Can anybody simply tell me how should I use BibTeX in TeX Live 2013? I saved my references in a .bib file and I write the following in my .tex file:  \documentclass{article} \begin{document} \bibliographystyle{plain}%Choose a bibliograhpic style % author~\cite{Meyer2000}. % \bibliography{Master} \end{document}   What I should do afterwards?  I compile it with BibTeX and PDFLaTeX but it does not help.

I've browsed the forums and found a number of posts that have addressed this issue, but none of the solutions seem to work for me. I have the following script that I just copied from the bibtex home page to get familiar with it. Instead of the citation number I get a question mark. I compile using Latex+Bibtex+Latex+Latex+PDFLatex+ViewPDF just as has been previously suggested and the problem persists.   \documentclass[11pt]{article} \usepackage{cite}  \begin{document}  \title{My Article} \author{Nobody Jr.} \date{Today} \maketitle  Blablabla said Nobody ~\cite{Nobody06}.  \bibliography{mybib} \bibliographystyle{plain} \end{document}   My bibliography (Bib.bbl)  @misc{ Nobody06, author = "Nobody Jr", title = "My Article", year = "2006" }    Looking at previous posts one thing that is concerning is that my .bbl looks empty as shown below. Further, I don't have a .blg  \begin{thebibliography}{}  \end{thebibliography}


Just a thought, I see that many questions arise with 'Blockchain' and to address that can we have separate community in the Stack Exchange network?  We do have a 'Bitcoin' community, can we make a Blockchain community in general?  If no, then please point me why we should avoid it?

I have an idea or subject that should have a Q&A, and want to propose a new site. How can I do this?  Related:


I initially set up my account --  -- in the summer of 2008 when the site was still very much in beta. Since I used myopenid.com for authentication and myopenid.com is no longer with us, I would like to apply the credentials I created for this account to my former account so I can keep using that account.  In another question --  -- it was mentioned that all you need to do is 'flag a moderator' to get access to an account which can't authenticated anymore (because the authentication services is gone).  How do I flag a moderator to get access to my old account?

Is there any way to get my old account + metadata back if I have lost an account ties to MyOpenID?


I have a copyright notice on my IEEE Journal that is overlapping with my text while using Lyx and I am not sure why it is happening or what I can do to fix the problem.  I have tried looking up ways to adjust the footer and even have seen this question asked by someone else , but no one has answered.  Here is an image of the problem I am describing:

I am trying to write a journal paper using the IEEEtran.cls template.  My problem is that the Publication ID Mark overflows into my thanks section.  This is the bottom of the title page:    From the documentation of IEEEtran.cls we see that:    I included the command \IEEEpubidadjcol into the second column. This prevents the overflow in the second column as you can see in my previous image, but lets the first column run freely.  I tried including \IEEEpubidadjcol into the first column aswell, but that causes compilation errors.  Please, could you give me some hint on how to solve this problem without doing something illegal with respect to the IEEE modus operandi?  EDIT:  As the answer suggests, the problem can be solved using the \IEEEpubidadjcol command twice. When I tried this, I got an error:  Infinite glue shrinkage found in box being split   In spite of this error a correct pdf is produced. The error goes away when I do not include packages fixltx2e and dblfloatfix.


If there was no time prior to the big bang and it was possible that it expanded and created the universe (and it happened) then, despite time doesn't exist there, if something is possible it will happen?

I saw  hosted by Stephen Hawkins.  And if I didn't get it wrong, it says that there was no time before the big bang, time was created there.  So how can anything happen when there is no time (eg: the creation of time and the universe)? Is this what he calls a 'singularity'? Which I could think like this: when there is no time nothing can happen, except during this singularity.  Of course I don't know of a law that says 'when there is no time nothing can happen..', I just came up with it, as something intuitive.


The exercise is the following: Suppose $F$ has right adjoint $G$ and $H$ has right adjoint $J$ ($F:\mathbb{A}\rightarrow\mathbb{B}$ and $H:\mathbb{B}\rightarrow\mathbb{C}$ with $\mathbb{A,B,C}$ categories). Prove that $GJ$ is the right adjoint of $HF$.   What is the best way to start with? I want to do this by the two-way-rule, thus by bijective correspondence, but i don't see how to start. Someone who can help me?  Thank you very much.

Does the composition of adjoint functors again form an adjunction?  Say $\langle F_1,G^1\rangle$ is an adjunct pair between two categories A and B and $\langle F_2,G^2\rangle$ is also an adjoint pair between the categories B and C, then would $\langle F_2\circ F_1,G^1\circ G^2\rangle$ be an adjoint pair between the categories A and C?  If not is there some way of obtain an adjunction given the assumptions made on the 4 functors, or by adding extra properties to the categories?  Particularly, here I am assuming A is the category $_RMod$ for some (apriori) arbitrary ring.


I found some old notes where someone suggest I run the following command to set some file permissions:  find /perl/lib/ -type f -exec chmod o+r \{\} \;   Would you happen to know what the \{\} part of the statement is doing?  Is it even necessary?  I tested running it a few times on some test files and it seems to do the same thing as removing the backslashes:  find /u01/app/oracle/product/12102/perl/lib/ -type f -exec chmod o+r {} \;   Any help you can offer would be appreciated.

The man page for GNU find states:    -exec command ;     [...] The  string `{}'  is  replaced  by the current      file name being processed everywhere it occurs in the      arguments to the command, not just in arguments where      it is alone, as in some  versions  of  find.     Both  of  these  constructions might need to be escaped      (with a `\') or quoted to protect them from expansion      by the shell.     That's from the man to find (GNU findutils) 4.4.2.   Now I tested this with bash and dash, and both don't need to have the {} being masked. Here is a simple test:  find /etc -name "hosts" -exec md5sum {} \;    Is there a shell, for which I really need to mask the braces? Note, that it doesn't depend upon whether the file found contains a blank (invoked from bash):   find ~ -maxdepth 1 -type d -name "U*" -exec ls -d {} \;  /home/stefan/Ubuntu One   This changes if the found file is passed to a subshell:  find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d {}' \;  ls: cannot access /home/stefan/Ubuntu: No such file or directory ls: cannot access One: No such file or directory   which can be solved by:  find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d "$0"' {} \;   in contrast to:   find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d "{}"' \;  /home/stefan/Ubuntu One   but that's not what the man page is talking about, is it? So which shell treats {} in a different way?


I am trying to solve by a different approach the fourth sum from ,  namely: $$S= \sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{1}{nm(4n+m)} =\int_0^1 \frac{\ln(1-x)\ln(1-x^4)}{x}dx= \frac{67}{32} \zeta(3) -\frac{\pi}{2}G$$    One way to solve it is similarly to my answer from there: $$S=\int_0^1 \frac{\ln(1-x)\ln(1-x^2)}{x}dx+\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$$ From  we know that: $$\small \int_0^1 \frac{[m\ln(1+x)+n\ln(1-x)][q\ln(1+x)+p\ln(1-x)]}{x}dx=\left(\frac{mq}{4}-\frac{5}{8}(mp+nq)+2np\right)\zeta(3)$$ Thus by setting $m=0,n,p,q=1$ in the first integral we get that: $$S=\frac{11}{8}\zeta(3)+\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx=\frac{11}{8}\zeta(3)+I$$ $$I=\sum_{n=1}^\infty \frac{(-1)^{n-1}}{n} \int_0^1 x^{2n-1} \ln(1-x)dx=\frac12\sum_{n=1}^\infty \frac{(-1)^n H_{2n}}{n^2}=\frac{23}{32}\zeta(3)-\frac{\pi}{2}G$$ And the result for $S$ follows. The last sum appears to be known, see $(659)$ from , or alternatively since $I=2\Re\left( S(i)\right)$ just use the following identity: $$S(x)=\sum_{n=1}^\infty \frac{x^n}{n^2}H_n=\operatorname{Li}_3(x)-\operatorname{Li}_3(1-x)+\operatorname{Li}_2(1-x)\ln(1-x)+\frac{1}{2}\ln x \ln^2(1-x)+\zeta(3)$$ However I am trying to find a different method since the result is quite nice and I believe there's a nicer way to solve the integral without using such sums.   Thus I would appreciate to get some help with the following problem:     Prove without using Euler's sum or polylogs that   $$\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx=\frac{23}{32}\zeta(3)-\frac{\pi}{2}G$$   I also tried to consider the following integral: $$J=\int_0^1 \frac{\ln(1+x)\ln(1+x^2)}{x}dx$$   So now I am after the following integral: $$I-J=\int_0^1 \frac{\ln\left(\frac{1-x}{1+x}\right)\ln(1+x^2)}{x}dx=\frac74 \zeta(3)-\pi G$$


Context:  I have an old working system with an Ubuntu version correctly running on it.  The problem to solve:  The wifi where I work does not reach every place in the office. The idea is to use this system as a bridge for extending the wifi range (please note that I am not even sure that the right word to use is bridge. If not, please correct me).  Questions:   is it possible to solve the problem with the solution I am proposing? Should I use two different wifi antennas? (of course, I have more than one if necessary) is there a standard procedure (or a ready-to-use OS) for that purpose? any advice or suggestions on how to do that? additionally, can I connect this system to a switch in order to provide internet access to other systems connected via eth?   Sorry for this newbie question. I am quite new with networking issues.

My house is wired for Ethernet but all the wires come to the basement which is where my dsl modem and my Netgear WNDR3700v3 wifi router is. I get practically no wifi signal upstairs but i have an Acer Revo upstairs running Ubuntu which is connected to my network with Ethernet and has wifi card built in (though I'm not using it). Is there a way I can make this into a repeater?   I've been reading up about it but there are some things I don't understand. I read that I need 2 wifi card and one needs have master mode. I don't understand what this means.  I also see that my WNDR3700 has an option to be a wireless base station and i can put in the mac address of 4 repeaters. Would I need to enable this to work with my revo as a repeater?


What is the word that describes a person who uses other people, generally for personal gain, without anything given in return? Maybe through blatancy or through manipulation. I was using extortionist, but I know that's not correct. To further explain; someone who keeps a relationship only for the benefits it provides.

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


Prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}},  \sqrt{2\sqrt{2\sqrt{2}}} \ $ converges to $2$.   My attempt  I proved that the sequence is increasing and bounded by $2$, can anyone help me show that the sequence converges to $2$? Thanks for your help.


