For $c > 0,$ find the limit, lim$_{n \to \infty}  n(\sqrt[n]{c} - 1)$   Ok, I am not exactly on sure how to do this. Though here are some of my thoughts:    lim$_{n \to \infty} (nc^{1/n} - n) = nc^0 - n = 0,$ and I don't think this can be correct logically. Also, I think we can make it a $\log$ function by doing it like this:  $(nc^{1/n} - n) = e^{\log(nc^{1/n} - n)}.$ But, then what? We can't distribute the log inside because that's not correct. I am lost. Any help?   Update: please don't mark this as a duplicate of , since the other question was not required to use L'hopital's rule, but I need to use that in my question.

I am trying to find the limit of:  $$\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$$  I know it should be very simple but I don't seem to get it. Thanks in advance for any help!


$$\lim_{n \to \infty}\left(\prod_{r=0}^{n/2}{\left(\frac{mn+1-mr}{mn+3-mr}\right)}\right)$$  Of course if we check out cases where it should telescope like $ m = 1, 2, \frac{2}{3}, \cdots$, we get closed forms - $\frac{1}{4}, \frac{1}{2}, \frac{1}{8}, \cdots$.  So, I was thinking if it has a closed form.   One can reduce it to   $\displaystyle \lim_{n \to \infty} \dfrac{\prod_{r=0}^n{\frac{r + p/m}{r+q/m}}}{\prod_{r=0}^{n/2}{\frac{r + p/m}{r+q/m}}}$, where $p,q$ are $1,3$ in the above problem     $$\displaystyle  = \lim_{n \to \infty}{\dfrac{\Gamma\left(\frac{p}{m}+n+1\right) \Gamma\left(\frac{q}{m} + \frac{n}{2} + 1\right)}{\Gamma\left(\frac{q}{m}+n+1\right) \Gamma\left(\frac{p}{m} + \frac{n}{2} + 1\right)}}$$   Now, how to find this limit? Wolfram Alpha now can find the limit quite fast for example for $(p,q) = (1,3)$, and $m=3$ it gives the limit $\frac{\sqrt[3]{2}}{2}$.

$$\displaystyle  \lim_{n \to \infty}{\dfrac{\Gamma\left(\frac{p}{m}+n+1\right) \Gamma\left(\frac{q}{m} + \frac{n}{2} + 1\right)}{\Gamma\left(\frac{q}{m}+n+1\right) \Gamma\left(\frac{p}{m} + \frac{n}{2} + 1\right)}}$$  This is from .   If we add one more variable -      $$\displaystyle L(p,q,m,t) = \lim_{n \to \infty}{\dfrac{\Gamma\left(\frac{p}{m}+n+1\right) \Gamma\left(\frac{q}{m} + \frac{n}{t} + 1\right)}{\Gamma\left(\frac{q}{m}+n+1\right) \Gamma\left(\frac{p}{m} + \frac{n}{t} + 1\right)}}$$   Then, the results I got from W|A are really interesting. They seem to follow the pattern which says      $\displaystyle L(p,q,m,t) = \dfrac{1}{t^{|p-q|/m}}$   If it is indeed true, how to prove it? Factorial approximations did not lead me anywhere.


My computer is presenting some weird behaviour, and I don't know what to try next to work out what's going wrong.  First the behaviour. The computer occasionally freezes. I can move the mouse, and the cursor changes (e.g., to a movement arrow, hand, text cursor etc). But nothing else on the screen moves. Counters don't count, windows don't move, clicks do nothing. Waiting doesn't help - it doesn't wake back up.  I can CTRL-ALT-F5 to an alternative terminal session and see what's running. Nothing seems to be maxing out any resources.  As far as I can tell, it's not tied to any one single application. I've tried to use the computer with different apps and it seems to still happen whatever I stop running, short of killing of Xorg and nautilus, obviously.  I've tried the xorg-edgers repo. No improvement. I've disabled compiz (I think) - no improvement. I've looked in a few log files but couldn't see anything that would indicate where the problem is (though I might well have been looking in the wrong place).  My next options are to reinstall and/or start swapping out hardware. But before I do that, can anyone tell me what can cause crashes like this, where the mouse can move but nothing else does? Or can anyone tell me which logs files I should be checking? Is there anything else I can try, to diagnose the problem? Is it likely to be a hardware issue?  The computer is a vanilla Dell XPS 8300 - details at  - except for the graphics card, which is an ATI Radeon X1300 Pro.

All operating systems freeze sometimes, and Ubuntu is no exception. What should I do to regain control when...   just one program stops responding? nothing at all responds to mouse clicks or key presses? the mouse stops moving entirely? I have an    In what order should I try various solutions before deciding to pull the power plug?  What should I do when starting up Ubuntu fails?  Is there a diagnostic procedure I can follow?


The  spell requires that you "can cast" the contingent spell (of fifth level or lower).  A  lets you store up to a single 5th-level spell by any caster (for example, a  cast by a friendly cleric) and later be able to cast it yourself (using the initial caster's modifier/DC if applicable) even if it's not normally on your list.  If you have a spell that you don't normally know inside your Ring of Spell Storing, can you then choose it as the contingent spell for contingency?

says:     Choose a spell of 5th level or lower that you can cast, that has a casting time of 1 action, and that can target you. You cast that spell--called the contingent spell--as part of casting contingency, expending spell slots for both, but the contingent spell does not come into effect.   Would one be able to use a spell that is cast from a  as the contingent spell?    For example: A bard casts  into the Reserve Ioun Stone and gives it to the wizard who then uses contingency along with the stored revivify to create an effect that would revive him upon falling unconscious. The wizard cannot cast revivify normally.  Would this work?    My specific concerns are:   Does having the spell stored in such a way count as a spell "you can cast"? Does the fact that the spell is stored in an item mean that it can't be cast as part of another spell as contingency requires? Is there any other reason why this would not work?


I am studying basic quantum mechanics in undergrad and have hit a wall. I understand that if a measurement is made for position, the wave function collapses into one of the eigenstates of position, i.e. a Dirac delta distribution, at the point where particle is found. If the particle is found at $x_0$, the wave function collapses into $\psi=\delta(x-x_0)$ The problem is that the delta function does not satisfy the basic requirements of a wave function, it is not finite at $x=x_0$. The problem also exists for other observables like momentum, where the eigenstate is not square integrable.

The way I've understood it is that eigenfunction of an operator are the different states which the actual wavefunction can take when the property/observable corresponding to the given operator is being observed.   For the Hamiltonian operator, the eigenfunctions are forms the wavefunction will take when energy is being measured. The probability that we get a specific state corresponds to the coefficient from fourier decomposition of the wavefunction.   I've also read/interpreted/misinterpreted that upon measurement of position, a wavefunction will collapse to a single spike with a specific value of position (determinate state of the position observable).  With all of the above in mind, is it correct to think that the eigenstates of the position operator are continuous, because the probability density function is continuous and we can get a spike anywhere?  Also, does this mean that the wavefunction takes the form of a spike when position is being observed, but a sine wave when the energy is being observed?  Edit: by continuous eigenstates I want to say that there is an infinite number of them.


While looking over the universal coefficient theorem, I was wondering whether we can assume that groups of the form $\mathbb Z^{\mathbb N}$ are free. If we replace $\mathbb Z$ by a field, the answer is yes, since we can take maximal linearly independent sets by Zorn’s lemma, and by taking denominators to show that this set spans the whole space. This technique seems to fail in an essential way over $\mathbb Z$, but is there any nice invariant we can use to properly show that $\mathbb Z^{\mathbb N}$ is not free?

From  I see that $\mathbb{Z}^{\mathbb{N}}$ is not a free abelian group. Someone can explain me why?  Thanks a lot!


I've set up an Ubuntu 10.04 LAMP server. I am going to set up multiple domains so that they will point to this server's IP. How to configure the server so, that it will serve a specific site (placed in a specific folder) according to a domain name which was used in the request?

I'd like to host two websites with different domain names, on a single server, with a single IP address.   I have a fixed IP address with my service provider. It points to my router which port forwards everything on port 80 to a mac mini server on my local network.  How would I get that mac mini server to host two different websites on the same IP address?  Do I need to play around with the DNS on the Mac, or on the router (which is the entry point for the fixed IP address)? IE on the local network, does each domain name needs its own IP address so that these can be resolved by the single server? Little confused as to where to start. Thanks for help.


$a$, $b$ and $c$ are positives such that $ab + bc + ca = 3abc$. Prove that $$ \sum_{cyc}\frac{a^2}{ca^2 + 2c^2} \ge 1$$   Here's what I did. My stupidity has reached a spiritual level.  We have that $ab + bc + ca = 3abc \implies \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 3$.  $$\sum_{cyc}\dfrac{a^2}{ca^2 + 2c^2} = \sum_{cyc}\dfrac{1}{c}\left(1 - \dfrac{2c}{a^2 + 2c}\right) \ge \sum_{cyc}\dfrac{1}{c}\left(1 - \dfrac{2c}{2c + 2a - 1}\right)$$  $$ = \left(\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}\right) - 2\sum_{cyc}\dfrac{1}{2c + 2a - 1} \ge 3 - \dfrac{2}{9}\sum_{cyc}\left(\dfrac{1}{c} + \dfrac{1}{a} + \dfrac{1}{c + a - 1}\right)$$  $$ = 3 - \dfrac{4}{9}\left(\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}\right) - \dfrac{2}{9}\sum_{cyc}\dfrac{1}{c + a - 1} \ge 3 - \dfrac{4}{3} - \dfrac{1}{18}\sum_{cyc}\left(\dfrac{1}{c - \frac{1}{2}} + \dfrac{1}{a - \frac{1}{2}}\right)$$  $$ = \dfrac{5}{3} - \dfrac{2}{9}\left(\dfrac{1}{2a - 1} + \dfrac{1}{2b - 1} + \dfrac{1}{2c -1}\right)$$  I am done with my life.

let $a,b,c$ be postive real numbers ,and such $$ab+bc+ac=3$$   show that   $$\dfrac{a^2}{a+2b^2}+\dfrac{b^2}{b+2c^2}+\dfrac{c^2}{c+2a^2}\ge 1$$   This problem is from Secrets In Inequalities volume 1  page 30,example 1.24. the comment.the  author this case is a bit more diffcult,But this author can't post solution.Thank you


Is there a possibility to define function in C that depends on data type. I want to define a function which uses different procedures depending on 1d array or 2d array as a argument.

Is there any way to achieve function overloading in C? I am looking at simple functions to be overloaded like    foo (int a)   foo (char b)   foo (float c , int d)   I think there is no straight forward way; I'm looking for workarounds if any exist.


