Fifteen people are sitting at a round table. There are 15 name cards on the table, but no one is sitting in front of their own name card. Show that you can rotate the table in such a way that at least two persons will sit in front of their own name card. How do I show this?   I know that you have to use the pigeonhole-principle, but I can't seem to understand in which way I can use this principle in this case.

Fifteen chairs are evenly placed around a circular table. On the table are the name cards of fifteen guests. After the guests sit down, it turns out that none of them is sitting in front of their own card. Prove that the table can be rotated so that at least 2 guests are seated in front of their own name card.  The extreme case is having swapped names in pairs i.e.   1 sits where 2 should sit and vice versa,  3 sits where 4 should sit and vice versa,...  Because no rotation will get two correctly seated, unless their number is odd from pigeon.  Missing something? Is this really the extreme case?


Suppose $x\in\mathbb{R}^n$ and $A\in\mathbb{R}^{n×n}$, and all entries in both of them are non-negative. Moreover, we have $$\mathbf 1^Tx = 1,$$ $$\mathbf 1^TA = \mathbf 1^T.$$ What is a sufficient condition for $$x,Ax,A^2x,...,A^{n−1}x$$ being linearly independent?

Suppose $x\in\mathbb{R}^n$ and $A\in\mathbb{R}^{n\times n}$. What is a sufficient condition for $$x, Ax, A^2x, ..., A^{n-1}x$$ being linearly independent?


The topography of an empty lake is given by a function f(x,y)=z. Each spring the lake is filled by water. The waterstand is given by a constant z=c, where c is a constant. How long is the shore of the lake?   What I am actually asking is: Is there any way to compute the lenght of a regular implicit curve?

While an explicit function $y(x)$'s arc length $s$ is easily obtained as  $$s = \int \sqrt{1+|y'(x)|^2}\,dx,$$   is there any formula for implicit functions given by $f(x,y) = 0$? One can use the implicit differentiation $y'(x) = -\frac{\partial_y f}{\partial_x f}$ to obtain  $$s = \int\sqrt{1 + |\partial_y f / \partial_x f|^2}\,dx,$$  but that still requires (locally) solving for $y(x)$. Is there any formulation that does not require this, e.g. another implicit equation involving $s$?    Thoughts so far:  One could rewrite $s$ as  $$s = \int |\nabla f|\, |\partial_x f|dx,$$  or symmetrize to  $$s = \int |\nabla f|\, \underbrace{(|\partial_x f|dx + |\partial_y f|dy)}_{(*)}/2$$  where $(*)$ might be strongly related to $|df|$ I guess (though it's not identical due to the $|\cdot|$), but then?


Sometimes LaTeX will give the warning like  Missing character: There is no <xxx> in font <xxx>!   How to test it (I mean a macro like \IfCharExist)? And how to replace this missing character with something else like \rule?

Because I began to use many Unicode characters (Japanese, some unusual diacritics, etc.) I switched from LaTeX to XeLaTeX to render my documents. Unfortunately, if a font is missing, the letters are simply left out (for example, when I had forgotten to specify the font for Japanese) without any error (and I can't seem to spot a warning either). I will read the result, but I prefer to get some early warning if some character isn't available. Is there any way to get a warning about characters that have not been rendered? An error would be even better.


Coming from Windows, I wished to change the Open Location... keybinding for my browsers. I was able to do it for Chrome by following the suggestions , but the same process does not work for Firefox.   I looked at the other answers where they  an Add-on called Saka but it is really complicated for me. All I wish is to have the following Keybindings.     Cmd ⌘   D   for Open Locations...  Cmd ⌘   L   for Bookmark this Page...   I am using MacOS Mojave (10.14.5) and Firefox (67.0)  I would be grateful if someone could help me figure this out.   Thanks,

I created the shiftcommandn shortcut for Firefox in Syst Prefs to match other browsers' behavior.     It registers in the Firefox Menubar.     But pressing the shortcut opens a new non-private window, and it loads there the first item in my "Top Sites".   I imagine I could create another shortcut to override this behavior, but what is this behavior? I don't see anything highlighted in the Firefox Menubar when I hit the shortcut. Or might there be another solution (other than using a different shortcut to open new private windows)?   Problem exists on both Mojave and High Sierra. Default Firefox shortcut (shiftcommandp) still opens a new private window.


Let $S_n$=$\sum_{k=1}^n\frac{1}{k}$. which of the following is true?   $S_{2^n}\ge\frac{n}{2}$ for every n$\ge1$. $S_n$ is a bounded sequence. $|S_{2^n}-S_{2^{n-1}}|\to0$ as n$\to\infty$. $\frac{S_n}{n}\to1$ as n$\to\infty$.   I have a confusion that whether $S_{2^n}$=$\frac{1}{2}+\frac{1}{2^2}+\dots+\frac{1}{2^n}$?  or $S_{2^n}$=$1+\frac{1}{2}+\frac{1}{3}+\dots+\frac{1}{2^n}$?

Let , $\displaystyle S_n=\sum_{k=1}^n\frac{1}{k}$. Which of the following is TRUE ? (A) $\displaystyle S_{2^n}\ge \frac{n}{2}$ for every $n\ge 1$. (B) $S_n$ is bounded sequence. (C) $\displaystyle|S_{2^n}-S_{2^{n-1}}|\to 0$ as $n\to \infty$. (D) $\displaystyle\frac{S_n}{n}\to 1$ as $n\to \infty$.  As the series is divergent , so (B) is FALSE. If (C) is TRUE then $\{S_n\}$ is a Cauchy sequence, which is NOT possible. Again , from Cauchy's first limit theorem , $\displaystyle\frac{S_n}{n}\to 0$ as $n\to \infty$. So it is FALSE. So finally , (A) is correct. Am I correct ?


I oftentimes have a dot on the review queues tab, normally indicating that there's stuff to review in the queues, yet nothing is available for reviewing, in both main and meta sites.   What does it mean when there's a dot on the review tab yet there's no review to perform in the queues?

I just noticed that the Close Votes review-needed indicator is red for me on ELL:    When I click on it, however, it shows that the queue has been cleared:    I've read the explanation about how the review-needed indicators work, but I didn't see anything that could explain what's happening:    I've tried refreshing the page in Firefox, and I've tried loading the page in Chrome, all with the same results.  Any idea what's going on?


True/False: If there exists $L \in \mathbb{R}$ such that $\lim_{n \to \infty }b_n=L$, and we know that $\sum_{n=1}^\infty a_n$ is convergent, then  $\sum_{n=1}^\infty a_nb_n$ is convergent. If $a_n,b_n \ge 0$ then this is true from the limit definition. But what happens if $a_n,b_n$ are not necessarily non-negative? Thanks!

Prove or disprove: if $\sum\limits_{n=0}^\infty a_n$  converges and $\lim\limits_{n→\infty}b_n =0$, then $\sum\limits_{n=0}^\infty a_n  b_n$ converges.  I tried this example $$a_n= b_n = \frac {(-1)^n} {\sqrt {n+1}},$$ this will show that $$\sum_{n=0}^\infty a_n  b_n = \sum_{n=0}^\infty \frac {1} { {n+1}},$$ which is the Harmonic series, diverges.   However, I tried every convergent test but I couldn't show that $$\sum_{n=0}^\infty \frac {(-1)^n} {\sqrt {n+1}}$$ converges.


I've been successful to achieve shade less material in Blender by following set up:    but is there any way we can allow these materials to cast shadows? Thanks.

Is there a way to make a true toon shader material in Cycles?  Here's, in order of importance, what would be ideal to find in such a shader:   Must use Cycles Must be an actual shader Must not rely on lighting Must be independent of camera position Must react directly to lighting rather than manually having to change it to emulate it Should be easily made into a node-group Should have the following configurability:   Main color Darkness color Shadow depth (how far the shadow goes from the unlit side)    Below, I'll be listing some already-found methods and their flaws:    Cycles's Toon BDSF:  Source: Blender  Result:    Node setup:    Cons:   Not a clear-cut two-color shading Reacts to diffusion of surrounding objects      Mask & Ramp:  Source:   Result:    Node setup (Compositor):    Cons:   Very grainy Does not support colour textures Not easy to change shadow depth in a nodegroup Not a material, requires compositor Requires use of object indexes     Shadeless Fresnel:  Source:   Result:    Node setup:    Cons:   Uses camera's direction Ignores lighting Not easy to change shadow depth in a nodegroup     Shadeless Normal:  Source:   Result:    Node setup:    Cons:   Ignores lighting Direction of shadow is manually changed Not easy to change shadow depth in a nodegroup   However, this one is easily the best one. It's pretty great, and would work still images very well.    That's all I've got. Does anyone else have any methods that fall under most of the criteria I listed above? Also note that OSL is totally fine, if it works.


From observer point of view an object, which falls into black hole never crosses its horizon. Then how does black hole appears and grows its mass?  Or does any black hole looks (and feels by all other information sources) for us like a void sphere with all mass around its horizon?

The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through?


\documentclass{article} \usepackage{wrapfig}  \usepackage{xcolor} \usepackage{lipsum}% dummy text only  \begin{document}  \lipsum[2] \begingroup \setlength{\intextsep}{0pt} \setlength{\columnsep}{5pt} \begin{wrapfigure}[15]{l}{6.5cm}     \begin{tabular}{@{}cc@{}}     \textcolor{blue}{\rule{3cm}{3cm}} &% Dummy image replacement     \textcolor{orange}{\rule{3cm}{3cm}} \\% Dummy image replacement     \textcolor{green}{\rule{3cm}{3cm}} &% Dummy image replacement     \textcolor{yellow}{\rule{3cm}{3cm}} \\% Dummy image replacement     \textcolor{red}{\rule{3cm}{3cm}} &% Dummy image replacement     \textcolor{brown}{\rule{3cm}{3cm}} \\% Dummy image replacement     \end{tabular} \end{wrapfigure}  \lipsum[2-4]  \endgroup  \end{document}    How do I create a label to place on each figure, a caption under the entire figure and also wrap all the figures and the caption in a box so it is separated from the main text that it is floated around? Thanks

I have an image wich is beside some text, and I would want to frame the image and the caption.  My code is for now:  \begin{wrapfigure}[4]{r}{8cm}     \centering      \fbox{\includegraphics[width=7cm]{Encodages}}     \caption[Différents encodages]{Différents types d'encodage pour «Wikipédia, l'encyclopédie libre»} \end{wrapfigure} BLABLABLA TEXT   but the fbox is only around the image. How could I do that?


