Like the Title, is this possible?   I only need the width and height, so loading the image into ram would be unnecessary.

Is there a cheap way to get the dimensions of an image (jpg, png, ...)? Preferably, I would like to achieve this using only the standard class library (because of hosting restrictions). I know that it should be relatively easy to read the image header and parse it myself, but it seems that something like this should be already there. Also, I’ve verified that the following piece of code reads the entire image (which I don’t want):  using System; using System.Drawing;  namespace Test {     class Program     {         static void Main(string[] args)         {             Image img = new Bitmap("test.png");             System.Console.WriteLine(img.Width + " x " + img.Height);         }     } }


What can be $P(0)$, when $P(x^2+1)=(P(x))^2+1$ and $P(x)$ is polynomial?  Let $P(0)=0$, then $P(1)=1$, $P(2)=2$, $P(5)=5$, $P(26)=26$, $P(677)=677$ ... and so on. Then $P(x)=x$, because all the points on $y=P(x)$ are $y=x$.  If $P(0)=2$, then $P(x)=(x^2+1)^2+1$ for the same reason.  But when $P(0)=3$, we have that $\lim_{x→∞}\log_xP(x)$ does not converge into an integer. So I think $P(x)$ cannot be a polynomial.  Then what are the values of $P(0)$ that makes $P(x)$ polynomial?

Find all polynomials $P$ such that   $$P(x^2+1)=P(x)^2+1$$


I've got the following class:  public class PopulateHasChildAccount {  public Boolean checkForChildren(Account acct) {     List<Account> childAccounts = [Select Id                                    From Account                                    Where ParentId = :acct.Id];     if(childAccounts.size() > 0) {         return True;     }     else {         return False;     } } }   ...and the following Trigger:  trigger PopulateHasChildAccountTrigger on Account (after update, after delete, after undelete) {  if(Trigger.isUpdate) {     for(Account a : Trigger.new) {         Account oldParent = new Account(Id = Trigger.oldMap.get(a.Id).ParentId);         Account newParent = new Account(Id = Trigger.newMap.get(a.Id).ParentId);         Boolean hasOtherChildren = PopulateHasChildAccount.checkForChildren(oldParent);          //more code             }         }     } }    }   But I'm receiving the following error when trying to save the Trigger: "Method does not exist or incorrect signature: PopulateHasChildAccount.checkForChildren(Account)"  I don't understand why. The class is public, the method is public and the class is instantiated. I'm very new to coding in general and Apex specifically. I keep seeing resolutions for this error saying to make the method static...but then I get an error saying constructors can't be static. In any case, why would it need to be static if I'm instantiating the class that's being passed into the method? (I hope that made sense...I'm never really sure.)

I have a call to a method in a class as follows:  String key1 = "test1"; String key2 = "test2";  long[] datalr = new long[] {}; datalr = TestClass.callerSub(key1,key2);   The test class is as follows:  public class TestClass {  Public TestClass { }  public long[] callerSub(string key1, String key2){  long[] datalr = new long[] {0,0};  datalr[0] = 2; datalr[1] = 3;  return datalr;  } }   I'm getting the following error in the first class:  Error: Compile Error: Method does not exist or incorrect signature: TestClass.callerSub(String, String) at line 54 column 12       which is the following line:  datalr = TestClass.callerSub(key1,key2);   The datalr data in the callerSub method is just an example above,  Any idea why?  Thanks


i am working with list insertion in map and not able to understand the insertion behaviour.  public class TestList {  public static void main(String[] args) {      String strarray[] = new String[5];      for(int i = 0; i < 5; i++ ){          strarray[i] = "Demo" + i;     }      Map<Integer, List<String>> cluesByText = new HashMap<Integer, List<String>>();     int j = 0;     for (String str : strarray) {          System.out.println(str);         List<String> s = cluesByText.get(str);         if (s == null) {             s = new LinkedList<String>();             cluesByText.put(j, s);         }          s.add(str);         s.add(str);         s.add(str);         s.remove(1);         // why it is storing without doing cluesByText.put(j,s);         j++;     }      //output is:      System.out.println(cluesByText);  } }   Problem  is  while doing  insertion  of list  into the map and then on changing the contents of list by insert/delete operation , it is getting reflected in the list which was stored in map in previous line.  final output coming on printing map contents is.  {0=[Demo0, Demo0], 1=[Demo1, Demo1], 2=[Demo2, Demo2], 3=[Demo3, Demo3], 4=[Demo4, Demo4]}   i am not able to understand why it happening in this way as  state of list is already been stored in map?

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


after running commandsudo apt upgrade i am getting the following error: `dpkg: error processing package libetonyek-0.1-1:amd64 (--configure):  package is in a very bad inconsistent state; you should  reinstall it before attempting configuration  Errors were encountered while processing:  libetonyek-0.1-1:amd64   E: Sub-process /usr/bin/dpkg returned an error code (1)`

I can't update my system because it freezes while installing a third-party update (zramswap-enabler)! Sometimes I get the following message in Update manager:  Could not initialize the package information An unresolvable problem occurred while initializing the package information. Please report this bug against the 'update-manager' package and include the following error message: E:The package zramswap-enabler needs to be reinstalled, but I can't find an archive for it.  I tried to remove the zramswap-enabler, but it's impossible because I get the following message: dpkg: error processing zramswap-enabler (--remove):  Package is in a very bad inconsistent state - you should  reinstall it before attempting a removal. Errors were encountered while processing:  zramswap-enabler E: Sub-process /usr/bin/dpkg returned an error code (1)  Actually I would really reinstall that package, but it is unable to do it! If I remove this third-party PPA then the system is warning me about a very very serious problem. So why can I not install/reinstall/remove/update this package and why freezes the updater if I try to update?


I've recently restored my interest on theoretical physics (I have a master degree in Electrical Engineering) and began my study with first volume of the Physics Course by Landau and Lifshitz. This is a very good and interesting book, and it just blows my mind (both in a positive and negative ways) - you spend really a lot of time trying to understand everything out of this textbook. Maybe someone can suggest somewhat sort of helping sidenotes for this book?

What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.?


why the following question is-> How to help them succeed? instead of How to help them TO succeed?

What is the correct way to use infinitive after the verb "help": with or without "to"?  For example:     Please, help me to understand this.   or:     Please, help me understand this.


I'm currently trying to adjust my document to the baseline grid and for that I want to change all margins of \chapter, \section, \subsection (and floats) etc. to multiples of the \baselineskip. I found that \titlespacing can do that, but it seems to generate errors.  \documentclass[paper=a5,pagesize]{scrreprt} \usepackage{titlesec} \titlespacing{\section}{0em}{2\baselineskip}{\baselineskip}  \begin{document}     \section{Test} % Missing number, treated as zero. \section{Test}                    % Illegal unit of measure (pt inserted). \section{Test}     Test \end{document}   I'm not sure what's happening here. I'm also getting Non standard sectioning command \section(titlesec) detected. Using default spacing and no format. warnings for all commands which suggests the packet might be incompatible with my class.  Is there any other way to do this?

I saw recepts from answers on  , and can I do this without titlesec, only with KOMA tools, f.e. via   \RedeclareSectionCommand[afterskip=<amount>,beforeskip=<amount>]{section} ? titlesec is fine, but it redefine some KOMA's features.    My MWE:  \documentclass{scrbook}  \usepackage{blindtext} \usepackage{atbegshi,picture,xcolor} %\usepackage{gridset}  % baseline grid \newcommand{\printbaselines}{%     \AtBeginShipout{%         \AtBeginShipoutUpperLeft{%             \color{red}%             \put(\dimexpr 1in+\oddsidemargin,             -\dimexpr 1in+\topmargin+\headheight+\headsep+\topskip)%             {%                 \vtop to\dimexpr\vsize+\baselineskip{                     \hrule                     \leaders\vbox to\baselineskip{\hrule width\hsize\vfill}\vfill                 }%             }%         }%     }% }%  \printbaselines  \begin{document}  \chapter{First} \section{Lorem I} \Blindtext[1] \section{Lorem II} \Blindtext[1] \section{Lorem III} \Blindtext[1]  \end{document}   I try set     \RedeclareSectionCommand[     beforeskip=-2\baselineskip,     afterskip=1\baselineskip]{section}       but it work only for first paragraph (and without \chapter), - on second paragraph syncing is lost.     I try use \vskipnextgrid from gridset after  \section but it not work with \chapter on some page with \section.     It is possible? (pdflatex)


I can't figure it out, minus 2 for me BUT for the 100th time, is it whom or which?  "...a group of people for whom I have the utmost respect for."  OR  "...a group of people for which I have the utmost respect for."

What is the correct relative pronoun for "government"? Which of the following phrases is correct? I am writing for an American [English] audience.     The Queensland Government, who licenses several casinos, ...   or     The Queensland Government, which licenses several casinos, ...


I have a Linux server which is compromised, I can see nasty looking perl scripts executing with root privileges. I want to get some data off it before I wipe it. How can I block all inbound and outbound traffic except for my ip? It's a Centos server I assume i can do this with iptables?  I'm aware a the server is rooted there is a possibility that attackers could have made changes on the server that would prevent this from working. Ill be testing to make sure and only have the server online for a couple of hours before it is nuked.

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.


I'm planning to use a  for a new 3D game engine I plan to work on, however I don't know how to approach the rendering side of things.  I can see two options here:   Every renderable game object has a RenderComponent, which stores a mesh and OpenGL-specific stuff like VBOs and VAOs. When the time comes to have update() called, it will use OpenGL to render itself. Every renderable game object has a MeshComponent. When it's time to render, the Renderer would go through a list of all MeshComponents, extract vertex and material information, and render it.   Which option would be most flexible if I want to implement things like post-processing (bloom, motion blur), skyboxes, LOD, blending/transparency or implementing a deferred renderer?

My E/C implementation is the basic one where Entities are just ID's, Components are data and Systems act on the Data. Right now I'm having trouble with object materials and rendering in general. For simple objetcs I have a ModelComponent, tied to a RenderSystem, ModelComponent has the vertex buffer ids that the render system uses. A simple MaterialComponent would probably have color or specular strenght, etc, but I wanted it to be flexible enough to allow for more than one render pass and general "effects" that are not as easy as a simple variable in the MaterialComponent.  Trying to solve these problems I came up with two solutions:  1 - Super-generic Material Component  Something like this:  struct Material : public Component {     ShaderData* shader;     std::vector<std::pair<std::string, boost::any>> uniforms;     [...] };   and in the render system I would loop and pass the uniforms to the shader. I suppose this would be slow, but fast enough for my purposes.  2 - Another layer of abstraction, MaterialData  Having a class to wrap specific materials, that could be inherited by whatever specialized  material, the base class would have something like void set_shader_constants(ShaderData* d) but the implementation is up to each class, and the MaterialComponent would have a pointer to a MaterialData object.  I'm not sure which approach I would prefer, but neither of these touch the subject of multiple passes, or other complex rendering techniques.  Any idea on how to accomplish this?


