I accepted the input from the user and stored it in the variable "n". But, when I try to execute this code, I get java.lang.NullPointerException.  public class JavaApplication58 {      public static void main(String[] args) {         int a[] = null;         Scanner sc = new Scanner(System.in);         int n = sc.nextInt();         for (int i = 1; i < n; i++) {             a[i - 1] = i;         }         for (int i = 0; i < a.length; i++) {             System.out.println("" + a[i]);         }     } }

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


I would like to re-use the titles of chapters and sections in a section on the structure of my thesis. How can I accomplish inclusion of the section heading, as it is for example used in the table of contents, in such a chapter?  A MWE illustrating my intentions goes as  follows:  \documentclass{article}  \begin{document}  \section{Introduction}  \subsection{Coarse Overview} \subsection{Structure}  In Section~\ref{sec:related_work} we talk about XXXX % XXXX should actually be "Related Work". In Section~\ref{sec:model} we talk about XXXX % XXXX should actually be "Model". In Section~\ref{sec:evaluation} we talk about XXXX % XXXX should actually be "Evaluation". In Section~\ref{sec:conclusion} we conclude.  \section{Related Work} \label{sec:related_work} \section{Model} \label{sec:model} \section{Evaluation} \label{sec:evaluation} \section{Conclusion} \label{sec:conclusion}  \end{document}

How can one get the current name of the following: Chapter, Section, Subsection(s), frame, label, mdframed?


There's no doubt a simple explanation for this, but since updating to Ubuntu 14.10 I've been having a problem with VLC 2.2.0.   It's nothing major but on all video whether from DVD or from the hard disk I'm getting a thin green line down the right hand side of the picture. It does not go away in full screen and seems to occur on all the video I have attempted to watch.  I have uninstalled and reinstalled VLC a number of times with no change. This does not occur on other media players such as SMPlayer.  If anyone could help me solve this, I'd be very grateful.   Thanks,  Ben

I am using Ubuntu 14.10 64bit and the latest version of VLC media player, when I play a video (MP4, MKV AVI etc... it doesn't matter) at the bottom of the screen there is a green line It isn't an issue with my OS, YouTube, and the default media player work fine. Has anyone else had this issue? and if so is there a fix or is it just a software bug?


I need a clarification on the semantics of Python.   Is it true that when Python encounters a statement of the form   x = some_term   a new object is being created, as specified by the process of evaluation of the term some_term?  Now suppose that the following lines have been encountered by Python:  x = the_term   y = the_term   Where the_term is some fixed term (assume that it does not contain any references to functions generating "random objects"). As I see this the behaviour of Python should be the following: first a new object O1 is created and associated with the name x. Then a second new object O2 is created and associated with the name y. Both names x and y are now in suitable namespace. Objects O1 and O2 are distinct objects, the are occupying different places in memory, and the got the same values. Hence the test   x == y    should return True, and test  x is y   should return False.  So tell me please why do I observe the following:  x=5  y=5   now x==y returns (of course) True, and x is y returns True.  But if we put:  x=99999999999999999999  y=99999999999999999999   now x==y returns (of course) True, and x is y returns False.  Could you tell me what is happening? What is the "real" semantics of Python (since the one I have described is clearly wrong, as these examples show)?

Why does the following behave unexpectedly in Python?  >>> a = 256 >>> b = 256 >>> a is b True           # This is an expected result >>> a = 257 >>> b = 257 >>> a is b False          # What happened here? Why is this False? >>> 257 is 257 True           # Yet the literal numbers compare properly   I am using Python 2.5.2. Trying some different versions of Python, it appears that Python 2.3.3 shows the above behaviour between 99 and 100.  Based on the above, I can hypothesize that Python is internally implemented such that "small" integers are stored in a different way than larger integers and the is operator can tell the difference. Why the leaky abstraction? What is a better way of comparing two arbitrary objects to see whether they are the same when I don't know in advance whether they are numbers or not?


I'm newish to Blender, following a Udemy course. Everything has been working fine, but now suddenly when I'm in edit mode and select a vertice / edge / face, the right click just drags the entire object around instead of transforming the object by moving the vertice / edge / face.  I don't mean that proportional editing is turned on (it was suggested that this has been answered elsewhere). This is not the same question. The entire object moves - with no changes or transforming actions. Dragging any vertice of face behaves like grab: the entire object moves.  Does anyone know why this might be happening?  Have I accidentally messed up a setting somewhere?   I added another mesh in the same file and I have the same problem. I opened a new file and created a mesh there and it works fine, so it's not my input device - I've obviously done something in this file that I don't understand. If anyone has any siggestions to help me troubleshoot this, I would appreciate it. And apologies if I'm missing something that should be obvious. Thanks! Georgie  As requested, this is the viewport:    You can see the vertex selected. Clicking on this to transform it just grabs the whole object. I'm not pressing G to grab.

My problem is that I sometimes lose the ability to independently translate or otherwise transform any parts of a single mesh. If I try, for example, to just translate several faces, edges, or vertices, then the entire mesh will stretch and displace itself in order to follow the translation. Or, alternatively, if I try to translate just one face then the whole mesh will move as if I'm translating in Object Mode.  I'm not really sure I know how to describe this problem properly. I don't even know how to reliably reproduce it. It seems to happen to any given mesh at random, and it doesn't stop happening to that mesh unless I delete and remake it.  I assume that I must be doing something wrong to cause this to happen. Does anyone have any ideas? Thanks.


I am trying to solve exercises from Pugh's Real Mathematical Analysis 2nd ed. and there is a question related to the connectedness of a disc. The question statement is as follows:  Is the disc minus a countable set of points connected? Path-connected? What about the sphere or the torus instead of the disc?  Intuitively, I think the disc is connected and also path-connected after removing those points. However, I would like to see proof of this. Can someone help me with that?

Here's a question that I share:  Show that if $D$ is a countable subset of $\mathbb R^2$ (provided with its usual topology) then $X=\mathbb R^2 \backslash D $ is arcwise connected.


We want to install several pc's with XUBUNTU from a usb stick. The user may not be asked any questions.   The installation must include kingsoft which is a dpkg. Is this possible?  Thanks  Joeri

I need a CD or USB stick, that will install Ubuntu on a completely headless machine. Stick CD in and restart, no keyboard or screen should be involved.  There are a few obstacles:   The language selection menu when you first boot the CD. The fact that the CD menu waits. The installer's asking questions during installation.


I have a simple shell script command like this which can be run via automator or workflow:  cd /Users/myuser/Documents/Code-Files/scripts/;  /usr/local/bin/node code_upload.js   I'd like to add this as a Quick Action to the MacBook's Touch Bar, how can I achieve this?  Thanks!

Is it possible to add an icon on the touchbar that would launch a custom application (to the right section that is always shown)? I want to add iterm2.


I have Windows 10, and nowadays as I use my laptop, my computer uses more and more RAM and CPU. If I don't do anything, happens the same, I left my laptop at home, and after 8-10 hours it uses 99% of my hardwares, and after a while my computer freezes and says, that I have to restart my computer, because I have no more RAM. I don't have any viruses, and yes, I disabled Superfetch also. The top 2, which uses, are always Service Host: Local System (mainly this one) and System.  Here's a picture after 10 minutes of run:    And here after 2 hours:     Expanded as requested:

Since I upgraded to Windows 10, my system has been consuming RAM excessively    I've been reading a bit and determined it's likely a driver leaking memory. So I got myself the Windows Driver Kit and tracked memory usage with poolmon:    However, I don't really know how to proceed from here. Is the item tagged "smNp" the culprit in this issue? How do I go from there to actually identifying the driver?  I tried some stuff like "C:\Windows\System32\drivers>findstr /s smnp ." but it returned no results. I also took a look at the pooltag.txt file and this is the description I found for it:      So yeah, any help would be appreciated. Thanks in advance.


For every $n\in N$, we have:$$a_{n}=\frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+...+\frac{1}{n^{2}}$$ Then let $\sum$ be: $$\sum =\frac{1}{a_{1}^{2}}+\frac{1}{4a_{2}^{2}}+\frac{1}{9a_{3}^{2}}+...+\frac{1}{n^{2}a_{n}^{2}}$$ Prove that $\sum \leq \frac{3n-2}{2n-1}$, $\vee n\in N,n\neq 0$ My attempts:  First I tried using $\frac{1}{n^{2}}<\frac{1}{n-1}-\frac{1}{n}$ and then I found $a_{n}< 2-\frac{1}{n},\vee   n>1$,  with $a_{1}=1$ $a_{2}< 2-\frac{1}{2}$ etc.  But then I arrived at $\sum \geq 1^{2}+3^{2}+...+(2n-1)^{2}$, but I need $\sum$ lower than something, not grater.  Then I found that $\frac{1}{n^{2}}>\frac{1}{n}-\frac{1}{n+1}$ , and I arrived at $a_{n}>\frac{n}{n+1}$, but in this case 4,9,..,n^2 don't simplify. Also I found that $a_{n}<\frac{4n}{2n+1},\vee   n\geq 1$(with induction) but $a_{n}$ has to be greater than something, so that $\frac{1}{a_{n}}$ and $\sum$ to be lower.  Any help would be appreciated.

Let $$x_n=\frac{1}{1^2}+\frac{1}{2^2}+\ldots+\frac{1}{n^2},\;\forall n\geq 1.$$ Show that $$\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq \frac{3n-2}{2n-1}.$$   I tried to prove it by induction  but I got a contradiction.


Consider the function $$f(x)= \begin{cases}       0, & \text{if}\ x\ \text{is rational} \\       x, & \text{otherwise}     \end{cases}$$  My question is - Is the function continuous at zero? I understood that the function is not continuous at any other points in $\mathbb{R}$. But for zero I think it is continuous as for any sequence $\{x_n\}_{n\in \mathbb{N}}$ consisting of rational and irrationals that converges to zero, the function takes the value $0$ for rationals which obviously converges to $0$ and for irrationals the function is the identity function which also goes to $0$ as $x_n$ goes to zero. Am I correct?  Thanks!

