ASCII characters in an image steganography
Steganography - How many bytes of information can you hide in a $1024 \times 768$ photo?
Yesterday, my laptop caught a virus which caused massive damage. Since them, I have been trying to recover important files before reformatting my computer, a task the virus has not made easy.   Restoration points predating the attack have been deleted.  Most of my folders show empty.  My Start menu is essentially empty, with the exception of Trillian and Mirror's Edge. The same goes for my Desktop, which only has programs which were installed after the attack.  Searching for files through my computer is pretty much useless, as it only rarely brings up anything. I suspect most of my files have not been deleted. While my folders show empty, uTorrent still does display them and I can open them from here. Unfortunately, when I select Open Containing Folder, the folder still shows as completely empty even if I'm currently watching a video from that very folder. Further adding evidence to the not-deleted-just-missing theory, the data recovery software I'm using (Restoration) cannot find only find an handful of the missing files.   If they were deleted, I could do a forensic recovery to get them back but since they're probably still somewhere on my computer, just out out of my reach, I can't find them.   Under those circumstances, is there a way I can recover those files? Android 4.1: How to check notifications are disabled for the application? So I have been extruding a cube to make a low poly banana and when I go from edit to object mode half the edges don't appear as well as half is dark.      I tried looking for an solution couldn't find one and its making me feel like I am doing something wrong so I decided to come here. Prove a assertion concerning Lebesgue space Let $f_n \in L^1$ such that $f_n\rightrightarrows f$. Then I want to conclude that If $\mu(X)&lt;\infty,$ then $f\in L^1$ and $\int f_n\to\int f$, so I want to make use of the Dominated convergence theorem, the thing is that I don't know which would be my dominating function.  I was trying to figure out if the measure could play that role, but after thinking a little bit I have realize that the measure doesn't have to be bigger than the absolute value of the functions of the sequence.  Another thing I was thinking of, is to apply Fatou's lemma, but I can't ensure that my functions are positive.  So, Can someone help me to prove this theorem please ?  Thanks a lot in advance :).    NOTE: I think this theorem is taken from Folland's Real analysis, modern techniques, and their aplications 2nd Edition :), This is to have all the definitions so we can talk the same language as in the book (this is, same notation and theorems or machinery) Was or is? Confusion My question is for example when closing a call with a customer which is the proper way? "Once again my was (name), have a great day!" or "Once again my is (name), have a great day!"   need this cleared up lol MySQL Seems to be crashing quite often, I'd say every hour or so.   The only thing running on this server that is using MySQL is a Drupal installation that I'm working on, there's only one person that's using it and it literally has around three pages - from what I can gather this seems to be a memory issue with innoDB? I'm not great at this stuff so I'm unsure.  Any guidance? Here's the relevant parts from my error.log  140216 14:20:01 [Note] Plugin 'FEDERATED' is disabled. 140216 14:20:01 InnoDB: The InnoDB memory heap is disabled 140216 14:20:01 InnoDB: Mutexes and rw_locks use GCC atomic builtins 140216 14:20:01 InnoDB: Compressed tables use zlib 1.2.3.4 140216 14:20:01 InnoDB: Initializing buffer pool, size = 128.0M InnoDB: mmap(135987200 bytes) failed; errno 12 140216 14:20:01 InnoDB: Completed initialization of buffer pool 140216 14:20:01 InnoDB: Fatal error: cannot allocate memory for the buffer pool 140216 14:20:01 [ERROR] Plugin 'InnoDB' init function returned error. 