When I boot up the computer, I'd like it to boot right to the Xubuntu desktop, rather than prompting me to login with lightdm. I'm aware that I can set up lightdm to not ask me for a password, but it still requires me to click the login button to get to the desktop. Is it possible to just skip lightdm entirely and go right to the desktop?  Thanks!

I want user foo to auto-login using LightDM (which has been used by Ubuntu since version 11.10). How would I do that?


On ios devices photos are stored in . I turned on the option to "send originals", so when I send a photo from my phone to my mac, it is in heic format. The conversion is only necessary once in a while when some website requires jpg-format. For my own purposes I'd like to stick to the more efficient heic-format. What ways are there to convert photos heic to jpg on macos? Assume the photo is on the mac file system. For solutions I would be specially grateful if you could take into account the following preferences:  Software that is available on macos by default Software available on homebrew Other ...

So, here’s the thing. I have a new iPhone and an old Mac. iOS 11 (still in beta as of today) and El Capitan (no more updates for this Mac). I use iCloud photo library in both devices. When I take a photo in the new format with my iPhone 7, is there any way to use it right away in my mac, without having to convert it in my iPhone first? I mean, can I get those photos synced through iCloud and converted locally on my Mac?  I have tried to find a third party software that could do that kind of conversion, but was not able to find any that would work on El Capitan. Any idea?


I am trying to log into technic launcher but for some reason it wont let me.  I have reset my password and username but it still says that the info I'm using is an invalid credential.   I have tried old usernames and passwords.  I know I'm using the right info because I have reset my name and password to see if that fixes the problem.

We just got a new laptop (ASUS) though we did have a mac.  We are trying to log onto Mojang to download Minecraft and it keeps saying, "The username and password are not recognized."   We have done all the usual procedures; we have reset the password, we are using the email, not the username to sign in, and it looks like the minecraft login servers are working etc. etc.  We quit Minecraft on the old computer and shut off that computer thinking that was the issue.   Still, we can't get onto Mojang.  We are accessing mincraft through firefox and trying to download it to the new computer but we can't get into the account to do that!  What in the world could be the issue?


Prove that there are no positive integers $a,b,n>1$ such that $(a^n-b^n)\mid(a^n+b^n)$  My approach:  Let $$\frac {(a^n+b^n)}{(a^n-b^n)}=k$$ where, $k$ is a positive integer  $$\therefore k=1+\frac {2b^n}{a^n-b^n}$$  Now, I am unable to prove that $\frac {2b^n}{a^n-b^n}$ is not an integer.  Please help me with my solution or provide a completely new solution.

I'm working through the problems in Niven's number theory book, and problem 46 in section 1.2 (page 19) has me stumped.     Prove that there are no positive integers $a, b, n > 1$ such that $(a^n - b^n) | (a^n + b^n)$.   I've tried playing around a bit (e.g. noticing that $a^n - b^n$ must divide $2a^n$ and $2b^n$), but in general I've just been going around in circles.  Can anyone please provide a (small) hint in the right direction?


I've heard that it curves twice as much is this correct?

I understand that a black hole bends the fabric of space time to a point that no object can escape.   I understand that light travels in a straight line along spacetime unless distorted by gravity. If spacetime is being curved by gravity then light should follow that bend in spacetime.  In Newton's Law of Universal Gravitation, the mass of both objects must be entered, but photon has no mass, why should a massless photon  be affected by gravity in by Newton's equations?  What am I missing?


I'm reading Courant's Calculus. There is an exercise: Prove the inequality $x+\frac{1}{x}\geq 2$.   I did the following: For the sake of curiosity, I did:  $$x+\frac{1}{x}\geq 2$$  $$x^2+1\geq 2x$$  $$x^2-2x +1\geq 0$$  And this is just $(x-1)^2$. Well, as the square of a real number is $\geq0$, then:  $$(x-1)^2 \geq 0$$  $$x^2-2x+1 \geq 0$$  $$x^2+1 \geq 2x$$  $$x+\frac{1}{x} \geq 2$$  Which is what was to be proved. Is it correct?

I was asked to prove that:   $$x + \frac{1}{x}\geqslant 2$$  for all values of $ x > 0 $  I tried substituting random numbers into $x$ and I did get the answer greater than $2$. But I have a feeling that this is an unprofessional way of proving this. So how do I prove this inequality?


I have some pretty invasive adware going on right now. It is in both Safari and Chrome, so I don't believe it is an extension (I have also looked through all extensions). I have also tried searching for all the recommended adware agents found on the Apple Support Forum (). I have also looked at recent downloads and I can't find anything suspicious.   I am wondering if anyone can recommend some safe software to target the adware.

Every time I click to open a link, other windows start opening. They all want to sell me Detox your Mac or have warnings about how my Mac is at risk or infected.  How can I check for malware?


I'm working on an android application and new to it.  I have to get date from user and then add 28 days and store it in database.  This is what I have done so far  private void saveDate() throws ParseException {     DatabaseHelper db = new DatabaseHelper(ActivityPeriodToday.this.getActivity());      String pDate = periodDate.getText().toString().trim();     String pTime = periodTime.getText().toString().trim();     String next_expected = getNextExpected(pDate);      boolean isInserted = db.insertPeriodTodayIntoPeriods(pDate, pTime, early_late, pDifference, pType, next_expected);      if (isInserted == true) {         Toast.makeText(ActivityPeriodToday.this.getActivity(), "Saved", Toast.LENGTH_SHORT).show();      } else {         Toast.makeText(ActivityPeriodToday.this.getActivity(), "Could not be saved", Toast.LENGTH_SHORT).show();     }  }  private String getNextExpected(String pDate) {     SimpleDateFormat sdf = new SimpleDateFormat("dd/MM/yyyy");     Calendar c = Calendar.getInstance();     try {         c.setTime(sdf.parse(pDate));     } catch (ParseException e) {         e.printStackTrace();     }      c.add(Calendar.DAY_OF_MONTH, 28);     return sdf.format(c.getTime()); }   But is code is not incrementing month.     Ex. If user selects 01/11/2016, then date is incremented and is saved   29/11/2016. But if user selects 16/11/2016 then saves date is   28/11/2016 but this should be 14/12/2016

I'm working with a date in this format: yyyy-mm-dd.  How can I increment this date by one day?


Let $$P=\prod_{k=1}^{2019} \operatorname{lcm}\left(1,2,\dots,\left\lfloor\frac{2019}k\right\rfloor\right).$$ Given that $P=n!$, find $n$.   This is the question provided, I do not really know how to approach this.

I try to prove the following formula:  $$n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$$  I noticed that  $\upsilon_{p}(\operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)) = s$ iff $\lfloor n/(p^{s+1}) \rfloor < k \leq \lfloor n/(p^{s}) \rfloor $


I think they both acceptable, but which one you recommend me to use in conversation.       If he were/was an elephant.     Isn't were sounds too formal/oldfashioned?

If I was... If I were...   When is it correct to use "If I was" vs. "If I were" in standard English?


I was thinking about something and I wish to share this thought with you in order to understand better something that bothers me.  Relativity theory says that the speed of light is the highest possible speed that can be developed. My question is: what is physical (and simplified) explanation for this? In other words, what is physical explanation beneath higher limit of speed? Taking classical example for a definition of speed as path divided by time (although aware it would be more appropriate to speak about waves) , what is possible explanation that something cannot travel more than 3*10^8 m in a second? Why not 3,1*10^8? What is physical constraint for that ?

I will try to be as explanatory as possible with my question. Please also note that I have done my share of googling and I am looking for simple language preferable with some example so that I can get some insight in this subject.  My question is what is so special about $c$? Why only $c$. Its like chicken and egg puzzle for me. Does Einstein reached to $c$ observing light or does he got to light using some number which turned out equal to $c$.   Why is $c$ not relative. If something has zero rest mass like a photon why they only travel at $c$ in vacuum and not with $c+1$ or $c-1$?


How can I produce the codes to get the symbols of pencil, ruler and compass in LATEX? I'm gonna write a sentence I can draw this figure by using simple tools in my presentation. So I prefer to include symbols pencil, ruler and compass instead of the words simple tools. Is it possible?

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


Say I have the following code    p {   display: inline; }  div {   display: inline-block;   width: 100px;   height: 50px;   background: black; }  <p>      Some  text      <div>      </div>     </p>     What is created is this    Here the inline and inline-block elements are not vertically centered. How would I make it look like this :

Why won't vertical-align: middle work?  And yet, vertical-align: top does work.   span{   vertical-align: middle; }
      Doesn't work.


I've just got new laptop with Intel Atom N2800 on the board (wiki says that it is 64 bit) from shop with preinstalled Windows 7 starter 32 bit, and I want to install ubuntu 12.04 32 bit (exactly 32 becouse it will couse much less amount of troubles in usage, AFAIK) in dual boot, so from  I know that  if the other systems (Windows Vista/7/8, GNU/Linux...) of your computer  are installed in EFI mode, then you must install Ubuntu in EFI mode too.   and from the same man page:  To install Ubuntu in EFI mode:     Use a 64bit disk of Ubuntu (32bit installer does not detect EFI)   So, after all of that:   How to know in which mode windows is installed? If it is in EFI - could I install ubuntu 32 bit with just BIOS? If it is yes again - how can I do that?    I have already spent the whole day trying to do that, until I noticed that my laptop has that UEFI and started to google what is that and how to deal with it.  Update:  Ok, now I know that windows is installed in BIOS/Legacy mode, thanks to user @magicandre1981, next question is how to finally install 32 bit ubuntu in dual boot?  What I have tried already:  At first - I'm not sure about UEFI - BIOS screen is in blue and white oldschool colors, there are some rows that says BIOS information, BIOS vendor etc, but at the same time there are row that says Compliancy: UEFI 2.3, PI 1.2.  So, my problem:   All the distros that I have tried - ubuntu 12.04, 12.04.2, 13.04, latest mint - when they are loading their LIVE  environment - nothing happens until I press any key - literally, even HDD activity led does no light up, I press space - a bit of loading process passes normally - changes picture on screen, lights HDD led, and then everythings hags and waits for the next press!   then... 12.04.x and mint does not installs at all - hangs at random step, 13.04 installs when I keep space button pressed, but dies on next reboot (I will try again if there will be no success with other distros).   One wild Russian translation of the whole mint distro finally succesfully installed, but I still have to do not free for example the alt during installation, work that concerned with HDD operations, reboot and etc. But at least it works after reboot:)  As still the same ubuntu man says:  In your BIOS, disable QuickBoot/FastBoot and Intel Smart Response Technology (SRT).   But I do not see this options in my BIOS!  Update 2:  I write ubuntu and other iso images to the flash stick using UltraISO, may be I have to try unetbootin for example?

