. So, I got $ V \subseteq \overline{V} \subseteq U$. But I am unable to prove that $A\subseteq V \subseteq \overline{V}$. I thought that I should let $V\subseteq \overline{V} \subseteq A$ but I am not able to find a contradiction. Can you please help with that?

I was given a claim:     Let $(X, \mathfrak{T})$ be a topological space. Then $X$ is a regular    space iff $\forall x \in X, \forall U \in \mathfrak{T}$ s.t. $x \in  U$, $\exists V$ such that $x \in V \subseteq \overline V \subseteq U$   Regular is defined as (similar to wiki):     If, given any point $x$ and closed set $F$ in $X$ such that $x$ does   not belong to $F$, they are separated by open disjoint neighbourhoods   I was stuck on a minor part of the proof and need some help!    $(\Rightarrow)$ Let $(X, \mathfrak{T})$ be a regular space. Then $\forall x \in X$, $F \subset X$, $F$ is closed and does not contain $x$, there exists open sets $U$ and $W$, such that $x \in U, F \subset W$ and $U \cap W = \varnothing$.  Since $U$ is open, for all points $X$, there exists an open set $V$ such that $x \in V \subset U$. (We have just produced $V$ in the claim)  Let $y \in F \subset W$ be another point. Then by definition of regular, $y$ is separated from any closed set. Consider the closed set $\overline V$, then we have $y \in W, x \in V \subseteq \overline V \subseteq U$. And since $U \cap W = \varnothing, y \notin \overline V$  ($\qed$ $\eop$ <--- how to generate end of proof symbol?)       There is something terribly wrong in the second last line of the proof   which I stated:      " $x \in V \subseteq \overline V \subseteq U$"      There is no insurance that such $\overline V \subseteq U$.  It is very likely that $U \subseteq \overline V$ instead.      How do I correct this line?


Or, I guess it could be worded, since when and why was it counted as part of a formal writing style to capitalize many general nouns? (After all, it's not German ...) This is also a trend in legal documents, however, I believe, attributable to the fact that certain terms (e.g. "Company") can have very specific definitions.  Here is the second paragraph of the .     We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.--Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.

It seems to have been common practice in the 17th and 18th centuries in English-language sources to capitalise the first letters of nouns, as in  At which Time he prov'd himself the Noah's Dove, that finding himself no Rest anywhere, was receiv'd again into his own Ark, and brought a peaceable Olive-Leaf in his mouth. —  (1685)  Most original sources I can find on the web have used modern rules for capitalisation, so I have a few questions:  Was the practice used for all nouns (Note mouth isn't capitalised in my quotation above.)? When did this practice begin? When and why did it end?


I have a number of clients that will never see an Internet connection, thus will never receive Windows updates that I need to somehow make happen.  I read a SuperUser suggestion from 2009 that spoke of Windows Server Updates.  I tried to download and install it on my Windows 8 (Internet connected one) and it said it was incompatible.  Any ideas as to where I can go to get the latest Win 7 and XP updates, burn them to disc and manually update my clients?

What options, if any, exist for offline update of Microsoft  Windows?  If a solution exists please list your experience using it.    Background:  If for any reason a computer does not have a connection to  the Internet or the connection is too slow to download  several hundreds of megabytes every so often some kind of  offline Windows Update is required.  In a multi-computer environment a lot of bandwidth (and thus in some cases money) and/or  time could also be saved if it is possible to update in an  offline manner.


I'm trying to prove with squeeze theorem that the limit of the following series equals 1: $$\frac{1+\sqrt{2}+\sqrt[3]{3}+...+\sqrt[n]{n}}{n}$$ For the left side of the inequality I did: $$\frac{1+\sqrt{1}+\sqrt[3]{1}+...+\sqrt[n]{1}}{n} <  \frac{1+\sqrt{2}+\sqrt[3]{3}+...+\sqrt[n]{n}}{n}$$ For the right side, at first I did the following: $$\frac{1+\sqrt{2}+\sqrt[3]{3}+...+\sqrt[n]{n}}{n} <  \frac{n\sqrt[n]{n}}{n}$$ But then I realized it wasn't true and that the direction of this inequality is the opposite. Do you have any idea which series with limit 1 is bigger from the original series? Thanks!

Does $\displaystyle\lim_{n\to \infty}\ \frac{1+\sqrt[2]{2}+\sqrt[3]{3}+\cdots+\sqrt[n]{n}}{n}=1$?   Thanks a lot for your time and help.


When I launch an FTP transfer from a client machine, it fails because it cannot connect to the server. With tcpdump I can see that the client sends a SYN to the server, and I can also see that the server received the SYN but it does not respond.    I made sure that the source/destination MAC address is correct, same for IP address.  There is absolutely no firewall rules whatsoever.  Any ideas how I can debug the issue?

