I would like to prove the following statement $$x^n-a^n=(x-a)\sum^{n-1}_{k=0}x^ka^{n-k-1},\qquad\forall n\in\Bbb N_0$$ I can easily prove it by induction using polynomial long division or series expansion however I am unsure whether or not these are "rigorous enough". I have thought about this for a while but is there a way to prove this statement in a more rigorous way? I think that the use of ellipses and "do this for the remaining $n$" gives me this uncertainty. Therefore I pose my question as follows:     Is there a rigorous way to prove this statement, or is the use of ellipses rigorous enough?   Thank you.


Let $X_1,X_2,...$ denote iid random variables such that $X_1$ is continuously distributed with density $p(x)$ and distribution function $F(x)$ where $F(0) = 0, F(x) > 0$ for all $x > 0$, and $p(0) > 0$. Let   $\hspace{15mm}Y = n\cdot  \min \{X_1,...,X_n\}$.  Then there exists a random variable Y such that:   $\hspace{15mm} Y_n \xrightarrow{D}Y$ as $n \xrightarrow{} \infty$.  What is the distribution function of $Y$?  I'm not sure how to proceed with this question. Any insight would be much appreciated.


Is Ubuntu 14.10 supported with Windows 8.1 preinstalled?

I have tried many times to install Ubuntu 14.10 on my Notebook of FUJITSU LIFEBOOK UH55/M.But it's always turned out something to be wrong, and it's just the Boot questions.  I installed Ubuntu 14.10 with UEFI, and with BOOT SECURE ON,because I want my pre-installed Win8 works between Ubuntu.  Now I doubt that Ubuntu 14.10 version is support UEFI or not,I followed many ways that INSTALL Ubuntu with SECURE BOOT ON. It seems not support my computer,by the way, if I have to try the Version 12.10?  OS           Windows 8.1 64 Bit. CPU          INTEL® Core™ i5-4200U PROCESS (1.60-2.60GHz) MEMORY       4GB(4GB×1)(DDR3L PC3L-12800) HDD          500GB HDD (HDD＋NAND FLASH MEMORY) DRIVE        NONE DISPLAY     13.3 HD フルフラットファインパネル（TOUCH）[1366×768] GRAPYICS    Intel® HD Graphics 4400 CAMERA  HD Webカメラ内蔵（有効画素数 約92万画素） INTERNET    LANなし, ワイヤレスLAN(IEEE 802.11a/b/g/n準拠) Bluetooth   Bluetooth® ワイヤレステクノロジー Ver.4.0+HS準拠 KEYBOARD    STANDARD KEBOARD（91KEY） POINTING DEBASE     フラットポイント内蔵


$\lim_{x \to 2} \frac{\cos{\left(\frac{\pi}{x}\right)}}{x-2}$ without using De L'Hospital

$$\lim_{x \to 2} \frac{\cos{\left(\frac{\pi}{x}\right)}}{x-2}$$  This limit is supposed be found without L'Hospital's Rule, but I have not been able to get close to the answer using conjugates, squares, Pythagorean Identity, half angle formulas or Squeeze Theorem. For each attempt, I expected at least one of  the well-known limits $\lim_{x \to 0} \frac{\sin{x}}{x}$ or $\lim_{x \to 0} \frac{\cos{x} - 1}{x}$ to come into use. They frequently did in my attempts but did not go anywhere. I have also been experimented substitutions but in vain.  How can this be solved without using L'Hospital's Rule?


I am trying to render a video (that is not a .dvd file) with audio using Blender. So far, I haven't had any success; all of my rendered clips have had the audio missing from the playback. I've tried a couple of different encoding and output options but nothing has worked so far (except for a .dvd file that I rendered originally).  What are my options for rendering a video with working audio?


Can I go out of LA airport during a layover without a visa?

I'm a Venezuelan citizen and am taking a long flight from Venezuela to Australia. I'm taking two connections and changing airplane two times; my schedule is: Venezuela-Mexico; Mexico-L.A., L.A-Sydney. In L.A. the layover is approximately seven  and a half hours long during the afternoon; I arrive at 2 and depart at 10 approximately. So I was thinking if it's possible to get out of the airport, and do some shopping or even going for dinner... I don't really know if I need a visa for this or which type should it be? Also I don't have any idea if the airport offers some type of luggage lockers or a luggage facility? From L.A. to Sydney I'm traveling by Qantas, in First Class. Is there anyone who knows if Qantas offers some type of luggage keeping service?  Sorry for the length I'll appreciate any info, or help. Thanks. I might sound like a newbie, but i don't even know if it's enough time for going downtown and then going back to airport...  I just don't want to expend 7 hours alone in the airport.


friend's      I have to parse the description from url,where parsed  content have few html tags,so how can I convert it to plain text.


Why does the padding in Merkle–Damgård hash functions like MD5 contain the message length?

I understand the need for padding in MD5. But why do we append the message length to the padding?  I heard it strengthens the hash but how?  Please provide an example if possible and how it applies to this quote:     The inclusion of the length-block effectively encodes all messages such   that no encoded input is the tail end of any other encoded input.   Why a message being the tail of another message is bad (if it is)?


How did Voldemort discover about his parents?

When Dumbledore told Voldemort that he was a wizard, Voldemort used to live in an orphanage. Voldemort's mother had died during his own birth and his father had left his mother even earlier.  Later, in his teen, he killed his father using the wand of his mother's father (Dumbledore discovered this using memories of various people).  But, Voldemort was an orphan with no link to his history. How did he come to know about his parents?


How would I make a custom environment to accomplish the following

\documentclass[12pt]{article} \usepackage{amsmath,amsthm,amssymb,amsfonts} \usepackage{enumitem}  \newenvironment*{exercise}{}   \begin{document}  \begin{exercise}{1.10.} Hello World\\ Hello world\\  Hello World \end{exercise}  \end{document}   How would I format this so that all instances of Hello World are aligned. That is that all the H's would be aligned. I am trying to replicate the format found in many mathematics textbooks which is why I am experimenting with theorem environments.


Does install another version of Ubuntu can solve the problem that "No wifi adapter found"?

my Ubuntu version is 18.04  levonvo 330-15IKB (Type 81DE) Laptop (ideapad) - Type 81DE


Is there a Windows exe that does nothing?

Is there a "noop"-esque exe somewhere as part of the Windows installation? I'm preparing some batch jobs and scheduled tasks, and for a couple reasons I'd like to reference an executable that does nothing -- i.e. launches with no visible window, and quits immediately.  Does such an executable exist in the usual Windows installation anywhere? or how can I come close? I do not want to have to depend on anything not already included in Windows.


Proof that a sequence of numbers must always contain a perfect square

Given $f(n) = n + \left \lfloor{\sqrt n}\right \rfloor$  Prove that for any natural number $n$, the sequence $n, f(n), f(f(n)),.......$ must always contain at least one perfect square.  Now obviously if we take $n$ to be a perfect square, we are done since the sequence contains $n$. So I started by looking at the behaviour of the function at $n = 2$, and within $2$ iterations we reach $4$. Then I looked at $n = 5$, and that reaches $9$ in $2$ iterations. However, $6$ is missed in the sequence as $f(5) = 7$ and this function is strictly increasing. So I looked at the sequence when $n = 6$, which reaches $16$ in $4$ iterations.   Trying to generalise this is a bit difficult, however, as I tried to let $k^2 < a < (k+1)^2$ for some natural number $a$.   Clearly, $f(a) = a + k$, however I am stuck here. Is this approach worth taking or is there something completely different required?


I have some important files on my PC, and it crashed. I tried to repair it but it didn't fix the issue. I installed Windows into another partition, hoping to gain access to the old Windows partition to recover the files, but I get "Access Denied". How can I fix this?


Opacity of background-color, but not the text

How do I make the cross-browser (including Internet Explorer 6) transparency for the background of a div while the text remains opaque?  I need to do it without using any library such as jQuery, etc. (But if you know of a library that does it I'd love to know so I can look at their code).


I have troubles writing a fraction whose items are words not numbers.  In a nutshell I should write:  minaccia/vulnerabilità   --> this is the numerator ----------------------  contromisure             --> this is the denominator   I simply do this, but it doesn't work.  \[ \frac{minaccia/vulnerabilit\'a}{contromisure}  \]   Can anyone help me?


Why is my question appearing on other websites?

I submitted a question on Stackoverflow:   Googling last night, I came across this post:   1) Why is my question on another site  2) Did I sign up for my information (even though it is only a question) to be shared with other forum communities on sites?  I might be missing the point here..


How to remove GNOME Shell from Ubuntu 20.04 LTS to install other desktop environment from scratch?

I have just installed the final version of Ubuntu 20.04 LTS desktop system from ubuntu-20.04-desktop-amd64.iso. After two days of testing I completely do not like its graphical interface - the GNOME Shell. Even installation of GNOME Flashback does not help either.  So I want to completely remove the GNOME Shell with all its trails from my system without re-installation. Just want to start from scratch like it was approximately if I have installed Ubuntu from .


Can I change the ipconfig names to the old convention? wlanX, ethX?

Some time ago there was a monumental change in the naming convention for networking in Ubuntu. wlanx became some strange vlp43txuv and eth0 became enpcl231.  Why it became to be an ordinary user like me can only imagine. It is not a good vision.  1 Is it possible to either change this globally on the system through alias, of sorts or  2 Is it possible to change it temporarily every time I run bash or some script?  It would make my life a lot easier to use the old naming convention as it is the quickest way to use. Now I have to check it every time because I cannot remember the new names at all.  If there are any hidden risks involved, please write those too. Perhaps a locked variable cannot work properly if an alias is changed and so forth.    EDIT: I came across this video on the different naming conventions that have been used. Here I found that the strange names comes from the PCI location    I forgot. The solution to my problem was just changing a line in grub as suggested in the duplicate thread. I did not have to change /etc/...


Compiler not throwing error message for wrong usage of variable as array

I came across the below problem in a book and on my system result is always "True" . As per my understanding, the reason for this is "int c" is optimized by compiler, hence the if() statement has no effect but i was under the impression that this would generate a error message for using c[a][b] as 'c' is not an array.    1 #include<stdio.h>   2    3 int main()   4 {   5         int a[2] = {0,0};   6         int b[1] = {0};   7         int c;   8         getchar();   9         if(a[b[c]] == c[b][a])  10                 printf("True");  11         else      12                 printf("False");  13 }   Can anyone please help me clear my understanding?


Is the tangent function (like in trig) and tangent lines the same?

So, a 45 degree angle in the unit circle has a tan value of 1. Does that mean the slope of a tangent line from that point is also 1? Or is something different entirely?


