Find the greatest value of $a^2b^3$ where $a,b$ are positive real numbers satisfying $a+b=10$.Determine the values of $a,b$ for which the greatest value is attained.   It is my question.I continuously tried to use weighted A.M-G.M. inequality, but unfortunately I found no way.I don't think it can be done using Tchebycheff's inequality or Cauchy-Schwartz's theorem. Please give me any hint for doing that.I also failed to solve another similar problem (but reversed. "Find $\min(3x+2y)$, where $x^2y^3$=48). If possible then please give me hint in that also. Thank you.

Find the greatest value of $a^2\cdot b^3$ where $a,b$ are positive real numbers satisfying $a+b=10$. Determine the values of $a,b$ for which the greatest value is attained.  At first I tried to find the value by putting $a=10-b$, I found a expression, but I got not way to do anything.   If we apply A.M-G.M. inequality, I think we found the minimum value or something else. It is a pre-Olympiad level problem. So I need some answers or some good hints.


I am a new blender API/addon developer. I am really bad at the mesh(bmesh) library. Do you guys know any guide or tutorial to use mesh library of blender API? the docs of Blender are really useless. I hardly understand it. I need more like a source with visual examples

Since asking for tutorials, videos, resources, links to other content or downloads is considered off topic here, this is a specifically created Community Wiki which gathers resources for Blender and it has been approved by the .  Just write in the appropriate answer/section. If you have concerns, questions, post a  question, so we don't clutter the comments, but you can link your meta question from the comments.  Questions regarding such resources are not allowed anymore, except for very specific and on topic requests (ask on  if you're unsure about your question). Follow the instructions made in the question about how to post, what can be posted, etc.  Learning             Assets    (also see: )   Reference Images/Blueprints (also see: )    Tools    (also see: )      Other   Special Interest ()     Also see the .


What is the difference between "someone is waiting for me" and "somebody is waiting for me?" Please make it clear for me.

Are there any subtle differences between "somebody" and "someone", or can they be used completely interchangeably? Similarly, can you imagine a situation in which you would prefer "anybody" to "anyone" or vice versa?


I have an interview coming up as an adjunct faculty for computer science. I am required to do a teaching demo for the interview. What is the best way to show the faculty my teaching style? I am using powerpoint to aid in my demonstration. I do not want to be the "person who reads off the powerpoint."  Thank You

A model lesson is a usual element in interviews for the faculty level positions. Normally this is not a full lesson but a 15-minute version which is performed in absence of actual students for just a few professors from a hiring committee. It is supposed to demonstrate "your teaching style", but by design this is clearly a different enterprise: you should "act normal" doing "the same" things    in a different time-frame,  for a different audience,  with completely different motivation and  under exorbitant cost of failure.   Having said this, I also acknowledge the model lesson as indeed a much needed element of the interview, which helps to assess a candidate's set of relevant skills.  The question is how one can ideally prepare to give such a model lesson. Putting aside obvious things like "structure of the talk," "clear slides," "projection of the voice," and "body language", which normally should be already trained by experience, are there specific things that should be taken into account for the model lesson only? What about techniques like jokes, questions to the audience (e.g. how many of you are familiar with the definition of the derivative), work in pairs, which you probably use in a real classroom — is it a good idea to demonstrate them in a room full of senior professors? I am a little confused.


I was a longtime windows/linux user and just purchased a Mac, everything is great except that I need a good download manager for Mac which works like Internet Download Manager for Windows, I know some things would be different but I am specifically looking for following feature   ability to resume downloads automatic capture of downloads from browsers such as firefox   I use Downthemall in firefox right now but it is not as reliable as it was on Windows.

What is a good Download Manager for Mac? Are there free ones available?


My question is connected with programming. I'm not sure how to name my class.  Should it be ItemQueue or ItemsQueue? We are talking about queue, which stores many items.  We can add new ones or remove existing. Similary, what about file list/files list? I have always wondered which form should I choose.

Possible Duplicates:             I'm wondering whether or not I should use a plural form noun with a collection name. For example, which one is correct, bookList or booksList (obviously they are variables in a programming language)?


Please someone tells me why, after installing Ubuntu 12.04, that my clock displays the incorrect time. My operating system time is delayed several hours, and I don't know how to fix it. Thank you.

Dual boot system Windows XP Pro and Ubuntu 12.04.  I have the bios set for the correct time and Ubuntu set for US Eastern time.  Ubuntu will boot up and the time will be off by -4 hours.  If I correct the time in Ubuntu then when I boot up in Windows XP the time will be off by + 4 hours.  This is a fresh install of 12.04. I did not have this problem before reinstalling Ubuntu.


Have you ever gotten an answer soooo good, you wished you could give a +20 instead of +1 ?  Bounty System  That's a good mechanism, but they're not always right for this situation:   Bounties are usually associated with giving incentive to answer or draw traffic. I would expect that most users offered bounties before getting an answer, not after. Bounties are usually offered by people with plenty of reputation. "New" users should be able to reward exceptional answers too.   Thanking in a comment  A warm comment on the answer is always nice, but I'm not sure comments are intended for saying thanks - but to clarify / improve the answer itself.  So what is the recommended way to reward this truly exceptional answer?  Other suggestions?  I know there is an answer of the week blog, is there a way to nominate an answer to be there? Sometimes exceptional answers are hidden in low-interest questions that receive less traffic - so those will never be upvoted enough to become noticed.  Or maybe instead of a single blog for the entirety of SO, there should be an entire section called "Answer of the week" with more than one answer (maybe on a per-tag basis). Answers should arrive there based on manual nominations and not on upvotes so unpopular questions will not be discriminated against.  Clarification:  It's not that I'm personally against bounties - I use them plenty of times. I'm mostly concerned about what other people tend to do. I suspect the bounty post-answer reward is not used as much as it should. I believe the majority of people don't consider bounties for this purpose.

Stack Overflow has been one of my best sources to gain knowledge on JavaScript.  Some answers have been exceptionally helpful - eye opening - and I'd like to know if there's a way to reward the authors beyond upvotes and bounties.


It's always taken for granted that the real number line is perpendicular to multiples of $i$, but why is that? Why isn't $i$ just at some non-90 degree angle to the real number line? Could someone please explain the logic or rationale behind this? It seems self-apparent to me, but I cannot actually see why it is.  Furthermore, why is the real number line even straight? Why does it not bend or curve? I suppose arbitrarily it might be strange to bend it, but why couldn't it bend at 0? Is there a proof showing why?  Of course, these things seem natural to me and make sense, but why does the complex plane have its shape? Is there a detailed proof showing precisely why, or is it just an arbitrary choice some person made many years ago that we choose to accept because it makes sense to us?

So, floor is a function that converts a real number to an integer. It rounds down. This makes sense; however, what about complex numbers? I know that depending on the number, it can be split linearly. However, I do not know what $\lfloor i\rfloor$ equals. Is there a clearly defined definition of $\lfloor i\rfloor$?


This is not a case of serial down voting.   This looks like a revenge kind of thing, at least it looks like that to me. What I am trying to do its to find out what can I do in this specific situation.   and  seem to be owned by the same user - :    I can't be 100% sure but it looks very suspicious.  I have received 2 down votes almost within the same time then about 20 minutes ago I have got another  - seconds after the question has been edited by mr S.  What can I do to prevent further down votes? I am aware of how the serial down voting system works but like I said this isn't the case specially that the user may have more than 2 accounts.   What does stackoverflow offer in terms of reporting suspicious down votes and multiple accounts users? I wouldn't want to stop contributing but if there is no way to report/stop such behavior from a pissed-off user then I am most likely going to reconsider the whole point of helping this community.

offers an answer to "How to report Sock puppets who upvote their own posts".  describes revenge voting.  Recently, I've downvoted an answer and added a comment. After submitting my answer to the same question, I noticed that the downvoted answer has been upvoted (within 2 minutes, probably a sympathy vote, I thought). I added more explanation to the downvoted answer, because the answerer believed that his answer was correct. A few minutes later, I received a downvote for my top upvoted answer. My answer became accepted, for which I received another downvote. I verified (Data explorer) that the specific user did not add new downvotes. So, I suspect this user of having a sock puppet, since the order of events were too coincidental.However, since the sock did not upvote the owner's post, flagging the post will probably not help. So, how can moderator's attention be requested for this case? Attachments: Comment chain:  Reputation mutation (the times do match):


Considering:  and   I do not agree with the current trend of validating every single feeling a child might have. I think it leads to entitled adults who think that their feelings are above everything else, adults who think they have the right not to be hurt or offended, ever. There's a difference between acknowledging a child's feelings ("I understand how you feel and why you feel like that"), and telling them it is OK to feel like that when it isn't. It is OK to feel hurt when someone insulted you. It is OK to feel sad when your friend moves to another town. It is OK to feel anger when you see someone abusing somebody else. It is not OK to feel envy of your friends toys. It is not OK to feel rage because you didn't get cake for dessert. And it is not OK to feel apathy because you had to write your name 5 times back at school. Sure, it's not easy for a child to discern when it is OK to feel some way, and when it isn't. That's why we parents are here: to help them learn.  What about the "bad" feelings of the child? Should they be mirrored or not? What do studies say in this regard?

The article  says,        Accept your children’s feelings.   ...   Instead, comfort your children and let them know you love them, rather than try to talk them out of how they feel.      Google says that “talk them out” means “to discuss a problem in detail” or “to settle something by discussion”.  According to the , correct interpretation is "to persuade someone not to do something".   Why is it a bad idea to tell a child not to feel bad about something? Won't that make the child stop feeling bad and be happy? Does this have any negative side effects?


I am trying to rotate the array by using following function:  def rotLeft(a,d):     temp=[]     temp.append(a[0:-1])     temp.insert(0,a[-1])     return temp   I should get output as 5 1 2 3 4   but I am getting 5,[1,2,3,4]  how to solve this problem

What's the difference between the list methods append() and extend()?


I’m taking a (non-student) job as a full time research assistant in a university engineering department, and am wondering what alternate title I could use for this on my resume that isn’t misleading.  Research assistant has a connotation of being a lower level student job, and I have a MS degree and ten years of work experience, so I’m hesitant to put that title on my resume.  If this was in industry I could use research engineer, but in academia, that has a connotation of someone who is a principle investigator and has a PhD.   My job description is a hybrid between these: I’ll be doing research and publishing, but in support of someone else’s project.  Also some departmental work setting up labs, learning and maintaining the equipment and helping teach students to use it.  Most of my time will be spent on research activities.  Suggestions for an alternate job title?

When applying for non-research related work in the commercial sector, how should confusion be avoided over the term "Research Assistant" being used in a CV?  Are human resources staff at companies, and recruiters, at risk of assuming "research" means market research, as opposed to scientific research, especially if they're skimming through the CV?