I have a Windows 7 x64 install USB and want to know if the installer has booted into EFI or BIOS mode.  I found a solution , but it doesn't work since notepad couldn't find: \Windows\Panther\setupact.log


When I go to the  and scroll all the way down, I see this collision:    The sidebar menu should probably not scroll once it hits the footer.  I'm using Chrome, if it matters.

Here is a screenshot from  page, with the floating sidebar: (all good so far)        After I scroll down to footer it just combines both:        Can it please be fixed?


How can I read a data from json separate file (f.e. 'data.json') in another file ('index.html') using javascript - in a simplest way ?  When I use it in the same file there is no problem:  data = '[{"name" : "Harry", "age" : "32"}]';             var j = JSON.parse(data);             document.getElementById('res').innerHTML = j[0].name;   But I cant manage to do that when I use external json file with:  '[{"name" : "Harry", "age" : "32"}]';   I'm looking for the SIMPLEST way (problably I'm missing some fundamental)

I need to do an  request in JavaScript. What's the best way to do that?  I need to do this in a Mac OS X dashcode widget.


I need to prove one thing: $$ n \ge 1: \sqrt{n} \le \sqrt[n]{n!} \le \frac{n + 1}{2} $$  The second part: $$ \sqrt[n]{n!} \le \frac{n + 1}{2} $$ is easy to proof.But the first is more complicated. Help please.

Show that if $n>2$, then $(n!)^2>n^n$.     My work: I tried to apply induction. So, at the induction step, I need to prove, $n^n>(n+1)^{n-1}$ Here, I tried to use induction again without any luck. I also took log of both sides, but I did not get anything. Please help!


So I was looking at the files in my computer and I happened to stumble upon the hidden files. What are these hidden files? namely .gnupg, .local, .mono, and .pki?

I saw so many hidden folders when I pressed Ctrl+H in my home folder ! their names are starting with a dot (.) ! like .themes , .config and etc.. Can I please get to know what can I do with those folders ? Or should I delete those ?


Today, I came into meta so that I could re-list (or make viewable again) a question that I had asked last week, as I have found more information on the topic, and feel the question with more information could be relevant again.  Now I can't find the original question and would have loved to have started with the original text from that question, simply add and re-submit / list.  Would it be possible to keep a running history of asked questions that have been closed by others, or even by ourselves within our profiles, so that we could return to them later?  Shouldn't this be part of your "Activity" anyway?

I would really like to see all of my questions and answers on the profile page, even if some of them were deleted, and I don't have enough rep to see them on the site. (Note that some questions are  after 30 days or 1 year, and the author might be oblivious about what happened.)   , the "deleted recent [questions/answers]" links in one's own user profile now list all respective posts that were deleted in the past 60 days, rather than just those that were originally posted in the last 60 days. , users with the "access to moderator tools" privilege (10k+ on designed sites, 2k+ on beta and non-designed sites) can use the search operator deleted:1 to see all their own deleted posts. , deleted questions and answers that were posted in the past 60 days, can be seen using the "deleted recent questions" and "deleted recent answers" links on the questions and answers tabs (at the bottom of the tab) in your user profile. For older posts: as of 2013-04-23 you can  if you already have a link to them, but they still aren't linked from the user profiles (not even just for you). Nor do you see inbox notifications for comments on them if you come back a few hours later. You have to have thought to bookmark your question, or you have to go digging for it in your browser history.


Defect Description Over at , I have enough rep to vote to close questions. I've been using the 'flag' option out of force of habit, but when I select that a question doesn't belong, it takes me to the close panel anyway and allows me to register my vote. However, once I have voted to close, what ends up happening in the UI is it improperly shows the new number of close votes and flags. Example Current Behavior Say I have a question with one vote to close it. Following the process in the defect description, I vote to close it as well. However, the UI takes my close vote, adds it to the existing count (1), then edits the count beside flag (my entry point) to show 2 flags in addition to the previous single vote to close.  Expected Behavior There should be two votes to close.  Additional Information If I refresh the page, the counts show correctly. In other words, the back-end code is fine, but the AJAX callback seems to edit the element I clicked rather than the element that represents the action I actually took.

When I'm using the Stack Exchange mobile view (specifically on my iPhone), after voting to close a question I am also shown the flag count. If I refresh the page afterwards, the flag count disappears and I don't think there is (or should be) any way that a non-moderator should see this.  Take for example . This is what I see before my close vote:    Additionally, the close vote dialog doesn't make it immediately obvious like the desktop version how the close votes are distributed, but this is a lesser issue:    After the close dialog is gone, I get the "x votes remaining" message, and I am also shown the flag count, which I don't think I should be able to see.


This short story is one that I may have encountered in the 90s editions of "Asimov's" magazine. Unfortunately, I am vague about the exact details.    A soldier returns to his own time from a horrendous battle in the distant future (he was on the winning side). He has been altered so that he is able to perceive across multiple dimensions/time lines. He enters a bar/tavern/eatery and witnesses another "veteran" (or being) abusing/threatening a woman he cares (cared) about. He is forced to kill this abuser across every dimension/time line he exists in, to protect this woman. In doing so, he must return to the future and fight in the war all over again.

I read this story in an anthology in the eighties or early nineties.  It was about an old man who lived outside a western-like town, though that might have just been how I imagined it.  He goes to town and some ex-military thugs are there causing problems.  Flaunting some odd interdimensional military tech of some sort.  He doesn't want to intervene as doing so would be bad but in the end he must.     By intervening, his military identity is revealed and that causes him (some paradox or causality law) to have to go back and fight the war again.   The war is at the end of time or the universe.  The man is maybe a colonel of the sky something... Not much to go on; I have been searching my collection and wracking my brain for years trying to recall the story.


Prove that $\forall n\ge0,43\mid 6^{n+2}+7^{2n+1}$ in three ways: a) Use mathematical induction b) Using techniques of modular arithmetic c) Without induction, nor modular arithmetic (Hint: use binomial theorem.)  a) Proof. Base case: $n=0$ WTS $\exists k\in\mathbb{Z},s.t. 6^{(0)+2}+7^{2(0)+1}=43k$ Let $k=1$, we have: $$36+7=43\tag*{hold}$$ Inductive step: Assume$$\exists k_1\in\mathbb{Z},s.t. 43k_1=6^{(j)+2}+7^{2(j)+1}$$ Show$$\exists k_2\in\mathbb{Z},s.t. 43k_2=6^{(j+1)+2}+7^{2(j+1)+1}$$ Let $$k_2=6k_1+7^{2j+1}$$ That $$43k_2=43(6k_1+7^{2j+1})=6(43k_1)+43(7^{2j+1})$$ By assumption $43k_1=6^{j+2}+7^{2j+1}$ have $$=6(6^{j+2}+7^{2j+1})+43(7^{2j+1})$$ $$=6(6^{j+2}+7^{2j+1})+301(7^{2j})$$ $$=6(6^{j+2}+7^{2j+1})+343(7^{2j})-42(7^{2j})$$ $$=6(6^{j+2}+7^{2j+1})+7^{2j+3}-6(7^{2j+1})$$ $$=6(6^{j+2}+7^{2j+1})-6(7^{2j+1})+7^{2j+3}$$ $$=6(6^{j+2}+7^{2j+1}-7^{2j+1})+7^{2j+3}$$ $$=6^{j+3}+7^{2j+3}=6^{(j+1)+2}+7^{2(j+1)+1}\tag*{$\square$}$$ b) $$\text{WTS }\forall x\ge0,6^{n+2}+7^{2n+1}\equiv0(\text{mod }43)$$ I first checked some "techniques of modular arithmetics" $\dots$  Theorem 3.1.2 if $a\equiv b(\text{mod m})$ and $b\equiv c\text{(mod }m)$, then $a\equiv c(\text{mod m})$ Theorem 3.1.3 When $a$ and $b$ are nonnegative integers, the relationship $a\equiv b\text{(mod }m)$ is equivalent to $a$ and $b$ leaving equal remainders upon division by $m$ Theorem 3.1.4 For a given modulus $m$, each integer is congruent to exactly one of the numbers in the set $\{0,1,2,\dots,m-1\}.$ Theorem 3.1.5 If $a\equiv b(\text{mod }m)$ and $c\equiv d(\text{mod }m)$, then $i)(a+c)\equiv(b+d)(\text{mod }m)$ $ii)ac\equiv bd(\text{mod }m)$ Theorem 3.1.6 If $a\equiv b\text{(mod }m)$, then $a^n\equiv b^n\text{(mod }m)$, for every natual number n. (from UTM "A Readable Introduction to Real Mathmatics" Chapter 3)  Proof. $$\vdots$$ c) $$\text{WTS }\forall n\ge0,43\mid 6^{n+2}+7^{2n+1}$$ Proof. Let $n\ge0$ Show $\exists k\in\mathbb{Z},s.t. 43k=6^{n+2}+7^{2n+1}$ Rough work: $$6^{n+2}+7^{2n+1}=6^{n+2}+\frac{7^{2n+2}}{7}=6^{n+2}+\frac{(7^2)^{n+1}}{7}$$ $$=6^{n+2}+\frac{(43+6)^{n+1}}{7}=6^{n+2}+\frac{{n+1\choose0}43^{n+1}+\dots+{n+1\choose n}(43)6^{n}+{n+1\choose n+1}6^{n+1}}{7}$$ $$=\frac{7(6^{n+2})+6^{n+1}}{7}+\frac{{n+1\choose0}43^{n+1}+\dots+{n+1\choose n}(43)6^{n}}{7}$$ $$=\frac{42(6^{n+1})+6^{n+1}}{7}+\frac{{n+1\choose0}43^{n+1}+\dots+{n+1\choose n}(43)6^{n}}{7}$$ $$=\frac{6^{n+1}(42+1)}{7}+\frac{{n+1\choose0}43^{n+1}+\dots+{n+1\choose n}(43)6^{n}}{7}$$ $$=43(\frac{6^{n+1}+{n+1\choose0}43^{n}+\dots+{n+1\choose n}6^{n}}{7})$$ Therefore I suppose to let $k=\frac{6^{n+1}+{n+1\choose0}43^{n}+\dots+{n+1\choose n}6^{n}}{7}$, but how do I prove this $k\in\mathbb{Z}$? Where should I start for b) ? Any help or hint or suggestion would be appreciated.

