uniform convergence of $f_n(x)=\left(\cos\frac{x}{\sqrt{n}}\right)^n$

Let a sequence of functions $(f_n)_{n\in \mathbb{N}^*}$ such that  $f_n(x)=\left(\cos\dfrac{x}{\sqrt{n}}\right)^n$ defined on $\mathbb{R}$         Show the pointwise convergence on $\mathbb{R}$   Show that the sequence converges uniformly on $[-A,A]$ with $A>0$        Pointwise convergence  I fund that $f_n(x)\longrightarrow e^{-x^2/2}$  Uniform convergence  I must show that $||f_n(x)-e^{-x^2/2}||_{\infty}\underset{n\to +\infty}{\longrightarrow }0$  My first idea  (*to be honest I've got no overview) is to write :  $\bigg|f_n(x)-e^{-x^2/2}\bigg|$, and I tried to find a bound.  As $1-\dfrac{u^2}{2}\le\cos u\le 1-\dfrac{u^2}{2}+\dfrac{u^4}{24}\iff 1-\dfrac{x^2}{2n}\le \cos\dfrac{x}{\sqrt{n}}\le 1-\dfrac{x^2}{2n}+\dfrac{x^4}{24n^2}$  Let $g_1(x)=1-\dfrac{x^2}{2n}$ and $g_2(x)=1-\dfrac{x^2}{2n}+\dfrac{x^4}{24n^2}$ and $M_1, M_2$ such that :  For $M_1$ that is but for $M_2$ I can find a finite bound  $$|g_1(x)|<M_1\quad \text{and}\quad |g_2(x)|<M_2$$   I repeat again I haven't got any overview about how to attack this problem


Rationale for commonly occurring DC voltage magnitudes in electronics

Is there some rationale behind the frequently occurring voltage magnitudes in circuitry and sensors, such as 3.3V, 5V, 12V, etc.


Let $A$ be an infinite set and B a countable set, show that $\vert A \cup B \vert = \vert A \vert$

Can someone please verify if my proof is correct, and add to it if it isn't?  Since we're given that $B$ is countable, we know $B$ is either finite or has the same cardinality as, say, the set $\mathbb{Q}$. So $\vert B \vert = \aleph_0$.  Similarly, if $A$ is infinite,  then we know the result $\aleph_0 \leq \vert A \vert$.  This implies that $ \vert B \vert \leq \vert A \vert$.  Then $\vert A \cup B \vert = \vert A \vert$.  Am I missing something here?


Why does == work on integers but not on strings?

I know this: When you use == to compare two objects it will compare the two instances of the object and check if they are the equal.  When you use .equals() it will compare the states of the 2 objects.   Let's say this is my code:  String string1 = new String("abc"); String string2 = new String("abc"); Integer integer1 = new Integer(5); Integer integer2 = new Integer(5); int int1 = new Integer(6); int int2 = new Integer(6);  if (string1 == string2)     System.out.println("The strings are equal"); if (integer1 == integer2)     System.out.println("The integers are equal"); if (int1 == int2)     System.out.println("The ints are equal");   Why will this code only print "The ints are equal"?


Well, for some reason that I will try to find out later, my TeX Live under Linux doesn't work anymore and I had to go through windows emulated system.  The file I work with include a \graphicspath command, but it seems that the "\" specific to windows path makes problem. The only I had to solve the error messages was to put all files in the same directory without spaces in the path.  Does anyone had experienced such kind of problems and solved it?  Thanks for help


I have seen in C++ program, during function declaration if there is no parameter for the function void is declared as parameter like this:  int F1(void)   How is it different than:   int F1()


How to enable switching between windows of chrome with CMD + ` on Big Sur?

I read in a lot of questions about this topic that cmd + `  should switch the windows, but it simply does not switch the windows, is there some other shortcut in Chrome that prevents this one from working?


This was posted in another question and below is the link.      Prove Theorem 2.5(iii), namely, that if $f$   is continuous at $a$ and $λ$ is a scalar, then $λ⋅f$ is continuous at $a$ i.e. $$0<|x−a|<δ⇒|λf(x)−λf(a)|<\varepsilon$$    Here $|λf(x)−λf(a)|<\varepsilon$ is not equivalent to $|λf(x)−λf(a)|<\frac{\varepsilon}{λ}$ but rather to $|λf(x)−λf(a)|<\frac{\varepsilon}{|λ|}$  My question is regarding the last inequality, shouldn't this be $|λf(x)−λf(a)|<\varepsilon$ instead?


XORing consecutive integers has an interesting property. Does anyone know why?

I hesitated to post on StackOverflow but I think the problem has little to do with programming and more to do with mathematics. So, here it is:  I wanted to compute the function $ f(n) = 0 \oplus 1 \oplus 2 \oplus \dotsb \oplus n$ in O(1) instead of O(n) so I computed $f(1), f(2),...$ to see the global look of the function and it appears that it has an easily identifiable pattern, which can be used to transform $f$ like so:  $$  f(n) = \left\{  \begin{array}{ll}   n  & \mbox{if } n \equiv 0 \pmod 4 \\                 1  & \mbox{if } n \equiv 1 \pmod 4 \\                 n+1  & \mbox{if } n \equiv 2 \pmod 4 \\                 0 & \mbox{if } n \equiv 3 \pmod 4 \\  \end{array} \right. $$   Does anyone know why the function has such pattern ?


Take an account without the "Critic" badge, upvote a question, immediately downvote it, then immediately cancel the downvote, and you get the critic badge.


Converting a method argument into an enum

I have an enum type defined like so:  public enum Status {     Active=1,     InActive=0 }   in my method can I cast the parameter into the enum like this:  public string doSomething(string param1, int status) { //will this work?       Account.Status = (Status) status; //or do i need to test one by one like this if(status == 0) {  Account.Status = Status.Inactive;  //and so on... } // end if }  // end doSomething


Is it possible to switch back to windows?

I have an hp 11-h110nr x2 and it originally ran on windows but I switched to Ubuntu and would like to switch back. How do I do this?


Detect an internet connection activation with Delphi

I've been using a 3G wireless card for a while and every time I connect, my anti-virus fires up the updates.  I'm wondering what is the Win32 API set of functions that I can use to, either, get notified or query about the event of an Internet Connection coming up?  And is there already a set of ported headers for Delphi?


Which of these sentences is correct?     The accent with which I speak   The accent which I speak with   Are they not the same?  While we are on the topic, I would greatly appreciate if you would tell me which one of the following sentences is correct and if the wrong one is not said at all.        They are a very proud people   They are very proud people    Cancer cells help invade   Cancer cells help to invade   Oxygen has a higher electronegativity   Oxygen has higher electronegativity


Element of order $l$ in $(\mathbb Z/p\mathbb Z)^\times$ where $p,l$ are primes.

Show that there exists, for $p,l$ primes, an element of order $l$ in $(\mathbb Z/p\mathbb Z)^\times$ iff $p-1$ is a multiple of $l$.  Firstly, if an element $a$ of order $l$ exists, since $a^{p-1}=1$, we have $l\mid p-1$. However I struggle with the other implication.


csquotes conflicts with quotation marks in Lua code

I received an  for my  package. Certain commands in my package fail when the following code is compiled with LuaLaTeX (XeLaTeX works fine):  \documentclass{article} \usepackage{fontspec, csquotes, lilyglyphs} \MakeOuterQuote{"} \EnableQuotes  \begin{document} \wholeNote \end{document}   Upon investigation I found that there are some quotation marks in the package code, and I assume this is the culprit:  \ifluatex \def\lilyGetGlyph#1{\directlua{documentdata.fontchar "#1"}} \fi   (For context: this can be found here: )  So I assume that the quotation marks in the \directlua command are expanded to "smart quotes" before the Lua code can be executed.   Is this assumption right? Is there anything I can do about it? Or do I have to accept and document the incompatibility?


chemformula: No auto-completion in TeXstudio?

I have trouble getting auto-completion to work with chemformula in TeXstudio. I have other packages working just fine.   The .cwl-file is showing up in "Options > Configure TeXstudio > Completion", and I have it ticked. However, it doesn't work when typing.  I have contacted Clemens Niederberger (who maintains the package), however he recommended I ask here instead.  It is mainly the \ch command I would like to have auto-complete, but all commands would be ideal.  N.B. I'm running TeXStudio 2.9.4 TeXLive 2015 (both newest, at the time of writing)


Remove space after figure and before text

I have a figure in my paper (I am using IEEEtran package). After this figure there exists a space between the figure and the text. How can I reduce the size of this white space. To be specific the space is between the caption of the figure and the text of my paper. Any suggestions?


Asking about position of an element in an order

Suppose we have a sequence of elements, for example of fruits on a shelf. Let's say I want to ask about the position of the apple in the sequence. The answer, of course, is an (ordinal) number. But what is the question I should use?  I construct tables with data and often there's a name of an element in one column and in the other column there's the ordinal number of the element. The column has got its name. Its name should be short and clear. A short question which the value (the ordinal number) responds to would be a proper name.  I have an impression that the name "Which" sounds bad because "which?" is a question one would ask if there was a small set of possible answers (for example "red, blue, green" or "first, second, third"). Here the ordinal number might be much bigger. "WhichOne" sounds like the better version of "Which", but still having the same problem. "WhichNumber" sounds extremely childish and in fact the answer to the question "Which number?" should be a (regular) number, not an ordinal number. "WhichInTheOrder" doesn't sound bad to me but I'm not sure if a native speaker would ask a question like "Which in the order is the apple?".  What would be the correct and specific question to ask in order to receive an answer like "The apple is 10th".?


Weird characters appearing in the console

I was using a Linux console and suddenly the format of the letters changed:    I probably pressed on the wrong keys. Any idea how to fix this?


How do I center text horizontally and vertically in a TextView?

How do I center the text horizontally and vertically in a TextView, so that it appears exactly in the middle of the TextView in Android?


I want to learn about compiling a kernel from scratch. How can I download the latest stable Linux kernel from , compile it, and install it in a VMware virtual machine? This is just for educational purposes.


The chain stay angle is the angle between chain stay and seat tube?

I need a new front derailleur for my Shimano Acera T3000 gear shift. I have to choose between:     They differ only in the chain stay angle they are made for. The info I find on what the "chain stay angle" is seems partly contradictory or unclear. So I want to make sure I got this: The chain stay angle is the angle between chain stay and seat tube - is that correct? Or more precise the angle between AB and AC with:  A: bottom bracket axis B: axis of rear wheel C: "middle point" at the top of the seat tube   Here's  with measured angles:  of the angles in question only the one between seat tube and chain stay (68°) falls into the interval [63,69] ... so, it has to be that one, I suppose. From my mechanical, geometrical intuition I don't see why that angle is relevant for the FD. It should be ∠(KK',KC) in my opinion!?


