Prove all zeros of a polynomial lie in $\{|z| > 1 \}$
Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.
How to change Gnome-Terminal title? I have several instances of terminals running in my working environment, what I would like is to set a specific title for each one, in order to have a clear idea what purpose the specific terminal serves i.e. Apache, editing_ini, postgres etc...  Of course from the command line. How to create a matrix with 20 columns in latex The code below works,  but when I add 10 more columns, it does not. So, how can I add ten more columns to the matrix below?  \documentclass{article} \usepackage{amsmath} \begin{document}  \begin{equation} \begin{bmatrix}  1 &amp; 0 &amp; 0 &amp; 0  &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 1 &amp; 0  \end{bmatrix} \end{equation}  \end{document} How can I type special symbols on my Android device like ☺ or ♥ as a regular character? Classic ASP SQL Injection Protection What is a strong way to protect against sql injection for a classic asp app?  FYI I am using it with an access DB.  (I didnt write the app) Good and easy way to share files on local machine I would like to have a directory that has following properties:    Many users can copy files into it  These files can be deleted/changed by these users (user A can delete/modify file that was copied into this directory)    it cant be done using normal file permissions (because permissions are retained on copy).  Here is what I found on the net:        Some use cases:    Sharing music on local machine  Simple git repository sharing (just make a bare repository writeable to many people) --- i know that there are solutions like gitosis Allow many developers to modify test instance of php app without giving them root (i guess they would copy files) --- I'm leading a team of nonprofit junior developers and I need to keep that one simple!    EDIT  AFAIK setting SGID bit is not enugh, it only affects newly created files --- and basic workflow for these use cases ivnolves copying and other operations (which cleave file's gid unchanged) How are House points tabulated/tracked? Why are the longer edges being beveled more? Let's have 2 numbers, N and K, where K divides N. The number of K-combinations from a given set S of N elements is a well known formula. Let's concatenate N/K groups (resulting in N elements) such as the resulting set is N. How many possibilities are there, i.e. what's the formula?  For instance:    N=4, K=2, C(4, 2) = 6 {1,2},{1,3},{1,4},{2,3},{2,4},{3,4}   The 3 possibilities are:     {1,2},{3,4}   {1,3},{2,4}   {1,4},{2,3}   I generated these combinations and I think the number goes like this:  (4, 2): 3 (6, 3): 10 (6, 2): 15 (10, 5): 126 (9, 3): 280 (10, 2): 945 (14, 7): 1716 (12, 4): 5775 (15, 5): 126126 (15, 3): 1401400   Apparently, the result always divides with (N-1). SQL Server Query Plan Hash Collision I'm wondering if anyone can shed light on a worry of mine that a query_plan_hash collision could cause a query to be executed as an entirely different query.  The hash is a 16 digit Hex that sp_help sys.dm_exec_query_stats says is a binary. Therefore it's only a 64 bit hash, and a collision seems very probable (considering SHA1 [160 bit] was just verified to have had collisions).  Would the plan_hash and the query_plan_hash both have to collide for this (query to be executed as an entirely different query) to happen?  I'm also curious if there is a setting somewhere in SQL Server that will allow us to change this hash to SHA2-512 (to reduce the possibility of a collision). Our data is very important.  I searched high and low via Google and Stack Exchange forums. RESTful Authentication What does RESTful Authentication mean and how does it work?  I can't find a good overview on Google.  My only understanding is that you pass the session key (remeberal) in the URL, but this could be horribly wrong. As someone who doesn't play Team Fortress 2, I occasionally get people asking me to trade, but I have no idea what's a "fair" price for these items. I don't really get this whole trading thing (I've seen people ask for "63 buds", I have zero idea what that means), but I don't want to get ripped off.   Some recent  examples would be:        How can I figure out how much an item is worth? What "lingo" do I need to know in order to trade? How to connect to device via SSH over direct ethernet connection How to prove this inequality $ x + \frac{1}{x} \geq 2 $ I was asked to prove that:   $$x + \frac{1}{x}\geqslant 2$$  for all values of $ x &gt; 0 $  I tried substituting random numbers into $x$ and I did get the answer greater than $2$. But I have a feeling that this is an unprofessional way of proving this. So how do I prove this inequality? Vandermonde identity corollary $\sum_{v=0}^{n}\frac{(2n)!}{(v!)^2(n-v)!^2}={2n \choose n}^2$ Why are all the textures in my file pink? How to compute $\lim\limits_{n\rightarrow \infty} \{(2+\sqrt{3})^{n}\}$, where $\{x\}$ is the fractional part of $x$? I've stumbled upon the following problem:  $$\lim_{n\rightarrow \infty} \{(2+\sqrt{3})^{n}\}$$  where "{}" notates the fractional part.  I've never studied this kind of problem, there exists any reference that I could read about this type of problem? Problem  For what natural numbers is $n^3 &lt; 2^n$?  Attempt @ Solution   For $n=1$, $1 &lt; 2$ Suppose $n^3 &lt; 2^n$ for some $n = k \ge 1$ It looks like the inequality is true for $n = 0$, $n = 1$ and $n\ge10$ But, how can I prove this through induction? What happens when many neurons have same weights? Does it make any sense to have two (or more) neurons in a neural network with the same weights? (intuitively it makes no sense, since all the neurons would behave the same way).   Please consider both the input and hidden layers. What if the weights are equal 0? How did Newton discover his second law? I've always assumed/been told that Newton's 2nd law is an empirical law — it must be discovered by experiment. If this is the case, what experiments did Newton do to discover this? Is it related to his studies of the motion of the moon and earth? Was he able to analyze this data to see that the masses were inversely related to the acceleration, if we assume that the force the moon on the earth is equal to the force the earth exerts on the moon?   According to , the  reads:     Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.   Translated as:      Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.   My question is how did Newton come to this conclusion? I get that he knew from  the idea of inertia, but this doesn't instantly tell us that the change in momentum must be proportional to the net force. Did Newton just assume this, or was there some experiment he performed to tell him this? Converting HTML to plain text in PHP for e-mail