Here's my attempt at trying to prove it by definition:  $$\exists \mathcal{E} > 0 | \exists N\in \mathbb{N}|\forall n > N:$$ $$|\sqrt[n]{n}-1|<\mathcal{E}$$  But from this point on, I'm not sure how to demonstrate that $N$. I tried applying the mean inequality, but when I do, the indexes cancel out and I get something like $1< \mathcal{E}$, which negates the proof. How can I proceed? I also don't know how to utilise the fact that the infimum is equal to one.

Let  $A = \left \{ \sqrt[n]{n} \mid n \in \mathbb{N}\right \}$. I need to find and prove the infimum of $A$.  Because $n \in \mathbb{N},$ we can know for sure that $\sqrt[n]{n} \geq 1$. (Does that need a deeper proof?)  Then to prove that $1$ is the infimum, for $\forall \varepsilon>0$, I need to find a certain $n \in \mathbb{N}$ that makes $$\sqrt[n]{n} < 1 + \varepsilon$$  How do I "engineer" that $n \in \mathbb{N}$ ?  What's the trick? Raising $\sqrt[n]{n} < 1 + \varepsilon $ to the power of $n$ doesn't really help.


I'm facing MTA poor reputation and I'm fighting against it since days without success. MTA poor reputation had plenty topics so I verify/modify many aspect of my configuration such as:   Verify blacklist IP Add reverse DNS on my ISP Match the smtp banner Add SPF allowing my smtp and webserver for my domain   Everything seems good from mxtoolsbox tools but ...  Talosintelligence rate the email reputation as poor. Since I make change on my SPF record, this reputation change from poor to neutral only for one day. There is something I forgot or don't understand and that why I post this topic here if anybody face and resolve this problem.  I investigate further and I think the problem can become from the DNS configuration: actually, MX record isn't FQDN, it show as: x.x.x.x.mydomainname.com (same for the reverse). Du to microsft  (old but seems good), I think I add to change my MX record as mailserver.mydomainname.com (and the reverse as well).  But I had to add an A record. My question is that I had to add it on my ISP DNS ? mailserver.mydomainname.com A x.x.x.x  should be good ?  Thanks you for reading me and for the help regards,

This is a  about Fighting Spam.   Also related:                    There are so many techniques and so much to know about fighting SPAM. What widely used techniques and technologies are available to Administrator, Domain Owners, and End Users to help keep the junk out of our inboxes?  We're looking for an answer that covers different tech from various angles. The accepted answer should include a variety of technologies (eg SPF/SenderID, DomainKeys/DKIM, Graylisting, DNS RBLs, Reputation Services, Filtering Software [SpamAssassin, etc]); best practices (eg mail on Port 25 should never be allowed to relay, Port 587 should be used; etc), terminology (eg, Open Relay, Backscatter, MSA/MTA/MUA, Spam/Ham), and possibly other techniques.


My 15 month old has suddenly started waking at night crying. We go into her room to try to comfort her, and sometimes bring her into bed with us, but our presence seems to make things worse. Sometimes she screams and becomes so hysterical that nothing will calm her down for 30 to 40 minutes. In between these episodes, and during the day, she is otherwise totally normal and her daytime behaviour has not changed.  Are we dealing with separation anxiety or is this closer to night terrors? She always seems awake and aware when she has a screaming jag. We haven't had trouble waking her, so I am thinking it could be separation anxiety. We recently took a 3 week vacation overseas and it was hard for her to adjust to the time change and jet-lag...could that be the reason for these outbursts?  Whatever it is, these tantrums are very scary...I am not sure now whether I should pick her up at night or not. I can't stand the thought of letting her scream alone...and when I go to her and try to comfort her while leaving her in the crib she becomes even more angry.

My son is 17 months old with a regular routine in a nuclear family.  0700 awake 0745 in nursery Full day of nursery 1730 pick up from nursery 1800 relaxing time with mum and dad 1830 bath time 1900 story / quiet time 1920 bottle of warm whole milk 1930 bedtime  As a family we have the usual toddler tears you would expect with bedtime and handle them accordingly but the real reason for this question occurs between the hours of 2300 and 0500. Randomly, for 4 to 5 minutes, he will wake up in absolute hysterics screaming for his mother.  His eyes are closed and when picked up to be soothed he will not recognise us and continue the episode.  He is, as far as I can tell, still asleep during these periods but the screams are deafening. I don't know if this qualifies as a night terror? Sometimes the episode will manifest itself with him pushing himself away from us to the floor and running into other rooms (asleep).  Normally he will settle by the stair gate clutching it and shouting as if he has been abandoned and we (parents) are downstairs instead of next to him. The only remedy we have found is to have one or two bottles of milk on hand to give to him which normally soothe his distress until he falls back asleep. Context His mother is a fairly normal sleeper but I am a  sleeper; dreaming/hallucinating as soon as I close my eyes and not waking for any amount of noise or distraction.  Often my dreams are in full colour and my partner can have full, lucid conversations with me whilst I sleep which I cannot remember.  However, in 32 years I have never had a nightmare that I can recall so I don't know how to approach my son to help him deal with this sleeping problem.  I always found Hynagogic sleep a pleasant experience. Do any parents or medical professionals on these forums have experience and/or advice on how to support my son?


The math club at my university spends its time solving problems from mathematical magazines (e.g. Mathematics Magazine). Let's assume I, as an undergraduate student, submit a solution to a challenge problem from such a magazine, and my solution is published. Is there any advantage to having one or more published solutions like this when applying to graduate school?  For reference, assume this is graduate school in math.

I have started solving problems from the American Mathematical Monthly. While I will definitely continue this, I am not sure how much this will help for math graduate school admissions (assuming I submit my solutions and they are recognized by the Monthly). How significant would multiple solutions to Monthly problems be in admissions? What about having the published solution to a problem? One issue is that I don't know how difficult the problems are presumed to be: all I know is that I personally have solved at least one of them!


I am trying to read 7M data from a file but it is failing. When I googled,I found that there is no limit for reading data.  My code given below is failing with segmentation fault.  char *buf = malloc(7008991); FILE *fp = fopen("35mb.txt", "rb"); long long i = 0; long long j = 0; while(fgets(buf+i, 1024, fp)) {     i+=strlen(buf);     if(i==7008991)break; } printf("read done"); printf("ch=%s\n", buf);   Need some help

What would be the most efficient method of reading a text file into a dynamic one-dimensional array? reallocing after every read char seems silly, reallocing after every read line doesn't seem much better. I would like to read the entire file into the array. How would you do it?


I'm using the ModelBuilder functionality in ArcGIS, and would like to take a raster that contains 4 bands, clip it with a polygon and then make NDVI from the clipped file. To do that, I need access to the different bands in the raster. In QGIS (where I'm coming from), some libraries don't preserve all 4 bands.   In QGIS, the raster calculator menu gave access to all of the bands, but ArcGIS doesn't seem to. Examples I've found breaks the raster into multiple entities in the model builder and works with those?  In ModelBuilder, how would you go about breaking the raster into its 4 bands?

I'm fairly new to ArcGIS and I get into trouble extracting a single band layer from a raster image .img in ArcMap that I want to use after in zonal statistics. So far, all help I found is to do the operation in the other way around and merge bands and some explanation by using the python code. But I would like to use ArcMap interface.  I tried to create a single layer from ArcCatalog and import it to ArcMap but I get a layer and not a raster. I also tried to import my image.img in ArcMap but then I don't find anything to extract only a specific band.


In regards to removing a program from a computer, I want to know why a program must be uninstalled versus deleting the program's files. I bet I can answer my own question by stating that programs must be installed in the first place and therefore must be uninstalled to remove.  However, I have always wanted to know some details as to why deleting a program's files (i.e. deleting its folder and all subfolders) does not effectively remove the program from my computer. Just seems like it would.

Uninstalling a lot of stuff at the same time takes too long. If I just remove the directory, it will probably leave some registry records and what else?


The best student in a school or university

Is there a word in English to qualify the highest-ranked student in a class in a year?  We are talking here about higher education, especially in the context of curricula that keep a given set of students over the course of several years, being ranked at the end of each year, possibly with competitive admission for the following year. The ranking is a weighted average of all marks obtained over the year.  I am looking for a single word, or expression, to quickly designate the one student with the highest ranking. If there is no such thing in English, then let's try to get the most concise and idiomatic definition.  In all cases, it is not emotionally connoted, i.e. not pejorative nor bragging.  For French speakers: I am looking for the translation of “major de promotion”.    EDIT: additional, not as much of a pure “word request” question: is this anything you should mention on a curriculum vitæ in the English-speaking world? If so, please mention whether the given word is appropriate for such a use  :)


Reviewing old homework sets for a class and I came across this integral:  $$\displaystyle \int_0^1 \int_0^{1-y} \cos\Big( \frac{x-y}{x+y} \Big) \; dx dy,$$  which the question suggests to evaluate using a change of coordinates; however, I haven't a clue where to begin to identify a useful change of coordinates.   I tried $u = x-y$ and $v = x+y$, but then wasn't sure how I'd convert the domain of integration.  After that, I looked to the given limits for inspiration and noticed that $0<x<1-y$ could be rewritten $y < x+y < 1$, so tried $u = x+y$ and $v = y$, which yielded   $$\displaystyle \int_0^1 \int_y^{1} \cos\Big( \frac{ u - 2y }{u} \Big) \; du\,dy,$$  but that doesn't seem any simpler than the original, to me.   Any advice would be appreciated!

Let $D$ be the region bounded by $x+y = 1$, $x= 0$, $y = 0$. Use the result of  to show that $$\iint_D\cos\bigg(\frac{x-y}{x+y}\bigg)~dx~dy = \frac{\sin 1}{2} $$   and graph $D$ on an $xy$ plane and a $uv$ plane, with $u = x-y$ and $v = x+y$.   I got the Jacobian determinant is $\dfrac{1}{2}$, but how do I get the limits of integration for $u$ and $v$?


I'm trying to colorize a SRTM raster in QGIS 2.10 following a tutorial found on the . My problem is that when I try to set the render type as single band pseudocolour in the Style Preferences, nothing happens and the raster rendering remains unchanged. Then when I open again the Style Preferences, everything is default-set.  What am I doing wrong ?

