Since some useful answers to other's questions sometimes later turn out be be wrong or receive comments that can provide valuable additional information, it would be great to be able to subscribe to comment-notifications on individual posts (that one doesn't own) instead of having to favourite the entire question. Maybe even with some noise filter like "only notify me of comments with at least [n] great comment votes" option.  This would also be useful to allow subscribing to the currently accepted answer to ones own questions, since

We are happy to announce that the  follow question and answer feature is now live across the Network, including Stack Overflow, all Stack Exchange sites, and all Meta sites. (International Stack Overflow sites will have it turned on in a day or two once we have translations all set.) You can follow any question or answer (that you did not author) by clicking on the [follow] button that is shown in the menu immediately below the post (alongside the [share] button):    After you have followed a post, you will get inbox notifications for all new answers (in the case where you followed a question), comments, edits, and notices. You will not receive notifications for any action that you performed. As was mentioned in the earlier post, we are not making changes at this point to the notifications received by a post owner, or due to @mentions. The initial release had been planned to only include question following. Thanks to many folks who chipped in over the past few weeks, we are happy to release both question and answer following at the same time. These are available in both the regular and mobile views. We are still planning on two more related releases:  Follows profile tab and question listing filter: A tab for follows will be added to your user profile activity page. Each user will be able to view this tab that will provide a listing of followed questions and answers, with standard sorts, and the ability to unfollow from the listing. Users (with the exception of moderators and authorized staff) will not be able to see this information about other users (nor will it be made public in the API, SEDE, or data dumps). We will be renaming the Favorites feature to Bookmarks. As we mentioned in the preview post, the feature will be the same as Favorites, with the name and icon updated to more accurately represent user expectations and usage. And you will be able to both "bookmark" and "follow" a question.  We hope that this new feature will allow you to have better access to the content that you care about and want to keep tabs on. Update (June 11, 2020): The user profile tab and the rename of Favorites to Bookmarks have been released.


In answers to Emacs-related questions, I often see key sequences displayed as a cool keyboard key icon wrapping the keystrokes.  :  How does one generate these?

How are people showing keyboard "glyphs" on Super User? I looked at the Markdown help page and it didn't show anything regarding this. Here is  (question has been deleted since this was asked, so an archive link is provided instead):


I am trying to retrieve some pieces of data from a URL using regular expressions in Javascript.    const url = "/node_modules/@company/dl-atoms-control/README.md";     The following RegEx retrieves text preceded by the string "dl-" In this case "atoms":    const molecularTypePlural = url.match(/(?<=dl-)\w+/gm)[0];     I now want to use molecularTypePlural in a second RegEx to retrieve the string preceded by "dl-atoms-" which in this case is "control". I can't hard code this because the molecularTypePlural variable will have different values with different URLs. I have tried the below:    const packageNameRegex = new RegExp(`/(?<=dl-${molecularTypePlural}-)\w+/gm`); const packageName = nodePath.match(packageNameRegex);     However the RegEx doesn't return any results. Logging packageNameRegex reveals that  the RegEx seems to be incorrectly formatted:  "/\/(?<=dl-atoms-)w+\/gm/"   I think it might be a problem with escaping special characters but I'm not 100% sure. Could anyone show me where I'm going wrong. Thanks

I would like to create a String.replaceAll() method in JavaScript and I'm thinking that using a regex would be most terse way to do it.  However, I can't figure out how to pass a variable in to a regex.  I can do this already which will replace all the instances of "B" with "A".  "ABABAB".replace(/B/g, "A");   But I want to do something like this:  String.prototype.replaceAll = function(replaceThis, withThis) {     this.replace(/replaceThis/g, withThis); };   But obviously this will only replace the text "replaceThis"...so how do I pass this variable in to my regex string?


If $f$ is an analytic function defined in the unit disk $\{z \in \mathbb{C}: |z| <1 \}$ where for any $n >0$ we have: $$\left|f\left(\frac{1}{n}\right)\right| \leq e^{-n}$$ Find $f$ I know this can be solved using Taylor coefficients of $f$ as that suggested in the practice textbook problem. However, I cannot figure how to find $f$. Does someone know how to solve this or have a link to a similar problem?

I'm talking about complex function   $f$ is analytic function on a region $D$ that include the point $z=0$. for every $n\in N$ such $\frac{1}{n}$ is in $D$ , the function follows this condition $|f(\frac{1}{n})| \leq \dfrac{1}{2^n}$   is that function must be constant ?


The attached photo is clicked in a professional DSLR camera. How can I get a similar effect of blurred lights in an ordinary digital camera, Or How can I edit a image later to get this similar effect?

I have a compact digital camera, and in macro mode I can manage to achieve a blurred background, if the background is far enough away. Can this be done when taking non-macro pictures, and if not, is there a way to simulate it?  When I shoot portraits with my brother's DSLR, it is quite easy to fade out the background. But with my point and shoot camera, I haven't been able to take such photos.   I choose a large aperture for my camera but it still doesn't work. I know that standing further and zooming will result in a smaller depth of field, but it doesn't seem to be enough to get the really nice "bokeh" look. I've tried macro mode, and that will work if the subject is close enough and the background far enough away, but how can it be done with non-macro pictures?   Why are DSLR cameras are so much better in this area? What are the general recommendations to do this using a compact or super-zoom camera?


If you try to delete a useless usage guidance excerpt, you can't save the edit, because you get an error message that "Wiki Excerpt is missing." No kidding. That's the whole point!  Why is the excerpt absolutely required once it is ever populated, even for tags that are reasonably self-descriptive? It's nice to want to have guidance for every tag, but often it's far more practical to just rely on the tag name, and stopping an editor in their tracks can be harmful if they're just trying to help by clearing away guidance that's outright counterproductive. For example,  on ELL: "For questions that use the word 'which'." How about we not include  in that, OK? In cases like this, it would be far better to have nothing at all than to have that bit of drivel.  Even . Please allow editor discretion, rather than enforcing an inconsistently and unrealistically high standard for fixes to terrible excerpts.

Sometimes a tag wiki excerpt or body ends up with unacceptable or useless content: plagiarized text that must be removed, or a totally unhelpful dictionary definition. (For example:  — and I've seen this situation many times before.)  The only way to get rid of that content is to submit replacement text that meets the minimum length requirement. This is not always easy as writing a decent wiki, and especially a decent excerpt, requires subject knowledge.  Currently the users or even moderators who are alerted to unacceptable content in a tag wiki cannot remove that content without providing their own, which they are not always in a position to do. Yet these wikis would be better off with no content than with either unacceptable or unhelpful content, or some content written by a non-expert in a hurry.  Please provide a way for users to blank a tag wiki excerpt or body. I'm not sure what the reputation requirement should be: same mechanism as for tag wiki edits (suggested edits with approval), or only done directly by a user with the trusted user (20k) privilege, or moderator-only.


I'm creating my resume, and I have to write about my education.  from 2007 until 2012 - I was a student (I'm not any more). Now I have to write that in sentence that has meaning.  1.  I had been studying economics from 2007 until 2012.  2.  I have been studying economics from 2007 until 2012.  Also, I want to stress this, that's why I'd like to use 'Continuous', but which one?

A. I have been studying English for one year. B. I had been studying English for one year.  Could one who hears those sentences argue that "A" case implies "and I am still studying it" whereas "B" case implies "and I am no longer studying it"? If so, how are different in time frame the following sentences?  I worked in Colombia for ten years when the manager sent me to Italy.  I have been working in Colombia for ten years when the manager sent me to Italy.  I had been working in Colombia for ten years when the manager sent me to Italy.   Please, consider that the real situation is that I worked in Colombia from 1963 to 1973 and, for some reason, 1, 2 or 3 must  be written today. However I'm under the impression that only the "3" case is grammatical or, in any case, correct in reference to the real situation, although "1" case seems to be salvageable deleting the preposition "for". Can anybody explain?


Triangle ABC is isosceles triangle with AB = AC. And angle A = 20°. Point D is on side AC such that angle CBD = 70°. Similarly, point E is on side AB such that angle BCE = 60°. Now, points D and E are joined. Then find measure of angle BDE. I found other angles. I tried using sine rule. But, its getting harder by applying sine rule. I don't know whether I am missing some important theorem.  Please help.  I'm sorry that I'm unable to provide diagram.

I've been running in circles and couldn't give a rigorous mathematical proof that the angle is x = 20°.     Any idea? This is my try:  I got the answer $x=20^\circ$ using a computer program:


Problem statement : Let $x,y$ be integers, show that if $xy$ divides $x^2 + y^2$ then $x=\pm y.$  What I have tried:   I can reduce this to the case where $\gcd(x,y)=1$, since if $x$ and $y$ have a common factor, $d$ say, then $d^2$  divides through both $xy$ and  $x^2 + y^2$   This then allows me to introduce another equation $1=ax+by$ for some $a, b.$  But I then get stuck ...

Show that $X+\dfrac{1}{X}$ is not an integer number for any rational $X$ and $X \neq 1, X \neq -1$    I think we can substitue $X=\dfrac{P}{Q}$ but I don't know if I can now assume that $\gcd(P,Q)=1$


So, I'm a third year student studying mathematics. My goal has always been getting a PhD in math. I'm currently doing ok with my math (taking grad courses and stuff). However, as many other students, I have to take courses outside math. I'm currently taking a labor studies class right now. All the class talks about is how bad America is treating its workers, and why don't we raise minimum wage to 50 dollars per hours to help the poor workers and stuff like that. I don't agree with everything I learn in class, and I show my disagree. As a result, the professor gives me terrible grades for saying my opinions. My question is: Will that bad grad hurt my future? Can I explain my situation in my application?

When applying to a PhD program in the US, how does the admissions process work? If an applicant is weak in a particular area, is it possible to offset that by being strong in a different area?  Note that this question originated from this . Please feel free to edit the question to improve it.


