Proof of a necessary and sufficient condition between annuli centered at the origin
When can we find holomorphic bijections between annuli?
How do I execute PHP that is stored in a MySQL database? I'm trying to write a page that calls PHP that's stored in a MySQL database. The page that is stored in the MySQL database contains PHP (and HTML) code which I want to run on page load.  How could I go about doing this? As of today I only knew about ubuntu-bug which I could use to report bugs about a specific program. But now I learned about apport-collect and apport-bug which basically are:  apport-bug - Reports problems to launchpad using Apport to collect a lot of information about your system to help the developers fix the problem and avoid unnecessary questions and answers.  apport-collect - Works as apport-bug but it send the information to an already existing bug report. In my case it was apport-collect 1060268 Thanks to Brad Figg in Launchpad.  Are there any other tools to report bugs? How do I create a new object using Python in Blender 2.80? As part of an existing add-on, I'm trying to create an object and add it to the scene using Python. I followed a Blender Cookbook tutorial found here: . I use the following code to do so:  emptyMesh = bpy.data.meshes.new('emptyMesh') theObj = bpy.data.objects.new("object_name", emptyMesh) bpy.context.scene.objects.link(theObj)   But I get the following error when I try to link theObj to the scene objects:  AttributeError: 'bpy_prop_collection' object has no attribute 'link'   This works just fine in Blender 2.76-2.79, but doesn't work in the 2.80 test build I downloaded. Was there a change to the Python API? Or is this maybe a bug in the test build? How do I cash a USD cheque in Europe, quickly? I'll receive a USD cheque shortly. I prefered payment by money transfer, but all attempts to do so - i.e. SWIFT/IBAN, Payoneer, transferwise - failed. Now I will receive a cheque by mail.  I contacted my bank and they say that they can cash a cheque for me, given a (prob hefty) fee. The bank employee was so kind to warn me, that in case of a cheque the funds are cashed, but reserved until the legal reimbursement period ends, which apparently is between 3 and 6 months.   Is there really no quicker way to receive payments by cheque and have access to the funds quickly? "In here", "from here", and "at here" I just read the discussed topic "look here vs. look at here":  It's got me wondering.  What is the reason for not using the preposition at before here?  Is it because here is an adverb and it is wrong to use a preposition before an adverb?  What if we use here with its nominal meaning, as in "get away from here", or "It's really hot in here", and then say "Look at here" meaning "Look at this place"?    If it is wrong and there is some other reason why at here is incorrect but in here and from here are correct, what is it? SPWeb.getFile(Url) exception : value does not fall within the expected range Meaning of symbols $\vdash$ and $ \models$ I'm confused about the use of symbols $\vdash$ and  $ \models$. Reading the answers to  and  I see that:  the turnstile symbol $ \vdash $ denotes syntactic implication. Then $ S \vdash \psi$ means that $\psi$ can be derived from the formulae in $S$  the double turnstile $ \models $, denotes semantic implication. Then the notation $A \models B$ means simply that B is true in every model in which A is true.  So I understand that, e.g., $(ZFC+ A) \vdash B$ means that $A \Rightarrow B$ is a theorem in ZFC and, in this sense $\vdash$ is a mathematical symbol for a theorem. While $(ZFC+ A) \models B$ means that $ B$ is true in every model of ZFC in which $A$ is true, and, in this sense $\models$ is not a mathematical but a metamathematical symbol.  I understand correctly? And those are the only uses of the two symbols? Steam Bollywood Achievement:     As Gandhi, win a cultural victory with   3 or fewer cities in your empire.   I wish to do this achievement on a Pangaea Standard map size or larger and on Prince difficulty or higher,  What tactics do people recommend to achieve this. Any tips on the use of, Social Policies, Wonders, Diplomacy, City States and Military. Arduino only works in root I've installed Arduino but as the title says, I can only upload with sudo. And yes my user is part of the dialout group so that's the weird thing.   Arduino did function before on my system. What could be wrong?  