Use mathematical induction to prove that 6(n+2) + 7(2n+1) is divisible by 43 for n >= 1.  So start with n = 1:  6(1+2) + 7(2(1)+1) = 63 + 73 = 559 -> 559/43 = 13. So n=1 is divisible  Let P(k): 6(k+2)+7(2k+1) , where k>=1  Show that P(k+1): 6((k+1)+2) + 7(2(k+1)+1) is true  = 6(k+1+2) + 7(2k+2+1)  = 6(k+3) + 7(2k+3)  I'm unsure where to go from here, I've tried several directions after this but have got nowhere. I don't know how to get the 43 or 559 out the front.  Any help would be great


I'm very new into Java and I've reached the chapter in my textbook that talks about interfaces. However, I am failing to see their use/point. I'm sure that they're not useless though and that it's just me not understanding the subject.  So, interfaces are like abstract classes and they only name methods, not their implementations. The first example provided in the book talks about having a class Shape, an extended class rectangle and the idea is to allow for a method to stretch the rectangle by its biggest side. So the code starts:  public interface Stretchable {     void stretch( double factor ); {   Then they describe the "point" of using it  public class Rectangle extends Shape implements Stretchable {    public void stretch( double factor )    {       if( factor <0 )       throw new IllegalArgumentException();        if( length > width )           length *= factor;       else           width*= factor;    } }   However, I fail to see what did I win there, by defining and implementing an interface. the interface was just void stretch( double factor); and I still had to define the same thing in the Rectangle class. What is the advantage in doing this, when I still have to define from scratch what the method of the interface is going to do in the class it's being implemented on?

So lets say I have this interface:  public interface IBox {    public void setSize(int size);    public int getSize();    public int getArea();   //...and so on }   And I have a class that implements it:  public class Rectangle implements IBox {    private int size;    //Methods here }   If I wanted to use the interface IBox, i can't actually create an instance of it, in the way:  public static void main(String args[]) {     Ibox myBox=new Ibox(); }   right? So I'd actually have to do this:  public static void main(String args[]) {     Rectangle myBox=new Rectangle(); }   If that's true, then the only purpose of interfaces is to make sure that the class which implements an interface has got the correct methods in it as described by an interface? Or is there any other use of interfaces?


Note: this proposal is the similar to a low-voted response to , added (by someone else) after the question was resolved.  The problem: downvotes without comments are annoying to responders, and ultimately do not provide any value to the poster or the SO community as a whole. Unless a response goes negative, there is no indication that the answer may be incorrect, and the responder does not learn why he/she is incorrect.  However, members of the SO community do not wish to fear retaliation for their downvotes, so do not want to be forced to provide a comment that explains their vote. Looking at other questions where this issue has been raised, it also appears that some people simply don't want to bother giving a reason for their downvote (although this attitude doesn't seem very community-oriented).  I propose that clicking the downvote arrow will require that the user enter a comment, then attaches that comment to the response/question without a username (or, if the DB schema requires a user, with a dummy username).  Yes, it's possible to game the system by typing "asdasdasdasdasd" (I think that's 15 characters). However, doing so will make clear to the downvoter that s/he is a borderline sociopath. More important, will signal to the responser -- and the community as a whole -- that the downvote was given without a lot of thought, and is therefore suspect.

I don't know if people don't explain why they up or down vote because they don't care or because they don't want the person to know they voted on an answer (or question)... But, it might be nice to be able to leave a comment anonymously as to why it was voted.  It could give us more insight as to people's thoughts on posts.    Really, I think this would come into play a lot more dealing with down votes more than up votes, but I could see it being beneficial in both situations.   See also


Can US Border Officials (e.g. Customs Officials at JFK Airport) legally require a non US citizen (whether a tourist, visa, or green card holder) for his or her passwords (phone, laptop, facebook, email, etc...)? Don't they need a warrant for that? Do different states have different rules?

I've read stories about border officials searching laptops when crossing the border in one direction or the other. Does this really happen, typically speaking?  As a US citizen, can I be forced to give them my laptop's password for any/no reason? I don't believe they are allowed to deny entry to the US to a US citizen? ....but who knows these days?  Canada can deny me entry for any reason, so that's fine. But in practice, does this even happen in either crossing direction?  EDIT - I've now made the trip. They didn't so much as glance in the direction of my laptop. My biggest issue turned out to be lack of international wireless data service!


If A is a symmetric matrix and $A^2 x = \lambda Ax$, does $x$ must be an eigenvector of $A$ with eigenvalue $\lambda$?

Let $A$ be a real symmetric matrix. Assume $A^{2}v=\lambda Av$ , can we somehow deduce $v$ is an eigenvector of $A$ with $\lambda$ as its corresponding eigenvalue? i.e $Av=\lambda v$. Thanks Edit: Also assume $\lambda \ne 0$ and we do not know if it is singular or nonsingular.


How could i fix this warning?      Type safety: Unchecked cast from List to List<ArrayObject>   List<List<ArrayObject>> detailList = search.getDetails(     (List<ArrayObject>) ((DefaultListBackedValueList) request.getAttribute(LIST)).getList());

In my spring application context file, I have something like:  <util:map id="someMap" map-class="java.util.HashMap" key-type="java.lang.String" value-type="java.lang.String">     <entry key="some_key" value="some value" />     <entry key="some_key_2" value="some value" />    </util:map>   In java class, the implementation looks like:  private Map<String, String> someMap = new HashMap<String, String>(); someMap = (HashMap<String, String>)getApplicationContext().getBean("someMap");   In Eclipse, I see a warning that says:  Type safety: Unchecked cast from Object to HashMap  What did I do wrong? How do I resolve the issue?


I am trying to design a comparator using a 741 IC, with a single supply of 12V. I have set the reference to 2V and I require the output to toggle between 12V to 0V. but the problem I am facing is the output is only going to 11V max and min of 2V. What is the reason behind the output saturation?

Simple enough question. Why not use a  in a target circuit or anyone's target circuit? What are the reasons not to use it? What might be the reasons to still choose this part?


Let $0<a<b $ and $ f: [a,b] \rightarrow [c,d]$ be an increasing bijection. Prove the following equality by area  $\int_{a}^{b}f(x)dx=bd-ac-\int_{c}^{d}f^{-1}(y)dy$.  Use integration by parts to prove the equality.  I honestly have no idea with this problem. I need full and detailed answer.

Is it true that  $$\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$$  Just making sure.   If not, how about:  $$\int_a^b f(x) dx = (f(b)-f(a))b - \int_{f(a)}^{f(b)}f^{-1}(x)dx$$   I'm having a hard time concentrating right now, and I'm trying to figure out how to get the area under a curve when the function is inverted.


Suppose there is a trademark called "Rubyblock" and you buy rubyblock.com and name your app "Rubyblock" is there some legal risk?  If yes, how do i can check this before to name the app and buy domain?

A search on google for "iphone developer" turns up loads of websites which have "iphone" in them, a trademarked name by Apple.  So I'm led to believe that having a domain such as iphonedeveloper.com is ok? Well, you're still using Apple's trademark, but it would be hard to brand yourself otherwise. You're an IPHONE DEVELOPER... right?  Well, what if I want to provide a website where users pay to get a list of the best offers from Ebay? I might have a domain like ebaydeals.com (I don't... i'm just speculating!).  Now I've heard that places like Ebay are really hot on the trigger and fire out emails to people who register domains like that straight away. But whats the difference?  In both cases I'm making money from the trademark, effectively, so is it just down to how lenient the company who owns the trademark is? Or are there rules? Is there a specific "line" you don't cross?  Thanks


I'm using a template for my thesis and now that I'm all done I want to set a formatting parameter different from the one in the template. When an image is supposed to show and it doesn't fit in the end of a page, it goes to the next page and the content in that previous page doesn't occupy a full page. The problem is that when that happens, LaTeX strecthes the spacing in the page so that the content fits the whole page, like so:  When I want it to keep the normal spacing, like so :  What command could be causing this? Or what would avoid it? I've Ctrl+F'ed \flushbottom and \raggedbottom and the only two entries I found made no difference so I really don't know what's causing this. Any tips?

I'm writing my bachelor-thesis and have a couple of small sub-sub-sections explaining conversions, like in the following  \subsubsection*{Assignment}  This document only explains non-compound assignments. The other kind, i.e \texttt{a += b}, is supported by the language too, but is not yet implemented.   \begin{itemize} \item If the first is an \texttt{auto} variable, no conversion takes place when assigning       the right hand side to the variable designated by the left hand side.  \item Otherwise, an assignment conversion takes place converting the given value to the type       of the designated variable.  \item Assignment requires an lvalue as the left hand side, and yields an lvalue result.  \end{itemize}  \subsubsection*{Multiplication} % ...   But latex renders it quite ugly with much space in between the items. I think it does so to fit the whole page. How can I tell it not to do so? Is what I'm doing right at all?