Let $X \subseteq \mathbb{R}^{n}$ be given by  $$ X = \left\{ (b_{1}, \ldots, b_{n}) \in \mathbb{R}^{n} \mid \sum\limits_{i=1}^{n} \frac{b_{i}}{i} = 0 \right\}$$  Then prove that $X$ is closed in $\mathbb{R}^{n}$.

Let $S,X$ be subsets of $R^n$ given by $$S=\{(a_1,a_2,\dotsc,a_n)\in R^n|\sum a_i^2=1\}$$ $$X=\{(b_1,b_2,\dotsc,b_n)\in R^n|\sum\frac{b_i}{i}=0\}$$  Then prove that $S+X$ is a closed set in $R^n$.


I was beginning to think I was getting the hang of the basics in Java, but then I found myself back in the dark.  The code here is quite meaningless, but my question is; if I type in "yo" to the question "What is your name", in my mind, the program should print "yo man!", but instead it prints "lala".    Why?  I don't understand.. :-/  import java.util.Scanner;  public class test {  public static void main(String[] args) {       System.out.println("What is your name?");     Scanner sc = new Scanner(System.in);     String str = sc.nextLine();      System.out.println("Hello, "+ str);      if (str == "yo"){         System.out.println("yo man!");      }     else System.out.println("lala");     sc.close();  }   }

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


anyone can help me with this question? I know that to prove continuity the left side limit must equal the right side limit, in this case is 3. But there is only one equation for me to do so, so any idea how to solve this question? Is it possible to choose a value less than 3 and a value more than 3 and sub it into the equation? If that’s the case the limit will not be the same. Really confused with this question, any help is appreciated. Thank you.

I am to show the continuity of this function with the help of $\epsilon$-$\delta$ argument.   The function is: $g: \Bbb{R} \rightarrow \Bbb{R}$, $x \mapsto x^2$.   Given the $\epsilon$-$\delta$ definition of limit, I tried as follows:   We must have: $|f(x)-f(x_0)|<\epsilon$, so then $|x^2-x_0^2|=|(x-x_0)(x+x_0)|=|(x-x_0)||(x+x_0)|$, so $|x-x_0|<\frac{\epsilon}{|x+x_0|}$. So now I will choose $\delta=\frac{\epsilon}{|x+x_0|}$.   Is it enough? I am writing this sentences like a machine, but I am not understanding intuitively.


The Sound Settings button on the panel app is also unresponsive, but it does open via PulseAudio. It's an HP 2000 laptop. I also have Ubuntu 16.04 installed on it, and the volume keys work fine on that OS. I'm fairly new to Ubuntu, so I am stumped.

I installed Lubuntu(14.04.2 LTS) in my Lenovo Z510.  The multimedia hot keys in my laptop is independent. Means to use multimedia keys I don't have to press Fn key. The brightness hot keys are working perfectly but only the volume buttons(mute, volume up, volume down) not working.  I tried  gsettings reset org.gnome.settings-daemon.plugins.media-keys volume-up gsettings reset org.gnome.settings-daemon.plugins.media-keys volume-down gsettings reset org.gnome.settings-daemon.plugins.media-keys volume-mute   but still nothing happens.


My user name on the system (Windows Server 2016) has special characters in it, such as äöü. When opening QGIS, the global variable user_full_name does not display the characters correctly, but makes ? in boxes instead (see image). I display the user name in a map layout, so it should be shown correctly.    I found a lot of resources online about characters not showing fine in database tables or shapefiles, but nothing concerning the global variables. I guess, the solution is simple, but I cannot figure it out.

This isn't a particularly major issue, but I've had this thing nagging me for a while. When looking at QGIS 3.4's global variables, user_full_name is assigned my given and surname, which includes a diaeresis (¨) somewhere in there. I can't seem to find any way to get QGIS to switch/adapt encoding and display the name correctly. The accented character gets switched to that ubiquitous black rhombus.  I looked for info on this behavior and found moderately similar issues like  and  but it's not exactly the same problem as it's not a geodata encoding issue but rather how QGIS deals with values pulled from the OS.  I have tried unchecking the Override system locale tickbox in Options|General as I prefer to use American English even though my OS is set to Canadian French. No effect to observe.  There's somewhat of a workaround right now which is to fix the name in the Project variable project_author as it is editable (it's filled with the offending global variable by default).  I'm curious to know, though, if someone has encountered this before and if there's a solution in QGIS.


I am tempted to install XtraFinder on my mac because of all the features it provides but am worried that it may leave my system vulnerable to a security breach.  The installation dialog box says the following     OS X 10.11 and later users should read about System Integrity Protection before installing.   I went to the link provided ():     You need to partially disable System Integrity Protection. I do not encourage you to disable System Integrity Protection. It makes your computer less safe.   The warning is something to do with code injection into Finder.   Does this mean that only XtraFinder is allowed to inject into Finder? Will this allow some other code to wreak havoc on my system? Will   installing XtraFinder make my system vulnerable?

While using OS X El Capitan 10.11.x, is it safe to disable System Integrity Protection? There are all these additional apps that modify folders and the dock that I want to install but you have to disable rootless first.  Good idea or bad idea?


I can show for any given value of n that the equation  $$\sum_{k=1}^n \cos(\frac{2 \pi k}{n}) = 0$$  is true and I can see that geometrically it is true. However, I can not seem to prove it out analytically. I have spent most of my time trying induction and converting the cosine to a sum of complex exponential functions   $$\frac{1}{2}\sum_{k=1}^n [\exp(\frac{i 2 \pi k}{n})+\exp(\frac{-i 2 \pi k}{n})] = 0$$  and using the conversion for finite geometric sequences  $$S_n = \sum_{k=1}^n r^k = \frac{r(1-r^n)}{(1-r)}$$  I have even tried this this suggestion I have seen on the net by pulling out a factor of $\exp(i \pi k)$ but I have still not gotten zero.  Please assist.

Possible Duplicate:          Prove $$\cos(\alpha) + \cos(\alpha + \beta) + \cos(\alpha + 2\beta) + \dots + \cos[\alpha + (n-1)\beta] = \frac{\cos(\alpha + \frac{n-1}{2}\beta) \cdot \sin\frac{n\beta}{2}}{\sin\frac{\beta}{2}} $$


I am relatively new to C and I came across a typedef for a structure with no name.   What is the point of it?  #define POLY(name,deg)    \     term name[deg] = {0};  typedef struct {   int coeff;   int exp; } term;

I have seen many programs consisting of structures like the one below  typedef struct  {     int i;     char k; } elem;  elem user;   Why is it needed so often? Any specific reason or applicable area?


I want to port 127:0.0.1:80 to the other machine via SSH, how can I do that? I tried adding -R 8000:localhost:80, but it doesn't work. By the way, PHP is also installed on localhost, maybe that's why?

I need to show somebody a website running on my local machine tomorrow. Normally I'd accomplish this by port forwarding on my local router but thanks to failing hardware and its replacement being awful, my current router doesn't let me do port forwarding.  So stuck with this delay and not wanting to push the whole thing onto a proper server, I had a crazy idea: Can I just forward my port to an external server over SSH?  I've done port tunnelling before but I usually do it the right way around:   I connect to a remote box and ask that port 12345 shows up on my local machine at port 12345. I start something on P12345 on the remote machine I can access it via localhost:12345   What I want to do:   Connect to a remote PC and ask that that its local P12345 fetch things from my local P12345 (over the tunnel) I start something on my local computer on P12345 Other people can access remote:12345 and see my localhost:12345


I have a PHP file i need the file to repeat every x hours after the PHP file is done,   Someone told me check out  watch -n x <your command>   but will this repeat after the PHP file is done?  Sorry I'm a newbie, Thanks for the answers!

I have setup a cron to execute one of my php scripts. But the problem is the php script is not being executed at all not even partially.  Here is the cron I have set up  45 23 * * * /usr/bin/php -q /var/www/myscript.php   I have tried the following   I removed the cron from normal user to root user still no results. I changed the permissions on the script using chmod +x /var/www/myscript.php I have used the command whereis php it gives the following  php: /usr/bin/php /usr/share/man/man1/php.1.gz    Now, I don't know what else I can do. Please Help.  P.S. I can execute the script manully and it runs perfectly.


I had a somewhat important file stats.txt, which I accidentally overwrote through a Matlab script (dlmwrite('stats.txt',...)). Is there anything I can do to recover this information? It comes from code that takes many hours to run, so I'd rather not have to do it all over again.  If it matters, I'm running Linux through a remote terminal (ssh-ing to my school's computer).

Is there a command to recover/undelete deleted files by rm?  $ rm -rf /path/to/myfile   How can I recover myfile? If there is such a tool how can I use it?


Given $n$ labelled nodes and $k$ edges, how many number of distinct connected undirected graphs are possible? There can be only one edge between a pair of nodes and cycles are allowed. I came up with following steps:  Find total number of possible edges with $n$ nodes, $t = (n * (n - 1)) / 2$ If $k \le t$, find $ret = t! / (k! * (t-k)!)$ i.e. tCk For $n - 1$ nodes, calculate:   $t1=$ total number of possible edges with $n-1$ nodes $r1=$ t1Ck $ret = ret - r1$   Repeat step $3$ for $n-2$, $n-3$ until $1$  The main idea here is to find all possible ways of choosing $k$ edges from total number of possible edges for $n$ nodes and then remove all possible ways of choosing $k$ edges from total number of possible edges for less than $n$ nodes (which would result in disconnected graph). It seems I am missing something, but I am not able to figure out what. Can someone please help?

Suppose that we had a set of vertices labelled $1,2,\ldots,n$.  There will several ways to connect vertices using edges. Assume that the graph is simple and connected.  In what efficient (or if there is no efficient way, you can just tell me whatever procedure you can think of) way do we be able to calculate the number of possible ways the graph can be made? (even if some graphs are isomorphic to each other, they are counted as separate cases.)


Given the extension $L = Q(ζ_7)$ of $Q$ where $ζ_7 = e^{2πi/7}$,  I had a small difficulty in first proving $L$ is the splitting field of $f(x) = x^6 + x^5 + x^4 + x^3 + x^2 + x + 1$ over $Q$ and that $f(x) = min_Q(ζ_7)$ before showing a further result here   So, for this, I know the six roots of $f(x)$ are $\zeta_{7},\zeta_{7}^{2},\zeta_{7}^{3},\zeta_{7}^{4},\zeta_{7}^{5}$ and $\zeta_{7}^{6}$ so $L = Q(ζ_7)$ is the splitting field of $f(x)$ over $Q$ but how to show $f(x)$ is irreducible over $Q$? I must be missing something simple here.