Lately, we've become aware of a TCP connection issue that is mostly limited to mac and Linux users who browse our websites.  From the user perspective, it presents itself as a really long connection time to our websites (>11 seconds).  We've managed to track down the technical signature of this problem, but can't figure out why it is happening or how to fix it.  Basically, what is happening is that the client's machine is sending the SYN packet to establish the TCP connection and the web server receives it, but does not respond with the SYN/ACK packet.  After the client has sent many SYN packets, the server finally responds with a SYN/ACK packet and everything is fine for the remainder of the connection.  And, of course, the kicker to the problem: it is intermittent and does not happen all the time (though it does happen between 10-30% of the time)  We are using Fedora 12 Linux as the OS and Nginx as the web server.  Screenshot of wireshark analysis    Update:  Turning off window scaling on the client stopped the issue from happening.  Now I just need a server side resolution (we can't make all the clients do this) :)  Final Update:  The solution was to turn off both TCP window scaling and TCP timestamps on our servers that are accessible to the public.


Operators related to physical transformations in quantum mechanics are usually unitary and linear except time-reversal which is both antiunitary and antilinear. What is the explanation for this difference?

I checked many books and they all state that  is . But why do we need it to be anti-linear? Please explain where this need actually arises.


I found this one on UserVoice, and I thought it was fitting to bring it up here for further discussion.  "Stack Overflow already works with Mobile Safari, but the experience is far from optimum. I believe an iPhone-optimized version (or maybe even a native client) would be perfect. I can help with either."  I personally think a some kind of mobile version of Stack Overflow would be great for using as a reference, but using it to ask questions would probably get cumbersome if you had to type up a long question with full description. However, using it to look up an answer when you're away from your desk would be awesome.  But, why not just use the regular Stack Overflow? Well, we all know that the small, touch screens get cumbersome to use when navigating websites built for desktops.

I like using Stack Overflow (or any other Stack Exchange sites) and was wondering if there was an app I could install on my phone or other device that would allow me to use the site on-the-go or straight from my desktop.  Some systems to consider:   Windows 8 Android iPhone/iOS   What are some apps that I could install to my computer or phone to enhance my Stack Exchange experience?


I have been digging the archives for eternity to find that Location Services and Auto-sync (assuming we ignored other factors such as Bluetooth etc -- because my focus is mainly about auto sync) are extremely battery hungry.  Although, i manually toggle the switches (GPS, BT etc) based on requirement. I have paid enough heed to notice the battery gain and drain caused by auto sync enabled and disabled.  I have read somewhere people claiming innocence of autosync. Basically, Their idea is that it doesn't constantly push all the data from server to my phone and vice-versa. instead, there is a thread meant to ask the server if there's something new (and events are created based on the responses).  So, shed some light on:  1) is auto sync really causing the depression to my battery?  2) what does auto sync really do (perhaps a geeky explanation please) ?  3) how many minutes/hours am i actually gaining or losing while leaving it ON or OFF ?  4) what other factors claim culpability as to battery drain?


There has been some turmoil lately, and many highly active users, moderators and community moderators have stepped down.   I'm wondering how/if this has affected the activity on various SE-sites (and SO in particular). What has happened to the question/day rate, answers/question, votes/post, number of users answering questions etc.  Is there any available information regarding this? Are there any clear trends? Does it at all affect the overall network activity?

Ever since Everything That Happened with Stack Exchange, it's understandable that many users are hesitant to get re-involved on SE.  It's understandable that  are deleting their own accounts, out of protest, or out of frustration, or for many other reasons.  But I have noticed that, at the very least on , where I spend most of my time, questions are getting fewer views and fewer answers, fewer votes are being cast, and fewer questions themselves are being asked.  I've also noticed that flags are taking a long time to be processed, probably because of the fact that Writing.SE .    Are other sites also experiencing inactivity?  Is this in direct correlation with Everything That Happened?  Is it just this site, or are other sites experiencing the same patterns as well?


Sometimes I am eager to see the activity of other users, who I am interested in . Is there any good way, except to search the id each time, to achieve this? Why can't stackoverflow have the follow feature?

I've been looking around and I can't seem to find an automatic (i.e. buzz- or Twitter-like) way to follow users inside Stack Exchange. Why haven't the developers added such a feature? It could help beginner users follow other beginners with the same interests. We would be able to learn from each others' questions and pitfalls. Also, it would reduce double posting.


I am trying to link my CSS file to the HTML but it doesn't seem to work and I do not see any errors on the syntax   <link rel="stylesheet" type="text/css" href="Project Website Styling.css">     Thank you

Is a URI (specifically an HTTP URL) allowed to contain one or more space characters? If a URL must be encoded, is + just a commonly followed convention, or a legitimate alternative?    In particular, can someone point to an RFC that indicates that a URL with a space must be encoded?  Motivation for question: While beta-testing a web site, I noted that some URLs were constructed with spaces in them. Firefox seemed to do the right thing, which surprised me! But I wanted to be able to point the developers to an RFC so that they would feel the need to fix those URLs.


this is my first time to install ubuntu, it seems a lot of effort on a dell xps 15, but for the last 12 hours or so I seem to be making progress. First of all ubuntu wouldnt load for me it was stuck on a black screen and also on purple load screen. I then pressed e while hovering over ubuntu in the grub menu and then I changed some things in here, I ran ubuntu and it worked perfectly.  However when I start ubuntu my changes are not saved and I am asking how can I make these changes permanent so that I don't have to update the grub every time I want to log into ubuntu.  I have googled this question and scoured the first couple of google pages for solution and none have worked in my case.    Can someone please enlilghten me on how I can just make my grub changes permanent... Thank you very much in advance!