I'm trying to use dpfloat to set two figures on a two-page spread. Because the figures are rather wide, I would like to use pdflscape to set these pages in landscape. However, the following fails when \begin{landscape} is on an odd page:  ... % This fails iff on an odd page. If I add \cleartoevenpage here it works \begin{landscape}   \begin{figure}[p]     \begin{leftfullpage}     ...     \end{leftfullpage}   \end{figure}   \begin{figure}[p]     \begin{fullpage}       ...     \end{fullpage}   \end{figure} \end{landscape} ...   When in the above example \begin{landscape} is on an even page (left page), then dpfloat behaves fine. If it begins on an odd page, dpfloat fails to float to an even page, and it reports  dpfloat moved a leftpage float from page 21.   100 times before crashing at the \end{landscape} line, perhaps because it is blocked by landscape (?). If I manually insert \cleartoevenpage before \begin{landscape} begins, it always works, however in that case I have blank paper before the float.  Here is a MWE that has similar but not identical symptoms. Instead of crashing when the landscape begins on an odd page, it floats to an even page but the page is not set in landscape.  \documentclass{memoir} \usepackage{dpfloat} \usepackage{pdflscape} \usepackage{tikz} \usepackage{kantlipsum}  \begin{document}  \chapter{Analysis}  \kant[3]  \section{Introduction}  \kant[4-7] % \kant[8-12] % Uncomment this line to be on an odd page and make landscape fail  \begin{landscape}   \begin{figure}[p]     \begin{leftfullpage}       \begin{tikzpicture}[scale=6]         \fill[blue] (0,0) rectangle(2, 1.2);         \end{tikzpicture}     \caption{Box plot of number of positions sent per iteration using this scheme}     \end{leftfullpage}   \end{figure}   \begin{figure}[p]     \begin{fullpage}       \begin{tikzpicture}[scale=6]         \fill[blue] (0,0) rectangle(2,1.2);         \end{tikzpicture}       \caption{Detailed plot.       \emph{Top}: overview. \emph{Bottom}: nightly curve.       \label{fig:overview}}     \end{fullpage}   \end{figure} \end{landscape}  \kant[1-3]  \end{document}   How can I set two figures in landscape on a two-page spread?


Winter Bash Box link not working properly

I tried to click the recently earned hat in Winter Bash popup box, but it is not working and no action to that click. Note it is working in Stack Overflow, but not in .


How do I perform an expandable string comparison?

I need to perform a string comparison (string equality). If the macro is non-expandable (e.g. contains \def or \let), it causes problems in the place where it is used.  I tried using \ifthenelse from the package with the same name, but it would seem it is not expandable (the same problems as when I use \def in the macro occur).  \ifthenelse{\equal{a}{b}}{if-case}{else-case}   How can I test the equality of two strings (#1 and a constant, for that matter) in an expandable way?


Error using SpeedFan - how can I control fan speed?

I'm new to the whole Linux concept. I start up SpeedFan and it comes up with a error saying "Privileged instruction". I'm very new to this, so if someone could tell me how to fix this step by step, it would be greatly appreciated.


Splitting field of $x^6+x^3+1$ over $\mathbb{Q}$

I am trying to find the splitting field of $x^6+x^3+1$ over $\mathbb{Q}$.  Finding the roots of the polynomial is easy (substituting $x^3=t$ , finding the two roots of the polynomial in $t$ and then taking a 3-rd root from each one). The roots can be seen  [if there is a more elegant way of finding the roots it will be nice to hear]  Is is true the that the splitting field is $\mathbb{Q}((-1)^\frac{1}{9})$ ? I think so from the way the roots look, but I am unsure.  Also, I am having trouble finding the minimal polynomial of $(-1)^\frac{1}{9}$, it seems that it would be a polynomial of degree 9, but of course the degree can't be more than 6...can someone please help with this ?


Find the limit of the recursive sequence

Definition  of  the  sequence :  $$a_1=a;\\a_2=b;\\$$ and $$\ \ \ a_{n+2}={{a_n+a_{n+1}}\over2}$$ for $n\geq 1$.  Find the limit of this  sequence in terms of $a$ and $b$.  Now in this case , taking $\lim_{n\rightarrow \infty}$  on  both sides does not help at all . So what I did was try to find the $n$-th term  in therms of $a$ and $b$ and then take $n$ to $\infty.$   So , using the given recursion formula I wrote down like  $7$-$8$  terms, grouped them  in  various  ways  but  still  could  not  get the pattern of the $n$-th term.   Terribly  sorry  for  the  lack  of  work/context  in this post of mine but  I tried  for like an hour  to figure  things out  but can't really put  those  scribbles  down  here.  Please  give  me  some  hints  as  to  how  to find the answer .  Thank you.


Show that $\lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{n^2+k^2}=\frac{\pi}{4}$

Show that $$\lim_{n\to\infty} \sum\limits_{k=1}^{n} \frac{n}{n^2+k^2}=\frac{\pi}{4}$$   Using real analysis techniques.


Why does /var/cache/apt/archives keep deleting files?

I normally download all .deb packages and just copy the packages from /var/cache/apt/archives directory to the rest of the computers, saving me to have to download all the updates and programs again. But since Ubuntu 11.04, the directory keeps deleting the oldest file or some kind of delete method that literally resets the amount of packages there. So then I need to download them again on the rest of the PCs. The files stay there for a couple of days, but then "magically" it's not there anymore after some days.   So what do I need to do to tell Ubuntu NOT to eliminate any files from /var/cache/apt/archives, not even the previous versions of the same package? I do not want it to delete anything from there.  Just to add, I install packages using aptitude or synaptic.


Unable to array values outside of function in shell script

I have the following script named run.sh:  #This is run.sh  prerequisite(){  config_file=./../config/config.sh source $config_file      echo "VAR1 inside prerequisite: $VAR1"     echo "country currency inside prerequisite: $country_currency[@]" }  LIST_OF_COUNTRIES=`cat country_list.txt`  transform() {     local country="$@"     prerequisite     echo "VAR1 inside transform: $VAR1"     echo "country currency inside transform: $country_currency[@]" }  transform ${LIST_OF_COUNTRIES[@]} & transformpid=$!  wait $transformpid  echo "Complete"   The content of my config.sh file is:  VAR1="value1" declare -a country_currency=( "INR" "USD" "JPY" )   When I run my run.sh file,  I get the following output:  VAR1 inside prerequisite: value1 country currency inside prerequisite: INR USD JPY  VAR1 inside transform: value1 country currency inside transform:   As I see from the output, the value of all the variables that I am sourcing from my config .sh file is getting fetching into the prerequisite function.  Whereas the values in the array are not getting fetched into the transform function. This is just a small snippet of code. I am doing multiple calls to the prerequisite function to dynamically source the values in my actual code. What am I doing wrong over here? Isn't the scope of the variable and the array that I have declared, supposed to be the same?


How do I access the BIOS on Kali Linux in order to change the username and password?

I just started using Kali, but I forgot what I used as password and username, so I want to know how change it. Can someone please help me?


How can I map the Caps Lock key to ShiftInsert on xubuntu

For a long time I have disabled my Caps Lock key using xmodmap.  However I would now like to map it to something useful, specifically Shift+Insert which does the same as the mouse middle button (if you have one).  I don't think this can be done simply with xmodmap because I don't think you can generate a Shift+key directly.  Can anyone suggest a simple way of doing what I want?


I am very new to photography and have been working my way through a few books and magazines trying to learn how to use my camera more effectively.  I keep getting stuck on the differences between the focal length, the aperture size and zoom. For example if I want to take a photo where the subject of the photo, say a flower, is In focus but everything else is blurred I have read that I need a large aperture to increase the depth of field but as I zoom in and out the largest possible apatutre changes.  Perhaps a poorly worded question but in essence what I am looking for is a simple explanation on the three subjects In the title, what effect they have on each other and what are the optimum setting for the effect I am after?   Thanks


Refer to the first answer here  , i want to do a block with items inside that keep position after overlay ?  ** Edited   I managed to do what I wanted naively because i don't know how it works with [<+->] \documentclass{beamer} \usetheme{Berlin} \begin{document}  \begin{frame}     \frametitle{Présentation de MedsoftWorks Consulting}     \begin{itemize}         \item<1->Ingénierie applicative          \item<5-> Développement web         \item<9> Digital et application mobile     \end{itemize}         \only<2-4> {\begin{block}{Les offres}            \begin{itemize}             \item<2-4> La formalisation des besoins.             \item<3-4> La conception de cahier de charge.             \item<4>  La réalisation du progiciel adapté à la            \end{itemize}                 \end{block}                }          \only<6-8> {\begin{block}{Les offres}           \begin{itemize}             \item<6-8> La gestion des moyens de paiement.             \item<7-8> La gestion de paiement sécurisé.             \item<8> Le Webmastering et maintenance.         \end{itemize}             \end{block}               }     \end{frame}  \end{document}


X unbiased coins. What is the probability that half of them exactly are heads. Please answer question where X= 20, 30, and 20000.


Existence of a prime number satisfying a certain condition

Does there exist a prime number $p$ such that there exist no prime numbers between $p$ and $p^n$, $n\geq2$, $n\in N$? If yes, what is the smallest such prime number?


Getting Null pointer Exception when loading a property file which is in computer

This is the code what i have written. but when i am trying to print key and value its getting null pointer.  My main concern is to load the keys and values from the property files and need to store in a map  Map<String, String> prop1 = new HashMap<String, String>(); Map<String, String> prop2 = new HashMap<String, String>();  public static void main(String args[]) {      Sample sample = new Sample();     sample.getLocaleOne(); }  public void getLocaleOne() {     Properties prop = new Properties();     InputStream input = null;      try {         File file = new File("Labels.properties");         System.out.println("file.getAbsolutePath());         input = this.getClass().getClassLoader().getResourceAsStream("C:/workspaceNewI18NChnages/customer/Labels.properties");          prop.load(input);          Enumertion<?> e = prop.propertyNames();         while (e.hasMoreElements()) {             String key = (String) e.nextElement();             String value = prop.getProperty(key);             System.out.println("Key : " + key + ", Value : " + value);         }     } catch (Exception e) {         e.printStackTrace();     } }


You know those jokes where someone has need for a number like for a WiFi password then they're given an integral so they'd just give up? People like sending me those cause I love math. But today I got a unique one.  $$\int_{-2}^2 \left(x^3\cos \frac{x}{2}\right)\sqrt{4-x^2} \, dx$$  Why is it different? Cause I evaluated it on Desmos and it's equal to $\pi$!  How is that possible? I'm trying to work around it and it's proving tricky. The much I know is if I can separate the square root term as an integral then it'll be the area of a semicircle with radius 2.


Show that number of solutions satisfying $x^5=e$ is a multiple of 4?

In a finite group, show that the number of nonidentity elements that satisfy the equation $x^5 = e$ is a multiple of 4.  I think that besides $ x, x^2, x^3, x^4 $ also satisfies the given equation but how can I show them distinct ?