I can't see this being asked before, although maybe I haven't searched enough.  If I go to my profile, click on All Actions and then the Comments tab, there is a long list (and multiple pages) of my past comments shown.         However, no year information is shown, only the month - even for comments posted over a year ago.         This is confusing, as it makes one wonder if the date (month/day) refers to this year. The presentation is the same, whether the same month and day of the comment is from this year or last year, or three years ago.  I was trying to locate an old comment, but was continually losing track of what year I was currently looking at, and had to click on random comments in the list to see to which year, that particular part of the comment list, pertained.  It would be nice to have the year added, or maybe "n years ago" (although this is not as good as having the actual year displayed.  This issue affects the Comments, Suggestions, Reviews, Revisions, Badges - in fact all of the tabs under All Actions.  It does not affect Reputation tab, maybe that sort of display could be used?

Here's :        At the moment, the latest entry there is October 13, which would be mistaken to mean October last year (2012), but it actually is October 2010. This applies to all the filters in the activity tab.


A level 11 Fighter makes 3 attacks per Attack action as per:  Extra Attack Beginning at 11th level, you can attack three times, instead of twice, whenever you take the Attack action on your turn.  According to Players' Handbook, any character can attack with both hands:  Two-Weapon Fighting When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.  If a level 11 Fighter is brandishing a light weapon in each hand, how many attacks do they make per turn? 4: 3 from the Attack action + 1 from the bonus action? Or 6: 3 from the Attack action + 3 from the Bonus action?

I have a 5th level fighter with the Two-Weapon Fighting fighting style.   What is the number of attacks I can make?   I say 4 attacks, but others say 3 because they say the rule on page 72 states that I get (only) 1 extra attack.


I will be traveling from India to Cuba with an connecting flight at Paris CDG airport to Cuba. The layover is 7hrs. Do I need a transit visa for the layover at Paris Airport?

I found many related questions on this site but I am still not sure about the rules. How can I decide if I need a visa to transit? Schengen members as of May 2021 are as follows:  Austria Belgium Czech Republic Denmark (excluding Greenland and the Faroe Islands - but an open border with the Schengen Area is maintained) Estonia Finland France (excluding overseas departments and collectivities) Germany Greece Hungary Iceland Italy Latvia Liechtenstein Lithuania Luxembourg Malta Netherlands (excluding Aruba, Curaçao, Sint Maarten and the Caribbean Netherlands) Norway (excluding Svalbard) Poland Portugal Slovakia Slovenia Spain (except Ceuta and Melilla) Sweden Switzerland


I'm using QGIS to produce thematic maps of 9 quantities (given in 9 columns in the attribute table) which have values broadly within the same range and I would like to plot them using the same intervals using 'Graduated' style.    However, while I can save a style, it saves the column name with it. When I load the style to attempt to apply it to another column, as soon as I change the column, it resets the intervals, which is exactly what I would like it not to do. Is it possible to somehow keep the interval ranges while changing the column?

For many of my datasets I have the same imported data duplicated numerous times, each iteration displaying the data values for a different column (in my case it's fish catch weight per gridded cell per year, so lots of iterations of the same grid, with a different pattern of values per year).  For presentation purposes, it strikes me as helpful to use the same scale for each year, so I go to the original data and divide the maximum value into (arbitrarily) 10 classes and manually input the values and labels after setting the desired colour ramp and input data field:   This is extremely tedious, not just the manual excel calculation part, but also the input interface for the values & labels*, hence my intention to make use of the 'save style' option. HOWEVER: when I save the style as QML and load it for the next layer, it saves everything - including the data field (in my case, year). When I change this field, QGis automatically generates the values & labels based on the data for that field, ditching all of the values & labels I set.   Is there any way to avoid this happening & thereby duplicate class number, values and labels for each field by simply loading a style? (somewhat meta) Am I going around this the wrong way, OR, is there a different face I could use to climb this mountain?


When I call reality() I want to print Royal Blue but I am getting Royal undefined I am just a beginner in JavaScript Please help me find out what is the problem.  var color = "Blue";  function reality() {   var color = "Royal " + color;   console.log(color); } reality();

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


I've got a simple program to swap 2 variables.  #include <stdlib.h> #include <stdio.h> int einlesen (void); int tausch(int,int); void ausgabe(int,int); int a,b,tmp; int main() {   printf("Bitte geben Sie 2 Zahlen zum Tauschen ein!");   einlesen();   tausch(a,b);   ausgabe(a,b); } int einlesen (void) {   scanf("%i%i",&a,&b); }   int tausch(int x,int y) !!!! {   tmp=a;   a=b;   b=tmp; } void ausgabe(int a,int b) {   printf("%i%i",a,b); }   It works, but my question is why the below doesn't work?  int tausch(int a,int b)

What is the difference between    a parameter passed by reference a parameter passed by value?   Could you give me some examples, please?


I intend to write to potential supervisors soon and I had a few questions.  I am currently in my second year of Masters of Neuroscience (In France, I'm Indian) and won’t finish until June 2018. I see some positions open that I really want and I don’t want to miss out on them but I also don’t want to write to them too soon.  When is the right time to write to them? What should the first email contain? I guess one should attach a CV but should I also send letters of recommendation?   Any tips on the scholarships and funding and what that requires?  Any other tips?

I'm applying for graduate school (PhD in computer science), and I'm considering writing to faculty whose research areas match with what I intend to pursue, to understand:   Whether they'd be looking for new students at all in the coming year? If they did, would they be potentially interested in my profile (I know no-one would guarantee an acceptance without me going through the process of application), but it would help to know if they would not be interested at all in me - which would leave me  free apply to other schools in which I get a neutral/positive response.   Keeping the above in mind, what would be the best way to introduce myself in the first mail?   What should be the salutation - I know "Respected Sir" sounds archaic, but was wondering if "Dear Professor X" sounded too informal or not! Do I state my credentials (details of where I did my undergrads/masters) first, or do I state my purpose in writing to him/her? How to mention my background concisely, without giving too much details, while at the same time not "underselling" myself as a potential grad student? I want to give a link to my resume/profile hosted on my website - should I embed the hyperlink, or is it better to write the link in plain text? How do I end such a letter - the obvious ones (such as "see you soon" or "till we meet again") being not quite suitable in this case)?   I'm basically afraid of saying too much (causing vexation) or too little (resulting in no response to my missive). I understand that the faculty are accustomed to seeing their inbox flooded with such mails each year, few of which ever get a positive response - which may not always be due to lack of an interesting profile, but the manner in which the mail is worded (Many professors have explicitly mentioned on their websites that they would not respond to generic "Do you have funding" type of queries no matter what the credentials of the student are!).   Though my interest is specific to CS, I believe it would apply to other fields as well. Also, I would be interested in the opinions of both present faculty members (who have to sort through such mails), and past applicants to grad-school (who have the experience of successfully writing to their advisers before applying)...


I'm having the a bit of a problem with accessing remote RedHat servers from a Windows machine using Cygwin SSH client.   What I do is I run some fairly time-consuming QA scripts on the remote RedHat machine by logging in from home Windows machine. At the client end I use Cygwin SSH in an ordinary Cygwin console window. As long as I'm working interactively (i.e. executing commands from the command line) everything is fine. When I start the script, everything works fine as well as long as the script produces any visible activity on the terminal, i.e. as long as it prints something to the screen. But if there's is a significant pause in the output, the connection to the RedHat machine eventually gets dropped with "Write Failed: Connection reset by peer" message.  Is this some sort of timeout/keep-alive issue? And if so, what do I have to configure to stop this from happening? And where (server side or client side)?

When I connect via ssh to certain servers, it timeouts and "freezes" the terminal (doesn't accept input, doesn't disconnect, can't Ctrl-C to kill the ssh process or anything).  This is in Ubuntu's gnome-terminal though it seems to be pausing the terminal input/output, and doesn't affect the operation of the GNOME Terminal software itself.  So less a bug with gnome-terminal than an annoying inconsistency with ssh.  So, is there a way to prevent/regain the terminal from ssh connections that have timed out?


Hi i am trying to understand the explicit casting in C++, and so playing around by creating different examples. Below i am giving an example which i think should be illegal as it changes the value of a const object. const char t='a'; const char *pc=&t; char *p = const_cast<char*>(pc); std::cout<<"Before changing t "<<*pc<<std::endl; *p='c'; std::cout<<"After channging t: "<<*pc<<std::endl;  After executing the program the value of the object t successfully changes to c as i can see it in the console. My question are as follows:  Shouldn't this be illegal since the whole point of having a const object is that it cannot be changed. What is the need of having this const_cast and it seems to me that it is dangerous in the sense that we are changing the const object. Is it perfectly okay to use const_cast like this?Again, if not then when should i use it?

I can't find much information on const_cast.  The only info I could find (on Stack Overflow) is:     The const_cast<>() is used to add/remove const(ness) (or volatile-ness) of a variable.   This makes me nervous.  Could using a const_cast cause unexpected behavior?  If so, what?  Alternatively, when is it okay to use const_cast?


I was wondering whether in football one can move the ball through the pitch in an unconventional way, namely by holding it:   on his forehead  between his head and shoulder between calf and thigh while jumping towards the goal by one foot   Are these things allowed?

On occasion you see sometimes players try this tactic where they squeeze the ball between two feet and hop across the goal line in an attempt to score. This is usually kids learning the game or adults goofing around.  Is this legal or must a ball be kicked across the line to count as a goal?


$sin(x)$ is the ratio between two sides of a triangle. One or more sides must be irrational for $sin(x)$ to be irrational. Why does a rational value of $x$ guarantee this?

My friend and I were discussing this and we couldn't figure out how to prove it one way or another.  The only rational values I can figure out for $\sin(x)$ (or $\cos(x)$, etc...) come about when $x$ is some product of a fraction of $\pi$.  Is $\sin(x) $ (or other trigonometric function) necessarily irrational if $ x $ is rational?  Edit: Excluding the trivial solution of 0.


I have a current copy of TF2 on Steam in my main PC. I have successfully moved copies of Steam games to my other PC. But with TF2, Steam is performing a 6GB download (6.5GB / 12.5GB). It is as if the backup didn't totally save the current image of TF2. The backup size is about 10GB.  Did anyone else experience it? How to avoid this (a.k.a perform a perfect no-download restore) ?

Since Team Fortress 2 is available for free, many of my friends have downloaded the game. Can I copy the game on a digital media (USB stick or external hard drive) without creating a problem with Steam? This will save me almost 6GB download.  EDIT: I said that this transfer must be made between two different user accounts.


