How do I list the conjugacy classes of $D_n$?
Conjugate class in the dihedral group
What is the result of $ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $ and why? How to insert spaces up to column X to line up things in columns? Auto generate an Index Is there any way to auto-gererate an index for the makeidx package? I've written ~270 pages and didn't think of adding \index{} everywhere.  Do I really need to go over everything and add \index{}? I have some files/directories on an external hard drive connected using USB to my Windows XP laptop. I am trying to delete those files but every time I try, I get an error "Cannot delete ....: Access Denied. Make sure disk is not full or write protected and that the file is not currently in use".  I checked that the directory is not is use. However, the permissions are set to read-only. Even if I remove the "read-only" checkbox, in Properties->Attributes, it automatically comes back again. How do I fix this? Is it a virus that is automatically changing it back to read-only?  regards,  JP I have a Python script which I would like to execute at every startup. I can run it by adding this to the startup applications:  python3 /path/to/script.py   That works, but it doesn't open a terminal window, so I can't see the program's output. How could I make it open a terminal window and execute the script in there?  Note: I get the window to stay open with input(' ') at the end of the Python script. Thanks! Rep value on the new flair is not updated There is an update issue with the new flairs. Yesterday I replaced all my flair snippets with the new ones, but the rep value on the "default theme" has not been updated. Here is a screeny:    The other themes show the correct value whereas the default one does not. How to identify "deictic center" for distinguishing "come" & "go"? Read this paragraph from this    My question is:  How to identify "deictic center" for distinguishing "come" &amp; "go"?  Let say I am at home &amp; I say "I am going to the zoo this evening", so the "deictic center" in this case is my home &amp; I move away my "deictic center".  But let say my friend Tom &amp; I currently at my home &amp; Tom said "Are you Coming to the zoo to see the lion?" &amp; I said "Ok, I am coming to the zoo this evening". So, the "deictic center" in this case is "the zoo" &amp; we move towards the "deictic center" (ie the zoo).  It feels like it is very arbitrary.  Note: See this , it said the selection of "deictic center" could be due to sympathy &amp; politeness. If a user is the type of person to consecutively get downvoted to potential negative reputation, so be it. What's the reasoning to maintain a minimum of one?  One reason that may justify this is of trying to not deter new users from the site who haven't read the FAQ and unknowingly and wrongly ask or answer a question. But most of us acknowledge this and not downvote in such a scenario.  So what's the reasoning behind this lower bound of 1? How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics? I used to think that "random effects model" in econometrics corresponds to a "mixed model with random intercept" outside of econometrics, but now I am not sure. Does it?  Econometrics uses terms like "fixed effects" and "random effects" somewhat differently from the literature on mixed models, and this causes a notorious confusion. Let us consider a simple situation where $y$ linearly depends on $x$ but with a different intercept in different groups of measurements:  $$y_{it} = \beta x_{it} + u_i + \epsilon_{it}.$$  Here each unit/group $i$ is observed at different timepoints $t$. Econometricians call it "panel data".    In mixed models terminology, we can treat $u_i$ as  a fixed effect or as a random effect (in this case, it's random intercept). Treating it as fixed means fitting $\hat \beta$ and $\hat u_i$ to minimize squared error (i.e. running OLS regression with dummy group variables). Treating it as random means that we additionally assume that $u_i\sim\mathcal N(u_0,\sigma^2_u)$ and use maximum likelihood to fit $u_0$ and $\sigma^2_u$ instead of fitting each $u_i$ on its own. This leads to the "partial pooling" effect, where the estimates $\hat u_i$ get shrunk toward their mean $\hat u_0$.  