Entire function so that $f\circ f$ don't have fixed points
Entire function problem: translation
I will go to France from 17/12/13 – 19/12/13, then I will come back to London. And again I will go back to Portugal and Spain from 26/12/13 to 03/01/14 which I will stay in Spain for the longest period. However, the Spanish consulate told me that I have to request for the visa from the French consulate.  The point is: Do I need to apply for a visa for a single trip two times (from French and Spanish consulate) or a single visa for multiple time (from French consulate). Below is the text in the file:  Pseudo name=Apple Code=42B state=fault  Pseudo name=Prance Code=43B state=good   I need to grep for "42B" and get the output from the above text like:   Pseudo name=Apple Code=42B state=fault   Does anyone have idea on how to achieve this using grep/awk/sed? BufferedWriter not writing everything to its output file Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$. Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.   I was thinking of showing $A$ is not invertible, meaning it has an eigenvalue of $0$. Since no matter the power you give to $A$, it is still not the identity, you can deduce that at least one eigenvalue is indeed $0$. However this doesn't work if you have different eigenvalues in the Matrix, so I got stuck.  Help will be most appreciated. Why do I get a segmentation fault when writing to a "char *s" initialized with a string literal, but not "char s[]"? I can't use the terminal while gedit command is running I recently installed 12.04. When I try to edit a file with gedit, I can't use the terminal until I close the editing file or I have to open a new terminal. But I think I didn't have this problem with 11.04, however I'm not sure. Is there anyway to avoid this and to use same terminal while editing files. I have hundreds of excel files which are all of the same format (i.e. 4 worksheets per Excel file). I need to combine all the files into 1 all singing and dancing file which must have the same format as the originals (i.e. maintain the four separate worksheets, which are all identically named).  While each file is structured the same, the number of columns (and the heading names) between sheet 1 and 2 (for example) is different. So it can’t be combined into one file with everything in one sheet!  There are two complications:   I need to create an EXTRA column in the merged file (on EACH sheet) to identify the source file (“file name”). The files contain a lot of zero data entries (e.g. 55 rows of useful data followed by hundreds of rows of zeros) which I need to remove from the merged file.   I’ve never used VBA, but everyone has to start somewhere I suppose. So I'm using an app that stores images heavily in the DB. What's your outlook on this? I'm more of a type to store the location in the filesystem, than store it directly in the DB.  What do you think are the pros/cons? Firefox - Websites with custom fonts not displaying Loading a package conditionally The paradox:    We have a circle and there is another circle with smaller radius. They are co-centeric.  If circle make full turn without sliding, both smaller and bigger circle make full turn too. If we assume that the passed road is equal to the circumference of circles. We have got smaller circle's radius is equal to bigger one's.  Unsatisfying Solutions I found:    "Do not assume that smaller circle's circumference is equal to passed road since the surface that contacts to the ground is bigger one. " // Okey but it does not explain the paradox, it explains just what is the wrong assumption (even does not explain why it is a wrong assumption.) It is undeniable that every point on both smaller and bigger circle will contact exactly one and only one point on their path. Therefore we can think that this is a bijective maps and smaller circle is isomorphic to bigger one. (Okey but ....)   Question: What is the true answer? What is wrong with the definition of circumference of a circle and relationship with its taken path. Create a table with LaTeX I need to copy a table from a pdf file to my LaTeX document. I know I have to do it by hand but still don't understand how to create a table with LaTeX. I know it's not possible to install a 32-bit driver in the traditional way, but I really cannot find a 64-bit driver for my memory card reader. Is there anyway I can somehow use this device with a 32-bit driver on a 64-bit Windows 7 installation?  I was thinking there might be a way to run a device in compatibility mode? Possibly even have a 32-bit device layer emulator or something?  I'm interested in any method to get this device up and running. In  as well as on Wikipedia the radial coordinate of the Schwarzschild metric is described as follows:     ...the r co-ordinate is the value you get by dividing the circumference of the circle by 2π.   This circumvents (no pun intended) the problem of talking about the path outwards from the singularity, but what about the circle itself: does it have the length we would measure when flying around it (however this is done) or is it a virtual circle assuming flat space, i.e. no mass at the center. Apparently,   $$ \sum_{n = 0}^\infty \frac{n}{2^n} $$  converges to 2. I'm trying to figure out why. I've tried viewing it as a geometric series, but it's not quite a geometric series since the numerator increases by 1 every term. Intuitive/direct proof that a rectangle partitioned into rectangles each with at least one integer side must itself have an integer side A challenge problem asked to show that if rectangle $R$ with axis-parallel sides is partitioned into finitely many subrectangles $R_1,R_2,\ldots,R_n$ (also with axis-parallel sides), such that each $R_i$ has at least one integer side length, then $R$ must also have at least one integer side length. The only proof I've seen, although simple, is quite unintuitive. Namely you look at the integral  $$ \int_R e^{2 \pi i (x+y)} dx dy $$ and note that the integral is $0$ if and only if $R$ has an integer side length, and then note that by assumption the integral is $0$ over all the $R_i$, hence summing the integral over all $R_i$ gives that the integral is also $0$ over $R$. Can someone give a more direct/intuitive argument that doesn't use voodoo like a complex-valued integral? Shift numbers into a different range I was wondering how can I shift my data that fall between a range lets say [0, 125] to another range like [-128, 128].  Thanks for any help Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$ Establishing a Basis for $F[x]/(f(x))$ Hypothesis:   $f(x) = a_0 + a_1 x + \ldots + a_n x^n \in F[x]$ s.t. $f(x)$ irreducible over field $F$. $deg(f(x)) = n \ge 1$. Let $V = (f(x)) \subset F[x]$.   Goal: Show that $\mathcal{B} = \{1 + V, x + V, x^2 + V, \ldots , x^{n-1} + V\}$ forms a basis for $E = F[x]/V$  Attempt:   Linear Independence: If this set weren't linearly independent, then a non-trivial $b_i \in F$ would satisfy  $$ b_0 + b_1x + \ldots + b_{n-1} x^{n-1} + V = 0 + V $$   But this would then imply that $b_0 + b_1x + \ldots + b_{n-1} x^{n-1}  \in 0 + V$. But this would contradict $V = (f(x))$ since it is impossible that $f(x)\,\,|\,\,b_0 + b_1x + \ldots + b_{n-1} x^{n-1}$ of strictly lower degree.  Now how would I show that this set spans $F[x]/V$? I installed Drush for the first time (so it may be a configuration error) and I'm trying to update to the latest core version of Drupal.  Drush is giving me this error - I'm on an OSX box.  dev5:clientnamedirectory my.name$ drush pm-update projects drupal-7.25 &lt;h1&gt;Additional uncaught exception thrown while handling exception.&lt;/h1&gt;  &lt;h2&gt;Original&lt;/h2&gt;&lt;p&gt;PDOException: SQLSTATE[HY000] [2002] No such file or directory in drupal_get_installed_schema_version() (line 155 of /Users/my.name/Sites/proface/includes/install.inc).&lt;/p&gt;  &lt;h2&gt;Additional&lt;/h2&gt;  &lt;p&gt;PDOException: SQLSTATE[HY000] [2002] No such file or directory in system_list() (line 165 of /Users/my.name/Sites/clientnamedirectory/includes/module.inc).&lt;/p&gt;&lt;hr /&gt;  Drush command terminated abnormally due to an unrecoverable error.