In a raster layer's Style Properties, I can choose pseudocolor render type, and choose a color ramp and classify the raster.      However, when I click the 'Apply' button, or click 'OK', the visualization of the raster never changes.  I was able to output a 'colorized' version of the same raster using GRASS plugin.  I also reinstalled QGIS 2.8, and was able to adjust and see a raster stylings using the steps I outlined above.  So, can anyone confirm this as an issue, or confirm that there's a mistake somewhere in my process?  I should note that I'm on a Mac, 10.10.4, and I'm using the QGIS provided by , 2.10.1-1 .  Update 1: Here's a screenshot of the rest of my settings.      I have Grayscale set to off in the Style setting.  Also, I don't believe grayscale/color-blind Preview is available on the Mac version of QGIS.  They're does't appear to be the option where it , in the Menu Bar under View / Preview / Photocopy (grayscale) etc.  Either way-- I added a shapefile to show color.  Update 2: I've experimented with setting color interpolation to discrete, linear, and exact, but still am not able stylize using Singleband pseudocolor.  I've also confirmed that the 'Render' box on the the main map view is checked.  Also, I am able to adjust Color Rendering settings, like Hue, Blending Mode, etc., and see the results when clicking 'Apply' or 'OK'.  Update 3: As other Mac users are confirming this, I think it may be a bug. I've created a bug report at the official .


I have a new MacBook Pro which I am not able to connect to my old iMac so I can use iMac as my secondary monitor. Details of MacBook and iMac MacBook Pro:  13-inch, 2019, Two Thunderbolt 3 ports iMac: 21.5 inch Mid 2011 Here is what I did but that didn't work:  Put a Thunderbolt cord into iMac and attached it to a Thunderbolt to HDMI Adapter Connected a new HDMI cord to the adapter (from iMac) to the MacBook Pro adapter Pressed Command + F2 on iMAC Nothing happened  Please help.

I have a Surface Pro 4 and an iMac (late 2019). I would like to connect my Surface Pro to the iMac to use the iMac screen as a second monitor.  Is that possible?  What are the requirements to use an iMac as a second screen?


My experiment had a 2x3 design with one covariate. If I analyse the results using an ANOVA, I get a strongly significant interaction between the two main factors (p<.001). If I add the covariate into the analysis and do an ANCOVA, the interaction between the two main factors is not significant (p=.252).  The covariate itself was not significant, nor did it have any significant interactions.  There are similar questions on this website, but I was hoping to understand what does such a result pattern say about the covariate? How should I interpret the results?  Adding the covariate was the novel feature of my study and therefore it is important to me to understand this interaction properly.  Is the covariate influencing the results?  EDIT:  I've been thinking about this all day and I guess the possible interpretation would be: When controlling for the covariate, the interaction of the main effects is no longer significant.  In which case I don't understand a couple of things:  a) Does that mean the covariate is responsible for the interaction?  b) Why is the interaction between FactorA*FactorB*Covariate not significant then?  c) Why isn't the covariate significantly interacting with anything at all, when its presence seems to be influencing the results?  EDIT 2:  Maybe I am doing something wrong, because it is not making much sense to me. Here are my results:    The last two pictures show when I run an ANOVA without the covariate (repeated measures, Factor 1 (2 levels). Factor 2 (3 levels).  The first three when I run an ANCOVA on the same factors, except I put in OptimismScore as a covariate.

I have initially run a 2x2x2 Anova and found some significant interaction between the independent variables. I then ran a ANCOVA where I added a covariate. I am confused with how to interpret the output from the ANCOVA as the significant interactions that I found with the ANOVA are now insignificant in the ANCOVA.


This is probably a naive question. Why is Entropy formula defined as the way what it is intead of more simpler formula? for example just P(x)*P(y) which I imagine can express uncertainty as well (0.5*0.5 > 0.4*0.6 > 0.3*0.7).

is the negative of the sum of the probabilities of each outcome multiplied by the logarithm of probabilities for each outcome. What purpose does the logarithm serve in this equation?  An intuitive or visual answer (as opposed to a deeply mathematical answer) will be given bonus points!


This function runs a number series known as the Collatz conjecture. What is its time/space complexity? def run(n):     i = 0     while n > 1:         if n % 2 == 0:             n /= 2         else:             n = n * 3 + 1         i += 1     return i

Most people with a degree in CS will certainly know what . It helps us to measure how well an algorithm scales.   But I'm curious, how do you calculate or approximate the complexity of your algorithms?


I have been using PVSTAR+ app which plaeyed youtube in the background and I could listen to youtube while its closed.  Youtube recently updated it's API so PVSTAR+ doesnt work anymore. it's also have been deleted from the store so I wont get any updates.  Is there an app that play youtube in the background and works now? And I dont want to use AudioPocket-it can't search youtube.  Thanks.

The stock YouTube app (here on 2.1-eclair, but applies to all android versions) stops playing when I minimised, switched to another application or even when I lock the phone. And when I resume it restart downloading the clip from the beginning. Is there any way that I can play YouTube clips in the background? Note, I only the audio to continue playing.


Is there a Unix command or shell script that takes a file argument and moves to the containing directory, ignoring the file part of the argument altogether?

I would find it very convenient to be able to use cd with a file argument.  cd myDirectory/anyname.anyExtension would be equivalent to cd myDirectory/  What would be the best alias or function to achieve this behavior ?  EDIT: Sorry I didn't mention it in the 1st place: I use zsh


In the Game of Thrones finale, S08E06 The Iron Throne we can see Bran the Broken being chosen as King of the 7 Kingdoms, but Sansa claims for the North to be independent hence making the realm of 6 Kingdoms.  We could expect the other Lords to step for their own realms and also asking for independency, especially Asha Greyjoy for the Iron Islands and the Dornish guy. These two Kingdoms have shown history of being reluctant to be part of a whole Westerosi Kingdom.

In the Game of Thrones Season 8 finale Sansa      demands the freedom of the North. North will be an independent kingdom.   Why did other houses remain silent. They could also demand the same for their own kingdom.  I could guess they are not very powerful to demand anything but there was no harm putting that in front of      the newly elected king.


I did a series of experiments in nodejs console:  > function a(){} undefined  > a [Function: a]  > a.name 'a'  > b = function(){} [Function]               // see, the name is empty  > b.name ''                       // further proof  > b = function b(){} [Function: b]  > b.name 'b'                      // now b behaves just like it's defined                          // by "function b(){}"   Judging from what I can test, function a() {} serves as a shorthand of a = function a() {}. Is this how engines like V8 internally do? Is there a difference between a and b in the above experiment?

I've recently started maintaining someone else's JavaScript code. I'm fixing bugs, adding features and also trying to tidy up the code and make it more consistent.  The previous developer used two ways of declaring functions and I can't work out if there is a reason behind it or not.  The two ways are:  var functionOne = function() {     // Some code };     function functionTwo() {     // Some code }   What are the reasons for using these two different methods and what are the pros and cons of each? Is there anything that can be done with one method that can't be done with the other?


I am trying to test out the renice command on my Mac, it seems to be having no effect. This is how I'm testing it:  I have a dual core CPU with hyper threading, so I run 6 instances of node -e 'while(1){}' which, combined, max out my CPU. (Alternatively, run while true; do echo running > /dev/null ; done if you dont have node.)  I then get a PID of one of the node processes, either by the activity monitor application or pgrep, and then run sudo renice -n 19 -p $PID.  By looking at the activity monitor application or htop, the CPU usage of all of the node processes are still equivalent:    My understanding was that the process that I reniced would have a low priority, and so would not use a significant amount of CPU time when there are other processes using it.  Am I misunderstanding something about renice? Or is this a bug in Mac OS?

I am trying to test out the renice command on my Mac, it seems to be having no effect. This is how I'm testing it: I have a dual core CPU with hyper threading, so I run 6 instances of node -e 'while(1){}' which, combined, max out my CPU. (Alternatively, run while true; do echo running > /dev/null ; done if you don't have node.) I then get a PID of one of the node processes, either by the activity monitor application or pgrep, and then run sudo renice -n 19 -p $PID. By looking at the activity monitor application or htop, the CPU usage of all of the node processes are still equivalent:  My understanding was that the process that I reniced would have a low priority, and so would not use a significant amount of CPU time when there are other processes using it. Am I misunderstanding something about renice? Or is this a bug in macOS?


I am working on a project using camera tracking. I have a solve error of 0.3, and when I set up the tracking scene, besides the fact that the camera is rotated incorrectly, everything works great. When I try to fix the camera's rotation, things get messed up.  I am wondering how I can fix this, am I doing something wrong? Thanks in advance!

I have been playing around with camera tracking and I'm happy enough with the tracking and alignment of the markers with the footage when viewed through the camera.    The problem is, when I am not looking through the camera I can see that the grid isn't aligned to the camera.    How do you correctly align the grid to this tracked camera? I have set a floor and two points for scale, also clicked setup tracking scene, but this just added cube and plane which were on the grid.


Implement char * ithword(char * str, int i) that will return the ith word in str. The words are alphanumeric and separated by non-alphanumeric characters. The function will allocate memory for the word returned, and return a pointer to it.  My approach is : Start traversing the string and count the numbers of spaces and non-alphanumeric characters and when the count reaches i-1, start printing till you get another space or non-alphanumeric characters.  Is it correct?