Sometimes I forget the exact name of a tool I'd like to use. Sometimes I remember parts of it, sometimes I only know what it's used for.  Is there a way to find out the name of the program from within the terminal?  E.g. search tool for "window positioning manipulation" -> wmctrl

As a Unix beginner, I often find myself wanting to know the name of the command that achieves a particular function I'm after. How can I go about finding out the name of the command, given a description of what it does?


I use,  egrep -rnw . -e "string"   a lot (in bash), but it would be nice to add some context to the returned results. This would be the line before and after it. Maybe the two lines before and afer it.   Is this difficult to do?   grep, egrep, pcregrep, etc. does not matter.  Thanks  PS. I just saw this:  which I didn't think of searching for "append".

Is there a way to output the neighbouring lines along with the line numbers while grepping the contents of a file? I'm trying to get outputs of the form:  $ ~/myscript.sh download file # 'download' being the pattern here 121: # and downloads with wget/curl, whichever is available. 122: download_file () { 123:  if which wget &>/dev/null; then ---------- 356: # Since the prerequisites are already installed, we may proceed 357: download_urls=("http://example.com/foo/bar.bz2" 358:                "http://d1.example.com/xyz/abc.tar.gz"   Of course, I know that I can get grep my pattern with the -n option and show some of the neighbouring lines from the obtained line number (say, by using any of the methods ), but is there a better way to do this?


In the Last Jedi, the Resistance, correctly assumes that      The First Order has a way of tracking them through hyperspace.   But why did they came to that conclusion, knowing that there is a technology that can signal your position across the entire galaxy?      Actually, Leia uses it so that Rey can find them   So why go straight to "a new technology has been developed" when the much simpler possibility "There is a tracker on one of our ships" (possibly hidden by a mole) was a valid possibility?

In The Last Jedi:     The Resistance fleet is tracked through hyperspace by the First Order after they make their jump away from their old base.   As soon as the FO ships appear, the Resistance immediately come to the (correct) conclusion as to the tech that was used.  Why would they assume the use of this tech, that they have never encountered before, as opposed to the more common technique of     tracking a ship through the use of a homing beacon.


I need to think of an example of a ring R with ideals I and J where I is an ideal of J and J is an ideal of R, but I is not an ideal of R.

If $R$ is a ring, J is an ideal in $R$, and $I$ is an ideal of $J$ (with $J$ considered as a ring), does it follow that $I$ is an ideal of $R$?  That is, is $I$ necessarily closed under multiplication by elements of $R$?  Surely $I$ is closed under multiplication by elements of $J$ (since $I$ is an ideal of $J$).  The "obvious" approach to proof fails so quickly that it must be false, that "an ideal of an ideal is not necessarily an ideal of the big ring".  Please provide a counterexample.  (Or a proof?)


I am curious one one would prove that a set of operators is "complete," which to my understanding means it can be used to represent all possible truth tables.  So normally if we had $\{\land,\lor, \lnot\}$ and a truth table what I do is look at where the outputs are true and then chain the expressions together with ors. For example in the truth table for XOR the output is true when either $p$ or $q$ is true but not both, so $(p \land \lnot q) \lor (\lnot p \land q)$.  Using this approach I think you can do it for any truth table so $\{\land,\lor, \lnot\}$ is complete.  Now let's say you want to show that some other set of operators are complete. Does it suffice to show that you can synthesize the $\{\land,\lor, \lnot\}$ operators?  For example let's say you asked me to prove:   Is $\{\land, \lnot\}$ complete? We can synthesize the missing "or" operation in terms of these two with with $p \lor q = \lnot(\lnot p \land \lnot q)$ Is $\def\nand{\barwedge} \{\nand\}$ (NAND) complete? Assuming $p \nand q$ is the same as $\lnot(p \land q)$ I can say $\lnot p = \lnot p \lor \lnot p = \lnot(p \land p) = p \nand p$, and then $p \land q = \lnot(\lnot(p \land q)) = \lnot(p \nand q) = (p \nand q) \nand (p \nand q)$. And if we absolutely needed $\lor$ we could just copy our example from earlier in terms of NAND: $p \lor q = \lnot(\lnot p \land \lnot q) = \lnot p \nand \lnot q = (p \nand p) \nand (q \nand q)$.   Am I way off base or is this a valid way to prove completeness? First by showing $\{\land,\lor, \lnot\}$ is complete via the process in my second paragraph, and then in the future, showing that any arbitrary set of operators can be used to synthesize $\{\land,\lor, \lnot\}$ (or if we wish to be minimal, $\{\land, \lnot\}$)?

For example $\{\land, \lnot\}$ apparently forms a functionally complete set as it can form any logical expression.  But I don't really know what this means or how you show it. Do we just show that some set is complete and then in the future if we have a new set, show that we can replicate the known operations with the new ones?  Do you have to find these strategically or is there a systematic way?


Correct me if I'm wrong, 'Gamora 2014' was last seen after she nut-kicked Quill and questioned Nebula if he is the one (her future lover).  Following the infamous 'Ironman' snap, we saw Thanos disintegrates into dust together with his minions.  Did 'Gamora 2014' suffers the same fate as 'Thanos 2014' too?  If no, does it makes sense, timeline wise, if this 'Gamora 2014' joined the third GOTG movie?

I noticed during the scene in Avengers: Endgame where, Quill and Thor are arguing over who's captain of the ship, Quill was looking at a picture of Gamora,       assumed to be (maybe accidentally?) dusted along with all the Thanos army by the Avengers' use of the Guantlet   Is it safe to say we still don't get Gamora back?


My cursor is currently at the end of Nicael's name, and the comment is long enough to send:    However, if I press enter with my cursor there, I can't send the comment - despite it being a valid comment. If I move the cursor to the non-user-ping text, I can press enter and send it. The same thing happens if the cursor is the the middle of the full name, or I am typing the name and it is partially complete - enough to show the auto complete:    This doesn't happen if the user I'm pinging has edited the post, and the auto complete doesn't show up:

Sometimes I want to post comments that include @-notifications but can't work the names into the comment text organically. In those cases, I write my comment out and then tack on a @JohnDoe at the end, which works just fine.  Well, it did work, until the otherwise-awesome new name autocompleter was introduced. Now I type out @JohnD and hit Tab, and the whole name appears, but I can't submit the comment by pressing Enter anymore. The Enter key just does nothing. And actually, it doesn't matter if I tab-complete the name or not.  I don't think it's just me because it happens on multiple computers, although they're both running Win7 Pro and recent Firefoxes. Also, I would understand — but disagree — if this was considered "not a bug, just reword all your comments that end this way."  EDIT: As the ever-intrepid pseudo-employee Tim Stone pointed out in the comments, what I initially reported is a special case of a more general problem: Enter submission of comments fails whenever the tab complete suggestions are being shown.


Suppose $X$ and $Y$ be metric spaces.Let $f:X\to Y$ be function which is Cauchy Continuous.Show that $f$ is continuous.  Cauchy Continuity:Let $X$ and $Y$ be metric spaces, and let $f$ be a function from $X$ to $Y$. Then $f$ is Cauchy-continuous if and only if, given any Cauchy sequence $<x_n>$ in X, the sequence $<f(x_n)>$  is a Cauchy sequence in Y.  I am planning to use sequential definition of Continuity but I am unable to produce a neat proof without completeness.Give me some idea!

Let $(X,d)$ and $(Y,\rho)$ be metric spaces and $f:X\to Y$ be a function and suppose for any Cauchy sequence $(a_n)$ in $X$, $(f(a_n))$ is a Cauchy sequence in $Y$.  Is $f$ continuous?  Let $f$ be continuous, is it uniformly continuous?


Sometimes, I miss a chrome notification. I want to see all notifications in some window or panel. Is this possible?

I get Chrome notifications from several websites and they work when I don't even have any tabs open for those sites.  But sometimes I get these Chrome notifications when I am not at my desk or looking at my laptop.  As some of these notifications are useful to me, I would like to be able to access any that I have missed.  Is there a way to view the notification history?


I have HP notebook with AMD Turion 64x2 processor with NVIDIA GeForce Go 6150 display adaptor. Which Ubuntu I can use 32 bit or 64 bit to dual boot with Windows 7?

What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit?


I would be very grateful for any help. I cant figure out why (probabilistic) public key encryption schemes can never provide perfect secrecy? Any Ideas?  Excerpt: In contrast to the private-key setting, perfectly-secret public-key encryption does not exist. (We stress that this holds regardless of how long the keys are and how short the message is.) In fact, given pk and a ciphertext c computed via c ← Enc_pk(m), it is possible for an unbounded adversary to determine the message m with probability 1.  (See comments for why this is not a duplicate.)

Assume there is a public-key encryption scheme $(KeyGen, Enc, Dec)$ with perfect correctness (i.e., for all messages M and valid key-pairs (PK,SK), we have $Dec_{SK}(Enc_{PK}(M))=M$).  Will there always be a function $A$ such that for all messages M and valid public-keys PK, $A_{PK}(Enc_{PK}(M))=M$?  In other words, can a computationally unbounded adversary decrypt the message, having only the public key?


Question     Suppose that f is bounded on $[0,b]$, and suppose $\int_{c}^b f $ exists for all $0<c<b$. Show that  $\int_{0}^b f$ exists.   I first think that consider the interval $[b/n,b]$ for $n\ge2$.  Since integrable for $[b/n,b]$, if I denote the set $A_n$ as the set of discontinuities for $[b/n,b]$.  By Lebesgue's theorem, measure of $A_n$ is zero.  Since countable union of measure zero set has measure zero, I can integrable over [0,b].  But I think this approach is wrong since $\cup_{n=2}^{\infty}[b/n,b]=(0,b]$.  Is this really wrong? If not, I can tell that f is integrable over (0,b]?  help me to solve this problem.  Note that here the integration is Riemann integration, not Lebesgue integration.

If $f$ is bounded by $M$ on $[a, b]$ and if the restriction of $f$ to every interval $[c, b]$ where $c$ in $(a, b)$ is Riemann integrable, then $f$ is Riemann integrable and that $\int _c^b f \to \int_a^b f$ as $c \to a+$.  I am stuck with this problem.


