Today I saw . It's pretty clear that Darth Sidious is hypercompetent at fighting, both with lightsabers and with the Force.   Comparing that to , Sidious looks like he's just sitting there and letting Skywalker pick him up and dump him in a hole. So why is he so passive once lifted by Skywalker? and furthermore, why doesn't he predict Vader's attack on him (like Snoke did with Ren in Episode V*)?    *Of course, Snoke doesn't do this so well, but you'd expect Sidious, being incredibly strong in the Dark Side as well as paranoid (he didn't sleep for fear of something happening while he was incapacitated, according to Wookieepedia), to at least be forewarned that something might be amiss with his apprentice.

I'm wondering whether this was a movie sin but his body position seemed to stay the same? Also why didn't he stop using Force Lightning? He continued to use it even as he was falling down.   I'm also wondering whether Palpatine meant to electrocute Vader or was it just a coincidence (because he kept firing Force Lightning) .  It makes no sense as he just stood there allowing Vader to throw him.


Suppose $f: (0, 1) \rightarrow {\rm I\!R}$ is continuous, with $c \in (0, 1)$, and suppose that $f'$ exists $\forall x \in (0, 1)$\{$c$}. Prove that if $\lim_{x\to\ c} \ f'(x) = K$ then $f'(c) = K$.  $$\lim_{x\to\ c} \ f'(x) = K \Rightarrow \forall \epsilon > 0, \exists \delta > 0 \text{ such that } |f'(x) - K| < \epsilon \text{ for } x \in (c-\delta, c+\delta)$$  Since $f$ is continuous and differentiable on the open interval we can use the Mean Value Theorem on $[x, c]$ where $x \in (c-\delta, c)$.   So $\exists x_1 \in (x, c)$ such that $f'(x_1) = \frac{f(x) - f(c)}{x-c}$.   By our limit definition $|f'(x_1) - K| = |\frac{f(x) - f(c)}{x-c} - K| < \epsilon$.   $$\Rightarrow \left|\frac{f(x)-f(c)}{x-c} - K\right| < \epsilon \text{ for } x \in (c-\delta, c)$$  We can use the MVT again on $[c, x]$ where $x \in (c, c+\delta)$, find an $x_2 \in (c, c+\delta)$ and get similar result.   $$\Rightarrow \left|\frac{f(x)-f(c)}{x-c} - K\right| < \epsilon \text{ for } x \in (c-\delta, c+\delta)$$  $$\Rightarrow \lim_{x\to\ c} \frac{f(x)-f(c)}{x-c} = K$$  $$\Rightarrow f'(c) = K$$  I'm not sure that I did this right - I'm not too comfortable with proofs yet (especially unfamiliar with using the MVT in proofs). I didn't use the fact that the domain of f is (0,1) which is concerning.

Let $f$ be a real-valued function continuous on $[a,b]$ and differentiable on $(a,b)$. Suppose that $\lim_{x\rightarrow a}f'(x)$ exists. Then, prove that $f$ is differentiable at $a$ and $f'(a)=\lim_{x\rightarrow a}f'(x)$.    It seems like an easy example, but a little bit tricky. I'm not sure which theorems should be used in here.    ==============================================================  Using @David Mitra's advice and @Pete L. Clark's notes I tried to solve this proof. I want to know my proof is correct or not.  By MVT, for $h>0$ and $c_h \in (a,a+h)$ $$\frac{f(a+h)-f(a)}{h}=f'(c_h)$$ and $\lim_{h \rightarrow 0^+}c_h=a$.    Then $$\lim_{h \rightarrow 0^+}\frac{f(a+h)-f(a)}{h}=\lim_{h \rightarrow 0^+}f'(c_h)=\lim_{h \rightarrow 0^+}f'(a)$$   But that's enough? I think I should show something more, but don't know what it is.


Compute the integral:  $$\iint_\sigma (x+y+z)\,\mathrm dS $$   on the cube $0\le x\le1, 0\le y\le1, 0\le z \le 1$.   I am really confused how should I compute it as I used to just take the projection of $\ z $ on the $\ xy $ plane but here the projection is just a square from $\ 0 $ to $\ 1 $. Trying to compute $\ \int_0^1 \int_0^1 (x + y) dy dx $ doesn't lead me to the right answer.

Evaluate the following integral $$\iint_S (x+y+z) \, dS$$  where $S$ is the surface of the cube $[0,1] \times [0,1] \times [0,1]$  Honestly, I don't know what to do. All I know is that you have to evaluate the integral for each of the 6 surfaces of the cube. The normals for them I can do and the equations of the planes, but other than that I couldn't do much.  Can someone break it down for me, please?  PS: No divergence theorem yet for me.


If I sign in to just one SE community, I'm automatically signed in to all other SE communities that I'm a member of. But this doesn't happen when I visit Area51.   There, I have to sign in separately, although I'm already online on other communities. Why is that?

I keep running across mentions-in-passing of Area 51 that make it sound like it’s obsolete, being sunsetted, or somehow posing a difficulty to Stack Exchange. One example I stumbled over just now while following up on the fixed CSS bug yesterday is representative:  I noticed that area 51 is not on either list. It and stack apps were not affected. –  hildred  @hildred Area 51 isn't getting a design lift any time soon, if ever. –  Anna Lear♦  @AnnaLear Is there any chance of removing the stupid Gravatar thing from Area 51? –  Catija  @Catija Not really. We aren't working on Area 51 in any meaningful way these days. –  Anna Lear♦   On their own these kinds of comments can be confusing or even alarming, so to clear the air: what’s really up with Area 51? N.B. that I'm neither complaining nor an alarmed Chicken Little myself — I ask because I think it would be useful to have a Meta.SE question people can link to for more information on why Area 51 is apparently developmentally unloved. :)


My friend just answered to one of my important questions. Now how should I reply to him?  1.Oh!That question had been on my mind for a long time, finally, I got my answer. ( Oh! I had that question on my mind for a long time, finally, I got my answer)                                     or   2.Oh!That question has been on my mind for a long time, finally, I got an answer.( Oh! I have that question on my mind for a long time, finally, I got my answer)  Basically, I am confused with had and have. Since that question is not anymore on my mind after having got an answer, which one of the above two sentences should be used?

My friend just answered to one of my important questions. Now how should I reply to him?        That question had been in my head for a long time, finally, I got my answer      or        That question has been in my head for a long time, finally, I got an answer.      Basically, I am confused with had and have. Since that question is not anymore in my head after having got an answer, what should be used? (I am also confused whether it is possible to use having instead.)


What do you think would be the requirements in getting admission in Hogwarts School of Witchcraft and Wizardry?  Would a child of 10 years old gain admission if he were to turn 11 in the months to come after July, for example December?  Will his/her relationships with anyone matter, like Draco Malfoy had relations with Death Eaters and other stuff like that?

So all wizards get an invitation to Hogwarts at 11... How do they know whom to invite?  If a wizard is Muggle-born, then nobody would know about their existence.  Or do they register some weird magical stuff being done by them before 11?


Is it true (and under which conditions) that the products of an non-square matrix $A$ and its transpose and vice versa (so the product of the transpose and $A$) share the same eigenvalues (multiplicities omitted)?

Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues.   I'm unsure how to approach this. I'm trying to assume that $\lambda$ is an eigenvalue of $A^TA$ with its eigenvector $\neq 0$ and use that to prove that $\lambda$ is also an eigenvalue of $AA^T$ with eigenvector $Ax \neq 0$, but I'm lost on how to actually state it with notation and build off it.  Should I be trying something else?


Let $|r| < 1$. How can I prove that $$\lim_{n \to \infty} \sqrt{n}r^n = 0?$$ I’ve tried taking logarithms and using l’hopital’s rule but am not really getting anywhere. Thanks!

I'm having trouble with proving the following for my math study:  Let $x$ be a real number with $|x| < 1$, and $q$ be a real number. Show that the series $\sum_{n = 1}^\infty n^qx^n$ is absolutely convergent, and that $\lim_{n \rightarrow \infty}$ $n^qx^n = 0$  I tried this:  $\sum_{n = 1}^\infty n^qx^n$ = $x + 2^q + 3^qx^3 + ...$ $= x(1 + 2^qx + 3^qx^2 + ...)$  So far, I don't know how I have to do this, I tried to apply the root test on this, but for that I would need to compute the lim sup of the series, so I thought that was not correct. Could you explain me how to prove this?  Thanks in advance!


Hi newbie in blender here.   does anybody know how to solve the problem?   Outside view show the whole 3d model, but on camera and rendered it comes out like this:

I'm having an odd issue - When I try to zoom in on a detail using my MMB, the "camera" in the 3D view seems to be cutting off the exterior surface of my object and showing me the inside instead. I'd expect this behavior, but only when I was much more zoomed in.  If I zoom out a bit (one click on the scroll wheel) then I can see the exterior as I intend.  Is there any way to adjust this behavior?  Thanks!


Prove  $(A^c)^c$ = $A$  $(A^c)^c = \{x|x\in (A^c)^c\}$  $(A^c)^c = \{x|x\notin A^c\}$ by definition of complement  $(A^c)^c = \{x|\ (x \in A)\}$ by definition of complement  Therefore   $(A^c)^c=A$  Is this proof ok, I'm not sure if its valid? thanks

Question states:  Prove the law of double complements for sets:  If $A$ is a set and $A^\complement$ is its complement than prove that:  $$ (A^\complement)^\complement  = A$$  I started with:  $$ A^\complement = U - A$$ where U is the universal set.  But I do not understand how to go further.


Could someone explain to me what !d command does? It seems to recall an old command (du -sh for me) but I have no idea how this command is chosen.

I used   history | less   to get the lines of previous commands and from the numbers on the left hand side I found the line I wanted repeated (eg. 22) and did  !22   at the command prompt and it worked -- executing the set of commands on the line I did at that time. I cannot figure out where the exclamation mark is used, what does it represent in terms of actions taken by bash, and where to use it. From the documentation I do not see an explanation that is 'tangible'.


I somehow rotated my view a few degrees to the side and I don't know how to reset it.    How can I reset the view?  Note: I don't have a number pad.

Lets say that I've rolled the view port with ⎈ Ctrl⇧ Shift Scrollwheel, and now want to get it back to its original orientation. How do I do that?


In beamer (presentation), I had seen example of insertion of a remark/small point during the presentation as below.  There, the author speaks (during presentation) as follows     "Consider the base case, namely when M/N is simple ... this work is done by Kleidmann, Liebeck,etc."   And while speaking this, he points out the names of Methematicians specifically as pointed below in slide.  Q. What are the commands to insert such pointing remarks, notes during slide presentation? (Please insert appropriate tag if necessary, since I do not have much idea of it.)