If a sequence $\{x_n\}$ has the property that $$\lim_{n\rightarrow\infty} x_{2n} = \lim_{n\rightarrow\infty}x_{2n+1} = L$$ Show that the sequence $\{x_n\}$ convergences to $L$.  I tried a proof by contradiction against the given information, then I considered saying that if all the subsequences of the already given convergent subsequences converge to $L$, then $\{x_n\}$ must converge to $L$.  What is the proper way to prove this?

Given a sequence $a_{n}$, if I know that the sequence of even terms converges to the same limit as the subsequence of odd terms:    $$\lim_{n\rightarrow\infty} a_{2n}=\lim_{n\to\infty} a_{2n-1}=L$$  Is this sufficient to prove that the $\lim_{n\to\infty}a_{n}=L$?    If so, how can I make this more rigorous?  Is there a theorem I can state that covers this case?


I have exactly the same problem as , but unfortunately no helpful answer was provided, and the OP accepted a non-answer! So I guess I should ask again, here.   Recently I am having streaming issues with my Netflix and Amazon Prime Instant Videos. Youtube videos, on the other hand, work just fine. I did ping tests at , and the tests were just normal.   I wonder whether is my ISP throttling the speed of HD video streaming? Is there any website that allows me to check this?

I’ve recently changed my ISP and noticed that I no longer can watch video sites like YouTube in real time; I need to wait for buffering first. On both ISPs, my speed was same 5 megabits per second.  I’ve checked normal download of files, and torrents, and they all work fine. Also, checked other video sites, same problem. Used other PC, same problem.


I would like to know is there any problem if we are not clearing or deleting an object that scope is complete program.  I believe the OS will cleanup the memory after executing the application.  This object is not going to use any socket or file operation, it will just allocate some memory for storing some data. may be int * x = new int[100];

Is it ever acceptable to have a  in your C or C++ application?  What if you allocate some memory and use it until the very last line of code in your application (for example, a global object's destructor)? As long as the memory consumption doesn't grow over time, is it OK to trust the OS to free your memory for you when your application terminates (on Windows, Mac, and Linux)? Would you even consider this a real memory leak if the memory was being used continuously until it was freed by the OS.  What if a third party library forced this situation on you? Would refuse to use that third party library no matter how great it otherwise might be?  I only see one practical disadvantage, and that is that these benign leaks will show up with memory leak detection tools as false positives.


Is there a word that implies that a person is educated and ignorant at the same time?   I tried ignorant, ignoramus and similar words but they imply that a person is uneducated and does not convey the sense of educated and ignorant. I searched up synonyms of ignorant and ignoramus but did not find the word I need.   In my native language we have a word which means "educated idiot." Is there any word for that? Thanks.

There was the following paragraph in the article that came under the title, “GOP and the rise of Anti-knowledge” written by  (October 29, 2015):     “English unfortunately doesn’t have a precise word for the German   “Fachidiot,” a narrowly specialized person accomplished in his own   field but a blithering idiot outside it. In any case, a surgeon is   basically a skilled auto mechanic who is not bothered by the sight of   blood and palpitating organs. We need the surgeon’s skills on pain of   agonizing death, and reward him commensurately but that does not make   him a Voltaire.”    In Japanese we have a word, 専門バカ, of which literal translation is “specialist idiot” meaning exactly same as defined the above - a narrowly specialized person accomplished in his own field but a blithering idiot outside it.  I’m really curious about the absence of short descriptions of the specialist who knows nothing more than his specialty area in English like German “Fachidiot,” and Japanese "専門バカ."  Isn’t there really any short word counterpart to “Fachidiot,” specialist’s ignorance, for instance, in English?  P.S.  I found "narrow-minded specialisit" as a German-to-English translation of "fachidiot" in the web site, Interglot translation dictionary.


How do I install itunes 64bits on Ubuntu 14.04 ? Using PlayOnLinux couldn't help me out to install the 64bit version of the latest itunes.

Is there an alternative to iTunes where I can buy music/back up phone?


Using Java I have conducted an experiment to determine which sorting method's (bubble or selection) runtime is faster. The program prompts the user to enter a number n which is the number of items in the array to sort. Then it creates and sorts 500 different arrays of this size and times the run to get an average time to sort using both sort methods. I used 500, 1000, and 2500 as test inputs for n. My results below show that selection sort runs faster than bubble sort, but both algorithms have a time complexity of O(n^2), so why is selection sort running so much faster?  TimeBubbleSort Class  public class TimeBubbleSort {     public static void main(String[] args) {          System.out.print("Enter a number of items in array: ");         Scanner scan = new Scanner(System.in);         int n = scan.nextInt();          long start_time = 0;         long end_time = 0;         long running_time = 0;         long final_time = 0;         BubbleSort bubbleSort = new BubbleSort();          for(int i = 0; i < 500; i++) {             int[] array = new int[n];             for(int j = 0; j < array.length; j++) {                 array[j] = (int)(Math.random() * n) + 1;             }             start_time = System.nanoTime();             bubbleSort.bubbleSort(array);             end_time = System.nanoTime();             running_time = end_time - start_time;             final_time = final_time + running_time;         }         System.out.println("The average time of each array took " +  (final_time / 500) + " nanoseconds");     } }   BubbleSort Class  public class BubbleSort {      void bubbleSort(int[] arr) {         int n = arr.length;         int temp = 0;         for (int i = 0; i < n; i++)             for (int j = 1; j < (n - i); j++)                 if (arr[j - 1] > arr[j]) {                     temp = arr[j - 1];                     arr[j - 1] = arr[j];                     arr[j] = temp;                 }     }      void printArray(int[] arr) {         int n = arr.length;         for (int i = 0; i < n; ++i)             System.out.print(arr[i] + " ");         System.out.println();     } }   TimeSelectionSort Class  public class TimeBubbleSort {     public static void main(String[] args) {          System.out.print("Enter a number of items in array: ");         Scanner scan = new Scanner(System.in);         int n = scan.nextInt();          long start_time = 0;         long end_time = 0;         long running_time = 0;         long final_time = 0;         SelectionSort selectionSort = new SelectionSort();          for(int i = 0; i < 500; i++) {             int[] array = new int[n];             for(int j = 0; j < array.length; j++) {                 array[j] = (int)(Math.random() * n) + 1;             }             start_time = System.nanoTime();             selectionSort.selectionSort(array);             end_time = System.nanoTime();             running_time = end_time - start_time;             final_time = final_time + running_time;         }         System.out.println("The average time of each array took " +  (final_time / 500) + " nanoseconds");     } }   SelectionSort Class  public class SelectionSort {     void sort(int arr[]) {         int n = arr.length;          for (int i = 0; i < n - 1; i++) {             int min_idx = i;             for (int j = i + 1; j < n; j++)                 if (arr[j] < arr[min_idx])                     min_idx = j;              int temp = arr[min_idx];             arr[min_idx] = arr[i];             arr[i] = temp;         }     }      void printArray(int arr[]) {         int n = arr.length;         for (int i=0; i<n; ++i)             System.out.print(arr[i]+" ");         System.out.println();     } }   Results Using Bubble Sort  Array Size of 500: took 284,979 nanoseconds  Array Size of 1000: took 960,067 nanoseconds  Array Size of 2500: took 7,448,865 nanoseconds  Results Using Selection Sort  Array Size of 500: took 107,035 nanoseconds  Array Size of 100: took 342,464 nanoseconds  Array Size of 2500: took 1,880,215 nanoseconds

How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related:


I'm stuck with this (should be easy) computation. I started by considering the most natural map $K[x,y] \to K[t^2,t^3]$ which is the one that sends $x \mapsto t^3$ and $y \mapsto  t^2$, and then extend by linearity. the map is easily seen to be surjective and factors through the quotient. The point is that I cannot find a way to show that the induced map is injective.. If I try to write down a general polynomial in two variables which is sent to zero I lose myself in the computations. Are there some other methods to show such claim?

How to prove that the ideal $I=(x^3-y^2)$ in $k[x,y]$ is prime?    I have constructed a map from $k[x,y]$ to $k[t]$, which maps $x$ to $t^2$, and $y$ to $t^3$. Then, I want to show that the kernel is exactly $I$. But the difficulty is that how to prove the kernel is contained in $I$.  Could you help me? Thanks a lot!


I'm trying to unwrap some new faces after fixing some topology on a model that is already textured (in particular at the edge of the mouth).  For some reason a number of faces just won't seem to unwrap or show up in the UV editor after I select and unwrap them. I've tried pinning vertices around them, messing with seams, and checked the normals, but no luck.  In the viewport, they seem to take the texture. But the faces/verts just aren't showing in the UV editor, so I can't get them in the right place.  The picture shows the gap in the UV where the new faces need to be and on the right are the faces I'm trying to unwrap.

When I unwrap the character I designed, I get only a few faces visible in the UV image editor, although all the faces are selected in the 3d viewport in edit mode.  Those faces are probably the one I added to "close" the character's head (for some reason I had a hole that I closed adding faces one by one and then checked to remove doubles). Maybe it's a coincidence.   And there is more: If I use 'circle select' (C + left-click) over "empties" area in the UV image editor (not in island mode), I can see that faces get activated in the 3d viewport (edit mode)! Of course, I have restarted Blender to see if the problem persists and it does.  All this weird behavior happens before I create an image. Once I create a new image or use an existing one as a UV, the meshes in the UV Image editor don't show up at all!   When I do all this process with the monkey figure I have no problem.  Could you have a look to my blend file and tell me what's wrong?    Blender 2.7.4 Mac OS X 10.10.3  My blend file:


I tried to make a game where you can destroy something when you swipe or tap. However, it says NullReferenceException & while the swipe control actually works, the gameobject can't be destroyed.  public class checkUp : MonoBehaviour { private Swipe swipe; private UIManager uiManager;  private void Awake() {     swipe = GetComponent<Swipe>();     uiManager = GetComponent<UIManager>(); }    // Update is called once per frame void Update() {     if (swipe.SwipeUp ) //NullReferenceException: Object reference not set to an instance of an object     {         Debug.Log("Passed!");         uiManager.destroyed = true;         Destroy(gameObject);     }   Here's the partial code from swipe:      if (swipeDelta.magnitude > 125)     {         //which direction?         float x = swipeDelta.x;         float y = swipeDelta.y;         if (Mathf.Abs(x) > Mathf.Abs(y))         {             //left or right             if (x < 0)                 swipeLeft = true;             else                 swipeRight = true;         }         else         {             // Up or down?             if (y < 0)                 swipeDown = true;             else                 swipeUp = true;         }     }

Since many users are facing the NullReferenceException: Object reference not set to an instance of an object error in Unity, I thought that it would be a good idea to gather from multiple source some explanation and ways to fix this error.  Symptoms I am getting the error below appearing in my console, what does it mean and how do I fix it?  NullReferenceException: Object reference not set to an instance of an object


Is it acceptable to assume unequal variance for my data to perform a t-test. If so, what is a justification for this?

