If $\phi$ is a morphism between groups $G$ and $H$, is $G$ isomorphic to  $$ker(\phi)\times im(\phi)$$ ? Why ? Thanks.

Suppose you have a group isomorphism given by the first isomorphism theorem: $$G/\ker(\phi) \simeq \operatorname{im}(\phi)$$ What can we say about the group $\ker(\phi)\times \operatorname{im}(\phi)$? In particular, when does the following hold: $$G\simeq \ker(\phi)\times \operatorname{im}(\phi)?$$ I ask this question because i want to prove that $GL_n^+(\mathbb{R}) \simeq SL_n(\mathbb{R}) \times \mathbb{R}^*_{>0}$, with $GL_n^+(\mathbb{R})$ the group of matrices with positive determinant. I proved that $SL_n(\mathbb{R})$ is a normal subgroup and that $GL_n^+(\mathbb{R})/  SL_n(\mathbb{R}) \simeq \mathbb{R}^*_{>0}$, using the surjective homomorphism $\det(M)$. I tried something with semidirect products but I got stuck.


Using the Well512 random number generator class in Java, how can one generate a random number with a range like 0 to 50?

How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum.


I'd like to switch off the registration window of a Windows 8.1 ASUS laptop at start up using the task manager.   The task manager does not seem to have a disable function for any particular task, so how do I turn this annoying window off at the start up?

There's a nifty new tab in the 'Task Manager' called 'Startup' where I can manage the program that run at startup.    BUT... It doesn't show all of the application that run at startup:    Some of the hidden culprits are:   Steam Skype Google Drive Dropbox Cisco VPN Java Update   "What about the registry?" Here's what's found in there:    Which doesn't contain all of the running programs.  How do I manage these startup applications from within Windows 8?


If have the following file /tmp/f1.txt file coming from the stdout redirection of the result of a PostgreSQL bash script execution :   id   -----  517  518  519  520  521  522 (6 rows)  INSERT 0 6   I wish I could iterate over those ids to perform other actions.  For now, I am able to retrieve the desired ids as follows (i'll always get 5 values ) :  cat /tmp/f1.txt | tail -n +3 | head -n5 -   This returns :  517 518 519 520 521   Which is exactly what I want.  So, the next step would be to read every single line. So in my case I'd store the result in a variable, and then read line by line :  LINES_UPDATED_CNT=$(cat /tmp/f1.txt | tail -n +3 | head -n${LINES} -) echo -e $LINES_UPDATED_CNT   My issue here is that this command yields the following result :  517 518 519 520 521 522   The newlines are lost, can't understand why. What would be the optimal way to do this, without wirting the cat/tail/head result into another file and reading it in a while ?  Thank you !

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?


I asked a question few days ago on Stack Overflow, but didn't got the specific answer for considerable amount of time. So to drew more attention to my question i started a bounty of worth 50 reputation on the question.  Now the bounty is in grace period, but I read it in bounty info page that there is no refund of reputation in case no answers are received as a result of bounty. Isn't it unfair to person like me who is having less reputation on Stack Overflow to loose such reputation without any expense? I didn't got the answer I wanted and still I lose my reputation. Why there is no refund of reputation if no answers are received in bounty period?

I have  with a bounty that will expire in a few days. It looks like nobody will get the bounty; only one answer was posted during the bounty period, and it has no upvotes.  In cases like this, the bounty is thrown away.  Why isn't it refunded instead, if no answerer has earned it?


If a player is a 2nd-level sorcerer, and sacrifices one of their 1st-level spell slots to get an additional sorcery point, could they use their 3 sorcery points to create another 2nd-level spell slot?

At level 6, a Sorcerer may have a maximum of 6 Sorcery Points. This is enough to create a level 4 spell slot. Would the Sorcerer be able to create a level 4 spell slot, even though he only knows level 3 spells, in order to cast a spell with a higher slot (such as Fireball to add an extra 1d6 to the damage and make it hard to Counter Spell)?


My simple calculator is trying to display the chosen operation of the user. I understand that in C, strings must be declared as 1D char arrays.  int a, b; int oper; //operation number char operName[15];  printf("\nEnter two numbers: "); scanf("%d%d", &a, &b); printf("\nYou entered: %d and %d", a, b);  printf("\nChoose operation:"         "\n1 = +"         "\n2 = -"         "\n3 = x"         "\n4 = /"); scanf("%d", &oper);   The code compiles and runs. But when executing the switch block, it stops working. I'm using switch to choose the appropriate operation name, and assign it to operName (so I can display the chosen operation before I do the actual operation).  switch(oper){     case 1:         operName == "Addition";         break;       .     .     .     default:         operName == "Invalid input"; }  printf("\n\nYou chose: %s", oper);   I read somewhere that I need to use pointers to prevent memory leaks, but I'm new to this so maybe there's an easier way.

I am a little surprised by the following.  Example 1:  char s[100] = "abcd"; // declare and initialize - WORKS   Example 2:  char s[100]; // declare s = "hello"; // initalize - DOESN'T WORK ('lvalue required' error)   I'm wondering why the second approach doesn't work. It seems natural that it should (it works with other data types)? Could someone explain me the logic behind this?


I have two cases for allocation of memory using new operator.  class xx{     public: int x;              xx(){}              ~xx(){} }; class yy : public xx {     public: int y;              yy(){}              ~yy(){} }; int main(int argc, char *argv[]) {     yy *y1 = new yy();  //y1 constructor is called     //CASE-1     yy *y2 = y1;     //CASE-2                  yy *y3 = new (y1) yy();      return 0; }   In CASE-1 I am just allocating y1 memory to y2 without destroying y1(shallow copy). Here constructor will not be called.   In CASE-2 I am allocating y1 memory to y3 to the address destroying y1. Here constructor of y3 will be called. But destructor of y1 is not called. According to my understanding application has to take precautions for null value check while using  y1 and y2 in future code.  So basically I want to understand the scenarios where CASE-2 is useful as compared to CASE-1. Thanks in advance.

Has anyone here ever used C++'s "placement new"? If so, what for? It looks to me like it would only be useful on memory-mapped hardware.


Based on other similar questions, I've determined that a familiar can attune to magic items. But can a familiar cast spells from the Ring of Spell Storing? The description of Find Familiar states "A familiar can't attack, but it can take other actions as normal." Does this mean if it could cast spells, it could only cast non-attacking spells?

Is it possible for a familiar to attune to and then wear or wield a magic item?


let x = {     name:"vin1",     oi:this,     ob:{         name:"vin2",         ob1:{             name:'vin3',             ob2:{                 name:"vin4",                 func:function(){                     console.log(name);  //  I want to access the name "vin1" here.                 }             }         }     } };   I found  answer which says it's not natively supported in JS. Any way to access the outer object property from the inner object?

Something like  var life= {         users : {              guys : function(){ this.SOMETHING.mameAndDestroy(this.girls); },              girls : function(){ this.SOMETHING.kiss(this.boys); },         },         mameAndDestroy : function(group){ },         kiss : function(group){ } };   this.SOMETHING is what I imagine the format is, but it might not be. What will step back up to the parent of an object?


I am using nonnegative matrix factorization, NMF (in its variant OPNMF, which is subject to additional orthogonality and $H = W^TV$ constraints) to factorize a dataset.  To find the optimal number of components in my data, I am doing split-half cross-validation. This means, I split my original dataset in two random splits for some thousands of times, and at each iteration I run opnmf on both splits for a given number of components K. Then I reconstruct the split matrices, in-sample and out-of-sample:  $\widehat{V_1,_1} = W_1*W_1^TV_1$ or $\widehat{V_1,_2} = W_2*W_2^TV_1$  and I calculate the reconstruction error by simple difference: $insampleRecErr = \widehat{V_1,_1} -V_1$ and $outofsampleRecErr = \widehat{V_1,_2} -V_1$   I do this for a large number of components, going up to almost the entire number of dimensions in my data.  However, the out-of-sample reconstruction error is not behaving as I expected. I was expecting the in-sample and out-of-sample reconstruction errors to follow the classic trend of being (1) monotonically decreasing for in-sample reconstruction, and (2) for out-of-sample reconstruction, to decrease until the optimum number of parameters, and then increase again when the model overfits.  What I see, instead, is that also the out-of-sample reconstruction error decreases monotonically at increasing number of components:   I tried creating synthetic datasets suited for testing NMF algorithms (via the synthethicNMF function in an R package), but I observe the same behaviour also in these artificial data.  This seems to suggest that it is related to NMF per se, and not my data.  Can anyone help me understand why is out-of-sample recontruction error also decreasing motonically?  In other sources (), this is not observed. So, it doesn't seem like it is a property of NMF to achieve better reconstruction at increasing number of components.  But if so, what would be a better way to assess generalization for NMF?  Thank you very much in advance!

Given a matrix $\mathbf V^{m \times n}$,  (NMF) finds two non-negative matrices $\mathbf W^{m \times k}$ and $\mathbf H^{k \times n}$ (i.e. with all elements $\ge 0$) to represent the decomposed matrix as:  $$\mathbf V \approx \mathbf W\mathbf H,$$  for example by requiring that non-negative $\mathbf W$ and $\mathbf H$ minimize the reconstruction error $$\|\mathbf V-\mathbf W\mathbf H\|^2.$$  Are there common practices to estimate the number $k$ in NMF? How could, for example, cross validation be used for that purpose?


I really need  /System/Library/Extensions/IOAHCIFamily.kext/Contents/PlugIns/IOAHCIBlockStorage.kext  It is necessary from OS X 10.9.5 (13F1911), that is, with all the latest changes, from just 10.9.5 is not needed.  My request how I can get this Apple software? Re-installing the OS from Recovery is very undesirable, since many valuable files are lost.  In addition, it will be restored from 10.9.5, but not from OS X 10.9.5 (13F1911)   can not solve the problem with the latest Apple updates. Specifically, my system has quite a few modifications I fear I’ll lose.   My English is likely bad here but I'm trying to say that I've spoiled the kext and all recovery methods are not suitable for one simple reason: in the version that I can download from App Store and in versions in /Volumes/Recovery HD/ com.apple.recovery.boot/BaseSystem.dmg updates of the latest releases are not implemented!  (It all happened because I'm trying to implement a patch has not attended to the preservation of the original version, that is that's such bad luck!).  UPD1: I found the required kext inside the "secupd2016-004mavericks.dmg" at the URL: , and solved the problem!  UPD2: no simple copying will produce the proper result, you need to implement kext:  sudo kextcache -system-prelinked-kernel sudo kextcache -system-caches sudo touch /System/Library/Extensions/ reboot   Thank you in advance for your help, and sorry for the bad english as I’m not a native writer or speaker.   Another question for the moderator: what does "duplicate" mean? What duplicates my simple request to help me get the the file which I need?

