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Heisenberg famously derived his uncertainty principle by considering the disturbance that a measurement would have on a small enough system.  Of course in the mathematical formalism of Quantum Mechanics the relationship is derived from more basic principles.  How does String Theory account for it? Heuristically, and mathematically? What can I do to lift a 10 year ban for making a mistake in my UK visa application? I am a Nigerian citizen.  In 2007 I was twice denied a visa to the UK.  Recently I was filling out an application for another UK visitor visa and by mistake I answered no to the question whether I had ever been denied a UK visa, instead of yes.  When reviewing my application, the visa officer found out about the previous visa rejections and as a result I got a 10 year ban on travel to the UK.  What can I do to lift my 10 year ban?   Will this ban affect my chances of obtaining a visitor visa to the USA? How to print a string at a fixed width? Transactions in .net What are the best practices to do transactions in C# .Net 2.0. What are the classes that should be used? What are the pitfalls to look out for etc. All that commit and rollback stuff. I'm just starting a project where I might need to do some transactions while inserting data into the DB. Any responses or links for even basic stuff about transactions are welcome. Very difficult integral (for me) Could someone point me to an online resource where I can look up  $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty \frac{\cos(\vec k\cdot\vec x)}{\sqrt{|\vec k|^2+m^2}}\,dk_1\,dk_2\,dk_3$$  where $\vec k$ and $\vec x$ are 3-vectors, and $m$ is a constant.  Also, if you know how to do it step by step and want to show off your fancy integration, that would also be very helpful.  Thanks ;) PHP conditionals, brackets needed? I was just browsing a forum and someone asked about a PHP file they had found on the web.  It has several spots like this in the code:  if ($REMOTE_ADDR == "") $ip = "no ip"; else $ip = getHostByAddr($REMOTE_ADDR);  I have always thought brackets are needed to enclose what you want to do if the condition is true.  Is there some other alternative, such as if it is on the same line you don't?  There is also another line like this: if ($action != ""): mail("$adminaddress","Visitor Comment from YOUR SITE",  My instinct is to say this wouldn't work, but I also don't know if it is an outdated PHP file and it used to work? How do I get rid of the noise on my Hayes Stroker Trail brakes How do I pick a part that goes into a breadboard when I order it? I have just bought some 555 timers and they are timers for microelectronic circuits...could anyone tell me what I need to search for in order to get larger ones which will fit a breadboard? Thanks This is Problem 6 of the 2007 Indian National Math Olympiad (INMO).  If $x, y, z$ are positive real numbers, prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2).$  My best idea was to expand this and simplify. Although that doesn't look very feasible. Another idea is to see that $x^2+y^2+xy \geq x^2+y^2$. Then we just have to show that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(x^2+y^2)(x^2+z^2)(y^2+z^2)$ if that is even true. Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$ What are the rules about using an underscore in a C++ identifier? It's common in C++ to name member variables with some kind of prefix to denote the fact that they're member variables, rather than local variables or parameters. If you've come from an MFC background, you'll probably use m_foo. I've also seen myFoo occasionally.  C# (or possibly just .NET) seems to recommend using just an underscore, as in _foo. Is this allowed by the C++ standard? What is EV, when used as an absolute measurement? Uncertainty principle and multiple observers My understanding is that an observer can measure the precise location of a particle so long as the corresponding uncertainty in momentum measurement is not an issue and vice-versa.    Say there is such an observer, interested in the precise position of a particular particle.  Now, consider a second, independent observer, unbeknownst to the first, who is trying to measure the exact momentum of the same particle without caring about the position.  As a thought experiment, we assume that the two observers are somehow able to access the same particle at the same time in some way without being aware of each other.  Can both observers get their desired results? What does "user was removed" mean and why did my reputation change because of it? Message appearing when a user was removed.     It seems I lost 1765 reputation points on Stack Overflow yesterday. The reason given in my history is "removed", with the description of "User was removed ()". I don't understand what that means. What caused this? Nonzero nilpotent elements in Zn So I've been stuck on this proof for the past threes days now. I keep going back and forth and making no progress.     Let $n\in \mathbb{Z}_{\geq 2}$. Show that $\mathbb{Z}/n\mathbb{Z}$ has a nonzero nilpotent element iff there is a prime $p$ s.t. $p^2$ divides $n$.   $(\Rightarrow)$ I know $a$ can be factored into distinct primes, so $a=p_1^{e_1}\cdot ...\cdot p_m^{e_m}$ then $a^k=p_1^{e_1k}\cdot ...\cdot p_m^{e_mk}$.  Also since $n|a^k$ so $a^k=nd$ for some $d\in \mathbb{Z}$.  $a^k=p_1^{e_1k}\cdot ...\cdot p_m^{e_mk}=nd$. So $nd$ has that distinct prime factorization.  Then I get lost on what to do. How to install Internet Explorer (multiple versions)? I am developing one site which has chat feature in Rails. I am using Ubuntu 12.04 LTS. I need to check that the site is IE9 because the chat feature using socket io of HTML5. I want to know that how to install IE9 in Ubuntu. I have looked at Chrome and Firefox extensions but if any standalone is available then please give me suggestion. Inexact measurement and wavefunction collapse Landscape printing from HTML I have a HTML report, which needs to be printed landscape because of the many columns. It there a way to do this, without the user having to change the document settings?  And what are the options amongst browsers. Why are Alkaline, NiMH, and Li-ion AA measured differently (mAh, mWh, etc)? Looking around Amazon, it seems that different types of batteries are measured differently:  Does anyone know why?   Li-ion are measured in mWh    (Cheap-Os)  3000mWh AmpTorrent  NiMH are measured in mAh      Alkalines are typically not measured   "Long Lasting" Duracell "Longest Lasting" Energizer    I assume that Alkalines are not measured for some sort of historical reason with marketing departments?  ... or is it that alkalines so mystical and unreliable that giving them a measurement is too aggressive? Or that switching to non-toxic / non-mercury was such a bad move in performance that measurements had to be removed in the 90s so people wouldn't know?  Perhaps NiMH are measured in mAh because the voltage can very so greatly and mWh doesn't make sense?  Are Li-ion measured in mWh because that's more consistent with non-battery measurements and they do deliver reliable voltage? Reading the book on which I'm learning English, I've come across a weird (for me) omitting the "to" in sentence: "I'd better go meet with him then."  Say, if it were "I'd better go to meet with him then.", would there be any difference between the two sentences? When I should prefer using one instead the other?  P.S. Sorry for my bad English. If I made a mistake somewhere, please correct me.