How do decision tree based ensembles like random forest deal with categorical ("factor") predictor variables? My guess would be that indicator variables are created for each factor via a one-hot-encoding (aka 1 of K coding) but I wonder if that is true? The reason I doubt it is that it seems that such a coding for a factor with many levels would of course results in many additional variables and the selection (random) of which predictors to consider for splitting at each node would not actually be picking "variable 1" or not, but instead would be selecting a potential subset of the indicators that resulted from "variable 1".   I was under the impression that Caret in R expanded all factors out using model.matrix in its train function before passing to (any) modeling algorithm including RF however so that made me reconsider.  Does anyone know how these things are treated?

I understand how best split is chosen for random forest for numerical predictors (features).   Numerical predictors are sorted then for every value Gini impurity or entropy is calculated and a threshold is chosen which gives the best split. But how best split is chosen for categorical predictor as there is no specific ordering?


for reading and searching for some phrase in packages documentation i use Acrobat Reader DC. it works fine for all packages except for beamer. in it only occasionally i find searched phrase, mostly results shows non related phrase in documentation pdf file. for example:    i wonder, if someone else experienced similar problems. is there a way to correct this behavior?

(This question is only as reference, I will add the answer myself)  Suddenly the search in the expl3 documentation interface3.pdf no longer works. As an example searching for "divis" gives this as the first hit:    In sumatra there is no problem, other files (e.g. source3.pdf) works fine. What could be the reason?)


How do I know my rank among all Stack Overflow users?  Where can I see a list of top users according to their rank on Stack Overflow?

It would be neat if you could see a users "User Rank" or "User Percentile Rating" within their profile. It could just be something like "Top 25%", "Within Top 250 Users", or "Rank: 4500 out of 6500 users", and would easily tell you where you rank based on score compared to all other users of SO.  This would increase the "game-iness" of SO, and would be another thing in addition to Score that would keep users wanting to increase their score. It would be like "Man I only rank within the top 1500 users, damn I need to get my score up to be within the top 500. That's be awesome! Gotta go answer more questions."  I know there's a similar request , but it's not the same as what I'm suggesting.


How do you calculate the sum of an infinite series like  $$ \sum_{n = 0}^\infty \frac{n}{2^\sqrt{n}}$$  //EDIT  //Ignore  I searched up how to find this with infinite geometric series solution which was  $$\frac{a}{1-r}$$  $a$ being first value and $r$ being common ratio. But I could not find common ratio.   Please give me common ratio of this series.  //Ignore  I have also tried limits like  $$ \lim_{a \to \infty} \sum_{n = 0}^a \frac{n}{2^\sqrt{n}} $$  but they don't actually give me a solid answer.  Correction  Prove this infinite series is convergent.

What is the value of  $$\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$$  It's clearly convergent but is it possible to calculate the sum?


Here:    It's given a reasoning that gives out the heat ball interior and its boundary, separated.  However, I have troubles seeing, why must the boundary be that?    Can one perhaps use the reasoning that since $y$ grows to the positive direction and since the inequality limits $y$ from above, then $y$s at the boundary satisfy the equality part of the inequality?  However, how do I know that $y$ actually attains that value?

I am learning Mean value property (MVP) of the heat equation. MVP of Laplace equation was relatively easy to understand I think it is because of the spherical symmetry. But I am not able to appreciate the MVP of heat equation. It's not very easy to imagine the "heat ball" in the following theorem from a :        Here are questions:        How do I define a heat ball?    How does it actually look like?


I'm trying to write a program that takes in a matrix full of 12-bit RAW sensor values (that range from [512-4096]) (512 is the BAYER sensor black level--> i.e. what pure black is defined as) and adjusts the EV of each pixel, excatly like the Adobe Camera Raw (ACR) "exposure" slider. I'm trying to figure out how it is done basically. I've looked up dozens of blogs that explain how EV is calculated and it seems to be:   seems to give the formula of: PixelAdjusted = Pixel * 2^EV  This just seems very wrong because an adjustment of 5 EV blows the picture wayyy out of proportion.. and I can't find any other resources online. Wikipedia has an excellent entry on  but it doesn't seem to have what I'm looking for either... any help on this?  Thanks!  Here is an example of what I mean:  RAW file in ACR with EV 0:   With EV 5:

Does anyone know of any algorithms or can explain mathematically how brightness (EV) is executed in post-processing? Does it adjust the level of brightness/RBG/contrast for each pixel? Does it relate to the histogram?  What are the technicalities of exposure compensation for an underexposed image in post processing?  EDIT: In  a link was posted. It  of changing the EV and it moves left/right. In Matt Grumm's answer, he states that each pixel is "multiplied" (which in my mind indicates that the histogram is moved up/down).  Can anyone explain why this is the case? (That EV changes from left to right)


There was a very similar question asked about 'last night' and 'yesterday night'  but I didn't really think the question was answered that definitively. Also, I thought about how we use other expressions that include last + date/time a bit more.  Is this because last Monday morning is unambiguous, and yesterday morning is also unambiguous whereas last morning is? Why doesn't last morning just mean the morning that passed if it is night time (and you are referring to a time in the same day), and if it is morning then it refers to yesterday's morning? I think this is still a probably with last Monday morning if you are using this expression on a Monday just after morning.

Is it proper to use the following expressions  I started to London yesterday afternoon . I started to London yesterday morning  I ask because it is supposedly correct to say 'last night'. Why don't we say 'last afternoon' or 'last morning'?


I want to use python regex to find the document class in a latex document.  A latex file contains \documentclass{myclass} somewhere near the top. I want to find myclass using regex.  This is what I've tried so far:  latex_text = "blank  /documentclass{myclass} words, more text /documentclassdoc{11} more words" s=re.search(r'/documentclass{(?P<class_name>.*)}', latex_text)   It matches: myclass} words, more text /documentclassdoc{11  How can I change it to only match myclass. It should also stop searching after it finds a match, as the document can get quite long.  I know the file should only have one documentclass, but I want to handle the case where there is more than 1 as well.

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


I've installed Edge Chromium on a server running Windows Server 2019.  The Server Manager now reports an error, that the edgeupdate service as stopped:    The eventlog shows an event id 0 for this and for the edgeupdatem service as well.  These two services are started by the Task Manager. You can start them at will, but they stop at once causing a new error - which, in fact, isn't an error, as the service is meant to stop after the update check - but annoying it is constantly having this event listed.   I might remove them from the Tast Manager to prevent this error, but how would Edge Chromium then be updated?

I just installed a fresh new Windows 2012 x64 Virtual Machine.  The very first thing I did was install Google Chrome.  When I went to the Dashboard, I get the following error (or it's made to look like an error).    So,   Anyone know what this error is all about? How can i 'fix' this?   Thank you kindly.  EDIT: Please don't suggest I uninstall G-Chrome as a fix.


Some months ago (when Meta was still Meta Stack Overflow), I got  that the time a flag get handled is increasing when the first flagging is trigged on a question older than one month compared to when it happens during the first hour. Recently  got implemented which according to me means the percentage of handled flags according to the question age drops. But proving so would require writing a query and as the implementation is still new it would be good to consider past handled flags. For such a query, I would need to access flags which got handled, but currently only PendingFlags with close votes are available on SEDE. The best would be an handled date for each flags. Since there is already a PendingFlags table, please also make handled flags available with there handled date also available on SEDE so I can output a graph of handled flag percentage over time. Update This question ask  asks for data on handled fags.  ask for accessing flagged data in general whether Pending or not which is considered as . Please don’t close it!

I'd love to see if there are trends over time, patterns of improving behaviour after being flagged, consistent reoffenders, most misused types of flag, etc.  I understand the who-said-what-about-who aspect would most likely cause this to be denied, but even anonymised data would be interesting to dig through.


I need to load data from a .txt file by using the following method:   public void getTextFromFile() {     File path = getExternalFilesDir(null);     File file = new File(path, "alarmString.txt");      int length = (int) file.length();      byte[] bytes = new byte[length];      FileInputStream in = null;     try {         in = new FileInputStream(file);          in.read(bytes);         in.close();     } catch (IOException e) {         e.printStackTrace();      }finally {           String contents = new String(bytes);         TextView clockTxt = (TextView) findViewById(R.id.clockText);         assert clockTxt != null;         clockTxt.setText(contents);     } }   When calling the method getTextfromFile();, under the onCreate(); the program crashes, with giving me the following error:   Caused by: java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.TextView.setText(java.lang.CharSequence)' on a null object reference   I have tried to:    Check if the id is correct.  Made sure that the correct layout is being called by setContentView(R.id.activity_main);  Making sure that the method getTextFromFile(); is being called under the setContentView();   Thanks!

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 want to make my dough for dinner rolls tonight in my bread maker and bake in the morning. Will this work? Also do I cut and shape before putting in the fridge for the night or do I do this in the morning before baking?  Thank you.

I would like to bake bread as soon as I get up.   Would it be possible to store bread dough overnight, perhaps in the fridge? For how long could I store it? Would it need to rise again next morning?