I know that editing the boot options line and adding 'nomodeset' solves the problem of my laptop during LiveCD mode, what I don't know is how to set it at boot up through Grub2 after I've installed Ubuntu.  So, my question is; how do I set nomodeset before I boot into Ubuntu?


Redirecting to HTTPS causes an error, Google should be indexing the HTTP version. How can I enforce that? I have no forms or logins on my website, I have no SSL certificate.  For example: Searching for paul and martin consultancy in Google returns the home page (second result) with an https:// protocol:    And clicking this link naturally results in the following browser error:    I am using this .htaccess:  Options +FollowSymLinks RewriteEngine On RewriteCond %{HTTP_HOST} ^example\.com$ [NC] RewriteRule ^(.*)$ http://www.example.com/$1 [R=301,L]

We have a busy website where we never used SSL. Recently its indexed by Google as https://www.example.com.  The users are getting security certificate errors.   In google webmaster tools we can only remove the relative URL. For example, any thing after http://www.example.com.   I am using IIS 6.0 to host the site .net website.   I have seen similar posts here and there and almost all of them recommend a redirect. I don't want to set up a redirect as it will slow down the site loading. I guess I would also need to setup a new website on IIS  with HTTPS protocol and then do the redirect to HTTP site?


Update  On a completely unrelated search, I have found this:  which lists a few possible options with about the same goals.  Original post  We have a desktop .Net/WPF app, with large (for a desktop app) amounts of data stored: it's has layouts, templates, products list and technical specs, and many more stuff.  Today it's stored in an Access DB, but we have hit the Access limitations pretty hard: it's not very fast, the DB weights 44Mb (which results in a large setup package), and more importantly, it's a pain to use with version control, because we can't merge the data from a branch to another. For instance, we might create a branch to add a few products, but then we have to add them manually in the trunk when we merge. We could use SQL scripts, but writing advanced SQL scripts for Access is a pain.  Basically, I want to replace the MS Access DB with another storage format, because Access is not well adapted.  I had tought of using JSON files that would be unzipped during or after install, but I'm a bit afraid of performance problems. I'm also thinking of splitting the data into multiple files with multiple formats, depending on its usage, but using different formats might get complicated or annoying to develop.  Performance  Some parts of the DB are accessed pretty often and should be performance-optimized, whereas others are accessed maybe 1 or 2 times per work session, and using a poor-performance but high-compression format could be OK.  Size  We want the installer to be the smallest possible, so the library should be small, and the format should use small files. Using a library that adds 5 Mb to the installer file is out of the question.  Compatibility  The software must be able to run on .Net 4 (not 4.5), and it would be great if it ran on Windows XP (even though we're thinking more and more of just abandoning it going forward, it's still more than 7% of our market share).  Moreover, it should not need to install a server (like MS Access or SQLite) because it will be installed on end-user's computers, and we don't want to bloat them.  Versionning  It should be easy to version the data and the DB structure. The file should either be a text file (like JSON), or scripts should be easy to run in the continuous integration platform (like SQL server).    So, which technology would you use that answers all these contraints ?  Thanks !

Could you recommend a lightweight SQL database which doesn't require installation on a client computer to work and could be accessed easily from .NET application? Only basic SQL capabilities are needed.  Now I am using Access database in simple projects and distribute .MDB and .EXE files together. Looking for any alternatives.


I just installed MacOS 11.3. I now have a folder on my desktop called Relocated Items.nosync. It contains a file called group.system_default inside Configuration/private/etc which the docs says is the default Apple would normally have installed but it left my modified file in place. I compared the two files. The difference is that the system default file Apple would have installed includes one additional line: _trustd:*:282:_trustd I have read that this process relates to security certificates and so this causes me a little concern. Does anyone have any insight what the best course of action is? Install Apple's recommended file including the trustd line? Or leave my modified file without that line in place? Do something else? Related thread on MacRumors:

After updating my macOS to 11.3.1 from 11.3, a directory named Relocated Items appeared on my desktop. A document in that directory explained a bit about what's going on. I will attach the text of the document below. so I viewed a diff between /etc/group and ~/Desktop/.../group.system_default and saw that the line containing _trustd:*:282:_trustd exists in group.system_default but not in /etc/group. Another odd thing I realized is the 'Date modified' on the file on group.system_default is 1. Jan 2020. This computer and the install are both from 2021. Can somebody explain what is going on? I am not sure which of the files came with the macos-update and which I suposedly modified in the previous version. I also don't understand what _trustd:*:282:_trustd means. Document in Relocated Items Directory  During the last macOS upgrade or file migration, some of your files couldn’t be moved to their new locations. This folder contains these files. Configuration files These configuration files were modified or customised by you, by another user or by an app. The modifications may be incompatible with the recent macOS upgrade. The modified files are in the Configuration folder, organised in subfolders named after their original locations. To restore any of the custom configurations, compare your modifications with the configuration changes made during the macOS upgrade and combine them when possible. Configuration files with the suffix "system_default" were edited or customised but the changes were allowed to remain installed. The system_default version of the file is provided to demonstrate what the Apple-supplied version of this file would look like. It is recommended you compare the two and evaluate whether you wish to integrate any changes Apple may have made to the default version.