I'm trying to iterate over the words of a string.  The string can be assumed to be composed of words separated by whitespace.  Note that I'm not interested in C string functions or that kind of character manipulation/access. Also, please give precedence to elegance over efficiency in your answer.  The best solution I have right now is:  #include <iostream> #include <sstream> #include <string>  using namespace std;  int main() {     string s = "Somewhere down the road";     istringstream iss(s);      do     {         string subs;         iss >> subs;         cout << "Substring: " << subs << endl;     } while (iss); }   Is there a more elegant way to do this?


the problem is when I click on cart object to make an order the app crashes and throws the NullPointerExcetion.  my Cart.java code is   public class Cart extends AppCompatActivity {      RecyclerView recyclerView;     RecyclerView.LayoutManager layoutManager;      FirebaseDatabase database;     DatabaseReference requests;      TextView txtTotalPrice;     FButton btnPlace;      List<Order> cart = new ArrayList<>();     CartAdapter adapter;      @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_cart);          //Firebase         database = FirebaseDatabase.getInstance();         requests = database.getReference("Requests");              public void onClick(DialogInterface dialogInterface, int i) {                         Request request = new Request(                         Common.currentUser.getPhone(),                         Common.currentUser.getName(),                         edtAddress.getText().toString(),                         txtTotalPrice.getText().toString(),                         cart                 );                  // send it to firebase                 requests.child(String.valueOf(System.currentTimeMillis()))                         .setValue(request);                 //Delete cart                 new Database(getBaseContext()).cleanCart();                 Toast.makeText(Cart.this, "Thank you, Order is placed!", Toast.LENGTH_SHORT).show();                 finish();             }         });     private void loadListFood() {         cart = new Database(this).getCarts();         adapter = new CartAdapter(cart, this);         recyclerView.setAdapter(adapter);     } }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I created a sample minimal directory structure with which I am able to re-create my linker error problem. Below is the directory structure I am having:  satyam@sat:~/cpp/build$ ls -R .: src  template  ./src: main.cxx  main.o  ./template: tmp.cxx  tmp.hxx  tmp.o   Content of each of the file is as below:  tmp.hxx  template <typename T> class Array { private:     T *ptr;     int size; public:     Array(T arr[], int s);     void print(); };   tmp.cxx  #include <iostream> #include "tmp.hxx"  using namespace std;   template <typename T> Array<T>::Array(T arr[], int s) {         ptr = new T[s];         size = s;         for(int i = 0; i < size; i++)                 ptr[i] = arr[i]; }  template <typename T> void Array<T>::print() {         for (int i = 0; i < size; i++)                 cout<<" "<<*(ptr + i);         cout<<endl; }   main.cxx  #include <tmp.hxx>  int main() {     int arr[5] = {1, 2, 3, 4, 5};     Array<int> a(arr, 5);     a.print();     return 0; }   First I moved to template directory and made object file of tmp.cxx with below command:  satyam@sat:~/cpp/build/template$ g++ -c tmp.cxx   Then I moved to src directory and made object file of main.cxx with below command:  satyam@sat:~/cpp/build/src$ g++ -c -I ../template/ main.cxx   Finally I tried to make binary in /cpp/build directory with below command and got this linker error:  satyam@sat:~/cpp/build$ g++ -o prog template/tmp.o src/main.o src/main.o: In function `main': main.cxx:(.text+0x4e): undefined reference to `Array<int>::Array(int*, int)' main.cxx:(.text+0x5a): undefined reference to `Array<int>::print()' collect2: error: ld returned 1 exit status   I tried looking on other threads of SO and found that including tmp.cxx file in main.cxx will resolve the problem, but I really don't want to go with that option as it doesn't looks right. Not sure where to look further.  Any help regarding this would be great.

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


$\lim_{n\rightarrow \infty} \sum_{i=0}^{n}\frac{e^{-n}n^{i}}{i!}\rightarrow \frac{1}{2}$  Tried: here suppose N is poission distribution with parameter n $\lim_{n\rightarrow \infty} \sum_{i=0}^{n} P(N\geq i) $ $= \lim_{n\rightarrow \infty} \sum_{i=0}^{n}(P(N=i)+P(N>i) + P(N<i)-P(N<i)) $ $= \lim_{n\rightarrow \infty} \sum_{i=0}^{n}(P(N= i)+P(i<N<i)-P(N<i)$ $= \lim_{n\rightarrow \infty} \sum_{i=0}^{n}(P(N= i)-P(N<i)$ ;  $(P(i<N<i)=0)$ $=\sum_{i=0}^{\infty}(P(N= i)-\sum_{i=0}^{\infty}P(N<i)$ $=1-\frac{1}{2}$ $=\frac{1}{2}$

I'm supposed to calculate: $$\lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\frac{1}{2}$, which is a pretty interesting and nice result. I wonder in which ways we may approach it.


So basically lets say I tell my familiar "go pick up my scroll" then after he flies to where my scroll is, can I dismiss him and recall him with the scroll next to me? Or does he simply drop the scroll when he's dismissed?

The Find Familiar spell states, in part:  As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons.  The question arising from this is:  Is this pocket dimension different for every familiar in the world? Thus being a personal pocket dimension? If this is true, then it should be able to store items given by its master for safe keeping away from anyone else, as long as these are items that a familiar could carry with it. Can the familiar bring small items with it into the pocket dimension for safe keeping?


The news is shocking to me.   vs     The news is shocking for me.   and     For me, the cooking style is useless   vs     To me, the cooking style is useless.    I think these two sentences are exactly the same. Is there anyone who can help me to tell the difference?

Which one should be used?      To me, it makes no difference, but I'm not really sure why.   vs     For me, it makes no difference, but I'm not really sure why.


I Am only 12 years old and I'm constantly wondering and trying understand how gravity really works. On YouTube everyone always talks about objects wrapping space time  around themselves and uses the analogy of a trampoline. I still don't understand gravity because if space were like a trampoline, then earth would be spiralling in towards the sun along with all the other planets, right? So could someone explain to me how gravity really works without the trampoline analogy.

It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force?  Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this?  When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place?


I have wrote this code to add text from one richbox to another without the stop words but it is copying all the text from richtext1         string[] Stopwords = { "a", "about", "actually", "after", "also", "am", "an", "and",  "any", "are", "as", "at", "be", "because", "but", "by", "could", "do", "each", "either",  "en", "for", "from", "has", "have", "how","i", "if", "in", "is", "it", "its", "just",  "of", "or", "so", "some", "such", "that", "the", "their", "these", "thing", "this", "to",  "too", "very", "was", "we", "well", "what", "when", "where", "who", "will", "with",  "you", "your"             };   This the code in the button that should do it  private void button2_Click(object sender, EventArgs e)         {             string st = richTextBox1.Text;             string[] split = st.Split(' ');              richTextBox2.Text = "";             int c = 0;             foreach (string s in split)             {                 if (!Stopwords.Contains(s))                 {                     richTextBox2.Text += s + " ";                 }                 else c++;              }         }   when I write if (Stopwords.Contains(s)) it prints all stop words in richtext1

Is there a way to make the following return true?  string title = "ASTRINGTOTEST"; title.Contains("string");   There doesn't seem to be an overload that allows me to set the case sensitivity.. Currently I UPPERCASE them both, but that's just silly (by which I am referring to the  issues that come with up- and down casing).  UPDATE This question is ancient and since then I have realized I asked for a simple answer for a really vast and difficult topic if you care to investigate it fully. For most cases, in mono-lingual, English code bases  answer will suffice. I'm suspecting because most people coming here fall in this category this is the most popular answer.  answer however brings up the inherent problem that we can't compare text case insensitive until we know both texts are the same culture and we know  what that culture is. This is maybe a less popular answer, but I think it is more correct and that's why I marked it as such.


On latest version Ubuntu 14.04 LTS, I have tried this :  sudo apt-get install yum   Then it says :  sudo password for user   And nothing gonna happen , if hit enter 3 times it says 3x incorrect attempt.  I'm beginner to Linux

I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7?


My aim is to proceed with a Heuristic calculation of the Tangent space to Aut(V) at the identity. However, I will have to prove the problem statement before I can proceed with that. My problem, Understanding the polynomial structure on the group Aut(V). The proper way of doing that would have to do with the symmetric algebra on the dual space, I don't wish to proceed this way. And I have been told to visualize the "coordinates" of the matrices as polynomials and work with that. If that is so, what would it mean for the "coordinate" to be "zero". Once this is certified I can proceed. This is what I have thought. Any other procedure, please, please let me know.

Let $k$ be an algebraically closed field. Let $A$ be a finite dimensional $k$-algebra, not necessarily commutative. Let $G = \text{Aut}(A)$ be the group of $k$-algebra automorphisms of $A$. I want to show that $G$ can be an affine variety in a suitable space $k^n$.


I am practicing some questions on convergence and divergence and stumble onto this problem.  Can anyone provide me some hints on how should I solve this question?   I already read a similar question on stackexchange but in the answers they have taken Xn=Yn, but I want to know, is the same true if both the series are different.

Could someone give me an example of two convergent series $\sum_{n=0}^\infty a_n$ and $\sum_{n=0}^\infty b_n$ such that $\sum_{n=0}^\infty a_nb_n$ diverges?


Here is the piece of code which contains two CSS elements. del and ins  I want to include the whole CSS code into Javascript... But the code is one level above my experience...  Here is the CSS code:  del {     text-decoration: none;     color: #b30000;     background: #fadad7; } ins {     background: #eaf2c2;     color: #406619;     text-decoration: none; }   And here is the piece of code which contains those classes:  convertChangesToXML: function(changes) {   var ret = [];   for (var i = 0; i < changes.length; i++) {     var change = changes[i];     if (change.added) {       ret.push("");     } else if (change.removed) {       ret.push("");     }      ret.push(escapeHTML(change.value));      if (change.added) {       ret.push('');     } else if (change.removed) {       ret.push('');     }   }   return ret.join(''); },   How to include CSS into Javascript here?  I don't want a separate CSS file ... Because I'm using a third party app called Storyline to create a web page and it's a lot easer to run a javascript code there without a css file

It's easy to set inline CSS values with javascript. If I want to change the width and I have html like this:

   All I need to do is:  document.getElementById('id').style.width = value;   It will change the inline stylesheet values. Normally this isn't a problem, because the inline style overrides the stylesheet. Example:

   Using this Javascript:  document.getElementById('tId').style.width = "30%";   I get the following:

   This is a problem, because not only do I not want to change inline values, If I look for the width before I set it, when I have:

   The value returned is Null, so if I have Javascript that needs to know the width of something to do some logic (I increase the width by 1%, not to a specific value), getting back Null when I expect the string "50%" doesn't really work.  So my question: I have values in a CSS style that are not located inline, how can I get these values? How can I modify the style instead of the inline values, given an id?


In R, Lets say that I have a set of x and y points, how can I get a geom_polygon to encapsulate all points, ie, what is the best way to create a 'bounding' polygon for the set?  library(ggplot2)  set.seed(1) x <- runif(100) y <- runif(100) mydata <- data.frame(x,y)  ggplot(mydata,aes(x,y)) + geom_point() + geom_polygon()   The above code is pretty clear that the result is unsatisfactory (result below).

