Why does an electric spark occur discontinuously while an electric arc is not extinguished as long as the current is maintained?
In my student book they separate these two and indicate that sparks need high voltage to occur while arcs need low voltage with normal or low pressure and electric arcs CAN come with heat and bright light. But when I search on the web many people said that arc is just a hotter version of spark. So what is the difference between them?
For which values of $x$, will $f (x) . f '(x) < 0$? Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically? Is there a way to exclude other particle systems from the effects of a Wind effect? I have a scene with a number of particle systems. I'd like to have a separate wind effect for my main scene and another for an extra: an emitter + wind-effect to blow leaves into my scene. I can't find any way to exclude, so here I am. At the very worst, I can just render the main scene and then render the wind effect and composite it, but I figured I'd check first. How do I integrate the following? $\int{\frac{(1+x^{2})\mathrm dx}{(1-x^{2})\sqrt{1+x^{4}}}}$ Can a bird, previously at earth potential, get electrocuted by landing on a powerline at high-enough voltage due to the initial "equalization charge"? At the voltage levels of typical overhead transmission lines in the US, a bird can land on one and be just fine (as long as it doesn't do something like spread its wings and touch a tree or something else at lower electric potential).  However, what about a hypothetical powerline at much higher voltage (as in tens of megavolts). Could landing on such a powerline fatally-shock the bird even though it does not complete a circuit for sustained current? (Assume that the distance is long enough that electrical arc'ing is impossible.)  NOTE: My understanding of what happens when a bird flies from an earth object to a powerline (please correct me if I'm wrong) is that - upon contacting the wire - its electric potential changes from earth-potential to the powerline's potential. In order for this to happen, there is an initial transfer of electrical energy (i.e. flow of charge i.e. current) from the powerline to the bird which "equalizes" their electric potential, which happens nearly instantaneously. If this is correct, then my question can be restated more generally as "Can an 'equalization charge' such as this result in a fatal shock, if the potential difference that it's equalizing is high enough?" Slipstream Windows 7 + Service Pack 1 MacPorts fails to find 'make' I've installed Xcode and MacPorts on a brand new mid-2013 MacBook Air, but MacPorts doesn't work, saying that it cannot find anything.  mba:~ cnst$ sudo port install wget Warning: The Command Line Tools for Xcode don't appear to be installed; most ports will likely fail to build. Warning: See http://guide.macports.org/chunked/installing.xcode.html for more information. ---&gt;  Computing dependencies for wgetError: Unable to execute port: can't read "build.cmd": Failed to locate 'make' in path: '/opt/local/bin:/opt/local/sbin:/bin:/sbin:/usr/bin:/usr/sbin' or at its MacPorts configuration time location, did you move it? mba:~ cnst$   And, indeed, there is no make or clang in the path, but it is definitely installed, though:  mba:~ cnst$ find /Applications -name "clang" -or -name "make" /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/clang /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/lib/clang /Applications/Xcode.app/Contents/Developer/usr/bin/make mba:~ cnst$   Why is there no make or clang in the path?  Why MacPorts doesn't work?  I notice that  mentions that you have to install something from ADC, Apple Command Line Developer Tools, but ADC doesn't work since last Thursday or Friday due to their security breach, so, the developer tools are nowhere to be found.  What's the proper solution here? Why does the Euclidean algorithm work for polynomials? What is the proof? Suppose I know that I can find the $\gcd$ of two integers with the Euclidean algorithm. What is the 'extension' so I can use this method also for polynomials?  Edit: I found an easy answer with less rigor which is approachable without knowledge of matrices:    also the first 3 subchapters of Is there a way to make PythonTEX compile as of today in Overleaf V2 ?  \documentclass[]{article} \usepackage[utf8]{inputenc} \usepackage{pythontex}  \begin{document} \begin{pyverbatim} def calc_ellipticity(theta, delta):     theta = np.deg2rad(theta)     psi = np.arcsin(np.sin(2*theta) * np.sin(delta))/2     return np.tan(psi) \end{pyverbatim} \end{document}   Compiling gives : ? PythonTEX ? How do Muggle Wars affect the magical world? This came up to me while I was reading the question about Magical being using firearms in battle to raise their power (which I think I have a good answer for, but it's too long to fit in this question... and it would also be inappropriate).  Anyways, I was reading it and then the following thought came into my mind: If wizards decided to use guns on their battles (the ones agains Voldemort for instance), that would create that opening for much bigger battles than we see in the books (after all even a muggle can fire a gun, so lots of guns + the Imperio curse, and presto manifesto (is that racist? talking about wizards and all) you have yourself an army). Those kinds of battles, however, would most definitely not go unnoticed by the muggles - even though they wouldn't be able to link it to magic.  