If $S$ is noetherian then $A^{-1}S$ is also noetherian for $A$ a multiplicative closed set

Is it true that if $S$ is noetherian then $A^{-1}S$ is also noetherian for $A$ a multiplicative closed set? A multiplicatively closed set implies closure under multiplication and inclusion of multiplicative identity. In addition the ascending chain condition of noetherian ring says that we have a sequence of ideals $\ldots -I_n\subseteq I_{n-1}\subseteq\ldots-I_2\subseteq I_1\subseteq S$ such that $I_n=I_{n=1}$ for some $n$. Then, does it imply that for the ring $A^{-1}S$, we multiply all the ideals by $A^{-1}$ to get an ascending chain condition? Will this do to prove that $A^{-1}S$ is noetherian? Or are there quick counterexamples?  Any hints? Thanks befrehand.


I want to know how to prove this:  $$ \sum_{k=1}^\infty \arctan\left( \frac{x}{k^2+a} \right)  = \pi \left\lfloor \frac{b}{\sqrt{2}} \right\rfloor     + \arctan\left( \frac{x}{b^2} \right)     - \arctan\left[ \tanh\left( \frac{\pi}{\sqrt{2}} \frac{x}{b} \right)                     \cot\left( \frac{\pi}{\sqrt{2}} b \right) \right] $$  for $0 \le a, b = \sqrt{\sqrt{x^2 + a^2} - a}$.  At least in the special case $x=1$,$a=0$  Thank you ..


Covering map between orientable compact connected surfaces without boundary with genus $g$

Similar to a previous question I asked, this is the other question that I couldn't answer in an exam I gave for my Topology course:  Suppose $g_1,g_2$ are non-negative integers such that $2-2g_2$ divideds $2-2g_1$. I have to construct a covering map $S_{g_1} \rightarrow S_{g_2}$, where $S_g$ is denotes an orientable compact connected surface without boundary with genus $g$.  Now, I attempted to try this problem for surfaces with smaller genera, for example a 2-torus and a 2-sphere. Clearly $2-2g$ is the Euler Characteristic of the said surface, and by classification of surfaces we have to only consider connected sum of 2-tori. So, I have $\chi(S^2)=2$, and $\chi(T^2) = 0$, here we have $2$ dividing $0$, hence I have to construct a covering map from $T^2 \rightarrow S^2$, and I have no idea how to move forward.  Addendum: I have to got great answers to my question here but I had a doubt when it comes to the points being mapped, specifically in Giulio Bresciani's answer. Clearly the handles of the figure is mapped to the handles in the figure above, but I'm unable to understand the mapping of the twist of the cover (above figure) to the extreme handles of the base (the figure below). Any help?


Interstellar Movie: Black hole shown in the movie

In the interstellar movie, the black hole shown has a ring of light orbiting around it. From what I know, (correct me if I'm wrong) that light is unable to escape the gravity of the blackhole and therefore is orbiting the blackhole. If it is unable to escape, why can we see that light?


Looking for title/author of SF novel about malevolent creatures/gods residing inside stars

One of whom destroys the Earth, perhaps accidentally, while fighting another... the plot also involves a human colony ship or planet that loses contact with the Earth; I think a small boy is also involved with the plot, although it's been 20-30 years since I read this story.  Any help would be appreciated!  It's driving my brother and me a bit batty.  Here's the batty brother's take: the main being has created others who are now at war, exploding stars. To escape, the main being accelerates the star of the human colony as a decoy. However, most of the story centers on some guy who winds up living forever, as they keep sticking him in cryogenic sleep and reawakening him. If memory serves me right, they abandon the colony planet for a while and move to asteroids as the star is weakening because it is using it's energy to accelerate. When it decelerates, it is the only star left in the universe. The one "being" was almost reduced to living off the energy of a black hole when it appears, and he sees it and sets off to go there, with a cryptic ending that the humans very well might fight him off.


How to change phone number in Google account?

I gave Google my phone number to verify it, not knowing that it would change it, and now my phone number is completely different? What have I done, and how do I unverify it and change my phone number back?


Proving that the groups $S_3$ and $D_6$ are isomorphic

In particular, $S_3$ is the group of permutations of $\{1,2,3\}$, and $D_6$ is the dihedral group of symmetries of the triangle (written as $D_{2\cdot 3}$). In generator-relation form, $D_6 = \left< r,s \mid r^3 = s^2 = e, rs = sr^{-1} \right>$.  I can intuitively see very easily that the two groups are isomorphic; the symmetries of a triangle can be viewed as orderings of the vertices (1,2,3).  However, proving this rigorously, I need some help.  Is the following proof correct?  Let $f : D_6 \to S_3$ be a homomorphism. Define $f(r) = (123)$ and $f(s) = (12)$. Then $$f(r)f(s) = (123)(12) = (13) = f(rs)$$  and we need this to equal $$f(sr^{-1}) = f(s)f(r)^{-1} = (12)(132) = (13)$$   which is indeed true. Since the order of $f(r)$ is $3$, and the order of $f(s)$ is $2$, and $f(r)$ / $f(s)$ cannot be produced using each other, the group $X = \left< f(r), f(s) \mid f(r)^3 = f(s)^2 = e, f(s)f(r)^{-1} \right>$ is isomorphic to $D_6$. But $X$ contains $6$ elements and so does $S_3$, so by closure in $S_3$, we must have $X = S_3$.     Are there any general tips for proving isomorphism? Is it a good idea to look at generators and relations between generators, and try to find a correspondence?  Thank you!


I have a summation series of the form: $n + n/2 + n/4 + n/8 + n/16 +\ldots  + 1$. Is there a formula for this series? Basically, the denominators are powers of 2.


How to find an equation of a plane when 2 lines lying on the plane are given ? Q)Find the equation of plane which contains the lines    $$(x-4)/1 = (y-3)/-4 = (z-2)/5$$ and  $$(x-3)/-2 = (y+3)/8 = (z+2)/-10$$


Do I have to take mana from my deck or hand when tapping a dual land?

I have a land card, for example  which reads "{T}: Add {R} or {W}." Do I take the mana from my library or my hand?


How do zoom, magnification, and focal length relate?

Zoom lenses and cameras with superzooms are often sold with a times ("×") zoom number — like a 12x zoom or 30x zoom. The question  explains how this relates to focal length numbers, like 70-200mm or 18-55mm. But how does ×-zoom relate to magnification, when used for macro or just to make something far away look bigger?  How can two 70-200mm lenses have different magnification?


How to disable Dark Mode in Google Chrome on macOS Mojave?

I have configured my installation of macOS Mojave to Dark Mode, because I prefer it over the Light Mode for some reasons.  The thing is that with the recent update, Google Chrome also automatically adopts the Dark Mode. I can't even see sometimes in which tab I'm in since it does not let me see clearly.    I have researched and found official Google Chrome Themes , but they seem to apply above the default Dark theme, which is not looking well.  If I disable Dark Mode in systemwide, I can see Google Chrome in Light Mode as usual, but I would love to see Google Chrome in Light Mode while using macOS Mojave in Dark Mode.  Is there a way to configure the desired behaviour.


Grub rescue no such device, also cannot access BIOS

I purchased an Acer Aspire M5-481PT-6688 which came preloaded with Windows 8. I wiped that, reinstalled my own bloatware-free copy, and tried to dual boot Ubuntu 13.04 on it. It has a hybrid drive, so when I installed it running alongside Windows, Ubuntu was installed to the SSD and Windows is on the HHD. I later removed Ubuntu via formatting the SSD and now I'm stuck at the grub rescue> prompt. The error says: no such device. No matter what key combo I press (F2, F8, F10, F12, Esc, Del) I cannot access my BIOS nor can I boot from the CD/DVD drive or USB.


Errors while installing Android Studio packages using PPA

I'm trying to install the Android Studio packages using a PPA with these commands:  sudo add-apt-repository ppa:paolorotolo/android-studio sudo apt-get update   But I keep getting these errors:  W: The repository 'http://ppa.launchpad.net/paolorotolo/android-studio/ubuntu zesty Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. E: Failed to fetch http://ppa.launchpad.net/paolorotolo/android-studio/ubuntu/dists/zesty/main/binary-amd64/Packages  404  Not Found<br> E: Some index files failed to download. They have been ignored, or old ones used instead.   As a result, the Android Studio isn't working either. How can I solve this problem?


Differences in meanings between 'in to' and 'into'

What is the difference in meaning between 'into' and 'in to'?   Is there a difference in meaning or with usage?    I was unable to find anything on other websites.


How does Mrs. Norris communicate with Mr. Filch?

I was petting my cat when I started musing, how does Mrs. Norris communicate/talk with Mr. Filch, the Caretaker at Hogwarts? Throughout the books it is mentioned that Mrs. Norris helps Filch to patrol the corridors. She acts as a lookout/spy/assistant to Filch, whereby she is often walking the corridors at night looking for law-breakers, and runs off to Mr. Filch to complain whenever she notices anything. She also polices the owls as well, apparently.  Well, is Mrs. Norris a magical cat? Mr. Filch is a Squib, so he does not have particular magical powers, but he still can see ghosts, dementors and thestrals, so does he have some special provisions to understand 'cat talk' or has an ability to talk with cats? 'Catsletoungue'? Would love to know!   Thanks.  Add: Ok even if Mrs. Norris could somehow meow to Mr. Filch to follow him to a particular place, which is understandable, how does Mr. Filch instruct Mrs. Norris where to go on, which corridor to patrol, which door to watch, etc., every single night?  For example.  "Sniff around, my sweet, they may be lurking in a corner."  Filch speaking to Mrs. Norris. (Sorcerer's Stone - Page 157)


As I understand, in JavaScript every object has a prototype and it exposes some default properties. I have the following code where I'm trying to set the Year property of two objects through prototype. But both the calls are failing.  How can I override toLocalString() for any object if I don't have access to the prototype? Please note that the following code is to test on the prototype property, but my intention is to override the toLocalString() method.  var car = {     Make: 'Nissan',     Model: 'Altima' };  car.Year = 2014; alert(car.Year);  alert(car.prototype); // returns undefined  car.prototype.Year = 2014; // Javascript error  // --------------  function Car() {     this.Make = 'NISSAN';     this.Model = 'Atlanta'; }  var v = new Car(); v.prototype.Year = 2014; // JavaScript error alert(v.prototype);


I know similar questions have been asked, but I couldn't find a solution because I'm not looking for a command to give new rights to the directory, I would like to understand it.  I'm very new to Ubuntu, have installed the server and Apache2 (not LAMP, or at least not aware of it).  I access the server by SFTP. I would like to move my existing website to the /var/www directory, but of course by default I don't have permission to copy files and folders.  I'm not looking for a code, but can somebody explain to a beginner: What is the way to go in such a case? I have trouble to believe that the first thing I have to do is to lower the permissions.  Thanks


I just discovered that chromium will only be released as a snap package.  How can I continue to get chromium, without snap? Is this possible without building from source?  Notes:   Please let's keep to the question as stated - not "what do you have against snap?" I'm not asking how to remove snap (I realize that would break Ubuntu)... just how to use chromium as it is now, a deb.     Update  No, this is not a duplicate of that linked question. I don't need to know "why it's a snap". I want to know how to use it without snap.  Right now there is building from source, and some random PPA mentioned below. I hope someone can advise us of trustworthy alternatives.


Self promotion answers that actually answer the question: Are they spam?