How do I add a neat polygon around a group of points on a scatterplot? I am using ggplot2 but am disappointed with the results of geom_polygon.  The dataset is , as a tab-delimited text file. The graph below shows two measures of attitudes towards health and unemployment in a bunch of countries:    I would like to switch from geom_density2d to the less fancy but empirically more correct geom_polygon. The result on unsorted data is unhelpful:    How do I draw 'neat' polygons that behave as contour paths around the min-max y-x values? I tried sorting the data to no avail.  Code:  print(fig2 <- ggplot(d, aes(man, eff, colour=issue, fill=issue)) +  geom_point() + geom_density2d(alpha=.5) + labs(x = "Efficiency", y = "Mandate"))   The d object is obtained with .  Solution:  Thanks to Wayne, Andy W and others for their pointers! The data, code and graphs have been . The result looks like this:


This user self answered :    How did he accept it so quickly? I thought there was a 48 hour delay between posting and accepting?

What does it mean to accept an answer? How do I accept an answer, and what are the rules? Can I accept my own self-answer? What are the reputation benefits? Which answer should I accept? Should I upvote the accepted answer? What should I do if none of the answers are suitable?      For more information, see "" in the .


Minor edits should be easy.  I don't mean trivial edits, but rather low character count grammar and spelling edits.  Changing a few characters to clean up the site makes the Internet better.  Discouraging users from making productive minor edits allows ugly obvious errors to persist.  Many answers or comments on questions on this subject are awfully negative: e.g.,              If someone sees a minor error and wants to fix it, why would we stop them?  If the issue is rep, just don't give any for such edits.  If the issue is bumping, don't bump such edits.  If the issue is that too many people have to review the edits, lower the rep limit for minor edits.  If you think that 2k rep users will somehow find it on their own or that flagging is the proper solution, you're introducing unnecessary bureaucracy.  If you think that everyone can see a grammatical error without cringing, you don't know developer types.  If you assume that there's always five more characters to change, you're encouraging gaming of exactly the sort you're trying to avoid.  Surely there's a better way?

Looking at  privilege, I find this to be a surprising requirement:  Try to make the post substantively better when you edit, not just change a single character. Tiny, trivial edits are discouraged.  What motivated this, or rather, what does this mean exactly? Does that, for example, include removing stuff like "Hi, all", and "thanks in advance"? [update] I was led to a  talking about this topic, but it has a million Comments, and doesn't really justify the rule (unless it's hidden in those million Comments). However, looking at Jeff's Comments gives me an idea that this was meant as a general guideline, instead of a hard-and-fast rule: If you edit a post, check elsewhere on that post if there are other improvements that can be made.


What is the difference between == and === in JavaScript?  I have also seen != and !== operators.  Are there more such operators?

I'm using  to go through JavaScript, and it's returning many suggestions to replace == (two equals signs) with === (three equals signs) when doing things like comparing idSele_UNVEHtype.value.length == 0 inside of an if statement.  Is there a performance benefit to replacing == with ===?   Any performance improvement would be welcomed as many comparison operators exist.  If no type conversion takes place, would there be a performance gain over ==?


Three events $A, B, C$ satisfy:  $P(A \cap B) = P(A) \cdot P(B)$  $P(B \cap C) = P(B) \cdot P(C)$  $P(A \cap C) = P(A) \cdot P(C)$.  Does this imply $P(A \cap B \cap C) = P(A) \cdot P(B) \cdot P(C)$?  How to prove that it's true or not?

The example in question is from Rick Durrett's "Elementrary Probability for Applications", and the setup is something like this:     Let $A$ be the event "Alice and Betty have the same birthday", $B$ be the event "Betty and Carol have the same birthday", and $C$ be the event "Carol and Alice have the same birthday".   Durrett goes on to demonstrate that each pair is independent, since for example,   $P(A \cap B) = P(A)P(B)$.   However, he concludes that $A, B$, and $C$ are not independent, since   $P(A \cap B \cap C) = \frac{1}{365^2} \neq \frac{1}{365^3} = P(A)P(B)P(C)$.  I understand the reasoning here, and that one can generally show that arbitrary events $X$ and $Y$ are not independent by showing that $P(X\cap Y) \neq P(X)P(Y)$.   I am a little new to probability, though, and don't understand why exactly $P(A \cap B \cap C) = \frac{1}{365^2}$.   My progress so far:   I do see why $P(A) = P(B) =P(C) = \frac{1}{365}$, and thus why $P(A)P(B)P(C) = \frac{1}{365^3}$.  It seems like the sample space $\Omega = \{ (a, b, c) \mid a,b,c \in [365] \}$ -- i.e., all of the possible triples of numbers from 1 to 365, where 1 denotes January 1st, 2 denotes January 2nd, etc. From that, I can conclude $|\Omega| = 365^3$, but I'm not sure where to go from here.   It seems like once a single birthday is chosen, the rest are completely determined if they're all equal to each other - is this a good direction to go in?


As far as I know a CM choke is nothing but a transformer(?).  How does it block common-mode noise and pass the signal of interest? Should we think of it as an LR filter? And how to size it if we know the signal of interest? A pictorial explanation with a circuit diagram ect helps to understand.  Edit:  Below are two scenarios where an isolated(floating/battery powered) sensor S signal is measured by an ADC device and the system is single ended. The coaxial cable’s two wires somehow are victim of CM noise. As you see the CM noise is the spike superimposed on the half sine wave desired signal:   So in the first scenario(upper diagram) I can see how the CM blocks this spike now. But in the bottom diagram there is an attempt to remove the same spike with a LPF where the LPF’s ground is the signal ground as usual. Will this attempt also remove the spike or not?

I'm trying to better understand the principles behind the common mode choke. I made a few drawings to clarify.    Differential Mode Signals  Differential currents (driven by differential voltages) create equal but opposite magnetic fields B in the inductor core:    These magnetic fields cancel each other out, so the net flux in the core is zero. As such, these differential currents don't "feel" any impedance.    Common Mode Signals  In contrast, common mode currents generate equal and additive magnetic fields in the core. That's why they "feel" a high impedance, and cannot get through (or getting through means they are highly attenuated).    But what exactly happens? I have several theories, which I will describe below.    Common Mode Signals - Theory 1  My first thought would be that the common mode signal hits the choke and creates a magnetic flux inside. By doing this, lots of energy is lost (hysteresis and perhaps other effects) as heat. Only a small part gets through:      What kind of common mode choke would behave in this particular way? "Burning up" the voltage spike seems a very desirable effect to me.    Common Mode Signals - Theory 2  Perhaps the voltage spike doesn't really get the chance to build up much magnetic flux in the core, or maybe the core is simply not "lossy" enough. The voltage spike bounces off the core and turns back. Only small part gets through:    Although the system on the right side of the choke is protected, the system on the left has to deal with reflected signals. Nasty things like standing waves might appear.    My questions  I've got a few questions for you:   Do you think theory 1 or theory 2 is most plausible? Do you think certain types of common mode chokes tend to behave as described in theory 1, others like in theory 2? Perhaps both of my theories are just plain wrong. If so, what actually does happen?   Please enlighten me.


I am developing a winform application. I have menu like Edit -> Copy and Edit -> Paste.  Instead of using     Clipboard class to do copying and pasting can I use Operating System's ability to Copy and Paste text, image, link, etc...

I have a windows forms application with controls like textbox, combobox, datagridview etc. These controls allow a user to use the clipboad, i.e. cut/copy and paste text. It is also possible to delete text (which is not related to the clipboard).  My application has a menubar with an Edit item containing Cut/Copy/Paste/Delete items, and a toolbar with these items as well. How can I enable/disable these items properly depending in the state of the control having the focus?  I am looking for a generic way, i.e. I look for an implementation I do once, and can reuse for the future independent of the controls my application will use.


I am using QGIS 2.14 and am working with two layers: a layer of US Census Blocks and a layer of information on internet providers within each block. The internet provider layer is a CSV flat file, and the census block layer is a shapefile from the US Census TIGER site. I'd like to be able to create a unified layer of internet providers with information on each so I can, say, click "Verizon" and see everywhere Verizon offers service, or select just those blocks where the minimum speeds are in excess of X.   I understand I can't do a simple Join because it only joins one row of the CSV to each census block. I have set up a Relation in the Project Properties, which reflects the data structure I want, but I can't figure out how to make it just display in the map as a new layer.  I also tried creating a new layer by joining the CSV to the census block layer, but QGIS complained it wasn't a valid shapefile.

I'm trying to create a join/relate in QGIS where I have a shapefile of buildings and to that I would like to join a non-spatial table (.csv-file) containing people who work in each building. So I have multiple records in my table that I would like to be able to join to my single features in my shapefile. I can only run a join in QGIS where the first record is joined to the shapefile feature (ie building) but subsequent records get removed. Could someone let me know how to complete this join/relate in QGIS?


Display is upside down but cursor is ok but the cursor clicks elsewhere as it were upside down as well.  You can see cursor in the pic

I just did a clean installation of Ubuntu 18.04.1 on a tablet which was previously running Ubuntu 17.10. Back then just after the installation the screen was rotated, but I was able to get it to work (I think it was running on Wayland).  Now with 18.04.1 the situation is similar: when Ubuntu first boots the login screen is upside-down, but that's not a problem. This time, after login, the screen is correctly oriented but the mouse cursor is upside down and mouse movements are inverted with respect to both axes. The problem is that when I try to click on something the click is registered on the position on the other side of the screen (symmetrically with respect to the center).   It almost seems like the screen (desktop, application, etc.) is correctly displayed, with also the mouse positioned correctly and moving as it should, but then the mouse cursor which is shown to the user is inverted, like if the screen had been inverted just before drawing the cursor.  I already tried the answers I could find, but none worked for me. Anyone have an idea of what's going on?  Thanks


I am trying to get most common words in a dictionary I created. I read about it an i saw that the answer is using sorted function and [:n] in order to ask for number of elements.  my problem is that my dictionary is a bit different to what I saw - it's like that:  [{"count":27,"stem":"obama","term":"obama"},{"count":20,"stem":"boehner","term":"boehner"},{"count":4,"stem":"tax","term":"tax"}, {"count":3,"stem":"daley","term":"daley"},{"count":3,"stem":"couldn","term":"couldn"},{"count":2,"stem":"trillion","term":"trillion"}]   so in this example obama is mention 27 time boehner 20 and tax 2 - so lets say I want to get top 5 most common words, how do I do that?