I want to do an AB test to check if one version does significantly increase revenue. Generically speaking I want to test whether the central tendency (mean) of 2 groups are different from each other on the basis of (unpaired) samples of the 2 groups.   My understanding is, that I could use the following approaches:   Student-t test, if the variance of both groups are the same and both are normally distributed Welch-t test (unequal variance t-test), if the variance of both groups might not be the same but both are still normally distributed Mann–Whitney U test (Wilcoxon rank-sum test), if I cannot make any assumptions about the distribution of both groups   But now I read () that I can always use the Welch-t test. The article argues that it is dangerous to make the assumption of equal variance and additionally that     the unequal variance t-test performs as well as, or better than, the Student's t-test in terms of control of both Type I and Type II error rates whenever the underlying distributions are normal.   And if the groups are not normally distributed, than I can just rank the data beforehand:     Thus, Zimmerman and Zumbo (1993) suggest that the unequal variance t-test can effectively replace the Mann–Whitney U test if the data are first ranked before the test is applied.    So the end conclusion is:     If you want to compare the central tendency of 2 populations based on samples of unrelated data, then the unequal variance t-test should always be used in preference to the Student's t-test or Mann–Whitney U test. To use this test, first examine the distributions of the 2 samples graphically. If there is evidence of nonnormality in either or both distributions, then rank the data. Take the ranked or unranked data and perform an unequal variance t-test.   So my question is:  Do you see any drawbacks in always using the Welch-t test instead of the Student-t test or Mann-Whitney test?


Let $G$ be a finite group, and $g$ be a an element of $G$. How could we go about proving $g^{|G|}=e$ without using cosets? I would admit Lagrange's theorem if a proof without talking about cosets can be found.  I have a proof for abelian groups which basically consists in taking the usual proof of Euler's theorem and using it in a group, I do not know if it can be modified to work in arbitrary finite groups.  The proof is as follows: the function from $G$ to $G$ that consists of mapping $h$ to $gh$ is a bijection. Therefore   $\prod\limits_{h\in G}h=\prod\limits_{h\in G}gh$ but because of commutativity $\prod\limits_{h\in G}gh=\prod\limits_{h\in G}g\prod\limits_{h\in G}h=g^{|G|}\prod\limits_{h\in G}h$.  So we have $\prod\limits_{h\in G}h=g^{|G|}\prod\limits_{h\in G}h$.  The cancellation property yields $e=g^{|G|}$.  I am looking for some support as to why it may be hard to prove this result without talking about cosets, or if possible an actual proof without cosets.    Thank you very much in advance, regards.

This is a very easy fact we use in Group Theory,  But somehow, I wondered that whether there may be another way (other than Lagrange's Theorem) to prove that the order of an element divides the order of Group.  I attempted to go on the term "exponent" of the Group (just assume that G is a Finite Group), which we may define the least common multiple of orders of elements in G. But this exponent divides $|G|$, since the order of each element divides $|G|$. So it became a little paradox.   Shall I think that; before teaching this fact in a Course, one should teach about Lagrange's first?


I'm working on a web app that accepts only social logins as authentication (Facebook and Google for now).  I've successfully implemented the login buttons following each site's instructions, and I use the email address associated with the service as their unique identifier and store it in PHP's $_SESSION variable to navigate through pages.  My question is whether or not I can assume there will be no vulnerabilities if I follow Facebook's and Google's implementation guidelines.  I assume using SSL to prevent man-in-the-middle attacks is a must.  What else can I do, or avoid, in order to securely handle each user's login and session?  Thank you for your suggestions.

What are some guidelines for maintaining responsible session security with PHP?  There's information all over the web and it's about time it all landed in one place!


Let $a_1, a_2, a_3, \ldots, a_{10}$ be ten randomly chosen real numbers in the interval [0,1].  Let $m$ be the maximal value out of these 10 numbers.  What is the expected value of $m$?   (i.e. If i had $n$ sets of 10 numbers and took the maximum $m$ for each set and averaged the values of all the $m$'s, what would this value become as $n \rightarrow \infty$?

What is the expected value of the maximum of 500 IID random variables   with uniform distribution between 0 and 1?   I'm not quite sure of the technique to go about solving something like this. Could anyone point me the right direction?  Thanks


I use \section, \subsection on my doc. I insert \section (and \subsection) before this command    \begin{table}[]     \centering         \begin{tabular}{@{}llr@{}}              \toprule   that create a table. I have the same block for 3 table. What I obtain are: two table, then the name of section and sub section and, at last, the third table. Why do the name of section and subsection are in the middle of the tabs?

Possible Duplicate:          I am trying to create a table after some text:  Some text. foobar foobar \\  \begin{table}[t] \centering \begin{tabular}{|c|c|c|c|c|c|} \hline  & a & c & & &  \\ \hline $\{X, X', Y\}$ & & b &  & &  \\ \hline \hline \end{tabular} \end{table}   However, the table is appearing before the text even though I type if after I type the text. Why?


How to draw this in TeXstudio? help me please.

I feel intimidated in learning TikZ. I was wondering if there are some nice materials (or just your replies) at different level:   for providing big picture, which is important to beginners to not lose direction during learning. for comprehensive reference.   Examples are important, but only examples are not always clear for understanding the big picture and organization.


A VPS running Ubuntu 14.04.5 LTS is consuming nearly 300% of CPU capacity.  It is identified running top as cER6XH.  Is there any way to track down what this process is and why it may be going rogue?

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


I switched from Windows to Ubuntu. The sound level is very low in Ubuntu. Please help me to solve the problem.

I have two laptops: Dell xps M1210 and Dell vostro 1400. On MS windows the output volume is so loud that I just need to set volume to around 20% to listen music and watch videos. I use Bose TriPort In-Ear Headphones most of the times. On ubuntu, even if I set 100% volume on the multimedia player, on the desktop volume manager as well, and also on the ncurses GUI of alsa mixer, I get very low volume output. Sometimes while playing some vidoes the volume is so low that I barely hear any words. I have struggled for two years since I started to use ubuntu to solve this mystery. The same sound card which gives excellent sound on MS windows fails miserably on GNU/Linux. Few weeks back I bought an Asus 100PX EEE PC. To my surprise even it also has the same issue. I have tried many versions of ubuntu and also I have done manual compiles of alsa modules without any success. I have asked and read about it in every possible forums and howto's. Nothing has helped me to address the issue.


I spent a lot of time trying to construct concrete example in the title. What I got so far was - structure lack associativity or structure is monoid ( contains identity). I spent hours of searching the web. Usually authors state some very advanced claim or state structure which is of course monoid or group. I have been offerd bicyclic semigroup - but this is monoid, so it doesnt meet the question. Lack of my success and negative response on mathstack would suggest this doesn't exist. However I doubt there is not possible multiplication table. Thank you all.

I tried to construct a Cayley table of an algebraic structure called inverse semigroup. No success so far. I just end up with more complicated structure (monoid, group). Thank you kindly. I may think, that this phrasing is more accurate and more to the point. Also, I have checked many sources and didn't find an example... One possibility would be, that it is not possible (which I doubt). Or why would it be not possible? One chance is to try for any set $X$, let $I(X)$ be the set of all partial bijections on $X \to X$, i.e. bijections between subsets of $X \to X$. The composite of partial bijections is their composite as relations (or as partial functions). In fact, any inverse semigroup is isomorphic to a sub-inverse-semigroup.


I'm no longer able to post questions on Meta. I get the "We are no longer accepting questions from this account" message. I have a large number of downvoted questions here. Well, actually, there were only two such questions, but I'm not arguing. It is a fair deal. Like in aviation, rules on stack exist for a reason.  I'm asking to be warned about such things. I've seen dozens of different informational banners and popups on Stack Exchange sites. They provide help, inform you about/explain something.  But I haven't seen a warning like I describe. It would be nice to have one. Or not?

Another "miséricorde":  Consider  (emphasis added):  I think its okay, please dont take any efforts for me. I personally do not feel the system helps ask good questions. I dont know why asking for a software in this case is bad. Basically I needed a command that would give me this data. There is no other way I could have asked the question. I could have changed the question just for the sake of changing. I feel I am better off elsewhere. Thanks for your very very prompt responses. Regards. Bye. – user1744649  We just lost another user due to inadequate guidance on what questions are allowed.  The  by the time they are banned has been proven incorrect. Given that , we need a better way to make sure that users can understand how to ask good questions and what types of questions are allowed. I suggest that we warn newcomers, in a clear but positive tone, when one of their questions has been closed, downvoted (to a score of -2 or lower), or deleted, so that they don't repeat the same mistake.  This is probably best done the next time the user asks a question, and should appear as an "interstitial" page prior to reaching the actual Ask Question form.  The page should not appear to users:  with at least 50 (or perhaps 75 or 100) reputation that have asked a good question since the last downvoted/closed/deleted question that have fixed a bad question and had it reopened/undeleted/upvoted.  The content of the page should be adapted based on the specific problem with the previous question.  I would imagine something similar to the following (example for a question closed as off topic on Super User):  Before you ask another question... One or more of your previous questions have been closed as off topic. The scope of on-topic questions is defined in the , as follows:  What kind of questions can I ask here? Super User is for computer enthusiasts and power users. If you have a question about …  computer hardware, computer software, or personal and home computer networking  and it is not about …  programming and software development, video games or consoles, websites or web services like Facebook, Twitter, and WordPress, electronic devices, media players, cell phones or smart phones, except insofar as they interface with your computer, issues specific to corporate IT support and networks, asking for a shopping or product recommendation,  … then you’re in the right place to ask your question!  Please make sure that the question you are about to ask is on topic as described above. If you need help determining whether your question can be asked on this site, you can ask for advice on  or . You may also want to edit your previous question to address any problems associated with it. To ensure a high standard of content quality and prevent disruption to the community, users who repeatedly post low-quality questions  Continue  The  doesn't address this issue as it is shown only to users with 10 reputation or less (rather than up to 50 and possibly higher) and does not address the specific problem with previous low-quality questions.  The point of this feature request is to provide a easily understood targeted message that actually teaches the user about what happened with the previous question he or she asked.  The EULA is generic and may not have conveyed the intended message clearly if the user still asked a low-quality or off-topic question. For reference,  currently has 143 reputation and the proposed message would probably have been shown after the first closed or deleted question. I know this can be a complex feature to implement, since it needs to be adaptive, but this should help eliminate confusion on what the rules are and minimize the incidence of good-faith users getting post-banned.