In the MWE below I want to place an "explanatory bubble" (see picture inserted below) pointing to the word "Integer" in the 8th line (the bubble should superimpose the text, a transparency effect such that the text behind the bubble is still weakly visible would be nice but is by no means necessary if this would make things significantly more complex) .  What is the most simple and elegant solution to do this?   \documentclass[10pt,xcolor=dvipsnames]{beamer} \usepackage{lipsum} \begin{document}   \frame{\frametitle{A Modern Exegesis of Lipsum}   \lipsum[1]   \begin{itemize}     \item WDQGCBIOZBWIWURZBBTBRTTVVUQRWXWTVEWQVY     \item BXWZTVWQTVCWRCQTVXTTQVRQXTRCVCVRTCVVTX     \item AUXZWTCVWVWUTVRTVCUZTEVWTVCUTVTVERVCTV   \end{itemize}   } \end{document}   The pdf output of the MWE:    The bubble should look somewhat like this:    PS: I saw  but it seems quite complicated to me -- hopefully there is a simpler solution to my problem. In case the solution involves TikZ some explanations would be appreciated since I have never used TikZ yet. NB: The solution should work with standard LaTeX and preferably not require PDFLaTeX.    EDIT: There is a follow-up question . The accepted answer to that question also gives an alternative solution to the above problem which may be more robust in combination with beamer than the solution suggested below.


I wonder if there is any way to show all post types in the same table of posts.  Let's say I've got 3 different post types: Movies, Books and Videogames.  Is there any way to show them all in a single table of posts?

I am building a site with 4 custom post types. To make things easier for our client/admin, I'm wondering if there is a way to merge those custom post types into one list in the backend? Like if you look at normal backend admin page with the list and columns of posts, can a page like that pull in 3 other post types for easy sorting/searching?  I can't combine the CPTs into one, they must remain seperate outside of one 'viewing' page in the admin area if possible.  Any thoughts on how to do this?? Or even where to start looking/thinkging of how to develop this?


I know this was asked many times before, but I couldn't find a recent answer, and it seems that Windows 10 has changed a lot and some answers went out of date in a year only! Where did these languages come from? They are not even present in the language settings. I didn't even install them and I don't even know what they are. Is there a recent way to prevent this (and fix it if it happened)?  My windows specs:

I just installed Windows Server 2016 in a development virtual machine and strangely there is an 'Unknown Locale (qaa-Latn)' listed in my language / input list (in the task bar) and it doesn't show up anywhere in the 'Clock, Language and Region' and > Language areas of the control panel nor in the newer Windows Settings dialog.  I have no idea how it got there and how I would remove it as it isn't listed anywhere explicitly.  Is there any way to remove this locale?  Update with more Details: This is/was a bare bones, fresh installation (using the Feb 2018 MSDN imnge of Windows Server 2016.. and I also tried re-installing it, again.. as new installation based on the RTM version of Server 2016 standard) without any 3rd party software. The only 'special' part is that it's running as a Hyper-V virtual machine (with Windows 10 Enterprise N being the host OS).


I am using Drupal 7 and have installed a translation module and enabled node and content translation, but I have a problem: In page /admin/content or node/add  the content name is not translated. I translate the content name string in the translation interface but they are not translated in related pages such add or manage content.  Please tell me how can I translate content type names.

I am developing a multilingual site that supports English and Norsk bokmal. I have set English as my default language. I wanted to translate the contents and the other things in the site.  My real problem started when I found that I was unable to see the translation of the content type's name. I went to admin/config/regional/translate/translate and translated everything, but still my content type's name is not translated.  I have attached a screenshot of the translation page. Still I don't find a way to translate the content type's name.


I've got an issue with setting an adapter to the ViewPager. Each time i get a NullObjectReference error. What's wrong with my code?  1) Layout:  <?xml version="1.0" encoding="utf-8"?> <LinearLayout xmlns:android="http://schemas.android.com/apk/res/android" android:layout_width="match_parent" android:layout_height="match_parent" android:orientation="vertical">  <android.support.v4.view.ViewPager     android:id="@+id/view_pager"     android:layout_width="match_parent"     android:layout_height="wrap_content">      <android.support.v4.view.PagerTabStrip         android:id="@+id/pager_header"         android:layout_width="match_parent"         android:layout_height="wrap_content"         android:layout_gravity="top"         android:paddingBottom="4dp"         android:paddingTop="4dp" />  </android.support.v4.view.ViewPager> </LinearLayout>   2) Java class:  public class FoodFragment extends Fragment {  Toolbar toolbar; ViewPager viewPager; TabsPagerAdapter pagerAdapter;   @Override public void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState); }  @Override public View onCreateView(LayoutInflater inflater, ViewGroup container,                          Bundle savedInstanceState) {      setRetainInstance(true);        ((AppCompatActivity)getActivity())     .getSupportActionBar().setDisplayShowTitleEnabled(true);     ((AppCompatActivity)getActivity())     .getSupportActionBar().setTitle(R.string.food);     toolbar = (Toolbar) getActivity().findViewById(R.id.toolbar);     toolbar.setBackgroundColor(Color.parseColor("#f6a632"));      pagerAdapter = new    TabsPagerAdapter(getActivity()    .getSupportFragmentManager());     viewPager = (ViewPager) getActivity().findViewById(R.id.view_pager);     viewPager.setAdapter(pagerAdapter);      return inflater.inflate(R.layout.fragment_food, container, false); } }   I always get this error when calling   viewPager.setAdapter(pagerAdapter); line.

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?


Let $f \in \mathbb{Z}[x]$.   And for more than 3 (i.e $\geqslant 4$) distinct $a \in \mathbb{Z}\ f(a) = 1$.   Prove that $\forall a \in \mathbb{Z} \ f(a)\neq -1$.  I have clearly no idea how to tackle this.   The only thing I've noticed (I'm pretty sure it is an obvious fact for the most of you) is that since polynomial is continuous function we have to prove that $f(a) > -1\  \forall a \in \mathbb{Z}$.

The question that I am trying to answer is :  Suppose is $p(x)$ is a polynomial with integer coefficients. Show that if $p(a) = 1$ for some integer a then $p(x)$ has at most two integer roots.  I have no idea how to get started. Any help would be awesome!


First I would like to say that I am new to Ubuntu and Linux.  I get an error with the make install when following the below instructions to install a Linux version of cpuminer-multi.     make: No rule to make target 'install'.  Stop.   I have placed what is in the folder that gets created when I attempt to install at the end. What am I missing?    SCRIPTS USED  sudo add-apt-repository ppa:ubuntu-toolchain-r/test sudo apt update sudo apt install gcc-5 g++-5 make sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-5 1 --slave /usr/bin/g++ g++ /usr/bin/g++-5 curl -L http://www.cmake.org/files/v3.4/cmake-3.4.1.tar.gz | tar -xvzf - -C /tmp/## Heading ## cd /tmp/cmake-3.4.1/ && ./configure && make && sudo make install && cd - sudo update-alternatives --install /usr/bin/cmake cmake /usr/local/bin/cmake 1 --force sudo apt install libmicrohttpd-dev libssl-dev libhwloc-dev git clone https://github.com/fireice-uk/xmr-stak.git mkdir xmr-stak/build cd xmr-stak/build cmake .. make install     FILES/FOLDERS GENERATED  build CMakeLists.txt doc LICENSE scripts xmrstak CI CONTRIBUTING.md Dockerfile README.md THIRD-PARTY-LICENSES

I was wondering about generic installations of all applications in linux. And what that means? Well, when I was using windows I knew that if I want to install an application I am double-clicking the .exe file and then next,next,next.  In linux, I have understood that maybe there is a common (not generic) way to install any application. Installing from source maybe? Well is there any step by step method that can be used to install  application like in windows or not?  I am asking because I do not want to keep asking the google, how to? So, I have managed to install recently from source freecad from  and I think that it would be a very nice start as common method, right?  But the thing then is where to find the right source and when an application has a very unique method of installation!


I want to compare the effect of a drug (immunomodulator) on antibody levels in a group of patients $(n=18)$. Blood samples were taken pre- and post-treatment in each patient and the means of antibody levels compared for each study subject. At this point I guess that the best and simplest option is a paired t-test.  However, in some cases, I have a different number of blood samples in the pre- vs. the post-treatment group. For example, for one patient I have $16$ samples pre-treatment and $5$ post-treatment.     Can I still use the paired t-test?  Should I use the independent t-test?

I have an existing data set that comes from the same group of people before and after they received a treatment.  The data set comes from when participants tested their blood sugar values over a 30 day period before receiving an insulin pump and a 30 day period after receiving an insulin pump. This data was obtained from user logs (archival data) and was not controlled to ensure that they were tested at fixed intervals. Participants tested themselves when they needed to test throughout the day for a period of 30 days.  My goal is to determine whether the average blood sugar across 30 days was different for the before vs after group.   Normally this would be a paired samples t-test but unfortunately the before and after group have an unequal number of data points with the after group having significantly more. People are testing more often after receiving an insulin pump.  What is the correct way to handle this?  I can collapse the data to find a mean for each participant before treatment and after treatment (across all participants) so that the data matches up and then run a paired samples t-test on this data but I think this is not the ideal solution.   Would a one way within subjects ANOVA be the appropriate test to run in this case?


When adding afterwards a character to a enumeration I do not succeed by going back with \vspace: The character C in the MWE is positioned too "high". Is there a possibility to achieve this? (I need to do this because I want to define an environment including enumerations with a symbol at the end.) \documentclass{article}    \begin{document}  \begin{enumerate} \item A \item B \end{enumerate} \vspace{-2\baselineskip} \hfill C  \end{document}

My self defined environment having a symbol at the beginning and at the end works fine for text without enumeration. When including enumerate the symbols are not there where desired. Is it possible to have the first symbol directly in front of "1." i. e. in the same line and the ending symbol in the same line as the last line of the enumeration? With \ignorespacesafterend and \unskip I did not succeed. \documentclass{article} \usepackage{amssymb} \newenvironment{myenv}{$\blacktriangleright$}{\hfill$\blacktriangleleft$}  \begin{document} There is a text.  \begin{myenv} And an example \end{myenv}  Here is another text.  \begin{myenv} \begin{enumerate} \item A \item B \end{enumerate} \end{myenv}  \end{document}


Is there anyone who can help me create a photorealistic star effect along the lines of this test video:    If you missed it, here's a screenshot (it's the blue one in front):    I'm aiming to get my star to be exactly like the front light blue one featured there in - a six pointer with thinner, sharper lines as opposed to the broader and more easily faded ones you usually get when you apply the glare effect.

