Proof Review: Fundamental group abelian if and only if isomorphisms are equivalent
Isomorphism equivalence implies fundamental group is abelian
How to search the internet for terms with special characters As I learnt from this , Google has no ability to search for special characters. Let's say I want to search for ss!. Are there any other search engines that can achieve this? Please do not propose any programming code search engines since this is a general search. Can't start ubuntu-desktop after upgrade to 18.04 After the restart step of upgrading Ubuntu to 18.04, tty is opening instead ubuntu-desktop. And when I enter my login name and password, I am still in the tty. This is happening again in every restart. How can I start the graphical desktop as normal? Difference between block size and cluster size In .NET, which loop runs faster, 'for' or 'foreach'? In C#/VB.NET/.NET, which loop runs faster, for or foreach?  Ever since I read that a for loop works faster than a foreach loop a  I assumed it stood true for all collections, generic collections, all arrays, etc.  I scoured Google and found a few articles, but most of them are inconclusive (read comments on the articles) and open ended.  What would be ideal is to have each scenario listed and the best solution for the same.  For example (just an example of how it should be):   for iterating an array of 1000+ strings - for is better than foreach for iterating over IList (non generic) strings - foreach is better than for   A few references found on the web for the same:               [Edit]  Apart from the readability aspect of it, I am really interested in facts and figures. There are applications where the last mile of performance optimization squeezed do matter. Neat series convergence result This is a nice problem on series convergence that I recently stumbled upon. Given a non-negative sequence of real numbers $(a_n)$ such that $$\sum_{n=1}^\infty a_n &lt; \infty,$$ show that there exists a non-decreasing sequence of non-negative numbers $b_n$ such that $$b_n \to \infty \quad\text{ and } \quad \sum_{n=1}^\infty a_n b_n &lt; \infty.$$ In other words, for every convergent series with non-negative terms, there is another convergent series with "substantially larger" terms.  I have a solution (see below), but maybe someone else has a different, simpler, and/or more elegant solution. I've installed emacsformacosx on my OSX box.  I'd like to shove my macmini in a data center and run it headless.  I've gotten x-windows working.  If I run xeyes, it displays on my Windows 7 client.  Emacs works from the command line on the osx box.  However, if I start up emacs from the windows client, it pops it up on the server instead of the client.  What am I doing wrong? I am looking to use Java to get the MD5 checksum of a file.  I was really surprised but I haven't been able to find anything that shows how to get the MD5 checksum of a file.  How is it done? How can I bump other users' unanswered questions? I'm looking around for answers to my questions on several Stack Exchange sites and the good boy that I am I don't want to ask duplicate questions.  Often I find that there are other people who asked the same questions, sometimes years earlier, but still don't have an answer. I'd figure I could bump these back to top, but if I don't have enough rep for a edit (or comment), how would I do that?  Or, in that case, I should just post a 'newer' version of the same question? I am crawling some data using Apache Nutch and storing it on my USB Drive. The OS itself is Ubuntu Live Boot OS. But for every restart or shutdown I am losing my data. I also tried suspending my Ubuntu user still data was not visible when I reinserted my live USB.  Is there any way I can keep the data intact and does not loose and application settings installations when I do restart Ubuntu.  Used USB installer provided by pendrivelinux.com at Server 2012 Core (no GUI): Remote Server manager not working I am trying cmd --> MMC --> Server Manager and then connecting to my Server 2012 no GUI  but i keep getting the following error The WinRM client cannot process the request  I am unable to upload images right now  This is not related to other post "How to Remote Manage Windows Server 2012 in Server Manager?" because title and description of that post is quite different from what i am asking Let $\mathbf{Y}$ be a random vector. Are $k$th moments of $\mathbf{Y}$ considered? I am self-learning on linear model theory right now, and one thing I find surprising is that although $\mathbb{E}[\mathbf{Y}]$ is defined for a random vector $\mathbf{Y} = \begin{bmatrix} y_1 \\ y_2 \\ \vdots \\ y_n\end{bmatrix}$, there is no mention of further moments besides the covariance matrix.  