I have a popup window where there are two onclick methods as "Submit" and "Discard".  When I click submit twice it insert two records that means duplicate record.   How can I avoid this?

I am working on a web application (J2EE) and I would like to know the options that are available for handling a double post from the browser.  The solutions that I have seen and used in the past are all client-side:   Disable the submit button as soon as the user clicks it. Follow a POST-Redirect-GET pattern to prevent POSTs when the user clicks the back button. Handle the onSubmit event of the form and keep track of the submission status with JavaScript.   I would prefer to implement a server side solution if possible. Are there any better approaches than the ones I have mentioned above, or are client-side solutions best?


I am trying to configure perl http api.  When I trying to run the perl script then it gives me error. Also I am not able to figure out how to install WWW/Curl/Easy package.  [emg@p1 ~]$ perl -c etc/ebe-http-custom.pl  Can't locate WWW/Curl/Easy.pm in @INC (@INC contains: /opt/perl-5.12.2-emg/lib/site_perl/5.12.2/x86_64-linux-thread-multi /opt/perl-5.12.2-emg/lib/site_perl/5.12.2 /opt/perl-5.12.2-emg/lib/5.12.2/x86_64-linux-thread-multi /opt/perl-5.12.2-emg/lib/5.12.2 .) at /opt/perl-5.12.2-emg/lib/5.12.2/Tumasms.pm line 5. BEGIN failed--compilation aborted at /opt/perl-5.12.2-emg/lib/5.12.2/Tumasms.pm line 5. Compilation failed in require at etc/ebe-http-custom.pl line 27. BEGIN failed--compilation aborted at etc/ebe-http-custom.pl line 27.

I get this error:  Can't locate Foo.pm in @INC  Is there an easier way to install it than downloading, untarring, making, etc?


I am coding a generic function that receives any entity class, accesses the database based on the class received and return an object filled with the contents returned from the database. Before someone asks, yes I am coding my own Entity Framework (just for fun!). What I already coded works if the class doesn't contain another class type. If the class contains another class inside I am trying to use recursive call to retrieve the object. In this case the generic type is changing and here is the point, the compiler doesn't accept a variable generic type. For example, suppose I have these 2 classes:  namespace Entities {     public class Order {         public int?Id { get; protected set; }         public DateTime Moment { get; set; }         public Client Client { get; set; }     }      public class Client {         public int?Id { get; protected set; }         public string Name { get; set; }         public string Email { get; set; }     } }   The generic function is: (simplified here and without the database access)  public static T GetById<T>(int? id) {     object obj = Activator.CreateInstance(typeof(T));     foreach (PropertyInfo prop in obj.GetType().GetProperties()) {         if (prop.PropertyType.Namespace == "Entities") {             int? idParent = n1; //where n1 is a value returned previously from DB             Type objType = prop.PropertyType;             prop.SetValue(obj, GetById<objType>(idParent)); //Compile error! "'objType' is a variable but is used like a type"         }         prop.SetValue(obj, n2); //where n2 is a value returned previously from DB     }     return (T)obj; }   It doesn't compile returning "'objType' is a variable but is used like a type". The code in the main program would have this line:  Order ord = GetById<Order>(1);   In this first call the type is known (Order) and the function works (without recursive call) returning the "Order" object but without the "Client" object. To retrive the "Client" object I need to call the function again (recursive call) but now the returned Type is unknown at compile time.  Does anyone have any suggestion?

What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod<T>() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod<T>()?         GenericMethod<myType>(); // This doesn't work          // What changes to call StaticMethod<T>()?         Sample.StaticMethod<myType>(); // This also doesn't work     }      public void GenericMethod<T>()     {         // ...     }      public static void StaticMethod<T>()     {         //...     } }


I am creating a portfolio site that I'd like pull in partial HTML files through an AJAX request. This is the basic HTML:
       // This will be replaced
     Click Me   The jquery code that I am using looks like this:      $( "#fire" ).click(function() {         $( "#portfolio" ).load("partial.html #portfolio > *");     });   This works, and I'm able to load the individual partial pages, but I cannot figure out how to have scripts run on the inserted HTML. I'm using Foundation Orbit, and I want to have these sliders function properly after the AJAX call. I thought maybe it was a conflict, so I also tried using slides.js, but that didn't work either. I have all the dependencies and needed scripts in my index file. What do I need to do to have the Orbit script apply to content on the page after the AJAX call?  I have a functioning plunkr that shows the problem I'm having. I'm just learning all this, so apologies if there is a super obvious answer, but I haven't found it on the site.  Here is the . It has a working Orbit slider to prove -- to myself -- that the script is working.   Thanks in advance!

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Consider a sequence $\{x_n\}$ in $S$. Where $S$ is a metric subspace. Given that every convergent subsequence of $\{x_{k(n)}\}$ converges to the same point say $x$. Prove that if S is compact, show that $\{x_n\}$ converges to $x$. Is my answer correct?

Let $(x_n)$ be a sequence of real numbers.  Prove that if there exists $x$ such that every subsequence $(x_{n_k})$ of $(x_n)$ has a convergent (sub-)subsequence $(x_{n_{k_l}})$ to $x$, then the original sequence $(x_n)$ itself converges to $x$ .              Thanks for any help.


How do we know that the number $1$ is not equal to the number $-1$? (I am not talking about the multiplicative inverse of an arbitrary field, but the integer/rational, real or complex number $1$.) Is that an axiom? Since someone in the comments asked for more background/motivation: I'm just a naive bachelor student and I wanted to prove that for any number $x$, $x=-x$ implies $x=0$ (which is true if and only if $1\neq -1$, see ). Why is this question different to the question in my last post? In my last post, I wanted to know if you can prove that $x=-x$ implies $x=0$ for an element $x$ of an arbitary field. It turned out that you can not (there are fields where this is not the case). In addition, it turned out that this is true if and only if $1\neq -1$. ($1$ stands for the multiplicative identity, not the number one.) Since we normally assume that $x=-x$ implies $x=0$ if $x$ for some number $x$ (at least in my lectures), I wanted to know wheter you can prove that $1\neq -1$ or not. (To be honest, I didn't think that you have to distinguish e.g. between the integer $1$ and the natural number $1$...) To put it into a nutshell: My first question was wheter you can prove $1\neq-1$ where $1$ stands for the multiplicative identity of an arbitrary field (the answer is no.) But we know that the answer is yes if $1$ stands for the integer/real number/complex number one, which led to this post.

Let $F$ be a field and $x\in F$. If $x=-x$ and $1\neq -1$, then $$0=\frac{x+x}{1+1}=\frac{1+1}{1+1}x=x.$$ This means that the statement in the title is true if and only if $1\neq -1$. But how do we know that $1\neq -1$ for an arbitary field?


As a 3K user with close privileges on MSO, if I accidentally flag a question as "It doesn't belong here or is duplicate", my flag is supposed to be automatically converted to a close vote.  However after the new close reasons were rolled out, there is an odd UI behavior that is initially showing it as a flag, and at the same time is showing me the flag count on the post.  After Flagging    After Refreshing Page  Once I refresh the page, all is well, and my flag is moved over to where it belongs and I can't see the number of flags anymore.    Steps to reproduce:   Find a crap question that needs closed Flag with "It doesn't belong here or is duplicate" Select appropriate reason* Enjoy seeing how many flags the question has. Refresh the page See the flag count disappear and your close vote displayed in the correct place.   As pointed out in the comments by Matt (and the current duplicate), the value next to "flag" might not be the flag count, but actually the correct close vote count in the wrong place.  Refreshing still corrects the UI bug regardless of what is actually displayed.  * - Since I've only figured out the reproduction steps this morning, I have only experimented with "Primarily Opinion based" and "Off-topic/Not a programming question".  I suspect all of the close reasons will behave the same and I don't want to randomly cast close votes to test unless the question deserves it.  (This has only been tested on MSO since it is the only site I have VTC privileges, but I would assume it behaves the same on all sites that have the new close system in place).

If I (as a user with vote-to-close privileges) click "flag" on a question, I see the ability to flag as "does not belong here, or is a duplicate".  Is this a ? I'm quite sure I didn't used to be able to see that.   Anyway, if I use that ("does not belong here, or is a duplicate") option and VtC the question, take a sip of my tea and continue about my daily business, upon submitting the "flag", the counter for the "flag" button gets set, not the "close" button.   This would seem like a definite .


I made a nice-looking tile texture:  Now I want to repeat it on x and y axes. Is there any easy way to do it?

Most people's question in this area is how to reduce repeating patterns, however I want to create them.  I'm creating 2d rendered tiles for my game, and I want to create procedural materials for my tiles that will seamlessly match. For that I need the cycles procedural textures to repeat on a predictable interval.  I've looked at similar threads, and they only deal with simple gradients, or images, not things like voronoi, musgrave, noise. I haven't been able to figure out how to scale/manupilate with math, the procedural nodes to any degree of repetition.