I saw this answer:    where the poster is trying to solicit a user for his product.   His answer though, is on topic and appropriate.     Is this spam?   I'm inclined to think not.  Should we remove/edit user contact info and just leave the product link?  Maybe?  Should we do nothing? ???  I saw related question:  but this is different because I believe this poster is trying to sell something.


Do I need to reboot my HTC Desire periodically?

I've had my HTC Desire for a couple of months now and it is awesome! (A huge improvement to my previous phone... Nokia 3315)  Though recently, I've realised that the phone semi-freezes more and more often - ie. when swiping between homescreens it will either pause/freeze and I will have to re-swipe to get it to change screens. Or worse, it just won't respond to any further swipes and I have to lock the screen then unlock to get the phone back into action.  Got quite annoyed at this (was probably happening once or twice a day) so I thought it might help to turn it off and on again. So I did - not sure if it was a placebo effect but it seems to have helped a bit?  So given that this is my first smartphone, I was wondering if it is 'normal' to need to restart the phone every so often. If so, how often is 'normal'? If not, what can I do to diagnose/fix this problem?


I will be apply for a short term study visa but my fathers bank statement which I will be using doesn’t show any activity in the past 6 months other than a deposit of 3,000 USD which he got out of an investment. The balance is 21,000 . Is it fine if the bank account isn’t very active ?


jQuery selector only works with elements generated on load in Laravel blade

In my blade view, I have rows of fields for each value in backend and at the end an empty text field. @php $x = 1; @endphp @foreach ($base_urls as $base_url)

{{ $x }}
         <input type="text" class="form-control" placeholder="Insert url or leave empty to delete" aria-label="Edit or remove url" name="base_url_{{ $base_url->ID }}" value="{{ $base_url->url }}" />
     @php $x++; @endphp @endforeach

{{ $x }}
     <input type="text" class="form-control" placeholder="Add url" aria-label="Insert url" name="base_url_" />
  When the user inputs something to the last empty field, I want another empty field to be generated, and so on. So I made a JS script called admin_panel.js that looks like this $('#base_urls_body form div.input-group:last-of-type input').change(function(e){     last_input_group = $('#base_urls_body form div.input-group:last-of-type');      if( $(e.target).val() != '' ){         last_input_group.after('

'+field_count+'
<input type="text" class="form-control" placeholder="Add url" aria-label="Insert url" name="base_url_" />
');     }  });   The field is being generated correctly, but the selector form div.input-group:last-of-type input is only detecting the input that was generated on page load, not the one generated with javascript  This is how I include my JS file in Laravel blade view. Its pushed to a stack in app.blade.php, the stack is called at the bottom of the body close tag. @push('admin_panel')      @endpush  Maybe since admin_panel.js is loaded after everything else it doesn't detect new changes? If I remove defer attr from the script tag, I can't use jQuery in my .js file. How can I fix this?


Why does my java program skip a if statement?

im only 15 and new to java so i am trying to build a simple calculator, but i cant seem to figure out why this if statement is being ignored. I have check to be sure that all values are being stored and yes they are so i can not see any other problems which would explain this. Any help would be great! Look for the comment in the second class //This if statement  The first class  public class CalculatorOperations {      double fnum, snum,answer;     String operation;      void plus(){          operation="+";         answer = fnum + snum;     }      void subtract(){          operation="-";         answer = fnum - snum;     }      void multiple(){          operation="*";         answer = fnum * snum;     }      void divide(){          operation="/";         answer = fnum / snum;     }      void invalidOperation(){          System.out.println("Invalid operation.");     }      void showAttributes(){         System.out.println(fnum);         System.out.println(snum);         System.out.println(operation);     } }   The second class      import java.util.Scanner;  public class calculatorApplication {      public static void main(String [] args){          CalculatorOperations Operators = new CalculatorOperations();         Scanner userInput = new Scanner(System.in);          String loop2 = null;         boolean loop;           while (loop = true){              // Getting input and storing it                 System.out.print("Please enter first number: ");                 Operators.fnum = userInput.nextDouble();                  System.out.println("TEST:"+Operators.fnum);                  System.out.print("Please enter second number: ");                 Operators.snum = userInput.nextDouble();                  System.out.println("TEST:"+Operators.snum);                  System.out.print("Please enter operation (+, -, * or /): ");                 Operators.operation = userInput.next();                  System.out.println("TEST:"+Operators.operation);                  // this if statement                  if (Operators.operation == "+") {                     Operators.plus();                  } else if (Operators.operation == "-") {                     Operators.subtract();                  } else if (Operators.operation == "*") {                     Operators.multiple();                  } else if (Operators.operation == "/") {                     Operators.divide();                  } else {                      Operators.invalidOperation();                 }                    System.out.println("Answer: " +Operators.answer);                  System.out.print("Would you like to do another sum? (yes or no): ");                 loop2 = userInput.next();            }           if (loop2.equals("yes") || loop2.equals("Yes")){              loop = true;                 System.out.println();                 System.out.println();             }else{                 loop = false;                   // Closes scanner to prevent resource leaks                  userInput.close();                 System.exit(0);             }                   }      }


What is the advantage of joining teams for competitive fighting tournaments?

I was just watching some footage from last year's EVO... and something is bothering me.  Why do some players affiliate with gaming 'teams' such as Complexity or Evil Geniuses?  I understand that in the Counter Strike or League of Legends scene, where there is a teamwork aspect to the game itself - those are the people that you play with, you work as a team, know each other's strengths and weaknesses etc.   However, in the hand-to-hand fighting games such as Marvel vs Capcom, the actual fighting is always 1v1, you don't have 'teammates' per se. In fact you probably spend more time fighting your teammates then you do rooting for them!  So what are the advantages of being part of a competitive team for fighting games?


I'm simulating a cloth. How can I bake the cloth simulation into keyframed vertices or shape keyed vertices?


Custom fields not useable in Approve/Reject Approval Request

I'm trying to get through my first SalesForce mod and it's definitely been a rocky path. I have one task I'm trying to do, but this section is holding me back.  I have two custom fields.  One a pick list and the other a text box. I have added them to the Approve/Reject Approval Request section in the Opportunity page. I added the fields through the Select Fields to Display on Approval Page Layout and they DO show up on the Approve/Reject Approval Request section. I added them in like ().  However, just the label for the fields show, the field itself is nowhere to be found and can't be used.    You can see and even use the fields when you open the Opportunity page itself, but when you go to use the Approve/Reject, you can't do anything with them or see any values.  I was never a SalesForce user and got this tossed in my lap and really don't know my way around yet. I appreciate any help on this!!  Thanks!!  Kurt


iPhone 7 and 7 Plus wallpapers in iOS 10

On apple.com some variations of this wallpaper are shown on iPhone 7 and 7 Plus screens:    I can't find them on my iPhone 7 (iOS 10.0.2). Are they available exclusively for 7 Plus?  Here the same question:  (but no answer).


Web and print versions of the same paper from one TeX file

I'm writing a term paper using LaTeX that includes a number of figures created using external tools. These figures are available in both bitmap and vector formats. Ideally I'd like to use the vector versions, of course, but these are fairly chunky (up to 40 MiB apiece), and if I include these rather than the bitmap versions, the resulting PDF for the paper is well in excess of 100 MiB.  This isn't a problem per se. However, I have to submit the paper in both paper and electronic form (by email), and emailing such a large file could be an issue. I've therefore wondered if there is an easy (!) way of producing two versions of the paper, one for printing (using vector graphics) and one for emailing (a ,,web version´´, using bitmap graphics) from the same TeX file. The TeX file is already suitably prepared, I merely need to ,,flip a switch´´ to produce either version, but I cannot produce both at the same time, with different names.  I'd like to avoid using makefiles etc.; my workflow's based on TeXstudio on Windows, so something that's pure TeX (well, LaTeX is fine) would be best. I've looked at \input and \include, but I'm wondering if there's any tricks or Best Current Practices where ideally, I only need to run xelatex termpaper.tex or so and get both termpaper-web.pdf and termpaper-print.pdf.  I do apologize for the relatively open-ended question. Thanks in advance!


Ubuntu 18.04.1 LTS update problems sudo apt-get update

Hello i have a problem with new update in ubuntu can someone help me  i have this error   ~$ sudo apt-get update Hit:1 http://si.archive.ubuntu.com/ubuntu bionic InRelease Hit:2 http://si.archive.ubuntu.com/ubuntu bionic-updates InRelease              Hit:3 http://si.archive.ubuntu.com/ubuntu bionic-backports InRelease            Get:4 http://security.ubuntu.com/ubuntu bionic-security InRelease [83,2 kB]     Get:5 https://dl.winehq.org/wine-builds/ubuntu bionic InRelease [4689 B]        Err:5 https://dl.winehq.org/wine-builds/ubuntu bionic InRelease                   The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 818A435C5FCBF54A Reading package lists... Done W: GPG error: https://dl.winehq.org/wine-builds/ubuntu bionic InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 818A435C5FCBF54A E: The repository 'https://dl.winehq.org/wine-builds/ubuntu bionic InRelease' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.


I've put together a system to parse JSON and render it with some simple CSS. Though, I've done this using a variable. I don't want to output the data within the script. Instead, gather it from a local or remote URL.     How could I gather the JSON data from a URL source and output it like I am now?  Update


This may sound like an odd question, but this is what I have the most trouble understanding on Stack Overflow (and other Stack Exchange sites). What is the correct way to upvote? Should I upvote every question I find interesting or should I do it sparingly. Could some of the more experienced users give a short list of their mental checkboxes they go through before upvoting?


What is the purpose of using both past participle and past tense?

So in the examples:   (1) They began cooking last night.   (2) They have begun cooking last night.   They literally both mean the same thing, and I am not sure in which context a person (speaking) would prefer one over the other. If anyone could explain, with examples, why this is?   Thanks.


Prove $\int_{0}^{\pi}\frac{x^2}{\sqrt{5}-2\cos{x}}dx=\frac{\pi^3}{15}+2\pi\ln^2{\left(\frac{1+\sqrt{5}}{2}\right)}$ without contour integration

Show that   $$\int_{0}^{\pi}\dfrac{x^2}{\sqrt{5}-2\cos{x}}dx=\dfrac{\pi^3}{15}+2\pi\ln^2{\left(\dfrac{1+\sqrt{5}}{2}\right)}$$    demonstrates how contour integration can be used to solve the above integral, but I'm interested in finding alternative methods.  I believe one might utilize the  in some way. My attempt: I tried to rely on the identity $$2\cos{x}=e^{ix}+e^{-ix}.$$  Can someone think of a solution to this integral which doesn't involve the residue theorem?  Thank you


How to map arrows with free group functor from Set to Grp

I am having a bit of trouble understanding the free functor, T: Set $\rightarrow$ Grp, where T($A$) = Free group generated by $A$. The question I have  in mind is how do I map arrows. In Set, the arrows are just functions from $A$ to $B$, with no regards to any structure whatsoever. But in Grp, the arrows are group morphisms. I cant figure out how to map my arrows in Set to a morphism between groups.  Any hints or insight is deeply appreciated  Cheers


I am confused about simple harmonic motion. I understand that it follows a sine wave but is it possible to explain why it does?