Why Fragment crashes on .hide() with .setCustomAnimations()?

xml:      <RelativeLayout         xmlns:android="http://schemas.android.com/apk/res/android"         xmlns:app="http://schemas.android.com/apk/res-auto"         xmlns:tools="http://schemas.android.com/tools"         android:layout_width="match_parent"         android:layout_height="match_parent">         <fragment                 android:id="@+id/the_fragment"                 android:name="com.example.MyFragment"                 android:layout_width="match_parent"                 android:layout_height="wrap_content"                 android:layout_alignParentBottom="true"                 tools:layout="@layout/fragment_my"/>        <Button                  android:id = "@+id/button"                 android:layout_width="wrap_content"                 android:layout_height="wrap_content"                 android:text="Show/Hide"/>      </RelativeLayout>   Code:      @Override                 public void onViewCreated(View view, @Nullable Bundle savedInstanceState) {                      super.onViewCreated(view, savedInstanceState);                      mMyFragment = (MyFragment) getChildFragmentManager()                                         .findFragmentById(R.id.the_fragment);                         ((Button)view.findViewById(R.id.button)).setOnClickListener(view->{         if (...){         //hide         getChildFragmentManager().beginTransaction() .setCustomAnimations(R.animator.slide_in_from_bottom, R.animator.slide_out_to_bottom)                                         .hide(mMyFragment)                                         .commit();          }else{         //show         getChildFragmentManager().beginTransaction() .setCustomAnimations(R.animator.slide_in_from_bottom, R.animator.slide_out_to_bottom)//in this line the app crash                                         .show(mMyFragment)                                         .commit();         }         });                                  }   The error occurs:  Process: by.gramophone.develop, PID: 21508     java.lang.NullPointerException: Attempt to invoke virtual method 'void android.view.ViewGroup.startViewTransition(android.view.View)' on a null object reference         at android.support.v4.app.FragmentManagerImpl.completeShowHideFragment(FragmentManager.java:1700)         at android.support.v4.app.FragmentManagerImpl.moveFragmentToExpectedState(FragmentManager.java:1797)         at android.support.v4.app.BackStackRecord.executeOps(BackStackRecord.java:792)         at android.support.v4.app.FragmentManagerImpl.executeOps(FragmentManager.java:2596)         at android.support.v4.app.FragmentManagerImpl.executeOpsTogether(FragmentManager.java:2383)         at android.support.v4.app.FragmentManagerImpl.removeRedundantOperationsAndExecute(FragmentManager.java:2338)         at android.support.v4.app.FragmentManagerImpl.execPendingActions(FragmentManager.java:2245)         at android.support.v4.app.FragmentManagerImpl$1.run(FragmentManager.java:703)         at android.os.Handler.handleCallback(Handler.java:739)         at android.os.Handler.dispatchMessage(Handler.java:95)         at android.os.Looper.loop(Looper.java:148)         at android.app.ActivityThread.main(ActivityThread.java:5417)         at java.lang.reflect.Method.invoke(Native Method)         at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:726)         at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:616)   UPDATE: But if I remove .setCustomAnimations(R.animator.slide_in_from_bottom, R.animator.slide_out_to_bottom) the error doesn't occurs


Origins of the nose-bleed in anime/manga

In a similar spirit to my , I wonder who was the first artist to feature a nose-bleed when thinking, shall we say, "provocative thoughts"?  Did it become popularized in anime/manga because of the popularity of the artist's work or because it is a common belief in japanese folklore?


Can't understand the limit solution to $\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$

I trying to solve the question:     $$\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$$     I know that i can proof $2^n>n^2$ in induction and i calculated the limit as "$∞^0$" that equals to $1$ but then i saw that the answer should be 2.  How is it 2?


We know the asymptotic density of primes. What about the asymptotic density of numbers with n prime factors?

Question in title. When I say n prime factors, I don't mean n distinct prime factors.


They are seems to be similar in meaning, however in a specific context Googling vote for the first.     ... teaching users for free.   I think free of charge(s) is more appropriate choice but I couldn't find convincing support for the idea.  Are those really equivalent and what is the best for the context? Is there another alternative?


Create node of same size as fitted node, but displaced slightly

I want to repeat a node multiple times, but displaced each time, something like:  However, in my case, the top node is a fitted node, that contains some other nodes. I do not know the size of the fitted node. So I dont know how big to make the nodes underneath. The nodes underneath should be blank, nothing drawn in them (unlike my example above). How can I create nodes that are the exact same size as the top fitted node? By the way, the code to produce the pictured example was: \begin{tikzpicture} \foreach \i in {1,2,3} {   \pgfmathsetmacro\exx{\i * 0.2};   \pgfmathsetmacro\exy{\i * 0.2};   \node [block, xshift=\exx cm, yshift=\exy cm] (inner_example) {This is some text}; } \end{tikzpicture}  (but in my actual case, I don't want to just repeat the drawing in each of the lower nodes, since it is a complicated picture, and seems wasteful to do so.)


How exactly does k-means clustering for categorical data work? I have a dataset which has several categorical features that can have 2,3,4,..,n values. I could one hot encode them, but I'm not sure if it even makes sense because k-means uses a distance metric. I looked into k-prototype clustering, but tried it on my dataset, but plotting it does not make sense when the y-axis and y-axis are just integer values that are small.


What does it mean if the status of manuscript changed directly from "editor assigned" to "reviews completed"?

I submitted a manuscript to a journal a month ago but the status was changed to "reviews completed" after "editor assigned," with nothing in between. What does that mean?


Redirects from http to https don't work if there's a slash directory for Joomla

Note: I cannot be root on example.com, so editing httpd.conf isn't an option.  I want anything from  to redirect to be https and including the slash directory. This is an example of the problem. The same problem if it is ... or ...  If the URL looks like this:  http://www.example.com/suggestions   It incorrectly redirects to the home page:  https://www.example.com/index.php   When the desired result is for it to redirect to here:  https://www.example.com/suggestions   Here is the .htaccess code I'm using:  RewriteEngine On RewriteCond %{HTTP_HOST} ^example\.com$ [OR] RewriteCond %{HTTP_HOST} ^www\.example\.com$ RewriteRule ^(.*)$ https://www.example.com/$1 [R=301,L]


How to get business map location displayed in the right hand sidebar of the Google search results page?

Does anyone know how to get your business map location displayed in the right hand sidebar of the Google search results page? As in the screenshot below:      I already added my business to this link: .  Is adding detail in above link enough or do I need to change my website coding?


Schengen travel for holder of Greek Blue Paper (Marriage)

I am a Tunisian citizen working in Greece and holding the blue paper. I am married to a Greek citizen and now waiting for the Residence permit. As far as I know, I am able to go back to my home country and other visa-free destinations (Turkey, Morocco etc). While I wait for my residence permit, am I allowed to travel to schengen countries if accompanied by my Greek partner? I appreciate your help :) Cheers!


Crossed & nested random effects Mixed Effects

Here comes my case:  I conducted an experiment with roughly the following design:  30 participants, each with a unique id, were asked to rank using a likert scale how much they liked images of forests. All the participants ranked the first 8 images and then the following 5 images were randomly drawn from a pool of 15 images. Therefore, in total each participant viewed 13 images of forests, but not all images were viewed by each participant. As the responses are ordinal I have gone with a cumulative link mixed effects model to preserve the structure of the data.   And here comes when I need your expertise. So far, I believe that the random terms of my model should take into account that:  Participants (id)  Image (id)   However, Im confused about how to incorporate the random effects as each participants views some but not all of the same images. Thus-far I have come to the conclusion and coded it as:   clmm(likert_Rating ~  Experience +  X.4 + X.3 + (1|part_id)+(1|Plot_ID), data=TotalF)  However, no matter how many models I try, I am never sure about what terms would be reasonable to include as randoms.  I would really appreciate if some of you could point me in the right direction as I am struggling to decide.  Many thanks for any help.


I just hit 200 reputations and saw big ads removed.  But they didn't bother me at all, so I would like to get them back to support the site.  Is there any way to do so ?


How to get the equation where a circle goes through three points

If I have the equation $ax^2+ay^2+bx+cy+d=0$ how do I get the equation where the circumference goes through the points P = (1,1), Q = (−1,−1) and   R = (−1,1)   I have it in mind to solve it with a matrix, but the instructions seem confusing to me, can I get some help?


Change Windows 7/8/10 system language - welcome screen, login, etc

Changing an admininstrator user language is pretty straight-forward, but it does not change the language of the Boot screen, Welcome screen, Login screen, etc...   Pretty much anything that's not on the desktop remains in the original language of the installation so it can look really ugly (for example, having a menu label in Spanish, and the menu items in English, etc.)  How to change that?  I've Googled this for hours and could only find answers about how to change the user language, which is completely irrelevant for this issue.


Estimating the integrated Tchebychev function and calculating its error

I would like to understand how to derive (2) from (1) below.     Problem:    If $\psi_1$ is the integrated Tchebychev function below   $$\psi_1(x)=\frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty}\frac{x^{s+1}}{s(s+1)} \left(\frac{-\zeta '(s)}{\zeta(s)}\right) \, ds \tag 1$$   where $c$ > 1, then   $$\psi_1(x)=\frac{x^2}{2}-\sum_\rho\frac{x^{\rho+1}}{\rho(\rho+1)}-E(x)\quad(2)$$   where the sum is taken over all zeros of zeta function in the critical strip. Which error term will be   $$E(x)=c_1x+c_0+\sum_{k=1}^{\infty}\frac{x^{1-2k}}{2k(2k-1)}$$   where $c_1=\frac{\zeta '(0)}{\zeta(0)}$ and $c_0=\frac{\zeta '(-1)}{\zeta(-1)}$.


When to use IMG vs. CSS background-image?

In what situations is it more appropriate to use an HTML IMG tag to display an image, as opposed to a CSS background-image, and vice-versa?  Factors may include accessibility, browser support, dynamic content, or any kind of technical limits or usability principles.


In general we know $A^{bc} = A^{cb}$ for integer $A$.  I want to extend this to the case $A=-1$.   For integers $a,b$ I guess the above relation holds,  \begin{align} (-1)^{2\cdot3} = ((-1)^2)^3 = 1 = ((-1)^3)^2 .\end{align}  But if we include the fraction  \begin{align} (-1)^{-\frac{1}{2}} &= ((-1)^{-1})^{\frac{1}{2}} = (-1)^{\frac{1}{2}} = i \\ &= ((-1)^{\frac{1}{2}})^{-1}=\frac{1}{i} = -i \end{align} this does not hold any more.   Is something wrong with my computation?


Why don’t I have the Get Windows 10 icon?

I want to get Windows 10, but I do not see this icon in the notification area (tray):    How do I get the icon to get Windows 10?


jQuery can't find element when it's parsed from JSON

At first I made a simple array just inside the .js file and wrote the function to make list items from it. Then clicking on freshly created li elements should do something.  //This code works  dic[0] = "decir"; dic[1] = "querer"; dic[2] = "poder";   $(document).ready(     function verbsarray() {          for (var i = 0; i < dic.length; i++) {                       var verbo = dic[i];                                          verbos += "
" + verbo + "
\n";         };                   $('ul.h_list').html(verbos);                        });      $(".h_li").click(function() {     alert("it works!");     //Dollar finds .h_li here }   Since that was a prototype, then I developed that function to take items not from the static array, but from loaded JSON. Function parses the needed items and again makes list items from them.  But the other function (that looks for clicked
) now doesn't work...  //this doesnt work :-(   function verbos_from_json () {      $.getJSON('verbos.json', function verbsarray(vjson) {         for (var i = 0; i < vjson.data.length; i++) {                    verbo = vjson.data[i].verb;                                      verbos += "
" + verbo + "
\n";         };                $('ul.h_list').html(verbos);         });          };  $(".h_li").click(function() {     alert("it works?.. no"); }


Using QGIS Vector->Geoprocessing Tools->Difference?