I read it when I was but a wee lad. The general summary that I can remember is:   Group of astronauts crash land (I believe they crash...I could be wrong though) on icy world They somehow end up below the surface into a long abandoned city of some alien race They begin to be followed by strange black glob-like creatures with green (maybe?) eyes. They follow but do not harm them. At some point they enter a structure and encounter a hologram of a different alien that tells them some history about a war with other aliens and basically having to sacrifice themselves to prevent the universe from being overrun or something along those lines. The explorers end up leaving the city and returning to their ship but there is a plot twist: they have a toast to the extinct race and say something along the lines of "to earth"...and it is revealed that the main characters are not humans but in fact have beaks and talons.   Anyway, as stated before I read this long ago and it was one of my favorite science fiction stories. I've been googling the little snippets that I remember for years but to no avail. Halp?

So my dad told me about a short story he had once read. It must be older like before 1986. It is about two men who traveled through space and found a dead planet. On it was what he calls a super museum. They set it up as a heritage/legacy for those in the universe that were intelligent enough to find it. As a twist it turns out that this planet is actually earth and that the men must have traveled to the future. (Kind of like planet of the apes)  I have found a few topics that looked similar. But it's not resurrection bij a.e van Vogt.(because they know it is earth they are visiting) Although this seems very similar. He also says it is not all the way back from michael Shaara.   Anybody have any idea? If it helps, the story was translated to Dutch and was in a book with other stories as well. I don't know if they were from one author or various. It has been bugging me for years as my dad always told me the story moved him deeply and as I love science fiction I would love to read it. Just found this site so thought to give it a go.thanks in advance!


Here is a proof that I am trying to solve: Show  that  if $p$ and $q$ are  distinct  primes,  then  the  group $\mathbb{Z}_p \times \mathbb{Z}_q$ is isomorphic to the cyclic group $\mathbb{Z}_{pq}$.  I have done a problem like this in the past but it was so long ago that I can't think of where to even start. Could someone give me at least a pointer on how I should do this?

In general, the group $\mathbb Z_{mn}$ under addition $\bmod mn$ is isomorphic to the direct product $\mathbb Z_m \times \mathbb Z_n$ if and only if $\gcd(m,n)=1.$ This is easy to see since $\mathbb Z_{mn}$ is generated by the element $(1,1)$, and if $\gcd(m,n)=1$, then this will only be zero if it is multiplied by itself $mn$ times (resulting in the cyclic group).   However I'm interested in constructing an isomorphism between the two groups as an explicit expression. I've been playing around a bit with some examples, one of which is the function $\phi : \mathbb Z_2 \times \mathbb Z_3 \to \mathbb Z_6$ where $\phi(a,b) = 3a + 4b \pmod 6$, which gives us the desired isomorphism. I'm interested here in the relationship between the integers $2$, $3$, and the coefficients $3, 4$ of $a$ and $b$. After playing around in Wolfram|Mathematica, I managed to obtain the following isomorphisms $\phi_{m,n} : \mathbb Z_m \times \mathbb Z_n \to \mathbb Z_{mn}$ for coprime $m,n$ in $\{1, 2, \dots, 10\}$.   First of all, the following results seem to hold in general.  $$\phi_{1, n}(a, b) = a + b \qquad \text{for all $n$}$$  $$\phi_{m, 1}(a, b) = a + b \qquad \text{for all $m$}$$  $$\phi_{2, n}(a, b) = na + (n + 1)b \qquad \text{for all $n$}$$ $$\phi_{m, n}(a, b) = K a + L b \iff \phi_{n,m}(a, b) = L a + K b \qquad \text{for all $m, n$}$$  Beyond this point, I could not spot a general pattern. The isomorphisms I obtained are:  $$\phi_{3, 4}(a, b) = 4a + 9b$$ $$\phi_{3, 5}(a, b) = 10a + 6b$$ $$\phi_{3, 7}(a, b) = 7a + 15b$$ $$\phi_{3, 8}(a, b) = 16a + 9b$$ $$\phi_{3, 10}(a, b) = 10a + 21b$$ $$\phi_{4, 5}(a, b) = 5a + 16b$$ $$\phi_{4, 7}(a, b) = 21a + 8b$$ $$\phi_{4, 9}(a, b) = 9a + 28b$$ $$\phi_{5, 6}(a, b) = 6a + 25b$$ $$\phi_{5, 7}(a, b) = 21a + 15b$$ $$\phi_{5, 8}(a, b) = 16a + 25b$$ $$\phi_{5, 9}(a, b) = 36a + 10b$$ $$\phi_{6, 7}(a, b) = 7a + 36b$$ $$\phi_{7, 8}(a, b) = 8a + 49b$$ $$\phi_{7, 9}(a, b) = 36a + 28b$$ $$\phi_{7, 10}(a, b) = 50a + 21b$$ $$\phi_{8, 9}(a, b) = 9a + 64b$$ $$\phi_{9, 10}(a, b) = 10a + 81b$$ If you want to try and generate a few yourself, here is the Mathematica function I implemented. I'm sure it can be optimised, but for the first 10 coprime integers it sufficed.  isomorphism[{m_, n_}] :=       Module[{x = Null},       For[i = 1, i < m*n,           i++, (If[#[[2]] == Table[i, {i, 0, m*n - 1}],           x = ToString[#[[1]][[1]]] <> "a+" <> ToString[#[[1]][[2]]] <>          "b"; Break[]] &) /@       Table[{{i, j},       Mod[i #[[1]] + j #[[2]], m*n] & /@       Table[{Mod[i, m], Mod[i, n]}, {i, 0, m*n - 1}]}, {i, 1,      m*n}, {j, 1, m*n}][[i]]]; x];   I'd appreciate if anyone can help me find the pattern to determine $\phi_{m, n}$ in general.


I'm running out of space on my root(/sda10). I want to merge the drive Ubuntu(/sda8 - 10 GiB) in my root(/sda10).  I don't have any unallocated space so.   Should I format the Ubuntu(/sd8) in ext4 format and then resize the /sda10 parition? I read here [ ] that GParted has to resize a partition above or below your partition that you need to extend -- which is a bit confusing.   Below is my parition screenshot.

I have two partitions, one of them has a file system and the other is unallocated.  How to merge two partitions?


I cannot figure out what is going on here. I have just installed Anaconda, and I am trying to get my #! /usr/bin/env python shebang to return the new interpreter. I have no python aliases, and ~/miniconda3/bin is the first entry in my PATH.  Even so, when I run env python -V I get Python 2.7.8, while if I run python -V I get Python 3.5.1 :: Contiuum Analytics, Inc.. This is very curious, and I cannot find any helpful discussions online.  type -a python gives the reasonable result:  python is /Users/aa/miniconda3/bin/python python is /Library/Frameworks/Python.framework/Versions/2.7/bin/python python is /Library/Frameworks/Python.framework/Versions/3.0/bin/python python is /usr/bin/python python is /usr/local/bin/python   hash -r python does not seem to help.  Thanks!

I have installed node.js at custom location and added the location to the $PATH in .profile file.  $ node --version v0.6.2 $ which node $ echo $PATH /usr/bin:/bin:/usr/sbin:/sbin:/usr/local/bin:/usr/X11/bin:~/Unix/homebrew/bin $ cat ~/.profile export  PATH="$PATH:~/Unix/homebrew/bin"   Node.js itself runs well. The problem is it is not listed by which command. So I can't install npm now. Because npm install cannot find the location of node.js. How can I make the node binary discovered by which?


I started using sed recently. One handy way I use it is to ignore unimportant lines of a log file:  tail -f example.com-access.log | sed '/127.0.0.1/d;/ELB-/d;/408 0 "-" "-"/d;'   But when I try to use it similarly with find, the results aren't as expected. I am trying to ignore any line that contains "Permission denied" like this:  find . -name "openssl" | sed '/Permission denied/d;'   However, I still get a whole bunch of "Permission denied" messages in stdout.  EDIT  As mentioned in the correct answer below, the "Permission denied" messages are appearing in stderr and NOT stdout.

Code   find / -name netcdf   Output  find: `/root/.dbus': Permission denied find: `/root/.gconf': Permission denied find: `/root/.gconfd': Permission denied find: `/root/.gnome': Permission denied find: `/root/.gnome2': Permission denied find: `/root/.gnome2_private': Permission denied


I'm quite new to testing with Mockito/Powermockito so I may have missed some important details about it. Here is a part of my code under test (I use the  library to encrypt the SharedPreferences data on my Android device):  public static boolean isTargetAddress(Context context, String address) {         EncryptedPreferences encryptedPreferences = new EncryptedPreferences.Builder(context).                 withEncryptionPassword(Constants.AES_PASSWORD).build();          Boolean bool = encryptedPreferences.contains("test");          return false; }   And this is my test case for this code:   @RunWith(PowerMockRunner.class) @PrepareForTest({EncryptedPreferences.class, EncryptedPreferences.Builder.class, Context.class}) public class BluetoothReceiverTest {     EncryptedPreferences encPreferences = PowerMockito.mock(EncryptedPreferences.class);     Context context = PowerMockito.mock(Context.class);      @Test     public void testNullTargetAddress() throws Exception {         PowerMockito.whenNew(EncryptedPreferences.class).withAnyArguments().thenReturn(encPreferences);          PowerMockito.doReturn(Boolean.TRUE).                 when(encPreferences).contains(Mockito.anyString());          PowerMockito.when(encPreferences.contains(Mockito.anyString())).thenReturn(Boolean.TRUE);          PowerMockito.when(encPreferences.contains("test")).thenReturn(Boolean.TRUE);          Assert.assertTrue(BluetoothReceiver.isTargetAddress(context, "test"));     } }   I want to mock the EncryptedPreferences class to test some edge cases of my program. The problem is that I get this error:  java.lang.NullPointerException     at com.lukanin.testappjava2.bluetooth.BluetoothReceiver.isTargetAddress(BluetoothReceiver.java:146)     at com.lukanin.testappjava2.bluetooth.BluetoothReceiverTest.testNullTargetAddress(BluetoothReceiverTest.java:37)     at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)     at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)     at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)     at java.lang.reflect.Method.invoke(Method.java:498)     at org.junit.internal.runners.TestMethod.invoke(TestMethod.java:68)   Line 146: Boolean bool = encryptedPreferences.contains("test");  Line 37: Assert.assertTrue(BluetoothReceiver.isTargetAddress(context, "test"));  What's wrong with my code? Why I can't mock the encryptedPreferences.contains(String str) method?  Is there any string like Mockito's MockitoAnnotations.initMocks(this); required for Powermockito in such case?  Edit 1:  I have read  and it's helpful, but doesn't address my problem.  I MOCKED the creation of the EncryptedPreferences object by using:  EncryptedPreferences encPreferences = PowerMockito.mock(EncryptedPreferences.class); PowerMockito.whenNew(EncryptedPreferences.class).withAnyArguments().thenReturn(encPreferences);   So then I think I can also mock the encryptedPreferences.contains(String str) method with   PowerMockito.when(encPreferences.contains(Mockito.anyString())).thenReturn(Boolean.TRUE);   But it doesn't work :(

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?