I am an undergraduate math student who loves mathematics very much, and I am confused by a math problem.  Given $1/3$, we know that $0.33...$ (there are infinite $3$s) is the decimal expression. But how can we prove that it is the only decimal expression of $1/3$?  Sorry for my mistakes for my wrong math typing and not good English. Thank you very much for your answers!

I'm a PreCalculus student trying to find a rigorous proof that $\displaystyle\frac{1}{3} = 0.333\ldots$, but I couldn't find it. I think (just think) that this proof would start by proving that  $\displaystyle\sum_{i=1}^{\infty}3\cdot10^{-i} = \frac{1}{3}$. My guesses (assuming that proving that $\displaystyle\sum_{i=1}^{\infty}\left(\frac{1}{10}\right)^i$ converges is trivial):  $\displaystyle\sum_{i=1}^{\infty}3\cdot10^{-i} = 3\cdot\sum_{i = 1}^{\infty}10^{-i} = 3\cdot\sum_{i=1}^{\infty}\left(\frac{1}{10}\right)^i = 3\cdot\left(\frac{1}{1 - \frac{1}{10}}-1\right) = 3\cdot\left(\frac{10}{9}-1\right) = \frac{1}{3}$.  Questions: is this completely rigorous? Which flaws could be found in this proof? How can I improve it?  PS. I'm not sure how to tag this. Feel free to edit, if necessary.


I have vector two sets of vector layers that won't show up together. One set shows up together and the other set together etc but they are of the same area.  The layers I was given did not have a defined spatial reference which I manually projected as the same as the data frame I specified so all layers now have same CRS...yet not showing up together. I have noticed they appear to have different extents... What should I do?

I put 4 different layers into my ArcMap document, but only one of them will show up on the map! I should be seeing the other 3 layers as well. When I do a Zoom to layer, I can see one layer, but I cannot figure out how to make the other 3 show up at once on top of each other.  Before I opened ArcMap, I used ArcCatalog where I right-clicked 3/4 of the shapefiles and  clicked Properties → Coordinate system → Import and then clicked on my Trees layer, which has the coordinate system I want the other 3 to have. But when I opened ArcMap the 4 layers did not overlap, nor could I move them above or below each other.


I want to delete duplicates totally from hashsets.  For example:   hashset names1 contains a, b, c, d  hashset names2 contains x, y, z, a    I want that hashset names3 should have b, c, d, x, y, z    Deleting the common element between the 2 hashsets and storing it in third hashset.how to do this?

That is, if I had two or more sets, and I wanted to return a new set containing either:   All of the elements each set has in common (AND). All of the elements total of each set (OR). All of the elements unique to each set. (XOR).   Is there an easy, pre-existing way to do that?  Edit:  That's the wrong terminology, isn't it?


Is there a limit to the number of times I can format a hard disk?  I tried to find this information , but I didn't find an answer.

I heard that doing too many Low Level formats can damage the hard drive. But it make things really fast and remove almost all the malware infections. So, my question is, how many times can we do the low level format safely without damaging the hard drive?


I have just shown that an integral domain $R$ is a unique factorization domain iff for every non-zero prime ideal $P$ of $R$, $P$ contains a non-zero prime, principal ideal.  I am then asked to show that if $R$ is a $PID$ then $R[[X]]$ (the ring of formal power series over $R$) is a $UFD$.  I have shown that $R[[X]]$ is an integral domain, so it remains to show that if $P$ is a prime ideal of $R[[X]]$, then $P$ contains a principal prime ideal. However, I am not very familiar with working with the ring of formal power series, so I cannot quite see what to do to get the desired result. I would appreciate any help that may be offered, thank you.

An exercise in my algebra course book asks to prove that if $R$ is a , then $R[[x]]$ is a , where $R[[x]]$ is the ring of formal power series over $R$. After some failed attempts at  proving the  I visited Wikipedia, which :     If $R$ is Noetherian, then so is $R[[x]]$; this is a version of the Hilbert basis theorem.   This is very useful, as $R$ is a PID and hence Noetherian. Unfortunately we only saw (without proof) Hilbert's basis theorem in the form     If $R$ is Noetherian, then so is $R[x]$.   I'm not sure how to conclude the Noetherianity of $R[[x]]$ from this. I know that $R[x]$ is a UFD because $R$ is (we saw this without proof), and have been trying to conclude the ACC in $R[[x]]$ from the ACC in $R[x]$, without success. I can prove the ACC if $R$ is a field, because then every $a_kx^k+a_{k+1}x^{k+1}+\cdots$ with $a_k\neq0$ is associate with $x^k$, hence every ideal is of the form $(x^k)$. (In fact this readily proves that $R[[x]]$ is a UFD.) If $R$ is not a field, say it has some non-invertible element $r$, then there are many more ideals such as $(r)$ or $(r+x)$.   I'm also facing difficulties at identifying the irreducible elements of $R[[x]]$. (I wish to prove that they are all primes in order to conclude the uniqueness of factorisation.) I have figured that they either take the form $ux+Px^2$ for some unit $u\in R^\times$ and some $P\in R[[x]]$ or have a non-zero constant term which is not invertible in $R$. The elements of the form $ux+Px^2$ are indeed primes, the difficulty lies in those with non-zero constant term.  Any hints at proving $R[[x]]$ is a UFD?


Egyptian passport holder, living in Kuwait, on Kuwait residence, also Bosnian passport holder. Traveling to Schengen, going out of Kuwait with Egyptian because of Kuwait residence in it, entering Schengen with different passport.

I am a citizen of two different countries, and have two passports.  How should I use my passports when traveling?


I'm new to JavaScript and since I'm trying to learn thru some exercises I'm having some problem understanding how to make this simple thing to work: var person = {   name: 'John Potato',   age: 31,   weight: '145kg',   birthday: 'Some day mid July' }  Then, after studying some things about Loops.. let counter = 0;  while(counter.length < person){   counter++; } console.log('The person has ' + counter + ' properties')  do{   console.log(counter++) } while(counter.length < person[prop]); console.log('The person has ' + counter + ' properties')  Thing is, neither of them work the way I'm expecting. All I want to do is to make it count the amount of properties there are inside the object 'person'

What's the fastest way to count the number of keys/properties of an object?  It it possible to do this without iterating over the object?  i.e. without doing  var count = 0; for (k in myobj) if (myobj.hasOwnProperty(k)) count++;   (Firefox did provide a magic __count__ property, but this was removed somewhere around version 4.)


Currently, I am writing a statement of purpose for the graduate program, and I want to describe my research experience. In particular, I want to write the following sentence:     I determined that the electromagnetic force is the main type of interaction between the droplets.   At the same time, I was recently corrected that the proper way would be to write     I determined that the electromagnetic force was the main type of interaction between the droplets.   as dictated by the "sequence of tenses" rule.  However, for me, it does not sound right. This phrasing creates a feeling that "the electromagnetic force was the main type of interaction between the droplets" somewhere in the distant past, and now it is not.  I read somewhere on the web that "sequence of tenses" may be violated in some occasions (for instance, while describing widely known scientific facts, e.g. "Newton discovered that the planets attract each other"). Would it be okay to violate "sequence of tenses", when describing my own scientific finding?  The other example that I am interested in is whether I should use     I understood how interesting it is to study physics.   or      I understood how interesting it was to study physics.

Which one is correct?        Centuries ago, people weren't aware that the planets revolved around the sun.   Centuries ago, people weren't aware that the planets revolve around the sun.      In my grammar book it has mentioned the first one as "grammatical correct sentence", but it has not done such a comparison.


How Can I download a file from a url, let's say:   https://example-my.sharepoint.com/personal/Documents/MyExample.docx   using c# and save it in a folder into my MVC Application on the server. Is there any way to do it?  Thanks.

What is a simple way of downloading a file from a URL path?


Is there a way to auto CC to a specific email adress all outgoing emails from a Gmail account?  I tried doing it with a filter but I don't have the option of CC. I know there is a script for GreaseyMonkey but it only works on Firefox and I need this to work on Chrome.

Is there a way to have a copy of any message sent from a Gmail account sent to another address?  I've got any messages coming to my address copied to another (see  for one solution, setting up filters is another), but I haven't yet found a way to have outbound messages automatically copied.  Is there a way?


I was reading "On choosing and bounding probability metrics" () and encountered the Lévy distance,defined by  $ d_L(\mu,\nu):=\inf\lbrace{}\varepsilon>0\,:\, \mu((-\infty,x-\varepsilon])\leq\nu((-\infty,x])\leq\mu((-\infty,x+\varepsilon]), \forall x\in\mathbb{R}\rbrace $  as a special case (on $\mathbb{R}$) of the Lévy-Prokhorov distance, defined by   $ d_P(\mu,\nu):=\inf\lbrace\varepsilon>0\,:\,\mu(B)\leq\nu(B^{\varepsilon})+\varepsilon,\forall \text{ measurable }B\subset\mathcal{X}\rbrace $  In the transcript it said that $d_P$ metrized weak convergence. It is clear that $d_L\leq{}d_P.$   Additionally it mentioned that $d_L$ metrizes weak convergence too, which I don't quite understand since it is only bounded from above by Lévy-Prokhorov. For it to metrize weak convergence it should have to be equivalent to $d_P$, which I don't believe it is. Or maybe I'm mistaken. Can anyone explain?  Thanks a lot.

Let $(S,d)$ be a metric space and let $\mathcal P(S)$ denote the space of Borel probability measures on $S$ endowed with the  $\pi:\mathcal P(S)\times \mathcal P(S)\to \mathbb R_+$ given by $$   \pi(P,Q):=\inf\{\varepsilon\geq 0:P(F)\leq Q(F^\varepsilon)+\varepsilon \text{ for all closed } F\subset S\} $$ where the $\varepsilon$-inflation of a set is given by  $  F^{\varepsilon} = \{x\in S:d(x,F)<\varepsilon\}.$  Another useful metric on $\mathcal P(S)$ is induced by the total variation norm, i.e.  $$   \rho(P,Q):=\sup\limits_{A\in \mathfrak B(S)}|P(A) - Q(A)| $$ where $\mathfrak B(S)$ is the Borel $\sigma$-algebra on $(S,d)$. I wonder if there are any interesting relations between these two metrics, $\pi$ and $\rho$. In particular, I know that convergence in $\rho$ implies the weak convergence and hence if $S$ is separable than it implies the convergence in $\pi$.   I wonder, however, if under some additional assumptions it is possible to derive some non-trivial bounds on $\rho$ if I know upper bounds on $\pi$. Or at least, if it is possible to upper-bound $|P(F) - Q(F)|$ for closed $F$ using $\pi$.


