Can I close my door with a torch?
If I'm floating in space and I turn on a flashlight, will I accelerate?
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$ I've already see a  by Marko Riedel which I list it follows:     The standard way to treat these sums is to integrate   $$ f(z) = \frac{1}{(z+\alpha)^2} \pi \cot(\pi z)$$   along a contour consisting of a circle of radius $R$ and with $R$ going to infinity and hence being larger than $\alpha$, where the circle does not pass through the poles on the real axis.   Now along the semicircle in the upper half plane we have   $$|f(z)| \le \frac{1}{(R-|\alpha|)^2}\pi \left|\frac{e^{i\pi R\exp(i\theta)} + e^{-i\pi R\exp(i\theta)}} {e^{i\pi R\exp(i\theta)} - e^{-i\pi R\exp(i\theta)}}\right|= \frac{1}{(R-|\alpha|)^2} \pi  \left|\frac{e^{2i\pi R\exp(i\theta)}+1}{e^{2i\pi R\exp(i\theta)}-1}\right| &lt; \frac{1}{(R-|\alpha|)^2} \pi   \frac{1+e^{-2\pi R\sin(\theta)}e^{2i\pi R\cos(\theta)}} {1-e^{-2\pi R\sin(\theta)}e^{2i\pi R\cos(\theta)}}$$   This last term is clearly $O(1/R^2)$ as $R$ goes to infinity as the quotient of the two exponentials goes to one since $\exp(-R)$ vanishes and there is no singularity when $\theta = 0$ or $\theta = \pi$ as $R\cos\theta = \pm R$, which is not an integer by the assumption that the circle avoids the poles and hence cannot be one.     My question: It is clear that for each $z=Re^{i \theta}$ , $f(z)=O(1/R^2)$ ，but can this guarantee that the last term on RHS is uniform bounded ? Since $\theta$ varies on a compact interval $[0, \pi]$ , I want to show that for each $ \theta \in [0, \pi]$ , and a fixed positive number $M \gt 1 $ there exist an open ball contains $\theta$ and a fixed $R_{\theta}\gt 0$ , for every $R \ge R_{\theta}$ and $x \in $ the open ball $$\frac{1+e^{-2\pi R\sin(x)}e^{2i\pi R\cos(x)}} {1-e^{-2\pi R\sin(x)}e^{2i\pi R\cos(x)}} \le M$$  For $\theta \neq 0,\pi$ , it is easy to find the desired $R_{\theta}$ and the open ball , but if $\theta = 0$ or $ \theta = \pi$ , for every open ball containing $\theta$ , it behave erratically near $\theta$ , I have no idea how to deal with this . Is redirecting homepage to a page with keyword it's targeting helps in SEO? How to call Apex REST API from Javascript? I have two different developer orgs. One contains apex REST web service, and I want to call that REST service from my second org. I have tried to call that REST service using normal ajax post request and forcetk.js, But I got following error     XMLHttpRequest cannot load   . Origin    is not allowed by   Access-Control-Allow-Origin.   I searched about this problem then I got to know that Salesforce never allows CORS (Cross-Origin-Resource-Sharing).  Initially I was using apex to call that REST web service, that time I was able to post data from apex. But as we have callout limitation in salesforce, I want to use javascript.  Can anybody please help me? The spell was cast without words, simply a flick of the Death Eater's wand, and a 'streak of purple flame' that lanced across her chest. It was later mentioned that the spell was weakened because of the lack of a verbal component, but still 'did enough damage as it was'. She was in the infirmary healing from the damage for some time. What spell was this? How do I turn off some formats in GeoServer's WMS? Adding an error on a dynamic referenced field Is there a way to add an error on a dynamically referenced field? Let's take this simple example:  opp.get('Name').addError('Invalid name');   This is not working, I'm looking for a similar minded way.  Thanks Conditions for vertical circular motion If a bob attached to a string is swinging in vertical circular motion, we say that the bob leaves the circular path when the tension in the string becomes zero, but even when tension becomes zero, there's always a component of the bob's weight towards the center of the circle. Why then does the bob leave the circular trajectory? What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$? What is the relation between the Higgs field and chirality? Wikipedia  that the spontaneous breaking of chiral symmetry "is responsible for the bulk of the mass (over 99%) of the nucleons".  How do the nucleons gain mass from the spontaneous breaking of chiral symmetry? Why don't leptons gains mass from it? What is the role of the Higgs field in this all? I am trying to put a server together to install Ubuntu. I bought an Intel S1200v3RPS motherboard and plugged an Intel Xeon E3 processor into it. I purchased a 1U chassis from Supermicro with a power supply.  The power supply does not have a 5-pin cable to the motherboard's Auxiliary Power Supply socket. A bit of research did not give any definite answer on the need for the 5-pin connection. The motherboard does not power on and the CPU fan is off. I tested the power supply on a desktop Intel motherboard and it works fine.   