I'm currently designing my first audio PCB. I've read a ton of discussions and guides about audio grounding, so I've decided to use single point grounding (with the point being last filter capacitor minus).   However, one question arised in my head and I haven't found an answer. Is it beneficial to the circuit to make a fill on the PCB, connected with ground at the single point?  It seems logical to me, that a fill on the PCB would reduce noise and crosstalk between signal traces, while connecting this shielding plane to ground in single point would eliminate all current return problems which normal ground fill would cause. Ideally, no current would flow through this plane, as whole circuit itself is connected following the idea of single point.  On the other hand, it could make the ground noisier, as the ground plane is sort of an antenna.  A following question would be - if my conclusion is correct, should I connect the fill to quieter preamp ground (which is more sensitive) or noisier power amp ground (which wouldn't care too much if its ground would collect some noise)?   Edit: To clarify: this is not a debate between single point and plane grounding. Grounding of the circuit WILL be done via routing components to the single point only by 1mm traces!   The point is: is it beneficial to put a separate fill on the PCB and connect it to the circuit ground in the single point (not connecting any component to the fill)? Will it increase or decrease overall noise if there is a screen added? Again - the fill will be connected to the ground at ONE POINT, no component connected to it. This is the PCB without any pours:  This is what my idea of screening fill would look like, notice that both bottom and top fills are connected to anything only under C8 cap, components are still connected to their single points:

Recently I had posted a seemingly innocent question on another forum. I was trying to keep a small and relatively simple circuit down to a 2 layer board and was asking about the shielding merits of a copper pour tied to analog ground, as opposed to dedicating unbroken separate plane used for ground. Though my question was only in reference to the shielding value of such a copper pour, a major controversy started on an entirely different point. In my layout I had created a virtual ground using the typical voltage divider feeding a unity gain configured OP amp, and then had run every single analog ground return to a point adjacent to the output of that virtual ground. I had also done a copper pour on the least busy layer and tied it to that same analog ground, again at that same single point. But there soon ensued a series of posts lambasting my use of such a convoluted "spider web" scheme, with many chiming in that I should just create a ground plane and just make all connections to the nearest available point of that plane ( through  via when necessary). Well doing so certainly makes for a cleaner and simpler layout visually. But having gone the "single point" route for so many years, and having mostly successful (meaning quite and stable) designs, I'm hesitant to change. Especially as some of the arguments spoke of single point grounds as something archaic, and relegated to vacuum tube circuits. What?   So anyway, just poking around, my research on the subject seemed to show two camps on this subject. One argument is that when an unbroken ground plane is available, it is always superior. The other argument says that if its a high frequency circuit a ground plane is better, but for a low frequency circuit (including audio), the single point ground method is better, mostly to avoid ground loops.  Of course I still have a dilemma, as prototype costs are constraining me to a 2 layer board if possible this time, and this means that my pseudo ground plane will, at best, be a copper pour, broken by some short traces here and there. But before adding that complexity or possible exception to the rule, I'd like to put this specific question out for general discussion: For an audio design involving OP Amps, when is a Single point" ground scheme the bast way to go, and when is just the simpler "nearest path to a ground plane" the better (or at least an adequate) choice.   By way of example, these two layered screen shots show two reasonably similar versions of the same board, which in reality is about 4" x 2.5". In the first you can see lots of long traces on both sides of the board culminating at a single pad labeled AGND. The second is nearly the same circuit, but this time the blue copper poor area is part of the analog ground net, so all those long traces have gone away in favor of the nearest path to the ground plane/ copper pour. Aside from all possible critique about other layout issues one might see, this is just an example. I'd really like to confine this discussion to the original question.   single point ground version   Nearest path to ground plane version


My computer speakers make a horrible sound while shutting down and I keep forgetting to turn them off before shutdown. I would like to prevent this with a "just in time" reminder. Something like a popup window that also delays shut down until I click a confirmation button would be great.

How can I run a command before the machine automatically shuts down?


I hope this question is not too generic.  Some weeks ago, I set up a new Q&A site for my collaboration.  I have added it to my search console dash board and I have submitted the sitemap.  Google lists 106 submitted URLs, but only 21 have been indexed. I can not see any errors on the dashboard.  Is this a normal behavior for a very low ranked web page? Should I just be patient and wait for people to link it more? Or is there something wrong with my configuration - somehow?

This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it?


Is it true that if we expand $(x+y)^n$ where $n$ is a prime number, then all the coefficients are divisible (except the first and last term) by $n$?  Note. There are many examples of when $n$ isn't prime, and the coefficients are not divisible by $n$.

I want to prove that if $p$ is a prime and $x,y \in \mathbb{Z}$, then $$(x+y)^p \equiv x^p+y^p \pmod{p}$$  So far I know that $$(x+y)^p = \sum_{k=0}^{p} \dbinom{p}k x^{p-k} y^k$$  A part of the above equation is supposed to cancel, I think, but I can't figure out a way how to make it cancel.


Since the last update whatever I do anything on my system a sound erupts like if i change the brightness using F2 and F3 keys or change volume or open any drive or folder or any file a voice repeats the whole process like on pressing down volumeF8 key a voice  volume  19 erupts from  speaker or I open any folder sound erupts that "new folder" is open.do anybody has idea what is happening on key press or opening any file or folder why this sound is coming whatever I do on my system. whatever I browse on Firefox any site anything I type it is repeated I am typing this question and it is being read out

I accidentally opened Orca Screen Reader from the Dash when I was trying to open Screenshot. Now everything I type or click on is spoken out loud.  How do I make it stop?  For reference, here is a screenshot of Orca Screen Reader running:


I am trying to play on a multiplayer for Minecraft on the PC.  All it says in the multiplayer server menu is "Scanning for games on your local network". However, it never finds the server.  How can I make this work?

My LAN server won't let my cousin join me or me join my cousin. It won't show up on the multiplayer screen - it keeps saying "scanning for LAN servers" but it never finds it. I am at his house and we use different computers but it won't connect. How can I fix this?


In TeX Live 2016 the following simple document fails to compile:  \documentclass[11pt]{scrartcl} \usepackage{amsmath} \begin{document} \[ \left( x+1 \right) \dots \left( x+8 \right). \] \end{document}   Several errors are thrown, the first of which are:  ! Argument of \zap@to@space has an extra }. <inserted text>                  \par  l.6 \[ \left( x+1 \right) \dots \left                                      ( x+8 \right). \] ?  Runaway argument? \left.......... ! Paragraph ended before \zap@to@space was complete. <to be read again>                     \par  l.6 \[ \left( x+1 \right) \dots \left                                      ( x+8 \right). \] ?    In addition, any of the following appear to cause the issue to go away:   Changing from scrartcl to article Removing the line \usepackage{amsmath} Not using \left( and \right) Using an earlier version of TeXLive   I'm assuming this is a bug somewhere, but I'm not sure how to fix it (other than just manually using \cdots instead of \dots, I suppose). Does anyone have any ideas on how to make things behave the way they should?  [EDIT: to clarify, compiling with PDFLaTeX, on TeX Live 2016, Arch Linux.]

I have the following MNWE and don't understand why this fails.   \documentclass{article} \usepackage{amsmath} \begin{document} $\dots \left. \right.$ \end{document}   Understanding the relevant code in amsmath proves to be rather difficult and I can't find a mention anywhere that this is somehow not OK to do. Of course I can use some of the more specialized dot commands to get rid of the guessing \dots does. I would be extra grateful for an explanation of what the trick with \uppercase in all the helper definitions(\striplong@...) and using \meaning in \mdots is.


I'm doing a little project for some class at my university. In one of my functions I have a list, like:   x = ["q0", "q1", "q2", "q3", "q4"]   What I want from that list is to create a dictionary, that I'll use to store values and then get the values like i was searching in a matrix, that combine the values of the list, like this:   dic = {("q0", "q1"): "", ("q0", "q2"): "", ... ("q3", "q4"): ""}   I did it this way:   part1 = x[1:] part2 = x[:-1] dic = {} for v in part1:     for r in part2:         if v != r and (r, v) not in dic.keys():             dic[(v, r)] = ""   I used a if because i don't want repeated values, like:   ("q1", "q1")   And I also don't want opposed values, like:   ("q2", "q3"), ("q3", "q2")   My question is if there is a better way of doing this. Better than using a for inside a for. (When I say better I mean faster) And if there isn't a better way, I wonder if there is a more clean way to write this code. Maybe using list comprehension.

I have a list with 15 numbers in, and I need to write some code that produces all 32,768 combinations of those numbers.   I've found  (by Googling) that apparently does what I'm looking for, but I found the code fairly opaque and am wary of using it. Plus I have a feeling there must be a more elegant solution.  The only thing that occurs to me would be to just loop through the decimal integers 1–32768 and convert those to binary, and use the binary representation as a filter to pick out the appropriate numbers.   Does anyone know of a better way? Using map(), maybe?


Do both of the following sentences have the same meaning?       1- My salary is twice higher than yours.   2- My salary is twice as high as yours.

What do the following sentences actually mean?  Are they the same in meaning?        The cost of living is twice as high in New York as it is in Tokyo.   The cost of living in New York is twice as high in Tokyo.   The cost of living in New York is twice higher than in Tokyo.   The cost of living in New York is two times higher than in Tokyo.      If they have the same meaning, then can I actually use them as a basis for composing other sentences having the same meanings? Such as:     1a. Your child is a hundred times as adorable as your pet dog.   1b. Your child is a hundred times adorable than your pet dog.      2a. Her room is twice as large as mine.   2b. Her room is twice larger than mine.


I can think of two times in the TV show when a White Walker has essentially caught a human, and then just let them walk away.   The survivor from the Night's Watch in the first episode. Samwell Tarly at the Fist of the First Men when he was too slow to run away.   Is there ever any explanation or evidence why the White Walkers would let lone humans escape?

In the first episode of the first season, , three rangers come across a wildling camp killed by a White Walker. The walker then kills 2 of the rangers, but allows Gared to live.                                  In episode 10 of the second season, ,  sees an army of wights led by a White Walker. The walker spares (ignores) Samwell Tarly but attacks the camp at the Fist of First Men. (Also noteworthy is that some wights also pass Sam just before the White Walker on his horse does, and either don't see him or ignore him.)                                  The walkers clearly spared these two people because they could have overpowered and killed either.  From a tactical point of view, the walkers gain nothing by sparing anyone. They are better off killing the person and thereby recruiting the person into their undead army. And the downside is that the survivor can warn others who would then flee the walkers. The result is that the walkers have fewer people to recruit because many humans fled.  Is there an explanation for why the White Walkers sometimes spare somebody?  I prefer an answer from the books, but I will take one from the TV shows.