Well, that thought brought up my one and final question, which I bring forth to you guys. Is there any mention on how the Wizards and Witches viewed the two world wars (which had taken part by the time Harry got to Hogwarts, and which he had probably heard about in muggle school), and what was the Wizards' part in it? What about the cold war? Did the magical world even recognise the existence of weapons such as nukes, which could render all life on earth extinct?  EDIT  DVK has brought up an  regarding the connections between the Second World War and the wizarding world (more specifically, the wizard Grindelwald). Although it doesn't fully answer my question, it does help by showing that there was indeed some form of connection between the two world at the time. If $x_1,x_2,\ldots,x_n$ are the roots for $1+x+x^2+\ldots+x^n=0$, find the value of $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$ Let $x_1,x_2,\ldots,x_n$ be the roots for $1+x+x^2+\ldots+x^n=0$. Find the value of   $$P(1)=\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$$   Source: IME entrance exam (Military Institute of Engineering, Brazil), date not provided (possibly from the 1950s)  My attempt: Developing expression $P(1)$, replacing the 1 by $x$, follows $$P(x)=\frac{(x_2-x)\cdots (x_n-x)+\ldots+(x_1-x)\cdots (x_{n-1}-x)}{(x_1-x)(x_2-x)\cdots (x_n-x)}$$    As $x_1,x_2,\ldots,x_n$ are the roots, it must be true that   $$Q(x)=(x-x_1)\cdots(x-x_n)=1+x+x^2+\ldots+x^n$$ and  $$Q(1)=(1-x_1)\cdots(1-x_n)=n+1$$ Therefore the denominator of $P(1)$ is  $$(-1)^{n} (n+1).$$ But I could not find a way to simplify the numerator.  Another fact that is probably useful is that  $$1+x^{n+1}=(1-x)(x^n+x^{n-1}+\ldots+x+1)$$ with roots that are 1 in addition of the given roots $x_1,x_2,\ldots,x_n$ for the original equation, that is  $$x_k=\text{cis}(\frac{2k\pi}{n+1}),\ \ k=1,\ldots,n.$$  This is as far as I could go...    Hints and full answers are welcomed. How to backup 20+TB of data? We have a NAS server at the company I work for that is being used for storing photography sessions. Each session is approximately 100gb. Over the last couple of years this server has accumulated 10+ TB of data, and we are increasing the amount of photoshoots exponentially. I estimate that by the end of next year we will have 20+ TB stored on this NAS. We are currently backing this server up to tape using LTO-5 tapes with Symantec BackupExec. Since the size of this server has grown, full backups of this server are not completing overnight. Does anyone have any suggestion on how to backup this amount of data? Should we be backing it up to tape? Are there any other options which may be better? I'm trying to identify a song by a female 80's pop group.   Here are the lyrics I remember:     It's the story of my life if you want to know   a play where everything is meant to be   you're the story of my life and I can't let you go Of course most languages have library functions for this, but suppose I want to do it myself.  Suppose that the float is given like in a C or Java program (except for the 'f' or 'd' suffix), for example "4.2e1", ".42e2" or simply "42". In general, we have the "integer part" before the decimal point, the "fractional part" after the decimal point, and the "exponent". All three are integers.  It is easy to find and process the individual digits, but how do you compose them into a value of type float or double without losing precision?  I'm thinking of multiplying the integer part with 10^n, where n is the number of digits in the fractional part, and then adding the fractional part to the integer part and subtracting n from the exponent. This effectively turns 4.2e1 into 42e0, for example. Then I could use the pow function to compute 10^exponent and multiply the result with the new integer part. The question is, does this method guarantee maximum precision throughout?  Any thoughts on this? Should a function have only one return statement? Is it fair to buy a return ticket I know I will never use just because it's cheaper? "Use Option as Meta key" with ability to type the # symbol I am using Terminal version 2.5, where I have two requirements:  I need to be able to type the Meta key. I need to be able to type the # character, too (Option+3 for the UK keyboard layout)  How can I satisfy both of these? By default, (2) is satisfied, but (1) is not. I can then turn on &quot;Use Option as Meta key&quot;, which satisfies (1), but breaks requirement (2). How can I have both? (It shouldn't be so hard for me to just be able to type.) Edit: what I'm looking for, for example, might be a way to just &quot;Use Option as Meta key&quot; for the left/right Option key, or a way to override the &quot;Use Option as Meta key&quot; for the sole exception of the # character. Protect email addresses in the user description from bots I've noticed that emails are not protected in the user description. For example  entered his email and when viewing the source code of the page it is plain text that malicious bots could harvest and exploit to spam. It would be nice if email addresses were automatically encoded to prevent this. JQuery to load Javascript file dynamically How do you update an Excel file (Data Refresh and update formulas) WITHOUT opening the file? I have an Excel file that want to update and save automatically with out having to open it or manually interact with.  Manually, I open the file up and hit data refresh which goes and does a SQL query and then hit F9 for the formulas to update and then I just close/save.    (I then would mail the file out to people using a perl script or use SAS JMP to run some numbers/charts and also mail them out.  Basically I need to script some things which require the XLS file to be updated.)