Output ls -l:  ls -l /dev/ttyUSB* crw-rw-rw- 1 root dialout 188, 0 apr  2 09:23 /dev/ttyUSB0 What translation occurs when writing to a file that was opened in text mode that does not occur in binary mode? Specifically in MS Visual C.  unsigned char buffer[256]; for (int i = 0; i &lt; 256; i++) buffer[i]=i; int size  = 1; int count = 256;   Binary mode:  FILE *fp_binary = fopen(filename, "wb"); fwrite(buffer, size, count, fp_binary);   Versus text mode:  FILE *fp_text = fopen(filename, "wt"); fwrite(buffer, size, count, fp_text); Status of B1/B2 visa after citizenship change? I have a valid B1/B2 visa valid to US till March 2019 on Indian passport, I changed my citizenship to Australian. Is my B1/B2 visa on Indian passport valid? Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty$. Prove that $f$ is uniformly continuous.   Since $f(x)\to 0$ as $x\to \pm\infty$ we have $|f(x)|&lt;\epsilon $ whenever $x&lt;-K$ and $x&gt;K$ where $K&gt;0$.  Also $f$ is uniformly continuous on $[-K,K]$ as the domain is compact.  Hence $f$ is uniformly continuous in $(-\infty,-K)\cup [-K,K]\cup (K,\infty)$.  But how to conclude that $f$ is uniformly continuous on $\Bbb R$ from above as I may chose $x\in (-\infty,-K);y\in [-K,K]$ ,how to conclude that $|f(x)-f(y)|&lt;\epsilon $ from above for a given $\epsilon$?  Please suggest the edits required. How to make the BibTeX reference list visible in a LaTeX document Im very new at LaTeX and I would appreciate some help solving this problem. I have created a BibTeX file containing all references to a document. In this text file BibTeX items are inserted and no other text are written, for instance @article{...}. When I call for this bib file from the main.tex file I use the commands:  \bibliographystyle{plain} \bibliography{thebibliography}   Now to my question. All i get when I compile this main.tex is the title (bibliography) for this chapter, otherwise the textfield is blank. Is this error occurring because I should write anything in the bib file or have I missed any lines in the main.tex file. How many Java string objects created in the code String s="abc"+"xyz";? Proof that $\frac {1} {2\pi i} \oint \frac {{\rm d}z} {P(z)} $ over a closed curve is zero. Prove that $$\frac {1} {2\pi i} \oint \frac {{\rm d}z} {P(z)} $$ over a closed  smooth simple curve that contains all of the roots of the polynomial $P(z)$ is either zero if $n \geq 2$ or equals $\frac{1} {a_0} $ if it's degree is $1$.   Proof: $n\geq 2$ $$\frac {1} {P(z)=(z-z_0)(z-z_1)\dots(z-z_n)}$$ So after partial decomposition of the fraction I'll have something like $$\frac {A} {z-z_0} +\frac{B} {z-z_1}+\cdots$$ where $A,B \in \mathbb{C}$ (Is this fact true that $A,B$ wont be polynomials and just coefficients I can see it why in an intuitive way but cannot write a full proof of it for the decomposition trying to get a linear system or something) then use Cauchy's theorem and integrate all of these on  different circles with their center at each root  and argue that  the integral is the same as the sum of those circle integrals. Now since $\frac {1}{z-z_n}$ will be analytic inside the circle when I'm integrating on circles that do not contain $z_n$  some  of those integrals  will be zero. and now since my curves are of the form $\gamma(t)=z_n+e^{it}$ , $t \in [0,2\pi]$ the rest of the integrals  will look like $$\int_0^{2\pi}  \frac{Aie^{ti}} {e^{it}}\,{\rm d}t $$  and all of them will be $A_i$.   Is my proof correct? Only part I cannot show is that I won't have any problem with decomposing the fraction. And I'm also using the assumption that after the decomposition I'll have as numerators simple complex numbers not not functions of any kind. Could Dark Matter form black hole? Some people speculate that the mysterious dark matter in the universe could be tiny black holes. But on the other side, could dark matter particles attract each other by gravity and finally form a black hole? Since dark matter is even more abundant than normal matter, the dark matter black hole should not be rare. Entire function with vanishing derivatives? Let $f:\mathbb{C}\rightarrow\mathbb{C}$ be an entire function. And assume that at each point, one of it's derivatives vanishes.  What can you say about $f$?  A hint suggests that $f$ must be a polynomial. How do I make Chromium use Flash from Google Chrome? Now, that Adobe has stopped issuing new releases for Linux desktops, the only option for users is to use Google Chrome, for those who want to use the latest Flash updates. I use Chromium. Is there any way to get Chromium use the Flash from Google Chrome? The reason I as this question is that I have noticed both these browsers run in the background, so technically, the browsers' plugins are available to use. Why is integration the inverse of differentiation, I mean why do I get the same function when I integrate and then differentiate the result? MySQL Replication : 1 Slave / Multiple Masters