Here is a beautiful circular paragraph I found in the TeXBook.      I would like to know how it and similar things could be typed.  Here is the code I found the TeXBook which I could not make compile in TeX or LaTeX (even after removing certain parts, trying to make it run on it's own).  \danger \TeX\ looks at the parameters that affect line breaking only when it is breaking lines. For example, you shouldn't try to change the ^|\hyphenpenalty| in the middle of a paragraph, if you want \TeX\ to penalize the hyphens in one word more than it does in another word. The relevant values of |\hyphenpenalty|, |\rightskip|, |\hsize|, and so on, are the ones that are current at the end of the paragraph. On the other hand, the width of indentation that you get implicitly at the beginning of a paragraph or when you say `^|\indent|' is determined by the value of\/ ^|\parindent| at the time the indentation is contributed to the current horizontal list, not by its value at the end of the paragraph. Similarly, penalties that are inserted into math formulas within a paragraph are based on the values of\/ ^|\binoppenalty| and ^|\relpenalty| that are current at the end of each particular formula. Appendix~D contains an example that shows how to have both ragged-right and ragged-left margins within a single paragraph, without using |\leftskip| or |\rightskip|.   I can separate the code for the paragraph on the left from the code for th circular paragraph.    \varunit=0.989pt % getting ready to make circular insert % \varunit=1.078pt was used with amr5: it had more letterspacing \setbox0=\vtop{\null \baselineskip6\varunit \parfillskip0pt \parshape 19 -18.25\varunit 36.50\varunit -30.74\varunit 61.48\varunit -38.54\varunit 77.07\varunit -44.19\varunit 88.39\varunit -48.47\varunit 96.93\varunit -51.70\varunit 103.40\varunit -54.08\varunit 108.17\varunit -55.72\varunit 111.45\varunit -56.68\varunit 113.37\varunit -57.00\varunit 114.00\varunit -56.68\varunit 113.37\varunit -55.72\varunit 111.45\varunit -54.08\varunit 108.17\varunit -51.70\varunit 103.40\varunit -48.47\varunit 96.93\varunit -44.19\varunit 88.39\varunit -38.54\varunit 77.07\varunit -30.74\varunit 61.48\varunit -18.25\varunit 36.50\varunit \fiverm \frenchspacing \noindent \hbadness 6000 \tolerance 9999 \pretolerance 0 \hyphenation{iso-peri-met-ric} The area of a circle is a mean proportional between any two regular and similar polygons of which one circumscribes it and the other is isoperimetric with it. In addition, the area of the circle is less than that of any circumscribed polygon and greater than that of any isoperimetric polygon. And further, of these circumscribed polygons, the one that has the greater number of sides has a smaller area than the one that has a lesser number; but, on the other hand, the isoperimetric polygon that has the greater number of sides is the larger. \hbox to 36.50\varunit{\hss[Galileo,\thinspace1638]\hss} }  \danger \parshape 16 3pc 26pc 3pc 26pc 0pc 24.69pc 0pc 23.51pc 0pc 22.73pc 0pc 22.20pc 0pc 21.85pc 0pc 21.65pc 0pc 21.58pc 0pc 21.65pc 0pc 21.85pc 0pc 22.20pc 0pc 22.73pc 0pc 23.51pc 0pc 24.69pc 0pc 29pc \vadjust{\moveright 28pc\vbox to 0pt{\vskip88pt\vskip-60\varunit   \vskip-3pt\box0\vss}}%

How do insert image between text and text wrap with shapepar or other package?


I'm creating a youtube channel where i will upload interesting videos of animals and humans. But don't know the name. Anyone please let me know common word including animals and humans?

Commonly, "animals" means "all animals, except humans". So is there a single word for "animals, including humans"?  Particularly, if you had a list of two choices, animal or human, what would you write as the heading?  Context: I'm building an input form for game designers to fill out about things you can encounter in a fantasy world. And one property of an encounter is whether it's an encounter with humans, animals, and possibly more categories to be determined later (e.g. spirits, monsters, undead?).


Is it possible to rename multiple files that share a similar name but are different types of files all at once? Example:  apple.png apple.pdf apple.jpg  Can I substitute the apple for something else, for example "pear"? If this is possible, what would the command be? Many thanks for your time!

How can Bash rename a series of packages to remove their version numbers? I've been toying around with both expr and %%, to no avail.  Examples:  Xft2-2.1.13.pkg becomes Xft2.pkg  jasper-1.900.1.pkg becomes jasper.pkg  xorg-libXrandr-1.2.3.pkg becomes xorg-libXrandr.pkg


I have just tried to upgrade my Ubuntu to Ubuntu 18, and at one moment I had to choose if it should install new version of a certain file or keep the old one, and I selected to see the difference. After which, I didn´t know how to close the window and return to upgrade so I pressed  Ctrl+X which terminated the process completely.   At first I could continue using Linux without any problems, but after I rebooted,  it started making problems. It shows a black screen where I can move with my mouse, but I can´t do anything else.  So I looked up online what I can do about it, and after trying everything with Booting in recovery mode, I have decided to install a new version of Ubuntu, while keeping the old data on the drive. But it seems that was not the solution either.    Any ideas ?

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I am confused about when to use Static variables/methods and exactly what they do. I know Static means that the variable or method becomes a part of the class and not an instance, but when do we use this? Also, if a variable is static, does that mean it is immutable like a final variable? Basically what is the use of Static?

To be specific, I was trying this code:  package hello;  public class Hello {      Clock clock = new Clock();      public static void main(String args[]) {         clock.sayTime();     } }   But it gave the error      Cannot access non-static field in static method main   So I changed the declaration of clock to this:  static Clock clock = new Clock();   And it worked. What does it mean to put that keyword before the declaration? What exactly will it do and/or restrict in terms of what can be done to that object?


I was trying to install a newer version of curl and when I ran: curl -V, the version number didn't change.  After running which curl, it displayed the path of the newly installed version: /usr/local/bin/curl. If I run /usr/local/bin/curl -V it displays the correct version.  The version being executed by curl seems to be in /usr/bin.  My PATH is: /usr/local/bin:/usr/bin ... etc, so it should be executing the /usr/local version.  Why is the output of which curl not the same as the program being executed by curl?

When I execute a program without specifying the full path to the executable, and Bash must search the directories in $PATH to find the binary, it seems that Bash remembers the path in some sort of cache. For example, I installed a build of Subversion from source to /usr/local, then typed svnsync help at the Bash prompt. Bash located the binary /usr/local/bin/svnsync for "svnsync" and executed it. Then when I deleted the installation of Subversion in /usr/local and re-ran svnsync help, Bash responds:  bash: /usr/local/bin/svnsync: No such file or directory   But, when I start a new instance of Bash, it finds and executes /usr/bin/svnsync.  How do I clear the cache of paths to executables?


I have made a project whose structure is like this    When I run my index.html from firefox, it is working fine.  But I open it with my chrome it is giving CORS error.     Now my problem is that chrome doesnot support file:// protocol ajax request & as I have distribute to my project to others I don't want other to run on firefox only.  Internally I am using ajax call in project, to load the resources. Can Somebody suggest how to bypass that ajax call to load resources?? Is there some solution or any third party js which can help me.  Note: Please don't suggest to use XAMPP, apache etc where I can put my project and run as localhost for chrome as I don't want user to force to download these to run my project. Please give other useful solution where I can do some change in code & it works for everyone.  Here are the links from which you could understand my problem better.

I'm working on a offline version of a website using jQuery and some xml files. I'm running in to a problem in jQuery when I do a $.ajax call on a xml file jQuery throws a error.  When I look at the error I can tell its loading the XML file because its in the error's responceText property. It seams to work just fine in Firefox.  This is how my call looks  $.ajax({     type: "GET",     url: "Modules/" + ModuleID + "/ModuleContent.xml",     dataType: "xml",     success: function(x) { xml = x; ProcessXML(); },     error: function(x) { alert(x.responceText); } });   When I run this on a web server it works just fine. Its only when I run it from the file its self when I have this problem.  Any ideas on how I can make this work in IE?  Edit: I found the answer to my problem.


I have the following assumption based on limited knowledge. A black hole appears dark to us because any light that would be emitted from it, and any light that passes nearby, is caught by the gravity well and either captured or bent from its original course.  If this is true, from any point within the gravity well or towards the center of a black hole, looking outward there would be immense amounts of light and radiation coming in.  Edit for specificity: The idea is not necessarily that a human or object would be looking out while at a point, but theoretically a fixed point that has light and matter passing by.  Of perhaps if we somehow invented something capable of not exceeding but matching the gravitational force and could stay still.  Or a sensor reading at a certain point, pointing a camera or infinite lumen sensor outward.

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


Prove the following statement $S(n)$ for $n\ge1$:  $$\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$$  To prove the basis, I substitute $1$ for $n$ in $S(n)$:  $$\sum_{i=1}^11^3=1=\frac{1^2(2)^2}{4}$$  Great. For the inductive step, I assume $S(n)$ to be true and prove $S(n+1)$:  $$\sum_{i=1}^{n+1}i^3=\frac{(n+1)^2(n+2)^2}{4}$$  Considering the sum on the left side:  $$\sum_{i=1}^{n+1}i^3=\sum_{i=1}^ni^3+(n+1)^3$$  I make use of $S(n)$ by substituting its right side for $\sum_{i=1}^ni^3$:  $$\sum_{i=1}^{n+1}i^3=\frac{n^2(n+1)^2}{4}+(n+1)^3$$  This is where I get a little lost. I think I expand the equation to be  $$=\frac{(n^4+2n^3+n^2)}{4}+(n+1)^3$$  but I'm not totally confident about that. Can anyone provide some guidance?

How can I prove that     $$1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$$    for all $n \in \mathbb{N}$? I am looking for a proof using mathematical induction.  Thanks


I have several Epic and Legendary skin shards. Do combining them increase my chances of getting a other Epic or Legendary skin shards?

If I reroll 3 skins of the same type, say 3 legendary skin shards, will I get a different legendary skin shard, or literally any random skin?


I wanna customize my registration form on drupal 7. I wanna add placeholders and remove the labels. How can I do that? Thank you

I would like to revise the default new user registration form in Drupal 7. Rather than to requst "username", I want to request "full name" with helper instructions to enter the text "username is your full name as you would normally use it."  There may be some other minor formatting changes I would like to make as well.  I cannot find an admin menu item to access anything relating to this question. And I am unable to locate a file within any director that has any text that would indicate it is the source for the new user registration form.  I realize this is a bit unconventional, however it is useful for our needs. I am aware of a module that allows the input of First Name / Last Name, but in processing it changes the input to first initial/lastname, ie Tom Thumb = username of "tthumb". The module "Realname Registration" would be just what I am looking for if it would only translate the username the same as the input.   That wouldn't necessarily solve the other formatting edits, but I would be very happy just to be able to manually edit the registration form help text under the username field, instructing the new user to register using thier real name.  Thanks for any help that you can provide.  J.M.


I recently upgraded my Ubuntu from 19.04 to 20.04. And as always, the first thing that happens is that all third party software sources are disabled.  I'm sure there are good reasons to do that and I don't mind going back in and re-enabling them afterwards. But it is such a trivial and half way mechanical task that I can't imagine that some tool doesn't exist to help user here.    Basically such a tool would check all disabled software sources with a comment like "Disabled by upgrade to.." (the exact wording eludes me) then look at the deb source, go out and check which Ubuntu release is the most recent under the "dist" folder, and enter that name in the Distribution field.  Do anyone know of such a tool?