I will be traveling to Prague in September for a university exchange as a student from Canada (for 4 months) although I hold dual citizenship as an Italian citizen (EU citizen). Due to my European citizenship (and passport), I understand that I do not need to get a student visa from the Czech embassy for my stay. Should I worry about not having a student visa? Can any one confirm this?  Also, if this is okay, what would be the best way to travel with my two passports?  Thanks.


I have recently decided to Ubuntu along the windows 7. when I arrived to the partition management section, I Created a root 30Gb partition from 70Gb usable space, so rest of the space got unusable and i couldn't create /home and swap partition. would you please help me to use this space? I'm a beginner. Thanks.

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


When I compile my tex file, it returns a wrong, "File `microtype.sty' not found. \usepackage"  How can I solve it?

I'm new to LaTeX, investigating using it for some work projects.  I'm using MiKTeX on Windows.  My employer's locked-down network blocks the application's automatic installation function.  I can take my laptop home and successfully install from there, but if I need a package in the middle of the day I'm stuck.  I am able to access the CTAN website and download the package files (.dtx or .ins?), but I don't know what do do with them.  How can I do a manual package installation?


How should we define set in ZFC?? I have heard sets are defined axiomatically in ZFC.But I have no idea why it is necessary to take zfc axioms to define set.It would be highly appreciated if anybody kindly explains it.Thanks in advance.

A set is defined as a collection of distinct objects.    Why have we defined a set to contain only distinct objects? Why is a collection of objects which may have identical objects not called a set? What is the benefit of defining a set, especially the way it is?


Consider the polynomial rings $k[\textbf{x}]:=k[x_1,...,x_m]$ and $k[\textbf{y}]:=k[y_1,...,y_n]$ where $m,n\in\mathbb{Z}_{>0}$ and let $I\subset k[\textbf{x}]$ and $J\subset k[\textbf{y}]$ be radical ideals. Then if we denote $k[\textbf{x},\textbf{y}]:=k[x_1,...,x_m,y_1,...,y_n]$, we have natural injections $k[\textbf{x}]\to k[\textbf{x},\textbf{y}]$ and $k[\textbf{y}]\to k[\textbf{x},\textbf{y}]$. Denote by $I^e$ resp. $J^e$ the extension of $I$ resp. $J$ along these injections. Then how can one show that there is an isomorphism of $k$-algebras $$ \left(k[\textbf{x}]/I\right)\otimes_k\left(k[\textbf{y}]/J\right)\cong k[\textbf{x},\textbf{y}]/(I^e+J^e)? $$ I am able to construct a morphism of $k$-algebras $$ \left(k[\textbf{x}]/I\right)\otimes_k\left(k[\textbf{y}]/J\right)\to k[\textbf{x},\textbf{y}]/(I^e+J^e)\\ \overline{x_i}\otimes 1\mapsto \overline{x_i},\quad 1\otimes\overline{y_j}\mapsto\overline{y_j} $$ by using the universal properties involved, where the overline denotes the respective class of the element underneath. Also, by the universal property of the polynomial ring we have a $k$-algebra homomorphism $$ k[\textbf{x},\textbf{y}]\to\left(k[\textbf{x}]/I\right)\otimes_k\left(k[\textbf{y}]/J\right)\\ x_i\mapsto \overline{x_i}\otimes 1,\quad y_j\mapsto 1\otimes\overline{y_j}. $$ But how can one show that the kernel of this homomorphism is given by $I^e+J^e$? That the latter is included in the former is straightforward, but I have no idea for the reverse inclusion.

While reading, there is an isomorphism that I'm having trouble fulling seeing.      If you have two algebras $A$ and $B$ over a commutative ring $R$, with $I$ and $J$ two sided ideals in $A$ and $B$, then you should have an isomorphism   $$ (A/I)\otimes (B/J)\cong (A\otimes B)/(I\otimes 1+1\otimes J). $$   Now there are bilinear maps from $A/I\times B/J\to (A\times B)/(I+J)$ and so the universal property of the tensor product gives unique maps $(A/I)\otimes (B/J)\to (A\times B)/(I+J)$. Does this somehow get to the isomorphism above, or am I completely off track? What is the quick way to see this? Thanks!


How can I export a specific menu out of wordpress? I have a list with many URLs and I need to copy it to multiple sites. But I don't want to do it manually.

When I do an export and import the menus get transferred but I have to set the Site Navigation Menu manualy. Obviously it's only a small detail but can I ask is this a bug or expected behaviour and is there any way to include the site navigation menu selection in the export file.   The same thing is the case for custom menu widgets.


Helo there,   just a quick question, I'm using a pseudo-classical pattern to create objects in JS and I was wondering how do I actually create a private method that is accessible only inside the object.   let's say I want to add a private method XY() to object Animal. Does this kind of pattern allow me to create a private method?    function Animal(name) {   this.name = name }  Animal.prototype = {   canWalk: true,   sit: function() {     this.canWalk = false     alert(this.name + ' sits down.')   } }   Thanks in advance, Alex

To make a JavaScript class with a public method I'd do something like:  function Restaurant() {}  Restaurant.prototype.buy_food = function(){    // something here }  Restaurant.prototype.use_restroom = function(){    // something here }   That way users of my class can:  var restaurant = new Restaurant(); restaurant.buy_food(); restaurant.use_restroom();   How do I create a private method that can be called by the buy_food and use_restroom methods but not externally by users of the class?  In other words, I want my method implementation to be able to do:  Restaurant.prototype.use_restroom = function() {    this.private_stuff(); }   But this shouldn't work:  var r = new Restaurant(); r.private_stuff();   How do I define private_stuff as a private method so both of these hold true?  I've read  a few times but it doesn't seem like "private" methods can be called by public methods and "privileged" methods can be called externally.


Perhaps showing my age here, but in "The Good Old Days", 10-foot squares were a standard map size. Each square on the map was 10 feet, and a 10-foot wide corridor was normal.  Now, having started gaming again, it seems 5-foot squares are standard.  So my question is: when did this change happen? Was it 3rd edition?

I was playing with  the other day and noticed a lack of a five-foot-unit of measurement. There are inches, feet, yards, meters and then fathoms (apparently, six feet). This tool seems fairly old, but the  says it was published in 2006.  At any rate, my question is as follows - when did the five foot square/hex become the standard unit of measurement in Dungeons and Dragons? Or, has it always been that? Call me a sucker for accuracy, but I've considered switching to meters more times than just for AutoREALM measurements.


Is there a way to convert Funtion {} to real function type ?  const foo = function(){ return 233 } const bar = { __proto__:  foo } foo.prototype == bar.prototype //true bar() //TypeError: bar is not a function foo // [Function: foo] bar // Function {}   'bar' is really close to 'foo', almost, but it cannot get call. What else it need to behave like 'foo'?

JavaScript allows functions to be treated as objects--if you first define a variable as a function, you can subsequently add properties to that function.  How do you do the reverse, and add a function to an "object"?  This works:  var foo = function() { return 1; }; foo.baz = "qqqq";   At this point, foo() calls the function, and foo.baz has the value "qqqq".  However, if you do the property assignment part first, how do you subsequently assign a function to the variable?  var bar = { baz: "qqqq" };   What can I do now to arrange for bar.baz to have the value "qqqq" and bar() to call the function?


I have 3 elder scrolls in my inventory that they won't let me remove. (Dragon,sun,blood). I finished dawn guard and defeated aldin which the scrolls are used for those quest lines. Why can't I remove them.

After completing the Dawnguard storyline in favor of the vampire hunters, I was able to give the 2 scrolls (sun and blood) to Dexion, however the dragon scroll remains in my inventory. Is there some special use for it? i've checked with Urag gro-Shub and he will not take it. Note that this is after I've completed the main questline.


I found this among a supposedly trivial Tetris console game code. wchar_t *screen = new wchar_t[]; unsigned char *pField; . . . screen[someMathIndex] = L" ABCDEFG=#"[pField[someOtherMathIndex]];  What is an wchar string in front of square brackets even mean? I can't even able to find a way to google it. Can you redirect me to some resource of this strange thing maybe.

As Joel points out in , in  (aka: K & R), there is mention of this property of arrays in C: a[5] == 5[a]  Joel says that it's because of pointer arithmetic but I still don't understand. Why does a[5] == 5[a]?


I mistakenly added some credentials to my code which should not be accessible to anyone.

I "accidentally" pushed a commit to GitHub.  Is it possible to remove this commit?  I want to revert my GitHub repository as it was before this commit.


I have looked for a single word to describe this feeling of what seems to be contradictory states of being. I know a (very) little German, and searched there as it seems that language has more words to express complex emotions and feelings. No luck. This to me might help to explain it. I recently watched a clip of a little boy that started really crying  after seeing and holding a kitten. His mother asked him,  Why are you crying?  He could barely get it out...and said,  It’s just so beautiful!

I was hoping for some help on this one. I'm looking for a word that carries all the connotations of "excruciating" (intense, prolonged, unbearable, torturous, etc) but relating to pleasure rather than pain.  I could potentially use "excruciating pleasure", applying it's lesser used meaning to imply "extreme/intense" - it might even be somewhat poetic, but there's an implication of masochism that doesn't really fit my narrative.  Any suggestions? I'm happy to to accept a clever protologism if no such word exists!  As an example:     The slow, seemingly endless mingling of their bodies was _______.


For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?

What different Ubuntu derivatives are there? And what is special with them?


First I set up /etc/apt/apt.conf to use my proxy and now I can update with sudo apt-get update. Now I want to add some ppas but can't.  I try to add a PPA behind my proxy so I set up http_proxy and https_proxy  export http_proxy=...... export https_proxy=.....   then I do   $ sudo -E add-apt-repository ppa:xorg-edgers/ppa gpg: keyring `/tmp/tmpf97t7hiy/secring.gpg' created gpg: keyring `/tmp/tmpf97t7hiy/pubring.gpg' created gpg: requesting key 8844C542 from hkp server keyserver.ubuntu.com gpgkeys: key 165D673674A995B3E64BF0CF4F191A5A8844C542 can't be retrieved gpg: no valid OpenPGP data found. gpg: Total number processed: 0   So then I try to add it manually:  $ sudo -E apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 8844C542 Executing: gpg --ignore-time-conflict --no-options --no-default-keyring --homedir /tmp/tmp.4ESVuO8uFh --no-auto-check-trustdb --trust-model always --keyring /etc/apt/trusted.gpg --primary-keyring /etc/apt/trusted.gpg --keyserver keyserver.ubuntu.com --recv-keys 8844C542 gpg: requesting key 8844C542 from hkp server keyserver.ubuntu.com gpgkeys: key 8844C542 can't be retrieved gpg: no valid OpenPGP data found. gpg: Total number processed: 0   Nothing I try works. Help.  Edit: Figured it out....The keyserver just wasn't working apparently keyserver.ubuntu.com is down permanently......Had to use:  sudo -E apt-key adv --keyserver hkp://subkeys.pgp.net --recv-keys C2518248EEA14886   Edit: It isn't a duplicate question....keyserver.ubuntu.com was down for me and had to user a different one. The other guys got it working with the default keyserver and only had to add their proxy. I had to add my proxy, plus manually add the gpg keys using a different key server.