Is there an addon, or an easy way to add  effects or  in Blender? I've been using Blender for a while now, and it's very time consuming to always have to export to another software to do them, and sometimes it's impossible if the scene is complex.


Which one of these questions is correct or both?  A     With whom do you watch movies?   B     Whom do you watch movies with?

I've been looking, but I have not come across this 'whom' related question anywhere.  Specifically in this circumstance, I feel 'with whom' flows more naturally but I remember someone suggested that 'whom with' is actually the proper order since it is referencing 'the people'     I am looking to find a friendly environment where I can enjoy my work and the people whom with I work.   Or     I am looking to find a friendly environment where I can enjoy my work and the people with whom I work.


Let $V$ be a Hilbert space with inner product $(\ ,)$ and norm $\|\cdot\|$. Suppose $a:V\times V\to{\bf R}$ is a bilinear continuous form. One can then define $A:V\to V'$ with $A(u)=\xi_u$ where $\xi_u(v)=a(u,v)$ for all $v\in V$. One can show by checking the definition that $A$ is linear.      Question: how to show that $A$ is continuous?     Suppose $u_n\to u$ in $V$. I end up with showing the estimate  $$ \sup_{v\in V, \|v\|=1}|a(u-u_n,v)|<\epsilon.  $$ For each $v$, by the continuity of $a$, one has for some constant $M_v$,  $$ |a(u-u_m,v)|\leq M_v\cdot \|u-u_m\|\tag{*} $$ But I don't see how to get a bound for $\{M_v:\|v\|=1\}$ so that (*) can be used.

In my numeric script there is a unproved theorem, saying that a bilinear form $a \colon V\times V \to \mathbb{R}$ on a normed vector space $V$ is continuous if and only if  $$|a(v,w)| \leq c \, \|v\| \, \|w\|$$ holds for all $v,w\in V$ for some $c > 0$.  My first question is: what is ment by a continuous bilinearform? Is it according to the norm $\| (v,w) \| := \max \{ \|v\| , \|w\| \}$ (which is equivalent to $ \|(v,w)\| = \|v\| + \|w\|$) ?   If so, then I agree that such a bilinear form is continuous but I don't see that a continuous bilinear form is bounded as above. Can anyone explain this to me?


I'm trying to recreate a similar effect,  I've tried to copy the text 6 times ( as the colours are ) and then use the pathfinder, to find the intersection, and color that in black, but it just doesn't work as nicely as this... any suggestions?  Many Many thanks, Giulia

I am trying to do an assignment and I need to do off registration. I cannot figure out how to get into the channels so I can move the colors to be off register. I can only figure out how to get into the separations, but it is not helping me. How can I make something off register? Thank you so much in advance! There aren't a lot of clear answers on Google.


I am not sure if my approach is on the right track for $\Rightarrow$, since I don't know how to proceed and reach the conclusion that $A$ meets each path-component of $X$? And I hope my approach to the other direction make sense?     $H_0(X,A) = 0 \iff A$ meets each path-component of $X$.   By Theorem 2.16, we have the exact sequence:  $$\cdots   H_0(A) \stackrel{i_*}{\to}  H_0(X) \stackrel{j_*}{\to}  H_0(X,A) \to 0$$  $\Rightarrow$: If $H_0(X, A) = 0$, then $H_0(X) = \ker j_*(H_0(X)) = \operatorname{Im}i_*(H_0(A))$. Because $H_0(X) = \operatorname{Im}i_*(H_0(A))$, we know $i_*$ is surjective.    Edit: I hope I figured this out?  The map $i_*: H_0(A) \to H_0(X)$ is surjective implies that the map $i_*: \bigoplus_\alpha H_0(A_\alpha) \to \bigoplus_\beta H_0(X_\beta)$ is surjective. That is to say that $\forall \beta, \exists A_\alpha : i(A_\alpha) \subset X_\beta$. Hence $A$ meets each path-component of $X$.    $\Leftarrow$: According to Proposition 2.7, for any space $X$, $H_0(X)$ is a direct sum of $\mathbb{Z}$'s, one for each path-component of $X$. So if $A$ meets each path-component of $X$, $H_0(X) = H_0(A) \approx \mathbb{Z}$. So the inclusion $i: A \to X$ induces a surjection $H_0(A) \to H_0(X)$.  So since $H_0(A) \to H_0(X)$ is surjective, $\operatorname{Im} i_*(H_0(X)) = H_0(X, A) = \ker H_0(X, A)$. Since the entire $H_0(X, A)$ lies in the kernel of $j_*$, $H_0(X, A) = 0$.

I've been doing some more exercises in , in particular the following:  Show that $H_0(X,A) = 0$ iff $A$ meets each path-component of $X$.  "$\Leftarrow$": Let $x_i \in A \cap X_i \neq \emptyset \forall $ path-components $X_i$. Then for any $x \in X_i$ there is a path $\gamma$ from $x_i$ to $x$. They therefore differ by a boundary: $\partial \gamma = x - x_i$ and therefore $\{ x \} = \{ x_i \}$ in $H_0(X,A) $. Therefore $H_0(X,A) = 0$.  "$\Rightarrow$" Now for this direction I'm not so sure and I'd be glad if you could give me a hint. Let $H_0(X,A) = 0$. By definition, the relative homology group is calculated from the following sequence of chain groups:  $$ 0 \rightarrow C_0(A) \rightarrow C_0(X) \xrightarrow{\partial_1} C_0(X) / C_0(A) \xrightarrow{\partial_0} 0$$  Then $H_0(X, A) = H_0(C_0(X) / C_0(A)) = ker \partial_0 / im \partial_0 = (C_0(X) / C_0(A) ) / im \partial_1 = 0$.  There are two cases where this equality holds:  (i) $C_0(X) / C_0(A) = 0$  (ii) $im \partial_1 = C_0(X) / C_0(A)$  In case (i), $A \cap X_i \neq \emptyset$ for all $X_i$.  In case (ii) I'm not sure how to proceed. Can you give me a hint? Many thanks for your help!  Edit Or maybe I could do the second direction like this:  $$0 = H_0(X,A) = \oplus_i H_0(X_i, A) \implies  H_0(X_i, A) = 0 \forall i$$  $$ \implies A \cap X_i \neq \emptyset \forall i$$?


was a gigantic engineering and colonisation idea from the 1920's. It involved building humongous hydroelectric dams and lowering the water level of the Mediterranean by something like 200 meters.  I want to ask whether that plan would have been possible, remotely feasible or just crazy.  Is this question suitable for any SE site at all?  What is the best site to ask it at? I have considered Earth Science and Engineering, but I'm not familiar with either site, so I'm not sure.

Is there a general discussion section for curious questions? Or are we simply left to swallow such curiosity because the results of it may or may not benefit a big crowd? Sample question There's an idiom, "It costs a moon". As of now NASA hasn't revealed if the Moon has precious elements. This brings some curious thoughts to me... What if the Moon has precious metals, gas, etc.? Does anyone own the moon or other planets in our solar system? Like Americans? Russians, Germans, Japanese, Chinese or British? Are there any constitutions that refrain anyone from such access or ownership to solar elements (either research wise or commercial wise)?


I am a beginner to blender and have somehow managed to hide the property editor in blender. Is there any way I can bring it back? Thanks

I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program.


On Quora, there is a feature to follow questions asked, either privately or publicly, so whenever one or more new answers are added, followers get notified. As far as I know, there is no feature like that on Stack Exchange. That is annoying me. Sometimes, there are very interesting questions to which equally interesting answers may be written anytime. Sometimes, any question may get one or more great answers even after a long period of time of being asked. I want to follow questions that interest me, so that if one or more new answers are added, I get notified, even it is years afters the question was first asked. Other people have suggested marking questions as favorite and checking them every once in a while, but I find it a bad idea, and that it will be time-consuming to do so. The placeholder in Title is "What's your bug, feature request, or meta-discussion topic? Be specific." So, this is my feature request. I hope that it will not fall on deaf ears.

I've come across a few interesting questions over the last few months on Stack Overflow. They're not necessarily questions I need an answer to, but the questions are nonetheless very interesting, and now I want to know what the answers are.  I don't want to add this question to my favourites because I have my really handy posts in there.   Ideally I would like to have another kind of shortlist to which I can add these posts. I would get notifications just as if it were my own post, without having these as favourites.  What do you think of that? It would be available only for questions, and you would receive notifications just like the author, for new answers and comments on the question (not comments on the answers).  You could browse the posts you're following, as well as stop following them.   The thing is sometimes I come across a semi interesting question and upvote and maybe even comment, but I never hear about it again, because sometimes it's just not interesting enough to remember.  Like I said in the comments, I don't feel like the favourite list is really for this. I want in-your-face red dot notifications for new answers on brand new interesting questions I find. The favourites is for that post with an answer that you know you'll need again.


I want to buy a new domain with a name that is so similar to my original website domain and redirect it in a 301 redirect to the original website. will this somehow affect the original website traffic?? Thanks

We have a ton of alternate domain names. What is the best strategy as far as SEO strategy is concerned? Do we want to 301 redirect them all to our primary domain or set up simple landing pages that link to the main site?


The way i interpret pseudo-forces is that its a mathematical correction that makes the conclusion of the observer in an accelerated frame correct.  And I also believe that this "pseudo-force" has no physical significance, that is, it isn't something actually acting on the body being observed.  While doing circular motion problems, while analyzing from the rotating frame, we add a pseudo-force in the outward direction.  Now, we *actually do feel an outward force * when we are in circular motion, (like when we are taking a turn on the road) and I have seen many textbooks attributing this to the "centrifugal force", which I believed to be simply a pseudo-force and thus, is not something that is physically affecting a body.  What is the correct explanation to this problem?  edit: I think I somewhat got the idea, but I still don't feel I can generalize it to other situations, like:  1)A liquid in a rotating tube (in a horizontal plane) moves Outwards  2)Suppose a block is kept on a rough rotating table,(the block also rotates).We say that friction provides the centripetal force. But say the angular speed is such that friction becomes insufficient to provide the force, and the block moves outwards. Also, from an inertial frame, if friction is acting towards the center, it means the body has a tendency to move away from the center.  Can these two situations be explained by the same, inertia arguement?