Can someone give me a hint how to the irreducibility of $X^{p-1} + \cdots + X+1$, where $p$ is a prime, in $\mathbb{Z}[X]$ ?    Our professor gave us already one, namely to substitute $X$ with $X+1$, but I couldn't make much of that.


I am trying to estimate the kernel density for number of days a child is sick. Around 73% of children report not being sick, i.e. zero. How do I estimate a kernel density for this censored variable using Stata?

plot(density(rexp(100))   Obviously all density to the left of zero represents bias.  I'm looking to summarize some data for non-statisticians, and I want to avoid questions about why non-negative data has density to the left of zero.  The plots are for randomization checking; I want to show the distributions of variables by treatment and control groups. The distributions are often exponential-ish.  Histograms are tricky for various reasons.    A quick google search gives me work by statisticians on non-negative kernels, e.g.:  .    But has any of it been implemented in R?  Of implemented methods, are any of them "best" in some way for descriptive statistics?  EDIT:  even if the from command can solve my current problem, it'd be nice to know whether anyone has implemented kernels based on literature on non-negative density estimation


I am writing a paper to a Springer journal and I am trying to use their \bibliographystyle{spbasic}.  I want to sort citation by appearance, hence the first citation in the article should be cited with [1] and second with [2] and so on. But citation is sort by the reference's alphabetically order.   \documentclass[smallextended]{svjour3} \begin{document} \usepackage[sort&compress,numbers]{natbib} .............. \cite{S1} .......... \cite{S2} \bibliographystyle{spbasic}  \bibliography{sssat.bib}   % name your BibTeX data base  \end{document}

I am writing a paper to a Springer journal and I am trying to use   \bibliographystyle{spbasic} However, instead of the number of the reference in the list of references I get something as:     [Hundsdorfer et al(1995)Hundsdorfer, Koren, van Loon, and Verwer]   followed by the citation  What should I do to get the number in the square brackets?  \documentclass[smallextended]{svjour3} \begin{document} \cite{Hundsdorfer:adv}  \bibliographystyle{spbasic}  \bibliography{moje.bib}   % name your BibTeX data base  \end{document}   I may have to do the bibliography manually, as no Springer provided bibtex style produces the output that can be seen in the journal articles.


If one wanted to say something like     no commas: Hello Pete, how are you?    or      commas: Thanks, Julia, this will be helpful!    would he need commas separating the different elements in the interjection or just the comma separating the interjection from the rest of the sentence/clause?

I see a lot of people saying things such as      Nice work, Nick   Or     Thanks, Mat   Is the comma really needed? I'm not 100% sure because my spelling and grammar is not great, but I think it reads very strange.


Let $f(n)$ be the function defined by  $$ f(n) = \frac 1{\sqrt{5}} \left[  \left(1+\sqrt{5}\over2\right)^n-  \left(1-\sqrt{5}\over2\right)^n \right] $$  How do you prove that $f(n) = f(n+2) - f(n+1)$ for all $n = 0, 1, 2, ...$ ?

Fibonacci numbers $f(n)$ are defined recursively:  $f(n) = f(n-1) +f(n-2)$ for $n > 2$ and $f(1) = 1$, $f(2) = 1$. They also admit a simple closed form: $$\sqrt 5 f( n ) = \left(\dfrac{1+ \sqrt 5}{2}\right)^n- \left(\dfrac{1 - \sqrt 5}{2}\right)^n \tag1$$  How to prove (1) using induction?  Remarks One could get (1) by the general method of solving recurrences: look for solutions of the form $f(n)=r^n$, then fit them to the initial values. But there should be a more concrete proof for this specific sequence, using the principle of mathematical induction.


How many maps $\phi : \mathbb{N} \cup \{0\} \to  \mathbb{N} \cup \{0\} $ are there with the property that $\phi(ab)=\phi(a)+\phi(b)$, for all $a,b \in \mathbb{N} \cup \{0\} $?  My Attempt is $$\phi(0)+\phi(m)=\phi(0) \implies \phi(m)=0\quad \text{ for all } m \in  \mathbb{N} \cup \{0\}$$  Hence there is only one such map.  Is it correct?

How to show that there are finitely many maps $\phi:\mathbb{N}\cup\{0\}\to \mathbb{N}\cup\{0\}$ with the property that $\phi(ab)=\phi(a)+\phi(b)$ for all $a,b\in \mathbb{N}\cup\{0\}$.


I'm writing my thesis in Overleaf. and I'm now trying to generate a content of figures using the command "\listoffigures", and now the content of figures is generated, but all citations become dosordered. :( \listoffigures \addcontentsline{toc}{chapter}{List of Figures} \clearpage  And when I delete the command "\listoffigures", they become again in the correct order (start from [1],[2],[3],[4]...). I also tried the command "\bibliographystyle{unsrt}" but it's not helping. \bibliographystyle{unsrt} \renewcommand\bibname{Reference} \bibliography{Reference}  The citations in the doc "Reference.bib" are generated by citaiv and copied to Overleaf. They are not in the order how I cited them, but I think it shouldn't be a problem. Doest anybody know why???

When using the \cite command in figure captions and the ieeetr bibliography style, then  BibTeX numbers the citations as appearing earlier than they do in reality (i.e. the first citation in the document ends up being [42]).  Is there any way to get BibTeX to ignore the \listoffigures section when numbering?


The question is, find the least number when divided by $36, 48$ and $64$ leaves remainder $25, 37$ and $53$ respectively. The answer is said to be $($the $\operatorname{lcm}$ of the three numbers $-11),$ where $36- 25= 48- 37= 64- 53= 11.$ Can anyone please give me the logic for doing this ? I am not familiar with the modular operator method. So any answer not using that would be helpful. Thanks

$$\begin{align*} x&\equiv 1\pmod2\\ x&\equiv 2\pmod3\\ x&\equiv 3\pmod4\\ x& \equiv 4\pmod5\\ x&\equiv 5\pmod6\\ x&\equiv 0\pmod7\\ \end{align*}$$  So the solution says we can eliminate $x\equiv 5(\bmod6)$ because the first two cases cover it, but I don't really know how it does. How do we solve it in cases like this where the moduli are not mutually relatively prime.


I have to decide if the function $f(x)=x\cdot \ln(x)$  in the interval $(0,+\infty)$ is uniformly cotinuous .

Show $f:(0,\infty)\rightarrow \mathbb{R}, f(x)=x\ln x$ on $(0,\infty)$ is not uniformly continuous.    I think that the general way to prove that something is not continuous in a metric space is to let $\epsilon=...$ and show that $\forall\delta>0$, $d'(f(x)-f(y))>\epsilon$. I can't use the Mean Value Theorem because we haven't gone over it yet.    Here's an attempt: Let $\epsilon=1$. Without loss of generality, let $x>y>0$. $|x\ln x-y\ln y|<|(x-y)(\ln x)|\leq|x-y||\ln x|$...$\delta=\frac{\epsilon}{\ln x}$ and therefore doesn't work for all $x$?


There's a mysterious blank space at the edges of the arrows between node 3 and node 9 below, whereas all the other edges are fine. How can I fix?    \documentclass[border=3mm]{standalone} \usepackage{tikz} \usetikzlibrary{matrix, calc, graphs, fit, backgrounds, positioning} \definecolor{myorange}{rgb}{1,0.8,0} \definecolor{mygreen}{rgb}{0.8,1.0,0.533} \begin{document} \begin{tikzpicture}[>=latex,thick,black!50,text=black, every new ->/.style={shorten >=0pt}, seqpoint/.style={   rectangle,minimum size=4mm,rounded corners=2mm,   inner sep=0,   thick,draw=black!50,   fill=myorange,   font=\footnotesize\sffamily }, func/.style={   rectangle,minimum width=16mm,rounded corners=1mm,   thick,draw=black!50,   fill=mygreen,   font=\ttfamily }, parentfunc/.style={   rectangle,minimum width=16mm,rounded corners=1mm,   thick,draw=black!50,   font=\ttfamily,   append after command={node[below right = 3pt of \tikzlastnode.north west, font=\ttfamily] {#1}} }, graphs/every graph/.style={edges=rounded corners}] \matrix[column sep=4mm, row sep=4mm] {  & \node (s1) [seqpoint] {1}; & \\ \node (s2) [seqpoint] {2}; & \node (s4) [seqpoint] {4}; & \node (s6) [seqpoint] {6};\\ \node (foo) [func] {foo}; & \node (bar1) [func] {bar}; & \node (bar2) [func] {bar};\\ \node (s3) [seqpoint] {3}; & \node (s5) [seqpoint] {5}; & \node (s7) [seqpoint] {7};\\ & & \node (baz) [func] {baz};\\ & & \node (s8) [seqpoint] {8};\\ & \node (s9) [seqpoint] {9}; &\\ & \node (quuxspace) []{}; & \\ & \node (s10) [seqpoint] {10}; &\\ & \node (tweedledee) [func] {tweedledee}; &\\ & \node (s11) [seqpoint] {11}; &\\ & \node (tweedledum) [func] {tweedledum}; &\\ & \node (s12) [seqpoint] {12}; &\\ & \node (s13) [seqpoint] {13}; &\\ }; \begin{scope}[on background layer] \node (quux) [parentfunc=quux, fill=mygreen!20, fit=(quuxspace) (s13) (tweedledee) (tweedledum)] {}; \node (isr) [parentfunc=isr, fit=(s1) (quux) (foo) (bar2)]{}; \end{scope} \graph [use existing nodes] { s1 -> s2 -> foo -> s3 -> s9;   s1 -> s4 -> bar1 -> s5 -> s9; s1 -> s6 -> bar2 -> s7 -> baz -> s8 -> s9 ; s9 -> s10 -> tweedledee -> s11 -> tweedledum -> s12 -> s13; }; \end{tikzpicture} \end{document}

When I use TikZ tree with nodes with rounded corners, the connecting lines do not touch the nodes (near corners) but end where would rectangle end. Is there an easy way around it?  \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture} [sibling distance=100]    \node[rectangle, draw, rounded corners = 3]{ }   child { node { } }   child { node { } }   ; \end{tikzpicture} \end{document}


Everyone knows that 1+1=2, but how would one mathematically prove that this equation is true? Or can you?

Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically?