I've deleted a system file from my Mac and need to get it back.  System files can include:   hidden files in the root of / - especially unix files in /private  /System files /Library files /Applications files that ship with the core OS   System files are not any app, user files or files that can be regenerated by a known sequence such as cache files, Spotlight index files, etc…    Canonical question and answer for .


Suppose that, $\lim\limits_{x\to x_0}f(x)$ and $\lim\limits_{x\to x_0}g(x)$ exist and $\lim\limits_{x\to x_0}g(x)\neq0$. Then, prove that $$\lim\limits_{x\to x_0}\frac{f(x)}{g(x)}=\frac{\lim\limits_{x\to x_0}f(x)}{\lim\limits_{x\to x_0}g(x)}$$

In real analysis, we have been asked to finish a proof of the quotient rule for limits (Given that $f(x)$ approaches $L$ and $g(x)$ approaches M as $x$ approaches a, prove that $\frac{f(x)}{g(x)}$ approaches $\frac{L}{M}$. I know that I could rewrite the quotient as multiplication and prove it that way but that is not the way the proof we are completing starts off. Here is how the proof in the book starts:  We showed in a previous exercise that $|g(x)| > \frac{|M|}{2}$ for all $x$ belonging to $D$ near $a$. In particular, $g(x)$ does not equal $0$ for all $x$ belonging to $D$ near $a$. Consequently, $\frac{f(x)}{g(x)}$ makes sense near $a$. Let $\epsilon > 0$ be given. The proof is based on the triangle inequality:  \begin{align*} \left|\frac{f(x)}{g(x)} - \frac{L}{M}\right| &= \left|\frac{f(x)}{g(x)} - \frac{L}{g(x)} + \frac{L}{g(x)} - \frac{L}{M}\right|\\ & = \left|\frac{f(x)}{g(x)} - \frac{L}{g(x)} + L \frac{M - g(x)}{Mg(x)}\right| \\ &\leq \left|\frac{1}{g(x)}\right| |f(x) - L| + \left|\frac{L}{M}\right| \left|\frac{1}{g(x)}\right| |M - g(x)|. \end{align*} We are expected to pick up the proof at this point.  I was thinking that since I want everything above $< \frac{\epsilon}{2} + \frac{\epsilon}{2}=\epsilon$, that I would construct $\epsilon_f$ and $\epsilon_g$ based on $\epsilon$. So, I said we want $|\frac{1}{g(x)}| |f(x) - L| < \epsilon/2$ and because the limit approaches $L$ end up with $\epsilon_f$ equals $\frac{\epsilon|M|}{4}$. I intended to do the same for the g part; however, when I go to define $\epsilon_g$ it involves $M$. Am I allowed to use $M$ in that definition for $\epsilon_g$? And if not, any ideas on where to go from here?  Thank you!!


So this boy in my class said to me, "notice me senpai".  What does it mean?     I think they like me, so does that have anything to do with it?

I'm new to anime and my friends really like it. They really like to say to me "notice me, senpai!" and I don't get the reference. I could be walking to class and one of my friends would say "Can you go to the canteen?" and I would say no I can't and then, they will say "NOTICE ME, SENPAI!" Can anyone shed some light on the "notice me, senpai" reference, please?


I am testing for normality. I have 5 subjects. I am looking to see the distribution for my baseline data. The normality score that I got for SW and KS contradict each other. SW said m data is normally distributed while KS says otherwise. How can this happen? What does it mean? And what should I do? Do I choose and pick either one?

I did a normality test for my data and as usual, SPSS will give both Shapiro-Wilk and Kolmogorov-Smirnov numbers. Is it okay if I choose to use only the number from Shapiro-Wilk? because the number from SW is the ones that showed significant level (0.183)  while KS is not (0.046). is there any references that I can use to support my decision as to using only SW when both SW and KS were given? thanks.


If 2 people are concentrating on different crusader's mantle and standing within the radius does the effect stack with another crusader's mantle causing 2d4 instead 1d4?

Recently played with a group, where 3 of their clerics would cast spirit guardians, claiming monsters in the area had to make 3 wisdom saves for 3d8 damage each, potentially adding up to 9d8 damage per round.  Is this any different then trying to have two casters cast insect plague or cloudkill on the same area, or bless on the same individual?


I am getting java.lang.NullPointerException and don't know exactly what is causing it. I know it has something to do with my getInput method, but I don't which line or lines is causing the error. Any help would be appreciated.   public class Input {  private Scanner scan;  //Checks input is an integer and bigger than 1 public int getInput() {     String input = scan.next();     int number = 0;     boolean isNumber = true;      while(isNumber) {         try {             number = Integer.parseInt(input);             if(number >= 1) {                 isNumber = false;             }         } catch (NumberFormatException e) {             isNumber = true;             System.out.println("Error: please enter a whole number that is bigger than 1");             input = scan.next();         }     }      return number;  }   }  public class Main  { public static void main (String[] args) {      Input userInput = new Input();     System.out.println("\t" +"Collatz Conjecture");     System.out.println("Please enter a value: ");     int n;     n = userInput.getInput();      System.out.println("Your number is " + n);    } }

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?


As someone close to being an adult and going to college, I have earned a small amount of money ($3000) and am looking to start my lifetime savings and get a head start by investing my money rather that simply holding it in a savings account.  Assuming that I can invest it any way I please, how can I best go about growing my money so I have a sizable amount by the time I graduate from college and need a house or car?  I currently have it invested in sector mutual funds but with the rise and fall of the stock market, is this really the best way to prepare long-term?

I am young, just started my career, and looking to begin investing so I can make my money work for me. I'm still living like I did in college (occasional purchase on myself, but most of it goes into savings) and I would like to take the extra money and invest it.   What would you suggest are the best options for me to begin? I was considering getting a personal investor [a financial advisor] for perhaps a year or so, but I've heard that they really are not worth the money. I wanted to get the input of the great minds here.


I think it's fairly well explained what powers were given to the One Ring, Elves, and Humans, but the dwarf rings are little explained in the series. Why were these rings important, or what kinds of powers did they give?

So, I've been reading Lord of The Rings, and other Tolkien books, and I've always wondered something. What did the other rings of power, given to the various races by Sauron actually do?


If one of my python files is called hello.py, is there a way to import it to my other python file, called main.py, in the following way:  main.py  name = "hello" import name   I get the following error:     ModuleNotFoundError: No module named 'name'

I'm writing a Python application that takes as a command as an argument, for example:  $ python myapp.py command1   I want the application to be extensible, that is, to be able to add new modules that implement new commands without having to change the main application source. The tree looks something like:  myapp/     __init__.py     commands/         __init__.py         command1.py         command2.py     foo.py     bar.py   So I want the application to find the available command modules at runtime and execute the appropriate one.  Python defines an __import__ function, which takes a string for a module name:     __import__(name, globals=None, locals=None, fromlist=(), level=0)      The function imports the module name, potentially using the given globals and locals to determine how to interpret the name in a package context. The fromlist gives the names of objects or submodules that should be imported from the module given by name.       Source:    So currently I have something like:  command = sys.argv[1] try:     command_module = __import__("myapp.commands.%s" % command, fromlist=["myapp.commands"]) except ImportError:     # Display error message  command_module.run()   This works just fine, I'm just wondering if there is possibly a more idiomatic way to accomplish what we are doing with this code.  Note that I specifically don't want to get in to using eggs or extension points. This is not an open-source project and I don't expect there to be "plugins". The point is to simplify the main application code and remove the need to modify it each time a new command module is added.


I have configured AIDE (Advanced Intruder Detection Environment) in my Centos7 VPS which has 2GB of RAM. After running AIDE --check I get the desired or the intended result. But when I check the available RAM the following is the result I get. The buff/Cache is almost full. Why is this happening?                total        used        free      shared  buff/cache   available Mem:           1.8G        249M        100M        9.8M        1.5G        1.4G Swap:          511M         15M        496M  Edit-- I want to know whether other AIDE users are experiencing the same issue or not. Does the memory used by the cache/buffer affect the overall server performance. I am using this VPS as a web server only.

This is a  about how Unix operating systems report memory usage.   Similar Questions:                    I have production server that is running Debian 6.0.6 Squeeze  #uname -a  Linux debsrv 2.6.32-5-xen-amd64 #1 SMP Sun Sep 23 13:49:30 UTC 2012 x86_64 GNU/Linux   Every day cron executes backup script as root:  #crontab -e  0 5 * * * /root/sites_backup.sh > /dev/null 2>&1   #nano /root/sites_backup.sh  #!/bin/bash str=`date +%Y-%m-%d-%H-%M-%S` tar pzcf /home/backups/sites/mysite-$str.tar.gz /var/sites/mysite/public_html/www mysqldump -u mysite -pmypass mysite | gzip -9 > /home/backups/sites/mysite-$str.sql.gz cd /home/backups/sites/ sha512sum mysite-$str* > /home/backups/sites/mysite-$str.tar.gz.DIGESTS cd ~   Everything works perfectly, but I notice that Munin's memory graph shows increase of cache and buffers after backup.  Then I just download backup files and delete them. After deletion Munin's memory graph returns cache and buffers to the state that was before backup.  Here's Munin graph:  Externally hosted image was a dead link.


I have no hints to get started. This is a really tough problem involving prime powers and it's the first time I have seen such question.  I need some good hints to get started. Thanks!  Please do not use congruence, limits or derivatives because they are out of scope of the chapter which has this question.

Let $p$ be prime number ($p\gt2$) and $a,b\in\mathbb Z$ ,$a+b\neq0$ ,$\gcd(a,b)=1$ how to  prove that $$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1~~\text{or}~~ p$$  Thanks in advance .