I have done extensive research, and yet there is no straightforward way to install the tor browser bundle on ubuntu 13.10 to work. Can anybody help me install the tor browser bundle?  Acer Aspire V5  Ubuntu 13.10

I tried to install Tor on my new version of Ubuntu, but it seems that Tor is not available in the repositories.  How else can I install and use Tor?


One thing my professor failed to explain was whether or not wrapper classes (such as Integer.* or Double.*) took up more RAM space because they have the format of an object reference and not a primitive data type.

Is the memory space consumed by one object with 100 attributes the same as that of 100 objects, with one attribute each?  How much memory is allocated for an object? How much additional space is used when adding an attribute?


$sampleText = "Episode 8 - Dansk dokumentarserie. Jørgen og John drar ut for å";   I need to convert it to json and encode it in a way to make it AJAX safe.  I tried following encoding :  //$name = htmlentities(utf8_encode($sampleText), ENT_QUOTES); //$name = htmlentities($sampleText, ENT_COMPAT, 'UTF-8'); //$name = htmlentities(utf8_encode($sampleText), ENT_COMPAT);   Sometimes it works but in some cases I get \. which makes json invalid.  Example : Gäster är kulturminster Alice \. Bah Kuhnke och komikern William Spetz.Kategori: TalkShow \..  Invalid JSON due to string \. :  [{"name" : "Humortalkshow."},   {"name" : "Temat 2013 var \."},   {"name" : "Talkshow \."}]   Could you please help me encode the foreign characters in a proper way.

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


I am Nepali passport holder traveling to Nepal with China Southern Airlines from New York. I have 6 hours transit (both back and to Nepal) in Guangzhou, China. I am not getting out of the airport. I wonder if I am eligible for 24-hour visa free transit. I am posting this because I saw nothing on this specific airport or China Southern Airlines online. Is Nepali passport has some rules on it?

I'm hoping to get a flight which requires me to be in China for 28 hours before the connecting flight out.  I'm happy to sit in transit if I have to.  However, I've read one site that said 12 hours is the maximum transit permitted.  Can anyone find either:   Definitive information saying how long transit in Beijing/Shanghai airports are for Or can I get a transit visa on arrival, in which case I'll go check out the city for a day ;)   I'm on a New Zealand passport if it makes a difference.  Failing all that I'll pick up a visa in Mongolia en-route, I'd just rather not have to waste a few days doing so if I don't have to!


Currently, I am making a program that detects a date in an HTML source and compares it to the current date.  While thinking out my code. I realized that I've run into a little problem. The HTML I'm scraping and comparing uses a format like this "December 23rd, 2014". What I have so far will not be able to compare to that.  My code that prints current date does not add a "st,nd,rd, or th" to the day of the month.  time = Time.new puts time.strftime("%B %d, %Y")   Can anyone find a solution for this?

I want to display dates in the format: short day of week, short month, day of month without leading zero but including "th", "st", "nd", or "rd" suffix.  For example, the day this question was asked would display "Thu Oct 2nd".  I'm using Ruby 1.8.7, and  just doesn't seem to do this.  I'd prefer a standard library if one exists.


I am writing my thesis for high school and i need to put an image after some text, but as i do as i always did with the \begin{figure} etc. it appear at the start of the page before the text I writed before, how should I solve this?

How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference


I'm trying to make a swap function in java but why is this not working?  void swap(int a, int b) {    int temp = a;    a = b;    b = temp; }

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


Is $\sqrt{x}$ uniformly continuous on $(0,1)$?  And can anybody give me a function that is uniformly continuous on some interval but $f^2$ is not?

Prove that the function $\sqrt x$ is uniformly continuous on $\{x\in \mathbb{R} | x \ge 0\}$.  To show uniformly continuity I must show for a given $\epsilon > 0$ there exists a $\delta>0$ such that for all $x_1, x_2 \in \mathbb{R}$ we have $|x_1 - x_2| < \delta$ implies that $|f(x_1) - f(x_2)|< \epsilon.$  What I did was $\left|\sqrt x - \sqrt x_0\right| = \left|\frac{(\sqrt x - \sqrt x_0)(\sqrt x + \sqrt x_0)}{(\sqrt x + \sqrt x_0)}\right| = \left|\frac{x - x_0}{\sqrt x + \sqrt x_0}\right| < \frac{\delta}{\sqrt x + \sqrt x_0}$   but I found some proof online that made $\delta = \epsilon^2$ where I don't understand how they got? So, in order for $\delta =\epsilon^2$ then $\sqrt x + \sqrt x_0$ must $\le$ $\epsilon$ then $\frac{\delta}{\sqrt x + \sqrt x_0} \le \frac{\delta}{\epsilon} = \epsilon$. But then why would $\epsilon \le \sqrt x + \sqrt x_0? $ Ah, I think I understand it now just by typing this out and from an earlier hint by Michael Hardy .


Is a one-time pad still breakable on a depth of 2+ if the plaintext is completely random?  I'm assuming this idea is wrong, mostly because it occurred to me, but let me walk you through my logic so you can concisely correct me:   A one-time pad is unbreakable on a depth of 1 because a comprehensive brute-force attack will yield numerous reasonable plaintexts. Upon a depth of 2 or more (e.g., the same pad used with multiple plaintext messages) it becomes breakable:  Brute-forcing message $A$ may result in (say) 10 plaintexts Brute-forcing message $B_n$ may result in 10 plaintexts each The key that commonly results in valid plaintexts is probably the one-time pad used.  If the plaintext is completely random, then this attack won't work, as there is no way to discriminate between "plaintext output" and incorrect outputs.   I was thinking of ways to pass encryption keys and IVs - which, if properly generated, should be very random data - between two systems.  Let's presume they have a trusted channel by which they can exchange the one-time pad, but wish to use an untrusted channel for exchanging more voluminous data.  They can use symmetric encryption to protect data across the untrusted channel if they have away to agree upon the keys used for the symmetric encryption.  If a one-time pad could be used to securely exchange symmetric keys across that untrusted channel, then the sparse use of the trusted channel (exchanging the one-time password) could enable encryption across the untrusted channel.  Would this, instead of a one-time pad, be a shared secret? A key derivation function?  Some "please don't beat me up" caveats:   Yes, I realize this sounds like I'm breaking the "never invent a new cryptosystem" rule, and I realize the importance of that rule.  Rather, I'm using this as a gedankenexperiment to understand encryption better, and/or as a way of identifying an existing model that describes what I'm suggesting. Yes, I realize SSL is the appropriate model for what I'm suggesting - the certificate exchange and handshaking is the "trusted channel", enabling symmetric encryption of the general data over the "untrusted channel".  I have reason to contemplate lighter-weight solutions.   I humbly appreciate any edification you can give me.

I understand the basics of OTP: $|\text{key space}| = |\text{plaintext space}|$ implies perfect security, key reuse destroys this.  Cryptanalysis on the $N$-Time Pad for $N > 1$ involves finding patterns in the ciphertext; this, however, all seems based on the premise that patterns exist in the plaintext (e.g. English language).  My question is: if $m_1$ and $m_2$ are two truly random strings, and they are both encrypted with the same OTP key to yield $c_1$ and $c_2$, is it possible to recover $m_1$ and $m_2$ from $c_1$ and $c_2$?  In other words: while "perfect security" (aka perfect indistinguishability) is obviously lost (constructing a distinguisher for two messages is trivial), is the plaintext still safe?


Should it be:  1KG or 1 KG?  1M or 1 M?  1PM or 1 PM?  1GB or 1 GB?  1Kmph or 1 Kmph?  1Kbps or 1 Kbps?  or anything else?

I remember reading somewhere that if a unit is abbreviated as one character, there must not be a space between the number and the unit (e.g., 5m, 26K). If the unit is abbreviated as two or more Characters, there must be a space between the number and the unit (e.g., "10 km", "USD 5").   Can you please help me find the source again? Is this recommendation correct?


Lots of symbols have their pronunciations. For instance, "$\tbinom {n}{k}$" is pronounced "$n$ choose $k$", and "$\forall$" is pronounced "for all".  The symbol "$\mapsto$" is used to represent a , as in $$x \mapsto f(x)$$ How to pronounce this symbol?

I am doing , and am having a few problems with function notation. I understand the form f(x).  What does the form f: x ↦ y mean? Could you also give one or two examples?  And, if possible, state your source. Thank you.


I was studying permutation groups from the book "Abstract Algebra and Applications" by Karlheinz Spindler in which page 553 I came across the following interesting problem. It is on the famous "The Fifteen Puzzle" for which I am unable to upload the picture but rather I would try to use mathematical notation.   Imagine the fifteen puzzle grid is being presented by the following $4\times 4$ matrix given by  $$\left[\begin{matrix} 1 & 2 & 3 & 4\\ 5 & 6 & 7 & 8\\ 9 & 10 & 11 & 12\\ 13 & 15 & 14 & \circ  \end{matrix}\right]$$ where $\circ$ is the empty place in the grid. We can slid the "numbered tiles" through blank space and are supposed to bring down the final structure as  $$\left[\begin{matrix} 1 & 2 & 3 & 4\\ 5 & 6 & 7 & 8\\ 9 & 10 & 11 & 12\\ 13 & 14 & 15 & \circ  \end{matrix}\right]$$  Now the questions are    Can some one tell me exactly what am I supposed to do now to solve the problem ?

You might know the :  $\hskip1.4in$  Concerning the solvability, Wiki says:     The invariant is the parity of the permutation of all 16 squares plus the parity of the taxicab distance (number of rows plus number of columns) of the empty square from the lower right corner. This is an invariant because each move changes both the parity of the permutation and the parity of the taxicab distance. In particular if the empty square is in the lower right corner then the puzzle is solvable if and only if the permutation of the remaining pieces is even.   I don't get what exactly is meant with the  in this special case?