For my Thesis I am stating a number of Theorems (Working Propositions actually). Using the theorem environment I do get some thing like:  WP1 My first WP  I create this by using   \begin{WP}    my first WP \end{WP}   I have defined the WP environment with  \newtheorem{WP}{Working Proposition}   However if I add a second (and a third etc) the numbering continues 1 , 2 ,3 etc  Occasionally I would like to be able to creat a WP2a and WP2b and then continue with 3.  When and where I extend to the a,b,c etc is random.  Help is appreciated.

I am trying to number my theorems as follows:  Theorem 1.A. First part of a theorem.  Theorem 1.B. Second part of the theorem.  Theorem 2. A theorem with no parts.  The following almost works:  \newtheorem{theorem}{Theorem} \newtheorem{theorempart}{Theorem}[theorem]   But it does not increment the theorem counter as I want, so that  \begin{theorempart}First part of a theorem. \end{theorempart}  \begin{theorempart}Second part of the theorem. \end{theorempart}  \begin{theorem}A theorem with no parts. \end{theorem}   gives:  Theorem 0.1. First part of a theorem.  Theorem 0.2. Second part of the theorem.  Theorem 1. A theorem with no parts.  Also, I don't know how to get the part-number to be a letter instead of a number.  I am using MiKTeX.


update-manager says there are no updates, but sudo apt --dry-run dist-upgrade says that the sudo package needs to be updated.  $ sudo apt --dry-run dist-upgrade Reading package lists... Done Building dependency tree Reading state information... Done Calculating upgrade... Done The following packages were automatically installed and are no longer required:   linux-headers-4.8.0-56 linux-headers-4.8.0-56-generic linux-image-4.8.0-56-generic linux-image-extra-4.8.0-56-generic linux-signed-image-4.8.0-56-generic Use 'sudo apt autoremove' to remove them. The following packages will be upgraded:   sudo 1 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. Inst sudo [1.8.16-0ubuntu1.4] (1.8.16-0ubuntu1.5 Ubuntu:16.04/xenial-updates [amd64]) Conf sudo (1.8.16-0ubuntu1.5 Ubuntu:16.04/xenial-updates [amd64])   But update-manager says:   The system is:  $ cat /etc/lsb-release DISTRIB_ID=Ubuntu DISTRIB_RELEASE=16.04 DISTRIB_CODENAME=xenial DISTRIB_DESCRIPTION="Ubuntu 16.04.2 LTS"   Is this ever expected behaviour, or is there indeed something weird going on?  I'll hold off for a day or so on doing the update, in case more details are needed.  Thanks.

Ever since I upgraded to 13.10, the software updater does not show all the available updates. Some will appear and can be installed just fine, but once it claims that all software is up to date, using sudo apt-get upgrade shows that there are still more packages waiting to be updated. I can update them via the command line, but that only solves things temporarily. I'm not sure why some show up and others don't. How can I make Update Manager update all packages?  Update-manager shows this:    But apt-get shows this:   Thanks!


It may be an odd question.  But, I particularly want to know the open's of cantor set with inherited topology of real line.

Does anyone know of any interesting subsets of the Cantor set? When I first started thinking about this, I thought that since the Cantor set $C$ is the intersection of disjoint unions of closed sets, those particular closed sets would be subsets of $C$. Those sets, however, happen to be intervals! The Cantor set contains no isolated points nor (open) intervals, so then what subsets does it contain besides $\varnothing$ and itself?


I want my table to appear as shown in the figure. Is it possible in Latex, and if it is how can it be done?

How to exactly make a rotated, multiple-row label (i.e., from) of a table vertically centered?  \documentclass[preview,border=12pt,12pt]{standalone} \usepackage{array,multirow,graphicx}  \begin{document} \begin{tabular}{|*5{c|}} \cline{3-5} \multicolumn{2}{c|}{\multirow{2}{*}{}} & \multicolumn{3}{c|}{to}\\\cline{3-5} \multicolumn{2}{c|}{}                     & a & b & c\\\hline \multirow{4}{*}{\rotatebox{90}{from}} & 1 & d & e & f\\\cline{2-5}                                       & 2 & g & h & i\\\cline{2-5}                                       & 3 & j & k & l\\\cline{2-5}                                       & 4 & m & n & o\\\hline \end{tabular} \end{document}


Confusion is because I hold a USA visa but not traveling TO the USA. I'm visiting Europe for tourism.  I am an Indian Passport holder, working in the USA (NOTE: Holding USA F1, Student Visa). I am visiting Sweden for New Year and have received a visiting visa (NOTE: Holding Schengen visiting visa ). I have booked British Airways flight transiting through London (NOTE: Same Terminal for arriving and departing flights at London, two hours apart). I have a return ticket confirmed from USA to Sweden to back to USA .  Would I need a Transit visa in this case?  UK GOV says:     You’ll need a visa to pass through the UK in transit (unless you’re   exempt) You should apply for a Direct Airside Transit visa if you   arrive in the UK on a flight and leave again without passing through   immigration control.      Exemptions You don’t need a visa if you have one of the following:      a visa for Canada, New Zealand, Australia or the USA (this can be used   for travel to any country) a residence permit issued by Australia or   New Zealand you have a common format residence permit issued by an   European Economic Area (EEA) country or Switzerland a resident permit   issued by Canada after 28 June 2002 a uniform format category D visa   for entry into a country in the European Economic Area (EEA) or   Switzerland an Irish biometric visa a Schengen Approved Destination   Scheme (ADS) group tourism visa where th e holder is travelling to to   the Schengen country that issued the visa a flight ticket from the   Schengen area, if you can prove that you entered the Schengen area in   the previous 30 days on the basis of a valid Schengen ADS visa a valid   USA I-551 Temporary Immigrant visa issued by the USA (a wet-ink stamp   version will not be accepted) a valid USA permanent residence card   issued by the USA on or after 21 April 1998 an expired USA I-551   Permanent Residence card issued by the USA on or after 21 April 1998,   with a valid I-797 letter authorising extension a valid standalone US   Immigration Form 155A/155B issued by the USA (attached to a sealed   brown envelope) All visas and residence permits must be valid.   Does point 1 apply as an exemption in my case?

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


I have a java application running on my local machine. I want to get the memory and CPU usage of that java application periodically using a java class. I can see the statistics of the application using JCONSOLE. But I want to get numerical values periodically using a java class. The solution should be applicable to both linux and windows platforms. How can I do this?

I'm currently building a Java app that could end up being run on many different platforms, but primarily variants of Solaris, Linux and Windows.  Has anyone been able to successfully extract information such as the current disk space used, CPU utilisation and memory used in the underlying OS? What about just what the Java app itself is consuming?  Preferrably I'd like to get this information without using JNI.


I have UITextField and i want allow user to type only up to 4 symbols. But i also want to allow them to erase symbols with keyboard (i mean, delete last and move caret for left. Symbol look like rectangle left arrow with cross on iOS keyboard).   For now i ended up with:  func textField(_ textField: UITextField, shouldChangeCharactersIn range: NSRange, replacementString string: String) -> Bool {     guard let text = textField.text, text.count < 4 else { return false }     return true   }   But i have no idea, how to let users to delete symbols. When text count become 4, i am not allowed to type or do any actions.

How can I set the maximum amount of characters in a UITextField on the iPhone SDK when I load up a UIView?


As a developer, I love writing code, and I like to think I'm fairly good at it.  However, my chosen field is Web Development, which almost always requires the developer to also act as designer.  I can tell if a design is good or not, I can offer suggestions to improve the layout or UX. But I cannot pick a color scheme, I cannot create a layout, and I am terrible at generating graphics.  As a developer, how can I pickup design?

I'm a web developer trying to become a web designer. But seems that I'm lost in the world of design.  But I don't know what to do, and from where should I start. I'm even unable to find good resources (of course, there are tons of resources out there, but I'm talking about good resources for web-design specifically)  I can tell if a design is good or not, I can offer suggestions to improve the layout or UX. But I cannot pick a color scheme, I cannot create a layout, and I am terrible at generating graphics.  As a developer, how can I pickup design?


Player 1 has A 8; Player 2 has A 9.  Community cards are A K 7 4 4.  Does player 2 win with a 9 kicker? Or is the K the kicker for both resulting in a tie?

In Texas Hold'em poker, there are some cases where a particular card, often called kicker, acts as a tiebreaker between players to determine who wins the pot, or if the pot has to be shared.  For some combinations such as three or four of a kind, there is no doubt: the kicker is the 5th card of the chosen combination, and determines the winner.  Example     Alice has 7 and 10   Bob has 7 and K   On the board are 7, 7, 2, 3, 4   In that case, both have a three of a kind. But because Bob has a king and Alice only a 10, he wins.  Most of poker websites explaining the rules clearly mention the role of the kicker applying to three of a kind and double pairs. But much fewer say something about colors, straights and full houses, and I found many contradicting answers. I also asked the question to some used online poker players and they also gave me contradicting answers.  I have tried to search for official tournament rules, but most of them only explain what happens with bad behaviors, bad deals, incorrect or confusing betting, showing cards when you shouldn't, acting when it's not your turn, etc. without mentioning subtleties about combinations at all.  To simplify my question, I will take three examples; I think it's better to start with examples before getting to the general answer if one exists. So, what's happening in the following 3 examples? Could you give a more generalized answer?  Example 1 - Flushes     Alice has 2♣ and 3♣   Bob has 4♣ and 5♣   On the board are 6♣, 8♣, 10♣, 2♥, 5♦   Contradicting answer 1: it's a tie, because the highest card included in the flush is the 10, which everybody chooses to include in their 5 showdown cards. Contradicting answer 2: Bob wins, because he has the greatest private card that is part of the flush  Example 2 - Straight     Alice has 6 and K   Bob has 6 and J   On the board are 4, 5, 7, 8, 10   Contradicting answer 1: it's a tie, because the greatest card in the straight is the 8 for both Alice and Bob Contradicting answer 2: Alice wins, because she owns an extra king, compared to the jack of Bob  Example 3 - Full house     Alice has 3 and 7   Bob has 3 and 6   On the board are 3, 3, 2, 2, 5   Contradicting answer 1: it's a tie, because one is supposed to choose only five cards to make a combination, and a full house is already five cards. There couldn't be any kicker, and thus their showdowns are strictly equals. Contradicting answer 2: Alice wins because of her extra 7, compared to the 6 of Bob  Thank you very much for your answers.  Note: I'm unable to post next to you, so I edit my own post; strange not be able to answer to an answer.  Ok, So if I summarize what you are saying :   In the flush case, Bob wins because at some point, their hand differs. Technically, I can continue comparing the highest private card to decide who wins. I had it correct. In the straight case, if the highest card of the straight is public, then it's technically always a tie, no matter what the players had as second private card (asuming that only one of the two cards was part of the straight). In a full house if both players have the same triplet and the same pair, it's always a tie, no matter what the players had as second private card (assuming again that only one of the two was part of the full house).   Please confirm me that what I summarized is correct.  Thank you for your answer.


