Understanding PDO prepared statements to insert data in a database
How can I prevent SQL injection in PHP?
Hi I don't know how to show that $\langle 2,x \rangle$ is not principal and the definition of a principal ideal is unclear to me. I need help on this, please.   The ring that I am talking about is $\mathbb{Z}[x]$ so $\langle 2,x \rangle$ refers to $2g(x) + xf(x)$ where $g(x)$, $f(x)$ belongs to $\mathbb{Z}[x]$. In class we've seen that $a$ (the weights) must satisfy $$X^T (y-Xa) =0$$  Here $X$ is a $(n\times d)$ matrix (so we have $n$ samples in $\mathbb R^d$)  let's denote the residuals $r = y-Xa$. In our class notes, it is written that     The normal equations require the residuals to be orthogonal to each of the columns of $X$.   Why?     Therefore, the solution of the linear regression is a projection of $y$ onto the subspace spanned by $v_1 , \ldots , v_d$ (the columns of $X$)   Can you please explain this? Given a polynomial $f(x)$ with integral coefficients and $f(x) = 37$ has 5 distinct integral roots, find the number of integral roots of $f(x) = 41$?  My Approach: Say $f(x) = (x-r_1)(x-r_2)(x-r_3)(x-r_4)(x-r_5)g(x) + 37$, where $r_i$ are the distinct integers.   Now for $f(x) = 41$ we have $(x-r_1)(x-r_2)(x-r_3)(x-r_4)(x-r_5)g(x) = 4$, so the factors can be $\pm 1, \pm2$ or $\pm 4$. Given $r_i$ are distinct at most two of them will give $\pm1$, then there can be both of $\pm 2$ or one of $\pm 4$. This is where I get lost, since even if I use all of $\pm1, \pm2$, I will be still be left with one $x-r_i$ factor. What about that? Does it matter that 37 and 41 are primes, or is it just a coincidence?  Thanks in advance. I would like to say something like     The boy, Adam's, favorite toy was a bike.   What is the proper way to say this? Add asterisk after labels in enumerate I would like to add an asterisk after certain labels in the enumerate environment. So for example  \documentclass{article} \begin{document}  \begin{enumerate}     \item Kuttel     \item* Daddeldu \end{enumerate}  \end{document}   but without the space between 2. und *. At  I've read that being $\sin(x)=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)!}x^{2n+1}$ by using  we get $\sin'(x)=\sum_{n=0}^{\infty}(2n+1) \frac{(-1)^n}{(2n+1)!}x^{2n}=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n)!}x^{2n}=\cos(x)$ but the page  says that if $f(x)=\sum_{n=0}^{\infty}c_n(x-a)^n$ then inside the radius of convergence of the power series we have $f'(x)=\sum_{n=1}^{\infty}nc_n(x-a)^{n-1}$ so shouldn't it be $\sin'(x)=\sum_{n=1}^{\infty}(2n+1)\frac{(-1)^n}{(2n+1)!}x^{2n+1-1}=\sum_{n=1}^{\infty}\frac{(-1)^n}{(2n)!}x^{2n}$?  Now I understand that this last result has a missing term due to the index of the series being $1$ and not $0$ but being the $1$ mandatory because of the above theorem and since trying to shift index doesn't help (we get $\sin'(x)=\sum_{n=0}^{\infty}\frac{(-1)^{n+1}}{(2n+2)!}x^{2n+2}$) how can the result that ProofWiki shows be rigorously justified?   (I mean, I think we can't just say "oh, there's a missing term!" after having applied the theorem and magically shift the index of the series to obtain the desired result) I want to digitize my old family albums using a scanner and there are lots of photos in them. Thus far, my method has been to scan 4 images at a time and then manually cropping them in a simple editor like Picasa or Windows Live Photo Gallery. This has been pretty time consuming as each scan is followed by 4 crop operations. Scanning each image individually would possibly be even more time consuming.  Is there any software or simple plugin (preferably free) that does this job? The best solution I have found is in , but that's an overkill. Is there a similar feature for one of the free photo editors like Paint.NET or GIMP? In the Linux system, we can use bellow command to enable packets forwarding:  ~ # sysctl net.ipv4.ip_forward=1 net.ipv4.ip_forward = 1   but how can I realize the same function in Windows?  I use Windows Server 2008 R2. Does text in brackets invoke the "an" vs. "a" rule? Drawing a 3D cylinder, and a circle shape on the x---y plane I'm trying to draw a cylinder on the three dimensional space, and I also want its projection on the x--y plane. I found the first answer  to be very useful. I just copy-paste it to my document, and modify it as follows (the modifications are only inside the \begin{tikzpicture} tags):   \documentclass[parskip]{scrartcl} \usepackage[margin=15mm]{geometry} \usepackage{tikz}  \pgfmathsetmacro{\xdeg}{30} \pgfmathsetmacro{\xx}{cos(\xdeg)} \pgfmathsetmacro{\xy}{sin(\xdeg)}  \pgfmathsetmacro{\ydeg}{120} \pgfmathsetmacro{\yx}{cos(\ydeg)} \pgfmathsetmacro{\yy}{sin(\ydeg)}  \pgfmathsetmacro{\zdeg}{80} \pgfmathsetmacro{\zx}{cos(\zdeg)} \pgfmathsetmacro{\zy}{sin(\zdeg)}  \newcommand{\tdcyl}[5]{% origin x, origin y, origin z, radius, height     \path (1,0,0);     \pgfgetlastxy{\cylxx}{\cylxy}     \path (0,1,0);     \pgfgetlastxy{\cylyx}{\cylyy}     \path (0,0,1);     \pgfgetlastxy{\cylzx}{\cylzy}     \pgfmathsetmacro{\cylt}{(\cylzy * \cylyx - \cylzx * \cylyy)/ (\cylzy * \cylxx - \cylzx * \cylxy)}     \pgfmathsetmacro{\ang}{atan(\cylt)}     \pgfmathsetmacro{\ct}{1/sqrt(1 + (\cylt)^2)}     \pgfmathsetmacro{\st}{\cylt * \ct}     \filldraw[fill=white] (#4*\ct+#1,#4*\st+#2,#3) -- ++(0,0,#5) arc[start angle=\ang,delta angle=-180,radius=#4] -- ++(0,0,-#5) arc[start angle=\ang+180,delta angle=180,radius=#4];     \filldraw[fill=white] (#1,#2,#3+#5) circle[radius=#4]; }       \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h         \tdcyl{0}{0}{0}{1}{3} % x y z   r h           \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}     \end{document}   I added another cylinder and tweaked the positions to fit what I need. This produces the following:      Which is almost what I want, except that I want to see the projection of that cylinder on the x--y plane, but unfortunately, the top cylinder hides the full circle. When I disable the top cylinder:      \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h            \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}   Now the projection is shown again:   But the top cylinder is missing...  How can I make the top cylinder transparent, or, alternatively, and even better; how do I create one long cylinder and emphasize its projection on the x--y plane?   BTW, what determines the position of the labels x,y,z in the above code? I want to reposition them so they won't overlap with the axis. Thanks in advanced! Why do popular but not ideal questions keep being closed? I notice a really worrying trend of some really popular questions being closed and eventually deleted. Some of them became legends already, like this one  ? Yes, it does not fit the format ideally, but what is point of obeying the letter of the law to such extent that it becomes ridiculous? Ok, closing is fine if community leaders became so pedantic, but why go so far as to even delete it? At this point it looks like burning old pictures just because you don't like them.  Update: Summary  For now I heard only two clear arguments:   Those questions pollute search results.  Those questions don't play well with enforcing question and answer standards.   Both of that statements are easily verifiable and to my experience are just false. How to specifically use ntfsundelete to recover directory This is a followup on my original post  which may be deleted in the future.  In the process of backing up my audio books, I "permanently" removed a folder (with subfolders) that I had already exclusively moved to that drive. It's path is /media/gratis/Seagate Expansion Drive/Audiobooks/Jason Dark. The sole folder in that should be called John Sinclair; but I'm not sure about that.  Which tool offers the best chances to recover those files? I haven't written plenty on that drive afterwards; so I hope for the best. It's not that other methods failed; I just cant get my head around what to do and I want to be cautious. It's a NTFS Drive.  According to testdisk it has an "EFI GPT" Partition table.  Disk /dev/sdb - 5000 GB / 4657 GiB - CHS 608001 255 63, sector size=512 - Seagate Expansion Desk, FW:9401   Information According to "Disks" (Ubuntu Standard Software):  NTFS; GUID Partition Table; [...] Partition Type: Microsoft Reserved   Attempt 1: First off, ntfsprogs seems to no longer be in repos (those mentioned by another user); but it is already installed on my machine so no problems there. I always get the error:     Access is denied because the NTFS volume is already exclusively opened. The volume may be already mounted, or another software may use it which could be identified for example by the help of the 'fuser' command. You can use force option to avoid this check, but this is not recommended and may lead to data corruption.   Although I only just plugged it in and even quit Nautilus by force (nautilus -q).   Therefore, I ran sudo ntfsundelete /dev/sdb2 -f. That gave me a list of a bunch of files, 205013 to be exact. Now, what I want is the content of the directory .../Audiobooks/Jason\ Dark/ to be restored. What do I have to do? It's contents are .m4b &amp; .opus files and folders, of course. How can I use the subdivision surface modifier to create more high poly meshes without ruining sharp edges? For example this mesh  The sphere should be subdivided but the rim of the cylinder should stay the same because it is a sharp edge. This is the result of the subdevision  How can I get sharp edges to not be affected by the sub surf mod? What 70s (60s?) TV show / TV movie had a generation ship whose inhabitants did not know they were on a spaceship? I have the vaguest memory of a TV show (maybe a BBC import?) in which the protagonists were moving through the sections of a massive generation ship whose inhabitants had forgotten that they were on a spaceship... I know there was an RPG with the same plot (which, after all, is a pretty great blank slate) but I definitely feel I saw this on a static-filled 13" B&amp;W TV back in the day... I need help identyfying this movie I once saw late night on TNT, late 90s or early 2000s.  