Let $h(x) = x$ for all rational numbers $x$ and $h(x) = 0$ for irrational numbers. I'm trying to show that $h$ is continuous at $x=0$ and at no any other point.  Defintion of continuity at $x_0$: $(\forall x)(\forall \varepsilon > 0)(\exists \delta > 0)$ such that $|x-x_0| < \delta \implies |h(x) - h(x_0)| < \varepsilon$.  For this part of the question I took $\delta = \epsilon$. Then $|x - 0| < \delta \implies |h(x)| < \varepsilon$ because if $x$ is rational, then $x < \varepsilon$ and if $x$ is irrational then $|x| < \varepsilon$.   Defintion of discontinuity at $x_0$: $(\exists x)(\exists \varepsilon > 0)(\forall \delta > 0)$ such that $|x-x_0| < \delta \implies |h(x) - h(x_0)| \geq \varepsilon$.  I tried to divide the problem into two cases:  1) If $x_0$ is rational, then $|h(x) - h(x_0)| = |h(x) - x_0|$. Then pick $x$ to be a irrational number. Then I have $|h(x) - x_0| = |x_0|$. And take $\varepsilon = \frac{|x_0|}{2}$.  2) Now if $x_0$ is irrational $|h(x) - h(x_0)| = |h(x)|$. Now here is where I was unsure of myself: If I pick $x$ to be a rational number, then $|h(x)| = |x|$. I was not sure about choosing $\varepsilon$ so that $|x| \geq \varepsilon$. Would it be valid to take $\varepsilon = \frac{|x|}{2}$? (I mean $|x|$ here and not $|x_0|$)  Could I get some feedback? Thanks!  Edit To finish off the last part, let $\varepsilon = \frac{|x_0|}{2}$. Now I want to choose an $x$ in the rational numbers. I also need to satisfy $x_0 - \delta < x$ (since $|x_0 - x| < \delta$) and $|x| \geq \frac{|x_0|}{2}$. So now I pick $x \in (|x_0|-\delta, |x_0|) \cap (\frac{|x_0|}{2}, |x_0|)$.


I'm an Nvidia GT 440 user. I can already click on the 1280x1024 option in monitors but as shown in the image below it outputs an error. The message says:The virtual size required doesn't fit the available one,plus it says the maximum size is 1024x768 I tried many things and i ended thinking that the problem could probably be the EDID info,so I installed the package read-edid. When i type      sudo get-edid | parse-edid   it prints this   If more explanation is needed I'll post it as fast as i can

I just updated from Ubuntu 10.10 to 11.04 and have an issue regarding the screen resolution. I have Intel integrated gfx chip and my monitor supports resolutions larger than 1024x768. (in 10.10 I've been using 1280x1024) But as soon as I upgraded, I'm stuck with 1024x768 resolution and seems I can't change it.  running xrandr In terminal yields the following results,   Screen 0: minimum 320 x 200, current 1024 x 768, maximum 4096 x 4096 LVDS1 connected 1024x768+0+0 (normal left inverted right x axis y axis) 0mm x 0mm    1280x800       58.1 +    1024x768       60.0*     800x600        60.3     56.2      640x480        59.9   VGA1 connected 1024x768+0+0 (normal left inverted right x axis y axis) 344mm x 194mm    1366x768       59.9 +    1360x768       60.0      1024x768       75.1     72.0     70.1     60.0*     832x624        74.6      800x600        72.2     75.0     60.3     56.2      640x480        72.8     75.0     66.7     60.0      720x400        70.1     1280x1024_60.00 (0xce)  109.0MHz         h: width  1280 start 1368 end 1496 total 1712 skew    0 clock   63.7KHz         v: height 1024 start 1027 end 1034 total 1063           clock   59.9Hz   What maybe the problem? Is it a bug? What kind of steps I should take in order to get a higher resolution? (changing xorg.conf maybe?) Any insight is highly appreciated. Thanks in advance.   UPDATE    Screenshot after running xrandr --addmode VGA1 1360x768  As you can see, side bar is not completely visible and Ubuntu logo at the task bar is missing. Also when you open an application, the Task bar of the application (where it should go to the top panel) is missing as well..


I have a 3- C-Media USB Headphone Set, a USB-Soundcard. I connected my head phones to it's headphone output. But even at level 2 of 100 in Windows 10, it is too loud. How do I make it even quieter?

Yes, I really am asking how to turn down the volume. But first, some more detail:  My headphones are   They are really loud. I usually have to keep them on the lowest setting. If the source material is louder than average, I have to lower the output volume in the player software.   Is there a way to can adjust the Windows 7 volume settings so that my normal listening volume is around 50% instead?


I have a string as a parameter in my method and i am trying to print the length of the string in which i have succeded but I want to add a zero in front of the length if it is less than 10.  I am getting the int cannot be referenced error, and not sure what the correct way of doing this is.  public void sendMessage(String message) throws ProtocolException {     physicalLayer.sendFrame("<" + "E" + "-"         + message.length().toString().padleft(2, '0')         + "-" + message + "-" + "00" + ">"); }   Thanks

How do you left pad an int with zeros when converting to a String in java?  I'm basically looking to pad out integers up to 9999 with leading zeros (e.g. 1 = 0001).


geocoder = new Geocoder(MapsActivity.this);                 List<Address> addressList = null;                 try {                     addressList = geocoder.getFromLocation(firstLocationLattiutde, firstLocationlongitude, 5);                 }                 catch (IOException e) {                     e.printStackTrace();                 }                  Address obj = addressList.get(0);                 add = obj.getAddressLine(0);                 guardAddress.setText(add);   but sometime it give error like this     java.lang.NullPointerException: Attempt to invoke interface method 'java.lang.Object java.util.List.get(int)' on a null object reference at com.example.fahadaziz.securityapplication.Services.MyService.onLocationChanged

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


Its a new installation. I ran mysql_secure_installation and set a password.  But I can still login with blank password. If I set -p it accepts my new password but also accepts blank password.  root@newserver:~# mysql -uroot  Welcome to the MariaDB monitor.  Commands end with ; or \g. Your MariaDB connection id is 46 Server version: 10.0.38-MariaDB-0ubuntu0.16.04.1 Ubuntu 16.04  Copyright (c) 2000, 2018, Oracle, MariaDB Corporation Ab and others.  Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.  MariaDB [(none)]> quit; Bye   There is only one root user account.  MariaDB [mysql]> select * from user\G *************************** 1. row ***************************                   Host: localhost                   User: root               Password: *lasdhjkladhailuhhiouaw            Select_priv: Y              Insert_priv: Y            Update_priv: Y

I've recently upgraded a system from Ubuntu 14.04 to 16.04 (mysql  Ver 15.1 Distrib 10.0.36-MariaDB) and noticed root can get in without a password eg:mysql -u root is empty.   Tried setting a new pass via mysql with UPDATE mysql.user SET authentication_string = PASSWORD('supersekrit') WHERE User = 'root'; however this didn't disable the empty password. Also tried running mysql_secure_installation to no avail.  Found a  about setting the plugin field in the user row to 'NULL'. I did that, but now root cannot login at all.   I followed the link to percona in the post, which states the correct way to do this is to run the following: ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'test';. This results in and error message -> ERROR 1064 (42000): You have an error in your SQL syntax...  Not quite sure what the correct way is to fix this. any ideas?  UPDATE: after setting the password for the root mysql account, Ubuntu 16.04 cron daemon is now throwing errors during logrotate. Looks like this issue is a rabbit hole.  I've emptied the root password for now until I can figure out what's borked with logrotate. Yeesh.  error: 'Access denied for user 'root'@'localhost' (using password: NO)'


IFS=$'\n' for CITY in $(cat /home/user/CT.txt) do  FILES=/mnt/dir1/dir2/$CITY/*  count=0 folder=''  for f in $FILES  do   echo "Processing $f file..."         ((count++))         folder=$f   # take action on each file. $f store current file name    #cat $f  done   Below is CT.txt content and directory structures :  cat CT.txt Test1 Test2 Test3  cd Test1/ |_dir1 exm.xls cd Test2 |_dir1 exm.xls   Output should:  i want only dir inside files should process under Test1 Test2 excluding .xls file

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?


As electrostatic force is a conservative force, but friction, occurring due to electrostatic forces is non-conservative.   A wider question would be: why is any force non-conservative if it is a consequence of electrostatic or gravitational forces (not talking about nuclear forces)?

Consider the mysterious force of friction. It drives our cars and bikes, slows them down, allows me to walk to the nearest dominoes store, allows me to eat my delicious pizza while ensuring that I stay sitting on the amazing seats provided by the pizza store.  Now friction is a non-conservative force we all know that amount of work done in dragging a body across a carpet depends on the exact route you take. However along with this practical experience I have also been taught that most interactions between everyday objects are a consequence of electromagnetic force which is conservative in nature. So my question how do several different Electromagnetic forces come together to make a new frictional force which is non-conservative in nature


I am 61 years old and have about $60,000 in credit card debt. I have about $130,000 in IRA mutual funds. I am also paying off 1st mortgage and a line of credit, so I am gaining equity with those. I am current on everything but am just paying min.s on credit card debt. Does it make sense to take a withdrawal from retirement accounts to pay off that credit card debt. All the cards have a min of 10 % up to 17%. I am not making any headway. Since I am over 59 would I be exempt from the 10% penalty?

The amount I have in RRSP savings is exactly equal to the amount I have in Home Equity Line of Credit debt (significant, but aside from home mortgage, my family has no other debt).    I know if I cashed out the RRSPs, I would be taxed, but since I've just changed careers and now have a much lower income, I'm tempted to cash in my RRSPs to cover the bulk of my HELOC so it's no longer looming over me.  Otherwise, it might take me forever to repay it.


If I'm launching a  (that requires the sacrifice a Goblin) and my opponent uses an  on the Goblin (or similar effects like the ability of a ) does this effectively counter my spell?

I have a question that bothers me after reading a part of the big book of rules :).  It's about the rule 717, illegal actions.     717.1. If a player realizes that he or she can’t legally take an action after starting to do so, the entire action is reversed and any payments already made are canceled. No abilities trigger and no effects apply as a result of an undone action. If the action was casting a spell, the spell returns to the zone it came from. The player may also reverse any legal mana abilities activated while making the illegal play, unless mana from them or from any triggered mana abilities they triggered was spent on another mana ability that wasn’t reversed. Players may not reverse actions that moved cards to a library, moved cards from a library to any zone other than the stack, or caused a library to be shuffled.   For example, player A plays a .     As an additional cost to cast Goblin Grenade, sacrifice a Goblin.   Goblin Grenade deals 5 damage to target creature or player.   It goes on the stack. Player B gains priority and casts a  on the only goblin of Player A.     Destroy target nonartifact, nonblack creature. It can't be regenerated.   The terror goes on the stack. Then both players agree to resolve the stack. The terror kills the last goblin standing and then the Goblin Grenade can't be cast because of the additional cost which can't be paid. So in my opinion that leaves two possibilities:   The Goblin Grenade returns to the zone it was previously from (the hand of Player A) The Goblin Grenade becomes illegal and gets countered, so it goes to the graveyard   Based on rule 717 I think it goes back to the hand but I'm not quite sure. :)


From Mac Lane:  I'm trying to prove the question at the bottom true, but I'm not exactly understanding how to jump between the different levels of abstraction.  If $B$ and $C$ are categories with one object each (say $B$ and $C$), then to satisfy the definition of a natural transformation it must be the case that if $g : B \rightarrow B$ is an arrow in $B$ (or an element of $B$) then $T(g) \circ \tau_B = \tau_B \circ S(g)$, where $\tau_B : S(B) \rightarrow T(B)$ is the natural transformation for each object (only one) in $B$.  It seems obvious that the above equality should imply the conjugacy relationship, but I'm not exactly sure where to bridge the gap between the "category with one element called a group" and the "group" itself.  Is the correct way of thinking this?:  Because the "group" $B$ with homomorphisms $T,S$ satisfies the axioms for the "category with one element called a group" and because we have the naturality relationship between the functors of the two "categories with one element called a group", we can replace the equation $T(g) \circ \tau_B = \tau_B \circ S(g)$ (that is in terms of arrows and objects) with their respective elements and products?