I'm trying to cite an article in a frame and display the URL at the same time (Beamer). But all I get for the citation is a print out of the key. As for the URL I can't make it work.   \documentclass{beamer} \usetheme{Warsaw} \usepackage[english]{babel}  \usepackage{csquotes}  \usepackage[]{biblatex} \addbibresource{science.bib} \begin{document} \begin{frame}      In  \textcite{Jilvero2012181} found in   --i want to print the url here--% \end{frame} \end{document}   science.bib is in the same folder with the main .tex document. The .bib file contains the following   @article{Jilvero2012181, title = "Heat requirement for regeneration of aqueous ammonia in post-combustion       carbon dioxide capture ", journal = "International Journal of Greenhouse Gas Control ", volume = "11", number = "0", pages = "181 - 187", year = "2012", note = "", issn = "1750-5836", doi = "http://dx.doi.org/10.1016/j.ijggc.2012.08.005", url = "http://www.sciencedirect.com/science/article/pii/S1750583612001909", author = "Henrik Jilvero and Fredrik Normann and Klas Andersson and Filip Johnsson", keywords = "Chilled ammonia", keywords = "Post-combustion", keywords = "\{CO2\} capture", keywords = "Aqueous ammonia", keywords = "Heat requirement " }   I am using TeXworks. Any suggestions?

How can I extract the value of the URL field of an entry in a .bib file?  I want to print it directly in the frame of my beamer document.   Additional info: (added July 20, 2014):  I can't provide the exact copy of the .tex file because it's very long now. In my preamble  I have   \usepackage{natbib,hyperref} \usepackage{bibentry} \bibliographystyle{apalike}   and in the document I have   \begin{document}  \nobibliography{database}  ....    \citet{Jilvero2012} % I want to print the URL here%   ...  \end{document}   this key is defined in my .bib file as   @Article{Jilvero2012,    Title                    = {Heat requirement for regeneration of aqueous ammonia in post-combustion carbon dioxide capture },    Author                   = {Henrik Jilvero and Fredrik Normann and Klas Andersson and Filip Johnsson},    Journal                  = {International Journal of Greenhouse Gas Control },    Year                     = {2012},    Number                   = {0},   Pages                    = {181 - 187},    Volume                   = {11},    Doi                      = {http://dx.doi.org/10.1016/j.ijggc.2012.08.005},   ISSN                     = {1750-5836},   Keywords                 = {Chilled ammonia},    Url                      = {http://www.sciencedirect.com/science/article/pii/S1750583612001909}  }


This is my regex expression WITH\s*\(.*\)\s*AS\s*   It is working when there is no line break. Here's the output: .  But it is not working when I introduce line breaks in between even though I am using \s* after AS. Here's the output:  Edit: Here's the regexr link:

For example, this regex  (.*)<FooBar>   will match:  abcde<FooBar>   But how do I get it to match across multiple lines?  abcde fghij<FooBar>


So here's the situation: I run live streams of video games, and I'd like to be able to read the stream chat and control my broadcast software while streaming, but with a fullscreen game this is extremely difficult. Some games can't be minimized, others will cause the stream to freeze while I'm minimized.  A lot of livestreamers use dual monitors to deal with this, they can stream from one monitor, and do the other things the audience shouldn't be watching on the other monitor, and it has the added effect of not breaking fullscreen games.  Unfortunately, due to space constraints it's not really feasible for me to get a second monitor right now. I figure there has to be someone else out there who had the same thought I did: virtual monitor. Is there anything that exists, software or hardware that would allow me to have two "virtual" monitors on one physical monitor? I figure I could use something similar to a KVM switch, or a software solution, but I don't really know.  Thanks in advance!

Is there such a thing?  I don't want multiple separate desktops, what I'd like to be able to do is split my main desktop into two areas so that an application in one when maximized won't take up the "Full" physical screen, but its portion of it.  I would like to be able to keep some apps maximized, but still view others off to the side with a single monitor.  Ideas?


I've applied for a visit visa to spend my paid annual leave with my fiancée - 10 days ( British Citizen ). Although I 've submitted all the requested documents ( signed application form, Employment letter, 6 months bank statements, salary slips for 6 months, copy of residency card, copy of my property contract, my old passport, my fiancee's bank statements for 6 months, mortgage statement, p60, invitation letter, copy of her passport ) they still refused my application although I've complied with my last visa conditions. Could you please help explaining this refusal letter?

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?


My if-then-else statement is always outputting the else outcome  import java.util.Scanner;   public class NiallScanner {  public static void main(String[] args)  {     System.out.println("Hello, What is your name?");     Scanner scanner = new Scanner(System.in);     String yourName = scanner.nextLine();     System.out.println("Is your name: "+yourName + "?");      Scanner scanner1 = new Scanner(System.in);     String isCorrect = scanner1.nextLine();      if (isCorrect ==  "Yes")     {         System.out.println("Thank you for your confirmation!");     }     else     {         System.out.println("Retry please.");      }  }   Any ideas why guys? I'm really new to java btw, so I may be overlooking basic coding errors.

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Observers at rest in gravitational fields will see infalling light signals as blueshifted.  Do inertial observers in free fall in a gravitational field see the same shift?  If someone is standing on a cliff at rest in the gravitational field and then steps off, do they instantly see a change in the blueshift as a result of being in free fall in an inertial reference frame?

I've heard that, from the perspective of an external observer, something falling into a black hole will eventually look "frozen": light waves will move to the infrared and further into lower frequencies.  But what about that unfortunate individual falling into such a black hole? What will he/she see when looking back at our universe?   For instance, I wonder, will it be the ultimate end of the Universe? Can someone who just crossed events horizon of the black hole still receive messages from our side?


Sometimes I get this odd behavior while using Google Chrome:    It appears only sometimes; I can usually get rid of it by refreshing. Is this from some extension? Should I suspect malware? What should I do to figure out what's injecting this stuff?  Also, subjectively speaking, Chrome's felt much slower lately.  edit: there is a rogue extension (). I will debug.  update: it was JQuery Injector, which has now been removed from the Chrome store.

What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


I want to perform one security mechanism, but I don't know whether it is possible.  I want to Shutdown/Turn Off PC/System when any USB device attach to it.

I know it has been discussed that it is not possible to start an application from an usb drive upon connection due to limitations of autorun (or autoplay??) in Win 7. But it is possible to create a scheduled task having an event type trigger. Surely there must be an event occurring when the drive -- or any USB device, for that matter -- is connected.    Does anybody have the slightest idea which Event ID should I use? Or at least what type of event? Where can I find the event in event viewer?


I would like to sort my records in ascending order and my string includes numbers in starting which are properties. I tried with the normal Order By clause but not getting an idea of what logic should I apply here.  Actual list:  5100 Estern Highway 1901 Wilsi Building 1205 Colorado highway 120 Sepulveda Whole Foods Business Building Ontario Tower Altron Tower 140 Sepulveda   Sorted list:  120 Sepulveda 140 Sepulveda 1205 Colorado highway 1901 Wilsi Building 5100 Estern Highway Altron Tower Ontario Tower Whole Foods Business Building  Thank you.

Is there an elegant way to have performant, natural sorting in a MySQL database?  For example if I have this data set:   Final Fantasy Final Fantasy 4 Final Fantasy 10 Final Fantasy 12 Final Fantasy 12: Chains of Promathia Final Fantasy Adventure Final Fantasy Origins Final Fantasy Tactics   Any other elegant solution than to split up the games' names into their components    Title: "Final Fantasy" Number: "12" Subtitle: "Chains of Promathia"   to make sure that they come out in the right order? (10 after 4, not before 2).  Doing so is a pain in the a** because every now and then there's another game that breaks that mechanism of parsing the game title (e.g. "Warhammer 40,000", "James Bond 007")


Every time I use the Array modifier with Object Offset, when I increase the count over 1, the duplicates begin to increase in size exponentially. How can I keep their size constant?

I'm somewhat new to blender (I've been using it for a few months but am still not fully comfortable with it). I'm trying to take a cylinder and duplicate it around an origin in a circular shape. I'm trying to get it to look something like this:    I looked up some tutorials on this, and they said to put an empty at the center of the rotation, and add an array modifier to the cylinder with "Object Offset" set to the empty. I did that, and instead of rotating around, the cylinders are getting scaled (it looks exponential). I'm not sure why this is happening. It's happened before but I wrote it off as some bad modifiers I applied earlier. But this is simply a cylinder and an empty. A screenshot of my setup and results is below:     It's kind of hard to see, but the empty is at the origin of the grid, inside the second smallest cylinder. The really small, thin cylinder is the one to which the modifier has been applied. Thanks!


Actually I am having list of 500 elements such as list = [1,2,3,4,5...500]  Now I want to create a batch of of 32 elements and store in nested list where the main list contains nested list of 32-32 elements and last nested list contains 20 elements such as: final_list = [[1,2,3,..,32],[33,34,35,..,64],..,[480,481,482,..500]]  I was trying with append from loop but not having exact idea how to do so. final_list = [] for itr in range(0,500,32):     final_list.append(l[0:itr])  Tried with various method but not able to find the correct logic. Any help would be great and thanks a lot in advance!!

I have a list of arbitrary length, and I need to split it up into equal size chunks and operate on it. There are some obvious ways to do this, like keeping a counter and two lists, and when the second list fills up, add it to the first list and empty the second list for the next round of data, but this is potentially extremely expensive.  I was wondering if anyone had a good solution to this for lists of any length, e.g. using generators.  I was looking for something useful in itertools but I couldn't find anything obviously useful. Might've missed it, though.  Related question:


The object is emitting too strong of a signal that it's unreasonable to consider it to be a mere chunk of scrap metal.      The object is emitting a too strong signal that it's unreasonable to consider it to be a mere chunk of scrap metal.   Actually the first one is the original sentence, but that kind of structure is rather unfamiliar to me. Could you let me know what's the difference or what's the correct usage here?

These kinds of expressions akin to measure quantifiers just blow my mind. For me it has to be "too big gulp of whiskey" and "too big sofa". Especially c), it sounds like you placed a part of the sofa in your room, not the entire thing. Can you break down and explain this structure?  a) "Could" is a little bit more difficult of a modal verb because it has many meanings. b) I took too big of a gulp of whiskey. c) I put too big of a sofa in my room, so there is no space.