As shown in , we make an assumption that the list of infinite sequences of binary digits is countable. After writing an enumeration, we complemented the diagonal elements to produce an element which isn't in the enumerated list. If the number $s$ is made up from complementing the digits of $s_i$ for $i=1,2,...,n$, then it is guaranteed that it is not one of the $s_i$s by construction. My problem is how do we know that it isn't one of the $s_j$s for $i=n+1,n+2,...$. The enumeration doesn't afterall stop at n---It goes like---${s_1,s_2,s_3,...,s_n,s_{n+1},s_{n+2},...}$. So our specially constructed $s$ can(infact must) fall in the list though it doesn't fall in the first $n \hspace{0.1cm}s_i$s. Contrastingly consider the proof that the rationals are countable, we construct a similar table(by dividing the row and column number of that table), at any step we can construct a rational which is not in that table by choosing a bigger row and or or a bigger column number, so we made a number which wasn't in the list but we don't say then that the set of rationals is uncountable. (Instead it is said we can make any rational number $c/r$ in finite number of steps.) Note that I have no problem in accepting the fact that the set of reals is uncountable (By Cantor's first argument), it is the diagonal argument which I don't understand. Also I think, this shouldn't be considered an off-topic question although it seems that multiple questions have been asked altogether but these questions are too much related and useful in drawing the (wrong)contradiction to Cantor's argument, so they have been asked. I have seen similar understanding problems with Cantor's diagonal argument in MSE but none match mine(probably) so this isn't a duplicate as well. If you think I missed some, please kindly comment down the link and I will have a look.

If we map every integer to a string that represents a rational number, and produce a number different from all the ones listed, we are essentially following Cantor's algorithm. But why does it not apply? Is it because we can't be certain that the number produced is a rational number?


I have Ubuntu 20.04. I want to install ubuntu 20.10 Groovy Gorilla without uninstalling 20.04 and just want to update it . How can I do that?

What are the different ways I can use to upgrade Ubuntu from one release to another?


How do i concatenate these two arrays to get the expected output?  let bidder= [   [1,2,3,4],   [5,6,7,8] ]  let arr1 = [9,10,11,12]    expected result  [ (4) [...], (4) [...], (4) [...], ]

How do I append an object (such as a string or number) to an array in JavaScript?


I have actually a batch on user, where user are activated or deactivated based on a criteria. In each execute I update my set of users, which in turn launch an @future method to recalculate the role for each user. The method need to be @future and is executed on trigger for user after update. The problem is that this generate the following error :    System.AsyncException: Future method cannot be called from a future or batch method:   I understood that as each execute is considered as a future call, I cannot execute another future from my trigger in each batch execute. So i decided to update all my users in my finish, which will call my future method, but now I am obtaining the following error :   System.LimitException: Too many future calls: 1   Does this mean that will not be able to execute a future method from a batch ??? If not, then how can I achieve this?  This is  not a duplicate of , because there it is doing callouts whereas in my case, I am recuring to @future because in a user trigger i cannot do any other DML. Also their hasn't been any best answer marked there.

I got a situation where i need to invoke future method from batch class. And i know that it is not possible to do. But there might be some workarounds to achieve it, right? And i dont want to invoke future method using shedule apex as my requirement will hit governor limits of "Total number of schedule jobs exceed". So i tried in below ways, but still fighting with same issue.  My design is  Scenario 1 :   Schedule Apex ===> 2. BatchClass (Runs every hour) (Generates a map with "N" records for every batch context, and passes it to Future method in an apex class)  ===> 3. Future method ( then it will login to a salesforce account and generates an attachment and sends an email to a corresponding email address) .   Scenario 2 :  Since, It is not possible to invoke future method from batch, i tried implementing an apex class with a normal static method  invoking future method and in a batch class, for every context i.e., execute() method, it will invoke a normal method which in turn invokes future method, but still got the same error      FATAL ERROR: Future method cant be called from future or Batch   ie.,   global class BatchClass implements Database.batachable<Sobject> {    global Iterable<ScheduledReport__c> start(Database.BatchableContext BC)  {         query=[];        return query;  }  global void execute(Database.BatchableContext BC, List<ScheduledReport__c> scope) {      FutureClass.normalMethod(mapRecords);   }    global void finish(Database.BatchableContext BC){   }  }   Future Class:   global class FutureClass {  global static void normalMethod(Map<> mapR) {      futureMethod(mapR);  }  @future(callout=true)  global static void futureMethod(Map<> m) {      //some code;   }  }   Scenario 3 :  Instead of invoking future class method from batch i tried updating list of records and done checkbox value to true and i've implemented after update event trigger to get the all the records in which checkbox values are true and from trigger i tried invoking future method , still didnt work , i got an error      FATAL ERROR: Future method cant be called from future or Batch   Please help me out.   Thanks !