So imagine you have a group $G$ and we consider the set of group homomorphisms from $\mathbb{Z}$ to  $G$ specified by  $\forall g$ $\in G$ $\exists$   $\phi(1)=g$. Each of these homomorphisms is in 1-1 relation with the elements of $G$.  Consider groups for a moment in the context of category theory, viewing the groups as one object categories and thereof group homomorphism as functors. What would a natural isomorphism mean in group theory terms for G?  My thoughts are that the natural transformations equate to maps between homomorphisms and since the homomorphisms are in 1-1 relation with the elements of G, then a natural transformation is a map between group elements, i.e another element of the group. I'm not entirely convinced by this.   Anyway continuing my reasoning a natural isomorphism is a map between the homomorphisms that has an inverse, the thing is in relation to the elements of G this is every element? Furthermore I'm looking to find an equivalence class defined by this natural isomorphism, is this just a collection of the elements that are each others inverses?  Thanks in advance for any assistance.


So I was looking through various proofs of the chain rule...and I came across  paper. The first proof given is complete and quite well-explained. But another simplistic proof is given in the end...which is mentioned as "technically incorrect". Can anyone tell me why?  Here is the incorrect proof in question:  $$\begin{aligned} (f \circ g)'(x) &= \lim_{h \to 0}\frac{f(g(x+h)) - f(g(x))}{h} \\ \implies (f \circ g)'(x) \cdot \left(\frac{1}{g'(x)}\right) &= \lim_{h \to 0}\left(\frac{f(g(x+h)) - f(g(x))}{h}\right)\cdot\left(\frac{h}{g(x+h)-g(x)}\right)\\ &= \lim_{h \to 0}\left(\frac{f(g(x+h)) - f(g(x))}{g(x+h)-g(x)}\right) \\ &= f'(g(x)) \\ \end{aligned}$$

Why is this proof not valid?  Here is my "rigorized" version: We write $$\frac{d}{dx}f\big(g(x)\big)=\lim_{b\to a}\frac{f\big(g(b)\big)-f\big(g(a)\big)}{b-a}=\lim_{b\to a}\left[\frac{f\big(g(b)\big)-f\big(g(a)\big)}{g(b)-g(a)}\cdot\frac{g(b)-g(a)}{b-a}\right]$$ Now we split the limit up to get $$\lim_{b\to a}\left[\frac{f\big(g(b)\big)-f\big(g(a)\big)}{g(b)-g(a)}\right]\cdot\lim_{b\to a}\left[\frac{g(b)-g(a)}{b-a}\right]$$ In the first limit, we can set $y=g(x)$. Then by differentiability, and hence continuity, of $g$, we have $y\to g(a)$ as $x\to a$. Therefore the first limit can be expressed as $$\lim_{y\to g(a)}\left[\frac{f\big(y\big)-f\big(g(a)\big)}{y-g(a)}\right]$$ So we get, by definition of the derivative, $$\frac{d}{dx}f\big(g(x)\big)=f'\big(g(x)\big)\,g'(x)$$  There are two objections given to this proof. The first is that one cannot multiply by the quantity $\big(g(b)-g(a)\big)/\big(g(b)-g(a)\big)$ as $g$ may be constant around $x=a$ and the expression would then be undefined. However, it seems obvious that we can simply consider the case of $g$ constant separately (and the case of $g'$ not defined due to 'infinite oscillations', the difficulty cited in the wiki article), where it is easily seen that the formula is valid. (Indeed, this exact point is made in the comments under the answer to .)  The second is that the limit substitution is not justified. I don't understand this either. That limit rule (in which such substitutions are allowed for continuous functions) could easily be proven, but that has nothing to do with the chain rule. This is the objection given in an answer to   I found three other relevant sources.   The first proof in the  explicitly avoids the proof above on the basis that the expression noted may be undefined. In the last page of  the author offers students $3$ points if they can explain why the argument I gave above is a flawed proof. In  the author similarly showcases the flawed proof, and then moves on to the 'real' proof.   The 'real' proofs are, shall we say, 'not pretty'. I am wondering if this salvaged version of the intuitive proof really does not work, and why?    EDIT: THEORETICAL ADDENDUM FOR THE CASE OF INFINITE OSCILLATIONS  Suppose that $g(a)=g(b)$ for infinitely many $b$ in all neighborhoods of $a$. Then I claim: if $g'(a)$ is defined, it must equal $0$.  Proof. The quantity $$\frac{g(x)-g(a)}{x-a}$$ can be made equal to $0$ by picking an appropriate $b$ in the interval $(a-\delta,a)\cup (a,a+\delta)$ regardless of how small $\delta>0$ is. Therefore there does not exist, for every $\epsilon>0$, a $\delta>0$ such that the difference quotient is always within $\epsilon$ of any limiting value not equal to $0$. For the limit $L\ne 0$, take $\epsilon=|L|/2$. As the limit must exist by hypothesis, it exists and equals $0$.  Next I claim: the chain rule is valid in this case.  Proof. The chain rule formula returns $f'(g(a))g'(a)=f'(g(a))\cdot 0=0$ in this case. We prove that, in fact, the derivative is equal to zero.   Because $g'(a)=0$, we can make $$|g(x)-g(a)|<\epsilon |x-a|$$ true for any $\epsilon>0$ by picking an appropriate $\delta>0$. Then suppose that $f'(g(a))=c$. We have $$|f(x)-f(g(a))|<\max\{|c+\epsilon|,|c-\epsilon|\}|x-g(a)|$$ for any $\epsilon>0$ when $x$ is sufficiently close to $g(a)$. So make $|x-a|$ sufficiently small for all conditions. Then we have $$|f(g(x))-f(g(a))|<\max\{|c+\epsilon|,|c-\epsilon|\}|g(x)-g(a)|$$ $$\frac{|f(g(x))-f(g(a))|}{|x-a|}<\max\{|c+\epsilon|,|c-\epsilon|\}\frac{|g(x)-g(a)|}{|x-a|}$$ But $$\frac{|g(x)-g(a)|}{|x-a|}<\epsilon^*$$ ($\epsilon^*$ the first epsilon) so we have $$\left|\frac{f(g(x))-f(g(a))}{x-a}\right|<\epsilon^*\max\{|c+\epsilon|,|c-\epsilon|\}$$ Therefore the difference quotient can be made arbitrarily small, and hence $$\frac{d}{dx}\left(f\big(g(x)\big)\right)=0$$ as was to be shown.


Do you know of any documentaries Like Fermat's last theorem or N is number? Story of a mathematician or a theorem.Dont know if this is a good site for the question.

This is an offshoot of the question on . I have listed a few videos/documentaries I have seen. I would appreciate if people could add on to this list.  $1.$ Story of maths      $2.$ Dangerous Knowledge    $3.$   $4.$   $5.$


Here is my raster map code and I want see pixel information like pixel value from it when I click on the map: const UnTiled = new ol.layer.Image({     opacity:0.9,     source: new ol.source.ImageWMS({         ratio: 1,         url: 'http://localhost:8080/geoserver/shomal/wms',         params: {                  'VERSION': '1.1.1',                 "STYLES": '',               "LAYERS": 'shomal:geotiff_coverage',               "exceptions": 'application/vnd.ogc.se_inimage',         }       })            });map.addLayer(UnTiled);

I have a problem with GetFeatureInfo (I'm working with openlayers).  In my HTML file I have this:

Sieraków MAPA

   And I want to show some info in div #info.  In javascript I have layer from geoserver:  var theurl = 'http://localhost:8080/geoserver/sierakow/wms';     var jeziora = new ol.layer.Image({           source: new ol.source.ImageWMS({             url: theurl,             params: {'LAYERS': 'sierakow:jeziora'},             serverType: 'geoserver'           })     });     map.addLayer(jeziora);      map.on('singleclick', function(evt) {             document.getElementById('info').innerHTML = '';             var viewResolution = view.getResolution();             var url = jeziora.getGetFeatureInfoUrl(               evt.coordinate, viewResolution, 'EPSG:4326',               {'INFO_FORMAT': 'text/html', 'FEATURE_COUNT': 50});             if (url) {               document.getElementById('info').innerHTML =                   '';             }     });   To do this I followed this examples:  I also try  with parsing but result is the same, nothing happend. My div #info is still empty and I don't know why.   Console show me this errors:  Uncaught TypeError: jeziora.getGetFeatureInfoUrl is not a function  Uncaught DOMException: Failed to execute 'getImageData' on 'CanvasRenderingContext2D': The canvas has been tainted by cross-origin data.   This is url:   http://localhost:8080/geoserver/sierakow/wms?SERVICE=WMS &VERSION=1.3.0 &REQUEST=GetFeatureInfo &FORMAT=image%2Fpng &TRANSPARENT=true &QUERY_LAYERS=sierakow%3Ajeziora &LAYERS=sierakow%3Ajeziora &INFO_FORMAT=text%2Fhtml &FEATURE_COUNT=50 &I=50 &J=50 &CRS=EPSG%3A4326 &STYLES &WIDTH=101 &HEIGHT=101 &BBOX=6919511.668971639%2C1779979.5230483634%2C6921441.703935839%2C1781909.558012564   And this error shows:  Refused to display 'http://localhost:8080/geoserver/sierakow/wms?SERVICE=WMS&VERSION=1.3.0&REQUEST=GetFeatureInfo&FORMAT=image%2Fpng&TRANSPARENT=true&QUERY_LAYERS=sierakow%3Ajeziora&LAYERS=sierakow%3Ajeziora&INFO_FORMAT=text%2Fplain&FEATURE_COUNT=50&I=50&J=50&CRS=EPSG%3A4326&STYLES&WIDTH=101&HEIGHT=101&BBOX=6918701.436880034%2C1786965.867550262%2C6920631.4718442345%2C1788895.9025144626' in a frame because it set 'X-Frame-Options' to 'sameorigin'.   I will be greatful for every tips how to do that :)


I can see among my friends that Ubuntu versions which were released in odd year (2019, 2017, 2015, 2013) were rarely used. In the past, I could see that people were using it evenly (11.04 and before), but since 2014 with 14.04 LTS, no one used 15.04 and 17.04. They are also using 18.04 now even when it is the end of 2019 (19.10 released). Or is it just me, my friends and my colleagues?

What are the differences between an Ubuntu Long Term Support release (LTS) and a normal release?


I'm relying entirely on the English Dubbed version. As far as I know, they only refer to each other as friends when speaking to other people. Is there an explanation as to why?