Bjarne Stroustrup, being asked if...  «Can I use "new" just as in Java?»   He answered «Sort of, but don't do it blindly and there are often superior alternatives.» and showed how to do that, with the following code:    void compute(cmplx z, double d) {     cmplx z2 = z+d; // c++ style     z2 = f(z2);     // use z2      cmplx& z3 = *new cmplx(z+d);    // Java style (assuming Java could overload +)     z3 = f(z3);     delete &z3;  }   I tougth that whatever the language be, the "new" works in the same manner i.e. allocates space for an object and assigns a pointer with the address of that object.   I'm wondering what's the difference (in terms of performence or whatsoever) between:  MyClass *ptr = new MyClass(); ... delete ptr;   and   MyClass& ref = *new MyClass(); ... delete &ref;    Any ideas about this?   Thank you

I know references are syntactic sugar, so code is easier to read and write. But what is the difference between a pointer variable and a reference variable?


I have a problem with inputs in the code. In the program I want to create a menu which allows us to put shapes in it. In the first option when I write square, circle or rectangle the program should ask me side, radius or height and width. However when I write the kind of the shape the program goes back to menu as nothing happened. Could you help?      import java.util.*;     public class test   {      public static void main(String[] args)       {          Scanner scan = new Scanner(System.in);          Scanner scan2 = new Scanner(System.in);          String kindofshape;          int choice, radius, width, height, side;           do          {             System.out.println("(1) Add a shape to the list");             System.out.println("(2) Get the total area of the shapes");             System.out.println("(3) Show information of the shapes");             System.out.println("(4) Quit");             System.out.println("Choice : ");             choice = scan.nextInt();              if (choice == 1)             {                 System.out.println("enter the type of the shape");                 kindofshape = scan2.nextLine();                 if(kindofshape == "circle")                 {                     System.out.println("enter the radius");                     radius = scan.nextInt();                               }                 if(kindofshape == "rectangle")                 {                     System.out.println("enter the width");                     width = scan.nextInt();                     System.out.println("enter the height");                     height = scan.nextInt();                    }                 if(kindofshape == "square")                 {                     System.out.println("enter the width");                     side = scan.nextInt();                  }             }          }while(choice != 4);        }   }

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


First :  function A() {          for (var i = 0; i < 10; ++i) {             //...         }         console.log(i); //i is undefined        // i dont get global i         for (i = 0; i < 10; ++i) {             //...         }      }   When i execute A() , i donot get global var i . But this:      function B() {        // i get global i         for (i = 0; i < 10; ++i) {             //...         }      }   When i execute B() , I get global i . So why i cannot get the global when i execute A() ?

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


If $$D_{2n} = \{r^i s^j, \quad 0 ≤ i ≤ n − 1, \quad 0 ≤ j ≤ 1 \}$$ is the dihedral group of order $2n$, show that the center of $D_{2n}$, $n > 2$ is the trivial subgroup if $n$ is odd, and is the subgroup $\{e, r^{n/2} \}$ if $n$ is even.  I don't know how to proceed with this one. Kindly help. Thanks in advance.

I have posted a proof below, and would appreciate it if someone could review it for accuracy. Thanks!   Problem:   Let n $\in$ $\mathbb{Z}$ with $n$ $\ge$ 3. Prove the following:   (a) Z(D$_{2n}$) = 1 if $n$ is odd.   (b) Z(D$_{2n}$) = {1, r$^k$} if $n$ = $2k$.   Note that $r$ and $s$ generate D$_{2n}$ with the group presentation { $r$,$s$ | $r$$^n$ = $s$$^2$ = 1, $rs$ = $sr$$^{-1}$ }   Proof:  part (a)   Let $n$ $\ge$ 3 where $n$ $\in$ $\mathbb{Z}$ and $n$ is odd.   For any x $\in$ Z(D$_{2n}$), x must commute with both $s$ and $r$, since both are in $D_{2n}$. Note that if $x$ commutes with both $s$ an $r$, then $x$ commutes with any element of $D_{2n}$ since $r$ and $s$ generate D$_{2n}$.    Then for any x$\in$ Z(D$_{2n}$), we have $xr$ = $rx$, where x is of the form $x$ = s$^j$r$^w$ (any such element can be arranged into this form via the relation $rs$ = $sr$$^{-1}$ and the fact that $r$ and $s$ generate D$_{2n}$). Note that since r and s have finite order, the exponents are modulo n and modulo 2 for $r$ and $s$ respectively.   Then we have  s$^j$r$^w$$r$ = $r$s$^j$r$^w$.   Which implies s$^j$r$^{w+1}$ = s$^j$r$^{w +- 1}$  In the case where the power of r on the RHS is $w$ - 1, it is clear we cannot have equality unless |r| = 1, which it is not. Note that if $j$ is even then we have only the $w$ + 1 case. Hence $x$ may be of the form $1$$r$$^w$ = $r$$^w$.   Also we have that x must commute with $s$, hence $s$$x$ = $x$$s$.   Then $s$$r$$^w$ = $r$$^w$$s$.  Which implies $s$$r$$^w$ = $s$$r$$^{-w}$.   Applying s$^{-1}$ to both sides we arrive at the task of finding when r$^w$ = r$^{-w}$ i.e when $w$ = $-w$. But since r has finite order we have:   $$ \bar{w} = (n-1)*w $$   where $\bar{w}$ is the residue class of w modulo n. Hence for some a $\in$ $\mathbb{Z}$$_+$   $$ w + an = wn - w $$  $$ 2w = wn - an $$ $$ 2w = n(w-a) $$   Now since 0 $\lt$ w $\le$ n we have that the LHS is greater than 0. Also since n $\ge$ w then (w-a) $\le$ 2, since otherwise the RHS would be greater than the LHS. So since n is odd we must have that (w-a) is even and hence (w-a) = 2, implying that 2w = 2n and hence n = w.   Hence x = $r$$^w$ = $r$$^n$ = 1. So Z(D$_{2n}$) = 1.   part (b)   From the argument above any x $\in$ Z(D$_{2n}$) must be of the form $s$$^j$$r$$^w$ for j even and j $\in$ $\mathbb{Z}$. Then x is of the form $r$$^w$ for $0$ $\lt$ w $\le$ $n$. Since $n$ is even we have the equation below is satisfied when $2w$ = $n$ or $w$ = $n$, since (w-a) $\le$ 2 but also (w-a) $\ge$ 0 for (w-a) $\in$ $\mathbb{Z}$$_+$.   $$ 2w = n(w - a) $$   Hence $r$$^w$ $\in$ Z(D$_{2n}$) when $2w$ = $n$, as desired.


I have searched for this, and while I have found questions that brush on the same issue, my question wasn't fully adressed by them. , namely, is very similar, but I still don't totally get it. So, let us have two containers, both of them have a volume of liquid $V$, bottom area $A$ and filled with the same fluid of density $\rho$. One of hem has a liquid column of height $h$ and the other one $H>h$.  According to hydrostatics, the pressure at the bottom of the containers is the following  $P1=\rho*g*h$ $P2=\rho*g*H$ $P2>P1$  On the other hand, we could look at the fluid as if all of its weight was being supported by the bottom wall (I realized that this might be my mistake while I was typing this. I'm gonna finish anyway to get some input from people who understand the issue better.) That assumption would lead us to:  $P1=\rho*V*g/A$ $P2=\rho*V*g/A$ $P2=P1$  Which is inconsistent with reality. I arrived at this problem by imagining what would happen if we put a very thin and long straw filled with fluid on top of a container, which would make the pressure $P2=\rho*g*H$ go really high by increasing $H$, which would mean that we could make any container fail by excessive stress if we put a long enough straw on top of it, which is absurd. In this case, the second analysis kinda makes more sense because if you don't increase the volume, you basically also don't increase the pressure, but I know this has to be wrong since pressure does depend on height of fluid column. I guess this is kind of two questions in one, as I have one question that asks for correction on the concepts I used to calculate something and another one which is the question about how the absurd situation doesn't happen. If you prefer to focus on "one question", please focus on the second one, since it is the one that I feel less able to tackle myself. FINAL ANSWER: I have been convinced. I thought the situation on the following video was absurd/impossible, and it isn't. My mind is settled. Thanks for your answers people!

The hydrostatic paradox, states that the      height of the water in any container is independent of the shape of   the container.     This does make sense since it is only the height of the fluid relative to ground which determines the pressure, and it is the pressure equilibrium that decides the shape of the fluid. But then consider the (B) container in the figure below.     The pressure at a particular depth say, $h$ is same as in the case of the cylindrical container. But in the cylindrical case (A), any element of fluid is in equilibrium because the difference in pressure of the fluid element above it and that below it exactly balances the weight of the element. Extending this argument to (B), for any element at the edge, the pressure of the fluid above is the same as in the case of the cylindrical container, but below it is the surface of the container. This container, is in equilibrium with the atmospheric pressure outside, and therefore, would be exerting pressure equal to the atmospheric pressure onto the fluid within, which would not be enough to maintain the equilibrium of the fluid element. How then can the equilibrium of the fluid element at the edge be explained?


For example, take the Wolverine character.  Wolverine in comics look like this:    Whereas in movies he looks like this:    Why are the costumes not the same in the comics and their movie adaptations?

I'm just wondering why Wolverine does not appear in his iconic costume when even in The Wolverine, there is apparently a deleted scene to show such a costume?    This deleted scene can be scene in the DVD/Home Release extras.


Is it dangerous to travel in Russia, as a dark-skinned Muslim?   while travelling by train from St Petersburg to Vladivostok. Skolkovo, Moscow Oblast Sankt-Peterburg, Russia Moscow, Russia   Robbery, racist attacks, forced feeding of pork and alcohol, and so on?  Explain why.

I was chatting with a friend after I saw his photos in Russia (Petersburg). He is a white British dude who has been to many, many, many countries. On the other hand, I am a pure Arab who looks like a typical Middle Easterner or North African, who has also been to many countries, but never to Russia or its neighbors.  Anyway, it seemed like he really liked Russia, so I told him it will be in my list. He told me "you do not belong".  At first, I wasn't sure what he did mean. He started explaining and told me stuff like "you will be hassled for no reason in some parts of the city" and "the police will stop you every few hundred meters asking for money". He made sure to make me believe that's all because I do not belong.  Can someone clarify this? Of course, some of this is hyperbole to help convey the point, but to what extent?  Note: The friend is . If you think the question is wrong, feel free to downvote him ;)


So far, this is my models.py page:  from django.db import models from datetime import date from django.conf import settings  class Star(models.Model):      thumbnail = models.TextField()     title = models.CharField(max_length = 200)     description = models.TextField()     star_power = models.TextField()      def __str__(self):         return self.title  class recent_update(models.Model):      title = models.CharField(max_length = 200)     description = models.TextField()     video = models.TextField()     date = models.DateField(("Date"), default=date.today)     ordered_videos = recent_update.objects.order_by('-created_date')      def __str__(self):         return self.title   yet my terminal says that recent_updates is undefined. I need to organize the model content so that the most recent model created comes at the top of the page; the oldest model goes at the bottom of the page.