I am trying to solve for the variance of $x[n]$, a time series process.  $$x[n] +a_1x[n-1]=w[n]$$where $w[n]$ is white noise with zero mean and variance $\sigma^2_v$. Also $|a_1|<1$.  I am aware that the equation can be solved using the Yule Walker Equations, but I was trying to solve it brute force using expectation.  Here is what I did:  Take the z-transform of the process, $$X(z) + a_1X(z)z^{-1} = W(z)$$ Solving for the system function, $$ H(z) = \frac{X(z)}{W(z)} = \frac{1}{1+a_1z^{-1}}$$ Inverse z-transform, $$h[n] = (-a_1)^nu[n]$$ Using convolution, $$x[n] = \sum_{k=0}^{n-1}(-a_1)^kw[n-k]$$ Solving for the variance, $$E[x[n]x^*[n]]=E[\sum_{k=0}^{n-1}(-a_1)^kw[n-k]\sum_{l=0}^{n-1}(-a_1)^lw[n-l]]$$ $$E[x[n]x^*[n]] = \sum_{k=0}^{n-1}(-a_1)^k\sum_{l=0}^{n-1}(-a_1)^lE[w[n-k]w[n-l]]$$ Since w[n] is a white noise process, $$E[w[n-k]w[n-l]] = 0, k\neq l $$ $$E[w[n-k][w[n-l]] = \sigma^2_v, k=l$$ So the expectation becomes, $$E[x[n]x^*[n]] = \sum_{m=0}^{n-1}(a_1^2)^m \sigma^2_v$$ Therefore, $$Var[x[n]]= \sigma^2_v \frac{1-(a_1^2)^n}{1-a_1^2} $$  But this is not correct, this answer is nonstationary, and we should expect a stationary solution for the zero mean white noise.  The correct answer is $\frac{\sigma^2_v}{1-a^2_1}$  It would be very helpful if someone could point out what I did wrong. I would like to solve this problem using this method. That way I can more appreciate using Yule-Walker equations. Thank you!

Consider a stochastic process $\{X_t, t = 1, 2, \ldots\}$ following the model $$X_t = \alpha X_{t-1} + e_t,$$ where $e_t \thicksim f$.  Can I say that the distribution of the initial point, $X_1$, is the same as $f$? Can I say that the stationary marginal density, if it exists, of $\{X_t\}$ is same as $X_2 (\stackrel{D}{=}\alpha X_1 + e_2)$?  I think that the stationary marginal density, if it exists, of $\{X_t\}$ is the same as $X_2$, but not necessarily same as $X_1$.


Is the word "dude" becoming gender neutral?  I don't think so, however, has modern usage changed?  Are there some recent examples of "dude" being used to refer to a woman or group of women?

OK . . . another one similar to   "Dude" is masculine; what is the feminine version?  The usage I'm thinking of is that "dude" nowadays is used primarily as a way to address a person very colloquially, e.g.:   "Dude, why are you squirting rubbing alcohol on the grill to start it up?" "Dude, pass me a brew."   Again as in the other "guys" case, it might be culturally acceptable to say "dude" to a female, but I'm not sure, and it feels a little wrong (and has for 30 years).  So what are some suggestions for acceptable female-gendered alternatives?   babe: might work, but sounds a little too diminutive (or does it?) dudette: cute, but hasn't caught on (but could it?)   Australians have "bruce" and "sheila" (I hear from the movies) but that just doesn't fly in AmE (and maybe that's already out of fashion).  What do Californians say (as "dude" in my description seems to come from there)? What do the surfers say?  Any suggestions? It may be the suggestion is that there is no perfect parallel.


I had this question where it was given $$a_n > 0$$ and $$\sum a_n$$ is divergent and I was to prove that $$\sum\frac{a_n}{1 + na_n}$$ diverges too, to be frank I could not make any worthy headway on this problem, so any ideas ?

A question from Rudin (Principles) Chapter 3:     Let $a_n\geq0$ and $\sum a_n$ diverges. What can be said about convergence/divergence of $\sum\frac{a_n}{1+na_n}$?   This one is being recalcitrant. Given that $x>y$ implies $\frac{x}{1+nx}>\frac{y}{1+ny}$ and when $a_n=1/n\log n$ the sum in question diverges, it seems plausible that in general the sum will always diverge, but I can't get a proof out. If it does diverge, it does so pretty slowly as $$\frac{a_n}{1+na_n}=\frac{1}{n}-\frac{1}{n+n^2a_n}\leq\frac{1}{n}.$$


All of the ways I have heard of to measure the passage of time involve measuring some sort of motion (e.g. vibrations of a cesium atom, movement of the hands on a clock, etc.).  Can the passage of time be measured without reference to any motion?

Imagine a perfect vacuum devoid of all matter and radiation. Irrespective of whether such a space can even exist, my intuition tells me that time would not exist within such a space. What this thought experiment tells me is that the human concept of time is basically that it's a measure of motion. Whether its a car speeding down a highway, skin on your face as the years go by, or photons, it's really all about motion. Now what about something like a gravitational field? Could that also be excluded from acting within a perfect vacuum?


Taylor Expansion of $\log(\frac{1+z}{1-z})$ around $z=0$  But $\log(1+z)=\sum_{n=1}^{\infty}(-1)^{n+1}\frac{z^n}{n}$  How can I continue from here?


when iuse the konsole for a period of time I sometimes have to scrollup to remind myself what has been going on but most of the text is green on black, warnings are purple and error messages are red.  It would be much easier to find my way around if text I type and or the prompt showed in a different color.

There are a number of tutorials/posts online (e.g. ) about how to customize your prompt in bash by setting PS1.  Is there a way to customize the color/bolding of the command I type?    In other words, as an example lets say that I wanted a green prompt, a bold blue command, and then output in whatever colors would be default.  In the example below, I already know how to make "joe>" show as green, blue, bold, whatever by setting PS1.  But is there a way I can I make git status show as bold for example?  joe> git status # On branch master # Your branch is ahead of 'origin/master' by 2 commits. # ...


i am taking a C pointer course on  this is the code in C: #include<stdio.h> int SumOfElements(int A[]) {     int i, sum = 0;     int size = sizeof(A)/sizeof(A[0]);     printf("SOE size of A = %d, size of A[0] = %d\n", sizeof(A), sizeof(A[0]));     for(i = 0;i< size;i++)     {         sum+=A[i];     }     return sum; } int main() {     int A[] = {1,2,3,4,5};     int total = SumOfElements(A);     printf("Main size of A = %d, size of A[0] = %d\n", sizeof(A), sizeof(A[0]));     printf("Sum of elements = %d\n", total); }  according to the output should be:  instead this code i got the output:  according to the tutorial he explained that when the complier see an array as function argument it does not copy the whole array, it just creates a pointer variable instead of creating the whole array. so in this case the compiler just copy the address of the first element in the array of the calling function(which is the main function). so the size of A in 's code is 4 which makes sense. but why my output of sizeof(A) is 8?

First off, here is some code:  int main()  {     int days[] = {1,2,3,4,5};     int *ptr = days;     printf("%u\n", sizeof(days));     printf("%u\n", sizeof(ptr));      return 0; }   Is there a way to find out the size of the array that ptr is pointing to (instead of just giving its size, which is four bytes on a 32-bit system)?


I didn't know the concept of domain/page authority in SEO until 1 hour ago. We have been blocking bots, crawlers, spiders and scanners in general directly from Apache through ModSecurity rules (custom rules).  We are only allowing bots from Google, Bing, Yahoo and other third party tools, but we block automated tools, risky countries (like Rusia, China, Ukraine, etc.), risky IPs and others since we've had negative traffic experiences and attacks in the past. Everything works fine now, but I'm afraid this can affect how some tools measures DA to all the domains we are hosting.  So, blocking bots affects DA results, like the ones in this page?   Thank you.

Google's new webmaster tools has a  section 'Index coverage'>'Excluded'>'Submitted URL not selected as canonical'.  I am getting 3 internal links in the section "Submitted URL not selected as canonical" of my website.   am not sure why these internal links are showing up there.  I had updated canonical tags for these 3 links.  (I am not sharing links cause may be my account marked as spam)   has some information about it, but doesn't say how to fix it:     Submitted URL not selected as canonical: The URL is one of a set of duplicate URLs without an explicitly marked . You explicitly asked this URL to be indexed, but because it is a duplicate, and Google thinks that another URL is a better candidate for canonical, Google did not index this URL. Instead, we indexed the canonical that we selected. The difference between this status and "Google chose different canonical than user" is that, in this case, you explicitly requested indexing.


I am making a new PC and I am going to see if steam works on ubuntu before installing windows 10. Because in the past, Steam hasn't worked on my ubuntu engines. So if it dosen't work, I want to wipe the SSD and replace ubuntu with windows 10. Like ubuntu, can you wipe the disk and install in the windows setup?

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


What is the formal name for a circle with a line through it (often red in color) indicating that something behind the line is "off-limits"?    For example, this sign indicating that one should not touch:

When my daughter asked me and my husband about a No Smoking sign, we explained that it means no cigarettes are allowed.  (We had to explain cigarettes to her too.)    Unfortunately, she now thinks that the red circle and diagonal line are called a "cigarette", so she'll talk about the cigarette in the No Parking sign:    Is there a name we can teach her for the red circle and slash?


I'm integrating Chat zendesk for my android app & I got this error NullPointerException: Attempt to invoke virtual method 'java.lang.String com.zopim.android.sdk.model.VisitorInfo.getEmail()'.  Any one know about it please let me know the solution. Thank you in advance.

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 do multivariate regression analysis for a dependent variable. unstandardized coefficient B for one of the independent variables was  2.314E-005 ,standardized coefficient Beta was 0.051, CI (0.000- 0.000), p=0.409. i want to know what is the this abnormal value of unstandardized coefficient 2.314E-005 means ?

I have a problem with the interpretation of a test result in which the p-value is 8.6e-28. How should it be interpreted? What is the e for?  Specifically, I used White's Test for the homoscedasticity assumption of a linear regression:  White's general test statistic :  150.0535  Chi-sq( 9)  P-value =  8.6e-28


In Relativistic Quantum Mechanics, Bjorken and Drell state that expanding the square root in the equation $$-\hbar^2\frac{\partial^2\psi}{\partial t^2}=\sqrt{-\hbar^2c^2\boldsymbol{\nabla}^2+m^2c^4}\psi$$ would result in a non-local wave equation. What exactly do they mean by this? One could argue that in order to compute $\psi$'s spatial derivatives at a certain point in space-time up to arbitrary order, one has to know the behavior of $\psi$ in points arbitrarily far from the point of interest, even if there is no world line linking those points. But if we were to solve a local equation such as the Dirac equation, we could do that nonetheless. Accordingly, I think there must be a deeper reason for the non-locality that Bjorken and Drell warn for.