Azure VM Nested Hyper-V VM Network Configuration

I'm trying to figure out how to share the internet connection from my HOST Azure VM to the VM's withing Hyper-V inside the HOST VM.  I've added two network interfaces to the HOST Azure VM each with static IP's configured.  Upon creating my Virtual Switch on Hyper-V i've associated the secondary NIC on the HOST machine and the internet connection is not passing through. I do have "Allow management operating system to share this network adapter" checked.  My intent is to create a Domain Controller with DHCP as a Hyper-V VM within my host machine and create subsequent Hyper-V VM's on the HOST machine for purposes of exchange, SQL, etc... But I need to get my primary Active Directory VM up and running and can't seem to figure out how to pass the internet connection from the HOST onto my first Hyper-V VM.  Any help, ideas, input appreciated.  Some context for this question: I'm investigating setting up a Hyper-V network for Microsoft Exchange. My plan is to create 1 Azure VM and install Hyper-V and multiple VM's inside for Active Directory, Exchange, DNS, DCHP to setup a public facing exchange server.


The rank of a square 2 by 2 block matrix with singular square blocks

I have tried to prove or disprove the following statement using Penrose-Moore pseudoinverses, but all of the literature on that subject seems to focus on the case $m \not= n$, i.e. rectangular matrices, rather than singular square matrices.  Let $M = \begin{bmatrix} M_1 & M_2 \\ M_3 & M_4 \end{bmatrix}$, where $M$ is a $2m \times 2m$ matrix, and $M_1 , M_2, M_3, M_4$ are $m \times m$ square matrices, all with determinant zero. Moreover, no two adjacent blocks of the $M_1, M_2, M_3, M_4$ are symmetric (hence the answers given  are non-examples, because all of the blocks are symmetric). Show that $M$ has determinant zero, or find a counterexample where $M$ is not singular.  Any help or insights with this problem would be greatly appreciated; I know this is probably a simple problem, but I am not sure how to apply the Laplace expansion in the case that the block matrices just have determinant zero, rather than being all zeros. This answer  says that the answer is affirmative and trivial, but I am not seeing it unfortunately. The condition regarding symmetry may seem random, but it is motivated by the fact that in such cases we can replace the blocks by their characteristic polynomial and still achieve desirable results. See, for example, here:


Shouldn't reviews be done a bit more carefully?

suggested edit made one change to the question -- changing the title to ALL CAPS.  I rejected it with a custom note and was pleased to see that the review was rejected by other reviewers as well.  However, out of curiosity, I looked at the  made by the user and ran into .  It is evident that the user has removed all the import statements from the code and the review was happily approved by three reviewers.  I don't quite agree that the review should have been approved.  Of course, I can rollback and make revision to the post in order to fix it but have some questions:   Does a mechanism exist for flagging such reviews? Shouldn't reviewers be given a break for permitting such changes?


Allow write access for regular user on CIFS share

I want to mount one of my media folders of my Synology DiskStation (DS414J, DSM 6.2) on my laptop (Manjaro running on Kernel 4.17.18) via SMB/CIFS. I set up a DiskStation user called media that has read/write access to this specific folder. I mount the folder with the following /etc/fstab entry:   //{disk station IP}/{folder}/ /home/{user}/NAS/{folder} cifs auto,x-systemd.automount,cache=none,rsize=130048,wsize=57344,users,user=media,pass={the password},workgroup=WORKGROUP,ip={disk station IP} 0 0   Mounting and read access works (I can access the files and e.g. play them with VLC) with the regular user. However, when I try to perform any write operations, I get "Permission denied" error.  Output of ls -la on the share shows following:  drwxr-xr-x 2 root root    0 01. Jan 2018   . drwxr-xr-x 2 root root    0 01. Jan 2018   .. -rwxr-xr-x 1 root root 5,8M 01. Jan 2018  '01.file' -rwxr-xr-x 1 root root 3,7M 01. Jan 2018  '02.file' -rwxr-xr-x 1 root root 3,2M 01. Jan 2018  '03.file'   How do I configure my laptop to allow my regular user to have read/write access to the share?


youtube-dl - download video from YouTube with subtitles - Tutorial

I downloaded Python and youtube-dl, on my desktop I saved the file yt-dl.py. My goal is to download video with subtitles. I opened cmd, wrote cd Desktop, pressed enter, after I dragged the file yt-dl.py on the cmd and then I don't know how download video with subtitles (I only know how download video without subtitles: after dragged file, I enter a space and after the link of video). What command could I use to download video with subtitles? (In the figure there is a mistake: the file is yt-dl.py instead of yt-dll.py)   Thank you for your time.  P.S. I tried the command --write-srt --sub-lang en '' found on  but it does not work. The link which I used is  instead of .    In the file yt-dl.py there is .


When I start my PC, my computer plays a loud BEEP for 2 seconds and after that it starts abnormally like press F1 To Start. I found some video in that many of the video tells to clean the RAM. After that I clean my RAM but it's not working.  So please tell how I get rid ofthis BEEP sound of CPU.


I want to change the color of UITabBar. I used UITabBar by the help of InterfaceBuilder but it doesn't provide the option to change the color of tabbar I want to change by tabBar color to Blue color can any one suggest me the best way of doing this work.  Thanks in adavance.


Can anyone please tell which ?     Or, if there is no particular theme, then how to tweak the code so as to have this kind of theme?  The Modified MWE is:  \documentclass[serif]{beamer}   \usepackage{hyperref}     \hypersetup{colorlinks=true, citecolor=blue, filecolor=blue, linkcolor=blue, urlcolor=blue}  \DeclareGraphicsExtensions{.pdf,.gif,.jpg,.eps}     \usepackage{subfigure}     \setbeamertemplate{caption}[numbered]     \usetheme{AnnArbor}  \definecolor{darkred}{RGB}{104,0,4} \setbeamercolor{palette tertiary}{bg=darkred}    \setbeamercolor{palette secondary}{fg=darkred!60!black,bg=yellow!85!orange}     \setbeamercolor{palette primary}{fg=darkred!70!black,bg=yellow!60!orange}    \setbeamercolor{frametitle}{fg=darkred, bg=yellow!60!orange }     \setbeamerfont{frametitle}{series=\bfseries}  \begin{document} \title{Are the Indian states fiscally sustainable?} \author[Santosh Dash]{Santosh K. ~Dash \inst{1}} \institute[] % (optional, but mostly needed) {   \inst{1}%   JNU, New Delhi}  \begin{frame}   \titlepage \end{frame}  \section{Introduction and Motivation} \begin{frame}{Introduction and Motivation}  \begin{itemize}   \item {Both States and Center.....}          \item Hence, we examine this issue.   \end{itemize} \end{frame} \end{document}   When i use that MWE, color of the title in the title page and section and sub-sections head appear in blue. I think it has to so something with hypersetup. I tried but i could not solve it. It should appear like the title page of the slide i referred to.


What's the problem here causing "Invalid memory reference (SIGSEGV)" when integers 10^8 and upwards are used as input?

I've used different values of n below and above 10^8. It works fine below it. But starts showing SIGSEGV once the input to n increases upto 10^8 or more. Why does this happen? My compiler is g++ 7.4.0 #include <iostream> #include <algorithm> using namespace std;  int main() {     long long int n, k, c = 0;              cin >> n >> k;     long long int arr[n];     for(long long int i =1; i <=n ; i+=2){         arr[c] = i;                  c++;     }              for(long long int j =2; j <=n ; j+=2){         arr[c] = j;                  c++;     }      cout << arr[k-1];          return 0; }


I check my Ubuntu 16.04 LTS system for available updates on a regular base. Ubuntu 18.04 LTS is not provided to download.


Proof that angle-preserving map is conformal

Let $\phi: S \to \bar{S}$ be a diffeomorphism between two surfaces in $\mathbb{R^3}$. Such a map is called conformal if for all $p \in S$, and $v_1, v_2 \in T_p(S)$ (the tangent plane) we have  $$\langle d\phi_p(v_1), d\phi_p(v_2) \rangle = \lambda^2 \langle v_1, v_2 \rangle_p$$  for some nowhere-zero function $\lambda$.  $\phi$ is said to be angle-preserving, if  $$\cos(v_1, v_2) = \cos(d\phi_p(v_1), d\phi_p(v_2)),$$  which I take to mean  $$\frac{\langle v_1, v_2\rangle}{\lVert v_1 \rVert \lVert v_2 \rVert} =  \frac{\langle d\phi(v_1), d\phi(v_2)\rangle}{\lVert d\phi(v_1) \rVert \lVert d\phi(v_2) \rVert} $$  From do Carmo, "Differential Geometry of Curves and Surfaces", 4.2/14:     Prove that $\phi$ is locally conformal if and only if it preserves angles.   The "only if" part is obvious, but how can the "if" portion be proved (i.e. how does preserving angles imply conformality)?


tikz-cd doesn't compile examples from the manual

I don't know if this a problem with my local TeX-Distribution (macTeX 2018) or with tikz-cd itself, how ever: I can't compile basic examples from the tikz-cd manual, like this:      \documentclass{standalone}     \usepackage[utf8]{inputenc}     \usepackage[ngerman]{babel}     \usepackage{xcolor}      \usepackage[T1]{fontenc}     \usepackage{lmodern}      \usepackage{amsmath, amssymb}       \usepackage{tikz-cd}      \begin{document}      \begin{tikzcd}         A \arrow[r, "\phi"] \arrow[d, red]                 & B \arrow[d, "\psi" red] \\         C \arrow[r, red, "\eta" blue]             &D \end{tikzcd}      \end{document}   The resulting output is   And the errors messages inside the log start with this error message:      ! Argument of \language@active@arg" has an extra }. <inserted text>                  \par  l.18        &D \end{tikzcd}  I've run across a `}' that doesn't seem to match anything. For example, `\def\a#1{...}' and `\a}' would produce this error. If you simply proceed now, the `\par' that I've just inserted will cause me to report a runaway argument that might be the root of the problem. But if your `}' was spurious, just type `2' and it will go away.  Runaway argument? ! Paragraph ended before \language@active@arg" was complete. <to be read again>                     \par  l.18        &D \end{tikzcd}   Any ideas what the problem might be? The macTeX-Distribution is complete and up-to-date as of april 4th 2019.


Install 10.8 on an external drive from 10.9

I have OS X v10.9. I downloaded v10.8 installer from the AppStore in order to install it on an external drive. However, when launching the installer it says that it can't be installed on this computer and give no option other than quit.  What's the easiest way to do install 10.8 on an external drive when I already have 10.9 installed?  I'm aware that there are some answers about downgrading from 10.9, but I wonder if there is any easier way than the hard process described in other places for downgrading.  Edit: THIS IS A MID-2011 MBP so it did not come with Macericks pre-installed.


Prove that the derivative of $x^w$ is $w x^{w-1}$ for real $w$

Can anyone give a proof of the derivative of this type of function? Specifically showing that  $\dfrac{d(x^w)}{dx} = wx^{w-1}$ for a real $w$?  I tried to use the Taylor series expansion for $(x+dx)^w$ and got the correct result. However, the proof of the Taylor series requires knowledge of the derivative of these functions. So this is essentially circular reasoning. I know that the same series is also given by the binomial expansion, but that's not entirely satisfactory either, because where's the proof that the binomial expansion works for all reals (isn't it only apparent for integers)? So far all of the arguments I've come across involve circular reasoning. I was thinking of showing that the binomial expansion is true for all reals using some form of proof by induction e.g. something like this.  I'm really not sure.