Is it possible to set the default sort order for a model to a field from a related model (rather than the integer key) i.e. something that yields a SQL order by clause with a field from both models? If so, how? I can do this via query_by but I can't figure out how to set it by default. Thanks.  class Foo(models.Model):     name = models.CharField(max_length=50)  class Bar(models.Model):     related = models.ForeignKey(Foo)     bar_date = models.DateField()      class Meta:         ordering = ('bar_date', 'related.name', )


I provided some feedback on an answer and downvoted it. Very soon after I received 3 downvotes for random answers I posted (which generally had upvotes) within the same minute and the answer I downvoted was removed.  Is behaviour like this captured and monitored? Whilst I cannot say for sure that a person did this maliciously, it seems likely in this case. I know it's only points so I don't mind but I am interested in what is done "behind the scenes" to stop this kind of behaviour.

I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back?


I'm having trouble working with strings in C. Excuse the informality, I'm usually on Math Stackexchange. Here is my function which takes an array of strings and returns a randomly selected one. randint(int n) is a function which returns a random integer from 1 to n.  int rand_word(const char ARR[]) {     int r = randint(sizeof(ARR));     return(ARR[r]); }   Here is my main():  int main() {     const char *WORDS[3];      WORDS[0] = "a";     WORDS[1] = "b";     WORDS[2] = "c";      printf("%s", rand_word(WORDS));      return 0; }   I expected to see either "a", "b", or "c" printed.  [Error] cannot convert 'const char**' to 'const char*' for argument '1' to 'int rand_word(const char*)'   Essentially my confusion is between data types. What have I done wrong? Thanks.

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


I am a member of both Quora and some Stack Exchange sites. Sometimes, I see that the same question is asked in both.   In such cases, is it OK for me to copy posts from Quora to Stack Exchange or vice-versa? Would I be violating any terms of service?

What with  today, possibly this is a good time to ask: who actually owns the copyright to questions, answers and comments submitted to StackOverflow and relatives?  Over in , we have the OP reaching the conclusion that SO owns the copyright and is licensing it under CC-Attribution-Sharealike, with no apparent confirmation or denial from staff, and in  we have a moderator asserting that Jeff owns the copyright to SO content.  As I note in a comment on the latter, though (which was met with deafening silence), I'm failing to find any evidence that this is the case.  I've looked for any kind of terms of service I may have agreed to indicating that I am signing over ownership of my words when I hit submit, and I can't find one.  Certainly the fact that I'm agreeing to CC-Attribution-Sharealike licensing is clear enough, but it seems to me as if I am retaining copyright while agreeing to those licensing terms, and S[OFU] is using what I have written under that license.  What's the deal?  Did I forget about something that I agreed to in the signup process (and if so, why can't I find it afterward)?  Do the owners and administrators of S[OFU] believe that they own copyright to the UGC?  Just what is going on here?  Edit as to why this matters (from answer comment thread): If I retain copyright, I can also choose to license the original content to other parties under other terms (such as using a zero-requirements license, using an attribution-required license without sharealike, etc). If SO has the copyright, I can't.


Searching for a job on SO Careers, you can check the Allows remote option. Then, all listed results will show a WORK REMOTELY sort-of tag.  Are both expressions synonyms or do they have a slightly different meaning?  And how can I distinguish those jobs where I can "sometimes" work from home from those ones where I can live, for instance, in another country?

When a posting is marked "allows remote", does it mean work in the office some days, work from home some days?  Or does it mean you could actually live out of town and maybe fly in as needed?  The reason I ask is I'm really interested in public facing software rather than internal/enterprise stuff, and most of that seems to happen in a few very expensive cities.  Given it's so hard to hire in places like SV/NYC, it seems like it could be a good scenario for companies if a developer had a really solid list of accomplishments, but I don't know how many companies think this way.


Where can I get a list of all the Stack Exchange sites available?  I have seen the list in the footer of Meta, but I'm not sure if this is the complete list.

Where can I find a list of all the Stack Exchange sites?  I need to ask a question about cars (where my total knowledge is about zero) but I can't find a cars Stack Exchange site - tried guessing all the obvious (and pun based) names.  I assume the list of a dozen or so at the bottom of this page is only a subset? There must be a site on a topic as geeky as cars!  A list of future/beta sites would also be useful - I found a few on topics I'm interested in only after they had been up for a while.


I want to add some days into a given date and below are my codes: Example: Given date = 2015/11/27 11:00, number of days = 2 My result should be 2015/11/29 11:00..  function setEndDate(date) {     var duration = $("#duration").val();     var dValue = parseInt($("#showDValue").val()) * 7;      if (duration == "Week(s)") {          date.setDate(date.getDate() + dValue);     } }   But i m getting error of this :  TypeError: date.getDate is not a function   Any solution?? Please help...

How can I redirect the user from one page to another using jQuery or pure JavaScript?


As a root user, I created a file in / directory. I can only read this file when logged in as normal user (say A) as expected.I changed the ownership to A.Now A can read as well as write.But when I try to delete it, permission denied message comes.Can anyone explain why?

If I create a file and then change its permissions to 444 (read-only), how come rm can remove it?  If I do this:  echo test > test.txt chmod 444 test.txt rm test.txt   ...rm will ask if I want to remove the write-protected file test.txt. I would have expected that rm can not remove such a file and that I would have to do a chmod +w test.txt first. If I do rm -f test.txt then rm will remove the file without even asking, even though it's read-only.   Can anyone clarify? I'm using Ubuntu 12.04/bash.


I've bought cheap Verbatim Vx500 SSD for my media server's boot drive. Cloned system drive to  it with Aomei Partition Asisstant and everything works. But today I've noticed that Windows10 thinks it is an HDD. It defrags it and in Task manager it aays directly type: HDD. How do I switch it to SSD? Is there some registry key for it?

I upgraded my old computer with a Samsung EVO 850. I did a clean Windows 10 installation.  Installed Samsung Magic and fixed all the AHCI settings. Now I have full 6Gb/s transfer speed.  However, my problem is Windows "Optimize Drives" tool wants to defrag my SSD like a hard drive. As far as I know, this is bad.  The rest of the OS works fine, and my 3rd party programs see that it's a SSD.  CPU: Intel Core i7 (4th gen) Mobo: Asus P7P55DE_PRO RAM: 8GB


We know that derivative of $x^n$ is $nx^{(n-1)}$ if $n$ is an integer. My question is how do we define derivative of $x^r$ is $r$ is an irrational number. For example what is the derivative of $x^\sqrt2$ or $x^\pi$?

Consider the real-valued function  $f(x)=x^r$ where $r$ is a real number.  (1) For what values of $x$ and $r$, is this function differentiable?  (2) How do you prove the power rule, when $f(x)$ is differentiable?  It would be nice if the proof is accessible to a 12th grade student.  EDIT: Perhaps, I have not been very clear about my question.  I am not satisfied with the "textbook proofs" I have seen.  Please established the existence (of the derivative) first before proving the power rule.  That is, please consider first question first.  This is the reason why I call the question a mathematical engineering question.  (If we can we bring high level math down to Grade 12 level, without loosing precision, then I call it good mathematical engineering.)


My son has played the small version of Minecraft on an Android tablet and wants the full version (either PC or Xbox 360), but we do not have Internet access at home. Will he be able to play the game?

My son would like to play Minecraft. If I download it to his laptop can he play it without an internet connection?


Let us have $a,b,c$ arbitrary positive numbers. Prove: $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \ge 3$ I have tried many things, but none of them seemed to work. Any ideas? (If duplicate, I am sorry, didn't see it yet) :)

Suppose $x,y,z$ are real positive numbers, prove that: $$\dfrac{x}{y} +\dfrac{y}{z} + \dfrac{z}{x} \ge 3$$ with equality when $x=y=z$.  Can someone help me find an easier solution? I started with assume only two are equal, without loss of generality, $x=y$. Then we get $$1 + \dfrac{x}{z} + \dfrac{z}{x}$$ $$1 + \dfrac{x^2 + z^2}{xz} = 1+ \dfrac{(x-z)^2 + 2xz}{xz} = 1 + 2 + \dfrac{(x-z)^2}{xz} \ge 3$$ To prove the general result I considered using a derivative with respect to $y$ to show that, starting with $x=y$ and increasing $y$ by a tiny amount, will show the equation's derivative as positive. I haven't gotten this to work yet. Any ideas?


How can I change the default icons for a particular file extension type , for example, the .tex file?  I have tried with      assogiate   , but it cannot do the job, it seems  I am using Ubuntu 12.10 with Unity desktop manager.

I'm trying to change the icon for application/x-hwp files. I've added the icons to the proper places, and checked it with assoGiate (after reading ). It shows that my desired icon is associated with the file type. Nevertheless, Nautilus is still showing the old icon. How can I make Nautilus show the correct icon?