140216 14:20:01 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed. 140216 14:20:01 [ERROR] Unknown/unsupported storage engine: InnoDB 140216 14:20:01 [ERROR] Aborting  140216 14:20:01 [Note] /usr/sbin/mysqld: Shutdown complete  140216 14:20:02 [Note] Plugin 'FEDERATED' is disabled. 140216 14:20:02 InnoDB: The InnoDB memory heap is disabled 140216 14:20:02 InnoDB: Mutexes and rw_locks use GCC atomic builtins 140216 14:20:02 InnoDB: Compressed tables use zlib 1.2.3.4 140216 14:20:02 InnoDB: Initializing buffer pool, size = 128.0M InnoDB: mmap(135987200 bytes) failed; errno 12 140216 14:20:02 InnoDB: Completed initialization of buffer pool 140216 14:20:02 InnoDB: Fatal error: cannot allocate memory for the buffer pool 140216 14:20:02 [ERROR] Plugin 'InnoDB' init function returned error. 140216 14:20:02 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed. 140216 14:20:02 [ERROR] Unknown/unsupported storage engine: InnoDB 140216 14:20:02 [ERROR] Aborting  140216 14:20:02 [Note] /usr/sbin/mysqld: Shutdown complete   EDIT The server is the lowest-spec DigitalOcean Droplet with 512MB RAM. This particular Droplet is running NodeJS, MySQL and Apache. There's a low-traffic static site, a Ghost blog and this Drupal site I'm developing.   Should I just upgrade the RAM, or is there something I can do to fix this? Find the smallest integer $n$ greater than $1$ such that the last $3$ digits of $n^2$ are the same as the last $3$ digits of $n$. Find the smallest integer $n$ greater than $1$ such that the last $3$ digits of $n^2$ are the same as the last $3$ digits of $n$.  So far I've got $n^2 = 1000k + n$ which means $n^2 ≡ n \mod 1000$. I  don't know how to proceed since 1000 seems to be a bit high. I know there is something wrong with this but I don't know where. It's some kind of a math fallacy and it is driving me crazy. Here it is: $$-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1?$$ How to solve the equation $\phi(n) = k$? Let $\phi(n) $ is the numbers of number that are relatively prime to n.   Then, how could we solve the equation $\phi(n) = k, k &gt; 0?$   For example:    $\phi(n) = 8 $  I can use computer program to check all numbers that are relatively prime to $n$, but I think there must be an easier way to approach this problem.    Base on this formula: $$\prod_{i=0}^{k} p_{i}a^{a_i} $$ The only thing I can see is n must not have a prime factor > 9, otherwise $\phi(n) &gt; 8 $. I really don't know where to start :( ? A hint would be greatly appreciated. Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials Suppose that $$Q(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0} $$and $$P(x)=b_{m}x^{m}+b_{m-1}x^{m-1}+\cdots+b_{1}x+b_{0}.$$ How do I find $$\lim_{x\rightarrow\infty}\frac{Q(x)}{P(x)}$$ and what does the sequence $$\frac{Q(k)}{P(k)}$$ converge to?  For example, how would I find what the sequence $$\frac{8k^2+2k-100}{3k^2+2k+1}$$ converges to?  Or what is $$\lim_{x\rightarrow\infty}\frac{3x+5}{-2x+9}?$$   This is being asked in an effort to cut down on duplicates, see here: Coping with  duplicate questions.  and here: . How do I create silhouettes in a studio environment? The trick to creating silhouettes in the field, as far as I know, is to use spot-metering and to expose for the background. However, this is a bit more difficult in a studio environment. What is the key to creating "artificial" silhouettes?  One solution that I'm considering is placing a bright flash directly behind the subject - would that work? Coordinate system for accurately calculating areas of polygons that cross UTM Zones? I have multiple polygons, all located offshore around the UK. I am trying to calculate the areas of these polygons in square kilometres, without splitting them by UTM zone.  Is it possible to do this accurately? I have been using World Mercator, but there are big distortions at this scale. If the polygons were limited to the east coast, say, I would use UTM31N. However, as they are all over the UK waters, I am unsure what to use.  Is there a coordinate system that covers this area? British National Grid does not extend far enough out to sea to be of use. Can you create images like this:    when you have something like  0 = green (#54ff00) 1 = white (#ffffff) 2 = red   (#ff0000) 3 = blue  (#0048ff)  Image (Python list of integers defined above): [[2,0,0,0,0,0,0],  [0,3,0,0,0,0,0],  [0,3,2,1,1,0,0],  [0,3,2,2,2,1,1],  [0,3,2,0,0,1,0],  [0,0,0,0,0,1,0],  [0,0,0,0,0,1,0]]   with TikZ?  