In the first and second seasons of SAO, Kirito seemed to be interested in more than one girl at the same time. At the end they are all friends and such, but they are all jealous of him and he likes them back and all.  Some would argue Asuna is the real girlfriend, but:   In the cave with Sinon (SAO II, ep.11, 20:30), Sinon asks "Is there someone you don't want seeing this?" Kirito shyly answers no. While introducing Asuna to Sinon, Kirito only said that Rika and Asuna were his friends. Asuna looked okay, a bit like she was thinking "Yeah I'm just his friend."   These two occasions got me wondering: is he playing them all at the same time or something?   What I'm asking for is something like a timeline, which shows when Kirito likes whom.


I have a business sim card with an Android phone. Now different employees have to make calls, we all work from home. Right now we switch the sim to the person who is working. I would like them to be able to log on to the phone over data/wifi and make the calls. Does anybody know a location  I have been looking for this a few weeks but cannot find a solution except GoIP + a PBX. All solutions I found for this are a bit too complicated for the time I want to invest in this.

I have 2 Android phones. First phone is in country A. Of course it has an Internet connection over WiFi. Second phone is in another country B, as me. So, I need to make phone calls while I'm in country B (over Internet) remotely using the phone and its sim-card, which is in counrty A. What Android software do I need?


Like in the title, is it possible. I was thinking about that last year but everybody told me that it's not possible due to controller issues. Today I revisited that idea after seeing awesome vids on youtube running two ssd in raid 0. I'm running 2xhdd in raid 0 and I'm wondering wether to change 2x64gb sdd raid 0 for system and 2xhdd for files.

I am wanting to replace my Operating sytem hard drive with 2 SSD drives. Well possibly just 1 but I am curious about doing 2 in a RAID-0 setup for even more improved speed.  What exactly would I need to run 2 SSD drives in a raid0 setup?


Hi there I have spent about an hour making some edits to my project only to find that for some reason all the cubes, that I had set to fall and bounce on the plane, now simply hover in mid air.  I have uploaded the project in question below. (or will try to) I would be very grateful of any help.   This question was removed as of apparently being solved by an answer given to another question which referenced to reseting the rigid body world cache. This would make sense as I have been editing the FPS. However I have never enabled rigid body world. And it has worked perfectly fine before. I actually originally downloaded this project as a template put have since heavily modified it. I have re downloaded that template and found that it too of course does not have a rigid body world enabled. I can not find out what is wrong because I have realised that I don't know how the cubes ever managed to fall to the ground.  Here is a link to the original template that I used.   Thanks for the quick response that I previously received.

I've set up the physics of a swinging wrecking ball and set the animation to run for 240 frames.  This was not long enough for the entire "swing" of the ball-and-chain.   I'm unable to reset the timeline, but I can set the end frame to (say) 1000 frames, but when I try to play the animation, the animation progress halts at frame 240 and I cannot get it to go any further.   There are no markers or keyframes in the timeline.  What should I do to "force reset" the animation-timeline, to allow changes to the length?


was migrated to Super User but then it was returned to Web Applications. Then it shows that it was "deleted" by a diamond moderator but later was undeleted by a now-former employee. I assume that the question was migrated for a second time but the migration was rejected because the diamond moderator mentioned that he didn't know why the question history shows that he deleted the question. While the question  on Meta Web Applications there wasn't any explanation of the last "undeletion".  This is the current body of the referred question  When I try to access  with DNS through 1.1.1.1, it doesn't work.  Why? % dig +nocmd +nocomments @one.one.one.one archive.is ;archive.is.                    IN      A archive.is.             49050   IN      A       127.0.0.3 ;; Query time: 139 msec ;; SERVER: 1.1.1.1#53(1.1.1.1) ;; WHEN: Thu Oct  3 17:12:50 2019 ;; MSG SIZE  rcvd: 44  %

A  appears to have been deleted, and deletion is attributed to a moderator,  deleted by Sathyajith Bhat♦ 12 hours ago , however,  (however, they did previously (unsuccessfully) tried migrating it to another site in the network where they're also a moderator, but migration was rejected by another moderator, it was then on hold on webapps, and then the hold was removed, which was supposed to have been the end of it).  Can someone explain what's going on here?  And restore the question that clearly wasn't meant to have been deleted, was a HNQ, and has 75 votes on the question, plus 74 votes on the top answer, and 56 on second answer; and 19 on third?  There's a lot of links to this question, too, and now they're all broken, making SE look like a community hostile to a popular question ontopic for the site it was on.


This is an identity put forward by Ramanujan (often used as "proof" of his genius):  $$ \frac{2\sqrt{2}}{9801} \sum_{k=0}^\infty \frac{ (4k)! (1103+26390k) }{ (k!)^4 396^{4k} } = \frac1{\pi} $$  How does one go about proving this? Alternatively, what does one need to know to be able to do so?  Any help is appreciated.

The following formula for $\pi$ was discovered by Ramanujan: $$\frac1{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^\infty \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}\!$$   Does anyone know how it works, or what the motivation for it is?


I was making a program where it would count how many times every word was used in a random paragraph. It compiles, but when i try to run it its giving me a NullPointerException.  Here's the code:  import java.util.StringTokenizer;   class Count {     int count;     String name;      void SetCount(int c, String n)     {         count = c;         name = n;     }      void Show()     {         System.out.print("Name=" + name);         System.out.print("Count=" + count);     } }  class Contains2 extends Count {     public static void main(String args[])     {         String s = "Once you have made it to the box office and gotten your tickets, you are confronted with the problems of the theater itself. If you are in one of the run-down older theaters, you must adjust to the musty smell of seldom-cleaned carpets. Escaped springs lurk in the faded plush or cracked leather seats, and half the seats you sit in seem loose or tilted so that you sit at a strange angle. The newer twin and quad theaters offer their own problems. Sitting in an area only one-quarter the size of a regular theater, moviegoers often have to put up with the sound of the movie next door. This is especially jarring when the other movie involves racing cars or a karate war and you are trying to enjoy a quiet love story. And whether the theater is old or new, it will have floors that seem to be coated with rubber cement. By the end of a movie, shoes almost have to be pried off the floor because they have become sealed to a deadly compound of spilled soda, hardening bubble gum, and crushed Ju-Jubes";         int size, i, count = 0, j;          size = s.length();         String[] test = new String[size];          Count[] c = new Count[size];          StringTokenizer st = new StringTokenizer(s, " ");             while (st.hasMoreTokens())         {             for (i=0; i < size; i++)             {                 test[i] = st.nextToken();                 c[i].SetCount(1, test[i]);             }         }          for (i=0; i<size; i++)         {             for (j=0; j<size; j++)             {                 if (c[i].name.equals(test[j]))                     c[i].count+=1;             }         }          for (i=0; i<size; i++)         {             c[i].Show();         }     }    }

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


I have a data set with a sample size over three million numeric values. Close to 20% are either 0 or 1, with the maximum being nearly 18500. So the data is clearly quite heavily positively skewed.  I am trying to categorize some of this data by putting it into bins of equal width, to use the Chi-sqaure test and Cramers V to look for associations between this variable and a categorical one, so I decided to try and find the optimal number of bins. Using the Freedman-Diaconis rule it gave me a value of 126044.0262335108, this is clearly a ridiculously large number of bins for the data.   Breaking the set into the Inter-decile range also proved fruitless giving me [0, 1, 1, 2, 3, 5, 8, 17, 47]  Reading elsewhere the square root of the sample size was suggested, this gave 1732.05081 which is more reasonable. However the method is quite crude.  I also looking into Doane's formula given . But reading up on this method it seems to have been based on an incorrect .  How should I deal with this level of skew in the data?  What is the best way to categorize this data?

I have a data set with a sample size over three million numeric values. Close to 20% are either 0 or 1, with the maximum being nearly 18500. So the data is clearly quite heavily positively skewed.  I am trying to categorize some of this data by putting it into bins of equal width, so I decided to try and find the optimal number of bins. Using the Freedman-Diaconis rule it gave me a value of 126044.0262335108, this is clearly a ridiculously large number of bins for the data.   Breaking the set into the Inter-decile range also proved fruitless giving me [0, 1, 1, 2, 3, 5, 8, 17, 47]  Reading elsewhere the square root of the sample size was suggested, this gave 1732.05081 which is more reasonable. However the method is quite crude.  I also looking into Doane's formula given . But reading up on this method it seems to have been based on an incorrect .  How should I deal with this level of skew in the data?  What is the best way to categorize this data?


Is it possible to type something such as "and" in between these two aligned equations where the arrow mentions?. If so, can anyone kindly tell me how to achieve this?   Here is the screenshot     and here is my code:   \begin{align*} \bigl(Sf\bigr)\bigl(v_{1},\ldots,v_{k}\bigr) &:= \sum_{\sigma\in S_{k}} f\bigl(v_{\sigma(1)},\ldots,v_{\sigma(k)} \bigr), \\  \bigl(Af \bigr) \bigl(v_{1},\ldots,v_{k}\bigr)    &:=\sum_{\sigma\in S_{k}} \bigl( \text{sgn\,}\sigma\bigr)  f\bigl( v_{\sigma(1)}, \ldots,v_{\sigma(k)} \bigr). \end{align*}

How do I reduce the vertical spacing of \intertext?


How can I convert String to enum value?   public enum Season {WINTER, SPRING, SUMMER, FALL} Season season1; String winterString = 'WINTER';  season1 = winterString; <-- This gives error of course, but is there a way to do it like in java?