I have a list of dictionaries and want each item to be sorted by a specific value. Take into consideration the list: [{'name':'Homer', 'age':39}, {'name':'Bart', 'age':10}]  When sorted by name, it should become: [{'name':'Bart', 'age':10}, {'name':'Homer', 'age':39}]


I had a NTFS partition on my ASUS laptop that had Windows 7 on it. I formatted it using Gparted Live CD because I thought there are some problems in Windows but then found out it was a problem of hardware... Now I would want to recover the partition and use the old Windows 7 that I had on it... Is it possible? :-)  Now I have 2 partitions on my laptop harddrive. 1st partition - NTFS that is empty (the one that I formatted) and has 200 GB and the 2nd partition - NTFS that has data on it and has 300 GB...  It was most probably a quick format since it took only like 1-2 seconds to format the partition... I didn't change the size of the partition or moved or resized other partitions on the harddrive...  I would want to "travel in time" and recover the partition, so that I would not have to install Windows 7 from scratch...

I've searched through several questions but didn't quite find anyone treating mine.  So, I have a 1TB external hard drive I use for backup purposes with only 1 NTFS partition. Today using DiskPart I formated that partition by mistake (who would have thought the disc count started in 0 and not in 1). The complete command I used was:  format recommended override quick label=Windows   So I performed a quick format, and from which I've read after a quick format it's possible to recover the data stored there. Anyway, as soon as I realized it wasn't the partition I wanted to format the one I specified I removed the access to my external drive to minimize possible damages.  Now, the MFT is the metadata part where the file name, creation date, access permissions and contents are registered; and it's mirrored too (so there's a copy of it somewhere in the disk). What I don't know is if a quick format erases that MFT mirror too, I hope not.  I'm running a program to recover files on it but I'll have to save the files to another location (once it's finished scanning, ~12 hours from now) and I don't quite have over 900GB of free storage where to put the data.  I would like to know if there's a program or procedure by which I could restore the old MFT in-place and have all the data that used to be in there accessible once again.  Any help or light you could shed on how to proceed or what programs to use is really appreciated.


I did this test in a HashSet comparision and equals is not being called   I would like to consider equals when farAway=false (A function to check two point distances)  Full compilable code, you could test it, and tells why equals is not being called in this example.  public class TestClass{      static class Posicion     {         private int x;         private int y;          @Override         public boolean equals(Object obj) {             if (obj == null) {                 return false;             }             if (getClass() != obj.getClass()) {                 return false;             }             final Posicion other = (Posicion) obj;             if ( farAway(this.x, other.x, this.y, other.y,5)){                    return false;             }              return true;         }          @Override         public int hashCode() {             int hash = 7; hash = 59 * hash + this.x; hash = 59 * hash + this.y;             return hash;         }           Posicion(int x0, int y0) {             x=x0;             y=y0;         }          private boolean farAway(int x, int x0, int y, int y0, int i) {             return false;         }     }      public static void main(String[] args) {         HashSet<Posicion> test=new HashSet<>();         System.out.println("result:"+test.add(new Posicion(1,1)));         System.out.println("result:"+test.add(new Posicion(1,2)));     } }   EDIT  -Is there a way to force HashSet add to call equals?

What issues / pitfalls must be considered when overriding equals and hashCode?


I have realtek rtl8723be network adapter. I have installed the diver from . I use following commands every time I turn on the computer:  sudo modprobe -rv rtl8723be sudo modprobe -v rtl8723be ant_sel=2   This worked well. But today I have problem with my wifi. It keeps disconnecting and the signal strength is really low even if the router is next to the computer. I don't see the other networks at all. I tried with ant_sel=1 too but no luck. My Ubuntu version is 16.04. Is there any way to troubleshoot and fix the issue?

I have a HP 14-AN001NA laptop. It came with Windows 10 installed on which the Wi-Fi worked fine anywhere in the house.   However I removed Windows 10 and installed Ubuntu 16.04 instead and since I have had terrible Wi-Fi anywhere aside from about three foot away from the router. I don't know if it's relevant but my Wi-Fi is not called wlan0 but wlo1 for some reason (I didn't change it).  When running lspci -knn | grep Net -A3     I get the following output:  05:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723] DeviceName:   Subsystem: Hewlett-Packard Company RTL8723BE PCIe Wireless Network Adapter [103c:81c1] Kernel driver in use: rtl8723be Kernel modules: wl, rtl8723be


I've been watching BlenderGuru's tutorials, and his lines in edit mode are much thicker than mine.    You can see, his lines are solid 2-3 pixel wide, mine are only 1. They also seem to disappear when I zoom in really close. Any fixes?

I'm a math teacher.  I like to use Blender to demonstrate some ideas when we talk about geometry in 3 dimensions, so I display it on our projector and the class will work together to edit some basic shapes.  I've changed the size of vertices so they are bigger and easier to see, but I haven't found a way to increase the size of edges.  Is there an option to do this?


I see so many users with a single gold badge "Famous Question" on stackoverflow. Why is the criteria to get the badge only 10k views? Stackoverflow is a very popular site. Its ranked very high in countries like India. For a site like stackoverflow, which attracts so many visitors a day,  this badge doesn't seem rare to get for a noteworthy question.  Why not raise the criteria to 20,000 views or even more?

Question-related badges are far too easy to obtain. Badges awarded to those who ask questions greatly outweigh those which are awarded for answers. Of course, it doesn't help that there are more question-related badges, however the main culprit is the set of badges which are based on question views: Popular Question (1,000 views), Notable Question (2,500 views) and Famous Question (10,000 views).    Firstly, lets take a look at the top three  for each category (Bronze, Silver and Gold):  Gold   Famous Question (62,192) Fanatic (8,076) Great Answer (6,928)   The Famous Question badge has been awarded more times than all other Gold badges combined.  Silver   Notable Question (345,834) Yearling (231,080) Necromancer (72,875)   There are more Notable Question badges than the second-most and third-most Silver badges combined.  Bronze   Popular Question (878,622) Student (606,325) Editor (477,659)   As you can see, the view-related badges dominate all 3 badge categories by a long way.    One of the most viewed questions on StackOverflow is "" with an impressive 573,219 views, 2,410 upvotes and 1,143 favourites.  This is a famous question.  The three most recent Famous Question badges were awarded for "", "" and "".  Combined these questions amount to 30,000 views, 6 upvotes and 0 favourites. One of which is closed!  These simply aren't famous questions.    Proposed Change  I think a more fitting system would be:   Popular Question : Ask a question with 5,000 views, at least 5 upvotes and 1 favourite. Notable Question : Ask a question with 15,000 views, at least 10 upvotes and 2 favourites. Famous Question : Ask a question with 75,000 views, at least 30 upvotes and 5 favourites.


I decided to write my thesis in LyX, got everything working nearly perfectly, but I found a strange problem which google cant help with... I tried to import citation from jabref to lyx, got only error "verify that lyx is running and the lyxpipe is valid" lyx running is, but when i tried to solve lyxpipe problem, I found out that I dont have lyxpipe (lyx and jabref were installed via ubuntu software center and after some searching, I found out that lyxpipe should be there, I tried to remove and reinstall lyx via software center, but still nothing), dont anyone knows whats wrong with my lyx?

I'm attempting to use the LyZ plugin for Zotero and LyX and it requires the LyX server to be present.  I've looked on the  for information and it makes reference to .lyxpipe.in and .lyxpipe.out but these are not present when I install LyX from the Ubuntu repository.  What are these files and how can they be created?


I have been trying to solve a question that arose in my mind a couple of days ago.  What is the sum of:     $1+4+9+16+25+\cdots +n^2$?   It is the sum of squares of each numbers starting from $1$ to $n$.  Can there be any formula for this sum?

I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals:  $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$  I really have no idea why this statement is true. Can someone please explain why this is true and if possible show how to arrive at one given the other?


I need help to create a circular diagram in Illustrator like this.  I need precisely to represent a percentage. How to do that ?  Thank you.

I'm trying to emulate this type of stroke:    So far, I've only been able to pen over the stroke and try to Minus it off (though I'm a rookie and still don't understand the whole pathfinder tool completely), but it's tedious and I'm not that great at it.  Suggestions?


I'm trying to use an iFrame to display an HTML webpage from an external source but, I can't get it to work with CSS.

I have a simple page that has some iframe sections (to display RSS links). How can I apply the same CSS format from the main page to the page displayed in the iframe?


I've been searching for the answer for a while, but I haven't been able figure it out.  I'd like to lower start time of my Mac's screen saver, but it's always disabled, and I cannot make it go up/down.     Any suggestions on how to fix this?  Thanks!

Can't believe that I have to ask this question, but...  How to I disable the screen saver on my 2014 MacBook Pro, running MacOS Sierra 10.12?  I have a need occasionally to keep the screen display on, but I might not use it for 20 minutes at a time. I want to disable the screen saver, but the button to adjust the time (I presume it has a 'None' option) is disabled.    How can I enable that dropdown, in order to change the 'Start after' time? Or is there somewhere else I should change it?  I know that I can use hot corners to disable screen saver, but that's too hacky - if I forget to put the cursor in the corner, it doesn't do it, and I only know when the screen saver comes on - which is frustrating.


I have given following differential equation:     $$y'(t) = a y(t) \cdot (b - y(t))$$   where $y(0) = y_0$ and $a,b,y_0 > 0$. How can I solve this differential equation?  I have tried to separate the variables and ended up with $$ \int a ~dt = \int \frac{1}{y(t)(b - y(t))}~dy(y). $$ I don't know how to go further, because I don't know how to solve the right-side integral. I would appreciate if you could help me solve the integral or solve the equation with another approach.   Note: I have the methods of a first year physics student available.

