Serialization compatibility Java 7/8
What is a serialVersionUID and why should I use it?
How was the bank robbery completed? In Now You See Me, when Morgan Freeman explains to the detective on how the Four Horseman robbed the bank, he mentions that they replaced the real money (while in the secured transport truck) with flash paper.  This does not explain how the paper in the bank got ignited, and no ignition/stimulator left in the scene as evidence.  Who/What/When ignited the flash paper in the bank on time?   There had to be some timer/delay mechanism on the platform, or something similar - but in the frames we see - there is nothing. Creating additional Virtual Host Ubuntu Server I am planning on doing a fresh install of Ubuntu and want to know what is the correct way to install ATI Catalyst Video Driver?      There are multiple valid answers for this question spanning over several versions of Ubuntu. For your convenience an index of each below: I have a file containing two columns and 10 million rows. The first column contains many repeated values, but there is a distinct value in column 2. I want to remove the repeated rows and want to keep only one using awk. Note: the file is sorted with values in column 1. For example:    1.123 -4.0 2.234 -3.5 2.234 -3.1 2.234 -2.0 4.432 0.0 5.123 +0.2 8.654 +0.5 8.654 +0.8 8.654 +0.9 . . . .   Expected output  1.123 -4.0 2.234 -3.5 4.432 0.0 5.123 +0.2 8.654 +0.5 . . . . Difficulty in creating macro '\newcommand' for the beginning and end of frames in Beamer Understanding English (Listening skills) The entire  site is blank right now.  The header and footer are shown, but no questions. How diodes protect H-bridge DC motor driver? I don't really understand how these diodes in this circuit and similar circuits (like driving a relay circuit) protects the controller circuit from the energy stored by the inductance of the coil. I really appreciate if someone could graphically explain it. ( I mean how the the diodes block the current and etc)  the second question about this circuit is the capacitor. what happens if it isn't there? Log4j Logging to a Shared Log File Is there a way to write log4j logging events to a log file that is also being written to by other applications. The other applications could be non-java applications. What are the drawbacks? Locking issues? Formatting? "modified" link in the home page questions list does not contain "?lastactivity" parameter I have just noticed that the "modified" link for  does not contain "?lastactivity" parameter in homepage questions list:        When , it's changing to https://meta.stackexchange.com/questions/253359/list-of-communities-with-base-css-updates-completed/286876#286876 as it should, and showing the deleted answer to those who can see it.  Other questions I checked are not affected. Possible way to reproduce might be question with zero answers, where the "modified" was caused by a now-deleted answer. In Dummit and Foote, Exercise 15.18 (p. 727 3rd edition) one is asked to prove that for a commutative ring with unity $R$, and $f$ a non-nilpotent element of $R$, that the localization $R_f$ is isomorphic to $R[x]/(xf - 1)$.  I have done this, using the strategy outlined in the problem, using the universal property of $R_f$ proved in Theorem 36. The problem I have is this:  If $R_f \cong R[x]/(xf - 1)$ and $\phi:R[x] \to R_f$ is a surjective homomorphism, it stands to reason that $\text{ker}(\phi)$ should be $(xf - 1)$. I cannot show this directly. The surjective homomorphism I have in mind is, for:  $p(x) = a_0 + a_1x + \cdots + a_mx^m$  $\phi(p) = \dfrac{a_0}{1} + \dfrac{a_1}{f} + \cdots + \dfrac{a_m}{f^m}$  It is clear to me that $\phi$ annihilates $(xf - 1)$, so that ideal is contained in the kernel. What I cannot show is the other containment, or equivalently:  If $\phi(g) = 0_{R_f}$ then $g(x) \in (xf - 1)$. The trouble I am running into is that $R$ might be a "bad" ring, containing a lot of zero-divisors, $f$ might even be a zero-divisor (being non-nilpotent is a considerably weaker property), so the usual polynomial tricks of the division algorithm or using the irreducibility of $xf - 1$ aren't much use, here.  I feel I am missing something obvious....what is it? Is there an upper limit to temperature in thermodynamics or statistical mechanics In many presentations of statistical mechanics where we have a system of particles having mass, such as the molecules of an ideal gas, the temperature is often equated to the average relative velocity of the particles. However no such velocity can exceed that of light. Is there therefore an absolute upper bound to temperature as well as an absolute zero? How is floating point stored? When does it matter? In follow up to , it appears that some numbers cannot be represented by floating point at all, and instead are approximated.  How are floating point numbers stored?  Is there a common standard for the different sizes?  What kind of gotchas do I need to watch out for if I use floating point?  Are they cross-language compatible (ie, what conversions do I need to deal with to send a floating point number from a python program to a C program over TCP/IP)? $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral Here is a fun integral I am trying to evaluate:  $$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \ dx=\frac{\pi \binom{2n}{n}}{2^{2n+1}}.$$  I thought about integrating by parts $2n$ times and then using the binomial theorem for $\sin(x)$, that is, using $\dfrac{e^{ix}-e^{-ix}}{2i}$ form in the binomial series.  But, I am having a rough time getting it set up correctly. Then, again, there is probably a better approach.   $$\frac{1}{(2n)!}\int_{0}^{\infty}\frac{1}{(2i)^{2n}}\sum_{k=0}^{n}(-1)^{2n+1-k}\binom{2n}{k}\frac{d^{2n}}{dx^{2n}}(e^{i(2k-2n-1)x})\frac{dx}{x^{1-2n}}$$  or something like that. I doubt if that is anywhere close, but is my initial idea of using the binomial series for sin valid or is there a better way?.  Thanks everyone. How can i integrate one SFDC org to another SFDC using Rest Api I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples. How to loop the particle simulation indefinitely? Should I vary input field lengths in a single page checkout form? Dynamic loading of python modules Why are map tiles being repeated? Using MapServer and Openlayers Title used for an autokrat in an Asimov story?