Find numbers from GCD and LCM
Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$
How can I generate PDF metadata from LaTeX? I am writing a document using LaTeX and generating PDF.  Can anybody tell me how I can generate the PDF metadata, e.g. author or title, from LaTeX?  On Windows XP, I am using MikTex's texify to generate the PDF.  On linux, I am using pdflatex to generate the PDF.  Any answers for either platform would be much appreciated! Is it supposed to be a HTML or an HTML I've seen many people who say:     This is a HTML page.   Yet I've also seen many people who say:     This is an HTML page.   Are both usages equally correct?  Or, which is the grammatically correct one?       Possible Duplicates: Smileys in LaTeX I would like to include smileys in my LaTeX document. Is there any package with lots of different smileys?  In mnsymbol and wasysym, I found some general symbols:  \documentclass{article} \usepackage{MnSymbol,wasysym} \begin{document} wasysym: \smiley{} \frownie{} \blacksmiley{}  MnSymbol: \(\smile{} \frown{}\) \end{document}     But I do not like the output. Actually, I am looking for smileys which look like "default smiles" in Google Talk, MSN, ... ;) &lt;- this one is my favourite. ;) Turning a cipher into a hashing function This is theoretical question. I'd like to know if it's possible (and what are eventually the consequences), not that I'm going to do it in one of my projects. ;)  The first hashing functions created were based on a symmetric cipher (just like the first Unix crypt was based on DES). The idea was simple. Use the password as key to encode a constant.  I'd like to know if it's still possible to convert any modern symmetric cipher into a hashing function (and second question: into a cryptographic hashing function). Is it possible (easier) to guess the key, when you have an encoded and decoded messages? Updating a field programmatically, hook_node_update Why is causality preserved in special relativity? PART 1: I was reading the article  Wikipedia. I couldn't understand this line:       "if the two events are causally connected ("event A causes event B"), the causal order is preserved (i.e., "event A precedes event B") in all frames of reference."     Is this an assumption or a consequence of STR? Please explain.       Note: My question consists of 2 parts this is the 2nd part. Below is a genral version of my previous question question:.   PART 2: Let there be three events $A$,$B$ and $C$ s.t: $C$ is the result of Simultaneous occurrence of $A$ and $B$. In other words $C$ occurs iff $A$ and $B$ are simultaneous. Now as we know in STR any two events separated in space are not simultaneous in different frames. So In some frames $C$ will occur and in some $C$ will not occur which will cause paradox. I tried many thought experiments to make such a paradox but i failed. In all the experiments that i thought i could not break the causality even by breaking the simultaneity because everytime the fact: "all signals move slower than light" preserved the causality.    So why causlity remains preserved always? Is it due to the fact that nothing can move faster than light? Negative values for AICc (corrected Akaike Information Criterion) I have calculated AIC and AICc to compare two general linear mixed models; The AICs are positive with model 1 having a lower AIC than model 2.  However, the values for AICc are both negative (model 1 is still &lt; model 2).  Is it valid to use and compare negative AICc values? Is it possible to instantiate an object at runtime if I only have the DLL name and the class name, without adding a reference to the assembly in the project? The class implements a interface, so once I instantiate the class, I will then cast it to the interface.  Assembly name:     library.dll    Type name:      Company.Project.Classname     EDIT: I dont have the absolute path of the DLL, so Assembly.LoadFile won't work. The DLL might be in the application root, system32, or even loaded in the GAC. How do I profile memory usage in Python? I've recently become interested in algorithms and have begun exploring them by writing a naive implementation and then optimizing it in various ways.  I'm already familiar with the standard Python module for profiling runtime (for most things I've found the timeit magic function in IPython to be sufficient), but I'm also interested in memory usage so I can explore those tradeoffs as well (e.g. the cost of caching a table of previously computed values versus recomputing them as needed). Is there a module that will profile the memory usage of a given function for me? Same e-mail user, different address? I was wondering why using foo.bar@gmail.com works but not foo.bar@outlook.com.  In Gmail, foo.bar@gmail.com and foobar@gmail.com (and any combination of periods in the username) is equivalent.  Is this a hidden feature in Gmail? Should questions include "tags" in their titles? Best way to remove an event handler in jQuery? I have an input type="image". This acts like the cell notes in Microsoft Excel. If someone enters a number into the text box that this input-image is paired with, I setup an event handler for the input-image. Then when the user clicks the image, they get a little popup to add some notes to the data.  My problem is that when a user enters a zero into the text box, I need to disable the input-image's event handler. I have tried the following, but to no avail.  $('#myimage').click(function { return false; }); How can I solve this quantum mechanical "paradox"? Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard deviation of momentum is $0$, but $\sigma_x$ must be finite. So we find that $\sigma_x\sigma_p=0$. Is something wrong with the uncertainty principle? I'm looking for a specific scifi book that I read years ago, I only partially remember the story, and I don't remember the author or the title.  What I remember of the story is:   An alien race picks up a signal from humans that includes instructions on how to make their own humans (genetic instructions). The humans grow up knowing they are created and are taught by the alien race. They are eventually given resources to build a ship, and go looking for their origins. They eventually find the solar system, but nobody answers. They find some stations orbiting earth and find that the station is very old, so old in fact that humans have long been extinct and other creatures have reached local space, and have been looking around the station as an archeological dig. I think they refer to two developed races from earth, but one developed from rats.   If anyone know what story this is, and can point me at it, its been driving me crazy for at least 15 years, and I think it's actually been much longer, since I can't remember when I read it. Prove $\sum_{d \leq x} \mu(d)\left\lfloor \frac xd \right\rfloor = 1 $ Slower download speed compared to Windows on Ubuntu 20.04 $n$ people attend the same meeting, what is the chance that two people share the same birthday? Given the first $b$ birthdays, the probability the next person doesn't share a birthday with any that went before is $(365-b)/365$. The probability that none share the same birthday is the following: $\Pi_{0}^{n-1}\frac{365-b}{365}$. How many people would have to attend a meeting so that there is at least a $50$% chance that two people share a birthday?   So I set $\Pi_{0}^{n-1}\frac{365-b}{365}=.5$ and from there I manipulated some algebra to get $\frac{364!}{(364-n)!365^{n}}=.5\iff (364-n)!365^{n}=364!/.5=.....$   There has to be an easier way of simplifying this. Convert line voltage heating system to use low voltage thermostats I currently have two line voltage ceiling radiant heating systems in my condo each with their own DPST thermostat. I'd like to use low voltage thermostats such as the nest. I found , but it only has 3 wires. Will this work with a system designed to use DPST thermostats? If not, is there something else out there that will allow me to use low voltage thermostats with line voltage heaters? Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$ I can't figure out an algebraic proof for the following identity:  $$\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$$  Combinatorical solution:  We can see that as choosing some from $n$ and the rest of $k$ from $m$, thus $k$ in total.  Or we could just choose $k$ from the union. (1, eval)('this') vs eval('this') in JavaScript?