When I upgrade from one version of Ubuntu to the next, the upgrade tool rightly disables all my PPAs, so that software compiled for or otherwise tied to the old version of Ubuntu does not interfere with the new version that I just upgraded to.  Is there any way to automatically re-enable and update any PPAs that provide packages for the new version of Ubuntu? For example, suppose I'm currently running Maverick, and I have two PPAs enabled, "foo" and "bar". Suppose that "foo" provides packages for both Maverick and Natty, while "bar" provides packages for Natty only. Is there a tool I could run after updating to Natty that would re-enable my "foo" PPA and update it to point to the Natty packages, while leaving the "bar" PPA disabled?


I am a bit confused on what this question is asking me to prove:  Prove $$ \exists z\forall x\in\mathbb{R}^{+}[\exists y(y - x = y/x)\leftrightarrow x \neq z]  $$  Am I asked to prove that there exists a z where the bi-conditional statement is true? Or is z a given and I should just prove the statement in the brackets for some z?  I put that thought aside and showed that the statement in brackets is true when z = 1, but I just want to be sure that I did what the question I was asked.

I have the following problem from the book "How to Prove it" by Daniel J.Velleman.  Prove that $$ \exists z\in \mathbb{R} \forall x \in \mathbb{R}^+ \left[\exists y \in \mathbb{R} (y-x=y/x) \leftrightarrow x \neq z \right]. $$  I have no idea how to deal with the existential quantifier at the beginning. I tried to negate it, but the rest is too complicated. Do you have strategic hints how to proceed? Allowed is first-order logic.  EDIT  Based and the response, I would propose the following proof and kindly ask the community to check if it is correct.  Proof: Let $z=1$, and let x be some arbitrary real number.   $(\rightarrow)$ Suppose $\exists y \in \mathbb{R} (y-x=y/x)$ and choose $y_0$ to be some real number such that $(y_0-x=y_0/x)$. Suppose $x=z$. Since $x=z$ and $z=1$, $x=1$. However, plugging $x=1$ into $y_0-x=y_0/x$ yields a contradiction, and thus, $x\neq z$. Hence, $\exists y \in \mathbb{R} (y-x=y/x) \rightarrow x \neq z$. Since $x$ was arbitrary, it follows that $\forall x \in \mathbb{R}^+ \left[\exists y \in \mathbb{R} (y-x=y/x) \rightarrow x \neq z \right]$. ($\leftarrow$) Suppose $x \neq z$. Since $z=1$, $x \neq 1$. Let $y_0=\frac{x^2}{x-1}$, which is defined because $x \neq 1$. Plugging into the equation $y_0-x=y_0/x$, we can verify that the equation holds for this particular value $y_0$. Hence, $x \neq z \rightarrow \exists y \in \mathbb{R} (y-x=y/x)$. Since x was arbitrary, it follows that $\forall x \in \mathbb{R}^+ \left[\exists y \in \mathbb{R} (y-x=y/x) \leftarrow x \neq z \right]$.   Therefore, the theorem follows.


Consider the series of functions $\sum z^n/n$ defined over the complex numbers.  By the Cauchy-Hadamard radius of convergence we have convergence when $|z|<1$, and divergence when $|z|>1$.  Now, what happens when $|z|=1$? For the concrete cases $z=1$ and $z=-1$ I can figure out that it diverges and converges, respectively.  But I am stuck trying to analyze what happens when the imaginary part of $z$ is not zero.  Also, does the series uniformly converge in the open disk of radius 1? My guess is not because of the divergence in $z=1$. Is this argument correct?

Inspired by the exponential series, I'm curious about where exactly the series $\displaystyle\sum_{n=1}^\infty\frac{z^n}{n}$ for $z\in\mathbb{C}$ converges.   I calculated $$ \limsup_{n\to\infty}\sqrt[n]{\frac{1}{n}}=\limsup_{n\to\infty}\frac{1}{n^{1/n}} $$ and $$ \lim_{n\to\infty} n^{1/n}=e^{\lim_{n\to\infty}\log(n)/n}=e^{\lim_{n\to\infty}1/n}=e^0=1. $$ So the radius of convergence is $1$, so the series converges on all $z$ inside $S^1$. But is there a way to tell for which $z$ on the unit circle the series converges? I know it converges for $z=-1$, but diverges for $z=1$, but I don't know about the rest of the circle. For what other $z$ does this series converge? Thanks.


My attempt...    By definition, whenever $|x- x_0| < \delta$ we have $|f(x) - f(x_0)| < \epsilon$. Observing that    \begin{align}  |f(x) - f(y)| &= |f(x -x_0 + x_0) + f(y)| = |f(x-x_0) + f(x_0) - f(y)|  \newline \newline &\leq \epsilon + |f(y) - f(x_0)| = \epsilon + |f(y-x_0)|... \end{align}      Here I need to choose a delta that can depends on $\epsilon$ and $y$ s.t. whenever $0<|x-y|< \delta$ then the above inequality is bounded by any $\epsilon$.     I'm also, in general, having trouble understanding this concept of continuity on an interval. I believe the structure of the definition is: for any $\epsilon> 0$ and any number $y$ in the interval, there exists a $\delta$ that depends on $\epsilon$ and $y$ such that for all $x$ in the interval and $|x - y | < \delta$ then $|f(x) - f(y)| < \epsilon$.     This definition makes me tempted to just choose y to be in the same delta neighborhood as $x$ in the given statement, but that constricts continuity to a small interval.    Edit: This question assumes no knowledge of Lebesgue measure theory.

The  asks about functions $f \colon \mathbb R \to \mathbb R$ such that $$f(x+y)=f(x)+f(y).$$ It is a very well-known functional equation, which appears in various areas of mathematics ranging from exercises in freshman classes to constructing useful counterexamples for some advanced questions. Solutions of this equation are often called . Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) Is there some overview of basic facts about Cauchy equation and related functional equations - preferably available online?


Coming from the  on RSA, I think I understand the following: RSA is based on generating an integer $n$ as the product of two large primes, $p$ and $q$, and encryption/decryption exponents $e$ and $d$ such that for any given plaintext $m$, $$(m^e)^d \equiv (m^d)^e \equiv m^{ed} \equiv m \mod n\,,$$ i.e. such that modular exponentiation with $e$ (encryption) composed in any order with exponentiation with $d$ (decryption) is the identity mapping on the plaintext. This works because $e$ and $d$ are chosen such that $$ed \equiv 1 \mod{|m|}$$ for any plaintext $m$, where $|m|$ denotes the order of $m$ in $\mathbb{Z}/n\mathbb{Z}$. This is done by selecting a multiplicative inverse pair $e$, $d$ in the ring of integers mod $\lambda(n)$, where $\lambda$ is ; and if I understand correctly the latter is essentially the least common multiple of the orders of all positive integers less than $n$ that are coprime to $n$, so that if $ed \equiv 1 \mod \lambda(n)$ is true then $ed \equiv 1 \mod |m|$ is too for all $m$ coprime to $n$, since $|m| \mid \lambda(n)$. But what happens if $m$ happens not to be coprime to $n$, i.e. if $m$ is either a multiple of $p$ or of $q$? What guarantees that in this case too the first identity shown above (the encryption-decryption identity) still holds? I thought along the lines of using , i.e. if I could prove that $ed$ was congruent to $p$ mod $\lambda(n)$, then $m^{ed} \equiv m \mod p$. But after some thought, this doesn't seem to lead anywhere.

I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but may be a question on here at some time) and came across something I had never seen before in any textbook description of RSA (Note: this comes from the beginning of ).  for any integer (message) $M$ which is relatively prime to $n$, $M^{\phi(n)} \equiv 1\pmod{n}$  The part I don't recall ever hearing in class, or coming across in a text book, or seeing in any description of RSA I've ever read is that $M$ and $n$ must be relatively prime. So, I decided to play around with a toy example of RSA to see what would happen. I use $p=13$, $q=31$, $e=7$ and $M=2p=26$ (for completeness: $d=103$, $\phi(n)=360$, $n=403$). I observed the following using my toy instance of RSA: $M^e\equiv M\pmod{n}$, $M^e\equiv 0\pmod{p}$ and $M^e\equiv M\pmod{q}$. Do these equivalences hold for all $M,p,q$ when $M$ and $n$ are not relatively prime? How would I prove this? What is the real-world effect of this?


I am trying to remove an item from the website using Javascript. Item is not available on the first load but available after some time or after some use event. So is there any way to remove an item that is not currently loaded?? Like lister('Classname') So when the item is available I can run some code to remove that.

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.


I'm trying to collect all players in the Arraylist with this (This is spigot 1.16.5): Arraylist constructor: public static ArrayList<Player> playerInGame = new ArrayList<>(); public void makePlayerWin(Player perdente) {         Iterator<Player> it = playerInGame.iterator();         if(!it.hasNext()) return;         Player players = it.next();         System.out.println(1);         if(playerInGame.contains(perdente) && players.getWorld() == Bukkit.getWorld(plugin.Game) || playerInGame.contains(perdente) && !perdente.isOnline()) {             System.out.println(2);             playerInGame.remove(perdente);             LobbyJoin(players);             players.sendTitle(plugin.cc("&6Hai vinto!"), plugin.cc("&7Sei tornato alla lobby!"));             playerInGame.remove(players);         }     }  But I get this error:

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


#include <stdio.h>  int main() {     int x = 1;      if (++x > 2,5)         printf("%d", ++x);     else         printf("%d", x++); }   I don't understand why the output is 3. ++x == 2 and 2 > 2,5 is false. But the compiler says the if statement evaluates to true.  What is the reason?


The buttons are too close (especially on high resolution) and I tend to hit Improve instead of Reject 1 out of 20 times or so.  Most times I simply cancel and reject the edit, but when it's a "test" I fail it and now I'm banned for 2 days of review.  It would be much easier if the Improve button was the rightest one.