Some guy took my Son's iPhone and took 1,200 photos within 12 minutes. He was able to use the camera from the lock screen without having access to the locked phone.  These photos completely wiped our family's Photo stream (and replaced our vacation photos with nonsense). Also, the storage was filled and my son couldn't even make a phone call before we deleted the 1,200 photos.  Deleting the photos was even more annoying. Can you imagine the tedious process of deleting 1,200 photos on an iPhone?  This was very annoying, and also a usecase Apple may not have thought of.   Somebody mentioned that you can disable control center on lock screen. (Settings>Control Centre>Access on Lock Screen). To my surprise, this brings back a camera button on the lock screen. So that didn't work.  An old post suggested that the only possible solution would be to completely disable camera and FaceTime. But this is not really a solution (would be comparable to painting the camera lens black).  Back to the question: In iOS9, how do I disable camera access on the lock screen?  Related (but not quite the answer):    – (Feb 2015, AskDifferent)  – 2014, Apple Support Forum  – 2013, Apple Support Forum

How to remove the camera button on the iPhone lock screen without removing the camera from the springboard  I don't want to allow people without access to take pictures using my phone (pictures are shared automatically by iCloud) But in the same time, I want to be able to use the camera from the springboard.  I'm searching for a native solution under iOS 8.x or later


I have a realm that i'm trying to make a welcome message appear only for the player who joined, each time they join. I've looked at some old videos and tried to update the code, but to no success. The best I could come up with is: /execute if score @p[scores={JoinGame=1}] JoinGame Ive already created a scoreboard that uses the score "minecraft.custom:minecraft.leave_game"  I'm pretty new to the new command block system, so a lot of this doesn't make much sense to me. Any help will be greatly appreciated!

I am working on a game that uses commands in such a way that players disconnecting then reconnecting could break the commands. I was wondering if there is a way to detect when players join the game in 1.13.2 and run a command to give them an item. When I researched this, I found solutions for older versions using /testfor or stat.leaveGame, but those seem to be outdated in 1.13. If someone could show me the commands to use as well as the layout for command blocks/redstone that would be great. It can be for the second time they join only, or for all times that they do. Thanks


I am making a game in java with lwjgl and slick. And I have a World that contains a arraylist with all items laying on the ground that it has to update. But when it updates the items a second time it throws a ConcurrentModificationException.  How can I fix this?  This is the full error:Exception in thread "main" java.util.ConcurrentModificationException     at java.util.ArrayList$Itr.checkForComodification(Unknown Source)     at java.util.ArrayList$Itr.next(Unknown Source)     at com.jakibah.infinyvale.World.HandleItems(World.java:43)     at com.jakibah.infinyvale.World.Update(World.java:65)     at com.jakibah.infinyvale.Game.Update(Game.java:29)     at com.jakibah.infinyvale.Canvas.CreateCanvas(Canvas.java:41)     at com.jakibah.infinyvale.Game.main(Game.java:16)  And this is my code:  World:  package com.jakibah.infinyvale;   public class World {  public Tile[][] map; private int TilesWide, TileHeight; public ArrayList<Item> items = new ArrayList<Item>();  public World(int volume) {      this.TilesWide = volume / 2;     this.TileHeight = volume / 2;     map = new Tile[TilesWide][TileHeight];     for (int i = 0; i < map.length; i++) {         for (int j = 0; j < map[i].length; j++) {             map[i][j] = new Tile(TileType.Test, i * 32, j * 32, 32);         }     } }  public World(int[][] newMap) {     this.TilesWide = newMap[0].length;     this.TileHeight = newMap.length;     map = new Tile[TilesWide][TileHeight];     for (int i = 0; i < map.length; i++) {         for (int j = 0; j < map[i].length; j++) {             switch (newMap[j][i]) {             case 0:                 map[i][j] = new Tile(TileType.Test, i * 32, j * 32, 32);                 break;             }          }     } }  public synchronized void HandleItems() {     if (!items.isEmpty()) {         for (Item i : items) {             i.Update();         }     } }  public Tile GetTile(int xplace, int yplace) {      if (xplace < TilesWide && yplace < TileHeight && xplace > -1             && yplace > -1)         return map[xplace][yplace];     else         return null; }  public void Update() {     for (int i = 0; i < map.length; i++) {         for (int j = 0; j < map[i].length; j++) {             Tile t = map[i][j];             t.Update();         }     }     HandleItems(); }   Item:  public class Item { private ItemType type; private Texture tex; private int x, y; private World w; private int texturefactor; private int durability; private int power;  public Item(ItemType type, Texture tex, int x, int y, World w,int texturefactor, int durability, int power) {     this.type = type;     this.tex = tex;     this.x = y;     this.y = y;     this.w = w;     this.texturefactor = texturefactor;     this.durability = durability;     this.power = power;     this.w.getItems().add(this); }  public void Draw() {     Canvas.DrawQuadTex(tex, x, y, texturefactor, texturefactor); }  public void Update() {     Draw();     CheckPickUp(); } public void CheckPickUp(){     if(Canvas.isColliding(Game.p.getX(), Game.p.getY(), Game.p.getX() + 32, Game.p.getY() - 32, x, y));     System.out.println("Colliding");     this.ToBag(); }  public void ToBag() {     Inventory i = null;     i = Game.p.getI();     Game.world.getItems().remove(this);     i.getInventory().add(new BagItem(type, i, tex, texturefactor, durability, power));   }

We all know you can't do the following because of ConcurrentModificationException:  for (Object i : l) {     if (condition(i)) {         l.remove(i);     } }   But this apparently works sometimes, but not always. Here's some specific code:  public static void main(String[] args) {     Collection<Integer> l = new ArrayList<>();      for (int i = 0; i < 10; ++i) {         l.add(4);         l.add(5);         l.add(6);     }      for (int i : l) {         if (i == 5) {             l.remove(i);         }     }      System.out.println(l); }   This, of course, results in:  Exception in thread "main" java.util.ConcurrentModificationException   Even though multiple threads aren't doing it. Anyway.  What's the best solution to this problem? How can I remove an item from the collection in a loop without throwing this exception?  I'm also using an arbitrary Collection here, not necessarily an ArrayList, so you can't rely on get.


Can someone please give me the prerequisites and mathematics required for string theory? Are there some good references to study it, both online and in a book? Please consider I am a newbie in string theory, and only about up to the level explained in Hawking's Brief History of Time and Penrose's Road to Reality. I would prefer something which does not omit rigor, but builds it up.Also, are there good online lectures on this?  (I have covered most of GR, but I am not really comfortable with advanced Quantum mechanics. I have studied QM only from Griffith's book, and a few McGraw hill lecture notes.)

I am in the last year of MSc. and would like to read string theory. I have the Zwiebach Book, but along with it what other advanced book can be followed, which can be a complimentary to Zwiebach. I would like a more mathematically rigorous book or lecture notes along with Zwiebach.   Specifically, mention whether the book discusses string theory   Rigorously? Intuitively?   What's the scope of the book? Does it cover the advanced materials, e.g. Matrix string theory, F-theory, string field theory, etc. Maybe even String Phenomenology?


I may have set a new world record in travel according to Google location history. I've noted that on Wed, 18th March 2014 I was in Sydney at 5:28pm, then in Sale Morocco at 6:06pm, then back in Sydney at 6:08pm. At this rate, I have travelled (according to google) 11,169 miles each way in about half an hour.   Also, I note on the 20th March 2014 that I did it again, this time:     5:25pm Sydney 5:27pm Jakarta 5:29pm Sydney 5:31pm Jakarta 5:44pm Sydney   Now I know that Google uses GPS satellites, Wi-Fi networks and the Cell networks to locate my location, but can it get the language, country and continent wrong all at once?

I have a major problem that I hope someone can help with. On my Google Maps feature under my Location History it shows a location that I was never at at any point, but when my wife happened to see that location she doesn't believe me that the GPS could be wrong and pinpoint that location if I was never there.  I was first wondering myself how could that could be possible if I was never there or my phone was never at that location that was 35 miles away from me and second is there any way I could prove the GPS being wrong? Can I contact Google Maps and can they give an official printout of that certain day and every location I was? I really need to prove my honesty to her and hope there is a way.


When we have a ratio of random variables, is their expectation/variance defined in the same way? That is, if we want to write out explicitly $E[\frac{X}{Y}]$ where X and Y are random variables, then   $$E[\frac{X}{Y}] = \int_\Omega \frac{X}{Y} p(x,y)dxdy$$  And similarly, is the variance of the ratio also defined the same way: $$V[\frac{X}{Y}] = \int_\Omega [\frac{X}{Y}-\mu_{\frac{x}{y}}]^2 p(x,y)dxdy$$  for some $\mu_{\frac{x}{y}}$?  This is a definitional question, I ask because I have not seen anyone write out the expectation of ratio of random variables explicitly.

I am confused about something very trivial.  Suppose that we have 3 random variables, such that:  $Z=XY$  I am trying to understand the relation between the following expressions:  $E_Z[Z] =? E_{X,Y}[XY] =? E_{Z}[XY] =? E_{X,Y}[Z]$  I can't decide which integrals below yield which expectation and which are equal:  a) $\int p(z) z dz$  b) $\int\int q(x,y) xy dxdy$  c) $\int\int p(xy) xy dxdy$  d) $\int p(z) xy dz$  e) $\int\int q(x,y) z dxdy$  where $p$ is the distribution for $Z$,and $q$ is the joint distribution for $(X,Y)$.  (a) is clearly $E_Z[Z]$.  (b),(c) I am not sure which one is equal to (a).  (d) xy should come out of the integral according to basic calculus and integral should yield 1 but they are dependent on z, so should they?  I think I am confusing myself with random variables vs. symbols in expressions.


Is the correct term, "well done to the English on their performance or performances."?  I believe "performance" to be the correct choice.

When I have to use information and performance I'm always confused.  However, I'm asking whether when I'm referring to more than one piece of information of performance I should use "information/performance is" or "information/performance are."


var json1 = {   "type": "FeatureCollection",   "features": [     {       "type": "Feature",       "properties": {},       "geometry": {         "type": "Point",         "coordinates": [           83.94299268722534,           28.218707821027166         ]       }     }   ] } var geolayer = L.geoJSON(json1).addTo(map);  geolayer.bindPopup(features.properties.name).openPopup()

Is it possible in Leaflet that popup opens on mouse-over, not on click?  This is working for just one marker at a time, but I need it for a bigger number of markers:  marker.on('mouseover', function(e){     marker.openPopup(); });


It should be a good idea to have some mechanism to request to the user who asked a question to mark the question as resolved. I know not all questions are resolved but some of them a lot of times are clearly resolved and the answer is still unmarked.  I'm talking about not only a reminder like the people asked for at , I'm talking about some kind of button that can be pushed by other users who think the question is clearly resolved and if an important number of users (this is the more difficult point... to determine how many is needed to do this) click on that "ask for a resolved mark", the question must be marked as resolved on any answer or a consequence can happen. This consequence could be the loss of some reputation points or something like that.  It's only an idea that must be polished. What do you think?

