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Run cmd.exe in Administrator mode without explorer.exe How to create posters using LaTeX Smallest Width for Galaxy S and Galaxy S2 Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$ I need to prove that if $f$ and $g$ are analytic in $D_r(z_0)$ and $g$ has a simple zero at $z_0$, then $$\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$$   When $f(z_0)\neq 0$ and since $1/g$ has a simple pole at $z_0$ $$\mathrm{Res}[f/g,z_0]=\lim_{z\to z_0}(z-z_0)\frac{f(z)}{g(z)}=\frac{f(z_0)}{g'(z_0)}$$ But what do I need to do when $f(z_0)=0$? Any help will be appreciated thanks Matching exact string with JavaScript How can I test if a RegEx matches a string exactly?  var r = /a/; r.test("a"); // returns true r.test("ba"); // returns true testExact(r, "ba"); // should return false testExact(r, "a"); // should return true I've been looking around on the internet and I can't find anything in depth on how the cable/connection functions. I've only been able to find simple pin out descriptions.  If someone can link me or point me in the right direction, I would be very grateful. Why does a translation matrix need extra row? Words that mean ''to say something unintentional'' I am looking for words that mean ''to say something unintentionally'' How do I access $HOME/storage Termux directory on Android Pie with a GUI File Explorer?  In Termux I print the working directory with pwd and it shows $HOME/storage as:  /data/data/com.termux/files/home   My internal storage looks like this:  . ├── Alarms ├── Android |   ├──data |   |  ├── ... |   |  ├── com.termux |   |  |   └── files |   |  |       └── 0 items |   |  └── ... |   └── ... ├── DCIM ├── Download └── ...   My external storage looks like this:  . ├── Android |   ├──data |   |  ├── ... |   |  ├── com.termux |   |  |   └── files |   |  |       └── 0 items |   |  └── ... |   └── ... └── LOST.DIR   Neither my internal storage, nor my sd card, contain a /data/ directory at the root level. Where is this /data/ directory? For that matter, where is the root /storage/ directory? Where is the root /emulated/ directory? Where are any of these directories and why cant I access any of them? BIGINT UNSIGNED value is out of range $\sqrt{1-x^2}$ is not a rational function If $k$ is a field in which $1 + 1 \neq 0$, prove that $\sqrt{1-x^2}$ is not a rational function. Hint. Mimic the classical proof that $\sqrt{2}$ is irrational   It seems rather odd to discuss the square root function in the context of an arbitrary field, but here goes nothing!  Proof:   Suppose that $\sqrt{1-x^2}$ is a rational function in $k(x)$. Then there exist polynomials $p(x)$ and $q(x) \neq 0$ that are relatively prime with $\sqrt{1-x^2} = \frac{p(x)}{q(x)}$; clearly we may take $p(x) \neq 0$. Then $1-x^2 = \frac{p(x)^2}{q(x)^2}$ or $q(x)^2(1-x^2) = p(x)^2$, which says $q^2 | p^2$, and since $q | q^2$, we can infer $q | p^2$. Moreover, since $p|p^2$ and $(p,q)=1$, then $pq|p^2$ or $q|p$, which contradicts the fact that the polynomials are relatively prime. Hence $\sqrt{1-x^2}$ cannot be a rational function.    How does this sound? Aside from the problem of discussing $\sqrt{~~}$ in the context of an arbitrary field, I am worried about not using the fact that $1+1 \neq 0$, at least not explicitly. Where exactly is this assumed used, if at all?  EDIT:  Suppose that $q(x) =1$, and let $f(x) = a_n x^n + ... a_1 x + a_0$. Then $1-x^2 = f(x)^2$. If $x=0$, $1 = a^2_0$ and therefore $a_0$ must be a unit. Letting $x=1$ we get $0 = (a_n + ... + a_1 + a_0)^2$; and letting $x=-1$ we get $0 = (-a_n - ... - a_1  + a_0)^2$. Since we are working in a field, there can be no nonzero nilpotent which means that $a_n + ... + a_1 + a_0$ and $-a_n - ... - a_1  + a_0$ are both zero. Adding the two equations together yields $2a_0 = 0$, and since $1+1 \neq 0$, $a_0 = 0$ which contradicts the fact that $a_0$ is a unit.   How does this sound?  Another attemtpt:  If $f(x)^2 = 1-x^2$, then $2 = \deg(f^2) = 2 \deg (f)$ implies $\deg(f) = 1$. Yet if $x=-1$, we get $f(-1)^2 = 1 - 1 = 0$ and therefore $f(-1)=0$ since there are no nonzero nilpotent elements in a field; similarly, $f(1)=0$. Since $1+1 \neq 0$, $f$ has two distinct roots in $k$ yet is only a $1$-st degree polynomial, a contradiction. Rainbow Six Siege Insane Load times? Computer or Internet? I have a high-end computer with decent ethernet yet whenever I join a game in Siege everyone finishes loading and it takes me 1-5 minutes. Is this because of my internet or computer?   Specs:  CPU - i7-7700k GPU - GTX 1080 16GG RAM 5900 RPM 4TB Hard drive Debian root partition resizing Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$ I need to show that the product of all the $n$th roots of unity is $(−1)^{n+1}$.   Is there a way to do this by induction? If there is, I can't seem to figure it out. Are there other, perhaps more efficient, methods of proof? Why isn't an infinite, flat, nonexpanding universe filled with a uniform matter distribution a solution to Einstein's equation? Logic Behind StackOverflow Question IDs We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? How to get Lookup ID from Search API with REST I'm trying to get the ID of a lookup field when using search api. My query looks something like this:  /_api/Search/query?querytext='ListId:12345678-1234-1234-1234-123456789012'&amp;selectproperties='Title,Company'   Where Company is the lookup field, in a specific list.  The result looks like this:  &lt;d:element m:type="SP.KeyValue"&gt;   &lt;d:Key&gt;Company&lt;/d:Key&gt;   &lt;d:Value&gt;Some company&lt;/d:Value&gt;   &lt;d:ValueType&gt;Edm.String&lt;/d:ValueType&gt; &lt;/d:element&gt;   I have created a managed property which looks like this: Altering layer's CRS to correct Layer Misalignment in QGIS I've got a vector layer in my project which isn't aligned with the rest of the project (see attached JPEG).  These are work files so I'm not sure when they were created or how they might have been messed with since they were created.  We moved from ArcGIS to QGIS a couple of years ago.  The infilled blue vector layer is the one I need to move, slightly north and east, so that it correlates to the blue line (also a vector).  All layers (and the project) are currently in EPSG:27700 - OSGB 1936.   If I need to create a new CRS based on OSGB 1936 and give it some new parameters, then how would I go about this?  Further information:  This is on Exmoor in SW England, and the data is uniformly almost exactly 8m out to the SW point to point - i.e I need to shift it 8m NE. Recursive cast from SimpleXMLObject to Array