I don't have very clear recollection about it. The movie was very strange. It all took place in a single room of a spaceship or an escape pod that had lost power. A woman and a man, or several men, were stuck in a ship or a spacepod that was somehow damaged or didn't have power.   The movie was entirely made of the dialogs between the woman and the man (or men). They would talk about what was happening outside, how to contact help, about their lives. During their conversation details about the world around them emerge. In this movie people have colonized the solar system but not moved outside it, and there is some sort of a war.  Other things I remember are that it was dark in that room. I think they used only a lightbulb or even direct starlight and sunlight (if they were far away from the sun), because there was no power. Also it was getting colder, becaus the ship's heating system was not functioning, and so it was losing its heat. The people would constantly complain about how cold it's getting. I think that the woman was the captain of the ship. She would sometimes go to the control cabin and try to do something to help their situation, either restore power or contact someone so they can be rescued.  What impressed me about it was how they managed to make it realistic. Because the actors would talk and act like it was all real, it made it somehow feel very realistic to me as well.  That's about it as far as I remember. Hope someone has watched this movie and can tell me what it is.  Update  I want to add a few more details about the movie. While I watched it in the late 90s/early 2000s the movie looked much older. It looked like a vintage B-Movie made in the style of the 70s or 80s. In particular the decor looked more like Alien 1 or Cosmos 1999.   I just watched the firefly episode and it can't be it. It has too much action, and the atmosphere is not dark enough. Does this polynomial evaluate to prime number whenever $x$ is a natural number? Short story or novel from the 1970s or before about two warring alien tribes A "non-believer" of C# was asking me what the purpose to extension methods was. I explained that you could then add new methods to objects that were already defined, especially when you don't own/control the source to the original object.  He brought up "Why not just add a method to your own class?" We've been going round and round (in a good way). My general response is that it is another tool in the toolbelt, and his response is it is a useless waste of a tool... but I thought I'd get a more "enlightened" answer.  What are some scenarios that you've used extension methods that you couldn't have (or shouldn't have) used a method added on to your own class? “All you have to do is read” vs. “All you have to do is to read” Remote Desktop Session Black after Minimize PROBLEM: When I minimize a remote desktop session and restore it, the remote desktop screen shows up black. This only happens when connecting to a particular computer.   DETAILS: If I start clicking around in the black area, portions of the screen will start redrawing and showing up correctly. For example, if I leave a window open in the remote session and click where that window is located on the remote computer, then that window--and only that window--will redraw, and sometimes a portion of that window won't redraw (usually the toolbar).  And to clarify--the window only has to be minimized momentarily, so it doesn't seem to be a timeout issue. Clicking or typing in the remote session still causes the remote computer to respond appropriately. Disconnecting from the session and reconnecting restores the whole screen image, as does clicking all over the place in the black image (causing each section to redraw).  CONFIGURATION: This problem only happens for me when connecting to a particular computer (a W2K Server box configured to allow remote administration) and only with certain client computers. I've tried 7 different client computers with various versions of Remote Desktop (the OSes were: Win2K, Server 2003, Server 2008, Windows 7 RC, 3 XP) and two of them exhibit the problem (one is one of the XP boxes and the other is Windows 7). Those same computers can RDP to other computers without problem.  RESOLUTION ATTEMPTS: I have tried the following:   Disable the LOCAL screen saver as mentioned on  Turned off bitmap caching in the client, as mentioned on many forums. Updated to version 6.1 of the remote desktop client Using mRemote (I doubted this would work since it uses MS's code for connecting to RDP servers) Turning off all video acceleration.   QUESTION: Any ideas on what is causing this?