Currently in my last year of high school, and I have always been told that  does not exist by my physics teachers. Today my girlfriend in the year below asked me what centrifugal force was, I told her it didn't exist, and then she told me her textbook said it did, and defined it as "The apparent force experienced towards the outside of a circle is the centrifugal force and is due to the mass of the object resisting the inward centripetal acceleration that the object is experiencing". I was pretty shocked to hear this after a few years of being told that it does not exist.  I did some reading and found out all sorts of things about pseudo forces and reference frames. I was wondering if someone could please explain to me what is going on? Is it wrong to say that centrifugal force does not exist?   This has always nagged me a bit as I often wonder that if every force has a reaction force then a centripetal force must have a reaction centrifugal force, but when I asked my teachers about this they told me that centrifugal force does not exist.


Freezer is failing and meat is thawing. Still refrigerator temp cold. Is it safe to refreeze?

I've often been told by people that I shouldn't refreeze meat (particularly hamburger meat) once it has been thawed.  However, this seems a little silly to me.  I can't imagine how meat that hasn't been bought fresh and local could find its way to my kitchen with out thawing and being refrozen a couple of times.  How much damage can one more thawing and refreezing really do?  Can it really be that dangerous disease wise? Or is this just one of those urban myths?


I have some issues with this exercise. How should I use induction on k? Maybe someone can give me a hint :)

I need to find a way of proving that the square roots of a finite set    of different primes are linearly independent over the field of    rationals.    I've tried to solve the problem using elementary algebra  and also using the theory of field extensions, without success. To  prove linear independence of two primes is easy but then my problems  arise. I would be very thankful for an answer to this question.


I am wondering why there is an article -a- before Merry Christmas Is it because it's a day or Christmas is countable? I couldn't explain it to my students in a transparent way.

"Mornings came and cast a blinding sunlight over everything, and he felt like nothing worthwhile could be accomplished."  For some reason, I feel like "a blinding light" is ok, but if its sunlight, then I should drop the "a" and write "cast blinding sunlight", but I'm not sure why I feel this way.   Can anyone offer some enlightenment?  edit - alternate phrasing, closer to being a literal translation: "Mornings came without warning, flooding the day with a strong sun, and he felt like nothing worthwhile could be accomplished."   I would still like an answer to the technical question of whether I should drop the "a", but would also appreciate knowing if anyone thinks option #2 is a better choice.


Find the limit for $\lim_{n\to \infty}\frac{n}{\sqrt[n]{n!}}$  I have no idea how to do this - they always say use the ratio test when there are factorials but the nth root stuff makes it so ugly and i can't get anything to come out of it. Does anyone know what process I should use?

Show:$$\lim_{n\to\infty}\frac{\sqrt[n]{n!}}{n}= \frac{1}{e}$$  So I can expand the numerator by geometric mean. Letting $C_{n}=\left(\ln(a_{1})+...+\ln(a_{n})\right)/n$. Let the numerator be called $a_{n}$ and the denominator be $b_{n}$ Is there a way to use this statement so that I could force the original sequence into the form of $1/\left(1+\frac{1}{n}\right)^n$


The last research aim to find gravitons which are boson, so if I correctly understand they are virtual particles.  Out of theorical assumptions,  Is there exist an experimental proof that the propagation of the gravity isn't instantly ?   I try my best to write correct english, I hope you understand my question.

In replying to a  I stated:     Gravitational waves have not been yet experimentally observed so as to have their velocity measured.   Which after the fact prompted me to try and verify it. I found a "speed of gravity" claimed measurement, which has been in a controversial discussion. In the last paragraph of  I found:     In September 2002, Sergei Kopeikin and Edward Fomalont announced that they had made an indirect measurement of the speed of gravity, using their data from VLBI measurement of the retarded position of Jupiter on its orbit during Jupiter's transit across the line-of-sight of the bright radio source quasar QSO J0842+1835. Kopeikin and Fomalont concluded that the speed of gravity is between 0.8 and 1.2 times the speed of light, which would be fully consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light.[18]   There has been criticism, described in the paragraph.   Has this matter been resolved ? is the measurement valid?  The speed of gravity has also been  calculated from observations of the orbital decay rate of binary pulsars and found to be consistent to the speed of light within 1% ( same link).  This is the speed that gravitational fields transfer information, and though the number itself depends on the theoretical framework solving for the system parameters it is true that just the existence  of gravitational damping in the binary system would imply that the speed cannot be infinite.  Along these lines I was wondering whether studying the second star in a binary system where the first has gone nova would not give a cleaner and model independent measurement of the speed of transfer of information gravitationally. In this day and age where everything is digital one should be able to have data on this from now on.     (Feb 11,2016) announced the observation of gravitational waves , at the same time  consistent with the speed of light being c, and thus measuring it. See the  for a summary.


The download page only mentions desktop pcs, so what version do I get for a Mac?

I am trying to download Ubuntu to put it on my daughter's MacBook (just installed new HDD, so no operating system on it)  But from my Windows PC all I can see is the Windows Ubuntu. Can I use that, or is there a specific place I can go to get the Ubuntu download for a Mac please?


This is the bind2nd definition:   template <class Operation, class T>     binder2nd<Operation> bind2nd (const Operation& op, const T& x)     {       return binder2nd<Operation>(op, typename Operation::second_argument_type(x));     }   And the key word typename can be used to:   In a template declaration, typename can be used as an alternative to class to declare type template parameters. Inside a declaration or a definition of a template, typename can be used to declare that a dependent name is a type.   So, I think typename is used to declare that Operation::second_argument_type is a type, but I want to know why we need to use typename here ?Can't we use it ? What is the advantage to use it ?

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


I’m experiencing a bizarre issue between PHP and MySQL. I have the following code to get values for an HTML table ($sortfield is set to table1.colb DESC or table1.colb ASC, depending on the test).  if (!($stmt = $db_handle->prepare("SELECT table1.cola, table1.colb ORDER BY ? LIMIT ?,20"))) {     exit('Prepare failed: (' . $db_handle->errno . ') ' . $db_handle->error); } if (!$stmt->bind_param('si', $sortfield, $start)) {     exit('Binding parameters failed: (' . $stmt->errno . ') ' . $stmt->error); } if (!$stmt->execute()) {     exit('Execute failed: (' . $stmt->errno . ') ' . $stmt->error); } $stmt->store_result();   This code executes with no errors, but the ORDER BY clause is totally ignored when its value is given as a variable. The results are sorted by table1.cola, as if ORDER BY were not present. If I replace ORDER BY ? with ORDER BY table1.colb (and modify bind_param accordingly), then the query behaves as expected and sorts by that column.  If I echo the complete statement with variables (i.e., echo "SELECT table1.cola, table1.colb ORDER BY $sortfield LIMIT $start,20") and manually run the result directly against MySQL, then the query works as expected.  $sortfield is taken from a GET method and processed by htmlentities() prior to statement preparation. It’s expected to be a string value, and that’s what it appears to be, so I’m quite confused about the outcome.

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


Suppose we have two lists a and b:  a = [1, 2] b = [3, 4]   Is there a quick operation that will return the list of tuples [(1,3), (1,4), (2,3), (2,4)]?

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


How do I set up a double elimination tournament with 18 participants. I can never get it to come out even.

I know that a double elimination bracket operates like two single eliminations: there is a "winners" upper bracket and a "losers" lower bracket.  My requirements   I need a logic for the Losers bracket players (not winners bracket). The general rule being that Losers fall down to the Losers bracket in the same position as they held in the winners bracket matches.....but that logic is not clear and neither are the conditions in which this is true. I want to understand the above logic assuming bye players not for the standard 2,4,8,16,32 teams scenario   Some links on brackets having byes


I'm trying to solve the problem that given any $x \in \mathbb{Z}/3705\mathbb{Z}$, I want to find all $x$ such that when mapped under the Chinese Remainder Theorem, is mapped to $(\bar{4},\bar{7})$ in $\mathbb{Z}/57\mathbb{Z} \times \mathbb{Z}/65\mathbb{Z}$.  Now I tried solving the system of congruences, $$x \equiv 4 \ (\text{mod} \ 57)$$ $$x \equiv 7 \ (\text{mod} \ 65)$$  Then I was left with, $$57k \equiv 3 \ (\text{mod} \ 65)$$ where $x=4+57k$. Now I could solve this by repeatedly adding (or subtracting) $65$ onto $3$, until I get a multiple of $57$. However when I typed it into Wolfram, the first solution that comes up is when I add or subtract $78$ and $38$ times respectively, which isn't exactly efficient in a test scenario. So I was wondering if there is some faster method to solve this question/system of congruences. Or some systematic way to find the number of times I need to add or subtract $65$.

When I am faced with a simple linear congruence such as  $$9x \equiv 7 \pmod{13}$$ and I am working without any calculating aid handy, I tend to do something like the following:  "Notice" that adding $13$ on the right and subtracting $13x$ on the left gives: $$-4x \equiv 20 \pmod{13}$$  so that $$x \equiv -5 \equiv 8 \pmod{13}.$$  Clearly this process works and is easy to justify (apart from not having an algorithm for "noticing"), but my question is this: I have a vague recollection of reading somewhere this sort of process was the preferred method of C. F. Gauss, but I cannot find any evidence for this now, so does anyone know anything about this, or could provide a reference? (Or have I just imagined it all?)  I would also be interested to hear if anyone else does anything similar.


I have a table contains tens, hundreds, or thousands numbers with or without decimal. I need those numbers to be aligned at ",", the decimal symbol (Indonesian). I try to use \newcommand\ph{$\phantom{1}$} but it doesn't work well. The number posisition didn't aligned at ",". Please help, thank you.  This is my MWE:       \documentclass[10pt,a4paper]{article}   \usepackage[utf8]{inputenc}   \usepackage[T1]{fontenc}   \usepackage{amsmath}   \usepackage{amsfonts}   \usepackage{amssymb}   \usepackage{graphicx}   \usepackage{multirow}   \newcommand\ph{$\phantom{1}$}    \begin{document}       \begin{table}[h]           \centering           \caption{Hasil Belajar Matematika}           \begin{tabular}{l|c|c|c|c}               \hline   \multirow{2}{*}{Statistik}& \multicolumn{2}{c|} {Eksperimen}&\multicolumn{2}{|c}{Kontrol}\\               \cline{2-5}               & {Pre-tes} &  Pos-tes  & Pre-tes   & Pos-tes   \\               \hline               Sampel          &   24      &    24     &        24 &  24   \\               Jumlah          &   928     &   1491    &   1184    &1585   \\                 Rata-rata       &   48,46   &    77,83  &    49,50  & 66,12 \\               Maksimum        &   75      &    100    &   70      &94     \\               Minimum         &   26      &    43     &   33      &35     \\                 Std. Deviasi    &   13,603  &    16,029 &   12,022  &15,066 \\               Varians         &   185,042 &    256,928&   144,522 &226,984\\               \hline           \end{tabular}       \end{table}   \end{document}