Recently, I have answered a few questions that were upvoted by factors more than the accepted answer, but not accepted. , at the time of my writing, has an accepted answer that the asker said was not what he wanted. I don't know why. In the future, when people view this, people might only look at the accepted answer and move on. Would it be possible to have a "community accepted" feature? Maybe only the people at the top can vote to accept it or something. How much rep, if any, should go to that person?


I am using tabularx environment and in the MWE I have three columns. The first column contains short text, the second column contains long text and the third column contains short text again. \documentclass{article}     \usepackage{tabularx}  \begin{document}  \begin{tabularx}{6cm}{|p{2cm}|b{2cm}|p{2cm}|}  short 1 & long text spanning more than one row & short 2 \\ \end{tabularx}  \end{document}  As expected, the result is that both short 1 and short 2 align to the bottom.  If I change the setting on middle column from b{2cm} to p{cm}, as expected both short 1 and short 2 align to the top. I would like to make short 1 align to the top and short 2 align to the bottom. How can I achieve that? Thanks in advance. EDIT: Following the suggestion by @NBur who pointed me out to , I've implemented the following changes: \documentclass{article}     \usepackage{tabularx}  \newcolumntype{C}{b{2cm}<{\vfill}}  \begin{document}   \begin{tabularx}{6cm}{|C|b{2cm}|p{2cm}|}  short 1 & long text spanning more than one row & short 2 \\ \end{tabularx}  \end{document}  Unfortunately this code brings up the text only by one line and not all the way up to the top of the cell, so it does not work.  Are there any other suggestions?

I'm newbie in TeX, so I've decided to ask for some help.   I'm working on technical documentation for my job and I need to create a 4-column table, where text in first two columns top-aligned and centered horizontally, last two aligned with last string of second column. But I can't achieve this.   I've tried this:   and this:   But the closest result which I able to obtain is:    So, last three columns is OK, first one - not, it should be top-aligned.  I was successful to overcome this by usage of \multirow environment, but it's should be implemented individually to rows. If' I'll do this for long tables - it'll make me insane. I want one fixed style in preamble, if it's possible.  Here is my table in main body:      %russian technichal standart documentation class      \documentclass[russian, 14pt, utf8, columnsxxiv, columnxxxi, columnxxxii, pointsection, hpadding = 10mm]{eskdtext}       %%%For working of eskdx, also cyrillic      \usepackage{xecyr}       %%%set TNR as main font      \setmainfont[Mapping=tex-text]{Times New Roman}       %%%Additional position options      \usepackage{float}       %%%advanced tables      \usepackage{tabularx}      \newcolumntype{Y}{>{\centering\arraybackslash}X}            \newcolumntype{d}{>{\centering}b{.25\textwidth}}      \newcolumntype{s}{>{\centering}b{.1\textwidth}}      \newcolumntype{a}{>{\centering}p{.25\textwidth}}       %%%redefine command for № -symbol, because eskdx quite old package      \renewcommand{\No}{\textnumero}       \begin{document}       \begin{table}[H]      \label{appA}      \begin{tabularx}{\textwidth}{a|d|s|Y}      \hline       Наименование & Основные технические данные & Кол., шт. & Примечание  \\       \hline      text text text text text text text & text text text text text text text text text text& {1} & text  \\       \end{tabularx}       \end{table}       \end{document}   I'll appreciate any help!


I overstayed my Post study work Visa (having lived and worked in the UK legally for 8years)  because I had just been divorced and didn't have the wherewithal to immediately relocate to in my home country (Nigeira)  I was removed from the UK voluntarily and given a 2 year ban but when I applied for a visiting Visa 1.5 years later, I was told my ban is for 10 years.  How do I overturn this BAN?

I am a Nigerian citizen.  In 2007 I was twice denied a visa to the UK.  Recently I was filling out an application for another UK visitor visa and by mistake I answered no to the question whether I had ever been denied a UK visa, instead of yes.  When reviewing my application, the visa officer found out about the previous visa rejections and as a result I got a 10 year ban on travel to the UK.  What can I do to lift my 10 year ban?   Will this ban affect my chances of obtaining a visitor visa to the USA?


I don't want to set any fixed heights to any element, is this possible?

text

What is the best way to vertically center the content of a div when the height of the content is variable.  In my particular case, the height of the container div is fixed, but it would be great if there were a solution that would work in cases where the container has a variable height as well. Also, I would love a solution with no, or very little use of CSS hacks and/or non-semantic markup.


Which phrase is correct on Canaries or in Canaries when it's about group of islands.

I'm sure virtually everyone agrees that people live on the Isle of Wight, but in Ireland.  Apparently the usage depends somewhat on physical size, but that can't be the whole story. How exactly do we decide which form to use? And are there any really glaring 'outliers' that don't fit the normal pattern?  LATER - I must just add that the most uncertain case I've found so far is The Falklands. Most people go for in there, but a substantial minority (about 1 in 3) opt for on.


I can see notifications from Stack Exchange app but the title / description is null:null.    I remember that the notification was about a new Meta question posted. I haven't had a chat ping yet, so can't test out. Other notifications(comments/answers) seem to be fine

I just received a notification with null:null title, it happened because someone has posted a comment on my answer.    I know question regarding null notification is already asked earlier  but this new issue is somewhat different than that issue. I assume here we just get null:null titled notification whenever someone post a comment on your answer.


Is it correct to assume that Property in Java it is simple getter and setter?

So, I have willfully kept myself a Java n00b until recently, and my first real exposure brought about a minor shock: Java does not have C# style properties!  Ok, I can live with that. However, I can also swear that I have seen property getter/setter code in Java in one codebase, but I cannot remember where. How was that achieved? Is there a language extension for that? Is it related to NetBeans or something?


For every real number $x$, if $x - \lvert x \rvert + \frac{1}{x} - \lvert \frac{1}{x} \rvert = 1$ then $x$ is irrational  If $x$ equals $\sqrt{2}$ I get an inequality... So is this claim false?

Prove : $$ \text{If } \; x-\lfloor x \rfloor + \frac{1}{x} - \left\lfloor \frac{1}{x} \right\rfloor = 1 \text{, then } x \text{ is irrational.}$$  I think the way to go here is to falsely assume that $x$ is rational, thus having $x=\frac mn$ with $m,n$ integers and go with that, we also know that $x$ with the celling belongs to the integers and that $\frac 1x$ with the celling gotta be a $0$. Still can't prove it. Thank in advance !


I was sitting **next to / by / by the side of / beside / close to ** my friend.  As a learner all of the preparations means near or close to to me.

"She came and sat by/beside/close to/next to/near me." To me, the bold lettered prepositions seem to have almost the same meaning. Is there any difference between them? If so, would you arrange them in order of the degree of closeness? From the closest to the least closest.


Inside the for loop, depending on if condition, files need to be created every time. While executing the code, NullPointerException pops up.      File[] tempDir=null;      for(  )     {     if(condition){         try {             tempDir[l]=new File(tempFileName);             if(l==0){                 tempDir[l++].mkdir();                 /*code*/             }             if (!tempDir[l].exists()){                 tempDir[l++].mkdir();                 /*code*/             }         }     }

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 tried to setVisible(null); but it produces an java.lang.NullPointerException. the JPanel setLayout(null); which I think is the issue, I don't know how to resolve it. I,m using a card layout to reduce windows in the application. Any help would be appreciated.  final JPanel Signin = new JPanel(); contentPane.add(Signin, "name_12988058891368"); Signin.setLayout(null);  JButton btnNewButton = new JButton("New button"); btnNewButton.addActionListener(new ActionListener() {     public void actionPerformed(ActionEvent arg0) {         Signin.setVisible(false);         Home.setVisible(true);     } }

To put it simple, there's a simple java swing app that consists of JFrame with some components in it. One of the components is a JPanel that is meant to be replaced by another JPanel on user action.  So, what's the correct way of doing such a thing? I've tried  panel = new CustomJPanelWithComponentsOnIt(); parentFrameJPanelBelongsTo.pack();   but this won't work. What would you suggest?


Does Windows 8 not support path longer than a certian length such as 256 characters? Such path is created under Linux, because Linux doesn't have such limitation. Thanks!

What is the longest file path that Windows can handle?


I have two sticks of RAM in my computer that I would like to sell or donate. From what I understand some RAM is volatile, losing all its contents when power is gone for a few minutes, and some is non-volatile, retaining that information after power is lost. I would like to know which kind of RAM I have and whether it is safe to give it to someone else. I am not very tech savvy, all I know about the sticks is that the manufacturer is Kingston, and when I open Task Manager it says that it is "DDR3" and the form factor is "DIMM". Thanks in advance.

If computer RAM was to be non volatile like other persistent storages, then there would be no such thing as boot up time. Then why is it not feasible to have a non volatile RAM module?


On my machine ( 25, Firefox 56.0) I got the error shown below. Suggestions?  I can't log in through Google because of this.

is error 404  Well, it seems that Wget picks it up so the last statement is false and the exact message is:  Error 6 (net::ERR_FILE_NOT_FOUND): The file or directory could not be found.   and it loads in Chrome once after I clear the cache but not after.


At the moment the Dialog quickly progress till the end and stays there for a few minutes and after that shows 0 seconds left for a minute or two after that before the copy operation is actually finished:    This is pretty much annoying.  Is there a way to fix this??

Whenever I try and copy a file to an USB flash disk, the progress bar runs till the end very fast and stops for an indeterminable time before it is complete.  Is there an issue with ubuntu or my flash disk is what I am not able to figure out. All I want is a realistic copy dialogue


In the article "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any multiple of φ(n).   Imagine I know the public and the private key. But what I really want is the factors of n, the p and q but I connot use any factorization algorithm in a large number of n.   In the Miller's article it is suppose to say how I can find the two factores, knowing the public and private key. But I cannot understand how exactly it is done. Does someone know? Or have a small example?   Appreciated

In the article , the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any multiple of φ(n).  Imagine I know the public and the private key. But what I really want is the factors of n, the p and q but I cannot use any factorization algorithm in a large number of n.  In the Miller's article it is suppose to say how I can find the two factors, knowing the public and private key. But I cannot understand how exactly it is done. Does someone know? Or have a small example?


While re-listening to Harry Potter and the Prisoner of Azkaban (audiobook), I noticed that after Sirius tried to get into the Gryffindor common room, and everyone goes to the Great Hall, Dumbledore only creates hundreds of sleeping bags, implying less than 1000 students. Is there any way to know how many students attended Hogwarts, or how many students are in each house?

