How GRE score affect your acceptance rate
How does the admissions process work for Ph.D. programs in the US, particularly for weak or borderline students?
Special Relativity - Regarding the Simultaneity of Events During the Train Paradox My questions concerns that classic train paradox, wherein there is a train and a tunnel of equal length, and the train is traveling and some fraction of the speed of light towards the tunnel.  According to the Special Theory of Relativity, an observer outside the tunnel will see the train length contracted (Lorentz Contraction), whereas an observer inside will see the tunnel contracted.   Additionally, suppose that there were doors at the ends of the tunnel and that the observer outside the tunnel closed both doors instantaneously when he/she saw that the train was completely inside the tunnel.  The classic resolution of this paradox invokes the non-simultaneity of events, explaining that the observer in the train sees the far door close first, and then, once the train has begun to exit the tunnel, looks back to see the door at the beginning close. Thus, both observers agree that the train does not touch the door when they are closed for an instant.  Now my questions.  Why is it that the observer on the train sees the far door close first? It seems to me that the information coming from the far door would reach the observer on the train only after the information from the other door is reach.   Under this interpretation, the observer on the train would observe the train getting hit by the doors. What if, by some means, this event can be explained in terms of a stationary observer too? Everyone always concludes that the train remains untouched by the doors, but really the only condition that needs to be met is that both observers must agree. Why can't they both agree that the train was hit?  So, to summarize.   Why is the door that is farther away from the train observed to close first? Why can't the other possible conclusion (both see a hit train) be observed? Automatically make various multiple stroke colour the same as various underlying fill colours. I have auto traced a photograph in illustrator - its got thousands of vectors once I expand it and illustrator has converted each of them to a filled colour - I want to now trace the edges of them with a grungy brush but using the underlying fill colour. Where in illustrator can I stroke or outline these fills using the underlying colour - surely this is something that the program automatically does?   I've found this script online but don't know how to implement it. I'm new to this so any help appreciated. Many thanks.   James   var idoc = app.activeDocument;   var sel = idoc.selection;    for (i=0; i&lt;sel.length; i++) {       var ipath = sel[i];       ipath.stroked = true;       ipath.strokeColor = ipath.fillColor;   } Can newsletters take into account a user's favorite tags on that site? Does adding two linear equations will result in a line which will pass through an intersection of the linear equations? I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two linear equations will result in an equation of a line which will pass through a point where two linear equations intersect?  If it is right then I completely don't understand why such a crucial point in understanding how to solve systems of equations is never properly taught even at a university level. Gaming the system for Populist badges Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A In the next proof we avail ourselves of the next lemma: For all sets A and B, ( A ∪ B ) - B = A. Proof: Let A and B be arbitrary sets and let x ∈ ( A ∪ B ) - B. x ∈ ( A ∪ B ) - B ⇔ x ∈ ( A ∪ B ) ∧ x ∉ B ⇔ ( x ∈ A ∨ x ∈ B ) ∧ x ∉ B ⇔ ( x ∈ A ∧ x ∉ B ) ∨ ( x ∈ B ∨ x ∉ B) For p ∧ ~ p ≡ F and p ∧ q ⇒ p where p and q are prepositions, ( x ∈ A ∧ x ∉ B ) ∨ ( x ∈ B ∨ x ∉ B ) ⇔ x ∈ A ∨ F By modus tollendo ponens, x ∈ A ∨ F ⇔ x ∈ A So then, x ∈ ( A ∪ B ) - B ⇔ x ∈ A And ( A ∪ B ) - B = A Therefore, the statement for all sets A and B, A ∩ B = ∅  implies ( A ∪ B ) - B = A is true trivially. Is this proof right? What is the best collation to use for MySQL with PHP? I'm wondering if there is a "best" choice for collation in MySQL for a general website where you aren't 100% sure of what will be entered? I understand that all the encodings should be the same, such as MySQL, Apache, the HTML and anything inside PHP.  In the past I have set PHP to output in "UTF-8", but which collation does this match in MySQL? I'm thinking it's one of the UTF-8 ones, but I have used utf8_unicode_ci, utf8_general_ci, and utf8_bin before. So I integrate the holomorphic function $\frac{e^{iz} -1}{iz}$ over the half disk in the upper half plane, let me name it $\Gamma$. By using Cauchy's theorem, it equals 0.  $$0 = \int_{\Gamma} \frac{e^{iz} -1}{iz} = \int_{0}^{\pi}(e^{iRe^{i\theta}}-1)d\theta + \int_{-R}^{R} \frac{e^{it}-1}{it}dt$$  ($Re^{[0, \pi]}$ and $t: [-R, R]$ being the respective parametrizations.)  