I want to align two numbers in two different rows the decimal point.    I do see a link for that here:   However, I don't understand how to incorporate that into my code.  What follows is a reduced version of my code.  \documentclass[12pt,english]{article} \usepackage{longtable} \usepackage{fullpage} \usepackage{times} \usepackage[flushleft]{threeparttable} \usepackage[font=large,labelfont=bf,tableposition=top,textfont=bf]{caption} \usepackage{tabularx} \usepackage{booktabs} \newcolumntype{C}{>{\centering\arraybackslash}X}  \begin{document}  \clearpage \newpage \begin{table}[!ht] \caption{Table Title} \def\arraystretch{1.05} \vspace{-0.2cm} \begin{threeparttable} \small \begin{tabularx}{\textwidth}{l*{10}{C}} \hline \hline \addlinespace & (1)  \\   Variable Name & 0.1234566  \\ & (0.1234566) \\ \hline \hline \addlinespace  \end{tabularx} \begin{tablenotes} \vspace{0.1cm} \footnotesize{  \item \noindent \hspace{-1.8mm} Notes:    \noindent Sources:   } \end{tablenotes} \end{threeparttable} \end{table}  \end{document}


So I have this i7 3.2Ghz 6-core dedicated server running Windows Server 2008, with a 1Gbps internet speed. Everything runs fine and nice, and the machine is strong enough to handle even up to 700 Mbps DoS attacks very easy.. no lag, no problem..  From time to time we were used to have big attacks but from only 1 or 2 IP at a time, so the CPU usage was always fine, until recently, we discovered a whole new level of DDoS attacks !  Some guy is flooding very small SYN packets, that are not exceeding 40 Mbps in total, but from thousand of IPs/botnets.. He is able to increase the CPU usage of the first COR up to its maximum, making the server almost down and not responding to RDP.. (The other 11 cors are empty, just chilling)  The TCP port that the attacker is targeting is a closed port, i think it's just the OS (Kernel in red) that's making all that mess.  I did some research, and (not sure) I think maybe the problem is something about IRQ balancing, like I need to balance that CPU usage between the other free cores..  Anyways, the big question is: Is it possible to fix this issue within the windows itself? How the hell can he kill my server with a 4% Network usage, when my server was able to stay alive even at 90% of the network usage before?! There must be a fix to this! Anyone know about balancing the 1st core to fix this? Please help with anything you have.

This is a  about DoS and DDoS mitigation.   I found a massive traffic spike on a website that I host today; I am getting thousands of connections a second and I see I'm using all 100Mbps of my available bandwidth.  Nobody can access my site because all the requests time out, and I can't even log into the server because SSH times out too!  This has happened a couple times before, and each time it's lasted a couple hours and gone away on its own.  Occasionally, my website has another distinct but related problem: my server's load average (which is usually around .25) rockets up to 20 or more and nobody can access my site just the same as the other case.  It also goes away after a few hours.  Restarting my server doesn't help; what can I do to make my site accessible again, and what is happening?  Relatedly, I found once that for a day or two, every time I started my service, it got a connection from a particular IP address and then crashed.  As soon as I started it up again, this happened again and it crashed again.  How is that similar, and what can I do about it?


I can't remove the indeterminate form $0 \cdot \infty$. I tried to write the limit as $$\lim_{x \to 0^-}e^{x \log \left(1+\frac{1}{x} \right)}$$ but it doesn't help.

Is there a way to find this limit without using L'Hôpital's rule. Just by using some basic limit properties.  $$\lim_{x\to\infty}\left(1+\frac1x\right)^x=e$$


Just switched completely from Windows to Ubuntu and am happy.   I have a problem; there is a folder called /root. I want to know how I could use the ls command to find out the owner and group associated with this folder, and what rights they each have.

I often see things like     read man xyz   For more information read xyz's man page.   see info xyz    so I wonder:   How can I get help on terminal commands generally? What exactly are these man and info pages?   How can I find and view them?


Given that a collection of classical particles can be modelled using Newton's three laws, it must be the case that both the conservation of momentum and the conservation of angular momentum are emergent features of Newton's three laws.  I can easily show the conservation of linear momentum from the third law, but how can the conservation of angular momentum be derived from Newton's three laws?

We know that angular momentum is defined as the cross product of position and linear momentum. By taking the time derivative, we can deduce that the time rate of change of the angular momentum equals the net torque.  Then why is the conservation of angular momentum considered a law, when we can easily show it is conserved when no net torque is applied, by using Newton's laws?  It truly confuses me.


I am unable get wireless or ethernet connection to work at all.  I have tried many things like trying to download the drivers while booting from the installation disc, and so forth, because this was the only time my laptop would pick up ethernet.   Inevitably this never worked because as soon as I booted without disc I was, once again, back to having no connections at all! I am unable pick up any connection whatsoever.

I'm having serious problems installing the Broadcom drivers for Ubuntu. It worked perfectly on my previous version, but now, it is impossible.   What are the steps to install Broadcom wireless drivers for a BCM43xx card?  I'm a user with no advance knowledge in Linux, so I would need clear explanations on how to make, compile, etc.    lspci -vnn | grep Network showed:   Broadcom Corporation BCM4322 802.11a/b/g/n Wireless LAN Controller [14e4:432b]      iwconfig showed:  lo        no wireless extensions. eth0      no wireless extensions.   NOTE: Answer below is updated every time new information is added and confirmed working.


In my company (as probably in many) we are struggling to share the knowledge. This goes from product-specific knowledge (which would not fit on Stack Overflow) to more broad knowledge like the one related to libraries or  bugs (to name a few possibilities). Once somebody finds a solution to a problem, usually they share it. But it may happen that they forget, or that they way they share it (an email, link on the wiki) is not good enough as users may no check it once the stumble upon the same problem. Probably most of them will just type the error on Google or Stack overflow. Knowing most developers just go to Stack Overflow to check for the issues, it would be worth to leverage this adding a system that facilitated the spread of knowledge in the company. I think it would be handy a system that would allow us to:  Create a list of questions (a private list as public lists are the same as tags) to which a given set of users can contribute adding existing or new questions, where we could search for issues in that list. Tags won't work as questions have a limit on the number of tags and it would pollute the questions with one tag per list, although the idea would be similar (private tags?). That way users have a place to check first of all. Notify members of the lists of new items (an  feed would work) Prioritize results on that list when searching  My questions are:  Do you have any suggestion on how to implement this given the currently available options on Stack Overflow? If it's not feasible, there is any way we can code a solution and contribute it back to Stack Overflow? (I suspect no as I've not seen the source anywhere, but I may have not looked at the proper place) If neither of both would work, how can we suggest this feature for future releases of Stack Overflow? This message is enough?  EDIT: My main point is that tags can be somehow limiting if you have a cross-tag interest. Maybe you can filter all queries with all the tags involved, but doing so will give back results that you may not want (due to quality or not being completely related) and it may be that your interest can't be expressed properly by grouping tags. Also, you may want to keep a set of questions that fit a specific theme relevant to you grouped and easily available. That could be done with the favorite flag. But you may want other people to see that list and  contribute to it questions that fit the theme. That you can't. For example, let's say me and my group are interested on issue that include:  2,  2.5,  3.0, CSS, , HTML5 and . We may find handy to have a list to store relevant questions (project gives error XYZ, why? check there) as it becomes part of a tool you use daily (Stack Overflow). Also, filtering by tags all these concerns would return an empty list, but we want to keep the relation somehow.

Is the Stack Exchange engine that powers Stack Overflow available to download or install internally for an enterprise or company?  I think Stack Exchange's engine is very great and could be very cool to use for internal enterprise patterns and practices, like the engine of Wikipedia.


I'm having trouble inserting an email address into a MySQL database.  I'm getting the dreaded 1064 error like so..  Error creating new user You have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near '@email.com, password, 20)' at line 1 -- 1064  So I'm guessing I need to escape the @ in the email variable?  But nothing i do seems to please Maria.  Generating the query in PHPMyAdmin was no help either. Any advice gratefully accepted.  // update SQL     $sql2 = "INSERT INTO members (username, email, password, balance) VALUES ($new_player, $new_email, $new_password, 20)";     if ($db->query($sql2) == TRUE) {             echo "** New User Created **
";                 } else {                 echo "Error creating new user " . $db->error." -- ". $db->errno ."
";     }

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


I am switching from windows 10 to ubuntu. So, I want to know that during ubuntu installation. The installer will format my whole hard drive or only instaling drive.  Please give reply fast I am waiting

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


I was wondering what this part of a c# winform does. public home() {     InitializeComponent(); }

What does InitializeComponent() do, and how does it work in WPF?  In general first, but I would especially be interested to know the gory details of order of construction, and what happens when there are Attached Properties.


EDIT: Let me break it down to something even simpler.  I understand that this is a  bug. I also understand that the deletion of a comment is implemented as a vote for deletion. The only thing I cannot get my head around is:   Why can we not change the text that is displayed? Is it because it would be too cumbersome to make this change implementation-wise? Is it just low-priority?   The second and third question are simple yes-or-no questions that I think I can expect an answer to. I apologize if I missed something important.    I recently deleted two of my comments and got the following warning:        Why is deleting my comment called a "comment vote"? Now, please read on before flagging it as a duplicate...  This is the same question as this one: . But unfortunately, nothing was done to fix the bug.  So, perhaps my question is rather: Why was this bug not addressed so far?  It has been around for a couple of years now and I'd really like to see a change to this misleading pop-up text.  N.B. I am not complaining about the time limit of 5 seconds. I am complaining about the wording.

I had an old question that I revisited in order to link it in a new answer. I noticed that in the comments Steven A Lowe had a funny comment that I -- at the time -- had responded to with "why can't I upvote comments?"  Well, of course, now I can.  So, I voted Steven's comment up then went to delete mine. I got the warning box that I can only submit comment votes once every 5 seconds. This seems like a bug to me. Deleting is not the same as voting.


In bash what does the syntax ||: do?    Example  $ ls foo ||:     Other than always return success, does this do anything else special?  Is the output of $ ls foo ||:; echo $? always zero, even if ls foo fails because foo doesn't exist?  I saw it in a script that begins with set -e.  So I'm guessing it ensures that no error occurs, thus the script does not immediately exit, even if a command suffixed by this returns an error.

I don't do terribly much shell scripting, so I was a little surprised when I was reading  and I saw the syntax they used in this documentation:     A non-zero return from the command in any submodule causes the processing to terminate. This can be overridden by adding || : to the end of the command.   I had to look up that || : was a shorthand for forcing a command to exit successfully.  Anytime I've had to make a command exit successfully, I used || true.  Is || : considered to be more idiomatic?