R formula when treating group as fixed:    y ~ x + group R formula when treating group as random:   y ~ x + (1|group)  In econometrics terminology, we can treat this whole model as a fixed effects model or as a random effects model. The first option is equivalent to the fixed effect above (but econometrics has its own way of estimating $\beta$ in this case, called "within" estimator). I used to think that the second option is equivalent to the random effect above; e.g. @JiebiaoWang in his highly upvoted answer to  says that      In econometrics, the random-effects model may only refer to random intercept model as in biostatistics    Okay --- let us test if this understanding is correct. Here is some random data generated by @ChristophHanck in his answer to  (I put  for those who do not use R):    @Christoph does two fits using econometrics approaches:    fe &lt;- plm(stackY~stackX, data = paneldata, model = "within") re &lt;- plm(stackY~stackX, data = paneldata, model = "random")   The first one yields the estimate of beta equal to -1.0451, the second one 0.77031 (yes, positive!). I tried to reproduce it with lm and lmer:  l1 = lm(stackY ~ stackX + as.factor(unit), data = paneldata) l2 = lmer(stackY ~ stackX + (1|as.factor(unit)), data = paneldata)   The first one yields -1.045 in perfect agreement with the within estimator above. Cool. But the second yields -1.026, which is miles away from the random effects estimator. Heh? What is going on? In fact, what is  plm even doing, when called with model = "random"?  Whatever it is doing, can one somehow understand it via the mixed models perspective?  And what is the intuition behind whatever it is doing? I read in a couple of econometrics places that random effects estimator is a weighted average between the fixed effects estimator and the "between" estimator which is more or less regression slope if we do not include group identity in the model at all (this estimate is strongly positive in this case, around 4.) E.g. @Andy :     The random effects estimator then uses a matrix weighted average of the within and between variation of your data. [...] This makes random effects more efficient[.]   Why? Why would we want this weighted average? And in particular, why would we want it instead of running a mixed model? What does 'per unit frequency' refer to? We were discussing Kirchoff's theorem on blackbody radiation in class today and the equation was: $$e_{f}= J(f,T)$$  $e_f$ was defined as power per unit area per unit frequency. What does per unit frequency refer to here? I know what per unit time means but don't understand 'per unit frequency'. Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.   I saw some proof of $\frac d {dx} x^n=nx^{n-1}$ using binomial theorem, which is only available for $n \in\mathbb N$. Do anyone have the proof of $\frac d {dx} x^n=nx^{n-1}$ for all real $n$? Thank you. remove isp-provided dns My isp provides a dns service; but unfortunately they do block certain sites. I would like to use opendns or google; but it seems like it doesn't work.    I have set up a wired connection; given a manual ip and entered opendns-ip's in the nameserver field (all through the gui). Still url's are being resolved through my ISP. I have tried to configure the same on my girlfriends laptop (win 7) and I also can't seem to do the setup. My previous computer also was a win 7 and had no problem. (so I believe the problem is 'me') If it were only one site, i could edit the hosts file; but I prefere to circumvent their whole dns server.  Is there something an isp can do to block the use of other dns-servers than theirs? Is it possible to re-route the ISP dns to the opendns? LibreOffice problem while openning a document My problem is that when I try to open one specific .odt document, I can't move the page or do anything except moving the mouse, which is useless. Also, the mouse, when I'm on the document, is freaking out switching between mouse and loader couple of times per second. It also becomes dark when I click on the document like if it's not responding. X Windows special programs: do some of these still exist? I am familiar with what partitions are, but I saw , and realised I didn't know what "aligned partitions" are.  So what does it mean to "align" partitions? What are the benefits, and the downsides? Why not group search results by thread? I like the new search, but the listing can become quite verbose. That is generally excellent because Stack Exchange is searching in more places. But now that you  to the original question, it becomes quite difficult to remember "that's not the question(s) I want &hellip; that's not the question(s) I want" when the questions' answers appear dozens of times scattered throughout the listings.  Why not group same-question entries together in the search results?  I realize that each individual post wont be sorted strictly "by relevance", but the most relevant question threads will be listed first&hellip; making it easier to skip over those entries once you decide that's not the question you're looking for.  