Not a year goes by where we don't see at least one person Sorted into each House, and it's usually a fairly even distribution.  The Sorting Hat doesn't get a chance to study the mind of each child before Sorting, so it can't Sort them relative to each other (top X in smarts go to Ravenclaw, 4 bravest to Gryffindor, etc)  What would happen if a Sorting occurred where all the witches/wizards were extremely intelligent?  Would they all get Sorted to Ravenclaw?  What if they were all extremely brave?  What if none of them were particularly smart or courageous, but they all wanted power?  We see that there's a fairly small number of beds per room in each dorm, would the Hat stop Sorting people into a House if it knew the House had no more beds?  If so, could Harry Potter have ended up in Hufflepuff if his last name had been 'Zimmers'?


I need to find arrival time in London Heathrow of the BA 677 flight on 31 july 2016. Can somebody help me? i tried flightstats and other websites but historical flight status check is not free. Thank you,  Takoz

Where can I find historical data on flights, specifically Delta international flights?  I need to find out about cancellations, diversions and any other flight data pertaining on particular route at a given time.  This source has to be official and stand up to legal scrutiny.


So, I was reviewing the Low Quality Posts review queue, when this item popped up in front of me:   I went down the page to see if the question was copied from a comment or something; and I found myself getting the following statement:     add comment (requires )      I understand it might(?) be because I was in a review queue and all, but I think either it should show     No comments allowed in review queues   or, pop-up a blue coloured modal (I don't remember what it is referred to as, exactly) with message similar to above one, instead of outright denying me the privilege to comment.

When reviewing an answer in the low quality queue the question doesn't believe that I have enough reputation to comment.        I can't remember if commenting on the post not actually being reviewed was ever allowed?


I have read that if we are using NAT, router knows where to send the incoming packets in the local network based on TCP/UDP port information. If this information can be used to uniquely identify each machine on a local network, then why is MAC address needed?

I understand that IP addresses are hierarchical, so that routers throughout the internet know which direction to forward a packet. With MAC addresses, there is no hierarchy, and thus packet forwarding would not be possible. So, MAC addresses are not used for packet transfer.  I don't think it sits there for no reason. So my question is, where exactly does a MAC address come into play during a packet transfer?


I am having a massive amount of trouble integrating this, I really have no clue how to get the answer in the book:     $$\int_{-\infty}^{\infty} \frac{x^4}{1+x^8}dx$$   I know I need to find the poles on this function, which is basically the value of $x^8 = -1$ or I could split it up like the following: $$x^8 +  1 = (x^4 + i)(x^4 - i)$$ With this I got the following poles (looking at $x^4 - i$), all have an order one: \begin{array} & x_1 = e^{\frac{i\pi}{8}} \\ x_2 = e^{\frac{3i\pi}{8}} \\ x_3 = e^{\frac{5i\pi}{8}} \\ x_4 = e^{\frac{7i\pi}{8}} \end{array} Now to calculate the residues I am trying to make use of the result that given a rational function $\frac{F}{G}$ such that both of them are analytic on a disk of radius $r$ with $G(z_0) = 0$ but $G'(z_0) \neq 0$ then we know that: $$Res(\frac{F}{G};z_0) = \frac{F(z_0)}{G'(z_0)}$$ With that I am having difficulty getting results that are useful, I maybe calculating wrong and I am not sure but I have been spending a long time on this one question. The solution in the book is $\frac{\pi}{4}[sin(\frac{3\pi}{8}]^{-1}$. I would like a step by step solution to this or at least some guidance because I really need to learn this and I am not sure how to do this properly. Thank you!

Compute the integral.   $$\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$$  The answer at the back of the book is  $$\frac{\pi}{4\sin(\frac{3\pi}{8})}$$


I am trying to write an adjacency list to save the graph. And here is my code, the class Graph has a member called Node. The Node can save any type of message, and many children with the cost to them. After Node thers is a nodes member to save all of the node in graph. template<typename T> class Graph { public:     struct Node {         using Ptr = std::shared_ptr<Node>;         T val;         std::vector<std::pair<Ptr, int>> children;         Node() {}         Node(T data) : val(data) , children() {}     };      typename std::vector<Graph<T>::Node::Ptr> nodes;     Graph(){}     Graph(size_t n) : nodes(n) {         for(auto node : nodes)             node = std::make_shared<Node>();     } };  Problem typename std::vector<Graph<T>::Node::Ptr> nodes; My compiler doesnot think Ptr is a valid type, here is the error type/value mismatch at argument 1 in template parameter list for ‘template<class _Tp, class _Alloc> class std::vector’  I can put the declaration of Node out of the Graph and make it a template to solve this problem, but why cannot this? System Info  Ubuntu 20.04 (WSL2) g++ (Ubuntu 9.3.0-10ubuntu2) 9.3.0  Already read

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


I always assumed that assigning computers to different workgroups was a way of effectively putting them on separate Windows networks. I just tried this, expecting computers in one workgroup to be invisible to computers in the other (and vice versa). Instead, all computers are still visible and accessible to one another.  If this isn't the purpose of changing workgroup names, what is?  EDIT: Ƭᴇcʜιᴇ007, this question is not a duplicate. I'm asking specifically what changing workgroup names achieves, not generally what workgroups are for. Could you please undo this?

In Microsoft Windows, what is the purpose of a Workgroup? I understand that a Domain allows the administration of security (user names, passwords, file access, etc.) to be centralized. But what does a Workgroup give you?


what sort of weight can I hang off a drywall screw stud?

I've always had the question of how much weight can a single screw into a drywall withstand?  For instance, I would like to do things like this:    It's hung with 5 screws. The whole thing weighs approximately 50kg (110 pounds) so we can say that each screw holds approximately 10kg (22 pounds).  The person who installed it said it was fine, but is it really?  Do somebody know a study or some numbers regarding how much weight this material can stand?  EDIT: Just to clarify, it's not screwed to the studs. It's screwed to the drywall.


public class Signup2 extends javax.swing.JFrame {  /**  * Creates new form Signup2  */ public Signup2() {     initComponents(); }  @SuppressWarnings("unchecked")   private void jTable1MouseClicked(java.awt.event.MouseEvent evt) {                                            int i=jTable1.getSelectedRow();     TableModel m=jTable1.getModel();     String reference_number;     reference_number=m.getValueAt(i,1).toString();     int no=0;     int n=0;String stm="";      try{         Class.forName("java.sql.DriverManager");         Connection con=DriverManager.getConnection("jdbc:mysql://localhost:3306/google_email","root","root");         Statement st=con.createStatement();         String q="select message,subject from message where reference_num='"+reference_number+"';";         ResultSet rs=st.executeQuery(q);                 while(rs.next()){                   readmessage.jTextField1.setText(rs.getString("Subject"));                   readmessgae.jTextArea1.setText(rs.getString("message"));               }        }        catch(Exception e){          System.err.println(e);       }      dispose();    readmessage rm=new readmessage();    rm.setVisible(true);     }                                       readmessage is the name of the jFrame  There is an error in this code in jtable1MouseClicked event. Actually, it's throwing a NullPointerException in the code:  jTextField1.setText("subject");  jTextArea1.setText("message");   Instead of setting in a field or area I just printed it and it worked. What is the possible reason for the error and how can I solve it?   error:    java.lang.NullPointerException     at Signup2.jTable1MouseClicked(Signup2.java:182)     at Signup2.access$100(Signup2.java:19)     at Signup2$2.mouseClicked(Signup2.java:69)     at java.awt.AWTEventMulticaster.mouseClicked(AWTEventMulticaster.java:270)     at java.awt.Component.processMouseEvent(Component.java:6536)     at javax.swing.JComponent.processMouseEvent(JComponent.java:3324)     at java.awt.Component.processEvent(Component.java:6298)     at java.awt.Container.processEvent(Container.java:2237)     at java.awt.Component.dispatchEventImpl(Component.java:4889)     at java.awt.Container.dispatchEventImpl(Container.java:2295)     at java.awt.Component.dispatchEvent(Component.java:4711)     at java.awt.LightweightDispatcher.retargetMouseEvent(Container.java:4889)     at java.awt.LightweightDispatcher.processMouseEvent(Container.java:4535)     at java.awt.LightweightDispatcher.dispatchEvent(Container.java:4467)     at java.awt.Container.dispatchEventImpl(Container.java:2281)     at java.awt.Window.dispatchEventImpl(Window.java:2746)     at java.awt.Component.dispatchEvent(Component.java:4711)     at java.awt.EventQueue.dispatchEventImpl(EventQueue.java:758)     at java.awt.EventQueue.access$500(EventQueue.java:97)     at java.awt.EventQueue$3.run(EventQueue.java:709)     at java.awt.EventQueue$3.run(EventQueue.java:703)     at java.security.AccessController.doPrivileged(Native Method)     at java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(ProtectionDomain.java:80)     at java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(ProtectionDomain.java:90)     at java.awt.EventQueue$4.run(EventQueue.java:731)     at java.awt.EventQueue$4.run(EventQueue.java:729)     at java.security.AccessController.doPrivileged(Native Method)     at java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(ProtectionDomain.java:80)     at java.awt.EventQueue.dispatchEvent(EventQueue.java:728)     at java.awt.EventDispatchThread.pumpOneEventForFilters(EventDispatchThread.java:201)     at java.awt.EventDispatchThread.pumpEventsForFilter(EventDispatchThread.java:116)     at java.awt.EventDispatchThread.pumpEventsForHierarchy(EventDispatchThread.java:105)     at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:101)     at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:93)     at java.awt.EventDispatchThread.run(EventDispatchThread.java:82)

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 am trying to understand the concept of event horizon and what really the word "event" means and have some questions. I apologize if the questions seem stupid or vague as I am not a physics student or professional: just someone who is curious.  As the black-hole sucks more and more mass, the gravity of the black-hole increases. Are things affected by this increased gravity not examples of events occurring due to changes (to the mass of the singularity) inside the (event horizon of the) black-hole ? In that case, isn't this an example of an event inside the black-hole influencing something outside it ?  Building on the same question: Couldn't gravity wave patterns during black hole collisions give us some insight into the geometry of the singularities inside the horizon ?  (Also, observing how the gravity envelope changes as mass (stars, planets, etc.) enter the horizon might provide clues on what is happening inside as the mass falls to the center. Also, If we are ever able to really observe closely and interpret BH collisions (probably even rarer), looking for changes to the gravity envelope past the moment when the two event horizons start merging could present interesting insights. However, I am not sure if we have such an advantage of observing (the changes in effects of gravity around) a BH from that many angles and at that precision today or not.)  Or is mass, somehow, also considered to be a property of the surface/event-horizon ?

My understanding is that light can not escape from within a black hole (within the event horizon).  I've also heard that information cannot propagate faster than the speed of light.  It would seem to me that the gravitational attraction caused by a black hole carries information about the amount of mass within the black hole.  So, how does this information escape?  Looking at it from a particle point of view: do the gravitons (should they exist) travel faster than the photons?