Remove All Windows, and reallocate space to Ubuntu Install

I bought a ibm thinkpad t430used and it came with Windows 10.  Since my SSD is only 120GB I wanted to remove windows, and reallocate that current 72GB that Windows 10 is using to my ubuntu install.  How can I do that?  My partitions currently look like:   Can someone please help? Thanks.


How to create a graphical application shortcut in awesome WM?

How do I create a graphical shortcut to run a program in awesome WM? An icon I can click to launch a program?  Right now, I can only run Firefox by either:   launching a terminal, then typing "firefox &", pressing Super+R and typing firefox, editing config files to add a keyboard shortcut.


Recently published paper deliberately not citing our very relevant work -- anything to do?

Note that the difference between this question and a related question () is that the authors in my question are fully aware of our work, whereas, in the related question, the authors were not aware of OP's work.  A recent paper did not cite our very relevant work.   There are significant overlaps among the scopes of the papers, and one of the important figures and the related conclusion are almost identical.  The leading author of the paper in question has been informed about our work even before we submitted the paper. I've asked for a reason for not mentioning it, and the answer was that our paper was noticed during the revision of the paper, and the authors do not feel obliged to mention it.   Is it OK to not mention a paper because of ``seeing it too late?'' Regarding this: does the date of submission/acceptance play a role?  Our publication date is before their submission date.


Chi-Squared Step of Vigenere Cipher Decryption

So, I have been assigned an assignment where I had to solve a Vigenere cipher.  Following along with  I managed to get all the way to the chi-squared step. But, that is the problem. Upon trying to code this, I found my results to be unfavorable. In fact, all of my results for the chi-squared probability test for each string were exactly the same. So, obviously I did it wrong.  I tried to use the formula on  to calculate this for each character, and for each string, I added them all together. Doing this leads to them all being the same total number for each string, which makes sense. But, if that is the case, how exactly do I use it to solve the cipher?  What I did:   Found the key length with I.O.C. (say it's 7) Create a string of all the 7th characters and the 1st Write a method to calculate chi squared value Calculate this for each character in each string from A-Z For each string, add up the probability of all the letters(PROBLEM)   What exactly am I supposed to do here? All of my "chi-squared" results are the same.  P.S. I found the keyword using a codebreaking website to clarify that my other information was right, but I would really like how do solve this last step.


New laptop with windows 7 via 8 downgrade, format and install windows 10, not activating

Just got a new laptop with Windows 7 (via 8 downgrade rights) installed on it.  I reserved a Windows 10 upgrade then installed Windows 10 via the .  So I skipped doing an upgrade to Windows 10 from 7.  Now Windows 10 says it cannot be activated. When I run slmgr.vbs /ato I'm told "The activation server determined the specified product key is blocked."  Is my only recourse to install 7/8 and then upgrade from that?  Seems really convoluted.


All my folders and files on my flash drive have been renamed automatically and I can no longer open them... I need those files

I opened up my flash drive this morning and all of my folders and files are normal, except for one folder and all its included files, which is the most important folder. The subfolders and files are renamed with bizarre characters and when I click to open them, a pop-up appears saying it's not accessible and the filename or directory name is incorrect. I don't want to reformat the flash drive because I'd lose all those files. Is there a way for me to restore it or something?  I would attach a screen shot, but apparently new users do not have that privilege. If you have a vague idea of what I'm talking about, let me know and I can email you screenshots so you can have a better understanding. Any help is greatly appreciated!


How to deep copy hashmap? I wanna make a copy of hashmap. When I change the keys and values in the copy, the original hashmap doesn't change. I cannot find a solution to solve this problem in the Internet. The function of putall() doesn't work.  HashMap<OWLClass, Set<OWLClass>> map1 ; HashMap<OWLClass, Set<OWLClass>> map2 = new HashMap<OWLClass, Set<OWLClass>>();   I tried   for(OWLClass map1.keySet()){         map2.put(a, map1.get(a));     }   and   map2.putAll(map1);   Both these methonds don't work.


Export each image from a collection in Google Earth Engine

I am trying to export each image in a filtered stack of Sentinel-1 images and cannot seem to get it right.   suggests using imageCollection.map() and a custom function (such as a geometric clip).  // Create a geometry representing an export region. var roi = ee.Geometry.Rectangle([-63.0, 9.2, -63.1, 9.3]);   // Load the Sentinel-1 ImageCollection. var sentinel1 = ee.ImageCollection('COPERNICUS/S1_GRD');   // Filter by metadata properties. var IW_H = sentinel1   // Filter to get images with VV and VH dual polarization.   .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))   .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))   // Filter to get images collected in interferometric wide swath mode.   .filter(ee.Filter.eq('instrumentMode', 'IW'))   // Filter IWs to get High res.   .filter(ee.Filter.eq('resolution', 'H'))   // Filter IW-Highs to get 10m res   .filter(ee.Filter.eq('resolution_meters', 10));   // Filter to get images from different look angles  var DescCollection = IW_H.filter(ee.Filter.eq('orbitProperties_pass', 'DESCENDING'));   var ClipFunc = function(iImage, geom) {   var iClip = clip(iImage, geom);   return(iClip); };   imageCollection.map(ClipFunc(DescCollection, roi));


Bootmgr is missing when booting with Ubuntu LiveUSB

I downloaded 64bit Ubuntu and I put it on my USB. It is bootable, and BIOS is configured to boot from it. But when I turn on the laptop with USB in it, it says:   Bootmgr is missing. Press Ctrl+Alt+Del to restart.   I have windows 7 64bit installed and I want to keep it. (dual boot or something)  Device: HP PAVILION G7 1303


What is the most rampant duplicate on Stack Exchange sites?

Strongly related:   This is not a question about how to deal with duplicates, it's a simple "meta" question:   What is the most rampant duplicate on Stack Overflow?    The particular duplicate must be "alive" on Stack Overflow (not merged or closed duplicate)  The duplicate-ness must be pretty unquestionable.    For example:   This is a duplicate of score 2 1.     merged ;-p    They are both so close that it makes little sense to have separate questions.   However, score 2 is pretty uninteresting.   (The rationale of this question is to find the duplicates so we can get the administrators to merge them. It is also to find better ways to find dupes in the first place, and perhaps turn finding duplicates into a game.)


using cmd prompt, how can I get the location of a share?  I know the name of the share, but when I remote onto the box, I can't see where the share location is.  net view shows me the names, but not the locations.


Option to flag/tag/bookmark a certain question/answer so that any edits/answers/comments show up in my Global Inbox

Note: This is not a duplicate of , since I am asking specifically about receiving notifications, nor is it a duplicate of , since I am asking about a separate facility to tag individual questions.    I'm asking this from the context of Puzzling.SE, although I'm sure it could be relevant for all SE sites.  Often, on Puzzling, a difficult puzzle will be posted.  I will look at it, and think, "That's really interesting; I'm curious to know what the solution is."  Sometimes I will favourite/bookmark it, and continue to go back to it to see if anyone has posted an answer/comment.  What would be much more helpful to me, is if I could click something that would add that question to my SE notifications, so I get notified when someone posts an answer or comments, in the same way I get notified for my own questions.  Since people use the "favourite" functionality for different things (as a temporary bookmark, or as a way to keep a list of best questions, or as a way to give kudos for an excellent question), it doesn't seem like it should be used for this.  Rather there should be a separate "flag" of some sort that can be applied.  Once I lose interest, I could uncheck it, and I would no longer get the notifications for that question.  On Puzzling there are also often puzzles that are worked on in a "group" format:  There are many bits to the puzzle, and different people offer solutions for each bit.  Thus it would also be beneficial to receive notifications of edits on answers I have tagged/flagged/marked.  I realize this aspect might be more difficult, since it doesn't mimic the notifications supplied for my own questions, but even if the notifications of answers/comments could be implemented, it would be very helpful.


I would like to know how the author got  $\frac{\sum_{k=1}^{n}\frac{1}{k}}{\ln(n)} \longrightarrow 1$  from $ \sum_{k=1}^{n}\frac{1}{k} =\ln(n)+\lambda+o(1)$    $$\frac{\sum_{k=1}^{n}\frac{1}{k}}{ln(n)}=1+\frac{\lambda}{ \ln(n)} +o(\frac{1}{\ln(n)})$$  when n goes to infinity we got that   $$ \frac{\sum_{k=1}^{n}\frac{1}{k}}{ln(n)}=1+o(0)$$


I have dates in 2 tables. Table student is as below:   ID|Name|Examdate 1  John 01/10/2015 2  Fred 11/12/2014   Table retake as below:   ID|RetakeDate 1  02/10/2016 2  05/11/2015   The IDs in retake relate to the students' IDs in student, i.e. they are the same.  I am trying to create another table where only students who have taken a retake after 12 months or more exist. The difference between examdate and RetakeDate needs to be >= 12months.  How do I achieve this?  There could be multiple rows in both tables for the same student. There will be multiple rows on both tables, as this will allow me to see how many times they have taken a retake and how many times an exam. At this moment in time I don't want to see if the retake is for the latest exam. I just want to see how many retakes they have taken all together. End result should be comparing each Exam date with Retake date. Some more explanation:     Q: So  if a student has dates in 2012, 2013, 2014 and then 2 retakes in 2016?       A: There should 3 rows in the result (one for each date)      Q: What if it's three exams – in 2012, 2013, 2014 – and (a) two retakes – in 2014 and 2016? or (b) one retake – in 2014? What should be expected as the result in each of those cases?          A: It doesn't matter. As long as the (a) retake was taken after 12 months or more, they should appear in the result.


Show there exist countable set containing an uncountable family $F$ of subsets such that $A,B \in F$ and $A \subset B$ or $B \subset A$

Prove there exists a countable set $C$ containing an uncountable family $F$ of subsets such that if $A,B$ are in $F$ and $A \cap B \neq \emptyset $, then either $A \subset B$ or $B \subset A$. I tried to show this by giving an explicit example, consider the set of integers $\mathbb{Z}$ and take it's power set $\mathcal{P} (\mathbb{Z} )$, I know that $\mathbb{Z} $ is countable and $\mathcal{P} (\mathbb{Z} )$ is uncountable , can you help?


When to use ArrayList, LinkedList, and Stack in Java?

How do I decide which data structure to use for a more efficient program? I mostly use ArrayList.  I checked out other questions but I was not fully satisfied. If someone could help me I would be really happy.


