Intersection using turf js
Polygon intersection using turf js
How can I execute an equivalent of `head -z` when I don't have the `-z` option available? From the movies we know that Obi-Wan Kenobi delivered Luke Skywalker to Owen and Beru Lars to raise on Tatooine shortly after Luke was born at the end of RotS (Episode 3).   The next think we know is Luke running into Ben Kenobi during A New Hope.   There seems to be a hint that there was at least SOME communication between Kenobi and Lars family based on him telling Luke:     Your father wanted you to have this when you were old enough, but your uncle wouldn't allow it.   (though it's possible that was referring to Kenobi offering to leave the lightsaber to Larses at the same time he dropped off Luke)  I was wondering if any details of what transpired between Kenobi and Larses in the years between RotS and ANH were noted in any canonical works (of any canon, including EU books/games/comics/etc...)? Let $A$ be the set of all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the following two properties. Let $A$ be the set of all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the following two properties:  (1) $f$ has derivative of all orders, and  (2) for all $x,y \in \mathbb{R}$, $f(x+y)-f(y-x)=2xf'(y)$.  Which of the following sentences is true?  (a) Any $f\in A$ is a polynomial of degree less than or equal to 1  (b) Any $f \in A$ is a polynomial of degree less than or equal to 2  (c) $\exists f \in A$ which is not polynomial  (d) $\exists f \in A$ which is a polynomial of degree 4  It is a problem from TIFR GS-2018. I have found polynomials upto degree 2 hold this properties but have to exclude the possibility of (c) and (d). I also found out if $f'(x)$ has at most one real root and clearly graph of $f$ is symetric about that root. How can I proceed further? Google Play: Error downloading app - insufficient space Natural Sounding Text to Speech? Java Manifest.mf classpath issues I've been trying to run a jar file - let's call it test.jar - that uses the Sybase jconn3.jar on a Unix system.  I have created a MANIFEST.MF file that has the following:  Class-Path: $SYBASE/jConnect-6_0/classes/jconn3.jar commons-net-1.3.0.jar   This gives a ClassNotFoundError. $SYBASE is the system variable that points to /opt/sybase13; I've also tried the following:  Class-Path: /opt/sybase13/jConnect-6_0/classes/jconn3.jar commons-net-1.3.0.jar   and  Class-Path: opt/sybase13/jConnect-6_0/classes/jconn3.jar commons-net-1.3.0.jar   However, if I copy the jconn3.jar file from the $SYBASE/jConnect-6_0/classes to the same directory as test.jar, and update my MANIFEST.MF to read as follows:  Class-Path: jconn3.jar commons-net-1.3.0.jar   The application runs as expected.  Now, I've been able to verify the jconn3.jar file works by copying it locally; my MANIFEST.MF file includes the path to my Main-Class, so that's not at issue here.  What do you think could be the problem? I've been looking at this thing for too long now. Thanks! How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$? I would like to find the apothem of a regular pentagon. It follows from   $$\cos \dfrac{2\pi }{5}=\dfrac{-1+\sqrt{5}}{4}.$$  But how can this be proved (geometrically or trigonometrically)? I want to write $ k = \{k1,k2,k3,...,kn\} $. How could I do this? What Did Lyanna Stark Say to Ned Stark? In the final episode of season 6 we see that Lyanna Stark is whispering something to Ned. What is she saying? Why are so many different types of objects white, yet appear gray when they are wet? There are many things with different textures that appear white – salt, beer foam, paper, shaving cream, snow, talcum powder, white paint, etc. The most common answer is all of the frequencies must be reflected in order for us to perceive white, which I already know. There must be more underlining details why such a huge variety of things are white. Furthermore, if you wet paper, snow or talcum powder, they appear off-white or gray. Why is this? How to use ssh to transfer files from computer a to local computer I am trying to get some files off of my school Linux account using ssh. I have got the connection to work using:  scp &lt;school_server&gt;: ~/folder I want ~/where I want to go.    