Total time taken for an accelerating frame in special relativity
Travel duration from Earth to a star at 9.8 m/s² acceleration
Continuously copy all file changes from one folder to another on change (Windows) I'm working on a massive Java web application which is kept under centralized version control, but the source files are used to build and run the actual server, which then copies all the files I work on into a random temporary directory while it's running.  My problem is that I need to either rebuild this huge application to see any changes to my files, or keep track of all my changes and copy over the files I've changed back to their source location before committing them back to source control.  My question is: is there a command line script I can run that will monitor any changes in the source folder and automatically copy changed files across to temporary folder X?  The idea is to remove the human point of failure in having to manually mitigate the two-locations problem. For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$ For a polynomial $p(z)=a_0+\ldots+a_nz^n$, prove there exist $R&gt;0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$.  I get $|p(z)|\geq |a_n|R^n$, which makes that factor of $1/2$ useless. So I must have done something wrong.  $$|\frac{\partial^n{f}}{\partial z^n}(P)|\leq \frac{\sup_{z\in \overline{D}(P,r)} |f(z)|k!}{r^k}$$. This is the Cauchy estimate.   $$|\frac{\partial^n{p}}{\partial z^n}(z)| = |a_n n!|$$ $$|\frac{\partial^n{p}}{\partial z^n}(0)|\leq \sup_{\zeta\in \overline{D}(0,|z|)} |p(\zeta)|n!/R^n$$ $$|a_n n!|\leq \sup_{\zeta\in \overline{D}(0,|z|)} |p(\zeta)|n!/R^n$$ $$R^n |a_n|\leq \sup_{\zeta\in \overline{D}(0,|z|)} |p(\zeta)|$$  There exist a $z_0$, such that $|z_0|&gt;0$ and $$\sup_{\zeta\in \overline{D}(0,|z_0|)} |p(\zeta)| = |p(z_0)|$$.  This is saying there exist a disk centered at the origin, such that $|p|$ is maximum on some point on the boundary.   Let $R=|z_0|$, we have $R^n |a_n|\leq |p(z_0)|$  Edit: I know what I got wrong. $z_0$ is just one point on the circle $|z| = R$. One can chose another point $z_1$ on the circle, such that $p(z_1)&lt;p(z_0)$. Solve $$u_{xx}-3u_{xt}-4u_{tt}=0$$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$.  My workings so far: I have factored the differential equation in the following way: $$(\delta_x-4\delta_t)(\delta_x+\delta_t)=0$$ where $\delta_x=\frac{\delta}{\delta x}$ etc. Now if we let $v$ be the solution to $(\delta_x+\delta_t)u$ then we have the following two equations: \begin{eqnarray*} (\delta_x+\delta_t)u=u_x+u_t=v\\ (\delta_x-4\delta_t)v=v_x-4v_t=0 \end{eqnarray*} Now for $v$ we simply find $$v=h(t+4x)$$ where $h$ is an arbitrary function of one variable. Now what remains is find $u$ such that $$u_x+u_t=h(t+4x)$$ I am stuck here, I thought about making a change of variables $\zeta=x+t$ and $\eta=x-t$ and thus using the product rule to show that $u_x=u_{\zeta}+u_{\eta}$ and $u_t=u_{\zeta}-u_{\eta}$ and thus $u_x+u_t=2u_{\zeta}$ and we need to solve $$u_{\zeta}=h(t+4x)$$ (I left out the factor 2 because $h$ is an arbitrary function). Do I simply integrate now and conclude $$u=f(\zeta)h(t+4x)+g(\eta)=f(x+t)h(t+4x)+g(x-t)$$ This seems wrong to me...  Some help would be greatly appreciated! I know someone or the other has asked about disabling ⌘Q, but I like the shortcut, and I use it often. However, I use an email client called Airmail that unfortunately does not keep a service (for notifications) running in the background when it is quitted. However, if I press the close button a service runs in the background, allowing me to receive notifications.  But since I have a habit of pressing ⌘Q all the time to close apps, I was looking into a way I could disable it for only Airmail.  Anyone know of a what to do this? I've been watching a lot of pro replays ever since the SC2 beta came out, and I've noticed that almost always, when Protoss research upgrades, the shields are the last research chosen. Why is that? Seems to me that if anything, shields should be the most important upgrade, as they affect all Protoss units and buildings. How can I add an empty directory to a Git repository? How can I add an empty directory (that contains no files) to a Git repository? What's different about photographing at sunrise vs. sunset? I usually get better light at sunrise (compared to sunset). I do though hate to wake up early in the morning to use that light ;)  What are the biggest differences between sunrise and sunset? Does an classical charge that is stationary in a gravitational field radiate? The well known Larmor formula tells us that an accelerated classical charge radiates a power proportional to the square of the acceleration. It has been  that a charge in free fall in a gravitational field does not radiate. Since gravity is locally equivalent to acceleration, one may wonder whether a charge at rest in a gravitational field radiates. The  is that it does. However this radiation is not  to an observer in the same reference frame! Apparently, the radiation does not carry energy or momentum, or it would be observable, in this reference frame and this would mean that charged matter behaves differently from neutral matter in gravity.    How does unobservable EM radiation without energy and momentum make sense (Q1)?  Does the physical origin of charge acceleration determine whether radiation is observable or not (Q2)?  Is the answer to the question in my title "It depends?"