How far I got  The following MWE defines all colors, produces a grid of the correct size (though the size is determined by hand):  \documentclass[varwidth=true, border=2pt]{standalone} \usepackage{tikz} \usepackage{xcolor}  \begin{document}     \newcommand\n{7}     \definecolor{green}{HTML}{54FF00}     \definecolor{wite}{HTML}{FFFFFF}     \definecolor{red}{HTML}{FF0000}     \definecolor{blue}{HTML}{0048FF}     \begin{tikzpicture}         \foreach \x in {1,...,\n}{             \foreach \y in {1,...,\n}{                 \begin{scope}[shift={(\x,\y)}]                   \draw [fill=green] (0,0) rectangle (1,1);                 \end{scope}             }         }     \end{tikzpicture} \end{document}   Of course, I could simpy make a lot of adjusted                   \begin{scope}[shift={(\x,\y)}]                   \draw [fill=green] (0,0) rectangle (1,1);                 \end{scope}   but I've wondered if this can (with reasonable effort) be done in TikZ / LaTeX.  My problem is giving TikZ the color array. I don't have any idea how to do this. I only know two types of looks in TikZ:  \foreach \x in {0,1,2,3,4,5}{...} \foreach \number in {1,...,\n}{...}   I have never seen a nested over a 2D-array. All I have seen so far were 1D-Arrays of tuples (with fixed tuple size). How to break multi digit number into separate digits in VHDL? I found the method .But I do not know how to perform this in VHDL. Let a fixed point number (12 downto -19) like 3456.478396 I need break this number entirely into separate numbers 3456.478396 --> 3,  4, 5,  6,  (dot) ,  4,  7,  8,  3,  9,  6...  into 11 integer type variables. How to perform this in VHDL?  signal example : sfixed(4 downto -4); --'example' contains 9.75 then it is storage as "01001.1100". --simply example ="10011100". --10011100 --&gt; integer 156   How to get back original 9.75 number from 156 to separate into single digits?  I USED,  library ieee; library ieee_proposed; use ieee.std_logic_1164.all; use ieee.numeric_std.all; use ieee_proposed.float_pkg.ALL; use ieee_proposed.fixed_pkg.ALL; use ieee_proposed.fixed_float_types.ALL; Neutrino project in Tamil-Nadu India In , the Indian government is going to start a neutrino project.  Questions:   Is it harmful for people who stay there?   Will this project affect any living beings? Does it cause any pollution? In comments, moderators have their diamonds in the OP rectangle:        And in the review (suggested edits), mods have their diamonds outside the blue OP background highlight rectangle:        Of course, it Doesn't Really Matter At All, but it is a small discrepancy (I am not saying that in the review, OP rectangles have a bigger padding). Prove that $\sum^{n}_{r=0}(-1)^r\cdot \large\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{3!}{2(n+3)}$ Why is the empty set considered an interval? This is a nice problem on series convergence that I recently stumbled upon. Given a non-negative sequence of real numbers $(a_n)$ such that $$\sum_{n=1}^\infty a_n &lt; \infty,$$ show that there exists a non-decreasing sequence of non-negative numbers $b_n$ such that $$b_n \to \infty \quad\text{ and } \quad \sum_{n=1}^\infty a_n b_n &lt; \infty.$$ In other words, for every convergent series with non-negative terms, there is another convergent series with "substantially larger" terms.  I have a solution (see below), but maybe someone else has a different, simpler, and/or more elegant solution. Short story about a man stranded on a red planet with a sentient hand as his friend I remember reading a short story 10 to 15 years ago about a man stranded alone on a red planet, where nothing would be green, and so he would miss that color. There was a sentient hand to keep him company, and it talked to him. I don't remember if the hand was a native life form or his own hallucination.  The story was not very old at that time, so it may have been written in the late 90s or 00s.