There was an earlier suggestion to  to prevent errant clicks.  I would suggest a similar thing (knowing the previous didn't get implemented for close votes) in the Suggested Edits queue.  The current order of buttons there is:  Approve Reject Improve Skip  Already twice today, I managed to mis-click on Approve when intending to Reject.  Having no confirmation or subsequent reason selection to make, my errant approvals were saved.  To remedy this, a better order might be:  Approve Improve Skip Reject   My (over?)thinking here is that:   Approve and Reject are really unlikely to be confused in a wild click A mis-click between Approve & Improve will do no harm if taken to the Improve screen,  and not a huge amount harm if Approved when intending to Improve. Between Improve & Skip an errant Improve can be backed out of  An errant Skip just kicks it down the road... Between Skip & Reject, an errant click on Reject gives can be backed out of on the reject reason An errant click on Skip just kicks your intended rejection down the road to someone else.   To maintain consistency with all the other queues, Skip probably needs to remain the right-most button. This doesn't deviate much from what is above in effectiveness. What's most important is to separate the Approve and Reject actions, approvals have no secondary screen.  Approve Improve Reject Skip


If I want to apply for a PhD scholarship that requires a cover letter, should I disclose that I have Asperger's Syndrome? If so, how detailed should I describe my condition? It's not something that I enjoy talking about, . Since I was only diagnosed recently, I'm thinking of writing a few sentences that mainly highlight the positive aspects, and how it could really benefit the research group. (I have worked as a teaching assistant, and have never gone through  so it should be OK.)  I have already told my professor about the AS, but was hoping to get further advice from folks in this forum.  Edit: This is what my careers advisor thinks. I want to show that I can add value to the research group -- these attributes are directly and indirectly related to AS.     I certainly think if it is something that you can manage well you don't need to disclose it at the beginning of the application process. If it's something that affects your working then you should disclose it. Either option I would present it in a positive manner. Ultimately you want to sell yourself for what you can do for them and how you can add value. Whether you disclose it in your letter or at a later stage of the process is up to you. Just keep it positive.

With Asperger's, the trick is always when to explain it (in a non-awkward situation). I'd like to avoid mentioning it if possible, but it has gotten to the point that I only mention it after committing a major social faux pas, in which case it might be seen as an excuse.  With ADD, this is an issue that happens when people explain things to me. I often don't parse things very well when they're communicated to me verbally since I do have attention lapses. That's the major issue, anyways.   With that said, I do (indirectly) imply that I have both diagnoses on my personal website.


I wonder if there is any difference in meaning between these?  It’s years since I rode a bike. (it’s = it is)  It’s years since I’ve ridden a bike. (it’s = it is)   Thanks  In the following link, below the phrase Since and tenses, there is what I have already excerpted from:

May I ask what the logic is behind using present perfect/infinitive + present perfect in "present perfect + since + present perfect" sentences?     it has been a while since I have enjoyed a party this much.   and     It's been a long time since I have read an interesting book.   Why is it not present perfect + past simple? I understand the "it's been" part, since it's something that is still relevant or going on. But if I'm referring to a specific past event, why should present perfect even be considered?  2) Also, I've seen people replace infinitive forms with present perfects:  "You must be surprised to receive a letter from me" = "You must be surprised to have received a letter from me"  Is there such thing as an infinitive present perfect? How is this construction possible?   Please help me understand!


How does a for-each loop works when it calls a method, either recursively or a different method?  Example:  for(String permutation : permute(remaining))     {           // Concatenate the first character with the permutations of the remaining chars       set.add(chars.charAt(i) + permutation);     }   By the way the method  permute  takes in a String and returns a set.  Thank you.

Consider:  List<String> someList = new ArrayList<String>(); // add "monkey", "donkey", "skeleton key" to someList     for (String item : someList) {     System.out.println(item); }   What would the equivalent for loop look like without using the for each syntax?


I use Outlook 2013 on a Windows 7 (64 bit) pc.   Whenever I try to shut down / restart my pc I see that windows 7 waits applications to close, when I press cancel I see an Outlook form:    Is there any way to prevent Outlook delaying shut down? Or set it to always permanently empty "Deleted items" folder without asking?

When I leave my PC, I shut it down. But when it is the turn to Outlook to quit, he wants me to confirm that I want to delete what is in the trash folder.     So when I leave without waiting for this dialog to appear and not answering it, the PC get stuck on that dialog and then the shutdown is cancelled.  Is there a way to avoid this Dialog box, and still have my outlook trash folder cleaned on exit?


How can I get google to recognize my different pages of my website?  Example:   I'm pretty sure it has something to do with my site-map, but how would I create one so that I could name each of those pages?

My website used to have sitelinks and now it doesn't. It's very possible that it's due to changing the website to a sidebar design instead of having an "interstitial" type landing page which limited the number of choices, but I'm not sure.  Here is how sitelinks might look for a site:    What are some things that I can do to improve my chances of getting sitelinks?


Guess I will multiply threads, but sorry, I'm still confused:  at Jan Kazimierz University in Lwow  or  at the Jan Kazimierz University in Lwow  I've found the second one more common, though I feel the first one is more appropriate because the university is named after a person (Polish King Jan Kazimierz)? I mean, you don't say at the Stanford University, do you?

Is the always used before the name of a school, college, or university?


When a light (photons) goes through two slits it creates interference patterns. if the light goes through a "single" slit, does it create interference patterns or does it behave like particles (photons)? is the pattern same for both particles and light waves if it is a "single slit"? In the double slit experiment, if you close one slit (or observe) it is said that light behave as particles (bullets) which means that through one slit light exactly behaves as stream of particles??

How can a light passed though a single slit produce a similar interference pattern to the double-slit experiment? How does the diffracted wave produce the points of cancellation and reinforcement, if there is only one wave?


I've gone through the dictionary definitions but I'm honestly still confused. Is there any distinction at all between them? Can someone please use an example to explain the four words and how they differ, if they do differ?

Meanwhile vs. meantime   Are they really the same? I've been using them interchangeably...


Let $C([a,b]) =\{f:[a,b] \to R |$f is continuous} with the supremum norm. Show that $C([a,b])$ is complete.  I want to show that if $(f_1,f_2,...)$ is a Cauchy sequence, then it is convergent. I already showed that $f(x)=\lim_{n \to \infty} f_n(x)$ exists. Then it is sufficient to show that $\lim_{n \to \infty} \|f-f_n\|_\infty =0$  So I got $\|f-f_n\|_\infty=sup\{|f(x)-f_n(x)| |x \in [a,b]\}$, I think I must use the property of compactness of $[a,b]$ but I don't know where and how to use it.

$C[a,b]$ is a normed vector space of all continuous complex valued functions on $[a,b]$, with supremum norm   $$\|f\|_\infty=\sup_{t\in [a,b]}|f(t)|.$$  The metric induced by the norm is  $$d(f,g)=\|f-g\|_\infty = \sup_{t\in [a,b]}|f(t)-g(t)|.$$  Show that $C[a,b]$ is a complete metric space under this metric induced by the supremum norm (i.e. show $C[a,b]$ is a Banach space).


These comments essentially explain it: (can be found )        Roombatron5000 added a related link. Then Shadow Wizard voted to close as a duplicate, but because the link has been given, the "possible duplicate" auto comment wasn't added.  I assume this is because the system doesn't allow multiple "possible duplicate" comments - one for each close vote. However, is there some way that it could look for the comment ID (or similar), rather than looking for a comment with the link in?  This matters less to the OP - as they see the "possible duplicate" banner, but other users may have missed it and not close voted it as well.  Related, possible duplicates:  and , but this is talking about it not appearing because of a different comment, not a possible duplicate comment.

Please refer to the following question:    The  had posted an  a while back.  I posted a comment referring to the same and voted to close the question as a duplicate of the referenced question.  Surprisingly, an auto comment saying "possible duplicate of ..." was not generated.  I agree that the referenced question shows up in the linked questions list but an auto comment ought to be generated.  Seems like a bug.    EDIT: I understand that the above behavior is by-design.  However, I'd say that the behavior in the following case should also be the same:  It's interesting to see that the auto comment would be generated if you were to add a comment linking to an answer and then voting to close the question as duplicate.  For example, observe the following question:


I am trying to put in order the returned date string from webService but the code below has not been working;  static func ConvertTStringToDate(dateString: String!) -> NSDate! { //      2014-06-28T00:00:00     var dateTime: Array<String> = dateString.componentsSeparatedByString("T")     var dateThrougTime: String = dateTime[0] + dateTime[1]      var dateFormatter = NSDateFormatter()     dateFormatter.dateFormat = "dd-MM-yyyy HH:mm"     var convertedDate: NSDate = dateFormatter.dateFromString(dateThrougTime)!      return convertedDate }

How do I convert, NSDate to NSString so that only the year in @"yyyy" format is output to the string?


Evaluate $$\int e^{2\theta} \sin (3\theta)\ d\theta .$$   I am little stuck as to what I can do after this point. Please tell me if my method overall is flawed:

$\int e^{2\theta}\ \sin 3\theta\ d\theta$  After Integrating by parts a second time, It seems that the problem will repeat for ever. Am I doing something wrong. I would love for someone to show me using the method I am using in a clean and clear fashion. Thanks.


prove that $$\sum_{k=1}^{n}{\sin(kA)} = {{\cos({A\over2})-\cos(nA+{A\over 2})}\over 2\sin({A\over 2})}$$using Telescoping series. How do i go about doing this?

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series:  $$\sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \cos \biggl( \frac{ 2 a + (n-1)\cdot d}{2}\biggr)$$  There is a slight difference in case of $\sin$, which is: $$\sum_{k=0}^{n-1}\sin (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \sin\biggl( \frac{2  a + (n-1)\cdot d}{2}\biggr)$$   How do we prove the above two identities?


In Epidemiology An Introduction Chapter 9，p165：CI for Risk data and Prevalence data: 95% CI= R±1.96×SE(R)SE(R)=[a(N-a)／N³]½ In Epuation，R=a/N，a to represent cases and N to represent people at risk. But how do I get an asymmetrical confidence interval for population rate like this?

I am studying how to construct a 95% confidence interval for odds ratio from the coefficients obtained in the logistic regression. So, considering the logistic regression model,  $$ \log\left(\frac{p}{1 - p}\right) = \alpha + \beta x  \newcommand{\var}{\rm Var} \newcommand{\se}{\rm SE} $$  such that $x = 0$ for control group and $x = 1$ for case group.  I have already read that the simplest way is to construct a 95% CI for $\beta$ then we applied the exponential function, that is,  $$ \hat{\beta} \pm 1.96\times \se(\hat{\beta}) \rightarrow \exp\{\hat{\beta} \pm 1.96\times \se(\hat{\beta})\} $$  My questions are:     What is the theoretical reason that justifies this procedure? I know $\mbox{odds ratio} = \exp\{\beta\}$ and maximum likelihood estimators are invariant. However, I do not know the connection among these elements. Should the delta method produce the same 95% confidence interval as the previous procedure?  Using the delta method,  $$\exp\{\hat{\beta}\} \dot{\sim} N(\beta,\ \exp\{\beta\}^2 \var(\hat{\beta}))$$  Then,   $$\exp\{\hat{\beta}\} \pm 1.96\times \sqrt{\exp\{\beta\}^2 \var(\hat{\beta})}$$  If not, which is the best procedure?