This is an extension of .  So, using the answer from the previous question I mentioned, I am able to make a generic utility that would convert/parse an Enumeration to a String.  Now the only problem I have with my solution is, I can't seem to refactor the code to my liking. It works the way I want it to, but it is a tad more on the code heavy side than I had hoped for. I was curious if there was a design pattern (or any other way to code it) to help solve this issue. I am thinking there is a creational design pattern that will help in this case. I would be easy if I had lambda expression but, Apex is not quite there yet ;).  The code I use has kind of patterns dug into it already. It uses the Strategy, Factory, and Template(ish) pattern I believe. I have the resources to find something to solve this issue (my favorite Design Pattern books), but nothing I can think of jumps out at me.  Here is the code for my utility for just one enumeration:  private interface EnumerationToStringHelper {     List<Object> ProvideEnumerationValues();     Boolean CompareEnumerationToString(String possibleEnumeration, Object enumerationValue); }  private class ExampleEnumToStringHelper implements EnumerationToStringHelperExampleEnum {     public List<Object> ProvideEnumerationValues(){ return (List<Object>)ExampleEnum.values(); }     public Boolean CompareEnumerationToString(String possibleEnumeration, Object enumerationValue)     {         return  ((ExampleEnum)enumerationValue).name().equalsIgnoreCase(possibleEnumeration);     } }  private static Map<Type, EnumerationToStringHelper> TypeToEnumerationMap;  private static void PopulateTypeToEnumerationMap() {     TypeToEnumerationMap = new Map<Type, EnumerationToStringHelper>     {         Type.forName('ExampleEnum') => new ExampleEnumToStringHelper()     }; }  public static Object ConvertStringToEnumeration(Type enumerationType, String possibleEnumeration) {     if(possibleEnumeration == null) return null;     if(TypeToEnumerationMap == null)         PopulateTypeToEnumerationMap();      EnumerationToStringHelper conversionAction = TypeToEnumerationMap.get(enumerationType);      if(conversionAction == null)         throw new EnumerationToStringException('The Type you enter is either a) not an enumeration or b) not a supported enumeration.');      for(Object particalarEnumValue : conversionAction.ProvideEnumerationValues())         if(conversionAction.CompareEnumerationToString(possibleEnumeration, particalarEnumValue))             return particalarEnumValue;     return null; }   public class EnumerationToStringException extends Exception { }   Now in order to use the utility, it is exactly what I hoped for.  return (ExampleEnum)RT_GeneralUtilities.ConvertStringToEnumeration(Type.forName('ExampleEnum'), 'Testing');   It is a little long, but it beats having the entire for loop for 12 or more different Enum types. That is why I wanted to build the utility - essentially for better readability and test coverage purposes.  The downside with this is I have to make a helper for every single Enum type. So it makes it kind of an eyesore maintainability-wise.    I was hoping there was a pattern I could implement to assuage that eyesore and make it appealing on both sides. Any suggestions?


How to find this sum : $\sum_{n=0}^\infty \dfrac{n^2}{2^n}$  $\sum_{n=0}^\infty \dfrac{n^2}{2^n}=\dfrac{1}{2}+\dfrac{4}{4}+\dfrac{9}{8}+\dfrac{16}{16}+\dfrac{25}{32}+\dfrac{36}{64}+\dfrac{49}{128}+\dots$ Now $\sum_{n=0}^\infty \dfrac{n}{2^n}\leqslant \sum_{n=0}^\infty \dfrac{n^2}{2^n}$ And I know that $\sum_{n=0}^\infty \dfrac{n}{2^n}=2$. But how to find this sum ? I am confused.Please give some hints.

I'd like to find out why  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6 \end{align}  I tried to rewrite it into a geometric series  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = \sum_{n=0}^{\infty} \Big(\frac{1}{2}\Big)^nn^2 \end{align}  But I don't know what to do with the $n^2$.


What is the appropriate way to encode and handle regressors that are nested? For example, a feature "Husband's age" is nested in the feature "Is married" in a sense that it's not defined unless "Is married" = 1. Should "Husband's age" be set to 0 or NA for those who are not married? Should we omit "Husband's age" from the model entirely and only use the interaction term "Husband's age"*"Is married"?  I guess this situation must be quite common, but I don't even know how to google it.

Consider a statistical problem where you have a response variable that you want to describe conditional on an explanatory variable and a nested variable, where the nested variable only arises as a meaningful variable for particular values of the explanatory variable.  In cases where the explanatory variable does not admit a meaningful nested variable, the latter is usually coded either as NA in the data set, or if it is coded with a value, that value is merely a placeholder that does not have any meaningful interpretation.  This situation tends to arise whenever you have an explanatory variable indicating the existence of a thing, and one or more nested variables describing the characteristics of that thing.  Some examples of this kind of situation in statistical problems are the following:   The explanatory variable is an indicator of whether a survey participant is married, and the nested variable is some characteristic of the spouse (e.g., education, age, etc.); The explanatory variable is an indicator of the presence of an item in a space, and the nested variable is a measure of some characteristic of the item (e.g., size, distance, etc.); The explanatory variable is an indicator of the occurrence of an event and the nested variable is a description of some characteristic of the event (e.g., duration, magnitude, etc.).   In these kinds of situations, we often want to build a regression-type model (in the broad sense that includes GLMs, GLMMs, etc.) describing the relationship between the response variable and the other variables.  It is not obvious how to deal with the nested variable in this type of model.  Question: How do we deal with the nested variable in this type of model?    Note: This question is designed to give a generalised answer to a recurring question on  regarding nested variables in regression (see e.g., , ,  and ).  This question is designed to give a generalised context-independent example of this problem.


a few minutes ago I changed my Ubuntu user password. Then I turned off the computer and turned it on. After I entered the new password, the system would tell me that the password was wrong. I tried to enter the old password, but without success. Now, I can't log into my computer and I can't even reset my password. What can I do?

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


I wonder if we need to use a question mark following "I wonder" for requesting something.   For example: I was wondering if you'd like to come to the cinema with me this evening?  Is using the question mark correct here?

Sometime, people put a question mark at the end of a sentence and use it to ask something. Instead using an interrogative sentence:     Do you like it?   You like it?   I think it is more often to someone who is not good at English.  As I am Korean, however, I realized that I also often and frequently violate Korean grammar. And I can't keep that all.  So, my question is:   Is it common for the native to use a declarative sentence as interrogative? Is it hard to understand in a short time? How are your societies tolerant to this?   Is this regarded as impolite or rude?


I can't decide, both sounds right and return results on Google.  So is it "any product group" or "any product groups"?  Context: The context is that some product can has sub-product that are part of groups, some have products and some don't. So I will add a method to know "any_product_groups?", "has_product_groups?", "any_product_group?", ... I'm not sure.  Example: "Has this product any product group(s)?"

This question has troubled me for ages despite my several attempts of looking it up in dictionaries or usage books. Do we say, "Do you have any ideas" or "Do you have any idea"? I do see an example where "any" means "it doesn't matter who/which/what", therefore "You can borrow any book you like." Also, does it matter between using it in questions and negatives?


Is there a predominant style in academic papers in computer science concerning the usage or the omission of the serial comma? What do ACM and IEEE do in general? I failed to find it out on my own. Is there any style guide of an academic publisher that suggests (or prescribes) that US-English papers in the two disciplines (mathematics, computer science) omit the serial comma in general?

According to the Wikipedia page for the , "Use of the comma is consistent with conventional practice" and "Use of the comma is inconsistent with conventional practice." Did the Oxford Comma come before its omission, or was the Oxford Comma traditionally omitted?  It makes logical sense that every item in a list would be separated in the same way: by a comma. If the Oxford Comma is conventionally correct, when and why did people begin to omit it?


I was making research about frameworks as a beginner JavaScript learner and I saw people also use libraries so I didn't understand what is the difference between them and why people use these libraries and frameworks ?

What is the difference between a framework and a library?   I always thought of a library as a set of objects and functions that focuses on solving a particular problem or a specific area of application development (i.e. database access); and a framework on the other hand as a collection of libraries centered on a particular methodology (i.e. MVC) and which covers all areas of application development.


So, the only thing I can think of is that Ubuntu did not correctly install some software as it doesn't recognize .run files. I checked "allow to run as executable file", but nothing.

My PC has both Ubuntu and Windows 7 installed. I have installed all my drivers in Windows like Nvidia graphics, motherboard etc. Shall I install them in Ubuntu too?  I looked on the web for my Nvidia drivers and I have found a .run file. How could I install it on my Ubuntu?


Let $X$, $Y$ be topological spaces and assume there exists a continous bijection $X\to Y$ and there exists a continous bijection $Y\to X$. Are $X$ and $Y$ homeomorphic?

I was asked the following question: if two topological spaces $X, Y$ are such that there exist a function $f:X\rightarrow Y$ continuos and bijective and a function $g:Y\rightarrow X$ continuous and bijective, then are the two spaces homeomorphic?  I would say that the answer is No, but I didn't find any counterexample so far.


I have two tables, table03 have 10 rows and table01 have 21 rows, now I want to get rows from table03 where they don't exist in table01, so far I wrote this query but it shows all rows of table03 even some rows doesn't exist on table01.  SELECT T3.`DateAdded`, T3.`Query_name`, T3.`Fund`, T3.`Ticker`  FROM `table_name03` T3 LEFT JOIN `table_name01` T1  ON T3.`DateAdded` = T1.`DateAdded`  AND `T3`.`Query_name` = `T1`.`Query_name`  AND `T3`.`Fund` = `T1`.`Fund` AND `T3`.`Ticker` = `T1`.`Ticker`   Table03:   Table01:


I always interpret "expletive you" as an imperative statement with an implicit subject of "I", although the (less than intelligent) speaker clearly doesn't think of it in this light.  Is there any basis for considering it otherwise?  P.S. - It seems to me that it would be so much easier for the submitter to type relevant tags in rather than this bizarre system - that I'm still struggling to decipher.

I heard that expression along with its derivatives so many times, in movies or otherwise, but I can't get it grammatically, meaning, does it stand for a complete sentence like "I will fuck you!" or "I want to fuck you!"? Or what?  Is it an imperative construction, or part of some other type of sentence with material deleted?  NB: This question is NOT about the meaning of this phrase (amply addressed in other questions on this site, such as ). It is about the structure of the phrase from a grammatical perspective, along with the common meaning of the expression.


Let $\{A_i\}_{i\in I}$ be a collection of subsets of a topological space $X$, such that $X = \bigcup_{i \in I} A_i$. Let $f:X \rightarrow Y$ be a map of topological spaces such that the restriction of $f$ to each $A_i$ (equipped with the subspace topology induced from $X$) is continuous.  Show that if each $A_i$ is closed, and $I$ is finite, then $f$ is continuous.  I understand that this can be solved by the pasting lemma, but I don't see how I can do it using both hypotheses that $A_i$ is closed and $I$ finite.