?   Note added:  I did not find the discussion at  and  sufficiently enlightening. Is there really any difference between the jackknife and leave one out cross validation? The procedure seems identical am I missing something? Subdivision surface modifier issue I'm following . After using Boolean I cleaned up the extra vertices. Edge flow looks fine on my mesh.   However, when I apply a Subdivision Surface modifier my mesh becomes really messy as if something is wrong with the edge flow.   Can you guys help spot the problem?  Mesh topology:    Subdivision issue: Pull down resistor on logic gate input I would like to use a pull-down resistor on the input of a NOT logic gate. I am using a 5V microcontroller, and I want to ensure that the input of the gate will never be floating (eg. microcontroller damage).  General information:  The logic gate I am using is a HD74LS04 inverter whose datasheet can be found . I am testing the output by placing my positive multi-meter lead on R4 and the negative lead on GND. With the digital pin floating, the output of 1Y is 4.33V. This is the expected behavior.  The logic gate requires a minimum of 2.0V for Vih. If I understand this circuit correctly, I expect the voltage at pin 1A to be 3.76V since R2 and R3 will form a voltage divider. This value seems plenty to signify a 'high' in the logic gate.  R2 exists to protect the digital pin. Ideally, I would have liked R2 to be 1KΩ. Increasing the value of R2 means I have to increase the value of R3 to maintain the same voltage divider. During testing I found that if R3 was any value over 3.3KΩ, the pin 1A would not get pulled down all the way if I left the digital pin floating.   Tests: If I disconnect everything except GND and Vcc and place the positive lead of my multi-meter on pin 1A (now floating) and the negative lead to GND, I read 1.49V. Placing a pull-down resistor (R3) on pin 1A to GND with a value of 100Ω changes the reading to 0.02V. Increasing the resistor's value to 330Ω increases the reading to 0.07V. At the value I need, 3.3KΩ, the reading increases to 0.60V. Finally, changing the resistor's value to 1MΩ increases the reading to 1.47V and actually changes the output of pin 1Y to low.  The test that uses the 3.3KΩ resistor is concerning. The reading I took (0.60V) seems to be approaching the Vil maximum of the logic gate which is 0.80V.   Questions:  This must be a trivial question, but why does an R3 value of 3.3KΩ not pull pin 1A all the way to GND? Is there a formula for determining the correct pull-down resistor value? Other answers I found on here simply state 10KΩ as a 'good' value for a pull-up resistor. I'm not sure where that value comes from or if it is applicable to a pull-down resistor.         &ndash; Schematic created using   Edit: Although Ignacio's answer technically answers the question, I thought I would share some information I found for others who may come across this question.  User 'Papabravo' on the  states that the calculation for a pull down resistor can be calculated by taking the Vil (0.8V) and dividing it by the "standard TTL load" of 1.6mA. As Ignacio pointed out, my specific logic gate can source up to 0.4mA, so the calculation would be 0.8/0.0004A which equals 2KΩ. For safety, I performed the calculation at 0.5V in order to give myself some headroom.  Other Resources: Meaning of Sun Lamp Size? In Cycles, a sun lamp is treated as infinitely far away - only the angle matters, not the position. Other lamps have their sizes defined in blender units: a point lamp with size 1 emits light from a area with size of 1. But if a sun lamp at infinity had a size of 1 blender unit, the angular arc of that sun would be nonexistent.  Clearly, when you change the size of a sun lamp, shadows get fuzzier or sharper. But what does that actually mean? What are you changing? What to do before root and flash my phone? Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem. Inverse of function is continuous or not? In Ubuntu ISO MBR, why does a GPT partition overlap the boot partition, and make MBR uneditable? I would like to have a paper's bibliography entries inside its .tex file instead of outside in a .bib file. Is this possible with biblatex?  My reason for asking this is that I want to find the most convenient way to produce documents that uses biblatex from just one file to make collaboration on papers easier and to be able to handle submissions of papers to journals. C++ inlining class methods causes undefined reference Is a NVIDIA GeForce with Optimus Technology supported by Ubuntu? I am considering buying a Dell XPS 15 laptop. The laptop has a Nvidia 420m card which should work with Linux but I keep reading that the Nvidia Optimus technology isn't supported on Linux. I am not really interested in switching from Nvidia to Intel to save power but need to know that the Nvidia card will in fact work if I installed Ubuntu.  If anyone has experience using a Nvidia card with Optimus technology or even better the exact laptop in question (Dell XPS 15 with 1GB NVIDIA® GeForce®  GT 420M) it would be great.  A major problem holding people back from adopting Linux is this sort of hardware issue. I am a long term Ubuntu user and supporter who can't afford to make a mistake with a purchase like this. I don't want to spend £500+ to find I have no graphics acceleration because Windows 7 is not an option. How to determine the class of a generic type?