The problem is...  $$ \frac{dp}{dt} = 10p(1-p),$$   $p(0)=0.1$.  Solve and show that $p(t) \to 1$ as $t\to \infty.$  I know this is probably really simple, I was trying to go down the line of finding a general solution and then imposing the boundary condition.  But I can't even see how to find the general solution... Then for the second bit taking the limit of the general solution $p(t)$?


i am looking for a method that i can't find anywhere, maybe i'm unable to search, i wish my single instance executable can be reopened by reopening its executable, let me explain better. I open the executable, the form hides, I re-open the exe and the form of the first executable returns to me without opening another instance, I hope I made myself understood i have this code in mainwindow.iniz... Process[] Processes = Process.GetProcesses();         int Count = 0;          foreach (Process Proc in Processes)         {             if (Process.GetCurrentProcess().ProcessName == Proc.ProcessName)             {                 Count++;             }         }         if (Count > 1)         {             Process.GetCurrentProcess().Kill();         }

Using C# and WPF under .NET (rather than  or console), what is the correct way to create an application that can only be run as a single instance?  I know it has something to do with some mythical thing called a mutex, rarely can I find someone that bothers to stop and explain what one of these are.  The code needs to also inform the already-running instance that the user tried to start a second one, and maybe also pass any command-line arguments if any existed.


I'm trying to substitute include guards in headers with same include guards, prepended with #pragma once:  #ifndef _HELLO_H #define _HELLO_H   Becomes:  #pragma once #ifndef _HELLO_H #define _HELLO_H   Also, i want to leave line endings as-is. If it was LF then use LF, if it was CRLF then use CRLF.  I came up with following command:  find . -type f -name "*.h" -print0 | xargs -0 sed -i -E -e 's/#ifndef ([a-zA-Z_][a-zA-Z_0-9]+)(\r?\n)#define \1/#pragma once\2#ifndef \1\2#define \1/g'   But i got just line endings replaced in all headers, and no #pragma once added.  Command executed within MSYS2 terminal under windows.

Consider the following text (incidentally, part of a MySQL dump):   CREATE TABLE `table` (   `id` int(10) NOT NULL auto_increment,   `name` varchar(100) NOT NULL default '',   `description` text NOT NULL,   PRIMARY KEY  (`id`),   FULLTEXT KEY `full_index` (`name`) ) ENGINE=MyISAM DEFAULT CHARSET=latin1; /*!40101 SET character_set_client = @saved_cs_client */;   I would like to remove the FULLTEXT key, and I also want to remove the trailing comma on the line above so that the SQL remains valid.  Can anyone come up with (and explain) a sed recipe to do this?


I've found ggmap's  function really useful over the years as it's got a 'fuzzy' search implemented by Google. However, I'm wondering if there are alternatives, because   geocode() seems unreliable sometimes overdependence on google it doesn't use/support open source API solutions   I've seen the   and  packages.   Has anyone else encountered this problem and discovered another solution, preferably using CRAN packages such as geonames?

I need to find a package in R or source code in R that performs batch geocoding using Bing, Yahoo, OpenStreetMap. Do you have any suggestions?


I am creating custom theme for Drupal 8. I am uploading the logo from theme setting, but I am not able to print the path of that logo. What I am doing to print the full path of logo is using {{ logo }}, but it is not working.  In Drupal 7 we can get the full path of logo with the following code.   <img src="<?php print $logo; ?>" alt="<?php print t('Home'); ?>" />   What is the equivalent for Drupal 8?

how can i show site logo, name and slogan Separately in custom area in my site theme, I now use this code to display theme, buts this code don't allow me to edit each of them Separately.  {{ page.header }}


Bash Reference Manual says     The use of time as a reserved word permits the timing of shell builtins, shell functions, and pipelines. An external time command cannot time these easily.    But it only compares reserved word time and external command time, and doesn't address the question:  Why does Bash implement time as a reserved word, instead of a builtin command?  What advantages can that give? What are other reserved words which can also be implemented as (builtin or external) commands? What are their advantages over their command counterparts? (Trying to figure out if their advantages are shared or specific to each of them)  For example,    the reserved word [[...]] versus the builtin command test or [ the reserved word select versus the builtin command read

In the Bash Reference Manual,      The use of time as a reserved word permits the timing of shell builtins, shell functions, and pipelines. An external       time command cannot time these easily.    Could you explain why the quote says that?  Is this because of the difference between a reserved word and a command, not just limited to the case of time? For example, how does the bash shell parse or interpret them differently?   Or is this only limited to the case of time? In the following examples,   why does the external time work on a shell builtin, and a pipeline, while the quote say it "cannot time these easily"?  External time on a shell builtin:  $ /usr/bin/time echo hello hello 0.00user 0.00system 0:00.00elapsed 0%CPU (0avgtext+0avgdata 1676maxresident)k 0inputs+0outputs (0major+78minor)pagefaults 0swaps   External time on a pipeline:  $ /usr/bin/time sleep 10 | sleep 5 0.00user 0.00system 0:10.00elapsed 0%CPU (0avgtext+0avgdata 1776maxresident)k 0inputs+0outputs (0major+79minor)pagefaults 0swaps  In the following example, why does the external time on a shell function fail? What does its error output mean?  $ function mytest () { sleep 10; }  $ /usr/bin/time mytest /usr/bin/time: cannot run mytest: No such file or directory Command exited with non-zero status 127 0.00user 0.00system 0:00.03elapsed 0%CPU (0avgtext+0avgdata 1252maxresident)k 32inputs+0outputs (0major+30minor)pagefaults 0swaps  It seems that the quote does not just apply to timing shell builtins, shell functions, and pipelines, :  $ time { echo hello; sleep 3; echo tim; } hello tim  real    0m3.002s user    0m0.000s sys 0m0.000s   $ /usr/bin/time { echo hello; sleep 3; echo tim; } bash: syntax error near unexpected token `}'   Why does the shell say "bash: syntax error near unexpected token }" in the case for command /usr/bin/time?


We know that the curl of an electric field is the rate of change of magnetic flux then why we have to calculate the curl of the curl of the electric field after that. What is the reasoning behind this Faraday's law $$ \nabla\ \times E = -\frac{\partial B}{\partial t} $$ Taking curl of the equation $$ \nabla \times \nabla\ \times E = -\frac{\partial (\nabla \times B)}{\partial t} $$ I would like to know what is the physical significance of taking the curl of the above equation?

I was trying to derive wave equation. We know that the curl of an electric field is the rate of change of magnetic flux then why we have to calculate the curl of the curl of the electric field after that. What is the reasoning behind this Faraday's law $$ \nabla\ \times E = \frac{\partial B}{\partial t} $$ Taking curl of the equation $$ \nabla \times \nabla\ \times E = \frac{\partial (\nabla \times B)}{\partial t} $$ I would like to know what is the physical significance of taking the curl of the curl of the electric field.


I've got a new home server with no keyboard, monitor, etc., but with the ability to boot from USB. I want to install Ubuntu Server on it, but can't work out how. If possible, I want a disk image that I can write to a USB drive to boot from which connects to the network and launches the ssh server, so that I can connect from my laptop and run setup from there.  Is this possible? What do I need to do?

This is tricky. I would like to install Ubuntu on a machine that is intended to work as server, and for some reason I do not have an option to connect a screen to it.  I expect this may be similar to remote installation. However, there is currently no OS on that machine, so I will have to set up everything from scratch.  On the other hand, I do have a physical access to that machine. Therefore I can get it to boot from a CD/USB. But that's not enough.  Is there a way to do such installation remotely? Is there a version of Ubuntu image that comes with a SSH server preinstalled, and starts it once booted, so that I can boot the machine with such image, connect to it via SSH and process the installation from a different computer?  If not, what other options do I have?


Just to be very clear, this question is very much related to, but distinct from a previous question I asked a few years ago:  - I still am not quite satisfied with SevenSidedDie's very excellent answer (they usually are, aren't they?). This question asks does light penetrate through the darkness spell or does darkness cast a shadow. And it is distinct from , which asks if the darkness blocks vision through it.  Is the Darkness spell visible from the outside? To make the question more clear, if darkness were cast on the surface of a flat plane, would I see a spot of darkness on the ground, or would I see a hemisphere above the ground?

In discussing , I came to realize that the real question was whether Darkness blocks vision or merely creates "darkness".    Per the wording of the spell:     Magical darkness spreads from a point you choose within range to fill a 15-foot-radius sphere for the duration. The darkness spreads around corners. A creature with darkvision can’t see through this darkness, and nonmagical light can’t illuminate it. (emphasis mine)   Normal darkness is defined in the game as creating a heavily obscured area and the only description added to the darkness is that it is magical, which (to me) just means that it is created by magic and is subject to the magical rules.    Darkvision is defined in the game as basically being able to see in darkness as if they were seeing in dim light. So, the text "darkvision can’t see through this darkness" merely means that it affects darkvision in the same way it affects normal vision. (See earlier versions of the spell below, which had similar wordings.)    I see nothing there that implies it is a barrier to vision, just an active  and utter absence of illumination.    Previous editions have varying descriptions.  and  give accurate accountings of the various versions.   The 1e Wizard version seems to actually imply a sphere of opaque blackness that even blocks infra/ultravision, while the 1e Cleric version is a reversal of the Light spell and creates totally normal darkness, with no block to special visions.   The 2e version is similar to the 1e Cleric spell. It creates an area of darkness "equal to an unlit interior room".   The 3.0e version comes closest to the 5e version. It "causes an object   to radiate darkness out to a 20-foot radius. Not even creatures who can normally see in the dark (such as with darkvision) can see in an area shrouded in magical darkness." Still no reference to any sort of opacity and the wording makes it clear that darkvision is being treated specifically here.   3.5e Darkness is similar, although instead of darkness, it creates "shadowy illumination". This affects darkvision as well as normal vision.   4e doesn't have a Darkness spell, but rather a Cleric Utility called Veil of Darkness, which creates "a zone that is heavily obscured and blocks line of sight." So, finally, a reference to opacity, in "blocks line of sight", although I question if opacity was the intent.


But now suppose the space is a ring of length $L$, it seems the derivation could work out exactly the same and we get $$\Delta p \Delta x \geq \hbar/2.$$  But since $\Delta x$ is limited, and if we choose an eigenstate of momentun, we can actually achieve $$\Delta p \Delta x = 0.$$  What's wrong here?

Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard deviation of momentum is $0$, but $\sigma_x$ must be finite. So we find that $\sigma_x\sigma_p=0$. Is something wrong with the uncertainty principle?