When I click "log out" the site shows me as being logged out, but I can log back in again by just choosing "Google" option from the log in page. I'm not taken to google.com to enter email/password again.    I've tested to repro, as below.     Before starting each test, I started with a clean browser - no cache, cookies, history - I wiped everything "log out" was done by the drop down menu OS: Debian 8 Browser: Iceweasel 31.8.0     TEST 1   Clicked "log in" on MSE Redirected to MSE login page (3 options) Clicked "Google" Redirected to google.com (login form) Entered credentials, was redirected back to MSE (was logged in) Clicked "log out" on MSE Redirected to log out confirmation page (clicked "log out") Redirected back to main MSE page shown as being logged out Click "log in" Clicked "Google" on login page Am logged in     The problem  After logging out and the site showing me I am no longer logged in, then clicking "log in" I am not redirected to Google to enter my credentials (email/password), when I should be as I had previously clicked "log out" on Stack site.    This means if I click "log out", someone/anyone with access to my computer can click "log in" and then click "Google" and are logged in to my account. I don't have this security issue personally, but many users might with shared devices, public computers, shared work PCs, etc.    Regardless of potential users this affects, I would have thought clicking "log out" would mean if I click "log in" on the same browser I would have to enter my credentials again with Google.      Other tests  TEST 2  The same happens on Stack Overflow following "TEST 1" exactly (so this not MSE specific).    TEST 3  It doesn't matter which site I log in and out of at all. Once I've been logged in, after clicking "log out", I can click "log in" and choose "Google" and without having to enter my credentials I am logged in to all sites again.    Even if I log out on one site, go to a site I've not been to yet, and click "log in" there.    Other  I don't have a Facebook or Stack account, only log in through Google, so cannot confirm if this is specific to Google auth or not.      Cookies  (This is mostly info Stack will use if needed/if it helps).    Based on TEST 1.    Before starting TEST 1:    0 cookies.    After logging in to MSE first time:    All cookies have the same following info:  Host: .meta.stackexchange.com Path: / Expires: At end of session Secure: No   Individual cookies (all contained the above info, but removed from below to shorten list; also removed "value" as it's pointless info):    Name: __cfduid HttpOnly: Yes  Name: __qca HttpOnly: No  Name: _ga HttpOnly: No  Name: _gat HttpOnly: No  Name: acct HttpOnly: Yes  Name: prov HttpOnly: Yes   After clicking "log out":    The same as above except cookie "acct" was no longer there, and an additional one only appeared after I'd clicked "log out":    Name: gauthed Value: 1 Host: meta.stackexchange.com Path: / Expires At end of session Secure: No HttpOnly: No   When I log in again (having logged out but now without having to re-enter credentials to log in):    "gauthed" is gone and "acct" returns.    "acct" is a different value to what it was when I was initially logged in.    The cookie "values" when I was first logged in are the same as when I have clicked log out (except for "acct" as that has gone) and the same as when I log in the second time (except "acct" which changes).

Why does logging in to Stack Overflow keep me signed in to my Gmail email after logging out and regardless of the Stay signed in checkbox?  Steps to reproduce:   Browse to  and confirm you are logged out Browse to  and confirm you are logged out Click login Click Google Enter Email/Password and confirm Stay signed in is unchecked Click Sign in Click logout (up top) Click Logout (down below) Browse to  and confirm you are still logged in Click Sign out <- Shouldn't clicking Logout on Stack Overflow be doing the same thing as this? Browse to  and confirm you are logged out     Answers are making sense but my frustration is that clicking Logout (twice) on StackOverflow essentially does nothing. If I proceed to click login and Gmail I am immediately authenticated because I still have an active Gmail cookie. In order to effectively logout I need to click Logout twice on Stack Overflow and then manually browse to  and Sign out.


I'm having trouble adding two normal maps to a leather seat. I'm using the principled shader and each normal map has it's own uv map. When I add the second normal map it adds unwanted distortion.

I made a high poly model and then baked its textures onto a low poly model. Now I want to give another normal map's details to the model. How can this be done?


When I put something after my domain name that doesn't exist I am taken to my 404 page, for example:  example.com/sdkjhfdsjk   But if I put something that exists as an image I am taken to the page for that, for example:  example.com/imagename  How can I turn this off. I only want to be taken to pages or posts that exist.  UPDATE: This has been  but the accepted answer to that does NOT fix this.  I added:  remove_action('template_redirect', 'redirect_canonical');   to my themes functions.php but the same action happens.

I notice that if I type in http://www.example.com/pag I can land on an existing page that has a name like http://www.example.com/page_five. I don't know exactly what causes this, but I want to know if there is a way to stop it from happening.


I'm trying to put together a comprehensive regex to validate phone numbers. Ideally it would handle international formats, but it must handle US formats, including the following:   1-234-567-8901 1-234-567-8901 x1234 1-234-567-8901 ext1234 1 (234) 567-8901 1.234.567.8901 1/234/567/8901 12345678901   I'll answer with my current attempt, but I'm hoping somebody has something better and/or more elegant.


I have the following string:     EN=sdfsdf, CN=User Name, CN=Users, DC=domain, DC=co, DC=il   I need to return the first string that starts with "CN=" and ends with an ",". In this case I need to return "User Name".  'CN=.*,'  returns  "CN=User Name, CN=Users, DC=domain, DC=co,"  How can I get the just the first occurrence?

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


Imagine I have something like:  numberlist = [0,1,2,3,4,5]  for number in numberlist:     print(number)   and it would print me every number, right?  But how can I print all these numbers in one line? I expect to get     0,1,2,3,4,5 or 0 1 2 3 4 5

I'd like to do it in Python. What I'd like to do in this example in C: #include <stdio.h>  int main() {     int i;     for (i=0; i<10; i++) printf(".");     return 0; }  Output: ..........  In Python: >>> for i in range(10): print('.') . . . . . . . . . . >>> print('.', '.', '.', '.', '.', '.', '.', '.', '.', '.') . . . . . . . . . .  In Python print will add a \n or space, how can I avoid that? Now, it's just an example, don't tell me I can first build a string then print it. I'd like to know how to "append" strings to stdout.


How can i round of to two decimal points with last decimal point can be either 0 , or 5   import java.text.DecimalFormat; import java.util.Collections; import java.util.HashMap; import java.util.Map;  public class Test {      public static void main(String args[]) {         String selling_price_beMod = "23.31";         double sell_price_d = Double.parseDouble(selling_price_beMod);         String selling_price = round(sell_price_d);         System.out.println(selling_price);     }      public static String round(double value) {          DecimalFormat df = new DecimalFormat("#.00");         return df.format(value);     }  }   When i run the below program the output is   23.31  In this case i want to make it display as 23.35  Please excuse if this is a wrong question and should be approached in a different way .

What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -> 0.91239 0.912300 -> 0.9123   What is the best way to achieve this in Java?


I captured this photo a few minutes ago :   The circle you see is the Sun :|. When I was taking this picture, I was in Live-View Mode with F/22 and no UV Filter. You think it's dangerous for my camera?  I've used Canon 60D with Canon 50mm 1.4 Lens

I want to experiment taking photos in which the sun appears. I'm afraid of what might happen if I take one with a narrower angle (where sun would be bigger). Can the lens act as a magnifying glass and burn the CCD or CMOS sensor?  Under which circumstances (zoom, exposure, aperture, etc...), can the sensor be damaged by the sun?


Does there exist a hash function $h$ and an input $x$ such that $h(x) = x$? I believe this is a special case of collision-resistance. I imagine such a case is guaranteed not to be possible (otherwise such a hash function wouldn't always be guaranteed to be useful), but how is such a case proven to not be possible?

I was wondering if there's any string that has a hash equal to itself, so that – when using any (none specific) hash function – the hash would be equal to that string?  so that:  hash(x) = x   Note that this is not an assignment or anything. I’m just curious and couldn't find any specific answer or reference. And I’m not sure how to go and prove/disprove that to myself!


We run quite a complicated Drupal 6 site with a lot of custom modules which was already migrated from D5. There are a few site administrators and we have had situations where a change in the settings of one module (usually something conflicting with Boost) has caused a problem with the site that is only detected later. We have no way to quickly tell which settings have been changed recently and what their previous values were.  Is there an additional module that hooks into to all variable_set() calls (for example) and logs the old and new values so that we can have an admin view listing all changes over time and which user made the change? It would be great to have an option to add a note to each item to explain why the change was made?  We try and share notes in our wiki on such changes but I think it would be much better if such data was available from inside Drupal itself.

I want to create a simple system for tracking changes to my Drupal configurations and knowing which modules are used by some configuration settings is crucial, but will be happy to use an existing one if it is good enough. Is there a module that implements this?


Prove the inequality: $|\arctan x-\arctan y|\le |x-y|;x,y\in\mathbb{R}$  What is the method for proving this inequality?

Why it is true that $|\arctan x-\arctan y|\leq |x-y|$? I have tried to use $\tan x$ but I didn't conclude to something.


How can I set the compression level for this command?  tar --lzma -cf files/compressed/lzma/archive.lzma -C files/original/ .   With --bzip I just use:  BZIP2=-9 tar --bzip2 -cf files/compressed/bzip2//archive.tar.bz2 -C files/original/ .   but with the --lzma option LZMA=-9 doesn't work.  Is this enviroment variable name incorrect? Where can I get the correct variable name?

So I need to compress a directory with max compression.   How can I do it with xz? I mean I will need tar too because I can't compress a directory with only xz. Is there a oneliner to produce e.g. foo.tar.xz?


There are many more that three visible wavelength in the visible EM spectrum, and yet we can model any color using only three primary RGB wavelength. Perception of an arbitrary color is equivalent of perception of a linear combination of only three fixed wavelengths that correspond to Red, Green, and Blue.  On the other hand, as far as I know, there seem to be no auditory "primary colors": you cannot fool an ear into believing that it hears an arbitrary frequency by starting with a small finite number of primary frequencies.  The question is about human olfactory sense: is it possible to fool the nose into believing it smells an arbitrary odor by offering a combination from a small collection of "primary smells"?

Millions of colors in the visible spectrum can be generated by mixing red, green and blue - the RGB color system. Is there a basic set of smells that, when mixed, can yield all, or nearly all detectable smells ?


Let's suppose we make this list  a=[1,2,3]   a can be sorted in 6 possible ways  a=[1,2,3] a=[1,3,2] a=[2,1,3] a=[2,3,1] a=[3,1,2] a=[3,2,1]   How do I make a function that automatically does that but with bigger lists?

How do you generate all the permutations of a list in Python, independently of the type of elements in that list?  For example:  permutations([]) []  permutations([1]) [1]  permutations([1, 2]) [1, 2] [2, 1]  permutations([1, 2, 3]) [1, 2, 3] [1, 3, 2] [2, 1, 3] [2, 3, 1] [3, 1, 2] [3, 2, 1]


Are there any conditions in which norm of inverse of a bounded operator T is equal to reciprocal of norm of the operator T.

I am a beginner of funcional analysis. I have a simple question when I study this subject.  Let $L(X)$ denote the Banach algebra of all bounded linear operators on Banach space X, $T\in X$ is invertible, then $||T^{-1}||=||T||^{-1}$? Is this result correct?