I found this script is running in my system without any knowledge.  #!/bin/sh if test -r /tmp/.txl/bash.pid; then pid=$(cat /tmp/.txl/bash.pid) if $(kill -CHLD $pid >/dev/null 2>&1) then sleep 1 else cd /tmp/.txl ./run &>/dev/null exit 0 fi fi   Also this script is being triggered by /tmp/.txl/upd >/dev/null 2>&1  Can anyone explain why this script is running  Any help will be appreciated..!

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


I have this question that I think  may be interesting to all maths' lovers.  We have $5$ rooms in a row : Room $1$-Room $2$-Room $3$-Room $4$-Room $5$.   There is a little mouse in one of the rooms. А cat tries to catch the mouse and put his leg into one room. If the mouse is in this room then he catches the mouse, otherwise the mouse moves to a nearest room. Тhen the cat again chooses any room etc.  What is the cat's algorithm for catching the mouse?

There are five boxes in a row. There is robot in any one of these five boxes. Every morning I can open and check a box (one only). In the night, the robot moves to an adjacent box. It is compulsory that he moves. I need a method to ensure that I can catch the robot within ten days. How to do so?


When the user is validated the client get the page contents of home.html in result instead of redirecting to the home.html.  Client side call:  $http({ method: "post", url: "http://localhost:2222/validateUser", data: {     username: $scope.username,     password: $scope.password }  }).then(function (result) {     if (result.data && result.data.length) {         alert('User validated');     } else {         alert('invalid user');     } });   Server side controller method:  module.exports.validateUser = function (req, res) {   User.find({ 'username': req.body.username, 'password': req.body.password }, function (err, result) {     if (result.length) {         req.session.user = result[0]._doc;         res.redirect('/home');     }else{         res.json(result);     }   }); };   Route in app.js:  app.get('/home', function (req, res) {     var path = require('path');     res.sendFile(path.resolve('server/views/home.html')); });

I'm using $.post() to call a servlet using Ajax and then using the resulting HTML fragment to replace a div element in the user's current page. However, if the session times out, the server sends a redirect directive to send the user to the login page. In this case, jQuery is replacing the div element with the contents of the login page, forcing the user's eyes to witness a rare scene indeed.   How can I manage a redirect directive from an Ajax call with jQuery 1.2.6?


i have huawei g5000-5000 mobile whith 512 mb ram which has 479 mb free and a quad-core processor.offlate i have seen it has 0mb free ram and i am not able to do any work.whenever i open any app it automatically closes. i dont have many app heavy game and no heavy app loaded on my phone.i jjst have whatsapp,ucbrowser,truecaller,etc which i think should not be a problem. i have an unrooted phone.so please tell me what to do?

I'm new to the ICS os, coming from Gingerbread from another phone. The phone's quite nice and fast when I first used it, but just this morning it started exhibiting weird actions. Camera360 doesn't open up automatically when I click it, the Camera closes for no reason, Pocket restarts when an article has an image, and TTPod resets the song to the previous song on my widget in the middle of a new song I'm playing.  I checked out the ram, and and was surprised to see 500+ mb used, 0 mb available. I looked at the list of programs and I see the usual culprits like Facebook, but the ram they're using doesn't add up to 500+ mb. Yeah, I know that the whole ram indicated isn't usable by the apps, but I don't think I've done anything to warrant the 0 mb. I close my apps. There are times when there's free 4 to 5 mb, but I think that too shouldn't be the case. I tried installing Advance Task Killer, it listed less than 10 apps, killed it, still the ram is what it is above.   I did a reboot, and now it reads 300+ mb usage, 200 something free.   What can I do? How do I ensure an app's closed on ICS? I installed GoLaucher because it has a handy task killer and I can see the ram freed in an instant, but I would like to know if there's a better way to handle the RAM.


I felt ill because I had drunk six cups of coffee.   I felt ill because I drank six cups of coffee.      I think both of them are correct. Do they differ in meaning?  I looked at this question here::      That question is about when to use the participles drank and drunk. This question's about whether we do or do not need to use a past perfect in the subordinate clause of a sentence like this. The linked-to post doesn't answer my question.

I am a bit confused in using drank and drunk. I know we use it with past tense but not when to use drank and when to use drunk.  What are the better ways to use these?  I , too, but it does not explain when to use which form.  What scenarios best suit each form?


It is known that $\mathbb{Z}[i]$ is a PID and that $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ is finite for all $(a,b) \in \mathbb{Z}^2\backslash \{(0,0)\}$.  My question :      Is there any result on the cardinal of  $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ ?

A very basic ring theory question, which I am not able to solve. How does one show that    $\mathbb{Z}[i]/(3-i) \cong \mathbb{Z}/10\mathbb{Z}$. Extending the result: $\mathbb{Z}[i]/(a-ib) \cong \mathbb{Z}/(a^{2}+b^{2})\mathbb{Z}$, if $a,b$ are relatively prime.   My attempt was to define a map, $\varphi:\mathbb{Z}[i] \to \mathbb{Z}/10\mathbb{Z}$ and show that the kernel is the ideal generated by $\langle{3-i\rangle}$. But I couldn't think of such a map. Anyhow, any ideas would be helpful.


let $H,K \subseteq G$ all be groups. A relation ~ on $G$ is defined by x ~ y $\iff x = hyk$ for some $h\in H$ and $k\in K$. I'm to prove that ~ is an equivalence relation on $G$.  I was just wondering if when I'm to prove reflexivity if this holds:  x~x:   $x = hxk$  $h^{-1}xk^{-1} = h^{-1}hxkk^{-1} = x $ , since $h^{-1} \in H$ and $k^{-1} \in K$ and so it's proven?  Ie it doesn't have to be the same element of $H$ and the same element of $K$ right?

Hei, guys!  I'm having some trouble with the next problem:  Let $A$ and $B$ be subgroups of $G$. Show that $\sim$ is an equivalence relation when it is defined as follows: $g\sim g'\Leftrightarrow g' = agb$ for some $a$ from $A$, $b$ from $B$.  Should I prove this is valid for any a and b? It says for some elements a and b. But I might as well take the unit element.   Could you give me a clue on how to solve it?  Cheers!


I was creating a basic application that takes input and stores it in a firebase database with auto incrementing but it crashes everytime giving a nullpointer exception. I think there is some problem in my dataholder java file but I can't fix it. I've tried changing arguments in dataholder file.i have checked my android manifest file for firebase services. Here's my dataholder java file public class dataholder {      String username,password1;      public dataholder(String username, String password1) {         this.username = username;         this.password1 = password1;     }      public String getUsername() {         return username;     }      public void setUsername(String username) {         this.username = username;     }      public String getPassword1() {         return password1;     }      public void setPassword1(String password1) {         this.password1 = password1;     } }  and MainActivity import androidx.annotation.NonNull; import androidx.appcompat.app.AppCompatActivity;  import android.os.Bundle; import android.view.View; import android.widget.Button; import android.widget.EditText; import android.widget.Toast;  import com.google.firebase.database.DataSnapshot; import com.google.firebase.database.DatabaseError; import com.google.firebase.database.DatabaseReference; import com.google.firebase.database.FirebaseDatabase; import com.google.firebase.database.ValueEventListener;  public class MainActivity extends AppCompatActivity {      EditText name;     EditText password;     Button login;       DatabaseReference reff;     dataholder obj;      long maxid = 0;      @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_main);         name = (EditText) findViewById(R.id.etusername);         password = (EditText) findViewById(R.id.etpassword);         login = (Button) findViewById(R.id.Login);          reff = FirebaseDatabase.getInstance().getReference().child("dataholder");         reff.addValueEventListener(new ValueEventListener() {             @Override             public void onDataChange(@NonNull DataSnapshot dataSnapshot) {                 if (dataSnapshot.exists())                     maxid = (dataSnapshot.getChildrenCount());             }              @Override             public void onCancelled(@NonNull DatabaseError databaseError) {              }         });          login.setOnClickListener(new View.OnClickListener() {             @Override             public void onClick(View v) {                   obj.setUsername(name.getText().toString().trim());                 obj.setPassword1(password.getText().toString().trim());                  reff.child(String.valueOf(maxid + 1)).setValue("obj");                 Toast.makeText(getApplicationContext(), "Data inserted ", Toast.LENGTH_SHORT).show();              }         });     }  }

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


I have  in play. We are playing with 3 people. If i beat one player, would the creatures he own die? So i would get 2/2 zombie tokens from his creatures?

In Magic: The Gathering, the rules for a player losing in a multiplayer game are quite complex, so I'd like to try to understand them by example. I would be happy to ask each of these situations as a separate question if that is preferred, but they all seem related, and I would love to have one place to look up all of these answers.  Let's say I'm playing with two friends, Bob and Chloe, in a simple free for all. Unfortunately, I lose. When I lose, suppose the following:   I controlled an  which has exiled Bob's , does he get his bear back? I have a  on the stack targeting Chloe, does Chloe take the 2 damage still? Earlier in the turn I cast  to prevent damage to one of Bob's . If it later takes 3 damage, will that damage be prevented? Something I controlled gave Bob a 1/1 soldier token. What happens to the token? Something Chloe controlled gave me a 1/1 soldier token. What happens to the token? I had a  enchanting one of Bob's army of . What happens to the bear? I had also played  on Bob's final . What happens to the last bear? Chloe had  my . What happens to the Clone? Are there any other situations specifically addressed by the rules?


I have to insert some wires into several electrical connections and have been getting conflicting information on whether or not they should be tinned before inserting.  I'm sure this is a quite simple question to answer with a picture so I have included one below.  To be clear, the screw itself does not make the connection here, but pulls the flat conducting plate on the bottom of the connection toward the flat conducting plate on the top.  Regardless, the connection is still supposed to be a friction fit held together by the force that you apply from tightening the screw.  I suppose the root of what I'm unsure about is whether making an electrical connection under mechanical pressure would suggest you should not tin the wires or if it is specifically the rotation and grinding on a tinned wire that would be caused by the screw that makes tinning these wires a bad idea.  I'm obviously no expert on this topic so any additional explanation on the thought process behind the answer is very welcomed.

This is subjective per say. But I am looking for other peoples experience.  If I am going to screw eight wires into daughter relay board's terminal block, is there a benefit or advantage to tinning the copper end before?  The environment that the units are to be installed is not near the coast and is not normally damp/wet. Rather dry and hot.