I've a problem at the office. We're behind a proxy (which is set and applied at ubuntu proxy settings) and when I try to add a repository from terminal, I get:      Error reading --some url here--: urlopen error [Errno 113] No route to host   I've tried with   Launchpad-getkeys script. I get this (image)      I've tried with another "hack", without luck   Press Alt-F2 and type gksu gedit /usr/lib/python2.6/dist-packages/softwareproperties/ppa.py Find line 88, change keyserver.ubuntu.com to hkp://keyserver.ubuntu.com:80 Save, close and reboot.    Does anyone know if I could solve this problem in any way? Thanks


Currently I have this:  However, I find this font more appealing:  How does on generally figure out which font is which (without formal training in typography), and how in this particular case to use the font specified in the second image? I know this is a rather ad hoc question, and SO favours more "conceptual" ones, but I simply cannot think of a better venue to post this question. EDIT: The  to the original pdf. I've used the pdffont and it mentioned something like Garamond and MacTimes.

Is it possible to identify the font used in a specific document/picture?  Answers to this question should identify:   Possible methods to do this (perhaps one answer per method) and adequately describe how to use it (as opposed to merely stating it); Ways of finding the identified fonts, if possible (free or not); and Any prerequisites associated with the method used, if required (for example, "In order to use method X, your document has to be in format Y").   This question is meant as an FAQ, based on an . Its aim is to facilitate the community with the general procedures involved in font identification. Similar cases are solved on a per-usage basis on 's  tag.


Should I post an answer to my own question if I obtain the answer through the hints in the comments section after a reasonable amount of discussion, or should I leave it to future readers to make their way through the comments?  Edit:There is a new link attached classifying this as a duplicate talks about the answer already being posted, whereas I'm talking of a situation where no answer is posted and the answer is arrived at in the comments.

Often you have a question, you can't find the answer on Stack Overflow so you search for it (or think a bit more). Having found the answer you'd like to keep a record so you can find it again later.  Before Stack Overflow I would write a blog post so I could search for it later. Jeff and Joel, I think, specifically said SO is a good place to replace these blog posts. So what is the best etiquette for adding your answer?   Just ask the question, then post your answer immediately and let voting sort the answers out. This is okay, but it looks like you are just trying to generate reputation, and other people often don't vote or answer, and a lot of the SO information is lost. Provide the answer in the question and ask the question phrased as "is there a better answer". This allows others to gain reputation, and doesn't look so greedy but makes your answer harder to vote on. Post your question, let others answer it. If no-one puts the answer you already found, then add it an hour or so later. If someone else gets it then accept their answer (or the best one). This is more selfless with reputation, but makes other people do work you have already done which feels a bit lazy and a waste of everyone's time.   Or maybe there is another way?


I am quiet new in projective transformation and I need to know and understand how can find the projective transformation matrix which transforms the set of points {{0,0,1},{0,1,0},{1,3,8},{1,4,6}} to the set {{1,0,0},{0,1,0},{0,0,1},{1,1,1}}. So, if I have the transformation mapping f defined by  f:A={{0,0,1},{0,1,0},{1,3,8},{1,4,6}} ----> B={{1,0,0},{0,1,0},{0,0,1},{1,1,1}}, how can find the matrix transformation which maps A to B.

I'm working on a project using Chrome - JS and Webkit 3D CSS3 transform matrix. The final goal is to create a tool for artistic projects using projectors and animation - somewhat far away from using maths... I'm using a projector to project several squares over several shapes - as seen in the picture. What I would like to do is for the user to draw 4 points on the screen (2D x and y) and from there extract a matrix object that I could apply to a regular DIV element of a dimension of 100px by 100px. By finding scaleX, scaleY, rotation, rotationX, rotationZ and probably some perspective that I could apply to the div to relatively match the surface. I'm not really familiar with geometry beyond sin and cos, and 3D in general and don't even know if that is something doable. If anyone could help me get started or point me in the right direction, I would greatly appreciate. Here is an animated gif (click to enlarge), hoping it makes it more clear to understand.


I have a series of PNG images that I've placed in the Video Sequencer.  I want to render them as an mp4 video, with a transparent background.  I've checked the Transparent box; selected FFmpeg video as the File Format; ticked the RGBA button; selected Quicktime as the Container; selected FFmpeg video codec #1; gone to Render Animation...and the resulting video cannot be opened with QuickTime Player ("file isn't compatible).  I then opened the same video in VLC, and the background is NOT TRANSPARENT.  I want to render the PNG images as an mp4, with a resulting transparent background.  I've tried many other Format/Container/Codec options as well, but cannot achieve a transparent background.  Hope this is concise enough that I might get some help? The file is here:

I have a series of PNGs that have transparent backgrounds.  When I place them on the strip in Video Editing and render, the background on the video is black.    I've made certain that the Transparent box is checked, and that any file formats, container or codec selections allow for RGBA, before rendering animation.  Still, the background of the video turns out black!  The file is here, and I'm desperate (and appreciative) for direction:   I would like to render the PNG files, within the Sequencer, as an mp4, WITH A TRANSPARENT BACKGROUND.  Hope this is descriptive enough to gather a response?


I went through the data sheet of STM32F4 and found the pin configuration of GPIOs. I don't understand the difference between these configurations:   Input floating Input pull-up Input-pull-down Analog Output open-drain with pull-up or pull-down capability Output push-pull with pull-up or pull-down capability   I have used some of these configurations by vaguely understanding it. Could you help me to understand how this works? What is the difference between these configurations?

I bought an . When I saw the reference manual, I saw that it has several I/O modes.  For input: floating, pull-up, pull-down For output: analog, open-drain, push-pull  I have already worked with AVR MCUs which have tri-state and pull-up. So I can understand pull-up and pull-down, but, I can't understand the modes floating, analog, open-drain, push-pull. What do these modes mean and when do I use which?


When should one consider converting continuous variable into categorical variable ? Are there guidelines ? Is it justified to bin skewed variable ? How should I determine the range / binning when I do the conversion ? For example, if I have Annual Income per year as a predictor how do I decide the the range / bins as 20k to 50k, 51k to 80k  and so on. Do the bins have to be equally spaced (fixed width) ? Is binning know to improve models like Random Forest ?

When should we discretize/bin independent variables/features and when should not?  My attempts to answer the question:   In general, we should not bin, because binning will lose information. Binning is actually increasing the degree of freedom of the model, so, it is possible to cause over-fitting after binning. If we have a "high bias" model, binning may not be bad, but if we have a "high variance" model, we should avoid binning. It depends on what model we are using. If it is a linear mode, and data has a lot of "outliers" binning probability is better. If we have a tree model, then, outlier and binning will make too much difference.   Am I right? and what else?    I thought this question should be asked many times but I cannot find it in CV only these posts


I have Windows 10 and Ubuntu 18.04. Is there any way I could temporarily  disable grub so that it would by default boot into Windows 10. I would like to undo it when I need Ubuntu and the dual boot screen back.

How do I set the bootloader so that in my dualboot with Windows 7/Ubuntu 11.04, Windows start up as standard instead of Ubuntu?


I have window 7 on a 1 TB HDD and I installed ubuntu also. I am not getting dual booting menu, I am not a computer expert, kindly say what I have to do?

I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this?


When you search for a village to attack, how does Clash of Clans choose an enemy village? Does it only choose villages by people with a similar amount of trophies, who are in the same league, does the town hall level also matter or is there anything else that influences the matchmaking?

Are battles determined by level or trophies? Just curious.


I am writing C code for 'password prompt' . I need to display * for every character the user enters . But I am not supported with getch(). So , I tried system calls .  for(i=0;i<5;i++) {     system("stty -echo");     scanf("%c", &a[i]);     system("stty echo");     printf("*"); }   I have tried to  turn off echo and get a char and display * enabling echo. But we know scanf continues until \n. So , i am unable to display * at once a char is got. Somebody help me pls. Also kindly suggest me any other better way.

I've been Googling around with no luck.  I'm looking for a way to do getc() or gets() or whatever that does not echo to the terminal.  I saw kbhit() but this doesn't appear to be part of ANSI.  Ideally, I'd like code that looks like  char s[100]; no_echo_gets(s); /* Won't echo to screen while being typed */ printf("%s\n", s);   Does anybody know a good ANSI compliant way to do this?


Let $G$ a finitely generated group. Prove that for a given natural $n$, there exists finitely many subgroups of index $n$ in $G$.  I tried to keep on this approach :   Here is my effort to edit or complete the above idea: My main emphesize is on this theorem:  If $H$ is a subgroup of finite index $n$ in a group $G$, Then there exists homomorphism $\phi:G\rightarrow S_n$ such that $Ker(\phi)=Core(H)=\displaystyle\bigcap_{x\in G}{xHx^{-1}}$.  As $G=\langle \{g_1,\cdots,g_m\}\rangle $, it's sufficient to find $\phi$'s effect over $g_i$s in order to determine whole $\phi$. Now $\phi(g_i)$ has $n!$ states to be chosen. Therefore, number of whole $\phi$s can be defined, are less than $(n!)^m$. But if we suppose number of such $H$s is infinite, we must have this fact that infinite number of $Core(H)$s are equal. Also if the left cosets of $H$ are $H,a_1H,\cdots,a_nH$, we can show $Core(H)=\displaystyle\bigcap_{i=1}^{n}{a_iHa^{-1}_i}$ Any idea is welcome for the rest. Thank You

Theorem: If $G$ is a finitely generated group, then it has a finite (maybe zero) number of subgroups of index $n$ for any $n\in \mathbb{N}$.   is a sketch of a proof. It consists of assuming such a subgroup $H$ exists, and allowing $G$ to act on $G/H$ by left multiplication. Such action defines a homomorphism $$\phi :G \rightarrow \text{Sym}(G/H)\cong \mathbb{S}_n$$  If $G=\langle g_1, \ldots ,g_r\rangle$, then the homomorphism is uniquely determined by where it sends the generators $g_i$. In particular, there are at most $(n!)^r$ such homomorphisms.  The last step of the proof requires one to notice that a different subgroup $H'$ of index $n$ in $G$ would produce a different homomorphism, and here is where I'm struggling. I've been able to show that $\text{ker}(\phi )=\text{core}(H)$, yet haven't been able to rule out the possibility of $\text{core}(H)=\text{core}(H')$.