In Lightning Component controller checking blank and undefined for a string variable.   var AccAsset = component.find("AccountAsset").get("v.value");   if(String.isBlank(AccAsset) || AccAsset == 'undefined'){         component.set("v.hasError", true);   }   This is throwing an error      "String.isBlank is not a function"

I have been using !$A.util.isEmpty(var) to check if value in empty/null/undefined in aura but this is not supported in LWC. What will be equivalent of this expression in LWC.   I don't want to write like if(this.var!==null && this.var!==undefined && this.var!=='')


I have a list of a few hundred addresses and have a day of the week matched with those days.  I need to know how many of the weekdays have a unique address associated with it.  For this example, Monday has 4 addresses but only 2 of them are unique:

I am trying to get a count of unique addresses from a list of a 1000 addresses in column A if they are in a specific primary week list in column B.  In this example, Monday has 4 addresses but only 2 on them are unique.


$L$ is a Lie algebra. If any finite dimensional repersentation of $L$ is completely reducible, then $L$ is semisimple.  I have already proved that $L$ is reductive, i.e. $\text{Rad}(L)=Z(L)$, by considering the adjoint representation. However, I stucked here and did not know what to do.

Let $k$ be an algebraically closed field of characteristic zero, and $\mathfrak{g}$ a semisimple Lie algebra over it. By Weyl's theorem, we know that any finite-dimensional representation $V$ of it is semisimple.   The question is: Is the opposite of this theorem also true, and if not, what is a counterexample?  NB by semisimple representation I mean a sum of simple representations and simple representation is the one that does not have a subrepresentation.


I want to select specific multiple files in windows explorer, to do that I used this:     explorer.exe /select, "c:\path\to\file.txt"   In PowerShell I made this:   $filenames = @("D:\imgs\a.jpg", "D:\imgs\b.jpg") foreach($fl in $filenames)  { Start-Process -FilePath C:\Windows\explorer.exe -ArgumentList "/select, ""$fl""" }   it works good, but two explorer.exe are running at the same time for each files in the $filenames array. I want to get selected files in single explorer.

I can display and select a single file in windows explorer like this: explorer.exe /select, "c:\path\to\file.txt"  However, I can't work out how to select more than one file. None of the permutations of select I've tried work. Note: I looked at these pages for docs, neither helped.


I am trying to mock HTTP method I created. For the get method, the test fail when trying to do POST\PUT, I am getting null exception.   I will put part of my code:  public HTTPResult httpPostPutGetRequest(String url, String jsonString, String requestMethod) throws Exception {     HttpURLConnection connection = connectionFactory.createURLConnection(url);     connection.setRequestMethod(requestMethod);     String result = null;     if (requestMethod == "PUT" || requestMethod == "POST") {          connection.setDoOutput(true);         connection.setRequestProperty("Content-Type", "application/json");         connection.setRequestProperty("Accept", "application/json");          OutputStreamWriter osw = new OutputStreamWriter(connection.getOutputStream());         osw.write(String.format(jsonString));         osw.close();   Then I am trying to mock it by the following:  public class StepdefsCommonTest {      private static final int PORT = 51234;     private static final String baseUrl = "http://localhost:" + PORT;     private HTTPResult result = null;      private String responseBody = "{blbl}";     private String responseMessage = "OK";     private int responseCode = 200;      public HTTPResult mockHttpRequest(String httpMethod) throws Exception {          HttpURLConnection mockHttpURLConnection = mock(HttpURLConnection.class);         URLConnectionFactory mockURLConnectionFactory = mock(URLConnectionFactory.class);          ByteArrayInputStream responseBodyInputStream = new ByteArrayInputStream(responseBody.getBytes());         when(mockHttpURLConnection.getResponseCode()).thenReturn(responseCode);         when(mockHttpURLConnection.getResponseMessage()).thenReturn(responseMessage);         when(mockHttpURLConnection.getInputStream()).thenReturn(responseBodyInputStream);         when(mockURLConnectionFactory.createURLConnection(baseUrl)).thenReturn(mockHttpURLConnection);          StepdefsCommon common = new StepdefsCommon(mockURLConnectionFactory);          HTTPResult res = null;          switch(httpMethod){             case "POST":case "PUT":                 try {                     res = common.httpPostPutGetRequest(baseUrl,responseBody,httpMethod);                 } catch (IOException e) {                     e.printStackTrace();                 }   I am getting null pointer exception for:  OutputStreamWriter osw = new OutputStreamWriter(connection.getOutputStream()); The exception I am getting:  java.lang.NullPointerException     at java.io.Writer.<init>(Writer.java:88)     at java.io.OutputStreamWriter.<init>(OutputStreamWriter.java:109)

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 the same exact problem as described in this SO post ("bash associative array key string with colon is giving error"):    The solution is to use declare -A but once I do this, my associative array ceases being global.  Is there a way to declare -A and having it global?  UPDATE: I tried declare -gA as described here:  but it doesn't work for me for some reason: As soon as exit the loop that populates my associative array (hashmap), the array gets unset.  Here is the actual bash code (the echo commands inside the loop are to verify that values are indeed extracted and assigned):  declare -gA HOSTS_START_MAP find "$TEMP" -type f -name "debug.log*" -exec grep -F "STARTING HOST " {} \; | while IFS= read -r HOST_START_LINE; do     if [[ $HOST_START_LINE =~ (.*)(DEBUG)(.*)(STARTING HOST)([ 0-9]*)(.*)(CALCULATION) ]]     then         HOST_START_TIME=$(echo "${BASH_REMATCH[1]}" | xargs)         HOST_NAME=$(echo "${BASH_REMATCH[6]}" | xargs)         # echo ">$HOST_NAME< ... >$HOST_START_TIME<"         HOSTS_START_MAP[$HOST_NAME]=$HOST_START_TIME         # echo $HOST_NAME --- ${HOSTS_START_MAP[$HOST_NAME]}     fi done  echo ${#HOSTS_START_MAP[@]} for MYKEY in "${!HOSTS_START_MAP[@]}"; do echo $MYKEY --- ${HOSTS_START_MAP[@]}; done

Why do I get different values for $x from the snippets below?  #!/bin/bash  x=1 echo fred > junk ; while read var ; do x=55 ; done < junk echo x=$x  #    x=55 .. I'd expect this result  x=1 cat junk | while read var ; do x=55 ; done echo x=$x  #    x=1 .. but why?  x=1 echo fred | while read var ; do x=55 ; done echo x=$x  #    x=1  .. but why?


As I understand images uploaded to stack exchange sites are stored in  . I recently noticed image included posts having broken links.  When clicked on the link it gives the error      This page isn’t working i.stack.imgur.com redirected you too many   times.   And ironically I can't put a screenshot here as well due to the same issue.  What has happened to image hosting server?

I just wrote a question before this one and had trouble uploading a screenshot. The drop your image dialog throws no warning or error, but after uploading it won't show.  I also noticed that other questions won't load their images. Could this be some issue with imgur or similar?  Example:     When opening the image in a separate tab, Chrome gives a "too many redirects" error:    This might be linked to


I have answered  on stackoverflow. I have answered this question after about 60 days and got 2 up-votes. I am not sure why I didn't get Revival Badge?

Formerly List of all badges with full descriptions.  What are badge name's requirements? Why didn't I get badge name ? Which badges can I earn multiple times?    Jump to:                    Note: Some badges are awarded based on score. The term score means the total number of upvotes minus the total number of downvotes.  Any badge with a *** next to it is one of 20 badges that count towards the  displayed on a moderator candidate in an election. The candidate score is a total of 40 points: the first 20 are awarded based on the user's rep divided by 1000 and rounded down; the second 20 represents the total number of unique badges earned of the 20 that count. Note that if the same badge is earned multiple times, it will only count once towards the candidate score.  Any badge with a "(retired)" next to it is no longer awarded, but is retained by users who previously earned them. See  for more info on what it means for a badge to be retired.       Visit the  of the  on any site to see a complete list of badges that you can filter by earned, unearned, or type.


I'm trying to export this Icosphere into Unity, but I want to have each poly be separate, with its own pivot point on its surface, and with the blue arrow on the manipulator widget facing out at 90 degrees from each poly, as if originating from the centre of the planet and passing through the poly. Currently every poly has the pivot point in the right place, but the orientation is wrong. How can I change this?

So,  Each of my polygons is a separate object. Their default normals point like this:   But their orientation or local axes are like so:   How can I make their local axes to be like so, but automatically?   I guess particles might be one solution for this exact case (if you emit new objects on top of the existing ones) but let's say the original objects are triangles and I wouldn't want to change their shape and pointing direction at all, only their local orientation axes, would that be possible?  Cheers!


If given a list of strings such as arr = ["abc", "efgh", "ij"], I want to know all the combinations starting from the first word to the last using recursion. so the output will look like this: aei aej afi afj agi ... chj  all the codes I see are just using the permutation of one string. I've been thinking that the concept is something like the fundamental counting principle like the one in the picture but I can't really put it into code.

How can I get the Cartesian product (every possible combination of values) from a group of lists?  Input:   somelists = [    [1, 2, 3],    ['a', 'b'],    [4, 5] ]   Desired output:  [(1, 'a', 4), (1, 'a', 5), (1, 'b', 4), (1, 'b', 5), (2, 'a', 4), (2, 'a', 5) ...]


TLDR: OK to repeat someone else's old, unanswered question if (as a creditless newbie) I can't vote it up or comment or otherwise help bring it to attention?  Details: I encountered an issue and wanted to ask a technical question (on Super User, as it happens; but I guess the question is relevant to all Stack Exchange sites). It's a rather obscure issue, and I assumed I may be the first to ask about it (and was skeptical that anyone would have a resolution).  But as I started typing the title, there was a suggestion ("Questions that may already have your answer") that linked to a question that someone else already asked, which is the exact question I had. I was happy to find this (and of course stopped typing my redundant question), but unfortunately, no one answered it yet.  But now, I wanted to vote this question up - and I can't. As a newbie, I don't have enough reputation. I also wanted (in a comment) to ask the person who posted this whether he had already found an answer somehow (it's been a while since he posted his question). But I can't do that either, for the same reason.  In such case: is it legitimate to somehow repeat the question? Or is that "littering" the site?

