Converting MYSQL table data directly to an XML in PHP
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A function that is continuous at the origin but not differentiable there Show that $f(x,y)=\dfrac{xy^2}{x^2+y^2}$ (with $(x,y)\not=(0,0)$ and $f(0,0)=0$) is continuous but not differentiable at $(0,0)$.  I tried to show continuity with an $\epsilon -\delta$ argument but I don't know how to factorize the expression so that I can have something useful.   For differentiability I think I should show that the partials are not continuous at $(0,0)$. But finding the partials is also painful. The prepositions “with”, “at” and “for” are also used to associate a business title with a company's name. It seems that they are interchangeable, with no (significant) difference in meaning. The following examples taken from The New York Times website seem to confirm that:      Until now, said Justin Nielson, a senior analyst for the media   research firm SNL Kagan, “there really hasn't been any direct   competitor . . .      “The consumer is still deleveraging,” said Jason Goldberg, a senior   analyst with Barclays. “It's not a lack of supply; it's a lack of   demand.”      “There’s the party of fear and the party of despair,” Nikos Xydakis, a   political analyst and an editor at Kathimerini daily, said.   Are they really the same as for meaning? If it isn't so, what is the difference between them? Why is AES considered to be secure? The security of RSA is based on the integer factorization problem, which is a very well defined and understood mathematical problem. This problem must be solved in order to fundamentally break RSA.   What about AES (and others based on the same idea)? Why is it difficult to break? Is there any mathematical principle that ensures its security? Why do we say there is an overall negative charge on the intracellular side of the plasma membrane at rest, and an overall positive charge on the extracellular side when both potassium and sodium are positively charged ions, and they are in relatively equal amounts on either side? It seems to me that both sides should be positively charged, and I can't get my head around it. Making a string out of a string and an integer in Python How to integrate Tikz code in SW? I'd like to know how to insert Tikz code in Scientific Workplace tex file. Since SW doesn't support Tikz directly, now I just create Tikz code in another tex editor and export as pdf. Then I convert pdf to images, and import images into SW. Examples and further results about the order of the product of two elements in a group Let $G$ be a group and let $a,b$ be two elements of $G$. What can we say about the order of their product $ab$?   says "not much":     There is no general formula relating the order of a product $ab$ to the orders of $a$ and $b$. In fact, it is possible that both $a$ and $b$ have finite order while $ab$ has infinite order, or that both $a$ and $b$ have infinite order while $ab$ has finite order.   On the other hand no examples are provided. $(\mathbb{Z},+), 1$ and $-1$ give an example of elements of infinite order with product of finite order. I can't think of any example of the other kind! So:   What's an example of a group $G$ and two elements $a,b$ both of finite order such that their product has infinite order?     Wikipedia then states:     If $ab = ba$, we can at least say that $\mathrm{ord}(ab)$ divides $\mathrm{lcm}(\mathrm{ord}(a), \mathrm{ord}(b))$   which is easy to prove, but not very effective. So:   What are some similar results about the order of a product, perhaps with some additional hypotheses? Can't use Shortcut key on linux mint 19 XFCE How do you document your databases? I find that most of my clients are not documenting their databases at all and I find that pretty scary. To introduce some better practice, I would like to know what tools/process people are using.   How do you document your database? (SQL-Server)  What tool do you use?  Documentation Storage Format for database schema/meta-data?   Word documents Excel spreadsheet Plain Text  Documentation process or policies?   I am not talking about reverse engineering / document a existing database, but mainly on the documentation best practices while you develop your system/database. How to restore original size and unboot my bootable USB pendrive I recently made my pen-drive bootable with Ubuntu 14.04. But I need to unboot my pen-drive now. I formatted my pen-drive once,But the size of the pen-drive still shows 2.25 MB. Whereas,this is an 8GB pen-drive. How can I get rid of this problem. I'm still using Windows 7. I read a book that answers one of my questions, and I would like to quote it as an answer. Is that illegal?    Thanks. Solve $$\int \limits_{0}^{\infty} \frac{\cos(x)}{\cosh(x)} dx$$ without complex integration.  This integral can be very easily solved with contour integration, but how can you solve it without taking a tour in the complex plane? Determine $\text{Aut}(S)$ where $S = \mathbb{Q}[x]/(x^2)$ Here's the problem: if $S = \mathbb{Q}[x]/(x^2)$, compute the group  of automorphisms $\mbox{Aut}(S)$.   