Henry looks into the camera and "gets shot" by Joe Pesci.  Why does he look to into the camera and "gets shot" by Joe Pesci?   I understand how meaningful the name of the song is but I don't understand the rest. I have heard it's related to The Great Train Robbery. Is this true?

At the end of ,       Henry is in the witness protection program and says "I get to live the rest of my life like a schnook."   Then, an image of Tommy appears, facing the camera and shooting at it several times. What is the meaning of this scene?


I'm using   to send emails. But my emails goes in spam folder. Here is code that I'm using for this.  <?php  $apiKey = "xxxxx.xxxxxx.xxxxxx";   require("sendgrid-php/sendgrid-php.php");  $from = new SendGrid\Email("Example User", "azeemhaider77@gmail.com");  $subject = "Sending with SendGrid is Fun";  $to = new SendGrid\Email("Example User", "axeemhaider@gmail.com");  $content = new SendGrid\Content("text/plain", "and easy to do anywhere, even with PHP");  $mail = new SendGrid\Mail($from, $subject, $to, $content);   $sg = new \SendGrid($apiKey);  $response = $sg->client->mail()->send()->post($mail);  echo $response->statusCode(); var_dump($response->headers()); var_dump($response->body());   Why this is not working why these emails move into spam folder ?

This is a tricky one and I've always relied on techniques, such as permission-based emails (i.e. only sending to people you have permission to send to) and not using blatantly spamish terminology.  Of late, some of the emails I send out programmatically have started being shuffled into people's spam folder automatically and I'm wondering what I can do about it.  This is despite the fact that these particular emails are not ones that humans would mark as spam, specifically, they are emails that contain license keys that people have paid good money for, so I don't think they're going to consider them spam  I figure this is a big topic in which I am essentially an ignorant simpleton.


I have a hp aspire one laptop Havnt used in some time and the password I thought it was isnt working. I want to wipe the password or the whole laptop but not sure how. It's running on Linux mint 17

I have a laptop with Debian on it, and I am going to sell this laptop.   Would it suffice to erase the Debian installation before selling it to completely clean up my laptop from my personal data, and if yes how can I uninstall Debian (so that there isn't any operating system on the laptop)?


Context: Equation 1 requires substituting A for B.  Does this mean all "A" in equation 1 is replaced with "B" or vice versa?

An awful lot of people seem to use the phrase "substitute X for Y" to mean "replace X with Y", while I've always used and understood it as "replace Y with X". This makes sense to me, given that a substitute is the replacement, not the thing which has been replaced.  I thought I might be able to figure things out from a dictionary, but now after seeing two sorts of definitions, I'm even more confused:   to put or use in the place of another to take the place of; replace   The first one suggests that the object will be the substitute (replacement), the thing put into place, while the second suggests that the object will be the thing which has been replaced.  Is one of these usages more correct in any sense? (I know this is probably a pointless question, since people will continue to speak the way they speak.) Is there perhaps a difference between American and British English?   And most importantly, is there any reliable way to tell what someone means when they ask how to substitute honey for sugar, or is the verb simply guaranteed to cause confusion?


A consequence of Lagrange's theorem in finite group theory is that $g^{|G|}=e$ for all $g\in G$.  I wonder whether this be generalized along these lines:     If $H$ is a subgroup of $G$ of finite index $n$, then $g^n\in H$ for all $g\in G$. $\qquad(\star)$   This is true when $H$ is normal, but not in general, as this counter-example shows:     $G=S_4$, $H=S_3$, $g=(234)$: $[G:H]=4$ but $g^4=g\notin H$.   A  says that, when $\gcd(|H|,n)=1$, $(\star)$ happens iff $H$ is normal.  Can $(\star)$ be true when $H$ is not normal? What other conditions on $G$, $H$, and $n$ ensure $(\star)$ ?

Let $G$ be a group and $H$ a subgroup with $[G:H]=n$. Is it true that $x^n\in H$ for all $x\in G$?   Remarks. The answer is positive whenever $H$ is normal, e.g., for $n=2$. In general, by using the normal core of $H$, one can find an $m\ge 1$ such that $x^m\in H$ for all $x\in G$.


I have a very dumb issue which I've been absolutely breaking my head over for a while now  ##########CODE 1 (STATIC)############## @app.route('/fromdb', methods=['GET']) def printall():  data = g.db.execute("SELECT TeacherInfo.Name, TeacherInfo.PhoneNo, TeacherInfo.HourlyRate, SubjectTable.SubjectName, SubjectTable.Grade, SubjectTable.Syllabus FROM SubjectTable JOIN TeacherInfo on SubjectTable.TeacherID = TeacherInfo.TeacherID WHERE SubjectName = 'Comp'").fetchall()    print(data)    return jsonify(details=data) ##########END CODE1###################   ##########CODE 2(DYNAMIC)############# @app.route('/fromdb', methods=['GET']) def printall():     x = request.json     p = x['SubjectName']     data = g.db.execute("SELECT TeacherInfo.Name, TeacherInfo.PhoneNo, TeacherInfo.HourlyRate, SubjectTable.SubjectName, SubjectTable.Grade, SubjectTable.Syllabus FROM SubjectTable JOIN TeacherInfo on SubjectTable.TeacherID = TeacherInfo.TeacherID WHERE SubjectName = ?", p).fetchall()    print(data)    return jsonify(details=data) ##########END CODE2###################   In the link above, there are two codes Code 1 works perfectly fine, I'm focusing on the 'WHERE SubjectName = 'Comp'' and WHERE SubjectName = ? here  I hard code the subject name into the query, and I get a JSON object with the results of the query  Now, in code 2, the variable 'p' contains the subject name and I'm able to retrieve it and print it. But the query isn't working, I'm getting a 500 error and I'm not sure how I pass it as a parameter in the query.  Could someone please help me out with this?

Using SQLite3 with Python 2.5, I'm trying to iterate through a list and pull the weight of an item from the database based on the item's name.  I tried using the "?" parameter substitution suggested to prevent SQL injections but it doesn't work. For example, when I use:  for item in self.inventory_names:     self.cursor.execute("SELECT weight FROM Equipment WHERE name = ?", item)     self.cursor.close()   I get the error:     sqlite3.ProgrammingError: Incorrect number of bindings supplied. The current statement uses 1, and there are 8 supplied.   I believe this is somehow caused by the initial creation of the database; the module I made that actually creates the DB does have 8 bindings.  cursor.execute("""CREATE TABLE Equipment      (id INTEGER PRIMARY KEY,      name TEXT,     price INTEGER,      weight REAL,      info TEXT,      ammo_cap INTEGER,      availability_west TEXT,     availability_east TEXT)""")   However, when I use the less-secure "%s" substitution for each item name, it works just fine. Like so:  for item in self.inventory_names:     self.cursor.execute("SELECT weight FROM Equipment WHERE name = '%s'" % item)     self.cursor.close()   I can't figure out why it thinks I have 8 bindins when I'm only calling one. How can I fix it?


I want the color of my div.navBtn elements to change through an animation effect. It isn't working out and I don't know why.  $(document).ready(function() {   $("button").click(function()   {     $("div.navBtn").animate(     {       width:'+=10px',       backgroundColor: "#aa0000"     });   }); });   backgroundColor is what does the actual color changing but it does not work. Width +=10 works perfectly, backgroundColor does absolutely nothing. Is the syntax wrong or something??? I copied "backgroundColor: "#aa0000"" from another help posting here. Does anyone know what the problem is?

I am trying to animate a change in backgroundColor using jQuery on mouseover.  I have checked some example and I seem to have it right, it works with other properties like fontSize, but with backgroundColor I get and "Invalid Property" js error. The element I am working with is a div.  $(".usercontent").mouseover(function() {     $(this).animate({ backgroundColor: "olive" }, "slow"); });   Any ideas?


When I try to flag a question on Stackoverflow from my Android phone (Google Nexus 4) with the Chrome browser (up-to-date), the textarea to add an answer is displayed above the "flag" box.  It only happens if the question have no answer yet.  See these examples :

The "Your Answer" textbox seems to be eating the flagging dialog as shown in Figure A.


I am studying category theory, and I think I often struggle between the fuzzy lines between Set as a category and then the category theoretic abstractions.  For example, take monomorphisms. I totally get the idea, but what does it mean for two morphisms to be equal, or not to be equal? It seems like the definition of a category (objects and morphisms between them) doesn't provide for the possibility of comparing morphisms... and yet, in things like monomorphisms, it only makes sense if there is an idea of different morphisms between the same objects that may or may not be equal.  I get that in set, since the underlying object are sets and the morphisms are functions between sets, it's possible that, say...  A = {1, 2, 3} B = {1, 2} f = 1 -> 1, 2 -> 1, 3 -> 2 g = 1 -> 2, 2-> 2, 3 ->1   But what in category theory allows me to distinguish between the morphisms f and g?

I am learning basics of the category theory (CT).  I do understand that CT is a modern powerful framework to describe various branches of mathematics in a unified way.  I do admit that category's definition tells a lot about the whole thing and focuses on the most important properties, shadowing unnecessary details. However, the more I go forward, the more it feels like it should explicitly require a notion of morphisms equality (like it does with morphism composition). It feels so because equality or inequality of morphisms arises everywhere, since the very beginning: any commutative diagram eventually reduces to an equality of two different paths and many other things involve equality as well. Even composition is defined grounding upon an (implicit) equality!  I'll try to give an example of my concern. Consider $\mathbb{SET}$. Its objects are sets and morphisms are functions. Now, let's recall that functions are sets as well - to be more precise, a function $f : A \mapsto B$ is a subset of a $A \times B$ obeying certain properties, which I omit. Thus, one could argue that $f$ is both a morphism between objects $A, B \in Obj(\mathbb{SET})$ and an object defined as a set of pairs $\{ (a_1 \in A, b_1 \in B), ..., (a_n \in A, b_n \in B) \}$ and those are equal because both are essentially exactly the same thing.  I hope my concern is clear and I need some kind of "conceptual insight" from knowledgeable people to move forward. Please give me the right perspective.


By meaningful I mean experimentally falsifiable.

I was surprised to only recently notice that      An object of any density can be large enough to fall within its own   Schwarzschild radius.   Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's.  Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards.  Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light.  Or Mt. Everest packed into one nanometer.  Reading on about this , it increases proportionally with total mass.  Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.  Question: For an object the , what would have to be its diameter for it to qualify as a black hole (from an external point of view)?  Would this not imply by definition that:   The Earth, Solar system and Milky Way are conceivably inside this black hole? Black holes can be nested/be contained within larger ones? Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside?