Someone else has already asked a question about the exact same problem that I am having. Unfortunately, the question does not have an answer yet. Follow-on questions to the original poster have gone unanswered. How do I get an answer to that question?  I can't upvote the question unless I have 15 reputation.  I don't have an answer to the question (yet), although I do have some more information about my particular instance of that problem that may lead to an answer. I don't see how to just comment on the question.  What choice do I have other than to start a new post with the same question (and be responsive when anyone replies)?


This should print "GLES2", but it doesn't. Is there a way to fix that?  #include <iostream> #include <string>  using namespace std;  class Rasterizer { protected:         virtual string get_driver_name() const { return "???"; }         Rasterizer(); };  class RasterizerGLES2 : public Rasterizer {         virtual string get_driver_name() const { return "GLES2"; } };  Rasterizer::Rasterizer() {         cout << get_driver_name(); }  int main() {         RasterizerGLES2(); }

Why the following example prints "0" and what must change for it to print "1" as I expected ?  #include <iostream> struct base {    virtual const int value() const {       return 0;    }    base() {       std::cout << value() << std::endl;    }    virtual ~base() {} };  struct derived : public base {    virtual const int value() const {       return 1;    } };  int main(void) {    derived example; }


I would like to try taking photo of shiny objects such as light sources, diamonds etc. I want to have them photographed without shining because I will try them on image processing programs and the more shining means the more problem at that photos.  Is there any comment ?  Thanks in advance,

I've been having the hardest time photographing objects that are encrusted in rhinestones and capturing their sparkle.  My understanding of sparkle is that it comes from two components: the dynamic range of our eyes and movement of our heads. Screens don't do a good job of reproducing the dynamic range that our eyes can see and still photos don't do a good job of reproducing movement.  I've looked at various other answers on this site, but I'm still left wanting a truly "sparkly" picture. I've tried:    (black acrylic did a pretty good job for this. It shows a reflection of the object, but effectively dimmed by a number of stops, so the bits that sparkle are still bright) Using a video of the object slowly moving, instead of still photos. This is probably the best option so far, but as one might imagine it's not always a usable option. Using a number of bright point light sources (e.g. non-diffused LEDs, xmas lights). , such as a flashlight/torch or non-diffused halogen lamp Long exposures, short exposures; narrow apertures, wide ones.   No matter what I do, I get more diffuse light (which is good for giving the overall appearance of the object), but very little sparkle. I understand that sparkle is small, bright points of light shining back at the camera, from the mirrored surface of the rhinestone facets, but somehow it never seems enough when captured by the camera.  Perhaps the real question is: how do you show sparkle on a low dynamic-range display? How do you capture it and if it's not easy to capture, is there a way to convince your eye to see something as sparkly?  Here's an example of a shot that I've been trying to make more sparkly:   (artwork by Judith Klausner, photo by myself)  The above photo was lit by a single halogen bulb above the camera and a flash pointed directly at it off to the right and above the camera. It was taken within a diffusion box with the front entirely open and black velvet on the left / back side, and black acrylic underneath it all. 90mm manual prime macro lens on a D600 at F16 with a 1.3" exposure.


Here is the code I am using for the output in the end  public static String processMessage(String input) {     String[] token = input.split(" ");     if (token[0] == "add")         return "yeah its a match";     else         return "not a match"; }   Here is the image of my test      Does anyone know what could be wrong?

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


class X {     public static void main(String...a)     {         String a = "meow";         String ab = a + "deal";         String abc = "meowdeal";         System.out.println(ab == abc);     } }   Am getting an output as false... why.  Am preparing for ocjp. I thin we have to get true. Beacuse ab contains "meowdeal". When am trying to assign "meowdeal" to abc this literal is already tehre in string pool. So ab and abc both are pointing to the same object. Then we have to get true.


I have this code. I have written the value of 'i' (in comments) that I expected as the correct output. But the outputs/alerts are different.  Fiddle:  Code:  var i = 10;  function outer() {     alert(i); // 10     var i = 5;     alert(i); // 5     function inner() {         var i = 20;     }     inner();     alert(i); // 5     if (1) {         var i = 30;     }     alert(i); // 5     setTimout(function () {         alert(i); // 5     }, 100); }  outer();   Can someone let me know the reason for the output? Or just the pointers where the specific concepts are explained?

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


Problem:     Let $f:X\to Y$ and let $F_i$ be a collection of closed sets such that $f|_{F_i}$ is continuous for each $i$ . Prove that $f$ is continuous over $\cup_{i=1}^m F_i$ ;$X,Y$ are metric spaces.   My attempt: Let $x_n$ be a sequence in $\cup_{i=1}^m F_i$ such that $x_n\to x$. Since we have finite number of closed sets we must have one $F_i$ such that $F_i$ will contain infinitely many terms of the sequence i.e $F_i$ will contain a subsequence say $x_{n_k}$ of $x_n$. Also $x_{n_k}\to x$. As $F_i$ is closed  so $x\in F_i$. As $f|_{F_i}$ is continuous then $f|_{F_i}(x_{n_k})\to f(x).$  But still I could not complete the proof.How to show that $f(x_n)\to f(x)$?

I was just trying to solve an exercise in Munkres' Analysis on Manifolds to get better at continuous functions and topology in $\mathbb{R}^{n}$, and I got stuck. Here it is:      Let $X = A \cup B$, $A$ and $B$ are subspaces of $X$. Let $f:X \rightarrow Y.$ Suppose that the restricted functions $f_{|A}:A \rightarrow Y$ and $f_{|B}:B \rightarrow Y$ are continuous. Show that if both $A$ and $B$ are closed in $X$, then $f$ is continuous.    Our definition of continuity is:  $f$ is continuous at $x \in X$ if for each open set $V$ of $Y$ containing $f(x)$, there is an open set $U$ of $X$ containing $x$ such that $f(U) \subset V$. $f$ is continuous if it is continuous at each point of its domain.  What I've tried so far:  Suppose $A$ and $B$ are closed in $X$. Suppose $A \cap B = \emptyset$. Then $X -A$ is open in $X$. But $X - A = B$ which is closed in $X$, which is a contradiction. Hence, $A \cap B \ne  \emptyset$. I'm not sure if this will be useful in the problem or not. If $x \in X$, then it's either in $A$ or in $B$. Suppose without loss of generality that it's in $A$. Then for all open sets $V$ of $Y$ s.t. $f(x) \in V$, $\exists$ an open set $U_{1}$ of $A$ s.t. $U_{1} \subset A, a \in U_{1}$ and $f(U_{1}) \subset V$. This is almost what we want, except that we want to find an open set $U$ of $X$ s.t. $U \subset A, a \in U$ and $f(U) \subset V$. This is because $U_{1}$ being open in $A$ does not necessarily mean that it's open in $X$ because $A$ is closed in $X$. (i know how to expand this argument out if needed) My idea now is to try to find a subset $U$ of $U_{1}$ such that $U$ is open in $X$. We have two cases:  (1) $U_{1}$ does not intersect the boundary of $A$. (2) $U_{1}$ intersects the boundary of $A$. Now I'm not sure what to do. I'm wondering if it would help to investigate the relationship between Bd(A) and Bd(B).. In any case (no pun intended), any help/advice would be greatly appreciated. :)  Sincerely,  Vien


I am viewing tags in Stack Overflow when I choose a tag the questions list for that tag appears I select one of the questions (everything is ok until now) but when I press back to go to the questions list the app takes me back to the tags list, this happens whether I have used the physical key or the button in the top left corner.   App Version: 1.0.89 Device Manufacturer: samsung Device Model: SM-N910C OS Version: 6.0.1 (N910CXXS2DQC5)

This looks a little bit like a variation on  but specific to the tags view.  Reproduction (app version 1.0.71):   Select any site (say Meta) from the sidebar Switch to the tags view using the top bar Choose a tag, any tag ( is nice)   optionaly refine your search with more terms  Go to any question found, go back   you end on the unfiltered tags view  Go back again   lucky you, your search is here


In what ways can we encourage musical aptitude in a two-year old?

My 1 year old daughter loves all kinds of music and rhythm. She dances and "plays" enthusiastically on both guitars, the piano and her toy glockenspiel. This has, since she was just four month, always been about me showing her that you can make noises on various instruments, and she then happily making as much noise as she can.  I think she's gotten the idea that different keys makes different notes, at least she like to play on all of them, and on the piano she also plays both hard and soft, but she still hasn't gotten the idea of rhythm. Her playing is always just about making notes as fast as possible, so I'm thinking that the next step is introduction to rhythms. She sometimes seems to try to clap her hands slower when I do it, but I'm not sure.  Any ideas or resources on how to introduce her to this would be appreciated.


According to Ohm's law,$$ \left[\text{voltage}\right]~=~\left[\text{current}\right] \times \left[\text{resistance}\right] .$$Does that mean if there is no resistance, then there can be no voltage? Why is that so? If you make a circuit with no load, and no resistors, why does the voltage have to be zero?

Imagine a circuit consisting of just a battery and conducting wires which have zero dissipativity so that there is no loss of energy( Zero resistance). If the wires are connected to both terminals the current will flow in the direction of lower potential. Can we say that there has been a voltage drop in the current in going from positive terminal to negative terminal? I asked this question because  voltage drop happens across resistor and I don't understand why it should occur only there. Because  I think, considering a positive test charge its electric potential should decrease  as it travel from higher potential to lower potential  whether any dissipation occurs or not.Does voltage drop refers to loss in total energy of electron i.e. because in this case KE + Electric potential will be zero and the total energy of electrons remains unchanged and thus we can says that voltage drop is zero. Is voltage drop(assumed here to mean loss in electric potential) equal to work output under normal conditions. I think no - because electric potential difference gets converted into kinetic energy of electrons out of which only some gets converted into heat or is it the case that in a resistor entire kinetic energy gets converted into another energy such as heat? Is electric field inside circuit constant? If yes how? Will not the shape of circuit matter?


Let $X$ be a normed linear space and, for any $x \in X$ and $r \gt 0$, let $T=\{y\in X: \|y-x\|\le r\}$ and $S=\{y\in X: \|y-x\|\lt r\}$.  If $z\in T$ and $z_n=(1-n^{-1})z$, for $n\in \mathbb{N}$, show that $\lim z_n=z$ and hence show that $\bar{S}=T$.   Below is the solution to the problem. But I think it's wrong. It shows that $\|z_n\|\lt r$, but we need $\|z_n-x\|\lt r$, where $x$ is a fixed point in $X$, to show that $z_n \in S$. How can I show this? Perhaps the problem is wrong? I would greatly appreciate any help.