I'm trying to use the Vector Geoprocessing Difference Tool in QGIS to "take a bite" out of one polygon using another in another layer. The tool menu Difference icon is exactly what I'm trying to do - it shows a circle that it "taking a bite" out of the overlapping corner of a rectangle beneath it.  I've tried every combination of input in the dialog (swaping input layer and difference layer, using selected polygons, etc.) I get three results: The union of the two layers (!), all of layer one, or all of layer two. I only get results by selecting "use only selected features". When I don't "use only selected features" it simply churns away and never produces anything at all.  The dialog seems simple and straight-forward, the operation is pretty basic, so I wonder what I am doing wrong.   Is there some twist or trick to this that I'm missing?   I've looked for detailed tutorials and/or instructions, but have not found any.


Displaying layout marks in a document set with different layouts

Is there any package that allows for the display of layout marks within a document where the layout changes several times throughout? I'm using the geometry facilities to issuing \newgeometry commands throughout my document, but it doesn't update the displayed layout and neither does the showframe package or the facilities of the memoir class.  EDIT: As Werner has pointed out, the showframe option of the geometry package displays correctly any updated page layout set by issuing \newgeometry commands.   My trouble came out of the fact that I'm issuing also \pagecolor commands and the page color seems to be hiding the layout lines typeset according to the geometry package. My confusion only worsened because the showframe package layout lines were not hidden by the page color (the package got the layout wrong on some pages, though). So, it all boils down to a conflict with the page color.   Even though I'm using geometry's showframe option for "debugging" ends, and I don't mind to have no page color at that stage of development, is it possible to override this problem and have at the same time both the page layout displayed by geometry as well as the page colored?   Btw, should I open a new question given that the problem is actually different from the originally posted one?


Hashmap throwing nullpointer exception when trying to get Integer value

I have the below code:   import java.util.HashMap;     import java.util.Map;      public class Pangram1 {          public static void main(String[] args)         {         Character [] ch = new Character[] {'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z'};         HashMap<Character,Integer> map1 = new HashMap<Character,Integer>();         String s = "The quick brown fox jumps over the lazy dog";         int count = 0;         int greater = 0;         for (char character: ch)         {             map1.put(character, count);         }          for(Map.Entry<Character,Integer> entry : map1.entrySet() )         {             System.out.println("key is" + "\t" + entry.getKey() + "\t" + "Value is" + entry.getValue());         }          for(int i = 0; i < s.length();i++)         {                Integer count1 = map1.get(s.charAt(i)); Line 28 --->            count1.intValue();             map1.put(s.charAt(i),new Integer (count1));               if(count1 > greater)             {                 greater = count1;             }         }          if(map1.values().contains(1) && greater == 1)         System.out.println("Pangram");         else if(map1.values().contains(0))         System.out.println("Not Pangram");         else if(greater > 1)         System.out.println("Multiple Pangram" + "\t" + greater);      }     }   I am getting this error Exception in thread "main" java.lang.NullPointerException     at Pangram1.main(Pangram1.java:28)  I have tried all ways such that there wouldn't be autoboxing/Unboxing problems but still exception throws up.   Could someone please help me with it ?  Thanks !!


Why is using the JavaScript eval function a bad idea?

The eval function is a powerful and easy way to dynamically generate code, so what are the caveats?


How to write "y^2" in latex ? I need that hook in mathmode. The error says to put the expression within $...$.


Regular expression: Split text by custom line terminator

I'm trying to build a regular expression to split a very long text string into components. Here's an example:  12345 2018-01-03 15:24:12 6789 STARTlorem ipsum dolor sit amet**STARTconsectetur adipiscing elit**   So far, I have something like this:  import re  example = r"12345 2018-01-03 6789 STARTlorem ipsum dolor sit amet**STARTconsectetur adipiscing elit**" str_regex = "(?P<id1>\d+) (?P<adate>\d{4}-\d{2}-\d{2}) (?P<id2>\d+) " + \     "(?P<firstpart>START.*\*{2})" m = re.search(str_regex, example)  m.group('id1') ## '12345' # This is OK  m.group('adate') ## '2018-01-03' # This is OK  m.group('id2') ## '6789' # This is OK  m.group('firstpart') ## 'STARTlorem ipsum dolor sit amet**STARTconsectetur adipiscing elit**' # This is where I'm lost: I'd like to match the text until the first occurrence of '**'   When I try to add a second part to the regular expression, it stops working:  str_regex = "(?P<id1>\d+) (?P<adate>\d{4}-\d{2}-\d{2}) (?P<id2>\d+) " + \     "(?P<firstpart>START.*\*{2})" + \     "(?P<secondpart>START.*\*{2}" m = re.search(str_regex, example) # This doesn't match anything anymore!   What I'd like to get is a regex that splits the example string as follows:  str_regex = "..." # What to put here to split the string? m = re.search(str_regex, example)  m.group('id1') ## '12345'  m.group('adate') ## '2018-01-03'  m.group('id2') ## '6789'  m.group('firstpart') ## 'STARTlorem ipsum dolor sit amet**'  m.group('secondpart') ## 'STARTconsectetur adipiscing elit**'   Notes:   It is guaranteed that there will be no other occurrences of double star (*) anywhere inside the strings. There will be always a header (containing id1, date and id2) and two contents parts (firstpart and secondpart). Anything else can (and will) be ignored   Can you point me in the right direction?


Does non-uniqueness of solution to 1st order ODE implies the existence of infinitely many solutions?

Consider the following initial value problem (IVP) to the first order ODE:   $$\tag{1} \dot x = f(t, x), \ \ \ x(t_0) = x_0.$$  The  describes when one has exactly one solutions. This is true (e.g.) when $f$ is continuously differentiable.   There are examples where uniqueness  and existence fails ( or ):   In all of the examples where I am aware of, whenever one has more than one solutions, one actually has infinitely many. Hence my question:   Can an IVP has more than one solutions, but only finitely many solutions?


Changing HISTTIMEFORMAT leaves entries with incorrect date

After exporting HISTTIMEFORMAT='%F %T' I tried to query history  But the result shows all the commands are executed on same day.  How can I check the actual date and time of actual command execution?


Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.

Let $R = \mathbb{Z} + x\mathbb{Q}[x] \subset \mathbb{Q}[x]$. Find the irreducibles of $R$. Show that the irreducible elements in $R$ are $\pm p$ for prime integers $p$ and the irreducible polynomials $p(x) \in \mathbb{Q}[x]$ whose constant coefficient is $\pm 1$. Prove these irreducibles are prime in $R$.  The first part is pretty clear. ($\pm p$ for prime integers $p$), if $\alpha \in R$ s.t. $\deg(\alpha)=0$ then $\alpha$ is a constant polynomial thus in $\mathbb{Z}$. If $\alpha$ is a prime then it is irreducible. Having trouble showing that for $p(x) \in R$ s.t. $\deg(p(x)) > 0$ with constant term $\pm 1$ are irreducible.


Ubuntu 20.10 server network is not starting on boot

I have just installed 20.10 server and I am unable to get the network to start on bootup. If I issue sudo dhclient eno1 the network starts successfully but I have to do this after every reboot. /etc/network/interfaces: auto lo iface lo inet loopback auto eno1 iface eno1 inet dhcp I've tried changing the order of this and also putting auto on one line with no success. This is the output from cat /etc/netplan/*.yaml #This is the network config written by 'subiquity' network: ethernets: {} version: 2


Evaluate the integral $\int\limits_0^{\pi}\log (1-\cos x)\, dx$

Question: What is the value of the integral $\int\limits_0^{\pi}\log (1-\cos x)\, dx$ Proceed: Let $I=\int\limits_0^{\pi}\log (1-\cos x)\, dx$, then $I=\pi \log 2+\int\limits_0^{\pi}\log \sin^2(x/2)\, dx$. What can I do now?


Equivalence principle and inertial frames

In Ta-Pei Cheng's Relativity, Gravitation and Cosmology book, he stated the equivalence principle as  Physics in a frame freely falling in a gravity field is equivalent to physics in an inertial frame without gravity.  But from wikipedia, an  is defined as a frame of reference that is not undergoing acceleration. So why is the freely falling frame of reference in a gravity field, which is accelerating, an inertial frame?


I'm messing around with Unity 2017's post processing tools while making a 2D game that benefits from the parallaxing effect using a perspective camera.  Please note that the game is mostly made using sprites.   Now, I have a playerGround, a backGround and a foreGround. I wish to blur the background and foreground only but not the playerground.  I'd like to know how to do this as playing with the focal length didn't do anything, everything receives the same blur amount regardless of the distance from camera.


So I bought 3 kgs of beef tenderloin, I put it in the freezer for 2 days, I got lazy and didn't cut them up. I figure I will cut them the day after so I let it thaw in the fridge, I store them in a bowl unwrapped, but then the day after I check it's still frozen. I decided to wait for another day, except that I got really lazy and waited till today 4th day in fridge. It's still kind of frozen and I barely smell anything. Should I discard the beef or is it still safe to eat?


What megapixel value is equivalent to which ISO film?

Is there some kind of equivalency table or formula that expresses what kind of pixels you need in a digital camera to have roughly the same quality as a particular ISO graded film? What other variables would influence this (focal-length, exposure time, etc)?


SQL Server Management Studio 2014 12.0.5000.0 "Invalid Column Name" Error

The following code executes as expected.  However, the editor shows red lines under attribute5 and WCC_ID in "h.attribute5 = i.WCC_ID" and states "Invalid column name" when the mouse hovers over the red lines.  These columns exist in the respective tables.  What is wrong with the SQL?   SELECT  * FROM ( SELECT attribute5 FROM OPENQUERY([FAMISPRO.WORLD],'SELECT attribute5 FROM FAMIS_EMP')  ) AS h INNER JOIN ( SELECT DISTINCT h.WCC_ID, h.KEYMARK FROM OPENQUERY ( PROJECT ,'SELECT * FROM ENTRY;' ) AS h LEFT JOIN ( SELECT * FROM OPENQUERY ( PROJECT ,'SELECT * FROM ENTRY;' )   WHERE EVENT = 'RETURNED' ) AS i ON h.WCC_ID = i.WCC_ID AND h.KEYMARK = i.KEYMARK WHERE i.EVENT IS NULL ) AS i ON h.attribute5 = i.WCC_ID;


In Game of Thrones season 7 finale the night king      breaks the wall with help of Viserion's blue coloured fire.   So was Viserion was breathing fire or something else?


Why can't we make a perpetual motion machine by using a magnet to pull up a piece of metal, then letting it fall back down?