I am currently creating a plugin with PyQGIS. The layers all come from a PostgreSQL database. Now I would like to include a table (without geometry) for a ValueRelation without the table appearing in the layer tree. How can I programmatically hide a layer using PyQGIS? By default, I load the layers as follows (without the database connection code): uri.setDataSource("schema", "table1", None) lyr_table1= QgsVectorLayer(uri.uri(False), "table1", 'postgres') QgsProject.instance().addMapLayer(lyr_table1)  How do I get access to the interface of the layer tree and which method can be used for hiding?

I have a number of layers in the Layers Panel inside a group but I don't want them shown (there's quite a lot so it looks untidy). These layers are also joined to several others. Is it possible to make these layers invisible to the user (i.e. not shown in the Layers Panel, it is not about setting the visibility of the layer) but can still be joined to other layers, or perhaps to make the group invisible? Closest I found was this post but hoping there's a more direct approach:


As a Linux newcomer that really wants to understand Linux rather than just work with it automatically, I understand that the term "Shell" basically describes a software layer which is above the kernel that includes services that can run and be manipulated by utilities much more "easily" then the kernel can. If I understand correct, web server software (such as Apache, MySQL and PHP) are titillates written in "high" programming languages and can use shell software pieces to operate together as a "Web Server" so that software from both layers will compromise that "Web server". If so, what is the difference between this software layer named "Shell" to the terminal I use in Ubuntu ? It seems to me that either there are two "Contexts" to the phrase "Shell" In Linux, or the terminal (such as Bash terminal) is mistakenly called "Shell" by some users.

I think these terms almost refer to the same thing, when used loosely:   terminal shell tty console   What exactly does each of these terms refer to?


What is a wave exactly? And why does it move like the way it does instead of following any random like pattern of motion, I mean why it moves in a semicircular pattern instead of semi square pattern?

I was watching an outtake of Prof. Brian Cox talking to a tv producer about "gravity waves".  Their discussion got a bit side-tracked, because the non-scientist didn't seem to understand what a wave "would look like", and also because there seemed to be some difficulties with the phrase "moving through", with Prof Cox saying that a wave doesn't move through space-time and then saying the ripples do.  I'm now not sure what moves when a speaker plays a sound; the air vibrates, but does "ripple outward"?  So, what is a wave?  Obviously, I'm really after a much simplified, probably broken, metaphor that allows me to visualise what a wave is. I understand that it will have flaws.  I forgot to include the youtube link, so here it is:


Is this true or wrong? How to prove it ？

I want to prove that a function $f:\mathbb{R}^n\rightarrow \overline{\mathbb{R}}$ that is continuous everywhere except for a set $E$ of Lebesgue measure zero is a Lebesgue measurable function. We know that $f$ is not continuous, so there are some open sets ${U_k}$ in $\overline{\mathbb{R}}$ such that $f^{-1}(U_k)$ is not open in $\mathbb{R}^n$. But $f^{-1}(U_k)\subseteq E$, and so $f^{-1}(U_k)$ is still measurable because it has measure zero. I don't know if this works, because I'm not sure if $E$ contains actually the preimage of those open sets $U_k$.


I recently started working in Blender through the latest Fedora distribution of Linux and completed my first project. When I went to render my animation and select the file format for the video, the only three Video file formats listed were AVI Raw, AVI Jpeg, and Frame Server. I want to render my animation as an MPEG, but am not currently able to. Please help.

I'm trying to render a video using blender, it have some images and sound, if I render it using just the default options I get no sound.  Searching on internet I found that I need to use other format than AVI JPEG to set some codecs options, I just have "AVI JPEG", "AVI RAW" and "FRAME SERVER". I'm keep looking but I can't found any information to solve my problem.  Im using fedora and actually I have  xvidcore-1.3.2-5.fc20.x86_64 ffmpeg-2.1.7-1.fc20.x86_64 packages installed.  EDIT: When I had the problem I had the last version of blender installed from , I also tried installing blender from dnf, also tried with , so  didn't solved my problem.


Let $X$ be the random variable which denotes the number of times a die has been rolled till each side has appeared. The order does not matter. We are trying to find $E[X]$.  Let $X_i$ be a random variable which denotes how many times a die has to be rolled till side i has appeared.  So,  $$E[X]= E[X1+X2+X3+X4+X5+X6] = E[X1]+E[X2]+E[X3]+E[X4]+E[X5]+E[X6]$$  $$E[X1]=E[X2]=E[X3]=E[X4]=E[X5]=E[X6]=6$$  $$E[X]=36$$?  Why is this solution wrong?

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'm trying to install a .cls file on a Windows 8 machine, using the editor TeXnicCenter and the distribution MikTex 2.9. I have been directed to other threads, but find them incomprehensible.  This is not a duplicate. None of the threads I have found have answered my question.  I installed the out-of-the-box version of TeXnicCenter from CTAN. I have downloaded the exam.cls class file which I would like to use. But I have no idea how to install it.  Every other thread I could find uses language I do not understand, e.g. local file trees, etc. Moreover, the instructions say "click start, ...". While Windows 8 does not have a start button.   I need a step-by-step guide on how to get this class file installed and working. I don't even know where the files are kept. I really am a newbie when it comes to doing anything other than typesetting. Please be kind and patient. Karma will reward you!

I'm new to LaTeX, investigating using it for some work projects.  I'm using MiKTeX on Windows.  My employer's locked-down network blocks the application's automatic installation function.  I can take my laptop home and successfully install from there, but if I need a package in the middle of the day I'm stuck.  I am able to access the CTAN website and download the package files (.dtx or .ins?), but I don't know what do do with them.  How can I do a manual package installation?


sudo commands are running without any passwords. I had not made any setting to make something like "sudo without password" This view show how sudois running without prompting for password   user@user:~$ sudo su -- root@user:/home/user# exit exit usrer@user:~$ who am i user   pts/0        2014-10-01 15:29 (:0) user@user:~$ sudo chown -R user:user /opt/lampp/htdocs user@user:~$ <br/>   Is this a system problem and need update or smth else I did updated my system yesterdaythis is /etc/sudoers `  # # This file MUST be edited with the 'visudo' command as root. # # Please consider adding local content in /etc/sudoers.d/ instead of # directly modifying this file. # # See the man page for details on how to write a sudoers file. # Defaults    env_reset Defaults    mail_badpass Defaults    secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"  # Host alias specification  # User alias specification  # Cmnd alias specification  # User privilege specification root    ALL=(ALL:ALL) ALL  # Members of the admin group may gain root privileges %admin ALL=(ALL) ALL  # Allow members of group sudo to execute any command %sudo   ALL=(ALL:ALL) ALL  # See sudoers(5) for more information on "#include" directives:  #includedir /etc/sudoers.d`   and sudoers.d  # # As of Debian version 1.7.2p1-1, the default /etc/sudoers file created on # installation of the package now includes the directive: #  #   #includedir /etc/sudoers.d #  # This will cause sudo to read and parse any files in the /etc/sudoers.d  # directory that do not end in '~' or contain a '.' character. #  # Note that there must be at least one file in the sudoers.d directory (this # one will do), and all files in this directory should be mode 0440. #  # Note also, that because sudoers contents can vary widely, no attempt is  # made to add this directive to existing sudoers files on upgrade.  Feel free # to add the above directive to the end of your /etc/sudoers file to enable  # this functionality for existing installations if you wish! # # Finally, please note that using the visudo command is the recommended way # to update sudoers content, since it protects against many failure modes. # See the man page for visudo for more information. #

I execute quite a lot of sudo commands.  I noticed that if I execute one and then another one within few minutes, the 2nd time I don't get the message:     [sudo] password for my_username:   but I do get it when there is more time between the execution of the two commands.  What's the period of time in which the message is not appearing? How can we check it / update it?


I have a Lenovo T470 laptop with a combined microphone/headphone jack. It is running Windows 7 with Realtek HD Audio 6.0.1.8142.  Whenever I plug headphones into to my laptop's audio jack, my laptop's internal microphone will stop detecting any sound. If I unplug my headphones, or if I use headphones that don't come with a microphone, the internal mic will start working again.  If I open Sound → Recording, it only lists a single sound device. This makes me think the headphones are overriding my default mic, rather than treating it as a separate device.    I have tried reconfiguring my mic as "Desktop Microphone" in Control Panel → Sound → Recording → Configure → Set up microphone, but it had no effect. Additionally, I could not find any way to disable the microphone in Realtek HD Audio Manager.  Why can't I use my laptop's internal microphone when headphones are connected?

I have a Samsung Series 7 NP700-Z5A, which has a dual-purpose mic/headphone jack.  In both Ubuntu 12.04 and Windows 7, whenever I plug in my headphones the internal mic goes completely dead. When the headphones aren't plugged in, the microphone is fine.  The hardware is Realtek HD audio and the driver version 6.0.1.6428 (on Windows, at least).  I have an inkling that it thinks my headphones are a microphone, but there seems to be no option (in either OS) to adjust this.  Why can't I use my laptop's internal microphone while my headphones are plugged in?


I have two monitors and I want the preview render to be on one screen and modelling it on the other. I can't do this because I can split the render and preview but they are in the same window.

I use dual monitor setup with diffrent screen layouts. So I have a "Default_l" screen layout and a "Default_r" screen layout. Is there a way to automate the change of the screen layout: When I change one screen layout for example from "Default_l" to "Compositing_l" the other screen layout also changes from Default_r to "Compositing_r"?


I have a 128GB SSD with Windows 10 installed on it and I also have a 1TB HDD on my computer. I want to dual boot Ubuntu along side with windows 10 but I don't know how much space I need to give to Ubuntu and if I should even install it on the same drive as windows, because I roughly have 60GB's on my SSD left but I thought it would be better to keep them like that since windows always has updates and that sort of stuff. I mainly use windows for gaming and pretty much everything, Ubuntu is for college programming purposes.  Sorry if I misnamed any term but I'm still a beginner to all this sort of stuff.

I have purchased a new SSD (120GB) and I had a HDD (1TB) already installed. I will install both Ubuntu and Windows on these drives. As the file space on the SSD is limited and I've read that writing to an SSD drive is discouraged, I would like to store most of the data on the HDD drive. I am aiming at faster system but also keeping the valuable data safe on the more reliable HDD and expanding the life span of the SSD.  I have already set up Windows on these drives (system files and applications on SSD, Users folder and ProgramData on HDD) and now it's time to set up Ubuntu.  So my question is which partitions I should create, on which drive should they be placed and how large they should be.  Based on my experience and articles I've read, I will probably create /swap, /home and / partitions.   Does it seem reasonable to place /swap and /home partitions on the HDD and / on the SSD?  And how large should / partition be?  Also, will the applications be installed in / partition? If so, is it rational to store the applications on separate partitions on the HDD instead of / on the SSD, and what should the size of the / partition be in this case?