Let $f:[0,1] \to \Bbb R$ such that for every $y$ either there is no $x$ such that $f(x)=y$ or there are exactly two such $x$. We are required to show that $f$ cannot be continuous. I have no idea how to prove this. Also is there a function which satisfies this?

This is from Apostol's Mathematical Analysis.  Let $f$ be a function defined in $[0, 1]$ such that for each real number $y$ either there is no value of $x \in [0, 1]$ such that $f(x) = y$ or there are exactly two such values of $x$. Prove that a) $f$ must be discontinuous on $[0, 1]$. b) $f$ has an infinite number of discontinuities in $[0, 1]$.  Long back I had tried to solve the problem. I reasoned for a) as follows: Suppose that $f$ is continuous and let $m, M$ be its minimum and maximum values on $[0, 1]$. Clearly if $m = M$ then $f$ is constant and clearly for every $x \in [0, 1]$ we have $f(x) = m = M$ which contradicts given property of $f$. So we must have $m < M$. Clearly there are now four distinct points $a, b, c, d$ in $[0, 1]$ such that $f(a) = f(b) = m, f(c) = f(d) = M$. By checking possible linear orderings of $a, b, c, d$ I could find a find a value of $y \in (m, M)$ for which there exist more than 2 values of $x$ such that $f(x) = y$. However this approach looks very clumsy and I suspect much simpler and easier proof is possible. Part b) seemed bit complex and my only guess was that probably $f$ was discontinuous on each subinterval of $[0, 1]$ but I could not prove this claim (may be the claim is wrong!). Perhaps there is a simpler solution to this part of the problem. Apostol's also asks to provide an example of such a function. Any hints on the overall problem will be appreciated.  Update: After looking at Marc's answer, I think I have found a way to show that there are infinitely many discontinuities. Earlier the solution was a part of the question itself but it made the question look quite lengthy hence I moved it to a separate answer.


I am trying to split text into words on the basis of space but I don't want to split words in single quotes into different words.  Here if you can see word 'fd f df' is converted into three words 'fd , f , df' but I want to get this as single word like 'fd f df'. const str = `TEST = 'fd f df' AND Pitch = 444` str.split(/\s+/) // ["TEST", "=", "'fd", "f", "df'", "AND", "Pitch", "=", "444"]  Any help will be appreciated. P.S : this quoted words could be repeated in text many time in any position.

I'm new to regular expressions and would appreciate your help.  I'm trying to put together an expression that will split the example string using all spaces that are not surrounded by single or double quotes. My last attempt looks like this: (?!") and isn't quite working. It's splitting on the space before the quote.  Example input:   This is a string that "will be" highlighted when your 'regular expression' matches something.   Desired output:  This is a string that will be highlighted when your regular expression matches something.   Note that "will be" and 'regular expression' retain the space between the words.


I'm desperately looking for the title of a fantasy series I read in the mid-90s. Hoping someone can find a clue from the details I can remember here:   Series had at least 5 or 6 volumes (at least, maybe more) Read in the mid-90s so could have been written in the 80's (or earlier?) I believe the series was complete when I read it. Story involves multiple worlds each centered on an "element" (a world with floating islands in the air, a world of lush nature, a lava world, a world made of a single giant ocean that nullifies all magic...) Story involves several protagonists from different worlds, all quasi-human in nature. Story starts with veteran assassin with a youngster fleeing in a castle, and I believe they are quickly involved with a sort of wizard who is actually a dragon in disguise. Wizard partially reveals existence of other worlds an world travel intervenes during 1st or second book. Another key character I remember is a kind of antagonist from a people who can only practice magic through tattoos on their bodies. The only body parts not tattooed are face and palm of hands.   Later in the books it is implied that these different "elemental" worlds were actually the Earth that was divided following a cataclysmic clash between science and magic in the past.

I'm trying to identify fantasy book series I encountered some time ago. Here are things I remember:   it was a fantasy setting but with some s-f elements; with many worlds and possibility to travel between them; resembling  setting a little, the two main races were non-human and probably hostile to each other,  a labyrinth (?), which somehow played an important role in the plot, a protagonist was some kind of emissary and was sent on a mission to another worlds  time period: 80s - 90s    Does anyone know what it is the name of the series?


I am running Wind River Linux 4.3 on an embedded Freescale single board computer (SBC). Output from uname -a:  Linux ge101 2.6.34.10-myname-grsec-WR4.3.0.0_cgl #1 SMP PREEMPT Mon Aug 26 01:35:35 PDT 2013 ppc ppc ppc GNU/Linux   There are several modules / processes running and creating log files that I am interested in collecting:   A kernel module logging to /var/log/messages A userspace application which is having its stdout redirected to a log file. This application is automatically started upon bootup by an init.d script. The script does this by the following: nohup ${executable_name} -C ${configfile_name} >> ${logfile} 2>&1 & This same userspace application writes other data to a separate file on the SBC's filesystem. A Python script using the logging module to write to a log file.   I am seeing a bizarre problem where these 4 log files occasionally are "corrupted" in the following way:   Anywhere between 78-309 NUL characters are inserted into the log file Text from another log file (40 or so lines) gets inserted into it When this happens, there is a chunk of data missing from the log file   Additionally, there are some instances where only the NUL characters are inserted, and no text from other logs gets intermingled in.  In a log file on the order of 100k lines, this behavior occurs 7-9 times.  The NUL characters by themselves would be fairly easy to remove during post-processing. However, the unexpected data showing up from other files is breaking parsing scripts. And of course, the missing chunk of data is the most troublesome.  Does anyone know what might cause this bizarre behavior to occur?

I have a small server which I use for testing and programming. Currently it runs Debian 9.4 stretch with 4.14.0-0.bpo.3-amd64 kernel.  Today I tried to connect through SSH but I couldn't then I tried to ping it and it was unreachable. Therefore I had to hard-restart it by unplugging power cable. Then I went to  /var/log/syslog  and I found a strange line containing exactly 6140 characters like the following  ^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@  then nothing else until new log entries of system restart. This is actually the first time it happens.  Does someone know what could it be?


I want to see which command gets executed when pressing a keyboard shortcut.  My use case: I have an external keyboard with no volume up/down keys (also no Fn + ...). The keyboard on my laptop has these keys. I want to define a custom shortcut for my external keyboard to execute the same command as the Volume control keys on my laptop-keyboard.  I found a lot of answers on how to create a custom shortcut but I could not find a way to see which commands gets executed when using an existing shortcut.

Is there any application (or sequence of commands) for this function: seeing the result of the actions, while using a GUI interface, being automatically translated into a Terminal (or similar CLI environment) on the same machine.  I saw this in action long years ago in VBA for Applications (for example the Macros in Excel). I wonder if there is same function in Linux.


Looking for title of short story, travelers come to Urth looking for help from an advanced civilization, against aliens, discover Urth inhabited by essentially backward farmers.  At the end of the story the people agree to help- by moving the planet to follow the aliens home.

First we are told that the Galactic Empire/Federation/Powers-that-be have kept the Earth locked up for being too warlike, but now their help is needed against invaders from another galaxy.  When the aliens land the first thing they meet is a talking bunny.      at the end when humans have accepted to join the fight the alien offers to send ships to transport them. The human leader tells that there is no need...  and the Earth accelerates away.   I must have read this sometime in the mid eighties, so no later than 84 or 85, but the story may be from the sixties or before.


$20=2^2\times5 $  My initial reaction was to write direct products between an abelian and non abelian groups — for example, $Z_5\times D_2$. However, I realized they are both abelian so I am a little stuck. I can't think of any subgroup that is not abelian. Could it be a semidirect product or something? If so, could you give me a hint? My knowledge of semidirect products is sketchy to say the least.

Find four groups of order 20 not isomorphic to each other and prove why they aren't isomorphic.   So far I thought of $\mathbb Z_{20}$, $\mathbb Z_2 \oplus\mathbb Z_{10}$, and $D_{10}$ (dihedral group), but I can't find another one. Would $U(50)$ work? I know it has order 20 and is cyclic but I'm not exactly sure how to move from there. Can someone to point me on the right direction?


Question: How would you prove the Taylor series for a function, and how would you find the exact value of it?   I know that$$e^x=\sum_{k=0}^{\infty}\frac {x^k}{k!}\\\frac 1{1-x}=\sum_{k=0}^\infty x^k\\\sin x=\sum_{k=0}^\infty \frac {(-1)^k}{(2k+1)!}x^{2k+1}\\\vdots$$  My question is: How would you prove the taylor expansion for any polynomial $f(x)$, and how would you evaluate the convergence?  For Example: With $e^x$, letting $x$ be a simple integer like $2$, we have\begin{align*}e^2=1+2+\frac 4{2!}+\frac 8{3!}+\ldots\tag1\end{align*} How would you solve for the exact value of $e^2$ when you have the infinite sequence? (Note that it does converge) And $x$ doesn't have to be an integer. It can also be a number such as $\pi\sqrt{19}$.\begin{align*}e^{\pi\sqrt{19}}=1+\pi\sqrt{19}+\frac {19\pi^2}{2!}+\frac {19\pi^3\sqrt{19}}{3!}+\frac {19^2\pi^4}{4!}+\ldots\tag2\end{align*} Which is intimating.

I know the Taylor Series are infinite sums that represent some functions like $\sin(x)$. But it has always made me wonder how they were derived? How is something like $$\sin(x)=\sum\limits_{n=0}^\infty \dfrac{x^{2n+1}}{(2n+1)!}\cdot(-1)^n = x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}-\dfrac{x^7}{7!}\pm\dots$$ derived, and how are they used? Thanks in advance for your answer.


In The Mandalorian Chapter 7: The Reckoning,      baby Yoda was shown to completely heal a wound using The Force (the final result was like the wound was never there). He even neutralized a strong poison in the system.   I didn't know that a force sensitive was capable of this. Has this Force superpower been shown before in the entire Star Wars universe (including Legends)?