Using slices error:  list_one = cards_18[0::3] # from index 0 to end, add 3 list_two = cards_18[1::3] list_three = cards_18[2::3]

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


Let $a_1$,$a_2$,$a_3$,.......,$a_n$ be $n$ such that each $a_i$ either $1$ or $-1$.If   $a_1 a_2 a_3 a_4+a_2 a_3 a_4 a_5+......+a_n a_1 a_2 a_3=0$,  then prove that $4$ divides $n$.  I tried this for small n and also observed different specific cases such as $a_1=1$ $a_2=-1$ $a_3=1$ $a_4=-1$.... etc.   But I am unable to circumvent anyway. Any kind of hints and full answers will be appreciated. Thank you all in advance.

It is known that $a_1, a_2, a_3, ... , a_n \in \left\{-1, 1 \right\}$ and $S = a_1a_2a_3a_4 + a_2a_3a_4a_5 + ... + a_na_1a_2a_3 = 0$  Prove that $n \equiv 0\space(mod\space 4)$  I know this problem can be solved using number theory, but I am looking for a solution utilizing the concept of invariance.   I was able to identify an invariant of sorts: even if you change the sign of any $a_i$, the sum will still remain congruent to same number $mod \space 4$. It can be proved using this invariant that no matter what values you choose for each of the $a_i$, $S \equiv 0 \space (mod \space 4)$. It is not yet clear how I can prove the required statement using this result.


I've got quite a few questions about capitalizing words in titles. I don't know if it's proper to include many questions in one topic, but I couldn't find anything of the sort when I gave the rules a glance. I've been studying how words work in titles and I'd like to think I know most things, but there are a few cases that I can't wrap my head around, as I can't find any specific information on them myself.  EDIT: I've trimmed the amount of questions down from seven to three after checking out some suggestions. The suspected duplicate article helped me out a great bit, and the title case converter was a great help. However, I haven't found a straightforward explanation to any of these remaining questions:   Should the word "the" be capitalized after certain symbols, mainly the ampersand (&)? I haven't been able to find a clear answer to this, I've mostly left "the" without capitalization but for example, writing "KC & the Sunshine Band" looks a bit off to me, so I'm wondering if this is an exception case. How do you capitalize words before and after commas? For example, if there was a title called "Come on, Let's Travel", should the "on" be capitalized in this case, or would it be considered the last word of a phrase? And in another case, there's a track with the title of "You, on the Dance Floor". Should the "on" be capitalized after a comma, or is it still left uncapitalized? How do you capitalize hyphenated words? This has been an absolute mystery to me and I can't seem to find many rules on how to capitalize hypnehated words and I can't figure out how they work; sometimes it seems you need to capitalize both parts of the word and sometimes it isn't so.

Are there any concrete rules that say which words (parts of speech) in a title should start with a capital letter? What would be a correct capitalization for the title of this question?


Today a  in English language learners concerning tenses in a short sentence with multiple verbs. Basically it was, which is correct?   I thought you wrote poetry. I thought you write poetry.   My answer (in summary) was that #2 sounded better. Some did not like the answer, thinking the usage to be ungrammatical. We even had a friendly chat about it. Lambie and Gustavson did their best to convince me. I ended up saying that the only basis I could fully agree with them is if tense agreement were grammatically required.  I'm not asking for up-votes (go down-vote the answer, and even this question, if you want), but I chose to escalate the question to the PhD and expert folks here to see if that grammatical requirement actually exists.  Lambie's final comment  was:     OK, call it agreement, that's fine. "I'm thinking I will buy some chicken." She was thinking she would buy some chicken. ...   People had to leave before I saw a difference and could comment on it. In his final example, the chicken buying was a single act. It happened yesterday and has nothing to do with today, except maybe dinner. 🍗 However, if she happens to be a professional chicken buyer, then that remains true.  The state of her professional chicken-buyerhood does not change with midnight.  Nor does the potential poet in the original question. So, today:   I think you write poetry.   Tomorrow, what will be this thought about (tomorrow's) yesterday? Did I think you are an ongoing writer of poetry, or that you were someone who once wrote poetry?  So that is my case as to why two tenses might be grammatically used in a short sentence.  Am I wrong?

I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense?


I want to write a bash shell script, it can accept parameters, and the parameter has prompt, example,   ./test.sh --version=1.0   value 1.0 is the real parameter for my shell, and --version= is the prompt  is there any easy way to do it like this?

I wish to have long and short forms of command line options invoked using my shell script.  I know that getopts can be used, but like in Perl, I have not been able to do the same with shell.  Any ideas on how this can be done, so that I can use options like:  ./shell.sh --copyfile abc.pl /tmp/ ./shell.sh -c abc.pl /tmp/   In the above, both the commands mean the same thing to my shell, but using getopts, I have not been able to implement these?


I am looking for a way to dynamically set the urxvt window title based on the command input.  Let's take an example.  If I run mplayer http://66.197.229.245:8082 in an urxvt window, I would like the  title of this window to be set to mplayer http://66.197.229.245:8082 or even better Terminal | mplayer.  Or if I run journalctl -b I want the window title to be set to Terminal | journalctl -b or better Terminal | journalctl.  Is this possible?

My Bash Prompt is currently setting the xterm titlebar using the following sequence:  PS1='\033]0;\u@\h>\w\007'   Is there an easy way to display the current command in the titlebar. For example, if I am tailing a file using tail -f foo.log, I want my titlebar to say tail -f foo.log.


I recently bought a new laptop from Best Buy and decided to boot Ubuntu on it.  The installation went on without a hitch except for the fact that Ubuntu can't seem to connect to the wireless card.  I enabled 3rd party software during the installation process and also tried some of the suggestions here:  But no luck. Here is the Output of lshw -C network:   WARNING: you should run this program as super-user.   *-network UNCLAIMED               description: Network controller        product: Intel Corporation        vendor: Intel Corporation        physical id: 14.3        bus info: pci@0000:00:14.3        version: 30        width: 64 bits        clock: 33MHz        capabilities: bus_master cap_list        configuration: latency=0        resources: iomemory:600-5ff memory:601d164000-601d167fff   *-network        description: Ethernet interface        physical id: 1        logical name: enp0s20f0u7        serial: d2:63:8d:38:84:17        capabilities: ethernet physical        configuration: broadcast=yes driver=rndis_host driverversion=22-Aug-2005 firmware=RNDIS device ip=192.168.42.246 link=yes multicast=yes WARNING: output may be incomplete or inaccurate, you should run this program as super-user.   And Here is the output of lspci:  00:00.0 Host bridge: Intel Corporation Device 8a12 (rev 03) 00:02.0 VGA compatible controller: Intel Corporation Device 8a52 (rev 07) 00:04.0 Signal processing controller: Intel Corporation Device 8a03 (rev 03) 00:07.0 PCI bridge: Intel Corporation Device 8a1d (rev 03) 00:07.1 PCI bridge: Intel Corporation Device 8a1f (rev 03) 00:0d.0 USB controller: Intel Corporation Device 8a13 (rev 03) 00:0d.2 System peripheral: Intel Corporation Device 8a17 (rev 03) 00:12.0 Serial controller: Intel Corporation Device 34fc (rev 30) 00:14.0 USB controller: Intel Corporation Ice Lake-LP USB 3.1 xHCI Host Controller (rev 30) 00:14.2 RAM memory: Intel Corporation Device 34ef (rev 30) 00:14.3 Network controller: Intel Corporation Device 34f0 (rev 30) 00:15.0 Serial bus controller [0c80]: Intel Corporation Ice Lake-LP Serial IO I2C Controller #0 (rev 30) 00:15.1 Serial bus controller [0c80]: Intel Corporation Ice Lake-LP Serial IO I2C Controller #1 (rev 30) 00:15.2 Serial bus controller [0c80]: Intel Corporation Ice Lake-LP Serial IO I2C Controller #2 (rev 30) 00:16.0 Communication controller: Intel Corporation Device 34e0 (rev 30) 00:1d.0 PCI bridge: Intel Corporation Ice Lake-LP PCI Express Root Port #9 (rev 30) 00:1f.0 ISA bridge: Intel Corporation Ice Lake-LP LPC Controller (rev 30) 00:1f.3 Multimedia audio controller: Intel Corporation Device 34c8 (rev 30) 00:1f.4 SMBus: Intel Corporation Ice Lake-LP SMBus Controller (rev 30) 00:1f.5 Serial bus controller [0c80]: Intel Corporation Ice Lake-LP SPI Controller (rev 30) 55:00.0 Non-Volatile memory controller: Samsung Electronics Co Ltd NVMe SSD Controller SM981/PM981   Any Help would be much appreciated!

Please note that this question is specific to Intel WiFi adapters.  My laptop is an HP ENVY with an Intel AX201 Wifi Adapter. I've dualbooted Ubuntu with Windows.  AX201 WiFi adapter is not supported by latest Ubuntu 18.04 version, because Ubuntu 18.04 comes with Linux Kernel 5.0, whereas support for AX201 comes built-in in Linux Kernel 5.2+. Canonical claims that Ubuntu 18.04 will get Linux Kernel 5.3 sometime next year. However, I wont be able to wait that long.  I tried downloading and installing Kernel 5.2.14, but I cant go beyond Grub: I get the error:     error: you need to load the kernel first.   Other option is to download the Intel Backport Driver, which I tried. That didn't seem to work either. As per the tutorials, I've restarted frequently, but that didnt work either.  Also I'm not quite sure if Intel IWLWIFI Backport driver supports AX201 in the first place.  WiFi works while I'm booted in Windows.  What should I do?  Thanks in advance!  UPDATE  I tried out @Pilot6's answer, and it worked. Thanks!  I have one last question: I've read that if you upgrade the Kernel beyond what Ubuntu 18.4 supports, its kinda unsafe (which I read as prone to system crashes).  I dont want system crashes because I have only one partition (root) for Ubuntu, and any crash would likely mean all my data is lost. One method forward would be to split my Ubuntu partition into root and home.  So if I want to access WiFi on my device safely without risking any crashes, what should I do?  My understanding of Ubuntu and Linux may be wrong as they are built on forum answers only. Please correct me if Im wrong anywhere.


How come that output of following programm is "pankaj", I was expecting a compilation error like "can not modify a constant string"  #include<iostream> using namespace std;  void fun(const char *a) {   a = "pankaj";   cout  << a; }  int main() {   const char *ptr = "GeeksforGeeks";   fun(ptr);   return 0; }

Why does the following code in C work?  const char* str = NULL; str = "test"; str = "test2";   Since str is a pointer to a constant character, why are we allowed to assign it different string literals?  Further, how can we protect str from being modified?  It seems like this could be a problem if, for example, we later assigned str to a longer string which ended up writing over another portion of memory.  I should add that in my test, I printed out the memory address of str before and after each of my assignments and it never changed.  So, although str is a pointer to a const char, the memory is actually being modified.  I wondered if perhaps this is a legacy issue with C?