I want to show that $$\int_0^{\pi} \frac{1}{(a+\cos\theta)^2}d\theta = \frac{a\pi}{(\sqrt{a^2-1})^3}; \;\;a>1$$ I've thought of making the change of variable: $\cos\theta = \frac{e^{i\theta}+e^{-i\theta}}{2}$ and $z = e^{i\theta}$ so that the integral became expressed in terms of $z$. However, I haven't been able to solve any of the new integrals and I'm a bit stuck. Would I have to solve it by using the residue theorem? Thanks!

How do you evaluate the following integral? Here we take $a>1$.  $$\int^{2\pi}_{0} \frac{1}{(a+\cos\theta)^{2}} d \theta=\frac{2\pi a}{(a^{2}-1)^{\frac{3}{2}}}.$$  I know I have to use the Residue Theorem, however, I am stuck on which contour to use, and also how to find the pole of the function. Any hints are greatly appreciated.


In worst case(failed to find sum ending up return false), what would be the complexity equation of the code and what's BigO of it? I put // and number of times either 1, n, n^2 that I think right. Could you check if I am calculating it right?  public static boolean hasSum(int arr[], int sum){          int n = arr.length;           //1          for(int i =0; i<n; i++) {           // 1, n, n             for(int j =0; j<n; j++) {      //1, n^2, n^2                 if(arr[i] +arr[j]==sum) {       //n^2                     return true;                 }             }         }       return false;      //1   (because it fails to find the sum) }   So what I have is 3n^2 + 2n +4 , which is O(n^2)  I think I may be right on BigO, but not sure about the equation that I made.  Is it correct?  Thank you!

Most people with a degree in CS will certainly know what . It helps us to measure how well an algorithm scales.   But I'm curious, how do you calculate or approximate the complexity of your algorithms?


I'm new to shell scripts and i use the below code to run a spring boot, however i need to have a progress bar to show the progress of starting the application.  I have tried with echo "waiting to start" but need to have a progress bar to show.  cd /var/develop/eureka-discovery-services/target pwd java -jar eureka-discovery-services.jar & while ! nc -z localhost 5001 ; do echo "Waiting to start"    sleep 2 done  cd /cd /var/develop/api-services/target pwd java -jar api-services.jar & while ! nc -z localhost 6001 ; do echo "Waiting to start"    sleep 2 done echo "All services started Successfully !!!"

When scripting in bash or any other shell in *NIX, while running a command that will take more than a few seconds, a progress bar is needed.  For example, copying a big file, opening a big tar file.  What ways do you recommend to add progress bars to shell scripts?


With whatever I do (php & meta Content-type headers as utf-8) and all the htmlspecialchars, utf8_de- and encode etc. I just can't seem to insert text the right way into the table. Even returning it in a div, checking with alerts etc. nothing seems to get this right:  This is inserted into the MySQL table:  Americaâ€™s Greatest Rock â€˜Nâ€™ Roll Band â€“ have   it should be:  America’s Greatest Rock ‘N’ Roll Band – have    in the jQuery script I use:    var ch_title = encodeURIComponent(ch_title); var ch_descr = encodeURIComponent(ch_descr);    the PHP insert script has:  $ch_descr = "$_POST[ch_descr]"; $ch_descr = nl2br("$ch_descr"); $ch_descr = mysqli_real_escape_string($conn,$ch_descr);   Does anyone know how to get this right?  Solution I used this to solve the problem, including the doctype and headers:  <!DOCTYPE html> <meta http-equiv="content-type" content="text/html; charset=utf-8">   and for PHP:  header ('Content-type: text/html; charset=utf-8');  $ch_descr = iconv('UTF-8', 'ASCII//TRANSLIT', $ch_descr); $ch_descr = mysqli_real_escape_string($conn,$ch_descr);

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.


In middle school I read a 'young adult' book - again I don't remember the name of the book or the author, and in this one, the year is more flexible, I got it from the school library in the mid-80s, which means there's a good chance it was originally published in the 60s or 70s.    In this story the protagonist is a teenager who wakes up from a coma in the future.  I specifically remember the opening scene when he wakes up - there's a guy with robot eyes (it turns out the doctor had somebody throw acid in his face prior to the events of the story) and three nurses who were identical (clones) but with brightly colored hair (blue, purple etc, at a time when dying one's hair as such was a lot more novel than it is now).  I can't remember what put him in the coma or why he was revived when he was (he may have simply woken up).    I recall a lot of it was about him trying to make sense of the new world he was in, and there was an ecology theme, cause the oceans were an oily yellow and lifeless (I remember one character telling him that maybe since he remembers the oceans as they were before mankind ruined them, that he'd be able to figure out a way to revive them - this seems like an insignificant detail, but I just read on the 'How to write an ident question' page that no detail is too measly), and the overall the state of society was worse than that of the one he'd left behind.   I also don't remember how this ends, although I'm pretty sure it was along the standard lines of 'hope for the future despite uncertainty'.

There's a book I borrowed from my grade 8 teacher's lending shelf (in Ontario, Canada) that I've been trying to identify for years. The main character was a man in a futuristic setting who... I think... had the secret to an improved version of the lifespan-extension serum everyone used. If I remember correctly, the flawed version caused people's skin to turn clear over the course of their extended lives. I think he was revived from some sort of stasis, but I can't be sure of that. I just vaguely remember a "stranger in a strange land" sort of cultural disconnect, him being cared for in some kind of hospital-like setting, and a sense that maybe the formula they want from him was invented by a now-dead family member of his. The most distinctive detail I remember was the love interest, a cloned nurse named "Eliza Tertia" who he encourages to break out of her role. (All the cloned nurses were named Eliza, and I remember "Eliza Duodecima" being the name of another one who is briefly seen.) I also remember the secret eventually being gotten out of him, only for it to be discovered that it's flawed, in that, while it does replenish the compounds that go missing in extended old age, it doesn't moderate their production. I don't remember if it was long enough to be a novel or if it was just a novella. My vague memories of the cover design and material suggest it was a 1970s printing or earlier, which would also fit with what I remember of the story's atmosphere.


First time poster here.  After installing High Sierra on my iMac (27", late 2012) my Boot Camp Windows 10 partition is no longer visible in the Startup Manager (accessed by holding Option-key on startup).  When logged into Mac OS, I can see the bootcamp-disk, and it's also visible in Startup Disk. Edit: it's visible in Finder, hence a different problem than described in other questions.  Edit: When I try to boot to Win from Startup Disk, the computer froze on first attempt. On second attempt, it displayed "no bootable device - insert disk and press any key".  I run OS X 10.13.2. Any help is greatly appreciated, thanks in advance! /Johan  Edit: the disk is a "fusion drive".  Edit: As a (at least temporary) solution, would it be possible to roll back the system using Time Machine, to before the High Sierra uppgrade?  Edit: I solved the issue by simply removing the bootcamp partition, starting from scratch with a new Win 10 installation. However, the Win installation failed several times. The installer wouldn't accept the bootcamp partition. After some googling I did a PRAM-reset, which did the trick. I don't know if this was caused by my original problem with the missing partition.  Thanks for the replies and suggestions, guys!

Suddenly my Boot Camp partition vanished: not visible in Finder, not visible on startup. In Disk Utility I can see the volume, but it's broken (verification log):  Verifying volume "disk0s4" Verifying file system. ** /dev/rdisk0s4 Invalid BS_jmpBoot in boot block: 2b0601 File system check exit code is 8. Error: This disk needs to be repaired. Click Repair Disk.   …and cannot be repaired:  Verify and Repair volume “disk0s4” Repairing file system. ** /dev/rdisk0s4 Invalid BS_jmpBoot in boot block: 2b0601 File system check exit code is 8. Updating boot support partitions for the volume as required. Error: Disk Utility can’t repair this disk.  Back up as many of your files as possible, reformat the disk,  and restore your backed-up files.   Before there was another message, something about   Mount of disk0s4 blocked by dissenter.   Terminal's diskutil list command:  #:                       TYPE NAME                    SIZE       IDENTIFIER 0:      GUID_partition_scheme                        *1.0 TB     disk0 1:                        EFI EFI                     209.7 MB   disk0s1 2:                  Apple_HFS Macintosh HD            596.5 GB   disk0s2 3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3 4:       Microsoft Basic Data                         199.3 GB   disk0s4   and another one:  sudo gpt -vv -r show /dev/disk0  gpt show: /dev/disk0: mediasize=1000204886016; sectorsize=512; blocks=1953525168 gpt show: /dev/disk0: Suspicious MBR at sector 0 gpt show: /dev/disk0: Pri GPT at sector 1 gpt show: /dev/disk0: Sec GPT at sector 1953525167      start        size  index  contents          0           1         MBR          1           1         Pri GPT header          2          32         Pri GPT table         34           6                 40      409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B     409640  1165055256      2  GPT part - 48465300-0000-11AA-AA11-00306543ECAC 1165464896     1269536      3  GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC 1166734432   397446048         1564180480   389343232      4  GPT part - EBD0A0A2-B9E5-4433-87C0-68B6B72699C7 1953523712        1423         1953525135          32         Sec GPT table 1953525167           1         Sec GPT header   Once, I had as similar problem after partition resizing and had successfully solved it with this guide. But here I see some differences - now naming is not detected and you can't see BOOTCAMP in Finder sidebar. So, I'm not taking chances and won't follow  until someone will advise me so.  iMac14,3 (21.5-inch, Late 2013) , OS X Yosemite (10.10.4)  Here is sudo fdisk /dev/disk0  Disk: /dev/disk0    geometry: 121601/255/63 [1953525168 sectors] Signature: 0xAA55      Starting       Ending  #: id  cyl  hd sec -  cyl  hd sec [     start -       size] ------------------------------------------------------------------------  1: EE    0   0   2 - 1023 254  63 [         1 - 1564180479] <Unknown ID> *2: 07 1023 254  63 - 1023 254  63 [1564180480 -  389343232] HPFS/QNX/AUX  3: 00    0   0   0 -    0   0   0 [         0 -          0] unused        4: 00    0   0   0 -    0   0   0 [         0 -          0] unused


I have waited for my favorite time period of in the evening.   Can this sentence make sense in meaning?

I have waited for the period of the day, in the morning.   Can the 'period of the day' and 'in the morning' be the apposition?


When I was but a young lad, I often heard the following saying;  If “ifs”and “ands” were pots and pans, we would never do the dishes.  There is also another similar saying;  If ‘ifs” and “buts” were candy and nuts, we would all have a Merry Christmas!  Which idiom came first?