In The Rise of Skywalker we see the Force      healing various people/creatures. The explanation given is that the healthy person gives some of their life energy to heal the wound.    In the book The Courtship of Princess Leia, Luke is lying dying after fighting with Force-wielding witches who ride Rancors (yes that is really a thing in a book and is the one thing I hope is seen on screen one day).  As Luke dies a number of creatures initially, and then plants, the earth, and I am pretty sure the water, all give a bit of their own Force to help heal him.   So is this reference to Force Healing in the book The Courtship of Princess Leia the first instance in canon of Force Healing?


I am matching whole words in a sentence using preg_match in PHP. This works fine. But it happens that sometimes a word is not matched due to one typo. For instance the official word is "Prader Willi syndrome". But then a biologist types "Prader-Willi syndrome" (the extra hyphen).   Is it possible to match words where you allow one typo using a regex?

I have a regex created from a list in a database to match names for types of buildings in a game. The problem is typos, sometimes those writing instructions for their team in the game will misspell a building name and obviously the regex will then not pick it up (i.e. spelling "University" and "Unversity").  Are there any suggestions on making a regex match misspellings of 1 or 2 letters?  The regex is dynamically generated and run on a local machine that's able to handle a lot more load so I have as a last resort to algorithmically create versions of each word with a letter missing and then another with letters added in.  I'm using PHP but I'd hope that any solution to this issue would not be PHP specific.


When you close VS with project files open, the next time you open that solution, it opens the same files.  Is there a way to prevent this?  Currently I try to remember to close all the open tabs before I exit.

Is it possible to open a project in Visual Studio 2008 without opening all the files that were previously opened last time I had the project open.  I have a habit of keeping many files open as I am working on them, so next time I open the project, it (very slowly) loads up a bunch of files into the editor that I may not even need open. I have searched through the settings and cannot find anything to stop this behavior.


How to append “.backup” to the name of each file in your current directory?

I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this?


In reference to your strengths and weakness. How to well describe composure as your strength. I am looking for a word/strength that represent ability to not to panic in any situation(especially difficult one).

What is an adjective to describe the duality of a first responder (such as an EMT responding to a terrorist attack) who is terrified for the wounded, yet simultaneously calm, detached, and capable enough to give aid?


As I was going through my dad's college magazine (of 1989), in the mathematics department quiz section, there was a question:     What is $i^i$, where $i=(-1)^{1/2}$, that is, is $i^i$ a real number, an imaginary number, or undefined?   I was suddenly taken aback, I mean how can be $i$ be raised to the power $i$, I thought may be Cartesian representation helps a bit in solving it but it led me nowhere so can anyone help?

I've been struggling with this problem, actually I was doing a program in python and did   1j ** 1j(complex numbers) (In python a**b = $a^b$ )   and found out the answer to be a real number with value $0.2079$, How to calculate this value of $i^i$?


So, in testing in the USA, an A is the best score you can get. Then comes B, which most students desire, and then comes a C, where you're on the verge of shattering your gradebook by getting a bad grade. Then there's D (even worse), and an F, where you will surely be very ashamed of yourself. Then, there's this alphabetical pattern, A, B, C, D, and then F. But where's E? Why isn't there an E in it? In an answer given, I want a historical explanation of this question that tells how these letter grades popped up, and why E dropped out (or was never included) in the USA. Thanks in advance!

Why do we use F for failing on an otherwise arbitrary alphabetic grading scale? Isn't E just as meaningful for failing as A is for excellent?  I'm more interested in a response on the history of how the current scale came to be.  (Edit: prompted from the comments below, I am asking about this situation within the context of the American grading system.)


My mom came from Venezuela to visit my sister and my family and after 6 months we applied for an extension of stay, she went to Mexico to visit my nephew and his wife but I want her to come back to the USA; how long does she need to be outside before she can re-enter the state?

I entered the USA on a three month visa waiver program from Australia. I am about to return to  Australia and would like to come back again to the USA. How long do I have to wait until I can re-enter the USA for another 3 months?


I have an object that is similar on one side and the other. However, the UV image editor UNwrapped it so that each half has slightly different vertex positions. How can I get it so that all the vertices line up?

Sometimes UV unwrap has several nearly identica islands. However, more often than not they differ a little. If I want to keep identical texture for these -- is there a good way to overlap them perfectly? I know I can do it vertex by vertex, but I hope there is a better way.  I know I can do it for the whole model if it is symmetrical with Symmetrize option from mesh menu. I am talking about selected islands, not all of them.


My Windows 10 was really slow, I was really frustrated so I decided to dual boot Ubuntu. I only put 100 Gigs on it because I wasn't sure if it was a great idea (I have 400gb in total). But it was a love at first test, so I wanna get rid (uninstall) of Windows 10 and put all the 400gb on Ubuntu. The question is, how do i go about doing that? thanks in advance.

I want to keep Ubuntu but remove Windows.


int a=7.78x100; int b=9.78x100;  The values stored after these operations are: a=778 and b=977 My question is that why is the value of b 977 and not 978;

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I am tasked with creating a program that uses functions to take a user input word, store it in an array,  and then display this word, the word in reverse, the word vertically, then the word reverse and vertical. For example:  Input:  array   Output:   array  ---- yarra  ----  a r r a y ------ y a r r a   So far, I have the code to store and display the word, I am just wondering what the best way to display this in reverse would be? The code so far:  #include <stdio.h>  void primaryFunction() {   char arrA[100] = {0};    int n;     //unsigned char ch;     unsigned int i = 0;     printf("Enter Your Word:\n");      for(i = 0; i<n; i++)     {     scanf("%c", &arrA[i]);     printf("\n%c",arrA[i]);      printf("%c",arrA[i]);                } }  int main(void) {   primaryFunction(); }   Any guidance can help. Thank you!!

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


For each positive integer n, let $\gamma_n = 1+\frac12+ \cdots + \frac1n -  \int_1^n \frac1x \, dx$. Prove that the sequence $\{\gamma_n\}$ converges.

I want to show that there exists a constant $\gamma\in\mathbb{R}$ such that   $$ \sum_{j=1}^N \frac1{j} = \log(N)+\gamma+O(1/N). $$  I know how to prove that the Euler-Mascheroni constant exists (which I believe $\gamma$ to be), but I am having trouble with the big-$O$ notation and the subsequent bounding. I've considered   $$ \left|\left(\sum_{j=1}^N \frac1{j}\right) - \log(N)-\gamma\right|\le |K/N| $$ for some $K$, and I was approaching this by trying to show the that the left side of the inequality decays faster, but so far am stuck. Any advice for this type of problem, or analogous ones, would be appreciated.  Thanks!


Let $R$ be a ring that satisfies ACC on the set of its left ideals and   $M$ be a finite generated $R$-module. Prove that every submodule of   $M$ is finitely generated.   I know that if $M$ satisfies ACC condition then every submodules of it are finite generated. I only want to show that $M$ satisfies ACC condition.  Help me some hints.  Thanks a lot.

Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.   Proof: Since $M$ is finitely generated module, there exists a free module $N$ such that $M \cong N/\ker(f)$ where $f:N \rightarrow M$. Since $N$ is free, it can be expressed as direct sum of isomorphic copy of underlying ring, i.e. $N \cong\bigoplus R$. Since $R$ is noetherian ring, $\bigoplus R$ is also noetherian. Since $\ker(f)$ is a submodule of $\bigoplus R$, $\ker(f)$ is also noetherian, which implies that $M$ is noetherian.  Is my proof correct? Is it true that direct sum of noetherian ring is noetherian?    Remark: Since $N$ and $\ker(f)$ are both noetherian, then $N/\ker(f)$ is also noetherian, and hence $M$ is also noetherian.  Since $M$ is finitely generated, the free module $N$ is of finite rank, and hence is isomorphic to finitely many copies of $R$.


Given a multivariate gaussian distribution of the form  $$\begin{pmatrix} y_{1}\\y_{2} \\y_{3}\end{pmatrix} \sim N\begin{pmatrix} \begin{pmatrix} 0\\0  \\0 \end{pmatrix}, &\begin{pmatrix} \sigma_{1}^{2} & 0 & \rho\sigma_{1}\sigma_{3}\\  0& \sigma_{2}^{2} & \rho\sigma_{2}\sigma_{3}\\  \rho\sigma_{1}\sigma_{3} &  \rho\sigma_{2}\sigma_{3} & \sigma_{3}^{2} \end{pmatrix}  \end{pmatrix}$$ Since it is known in the gaussian distribution that zero covariance implies independence then is it safe to write the likelihood as: $$f(y_{1},y_{2},y_{3})=f(y_{3}|y_{1},y_{2})*f(y_{1})*f(y_{2})$$  If yes, then how can we write  $f(y_{1},y_{2},y_{3})$  PS : A similar question has been asked in cross validated :

I would like to find a computationally quick and sufficiently accurate way (i.e., either analytically or numerical approximation) to compute a conditional probability for a specific multi-variate normal distribution, which is defined as follows:  Let $X_1, \dots, X_n$ be n independent (univariate) normal random variables. And let $A_1, \dots, A_k$ be defined as sums of subsets of those random variables, i.e.,: $\forall i: A_i = \sum_{j \in S} X_j$, where $S \subseteq \{1,\dots, n\}$.  I am looking for the following conditional probabilities of $A_i$:  Pr[ $A_i \leq x$ | $A_j \leq t$ $\forall j \in C$ and $j \neq i$ ], where $x$ is any number smaller than $t$, and $C \subseteq \left\{ 1,...,k \right\}$ is a subset of all possible variable indices on which the probability is conditioned. So the condition is on several $A_j$'s.  To the best to my knowledge, the conditional density of a multi-variate normal density is generally not a (uni-variate) normal distribution. I tried via Monte-Carlo simulation, but approximation is not sufficiently accurate when using 500,000 samples, 2000 bins (to classify the results) for a "problem" with 50 random variables, i.e. n=50.  Analytically that doesn't seem to be trivial. I have asked quite a few Statisticians around me and so far we haven't found a solution.


If $v$ is a column vector, then how many non-zero eigenvalues does the matrix $vv^T$ have? What are the eigenvalues? What are the corresponding eigenvectors? What are the eigenvectors corresponding to the zero eigenvalues?  [Note: This is not homework]

Given a column vector $v$ in $\mathbb{R}^n$, what are the eigenvalues of matrix $vv^T$ and associated eigenvectors?  PS: not homework even though it may look like so.


I've seen the proof of $\lim_{x\rightarrow0} \frac{\sin(x)}{x}=1$ but it uses the fact that $\tan(x)>x$ which in all places says it is obvious but this is maths and a I'd like to see a purely rigorous proof. If anyone knows about please comment and thanks in advance.