I am running Ubuntu 12.04 on an IBM T43 laptop.  I hadn't used the laptop for a few weeks and forgot the password so reset it using the info found on here but now after entering the password the screen just keeps asking for the password again ???  ls -l /home returns dr-x------  I can login OK as 'Guest' and use internet but cannot use my own personal login.  Any idea what is wrong and how to fix it?

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


I have this homework question.  "For any integer $a$ and $b$, prove that $\gcd(a,b) = \gcd(3a+5b,11a+18b)$."  I know that if $ g = \gcd(a,b)$   and   $h = \gcd(3a+5b,11a+18b)$   then   $g = h$   iff $g \leq h $ and $h \leq g$.  I successfully proved that $g \leq h$.   Now, to prove that $h \leq g$, I need to prove that $h\mid (a,b)$, but I can't seem to find how I should prove this.  $\because h = gcd(3a+5b,11a+18b) \Rightarrow h \mid (3a+5b)$   From here I'm stuck on how to get $a$ and $b$ seperate.   Any hint would be very helpful.   Edit: Since this question was marked duplicate and I was given these ,, links to check, I did check them and didn't find my answer because all of these questions have given that $gcd = 1$, whereas my question doesn't tell if $gcd = 1$ and furthermore these questions are a bit complex for me to understand since I'm a new learner of number theory.

I'm having problems with an exercise from Apostol's Introduction to Analytic Number Theory.     Given $x$ and $y$, let $m=ax+by$, $n=cx+dy$, where $ad-bc= \pm 1$. Prove that $(m,n)=(x,y)$.   I've tried to give a proof, but I suspect it's wrong (or at least not very good). I would be very thankful for any hints/help/advice!  My proof:     We observe that since $ad-bc= \pm 1$, $ad=bc \pm 1$, and $(ad,bc)=1$.   Now, $(a,b) \mid m$ and $(c,d) \mid n$ but      $$(a,b) = ((d,1)a,(c,1)b)=(ad,a,bc,b)=(ad,bc,a,b)=((ad,bc),a,b)=(1,a,b)=1.$$      Similarly, we determine $(c,d)=1$. So, $1=(a,b) \mid m$ and $1=(c,d) > \mid n$. But $(x,y)$ also divide $m$ and $n$. Since $(x,y) \geq (a,b)=(c,d)=1$, this implies that $(x,y)=m,n$. Hence   $(m,n)=((x,y),(x,y))=(x,y)$.


I have recently signed up with netflix and have followed procedures in updating chrome and set up user agent switcher but when I try to change playback settings in netflix to html5 the setting is not available.

Is there a way to stream Netflix content to my Ubuntu machine?


Due to some iCloud struggles, I had recently occasion to sign into and out of iCloud on OS X a few times recently.  Interestingly, when I have 2FA enabled on my iCloud account, OS X asked for the screen lock passcode to my iPhone when signing in to iCloud, and would not sign in without it (no .  After the initial sign in succeeds, it prompts for the iCloud password again, and this time asks for the 2FA code.    This was a surprising and unexpected part of the authentication flow.  Does anyone know why iCloud / OS X / iOS interact in this way?

During iPhone update to iOS 10.3.1, I was asked for my password using the correct machine name for my Mac mini. To be clear, the request was not for my iCloud password, my actual local user account password for macOS. This can also happen in the other direction - setting up a Mac may ask for verification for you to enter your iPhone / iPad passcode (and not your iCloud password)  I could not find any information about this kind of access. I was thinking it was security for iCloud and possibly related to two step authorization or two factor authorization. This is the first time I can think of that I entered a desktop password outside of that actual desktop.  I don't have a screen shot but I recall an implication that some files in my Mac are encrypted and need my password. '... need to enter the password for .'   Are there settings I can I control this assuming it's a legitimate part of iCloud setup process or iOS setup process?


After upgrading to Ubuntu 12.10, I have been unable to restart my Oracle virtualbox.   jan@jan-System-Product-Name:~$ sudo /etc/init.d/vboxdrv setup sudo: /etc/init.d/vboxdrv: command not found   Where do I go from here? Can anyone help, please?  I tried to install virtualbox via these commands:   echo "deb http://download.virtualbox.org/virtualbox/debian $(lsb_release -sc) contrib" | sudo tee /etc/apt/sources.list.d/virtualbox.list wget -q http://download.virtualbox.org/virtu...racle_vbox.asc -O- | sudo apt-key add - sudo apt-get update  sudo apt-get install virtualbox-4.2   Attempts to install via package manager vbox would not start. These error reports are received:      Because the USB 2.0 controller state is part of the saved VM state, the VM cannot be started.To fix this problem, either install the 'Oracle VM VirtualBox Extension Pack' or disable USB 2.0 support in the VM settings (VERR_NOT_FOUND).  Result Code:  NS_ERROR_FAILURE (0x80004005) Component:  Console Interface:  IConsole {db7ab4ca-2a3f-4183-9243-c1208da92392}    I installed the extension pack, no change in result.   I have added myself as user, but the error report says user must be added, when I redo add user, it says user is already added.   The following outputs were also received:         Failed to open a session for the virtual machine Nuwe skelm.   Implementation of the USB 2.0 controller not found!   I cannot access the USB 2.0 setting to disable it. Where do I go from here, please?

Since upgrading to Ubuntu 14.04, When I launch my VirtualBox virtual machine I get:  Failed to open a session for the virtual machine win7pro32bit. Implementation of the USB 2.0 controller not found! Because the USB 2.0 controller state is part of the saved VM state, the VM cannot be  started. To fix this problem, either install the 'Oracle VM VirtualBox Extension Pack'  or disable USB 2.0 support in the VM settings (VERR_NOT_FOUND).  Result Code: NS_ERROR_FAILURE (0x80004005) Component: Console Interface: IConsole {8ab7c520-2442-4b66-8d74-4ff1e195d2b6}   The solution to the  does NOT fix the problem:  sudo apt-get purge virtualbox sudo apt-get autoremove sudo apt-get update sudo apt-get install virtualbox   UPDATE: Also happens when upgrading VirtualBox itself to 5.0, within existing Ubuntu 14.04.


If I have a sequence $(a_n)_{n=0}^{\infty}$, and I have defined the exact same sequence, just for it to start at $n=1$, which means $(a_n)_{n=1}^{\infty}$, I have found the limit of $(a_n)_{n=1}^{\infty}$. My question: is there a theorem that shows that $\lim_{n \to \infty} (a_n)_{n=0}^{\infty} = \lim_{n \to \infty} (a_n)_{n=1}^{\infty}$? Here are the sequences for reference: $$ (a_n)_{n=0}^{\infty} =\left\{\begin{matrix} a_0=r & \\  a_{n+1}=\cos(a_n) &  \end{matrix}\right.$$ $$ (a_n)_{n=1}^{\infty} =\left\{\begin{matrix} a_1=\cos(r) & \\  a_{n+1}=\cos(a_n) &  \end{matrix}\right.$$ Thanks a lot!

I want to show that a sequence $(a_n:n \in \mathbb N)$ converges to a limit $L \in \mathbb R$ if, and only if, an N-th tail of the sequences converges to $L$ for some $N \in \mathbb N$. For each $N \in \mathbb N$, an N-th tail sequence can be defined as $(t_n:n \in \mathbb N)$ where $t_n := a_{N+n}$.  Using the definition of a limit for the sequence $(a_n:n \in \mathbb N)$, we have the following:  For every $0 \lt \epsilon$, there is a natural number $N_{\epsilon} \in \mathbb N$ such that for all $N_{\epsilon} \lt n$, $|a_n - L| \lt \epsilon$. But I'm not sure what to do next in order to show that the $N$-th tail converges. Which natural number should I choose for the $N$-tail? Any help would be much appreciated.


I understand you can probably just post a question and tag it as  to suggest one, but I was wondering what goes behind the scenes when determining whether or not a badge should be implemented? Are there things to keep in mind before suggesting a new badge?

Are there ever going to be more badges added, and possible to get?


Let $X$ be a metric space and $Y$ a topological space. Then for any map $f: X\to Y$, $f$ is continuous at point $x\in X$ if for every sequence $\{x_n\}\subset X$, $\lim_{n\to \infty}x_n=x\Longrightarrow \lim_{n\to \infty}f(x_n)=f(x)$. My question is, if we weaken the condition and let $X$ be a common topological space, does the extended proposition still hold? Thanks in advance.

We say that a function, $f: X \to Y$ ($X, Y$ are topological spaces) is sequentially continuous if $f(x_n)$ converges to $f(x)$ whenever $x_n$ converges $x$. Give an example of a function that is sequentially continuous but not continuous.  I tried letting $X$ be $\mathbb R$ with cofinite topology and $Y$ be $\mathbb R$ with discrete topology where $f$ is identity map but $f$ is neither sequential continuous or continuous. There are no simple solutions online since most use ordinal sets and we have not yet covered that in our topology class.


I tried to change permission but it cannot.it says permission denied and operation denied how can i change the mode.. i tried every thing..    I have tried using sudo, but it gave this error  sudo chown bin ns-allinone-3.21 sudo: error in /etc/sudo.conf, line 0 while loading plugin sudoers_policy' sudo: /usr/libexec/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins)

I'm logged into a server as user "ubuntu" and I've got files that look like this:  -rw-rw-r-- 1 www-data www-data 33150 2012-06-04 22:17 file-a.png -rw-rw-r-- 1 www-data www-data 36371 2012-06-04 22:15 file-b.png -rw-rw-r-- 1 www-data www-data 41439 2012-06-04 22:16 file-c.png   The ubuntu user is a member of the group www-data:  groups ubuntu   produces  ubuntu : ubuntu www-data   So shouldn't I be able to change other permissions since I have access to the file? I'm not an expert on the user/group stuff. So this is just perplexing me.  I'm trying to run:  chmod o-r *  I realize I can do it with sudo, easily, but I'm trying to understand why I can't modify the files without sudo.


I'm an eighth grader working with a graduate student on some math over the summer. He presented me with the following question: We have a cube formed of 27 small, congruent cubes. A worm sits in the central cube, and has the goal of going through every small cube exactly once. It can get from one cube to an adjacent cube only through the midpoint of the face; it cannot travel diagonally. Can this be accomplished?  After several attempts at this problem, I have been unable to find a method of solving it, and am currently trying to restrict the possibilities by figuring out which cube or class of cube (corner, center of a face, etc.) the worm has to finish its task in.   Before writing this question, I looked into the wood worm in a cube () problem that has already been asked here, but that problem had not in fact been given a clear answer and was closed for lack of important details.  I have been introduced to Hamiltonian Paths and Circuits, but these concern paths starting at a vertex of a graph; not the center.