I am currently porting some code from Visual Studio to Mingw GCC. It seems there is a problem when I attempt to use a static variable . This code works fine in Visual studio so I am not sure what the problem might be here. I have pasted an outline of what the code looks like. If this is insufficient I could put in more.  Header file: .h namespace LG_Wrapper {     template <LG_Thread Thread>     class EffectApplication : public ktApplication     {     public:     static EffectApplication<Thread>& GetInstance();     protected:         .....         .....         static boost::recursive_mutex mResource;       } }  DECLARE_LEGACY_TYPES(EffectApplication);   Source File: .cpp namespace LG_Wrapper {      template<>     boost::recursive_mutex  EffectApplication<LG_Thread_NAME>::mResource;  //LG_Thread_NAME type discussed below      template <LG_Thread Thread>     EffectApplication<Thread>& EffectApplication<Thread>::GetInstance()     {         boost::recursive_mutex::scoped_lock mutex( mResource ); //Error with mResource          static EffectApplication<Thread> instance;         return instance;     }     .... }   Now I am not sure about the LG_Thread_NAME type.  After going through the code I noticed that I define the following in the project settings  LG_THREAD_NAME=GAME   This definition comes into play with this macro somewhere else in the code  #define DECLARE_LEGACY_TYPES(...)   I am having issue accessing mResource The code builds fine if I comment out the statement  boost::recursive_mutex::scoped_lock mutex( mResource );   Any suggestions on why I might be getting the following error with the above code ?  (.text$_ZN10KT_Wrapper17EffectApplicationILNS_9LT_ThreadE0EE11GetInstanceEv[_ZN10LT_Wrapper17EffectApplicationILNS_9LT_ThreadE0EE11GetInstanceEv]+0x11): undefined reference to `LT_Wrapper::EffectApplication<(LT_Wrapper::LT_Thread)0>::mResource'   Update: I am certain that there is something wrong with the variable mResource because in the static method. If I do this it builds fine    boost::recursive_mutex l; boost::recursive_mutex::scoped_lock mutex( l );   Duplicate Question Issue: I am not sure how this question is a duplicate of the links provided. In all the links provided the ops have not initialized their static variables. Here I have initialized my static variable outside the class.

Can anyone explain why following code won't compile? At least on g++ 4.2.4.  And more interesting, why it will compile when I cast MEMBER to int?  #include <vector>  class Foo {   public:       static const int MEMBER = 1;   };  int main(){       vector<int> v;       v.push_back( Foo::MEMBER );       // undefined reference to `Foo::MEMBER'     v.push_back( (int) Foo::MEMBER ); // OK       return 0; }


I am trying to make an array of N+1 bins for a distribution of N discrete scores.  I assumed numpy's arange could be used for that. However, the function gives me odd values, which have a significant effect on the resulting numpy histograms. Here's a minimal example:  n = 10 a = np.arange(0, 1.01 + 1/n, 1/n)  print(a) for i in a:     print(i)     [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.  1.1]  0.0 0.1 0.2 0.30000000000000004 0.4 0.5 0.6000000000000001 0.7000000000000001 0.8 0.9 1.0 1.1   The fact that simply printing the array outputs seemingly normal values is extra misleading. This is a big issue if I want to use this array as a bins argument to numpy's histogram() function because my values are k/10 decimals. In particular, all data points with the value of 0.7 will be placed in the [0.6000000000000001, 0.7000000000000001] bin, whereas I'd expect them to be inside [0.7, 0.8], as per np.histogram() documentation.  The question is whether this is a bug or a feature.

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


I'm making a chat-mockup for with html, css and AngularJS for a school assignment that looks a bit like this (very basics)  HTML

User

Content

     <input type="text" class="chat-msg-text-input" />     <button data-ng-click="addMessage()">Send</button>
   CSS  .chat-box {     border: 1px solid black;     padding: 10px;     height: 200px;     overflow: auto; } .chat-msg-user {     border-bottom: 1px solid red; } .chat-msg {     border: 1px solid red; }   Angular  $scope.addMessage = function(){     $scope.tempMessage.id = $scope.chat[0].chatmessages.length;     $scope.tempMessage.user = $scope.user.name;     $scope.tempMessage.sendDate = $scope.dateToString(new Date()).split('-')[0];     $scope.tempMessage.sendTime = $scope.dateToString(new Date()).split('-')[1];      $scope.chat[0].chatmessages.push($scope.tempMessage);      $scope.tempMessage = {};  };     As seen in the Fiddle I have a set height for the .chat-box and when the message overflow it the scrollbar appears (I'm not using JQuery, just for demo purposes).  Right now the .chat-msg is appended to the bottom of the .chat-box as I want it to, but you have to scroll down manually to see the latest messages. What I want is that it automatically scrolls down to the latest messages.  How do I do this? May it be with html, css or AngularJS  EDIT  Got it working using somae AngularJS in combination with the answer to .  Made a AngularJS function containing the answer which is called after ng-repeat ends.  /EDIT

I am creating a chat using Ajax requests and I'm trying to get messages div to scroll to the bottom without much luck. I am wrapping everything in this div: #scroll {     height:400px;     overflow:scroll; }  Is there a way to keep it scrolled to the bottom by default using JS? Is there a way to keep it scrolled to the bottom after an ajax request?


So I did player.forceav speedmult 10000000 as a joke and now I can't play. The character is stuck in a infinite running loop. How do I undo this so I can continue my game?

So, I was messing around in the Skyrim console and increased my speed a lot. Now I want to reset my speed but the command player.setav speedmult 100 isn't working. Is there any way to reset this?


i am trying to get date from a timestamp which is coming from an api ,but it will shows the wrong date.  <?php  //its from the api also its timestamp of the today  $timestamp="1460364355000";  //  but it will shows the wrong date. echo date('Y/m/d',$timestamp);  ?>   When i check the above timestamp  it will shows the correct date ,but using  php i will get the wrong date.

I Have a string that is equal to a date, represented as the number of milliseconds since the Unix epoch.  I am trying to output it into d-m-Y.  The string I was given was "1227643821310", and I am told that the result should be equal to 2-12-2008, but I keep getting a result of 25-11-2008  My code is as follows:  $mil = 1227643821310; $seconds = $mil / 1000; echo date("d-m-Y", $seconds);   Any ideas as to why this might be?


Given three fixed integers $a,b,c$. I am asking if one can find an integer $y$ such that the quotient $$x= (ay+b)/c$$ is also an integer. There is no restriction on the values of $y$.

I am taking a number theory class, and I was not able to solve this homework problem.   Let $a,$ $b,$ and $m$ be constant positive integers. For which positive integer values of $n$ does $a|mn-b?$   I tried this out for a couple of values, and the values of $n$ satisfying this expression seem to occur in a cycle.  (For example, let $m=2019,$ $a=20,$ $b=19.$ The values of $n$ that work are $1,21,41,61,....$) However, I am not able to show that this always happens.


Let $f$ be a polynomial in the variables $x_1, \ldots, x_n$, where $n > 1$, and with coefficients in $\mathbb{Z}$.   Are there convenient assumptions on $f$ to make the following implication? Assume that $f$ is irreducible in the ring ${\mathbb Z}[x_1, \ldots, x_n]$, then $f$ is irreducible in $\mathbb{Q}[x_1, \ldots, x_n]$.   For instance, if $n = 1$, you would require that the leading coefficient of $f$ is equal to $1$ (Gauss lemma). Are you aware of a similar condition in case $n > 1$ ? Thank you.

Gauss's Lemma for polynomials claims that a non-constant polynomial in $\mathbb{Z}[X]$ is irreducible in $\mathbb{Z}[X]$ if and only if it is both irreducible in $\mathbb{Q}[X]$ and primitive in $\mathbb{Z}[X]$.   I wonder if this holds for multivariable case.      Is it true that a non-constant polynomial in $\mathbb{Z}[X_1,\dots,X_n]$ is irreducible in $\mathbb{Z}[X_1,\dots,X_n]$ if and only if it is both irreducible in $\mathbb{Q}[X_1,\dots,X_n]$ and primitive in $\mathbb{Z}[X_1,\dots,X_n]$?    Thank you for your help.


Basically, I'm trying to find out the correct order of the FNAF games, including the book, which seems to be the last.  Since there are five games out now, a lot of timelines are obsolete and don't include the FNAF Silver Eyes book.

I'm curious what the timeline is for the events so far for all the games of Five Nights at Freddy's.  From playing FNaF 3 I'm not sure if I'm wrong but it seems to take place shortly after the events after FNaF2, which happens after FNaF1, but some people have been telling me it's the other way around, in that FNaF 3 comes first, then 1 & 2.  How do 4 and the two un-numbered sequels factor into this?


I registered a post type of 'product', and also registered a taxonomy 'poruct-cats' for this post type.  When I want to access to product-cats it seems like below:  example.com/poruct-cats/a-product-name   The above url is not seo friendly.  I Like the url be like below:  example.com/product/poruct-cats/a-product-name   I spent lots of time for reading about WordPress rewrite in codex but I finally could not do that.  Any suggestions is appreciated.

I think thats a quick one:  I've got:   Custom post type: Food  Custom taxonomy (Registered to Food): Fruits Terms in Fruits: Apple, Orange, Cherry   If I type in example.com/food?fruits=Apple,Cherry, I get all posts in Fruits with the terms Apple and Cherry, thats great!  But I would like to type in example.com/food/fruits/Apple,Cherry or example.com/food/Apple,Cherry to get the same result.  I´ve tried different permalink and rewrite plugins related to custom posts but nothing helped.  Thank you,  David


I'm using Windows 10 Pro build 19042.330 and the Insiders Edition. For several months now I've been experiencing the following problems (even AFTER resetting Windows to factory defaults): I work as a software developer and several times a day, Windows changes my keyboard layout (I use a German keyboard, and it's changed to English (UK)). My system language is English (UK), but with only the German keyboard configured. I'll add some screenshots.   However, the taskbar would indicate otherwise:  I've not been able to discern the key combination to switch between these keyboard layouts, in fact I'm beginning to think there isn't one and that it's random. Is there a way to disable the second (apparently configured) keyboard layout? It's not that I can't type with the English layout, but having gotten used to the German layout, it's somewhat confusing when all of a sudden a question mark appears where a dash should be.