The Wikipedia  has a derivation of the Klein-Gordon equation.  It gets to this step:  $$\sqrt{\textbf{p}^2 c^2 + m^2 c^4} = E$$  and inserts the QM operators to get  $$\left( \sqrt{ (-i \hbar \nabla)^2 c^2 + m^2 c^4 } \right) \psi = i\hbar\frac{\partial}{\partial t} \psi$$  The article then says     This, however, is a cumbersome expression to work with because the differential operator cannot be evaluated while under the square root sign. In addition, this equation, as it stands, is nonlocal.   To fix this, the first equation is squared instead to get  $$\textbf{p}^2 c^2 + m^2 c^4 = E^2$$  after which the QM operators are inserted and the expression is simplified to get  $$-\hbar^2 c^2 \nabla^2 \psi + m^2 c^4 \psi = -\hbar^2 \frac{\partial^2}{\partial t^2} \psi$$  A couple things I don't understand.  First, are the solutions to this differential equation not exactly the same as the solutions to the first differential equation?  Both sides of the starting equation were squared, so it seems to me that regardless of the particular form of the resulting differential equation, both of them should have the exact same set of solutions.  Secondly, why is the first differential equation cumbersome to work with?  It seems like it would in fact be easier to work with, since the operator under the square root could be expanded in terms of a Taylor series and then you have an equation that is first order in time.  And finally, can someone elaborate on what nonlocal means? The linked article on the Wikipedia page didn't entirely help me understand it.


The problem that I am running into is that 'data' variable is not being set whenever I try to read in the json object. I only get an empty set. Below I have the code and the outputs.   import json  data = []  def add(name, amt):   data.append({"ticker": name, "amount": amt})  def write():   with open('portfolio.json', 'w') as file:     json.dump(data, file)  def load():   with open('portfolio.json', 'r') as file:      data = json.load(file)  def main():   choice = input("Do you want to add vals? (y/n): ")   if choice == 'y':         add('btc', 43.2)     add('xrp', 256.5)     add('xmr', 655.3)     print(data)     write()    if choice == 'n':     load()     print(data)  main()   Output 1:  Do you want to add vals? (y/n): y [{'ticker': 'btc', 'amount': 43.2}, {'ticker': 'xrp', 'amount': 256.5}, {'ticker': 'xmr', 'amount': 655.3}] Press any key to continue . . .   So now the file 'portfolio.json' contains the json object with all of the data, correct? So, now when I try to read that in, this is what I get:  Output 2:  Do you want to add vals? (y/n): n [] Press any key to continue . . .   As you can see, the data variable is just an empty set, and it is not taking in the data. However, if I were to go inside the load function and print out the data variable, I would get my value.

How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access?


I have a process that runs on a @reboot cron job.  The process needs to run an executable file.  I have noticed that I have to put the executable in /usr/bin/.  I can't just put it in a folder in my $PATH list.  So my question is, if processes run by cron jobs do not look in the $PATH list of directories, where do they look?  Obviously they at least look in /usr/bin/.

Cron doesn't use the path of the user whose crontab it is and, instead, has its own. It can easily be changed by adding PATH=/foo/bar at the beginning of the crontab, and the classic workaround is to always use absolute paths to commands run by cron, but where is cron's default PATH defined?  I created a crontab with the following contents on my Arch system (cronie 1.5.1-1) and also tested on an Ubuntu 16.04.3 LTS box with the same results:  $ crontab -l * * * * * echo "$PATH" > /home/terdon/fff   That printed:  $ cat fff /usr/bin:/bin   But why? The default system-wide path is set in /etc/profile, but that includes other directories:  $ grep PATH= /etc/profile PATH="/usr/local/sbin:/usr/local/bin:/usr/bin"   There is nothing else relevant in /etc/environment or /etc/profile.d, the other files I thought might possibly be read by cron:  $ grep PATH= /etc/profile.d/* /etc/environment /etc/profile.d/jre.sh:export PATH=${PATH}:/usr/lib/jvm/default/bin /etc/profile.d/mozilla-common.sh:export MOZ_PLUGIN_PATH="/usr/lib/mozilla/plugins" /etc/profile.d/perlbin.sh:[ -d /usr/bin/site_perl ] && PATH=$PATH:/usr/bin/site_perl /etc/profile.d/perlbin.sh:[ -d /usr/lib/perl5/site_perl/bin ] && PATH=$PATH:/usr/lib/perl5/site_perl/bin /etc/profile.d/perlbin.sh:[ -d /usr/bin/vendor_perl ] && PATH=$PATH:/usr/bin/vendor_perl /etc/profile.d/perlbin.sh:[ -d /usr/lib/perl5/vendor_perl/bin ] && PATH=$PATH:/usr/lib/perl5/vendor_perl/bin /etc/profile.d/perlbin.sh:[ -d /usr/bin/core_perl ] && PATH=$PATH:/usr/bin/core_perl   There is also nothing relevant in any of the files in /etc/skel, unsurprisingly, nor is it being set in any /etc/cron* file:  $ grep PATH /etc/cron* /etc/cron*/* grep: /etc/cron.d: Is a directory grep: /etc/cron.daily: Is a directory grep: /etc/cron.hourly: Is a directory grep: /etc/cron.monthly: Is a directory grep: /etc/cron.weekly: Is a directory /etc/cron.d/0hourly:PATH=/sbin:/bin:/usr/sbin:/usr/bin   So, where is cron's default PATH for user crontabs being set? Is it hardcoded in cron itself? Doesn't it read some sort of configuration file for this?


My mother tongue is Latin-based so I'm used to differences in male/female for neutral words. I don't know how this would work with some words in English.  If the "victim" in a sentence is neutral (ie: it could be either a man or a woman, in this context it makes absolutely no difference and we don't know if it's a man or a woman), should I use "his" or "her"?  My instinct would tell me to use his but I seem to remember encountering her in such a neutral situation before.  EDIT:  Here is the exact sentence (it's from a IT Security paper I'm writing):     Finally the paper will demonstrate how the attacker may control the   contents of the web pages delivered to the victim as well as redirect   his downloads towards malicious files.   As you can see I used his here, is that correct?

Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end.


Within MCU canon, what was Yondu's motivation to travel to Earth, only abduct Quill, and then raise him as his son?  It seemed to me that Yondu and his crew of Ravagers had more rewarding things to do if they were going to travel all the way to Earth, and had more rewarding uses for Quill than making him an adopted son. Or am I missing something?

During the movie, we learned that Ego tried to reproduce the Celestial gene by having a lot of children and then having them delivered to him. I am not sure if Yondu was contracted for all of them but he definitely delivered at least a few of them since he broke the ravager code and got banned for dealing in kids.  My question is: why did he stop with Peter? Was Peter the last one on the contract or did he keep on delivering some but just not Peter?  Also, why didn't Ego seek out Yondu to get his kid back?  I don't think this was touched on in the movie. This was slightly mentioned here () but that is not answering my question.  I think Yondu said it was because he could get to places where the Ravagers could not since he was a kid but that would have been true with all the others kids he abducted for Ego.


Should I use is or are?, Personally I think the correct answer is using is but I have a little doubt in my mind. Can someone help me out? Thank you

The furniture in our classroom ___ uncomfortable.   Should I use is or are here? I found on the internet things like all of furniture is and house full of furniture is.  But nothing about my example. Personally I think that correct is is, but website where I found this says that correct is are. So I'm writing here to find out.


I've been reading this question on StackOverflow , but I'd like to know if changing the favicon daily mess up any SEO or raise any concerns with search engines?   I am using Ubuntu's Apache.

I'm looking for advice about favicons and their impacts on search engines. Recently I noticed a site which changes its favicon every time you load another page without losing overall recognition of the favicon style. I'd like to incorporate this into my site as well but am I taking any SEO risks here?


I added a comment to the top answer , I but couldn't get the code to format correctly. I made sure I was entering the four spaces.  The comment was only editable for 5 minutes, and it now appears too late to fix it. What should I do? The comment is important in explaining why I unaccepted the answer.

I see some people write comments that are for example - in italics.  I do not see any way of doing that while writing my comments. Why is it so?


Is the infinity of irrational numbers equal to the infinity of rational numbers? Or is one is greater than other? And what is the proof? I could not find out a rigorous proof about this.  P.S. I am interested in which set of numbers is more dense - rational or irrational. Other similar questions do not consider the density of the numbers.

There exists an infinite amount of rational and irrational numbers. But is there more irrational numbers than rational? And if so can a ratio of one to the other be calculated?


Can anyone point me to where the formula is for calculate the values that populated a t-table?  For example, I am trying to figure out how I find the critical t-table values for a unique confidence interval (say 43%)?

I am searching for the formula that will generate the critical values in a t-test instead of using a static critical value table.   I am programming in Java and not R so the qt() function is not what I am looking for.  Any help is appreciated.


I'm a druid looking to select just one feat to boost my CMD. No level restrictions. I have found Defensive Combat Training but is there anything that increases CMD even more?

I'm looking for feats or other permanent class features that can increase my CMB for purposes of grappling with my druid character. The grappling would be almost always occurring while in wild shape form.   I do not want gear suggestions (permanent or consumable), spells, or other temporary buffs. I would like to know of feats for even higher levels which I do not qualify for at the moment 1–20 level.   Current stats:  Level 2 Human Druid Str 18, Dex 13, Con 14, Int 9, Wis 15, Cha 7 Feats: Improved Initiative, Improved Spell Sharing


I need help with solving the following diophantine equation: $$x^2+y^2=2018$$  Thanks a lot in advance!

Can $2018$ be written as a sum of two squares? If it can be, what are the numbers?  I know the first answer is it can be because $2018=2\times1009$ and $1009\equiv 1 \pmod{4}$. But I cannot find the numbers.


How to prove the following version of the Hilbert basis theorem:     $R$ is Noetherian if and only if $R[|x|]$ is Noetherian.   Of course, in view of the isomorphism: $$\frac{R[|x|]}{(x)~R[|x|]} \simeq R$$ one direction follows. I'm struggling to come up with a proof for the converse. Any help is much appreicated.

Let $R$ be a Noetherian ring. How can one prove that the ring of the formal power series $R[[x]]$ is again a Noetherian ring?    It is well-known that the ring of polynomials $R[x]$ is Noetherian. I try imitating the standard proof of the fact by replacing "leading coefficients" by "lowest coefficients", but it does not work.


Some months ago, I could see who closed a question, but not anymore? I screenshot .

Megan has written a .  I've seen a bunch of discussion about it on chat - but it feels like having it purely on the blog is a little clunky.  So specifically - what does the MSE community feel about the proposed post notices for closed questions? What's missing, or what should be added? What are some of the lessons we've learnt that could be helpful here?


A local teen gets the high score on an arcade game, and he wins a real life replica of the main enemy in the game. It arrives at his door one day. At first he and his (I'm pretty sure girlfriend, maybe sister?) are enamoured with it, but then it tries to kill them and their friends and family. There is one scene I remember where the robot picks up a long kitchen knife in its arm, and it rotates quickly.   I thought the movie was called "Hover" for some reason, but that's not it. The robot was short and red I think.