How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution.  This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, that proving the above statement is enough for proving the continuity of $\sin$, but I can't find out how. Any help is appreciated.


I am trying to implement a matrix class.  Class Definition  template <typename T> class Matrix { private:     int size;           //size of matrix     T value;     T ** M; public:     Matrix(int m = 2);     Class implementation  /* Matrix constructor */ template <typename T> Matrix<T>::Matrix(int m) : size(m), value(0) {     M = new T*[size];     for (int i = 0; i < size; i++)     {         M[i] = new T[size];         for (int j = 0; j < size; j++)         {             M[i][j] = value;         }     } }   This is how I create an object:  Matrix<int> A = Matrix<int>(3);   I keep getting this error:      Error 2   error LNK2019: unresolved external symbol "public: __thiscall   Matrix::Matrix(int)" (??0?$Matrix@H@@QAE@H@Z) referenced in   function _main   Any ideas what can be causing this?

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


राम (hindi language)  I am working on a table where many rows contains value like this &#2352;&#2366;&#2350; it shows in browser like राम  and many rows already contains राम  but I want to replace all encoded value with decode values for this i used find replace query also put data in form and updated but every time db stores encoded  value  Structure of table  hindi   varchar(256)    utf8_unicode_ci   what i did  <?php echo $queryfetch="select hindi from users where id='2'"; $resultfetch=mysqli_query($c,$queryfetch); while($row  =   mysqli_fetch_array($resultfetch)) { echo $queryupdate="update users set hindi='".html_entity_decode($row['hindi'])."' where id='2'"; $resultupdate=mysqli_query($c,$queryupdate); } ?> select hindi from users where id='2'  update users set hindi='राम' where id='2'  ** sql before =&#2352;&#2366;&#2350;  **sql after = à¤°à¤¾à¤®**

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I try to find any solution with sort multi-dimensional arrays, but don't see anything match my requirement.  Here is my example that I want.  I want to sort below array by "views" DESC  $arr = array( 0=>array(     'id'=>11,     'views'=>10,     'title'=> 'html' ), 1=>array(     'id'=>12,     'views'=>4,     'title'=> 'Java' ), 2=>array(     'id'=>13,     'views'=>100,     'title'=> 'Boostrap' ) );   to  $arr = array( 0=>array(     'id'=>13,     'views'=>100,     'title'=> 'Boostrap' ), 1=>array(     'id'=>11,     'views'=>10,     'title'=> 'html' ), 2=>array(     'id'=>12,     'views'=>4,     'title'=> 'Java' ) );   without loop in php.  How can I do this.

I have CSV data loaded into a multidimensional array. In this way each "row" is a record and each "column" contains the same type of data.  I am using the function below to load my CSV file.  function f_parse_csv($file, $longest, $delimiter) {   $mdarray = array();   $file    = fopen($file, "r");   while ($line = fgetcsv($file, $longest, $delimiter))   {     array_push($mdarray, $line);   }   fclose($file);   return $mdarray; }   I need to be able to specify a column to sort so that it rearranges the rows.  One of the columns contains date information in the format of Y-m-d H:i:s and I would like to be able to sort with the most recent date being the first row.


I'm trying to change how the categories and subcategories are displayed in a post. As you can see in the following image, the Category (España) is displayed before the subcategory (Valencia), but I'd like it to be displayed the other way around: Valencia, España.  I guess it is something simple which I'm not able to see. Any help would be much appreciated. Best, M.


It is not difficult to prove that $0/0$ is not equal to any constant $c \ | \ c/c = 1 \ \land \ c \in \mathbb{R} \cup \mathbb{C}$.  First assume that $0/0 = c$. Consider the true equation $2\times0=0$. Based on our initial assumption, dividing the equation by zero gives $2\times0/0=0/0 \ \Rightarrow \ 2c=c$. Based on our definition of $c$, dividing the equation by $c$ gives $2=1$. However, $2 \ne 1$. $\ \therefore\ $ $0/0 \ne c.\quad\blacksquare$  Sorry for the incomprehensible spacing. Anyways, whenever I attempt to prove that $0/0 \ne 0$, I always end up arriving at $0=0$. Can someone find (or make) a proof? I couldn't find one online either.  Just some clarifications: In in the argument that ends with a box, I am attempting to prove that $0/0 \ne 0$.  Extra clarifications: This is not a duplicate. I am not asking for an intuitive proof that division by zero is nonsensical. I am asking for a concrete mathematical proof that $0/0 \ne 0$. And sorry about my previous edit, that was incorrect but I fixed it.

Possible Duplicate:          What will be the answer if zero$(0)$ divided by zero$(0)$ Why It is un answerable?   $$\frac 00=\space ?$$ Thanks in Advance, Vicky


HttpRequest req = new HttpRequest();  req.setEndpoint('callout:Google/maps/api/place/findplacefromtext/json?');         req.setHeader('key', '{!$Credential.Password}');         req.setMethod('GET');         Http res = new Http();         HTTPResponse res = res.send(req);          Since Google API allowsing us to use ApiKey and we do not need to do Outh2 in that case. I am using APIKEY in password option in Named Credential. I have checked Allow Merge Fields in HTTP Header option.  Error I am getting:  "error_message" : "You must use an API key to authenticate each request to Google Maps Platform APIs.

I have a named credential as follows:  Name   Test_Credential URL    https://www.somesite.com Identity Type    Named Principal Authentication Protocol    Password Authentication Username   foobar Password   mySomeSiteDeveloperKey Generate Authorization Header   FALSE Allow Merge Fields in HTTP Header    TRUE Allow Merge Fields in HTTP Body     TRUE   The service that I am trying to authenticate against uses URL parameters to pass in the developer key and username. Is there any way to use  to pass those in to the URL?   The Named Credential attributes seem not to get decoded until the request is actually sent, as debugging the endpoint, or headers if I set them per the linked doc, show the un-merged data. I can get the callout to go to the right place, and return the expected error because the auth information is not provided. Anybody know of a "show me my HTTP request" site that I could point to to get a better idea of how this works?  I've tried both of these:  req.setEndpoint('callout:Test_Credential/api/action?id={!$Credential.Password}&account={!$Credential.UserName}');  req.setEndpoint('callout:Test_Credential/api/action' + '?id=' + '{!$Credential.Password}' + '&account=' + '{!$Credential.UserName}');   (Edited to remove the part about $Credential vs. $Test_Credential as I was able to determine that it is the former, and see the merged creds by calling out to .)


I'm the new to Ubuntu. Recently, I downloaded the ISO image (32-bit). I have a laptop in which Windows 7 is pre-installed and now I want to install Ubuntu alongside Windows 7. I have burned a DVD for it but I don't know how to install it.

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


I have vim version: 2:7.4.052-1ubuntu3 installed.  How do I update to the latest version using the terminal?

I'm on Ubuntu 12.04 and want to know how to update Vim via the command line. What is the command to update this?


What is a nerve compared to a neuron? Is it a collection of axons alone or does it include cell body too? I'm pretty confused of what actually the "nerve" is composed of. I had imagined that the nerve is actually having a no of neurons synapsing together but I guess it's not so.. Pls do make a clear demarcation between a neuron, nerve,  nerve fibre, ganglia, nuclei

This question has haunted me for two years.    mentions :      A nerve is an enclosed, cable-like bundle of axons (the long, slender projections of neurons) in the peripheral nervous system. A nerve provides a common pathway for the electrochemical nerve impulses that are transmitted along each of the axons to peripheral organs.   Okay, my book also defines like that. But if the nerve runs only with bundles of axons, where then are their soma located?   They say nerves are formed of many axons bundled together. Now, if there are axons, there must be soma, but they do not form nerve & hence are not present in nerve. So, where are they? Are they present at the beginning of the nerve?   Also, nerves communicate with each other. Books picture this as two neurons one above other; the above one sends impulse through its terminals to the dendrites of the neuron below it. So, how do these two neurons constitute a nerve?? After all, they now contain the cyton?? So, how do neurons one above other form nerve as they now contain the soma??   PLz explain.


Intel has two version of the Q9550 cpu, one of them is a 95W and the other is a 65W. But I didn't find anywhere on how to tell whether you have one or the other.  Is there anywhere to check for that?  (I use Arch Linux, if that matters.)

I have a Intel Xeon CPU at 3.06GHz with 512KB cache size.  I was wondering if the on-chip cache for the machine is L1 or L2. Is there a way of knowing that through a Unix command?


I sometimes use "manner" to use noun-phrases as adverbs, like "in the manner of a vigilant watchdog". If I reverse the order, does the noun phrase then have to be hypenated? Like so: "in a vigilant-watchdog manner"

Some compound words are written without hyphens (nonaggression, nonbeliever), some with hyphens (well-intentioned), and others with spaces (post office).  Is there a rule or good guide as to which option should be used?


Prove that given any $17$ integers, there exist nine of them whose sum is divisible by $9.$  I'm pretty sure we have to use the pigeonhole principle, with the possible remainders as the pigeonhole, but that gives a lot of possibilities and I don't know where to start.  I tried to compare it to this question which was easier to solve:  Prove that given any $5$ integers, there exist three of them whose sum is divisible by $3.$

There was a problem in a recent programming competition which my friend solved by assuming the following conjecture:     Show that for any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.   I have thought about this problem for a while but can't seem to prove it, but I couldn't come up with a counter-example either.    A similar problem has a well-known solution: show that for any set of $n$ integers, there is a non-empty subset whose sum is divisible by $n$.  The proof goes as follows. Suppose the set is $\{x_1, x_2, \dots, x_n\}$ and hence define $s_i = \left(x_1 + x_2 + \dots + x_i\right)\bmod n$, with $s_0 = 0$. Then we have the set $\{s_0, s_1, \dots, s_n\}$ with $n+1$ elements, but each $s_i$ can take only $n$ distinct values, so there are two $i, j$ with $i\neq j$ such that $s_i = s_j$. Then $s_j - s_i = x_{i+1} + x_{i+2} + \dots + x_j$ is divisible by $n$.  However, this approach can't directly be applied to this problem since now we need to ensure that we choose exactly $n$ integers.


A user posts an answer that is wrong content-wise, meaning that it does not fit under any of the flags.  Now, it has received a huge amount of downvotes.  Can the user just delete it and add a new, exactly-the-same answer?