Induction, 0'1 and 1's sequence fun question

010 can we generated. If s is a sequence which can be generated by these rules, then 01s, 10s, 0s1, 1s0, s01, and s10 can all be generated.   -Prove (by induction?!) that in any sequence generated by these rules, there are more 0's than 1's   Without using the principle of induction my best guess was that rule 1 is the base case hence there will always be one 0 more than 1. The order in which the sequences are displayed do not matter because they just add one 0 and one 1 to the sequence s. BUT the question demands induction.. I can't see any other way to explain it rather than the way I just did.  PART 2 (if you're bored :p) Again, consider sequences of 0's and 1's, this time generated according to the following rules: 10 can be generated.  01 can be generated.  If s is a sequence which can be generated by these rules, then 0s1 and 1s0 can be generated by these rules.  If s is a sequence which can be generated by these rules, then the sequence ss (s followed by another copy of s) can be generated.  If s is a sequence which can be generated by these rules, and s is of the form t00 or t11 for some smaller sequence t, then t itself can be generated.  Prove that no sequence with an odd length can be generated by these rules.


How do I pack textures for sending off to a render farm

Whenever i try to send a project off to a render farm such as sheepit, it says it needs the textures packing with the file in order to render correctly.  How would I do this?


So I ran accross the following problem today on a forum:     "In an attempt to reduce male birth rates, feminists have passed a law   which forces families to stop having children after their first male   child. After this law is passed, what is the expected ratio of male   children to female children?"   It's unclear whether families are supposed to continue having children until their first male child or if they may stop at any earlier point, but let's assume the former. Let's also assume that everybody obeys the law, and that either sex has an equal chance of being born.  I thought I had a simple solution, because the problem is logically equivalent to the following process:        Generate N infinite random sequences of boys and girls   Cut each sequence after the first occurrence of a boy   Concatenate the results and measure the ratio of boys to girls      This is equivalent to generating a random sequence of boys and girls by stopping at each boy but then continuing again (up to N times), so the only difference from a normal random sequence is that this sequence always ends with a boy. However, if N grows to infinity, it seems like this last element (which can never be reached) becomes irrelevant, so the ratio of boys and girls should be 1:1 like in a normal infinite random sequence. This seems perfectly logical to me, but a few people kept insisting that it is wrong, ranting about "biased estimators" and claiming that the real ratio will be biased in favor of females.  Is my reasoning flawed? If so, why?  [EDIT]  Contrary to some suggestions, I don't think this question is a duplicate. It asks about the validity of a particular approach to solving the problem, not just for a solution.


How to give NSWindow a particular background color

I am writing a cocoa application which has a NSWindow. I want to change the background color of the window to a specific color. But the window properties in the inspector only provide "Textured Window" alternative. How can I make the color of the window as desired?


I'm looking for some advice on how to determine how accurate a forecast is.  Basically, what I have is 23 years of competitive results for a particular sport (10000+ matches). The matches are broken down into team, division, home, away, and neutral matches, as well as score. From this I was able to determine each team's for and against scores for each year, depending on the division of their opponents and venue. However, I'm trying to determine the best method of forecasting the scores going forward (about 12 months).  My first thought was to use forecast the averages and backtest then vis-a-vis the the historical results. This leads to some differences (obviously), but I can't determine how significant these differences are.  As an example, I used 10 teams, and forecast using the proceeding 5 year period. When I got the average of the average differences between actuality vs forecast, I got 0.44 (e.g. average of the average of 18 data points per team for 10 teams). If I change it to a 4 year period, it (obviously) changes, in this case to 0.75.  Is this the correct way of determining the best forecast model or if there is a a more correct method, that is widely accepted, for determining which forecast model is most accurate?  BTW: doing this in Excel, so answers with Python, R, or other programs, while useful, are not great.


I have the equation $ \mathbf{x}^T A \mathbf{x} = b $, where $b$ is a scalar, $\mathbf{x}$ a vector of size $M$, and A a matrix of size $M\times M$. $b$ and $\mathbf{x}$ are given.   How many such equations do I need to find the (common) $A$, and how do I do it?


I have created bootable usb drive following , specifically following the instructions under  Windows 10 bootable USB using WoeUSB  I have disabled secure boot in bios and boot type is set to UEFI, when i boot from the usb the system restarts after 3 seconds and when the second time the system starts it goes straight to Ubuntu. I have no idea how to successfully boot into usb drive and install windows 10.


why blender crash after tray subD complex shape?

i have decent pc ryzen 9 3900x 32 gb and gtx 1660 super. now i modeling turntable and have some problem not just now but often when i worked on complex shape blender start work very slow or even crash...here is example of object


At most finitely many (Hamel) coordinate functionals are continuous - different proof

If $X$ is a vector space over $\mathbb R$ and $B=\{x_i; i\in I\}$ is a Hamel basis for $X$, then for each $i\in I$ we have a linear functional $a_i(x)$ which assigns to $x$ the $i$-th  coordinate, i.e., the functions $a_i$ are uniquely determined by the conditions that $$x=\sum_{i\in I} a_i(x)x_i,$$ where only finitely many summands are non-zero.  If $X$ is a Banach space, then at most finitely many of them can be continuous.  I have learned the following argument from comments in .     Suppose that $\{b_i; i\in\mathbb N\}$ is an infinite subset of $B$ such that each $f_{b_i}$ is continuous. W.l.o.g. we may assume that $\lVert{b_i}\rVert=1$.      Let   $$y:=\sum_{i=1}^\infty \frac1{2^i}b_i.$$   (Since $X$ is complete, the above sum converges.)      We also denote $y_n:=\sum_{i=1}^n \frac1{2^i}b_i$. Since $y_n$ converges to $y$, we have $f_{b_k}(y)=\lim\limits_{n\to\infty} f_{b_k}(y_n)=\frac1{2^k}$ for each $k\in\mathbb N$. Thus the point $x$ has infinitely many non-zero coordinates, which contradicts the definition of Hamel basis.   I have stumbled upon  in the book Christopher Heil: A Basis Theory Primer. Springer, New York, 2011. In this exercise we are working in an infinite-dimensional space $X$. Basically the same notation as I mentioned above is introduced, $a_i$'s are called coefficient functionals and then it goes as follows:     (a) Show by example that it is possible for some particular functional $a_i$ to be continuous.      (b) Show that $a_i(x_j) = \delta_{ij}$ for $i,j\in I$.      (c) Let $J = \{i\in I : a_i \text{ is continuous}\}$. Show that $\sup \{j\in J; \lVert a_j \rVert<+\infty\}$      (d) Show that at most finitely many functionals $a_i$ can be continuous, i.e., $J$ is finite.      (e) Give an example of an infinite-dimensional normed linear space that has a Hamel basis $\{x_i; i\in I\}$ such that each of the associated coefficient functionals $a_i$ for $i\in I$ is continuous.   The part (c) can be shown easily using  (a.k.a. Uniform boundedness principle). But I guess that the author of the book has in mind a different proof for part (d) from what I sketched above, since (c) is an easy consequence of (d) -- so he would probably not be put the exercises in this order. (But maybe I was just trying to read to much between the lines.)  Question: I was not able to find a proof od (d) which uses (c). Do you have some idea how to do this?  NOTE: My question is not about the parts (a), (b), (e). I've included them just for the sake of the completeness, in order to include sufficient context for the question.


$p$-groups have normal subgroups of each order

Suppose $|G|=p^n$. Then $G$ has a normal subgroup of order $p^m$ for every $0\le m\le n$.   By induction. It is clearly true for $n=0$. Now suppose $k<n$ and $H_i$ is a normal subgroup of $G$ of order $p^i$ for $i=0,...,k$.  I read in another thread that if we consider $Z(G/H_k)\neq 1$ and the Cauchy's theorem, this will provide us a group of order $p^{k+1}$. I don't see why yet.  By that theorem there exists $gH_k\in Z(G/H_k)$ with order $p$. How can we construct a group of order $p^{k+1}$ from here?  Thank you.


$\phi: M_2(\mathbb{Z})\to \mathbb{Z}$ is necessarily trivial

Let $\varphi: M_2(\mathbb{Z})\to \mathbb{Z}$ be a ring homomorphism. Then $\varphi$ is necessarily trivial.  My reasoning:  Suppose not. Then $\varphi(I)=1\implies \forall A\in M_2(\mathbb{Z}),\exists A^{-1}\in M_2(\mathbb{Z})$ such that $\varphi(I)=\phi(A)\phi(A^{-1})=\phi(A)\phi(A)^{-1}=aa^{-1}$. However, only $1$ and $-1$ have multiplicative inverses in $\mathbb{Z}$. Hence, if $A\ne I$, then $\phi(A)^{-1}$ may not exist. This implies that $\phi$ must be trivial (that is, map everything to $1$). [For if $\phi(A)=0$ for all $A\ne I$, then $\phi(A)^{-1}$ admits division by $0$].  Do you think this is correct?


Why is this sentence wrong? "He went to home."

Why is this sentence wrong?     He went to home.   is it correct in this way?     He went home


Is a bank account or branch manager able to give higher interest rates on CDs to preferred clients?

Can an account manager or branch manager of your bank give you higher interest rates on savings or CDs (Certificates of Deposit) if you are a preferred client?  For instance, if a long time client who held funds at the bank for a long time was thinking of moving their funds to a different institution would the manager have the authority to match the other bank's rates?


Show some sort of popup if a user uses code in their post and does not format it correctly

For example I have seen people post questions and answers like this:     You should use  instead of  because  does not do what you think it should do and  does what you want.   But it should have looked like this:     You should use <tag> instead of <othertag> because <othertag> does not do what you think it should do and <tag> does what you want.   Some users do not even realize that they are making those kinds of mistakes!  There should be a popup of some sort that wars you that you might not have indented or backticked code, because if you do not do those things your post will not look correct!


Relationship between logistic regression and Softmax Regression with 2 classes

Suppose we have data matrix $X$ which is $n\times p$ matrix ($n$ data points, and $p$ features including intercept), i.e., we already add the intercept term (append $1$ column) to $X$   For logistic regression (binary classification), the model parameters / regression coefficients $\beta$ is a length $p$ vector. For softmax regression (multi-class classification), the model parameters $W$ is $p \times m$ matrix, where $m$ is the number of classes.   Now, suppose we set $m=2$, then $W$ is a $p \times 2$ matrix. They are the same model, so the number of parameters CANNOT be doubled and we should be able to derive one from another.   So, my question is  What is the relationship between $\beta$ and $W$?


How to run xfce-terminal with different commands per tab and keep using the tabs after the commands have returned?

To keep the overview I like to place multiple commands always in the same order and start them automatically together (gradle, git, database, scala-REPL, jboss...)   -H (hold) seems to mean that the terminal isn't closed after termination, but how do I terminate such a process willfully? Not at all? In such a way that I can continue to use the terminal.   I'm using xubuntu with with xfce4-terminal and bash. Is there a better GUI-solution to startup multiple commands, with the ability to continue working in that window/tab?  Update: If you don't know these commands: Jboss and gradle are continously producing output, which you don't want to have intermixed in the same terminal. And sometimes they need to be interrupted with ^C, and restarted. I don't like to reopen an xfce4-term and navigate to the directory I need to act in.  Database and scala-REPL are interactive so there is no sense in starting them in the background.   My current startup-script just navigates to the desired directories, and opens all tabs in the right order to find them always at the same position, naming every tab for its purpose:  xfce4-terminal -T eclipse   --working-directory=/home/stefan/oximity -e "/opt/eclipse/eclipse" \     --tab -T arandr --working-directory=/home/stefan/oximity -e "arandr /home/stefan/.screenlayout/oximity.sh" \     --tab -T bash       --working-directory=/home/stefan/oximity \     --tab -T gradle     --working-directory=/home/stefan/oximity/med \     --tab -T git        --working-directory=/home/stefan/oximity/med \     --tab -T mysql      --working-directory=/opt/mini/mysql \     --tab -T jboss      --working-directory=/opt/mini/jboss \     --tab -T jboss-log  --working-directory=/opt/mini/jboss/standalone/log \     --tab -T scala-REPL --working-directory=/home/stefan/proj/mini/forum -e /opt/scala/bin/scala   Eclipse and arandr are detached from the shell and run in their own window, so there the -e (execute) param works. I think for the scala-REPL it works since it is the last command in the list.