I, like many other Steam users, own quite a few games, and have trouble ever deciding which ones to try next. My favorite metric these days is the user review scores, but I can find no way to apply this to my library.  I did find this question:  However, the accepted answer is from back in April (before the discovery update) and the additional answer added in September doesn't address all the possibilities I am looking for insight on.  I have dug around and can find no indication of being able to search by anything other than the available columns in list view (name, metascore, last played etc.) However, I know that the core search now shows which titles are in your library. Is it possible to use the general search and filter by only the titles in your library? (The answer to this according to the Sep. answer on the aforementioned question is No)   Is there anyone who has come up with some sly way of helping filter down lists to a close approximation of your owned games. If so, then I could leverage the additional useful sortations found in general search (user review and release date for sure) also having the ability to filter on things like number of players, features and everyone else's tags.  I have tried various tricks to get the search to filter in unpublicized ways, is there a super-user out there that has cracked this nut or is it truly not possible at this point?

My game list is approaching 100 games and it is starting to get difficult to sort them. I've categorized them by genre but it's still difficult to find them (and my backlog is getting bigger).  I also have Steam installed in more than one computer so I have to repeat the sorting for each one of them.  Is there any option to have the games ordered in a nice and clean way?  Edit: About the library sync between computers it could be  problem.


I've read  but I don't know how to use the same method to prove my example. Induction seems very long and unnecessary. I tried to come up with something using:  $n^7 \equiv n \mod{7}$ and $n^{11} \equiv n \mod{11}$  but I am not sure that's useful. I am now assuming I have to show that $n^{31} - n$ is a multiple of 7 and 11 and thus a multiple of 77. How do I arrive in this conclusion?

I'm asked to show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$. I've tried to tackle this using Fermat's Little Theorem and Euler's Theorem, but I can't even get started. My main problem seems to be the "for every $a \in \mathbb{N}$" part, because if it restricted $\gcd(a, 1001) = 1$ I would be able to factor out 1001 and try to show that it's factors divide $a^{61} - a$. I'm kinda lost here. Any help is appreciated.


So I was trying to code a viewer class and then create a list which is based on these viewers as another Class called ViewerList.  Usually everything should work but somehow it doesn't let me use the methods "toLine()" and "getName()". If anyone here could help me it would be awesome.  As in title the only error-report i get is NullPointerException.  This is the Viewer class:  public class Viewer {  private int points = 0; private String name;  public Viewer(String name, int points) {     this.points = points;     this.name = name; }  public int getPoints() {     return points; }  public String toLine() {     String line = getName() + " " + getPoints();     return line; }  public void addPoint(int amount){     points += amount; }  public String getName(){     return name; }   This is the ViewerList class:  public class ViewerList {  private Viewer[] array; private int nextFreeSlot = 0; private int count = 0;  public ViewerList(int capacity){     array = new Viewer[capacity]; }  public void add(Viewer o){     if (nextFreeSlot == array.length) {         throw new IllegalStateException("Liste ist voll!");     }     array[nextFreeSlot] = o;     count++;     nextFreeSlot++; }  public Viewer[] getArray(){     return array; }  public Viewer get(int index) {     return array[index]; }  public int getCapacity() {     return array.length; }  public int getElementCount() {     return count; }  public void addPoints () {     if(array.length > 0){         for(Viewer v  : array){             v.addPoint(1);         }     } }  public int getPointsOf(String viewerName) {     int points = 0;     String vName = "";         for(Viewer v : array){                 vName = v.getName(); // The v.getName() method is an error here             if(viewerName.equals(vName)) {                     points = v.getPoints();             }          }      return points; }  public boolean contains(String name) {     boolean contains = false;         for(Viewer v : array){             if(name.equals(v.getName())){ // also here i get the NullPointerException                 contains = true;                 break;             }         }     return contains; }   }  Also if you need the stack trace then here it is:  java.lang.NullPointerException     at bot.PointList.getPointsOf(PointList.java:50)

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?


Can anybody show me how to do the boxes in the image attached in latex.   Thanks ahead

I have several frameboxes in my document, using the following command:  \framebox(115,115){ R-Sq: \newline For example}    I want to force a new line, but neither \newline or \\ appear to work. Is there any other way of doing this?


$y^2 = x^3 + mx + c$    An elliptic curve in the form defined in Wikipedia $y^2 = x(x-A)(x+B) = x^3 +(B-A)x^2 + ABx$     Frey's curve  has no term in $x^2$, but $2$. does because from Fermat, $A=a^n$ not equal to $B=b^n$   Question: Is there a simple way to transform Frey's curve with given $A,B$ into form $1$.  (Has it got anything to do with Weierstrass ?)

I understand, on  a layman's level, Fray's motivation to write an elliptic equation corresponding to an assumed solution to FLT. My question is, how technically is Frey's equation derived?   $1.$ FLT : Contradiction. There exist integers $A,B,C,n>2$ such that $A^n + B^n = C^n$  $2.$  Frey: $y^2 = x(x-A^n)(x+B^n)$  $3.$  Elliptic curve $y^2= x^3 + ax + b$    $4.$  The curve is not modular. => not elliptic => FLT  proved.   I need is the algebra to go from 1. to 3. above.  Assume Numbers A,B,C such that A^n + B^n = C^n contradicting FLT.  $y^2 = x^3 + ax + b$ an elliptic curve in Weirstrass form. I am guessing A and B go unchanged into x(x-A^n)(x+B^n)   Is that correct ?  Expanding 2. I get a term in x^2 , there is none in 3. This is my problem.  What does a $2$ dimensional graph of the Frey curve look like ?


I'm making a presentation and want to insert a comment, like a pop up comment, which contains some equations in math style. For example:  \documentclass{beamer}  \usepackage{pdfcomment}  \begin{document}    go back to the last equation. \pdfcomment{$x^{2}+2x-1=0$ }  \end{document}   My problem is that the equation above doesn't appear in the math style  $ x^{2}+2x-1=0.$  Is there another way to do this?

My goal : I correct copies from students that I scan to pdf. I wish I could make the annotations on the scanned copies rather than on the physical paper. Today, I have to scan the copies again to have my annotations transferable to students by email. Since most of the annotations are similar, I wish to have a stock of annotations I could transfer on the copies.  I went through a lot of technologies, including many "StackExchange Questions" here. I considered pdfcomment, cooltips, fancytooltips, the OCG family (ocgx, ocgp, ocg2, ...), etc.  Two tracks attracted more specifically my attention :    pdfcomments : I like the mouseover to see the comment, the capabillity to move the annotation around so I can have a stock on a pdf and I can copy it onto the scanned copies. This would be my choice if there was not a main drawback : it accepts only plain text when I need to use mathematical notations. (It needs selected pdf readers). Because you can move comments, you can put them on any pdf, even if it is not compiled from Latex or if you don't have the source. fancytooltips : I like the mouseover to see the comment, and the capability to use LaTeX mathematical formulas and images. Drawbacks : I can't move the annotation from a pdf document to the copies. (It works with very few pdf readers.) . I am not sure whether I can put tips on non Latex pdfs.   Is there a way to have pdfcomment have images/Latex mathematical formulas (or references to formulas that can show with a mouseover) ? Or is there a way to transfer fancytooltips to a non Latex pdf ? Or are there other techniques to achieve the goal ?


I understand that if two coprime integers a and b are such that $ab=x^2$,  then a and b must also be perfect squares.   Are there any similar properties if $ab=y^3$?

I'm trying to do the following exercise from Neukirch's Algebraic Number Theory (exercise 2, $\S 1$, chapter 1):  Show that, in the ring $\mathbb{Z}[i]$, the relation $\alpha\beta=\varepsilon\gamma^n$, for $\alpha,\beta$ relatively prime numbers and $\varepsilon$ a unit, implies $\alpha=\varepsilon^{\prime}\xi^n$ and $\beta=\varepsilon^{\prime\prime}\eta^n$, with $\varepsilon^{\prime},\varepsilon^{\prime\prime}$ units.  My attempt: once $\alpha$ and $\beta$ are relatively prime, $\alpha\nmid\beta$ and $\beta\nmid\alpha$. Therefore $N(\alpha)$ and $N(\beta)$ are relatively prime too (where $N(a+ib)=a^2+b^2$). Therefore,  $$N(\alpha\beta)=N(\alpha)N(\beta)=N(\varepsilon)N(\gamma^n)=N(\gamma)^n=(p_1\cdot\ldots\cdot p_r)^n=p_1^n\cdot\ldots\cdot p_r^n$$  And once $N(\alpha)$ and $N(\beta)$ are relatively prime, we have (if necessary, we reorder the $p_i$'s):  $$N(\alpha)=p_1^n\cdot\ldots\cdot p_k^n=(p_1\cdot\ldots\cdot p_k)^n=N(\xi)^n=N(\xi^n)$$ and $$N(\beta)=p_{k+1}^n\cdot\ldots\cdot p_r^n=(p_{k+1}\cdot\ldots\cdot p_r)^n=N(\eta)^n=N(\eta^n)$$  And the result follows.  But I'm not sure about one step. It is $\alpha$ and $\beta$ relatively prime $\Rightarrow$ $N(\alpha)$ and $N(\beta)$ relatively prime. I know that if $\alpha|\beta$ then $N(\alpha)|N(\beta)$, but the previous assertion is not necesseraly true, and if it is, and don't know how to prove it. If it is true, the result follows, unless I made something wrong in the rest of the proof.  That's it. If you know another way of doing the exercise, please show me.


I have an array of bar buttons that I normally set with something like:    NSArray *leftButtonArray = [[NSArray alloc]initWithObjects: backBarButton, separator1,postBarButton, separator1, memeBarButton, separator1, pollBarButton, nil]; self.navigationItem.leftBarButtonItems = leftButtonArray;   However, I want to change these buttons on the left to instead be center aligned. Anyone know how I can do that? Providing an example or using my buttons to do so would be a plus.   Thanks!

I have three UIBarButtonItem created as below. They align left and I'd like to align center so there isn't a gap on the right side. I don't see an align property on UIToolBar. Is there another way to accomplish this?  //create some buttons UIBarButtonItem *aboutButton = [[UIBarButtonItem alloc] initWithTitle:@"About" style:UIBarButtonItemStyleBordered target:self action:@selector(showAbout:)]; [toolbar setItems:[NSArray arrayWithObjects:settingsButton,deleteButton,aboutButton,nil]]; //Add the toolbar as a subview to the navigation controller. [self.navigationController.view addSubview:toolbar];


I have read lots of paragraphs on w3schools that are telling us to avoid "new" when there is an another option. "new" Keyword is easy to use so why are they telling us to avoid it? What are the advantages of using literals?   var family = [ new Person("Bob",13), new Person("Bo0",103), new Person("hfg",163), new Person("timmy",6) ]   instead of this  var family = new Array(); family[0] = new Person("alice", 40); family[1] = new Person("bob", 42); family[2] = new Person("michelle", 8);   which one is better or wise?  English is not my native. Please correct mistakes if possible.  Thanks.