Currently, I am using below tag to detect whether VF Page is embedded in lightning or Classic or Mobile devices. Below the line of code return values as Theme3, Theme4t, Theme4u etc. These values can be changed by salesforce at any time.   var currentUserContext = "{!$User.UIThemeDisplayed}";   Instead of below lines, is there any other way we can check whether VF page is loaded in Lightning or classic or S1 mobile app.

I have a Lightning Components and need to know if it is running inside of a Community or in Lightning Experience.  Is there a way to detect the running context?  Right now I'm checking document.location against a hardcoded Community-path but I need a general solution.  Best Idea I have so var to make it dynamic is to check for '/s/' in the URL. But I'm not sure if this is reliable for all possible Community pages. Also it feels like an hack.  After detecting the context, I also need to get the URL Prefix from the community. Again I could cut it out of the path, but would prefer otherwise.    Googling around didn't brought much. So far I found some context-aware unanswered questions here:


A basic limit question I don't quite understand... The question is as $$\lim_{x \to 5} \sqrt{x-5}$$ and solve for the limit. When I plug in $5$ I get the answer zero, but when I tackle this question graphically the limit does not exist as nothing comes from the left of $5$.  Could anyone clear this up for me? Thanks.

What is the limit of $\sqrt x$ as $x$ approaches $0$? I asked a few people and they all gave me two different answers. Some said that the limit is $0$, and other say that the limit is not defined because the right-hand limit is $0$ while the left-hand limit is undefined. I'm confused. please help!!


This is sort of an SO zeitgeist question.  I thought I might dig into the python backlog (there are 800 pages of questions) to clear out of some of the fluff - there are a lot of questions that are basic python questions, i.e. along the lines of 'how do I write a list comprehension?' They are question and answer, so short-term they serve a purpose; long term, they probably don't. Then I started wondering about why they should be closed... if you go scrolling back through pages of old questions, closed questions appear there. (anyways, I don't have rep to vote to close yet anyways, so it doesn't matter).   In any case... while I get a lot of value out of this site, there are some parts of the moderation system I don't completely understand, so I thought I'd ask - this particular question is a symptom, not really the underlying question, but maybe it will help.  The difference between these old questions that are closed, and old questions that aren't closed, appears to be nothing - they still show up in browsing, they still show up in search results. As the short FAQ says, the best answers and questions appear by voting them up or down. Voting a 'bad' question down pushes it out of visibility most of the time anyways.   What value is gained by closing them, as opposed to just voting them down?

Having been a member of Stack Overflow for a year, I have participated in reviewing close votes and flagging questions if I found any duplicates. However, I don't understand the purpose of closing a question.  As per myself, the main purpose is keeping the site clean and make a better place.     I still see closed questions on the site that are a year old.  When will these questions be deleted?   Also, when a question/answer does get deleted, it is still visible to 10k users, even if it is deleted by the owner.   Every day I participate in reviewing close votes, but the question arises why we are preserving these questions and answers even after they are closed.


We can solve the Schrodinger equation for the Hamiltonian operator from the classical Hamiltonian of hydrogen bound state, consisting of proton and electron attracting each other electrodynamically, to get the eigenfunction, which is corresponding to stationary bound state we wanted to find.  But It must also be possibly explained through QED, but maybe rather complicated way. I can't even imagine the way it does. Could anyone explain it for me possibly qualitatively?

I am a beginner in QED and QFT.  What is known (or expected to be) about bound states in QED? As far as I understand, in non-relativistic QM electron and positron can form a bound state. Should it be true in QED? Most of the basic text books on QFT I known treat QED with perturbative methods which do not help to study bound states. Is there a literature to read about it?  UPDATE: According to , electron and positron form a positronium. It is an unstable particle which can annihilate to two photons. In particular electron and positron cannot form a bound state. But still there is a logical possibility that several electrons and positrons can form a bound state (though probably once one has at least one electron and one positron, they will necessarily annihilate. Is it true?)  On the other hand, if one considers QED with both electrons and muons, then electron and antimuon form muonium. Clearly they cannot annihilate to photons. However in  in wikipedia it is claimed that muonium is unstable. Is it due to some effects of QED or due to actual presence of other, say weak, interactions?


Twins is a 1988 comedy featuring Arnold Schwarzenegger and Danny DeVito as genetically engineered twins. The fact that they’re genetically engineered is used to explain the differences between Arnold and Danny, but the movie would’ve probably worked as well if they would’ve been regular brothers. , .  If they would have been is something I would never say. In my dialect, if they had been is the correct choice. And I don’t think I’ve ever heard the if they would’ve been construction from anyone here in the middle of Ireland, or even from anyone on this side of the Atlantic, but it is certainly common online. I suspect that this is currently a purely American phenomenon, but I could well be wrong about that. I am not sure what search terms to use to do my own research. The phrase “double conditional” is one I came up with as I asked this question. I’m certain it’s not the standard term used to describe this usage. And most results from a search are about programming languages. However, I did turn up a couple of relevant references.  DEAR GRAMMAR LADY: A prominent scholar made the following statement in a recent article. “If we would regard religion as a work of art — as a piece of music — we would have a different understanding of it.” The “would” in the first clause strikes me as being incorrect usage/phraseology; i.e., I had expected “If we regarded or if we were to regard.” (sic) Could it be that even scholars of great renown are capable of such blatant mistakes? ANSWER: You are correct. She is guilty of what I call the “double conditional.” Mary Newton Bruder, The Grammar Lady, .  I also found , but it goes off topic almost immediately.

This has been bugging me for some time; I tried to look for previous questions here but my language tools may not be sharp enough to phrase my query correctly so please forgive me if this has already been posted here.  Speakers of English as a foreign language tend to incorrectly use the word "would" when using some particular subjunctive constructs. Here is  (this time presumably by a native English speaker):     If that would happen, you won’t be alone.     (One correct version being "If that happens, you won't be alone".) I have detected this in speakers of a number of languages so I feel this is more likely to be a feature of the English language itself than a carry-over from their native language.  I have a faint intuition that this is because , and it certainly doesn't help that , but I can neither make that precise nor even really phrase a concrete question. Can someone shed some light on this?    Edit: just to provide some real-world examples of what I mean, here is one example taken from :     Publish or Perish is designed to empower individual academics to present their case for research impact to its best advantage. We would be concerned if it would be used for academic staff evaluation purposes in a mechanistic way.   This is obviously ungrammatical (to me), but I'm not sure how to characterize the mistake, or what the likely causes are (e.g. whether it follows from analogous constructions in other languages).


We all know that the fundamental particles to be controlling the electric and magnetic forces in our universe are obtained in pairs(electrons and protons, north pole and south pole.) Likewise I guess it is safe to assume that even the weakest long range force,Gravity, also follows the same. So, is anti-gravity real or just a rubbish idea of my tiny brain?Also I think this might be related to the Quantum realms.

Confinement of antihydrogen might help provide a future answer.


I have 2 Files:  C:\Program Files\MyApp\images\image.png  C:\Users\Steve\media.jpg   Now i want to calculate the File-Path of File 2 (media.jpg) relative to File 1:  ..\..\..\Users\Steve\   Is there a built-in function in .NET to do this?

There's a part in my apps that displays the file path loaded by the user through OpenFileDialog. It's taking up too much space to display the whole path, but I don't want to display only the filename as it might be ambiguous. So I would prefer to show the file path relative to the assembly/exe directory.  For example, the assembly resides at C:\Program Files\Dummy Folder\MyProgram and the file at C:\Program Files\Dummy Folder\MyProgram\Data\datafile1.dat then I would like it to show .\Data\datafile1.dat. If the file is in C:\Program Files\Dummy Folder\datafile1.dat, then I would want ..\datafile1.dat. But if the file is at the root directory or 1 directory below root, then display the full path.   What solution would you recommend? Regex?  Basically I want to display useful file path info without taking too much screen space.  EDIT: Just to clarify a little bit more. The purpose of this solution is to help user or myself knowing which file did I loaded last and roughly from which directory was it from. I'm using a readonly textbox to display the path. Most of the time, the file path is much longer than the display space of the textbox. The path is supposed to be informative but not important enough as to take up more screen space.  Alex Brault comment was good, so is Jonathan Leffler. The Win32 function provided by DavidK only help with part of the problem, not the whole of it, but thanks anyway. As for James Newton-King solution, I'll give it a try later when I'm free.


When you back up the car you're going to back it up until your body is even with the middle portion of the trunk on the other car. Then at that point you're going to turn your wheel all the way to the right, and you're going to create an angle. What you're going to do is your car is going to be in a position like this when you turn the wheel to the right, OK.    I have a greatvdeal of time figuring out what all these going to s really mean . Does all of them mean the same here? I know what it means. It is talking about something that would hapoen in the future. But all these in this short speech is confusing .

Today I want to be able to give you some good tips on parallel parking. It's part of your road test. It's something you need to learn. For most new drivers it's real difficult, because they're not able to judge angles. And parallel parking is all about angles. I'll take you through a typical parking, I'll take you through how I teach it , and maybe that'll help you in passing your road test. The first thing you want to do is you want to pull over over and you want to stop alongside a parked car. Typically, an inspector will give you a command to pull over, stop next to the red or blue car. You're just going to pull over, put your blinker on to the right, and pull over even with that car.     taken from a series of videos teaching driving   Why did the man use  be able in his speech? What is the difference between be able and I would like to or I want ? I mean what the listener should make of  I want to be able to give you ...  . Why did not he say I want to give you... ?  When he says I'll take you through a typical parking , I get the meaning of take one through ,It means I am going to teach you , isn't it? But my real concern is what the second I'll take you through means, while saying I'll take you through how I teach it . Perhaps it doesn't mean I will teach you that how I teach it ! , does it? The man always says the first thing you want to do . Why does not he say the first thing you should do , the first thing you need to do ? What are the diffrences in meaning? Isn't it unnatural saying you want to do ? In the last sentence he says You're just going to pull over, is the use of going to just weakening would and will? I think here it means something else. I think it means you just want to or you just start


I want to fill this shape with a gradient, but because it's divided it won't fill it completely, leaving a gap between subshapes. How can I join these subshapes? I can't use pathfinder because it will just create another stroke between subshapes, but won't fill the gap. Fill tool doesn't really work here: It fills the gap, but if I try to divide this shape once again, the fill color will just vanish.