I'm aware that the angle in radians is 1 when the arc length is equal to the radius. However, I wonder if this is exactly where radians come from. Have we set radians like this (like we set $i^2$ to $-1$) or is there something more to it?

I have learned about the correspondence of radians and degrees so 360° degrees equals $2\pi$ radians. Now we mostly use radians (integrals and so on)  My question: Is it just mathematical convention that radians are much more used in higher maths than degrees or do radians have some intrinsic advantage over degrees?  For me personally it doesn't matter if I write $\cos(360°)$ or $\cos(2\pi)$. Both equals 1, so why bother with two conventions?


While talking with a friend about the number $16$, I began thinking about what two positive rational numbers, $n$ and $m$, satisfy the condition that $n^m$ = $m^n$ where $n$ and $m$ are not equal. $2$ and $4$, as discussed with my friend, are the first pair of integers to do this, and seem to be the only pair to do this after brute forcing combinations in a python script. It seems like there should be more possible pairs, so are $2$ and $4$ the only positive rational numbers to satisfy these conditions?

We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$. Is there another pair of integers $x, y$ ($x\neq y$) which satisfies the equality $x^y = y^x$?


I already  but i but i cant able to understand, so if you explain for below example, it will help me to understand clearly.....  for example, If an order came from Government to people     Education is Compulsory up to age 15.   or      Education is Mandatory up to age 15.   what is the exact difference?   which order has the highest order priority to people?

What is the difference between mandatory and compulsory? Are they synonyms? Can they be used interchangeably especially with regard to something you must do?   Writing the essay is a mandatory task.  Writing the essay is a compulsory task.


I need a specific divis / hyphen character or more than one randomly show  This code is not working at the present.  Does anyone have any suggestions?  \documentclass{minimal}  \usepackage{blindtext}  \usepackage[htt]{hyphenat}  \newsavebox\leftarrowbox  \sbox\leftarrowbox{$\leftarrow$}   \makeatletter \renewcommand*{\BreakableSlash}{%  \leavevmode \prw@zbreak /%  \discretionary{\usebox\leftarrowbox}{}{}%  \prw@zbreak }  \makeatother   \begin{document}   \parbox{40mm}{%  \texttt{/etc\fshyp really\fshyp long\fshyp directory\fshyp name/ \blindtext}%  }   \end{document}

I am setting e.g. directory names in a typewriter font. These names can become long. With the hyphenat package, I enabled hyphenation. Now, what is missing, is that the hyphenation character is replaced e.g. by a backwards oriented arrow.  Thus, what I want to do is something like  \usepackage[htt]{hyphenat} \newcommand{\origttfamily}{}% \let\origttfamily=\ttfamily % \renewcommand{\ttfamily}{\origttfamily \hyphenchar\font\ensuremath{\hookleftarrow}} \begin{document}   \texttt{/etc/really/long{\fshyp}directory{\fshyp}name/} \end{document}   However, \ensuremath{\hookleftarrow} does not work in this case - it is not a single character.  Can somebody point me towards a solution? Thanks a lot!  (moved from )


I answered this question and automatically I was downvoted, an the answer was deleted, I think this is not correct  The question:

The following scenario happened to a question of mine today:   I asked a question to a topic I'm pretty new to. Someone answered the question, it absolutely satisfied my points, so I upvoted and accepted it.   But a few minutes later he got heavily downvoted because (as I understand it) the way he explained the points were completely wrong and they said his words just show he has no clue about the topic.  So he deleted his answer, which made me sad as I thought it will be lost.  But it wasn't.  His answer is still in the question. It has a weak colour, as an answer has of my own after I deleted it. But why? Is this just to me, as I'm the one who upvoted it? Or is it because at the point he deleted it, it was the accepted answer?  And is this just visible to me?  Or anyone can still see it?  And I also noticed he still has the +2 rep he got left from his answer (after downvoting) so is this really a deleted answer?  What's going on?


I have noticed that many French diplomas contain the mention "Pour en jouir avec les droits et prérogatives qui y sont attachés", which can be translated into "[The diploma is conferred upon Mr. X and gives the Y level] to be enjoyed with all rights and privileges pertaining thereto."   What does "to be enjoyed with all rights and privileges pertaining thereto" mean on a French diploma? I.e., what are those rights and privileges? For example, if someone obtained the , what rights and privileges does that give?  I'm not sure whether it refers to some legal consequences, academic consequences, or something else, so that's why I don't post on Law.SE.  Examples:

It is common language in graduation ceremonies, at least in the United States, to hear a degree conferred with "all the rights and privileges pertaining thereto." How would one discover what the rights and privileges pertaining to a MA or PhD degree actually are?