Say I have a well updated Linux VPS serving HTTP content on port 80 using apache. What would I gain by enabling IPtables?   I can see no obscurity gains since the machine has a port open. Also, since the machine is constantly updated I trust the kernel to securely handle incoming requests on closed ports, which is reasonable right? I hear everywhere that I need to enable iptables but I fail to see the gains. Am I missing something?

I admin a handful of cloud-based (VPS) servers for the company I work for.   The servers are minimal ubuntu installs that run bits of LAMP stacks / inbound data collection (rsync). The data is large but not personal, financial or anything like that (ie not that interesting)  Clearly on here people are forever asking about configuring  and such like.   I use a bunch of approaches to secure the servers, for example (but not restricted to)   ssh on non standard ports; no password typing, only known ssh keys from known ips for login etc https, and restricted shells (rssh) generally only from known keys/ips servers are minimal, up to date and patched regularly use things like rkhunter, cfengine, lynis denyhosts etc for monitoring   I have extensive experience of unix sys admin. I'm confident I know what I'm doing in my setups. I configure /etc files. I have never felt a compelling need to install stuff like firewalls: iptables etc.  Put aside for a moment the issues of physical security of the VPS.  Q? I can't decide whether I am being naive or the incremental protection a fw might offer is worth the effort of learning / installing and the additional complexity (packages, config files, possible support etc) on the servers.  To date (touch wood) I've never had any problems with security but I am not complacent about it either.


There are some pairs of words that are spelled the same, aside from capitalization, but pronounced differently. One example of this is Polish - polish. I remembered another pair but forgot it. Can somebody help?  The following question is related, but not the same because it only asks about words with different meanings, and doesn't specify that they must have different pronunciations: ""

What words change meaning when the first letter is capitalised? The only word with this property that comes to mind is polish/Polish (the pronunciation also changes in this case, but that's not a necessity part of what I'm asking for).


I have a build script that executes a long command that produces lots of output which went like this:  ./compile   In order to troubleshoot compilation performance, I want to use ts (from ) which prefixes each output line with a timestamp.  So I updated my script like this:  bash -c "./compile | ts '[%Y-%m-%d %H:%M:%S]'"   This works, but now the exit value is always 0, event when compile fails (I think, because ts exits without an error).  How can I update my script to return compile's exit code while using ts?

I have two processes foo and bar, connected with a pipe:  $ foo | bar   bar always exits 0; I'm interested in the exit code of foo. Is there any way to get at it?


My code works fine for 10000 but not for 100000 numbers.  The error occurs at  result.add(next); result.addAll(mergeInt(left,right));   Here's the code:  private static ArrayList<Integer> mergeSortInt(ArrayList<Integer> array)     {         if (array.size() <= 1) return array;          ArrayList<Integer> left = new ArrayList<>();         ArrayList<Integer> right = new ArrayList<>();          for (int i = 0; i < array.size() / 2; i++)         {             left.add(array.get(i));         }         for (int i = array.size() / 2; i < array.size(); i++)          {             right.add(array.get(i));         }          return mergeInt(mergeSortInt(left), mergeSortInt(right));     }      private static ArrayList<Integer> mergeInt(ArrayList<Integer> left, ArrayList<Integer> right)     {         if (left.size() == 0) return right;         if (right.size() == 0) return left;          ArrayList<Integer> result = new ArrayList<Integer>();          int next;          if (left.get(0) > right.get(0))         {             next = right.get(0);             right.remove(0);         }         else          {             next = left.get(0);             left.remove(0);         }          result.add(next);         result.addAll(mergeInt(left,right));          return result;     }   What exactly is a StackOverFlowError? And why does it only occur for a larger amount of numbers?  Thanks in advance :)  EDIT:  I don't really see how this is a duplicate since I'm also asking for help specifically with my  code.

What is a StackOverflowError, what causes it, and how should I deal with them?


I know this may sound weird. But could a photon be given mass? And if so what would the effects be?

Why can't photons have a mass? Could you explain this to me in a short and mathematical way?


How can I see that $${2^k-1\choose a}\equiv 1\mod 2$$ for $0<a<2^k$?  I tried playing around with ${2^k-1\choose a}=\frac{(2^k-1)!}{a!(2^k-1-a)!}$ but it didn't get me very far.

Kinda stuck on this one. Help is appreciated. I'm going for either a direct or contrapositive proof.     Prove: If $n=2^k-1$, for $k\in\mathbb{N}$, then every entry in Row $n$ of Pascal's Triangle is odd.   I've been considering entry $i$ in row $n$ of Pascal's Triangle, so for $0\leq i\leq n$, we have: $$ \binom{n}{i} =\frac{n!}{i!(n-i)!} =\frac{(2^k-1)!}{i!(2^k-1-i)!} $$ I've tried manipulating this in a bunch of ways, including using the fact that $\binom{n}{i}=\binom{n-1}{i-1}+\binom{n-1}{i}$, but nothing's panned out.


I have to evaluate the following limit of a sum: $\lim_{n\rightarrow\infty}  (\sum_{k=1}^{n} (\int_{0}^{\frac{π}{2}}(\sin(x))^{k}dx))$. I ended in $\lim_{n\rightarrow\infty}  (\int_{0}^{\frac{π}{2}}(\sum_{k=1}^{n} \frac{(\sin(x))^{n}-sin)}{\sin(x)-1})dx$. From here on however I am unsure if I can introduce the limit under the integral or how to continue.

Compute $$\displaystyle \lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx.$$   I tried writing $\displaystyle \lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx = \lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \frac{1-(\sin{x})^{n+1}}{1-\sin{x}}dx$, but I don't know how to continue form here.  I know that the limit diverges to $\infty$, but I don't know how to prove it.


Both these joins will give me the same results:  SELECT * FROM table JOIN otherTable ON table.ID = otherTable.FK   vs  SELECT * FROM table INNER JOIN otherTable ON table.ID = otherTable.FK   Is there any difference between the statements in performance or otherwise?   Does it differ between different SQL implementations?

I am wondering how to differentiate all these different joins ...


I just heard about new theories proposed by Erik Verlinde about the fact that Gravity doesn't exist..or at least it's not a foundamental force. My question is : if this is true what are the implications on current models like string theory , eternal inflation ecc ecc ? what can change in the understanding of our universe ?

Recently, there was a rapid communication published in Phys.Rev.D (), titled "Gravity is not an entropic force", that claimed that , disproves Verlinde's entropic approach to gravity.  The neutrons experiment gave results consistent with the predictions of Newtonian gravity for the lowest energy state.  As I understand it, the author claims that the fact that Verlinde's entropic force comes from a thermodynamic process that is irreversible (or approximately reversible), leads to non-unitarity in the evolution of quantum systems. The non-unitarity then exponentially suppresses the eigenfunctions, predicting results very much different than the Newtonian. Thus, that experiment is in contradiction to what is expected if Verlinde's approach is correct.  My questions are,   First of all, is there anything else essential that I am missing? Is there any response to that argument? Is that a fatal problem with Verlinde's entropic approach? Is that a fatal problem for any entropic approach?   Updates on the discussion:   There is also this recent comment  Once more: gravity is not an entropic force


In the paper "Violating Bell inequality by mixed spin 1/2 states: necessary and sufficient condition" () by three Horodecki siblings, it is stated that an arbitrary two qubit density matrix can be written in the following form:  $\rho = \frac{1}{4}(I \otimes I + r \cdot \sigma \otimes I + I \otimes s \cdot \sigma + \Sigma_{i,j=1}^3t_{ij}\sigma_i \otimes \sigma_j)$  where $r$ and $s$ are some vectors.  I understand how $I$ and $\sigma_i$ for $i=1,2,3$ form a basis for operators on a single qubit so taking pairwise cross products of each forms a basis for operators on two qubits. But why does the coefficient of the $I \otimes I$ have to be $\frac{1}{4}$?  As a side question, the paper also says $t_{ij}=tr[\rho\sigma_i \otimes \sigma_j]$. Why is that the case?  Edit: The other page linked doesn't answer either of my questions. They say that $I,\sigma_i$ form a basis, but don't explain why $\frac{1}{4}$ is the coefficient. It also doesn't mention my second question.

I was reading the paper . The author defines a generic two qubit density matrix as $$ \rho=\frac{1}{4}\left( I \otimes I + \vec{r_{\rho}} \cdot \vec{\sigma}\otimes I + I \otimes \vec{s_{\rho}} \cdot \vec{\sigma} + \sum_{i,j=x,y,z}T^{ij}_{\rho} \sigma_i \otimes \sigma_j \right) \, . \tag{1} $$  How is it obtained and what are the constraints over $T^{ij}_{\rho}$ ? Also, seeing that it has some symmetry can a general 3 qubit density matrix be written as  \begin{align} \rho = \frac{1}{8} &\left( I \otimes I \otimes I + \vec{r_{\rho}} \cdot \vec{\sigma} \otimes I \otimes I + I \otimes \vec{s_{\rho}}\cdot \vec{\sigma} \otimes I + I \otimes I \otimes \vec{t_{\rho}}.\vec{\sigma} \right. \\ &+ \sum_{i,j=x,y,z}T^{ij}_{\rho} \sigma_i \otimes \sigma_j \otimes I + \sum_{i,j=x,y,z}U^{ij}_{\rho} \sigma_i \otimes I \otimes \sigma_j \\ &\left. + \sum_{i,j=x,y,z}W^{ij}_{\rho} I \otimes \sigma_i \otimes \sigma_j +\sum_{i,j,k=x,y,z}X^{ij}_{\rho} \sigma_i \otimes \sigma_j \otimes \sigma_k \right) ? \end{align} Here $\vec{r_{\rho}}, \vec{s_{\rho}}, and \vec{t_{\rho}}$ are 3 dimensional vectors with real components and each having magnitude $\le 1$.  EDIT:  I get the fact that tensor of pauli matrices acts as a basis but can't get the condition on $T_{ij}$. I was able to work backwards to see that $T_{\rho}^tT_{\rho}$ has to be such that its maximum eigen value is $\le 1$ so that CHSH inequality is only violated at maximum upto $2\sqrt{2}$. So if this condition is not followed then $(1)$ should not be a valid density matrix. The form given in $(1)$ is already hermitian and has trace 1. So for $T_{\rho}^tT_{\rho}$ having maximum eigen value $\ge1$ $(1)$ might not be a positive operator but I am unable to prove that.