Suppose that $\{A_i\}$ is a finite collection of closed sets in $X$ such that $X = \bigcup A_i$, and $f : X \to Y$ restricted to each $A_i$ is continuous. Then $f$ is continuous.   Okay. The base case ($n=2$) is just the pasting lemma. I am having a little trouble with the inductive case, specifically with what the hypothesis is and how to deal with continuity with respect to subspaces. I believe the inductive hypothesis is to assume that any function over a topological space that is the union of $n-1$ closed sets such that the function restricted to each of these $n-1$ closed set is continuous must be continuous over the whole space. Then I assume I have a topological space $X = \bigcup_{i=1}^n A_i$, where each $A_i$ is closed, and a function $f : X \to Y$ such that $f|_{A_i}$ is continuous for each $i$. Thus $X = \bigcup_{i=1}^{n-1} A_i \cup A_n$, where $C = \bigcup_{i=1}^{n-1} A_i$ is closed since it is a finite union of closed sets. If I can show $f|_C$ is continuous, then I simply apply the pasting lemma to finish the problem. Give $C$ the subspace topology, and notice that each $A_i$ is closed in $C$. Thus we have a topological space $C$ that is the union of $n-1$ closed. But do I still have continuity $f$ restricted to $A_i$ since I am no longer considering them subspaces of $X$ but of $C$? When one says $f|_{A_i}$ is continuous, is one saying that $f$ is continuous when restricted to $A_i$ and $A_i$ is given the subspace topology?  EDIT:  I think I figured out the lemma I need. Claim: Let $A$ and $C$ be subspaces of $X$ such that $A \subseteq C$. Topologize $C$ with subspace topology with respect to $X$. Then the subspace topology on $A$ as a subspace of $X$ (call it $\tau_X$) is the same as the subspace topology of $A$ as a subspace of $C$ (call it $\tau_C$).   Proof: Let $U$ be open in $X$. Then $A \cap U$ is some open set in $A$ as a subspace of $X$. Since $C$ is a subspace of $X$, $C \cap U$ is open in $C$ as a subspace of $X$. Then $A \cap (C \cap U) = (A \cap C) \cap U = A \cap U$ is open in $A$ as a subspace of $C$, thereby proving $\tau_X \subseteq \tau_C$. Now let $O$ be some open set in $C$ as a subspace of $X$. Then $A \cap O$ is some open subset of $A$ as a subspace of $C$. But $O = C \cap U$ for some open set in $X$. Therefore $A \cap O = A \cap (C \cap U)= A \cap U$, which is also open in $A$ as a subspace of $X$. Hence $\tau_C \subseteq \tau_X$  Kind of obvious. But it was hard to spot the need for this lemma when I was considering subspace of subspaces and continuous functions, etc. Am I right in thinking this is the lemma I need?


Never fear I can in fact remember more about it than that! The cover was black and it had a silver snake eating its own tail on the cover. The book was about a boy who is hired by a company to travel (with a girl and another boy (the drummer)) to another world/alternative reality and there they discovered another girl who turned out to be his dead twin sister.   He was some hero or something and they found something out about the company they were hired by and at one point he was almost killed but got a scar next to his right (or maybe left) eye that made him or marked him as the seer? His twin gave him a bracelet shaped like a snake biting its own tail and that meant something important... The Snake was also the symbol/logo of the company.   In the end he went home and spoke to him mom about his twin and I remember it being the first book in a series.

I remember this book from my early teen years, although what I remember makes it seem incredibly bizarre, but from what I remember, it was really enjoyable. I'm sure I read it before I read the "Mister Monday" series, by Garth Nix. I don't believe all of the series was available, if that helps narrow down a time frame.  I have a feeling this book was part of a series too. And it is based around a young male protagonist and, soon, a girl and another boy, whom he befriends.  I believe the first chapter of the first book starts with the protagonist answering a phone call. One of the questions he is asked is; How did the dinosaurs die? He initially believes this to be one of those radio shows, so he tries to be funny in his answer, which is; they died laughing. I'm sure they ask him about his sleeping habits, and he admits to falling asleep very easily, almost on command. This leads the boy to being recruited by an organisation which uses sleep as a way of entering and exiting some sort of world, or other time. There is something dangerous about it too, as I remember something about: trying to go deeper, or further, caused the person's heart to race to the point of an attack.  When he first travels to this place, it's like the beginning of time. The place is beautiful, and untouched. The protagonists male friend befriends a black panther cub, which I'm sure follows him around when they return.   This is when I lose track of the story and just remember snip bits;  The male friend is a skilled drummer and is able to tap into the 'beat' of the world, and stop time from travelling backwards - I believe this is in the second book.  The female friend is a skilled debater with unmatched logic, and during an argument with (some sort of boss bad guy), she uses the argument of a never ending cycle, a snake biting its tail. I'm sure she also had a bracelet of a snake biting its tail too, with green eyes?  There is a point where they are traveling through a cave of jewels. The protagonist collects some. They then come to a seemingly dead end, however, by giving up everything they  covet, such as the jewels, the characters are able to ascend to the village above.   Sorry for the long post, but I thought adding as much as I know might spark an answer from someone. :).   Thank you for your time.


I think an update may have created a network problem on Artful ardvark. How do I delete the last update? I can't connect to a network to update any patches.  I can not connect to a wireless network. I used to be able to connect and then a few days ago it started disconnecting and reconnecting. After that it would no longer connect. I could connect to a wireless printer and print. I need solutions that don't include connecting to the internet to update or get any packages as I can't do either.

This has happened to me many times in the last 5 years: an upgrade broke my system. Each time I end up with this situation, I have to reinstall the whole system, which is really annoying.  Is there any way to roll back the most recent upgrade to be able to have a functional system without reinstalling? If not, which is the best way to suggest this as a top priority idea?   I read this idea was described in brainstorm.ubuntu.com, but it feels it is dead... and the forums are full of examples of upgrades breaking things, that's why I feel something needs to be done about this topic. Thanks!


How can I get realtime alerts on answers to my questions? i.e. when someone answers my question I want an immediate notification so I won't have to wait for the daily email.

Is there a way to subscribe to a question and be notified more frequently than once a day?  I'd like to be notified immediately on any posts to a question.


XNOR has two definitions:  \$1^{st}:XNOR=NOT(XOR)\$  \$2^{nd}: XNOR(A,B)=\overline{A}\cdot\overline{B}+A\cdot B\$  The problem is that these definitions are not equal in Odd inputs, the second definition acts as xor at odd inputs.  is the second really a definition or is it just the SOP of the first definition at 2 inputs?

I've just started studying computer engineering, and I'm having some doubts regarding the behavior of the XOR gate.  I've been projecting circuits with Logisim, whose XORs behave differently from what I've learnt. To me, it should behave as a parity gate, giving a high output whenever the inputs receives an odd combination. It doesn't, though, for more than two inputs. How should it behave?  I also read in a book that XOR gates are not produced with more than two inputs. Is that correct? Why?


The original question is asking for the following:  Find all ordered pairs of positive integers $(x, y)$ for which $3^y = x^2 + 56$.  I've found a solution I believe to be the only solution, but I'm struggling to prove it's the only solution. $(5,4)$  When I see a problem like this, I initially think to use modular arithmetic to find the pattern of the answer.  For example, taking each side of the equation $\mod 4$ shows that $x$ must be odd and $y$ must be even.  $\mod 3$ shows that $x$ is not divisible by $3$.    Using a spreadsheet and running all $\mod \ $ from $2$ to $81$ and looking at the remainders for $x = 1$ to $250$ shows that $x = 5$ is the only possible solution, but obviously this is not a proof. I'm struggling to find the steps necessary to prove this answer.    I've also simplified the equation to have $y=\frac{\ln(x^2+56)}{\ln(3)}$, but I don't know how to show the only time $y$ is an integer is when $x=5$. (Perhaps I am wrong and more solutions exist). Any help would be appreciated.

First of all, $n$ is even (find that out by trying to see what kind of remainders you can possibly get when dividing everything by 4). So $n=2m$, $m\in N$.  $ x^2 + 8 = 3^{2m} \Rightarrow x^2 - 1 = 3^{2m} - 9 \Rightarrow (x+1)(x-1) = (3^m + 3)(3^m - 3) \Rightarrow x$ is odd.  That's all I've tried so far. I'd like to get some help. Thanks.


(Sorry to re-post this, I have lost access to my original account.)  I've recently installed Kubuntu 18.04.3 on a new AMD Ryzen 3000-series-based system. The system is installed on a SATA SSD, specifically on an Ext4 partition, with a SATA HDD formatted in NTFS mounted for storage. The system has been in use for a few days, with a maximum uptime of two days (so far).  My issue is this: the HDD indicator light on the case flashes every 1-3 seconds, even when the system is idle, and there is no obvious reason to access the disk. The flashes are not regular: sometimes the light is dark for as long as 3 seconds (obviously it is difficult to time such short intervals -- I am approximating), sometimes there are a few quick pulses less than a second apart. The flashes seem to vary in duration as well -- sometimes very brief, sometimes nearly a second. Unmounting the secondary HDD does not appear to have any effect.  Some searching lead me to try iotop. I ran sudo iotop -Pao, and waited until 10 flashes of the HDD light had occurred. This is the result:   6887 be/4 root          0.00 B      0.00 B  0.00 %  0.02 % [kworker/u64:1-events_power_efficient]   433 be/3 root          0.00 B      0.00 B  0.00 %  0.02 % [jbd2/sda2-8]  6302 be/4 root          0.00 B      0.00 B  0.00 %  0.01 % [kworker/u64:0-events_unbound]   The "kworker" processes seem to switch between various states, such as "events_power_efficient", "events_unbound", and "events_freezable_power_". The jdb2 process does sometimes write to disk, though that was not observed here (even though, as I said, 10 flashes of the HDD light occurred). The computer was otherwise idle during this test.  My searches also lead me to check /var/log. The result of ls -lth | head is as follows:  -rw-r-----  1 syslog adm             951K Aug 27 19:49 kern.log -rw-r-----  1 syslog adm             594K Aug 27 19:49 syslog -rw-r-----  1 syslog adm             528K Aug 27 19:49 ufw.log -rw-r-----  1 syslog adm              53K Aug 27 19:48 auth.log -rw-r--r--  1 root   root             40K Aug 27 19:15 Xorg.0.log -rw-rw-r--  1 root   utmp             79K Aug 27 18:29 wtmp -rw-r--r--  1 root   root              55 Aug 27 16:28 prime-offload.log -rw-r--r--  1 root   root              30 Aug 27 16:28 prime-supported.log -rw-r--r--  1 root   root            1.2K Aug 27 16:28 gpu-manager.log   I have no experience interpreting log files, so I don't know if anything here is out of the ordinary.  If the kernel version is relevant, the output of uname -r is 5.0.0-25-generic.  My questions are, 1. Why is my HDD light flashing, even though there is no obvious disk activity, 2. Does this indicate some kind of problem with my system that needs to be fixed, and 3. If so, how do I fix it? The light itself does not bother me -- if this is just a sign of a normal, healthy Ubuntu install, then no problem. My concern is that something is wrong, and if so, I would like to fix it.  Thanks in advance for your time.  In response to heynnema (in the original posting of this question), the issue occurs even at the log-in screen, before I log in. So, it is not tied to my user account. However, it does not occur in the BIOS, suggesting that it is specific to Kubuntu (or at least, to the SSD Kubuntu is installed on).


I came across the chain rule for limits the other day and it interested me quite a bit and surprisingly I couldn't find the proof on the internet anywhere. From what I understand the chain rule for limits states that if:  $$ \lim_{x\to c} g(x)=M$$ and $$\lim_{x\to M} f(x)=L$$ then$$\lim_{x\to c} \ f(g(x))=L$$  1.Under what conditions does this hold true?  2.What is the epsilon-delta proof for the rule?