I have a list of Cell object that represent a board game inside the board class.  Cell boardGame[][] = new Cell[8][8];   I needed a temporary cell to try the player move on him and compare it to the other cells, so I though that I could use a java pass-by-value to do it.  test(board.boardGame); board.printBoard();   private static void test(Cell[][] boardGame) { Cell c = new Cell((new Soldier(ChessPiece.QUEEN, Color.WHITE)), 7, 4);     boardGame[7][7] = c;  }   I read some post about java here, but apparently I still didn't catch it 100%.  I expected to see only one white queen on the board, but I saw two. I know that if you pass a reference you can change its values, but I though that if I would pass the array itself its members won't be modified unless I would execute a return.  Please help me to understand this subject better. Thanks  Edit:  I think I don't understand when it called attributes and where it doesn't. I though the different it if you are call "new" or not.  When its part of another object it called attribute right? but every object can be created as part of another object. I can create a new string in dog class and then create the dog class in the animal class and then create it in another class. So only the top class is in the stack?  For exemple:  public class Board  { //fake class      int num= 0;     public void test(int i){         i = 1;     } }   and on another class:      public class Main {         static void outsideTest(Board board){             board.num = 1;         }     public static void main(String[] args) {         Board board = new Board();         System.out.println(board.num);         board.test(board.num);         System.out.println(board.num);         outsideTest(board);         System.out.println(board.num); } }   Now I didn't understand why on test() method the num didn't change and on outsideTest() the num change, num as been created in the heap because its part of the board object, so its need to be changed on both cases no?

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


Say we let $f$ be a real-valued function, let $S\subseteq \text{dom}(f)\subseteq R$, let $a\in \bar{S}$, and let $L\in R$.  We know the $\delta -\epsilon$ condition for $\lim_{x\to a} f(x)=L$ is:  $$\forall \epsilon >0: \exists \delta >0: \forall x\in S: |x-a|<\delta \to |f(x)-L|<\epsilon.$$  So given all that, how can we show $\lim_{x\to 0}x \cdot \sin(\frac 1 x )=0$ by proving the condition I wrote above, for $a=0$, $S=(0,\infty)$, $f(x)=x\cdot \sin(\frac 1 x)$ for all $x\in (0,\infty)$, and $L=0$?

How to find limit as $x \to 0$ of $x\sin(1/x)$?    For $x^2\sin(1/x)$, I know it's $0$ since by the Squeeze theorem, $-x^2 \le x^2\sin(1/x) \le x^2$, but for $x\sin(1/x)$, I run into some problems when applying Squeeze theorem.


<apex:repeat value="{!mapOfID [Lpartner]}" var="InvestorDistributor" rendered="{!mapOfID[Lpartner] == true}">

                          {!InvestorDistributor.Name}"             	                          <apex:outputText value="{0,date,MM'-'dd'-'yyyy}">             <apex:param value="{!InvestorDistributor.navpeII__Distribution_Date__c}"/>              </apex:outputText>             	             {!InvestorDistributor.navpeII__Total_Distributions__c }"

        <apex:variable value="{!totaldistribution+ InvestorDistributor.navpeII__Total_Distributions__c }" var="totalContribution" />     </apex:outputPanel>                   </apex:repeat>

is it possible to check for a specific key in a map i.e., whether it exists or not in VISUALFORCE page?  Based on this i need to render a pageblocktable.


Let $\mathbb{D}=\{z\in \mathbb{C} \,\,|\,\,|z|<1\}$. Prove that, if $\{w_1, \,...\,,w_n\}\subset\mathbb{D}$, then there exists a point $z_0\in \mathbb{D}$ such that:  $$|(z_0-w_1)...(z_0-w_n)|=1$$  [Hint: use the Cauchy inequalities or the maximum modulus principle]   My idea initially was to prove, somehow, that $\exists\alpha\in\partial\mathbb{D}$ with $|P(\alpha)|>1$, where $P(z)=(z-w_1)...(z-w_n)$. If that is true, than from the maximum modulus principle:  $$\sup_{z\in\mathbb{D}}|P(z)|=\max_{z\in\partial\mathbb{D}}|P(z)|>1$$  That means $|P(\beta)|>1$ for some $\beta\in\mathbb{D}$ close enough to the border. Since $|P(0)|=|w_1|...|w_n|<1$ and |P| is continuous, from the intermediate value theorem, $|P(z_0)|=1$ for some $z_0\in\mathbb{D}$.  But I'm having trouble to prove that such $\alpha$ exists. Any ideas?  Thanks!

$n$ points $z_1,z_2,\cdots,z_n$ in the unit open disk are given. Prove or disprove that there exists $z$ in the unit circle such that $\prod_{i=1}^n |z-z_i|^i \ge 1$.  I think it can be solved by elementary analytic methods but no idea.


I have a table in mysql called messages. I use the following code to call date from my table and print them.  <?php $message_query = mysql_query(" SELECT `messages_id`, `from_id`, `message`, `date` FROM `messages` WHERE `group_hash`='$hash' ORDER BY `date` ASC ");  while($run_message = mysql_fetch_array($message_query)){     $message = $run_message['message'];     $print_message = substr($message, 0, 100); }   echo "$print_message";   ?>   I use the function substr() to give me a certain number of characters of the message that will be displayed. Messages are writen in Greek language and stored in field message which has type = utf8_general_ci. Everything works fine and the message dispalyed correctly. The only problem is that when a word that is printed cutted off, I get at the end of the word a symbol like ? in a rombus. When the word that printed does not cutted off, I don't get it. Any idea how to fix this?

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


I have install VGA driver and after that the prompt worrying message to me disabled UFHI and I say use after that asked me password, aftet I reboot system I enter password loop. After entering the password the ask me again for password.

