Hairy ball theorem for $S^2$
A smooth vector field on $S^2$ vanishing at a single point
What is the purpose of  in Python — especially with respect to when I would want to use it, and when not? How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$ Let $H,~K$ be the Hilbert space. if $\{v_{j}\}_{j\in J}\subset H$ and $\{w_{i}\}_{i\in I}\subset K$ are the orthonormal bases, then how to construct the isomorphic mapping: $H\otimes K \rightarrow \bigoplus\limits_{i\in I}H$. Here, the $H \otimes K$ is the tensor product of two Hilbert space. Can I use a USB stick for a normal install? (to get platform adaptability) So I know I can make a persistent LiveUSB whereby there would be anywhere up to 4GB (I think that's the max) of persistent storage for downloads, etc.  I am asking the opposite, in a sense. I'd like to configure a USB install to have the platform adaptability that a Live OS offers while fully utilizing the 120GB of space I have.  In essence I'm hoping to have a boot up install that reconfigures most/all the hardware/drivers as necessary every boot as I'd like to be able to boot off of it on nearly any machine. (Within reason - they will all be 64-bit)  The biggest gripe with doing multi-platform booting is the video driver stuff. Sometimes the system I'm booting off of is AMD, sometimes Nvidia, sometimes Intel.  Alternatively, a usable answer may be a way to better configure the LiveUSB setup for more storage utilization and customization. I have a graphic on the clipboard on OS X.  What's the quickest way to get it onto disk as a png or jpg? Why are extra dimensions necessary? Some theories have more than 4 dimensions of spacetime. But we only observe 4 spacetime dimensions in the real world, cf. e.g.  Phys.SE post.   Why are the theories (e.g. string theory) that require more dimensions taken seriously by scientists?  Is there any proof that these extra dimensions exist? Is there a simple layman's explanation for the need [or strong hint] for extra dimensions? "like I" or "like me"? In high school we learned to say "than I" and "as I" because you could potentially add an "am" to the end of the sentence.  Examples:  "She is smarter than I."  (Think: "...than I am.") "He is as tall as I."  (Think "...as I am.")  So analogously, shouldn't it be "like I" as well:  "He is sincere, just like I."  (Think: "... like I am.")  But universally, it seems that we use "like me".  Where does this reasoning break down?  Is there history here? android expandablelistview how to set space between groups items How t show $f=g$ almost everywhere How to install apps which require a newer version of iOS on a 1st gen. iPad? Fantasy novel with amnesiac witch, impotent soldier and cursed animals The story is set in a vaguely medieval world in which a young woman has been cursed by the evil witch who has enslaved her and caused her to lose her memory. With the aid of her talking animal friends who have also been cursed (toad has a huge stone under his tongue meaning he can't feed and a crow with a gem embedded in its wing and there's a little grey kitten too who never grows up) she sets out on a journey to break the curse for herself and her friends. Along the way she meets an injured unicorn and a horny-but-moral soldier rendered impotent by a curse after refusing the disguised witch's sexual advances.  After adventures there's a 'happy ever after' for all of the heroes and the witch meets a sticky end.    In the UK the book had a deep red cover with an illustration. I read it in either the 1990's or the early 2000's. Cracking book, definitely for adults given some of the situations, language and humour. When clicking &quot;edit&quot; I see:  Your edit will be placed in a queue until it is peer reviewed. We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.  Like:     Likewise, when I am not logged in, clicking &quot;improve this question&quot; or &quot;improve this answer&quot; shows:  You are not . Your edit will be placed in a queue until it is .  And when I click 'Save', I get:  Thanks for submitting an edit. It is only visible to you until it's been approved by trusted community members  Like:     Who can suggest an edit? Where do suggested edits go? Who can vote on a suggested edit? How do suggested edits get reviewed? Can I earn reputation? What about abuse or bad edits? Sometimes the Community user approves or rejects my edit. Why is that? When can I not suggest an edit? Is there a minimum change requirement for a suggested edit? How do I check my suggested edit history? I disagree with the reasons why my suggested edit was rejected. What can I do? How do I know whether there are edits waiting for review? Someone suggested an edit to my own post, and the reviewers took the wrong action. What can I do? Are tag wikis included in this scheme? What do the &quot;Improve Edit&quot; and &quot;Reject and Edit&quot; buttons do? Why are apparently valid links to rejected edits resulting in 404 errors?   For more information about editing, see &quot;&quot; in the . "Mixed declaration and code" warning, is it worth addressing? Adding my launcher to the Unity Launcher automatically. How? Please add a system to allow file uploads attached to questions and answers I posted a question and a couple of respondents asked for the source code. I could only post portions of the code.  If attachments were allowed I could have uploaded a .zip file with the whole application.  Will this be a feature in SO? Let $\{f_n\}$ be a sequence of analytic functions on a region $\Omega$ with $|f_n| ≤ 1$ on $\Omega$. Let K be compact and contained in $\Omega$. Suppose $\{f_n\}$ converges at infinitely many points in K. Then is it true or false that $\{f_n\}$ necessarily converges at every point of $\Omega$? Making a (simple) directory tree Light clock with mirrors on a moving train While watching  play for the gold medal in London 2012, I noticed Williams was going about her business while Sharapova was grunting each time she hit the ball.  After doing some , grunting in tennis dates back to 1962. Although men grunt, women draw more attention due to their high-pitched grunts. In addition, there is an initiative to eliminate excess grunts in the next generation of tennis players.  Another quote from said research says:     "I have not found in my 32 years anybody who says grunting or not   grunting has an empirically positive or negative effect on performance   -- it's all about belief system."   What is this "belief system?"  If grunting is not related to performance, why do tennis players do it excessively? Is it valid to have more than one question mark in a URL? Why shouldn't we allow NULLs?