I'm looking for a movie that was set in the US, and all the characters (including the robot) spoke English.  I can't recall the exact plot, but mostly it was about an innocent game robot that shoots small objects for fun and becomes dangerous, because its AI made a wrongful choice about 'winning the game'. The robot starts to arm itself with more dangerous objects (not sure but knives and stuff) and starts to attack people.  It was overall supposed to be fun and adventure movie for kids. Color movie, and probably made in 80~90's.   There is a recurring scene when the robot detects an aggressor, it scans and loudly announces "enemy one, enemy one". The robot was somehow looking similar to Wall-E, and had a saucer-like head part.


I have a tourist visa B2 and I am planning to visit the US in march 2018, my passport is valid for 10 years but my visa will expire on July 2018. I would like to know if there are any limitations of entering the US with a visa validity of less than 6 months. thanks!

My visa is expiring in May 2016 and I want to visit USA in March to 2 weeks on a business trip. Can I run into any troubles or there be any issues in getting I-94 upon reaching USA.


how would I find the mgf of a gamma rv with parameter k > 0 and λ > 0 ?

If I have a variable $X$ that has a gamma distribution with parameters $s$ and $\lambda$, what is its momment generating function.  I know that it is $\int_0^\infty e^{tx}\frac{1}{\Gamma(s)}\lambda^sx^{s-1} e^{-x\lambda}dx$ and the final answer should be $(\frac{\lambda}{\lambda-t})^s$, but how can i compute this?  P.S. I know that there are other questions on this site about the MGF of the gamma distibution, but none of those use this specific definition for the density function of a gamma distribution. And I would like to see it with this one. Thanks a lot!


Can anyone explain how to calculate the remainder for types of problems like this:     $2^{2131312213123}$ divided by 100      $13^{6601}$ mod 77

How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and .


I need to integrate,  $$I=\int_0^\infty\int_0^\infty \frac{e^{-(x+y)}}{x+y}\ dx\ dy$$  I tried using integration by parts for the first integrand but I am getting its value as zero.

Question : The integral   $$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} \mathop{dx}\mathop{dy} $$  is   (a) infinite   (b) finite but can not be evaluated in closed form   (c) 1  (d) 2 .  I tried substituting $u=x+y$ and $v=y$ that led me no where . I'm not even sure about convergence of integral .Any help would be greatly appreciated .


Can someone please verify whether my proof is logically correct? :)     Let $p\geq 2$. If $2^{p}-1$ is prime, then $p$ must also be prime.   Proof:  Let $p=a\cdot b$ with $a>1$ and $b>1$ being integers. Then   $2^{p}-1 =2^{ab}-1=(2^{a}-1)(2^{b(a-1)}+2^{b(a-2)}+\cdots +2^{a}+1) = (2^{b}-1)(2^{a(b-1)}+2^{a(b-2)}+\cdots +2^{b}+1)$   where $2^{a}-1>1$ and $2^{b}-1>1$ since $a>1$ and $b>1$. If p is composite with $p=a\cdot b$ and $1<a<p$, then $2^{p}-1$ is composite, since $2^{ab}-1$ is divisible by $2^{a}-1$. $\square$     I don't understand why it is showing if $p$ is composite, then $2^{p}-1$ is composite though.

Would the following be a valid proof?  Let $r$ and $s$ be positive integers, then the polynomial $x^{rs}-1=(x^r -1)(x^{s(r-1)}+x^{s(r-2)}+\cdots+x^r+1)$.  So if $p$ is composite (say $rs$ with $1<s<p$), then $2^p-1$ is also composite (because it is divisible by $2^s-1$)


So I was given this problem:     Let $\vec{a} = \begin{pmatrix}x_a\\y_a\\z_a\end{pmatrix}$, $\vec{b} = \begin{pmatrix}x_b\\y_b\\z_b\end{pmatrix}$, and $\vec{c} = \begin{pmatrix}x_c\\y_c\\z_c\end{pmatrix}$.   Show that $(x_a,y_a,z_a)$, $(x_b,y_b,z_b)$, and $(x_c,y_c,z_c)$ are collinear if and only if   $$\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = \mathbf{0}.$$   I tried plugging it in and it looks like it is true:     Let $\vec{a} = \begin{pmatrix}2\\4\\6\end{pmatrix}$, $\vec{b} = \begin{pmatrix}4\\8\\12\end{pmatrix}$, and $\vec{c} = \begin{pmatrix}8\\16\\24\end{pmatrix}$.   $$\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} =\begin{pmatrix}0\\0\\0\end{pmatrix}  +\begin{pmatrix}0\\0\\0\end{pmatrix}  +\begin{pmatrix}0\\0\\0\end{pmatrix}\\ = \begin{pmatrix}0\\0\\0\end{pmatrix}\\ $$   How could I prove this to be true? I am not entirely sure where to begin.

Let ${a} = \begin{pmatrix}x_a\\y_a\\z_a\end{pmatrix}$, ${b} = \begin{pmatrix}x_b\\y_b\\z_b\end{pmatrix}$, and ${c} = \begin{pmatrix}x_c\\y_c\\z_c\end{pmatrix}$. Show that $(x_a,y_a,z_a)$, $(x_b,y_b,z_b)$, and $(x_c,y_c,z_c)$ are collinear if and only if ${a} \times {b} + {b} \times {c} + {c} \times {a} ={0}.$  Hello,  Is there any other way to do this problem without bashing?  I can't seem to find a nice and slick solution to this.  Thanks in advance!


How can I delete any system app? I deleted a wallpaper app in my app folder but I don't see any changes? I want to delete some apps especially default factory-installed apps. Is there a simple way?

I'm using a Samsung I9000 and I have some annoying apps that came pre installed by the phone vendor, like a music store, a custom web browser and other memory leaking apps.  Those crappy apps can't be uninstalled neither by Manage applications tool, nor by editing the apps tiles in the front menu.  I guess I have to be a root user or something to get rid of those apps, but I don't know how.


I want to make an all out Mage character in Skyrim... No weapons or armor (except for Mage attire). What class would be best for this way of playing?

I am having trouble choosing a new character on my new game in Skyrim. I don't know whether I would like to be a Mage, Warrior or Thief. I like the sound of Thief because gold is involved, warrior because I like to be able to get in there and take damage...and deal it. And mages are cool because spells are effective against most enemies and you can upgrade your magika until you are unstoppable and learn awesome spells.  So, I'm quite stuck on choice and who would make a good vampire as well? Most people say Dark Elf, but what do you think?


Let $f\in C^{\infty}[-1,1]$ and let $M$ be a constant such that $|f^{(j)}(x)|\le M$ $\forall j\in \Bbb{Z}_{+}$ and $x\in [-1,1]$. Prove that if $f({1\over k})=0$ $\forall k\in \Bbb{N}$ then $f=0$.  I don't know what to do. I guess it has something to do with Taylor expansion and the remainder corollaries but I don't know it well enough to understand how to apply it in here. I would appreciate your help.

Let $f\in C^{\infty} ([-1,1])$ and suppose there's a constant $M>0$ such that $|f^{(j)}(x)|\le M:\forall j\in\mathbb N$ (including zero) and for all $x\in [-1,1]$. Prove that if $f(\frac 1 k)=0 :\forall k\in \mathbb N$ then $f(x)=0 :\forall x\in [-1,1]$  I understand that the function is always smooth and Lipschitz, so it's always uniformly continuous too. So it can't be that $f(\frac 1 k)=0$ and for the closest irrational number say $y$ we will have $f(y)\neq0$ because that will contradict uniform continuity. It's a bit similar to Dirichlet function. If I'm right then it can be proved without using the fact that the function is smooth and I should be able to find for $f^{(0)}$ a contradiction which should be enough but it doesn't feel right if I'm not using parts of the question. Also, I'm not sure on how to formally express the counter example, should i use the $\epsilon - \delta$ ? Heine with two sequences ?


Let $A = \frac {\Bbb C[X,Y]} {\left ( X^2 + Y^2 - 1 \right )},$ $x,y$ denote the images of $X,Y$ in $A$ respectively. If $u = x + iy,$ then prove that   (a) $u$ is a umit in $A,$ and   (b) $u-i$ generates a maximal ideal of $A.$  I assume by image of $X$ and $Y$ it is meant that the image of $X$ and $Y$ under the quotient map $f : \Bbb C[X,Y] \longrightarrow A$ defined by $$P(X,Y) \longmapsto P(X,Y) + \left (X^2+Y^2 - 1 \right ),\ P(X,Y) \in \Bbb C[X,Y].$$ Then $x = X + \left (X^2 + Y^2 - 1 \right )$ and $y = Y + \left (X^2 + Y^2 - 1 \right ).$ If we denote the identity of $A$ i.e. $1 + \left (X^2 + Y^2 - 1 \right )$ by $\overline {1},$ then we get $x^2 + y^2 = \overline {1}\ $ i.e. $\ u \cdot (x-iy) = \overline {1}.$ Since $x-iy \in A$ (Since it is the image of $X - i Y \in \Bbb C[X,Y]$ under the quotient map $f$), so it follows that $u$ is a unit in $A,$ which proves (a). How do I prove $(b)$? Any help will be highly appreciated. Thanks in advance. EDIT $:$ $A$ is isomorphic to $\Bbb C [x,y],$ as rings. Any maximal ideal of $A$ corresponds to the maximal ideal of $\Bbb C[X,Y]$ containing $\left (X^2 + Y^2 - 1 \right ).$ So $x+iy-i$ generates a maximal ideal of $A$ iff $\left (X+i(Y-1), X^2 +Y^2 -1 \right )$ is a maximal ideal of $\Bbb C[X,Y].$

Let $A = \frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$  Let $u=X+iY.$ Show that $(u-i)$ is a maximal ideal of $A.$  Any ideal of $A$ is an ideal of $\Bbb C[X,Y]$ containing the ideal $\left ( X^2+Y^2-1 \right ).$ Need only to show that $(u-i)$ is maximal with respect to all the ideals of $\Bbb C[X,Y]$ containing $\left ( X^2+Y^2-1 \right ).$ It is easy to show that $X^2+Y^2-1 \in (u-i)$ since $$\left ( X +i \left (Y-1 \right ) \right ) \cdot  \frac {\left (X^2+Y^2-1 \right ) \left (X-i \left (Y-1 \right ) \right )} {X^2+ \left (Y-1 \right )^2} = X^2+Y^2-1.$$ But how do I prove that $(u-i)$ is maximal with respect to all the ideals of $\Bbb C[X,Y]$ containing $\left (X^2+Y^2-1 \right )$?  Any help will be highly appreciated. Thank you very much.