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


I am trying to understand how Attribute Base Encryption (ABE) works. So, after downloading libfenc library from , I built the source code on Ubuntu 12.04 without any error.  Afterward, I tried to follow the library  as follow:  Create the master secret and public parameters: abe-setup -m CP  Generate key for user's attribute: abe-keygen -m CP -a 'ONE,TWO,THREE,FOUR,FIVE' -o userCP.key  Encrypt the input file under a given policy: abe-enc -m CP -i filename.txt -p "((ONE and TWO) or THREE)" -o outfile   With each executed command a file is generated (three files among which the encrypted file is created). Now, when I try to decrypt the encrypted file "outfile" using: abe-dec -m CP -k userCP.key -f outfile.cpabe no file is generated at all, and I don't know if the encryption mechanism works or not !! does the code works or not !! am I missing something ? EDIT () Through this question I am seeking understanding the ABE encryption. It is not about the library AT ALL. it is about the basic understanding of the ABE mechanism. Believe me, the code itself is useless.

Can someone explain what  is?  I was searching for a book or something that can help me in this regard but so far I have found none. Google also returns practically nothing aside from the papers.


I have these operators +=, -= etc. in Math mode. LaTeX introduces space around single character operators. So I get + = and - = instead.   However, in my case I want no space between the + and the =, and similarly between the - and the = in the second operator.  How do I make them near each other such that there are is no horizontal space between them? I tried to put them in \mathit but it didn't have any effect.

This is a very short question and hopefully there's a short answer. I know I can use \stackrel{top}{bot} to vertically merge two symbols into one with top on top and bot on the bottom. Is there something similar for left-right merging? I ask because I want to make a += symbol (for an additive update step in code). If there's already a symbol for that, that would be OK too.


New to java and would like to understand what is different (if any) between these two declarations/instantiations:  Double[] aRRAY = new Double[] {1.2, 1.3};  and  Double aRRAY [] = new Double[] {1.2, 1.3};  Note the different positions of the square brackets on the left side in code snippets 1 and 2. Is there any difference ultimately? If so what is it?

I have recently been thinking about the difference between the two ways of defining an array:   int[] array int array[]   Is there a difference?


I read a book in the 60's when I was a child.  The narrator or main character arrives at an island, due to a shipwreck or some other disaster, and discovers a utopian society.  The families there have taken on the letters of the alphabet as their last names (Mr. A, Mrs. B, etc.)  There are only twenty families as there would be confusion if someone were named "U" (call out "Hey U," and everyone would react). I believe that is the reason why the narrator is told he cannot stay. Any ideas what book or short story this may be?

I recall reading a novel length work 30+ years ago.  It was loosely based on  I recall the Jules Verne story being mentioned in this work, but as fact not fiction. Something like "I realized I could beat the record of 80 days to get around the world".  A male character is traveling by balloon (or there is a balloon at the end, or both), some how gets most way around the world very quickly and lands on an island where a group of people have a futuristic society mostly based on good use of current technology. It may also have been that he was shipwrecked on the island and left in a balloon, traveling fast when the volcano erupts.   I recall one scene where the tables and chairs in the dinning hall, sink into the floor, leaving the table tops flush with the floor for quick easy clean up.    The island is a volcano and diamonds from the volcano play a part some how. I have Googled around for it, but I can't remember the title, author or how many days it took.  There are a lot of hits related to "Around the world".


Let $F$ be an arbitrary field, I need to prove that $x^2 - x + 1$ divides $x^{10} - x^7 + x^4 + ax + b$ for some $a, b \in F$  The difficulty that I am currently facing is that since $F$ is an arbitrary field, $x^2 - x + 1$ might be irreducible over $F$ and so I cannot solve it by factoring $x^2 - x + 1$. I also try to use the division algorithm to prove it using contradiction by assuming $x^2 - x + 1$ don't divide it, and hopefully something would happen to the remainder but this leads to a dead end as well. So any help would be appreciated.

The following question was asked on a high school test, where the students were given a few minutes per question, at most:     Given that,   $$P(x)=x^{104}+x^{93}+x^{82}+x^{71}+1$$   and,   $$Q(x)=x^4+x^3+x^2+x+1$$   what is the remainder of $P(x)$ divided by $Q(x)$?     The given answer was:     Let $Q(x)=0$. Multiplying both sides by $x-1$:   $$(x-1)(x^4+x^3+x^2+x+1)=0 \implies x^5 - 1=0 \implies x^5 = 1$$   Substituting $x^5=1$ in $P(x)$ gives $x^4+x^3+x^2+x+1$. Thus,   $$P(x)\equiv\mathbf0\pmod{Q(x)}$$     Obviously, a student is required to come up with a “trick” rather than doing brute force polynomial division. How is the student supposed to think of the suggested method? Is it obvious? How else could one approach the problem?