It is not necessarily true that the closure of an open ball $B_{r}(x)$ is equal to the closed ball of the same radius $r$ centered at the same point $x$. For a quick example, take $X$ to be any set and define a metric $$ d(x,y)= \begin{cases} 0\qquad&\text{if and only if $x=y$}\\ 1&\text{otherwise} \end{cases} $$ The open unit ball of radius $1$ around any point $x$ is the singleton set $\{x\}$. Its closure is also the singleton set. However, the closed unit ball of radius $1$ is everything.   I like this example (even though it is quite artificial) because it can show that this often-assumed falsehood can fail in catastrophic ways. My question is: are there necessary and sufficient conditions that can be placed on the metric space $(X,d)$ which would force the balls to be equal?


I'm working in Android Studio 3.0.1. I created a EditText in which I write a text now I want when user long press that text it get copied in clipboard.  I used a method here (which is not working)   ClipboardManager mClipboard = (ClipboardManager) getSystemService(CLIPBOARD_SERVICE);         mEditText.setText(mClipboard.getText());  It says Method Invocation 'get text' may produce 'java.lang.NullpoinyerException' I need help what should i do ?

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?


Every time I scan my 35mm negatives, there is always a lot of dust, even after using a rocket duster and wiping with a microfiber cloth. What sort of equipment exists in order to get rid of the dust? I’m using a dedicated 35mm scanner that has IR dust removal, but that too isn’t that great. I try deleting every dust particle manually in Photoshop, but as you might imagine, it takes hours and is far from completely effective, especially with larger particles. Do you think it would be better just to make prints with an enlarger and then scan those?

What is a proper way to clean a 35mm negative film stripe before scanning?   What chemicals can remove fingerprints, dust that does not come off by blowing, or strains of glue? What type of cloth does minimal damage when rubbing off dirt?


My website is based in the UK with a .co.uk domain. We are now expanding into the US. I' m wondering whether I should use .com or .us for this domain? If I use .com, will this appear in the UK over my .co.uk domain?

When I set up a site in multiple languages, how should I set up my URLs for search engines and usability?  Let's say my site is www.example.com, and I'm translating into French and Spanish. What is best for usability and SEO?  Directory option:  http://www.example.com/sample.html http://www.example.com/fr/sample.html http://www.example.com/es/sample.html   Subdomain option:  http://www.example.com/sample.html http://fr.example.com/sample.html http://es.example.com/sample.html   Filename option:  http://www.example.com/sample.html http://www.example.com/sample.fr.html http://www.example.com/sample.es.html   Accept-Language header:  Or should I simply parse the  header and generate content server-side to suit that header?  Is there another way to do this? If the different language versions don't have different urls, what do I do about the search engines?    UPDATE 2011-12-06  Google has new recommendations for meta tags for explicitly pointing to other language content: .  UPDATE 2012-05-25  Related but not precisely:   UPDATE 2013-06-12  includes discussion of several URL schemes directly relevant to the question.


Looking for old time radio show OTR story with this plot.  A passenger spaceship for some reason has to make the choice to self destruct because if it doesn't it will impact a major city and be like small extinction level asteroid crash.  I don't think this was a normal episode of a series like dimension x because I've listened to the classic major series, but maybe I've missed it.  I heard this from a school library tape set of radio shows that included a lot of radio shows and Orson Welles stuff.

I'm trying to pin down a memory of a short story which I first read sometime in the early-to-mid 1980s (in an anthology I found in a school library, I think). I later found it again in another book, in another library, sometime in the 1990s. I remember the general plot, but not who wrote it. I have the impression that the story was already pretty old before I first ran across it.  Here's the plot outline:   As the story begins, a spaceship containing hundreds (or even more?) of passengers is returning to Earth from some other planet. Something goes terribly wrong, and they lose the main engine. (Which may have been the only engine -- I'm not sure of the technical details.) I don't recall if it was accident, sabotage, a meteor strike, or what, but their main means of propulsion is gone, with no hope of fixing it any time soon.  The timing is terrible. The ship is still on a trajectory that has it approaching Earth at high speed, and it badly needs to decelerate if there's to be any hope of touching down safely instead of slamming into the planet so hard that it will inevitably kill everyone aboard. But now the ship can't decelerate (nor change course to miss Earth entirely, which could have bought them valuable time), and there's only a matter of some hours left before the projected time of impact.  Some political and military leaders meet on Earth for an emergency conference  to discuss their options. What it comes down to is that a) there is no way to save the passengers and crew of the ship, no matter what they do, but b) if they do nothing at all, this will also mean the tragic deaths of millions of other civilians in the region which the ship will crash into. Not so much because of the shock of impact, but because of the sound in the minute or so before that. My memory gets blurred on the physical details of what makes the sound so bad . . . but I think the general idea may have been that such a huge metallic mass, moving so incredibly fast as it comes down toward the Eastern Seaboard of North America (or perhaps some other densely populated bit of the globe?), will be "screaming" in such a way that the vibrations racing through the air will shatter zillions of pieces of glass and/or otherwise cause huge numbers of fatalities down on the ground, even before the ship strikes whatever bit of the Earth's surface it is projected to strike.  The final decision is that the lesser of two evils is to send up a missile (nuclear warhead, I think?) to vaporize the ship before it comes plummeting through the air near an urban area.  I think that the officers aboard the ship either already knew, or very strongly suspected, that everyone aboard was doomed after the main engine had dropped dead. But the Captain and his loyal subordinates do their best to maintain a stiff upper lip in order to prevent mass hysteria from breaking out among the passengers. There's one bit where it is announced that a rescue ship is coming up from Earth to pull alongside the falling ship and then they'll transfer the passengers to safety. I believe the Captain knows darn well that the laws of physics do not make such a maneuver possible at this late date, and thus "a rescue mission" cannot be the intended function of the fast-moving blip on the radar screen that is headed straight for his ship, but he sees nothing to be gained by telling everyone the truth. So most of them die in blissful ignorance.


If $A$ is matrix from $M_{n-1,n}$ such that sum of all elements in row is zero.  Prove  det$(AA^T)=nk^2$, for some $k\in\mathbb{Z}$.  I tried to solve it, but I’m really confused.   I know that $A[1, 1, \dots, 1]^t= 0 * [1, 1,\dots, 1]^t$  So zero is eigenvalue of $A$, so it's singular and $\det A=0$.   So $\det(AA^{T})=\det(A)\det(A^T)=\det(A)\det(A)=\det(A^2)=0$   Is this correct? Is there any other way to solve this?  Thank you in advance.

Problem: We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of elements in each row is zero. Prove that $\det(AA^T)=nk^2$, where $k\in \mathbb Z$.  What have I considered so far:   First I thought, since sum of all elements in each row is zero, zero is eigenvalue of $A$ but $A\in M_{(n-1)\times n}(\mathbb Z)$ confused me. I see that $AA^T$ will be $(n-1)$ by $(n-1)$, so I tried calculating $AA^T$ but I failed to see any connection.   I did some research and found  question but we had no mention of it, which makes me believe I am on the wrong track.  Thank you all for your help.


I have recently begun programming at university and I am a little stumped with one of my tutorial problems.  I basically need to create a method within a class which uses the Random.nextInt() method to flip a coin, assigning and saving the value once the process has been run.  MY current attempts include this:  public void Flip() {  int flipResult;  flipResult = mRandNumGen.nextInt(1);  if(flipResult == 0) { mFace = 'H'; } else { mFace = 'T' }  }   mFace and mRandNumGen are variables which have been declared already outside the specific method. What exactly is going wrong here? I can't for the life of me get this to work :/

How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum.


Following code read a piece data from given DataRow(modelValue) and parse it to a nullable DateTime instance.  Question: Please see the code sections under L1 & L2 where both are technically equal (If i am not making any schoolboy error). However, L1 works as expected but not L2. I am getting      there is no implicit conversion between null and datetime   when I execute the code under L2. Can someone advise me ?          DateTime? CallBack;          var callBackDate = modelValue["CallBack"] == DBNull.Value ? null : modelValue["CallBack"].ToString();         //Parsing         DateTime cdate;         if (!DateTime.TryParse(callBackDate, out cdate))             cdate = DateTime.MinValue;           //L1         if (cdate==DateTime.MinValue)             CallBack = null;         else            CallBack = cdate.Date;         //L2          CallBack = cdate == DateTime.MinValue?null:cdate.Date;

EmployeeNumber = string.IsNullOrEmpty(employeeNumberTextBox.Text)     ? null     : Convert.ToInt32(employeeNumberTextBox.Text),  I often find myself wanting to do things like this (EmployeeNumber is a Nullable<int> as it's a property on a LINQ-to-SQL dbml object where the column allows NULL values).  Unfortunately, the compiler feels that  There is no implicit conversion between 'null' and 'int'  even though both types would be valid in an assignment operation to a nullable int on their own. Using the null coalescing operator is not an option as far as I can see because of the inline conversion that needs to happen on the .Text string if it's not null. As far as I know the only way to do this is to use an if statement and/or assign it in two steps.  In this particular case I find that very frustrating because I wanted to use the object initializer syntax and this assignment would be in the initialization block... Does anyone know a more elegant solution?


We've got a party with a Celestial Mystic (Book of Exalted Deeds), and I was reading about his level 9 ability, which grants him DR 10/Unholy. Would this be different from DR/evil, as in it would only be breached by unholy weapons, and not attacks from evil outsiders?   I'm asking this because I haven't seen any monsters or anything that have things like DR/Unholy, Holy, Axiomatic, etc... it's usually just Good/Evil/Lawful/Chaotic. Has anyone seen any material throughout the books like this? My intuition tells me it's a typo and should be DR 10/evil, but the errata doesn't say anything about this.  Thanks!

We've got a party with a Celestial Mystic (Book of Exalted Deeds), and I was reading about his level 9 ability, which grants him DR 10/Unholy. Would this be different from DR/evil, as in it would only be breached by unholy weapons, and not attacks from evil outsiders?  I'm asking this because I haven't seen any monsters or anything that have things like DR/Unholy, Holy, Axiomatic, etc. It's usually just Good/Evil/Lawful/Chaotic. Has anyone seen any material throughout the books like this? My intuition tells me it's a typo and should be DR 10/evil, but the errata doesn't say anything about this.