If $$\displaystyle \lim_{x \rightarrow c}f(x)=l$$ and $$\displaystyle  \lim_{x \rightarrow l}g(x)=L$$ and $f(x) \neq l$ in some punctured   neighbourhood of c,      then $\displaystyle \lim_{x \rightarrow c}g(f(x))=L$.   Note that the first two conditions are insufficient for the conclusion to hold. (For a clear example, see the first comment in  .) But if all three conditions are satisfied, the conclusion may be drawn.  This is because the 3rd condition ensures that near $c$, $gf$ won't be forced to take the value of $g$ at $l$. I.e. $\displaystyle \lim_{x \rightarrow c}gf(x)$ will be equal to $\displaystyle \lim_{x \rightarrow l}g(x)$ instead of necessarily being equal to $g(l)$. (Note that $\displaystyle \lim_{x \rightarrow l}g(x)=g(l)$ iff. $g$ is continuous at $l$.)  So that's my informal explanation for the theorem. But I'm having difficulty writing down a proper proof. Please use the sequential definition of limits (instead of epsilon-delta), if required.


As described :  $$\frac{a}{b} \bmod{n} = \left((a \bmod{n})(b^{-1} \bmod n)\right) \bmod n$$  When I apply this formula to the case $(1023/3) \bmod 7$: $$\begin{align*}     (1023/3) \bmod 7 &= \left((1023 \bmod 7)((1/3) \bmod 7)\right) \bmod 7 \\                    &= ( 1 \cdot (1/3)) \mod 7 \\                    &= ( 1/3) \mod 7 \\                    &=   1/3 \end{align*} $$ However, the real answer should be $(341) \bmod 7 = \mathbf{5}$.  What am I missing? How do you find $(a/b) \bmod n$ correctly?

For example: $$7x \equiv 1 \pmod{31} $$ In this example, the modular inverse of $7$ with respect to $31$ is $9$. How can we find out that $9$? What are the steps that I need to do? Update If I have a general modulo equation: $$5x + 1 \equiv 2 \pmod{6}$$ What is the fastest way to solve it? My initial thought was: $$5x + 1 \equiv 2 \pmod{6}$$ $$\Leftrightarrow 5x + 1 - 1\equiv 2 - 1 \pmod{6}$$ $$\Leftrightarrow 5x \equiv 1 \pmod{6}$$ Then solve for the inverse of $5$ modulo 6. Is it a right approach? Thanks.


Note: please English is not my first and here I saw people use hard words I can not understand. please consider simple words, thank you. If I bought an item 3 times at different prices. the average formula will give me the average of this.   ($5 + $10 + 15)/3 = $10  The problem is if bought different quantities each time with different prices. Does the previous average formula represent this situation?   $5 - 1200 items   $10 - 5   $15 - 20  I did this and I am not sure it is correct $5*1200 = $6000 $10*5   = $50 $15*20  = $300  I summed all the total prices $6350 then divided it into a total of items 1200+5+20 = 1225. $6350/1225 = $5.18   is this consider average and is this correct?

What is the difference?For what kind of purpose do we use the weighted average method?Why don't we instead always use the normal average method?and also,how to get the weighted average of some numbers?Also,do we have first to get the mean(normal average) of numbers in order to get their weighted average?  Thank you so much.


How to remove special character in a string. Example: Actual string is 'xx' but we are getting unicode character in string as âxxâ Please suggest ways to remove special character(â) in above string with python3.

I have a Unicode string in Python, and I would like to remove all the accents (diacritics). I found on the web an elegant way to do this (in Java):  convert the Unicode string to its long normalized form (with a separate character for letters and diacritics) remove all the characters whose Unicode type is "diacritic".  Do I need to install a library such as pyICU or is this possible with just the Python standard library?  And what about python 3? Important note: I would like to avoid code with an explicit mapping from accented characters to their non-accented counterpart.


Let me clear you first that I'm not a college student and this is not my home assignment. I am just curious to know the solution of this question which was once asked to me. I think this is a nice and tricky question which I feel worth sharing.The question was--  How do you input a string(said in general sense, independent of programming) from a user and print reverse of it in C/C++ without using array or any library function for reversing the user input?  I am unable to break-into this. Help please  Note: Members are marking it as a duplicate for  question. But All answers to this are either using library functions or using a pointer to char array(char *). None of them is allowed in my case. Please review  it once again

How do you reverse a string in C or C++ without requiring a separate buffer to hold the reversed string?


I am a beginning photographer with a Canon Rebel XTI. I'm trying to get indoor portraits of my son, but I can't seem to get non-blurry photos because the shutter speed is too slow as I need to let the light in, however he is moving thus causing the blurriness. Whenever I change the shutter speed, the photos become too dark. If anyone has any tips, techniques or settings on the camera they could suggest that would be most appreciated. Maybe I need a different lens?   Thank you!

I'm a mom who is obsessed with taking photos of my now 2 year old daughter.  I currently have a Nikon j1 which I like, but I find the shutter speed is still a bit slow and when you're trying to take photos of a speedy little girl, I end up with a lot of blurry images.  So I'm looking for a camera with a very fast shutter speed that will allow me to take good photos of a very fast moving child.  Also that can take photos in low light. I've been looking at the canon eos rebel but I'm not sure. Would like it to be able to take videos as well. Any advice?


Does $e^z -z$ have any zeros?   By plotting the functions $e^z$ and $z$ in the real line, I have seen that this equation does not have any zeros in the real line. Can the same thing be said for the complex plane? Being an entire function, I know that it assumes every finite complex number except atmost one. But what about the zero? Please help.

(p.236)  has a proof that the equation $e^z-z=0$ has infinitely many complex solutions:    I'm curious if there are any particularly elegant ways to see this, other than that given in the text.


I rolled doubles three times in a row, and I landed on Illinois Avenue on my last roll. I want to buy it, but since it's my third double I'm going to jail. I want to buy it right now at the regular market price instead of at an auction because the other players have a ton of money and may bid very high for Illinois Avenue.   Can I buy it now? Thanks!

In Monopoly, when you roll doubles a third time, you go to Jail.  But do you get to interact with the space first?  More specifically, do you get to do any of the following first?   Pass go  Draw a Chance or Community Chest card Pay Luxury Tax or Income Tax  Pay Rent


Would it be possible to program an alert where a bar would pop-up (similar to "A new Answer/Comment has been posted click to load") which would show if a user is currently writing a comment or writing an answer?  Seems to be a decent number of "quick answers" where two people give a very similar answer at the same time not knowing someone else is already working on a solution.  See  for more on how this can be helpful for "quick replies" versus "thought out replies".

When a question is open, it would be nice to see that there are X people (or preferrably a list of the X people) who are in the process of writing an answer.  For simple questions, usually once I'm about to hit the "post your answer question" I get the "there are 3 new answers, click here to load them" nag.


A brother applied for a UK visit visa, he is self employed (a CEO/Business owner) and applied for a Visit Visa using only  his company bank statement to apply.  The commission refused the visa thinking that he used his personal bank statement, so they indicated that his salary didn't reflect in his personal bank statement and the monthly inflows were more than his stated monthly salary.   Clearly who ever worked on the documents assumed it was his personal bank statement so passed judgements indicating that his personal bank statement indicated undisclosed sources of funds hence the refusal.  If only they had taken time to read through they would have realized it was his company statement and not a personal statement.  He was informed that he cannot appeal  What can he do about this error ?

I have applied recently for a general visitor visa to the UK to spend 10 days during Christmas with my British unmarried partner and it has been turned down.   The Entry Clearance Officer stated on his refusal notice the following:     I note that you have never previously travelled to the UK or any country with similar immigration requirements and you therefore do not have a history of travel and compliance to consider.      You have submitted an employment letter to confirm your occupation in KSA but I am required to also assess your personal, domestic and economic circumstances in determining whether you are genuine visitor travelling to the UK for the period and purpose you state.      You claim an income of SAR ........ per month which equal ........ GBP and from the evidence submitted this appears to be your sole source of income.   I note that this monthly income is reflected on your bank statements. However, the bank statement you have presented show a recent large deposit that are in excess of your stated income and inconsistent with the account history. You haven't provided evidence toward the origin of this recent deposit and in the absence of reasonable evidence I am not satisfied that these bank statements accurately reflect your personal circumstances.      In view of the above, I am not satisfied you have demonstrated that your circumstances are as you claim and therefore I am not satisfied that you're travelling to the UK for the period and purpose you stated. 41(i)and(ii).   Its true that I have deposited that sum of money right before I apply and it was a commission I received from work earlier this month.   So, could you please give me your advice on the above as I am planning to apply again soon. and how to avoid my application being refused again?


By far, these infinite series and sequences have been my biggest problem in calculus 2, and this problem really puts my limited knowledge to the test.  I have found that posting these pictures helps show everyone what I have learned so far, and then I'll try to solve it myself.  Chapter and section names:    Rules that my book gives me to solve these problems. This shows more of what I should and do know:    Looking at those rules, it doesn't really even seem to help me with this problem. The only way I could see this being solved with what I know is with the integral test.  Also, note that it starts at 2 (I almost missed that myself).  If I'm going to try to use the integral test, then here is my book's definition of it:    And here is the question again: Determining if the series $\sum_{n=2}^\infty {1\over {nln(n)ln(ln(n))}}$ is convergent or divergent and justifying the answer. I honestly don't know where to start with this one, I would try but there are a lot of changes from previous questions, and it makes it a lot harder.  Any help is greatly appreciated. Thank you.

I'm being asked to determine if $\displaystyle\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ converges. So, using Cauchy's Condensation Test, I reduced the problem to one of determining the convergence of $\displaystyle\sum\limits_{n=3}^\infty\frac 1{n\ln (n\ln 2)}$. Am I on the right path, and how do I proceed from here?


I wonder how to calculate the following limit: $$ \lim_{n\rightarrow\infty}\frac{1+n+\frac{{}n^{2}}{2!}+\cdots +\frac{n^{n}}{n!}}{e^{n}} $$ In the first sight, I think it should be zero, because exponential function is much faster than polynomial. But the upper of the expression is the Maclaurin polynomial of $e^{n}$. With the growth of n, it approaches to $e^{n}$. Consider there is a roughly way to estimate the remainder of $e^{n}$ rather than $$ R_{n+1}(n)=\frac{\xi^{n+1}}{(n+1)!}     \ for  \ \ \xi\in(n,+\infty) $$ Because $$ \frac{1+n+\frac{{}n^{2}}{2!}+\cdots +\frac{n^{n}}{n!}}{e^{n}}=1-\frac{R_{n+1}(n)}{e^{n}} $$ But it's hard to continue.

I'm supposed to calculate: $$\lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\frac{1}{2}$, which is a pretty interesting and nice result. I wonder in which ways we may approach it.


I would to call my subs without using parentheses around the argument lists. For example, I'd like to use  mypush \@list, $item;   instead of  mypush(\@list, $item);   To accomplish that, I've declared my sub with a prototype.  sub mypush (+@) { push shift, @_ }   In fact, that also allows me to the following, but that's just a bonus:  mypush @list, $item;   Other than having to declare subroutines with prototypes before using them anywhere in the code, is there any serious drawback to using prototypes in Perl?  Code looks definitely cleaner to me. But where in general can prototypes go wrong? When would I regret it?