Need explanation for $CY_3$ folds comes first rather than algebraic curves comes first

The example I am aware of so far is quintic 3-fold equipped with $SU(3)$ holonomy. Why it is more natural to talk about $CY_3$ folds or Calibi-Yau 3 folds without talking about algebraic curves in string theory? Why it is not more natural to talk about curves first? Or why it is more intuitive to movtivate 3-fold first rather than motivate ? Reminder: This is not a popular science question. I need mathematical and theoretical physics justification. Please give me the reference if possible.


How can I tell if my iOS device is currently jailbroken?

How can I find out if my iOS device has been jailbroken (with a drive-by exploit for example)?  Is there an app for that?


Searching on users page and sorting by reputation

So I feel like this is either a dumb question or a dupe, but here we go... If I go to the "Users" page on a site and search, and then sort by all-time reputation (as ), I get very confusing results:  I don't understand how these are sorted. There is one person with over 1K rep, and they are not (in any way that I can see) placed above the person with 1 or 19.  How are these sorted?


If a different question contains the correct answer, should the question be marked as a duplicate?

The situation I am referring to is . The situation is as follows:  Question A is created with a certain question. Question B is an older, entirely different question, but the discussions in the comments and answers provide the solution to A. Question A has been marked as a duplicate and is now linked to Question B.  This methodology seems counter-intuitive to me. If I visit the site and happen to search for something similar to Question A, I am redirected to Question B and become confused, since I see no correlation and have no interest in plowing through the comments and answers to find the answer to my question. What is the general consensus here? Do I stand alone in my reasoning?


whats is the applications of the minimization of eigenvalue in the real life ( physics,the natural sciences...)

let $\lambda_{1}(\Omega),\lambda{2}(\Omega),\lambda_{3}(\Omega)...$ the eigenvlues of the laplacian Operator with Dirichlet condition on the boundary on $\Omega $  the classical spectrale optimisation problem is : $$ min\{\lambda_{k}(\Omega),\; \Omega\subset \mathbb{R}^N open ,\; |\Omega| = c\;\},$$ where  $|.|$denoted the  Lebesgue measure , $c>0$, $k \in \mathbb{N}^{\ast}$ and  $\lambda_{k}$ is the $k-$eme eigenvalue of Dirichlet-lapalacian on $\Omega$.  I would like to know what is the application of this Problem (For the laplacian or another Operator) in the physics or the natural sciences..  thank you for your answers


Is there a relationship between the unbounded infinities and uncountable infinities?

When a function f increases without bound we say $f(x)=\infty$. How does this idea relate to, if at all with the infinite sets we study in set theory?  To give a better understanding of why I'm bringing this up let me present and example,  Take $$\lim_{x\to2}f(x)$$ where $$f(x) = \frac{3}{(x-2)}$$ the graph of which is     Now obviously $\lim_{x\to2}f(x)$ does not exist but could we in some context say that $\lim_{x\to2}f(x)$ corresponds to(or is even equal or equivalent to) a set $\mathscr M$ such the |$\mathscr M$| = |$\mathscr{R}$|. In other words, if they are related then how is that and if not, why not? Thanks in advance.


I ran a regression analysis to predict performance on an exam, calculated residuals and took an average and sum of the residuals and the result was ~ -0.011 (for average) and -2.34 for the sum of residuals.  This was when the calculation was done on Excel.  Using SPSS, when I requested for residuals to be saved while running the regression and then did a descriptive statistics for those residuals, the average was 3.4 E-14 and the sum was 0.0000.  I'm not sure why two programs would result in vastly different values.  Also, a tad confused as to what could be causing the negative value for sum of residuals despite the plots not revealing any glaring homoscedasticity or outliers.  With regards to the sum/average of residuals being equal to zero, does the value have to exactly zero or does it have to be something with a really negative exponent to qualify as zero?  What would be considered close to zero or almost zero in terms of a threshold?  If there are references that could be provided for this threshold or range, that would be much appreciated too.   Thanks!


I put together a sample scenario of my issue and I hope its enough for someone to point me in the right direction.  I have two tables  Products    Product Meta    I need a result set of the following


Do the Q have rules comparable to Starfleet's Prime Directive?

They're obviously not opposed to messing with other races but do they place limits on their interference and/or interactions?  We have witnessed Q (John de Lancie) change or alter many things for his amusement, but he only goes so far and usually puts things back as they were when he gets bored or done with whatever he's up to. I have never seen them 'advance' a civilisation, though Q has saved one or two.  Do they have a rule for this?


Formula to calculate Level and Current Experience from Total Xp

So I'm building a mobile game where I have simple XP progression system that goes like this: Level1: 0-399 Total XP Level2: 400-1199 Total XP Level3: 1200-2399 Total XP So basically for the first level the player needs 400 XP to level up. Once it reaches that the exp bar goes to zero and then needs 800 XP to level up, the XP bar goes to 0 and needs 1200 and so on. I was wondering if there is a formula in order to calculate the current level of the player and the current experience (i.e. 400/800 when it has 800 total XP) from the Total XP. EDIT: So I found the formula Level = Floor(1/20 (10 + sqrt(2) sqrt(50 + TOTAL XP))) but I still can't figure out the formula to find the Current XP Thank you


Problem installing g++ ccompiler on Ubuntu 14.04

I tried to install g++ using packages from another user. offline..but there were errors. After connecting to the net I tried to install using sudo apt-get install g++, but it gave the following output:  gstreamer0.10-alsa is already the newest version. qtdeclarative5-ubuntu-ui-extras-browser-plugin is already the newest version. python-gconf is already the newest version. gstreamer0.10-tools is already the newest version. libglib2.0-0 is already the newest version. gir1.2-peas-1.0 is already the newest version. libatk-bridge2.0-0 is already the newest version. gnome-session-bin is already the newest version. libgomp1 is already the newest version. libmessaging-menu0 is already the newest version. usb-creator-gtk is already the newest version. libgnome-desktop-3-7 is already the newest version. software-properties-gtk is already the newest version. gnome-control-center-shared-data is already the newest version. unity-scope-gourmet is already the newest version. libcupsimage2 is already the newest version. growisofs is already the newest version. libjson-glib-1.0-common is already the newest version. activity-log-manager is already the newest version. libio-string-perl is already the newest version. qtdeclarative5-qtfeedback-plugin is already the newest version. gnome-power-manager is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   and many more lines like this....but g++ is still not installed


Disable visual volume display on top left on windows 10

How can i disable the visual volume overlay which appears at the top left on windows 10? It is very annoying if I change the volume then I have to wait 3-4 seconds till it dissapears, and I can't click anything which lays behind it during this time.  Is there a registry entry or something which I can set to false?


Does moving apps to the SD card negatively affect performance?

Does moving an application to the SD card negatively influence I/O performance of the app or of Android in any way, in particular loading times?


How is the concept of "work done" useful?

There are many questions on this site about the confusion caused by the definition of work done $W = \vec{F} \cdot \vec{s}$. Look over to the related column on the right you'd see how many there are:          I am glad the users are gracious enough not to mark them as duplicates, and I hope this hospitality can extend to my question which may result in opinionated answers.  Since most of the confusion surrounding work done is related to that, despite having a unit of energy, it does not provide much useful information regarding energy state of the parties involved. For example in the first link it was asked "How is the work done to push a planet over 1m with 1N the same as pushing a feather over 1m with 1N?" I might as well have asked about the work done of applying a force of 1mN to a particle of any mass travelling at 0.9c for 1s, because contrary to intuition implied by work done, displacement, absent from a force field, means nothing to energy state or energy transfer, and yet work done is defined with respect to displacement.  In the rare occasions that work done is used in a constructive manner, such as inside a gravitational field or between capacitor plates, it is being equated to other energies (KE, PE), whereas those energies on their own are sufficient to describe the energy states and the use of work done is redundant.  The question: In what scenarios is "work done" uniquely useful both as a concept and as a practical tool aside from the mathematical definition and in examinations? Note that I am seeking insightful examples as to when work done is a useful definition to assist problem solving (outside textbook exercises) without causing more confusion than problems it can solve. Like all definitions, there are useful ones, and not so useful ones. The vast number of work-related questions on this site alone proves the utility of this question. The philosophical aspects has been touched upon in .  I am not disputing its validity. Please do not rehash the definition.


Im stuck today with a java error on an eclipse 3.8 platform.  I try to generate a simple MenuBar on a JFrame. The JMenuBar contains the JMenu("Help") and the JMenu contains a JMenuItem("Quit"). The class extends a JFrame. With the function (this.)setJMenuBar(MenuBar); I try to set my MenuBar to my JFrame, which should work fine as long I just have one MenuBar.  GUI-class code:  import javax.swing.*; import java.awt.*;  public class Taschenrechner extends JFrame{  //Instanzvariablen im Zusamenhang mit dem Menu private JMenuBar MenuBar; private JMenu MenuHelp; private JMenuItem MenuHelpQuit;  public Taschenrechner() {     super();      //Flaeche festlegen     this.setSize(300,300);      //Menukomponenten definieren     MenuHelp= new JMenu("Help");     MenuHelpQuit=new JMenuItem("Quit");      //Menukomponenten zusammensetzen     MenuHelp.add(MenuHelpQuit);     MenuBar.add(MenuHelp);     this.setJMenuBar(MenuBar); } }   my main-class code (declare objekt and setVisible):  public class Taschenrechnerstart {  public static void main(String[] args) {     Taschenrechner taschenrechner1 = new Taschenrechner();     taschenrechner1.setVisible(true); } }   Now on starting the code I get a NullPointerException-error in the GUI-class on line:  MenuBar.add(MenuHelp);   and a NullPointerException-error in the main-class on the line:  Taschenrechner taschenrechner1 = new Taschenrechner();   Does someone have an idea why my code isn't working?


Why are redheads called "gingers" when ginger is yellow?

The term "ginger" is often used as a slang term for someone with bright red hair.  But ginger (the spice) is   Where does this term come from, then?


How to get started with learning electronics?

My main goal is to be skilled enough to design printed circuit boards to build devices like a basic smart watch and other simple projects. How do I get started ?


If $v_1,...,v_r$ are eigenvectors that correspond to distinct eigenvalues, then they are linearly independent.