I’m interested in the origin of the idiom:     If "ifs" and "buts" were candy and nuts, we'd all have a merry Christmas.   When was it first used? Is this the original idiom, or was there an older version? Furthermore, how should its meaning be interpreted?


On my web server - runnnig LAMP - I have a Wordpress installation, where I'd like to set the ownerships/permissions like this:  my-username is the owner of all files while the owner group is www-data (chown -R my-username:www-data). I've set chmod -R 775 on whole installation folder, so users in owner group should be able to write the files/folders. For some reason Wordpress can't write them, the only configuration when it works is when www-data is owner user (chown -R www-data:www-data).  The problem with that, is that I use Gulp to compile my assets, and Gulp can only run if the owner of the files it needs to write, is the user who runs Gulp from the command-line (my-username in this case). I've also tried setting chown -R www-data:www-data and include my-username in www-data group, so that my-username running Gulp would have write permissions (I can write files in the terminal), but Gulp would not work.  How should I set this up, so that both Wordpress(www-data) and Gulp(my-username) could have working write-permissions? Why is having group-permissions not enough?

I have an ec2 instance on AWS which already installed a few Wordpress-es in it.  I want to set things up to let more people handle their own projects, with me also being able to go into the server using terminal if I still want to.  I have been following tutorials such as  and a few others.  I figured all of them just teach users how to sftp into their own home folder, also the steps keep saying addUser but some users already existed and removing them might cause some issue.  How can I give existing users the permission to use SFTP for Wordpress projects?  Let's say all my Wordpress projects are already under /var/www/ which has already been set up with www-data:www-data.  Really new with setting things like this.  Thanks in advance for any help.


I'm looking at some small assembler codes and I'm having trouble understanding the TEST instruction and its use. I'm looking at the following code at the end of a loop:  8048531:    84 c0                   test   al,al 8048533:    75 dc                   jne    8048511 <function+0x2d>   The way i understand TEST is that it works a bit like the AND operator and it sets some flags. I guess I don't really understand how the flags work. test al,al to me looks like it checks the same lower bits and will always get the same results.   Can someone explain?

I am trying to understand some assembly.  The assembly as follows, I am interested in the testl line:  000319df  8b4508        movl   0x08(%ebp), %eax   000319e2  8b4004        movl   0x04(%eax), %eax   000319e5  85c0          testl  %eax, %eax   000319e7  7407          je     0x000319f0     I am trying to understand that point of testl between %eax and %eax? I think the specifics of what this code isn't important, I am just trying to understand the test with itself - wouldn't the value always be true?


I have a python script that accepts file names as arguments and performs operation on those files. Currently the script is in the same directory as the files it operates on. But I want to be able to run my python script from anywhere in the operating system. When I give the file name as argument to the script, it should know exactly which directory to look for regardless of where the python script is running in the system. How can I achieve this in python?  Here is the relevant portion of the script. Can I just hard code the path?  The type_mapping_file will be the filename passed into the script as an argument.  data = None with open (type_mapping_file, "r") as myfile:     data=myfile.read()  if(data is not None):     request_params = {'type': type_name, 'index': index_name}      send_http_request("/index/type/create", request_params, base_url, post_body=data)   Thank you in advance.

I have scripts calling other script files but I need to get the filepath of the file that is currently running within the process.   For example, let's say I have three files. Using :   script_1.py calls script_2.py.  In turn, script_2.py calls script_3.py.    How can I get the file name and path of script_3.py, from code within script_3.py, without having to pass that information as arguments from script_2.py?  (Executing os.getcwd() returns the original starting script's filepath not the current file's.)


I'm trying to install ns3 and, before that, I need to run the command below: sudo apt install gir1.2-goocanvas-2.0 python-gi python-gi-cairo python-pygraphviz python3-gi python3-gi-cairo python3-pygraphviz gir1.2-gtk-3.0 ipython ipython3  After running this command, I get this error: The following packages have unmet dependencies:  ipython : Depends: python-ipython (= 5.5.0-1) but it is not going to be installed  python-gi : Depends: python2 (< 2.8) but it is not going to be installed              Depends: python2 (>= 2.7~) but it is not going to be installed              Depends: python2:any (< 2.8)              Depends: python2:any (>= 2.7~)  python-gi-cairo : Depends: python-cairo (>= 1.11.1) but it is not going to be installed                    Depends: python2 (< 2.8) but it is not going to be installed                    Depends: python2 (>= 2.7~) but it is not going to be installed                    Depends: python2:any (< 2.8)                    Depends: python2:any (>= 2.7~) E: Unable to correct problems, you have held broken packages.  What should I do to solve this problem?

After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


Let $A \in \mathbb{R}^{n \times n}$. Then $\operatorname{rank} A \leq 1$ if and only if $A = xy^T$ for some $x, y \in \mathbb{R}^{n \times 1}$.  Need help. I can't find sufficient facts nor theorems to support my proof on the statement.

Let $A$ be an $n\times m$  matrix. Prove that $\operatorname{rank} (A) = 1$ if and only if there exist column vectors $v \in \mathbb{R}^n$ and $w \in \mathbb{R}^m$ such that $A=vw^t$.    Progress: I'm going back and forth between using the definitions of rank: $\operatorname{rank} (A) = \dim(\operatorname{col}(A)) = \dim(\operatorname{row}(A))$ or using the rank theorem that says $ \operatorname{rank}(A)+\operatorname{nullity}(A) = m$. So in the second case I have to prove that $\operatorname{nullity}(A)=m$-1


If we build a number as follow:  $$N=7+\sum_{k=1}^n6\times10^k$$ we find: $$N^2=9+\sum_{k=1}^n8\times10^k+\sum_{j=n+1}^{2n+1 }4\times10^{j}$$ that means for example:  $67^2=4489$, $667^2=444889$, $6667^2=44448889$ and so on. How can we prove that given an arbitrary $n$ and a number $N$ built as above, the square of $N$ can be obtained by th equation for $N^2$? Thanks

Prove that in a sequence of numbers $49 , 4489 , 444889 , 44448889\ldots$ in which every number is made by inserting  $48$ in the middle of previous as indicated, each number is the square of an integer.


I've been looking for a program ,or a widget, that could search for lyrics, download them and add them to iTunes (or display the lyrics while I'm playing a song).  All those I could find were outdated and didn't work correctly.  There are other program that can search for the lyrics but do not add them to iTunes, others that display lyrics already in iTunes but not both.  iTunes version : 12.3.0.44  OS X version : Yosemite (10.10.5)

Is there a way to automatically download lyrics in iTunes?


Let $g:U \rightarrow \mathbb{C}$, be defined for every $r \in (0, \infty)$, and $\theta \in (0, 2\pi)$ as $g(re^{i\theta}) = \sqrt[n]{r}e^{i\frac{\theta}{n}}$.  I have to show that g is well defined and holomorphic without using the Cauchy-Riemann equations. I know that, as $U$ is simply connected, if the 1-Form $w = \frac {g(z)}{z^2+1}$ is holomorphic then it is also local exact (Goursat´s theorem), but I do not really know if this theorem works for this case, as the implication goes to the other direction that I want.  Thank you in advance

It is true that given a domain $D$ and a function $f$ that is holomorphic and not vanishing in $D$, then a branch $\varphi$ (with $\varphi$ continuous) of $f^{1/n}$ in $D$ is holomorphic in $D$ ().   My question is, does the statement remain true if we remove the non-vanishing condition? I haven't been able to find a counterexample or a proof on that more general case.


I need to add the following repo in ubuntu 16.04:  deb http://apt.llvm.org/trusty/ llvm-toolchain-trusty main  I attempted to add that repo by typing following command:  sudo add-apt-repository "deb http://apt.llvm.org/trusty/ llvm-toolchain-trusty main"  I want to add that repo because I want to install packages from there.  I see that after the add-apt-repository command there is an entry added in /etc/apt/sources.list  but when I am trying to install the package using sudo apt-get install clang-3.4 I still get error:  Reading package lists... Done Building dependency tree        Reading state information... Done Package clang-3.4 is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'clang-3.4' has no installation candidate

What does the above Error mean? What is an installation candidate?  I was trying to do  sudo apt-get install munin-memcached     and I get this message:  Reading package lists... Done Building dependency tree        Reading state information... Done Package munin-memcached is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package munin-memcached has no installation candidate   I googled for the problem and someone said to do a apt-get upgrade but it still did not solve my problem.


$$\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac {1} {k+n} = \ln 2$$  I'm supposed to find the limit and get the right part as an answer. I don't know what to do with it. Could someone explain?

What is the sum of the 'second half' of the harmonic series?  $$\lim_{k\to\infty}\sum\limits_{n=k+1}^{2k}{\frac{1}{n}} =~ ?$$  More precisely, what is the limit of the above sequence of partial sums?


I know $\int_0^{+\infty}\sin(x^2)\ \mathrm dx$ converges, but $\sum\limits_{i=1}^{\infty}\sin(i^2)$ diverges. How to prove it?

Does the series $\sum \limits_{n=1}^{\infty} \sin(n^2)$ converge?  I think I've tried everything, I have no more ideas.


Suppose I have a hellp.py python file. I found that I only can type command: python hello.py to run my command line, but how can I just type ./hello so that my system can run my hellp.py file?

I just installed a linux system (Kubuntu) and was wondering if there is a program to make python programs executable for linux.


So I have someone who is interested in a sugar daddy/sugar baby arrangement but in order to receive the money he wants my mobile banking username and password. Is it a scam ?

Someone is offering to pay me in a sort of sugar daddy/sugar baby arrangement. They want to make online deposits to me, and they're asking me for my online banking username and password. Is that information alone enough for them to be able to take my money out of my account, or am I safe?


I was given the hint to split it into two cases ($|a| - |b|$ being positive and negative) and then use the triangle inequality. However, since the triangle inequality says that $|a+b|$ is less than or equal to $|a| + |b|$, so I don't see how I can use that to help since I'm dealing with subtraction. I've tried using the definition of absolute value, and I was able to find that $||a| - |b||$ = $|a| - |b|$ in my first case, but I couldn't do much with that.

I've seen the full proof of the Triangle Inequality  \begin{equation*} |x+y|\le|x|+|y|.  \end{equation*} However, I haven't seen the proof of the reverse triangle inequality:  \begin{equation*} ||x|-|y||\le|x-y|. \end{equation*} Would you please prove this using only the Triangle Inequality above?  Thank you very much.