Is there any way to fill grouped objects background in Illustrator?  Below is example how i want it, right now i simply just put white square behind them.


I am trying to find a good word or phrase to describe someone who (or the act of someone which) tries to benefit from everything someone else has or does.  The context is, on a personal level.   For example, a friend, parent or someone else tries to be included in all of the good things that come out of your hard work.  A more concrete example may be "My friend Sam is always pushing to drive my new car, stay at my new house, go out when I get paid knowing I'll pick up the tab, inviting herself and her child to any of my interesting outings for the child's benefit. Sam is ______".  I do want to make the distinction that this should not be strictly related to money. It's just one person who uses someone else's advantageous situation to benefit, at every possible opportunity. The word/phrase I am looking for should describe either that person or their act.

What would you call someone who isn't afraid to ask for money or any kind of favor or who misinterprets someone's generosity for a consistent resource for what they need?


I have a very long equation. The MWE is:      \documentclass[12pt, A4paper]{article}     \usepackage{lipsum}     \usepackage{amsmath}     \usepackage[left=2cm, right=2cm, top=2cm,bottom=2cm]{geometry}      \begin{document}  \lipsum[1]      \begin{align*}     \sqrt{A^{2}+4B^{2}\times {PC^R}^{2}+4AB\times{PC^R}}&=\sqrt{\sigma_{11}+\sigma_{55}M_{1i,t}^2+\sigma_{77}M_{2i,t}^2+2\sigma_{15}M_{1i,t}+2\sigma_{17}M_{2i,t}+\sigma_{57}M_{1i,t}M_{2,it}} \\     &+\sqrt{4 PC^2\left[{\sigma_{22}+\sigma_{66}M_{1,it}^2+\sigma_{88}M_{2,it}^2+\sigma_{26}M_{1,it}+\sigma_{28}M_{2,it}+\sigma_{68}M_{1,it}M_{2,it}}\right]} \\     &+\sqrt{PC\left[\sigma_{12}+\sigma_{16}M_{1,it}+\sigma_{18}M_{2,it}+\sigma_{52}M_{1,it}+\sigma_{56}M_{1,it}^2+\sigma_{58}M_{1,it}M_{2,it}\right]}\\     &+\sqrt{PC\left[\sigma_{72}M_{2,it}+\sigma_{76}M_{2,it}M_{1,it}+\sigma_{78}M_{2,it}\right]}     \end{align*}  \lipsum[1]          \end{document}   As you can notice the equation reaches the end of the page. I know that I could try to make some simplifications or I could even split the RHS in more bits, but this are options that for some peculiar reasons are not useful to be followed.   Any suggestion on how I can shrink the equation and align it to the body text? Thanks in advance.

I want to show the derivation of a formula where I encounter long formulae. Unfortunately the derivation is very complex, so I have to show some intermediate steps.  My problem is, that I want to mix the behaviour of multline with align. The first line should be aligned left and the whole rest should be aligned right with respect to the longest line. This block should be aligned at the =.  At the moment, I use the align environment. But in this case, the first line is still aligned left to the $ of the other lines.  Important note: I don't like magic numbers. So I prefer solutions which are completely automatic.    My approach so far:  \documentclass{scrartcl} % Kodierung \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} % Sprache (neue deutsche Rechtschreibung) \usepackage[ngerman]{babel} % Mathematik \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb}  \begin{document}     \begin{align}         (a+b+c+d+e+f) \\ % aligned left         % the following block should be aligned right         &= a+b+c+d+e+f+g+h+i+j+k+l+m+n\\     \begin{split}         &= a+b+c+d+e+f+g+h+i+j+k+l+m+n \\         & \quad +o+p+q+r+s+t+u+v+w+x+y+z+1+2+3+4     \end{split}\\         &= a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p     \end{align} \end{document}


We have a bag with 4 balls, one white, one black, one blue and one red. We are drawing balls with replacement. Find the expected value of the number of tries needed to draw all four colours.  More general: We have a uniform discrete distribution. What is the expected value of the number of tries needed until all elements of the sample space have occurred.

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic?


I am using vodafone dongle but when I am using it ,it is detected inside computerwhile connecting take long time  but can not connect to internet

I have connected the dongle to my laptop, it shows in network manager with my network provider name (tata docom), but can't connect to internet. How can I fix this? Writing in terminal  lsusb  command gives following output Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub Bus 001 Device 003: ID 19d2:0143 ZTE WCDMA Technologies MSM   here ZTE wcdma is my dongle device  Device: usb0 ----------------------------------------------------------------- Type:              Mobile Broadband (GSM) Driver:            cdc_acm State:             disconnected Default:           no Capabilities:


When I point a laser at a wire , a circle of light appears on a wall behind it . why this happens.  What is the circle of light and why does it appear?  Could anyone give some tips on what I should search for or any references?   wire have diameter 3.17 mm   PS.I don't good at English,,, sorry   Wire perpendicular to the projection screen   Laser under on the wire Then born circle of light

So, when I point a laser at a piece of wire (pointed at a specific angle), a circle of light appears on a wall behind it (see image below). I am trying to see why this happens and if there are any readings on this. Could anyone give some tips on what I should search for or any references?   ()  So this is a problem for a physics tournament, but I haven't tried it myself yet. However I have found a video depicting what I mean.


Is it possible to find the index of a list in a for loop without using a generator?  for character in string:     if character == "a":         print(get_index_somehow)   I am aware that you could use a generator in a for loop and get the index that way  for i in range(len(string)):     character = string[i]         if character == "a":             print(i)   Just curious if it's possible

How do I access the index in a for loop like the following?  ints = [8, 23, 45, 12, 78] for i in ints:     print('item #{} = {}'.format(???, i))   I want to get this output:  item #1 = 8 item #2 = 23 item #3 = 45 item #4 = 12 item #5 = 78   When I loop through it using a for loop, how do I access the loop index, from 1 to 5 in this case?


We currently have around 20 apex classes and 5 triggers which are not used in our production org. We want to delete them in our production instance. We dont have ant scripts ready yet to be used for our deployments and so we cannot use destructivechanges file. Currently our production deployments are done by our support team and they need documentation from us to do these deletes. Changesets do not allow to delete apex classes and triggers. So what is the best way to delete these apex classes and triggers from production?

I was recently told (  ):     You cannot delete a class in production directly. You will need delete   the class from your sandbox and then deploy the deletions to your   production org.   When you deploy from sandbox to production, the   missing classes will come up in red and you can choose to deploy these   deletions to Production.   However, I'd like some clarification because finding information on how to do this is like pulling teeth, unfortunately.  Am I supposed to:   Delete the Trigger in Sandbox Make a deployment package in Sandbox Add the Trigger which is going to be listed in RED now Deploy (and that deletes it from Production)?   I am not seeing deleted Triggers in Red in Sandbox.  Are they NOT listed under "Triggers" for deployment, but elsewhere?   Frustrated = true.   Does this ONLY apply to Classes??  UPDATE:  I just tried again, with a CLASS, and it still doesn't show up at all as a Deployable package (red or not) after I delete it in the Sandbox.  UPDATE 2:  I was just able to delete a class, that I know was written via IDE from a third party, in both Sandbox and Production.  So now I'm wondering if it has to do with where it was originally deployed from (if from IDE, IDE can delete it - it from Sandbox, you have to jump through hoops).  :-(


We have a 2012 Server which is failing to install updates, just searching online, WSUS forever to get updates. I tried rebooting and running the WSUS stop, renaming the Softwaredistribution folder and tried to install some patches manually, but the installation is taking forever too.  Even the manual installation is also taking forever. I checked windowsupdate log file and the logs says no approved patches, but when i checked online and for WSUS updates, for the effectiveness, it is taking forever to search for updates.  Please help me in getting this resolved.  Thank you.

I recently inherited the management of a Windows 2012 server at a remote site.    I checked Windows Update and it has not been updating since March.  When I tell Windows to check for updates, it acts like it is checking, but it seems to say that for hours.   If I attempt to restart the windows update service, it seems to never be able to shut down.  My only remedy seems to be rebooting to get back to the point where I can tell Windows Update to check for new updates.    The last successful check for updates says March 20.  The last time updates were installed says March 17 (failed).  The update history shows that one update failed for March 17, a printer driver update, but the history shows 13 failed updates for Feb 17.  Not sure what else to try.


Suppose $f(x)$ defines on the bounded interval $I$. Prove that $f(x)$ is uniformly continuous on $I$ if and only if the image of each Cauchy sequence under $f$ is also a Cauchy sequence.   The "only if" part is easy. For the "if" part I can prove that $f$ is continuous on $I$. But how to prove it's uniformly continuous? I try to prove by contradiction, but could not get a Cauchy sequence.

Let $f$ be a continuous function. If $f$ is uniformly continuous then it maps cauhy sequence into cauchy sequence. Is the converse true? That is if $f$ maps cauchy into cauchy gives the uniform continuity of $f$. I think it's no. Can suggest a counter example


I was in dual-boot. using Ubuntu and Windows I have recently re-installed windows, now I'm having troubles with boot. It is always booting with windows, it's not showing options to choose between win and ubuntu (it starts to win automatcally). I am using ubuntu 16.04  How can I fix it?   Thank you.

I went ahead and installed windows 10 on my windows 8 and Ubuntu dual boot PC. All went smooth and Windows 10 works perfectly however the computer automatically boots to Windows and the grub launcher is missing. The partitions are still there I just need some help getting Ubuntu back. Thank you in advance!   Edit: I found a way around it. I don't know of this works for everyone but I went in to the control panel and went to update and recovery. Then I went to recovery and booted into uefi.  Then I selected boot from device and my Ubuntu partition was there and I could boot into it.  Feel free to post other solutions though!