Obviously, a perpetuum mobile isn't possible by any law in physics, because energy can't be "created" or "destroyed", only transformed. This said, I've had an idea for a perpetuum mobile and can't seem to find my mistake (I'm actually very close to building and trying it).  Here's the plan:  Take a piece of wood and attach its upper end to a screw so it can swing like a pendulum. Then, attach a magnetic metal at the lower end of the wood. Now, place two magnets at each side of the pendulum, so that at the maximum amplitude, the metal will barely touch the magnets and will swing back, due to its weight. Now, in my head, if you give the pendulum a little impulse, it will swing up in one direction and get attracted by the magnet just a tiny bit. Thus, on the "way back", it will have a slightly higher amplitude. So it swings to the other side, closer to the magnet, which will pull the pendulum a bit more upwards, thus increasing the amplitude furthermore. This could theoretically go on and the pendulum will never stop, it will actually gain more momentum at the start.  So the conditions are:   The Metal must be heavy enough so it doesn't stick to the magnets The Metal must be magnetic enough so that we gain amplitude instead of losing it each swing   And that's basically it. I am aware that the construction couldn't work, but struggle to find where I made my mistake. Anyways, if it does work and you guys build it before I do: I want 50% of all profits and want you to name it Perpenduluum Mobile :D


How to convert a known one-dimensional array into a two-dimensional array by python but without using numpy? (just using basic python language)) e.g suppose you have an one dimensional array with 100 elements, now you need to use python to transfer it into a 10x10 matrix but without using numpy. You can only use the basic python language, like for loops.


Maxtor 500GB external hard drive not being detected but power is going to it?

I have 2 * Maxtor Onetouch 4 Lite 500GB external hard drives (part no. 9NT2A4-500). They both used to work fine on my old laptop (an Acer) but I have not used them for about a year, since my laptop was stolen and I got this one (also an Acer [Aspire 7738G]). I have one plugged into the mains with one of the leads I believe was supplied with them. It appears to be receiving power as it is warm and the power light (on the unit itself) is on; also the mains adapter is fairly warm.  I also have it plugged into my laptop with a USB lead which I have tested on my mp3 player (so I know it works). However my hard drive is not showing on my computer. I have tried checking for new hardware, installing the software that was supplied with it, checking drive letters in case it is registered as C: or something stupid, checking for problems etc... I can't find any cause for it to do this. It does appear to be starting up and, possibly, shutting down and restarting constantly (that's what it sounds like altho I can't be certain).  I have had both hard drives stored in different places for the last year and they're both doing the same thing.. if it was only one then I'd guess it had got damaged or corrupted or something but since it is both I doubt this is it. The only things in common with both of them are the leads and the laptop, however I know the USB lead works and guess the mains lead works as there is power going to the unit.  Has anyone come across this before or does anyone have any idea what the cause / solution to the problem is? Any help would be greatly appreciated.  Regards, Richard


How many USB's can I connect to a PC running Windows and what drive letters do they get assigned?

Consider the following scenario: On my PC I have only one partition, with the drive letter C. If I connect a USB hub or more, what happens / which drive letters get assigned to the USBs if they exceed the A to Z available list of drive letters? If I connect for example 50 USB memory sticks - how will the drives get named after A to Z will get used, for the remaining number of USB memory sticks?


Story where radically different cultures live together and are defined by rulesets, some choose not to see each other, a house is used as a spaceship

I think this novel came out in the 2000s.  There are many cultures that live close together but are very different, for example some pretend to be pre-industrial.  One of the main characters is a youth who grew up in a pretend pre-industrial society and is now exploring the rest of the solar system? ring-world?   Each culture experiences their own reality that is defined by a ruleset.  One of the rulesets becomes aggressively self-propagating and this is the problem that drives the plot.  At some point a tumbling house, just a normal house, is used to travel across space.


How can I find what is using the rest of my drive?

I am using a Macbook air.  64GB.  My user directory has used 20.47GB  Disk Utility shows 'Other' is 41.33GB and I only have 2.9GB free.  What tools or command line commands can I use to find out what is taking up large amounts of this.  I can use finder with all files and sort by size but that is already about my directory and the space taken seems outside of my directory.


I want to get the progress of my AJAX request - how much has been downloaded so far out of how much the file is. For example, I am downloading a large picture with AJAX so I can put the content in a DATA url (this may not be the best way to do that, it's just a example.)   So, I make the AJAX request to some host I have no control over (flickr), and report the progress back to the user. I cannot find a way to do this without a server-side script or something like that. Preferably the solution would use JQuery, because that is what I use for my website. Thanks! Isaac


How to "globally" reduce space in equation to get compact or narrow formed equations?

The above one is done by Word, the below equation is done by LaTeX. How can I get the compact form like Word "globally"?  Here's my code: Please take a look at and give me some advice ....   thank you  \documentclass[a5paper, 10pt, twoside]{book} \usepackage{geometry} \geometry{voffset=10pt, tmargin=1.2cm, bmargin=1.5cm, lmargin=2cm, rmargin=1.5cm }  \begin{document}  The equation is given as:  \begin{equation} \frac{1}{2} \left[ \frac{h_{\underline j}}{h_{\underline i}}  \left\{ \frac{\partial}{\partial q^i} \left( \frac{\hat{u}^{\underline j}}{h_{\underline j}} \right) + \left( \frac{\hat{u}^{\underline m}}{h_{\underline m}} \right) \Gamma^j_{mi} \right\}   + \frac{h_{\underline j}}{h_{\underline i}}  \left\{ \frac{\partial}{\partial q^i} \left( \frac{\hat{u}^{\underline j}}{h_{\underline j}} \right) + \left( \frac{\hat{u}^{\underline m}}{h_{\underline m}} \right) \Gamma^j_{mi} \right\} \right] \end{equation}  \end{document}


Prove or disprove: $\sum a_n$ convergent, where $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$.

Let $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$. Show that $a_n>0\  \forall\  n\ge1$.   Prove or disprove: $\sum\limits_{n=1}^\infty a_n$ is convergent.     I can't show that $a_n > 0\  \forall n\ge1$. I tried using induction but it wouldn't work.  Attempt: $$ \begin{align} 2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}&=(2\sqrt{n}-(\sqrt{n-1}+\sqrt{n+1}))\cdot {2\sqrt{n}+(\sqrt{n-1}+\sqrt{n+1})\over2\sqrt{n}+(\sqrt{n-1}+\sqrt{n+1})}\\&={2n-2\sqrt{n-1}\cdot\sqrt{n+1}\over2\sqrt{n}+(\sqrt{n-1}+\sqrt{n+1})}\end{align}$$ (The calculations are true for sure. No check is desired.) Denote $$a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}={2n-2\sqrt{n-1}\cdot\sqrt{n+1}\over2\sqrt{n}+(\sqrt{n-1}+\sqrt{n+1})}\text{ and }b_n={1\over n^{2}}.$$   Then  $$\begin{align*} \lim_{n\to \infty}{a_n\over b_n} & =\lim_{n\to \infty}n^{2}{2n-2\sqrt{n-1}\cdot\sqrt{n+1}\over2\sqrt{n}+(\sqrt{n-1}+\sqrt{n+1})} \\ &=\lim_{n\to \infty}n^{2}\lim_{n\to \infty}{2n-2\sqrt{n-1}\cdot\sqrt{n+1}\over2\sqrt{n}+(\sqrt{n-1}+\sqrt{n+1})} \\ &=0 \end{align*}$$ By the comparison test for series convergence, since $\lim_{n\to \infty}{a_n\over b_n}=0$, then if $b_n$ converges, which it does, so does $a_n$.


I am currently writing a project report, and have come across a strange thing.   While making the title page, when I insert the title, if I wrote \textbf{\LARGE{Multi-Server Authentication Scheme Using Biometrics}} the output came as this:    But if I change the code to \LARGE{\textbf{Multi-Server Authentication Scheme Using Biometrics}}, the output looks like this:    Although the above solved my problem, I am curious to know why this happens. The rest of the code needed to fully reproduce this is:  \documentclass[12pt,a4paper]{report} \begin{document} \begin{center} {here goes the above codes for the title} \end{center} \end{document}


I am writing an assignment, and I need to say, "6", "year","old", and "girl". I wrote 6 year old girl, but I keep getting a blue underline suggesting it is grammatically incorrect. How should I be writing this, and why?


What am I supposed to say if I want to say that I don't possess ssomething? here are some sentences I have trouble with:  1-I have nobody or I don't have anybody?  2-There isn't any sugar or there's no sugar?  3-I have no knives in my bag or I don't have any knives in my bag?


How does the URL change without refreshing the page?

when I click in the comments section where it says "x More...".  How this this URL trickery happen?


How to get rid of banding in illustrator while using gradient?

How to get Rid of Banding in illustrator while using Gradient


I need a method for adding "business days" in PHP. For example, Friday 12/5 + 3 business days = Wednesday 12/10.  At a minimum I need the code to understand weekends, but ideally it should account for US federal holidays as well. I'm sure I could come up with a solution by brute force if necessary, but I'm hoping there's a more elegant approach out there. Anyone?  Thanks.


Have I used "whom" correctly in the following sentence? Rarely a day goes by here that I don’t witness this core value manifesting itself in a myriad of thoughtful, sincere, acts of kindness toward our residents, many of whom have enriched our lives beyond measure.


Effect of space time relativity on the age of the universe?

So we all heard about the twins paradox to explain einstein's time space relativity.  Wikipedia Quote :" In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. "  So what if the universe has been travelling at varying speeds (increasing or descreasing), wouldn't this effect our measurements on age of the universe?


What is the best way to implement a "timer"?

What is the best way to implement a timer? A code sample would be great! For this question, "best" is defined as most reliable (least number of misfires) and precise. If I specify an interval of 15 seconds, I want the target method invoked every 15 seconds, not every 10 - 20 seconds. On the other hand, I don't need nanosecond accuracy. In this example, it would be acceptable for the method to fire every 14.51 - 15.49 seconds.


How can I import a VMDK disk image to an AWS EC2 t2.micro instance on us-east-1e region using an S3 bucket on us-east-1?