By splitting the left integral in two, I get $\int_{0}^{\pi} e^{iRe^{i\theta}}d\theta \rightarrow 0$ by dominated convergence, and $\int_{0}^{\pi} -1d\theta = -\pi$. By making $R \rightarrow \infty$, I'm left with  $$\pi = \int_{-\infty}^{\infty} \frac{e^{it} - 1}{it}dt = \int_{-\infty}^{\infty}\frac{\sin t}{t}dt + \int_{-\infty}^{\infty}\frac{\cos t -1}{it}dt.$$  How do I get rid of the integral on the right? I welcome all feedback. How is canon determined for the works set in the world of ASOIAF? Upgrade to the specific php 7.1/7.2 from php 7.0 in Ubuntu 16.04 How can I upgrade to php 7.1 from php 7.0 in ubuntu 16.04 ?  If I do a php -v I get this message:  PHP 7.0.8-0ubuntu0.16.04.3 (cli) ( NTS ) Copyright (c) 1997-2016 The PHP Group Zend Engine v3.0.0, Copyright (c) 1998-2016 Zend Technologies     with Zend OPcache v7.0.8-0ubuntu0.16.04.3, Copyright (c) 1999-2016, by Zend Technologies Should methods in a Java interface be declared with or without a public access modifier? Should methods in a Java interface be declared with or without the public access modifier?  Technically it doesn't matter, of course. A class method that implements an interface is always public. But what is a better convention?  Java itself is not consistent in this. See for instance Collection vs. Comparable, or Future vs. ScriptEngine. I have an URL structure like the following:     sitename.com/cellphone/nokia/galaxy-5678-nokia-cellphone-from-abc/   For more example:     sitename.com/cellphone/motorolla/new-motorolla-gta800-cellphone-from-zxy/   The directory structure is like the cellphone is the main directory of the module and the words like Motorolla and Nokia are subdirectories which are categories and then comes the title of the cellphone.  Here the word cellphone and Nokia in the first link and cellphone and Motorolla in the second link are repeated.  Is it any kind of keyword stuffing? will it be penalized by Google? Solving trigonometric equations of the form $a\sin x + b\cos x = c$ Suppose that there is a trigonometric equation of the form $a\sin x + b\cos x = c$, where $a,b,c$ are real and $0 &lt; x &lt; 2\pi$. An example equation would go the following: $\sqrt{3}\sin x + \cos x = 2$ where $0&lt;x&lt;2\pi$.  How do you solve this equation without using the method that moves $b\cos x$ to the right side and squaring left and right sides of the equation?  And how does solving $\sqrt{3}\sin x + \cos x = 2$ equal to solving $\sin (x+ \frac{\pi}{6}) = 1$ How to show that $P(A\cup B) = P(A) + P(B) - P(A\cap B)$ Say we have a venn diagram with A on the left, intersection C in the middle and B on the right.   I want to show that $P(A\cup B) = P(A) + P(B)  - P(A\cap B)$  I know what it can be written as A+B+C, but a lot of the proofs  go from:  $P(A\cup B) = P(A) + P(B)  + P(C)$ to  $P(A) + P(B) = P(A\cup B)  + P(C) $  and then rearrange to  get the proof and get $P(A\cup B) =P(A) + P(B)-  P(C) $ . I just don't get how the left side of the inequality get go from $P(A\cup B)$  to $P(A) + P(B)$. Doesn't that only happen if we assume that they are disjoint. In this case, do we assume that they are disjoint? I know how to write the proof but just having a hard time actually understanding it. Redirect output from all commands to file, not just last What is the best way to unit test a method that calls into multiple methods, for example:  modify(string value) {     if(value.Length &gt; 5)  replaceit(value);      else changeit(value); }   This pseudo code has a modify method that (currently) calls either replaceit() or changeit(). I have already wrote tests for replaceit and changeit, so writing a new test for modify will be 99% the same set of code.  I need to test it thought because it may change in the future.    So do I copy paste the existing test code?  Move the test code to a common function?  Any other ideas?  I'm not sure of the best practice here. So I am on Minecraft playing on my friends world (Not server). However, they won't go online for no reason. I want to go continue my work on that world and not start brand new on survival again. I've already made a lot of progress and would not like to lose it, can somebody help? I've already tried to get answers but they are either too complicated or for servers like IP. Enable External Sharing Programmatically We have a scenario on which we are creating site collections from a provider-hosted app. Some of these site collections will be used by external users. Is there a way from CSOM (server-side) to enable external sharing on the site collection? I haven't found any resources stating whether this is or not doable.  I'm trying to replicate the settings you can specify at the site collections page on the tenant admin site:    Thanks! SQL: Get records created in time range for specific dates How to create a desktop shortcut in Unity? Is there an easy way to create a desktop shortcut for an application in Unity? The ability to right click or drag and drop icons to the desktop in Unity does not seem to be there.