But when it goes to transfer folder it gives me the message:  not a regular file    The file contains .java files, and I want the whole folder. How do I flatten this vector logo leaving only the visible black paths? I dont have a clue about the proof in the reverse implication on the iff statement.  I will show what I have by now:  1) A cofinite topology implies that any infinite subset in $X$ is dense. Let $U\in\tau$ and is cofinite topology so $U=X-\bigcup_{k=1}^{n}\{x_k\}$.  Let $V\in X$ an infinite subset then $$V\cap U=V\cap(X-\bigcup_{k=1}^{n}\{x_k\})=(V\cap X)-(V\cap \bigcup_{k=1}^{n}\{x_k\})=V-(V\cap \bigcup_{k=1}^{n}\{x_k\})$$  and cause $|V|\ge\aleph_0$ and $|\bigcup_{k=1}^{n}\{x_k\}|=n\in\Bbb N\,$ we have that $|V\cap \bigcup_{k=1}^{n}\{x_k\}|\le n$. And finally is obvious that $V-(V\cap \bigcup_{k=1}^{n}\{x_k\})\ne\emptyset$ so any infinite subset is dense on $X$.  2) A cofinite topology implies a $T_1$-space. Let $x, y\in X$ and $U\in\tau: U=X-\{y\}$ so $x\in U\land y\notin U$. We can define too $V\in\tau:V=X-\{x\}$ so $x\notin V\land y\in V$ then a cofinite topology is a $T_1$-space.  But my problem is that I dont have a clue to prove the reverse implication i.e. if we have a $T_1$-space where every infinite subset is dense then it is a cofinite topology. Some hint? Some advice or correction in the proof of above? Thank you in advance.    I will complete the proof with the advice of @Cameron Buie.  1) A $T_1$-space implies that any finite subset is closed. Let the singleton $\{x\}\subset X$. Then $\overline{\{x\}}=\{x\}\cup\{x\}'$ where $\{x\}'=\{y:(\forall U\in\tau : y\in U)\land x\in U\}$, but because we are in a $T_1$-space exist some $U$ for any points $x,y\in X: x\in U\land y\notin U$ so $\{x\}'=\emptyset$ then $\overline{\{x\}}=\{x\}$ and is closed.  This means that for every $T_1$-space it cofinite sets are open.  2) If any infinite subset is dense on $X$ it means that the closure of any infinite subset is $X$ so the only closed sets are finite (and $X$ itself), so the topology is cofinite. I'm curious whether I can find the overlap $\langle q | p \rangle$ knowing only the following:   $|q\rangle$ is an eigenvector of an operator $Q$ with eigenvalue $q$. $|p\rangle$ is an eigenvector of an operator $P$ with eigenvalue $p$. $Q$ and $P$ are Hermitian. $[Q,P] = i \hbar$.   I'm asking because books and references I've looked in tend to assume that $Q$ is a differential operator when viewed in the $P$-basis, then show that it satisfies the commutation relation. (I haven't read one yet that proves that the form given for $Q$ is the only possible one.) I've heard, though, that we can work purely from the hypothesis of the commutation relation and prove the properties of $Q$ and $P$ from it. Line integration in complex analysis When should I load assets for optimal performance? I'm writing a game using LWJGL and Java, and was wondering if there were best practices for when to load resources.  I have seen examples that load all resources when initializing the game (XNA), ones that load the new resources needed for each level while referencing the already loaded assets again. Evaluating limit (iterated sine function) The limit is   $$\lim_{x\rightarrow0} \frac{x-\sin_n(x)}{x^3},$$  where $\sin_n(x)$ is the $\sin(x)$ function composed with itself $n$ times:  $$\sin_n(x) = \sin(\sin(\dots \sin(x)))$$  For $n=1$ the limit is $\frac{1}{6}$, $n=2$, the limit is $\frac{1}{3}$ and so on.  Can we define a recurrent relation upon that given hypothesis? Also, how do I involve $n$ into calculation, because the final limit will depend on it?  Any suggestions on how to tackle this?  Thank you! Why won't Amanita move in and settle down? I keep getting an alert that Amanita would like to settle down. I have a house ready for them however they still won't move in. Who is this NPC and why won't they settle down? Some people love creating or fostering the creation of events that are noisy, chaotic and fun, such as parties, arguments, reunions, etc. Sometimes there's a negative connotation to this (like in provoking an argument), but sometimes there is not (like in organising a big, noisy party).  The word I'm looking for would be the English equivalent to the Spanish armadanzas, just in case this is helpful.  Any ideas? Memory allocation for member functions in C++