I've recently purchased a reserved EC2 micro instance on region eu-east-1e.  I am having trouble importing a virtual machine using ec2-api-tools:  ec2iin -t t2.micro "CentOS 7 x86_64-disk1.vmdk" -g my-launch-config -f VMDK -a x86_64 -p Linux  -b mybucket -o MYID -w MYSECRETKEY +A -s 10  -d importingMinimalCentos764VMDK --region us-east-1e --subnet mysubnetid   output:  Requesting volume size: 10 GB ERROR: Unable to create signed manifest URL. Cannot access/create bucket: mybucket : com.amazonaws.AmazonClientException : Unable to execute HTTP request: mybucket.s3.us-east-1e.amazonaws.com   Which makes sense since the address of my bucket is mybucket.s3.us-east-1.amazonaws.com, but if I choose that region then I get a different error:  Client.InvalidParameter: Subnet 'mysubnetid' is in the availability zone 'us-east-1e'. (Service: AmazonEC2; Status Code: 400; Error Code: InvalidParameter; Request ID: 6e6d886f-2932-42f8-b771-b99475371bc6)   If I keep the region us-east-1 and ommit the --subnet mysubnetid then I still got a problem, since apparently I cannot create a t2.micro on us-east-1:  Client.Unsupported: The requested configuration is currently not supported. Please check the documentation for supported  configurations. (Service: AmazonEC2; Status Code: 400; Error Code: Unsupported; Request ID: 91fe5c48-2a0e-45bc-90fb-d7a 581fc3780)   There is no way to create a bucket on us-east-1e region. It is not listed and the command line tool aws s3 mb s3://mybucket --region us-east-1e gives an error, region not found when I try.  How can I fix this? I just want to upload and convert my VMDK to launch the t2.micro I've reserved and I need a bucket on the same region for that! I suppose I can do it in another region, then crate an image, then move the image to my desired region. But will I be able to export any changes to that instance? (when I tried to export an image before I got an error like you can only export imported instances, that's why I am creating a VMDK VM and importing it: so I can export it later, anytime I want)


Is there any 'flavour' of ubuntu that comes with East Asian language support? Or does anyone have a suggestion about what 'flavour' is more suitable for working with Chinese, Japanese and Korean? I still prefer to have the default system langauge English.


cannot read field because is null java textfields

I am getting this exception there Exception in thread "AWT-EventQueue-0" java.lang.NullPointerException: Cannot read field "imeField1" because "controller.evidencijaController.view" is null at controller.evidencijaController.spremiPodatke(evidencijaController.java:14) package controller;   import javax.swing.*; import java.sql.Connection; import java.sql.DriverManager; import java.sql.SQLException; import java.sql.Statement;  public class evidencijaController {     private static view.evidencijaView view;     private model.evidencijaModel model;     public static void spremiPodatke (String imeTurista, String prezimeTurista, String oibTurista, String mailTurista, String mobTurista) throws SQLException {         if(view.imeField1.getText().isEmpty()){             JOptionPane.showMessageDialog(view, "The ID cannot be null!", "Invalid info", JOptionPane.WARNING_MESSAGE);         }else{             Connection connection = DriverManager.getConnection("jdbc:mysql://localhost:3306/rezervacijalucica","root","");             Statement statement = connection.createStatement();             statement.executeUpdate("INSERT INTO turist(imeTurista, prezimeTurista, oibTurista, mailTurista, mobTurista) VALUES("+imeTurista+","+prezimeTurista+","+oibTurista+","+mailTurista+","+mobTurista+";)");         }     }```


My intention is to import a .py module that is passed as an argument:  module = str(sys.argv[3]) mymod = __import__(module)   However, I run into "ImportError: Import by filename is not supported.". Note that the passed module name is different on different invocation, and there is no common file path. What would be the workaround?


My party went up against two wizards. Wizard NPC 1 cast a spell, and Wizard PC used their reaction to Counterspell to try to block it. Wizard NPC 2 counterspelled Wizard PC. I have two questions about this:   Is there any defence against this? If it was just one NPC Wizard, could they use their reaction, during their turn, to counterspell the PC Wizard's counterspell?


How to combine two lists in one list? using notepad++ regex?

I have a list of textfile such as below example:  username1 username2 username3   I want a regex that can make it like following example:  username1:username1 username2:username2 username3:username3   etc..  I've tried many regex with failed attempts.  hopefully somebody can help me..  thank you in advance. regards.


This proof has surely been addressed before on here, but I'm writing the proof from scratch, without looking at other variants of it, and hoping that someone could critique it, as I'm still somewhat new to proof-writing and very new to analysis.  All comments on content, style, elegance (especially lack thereof, in my case) and so forth are very much welcome and appreciated.  Theorem. Let $A$ be a nonempty set of real numbers which is bounded below. Let $-A$ be the set of all real numbers $-x$, where $x \in A$. Prove that $\inf A = - \sup \left(-A\right)$.  Proof. Let $A$ be a nonempty subset of $\mathbb{R}$, and $-A$ to consist of the negations, $-x$, of all $x \in A$. The infinium of $A$ has the properties that \begin{align*} \forall x \in A, \inf A \leq x \ \wedge \ \forall y\in A, \left(y \leq x \implies y \leq \inf A \right), \end{align*}  i.e., $\inf$ is both a lower bound of $x$ and the greatest of such lower bounds. Multiplying these expressions through by $-1$, which yields elements in $-A$, gives \begin{align*} \forall -x \in -A, -\inf A \geq -x \ \wedge \ \forall -y \in -A, \left(-y \geq -x \implies -y \geq - \inf A \right), \end{align*} so $-\inf A$ is an upper bound of $x$ and the smallest of such upper bounds, in which case we have $-\inf A = \sup \left(-A\right)$. Multiplying this equation through by $-1$ yields our result, $\inf A = - \sup \left(-A\right)$.     How does this look?


I have ubuntu installed as the sole OS on a T420. Before this I had installed the #! distro (and Xubuntu before that) and wireless worked seamlessly on either. My home hotspot shows up but when I click on it tries for a while before disconnecting.  Before going into the problem further, I wanted to double check that I entered the wifi password for my home network correctly. I went to Edit Connections >> Wi-Fi Security and changed the key, but it is still not able to connect. So I think the password is definitely correct. I don't understand why it can't connect now.


I wish to add Ubuntu 64 bit to Windows 8, and the installation guide mentions booting from USB or DVD. If I burn the downloaded Ubuntu to an empty USB stick, then put the stick into my computer, what happens next?


Show root test is stronger than ratio test

Let $a_n$ be a sequence of real positive numbers. Show $$\liminf_{n\to  \infty} \frac{a_{n+1}}{a_n} \leq \liminf_{n\to \infty}\,(a_n)^{1/n}  \leq \limsup_{n\to \infty} \, (a_n)^{1/n} \leq \limsup_{n\to \infty}  \frac{a_{n+1}}{a_n}.$$   Here's the proof I had in mind, and I'm interested to know if anyone knows a simpler one, or if anyone can find a gap in my logic.  Suppose $\liminf_{n\to \infty}(a_n)^{1/n}=L_1$. Then we have a subsequence $a_{n_k}$ such that $(a_{n_k})^{1/n_k}\to L_1$. Now   $$(a_n)^{1/n}=\left( \frac{a_n}{a_{n-1}} \frac{a_{n-1}}{a_{n-2}} \dotsb \frac{a_2}{a_1} a_1 \right)^{1/n}\\ \log\left( \sqrt[n]{a_n} \right)=\frac{\log\left(\frac{a_n}{a_{n-1}}\right) +\dotsb +  \log\left(\frac{a_2}{a_1}\right) + \log(a_1)}{n}.$$  If $\log(\sqrt[n_k]{a_{n_k})}\to \log(L_1)$, then we can show by contradiction that $\forall \epsilon$ there are arbitrarily high $n_l$ such that $$\frac{a_{n_l}}{a_{n_l -1}} < L_1 + \epsilon $$  If not, then eventually the averages on the right-hand side would be too large.


How to protect my galaxy S9 from data recovery after factory reset?

I have a Galaxy S9 that I will send to Samsung in a couple of days for the trade-in program and I want to delete everything on it in a way that it cannot be recovered even after a factory reset. From my limited research, there are people who recommend encrypting the phone before doing the reset as this will ensure the data is just noise and unreadable after the reset. But there is no option on my S9 to encrypt the phone as I saw on the youtube videos, and after a quick search I found out that S9's are encrypted by default. So is it safe to just factory reset it since it's encrypted by default anyway? I'm not that good when it comes to tech and stuff, what would you guys recommend I do? Thanks for the response.


While going through some of my notes, I came across a formula for evaluating an integral of the form: $$\int_0^\infty {\frac{dx}{x^n+1}} = \frac{\pi}{n\sin(\frac{\pi}{n})}$$  I was wondering if any other formulas exist for solving more complicated integrals where an antiderivative can't easily be found. If you could also include a proof of said formula, that would also be greatly appreciated.  Thanks in Advance!


I tried the first experiment in chapter 5 in the Metafontbook: ran mf, typed \relax and drawdot (35,70); showit;.  This opened a window entitled Metafont, but containing nothing.  What's missing?  Using TeXlive 2020 on Linux. PS. After adding drawdot (65,70); showit; I see both dots. PS II. Which have now disappeared, after I changed window-manager workspace and back. PS III.  Typing showit; before the first drawdot opens a window and allows the first dot to be seen, but after having switched workspaces and back, I haven't found any way of bringing the picture back, short of drawing something more and showing it.


What year was the spell Lumos taught at Hogwarts?

In the Harry Potter world; what year do they teach Lumos to the students? Is there any in canon examples of what school year the teachers teach the young Wizards and Witches the spell Lumos?


Let $A=3^{105} + 4^{105}$. Show that $7\mid A$.  My attempt-   I tried to convert $3^{105}$ like this: $3^{105}\equiv 3\cdot(3^2)^{52}\equiv 3\cdot 9^{52}\equiv 3\cdot2^{52} \pmod 7$. And for $4^{105}$ I tried the same way to convert it into $4\cdot 2^{52}$ but that's not possible and I'm getting $4^{79}\cdot 2^{52} \pmod 7$. I had the idea of doing it in $3^{105} + 4^{105}\equiv 3\cdot2^{52}+4\cdot 2^{52}\equiv 7\cdot2^{52}\equiv 0 \pmod 7$.  But I'm getting $4^{79}$ making it complex.  Can anyone suggest me some easier method? Please.


What is the appropriate ability modifier for hurling a Javelin of Lightning?

Is it Strength because it's a Thrown javelin (like a regular javelin), or Dexterity because of the wording of the descriptive text below? Specifically: 'make a ranged weapon attack' implies Dexterity to me.      This Javelin is a Magic Weapon. When you hurl it and speak its Command Word, it transforms into a bolt of lightning, forming a line 5 feet wide that extends out from you to a target within 120 feet. Each creature in the line excluding you and the target must make a DC 13 Dexterity saving throw, taking 4d6 lightning damage on a failed save, and half as much damage on a successful one. The Lightning Bolt turns back into a Javelin when it reaches the target. Make a ranged weapon Attack against the target. On a hit, the target takes damage from the Javelin plus 4d6 lightning damage.      The javelin's property can't be used again until the next dawn. In the meantime, the Javelin can still be used as a Magic Weapon.


Many are familiar with this popular illusion where a single shade of color appears to be two different shades, depending on what color surrounds it    The orange dots in the image are actually the same color, even though they appear to be clearly different. A detailed explanation can be found .  Since the perception of a color is affected by what colors it is next to, I wonder, is there information out there for how to correct for this phenomenon?  What I mean is that, suppose I see a color out "in the wild", such as on a color swatch or on someone's web page. I found out what color it is-- say, Coral Pink, #F88379. Then I decide I want to use it in a color scheme. But, because of color constancy, when I place it next to my other colors, it would appear to be slightly different than it would in other contexts.   Has anyone mathematically determined how to correct for this effect? Is there a program I can use to help me do so?


I cannot boot to the desktop because I filled the file system. How do I reclaim some space?

My memory is completely full when I tried following the data recovery and copied the wrong file using command line tool Test Disk. As it was taking so long to copy, I turned it off and I realized I copied the wrong file. Now my laptop memory is now full and lead me to more problems.  I have had similar problems to :       Now my screen keeps blinking:   Can anybody help? Many thanks. Wish you all the best.