I'm writing a little text, but for some reason it won't compile when I do:  \begin{prop}[Existência de $\sqrt[n]{a}$, $a > 0$, $n \in \mathbb{Z}_{>0}$] Sejam $a >0$ e $n \in \mathbb{Z}_{>0}$. Existe $b \in \R_{>0}$ tal que $b^n = a$. \end{prop}   because of the \sqrt[n]{a}. I'm pretty positive that this is the problem, because when I take it off it all compiles normally. I don't know what it wants me to do to fix this. The warnings are:     Argument of \@sqrt has an extra } \begin{prop}[Existência de $\sqrt[n],      Paragraph ended before \@sqrt was complete \begin{prop}[Existência de $\sqrt[n]      Something's wrong--perhaps a missing \item. \end{prop}      Missing } inserted \end{prop}   They don't make any sense. How to fix?    In case it is needed, the piece of code before:  A ideia para verificarmos as desigualdades acima se resumiu a eliminar os termos positivos, e usar que: \[n > 1 \implies n^m > n \implies \frac{1}{n^m} < \frac{1}{n} \implies -\frac{1}{n^m} > -\frac{1}{n},\quad \forall\,m \in \mathbb{Z}_{z>0}.\]  Por fim, agrupando termos pares e ímpares temos: \[ \sum_{i=0}^n {n \choose i}b^{n-i} = b^n + \sum_{i=1}^{n}{n \choose i}b^{n-i} = b^n + \sum_{i=1}^{\lfloor n/2\rfloor} {n \choose 2i}b^{n-2i} + \sum_{i=1}^{\lfloor (n+1)/2 \rfloor} {n \choose 2i-1}b^{n-(2i-1)},  \]onde $\lfloor \cdot \rfloor$ é a \emph{função piso}.  \newpage  \begin{prop}[Existência de $\sqrt[n]{a}$, $a > 0$, $n \in \mathbb{Z}_{>0}$] Sejam $a >0$ e $n \in \mathbb{Z}_{>0}$. Existe $b \in \R_{>0}$ tal que $b^n = a$. \end{prop}   and my preamble:   \documentclass[a4paper, 12pt]{article} \usepackage{amsmath, amssymb, amsfonts, amsthm} \usepackage[brazil]{babel} \usepackage[utf8]{inputenc} \usepackage{indentfirst} \usepackage{multicol} \usepackage{gfsartemisia-euler} \usepackage{graphicx} \usepackage[T1]{fontenc} \usepackage{stackrel} \usepackage{cancel} \usepackage{caption} \usepackage{enumerate} \usepackage{mathrsfs} \usepackage[bottom=3cm,top=3cm,left=3cm,right=2cm]{geometry}  \headheight 20mm      % \oddsidemargin 2.0mm  % \evensidemargin 2.0mm % \topmargin -40mm      % \textheight 250mm     % \textwidth 160mm      %   \newcommand\pair[1]{\langle{#1}\rangle} \newcommand{\R}{\mathbb{R}} \newcommand{\V}{\mathcal{V}} \newcommand{\diag}{\mathrm{diag}} \renewcommand{\d}{\mathrm{d}} \DeclareMathOperator{\senh}{senh} \DeclareMathOperator{\sen}{sen} \DeclareMathOperator{\tg}{tg} \DeclareMathOperator{\cotg}{cotg}  \newtheorem{teo}{Teorema}[section] \newtheorem{cor}{Corolário}[section] \newtheorem{lem}{Lema}[section] \newtheorem{prop}{Proposição} \newtheorem{defn}{Definição}[section] \newtheorem{Ex}{Exemplo}[section] \newtheorem{obs}{Observação} \newtheorem{ex}{Exercício}  \newenvironment{dem}{\smallskip \noindent{\bf Demonstração}: } {\begin{flushright} $\qedsymbol$\end{flushright}\smallskip}

My questions concerns the following MWE:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{datavisualization} \usetikzlibrary{datavisualization.formats.functions} \begin{document} \tikz[scale=4]     \datavisualization[         school book axes,         visualize as smooth line=myfunction,         myfunction={pin in data={text=$f(x)$}}]     data [set=myfunction, format=function] {         var x : interval [0:1];         func y = \value x^2;     }; \end{document}   which makes the following pretty graph:   The problem is that when I try to change my label text from $f(x)$ to $f[x]$ I receive the error Missing $ inserted. on the line containing };.  I figure it probably has to do with TikZ parsing the brackets before math-mode gets to them, but I don't know how to fix it. I tried replacing [ and ] with \[ and \] but this didn't help at all. I also realized that I could replace $f[x]$ with $f$[$x$], but this seems like the wrong way to go.  How can I include brackets in my label?


I am looking for lens help!  I am new to the DSLR world and just got a Canon T5.I posted on a local group looking for someone selling lenses. One person has gotten back to me so far and below is what they said they are selling:.   Minolta F=28mm 1:3.5 Minolta F=135mm 1:2.8 telephoto lense F=135mm 1:2.8   I have a few questions: -can I use these with a canon t5? -are they auto focus? -are they good lenses? -what's the difference between the second and third one? -what would you say is a reasonable offer for these? Thanks!!!!

I've got some lenses of brand X, but I've just got a new camera of brand Y. How can I tell if it's possible to use my lenses on my camera? I accept that I may lose a lot of automatic functionality like autofocus, aperture control and metering when using an adapter to connect the two.


Tamil progressively overlaps and combination letters (உயிர் மெய் எழுத்து) do not merge in Xfce4 terminal:    Changing font and encoding doesn't help. how to overcome this?

I am trying to process telugu text with Python. Text is rendering correctly in chrome browser like this.     Unfortunately it is not rendering correctly in default terminal or python shell in terminal.      Can you help in finding what is causing the problem?  What I have tried so far:  Installed all available telugu fonts  sudo apt-get install fonts-telu-extra fonts-telu fonts-lohit-telu   Setup unicode support in terminal   locale              LANG=en_US.UTF-8 LANGUAGE=en_US.UTF-8 LC_CTYPE="en_US.UTF-8" LC_NUMERIC="en_US.UTF-8" LC_TIME="en_US.UTF-8" LC_COLLATE="en_US.UTF-8" LC_MONETARY="en_US.UTF-8" LC_MESSAGES="en_US.UTF-8" LC_PAPER="en_US.UTF-8" LC_NAME="en_US.UTF-8" LC_ADDRESS="en_US.UTF-8" LC_TELEPHONE="en_US.UTF-8" LC_MEASUREMENT="en_US.UTF-8" LC_IDENTIFICATION="en_US.UTF-8" LC_ALL=en_US.UTF-8   Enable te_IN in /etc/locale.gen  Setup telugu language from Language Support.  Download custom telugu fonts and load them.  None of these have solved the problem. Without proper rendering, it is very hard to understand text. Any help in troubleshooting this is highly appreciated.


In X-Men: The Last Stand Professor X dies, so how is he alive in X-Men: Days of Future Past? That makes no sense if he dies before they reach that future.

I remember watching X-Men 3 and seeing Charles Xavier get disintegrated by Phoenix, however the post-credits scene and his appearance in later movies indicate that he actually survived. How is that possible?


I am creating a basic GUI application which implements  method using PyQt5, and having trouble creating Qlbales dynamically i.e. I want to display the results in these labels, and the number of labels is based on the number of inputs by the user so it varies. I could create the maximum number and then use just the ones I need, but I am sure there are neater and more effective solutions.  I have tried with exec and eval (I know it is poor approach), but nevertheless I have not succeeded. I think eval fails to read element from the list somehow, not sure. Here is what I've tried (i+5 because I have 4 more labels) :  def set_result_labels(self):          font = QtGui.QFont()         font.setPointSize(15)         for i in range(len(self.text_parties_names)):             exec(f"self.label_{i+5} = QtWidgets.QLabel(self.centralwidget)")             eval(f"self.label_{i+5}.setGeometry(QtCore.QRect(640, {(i+5)*40}, 50, 50))")             eval(f"self.label_{i+5}.setFont(font)")             eval(f"self.label_{i+5}.setText(self.text_parties_names[i])")    and self.text_partirs_names is list with the names from textEdits (user input):  def get_parties_names(self):         for text_edit in self.text_edit_parties_list:             if text_edit.toPlainText():                 self.text_parties_names.append(text_edit.toPlainText())

Suppose I have a python object x and a string s, how do I set the attribute s on x? So:  >>> x = SomeObject() >>> attr = 'myAttr' >>> # magic goes here >>> x.myAttr 'magic'   What's the magic? The goal of this, incidentally, is to cache calls to x.__getattr__().


Say I have      x = [[0,0]]     y = x[-1]   Then why does      y[1] += 1   give       x = [[0,1]]     y = [0,1]    That is, I'm confused as to why it also changes what x is, even though I only specified something to do with y?

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


I want to axiomatize "the concept of set" in my head, but every time I face some circular definition or intuition.   In predicate logic, we quantify over some "Universe of Discourse". Intuitively Universe of Discourse is a set, a collection. But then, in naive set theory or axiomatic set theory, we define "set" by using quantifiers (over Domain of Discourse)... Isn't it circular?  I mean, we assume that "Universe of Discourse" is some kind of "set", then by using first order predicate logic we define set again?

I wonder about the foundations of set theory and my question can be stated in some related forms:   If we base Zermelo–Fraenkel set theory on first order logic, does that mean first order logic is not allowed to contain the notion of sets? The axioms of Zermelo–Fraenkel set theory seem to already expect the notion of a set to be defined. Is there are pre-definition of what we are dealing with? And where? In set theory, if a function is defined as a set using tuples, why or how does first order logic and the axioms of Zermelo–Fraenkel set theory contain parameter dependend properties $\psi(u_1,u_2,q,...)$, which basically are functions?


A pair of users seem to be hitting several sites with poor or plagiarized answer, and the first user immediately accepts the answer of the second. I've notified mods on both sites, but suspect this pair are hitting more sites. Anything else I can do to help stop them?  For example:

Normally new users are not allowed to up-vote until they gain a bit of reputation by receiving up-votes or accepts from the community of a site.  But this has a weak point that is being exploited:     A number of new users post, answer, and accept each others'    off-topic questions before we can close them (in less than 5 min).    Accepting each others' answers gains them enough reputation to    start up-vote each others' posts.   We are closing them and the moderators clean up afterwards but  this keeps happening over and over again and becoming frustrating  to the extent that I think a systematic solution might be required. Is there a system to prevent this kind of circumvention of  the reputation requirements using accepts by new users?  One possible solution might be to change the system so accepts from users who do not have enough reputation to up-vote  do not give any reputation (at least until the answer gets an up-vote).