Google searching hasn't turned up much. Are $k$th (raw) moments of $\mathbf{Y}$ considered, or is there a different idea I don't know about?  I am learning from the text  (the TOC starts in p. 17 of the linked file). By "considered," what I mean is is there such a thing as $\mathbb{E}\left[\mathbf{Y}^k\right]$, and if so, how would such a concept be defined? The book I have only covers the first raw moment, and I find it a bit strange that there is no mention of how to define $\mathbb{E}\left[\mathbf{Y}^k\right]$ given my experience in univariate probability, nor do I have the expertise to define it.  Furthermore, if $\mathbb{E}\left[\mathbf{Y}^k\right]$ isn't defined, is there perhaps a related concept that I don't know about that is used instead? Why is this regex allowing a caret? Let $f$ be a measurable function on a measure space $X$ and suppose that $fg \in L^1$ for all $g\in L^q$. Must $f$ be in $L^p$, for $p$ the conjugate of $q$? If we assume that $\|fg\|_1 \leq C\|g\|_q$ for some constant $C$, this follows from the Riesz Representation theorem. But what if we aren't given that such a $C$ exists? SQL - an error occurred during the pre-login handshake Is there a good resource or tool to help build a palette/color scheme around colors I select? No matter how nice the composition, flow, and lines of my design are, if I am not copying directly from nature, I have a very difficult time picking a decent color scheme.  It either looks too drab, or too garish.  Is there a good resource that will help me to choose a color scheme that has 2 or 3 colors, and the colors do not clash?  I'm not looking for specific colors or color schemes.  What I need is a resource that will help me choose a color (or colors) that go nicely with, or provide a good accent to, whatever main color I am working with on the design. Tweak showlabels/showkeys - wrap the label When looking at a PDF document I often want to zoom-out to scroll quickly to its contents and get an overview.  However, when I zoom-out past a certain threshold (it seems to differ per PDF) Safari thinks I want to see the tab overview:    I have never found a use for this function, so it only causes annoyance.  Can I turn this tab overview off somehow? A solution that uncouples the pinch-to-zoom gesture from the functionality would also work.  I'm on Mountain Lion 10.8.5 with Safari 6.1.3. How to install LXDM instead of GDM3? I'm running Debian Wheezy and my default Display Manager is GDM3, and I would like to replace it with LXDM. The problem is that I'm trying to run # apt-get install lxde and it's not working, what am I doing wrong?  My /etc/apt/sources.list is:  deb cdrom:[Debian GNU/Linux testing _Wheezy_ - Official Snapshot i386 DVD Binar$  deb http://ftp.br.debian.org/debian wheezy main deb-src http://ftp.br.debian.org/debian/ wheezy main  deb http://security.debian.org/ wheezy/updates main contrib deb-src http://security.debian.org/ wheezy/updates main contrib Is it true that smell is lost flavor? This is a maxim that I hear frequently, especially as a defense of cooking methods that don't produce a lot of aroma: if the aroma is in the air, it means it's left the food.  As an example, some people complain about the lack of aroma produced in sous vide cooking, to which the sous vide advocates retort that this is evidence that more flavor is in the food.  Likewise, I recently saw , where he went for a low-and-slow approach that produces little aroma: here, too, he claimed the flavor-retention defense to its lack of appeal. "Don't be disappointed, but my roasting technique doesn't flood your kitchen with good Sunday roast smells. This is a good thing, because smells are lost flavor" he said, while "SMELL = LOST FLAVOR" popped up on the screen.    I suppose it stands to reason, and that's the appeal of this explanation, but is it the truth? Does smelling a food necessarily imply that the final product will be less flavorful, and is it strictly because the aroma is escaping? Time reversal symmetry and T^2 = -1