Consider:     Childhood never comes again in life.    What might be single word that means never come again in life?

What is the word/phrase to mean something that just happens once? For example,     I have often been told/expected to do this and not to do that. I become aimless   and gradually lose the idea of who I am. I ask myself "What is the point?" If   life is just once thing, why can't I live my life in my own way,   the way I think is right and suitable to me? If I cannot, I would   rather live a shorter life.


There are some books on the table. If you group them by 3, you get some number of full groups and 2 books remain; if you group them by 4, you get some number of full groups and 3 books remain; if you group them by 5, you get some number of full groups and 4 books remain. What is the number of books on the table, if it is less than 100?

Find natural number $x$ so that $$\begin{align}x&\equiv 9\pmod{10}\\ x&\equiv8\pmod9\\ &\ \ \vdots\\ x&\equiv 1\pmod2\end{align}$$


I've defined  \newcommand{\foo}[1]{\textbf{#1}} \newcommand{\bar}{\foo{Bar}}   Now, when I compile  \bar tender --- tend your \bar.   I would like to get     Bar tender - tend your Bar.   but what I actually get is     Bartender - tend your Bar.   It seems that if I use \foo{Bar} directly, I get what I want.  How can I get the output I expect by changing the command rather than the invocation? I'd rather not use \xspace unless absolutely necessary.

I have a definition:  \newcommand{\arnold}{Arnold Schwarzenegger}   When I refer to it by:  \arnold is a   it is rendered as:   Arnold Schwarzeneggeris a    In order to have a space in front of "is" I would need to write  \arnold\ is a   Is there some other shorter way?


When an ignored user joins a chat room, their avatar is shown in half size in the user list to the top right. The container that contains the avatar retains its full height, so everything is pushed down by half an avatar's height on my screen when an ignored user joins.    More specifically, the ignored class seems to be added on the user container. It resizes the avatar, but the height of the container is governed by #present-users > .present-user, #present-users .more, which makes the height 32 pixels. I believe .present-user.ignored should set the height to 16px to match .ignored .user-gravatar32.

When I ignore a user, the avatar list looks weird.    The blank line beneath the row with the avatar of the ignoree is quite annoying.    I use Google Chrome on OS X.  There was a  tagged  but it still looks weird.


What are the number of dissimilar terms in the expansion of $(x+\frac{1}{x}+x^2+\frac{1}{x^2})^{15}$?  I know how to solve this kind of problem. First I would arrange the term into a binomial expression. The expansion will have $(n+1)$ dissimilar terms. But how can I arrange it into a binomial expression?

Find the number of dissimilar terms in the expansion of $$\bigg(x+\frac{1}{x}+x^2+\frac{1}{x^2} \bigg)^{20}$$  Could someone give me some hint to proceed in this question. I used $x+1/x=t$ and wrote expansion as $(t^2+t-2)^{20}$ but even this does not convey much information. Please help.


I have downloaded the Second Life package for Ubuntu 14.04 but I am unsure how to run it. What file do I have to click on to set it up?

I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file?


In Windows 10, when I used to type cmd in Run. The PowerShell was used to open inside black cmd like window.   My friend has somehow made cmd open cmd.exe, which was default in the previous version of Windows, but not Windows 10. Now he doesn't remember how he did.   How do I reset to open PowerShell inside cmd?

Shift-rightclicking an empty spot in Explorer displays "Open with PowerShell" instead of "Open with Command Prompt" since the  (2017-04). How can I get the old behaviour back where it shows "Open with Command Prompt"?  I tried changing the setting "Show PowerShell instead of Command Prompt when rightclicking the Start Menu or pressing Windows + X" to off, but that didn't change the shift+rightclick menu.


What are the different unusual subjects in number theory? I am adviced sometimes to think before going into research in number theory as these subjects like number theory, algebraic geometry are highly old and most the works are done so that a people need a lot of prerequisites to go into that subject and the problems are tough. That's why I am bit nervous. Is it really true? I have come to know about different areas in number theory like ergodic number theory, probabilistic number theory, modular forms and I have studied elementary, algebraic as well as analytic number theory a bit and I love studying number theory. If the subject would be very terse in research then it would be very difficult to work with it. So I am worried. Please give me some advice.

I know little about number theory even after reading its Wikipedia article.    I was wondering if the subjects studied by number theory is only about integers or even more restrictedly natural numbers or prime numbers, and how they are related to other types of numbers such as rational and irrational numbers? In number theory, are the real numbers also studied? If yes, what aspects of real numbers are studied in number theory?   Are real numbers studied just as generalization from integers and rational numbers? Or are they also studied standalone independently of integers and rational numbers?  If they are also studied independently of integers and rational numbers, is the set of real numbers, $\mathbb{R}$, regarded as a 1-dim Hilbert space with dot product being inner product and the induced topology, just as how it is studied in real analysis? Is $\mathbb{R}^n,     n \in \mathbb{N}, n>1$ studied in number theory? Can I say what is studied in real analysis about real numbers is part of number theory?  When studied independently of integers and rational numbers, is $\mathbb{R}$ regarded  as a special kind of algebraic structure studied in abstract algebra? Similar questions for complex numbers, to those for real numbers in 2. Especially are there differences between how complex numbers are studied in complex analysis, in algebra, and in number theory?    Thanks and regards!


So basically what I'm trying to do is have a boss spawn (ever 10 levels) and have every other enemy currently on screen removed. All object are in a linkedlist and extend GameObject.   In GameObject I have removed as a boolean and:  public GameObject(float x, float y, ID id) {     this.x = x;     this.y = y;     this.removed = removed;     this.id = id; }   Going off another suggestion from a previous thread, in the handler I have:  for (int i = 0; i < object.size(); i++) {          if (object.get(i).removed == true)               object.remove(i);     }   The way I'm checking the level and removing the enemy is (basic enemy line 41) This is in the basic enemies class:  if(hud.level % 10 == 0) {         this.removed = true;     }   Every time I run the code and an enemy spawns in it throws a nullPointerException at line 41 of basic enemy. Full error is:  Exception in thread "Thread-0" java.lang.NullPointerException at BasicEnemy.tick(BasicEnemy.java:41) at Handler.tick(Handler.java:13) at Game.tick(Game.java:92) at Game.run(Game.java:73) at java.base/java.lang.Thread.run(Thread.java:844)   The int level is public and set to 1 at the start  I'm not very good with LinkedLists so this is pretty confusing atm.   edit  hud.level is   public int level = 1;   HUD is the class which keeps track of overlays, current level, and score the code for increasing score and level is:   public void tick() {      HEALTH = Game.clamp(HEALTH, 0, 100);     greenValue = Game.clamp(greenValue, 0, 255);      greenValue = HEALTH * 2;      score++;  }   Level:  public void tick() {     scoreKeep ++;      if(scoreKeep >= 100) {         scoreKeep = 0;         hud.setLevel(hud.getLevel() + 1);

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've noticed in other people's code that methods returning generic collections will almost always return an interface (e.g. IEnumerable<T> or IList<T>) rather than a concrete implementation.  I have two related questions. Firstly, why (if at all) is it considered better to return an interface? Secondly, is there a collection interface that includes the Sort method (as List<T> does)?

Can anyone explain to me why I would want to use IList over List in C#?  Related question:


If yes, could the same photon hit multiple targets as it expands? If not, how does the photon acquire the wave-ness if it is not born as a spherical wave? Also, in second case, how can multiple photons synchronize to make up a single wave front?

When an excited state couples to the vacuum, it has an infinite number of directions of the quantized electromagnetic field to couple to. Does it evolve into a superposition of all those directions at the same time and only collapses once the photon is measured, or does it couple to only one? (Or, of course, is there no experimental way to tell?)


I am working with iCloud, iPhone and Macbook Pro on Yosemite.   I receive ICS calendar invites via mail from a user using Outlook. When I click on the ICS file in the mail, it opens and I can add it to my calendar without a problem. It also syncs nicely on all my devices.  However, the sender of the invite does not get a confirmation, in the meeting properties I'm shown as "did not reply". When I open the invite in my calendar, I have no option to accept or send a notification.   In short: ICS invites are added to my calendar but the organizer does not receive a notification.   How can I send an accept notification?

I'm using Apple mail with a fresh install of MacOS and I'm missing the Accept/Maybe/Decline buttons on calendar invites. My company uses a Exchange 2013 server and some other users do see the buttons. For me, I just see an email with an attached .ics file for the same invites.  Expected behavior seen by some people....   How my mail app shows it...


I am trying to color tr with .click event using jquery.  My code has no problem with coloring the first row which is static, but other rows, created with jQuery don't want to color.  I have no idea why is not working on other rows.  $(function () {     $('tr').click(function () {         $(this).toggleClass("obarva");     }); });   Here is my existing code: `

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


When I connect my external hard disk to my Ubuntu device and delete some files and folders from it, they are not actually deleted as they still preserve space but I do not see them.   However, when I connect the hard disk to a Windows machine, I see a folder .Trash-1000 contains some files and folders, and when I delete them from there, I get the space freed.  1) How can I delete my files and folders from the external hard disk to the rubbish bin and free their space in Ubuntu?  2) How can I see the .Trash-1000 folder in the external hard disk from my Ubuntu machine?

Using Ubuntu 11.10, I accidentally deleted a file that was approximately 700 MB. I tried to find it in the in following locations, but couldn't:  /home/user/.local/share /home/user/ <-- there was no folder .Trash /home/user/Desktop/ <-- there was no folder .Trash   So where did .Trash go in Ubuntu 11.10 onward? I use the Gnome environment.