Prove:     If $v_1,...,v_r$ are eigenvectors that correspond to distinct eigenvalues $\lambda_1, ...,\lambda_r$ of an $n \times n$ matrix $A$, then the set $\{v_1,...,v_r\}$ is linearly independent.   Please give an example and tell me how this theorem works!


Why can't we use due to in 'The picnic was cancelled due to the rain.'?

I obtained the following sentences at this website .  The picnic was cancelled due to the rain. The picnic WAS CANCELLED BECAUSE OF THE rain.  The first sentence is wrong but the second is correct. Why can't we use 'due to' in the first sentence?  Another source (from Magoosh)  suggests that the first sentence is wrong. The reason provided by Magoosh is as follows:  "The picnic was canceled, because of rain" or "Cancellation of the picnic was due to rain" or "The cancellation, due to rain, was a problem for ...." The word "due" is an adjective, a noun modifier. It is allowed to modify a noun, as it does in the second and third structure here. It cannot modify the action of a verb, as the original has. For that, we need "because of," which opens a preposition phrase that can modify verbs.


Different from x Different to x Different than

In the following sentence:     "When I visited my old school after so many years, it looked completely different in the classrooms and the backyard /from what/to what/than/ it had been when I was a little boy.">       Are the three options acceptable in spoken English ?


I am an economist so my academic career has been spent on interpreting beta hat rather than optimising y hat. But I've become quite fascinated by neural networks so I wanted to get some things clarified.  So a 'regular' linear regression is an array of attributes with one hidden layer consisting of a single neuron. If we use the sigmoid activation function we get the logit model. Both of these I am very familiar with and I have used the first one for casual inference for many years (i.e., when can the beta's in y = BX + e be interpreted as causal effects on y).  My confusion arises when the hidden layer(s) have several nodes. I recall watching some TensorFlow lecture where it was said that the different nodes find different patterns. So in the MNIST dataset for example, if we wanted to detect the number nine, we know that it is composed of a circle with the bent line and a seven is a straight line combined with another straight line etc. So the different nodes in the hidden layers capture these patterns (please correct me if my interpretation here is incorrect).  So for image classification problems I kind of see the role different neurons play. But what about the case of regressions? Say I have a bunch of data about houses, what role do the different neurons play then? In the linear regression:  $Houseprice_{i} = a + \beta_1*size_{i} + \beta_2*No.Rooms_{i} + \beta_3*HasPool_{i} + e_{i}$  Each beta/weight tells me the effect each attribute has on the house price. But this requires just one hidden layer with a single neuron and an activation function that just maps to itself. If I add a bunch of hidden layers with several neurons I will most likely get a better prediction for the house price but how do I interpret the weights, number of neurons and number of hidden layers?  Any clarification would be greatly appreciated!


I [had]/[have] been in a pretty good mood so far

CONTEXT: John to Bob: "I was wondering if you could lend me some money, Bob." Bob to John: "I've been in a pretty good mood so far, so stop bringing me down with that nonsense." Chris to Bob: "What did you just say to John?" Then Bob says to Chris one of the sentences below. SENTENCES:  I told him that I have been in a pretty good mood so far, and asked him to stop bringing me down with that nonsense.  I told him that I had been in a pretty good mood so far, and asked him to stop bringing me down with that nonsense.   QUESTION: Are both sentences correct? I'm wondering about the bolded part.


I am trying to prove that not both integers $2^n-1,2^n+1$ can be prime for $n \not=2$. But I am not sure if my proof is correct or not:  Suppose both $2^n-1,2^n+1$ are prime, then $(2^n-1)(2^n+1)=4^n-1$ have 2 precisely two prim factors. Now $4^n-1=(4-1)(4^{n-1}+4^{n-2}+ \cdots +1)=3A$. So one of $2^n-1, 2^n+1$ must be 3. which implies $n=1$ or $n=2$ (rejected by assumption). Putting $n=1$, we have $2^n-1=1$ which is not a prime. Hence the result follows.  I also wanna know if there is alternative proof, thank you so much.


Difference in "sourcing" from a file in bash

What is the difference between the following two commands to source a file and then print the env variables?  sh -c . envvars.sh; env   And:  ./envvars.sh; env   More specifically, what do the following do:  ". envvars.sh" vs. "./envvars.sh"   And:  "sh -c envvars.sh" and "./envvars.sh"


Encrypted vs unencrypted digital signatures

Is there a difference in terms of security between    An encrypted stream of bits obtained by encrypting a plaintext concatenated with it's signature  $ C = E_k(plaintext||\sigma)$  where $E$ is a symmetric or asymmetric encryption function, II is a concatenation operator and   $\sigma=h(plaintext)^k$   where $h$ is a secure MAC (the key is assumed to be the same).  A bit stream obtained by concatenating a ciphertext and the signature over the its corresponding plaintext  $C=E_k(plaintext)||\sigma$  where   $\sigma=h(plaintext)^k$ A stream obtained by encrypting the ciphertext of the plaintext concatenated with the signature over the respective ciphertext  $C=E_k(E_k(plaintext)||\sigma)$  where  $\sigma=h(E_k(plaintext))^k$   Also, is there any risk due to using the same key for both encrypting and signing? I don't refer to the cases that do not involve recovering the key through other means other than passive or active attacks.


Importance of intercept term in regression equation

What is the actual importance of an intercept term in a regression equation? If regressors include variables like age, height, weight and gender(1= male, 0= female), should the equation have an intercept term?


My PS3 controllers have died and are not charging

It has been some months since I've turned on my Playstation 3. Today, when I turned it on with my controllers, it didn't work. I thought "Hey, the battery surely ran out", so I tried to charge them but they don't seem to be charging at all. Could it be that they're officially weight papers by now?


ArcSDE error: "Maximum number of connections to instance exceeded "

I have an ArcSDE error: " **Failed to connect to database. Maximum number of connections to instance exceeded "*  Did what ESRI recommended :"      Check the value set for the CONNECTIONS parameter in the SERVER_CONFIG   or sde_server_config ArcSDE system table to be sure it is sufficient.   If it is not, increase the number of allowed connections using the   sdeconfig command with the alter operation"   and still nothing works on my database server. (I can't create features, import, etc).  We use a Microsoft SQL Server. And it's an enterprise geodatabase.     Apparently it was a schema lock. I had a map service started which used that geodatabase. So how can I edit the geodatabase and have a started map service in the same time. I've already created several versions and tried to publish just the versions, but they still lock my gdb.


When do we calculate the population parameter instead of sample statistics?   If there is a this kind of case which statistical tool should we use population parameter or sample statistics?  A car company wants to know the average age of cars of their brand that are still on the road. How would you define the appropriate population? Will the car company calculate a population parameter or sample statistic? Why?


I'm working with linguex package. How can I draw underarrows to represent movement? I'm interesting in producing something like this:    Thanks!


How can I wake-up a PC using a command? (i.e. equivalent to moving a mouse, etc)

It doesn't seem like this would be very difficult, but how can I wake-up a PC by doing the equivalent of moving a mouse or pressing keys on a keyboard?  My PC is running Windows 10 and I only have the monitors enter sleep mode after 15 minutes.  The rest of the PC is still awake and doesn't use hibernate, etc.  I'm trying to use EventGhost to receive a TCP/IP command that tells the PC to wake up the displays but it's proving quite difficult.


Why does entropy of an ideal gas break the third law of thermodynamics?

I was recently looking at the entropy equation for an ideal gas, show below  $$S=NR\left\{\frac{5}{2}+\ln\left[\frac{V}{N}\left(\frac{2\pi mRT}{h^2}\right)^{3/2}\right]\right\}$$  And what troubles me is as $T\rightarrow0$ then entropy become negative, which violates the third law of thermodynamics, how can this be?


how to know which method is calling other method in javascript

consider i have many methods in jscript..  method1()  method2()  method3()  Now method1() and method2() are independent. where method3() is called by both the methods. I want to know from which method method3() is getting called. either method1() or method2()


I have been watching lectures on real analysis by Prof. Francis Su (Harvey Mudd College) on youtube and in the 20th lecture he defines limits of functions. He says the main idea for a function to have a limit at a point is that as the points in the domain gets closer and closer to a point, their corresponding images gets closer to a point in the co-domain. The definition of limit given by him is as follows:  $X, Y$ are metric spaces, $E \subset X$ and $p$ is a limit point of $E$.   Let $f: E \rightarrow Y.$  To say "$f(x) \rightarrow q$ as $x \rightarrow p$" or "$\lim_{x \to p} f(x) = q$" means that $\exists$ $q \in Y$ such that $\forall$ $ \epsilon \gt 0,$ $\exists$ $\delta \gt 0$ such that $\forall$ $x \in E$  $0 \lt d_X(x,p) \lt \delta \implies d_Y\left(f(x),q\right) \lt \epsilon \tag 1$  In this definition let X = Y = $\mathbb R$. I don't understand why this definition works. How does this definition reflects closeness i.e as points gets closer to $p$ their images get closer to $q$ and also why don't we say   $d_Y\left(f(x),q\right) \lt \epsilon \implies 0 \lt d_X(x,p) \lt \delta $  instead of $(1)$? If there are any mistakes in the question then please suggest.


I'm trying to show explicitly that $A$ is isomorphic to $H_n(B^n,S^{n-1},A)$ by the map $a\mapsto [a\cdot f]$. Where $f$ is a homeomorphism from $\Delta^n\rightarrow B^n$ that restricts to a homeomorphism from $\partial\Delta^n \rightarrow S^{n-1}$.  I am getting confused with how to work with elements in $H_n(B^n,S^{n-1},A)$.   From what I understand $H_n(B^n,S^{n-1},A)=H_n(C(B^n,S^{n-1},A))$ where $C(B^n,S^{n-1},A)=C(B^n,A)/C(S^{n-1},A)$.  This gives that $[g]\in H_n(B^n,S^{n-1},A)$ is $g+Ker(\delta_n:C(B^n,S^{n-1},A)\rightarrow C(B^n,S^{n-1},A))$. But I do not see how to work with this


For $p$ prime in $\mathbb{Z}[i]$, show $p \equiv 3 \mod 4$ using ring theory.

Just building on , where we showed that an odd number $p$ is prime in $\mathbb{Z}[i]$ if and only if $x^2+1$ does not have roots in $\mathbb{Z}/p\mathbb{Z}$.  The last part of this exercise is to show, in this case, that the multiplicative group of units of $\mathbb{Z}/p\mathbb{Z}$, denoted by $(\mathbb{Z}/p\mathbb{Z})^\times$ does not have an element of order 4, and $p \equiv 3 \mod 4$.  We can also conclude that $p \not\equiv 0,2 \mod 4$ because $p$ is odd.  Here is where I am getting a bit stuck. I assume the point is to show that if we assume that $p \equiv 1 \mod 4$, for example, $p = 5$, then $x^2+1$ has roots in $\mathbb{Z}/5\mathbb{Z}$. Here, $x^2+1 = 0 \mod 5$ for $x=2$. By the previous proposition, then $p$ is not prime in $\mathbb{Z}[i]$.  I am lacking the general statement of this proof. How can I go from assuming $p \equiv 1 \mod 4$ to $x^2+1 \equiv 0 \mod p$, in a general way?