My Samsung stove is model NE59J7750WS – Nancy 1 hour ago   delete   If I enter 150 I get 1.50 minutes. If I enter 500 I get 5 minutes. If I enter 5 I get 5 minutes. There is nothing on the display panel to show hr. When I push the Cooking Time button this shows up: _ _ _ min. There is an arrow pointing to the right above this. I can't push it or anything. My problem is cannot set for say 5 hours. Samsung told me to enter 5 0 0, but I just get 5 minutes. There is no..... _ hr _ _ min.....like I have seen online in some pics. – Nancy 1 hour ago   delete

Why does the Cooking Time not allow me to enter hours?  All  I get is Minutes. What is that flashing arrow above where the digits are for the time? No matter when I enter amm I can get is seconds or minutes for the maximum if the three digits I can enter.  Thanks for any help


I am new to sequences and encountered a task where I am to show that a sequence $(a_n)$ that fulfills the following criteria is a Cauchy sequence. $\forall n \geq 2 : |a_{n+1} - a_n| \leq L \cdot |a_n - a_{n-1}|$ with $0 \leq L < 1$. This means that the following is true as well: $|a_{n+1} - a_n| \leq L^n \cdot |a_1 - a_0|$ $\frac{|a_{n+1} - a_n|}{|a_1 - a_0|} \leq L^n$ Since $L^n$ converges to $0$ and we have the quotient of two absolutes, I can use the Squeeze theorem to conclude that the sequence $(a_n)$ converges to $0$ as well. Every convering sequence is a Cauchy sequence which concludes my proof. However, I am really unsure because I also found sequences that look like they would fulfill the description but are not converging like this one:  Where did I go wrong and how can I show that it is a Cauchy sequence? I was made aware of a post dealing with the same problem and using Cantor's lemma:  However, I am not allowed to use Cantor's lemma for this task, so any help would be appreciated.

I was given the following question: Let $q$ be a real number such that $0 < q < 1$, and let ${a_n}$be a sequence that follows the rule : $|a_{n+1}-a_n| < q|a_n-a_{n-1}|$ for any $n>1$. Prove that ${a_n}$ converges. I already know this can be proven using Cauchy's criterion, but I had a different proof in mind (using Cantor's lemma), and wanted to know if it's valid, or if I might be mistaken. So here it is: First - I prove that the sequence is bounded. Since the sequence is bounded, the set of its members (and the set of any sub sequence of ${a_n}$) has a Supremum and an Infimum. Then, for any natural number $k$, I define the closed interval $A_{k}$, such that $A_{n}=[\inf(a_k), \sup(a_k)]$, where inf and sup of $k$ are the Infimum and Supremum of the set of the members of $a_n$, starting from $a_k$ (meaning, any member with an index greater than or equal to $k$). Naturally, $A_1$ is the "biggest" interval, and because of how the sequence is defined, $A_{n+1}$ is always a proper subset of $A_n$ for any $n$. Now I use Cantor's lemma - because the interval gets infinitely smaller and smaller (after n iterations, it gets at least $q^n$ times smaller), the intersection of all intervals $A$ (meaning, $A$ of $n=\infty$) contains one single point, let's call it $L$. Now, I state that $L$ must be the limit of $a_n$ - for any epsilon, there exists a natural number $k$, such that for any $n>k$, $A_k$ is contained in the epsilon neighborhood of$ L$, and therefore all members of $a_n$ starting from $a_k$ are in the epsilon neighborhood of $L$, which means $L$ must be the limit. So do you think this is a valid proof? Or am I making some false assumptions? I know this proof is a bit longer than using Cauchy's criterion, but I like it better because I feel like it gives a better explanation as to 'why' the series converges. Thanks in advance!


Do subclasses have all the variables and methods of the parent class? Including the Private properties and methods of the parent class?  Or does the subclass have only accessible variables and methods of the parent class? Like public, default, protect?

In Java, are there clear rules on when to use each of access modifiers, namely the default (package private), public, protected and private, while making class and interface and dealing with inheritance?


I need your help with this one. I have to form a regex that accepts only 8 digits (no letters) with no or less than 3 dashes.  It should accept these examples:  12345678 1234 5678 1234-5678 123-45-678 12-345-678   It should not accept these examples:  1234 (less than 8 digits) 123456789 (more than 8 digits) -12345678- !@@#$% 12ABCBDEF (with letters) 12-34-56-78 (more than 3 dashes)   Any help is appreciated.

I'm trying to put together a comprehensive regex to validate phone numbers. Ideally it would handle international formats, but it must handle US formats, including the following:   1-234-567-8901 1-234-567-8901 x1234 1-234-567-8901 ext1234 1 (234) 567-8901 1.234.567.8901 1/234/567/8901 12345678901   I'll answer with my current attempt, but I'm hoping somebody has something better and/or more elegant.


Let G be a finite group and H a subgroup of G. Let a be an element of G and aH = {ah : h is an element of H} be a left coset of H. If B is an element of G as well show that aH and bH contain the same number of elements in G

*****************updated question**************  The question starts off like this:   Let $H$ be a subgroup of a finite group $G$. Prove that $|Ha| = |Hb|$ by proving that there exists a bijection $f : Ha \rightarrow Hb$. Find this bijection.   I know that I have to show injective and surjective but want to know if anyone thinks this is correct in this fashion  $$Let\ a\in G, \ y, x \in Ha,then \ x=ra, y=sa\ for\ some\ r,s \in H. $$ $$we\ define\ f:Ha \rightarrow Hb\ by \ f(x)=hb$$ $$suppose \ f(x)=f(y)$$ $$rb=sb\ for\ some\ r,s \in H$$   $$r=s$$   $$xa^{-1}=ya^{-1}\ (from\ x=ra\ and\ y=sa)$$ $$x=y$$ This shows injective. for the onto part this is really wanted to check $$let\ x\in Ha, y\in Hb\ and\ a,b \in G\  such\ that$$ $$x=sa,\ y=sb\ for \ some\ s \in H$$ $$then\ f(x)=sb$$ $$=yb^{-1}b\ (from \ y=sb)$$ $$=y$$ Thus, we have shown that $\forall y \in Hb, \exists\ x \in Ha \ such \ that f(x)=y  $  here we have shown the function is also surjective and hence a bijection exist between $Ha$ and $Hb$ and therefore we know then  $|Ha|=|Hb|$


I have an array ['cat','dog','rabbit','snake','sheep','cow','horse','pig'] and I want to output every combination of the elements, while also removing elements until the the data set includes one of each animal.  ['cat','dog','rabbit'] ['cat','dog',] ['cat'] ['dog','rabbit'] ['dog'] ['cat','rabbit'] ['rabbit']   but with a lot more data etc...  Are there any modules to help with this?  Thanls

I have a list with 15 numbers in, and I need to write some code that produces all 32,768 combinations of those numbers.   I've found  (by Googling) that apparently does what I'm looking for, but I found the code fairly opaque and am wary of using it. Plus I have a feeling there must be a more elegant solution.  The only thing that occurs to me would be to just loop through the decimal integers 1–32768 and convert those to binary, and use the binary representation as a filter to pick out the appropriate numbers.   Does anyone know of a better way? Using map(), maybe?


Why do we not observe any free quarks or gluon, but only particles that are built out of them, such as mesons and baryons? How does this phenomenon emerge from QCD?

I simply know that a single free quark does not exist. What is the reason that we can not get a free quark?  If we can't get a free quark then what is single-top-quark?


constract a sequence of functions on [o,1] each of which is discontinous at every point on [0,1] and which converges uniformly to a function that is continous at every point

Construct a sequence of functions on [0,1] each of which is discontinuous at every point on [0,1] and which converges uniformly to a function that is continuous at every point?


I have a world and I'm making this secret password lock with redstone and all that I need is about 2 stacks of paper so I need help finding sugar cane so I can make a farm and so I can finish my secret lock

I played several hours a started three different worlds in Minecraft, but I have never found any sugar canes. I read on Minecraft wiki to search near water but still no luck. Do you have more hints? Is it possible to re-create an environment that allow sugar canes to naturally grow?


Inspired by this question:   Here's the scenario:  A party member wants to fool an enemy into thinking that they are casting a spell. They take out components, do hand gestures, and starting chanting but do not actually initiate the casting of any spell. The enemy, fooled by this, casts counterspell at the pretend-spellcaster. How does this resolve?  Is counterspell successfully cast (obviously with no effect)? If so, is the slot used to cast counterspell lost?  Or, can counterspell not be initiated in the first place (since there is no real spell being cast)?

There are many spells which explicitly target creatures:     Choose one creature within range   The target creature is normally supposed to make a saving throw in this case.  What happens when the caster chooses a creature, that is actually an object? For instance, a scarecrow, a mannequin, an illusion, or a corpse.  Examples:   An evil mage is hiding in the bushes. He casts an illusion of himself on the road, using the Silent Image spell. A PC sorcerer walks down the road, sees the illusion and casts Magic Missile on it. A cleric is standing near a pile of dead bodies. He has suspicions that a few corpses are actually undead creatures. He casts Sacred Flame on every corpse, see which if them succeed, hence, reveals the undead. A wizard casts Acid Splash on a mannequin, trying to damage it with acid.   Possible outcomes I can think of are:   The caster cannot even try to cast the spell, regardless of their information about what the target actually is. The caster tries to cast the spell, the casting fails, not expending the spell slot. The caster casts the spell, it expends the spell slot, then fails. The caster casts the spell, but it hits the original and not the illusion. The caster casts the spell, it flies to the target illusion but deals no damage to it (passes through it).   References in the rules and Sage advice  I was trying to investigate, but it didn't make things clearer:    has an answer, that Magic Missile won't hit. It says nothing about if it can be targeted at all, it leaves it up to the DM. Magic Missile automatically finds the original, even when the caster targets an illusion. At least . Now . This supports the counter-intuitive option 4.   on the other hand   , if there were no perceivable effects (let's say you can try to cast the Command spell on an illusion). That assumes that casters can waste their spells on illusion, which means they at least can target it. This supports options 3 and 5.