Calculate the following integral when $a^2+b^2=1<c$  : $\int_{0}^{2\pi}\frac{dt}{acos(t)+bsin(t)+c}$ I thought maybe setting $\cos(t)=\frac{z+z^{-1}}{2},\sin(t)=\frac{z-z^{-1}}{2i}$ and then try to calculate but not sure about if it's the right way to do ti

Let $a,b,c\in\mathbb{R}$ such that $\sqrt{a^2+b^2}=1<c$.  Find $I:=\int_{0}^{2\pi} \frac{1}{a\cos(t)+b\sin(t)+c}dt$.  So, I set $z=e^{it}$ and then $dz=ie^{it}dt$ and so $\frac{dz}{iz}=dt$. Therefore,  $\begin{align*} I & =\frac{1}{i}\int_{|z|=1} \frac{dz/z}{a\cdot\frac{z+z^{-1}}{2}+b\cdot\frac{z-z^{-1}}{2i}+c} \newline &=\frac{2}{i}\int_{|z|=1} \frac{dz}{a\cdot(z^2+1)-ib\cdot(z^2-1)+2cz} \newline &=\frac{2}{i}\int_{|z|=1} \frac{dz}{(a-ib)z^2+2cz+a+ib}\newline &= \frac{2}{i}\int_{|z|=1} \frac{dz}{(z-z_+)(z-z_-)}\end{align*}$  Where $z_{\pm}=\frac{-2c\ \pm\ \sqrt{4c^2-4(a+ib)(a-ib)}}{2(a-ib)}=\frac{-c\ \pm\ \sqrt{c^2-(a^2+b^2)}}{(a-ib)}=\frac{-c\ \pm\ \sqrt{c^2-1}}{(a-ib)}$.  Therefore, if we define $f(z)=\frac{1}{z-z_-}$, we get that $f$ is analytic in $\{z:|z|\leq 1\}$ since  $$|z_-|=\Bigg|\frac{-c-\sqrt{c^2-1}}{a-ib}\Bigg|=\bigg|c+\sqrt{c^2-1}\bigg|>|c|>1$$  Finally from Cauchy's Integral Formula:  $$I=\frac{2}{i}\cdot 2\pi i\cdot f(z_+)=4\pi \frac{1}{z_+-z_-}=\frac{2\pi(a-ib)}{\sqrt{c^2-1}}$$ Which is not always real... So my question is what is the problem.  Moreover, sometimes it is correct, e.g. $a=1,b=0,c=2$ gives the correct answer $\frac{2\pi}{\sqrt{3}}$.


In bash, how do I check if a string variable matches a given regular expression? It should be the fastest and most portable (OS X, Linux) method possible.  Basically I want:  if [ $MY_VAR matches '[A-F0-9]{8}-[A-F0-9]{4}-[A-F0-9]{4}-[A-F0-9]{4}-[A-F0-9]{12}' ]; then     echo 'matched' fi

I want to check if a variable has a valid year using a regular expression. Reading the  I understand I could use the operator =~  Looking at the example below, I would expect to see "not OK" but I see "OK". What am I doing wrong?  i="test" if [ $i=~"200[78]" ] then   echo "OK" else   echo "not OK" fi


I would like to use my ageing 27" iMac (mid 2010 model) as a second screen for my mid 2015 5k model as my even older 24" Cinema Display finally gave up the ghost. I have tried hooking them up using a lightning cable and putting it in target display mode using the standard Command+F2 and also Command+Fn+F2 but nothing happens. Do I need a thunderbolt > mini displayport cable/adapter or mdp > mdp? It would be great if anyone can share any experience of this before I buy one. Thanks.

I have a Surface Pro 4 and an iMac (late 2019). I would like to connect my Surface Pro to the iMac to use the iMac screen as a second monitor.  Is that possible?  What are the requirements to use an iMac as a second screen?


I have an FT232RL connected to an AVR Atmega2184P (running the Arduino core) UART. The microcontroller has two power supplies - a LiPo battery (VBat), and USB power (Vin). The way I've designed the circuit is that if the USB is plugged in the battery is disconnected from the circuit and Vin powers the entire circuit. When the USB is unplugged, VBat takes over  The VCC and VCCIO on the FT232 is connected to Vin. Therefore the FTDI chip should only be powered on when the USB device is connected.  I'm noticing weird behavior when the battery is plugged in but the USB is not. As soon as I initiate the UART bus on the microcontroller, and current is sent down the RX and TX lines, the FT232 powers itself up. What is strange is the power is then transferred into the Vin power rail.   This is affecting other parts in my circuit that rely on there not being any power in Vin when the USB is unplugged. If my code doesn't initiate the UART bus, everything works as it should.  Has anybody seen this behavior? I can't see any reason why the FTDI chip would be relaying power back into the VCC line.  I've tested this with multiple processors (different Arduino boards), and multiple FTDI breakout boards. Initially thought it might be a chip issue, but the behavior described is consistent across each device.

This is the most interesting thing I have seen! I have built a  that sends data (D0-D7) to a DAC (ADV2175). The design worked fine and I just have a low frequency alias noise (). This noise was present on all my ground planes (This is in prototyping stage and that's not unexpected from the test PCB).  I started tracing the noise path by disconnecting wires to see when the noise is gone. Surprisingly even after disconnecting all VCC and GND connections (+ all VREF and logics gone to 0 or 1) the noise was present yet. The more unexpected behavior is when the DAC is just connected to DATA port+ CLK pin (all coming from the source FPGA, NO VCC or GND), it continues working and a sine wave is produced (but with the same noise)!!!  First I thought it may receive its VCC/GND form the logic 1/0 fed into it but if it was correct, it should not have produce 0x00 and 0xFF levels, but it makes those levels correctly (I changed 0xFF data stage to another level and a notch appeared on top of the waves. this shows it can build oxFF correctly).    This is a big challenge for my PCB design, as if this device really takes its GND from the data port, instead of the dedicated pins, I will have a hard time for designing a reliable ground plane for it (the return voltage should go back to a logic noisy environment and analog-digital ground plane isolation may be impossible).  Can anyone explain what is happening there?


If I have a bash script in my home directory and call for it to execute from my Desktop, is it possible for the script to know the request to execute came from the Desktop? I've figured out how to get the path of where the script file is, but I want to know where the request came from.  Thanks!

How do I get the path of the directory in which a  script is located, inside that script? I want to use a Bash script as a launcher for another application. I want to change the working directory to the one where the Bash script is located, so I can operate on the files in that directory, like so: $ ./application


Last night I decided to upgrade my phone to Android 6.0 and noticed I am unable to log into the app anymore. I have always used Google as my login for the site and I was logged into the app just yesterday, before upgrading to 6.0.  I double checked that I don't have a password associated with my account by using the "forgot" link and did get back a confirmation email saying that I don't have a password associated with my account and that I can login using my Google account.  Yet this is what my login screen looks like on my 6.0 phone.    And on my 5.1.1 tablet it looks like this.    Looks like a new permission model issue causing the Google login not to show up on Android 6.0, and because I do not have a password associated with my Stack Exchange account, I am unable to login.

I registered this ID with my Gmail account, and logged in successfully via web browser. However, while I was trying to log in on the Stack Exchange app in my Android Phone, I don't see any option to log in with Google:    I was told that no user was found with my Gmail account. It is amazing that I can log in via web browser, but cannot do so with the same Gmail account via app. How can I do that?  Just to compare, here is a "normal" login screen of another user:    Where did the Google login go and how can I bring it back?  My app version is 1.0.73, phone is Coolpad 8150D with Android version 4.0.3, kernel 3.0.8.


I have a slide with three blocks, say 1, 2, 3a, and 3b, where 3a and 3b have exactly the same height (they are the same equation with some change of variable). I want to use \pause and \only to obtain the following:   only 1 (click) -> only 1 and 2 (click) -> 1, 2, and 3a (click) -> 1, 2, and 3b   while maintaining the exact same positioning of each block as in the last two slides. Here is my tentative example: what happens is that Block 1 and Block 2 appear in the center of the slide as no third block is going to appear.  \begin{frame}[c]{Title}     Block 1         \pause     Block 2         \pause     \only<3>{         Block 3a     }     \only<4>{         Block 3b     } \end{frame}

I want to have a slide in beamer with itemize exposing new line on each click while at the bottom part of the slide there are some equations. This is my attempt  \begin{frame}   \begin{overprint}{\textwidth}     \leavevmode     \begin{itemize}[<+->]     \item <1-> Poisson Boltzman equation (PB)     \item <2-> Debye-H\"uckle equation  (DH)     \item <3-> The naive approach - applying (DH) equation to PE     \end{itemize}   \end{overprint}   \begin{tikzpicture}     \node at (0,0) {};         \node<1,2> [text width = 20cm]at (10.5,-1) {$ \nabla^2 \phi =\sum_i \frac{n_i q_i\text{e}^{-q_i \phi/kT}}{4 \pi \epsilon}$};         \node <2> [text width = 20cm]at (10.5,-2) {$q_i \phi/kT \ll 1 \Rightarrow \nabla^2 \phi \simeq \kappa^2 \phi$};         \node <2> [text width = 20cm, font=\footnotesize]at (10.5,-2.5) {$\kappa^2 = \lambda^{-1/2} =  \sum_i \frac{n_i q_i}{4 \pi \epsilon}$};         \node <3> [text width = 20cm] at(10.5,-1) {$\frac{F_{el}}{VkT} = - \left ( \frac{ 4 \pi e^2}{\epsilon kT}     \sum_{i=1} n_i z_i^2 \right )^{3/2} \left ( 12 \pi \right )^{-1}$};   \end{tikzpicture} \end{frame}   However, the itemized line jump up and down between slides. I've tried to use itemize without any environment surrounding it. I've also tried to use overlayarea instead of overprint. How can I keep the line position constant?  I've uploaded a gif animation to display this. On my machine it run really fast and I can't fix this. Hope the problem is understood.   When I run this, I get


How can I read a .txt file in python and write those contents into a .md file without any change in content. I have googled enough but couldn't find a proper answer . ?

How do I copy a file in Python?  I couldn't find anything under .


I made a code for Binary Search Tree. It has only Insert function. I am getting an error at insert() function's while condition.   Exception in thread "main" java.lang.NullPointerException     at tree.LinkNode.insert(BST.java)     at tree.BST.main(BST.java)   I have initialised the Dynamic variable stub in the insert() function using keyword new.  Where did I go wrong?  The code has three class:   BST (contain the main() class) LinkNode (contains LinkNode references and the insert() function) MyLinkNode (A class to initialise  the root node)   Code:  public class BST {      public static void main(String[] args){     MyLinkNode start = new MyLinkNode(42);     LinkNode node = new LinkNode();     node.insert(start.root, 36);     } }  class LinkNode{      LinkNode leftnode;     LinkNode rightnode;     LinkNode parentnode;     int value;       public LinkNode() {}       public String insert(LinkNode root, int val){         LinkNode stub = new LinkNode();         stub = root;         while(stub.leftnode == null || stub.rightnode == null){             if(stub.value < val){                 stub = stub.leftnode ;             }             else if(stub.value > val){                 stub = stub.rightnode;             }             else{                 System.out.println("You Cannot insert a value that already exist in the tree.\nPlease insert a different value");                 return "";             }         }         stub.value = val;         stub.leftnode = null;         stub.rightnode = null;         this.parentnode = stub;         return "Insertion Succesful";     } }  class MyLinkNode{      LinkNode root;      public MyLinkNode(int val){         root = new LinkNode();         root.value = val;         root.parentnode = null;         root.leftnode = null;         root.rightnode = null;     } }

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 purchased a Rail and Fly ticket once,  after I already had bought the plane ticket. I ended up picking my luggage st the normal luggage belt,  and carrying it to the train station myself. However,  I saw signs saying I should pick them up st the Lufthansa Center at the train station.   I now have relatives flying in to Germany for the first time and want to make sure:  Is there a way to find out beforehand where the luggage has to be picked up?