First off, I have the solution and I know it's isomorphic to the multiplicative group $\mathbb{Q}\backslash\{0\}$, so I'm trying to understand it. It uses what is called the substitution principle and the fact that the restriction of any endomorphism $\phi: \mathbb{Q}[x]\to \mathbb{Q}[x]$ to $\mathbb{Q}$ is the identity. It says that these two facts implies that the endomorphisms of $\mathbb{Q}[x]$ are in 1-1 correspondence with $h \in \mathbb{Q}[x]$, where the endomorphism corresponding to $h$ is $\phi_h : \mathbb{Q}[x] \to \mathbb{Q}[x]$ given by $\phi_h(f) = f(h)$ for $f \in \mathbb{Q}[x]$. I guess I just don't understand how it applied the substitution principle? It's probably obvious, but for some reason I am not getting it.  An explanation would be greatly appreciated! Or if you have a different solution, that'd be cool too. Thanks!! Can I run out of disk space by creating a very large number of empty files? It is well-known that empty text files have zero bytes:    However, each of them contains , which according to my research, is stored in , and do use space.   Given this, it seems logical to me that it is possible to fill a disk by purely creating empty text files. Is this correct? If so, how many empty text files would I need to fill in a disk of, say, 1GB?    To do some checks, I run df -i but this apparently shows the % of inodes being used(?) rather than how much they weigh.  Filesystem             Inodes  IUsed    IFree IUse% Mounted on udev                   947470    556   946914    1% /dev tmpfs                  952593    805   951788    1% /run /dev/sda2            28786688 667980 28118708    3% / tmpfs                  952593     25   952568    1% /dev/shm tmpfs                  952593      5   952588    1% /run/lock tmpfs                  952593     16   952577    1% /sys/fs/cgroup /dev/sda1                   0      0        0     - /boot/efi tmpfs                  952593     25   952568    1% /run/user/1000 /home/lucho/.Private 28786688 667980 28118708    3% /home/lucho Do trees really get a large share of their mass from the carbon in the air? I remember hearing that trees and other plants actually obtain a large amount of their mass from the carbon floating in the air, not the ground beneath them. Does the makeup of air actually contain enough carbon to support this theory, and is a tree's surface area actually large enough to obtain the amount of carbon it needs directly from the air? What focal length lens do I need for photographing the moon? I would like to know whether it is possible to photograph moon without any flaws with a canon EOS 550d..   Also to get an image of the moon as close as the following image, what kind of equipment(lens,etc) is need to be used with the 550d Body In Avengers: Endgame,       Thanos was able to stop and catch Mjolnir and Stormbreaker mid-air as both Captain America and Thor used/called them BEFORE he got the Infinity Stones.   Since this character is clearly not worthy and had no super powers at the time, how were they able to wield Thor's Mjolnir and Stormbreaker, when even the Hulk couldn't do it in The Avengers? Parse RSS with jQuery I want to use jQuery to parse RSS feeds. Can this be done with the base jQuery library out of the box or will I need to use a plugin? From a previous question, we have that $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[4]{3})$, and I am assuming that we would need to use this to justify the answer to the question.   Would it be right to use some idea of a splitting field here? Or is it something to do with $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ not containing a primitive 3rd root of unity?   This is a past exam paper question worth 8 marks, so it doesn't seem like it's a few lined answer, but I am a little stuck on where to go. Why do snap-packages exist - is there a real need? Assumptions  Honestly, I do not know much about  snap-packages - but this is irrelevant for this question - see below. I assume the system is significantly different from the existing one.  Does the change make sense?  Is there an actual need, strong enough? That is - is there a new use case, that is important enough to develop a new format - and the associated infrastructure?  Was it not feasible to change the current method to cover the new use cases too?  Or am I missing the point?  It is possible that what I see is mostly marketing - new names and presentation for minimal technical change, to get a chance that any body assumes it as "new and better" and it may be actually used. Also, it may be that the new packages are so closely based on the existing format that it is mostly a change in presentation to the user. That could be a good solution, of course. In this case, this question would have not much relevance.  Then, I would hope that is still useful enough to answer to side aspects.  Just let me know if the question is not helpful or confusing to new users, I'm happy to delete it.  So, why do they exist?    Background  My first reaction was "That makes no sense!"  This is similar to a situation where, on the physics site, someone asked, unhappy, why nobody discusses his brilliant new ideas in answers. It looked strongly like crackpot ideas; So far from actual physical knowledge that it was hard to find a point to even start. I wrote an answer that did not touch his ideas with a single word, but explained why one would just not discuss assuming crackpot ideas - not the first case of that. The answer was actually hitting the point, I think.    If my assumptions were right, this case is similar.    But then, maybe not - let's see.