Why $O(n)$ has exactly two connected components?
How many connected components does $\mathrm{GL}_n(\mathbb R)$ have?
How to show to the user a progression in a script? Do I require airport transit visa at Frankfurt? I am flying from Mumbiai to Montego Bay via Dubai and Frankfurt as my final destination. Do i require airport transit visa at Frankfurt. i will be having invitation letter from husband and  even visa from Montego Bay. Remove HTML Tags from an NSString on the iPhone Midpoint-Convex and Continuous Implies Convex Given that $$f\left(\frac{x+y}{2}\right)\leqslant \frac{f(x)+f(y)}{2}~,$$ how can I show that $f$ is convex. Thanks.      Edit: I'm sorry for all the confusion. $f$ is assumed to be continuous on an interval $(a,b)$. I am trying to take pictures of large rugs. The rug size is about 10mx5m, and I'm  planning to purchase , and Canon 7D Mark II with Canon EF 50MM F/1.2L USM lens, since we need high quality images.  We want to set up a studio to take giga-pixel quality images of the large rugs for museum conservation purposes  Could you please suggest the best way for mounting the camera to the ceiling, and any other recommendations for my camera/lens setup, and required lighting? It will be  an indoor shoot. Just we want to setup a studio to shoot the large rugs. If you draw two cards, what is the probability that the second card is a queen? Consider the sequence defined as  $x_1 = 1$  $x_{n+1} = \sin x_n$  I think I was able to show that the sequence $\sqrt{n} x_{n}$ converges to $\sqrt{3}$ by a tedious elementary method which I wasn't too happy about.  (I think I did this by showing that $\sqrt{\frac{3}{n+1}} &lt; x_{n} &lt; \sqrt{\frac{3}{n}}$, don't remember exactly)  This looks like it should be a standard problem.   Does anyone know a simple (and preferably elementary) proof for the fact that the sequence $\sqrt{n}x_{n}$ converges to $\sqrt{3}$? What is the standard interpretation of the order of operations for an expression involving some combination of grouping symbols, exponentiation, radicals, multiplication, division, addition, and subtraction? On the first puzzle of the quest Under Saarthal (the one with the six pillars), I enter the correct combination, but the door still doesn't open, and arrows are still shot at me. I've reloaded the game a couple hundred times, I've left the room, and it still doesn't work. What do I do? Android OS without Google Services? Why is this markdown for a link not showing properly? The Stack Exchange (Personal Productivity) markdown  is showing literally rather than as a named link. Don't know why. Reviewer Stats showing wrong count I have totally reviewed 716 suggested edits, but it shows I've approved 486 suggestions and rejected 228.     I searched about it on meta. But, can't get solution. I thought that some of my reviewed posts might get deleted. So, I went to the review history and found      .   It should be a bug. Blender 2.79b is installed (from .exe) on my computer, currently. And I just downloaded the Blender 2.8 release candidate 2 (.zip).  When I create something in Blender 2.8, after I save it, I cannot open it again because the computer tries to open the blend file in version 2.79b. And manually selecting the 2.8 version from zip file does not work.  How can I open my blender 2.8 files? Do I have to delete Blender 2.79b? Allow retracting a moderator flag if the post has been deleted and I don't have enough reputation to see deleted posts Currently, custom flags for moderator attention are not automatically invalidated (marked helpful) when a post gets deleted. Ordinarily, one can retract a moderator flag by going to the post, clicking &quot;flag&quot;, and then &quot;Retract Flag&quot;. This works even if the post has been deleted, provided they can see the post (they have 10,000+ rep, it's their own post, or they have answered it). However, it's not possible to self-remove a flag on a deleted post if they can't see the deleted post, because they can't get to the &quot;flag&quot; button. Is this intended? If not, can this ability please be implemented? As Aurora0001 commented, there is no server-side check, the button is just not visible. Can this please be implemented on the website, or is the fact that it's possible server-side a bug that will soon be fixed by removing it? Android app - can I see interesting questions? On the website the default list of questions displays interesting tab (which I believe has questions based on my highest scoring tabs). That's very convenient and allows me to check new questions that are relevant for me easily.   Can the same view be added to the mobile app? Evaluate this power series Evaluate the sum  $$x+\frac{2}{3}x^3+\frac{2}{3}\cdot\frac{4}{5}x^5+\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}x^7+\dots$$  Totally no idea. I think this series may related to the $\sin x$ series because of those missing even powers. Another way of writing this series:  $$\sum_{k=0}^{\infty}\frac{(2k)!!}{(2k+1)!!}x^{2k+1}.$$ How to use Launchctl for schedule application I try to work with Launchctl and have a question:  How can I set up an application to run in a few minutes using Launchctl? (for example, open the program MyApp.app with arguments "hello" "world" Every 10 minutes)  I know that it can easily be done by creating Launch Agent, I looking for a way to do it using Launchctl directly to programmatically. How to achieve this smudge effect in photoshop? I have a correlation matrix of security returns whose determinant is zero. (This is a bit surprising since the sample correlation matrix and the corresponding covariance matrix should theoretically be positive definite.)  My hypothesis is that at least one security is linearly dependent on other securities. Is there a function in R that sequentially tests each column a matrix for linear dependence?  For example, one approach would be to build up a correlation matrix one security at a time and calculate the determinant at each step. When the determinant = 0 then stop as you have identified the security who is a linear combination of other securities.  Any other techniques to identify linear dependence in such a matrix are appreciated. Changing website favicon dynamically I have a web application that's branded according to the user that's currently logged in. I'd like to change the favicon of the page to be the logo of the private label, but I'm unable to find any code or any examples of how to do this. Has anybody successfully done this before?  I'm picturing having a dozen icons in a folder, and the reference to which favicon.ico file to use is just generated dynamically along with the HTML page. Thoughts?