The exact question is- Find the real value(s) of $a (a \ne -1)$ for which the limit $$ \lim_{ n \to \infty} \frac{ 1^a+2^a\cdots+n^a}{(n+1)^{a-1}[ (na+1)+(na+2) \cdots+(na+n)]} = \frac{1}{60}$$  I simplified it a bit to get that limit. However,  I got the answer from Wolfram Alpha $\frac{1}{a+1}$ without a solution and an assumption that $|a|<1$ however the answer that I got on further solving (and given) is $a=7$ and $a=-\frac{17}{2}$  How is it solved?

By considering:  $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^1}{n^{2}} = \frac 1 2$$ $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^2}{n^{3}} = \frac 1 3$$ $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^3}{n^{4}} = \frac 1 4$$  Determine if this is true: $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}} = \frac 1 {{m+1}}$$  If it is, prove it.  If it is not, evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{{m+1}}$.


My name is Tracy. I'm South African and hold a South African passport. I recently moved to Italy. I will be on a Sapphire Princess cruise ship from 4th of April which starts in Messina until 18 May where it ends in  Southampton. The ships home port is Southampton.  I will disembark the ship in Southampton and return back to Italy. I'm legally married to an Italian, and therefore I hold    legalised Marriage Certificate  Residence card for family member of a European citizen  Italian Teserra senitaria card  Italian identity card    To fly from Southampton with the following documents and accompanying my husband, will I need a visa to transit through UK?

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


I uninstalled my windows through OS-Uninstaller in Ubuntu. But now i am unable to access any of the disk partitions. I am getting following error:   Error mounting /dev/sda7 at /media/devil/Programming: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda7" "/media/devil/Programming"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda7': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option.   What to do? I guess I have to install windows again.. right?

Sorry if this question is already solved.  I changed my Operating System, from Windows to Linux Ubuntu 13.04.   I have 2 partitions:   C: (system) and  M: It's NTFS; there I have my information, music, photos. When I want to access the Disk to use the information, I can't get past this error:   Error mounting /dev/sda2 at /media/love/Mis Archiivos: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda2" "/media/love/Mis Archiivos"' exited with non-zero exit status 14:  The disk contains an unclean file system (0, 0).  Metadata kept in Windows cache, refused to mount.  Failed to mount '/dev/sda2': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown  Windows fully (no hibernation or fast restarting), or mount the volume  read-only with the 'ro' mount option.    Clarification: I don't have 2 OSes. I only have Linux installed.


Completely 100% new to Linux.  I recently partitioned my drive to run Windows and Ubuntu simultaneously. Ubuntu installed fine, but then I installed Win7 and suddenly Ubuntu disappeared from the boot options.  This is probably semi-duplicate, but the answers to the other questions insinuated there was something wrong with "GRUB" something. The suggested solution seemed to depend on the Linux terminal. Maybe I'm missing something trivial, but I don't see how I access the terminal at this point. Can I fix it via Windows somehow?

My system was configured to dual boot Ubuntu 12.04.1 LTS and Windows 7. Today I got my hands on the MSDN release of Windows 8 and I installed it over my Windows 7. Now the computer just boots to Windows 8 directly without loading the GRUB screen.  So I followed the steps as suggested in: . Running this command:      ls -l /dev/disk/by-label/   gives the following output:      total 0     lrwxrwxrwx 1 root root 10 Sep 11 07:51 Entertainment -> ../../sda2     lrwxrwxrwx 1 root root 10 Sep 11 02:45 PENDRIVE -> ../../sdb1   Also fdisk -l command gives this as the output:      Disk /dev/sda: 320.1 GB, 320072933376 bytes     255 heads, 63 sectors/track, 38913 cylinders, total 625142448 sectors     Units = sectors of 1 * 512 = 512 bytes     Sector size (logical/physical): 512 bytes / 512 bytes     I/O size (minimum/optimal): 512 bytes / 512 bytes     Disk identifier: 0x1246aa23         Device Boot      Start         End      Blocks   Id  System     /dev/sda1   *        2048   319582199   159790076    7  HPFS/NTFS/exFAT     /dev/sda2       319582208   602906623   141662208    7  HPFS/NTFS/exFAT     /dev/sda3       602908672   625135615    11113472   83  Linux      Disk /dev/sdb: 1939 MB, 1939865600 bytes     64 heads, 63 sectors/track, 939 cylinders, total 3788800 sectors     Units = sectors of 1 * 512 = 512 bytes     Sector size (logical/physical): 512 bytes / 512 bytes     I/O size (minimum/optimal): 512 bytes / 512 bytes     Disk identifier: 0xc3072e18         Device Boot      Start         End      Blocks   Id  System     /dev/sdb1   *        2248     3788799     1893276    c  W95 FAT32 (LBA)   So I assume that I have to run this: sudo grub-install /dev/sda3 to get GRUB up and running. But I am getting this error:      /usr/sbin/grub-probe: error: cannot find a device for /boot/grub (is /dev mounted?).   Can anyone please guide me in the right direction? The current Ubuntu installation is far too customized to my needs to lose it to a boot manager issue! Any help is much appreciated!


So recently I bought a used lens - Canon ef 28-80mm f/3.5-5.6 usm with the metal mount but it came with no lens cap and I want to buy one now but I can't see the diameter of the lens on it anywhere which I need to buy a lens cap, do any of you guys have this lens or happen to know the diameter of it?   Thanks!

I have an older Olympus OM 50mm lens that I'd like to get a matte box for, as I'm going to use it for video on a 550D. However, I can't seem to figure out what the thread diameter is. There are no markings on the lens itself to indicate what diameter. How do I figure this out?    Here's the lens I have. It's the standard 50mm ƒ/1.8 kit lens that came with many Olympus OM lenses in the '80s


Browsing the new questions queue in , I see several rapid-fire questions from an  with a spam-like name:     is quite forthcoming about it's intent:      However, there is no visible solicitation activity besides the account name and description. Questions appear to be clear and on-topic, and they enjoy neutral to positive reception (that I can see; I am not 10k).    This is an established account (+1k rep) on four Stack Exchange sites, with +6k rep on Math.SE. As such, I am inclined to let it go where I would have otherwise flagged it.  Should this type of "passive" spam be given leeway, considering it promotes an in-network community resource in a non-disruptive manner, or is spam spam and should be treated as such?  I understand that 100% is easier than 98%, but I would like to know the community's position on this.

Is it permissible to use your SE display name to advertise another SE site or Area 51 Proposal? Is this scrupulous or laudable?   I don't refer to my comment box. For example, could I change 'LePressentiment' to 'Commit to Law SE' to advertise the  proposal?


How does Einstein got  equivalent mass- energy equation E=mc2 ?

Most people know the famous equation:    What were his steps of thinking for this equation that helped us discover so much about our world?


In the Google , I discovered that the developer often uses an awkward way of executing JavaScript code:  Instead of doing  var a = foo(bar);   I see this:  var a = (function() {   return foo(bar); })();   What is the reason to do it the weird way?

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


How are commutators the mathematical basis for ? What makes one say that commutators imply uncertainty principle or vice-versa?

states that:    $$\sigma(x)\sigma(  p_x )\ge \frac {\hbar}{2}.$$  What is the scientific proof of this principle?


I'm having some trouble regarding the layout of nested subscripts/superscripts when used as underscored argument of argmin/min/max operators.  I have defined \argmin{} operator as:  \DeclareMathOperator*{\argmin}{arg\,min}   and then used inside:  \[\bm \theta_c^p \coloneqq  \adjustlimits\argmin_{\bm \theta_c \in \mathbb{R}^{n_{p} } }  \max_{\bm \theta \in \mathcal{D}_{\bm \theta}} \left\| \bm \theta - \bm \theta_c \right\|_p \]   in order to get:    My issue is that the actual output is not completely satisfactory mainly owing to wrong size of the subscript 'p' of 'n': they are both scriptscriptstyle so they have the same size and it results in a quite odd layout. I have already tried manipulating the size with no success whatsoever, even with \scalebox.  Which could be a simple and clean solution to this problem?  EDIT: I removed the part of the question that makes it a duplicate, the rest of the question is completely different from the "height issue" of adjacent operators (thanks to the use of \adjustlimits it is not an issue anymore)

I have a problem with the subscript under the sum,  \sum_{i \in X} \sum_{i \in \bar{X}}   for example gives the subscript at different heights for each sum. Does anyone know how to fix this?


$\displaystyle \frac{4}{20}$+$\displaystyle \frac{4.7}{20.30}$+$\displaystyle \frac{4.7.10}{20.30.40}$+...  Now  I  have  tried  to  solve  this  in  a  usual  way,  first  find  the  nth  term  $t_n$.  $t_n$=  $\displaystyle \frac{1}{10}$($\displaystyle \frac{1+3}{2}$)  +  $\displaystyle \frac{1}{10^2}$($\displaystyle \frac{1+3}{2}$)($\displaystyle \frac{1+6}{3}$)  +  ...+  $\displaystyle \frac{1}{10^n}$($\displaystyle \frac{1+3}{2}$)($\displaystyle \frac{1+6}{3}$)...($\displaystyle \frac{1+3n}{n+1}$)  =$\displaystyle \frac{1}{10^n}\prod$(1+$\displaystyle \frac{2r}{r+1}$)  ,  $r=1,2,..,n$  =$\displaystyle \prod$($\displaystyle \frac{3}{10}-\displaystyle \frac{1}{5(r+1)}$) thus,  $t_n=$ (x-$\displaystyle \frac{a}{2}$)(x-$\displaystyle \frac{a}{3}$)...(x-$\displaystyle \frac{a}{n+1}$),  x=$\displaystyle \frac{3}{10}$,  a=$\displaystyle \frac{1}{5}$  Now  to  calculate  $S_n$,  I  have  to  find  the  product  $t_n$,  and  then  take  sum  over  it.  But  this  seems  to  be  a  very  tedious  job.  Is  there  any  elegant  method(may  be  using  the  expansions  of  any  analytic  functions)  to  do  this?

How to find infinite sum How to find infinite sum $$1+\dfrac13+\dfrac{1\cdot3}{3\cdot6}+\dfrac{1\cdot3\cdot5}{3\cdot6\cdot9}+\dfrac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $$   I can see that 3 cancels out after 1/3, but what next? I can't go further.