In another , a user pointed out that the new keyword was dangerous to use and proposed a solution to object creation that did not use new. I didn't believe that was true, mostly because I've used Prototype, Scriptaculous and other excellent JavaScript libraries, and everyone of them used the new keyword.  In spite of that, yesterday I was watching Douglas Crockford's talk at YUI theater and he said the exactly same thing, that he didn't use the new keyword anymore in his code ().  Is it 'bad' to use the new keyword? What are the advantages and disadvantages of using it?


I’m taking MIT ocw single variavle calculus now, and I found I need some books to help with studying. I know Stewart or Thomas calculus is famous for calculus. But I think it’s too huge. And that’s the reason why I have tried to take online lecture. So could you please recommend some calculus books to practice exercises? I want a books which are not huge like Stewart, have some challenge problems, not much focused on analysis. I read some people recommend books, but I think it’s more focused on analysis than calculus.

This question is a  of the common question asking for calculus references. It is here to  away the repetition, and give a canonical resource for calculus references.      I'm looking for a resources to learn single-variable calculus.


Installed Ubuntu 20.04.1 LTS on USB key using Rufus. This seemed to go fine. When I boot from usb key on windows 10 machine I get a black screen and hear a 3 note chime...and then nothing- just a black screen.  Any help greatly appreciated. Machine is a bit older- came with Windows 7, but I wiped and installed Windows 10.  900 GB free disk space; 4 GB RAM

This question is asked often in Ask Ubuntu, sometimes with few hints about the situation.   Please provide a list of possible reasons to help troubleshoot the problem.


There is a trademark product that is registered with all-caps (example: ). However, the all-caps formatting is usually considered bad practice, so the spelling with only title-caps (Matlab) has been used very widely.  The brand-book from the trademark owner insists on the usage of the all-caps term (; however, the brand-book is directed for :     Audience for This Guide      The brand guide is for MathWorks distributors, external creative contractors, and agencies who create MathWorks materials.   and not necessarily other users.  My questions (assuming this question has nothing to do with legal documents, where such stuff might matter):   Do I violate any common spelling practices by using a better-looking and easier typable title-caps spelling (e.g., Matlab) as opposed to the trademarked spelling? Would the answer change if we are talking about publishing in a reputable journal? (assuming the style guide of the journal omits this issue) Is there general consensus about all-caps trademarks being a bad practice?

I am writing a letter to apply for entry into a graduate-level university program through my company. I am struggling on how to write the name of the company in the letter. The company's trademark is to write the name in capital letters (and we are encouraged to do so in work communication) but this seems out of place to me in the formal letter.  Example:   "... to apply for entry to the MYCORP Leadership program beginning in..." "... to apply for entry to the Mycorp Leadership program beginning in..."   I'm currently leaning toward option #2 even though this isn't consistent with the company's preferred branding.


I know that a generating function for the Zeta function at the even integers already exists, but how about the Zeta function at the odd integers?  I've done some research, and found some alternative formulas for the harmonic numbers that allowed me to create a generating function for $\zeta(2k+1)$, but I'd like to know if it'd be new.  That would be nice if the answer is no, after all, it gets me really frustrated when I find out that all my discoveries in Math are actually just rediscoveries. And that's been the case in like 99% of the times I found something.  Just found out the answer is yes, but my formula is different anyway, less bad.

I know some nice ways to prove that $\zeta(2) = \sum_{n=1}^{\infty} \frac{1}{n^2} = \pi^2/6$.  For example, see  or the answers to the question "?"  Are there any nice ways to prove that $$\zeta(4) = \sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}?$$  I already know some proofs that give all values of $\zeta(n)$ for positive even integers $n$ (like #7 on Robin Chapman's list or Qiaochu Yuan's answer in the linked question).  I'm not so much interested in those kinds of proofs as I am those that are specifically for $\zeta(4)$.  I would be particularly interested in a proof that isn't an adaption of one that $\zeta(2) = \pi^2/6$.


If $x$ and $y$ are irrational numbers then $x$ to the power of $y$ is irrational I am asked to prove or disprove this statement. To do so I got an idea to use the contra-positive, for that I need to prove if $x$ to the power of $y$ is rational then $x$ and $y$ are rational. I took $\ln$ for both sides, because keeping some element in power would make the sum more difficult, now I have $y\ln(x) = \ln(p/q)$. How could I show that $x$ and $y$ are rational?

Can an irrational number raised to an irrational power be rational?  If it can be rational, how can one prove it?


I‘m not very versed in Gödel‘s incompleteness theorem but in a naive way: If a statement of existence is not provable, there you cannot find an example which fulfills the statement (otherwise the statement would be provable with this example). But when there is no element which fulfills the statement, doesn’t that imply that the statement ist false? I thought about that one in the context of the measure problem - because the statement $$\exists \text{ measure function } \mu: 2^{\mathbb R} \to [0,\infty] \, \forall I = [a,b] \subseteq \bar{\mathbb R}: \mu(I) = b - a$$ is neither provable nor refutable. But if I cannot prove there is a measure function, I cannot find a $\mu$ for which the statement is true. Because finding such a $\mu$ would prove the statement. But when there is no such $\mu$, the statement of existence is false, isn‘t it? Where is my mistake in thinking?

states that "...For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system".  What does it mean that a statement is true if it's not provable?  What is the difference between true and provable?


I want to copy a file via ssh when I've logged in. What scp does is that it copies the files by login, password, path. What I want is to be able to do the same thing when I'm "inside", ideally without providing the login and password:  $ ssh root@123.123.243.63 root's password:  Welcome to ..... Last login: .... root@folder1:~# // How do I download (or upload) the files when I'm here?

If I'm logged in to a system via SSH, is there a way to copy a file back to my local system without firing up another terminal or screen session and doing scp or something similar or without doing SSH from the remote system back to the local system?


So.... in brazilian regulated academic works we have a distinction between tables where the lines are separated by borders and tables that have all borders enable; I dont really know how to translate that to english, so I will just refer to one kind as SMALL TABLES and BIG TABLES; The thing is: I need to indicate the ocorrency of those kinds of tables in different list of tables; so I would need a list for the small tables and a different one to the big tables; Its there a way to create this different set of tables so that I can display this two types in different lists?

I’m writing a document in the latex and it contains some BNF grammar noations in several places of the documents. (I used verbatim package in order to write these BNF grammar notations)  Now I want to add a new section to the document that shows name of all grammar notation and their page numbers. This should be similar to “List of Figures” page.  I’m new to Latex and your help will be very helpful for me.  Thanks


Reading some articles and Silvermann's "The arithmetic of elliptic curves" I found these two different definitions for good ordinary reduction.  Silvermann, with Theorem V.3.1, says that an elliptic curve defined over a finite field with characteristic $p$ is ordinary if, for example, $E[p^r]=\mathbb{Z}/p^r\mathbb{Z}$ for every $r\in\mathbb{N}$. This implicitely says that an elliptic curve $E/K$ defined over a number field has (good) ordinary reduction at a place $v$ of $K$ if the reduction $\tilde{E}_v$ is ordinary.  From the other hand, I read in many articles that for elliptic curves $E/\mathbb{Q}$ the condition of having a (good) ordinary reduction at $p$ is equivalent to the condition \begin{equation*} p\nmid a_p:=p+1-|E(\mathbb{F}_p)|. \end{equation*}  Why is the last condition equivalent to the first?

Let's consider an elliptic curve over a finite field $\mathbb F_p$.  The trace of the Frobenius homomorphism is defined as:  $$a_p=p+1-\#E(\mathbb F_p)$$  See for example .  I read that this value is zero if and only if the elliptic curve is supersingular. Unfortunately there is no proof give. So I am looking for a proof of this. (For example a good reference).


I want to store boolean arraylist in local file and load values in onCreate(). I'm using  public void saveBoolean(String fileName, ArrayList<Boolean> list){     File file = new File(getDir("data", MODE_PRIVATE), fileName);     ObjectOutputStream outputStream = null;     try {         outputStream = new ObjectOutputStream(new FileOutputStream(file));     } catch (IOException e) {         //     }     try {         outputStream.writeObject(list);     } catch (IOException e) {         e.printStackTrace();     }     try {         outputStream.flush();     } catch (IOException e) {         //     }     try {         outputStream.close();     } catch (IOException e) {         //     } }   and  private ArrayList<Boolean> getSavedBooleanList(String fileName) {     ArrayList<Boolean> savedArrayList = new ArrayList<>();      try {         File file = new File(getDir("data", MODE_PRIVATE), fileName);         ObjectInputStream ois = new ObjectInputStream(new FileInputStream(file));         savedArrayList = (ArrayList<Boolean>) ois.readObject();         ois.close();     } catch (IOException | ClassNotFoundException e) {         e.printStackTrace();     }      return savedArrayList; }   but it invokes NullPointerExcpetion when attempt to initialize custom view listview. I'm also saving and loading string and integer lists like this, string list is loaded but integer and boolean lists are not initialized so length is 0 and my code loading value at listview position so it invokes error because length is 0 while inxed is for example 2. Is here any way to save/load integer and boolean list into file or I must convert booleans and integers into string before saving? Thanks for every reply.

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'm trying to automate a nightly backup with the following cron jobs (IPs and password redacted. of course):  [root@katexic ktxc]# crontab -l 30 3 * * * /bin/tar -czf /backup/ktxc/ktxc-`date '+%m%d%y'`.tar.gz /var/www/ktxc.to;scp -i /root/.ssh/id_rsa /backup/ktxc/ktxc-`date '+%m%d%y'`.tar.gz backup@111.22.33.44:/home/backup/backups 45 3 * * * /bin/tar -czf /backup/katexic/katexic-`date '+%m%d%y'`.tar.gz /var/www/katexic.com;scp -i /root/.ssh/id_rsa /backup/katexic/katexic-`date '+%m%d%y'`.tar.gz backup@111.22.33.44:/home/backup/backups 00 4 * * * /usr/bin/mysqldump -u ktxc_yourls -pxxxpasswordxxx ktxc_yourls | gzip > /backup/ktxc/ktxc-mysql-`date +\%m\%d\%y`.sql.gz;scp -i /root/.ssh/id_rsa /backup/ktxc/ktxc-mysql-`date '+%m%d%y'`.sql.gz backup@111.22.33.44:/home/backup/backups   These work fine from the command line, but not when the cron daemon tries to run them. In the /var/log/cron I see messages like:  Jun 10 03:30:01 katexic CROND[7437]: (root) CMD (/bin/tar -czf /backup/ktxc/ktxc-`date '+) Jun 10 03:45:01 katexic CROND[7445]: (root) CMD (/bin/tar -czf /backup/katexic/katexic-`date '+)   I assume that there's some problem with the + sign in my commands? How do I fix these so they run properly as cron jobs?  This isn't solved by the troubleshooting in  because that doesn't, afaict, cover special characters and the like and the error in the log is the same as cron sends to my email.