I am arriving at Frankfurt International Airport Terminal 1. I have a  ticket in co-operation with Deutsche Bahn. I would like to know where I should collect my luggage. The last time when I booked, I was able to pick up my baggage at the AIRail terminal in Frankfurt. It was really convenient as I did not have to drag my luggage through the entire length of the terminal. Is this true also with the Rail&Fly ticket? What is the difference between these two types of travel - AIRail and Rail&Fly??  Additionally, I would like to know if the Rail&Fly is valid für using the S-Bahn lines (S2&S3) in Stuttgart (VVS)?


How can I change the projection of a global map so it is centered on a certain coordinate with QGIS? I know types of maps with varying centers exist, but those centers are (at least on the projections I know) always still on the equator (or polar) and not, for example, somewhere in the northern hemisphere. I am asking because I have got a georeferenced global map and I want to project it so that the most accurate part of it is Central Europe and not West Africa. Thanks

I'm a bit of a novice with QGIS, so this is really throwing me for a loop.  For the maps I'm intending on making, an azimuthal orthographic projection would be my preference.   For example, one map I'm trying to recreate is this map of the Pacific islands :    I've been using the NaturalEarth Quick Start package, which has been a really good launching-off point, but I'm running into some issues at the horizon of the orthographic projection.  I've tried adding a custom projection:  +proj=ortho +lat_0=0 +lon_0=170 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs   But that gives the following map:    Which certainly is close to being right, but the ocean is obviously being cut off in the Arctic and on the southern horizon.  I understand the issue is that naively mapping layers described in WGS 84 to an orthographic projection leaves you with artifacts at the horizon, but how do I fix it?    I first tried to use the Clip to Hemisphere plugin described in , but it seems incompatible with QGIS 3; when I try adding the plugin, QGIS3 gives an error message and places it in the "Invalid" section of the Plugins window.    I then tried both solutions presented at  Again the issue is with QGIS 2/3 incompatibility.    For Solution 1, both Numerical Digitize and CAD Tools are again incompatible with QGIS 3 and give the same result as Clip to Hemisphere.    For Solution 2, I can't disable on-the-fly-reprojection in settings since that setting was removed in QGIS 3.


New to Ubuntu, and recently updated to 16.04 (yes, yes, I probably should have waited being new and all).  Generally it's working well...but I'm having some update problems. The dreaded red triangle in the upper righthand corner. I've tried doing some searching on my own, but to no avail. When I tried updating through the software update, I get the following notice.  W: http://dl.google.com/linux/chrome/deb/dists/stable/Release.gpg: Signature by key 4CCA1EAF950CEE4AB83976DCA040830F7FAC5991 uses weak digest algorithm (SHA1),  W: There is no public key available for the following key IDs: 1397BC53640DB551, W: The repository 'http://ppa.launchpad.net/conscioususer/polly-daily/ubuntu xenial Release' does not have a Release file, W: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.,  W: See apt-secure(8) manpage for repository creation and user configuration details.,  E: Failed to fetch http://ppa.launchpad.net/conscioususer/polly-daily/ubuntu/dists/xenial/main/source/Sources  404  Not Found,  E: Failed to fetch http:// ppa.launchpad.net/conscioususer/polly-daily/ubuntu/dists/xenial/main/binary-amd64/Packages  404  Not Found,  E: Failed to fetch http:// ppa.launchpad.net/conscioususer/polly-daily/ubuntu/dists/xenial/main/binary-i386/Packages  404  Not Found,  E: Some index files failed to download. They have been ignored, or old ones used instead.   Now, I'm not an idiot, and have checked around to see if I could find the problem myself, but nothing seems to be posted for this problem in 16.04. Can anyone help?

PPA seems to be constantly offline. Whenever I use sudo apt-get update, this error is shown:  W: Failed to fetch http://ppa.launchpad.net/ 404  Not Found   How do I fix these errors?


I've noticed this happening recently:  when I flag useless comments, they seem to disappear get burninated immediately.  My guesses:   they only disappear for me each of my flags has coincidentally made the post hit the automatic deletion threshold  they actually disappear get burninated because I'm awesome something else?   What's really going on?

I posted a comment on the . My comment was:  You will have to work on your [accept rate](http://meta.stackexchange.com/questions/5234/how-does-accepting-an-answer-work). Currently it's catastrophic. Zero as in a singularity inside a black hole.  This comment was deleted by someone. I would like to know if showing users that don't know how to accept answers is considered as a bad thing so that I stop doing it or if not why would my comment have been deleted and do only moderators are InRole to delete comments.


How can I remove the Guest account from my admin account? Because there is no use of have a password for the admin account will the guest is open to anyone.

How do I disable the guest session in Ubuntu 11.10 or higher? I don't want people to be able to use my computer without using a password to log in!


I am having some confusion while using PageMessages and Messages in my VF Pages. I'm using an apex controller to pass a message to my vf page but the problem is that if I use PageMessages then it showing the default validation error messages on that page. And if use Apex:messages then the error messages don't show up at all...

I have always been curious what are the exact differences between all of the messaging options Visualforce provides, such as apex:message, apex:messages, apex:pageMessage, and apex:pageMessages. The description the Salesforce documentation at times can be rather cryptic.  <apex:message>      A message for a specific component, such as a warning or   error. If an  or  component is not   included in a page, most warning and error messages are only shown in   the debug log. -      <apex:messages>      All messages that were generated for all components on the current   page. If an  or  component is not   included in a page, most warning and error messages are only shown in   the debug log. -      <apex:pageMessage>      This component should be used for presenting custom messages in the   page using the Salesforce pattern for errors, warnings and other types   of messages for a given severity. See also the pageMessages component. -      <apex:pageMessages>      This component displays all messages that were generated for all   components on the current page, presented using the Salesforce   styling. -     So, most of that sounds relatively similar. What are the differences and what are the use cases for each?


People have asked similar questions in the past:  is from September 2012  I haven't found a single post where someone used a tab character and intended for it to be anything other than 8 spaces.  On the other hand, I've seen numerous edits where people have to correct the indentation because of how tabs are handled.  Should tabs be treated as 8 spaces?

Related:       Note that this question, while related, is not the same as the ones linked.  In many cases, when people put code into questions or answers, they copy/paste the code from their editor.  If their editor is using tab characters, the formatting will be broken after the post is submitted.  For example, if a code is indented using TAB characters, then one TAB character in the beginning of a line will be treated as one level of indent and align with the left edge of the code, effectively indenting equally to 4 spaces.  However in the post editor it looks indented twice - the same as 8 spaces.  I often edit other people's posts to improve code formatting and I find this TAB issue being the biggest annoyance.  Most of the times (I think) on SO, we use 4 spaces to format/indent the code.  I think it would be an easy thing to auto-expand TAB characters inside <code> blocks by replacing them with 4 spaces when the post is submitted.


Is it true to say that if $a_n \geq b_n$ then $\lim \limits_{n \to \infty}(a_n) \geq \lim \limits_{n \to \infty}(b_n)$ and if not can I have a counter-example?  Thanks!

Theorem  Let $\{a_n\}$ and $\{b_n\}$ be convergent real sequences. Assume that there exists a $N\in\mathbb{N}$ so  $a_n\le b_n$ (eq. 1)  for all $n\ge N$. Then  $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$.  My attempt at proving  Let $a=\lim_{n\to\infty}a_n$ and $b=\lim_{n\to\infty}b_n$. $a$ and $b$ are real numbers because the limit of a sequence of real numbers is a real number (which is a corollary in my textbook). For proof by contradiction, assume  $b<a$.  Let $\epsilon=\frac{a-b}{2}$. Then we can find $N_a,N_b\in\mathbb{N}$ so  $|a-a_n|\le\frac{\epsilon}{2}$ when $n\ge N_a$, (eq. 2)  $|b-b_n|\le\frac{\epsilon}{2}$ when $n\ge N_b$. (eq. 3)  In a textbook I found that I should do the following:  Choose a $n$ so $n\ge\max(N,N_a,N_b$), then eqs. (1-3) are satisfied. Then  $a-\epsilon\le a_n+\frac{\epsilon}{2}-\epsilon$  How do I get that last thing? Is it necessary to do a proof by contradiction or can one do a direct proof?


Moore's law states that computer power doubles in every 18 months (more formally: "the number of transistors in a dense integrated circuit doubles about every two years."). Statistics suggest that this observation should be correct, but aren't quantum computers much more powerful than just double-powered classical computers? More interesting question is, is there even a way to improve the power of quantum computers?

Plain and simple. Does  apply to quantum computing, or is it similar but with the numbers adjusted (ex. triples every 2 years). Also, if Moore's law doesn't apply, why do qubits change it?


If we define $G_0 = 10^{100}$, and $G_n = 10^{G_{n-1}}$ (hence $G_0$ is a googol, $G_1$ is a googolplex, $G_2$ is a googolplexian), for what first value of n will $G_n$ exceed Graham's number?

When numbers get as large as Graham's number, or somewhere around the point where we can't write them as numerical values, how do we compare them?  For example:  $$G>S^{S^{S^{\dots}}}$$  Where $G$ is Graham's number and $S^{S^{S^{\dots}}}$ is $S$ raised to itself $S$ times and $S$ is Skewes number.  It appears obvious (I think) that Graham's number is indeed larger, but how does one go about proving that if both numbers are "so large" that they become hard to compare?  More generally, how do we compare numbers of this general size?  As a much harder problem than the above, imagine a function $G(x,y)$ where $G(64,3)=$ Graham's number.  The function $G(x,y)$ is as follows:  $$G(x,y)=y\uparrow^{(G(x-1,y))}y$$  Where $G(0,y)$ is given.  I ask to compare $G(60,S)$ and $G(64,3)$


My Wordpress Dashboard is suddenly quite buggy. To be specific just the admin menu is buggy. When I navigate somewhere in admin area some of the menu items disappear as you can see on the following screen.    After I move mouse over the menu some items re-appear but not correctly positioned as you can see on the next picture (see Updates text).    After I reload the page once or twice (reloading the same page, not navigating somewhere else) or Collapse and Expand menu again menu is fixed.   I don't use any plugins. I have tried to update Wordpress (manually) but it didn't help. I am currently using Wordpress 4.3, Google Chrome  45.0.2454.85 (Official Build) (64-bit), and Ubuntu 15.04.  I have just tested FireFox and there seams to be everything OK so it seams to be something with Chrome, but when I've checked console (in Chrome) there are no errors. The errors might have something to do with Chrome recent update.

I'm having an issue with my admin menu in WordPress. As you can see in the image below the formatting of the menu is out of order. This happens whenever I first land on one of the admin pages but if I refresh the page the menu looks fine. I tried disabling my plugins but none of them seem to be causing the issue.