From The Silence of the Lambs (1988):  "Marilyn Sutter saw it upstairs. Chilton was blowing off about "The Search for Billy Rubin." Then he went to dinner with a television reporter. That's where he was when Lecter took a walk. What a pluperfect asshole."  While I am aware of the pluperfect tense, the above usage of the word strikes me as rather exotic. ODO only lists the grammatical definition in its . But it provides an additional definition under its :  [as modifier] more than perfect: they have one pluperfect daughter and are expecting an ideal little brother for her   defines its alternate sense as utterly perfect or complete along with a note on its origin:  late 15th century: from modern Latin plusperfectum, from Latin (tempus praeteritum) plus quam perfectum  I'm curious as to how this odd-sounding construction made its way from the grammar book into common parlance. Is it used in this sense only in the US? Is it still in use? (Although I see it used in other languages, I believe that pluperfect is no longer the term of choice in English grammar.)


Can an unconscious creature hold their breath?

Does an unconscious creature or PC automatically hold their breath as pertaining to suffocation?  As pertaining to this question:      A creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).   When a creature runs out of breath or is choking, it can survive for a number of rounds equal to its Constitution modifier (minimum of 1 round). At the start of its next turn, it drops to 0 Hit Points and is dying, and it can’t regain Hit Points or be stabilized until it can breathe again.   The question revolves around the first part “A creature can hold its breath. As opposed to A creature holds its breath


How to write a test class for a scheduleable class that sends an email?

I am fairly new to apex testing and am completely lost on how I am supposed to test a schedulable class that regularly sends an email. The class that I have written is below. It is very simple, and its only function is to regularly send the same exact email to the same exact people everyday. Note that anywhere there is an 'X' is actually something else, I just put 'X' there for privacy reasons. Any advice on how to test this would be immensely appreciated. public class SendSurveyEmail implements Schedulable { public void execute(System.SchedulableContext sc){     Messaging.SingleEmailMessage message = new Messaging.SingleEmailMessage();     message.setUseSignature(false);      message.setBccSender(false);      message.setSaveAsActivity(false);           EmailTemplate emailTemplate = [Select Id,Subject,Description,HtmlValue,DeveloperName,Body from EmailTemplate where name = 'X'];     message.setTemplateId(emailTemplate.Id);          User[] allUsers = [SELECT Id, Email FROM User WHERE isActive=:true];     String[] toEmails = new List<String>();     for(Integer i = 0; i < allUsers.size(); i++){         String email = allUsers[i].Email;         if (email.contains('X')){             toEmails.add(email);                 }     }     message.setToAddresses(toEmails);          String surveyLink = 'X';     message.setPlainTextBody(surveyLink);      }


How can I activate a text input element by pressing enter?

I've got this input element for searching for an adress: <input type="text" id="searchAdress"/>  Next to it is this button: <button type="button" id="add" onclick="addAdress()">Add</button>  Which activates the javascript function "addAdress" which makes the searching for an adress work. It contains this: function addAdress() {      let adress = $('#searchAdress').val();  Right now you have to move your mouse away from the input field and click the "add" button to activate "addAdress", is it possible to also activate "addAdress" by pressing enter? So that you can search for an adress by pressing the button or by pressing enter.


As we can usually predict the various forces that a body might be undergoing based on its position and its velocity.Hence what is the need of acceleration?


Which is the best torrent client for Ubuntu 14.10?

I searched utorrent site, but it is given for lower versions of ubuntu. Which one do you suggest ?


How to compare 2 regression slopes with R?

I have to compare the slopes of 2 regression lines with R. The 2 regressions are made with the same parameters in 2 different locations.  I did my regressions with the function lm(). Now I have the results but I don't know how to compare them..  I tried with student test or ANOVA but it requires more than the 2 slopes.  I looked for an answer during something like 2 hours but didn't find, so I ask the question here : How should I do my test?   Thank you in advance, b.raoul


I have a company webpage at "example1.com" and was developing a new webpage at "exemple2.com" (because it was everything already set).   When I finished the page, I updated my "example1.com". So, at this time both "example1.com" and "example2.com" had the exactly same code.  Couple of day later I disabled my "example2.com" site by removing its DNS configs.  But... The root page on google was indexed on "example2.com" and when I removed this domain (and forbidden google to index them at the search console), my root page from "example1.com" didnt get indexed.  So... I have all my pages from "example1.com" indexed (about 6 pages), and my root page isnt indexed... I already try the manual index at search console, but nothing until this moment...  Any tips on how I can solve this? Or this is one of the cases that I just need to wait a month or so?  Thanks!!


'had better not entangle' v 'had better not to entangle'

Can I write this sentence:     He said Carter had better not entangle the US in problems like those   in Afghanistan, Somalia and Iraq.   Like this:     He said Carter had better to not entangle the US in problems like those   in Afghanistan, Somalia and Iraq.   ?  If so, what's the difference between the meaning of both sentence?


I washed and dried my passport by mistake, do I need a new one?

Around two years ago I washed and dried my passport by mistake at the laundry room. My ID, my old US student visa and my stamps from european countries are still readable but the pages are not "flat" anymore and the front cover is kind of erasing (some parts of the Brazil symbol is gone).   In April I'll travel to US for a conference, I'll need to get a new US visa (B1/tourism visa) but I'm worried if my passport is not "good to go" anymore because it was "washed and dried". Apparently there is an electronic chip in it and I don't know if it is still working.  Should I get a new passport or can I save some money and time and use this one? It expires only in 2019.


I am always in a doubt on when I should reference and when I should use a variable pass. For example, one of the API is called by the JOBJECTs -  QLIST retrive_cinemas(QString& options) {    return (staticobject::getcinemas(options)); }   or  QLIST retrive_cinemas(QString options) {    return (staticobject::getcinemas(options)); }


How to blur a section in a video that is already uploaded?

I realized I opened a Chrome tab that I don't want shown in the video. The video already had 500 views and thumbs up, etc. I don't want to take it down just to re-upload it.  Is there a way using YouTube effects to blur parts of a video, or cut part of it out?


How to block SMSs from certain "named" senders?

There are many tools around to block unwanted SMSs. Samsung Galaxy S3's Jelly Bean offers a native call&sms blocker too. But some senders are not phone numbers, they are alphanumeric strings. I would like to get rid of this spammer, and my provider says they can't block SMSs on their own. Currently, I wouldn't like to block "anonymous" SMS because I haven't yet received spam (better say mobbing) from undisclosed/private senders. I've tried to use , but it doesn't seem to support named senders too. Any suggestions on how to deal with this?


Minimum value of the expression given below.

Is $a,b,c$ are three different positive integers such that :  $$ ab+bc+ca\geq 107 $$  Then what is the minimum value of $a^3+b^3+c^3-3abc$.  I expanded this expression to $(a+b+c)((a+b+c)^2-3(ab+bc+ca))$ and tried to find the minimum value of $(a+b+c)$ by AM-GM inequalities but the problem is that the minimum value occurs at scenario where $a=b=c$, which is ommitted by assumptions of this question. I'd appreciate some help.


Mass defect- From where mass is being lost?

As a school student, I have wondered while studying mass defect the following mysterious problem  My assumption   Just like a car's mass is constituted by each part of it(i.e total mass of car will be equal to mass of body+engine etc..), I assume that the mass of nucleus is the sum total of the mass of the particles the nucleus contains, i.e  mass of nucleus =mass of protons +mass of neutrons I assume all the protons, neutrons  are exactly the same, they have (each kind) exactly same mass I assume the charge of proton is distributed uniformly.   Details    A quote from Wikipedia:      It is observed experimentally that the mass of the nucleus is smaller   than the number of nucleons each counted with a mass of 1 a.m.u.. This   difference is called mass excess.   The mysterious problem I encounter  There is no change in the number of neutrons or protons in the nucleus of the atom. And my idea was as the mass of nucleus is the total mass of protons and neutrons, if the mass of nucleus is to change what I can think about the possibilities are   Either the number of neutrons or number of protons should change In order to fit the 2nd assumption, some part of the mass of every neutron and every proton will go (probably as energy) so that all the protons are same and all the neutrons too are same.   The 1st possible explanation is obviously wrong as we don't see any change in the number.  The 2nd possible explanation is just 'like a reason for the sake of giving a reason' logically difficult to convince myself. If that were true there should have been many types of protons and different types of neutrons (both classified according to their mass), which again is un-intuitive.  The question   What's the possible explanation to the question from where the mass is being lost? Either one of my assumption is wrong (but isn't my assumption just logical?) or there should be some other reason how the mass can vary (may be we should better define what is the mass of the nucleus). In that case, another question , If my assumption 1 is false What constitute the mass of a nucleus?  Isn't there something like a standard proton or a standard neutron (By standard I mean a fixed mass fixed charge etc) By my third assumption, If the proton loses some mass shouldn't it lose some of it's charge. And suppose we forget E=mc^2 can't we say the difference in the potential energy of electron-proton (as it changes when the charge changes) is an explanation of how the nucleus gets binding energy.


How to add saved password to Chrome manully

Chrome doesn't offer to save passwords at some sites, is there any way to add the passwords manully?


Can an opposing player take the ball from the goalie, inside the goalie's area, when the goalie has placed it on the ground to kick it?  The ball is no longer in the goalie's hands at this point, but rather, has been placed on the ground. Which rule in the FIFA rules explains this best?


Is set theory the most fundamental aspect of mathematics?

First of all I apologize if this question is too out of topic but it's been bothering me for a while.  From what I've gathered after years of study it seems that set theory is essentially the foundation of modern mathematics.  Now, I've been studying formal logic for a while and it seems to me that logic is even more fundamental than set theory in the sense that we rely on it to prove things about sets. However, from what I've read we also rely on set theory to prove things about logic.  I realize that formal logic is not the same as naïve logic. But if we expect to have a solid foundation for mathematics, shouldn't we have a rigourous approach to the way we reason that is independent from set theory? Is such a thing even possible?  In a nutshell, is it possible to have a reasonable framework for logic that is rigourous and independent from set theory?  I'm sorry if this question is too vague. And maybe a lot of people don't really care as long as everything makes sense. But since modern mathematics is so concerned with consistency and rigour, how do we know logic itself isn't flawed?  I would really appreciate your insight on this topic! Thank you!  PS: Please let me know if this question isn't appropriate for this forum.


I have a following code and in this news_date is of datatype DATE.  <?php       $news_id=$_REQUEST['id'];            $result = mysql_query("select news_title, img_name, news_date, news_desc from news where news_id=".$news_id);         $row=mysql_fetch_array($result);       ?>   .     <div class=news-date>         <?php echo $row['news_date'] ?>     </div>   This gives me date in "YYYY-mm-dd" format.  How can i change it to "mmmm-dd-yyyy" i.e. October 24, 2013 or similar


kill Ubuntu 13.10 then install 14.04 fresh

I am fed up trying to upgrade to 14.04  I have tried everything I can find from Ask and nothing is helping. Can I just kill it and install 14.04? Or uninstall completely than boot up with a 14.04 disk?  Please dont make me go back to Gates!