Consider what we have now &mdash;  Apple SE > Search "Exchange contacts"   A: Exchange contacts do not appear in iCloud A: Exchange contacts do not appear in iCloud Q: iPhone Contact Sync A: How to use Gmail contacts on an iPod Touch A: Exchange contacts do not appear in iCloud A: Exchange contacts do not appear in iCloud A: How to use Gmail contacts on an iPod Touch A: Exchange contacts do not appear in iCloud A: Exchange contacts do not appear in iCloud A: iPhone Contacts Sync Q: Best way to transfer iphone contacts away from Exchange server Q: Can I use Google's new CardDAV-based contacts sync to sync between my Exchange contacts and … A: How to delete contacts from iPhone? A: Can I use Google's new CardDAV-based contacts sync to sync between my Exchange contacts and … : etc, etc. :   Once I realize I don't want that iCloud question&hellip; or that iPod Touch question&hellip; or that sync question &mdash; or a dozen others &mdash; it becomes extremely cumbersome to remember and search the listings for questions I didn't eliminate yet.  I'm not suggesting rolling up the results back to the original question&hellip; just grouping these posts together (I like seeing each answer-match with the text excerpt underneath). But once I eliminate the question entirely, it would be nice to scroll past those entries to continue my search&hellip; without all the noise of those entries reappearing over and over again in the search results. How to Combine IN-Opeator with LookupIds in a caml-query? Local TLD vs. .com and .com/nl vs .nl I basically have 2 questions about local TLD vs .com.  First question: There already exists a website "keyword.nl" with a crappy website, no SEO optimisation. Is it possible for a website "keyword.com" to rank higher than the "keyword.nl" website on "google.nl" when searching for "keyword"? Or will it always display the .nl website higher because it's a local TLD and the URL consists entirely and only from the searched keyword and it's searched on the .nl version of google?  Second question: I know it's good for SEO to have many websites link to your website. But I also read that local TLD's will score higher on that specific google TLD (.fr website will rank higher in google.fr, etc.) With both those facts in mind, is it better to create a "keyword.com/fr/" and "keyword.com/nl/" website or a "keyword.fr" and a "keyword.nl" website? (In other words, .com/langauge for more links to the website, or a "keyword.local-TLD" website for every different language version of the website) Or maybe even a subdomain? ("fr.keyword.com?")  Kinda new to this, so thanks in advance!  --Edit: additional info--  The reason that I phrased the original question like this is because I wanted to keep the question strictly "webmaster-side". However I feel like maybe I should clarify the background of this question more thoroughly, so the question becomes more clear, and thus the answer. But I don't know if this would make the question a more legal one instead of a "webmaster" one, so please correct me if this is the wrong place to post this question.  I'm a student working on websites in my sparetime, I have basic knowledge about SEO, but that was all local, for companies operating only in one country. However this time a friend contacted me who wants to found a company called "X" (e.g). He wants to ship/operate to multiple countries, but he will first found it (and he himself) lives in The Netherlands (.nl). However there already exists a company in The Netherlands called "x" with the website "x.nl". As far as I understood, the fact that both the companies are called "x" doesn't matter, in trademark/company registery terms, since they are both operating in different work sectors.    But the main issue here is, could my friends website "x.com/nl" outrank the "x.nl" on "google.nl" if you only search on the brand name; "x"?  @Closetnoc:  Hi, thanks a lot for your answer, it gave me some clarification however I feel you misunderstood my first question because of my use of "keyword.com" as an example URL. So I don't really know what conclussion I should draw from your first answer. I updated my question with additional info to clarify it more broadly. From your second answer this is what I understand: A .nl URL will not do that great on google.com, however a .com URL can do just as well as a .nl search on google.nl? So considering the info above, it's best to go with a x.com/fr and a x.com/nl URL, right? Please correct me if I misunderstood. However, if so, that still leaves the first question, if a "x.nl" is already taken, could a "x.com/nl" still outrank it at "google.nl"? Maximal ideals in the ring of real functions on $[0,1]$ Let $S$ be the ring of all continuous functions from $[0,1]$ to $\mathbb R$. How to prove that all maximal ideals of $S$ have the form $M_{x_0}=\{f\in S \mid f(x_0)=0\}$?   Thanks in advance. Continuous function whose right hand derivative equals 0 is constant?