i figured out how to draw the 3d effect cubes, but now im facing the issue of the border lines extending beyond the points where they meet. i know that by doing "draw=none" i can turn these off, but i prefer the borders. is there an obvious fix for this? (also, I have seen rounded corners, but I'm not wanting to go this route either)  Here's the code:  \documentclass[border=.5cm]{standalone}  \usepackage{xcolor} \usepackage{tikz} \usetikzlibrary{positioning}  \begin{document}  \pagecolor{black}  \begin{tikzpicture}[on grid, font=\sffamily, line width=.2mm]  \draw[draw=white, fill=blue!65, yslant=-0.5] (5,5) rectangle (6,6);  \draw[draw=white, fill=blue!95, yslant=0.5] (6,-1) rectangle (7,-0);  \draw[draw=white, fill=blue!45, yslant=0.5, xslant=-1] (6,0) rectangle (7,1);  \end{tikzpicture}  \end{document}     Also, here's a screen grab of the problem (it happens on other corners too):

Am trying to draw a simple rectangle and there seems to be minor issue with two of the endpoints (f and d in the following). I tried line cap=rect as suggested by  but that did not seem to work.  The resulting image:    \documentclass{standalone} \setlength\PreviewBorder{5pt}%  \usepackage{tikz}  \newcommand*{\Width}{2.0} \newcommand*{\Height}{3.0} \newcommand*{\Depth}{1.0}  \begin{document} \begin{tikzpicture}%     \coordinate (A) at ( 0,       0,     \Depth);%     \coordinate (B) at (\Height,  0,     \Depth);%     \coordinate (C) at (\Height,  0,      0);%     \coordinate (D) at (\Height, \Width,  0);%     \coordinate (E) at ( 0,      \Width,  0);%     \coordinate (F) at ( 0,      \Width, \Depth);%     \coordinate (G) at (\Height, \Width, \Depth);%     \coordinate (H) at ( 0,       0,      0);%     %     \draw [blue, ultra thick,line cap=rect]%         (A) -- (B) -- (C) -- (D) -- (E) -- (F) -- cycle;%     \draw [blue, ultra thick,line cap=rect]%         (B) -- (G) -- (F) -- (E) -- (D) -- (G) -- cycle;%      \path (D)  [right] node {$d$};% Problem Point 1     \path (F)  [left ] node {$f$};% Problem Point 2 \end{tikzpicture}% \end{document}   This problem about  seems related, but I do not understand how to adapt that to my problem.


I had been using my phone for last 1.5 year ( Lava z90). But recently it's power off button and volume buttom are not working and also my usb debugging is turned off.2 days back my phone is switched off and I am not able to swich on it. Is there a way to turn it on?

I got an old phone: an HTC WildFire S. Everything works fine, except that the power button has gone bad. Can I start the phone from my computer over a USB connection somehow?


In this sentence      My sister told me that she didn't want pancakes for breakfast.   The sentence would still make sense even if the word "that" is taken out. How would one decide to use the word "that" in a sentence? Is it considered better writing when "that" is not used when it is not required?

He will understand that I was not joking.   He will understand I was not joking.  Which of the sentences is correct? Are there any specific rules about the use of "that" in the sentences I reported as example?


I have noticed that the iOS app isn't highlighting syntax correctly, even with the explicit comment:  <!-- language: whatever -->   For example, compare  in Chrome for iOS (47.0.2526.107):    with the SO app (1.4.2.3):

I've just noticed viewing a Python  (since modified: see ) on Stack Overflow that the Android app shows new (incorrectly) highlighted as a keyword which differs from the normal render from the web page.    While it should look more similar to:    Notice no highlighting for new.


I am planning on setting a server which will be running 24/7, for educational purposes mainly. The machine will also serve as a HTPC occasionally since it will be connected to my TV.  That being said i am wondering if there is any significant performance loss or/and resources usage between the desktop and server versions.   PS. I know i can just dual boot and install windows but i'd rather stick with just one OS if the performance is not that big of a deal  thanks in advance

What's the difference between the server version of Ubuntu and the desktop version?


I run the following program in Java:      public class foobar {     public static void main(String[] args) {      ArrayList<float[]> arr = new ArrayList<float[]>(10);      for (int i=0; i<10; i++){         int k = i + 10;         float[] foo = new float[5];         foo[2] = k;         //System.out.println(Arrays.toString(foo));         arr.add(foo);         foo[0] = 11;         foo = null;     }      for (float[] item:arr) {         System.out.println(Arrays.toString(item));     }      } }   and it outputs,  [11.0, 0.0, 10.0, 0.0, 0.0] [11.0, 0.0, 11.0, 0.0, 0.0] [11.0, 0.0, 12.0, 0.0, 0.0] [11.0, 0.0, 13.0, 0.0, 0.0] [11.0, 0.0, 14.0, 0.0, 0.0] [11.0, 0.0, 15.0, 0.0, 0.0] [11.0, 0.0, 16.0, 0.0, 0.0] [11.0, 0.0, 17.0, 0.0, 0.0] [11.0, 0.0, 18.0, 0.0, 0.0] [11.0, 0.0, 19.0, 0.0, 0.0]   From what I understand, Arraylist only stores a reference to the object (a float array in this case). However, since array foo is only valid within the for loop's scope in this case, why does arr not end up with null values after the for loop? Why is the change foo[0]=11 reflected, but not foo=null?

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?