In   asserted:     I would advice you not to use prototypes. They have their uses, but not for most cases and definitely not in this one.   Why might this be true (or otherwise)? I almost always supply prototypes for my Perl functions, and I've never before seen anyone else say anything bad about using them.


I am interested in running a single Windows program on my Macbook. I have looked at various options, including bootcamp, however since it is only a single program, I was looking for a way to minimize the amount of storage used. I also had the same problem while looking at virtual machines. The program is a tutor.com classroom that is an online tutoring application. It is an .msi file. I have tried seeing if this program is compatible with Wine, but it is not. I am not too familiar with any of these methods. Any help would be appreciated.

My question is actually fairly simple: is there any way i could run windows programs (for example PC games) on my iMac? (i am currently running OSX Snow Leopard). I know about things like VirtualBox and Parallels to run windows itself, but is there a Mac application that will allow me to run .exe programs and the like?


I'm writing a Apex class to auto delete Case records of record type claims and service failure with created date older than 6 Years here is the code. But i'm failing to Refer the record type in the code can i get some help on it   global class DeletecaseBatchClass implements Database.Batchable<sObject>{     global DeletecaseBatchClass(){     }      global String query;     global Database.QueryLocator start(Database.BatchableContext BC) {         query = 'SELECT Id, createddate, RecordType.Name from case where createddate < date.today()-2190 AND RecordType.Name IN ()';         return Database.getQueryLocator(query);     }      global void execute(Database.BatchableContext BC, List<case>scope){         delete scope;     }      global void finish(Database.BatchableContext BC){     } }

I know of two approaches to get the recordtype id of a particular record type   Use SOQL   RecordType RecType = [Select Id From RecordType  Where SobjectType = 'Account' and DeveloperName = 'Business'];    Benifit here is if the admin changes the name of the record type, the code still works as we can use developer name   Using Describe  Map<String,Schema.RecordTypeInfo> rtMapByName = d.getRecordTypeInfosByName(); Schema.RecordTypeInfo rtByName =  rtMapByName.get('Business');    Saves on SOQL limits but uses a describe call.  What would be your choice and why   EDIT : Usage is for setting up recordtype while inserting records in apex or trigger


Finding value of  $\displaystyle \int\frac{\sec x}{\sqrt{3+\tan x}}dx$   Try: Let $\displaystyle I = \int \frac{\sec x}{\sqrt{3+\tan x}}dx,$ Put $3+\tan x = t^2$  and $\sec^2 xdx =2tdt$  So $\displaystyle I = 2\int \frac{1}{\sqrt{t^4-6t^2+10}}dt$  could some help me how to solve it, Thanks

Evaluate the following integral.$$\int \frac{\sec x}{\sqrt{3+\tan x}}dx$$  On putting $t=\tan x$ I am getting $$\int\frac{1}{\sqrt{(t^2+1)(t+3)}}dt$$.  How should i proceed from here.


I have n jars with same functionality but different package name ( since different         regions).     I have same operation performed using this n jars.  Now I want to load the corresponding region of jars, for my operation. What is the best design pattern to use in this case.  I tried with reflection by changing the package name and loading dynamically. But is there any best pattern available for this case ?

Why is it so hard to do this in Java? If you want to have any kind of module system you need to be able to load JAR files dynamically. I'm told there's a way of doing it by writing your own ClassLoader, but that's a lot of work for something that should (in my mind at least) be as easy as calling a method with a JAR file as its argument.  Any suggestions for simple code that does this?


I am flying back to the US (Oakland) from Cancun through Guadalajara. We did not clear immigration or customs in Cancun, because the first leg was domestic, but it appears that we don’t need to clear immigration in Guadalajara, either. We were able to transfer flights without having to pass an immigration checkpoint. Currently, we are waiting at the gate in GDL. Is this any cause for worry, since it doesn’t look like we need to register an exit from Mexico?

For a long time, I thought Mexico completely lacked exit formalities. Turns out they do have exit stamps (note how it says S=Salida rather than E=Entrada).  Is this only the case at land (and perhaps sea) crossings, or airports as well?


I'm using MikTeX and WinEdt for writing an IEEE conference paper. To create a neural network structure I used this code :  \begin{figure} \begin{tikzpicture}[ init/.style={   draw,   circle,   inner sep=2pt,   font=\Huge,   join = by -latex }, squa/.style={   draw,   inner sep=2pt,   font=\Large,   join = by -latex }, start chain=2,node distance=13mm ] \node[on chain=2]   (x2) {$x_2$}; \node[on chain=2,join=by o-latex]   {$w_2$}; \node[on chain=2,init] (sigma)   {$\displaystyle\Sigma$}; \node[on chain=2,squa,label=above:{\parbox{2cm}{\centering Activate \\ function}}]   {$f$}; \node[on chain=2,label=above:Output,join=by -latex]   {$y$}; \begin{scope}[start chain=1] \node[on chain=1] at (0,1.5cm)   (x1) {$x_1$}; \node[on chain=1,join=by o-latex]   (w1) {$w_1$}; \end{scope} \begin{scope}[start chain=3] \node[on chain=3] at (0,-1.5cm)   (x3) {$x_3$}; \node[on chain=3,label=below:Weights,join=by o-latex]   (w3) {$w_3$}; \end{scope} \node[label=above:\parbox{2cm}{\centering Bias \\ $b$}] at (sigma|-w1) (b) {};  \draw[-latex] (w1) -- (sigma); \draw[-latex] (w3) -- (sigma); \draw[o-latex] (b) -- (sigma);  \draw[decorate,decoration={brace,mirror}] (x1.north west) -- node[left=10pt] {Inputs} (x3.south west); \end{tikzpicture} \caption{NN} \label{fig_neuron} \end{figure}   How can I minimize size of total figure? It is a little big for two column article.

I have a simular issue to the question asked in :  I have tried the solution provided by Jake. This makes that my picture fails to resize (scale) as i intend.  Whether i give Set scale=0.4 or Set scale=0.8 The size of the  picture remains the same  This is the code i use:  \begin{figure}[ht!] \centering \begin{tikzpicture}[Set scale=0.4, every node/.append style={transform shape},] % STYLES \tikzstyle{every node}=[rectangle,rounded corners, minimum width=100pt,     align=center,node distance=3cm,fill=black!10,inner sep=5pt,text width=3cm,minimum height=1.75cm,>=stealth,text badly centered] % Draw forces \node [force, above of=rivalry] (top) {Firm strategy, structure and rivalry}; \node [force, left=1cm of rivalry] (left) {Factor conditions}; \node [force, right=1cm of rivalry] (right) {Demand Conditions}; \node [force, below of=rivalry] (bottom) {Related and Supporting industries}; %%%%%%%%%%%%%%%% % Draw the links between forces \path[<->,thick]  (left) edge (right) (left) edge (top) (left) edge (bottom) (top) edge (right) (bottom) edge (right); \path[<->,thick]  (bottom) edge (top); \end{tikzpicture} \caption{Porter's Diamond source:~\cite{Porter:1980}}% \label{fig:diamond}  \end{figure}


I want to swap the field in the ConvexHull class just like swap( points[0], points[1] ).  How do I have to do?  public class ConvexHull {     List<Point> points;      public void run ()     {         Point.swap ( ref points[ 0 ], ref points[ 1 ] );  //Error!!     } }  public class Point {     private double x, y;      Point () { x = y = 0; }     public static void swap(ref Point a, ref Point b) {         Point c = a;         a = b;         b = c;     } }

Can I pass a property as an "out" or "ref" parameter if not then why not?   e.g.  Person p = new Person();    . . .  public void Test(out p.Name);


I have a JS file exporting an array of objects. Each object contains a property with a URL strings. Here's an example: export const data = [   {     name: 'aaa',     content: 'Click here or here'   },     {     name: 'bbb',     content: 'Click here or here'   } ]  Notice the title property on each link, which may be empty or include some text. In my IDE (Webstorm) I want to search for every occurence of title, including the double quotes and the text between them or with empty double quotes. Essentially I want to be able to find each occurence of title="some text" and title="". Webstorm support searching with RegEx, but I have to idea how to construct such expression. I tried title=["]\D["], title=["]\w\s["], ["][a-zA-Z]["] and a few more... None of them worked. Any ideas how to construct such RegEx?

I have a txt file which actually is a html source of some webpage. Inside that txt file there are various strings preceded by a "title=" tag.  e.g.   <div id='UWTDivDomains_5_6_2_2'  title='Connectivity Framework'>    I am interested in getting the text Connectivity Framework to be extraced and written to a separate file.  Like this, there are many such tags each having a different text after the title='some text here which i need to extract '  I want to extract all such instances of the text from the html source/txt file and write to a separate txt file. The text can contain lower case, upper case letters and number only. The length of each text string(in characters) will vary.  I am using PowerGrep for windows. Powergrep allows me to search a text file with regular expression inout. I tried using the search as        title='[a-zA-Z0-9]  It shows the correct matches, but it matches only first character of the string and writes only the first character of the text string matched to the second txt file, not all string.   I want all string to be matched and written to the second file.  What is the correct regular expression or way to do what i want to do, using powergrep?  -AD.


I downloaded Ubuntu, and now have a Ubuntu folder in "Programs" on my C drive. It has an install icon in the foldeer, but it doesn't do anything. What do I do next to install Ubuntu?

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


For n $\in$ N let $\beta(n)$ denote the number of digits used in the binary representation of n. For example         $\beta(1)$ = 1         $\beta(2)$ = 2         $\beta(3)$ = 2         $\beta(4)$ = 3 Find a closed formula for an arbitrary n $\in$ N  where N is the set of natural numbers.  So what I have is the representation of n = 1...12 in binary so,         n = 1: $2^0$          n = 2: $2^1$         n = 3: $2^0$ + $2^1$          etc. But the closed form solution isn't apparent

I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof?


I have following output from Protractor test and I'm trying to parse and find name of failed spec:  Specs: /var/lib/jenkins-slave/workspace//tests/js/e2e/ui_e2e/tests/test_one.js Selenium URL: http://10.20.40.54:4444/wd/hub  ..... number of different strings here....  Executed 25 of 25 specs SUCCESS in 1 min 23 secs. ----- Specs: /var/lib/jenkins-slave/workspace//tests/js/e2e/ui_e2e/tests/test_two.js  ..... number of different strings here....  UnknownError: Due to a previous error, this job has already finished. You can learn more at   I'm using following regex:  (?:Specs:)(?:[\s\S])*(?=UnknownError(.*?))   However, it matches too wide section from first string, swallowing string with test_two.js.  How can I avoid swallowing and narrow match to have it like:  Specs: /var/lib/jenkins-slave/workspace//tests/js/e2e/ui_e2e/tests/test_two.js  ..... number of different strings here....  UnknownError: Due to a previous error, this job has already finished. You can learn more at

I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}?