I recently downvoted an answer on SO because I believe it didn't actually answer the question, and before I could add a comment, the answer had been deleted. Two minutes later, I looked at the question again, and the same user had re-posted his answer, without the downvote.  I've seen this guy remove answers with negative feedback/downvotes in the past and repost them exactly as they were. My biggest concern is that by getting round the system this way will hide legitimate feedback that may be very relevant to whoever asked the original question.  I feel there's an argument for requiring a vote to close ANY answer or question with any kind of feedback. Personally, I've only ever deleted one question that had answers, because I realised there wasn't an easy way to explain what I was asking, and realised shortly after I posted it that it wasn't possible anyway.


I want to factor the $X^5 + X^3 + X^2+1$ into irreducible factors in the field $\mathbb{Z} / 2\mathbb{Z[x]}$. I'm new in abstract-algebra, so I couldn't apply ideas from similar tasks to this one. So, can someone explain it for me on this case? Looks like I have to brute-forse some roots and then compose their multiplies into $\mathbb{Z} / 2\mathbb{Z_{[x]}}$, but I'm not sure.

$$x^3+x^2+x+1$$  $$x^5+x^3+x^2+1$$  $$x^5+x^3+x+1$$  I've tried applying Eisenstein criterion but I can't figure it out. Thanks in advance.


I have an iPhone 5 (iOS 7.0.2) which is locked and I can't unlock it because I've forgotten my Apple ID.  Is there any solution?

Apple showed this new feature in iOS 7 called Activation Lock, that if you enable "Find My iPhone" on a device that is lost or stolen, a person that finds/gets the iPhone will not be able to wipe it or reset it. I'm curious whether the lock is designed to prevent these avenues to defeat the lock:   Can they completely drain the battery and leave the phone in that state for a couple of months and then try it? Or, can they use any third-party software that can access iPhone from outside the iTunes and wipe it that way? Or, can they simply "jailbreak" it and forget about this Activation Lock?   By what methods can this lock be defeated or bypassed?


I tried to edit my rc.local file in order to use a script with parameters on startup but it doesnt exist. I am using Kubuntu 18.04. Has it been removed?

I am setting up quota on my Linode server running Ubuntu 16.10, and I get the following error      Cannot stat() mounted device /dev/root: No such file or directory   So to fix this, I reached  for the fix which is done by adding   ln -s /dev/xvda /dev/root /etc/init.d/quota restart   to the /etc/rc.local. But Ubuntu 16.10 doesn't uses rc.local anymore instead uses . What is the alternative for rc.local, How can I run the above commands on startup?  Also I enabled the service using systemctl enable rc-local.service but it didn't work for me. Any lead would be appreciated.


I have a problem with my grid. It doesn't want to center vertically even when using the properties "align-items: center" and "align-self: center"    .citations {     background: #1070b4;     margin-top: 88px;     height: 600px; } .citations-grid {     width: 100%;     max-width: 1290px;     height: auto;     display: grid;     margin: 0 auto;     grid-template-columns: repeat(auto-fill, 625px);     justify-content: center;     align-self: center; }

“La musique commence là où s'arrête le pouvoir des mots.”
 - Richard Wagner

“La musique est la langue des émotions.”
 - Emmanuel Kant

 “La vie sans musique est tout simplement une erreur, une fatigue, un exil.”
 - Friedrich Nietzsche

I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. I found some solutions, but all of them are missing Internet Explorer 6 support.
Div to be aligned vertically
   How can I center a div vertically in all major browsers, including Internet Explorer 6?


Let $R$ be a ring and let $I,J,K$ be its ideals. Let $I=(0:J)=\{r\in R \mid rJ = 0 \}$. Then $I$ is called the annihilator of $J$. Now let $I=(K:J)=\{r\in R \mid rJ \subseteq K \}$. Is there a name for $I$ in this case with respect to $J$? ($I$ is ... of $J$?)

Wat exactly does the notation $$A : (BC)$$ mean? We are talking about fractional R ideals. From definitions i get, if $$a \in A:(BC)$$ then $$a(BC)\subset A$$  But what am i saying exactly?  I hope someone can explain this to me.


main function is part of the class therefore we should be able to access root as it is instead of tree.root after creating an object of the class, as instance variables are accessed using this variable inside instance method?  class Main {       Node root;      Main()      {          root = null;      }       public static void main(String[] args)      {          Main tree = new Main();         //  tree.root = new Node(1);          }  } ```

To be specific, I was trying this code:  package hello;  public class Hello {      Clock clock = new Clock();      public static void main(String args[]) {         clock.sayTime();     } }   But it gave the error      Cannot access non-static field in static method main   So I changed the declaration of clock to this:  static Clock clock = new Clock();   And it worked. What does it mean to put that keyword before the declaration? What exactly will it do and/or restrict in terms of what can be done to that object?


Elements $a$ and $b$ of an integral domain are associates if   $a\mathrel{\vdots}b$ and $b\mathrel{\vdots}a$   I have proved this fact. Then I tried to find out $a$ and $b$ which divide each other and does not associate. This may happen only in non-integral domains of course. But I couldn't find an example. Can someone suggest one?  Definition of associates.     $a$ and $b$ are associates if $a=b\epsilon$ where $\epsilon$ is   invertible element of the ring.      $a\mathrel{\vdots}b$ means $a$ is divided by $b$. ($a=bc$). It is the   same as $b|a$.

Recall the following relevant definitions. We say that   $b$ is divisible by $a$ in $R$, or $a\mid b$ in $R$, if $b = r a$ for some $r\in R$. $a$ and $b$ are associates  in $R$ if $a\mid b$ and $b\mid a$, (or, equivalently, if $aR = bR$). $u\in R$ is a unit if it has a multiplicative inverse (a $v\in R$ such that $uv=vu=1$). $a$ and $b$ are unit multiples in $R$  if $a = ub$ for some unit $u\in R$.   Given these definitions, my question is,     If $R$ is a commutative ring with unity and $a,b\in R$ are associates in $R$, are $a$ and $b$ unit multiples in $R$?   I was told that this not always true. But I encountered some difficulties in finding a counterexample.


When trying to use hyperref on Overleaf, I am getting the following warning: Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):  removing `math shift' on input line 246.  As you see, it's a reasonably long document, but the code that gets into conflict is the one that follows. It's in portuguese, but essentially I'm trying to create a section to talk about tensor spaces. \subsubsection{Produto Tensorial e o Espaço $T^{r}_{s}$}   On the preamble, I have: \usepackage[colorlinks,citecolor=blue]{hyperref}   As I'm new to LaTeX, it might be the case that I am using a wrong command to embed math into text, but I want to be sure that this is solved for future projects. Thanks in advance!

Possible Duplicate:          The following code:  \subsection{The classes $\mathcal{L}(\gamma)$}   generates the errors:  Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `\gamma' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   What do I have to do to keep \gamma in the subsection, so that it is also listed in the table of contents?


I bought a used 80GB SSD on eBay and checked it with CrystalDiskInfo.  Its saying 36,000GB have been written on the SSD. How much data can be written before failure?

Some Sold State Disks (SSD) have a  (MTBF) of 2,500,000 hours. If you divide that by the rough number of hours in a year you get 2500000÷(365×24) ~= 285 years before there is a problem.  I know that the first generation SSD's used to have a short life - but now the estimated time before they fail seems absurdly high. Most warranties only cover them for 1-3 years it seems.  How long are the modern, SATA III drives supposed to last?


This is a follow up of my previous question . Say we have a Python file with this content:  hello.this_is("bla bla bla") some random text hello.this_is('hello hello')  hello.this_is("bla") hello.this_is("1hello")  hello.this_is("2hello") other stuff   I want to extract all the strings within quotes in hello.this_is(, either single or double quotes, so my output is like:  bla bla bla hello hello bla 1hello 2hello   From the answers on the other question I ended up having this expression:  grep -Po '(?<=hello\.this_is\((["'\''])).*(?=\1)' file   Which works well... unless there are two matches of hello.this_is() in the same line and using the same kind of quotes. In that case, the output is like:  bla bla bla hello hello bla 1hello")  hello.this_is("2hello    # this is wrong   That is, the .*(?=\1) is a greedy match, so it matches until the last occurrence of the captured group happens again, instead of matching two different patterns.  How can I change the regex in Grep so that it matches everything up to the next captured group in a non greedy way?  To have a very simplified example, it would be like if we want to get all the numbers between the "hello" text in "hello23hello24hello25". Ideally you would get "23" and "24", but instead I get:  $ grep -Po '(?<=(hello)).+(?=\1)' <<< "hello23hello24hello25" 23hello24   Using a more representative example, let's say we use the capture group to match either "hello" or "hillo" in this example:  $ grep -Po '(?<=(hello|hillo)).+(?=\1)' <<< "hello23hello24hello25hillo26hillo27" 23hello24 26   While the desired output would be "23", "24", "26".  I was thinking of replacing the .+ pattern with something like [^\1]+ so it matches everything but the captured group... but it does not work.

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


I know how to hide a volume with DISKMGMT.MSC (Right click, Change Drive Letter and Paths, and remove the drive letter),    but here I want something a little bit different:   I would like to still have the disk mounted as E: (thus we can launch a program there, we can access it via cmd.exe, symlinks to E:\mydirectory\ will still work, etc.)  but just not see it in the Computer Explorer view:    How to do this?  (I'm admin, and there is only 1 user account).    Note:  doesn't work, no option to remove E: only appears in the list:

I need to hide the D: drive for specified users on Windows 7. How can I do that?


My attempt The problem can be reduced as distributing 5 elements among 4 elements. The only way to do this is by making groups of $2,1,1,1$ So number of ways are $$\frac{ 5! \times 4!}{2!\times 1! \times 1! \times 1! \times 3!}$$ $$=240$$ But the answer is $44$ This was just my attempt, which is wrong. What is the correct way to solve it?

I understand the whole concept of Rencontres numbers but I can't understand how to prove this equation  $$D_{n,0}=\left[\frac{n!}{e}\right]$$  where $[\cdot]$ denotes the rounding function (i.e., $[x]$ is the integer nearest to $x$). This equation that I wrote comes from solving the following recursion, but I don't understand how exactly the author calculated this recursion.  $$\begin {align*}  D_{n+2,0} & =(n+1)(D_{n+1,0}+D_{n,0}) \\ D_{0,0} & = 1 \\ D_{1,0} & = 0  \end {align*} $$