A woodworm is sitting at the centre of a cube that's divided into 3^3 identical cubelets. The woodworm can go from the centre of one cubelet to the centre of another in any edge-parallel direction. The woodworm would like to eat its way through the cube such that it visits the centre of each cubelet exactly once. Is this possible?


I would like to ask for help regarding writting bibliography. In bibliography section the Latex compiler puts huge gaps between the words. I would be grateful if someone could tell me how to get rid off them.  The code:  \begin{thebibliography}{99}     \bibitem{tesla}     \emph{Model S $\mid$ Tesla}.Tesla [online].[cit. 2017-04-29]. Dostupné z: https://www.tesla.com/models  \end{thebibliography}

A picture is worth a thousand macros:    I don't blame LaTeX for having difficulty in formatting this entry.   What can I do, however, to alleviate the effects and avoid the Word-like indentation?   A related question suggested by the site is  which indeed produces a better aligned entry:   While I like the sane alignment, I'm not not very happy with the switch to a monospaced font (while it works in the regular text, in bibliographical entries it attracts too much attention and takes too much space).  Any other suggestions?  The entry for the above test bibitem is:  \begin{thebibliography}  \bibitem{anything-here} "Lorem Ipsum Society, \emph{dolor sit amet, consectetur}, May 2010 retrieved on Oct 16, 2010 from http://www.lorem-ipsum.com/whatever-here/about\%20something/here\%20takes/space\%20in\%20a\%20long/url\%20foobar.aspx   \end{thebibliography}


Find $m$ such that $\displaystyle\int_{-\infty}^\infty \frac{1}{(1+x^2)^m} \, dx$ is finite.  I tried to substitute $x$ with $\tan\theta$ but got stuck.

For what value of $C$ and $m$ can the following function be probability density function?  $$f(x)=C(1+x^2)^{-m}$$


There is so much information out there on Ubuntu, I’m not sure where to look.  I’ve been using some images for my odroid SBC, and older images used to have a file /etc/network/interfaces.d/eth0 where I would set a static ip address.  On newer images, that file is gone, and in fact there are no files in that directory at all.  Did something fundamental happen to the way interfaces are now configured?

I updated a virtual machine running Ubuntu server 15.04 to the just released new stable 15.10.  There were no apparent problems, but after reboot the machine lost its network connection. lspci showed the correct card and lsmod proved that the driver had been loaded.  Hints about editing or removing /etc/udev/rules.d/70-persistent-net.rules did not succeed (still no network, no new file), the famous /lib/udev/write_net_rules did not even exist.  I don't have much clue regarding udev and systemd, so it took me some time to find in /sys/class/net that the network interface name changed. It became ens32, which was renamed from eth0. After I changed /etc/network/interfaces network communication was enabled again.  But - why does this happen at all? And if it happens, shouldn't the interfaces file be updated automatically?  Now that I deleted the virtual network card and created another one, eth0 becomes eno16777728, which is not so, uhm, nice.  Should this behaviour (at least that of the upgrade procedure) be reported as a bug?  Furthermore, is /etc/udev/rules.d/70-persistent-net.rules obsolete now? And (although only partly related) what about /etc/udev/rules.d/70-persistent-cd.rules?)  Edit - additional question (after accepted answer) The dependency of /etc/network/interfaces from the actual interface name bothered me. I tried a new installation of *ubuntu in another virtual machine. To my surprise, /etc/network/interfaces contained a reference to the loopback device only. However, with my original VM this change prevented the network to come up. So what else do I need to change?  Edit Well, from another test I found that a new Ubuntu Server has the network interface card in /etc/network/interfaces, while XUbuntu has not. Maybe it is using network-manager or something else.


I know that the integral looks like like the anti-derivative of $\arctan$, but i don't know how to use this fact so I tried to use a fraction decomposition to: $$\frac{1}{(x^2+1)^2}$$ to solve the anti-derivative : $$\int \frac{1}{(x^2+1)^2}\, dx$$ so :$$\frac{1}{(x^2+1)^2}=\frac{A}{x^2+1}+\frac{B}{x^2+1}\iff \frac{1}{x^2+1}=A+B$$ $$1+0x^2=(A+B)x^2+(A+B)1$$ Thus I got this system of equations: $$\cases{A+B=1 \\ A+B=0}$$ Which is impossible. I also tried to use substitution but it didn't help me.

I am in the middle of a problem and having trouble integrating the following integral:  $$\int_{-1}^1\frac1{(1+x^2)^2}\mathrm dx$$  I tried doing partial fractions and got:  $$1=A(1+x^2)+B(1+x^2)$$  I have no clue how to solve this since it is obvious there is no way to cancel out either $A$ or $B$ to get the other variable. Please guide me.  Thank you.


The robber wouldn't say where he had spent all the money. The robber didn't say where he had spent all the money.   What's the difference between two sentences?

What is the difference between would not and did not?  For example:     I called my girlfriend but she wouldn't stop.   I called my girlfriend but she didn't stop.


I have a Huffman Tree, and a character, and I want to return what that character's encoding within the Huffman Tree should be.  I've implemented it using the breadth-first traversal method, and each time I'm checking the left and right tree, I'm checking if the tree's data is equal to character I'm looking for. Each time I go right or left, though, I add 0 or 1 to the encoding so far. Eventually, when I find the character equal to the tree's data, I return that tree's encoding value.  Code:      public static String findCharEncoding(BinaryTree<CharProfile> bTree, char character) {         Queue<BinaryTree<CharProfile>> treeQueue = new LinkedList<BinaryTree<CharProfile>>();          // Create a TreeWithEncoding object from the given arguments and add it to the queue         treeQueue.add(bTree);          while (!treeQueue.isEmpty()) {             BinaryTree<CharProfile> t = treeQueue.remove();  ->          if (t.getLeft().getData().getCharacter() == character) {                 return t.getLeft().getData().getEncoding();             }             if (t.getLeft() != null) {                 t.getLeft().getData().setEncoding(t.getLeft().getData().getEncoding() + "0");                 treeQueue.add(t.getLeft());             }              if (t.getRight().getData().getCharacter() == character) {                 return t.getRight().getData().getEncoding();             }             if (t.getRight() != null) {                 t.getRight().getData().setEncoding(t.getRight().getData().getEncoding() + "1");                 treeQueue.add(t.getRight());             }         }          // If it gets to here, the while loop was unsuccessful in finding the encoding         System.out.println("Unable to find.");         return "-1";     }   Which I've implemented as follows:          for (int i = 0; i < charOccurrences.size(); i++) {             char character = charOccurrences.get(i).getCharacter();              charOccurrences.get(i).setEncoding(findCharEncoding(huffmanTree, character));             System.out.println(charOccurrences.get(i).getEncoding());         }   CharProfile is a custom class that holds the character value, the probability of the character and the encoding.  It keeps returning a NullPointerExceptionError at the line if (t.getLeft().getData().getCharacter() == character) {, which I've indicated with an arrow. I've tried and tried, but I can't seem to figure out why, other than the fact that it's t.getLeft().getData() that's returning the error, not the whole thing, or t.getLeft(), but I still can't figure out why.

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?


My bike for 2 days started to squeal whenever I use my back brakes it has been really annoying and I am trying to fix it. Please give me any suggestion that can help this problem

I bought a Schwinn Frontier Sport few months ago and started riding happily. After a few weeks my front rim brakes started creaking. It's so annoying in public places. My rear brake doesn't produce any sound but isn't as powerful as the front brake.  The retailer says cleaning would solve the front brake's issues and I got it cleaned, but nothing changed. Is there something I can do something myself to fix this?


I'm helping a customer stand up an Azure environment and they decided to stand up a server (DC) on their own without asking for help.   The only access method is supposed to be IPsec, but they forgot to disable the Azure-assigned public IP while standing up the server, so their DC ended up public on the Internet with no firewall whatsoever - including Windows Firewall (disabled while troubleshooting other networking/replication issues).  The symptoms that led to this discovery were random account lockouts originating from Chinese IP addresses in the Security log on the domain controller.  I've since fixed the situation by re-enabling Windows Firewall, creating an Azure security group, and deleting the public IP so that it's secured by IPsec. I also recommended they just decommission that server entirely and spin up a new one.  But I'm still curious - what attack surfaces are there for a domain controller that has no firewall whatsoever on the open Internet? If they decide not to decommission it, is there anything to look for in terms of compromise?

This is a  about Server Security - Responding to Breach Events (Hacking)   See Also:                  Canonical Version I suspect that one or more of my servers is compromised by a hacker, virus, or other mechanism:   What are my first steps? When I arrive on site should I disconnect the server, preserve "evidence", are there other initial considerations? How do I go about getting services back online? How do I prevent the same thing from happening immediately again? Are there best practices or methodologies for learning from this incident? If I wanted to put a Incident Response Plan together, where would I start? Should this be part of my Disaster Recovery or Business Continuity Planning?   Original Version       2011.01.02 - I'm on my way into work at 9.30 p.m. on a Sunday because our server has been compromised somehow and was resulting in a    attack on our provider. The servers access to the Internet   has been shut down which means over 5-600 of our clients sites are now   down. Now this could be an FTP hack, or some weakness in code   somewhere. I'm not sure till I get there.      How can I track this down quickly? We're in for a whole lot of   litigation if I don't get the server back up ASAP. Any help is   appreciated. We are running Open SUSE 11.0.            2011.01.03 - Thanks to everyone for your help. Luckily I WASN'T the only person responsible for this server, just the nearest. We managed   to resolve this problem, although it may not apply to many others in a   different situation. I'll detail what we did.      We unplugged the server from the net. It was performing (attempting to   perform) a Denial Of Service attack on another server in Indonesia,   and the guilty party was also based there.      We firstly tried to identify where on the server this was coming from,   considering we have over 500 sites on the server, we expected to be   moonlighting for some time. However, with SSH access still, we ran a   command to find all files edited or created in the time the attacks   started. Luckily, the offending file was created over the winter   holidays which meant that not many other files were created on the   server at that time.      We were then able to identify the offending file which was inside the   uploaded images folder within a  website.      After a short cigarette break we concluded that, due to the files   location, it must have been uploaded via a file upload facility that   was inadequetly secured. After some googling, we found that there was   a security vulnerability that allowed files to be uploaded, within the   ZenCart admin panel, for a picture for a record company. (The section   that it never really even used), posting this form just uploaded any   file, it did not check the extension of the file, and didn't even   check to see if the user was logged in.      This meant that any files could be uploaded, including a PHP file for   the attack. We secured the vulnerability with ZenCart on the infected   site, and removed the offending files.      The job was done, and I was home for 2 a.m.            The Moral   - Always apply security patches for ZenCart, or any other CMS system for that matter. As when security updates are released, the whole   world is made aware of the vulnerability.   - Always do backups, and backup your backups.   - Employ or arrange for someone that will be there in times like these. To prevent anyone from relying on a panicy post on Server   Fault.