PDF and CDF of sum of random variables with different distributions

This may sound too trivial but I am having difficulty to solve an assignment problem where I need to determine the distribution and density of a random variable $Z$ which is the sum of random variables with different distributions.  In general, what is the technique to find the distribution and the density when there are random variables of different distribution?


Can't boot Ubuntu Live from USB (initramfs) unable to find a medium containing a live filesystem

I'm looking for a bit of advice regarding Linux Live booting from USB. So I tried building a bootable Persistent Ubuntu Live USB the following way:   downloaded Ubuntu 16.04.3 LTS ISO,downloaded Linux Live USB Creator,  followed the LiLi USB Creator wizard, says everything is fine.     I choose USB to boot from and I'm presented with the Ubuntu boot menu. From there, no matter if I choose Persistence, Live or Integrity Check I always get an error that doesn't allow me to actually get to Ubuntu proper:      I'd like to mention that I'm using a fresh Windows 10 and a brand new USB stick (16GB, usb3.0) and my motherboard is MSI 970 Gaming. I'm quite a beginner on Ubuntu.


How can I merge multiple bookmark (html format) files?

I am looking for a way to merge a bunch of different bookmark files without importing duplicates (or creating empty folders ... im looking at you firefox+bookmarkdd!).  I'm not looking to sync amongst browsers or computers, this is a one time merge of a bunch of different files.  Ideally I wouldn't have to install anything, as such I'd also be open to scripted solutions.


Why does my Pokémon Gold cartridge seem to forget saved gameplay?

I recently bought a copy of Pokémon gold version at a car boot sale. I played it for a while but then I had to stop, so I saved and then turned the game boy off, and took the game out. The next day when I put it back in my Game Boy and switched it on, all my save data was gone and the only options were New Game and Cancel.   I checked online to see if it was fake, but it looked the same as all the real ones. I also compared it to my Pokémon  red which I know is genuine, and all the details of the cartridge were the same (except for colour and sticker of course) here are some pictures of the comparison between the two games      Does anyone know whether this copy of Gold IS fake? How can I tell? Or is it just broken?


hiding discussions originating from religion.SE from the "hot-network-question" list on scientific SE websites

Here I mention only hiding from hard-science SE websites : maths, phsycis, chemistry, earth science, etc. And I explained why with a simple and verifiable argument : religions are considered anti-scientific (the opposite of science) by so many professional scientists recall that many of those websites are mainly used by professionnal researchers, the same people who answered to those famous surveys on religions.  Given that religions are considered anti-scientific (the opposite of science) by so many professional scientists, wouldn't it be a good idea to hide from the "hot-network-questions" the  discussions originating from ,  or  when we are on one of those  ? And isn't there a huge bias in favour of downvotes here ? Even if you don't agree, the question isn't "stupid" nor "crazy".


Kickstart for installing EFI bootloader on BIOS machine

Is it possible to generate  from within a BIOS machine? If so, how do you make this bootloader installation with Kickstart? AFAIU bootloader kickstart command installs the bootloader for BIOS as it is running in a BIOS machine.   EDIT:  We are trying to build a disk image with Koji. To do so, it spawns a QEMU VM, which by default is using BIOS. Then it runs a kickstart file for configuring it. We want this configuration to allow this image to run on both BIOS and UEFI machines. Avoid having one image for each. We have seen that this is possible with  as it boots fine in both.


If we are given $20$ people , what is the probability that among the $12$   months there are $4$ months containing exactly two birthdays and $4$ months   containing exactly $3$ birthdays .   I tried , that I even not able to start it .


Show $\sqrt{1+\sqrt{2}}$ is algebraic over $\mathbb{Q}$ with degree $4$      Let $\alpha=\sqrt{1+\sqrt{2}}$, and it is a root of $f(x)=x^4-2x^2+1\in \mathbb{Q}[X]$, so $f(x)$ is irreducible in $\mathbb{Q}[X]$, thus $\alpha$ is algebraic over $\mathbb{Q}$.   Clearly, $\alpha$ is not a root of polynomial with degree one.  How to show $\sqrt{1+\sqrt{2}}$ has degree $4$? My thought is let $g(x_1)=a_1x^2+b_1x+c_1, q(x)=a_2x^3+b_2x^2+c_2x+d$ and let $g(x_1)=0$, $q(x_2)=0$, but is seems not right. Can anyone give a hit to do it? Thanks


glb/gltf export for three.js with color and shading?

I'm very new to blender and am trying to export a model from blender for use in three.js. From what I've read, the best way to do this is to export it as a glb/gltf file. I can get the file to export, but it loses most of the color and all of the texture I've added. I added the color and texture via the shading tab and I made sure that I have enabled it to export with materials. Am I missing something or is this just not possible? Color and texture added via shading tab:  What the model looks like in blender:  What the model looks like in three.js:


Is there a way to use JAVA on Ubuntu after FF stopped NPAPI support?

Mozilla announced that NPAPI will not be supported since the released version 52. This means that Java will not be supported either.  Chromium based browsers do not support java for some time already.  At java.com they suggest using Internet Explorer or Safari.  I am using a Java app to sign banking documents. Is there any way to use Java in Ubuntu?


\docsvlist and nested functions: unwanted large spaces

I would like to iterate through a comma separated list to translate some words. I already found how to do so using \docsvlist from the etoolbox package. However, there is a large space printed before the first word and between the words when there should only be a "normal" space after the printed comma. I think the problem comes from the nesting of the \ifstrequal commands used for the translation. Below is a MWE including an example calling all the possible translations and another example calling only the first translation to show the impact of the nesting. How can I avoid these additional spaces? MWE \documentclass{article}  \usepackage{etoolbox}  \begin{document}          \newcommand\TranslateAnimal[1]{         \ifstrequal{#1}{Cat}{Chat}{             \ifstrequal{#1}{Dog}{Chien}{                 \ifstrequal{#1}{Mouse}{Souris}{                     \ifstrequal{#1}{Bird}{Oiseau}{                         \ifstrequal{#1}{Horse}{Cheval}{                             #1 % If there is no known translation         }}}}}     }      \newcommand{\TranslateAnimalList}[2][,]{         \def\nextitem{\def\nextitem{#1}}% Separator         \renewcommand*{\do}[1]{\nextitem\TranslateAnimal{##1}} % How to process each item         \docsvlist{#2}% Process list     }      There are additional large spaces before the first word and after words: \TranslateAnimalList{Cat,Bird,Dog,Horse,Mouse,Seal,Donkey}          Compare with: \TranslateAnimalList{Cat,Cat,Cat,Cat,Cat,Cat,Cat} where there is only a large space before the first word  \end{document}


View my questions with unaccepted answers

There is this new acceptance rate feature that appears beneath my signature card when I ask a question.  How do I display all my questions with unaccepted answers? How can I easily see the list of questions that have not been checked as accepted?


I have the /usr/lib/systemd and /etc/systemd directories, and systemd is running.  But I also have the /etc/init/ directory, with several .conf configuration files, I thought this was a sign of Upstart.   And I also thought Debian had moved to System V starting release 7. But that would imply having a /etc/inittab (that I don't have) directory, wouldn't it?


I feel intimidated in learning TikZ. I was wondering if there are some nice materials (or just your replies) at different level:   for providing big picture, which is important to beginners to not lose direction during learning. for comprehensive reference.   Examples are important, but only examples are not always clear for understanding the big picture and organization.


Unable to prove this by mathematical induction

I have the question:  $$1 + 8 + 27 + \dots + n^3 = \frac {n^2(n+1)^2}n$$  But doesn't this fail the base case? If we plug in a $1$ on both sides of the problem we get $1 = 4$. Which is not true. Does that mean we can't prove this further?  Any help would be extremely appreciated!


I would like to center a figure made on Tikz. This figure has a specific size which is wider than \textwidth,  and it needs to be centered. All options I see use \resibox or \makebox to center the figures. But I don't want to change the figure size. Are there any option or command to allow this?   Thanks very much in advance. Kind regards,  German  === SOLUTION == As Mr @David Carlisle commented below, the solution is uncomment the \makebox and set the scaling to 0pt as follow:  \begin{figure}[h!] \centering   \newlength\figureheight  \newlength\figurewidth  \setlength\figureheight{6cm}  \setlength\figurewidth{1.2\linewidth} \begingroup     \fontsize{8}{\baselinestretch}\selectfont     \makebox[0pt][c]{     \input{VoltFRFFreq.tikz}     %} \endgroup \caption{A plot of a sphere} \label{fig.freq} \end{figure}   Thanks again to all people!!  -- EDIT's --- P.D.-I forgot to mention I use XeLaTeX, I hope it helps. Kind regards, P.D.D- The code is  \begin{figure}[h!] \centering   \newlength\figureheight  \newlength\figurewidth  \setlength\figureheight{6cm}  \setlength\figurewidth{1.2\linewidth} \begingroup         \fontsize{8}{\baselinestretch}\selectfont         %\makebox[\figurewidth][c]{     \input{VoltFRFFreq.tikz}     %} \endgroup \caption{A plot of a sphere} \label{fig.freq} \end{figure}


I would like to map the AltGr key on my keyboard to produce Ctrl+Alt. I am aware of xkb and xmodmap. As far as I could tell, however, using those you can only map from key combinations onto single keys, not the other way round.


After I installed ubuntu I tried to install windows back, around 3 weeks after. Now every time I try to reinstall Windows it says:  "Please insert proper boot device"  After uninstalling ubuntu it is still a boot partition in the bios. Does anyone know how I could install Windows back? The only reason why I want to do this is because Ubuntu can't play many games and I am a PC gamer.


Notational confusion about the reading of $\mathrm{d}x^2$

I've already tried to ask this question (), but people seems to misunderstand what I was trying to express, so I decided to ask it again.  My question is, if one writes $\mathrm{d}x^2$ (which is kind of a differential expression), should it be read as $$(\mathrm{d}x)^2$$ (differential of x, but squared) or $$\mathrm{d}(x^2)$$ (differential of $x^2$)?  The question can also be asked in a different way: if I want to express $(\mathrm{d}x)^2$, do I have to explicitly write the parentheses or just write $\mathrm{d}x^2$?  Keep in mind that I'm not asking about the meaning of the differential, but instead the notation related to it.


How can I change the registered name in Windows 7 to my own?

how do I change the registered name in Windows 7 to my own name?


How do I load levels using a tile map in java

I'm creating a game and I would like to load levels in the game using a tile map.  this is the TileMap class code:          for(int row = 0; row < mapHeight; row++){             for(int col = 0; col < mapWidth; col++){                  if(tile[col][row] == "1"){                     handler.addObject(new Block(col * tileSize, row * tileSize, ID.Block, ss, 1, handler));                 }                  if(tile[col][row] == "&"){                     handler.addObject(new Player(col*tileSize, row*tileSize, ID.Player, handler, game, ss, 2));                 }             }         }   With this code I just get a blank screen. How do I fix this? Is there a better way? Thanks!


Let $R$ be a ring with identity $1$ and let $a\in R$. If there exists a unique $b\in R$ such that $ab=1$, prove that $ba=1$ and $a$ is a unit.