We have a 200 sided fair die with faces numbered 1 through 200 and want to know how many rolls are expected to roll a 1. How would I go about calculating this?

Given a discrete random number generator, such as a six-sided die, what is the expected value of the number of rolls necessary to roll a specific number (e.g. a six)?   I think the result should be given by E$\langle$rolls$\rangle$ = $\frac{1}{6}\sum_{n=0}^\infty{(\frac{5}{6})^n(n+1)}$, but I don't know how to calculate the convergence of that sum.  Also, how do I calculate the variance?


I'm thinking about this question and no elegant idea comes to my mind. Prove that the field of fractions of $\mathbb R[x,y]/(x^2+y^2-1)$ is isomorphic to $\mathbb R (t)$.

This problem goes as follows:     Prove that $\mathbb{Q}[x,y]/\langle x^2+y^2-1\rangle$ is an integral domain and that its field of fractions is isomorphic to the ring of rational functions $\mathbb{Q}(t)$.    The first part is straightforward, $x^2+y^2-1$ is irreducible in $\mathbb{Q}[x,y]$, and  hence a prime ideal, as $\mathbb[Q][x,y]$ is a euclidean and hence a UFD. The quotient by a prime ideal is an integral domain.   How do I do the second part? I guess, I have to set a isomorphism by making a substitution such that only one variable remains. But I don't see how $x^2+y^2-1$ is going to help me make a choice.


I need a rigorous proof that verify why the limit of $\dfrac{\sin(x)}{x}$ as $x$ approaches $0$ is $1$.  I tried before but i do not know how start this proof. I would appreciate if somebody help me. Thanks.

How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution.  This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, that proving the above statement is enough for proving the continuity of $\sin$, but I can't find out how. Any help is appreciated.


I am looking to create a cleric in e5 DnD. I was wondering if it is possible, to make a neutral good cleric, that still uses Death Domain.  My idea was, that he sheperds the souls of the dead to their corresponding plane (of death?). That would be a good deed.

Basically, me and my friend have been arguing for 2 months over the Death domain cleric alignment. He keeps referencing the DMG's quote of "The gods of death domain embody murder" and the fact it is a villainous class option. My evidence is all the neutral deities (Wee-Jas, Raven Queen, etc.) that have death domain in their suggested domains. Who is right?


I'd like to create a scene in Blender 2.8 and render an HDRi environment texture from it. Is that possible? I expect I'd create a sphere, texture it appropriately, add some distant objects, put the camera at 0,0,0... but how to set up a camera type to record the 360-degree view as a properly formatted HDRi (e.g. equirectangular float EXR)?

Is it possible to render 360° panoramic images in Blender, usable to make a 360° pano presentation?


At this point, when starting with new implementations is it better to go with Lightning Framework for UI and better UX, or to continue with Visualforce based UIs?

As a developer, just curious to know what's the future of Visualforce (pages, components, email templates, etc..) ??  I believe for sure there will be backward compatibility so that the existing ones will still run.  But what's gonna happen next (say after couple of releases when lightning becomes GA & goes mainstream). ??    will Salesforce stop customers from using VF for new development ? will VF & L work together (like embed one in another or call one from another) is it possible to migrate / upgrade existing VF to L without rewriting ?   Just a few questions i can think of now.. but in general if any of you know more details on these, please share with us..  Thanks


I was trying to solve a probabilistic problem and I found I had to use the equality $\displaystyle\sum^{N-r}_{x=0}\begin{pmatrix} N-x \\ r \end{pmatrix}=\begin{pmatrix} N+1 \\ r+1 \end{pmatrix}$ in an intermediate step. I verified it with Wolfram Alpha, but I really can't come up with a proof (I tried expanding everything out but find no clue in the end). I hope I can find a proof here and it is even more delighting if someone is willing to teach me some typical ways of proving equations involving combinations and permutations, which seem to be unmentioned in the textbook I am currently using.

After reading , the most popular answer use the identity $$\sum_{t=0}^n \binom{t}{k} = \binom{n+1}{k+1}.$$  What's the name of this identity? Is it the identity of the  modified.  How can we prove it? I tried by induction, but without success. Can we also prove it algebraically?  Thanks for your help.    EDIT 01 : This identity is known as the  because, on Pascal's triangle, when the addends represented in the summation and the sum itself are highlighted, a hockey-stick shape is revealed.


My Ubuntu was running very nice. I can access all drive.i use two os windows8 and Ubuntu. But when i shut down my Ubuntu os and start with windows 8 and i copy a folder from c(desktop) drive to movies (F drive) and i shut down pc and again start pc with Ubuntu then i can not access any drive. (Software is root Drive).   Unable to access “Software”  Error mounting /dev/sda6 at /media/kalyan/Software: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda6" "/media/kalyan/Software"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda6': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option.    can you give me a solution please?

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


I want center of $GL_n(\Bbb R)$.   Artin, in his book Algebra, hints that, 'You are asked to determine the invertible matrices $A$ that commute with every invertible matrix $B$. Do not test with general matrix $B$, test with elementary matrices.'    I know that  and  generate $GL_n(\Bbb R).$ I also see that Row-multiplying transformations (unless all diagonal entries are 1's) and Row-addition transformations (unless all off-diagonal entries are 0's) don not commute with each other, so only elenentary matrix in center is $I$.  What I don't get is:  1. How do we derive from this that $cI$ is in center for any $c\in \Bbb R$? (I can see $cI$ in center, but, it did not click me, because I thought this way: since center is subgroup, $\langle I\rangle$ is in center, but $\langle I\rangle=\{I\}$. Where did I not think through?)  2. No other matrix is in center?

Find the center of the group  $\operatorname{GL}(n,\mathbb R)$ of invertible $n \times n$ matrices.  Please can someone please help me? I know that by definition the center $Z$ of a group $G$ is defined by $Z(G) = \{g \in G\ |\ ag = ga ,\, \forall a \in G\}$.  I know that the identity matrix commutes with any matrix. I also notice by computing several matrix products that if we have a matrix with a main diagonal and all other entries are zero, then the given matrix commutes. In addition, I know that the determinant cannot be zero since zero times another matrix will only be zero. Please I would really appreciate the help. Thank you.


I have a new Windows 10 EFi formatted drive, and I am wondering what is the proper way to customize the boot menu logo and the name? For example, changing the orange drive logo to a picture, or changing the boot menu name "EFI Boot" to "My Drive".  My Mac is running macOS Catalina.

After successfully installed Linux and Windows along with macOS High Sierra on my Macbook Pro 2013 13" with help from Mr. David Anderson (a great contributor here). Now I wonder how to change the icons for my Windows (installed on a separate internal SSD) and give MacOs Partition Icon of MacOs so that the startup manager will be beautifully labeled and easy to see. Thank you for the help in advance!  Current startup manager conditions:   My diskutil list:  /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *250.1 GB   disk0    1:       Microsoft Basic Data BOOTCAMP                250.1 GB   disk0s1  /dev/disk1 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *240.1 GB   disk1    1:                        EFI EFI                     209.7 MB   disk1s1    2:                 Apple_APFS Container disk2         151.8 GB   disk1s2    3:       Microsoft Basic Data                         7.9 GB     disk1s3    4:       Microsoft Basic Data                         79.9 GB    disk1s4  /dev/disk2 (synthesized):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      APFS Container Scheme -                      +151.8 GB   disk2                                  Physical Store disk1s2    1:                APFS Volume MacOsX                  14.6 GB    disk2s1    2:                APFS Volume Preboot                 24.5 MB    disk2s2    3:                APFS Volume Recovery                512.1 MB   disk2s3    4:                APFS Volume VM                      4.3 GB     disk2s4


I am using   which is on Android 2.2 . Currently device showing The application google services framework (process com.google.process.gapps) has stopped unexpectedly I didn't get any support from the nikai site. How can i rectify and overcome the problem

How to fix the application Google Services Framework (process com.google.process.gapps) has stopped unexpectedly error? It's showing like 10,000 times and I can't get into the Play Store or the browser.


Without using induction, how can it be proved that 7 divides $3^{2n+1}+2^{n+2}$ for each $n\in\mathbb{N}$? I tried to expand it using $\frac{x^{n+1}-1}{x-1}=1+x+..+x^n$ but I had no success. It would be great if more than one proof is provided.

Expanding the equation out gives  $(3^{2n}\times3)+(2^n\times2^2) \equiv 0\pmod{7}$   Is this correct? I'm a little hazy on my index laws.  Not sure if this is what I need to do? Am I on the right track?


I want to know the orientation of a certain face by knowing the z vector(direction vector) of its normal. How do I let Blender display the values of the normal of a face?

We want to see the three values of a normal of a face when we select it in edit mode. How to do so?    Is there any add-on showing these sort of info realtime?  Update: It seems the accepted answer does not result correct normal vector!! In the following figure the normal vector of the selected face obviously is not (0,0,-1)!


I had a midterm exam today about group theory and I were asked to prove the following theorem:     Let $G$ be a group. Prove that if $X,Y\triangleleft G$ and $G=XY$ that $X\cap Y=\{e\}$ then $G\cong X\times Y$.   I really have no idea where to start proving this theorem. Also I tried to find a previous thread about this question but without any luck.  How to prove this theorem?

Let $K$, $N$ be normal subgroups in $G$.  I would like to show that if $K\cap N=\{e\}$, then $KN\cong K\times N$.  My original thought was to invoke the first Isomorphism theorem.  Therefore I would have to find an appropriate mapping $\varphi$ whose kernel is $\{e\}$.    In a previous exercise, I showed, again by the first Isomorphism theorem that   $$\frac{KN}{K\cap N}\cong\frac{KN}{N}\times\frac{KN}{K}$$  thus, if $K\cap N=\{e\}, $ i would just have to show that $\frac{KN}{N}=K$ and $\frac{KN}{K}=N$.  Thus my idea was to prove that under the condition that the intersection of $K$ and $N$ that elements in $KN$ can commute freely.  We know that $KN=NK$, but this does not imply commutativity, only that if $kn\in KN$, then $kn=n'k'$ with $n$ not necessarily equal to $n'$ and such with $k$.  I just can't come up with a commutativity proof.  EDIT: I forgot to define $KN=\{kn|k\in K, n\in N\}$.