I would like to buy a new power supply but could not find one which expressly stated that it comes with the 5-pin aux power supply cable. Any recommendations on a power supply unit for this motherboard would be helpful. Any comments on the problem would be greatly appreciated. Can mobs go through doors? I was wondering if mobs can go through doors or not. It's the difference between me just putting up a door to my house, or putting up dirt instead. The level 4 spell Polymorph requires concentration to maintain.  The subject retains their personality and alignment, but they have the mental statistics of the new form, which must be a beast and cannot speak or cast spells.  If a caster targets themselves with this spell, can they concentrate to maintain it, or does this depend on the mental statistics of the beast form they choose?  This situation certainly occurs in practice, since Wizards reaching level 10 in the School of Transmutation gain the Shapechanger feature.  This allows them to cast Polymorph, but only upon themselves and only to change into a beast of CR 1 or lower.  Beasts with CR 1 or less range in Intelligence from the Giant Eagle (Int 8) to the Frog (Int 1). How can I find tv shows/films similar to one I like? As a general case, how can I find movies or TV shows similar to an existing movie or TV show that I like? Let $ D = 2^\mathbb{N} $, i.e., D is the set of all sets of natural numbers.   What's the meaning of this definition? Intuitively, I would suggest that $ D = \{1,2,4,...\} $ but the explanation "set of all sets" leads me to the guess that this is wrong. Can a decision in a node of a decision tree be based on comparison between 2 columns of the dataset? Assume the features in the dataframe are columns - A,B,C and my target is Y  Can my decision tree have a decision node which looks for say, if A&gt;B then true else false? I was recently watching Episode 3 and a few clone wars episodes, and I found myself thinking during the opening battle between the Republic and General Grievous' forces above Coruscant, on a planet so densely populated where potentially thousands of inhabitants can be killed from a drifting capital class ship with a decaying orbit during space battles what defenses are in place?  Is there any instances of some form of emergency services that tractor beam chunks of debris to safe landing places or repulsor towers that can slow or suspend it until it can be taken apart safely? Even disintegration lasers or emergency force field generators like the types deployed on Hoth as they must have the energy output capable of sustaining it. This IS the galactic capital so must have some advanced tech at its deposal. Even now in our own development humans have certain preventative measures for all types of threats and ways of tracking them, plus responses or fall back plans. Someone mentioned that "veiling glare" or "veiling flare" was to blame for reduced contrast in a photo. What does this mean exactly?  What causes veiling glare, and how can it be avoided? How does it relate to those floating polygonal lens flares one often sees in movies? Bluetooth is on but can't find or be found by any other devices.  Output of sudo service bluetooth status:  ● bluetooth.service - Bluetooth service    Loaded: loaded (/lib/systemd/system/bluetooth.service; enabled; vendor preset: enabled)    Active: active (running) since ხუთ 2015-06-04 22:33:18 GET; 13min ago  Main PID: 26678 (bluetoothd)    CGroup: /system.slice/bluetooth.service            └─26678 /usr/sbin/bluetoothd -n  ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPAG ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPHS ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSource ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSink ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPAG ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPHS ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSource ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSink ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Adapter /org/bluez/26678/hci0 has been enabled ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Adapter /org/bluez/26678/hci0 has been enabled   Output of lsusb:  Bus 003 Device 005: ID 0a5c:21d7 Broadcom Corp. BCM43142 Bluetooth 4.0   How can I fix it? On Windows 7, is there a command prompt line that can start cmd as an administrator? On Linux, we can use  sudo bash   to run a shell as the superuser.  On Windows 7, we can use     Start menu -> (in search box, type) cmd -> Right click on search result and choose Run as Administrator   to run a command prompt as an administrator. Is there also a command prompt line that is like Linux's sudo or su so as to start a shell as an administrator? Float/double precision in debug/release modes Do C#/.NET floating point operations differ in precision between debug mode and release mode?