This is a  about using cron & crontab.   You have been directed here because the community is fairly sure that the answer to your question can be found below. If your question is not answered below then the answers will help you gather information that will help the community help you. This information should be edited into your original question.  The answer for 'Why is my crontab not working, and how can I troubleshoot it?' can be seen below.  This addresses the cron system with the crontab highlighted.


If I look under Settings >> Keyboard >> Shortcuts, I don't see anything related to Control-C, -X or -V.  Where are they defined?  And how?  Suppose I want to change their actions to some other shortcut key, how would I do it?    With help in the comments, I am able to define a hotkey to do the paste action using xdotool: xdotool key --clearmodifiers ctrl+shift+v.    In addition, I would like to add a script: xdotool key --clearmodifiers ctrl+shift+v && some_script.  That fails, but with further help from the comments, I'm finding that /bin/bash -c "xdotool key --clearmodifiers ctrl+shift+v && some_script" does work!

I'm trying to simulate a media key press using a custom shortcut.  So far, I've been able to achieve the simulation I need using the command:  xdotool key XF86AudioPlay   It works perfectly, it pauses or starts the music player every time it is run.  The problem comes when trying to run it as a shortcut.  First I tried to run an alias with a custom shortcut, but it did not work.  As explained on :     The commands run by keyboard bindings are not parsed via a shell. Your best bet is to create a directory bin in your homedir.   Next I created the suggested script and named it simplay:  #!/bin/sh xdotool key XF86AudioPlay   It is located inside a bin folder which is part of the PATH, this works fine and can be run from any location.  When trying to create the Custom Shortcut, I was unable to get it to execute, the configuration is the following:  Name: test Command: simplay  Shortcut: Ctrl+Alt+R   After searching a bit more I found another way to execute the shortcut:  gnome-terminal -e simplay   I tried it on a terminal and noticed that when executing it it would rapidly open a new terminal window, execute the child process, pausing the music and immediately close the window.  I changed the command on the shortcut and when hitting it I noticed the same behavior opening a terminal and immediately being closed but this time the child process did not pause the music, which makes me think that the script has been called on all my previous attempts but it is somehow not being able to execute.  How can I solve this problem according to your knowledge?


Is there any short enhanced form of for loop which we can use for primitives. I have do the legacy code for looping on to primitives, like this  for(int i=0; i<10; i++){ }   Although for objects, we have ehanced for loop like  for(MyObject m : myObjectList){ }   Is there any similar option for primitives also?

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


As in question, how can we assign an icon here?    Regards

As from the screenshot below, there is a duplicate icon of the xfig program. Sometimes with different programs same thing happens.    Any ideas how to solve this?


I've got two I2C Slave ATTiny85 chips both running at 16MHz with external crystals. Can they both share a single crystal with the 22pf caps? Is there anything wrong with this?   I don't have any free pins on the ATTinys to route a clock signal out of one ATTiny into another.   If there's some type of external clock circuit, how is that constructed and connected/shared with both ATTinys.         – Schematic created using

How do I share a single crystal (not a complete oscillator module) between two micros? Is it OK to just connect everything as normal for the first micro and also directly connect its XO to the XI of the second microcontroller? I expect to place the micros very close together on the board.


I am trying two ways to implement this situaiton: when a test-button is clicked, a text Hello World is displayed at <p> element test-text Method 1 function showText(test_button_id) {     let test_text = document.getElementById("test-text")     test_text.innerText = "Hello World";  }  let test_button = document.getElementById("test-button") test_button.addEventListener('click', showText('test-button'))  Method 2 let test_button = document.getElementById("test-button") let test_text = document.getElementById("test-text")  test_button.addEventListener('click', () => {         test_text.innerText = "Hello World"; })  Method 2 works. Method 1 does not. What is wrong with the way I am calling the function in addEventListener? I know the argument test_button_id is not doing anything in this code. I intend to parse it in if the code works. Thanks.

The situation is somewhat like-  var someVar = some_other_function(); someObj.addEventListener("click", function(){     some_function(someVar); }, false);   The problem is that the value of someVar is not visible inside the listener function of the addEventListener, where it is probably being treated as a new variable.


My OS is 10.6.8.  Yosemite is no longer available in US.  But Sierra needs 10.7 to download. Help! I'm stuck in a loop!  And cannot install my new printer until this is resolved. :/

I want to update from Mac OS X 10.6.8 to the newest version which is macOS Sierra. My Mac should be able to run this version of macOS. If I try to download the update on the App Store it fails because I need Mac OS X 10.7 at least.  What can I do to upgrade my Mac?


I’m trying to track when United Airlines flight UA4944 from Newark (EWR) departed and landed at Albany Airport (ALB) on 26 Nov 2018.  Could anyone help me with the flight information?

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


I was comparing the statement of the  on Wikipedia to an  I found geared towards laymen. The propositions differ slightly, but they would be equivalent if the following were true:     If $a$ and $b$ are coprime, and $a + b = c$, is $c$ coprime to both $a$ and $b$?   By , if (without loss of generality) $a > b$, then $a$ and $c$ must be coprime: the first iteration of the algorithm subtracts $c = 1*a + b$, and then you're left with $a$ and $b$, which are coprime by proposition and so generate 1 as the final result.   If $b$ is prime, I can imagine a proof by contradiction via the .   For more complicated $b$ I am not sure it holds.

Let $a$ and $b$ be two integers such that $\left(a,b\right) = 1$. Prove that $\left(a+b, ab\right) = 1$.   $(a,b)=1$ means $a$ and $b$ have no prime factors in common  $ab$ is simply the product of factors of $a$ and factors of $b$.  Let's say $k\mid a+b$ where $k$ is some factor of $a$.  Then $ka=a+b$ and $ka-a=b$ and $a(k-l)=b$.  So $a(k-l)=b, \  a\mid a(k-1)$ [$a$ divides the left hand side] therefore $a\mid b$ [the right hand side].  But $(a,b)=1$ so $a$ cannot divide $b$.  We have a similar argument for $b$.  So $a+b$ is not divisible by any factors of $ab$.  Therefore, $(a+b, ab)=1$.  Would this be correct? Am I missing anything?


I am building a map based of a simulation world and I am trying to build an OP sword for myself as a test runner. I have part of the command, I just need help sticking the {Unbreakable:1} into the command  Current command:   /Give Hydrotronics diamond_sword 1 0 {display:{Name"Valkyrie's Lance",Lore:[The Ragnite Hums As The Lance Rests In Your Hands]},ench:[{Id:16,Lvl:200},{Id:19,Lvl:3},{Id:20,Lvl:13},{Id:20,Lvl:13},{Id:17,Lvl:30},{Id:34,Lvl:10}]}   I tried removing Id:34 (Unbreaking) and replacing it with {Unbreakble:1} but the Unbreakable didn't come through.

I have two commands I'd like to combine into one, but I'm not sure how to go about combining them. Is this possible?   Here are the commands. They work individually, I just can't seem to get them to work together:  /give @p jukebox 1 0 {CanPlaceOn:["minecraft:melon_block"]}     /give @p jukebox 1 0 {display:{Name:"Box"}}   Can you help me to add one of the commands to the other one?


What is the difference between cp fileA fileB and cp -- fileA fileB in Linux?

I have seen -- used in the compgen command.  For example:  compgen -W "foo bar baz" -- b   What is the meaning of the -- in there?


I have a time series going from 2013 until late 2016. I am using the auto.arima function in R to forecast the next 12 months. I get the following where the black line are my observations and the blue line is my prediction.  fcast <- forecast(auto.arima(a.ts)) plot(forecast(fcast, h = 12))      However when I use this custom arima function I get a much better result  fit <- arima(a.ts,seasonal=list(order=c(0,1,0),period=12)) plot(forecast(fcast, h = 12))     Why is the auto.arima function not producing a result that doesn't seem anywhere near as good. I know they are using different parameters but I would have thought that auto.arima would have found the best parameters and forecasted using those?

I am surprised how often the auto.arima function from the "forecast" package in R returns straight linear forecasts when there appears to be fairly strong seasonality in the historic data.  I've attached an example:      tpits=ts(TPI,start=c(1986,1),end=c(2020,1),frequency=1)     fit=auto.arima(tpits)   The data is annual and varies significantly but the forecast is completely linear.  What am I doing wrong?


Hi I am a bit of a science noob but anyway I'm writing a little Sci-fi story and I just want to know if there is a substantial difference in perceived time passed at point A and point B if Point A is on the tip of our galaxies outer edge and point B is say two thirds of the radius in (from the outer edge of the galaxy)?  Just because I was going to have two alien factions fighting over outer territories for research purposes (There home worlds are closer to the center of the galaxy so if they conduct research out there on weapons and stuff they can get a leg up on the competition because they have more time to do research, IDK if I'm explaining it well but I think you'll get what I'm Saying).

I understand that time is relative for all but as I understand it, time flows at a slower rate for objects that are either moving faster or objects that are near larger masses than for those that are slower or further from mass.  So, the illustrative example I always see is that if I were to leave earth and fly around at near light speed for a while or go into orbit around a black hole the time I experience would be substantially shorter than for those I left behind at home on earth and I'd come back to find that I've only aged however long I felt I was gone by my own clock but that on Earth substantially more time would have elapsed.  Following through on this model, the stars in orbit around the black hole at the center of the Milky Way are aging much much slower (relative to us), right?  So does it not follow that the center of the galaxy is some appreciable (I have no idea how to go about putting this in an equation so will avoid guessing at the difference) amount "younger" than the stuff further away from the center?   If this is not true, could someone please explain why not, and if it is true, can someone please point me to where I can calculate the age of the center of the galaxy :-)  And to be clear... what I'm asking is... if there was an atomic clock that appeared at the center of the galaxy when the center was first formed, and we brought it through a worm hole to earth today - how much time would have elapsed on that clock vs. the age we recon the galaxy currently is? (13.2 billion years)