How to embed wireless network drivers in iso file
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Let $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$   Show that $X$ is Hausdorff if and only if $D$ is closed in $X \times X$.   First, I tried to show that $X \times X \setminus D$ is open using the fact that $X \times X$ is Hausdorff (because $X$ is Hausdorff), but I couldn't find an open set that contains a point outside $D$ and is disjoint to it... How do I set up an email server? Why can my keyboard only digest 6 keypresses at a time? When I slam my hand onto my keyboard, only a maximum of 6 keys will be registered, I've tested this for the past few minutes and was unable to get more than 6. Is this the same on all keyboards? If not, what would be the distinguishing factor, If yes: why 6 specifically?  For clarification: I do not have a usecase for this, I am simply curious tar files only, no directories Limits of trig functions How can I customize different nodepart with different textures? My question is how can I customize hatch patterns(grid, vertical line, etc.) for different nodepart in a node?  The following is a failed try.  \documentclass[border=2mm,convert]{standalone} \usepackage{tikz} \usetikzlibrary{shapes.multipart,patterns}  \begin{document} \begin{tikzpicture} \node[rectangle split,rectangle split parts =2,rectangle split part fill={red!30,red!10}, rectangle split part pattern={grid,},draw]{one \nodepart{second}two}; \end{tikzpicture} \end{document} Possible Duplicate:          I was thinking about making a pacman clone, I know there is a similar question here  , but I know i can't use the original art from the game because it belongs to Namco, so if I design a character that has the shape of the slice circle it will look exactly like pacman, maybe if I use green instead of yellow? Also if the game plays like the original pacman, it is wrong?  I just want to make the game as a personal project and and publish it in my site without getting in trouble Looking for the title of a book about alien invasion, mining asteroids and using lasers to defend earth What I remember of this novel/series is that the main character creates solar laser satellites and mines asteroids to create more satellites to defend Earth from aliens. Later on, he uses the hollowed out asteroids as a base and eventually as an armored fortress to repulse the alien fleets. I last remember the main character attempting to hollow out more asteroids to defend and attack the aliens eventually. Beamer: PDF presentation viewer to play embedded videos and show elapsed time Let $A$ be an $n \times n$ matrix with real enteries. Define $\langle x,y\rangle_A = \langle Ax,Ay\rangle, \quad x,y \in \mathbb R^n$ , where $\langle,\rangle$ is a standard inner product on $\mathbb R^n$. Then  $\langle x,y\rangle_A$ is an inner product iff  1)  $\ker A = \{0\}$.  2) $\operatorname{rank} A= n$.  3) all eigenvalues of $A$ are positive.  4) all eigen value of $A$ are non negative.  Clearly if $\ker A \neq \{0\}$, then there exist $x \neq 0$ such that $Ax =0$, then $\langle Ax, Ax\rangle_A = 0$, then $\langle ,\rangle_A$ is not inner product, so $\ker A = \{0\}$, thus rank of $A$ is $n$.  I am unable to check the 3) and 4) option. Please help to check the other option. Thank you Changing the keyboard layout turns off the numlock I have already read        and many others   But I still have the following problem:   On one hand I've been told that if pure rotation takes place then the object goes on forever. This must imply no frictional force in any form acting on the body. On the second hand I've been told that during pure rotation(no external forces like wind) on a plane surface friction acts opposite to velocity of center of mass (accompanied by change of normal) and slows it down.     Both seem logical enough: The point of contact doesn't slip therefore no friction is required; So no retarding force and it must go on. Things don't go on forever; Friction must be present to slow it down.    So, which hand is correct? Or is there a third hand altogether? Transforming the dummy values to be able to take logs I have a panel data model with double-log functional form. I have 4 variables, one of which is a dummy. What is the best way to transform the values of 0 for my dummy to be able to take natural logs (since you can't take logs from zero)? I have found 2 options so far, but I dont know which is the best (or perhaps there is a 3rd option).  1) Transform all the values of 0 into a very small value (0.00000000001) and then take the logs. I'm not sure this wouldn't still change the outcome of my model quite a bit. 2) Change the values of 0 into 1 and the dummy values of 1 into e (the base of natural logarithm). The log of this newly defined dummy then takes on the values of zero and one and the interpretation of my betas would remain the same. How does Java's PreparedStatement work? Why shouldn't I prefix my fields? I've never been a fan of Hungarian notation, I've always found it pretty useless unless you're doing some really low level programming, but in every C++ project I've worked on some kind of Hungarian notation policy was enforced, and with it the use of some 'not-really-Hungarian' prefixes as m_ for fields, s_ for statics, g_ for globals and so on.  Soon I realized how much useless it was in C# and gradually started to drop all of my old habits... but the 'm_' thing. I still use the m_ prefix on private fields because I really find it very useful to being able to distinguish between parameters, locals and fields.  The  says I shouldn't, but it does not say why (the way e.g. Google's conventions generally tend to rationalize their prescriptions).  Are there reasons why I shouldn't or is it only a matter of style. If it is the latter, are prefixes generally considered a bad style and can I expect negative reactions from other people working on the codebase? Converting a list of tuples into a dict I have a list of tuples like this:  [ ('a', 1), ('a', 2), ('a', 3), ('b', 1), ('b', 2), ('c', 1), ]   I want to iterate through this keying by the first item, so, for example, I could print something like this:  a 1 2 3 b 1 2 c 1   How would I go about doing this without keeping an item to track whether the first item is the same as I loop around the tuples? This feels rather messy (plus I have to sort the list to start with)... get exact file create time windows 7 I'm trying to figure out exactly when I created a file. Windows 7 thinks I don't know how to subtract two times, and tells me it was created "1 hour ago." I need a little more detail than this, but I can't seem to find a setting to toggle this "feature" off.  Example below: I recently saw a question about a problem (or possible bug) with some product on Stack Overflow. At first, I wanted to suggest that the asker post his question to that product's support forum.  When searching for the URL of that forum, I noticed that the product developer closed its support forums and now advises users to post all their questions on Stack Overflow instead.  Is this within the intended use cases of Stack Overflow, or is this abuse? Say there are $m+n$ elements split into two groups ($m$ and $n$). The variance of the first group is $\sigma_m^2$ and the variance of the second group is $\sigma^2_n$. The elements themselves are assumed to be unknown but I know the means $\mu_m$ and $\mu_n$.  Is there a way to calculate the combined variance $\sigma^2_{(m+n)}$?   The variance doesn't have to be unbiased so denominator is $(m+n)$ and not $(m+n-1)$. Can 12 teams in 6 disciplines play 6 rounds without repetition?