So I recently did a clean install of Windows 10 English. I configured it to have English UI language but Norwegian keyboard. I have several problems with that setup:   The keyboard language keeps switching to English constantly I can't see the language bar nor the language toggle popup when I swap:     I have bound the Norwegian keyboard layout to Shift+Alt+0 and that works, but it's annoying to have to do that every 5 minutes. Also I find it weird that I can't see the language bar neither on the desktop nor on the toolbar.  Anyone have any idea of what might be wrong?  Here are some screenshots of my settings:          P.S. The only time I see the language toggle popup is actually when I'm logged out in the lock screen and press Win+Space. Nothing happens if I do that after being logged in.


$\forall\; n \geq 3  \;\;\exists (x,y) \in \{2m+1;m\in \mathbb{N}\}^2$ such that $2^n=7x^2  + y^2 $  I proved it by induction and I'm curious how you guys would you show it.

Prove or disprove that,     There always exists a solution of the equation, $$n^m=x^2+py^2$$ with odd $x$ and $y$ and for all $m\geq k$ for some positive integral $k$. Here $p$ is an odd prime and $n\in 2\mathbb{N}$. Is $k$ dependent on $n$? If so then find a way to calculate the value of $k$.   This is basically one of my conjecture which I am trying to prove for quite sometime. Unfortunately, I have progressed very little in this problem. So far I have been only able to prove that for all $m\geq3$ , $n=2$ and $p=7$ there is always a solution of the equation meeting the constraints.   Any idea how to tackle the problem?    Update  After D. Burde's answer of the original problem (see below) I am now interested in finding all $(n,m,p)$ triplets such that the equation holds. Any ideas regarding this problem?


So the title of the question is quite broad, I've seen a few of questions in the site regarding this particular topic (quite a few actually, so let me know if this is somehow a duplicate). My problem is the following, I am working on my PhD thesis, and so far me and my supervisor have collaborated in a few articles (that somehow constitute the body of my thesis). Right now I am working on a particular article (on which I've made all the work). The fact is that my supervisor, and apparently all the members of my faculty tend to put authors in alphabetic order. The fact is that my last-name starts with a "T" so by using their logic I will almost surely  end-up being the second\third author. I don't feel this is actually fair, since after some search online I've seen that in general the order of the authors reflects somehow how much work was done by each one. So it seems strange for me to be like "coauthoring" my own PhD thesis. What should I do? I don't want to appear pretentious, or rude in front of my supervisor, but I don't think it's fair for me either. Do you have some advice on what to do? In case it's relevant my field of research is pure math.

Using alphabetical ordering for authors' names is a long established tradition in mathematics. In the situations of extremely unequal contributions, is it reasonable to break from this tradition?  Has there been any examples?  If it is common, what is the threshold for breaking from alphabetical ordering?


Is there a filter or material that allows a variable amount of light through based on intensity? So the brightness of highlights would be reduced, while shadows would be less, or not at all, affected. If such a filter were to exist, it would result in increased dynamic range.  I am not referring to ND filters because, if I understand correctly, they cut light uniformly across a scene. (See )  A serious problem with this idea that I did not consider earlier is that a filter made from such a material, if it does exist, would ultimately behave as an ND filter because light passes through the filter from all directions ().

When processing sound, one can use a  to reduce the dynamic (DR) range of the signal. In photography, we often run into the problem of scenes with DR larger than the sensor's capture ability. For example, shooting a person on a white snow background. This leads to either the subject is underexposed, the snow is overexposed or both.  A Neutral Density filter is used to reduce the amount of light received by the sensor. However, a uniform filter does not (theoretically) reduce scene DR. Graduated ND filter can be helpful in some cases, but the use is very specific.  Is there a device (material) that can reduce the received DR? Preferably, a passive device (like a lens filter)?  Obviously, in the sound compressor example above, the DR of the signal chain has to be able to accommodate the original DR in order to prevent unwanted clipping and distortion. In Digital Photography, this is equivalent to a high DR sensor, and the compression itself is equivalent to HDR tone mapping.


can you please someone explain to me the diffrence between the 2 statements:  l = [[None] * 3] * 4 for i in range(4):     for j in range(3):         if i == 0:             l[i][j] = 0 print(l)   M = [[None] * 3 for _ in range(4)] for i in range(4):     for j in range(3):         if i == 0:             M[i][j] = 0 print(M)   the output:  [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]] # first statement [[0, 0, 0], [None, None, None], [None, None, None], [None, None, None]] # second statement

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


How should you ask a question where the aim is to collate multiple peoples expertise on one subject matter rather than a pure question answer set up. For example:  What ways have people modelled evapotranspiration using satellite data? I have found x,y,z but want to know if there are any additional methodologies.   I know you can use community wiki when answering a question, but not sure what the format should be where one answer will most likely only ever form part of the overall answer.

There are absolutely loads of payment gateways out there, and I'd like a comprehensive list of them. There's already a question asking for the "best" ones,  and another asking for ones suitable for a charity .  Would such a question be on topic? And would it need to be CW? The obvious way to do it is to have one CW answer and edit all other answers into it. I don't know whether the question itself should be CW, or just the main answer.


I was just thinking theoretically on how long I would be able to run a circuit on a capacitor.  I'm wondering - is my approach for this approximate calculation correct?  Let's say the circuit consits of one Arudino (5V) and one other sensor (5V). Let's say that the total current draw of the Arduino + Other Sensor is 150mA at 5V (asssume constant draw)  Now, I model this cirucuit as a resistor of resistance R = (5V)/150mA = 33ohms.   Next, I choose a capacitor of capacitance 1F with a rating of 10V. Now, I can model my entire circuit as an RC circuit with a 33ohm resistor and a 1F 10V capacitor. The time constant of this circuit is thus (33)(1) == 33. Thus, in a discharging configuration, the capacitor will deplete by 63% of it's total charge in one time constant (33s).   Next, I consider the fact that my circuit needs 5V to run and thus I cannot utilise the full capacity of my capacitor. I assume that I will be using some sort of LDO that provides stable 5V to my circuit for any voltage of the capacitor above 5.3V (5V + LDO drop out).  By the equation Q = CV - if it takes 33s to deplete charge on the capacitor to (100-63)=36%, then it will also take 33s to reduce the voltage across the capacitor from 10V to 36% of 10V which is 3.6V.  By a rough estimate then, I assume I'll get somewhere between 10-20s of usable time.   Is my thought process correct (I know it's very rough calculations) - particularly about modelling the circuit as a resistor?

For the purpose of a project I wish to power an arduino using a supercapacitor charged to 5V. The supercapacitor will be fed straight into the power Vin and GND terminals on the Arduino. No power plug or USB connected to a computer will be connected, so all power is to be drawn from the supercapacitor. Previously I have powered the board using a 0-12V variable voltage supply, and the arduino draws between 20 and 35 milliamps.  My question is this, if I connect the supercapacitor straight to the arduino board, will the arduino govern how much current to draw from the supercapacitor? Or will I need to place a resistor in series with the supercapacitor discharging in order to regulate current and stop the supercapacitor rapidly discharging and frying the board?  Lastly is this feasible at all? I am aware that as the 5V from the supercapacitor will drop off the period during which the arduino will run is limited.  Any advice is appreciated as I  do not wish to fry my Arduino board attempting this.


How do I make an object glow?    I've tried everything to make it glow but it isn't. I even made a separate material and added the texture again and used a mix shader to mix the texture and glow.

I have a node setup and got this effect.    Node setup    Result    Need to have a outer glow to the object like this  Outer Glow    What extra node i have to add to get the above result to glow my object. Any suggestion or help. Thanks


I'm well aware that bacteria can grow on food left out overnight and should probably be thrown out afterwards. But, what about in instance of soups or stews, where the soup/stew goes directly from the cooked pot to a CLOSED pyrex container.  I would think since the food is starting off quite hot and immediately put in a air-tight container it is semi-akin to the canning process.  So all in all is there any scientific evidence that would allow me to believe that the way this food was "left out" is safe or nearly safe?

If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?


so , i started making a short film of a robot mystery , and had made a few renders , it was all okay , until i made my 5th render , the whole lighting system glitched and the lights started pitching to purple , first i thought , that my hdri might have caused the problem but the hdri is attached but still , this is the problem PS , im a noob

I made a character, and its one of my first times texturing, and I saved my character into a new folder, and when I came back to the model ALL the textures were pink, I used to know what to do, but I stopped texturing, how do I bring my textures back?


"the girls' nose" or "the girls' noses"?  We are talking about the nose of many girls.

After the therapy, eight children (43%) became able to crawl/move on their back.   Or should I use "on their backs"?   Singular because each child only has one back, or plural because we're dealing with eight backs?


I don't want to display any number with Algorithm. like Algorithm 1. I have typed   \begin{algorithm}  \label{euclid}  \caption{\textbf{Deep Network}}  \begin{algorithmic}[] --------------------- \EndProcedure  \end{algorithmic}  \end{algorithm}   In output it display Algorithm 1, whereas I do not want the number 1 to be displayed.  Any suggestions please.

My problem is that I do not know how to disable the numbering for algorithms. I have created an algoritm and its number is "Algorithm 1", but I want to have "Algorithm".  \documentclass{article}  \usepackage[noend]{algorithmic}  % Hide endif .etc  \usepackage{algorithm}  \algsetup{indent=2em}  % Default 1 em  \renewcommand{\algorithmiccomment}[1]{\hspace{2em}// #1}  % Change to C-style comments, though still ugly  \begin{document} \begin{algorithm}     \caption{MyAlgorithm} \label{alg:MyAlgorithm}     \begin{algorithmic}[1]     % Default no line numbering        \end{algorithmic} \end{algorithm}  \end{document}


I get this error after adding the repository to install wine any suggestions?  E: Failed to fetch   403  Forbidden   E: The repository 'http://ppa.launchpad.net/jonathonf/python-3.6/ubuntu focal 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.

When updating, I get the following error message:   W: The repository 'http://ppa.launchpad.net/mc3man/trusty-media/ubuntu xenial Release' does not have a Release file.   Here, I find another statement on this error:   This recommends removing certain PPAs; and, I'm not sure if I should do that since it might mean not getting the updates that I need.    Is this what I should do?