Steepest descent method and how to find the weighting factor
Optimal step size in gradient descent
Distorted Cabin & Oily Sheen: What is going on in this paragraph? What are the pros and cons of engineered hardwood? Are there any downsides to engineered hardwood? I'm looking to install hardwood in dining room and kitchen areas. $\sqrt[31]{12} +\sqrt[12]{31}$ is irrational Prove that $\sqrt[31]{12} +\sqrt[12]{31}$ is irrational.   I would assume that $\sqrt[31]{12} +\sqrt[12]{31}$ is rational and try to find a contradiction.  However, I don't know where to start. Can someone give me a tip on how to approach this problem? Suppose that G is a group and N &lt; G a normal subgroup. Assume that there is no normal subgroup M &lt; G with N &lt; M. Prove that G/N is simple.  This problem is really throwing me for a loop. The concept of quotient groups and how they relate to simple subgroups is confusing me, and so I am not really sure how to begin. If a simple subgroup's only normal subgroup is itself (and the trivial group), then G/N being simple would be proving that when multiplying the entire subgroup N by an element g for all g in G, that the collection of those sets cannot be broken into smaller normal subgroups? In  answer to the question "why does the moon have the same rotation and revolution periods?", we read:     The mass and speed of rotation of the Earth influence the moon in that some of its rotational energy is actually transferred to the moon. (...) Many of the moons in the solar system have also reached this point of equilibrium. In Jupiter, the moons Amalthea, Thebe, Io, Ganymede, Callista, and Europa, all have identical rotational and revolutionary periods.    My two questions are:   Can we show the mechanics of this quantitatively?  Does the system Earth-Sun experience the same phenomenon, in some measure? Will then the earth slow down its rotation speed until it will show always the same face to the sunlight? In this last case, on which timescale? A  is formed when a raindrop refracts light, but why then does the whole sky not become a huge rainbow when it rains? Would the light not be dispersed into ordinary white light? What causes it to look as if each end is nearly touching the ground? Why "be king", not "be a king"? I've heard people say "be king" (as in "I can't wait to be king") in movies and TV. Why don't they say "be a king"? Which is correct? Let $X_1, X_2, \ldots X_n$ be random variables with mean $\mu$ and variance $\sigma^2$. We define the sample mean $\bar{X} = \sum_{i = 1}^n X_i$.  I am having trouble understanding why the variance of $\bar{X}$ is $\sigma^2 / n$.  Here is what I worked out thus far:  $$\begin{gather} \sigma_\bar{X}^2 = E((\bar{X} - \mu)^2) = E(\bar{X}^2 - 2\bar{X}\mu + \mu^2) = E(\bar{X}^2) - 2\mu E(\bar{X}) + E(\mu^2) = E(\bar{X}^2) - \mu. \end{gather}$$  However, I'm not sure what to do with the $E(\bar{X}^2)$. How do I change the extension of multiple files? I would like to change a file extension from *.txt to *.text. I tried using the basename command, but I'm having trouble on changing more than one file.  Here's my code:  files=`ls -1 *.txt`  for x in $files do     mv $x "`basename $files .txt`.text" done   I'm getting this error:  basename: too many arguments Try basename --help' for more information I want to import graphics into my main input file using the macro \includegraphics. It does not work if the filename contains spaces.   also discusses this subject, but there is no solution there.  My compilation routine is latex->dvips->ps2pdf (because of PSTricks). What are the best ways to improve a site's position in Google? Managing error with GPS routes (theoretical framework?) I'm looking for the appropriate theoretical framework or speciality to help me deal with understanding how to deal with the errors that the GPS system has - especially when dealing with routes.  Fundamentally, I'm looking for the requirements on the data and any algorithms to use to be able to establish the length of a trail. The answer needs to be trustworthy.  A friend of mine was the race director of a race which was billed as 160km but the Garmin watches everybody has makes it more like 190km+. It caused quite some grief at the finish line, let me tell you!  So my friend went back to the course with various GPS devices in order to remap it and the results are interesting.  Using a handheld Garmin Oregon 300 she got 33.7km for one leg. For the same leg on a wrist watch Garmin Forerunner 310xt it came out to 38.3km.  When I got the data from the Oregon it was obvious that it was only recording data every 90 seconds or so. The Forerunner does it every couple of seconds.  When I plotted the data from the Oregon I could see that it got confused by some switchbacks and put a line straight through them and a curve was made a little less.  However, I muse that the difference in the recording frequency is much of the explanation. i.e. by recording every couple of seconds the Forerunner is closer to the real route. However, there will be an amount of error because of the way GPS works. If the points recorded are spread around the real route randomly (because of the error) then the total distance will be larger than the real route. (A wiggle line going either side of a straight line is longer than the straight line).  So, my questions: 1. Are there any techniques I can use on a single dataset to reduce the error in a valid way? 2. Does my theory about the difference in recording frequency hold water? 3. If I have multiple recordings of the same routes are there any valid techniques to combine them to get closer to the real route?  As I say, I don't really know what to search for to find any useful science about this. I'm looking for ways to establish just how long a given piece of trail is and it is very important to people. An extra 30km in a race is an extra 5+ hours we weren't expecting.  As requested here is some sample data:       Thanks for any advice you can give. Are there 'stack' sites for Mac or Windows? There is Ubuntu and Unix/Linux site but is there special 'stack' site for Mac and Windows?  For context, the question I am looking to ask: I accidentally connected a Windows NTFS formatted HDD to a Mac. And the Mac (may be) quick-formatted it. I think that the information is there, but the FAT table is gone. How I can recover the information. How to enable linking floating point library in TurboC? Double SOCKS5 proxy using SSH I was searching for a way to connect to one of my servers who is behind a jumpbox via SSH. I was able to do so by running the following command:  $ ssh -tt ptitpou@jumpbox ssh -tt ptitpou@targetserver   Now, I want to be able to use that server to access webservers on targetserver's network. For that, I followed  and I was able to successfully access the websites. The command I used was:   $ ssh -L 127.0.0.1:9999:localhost:9696 -tt ptitpou@jumpbox ssh -D 9696 -tt ptitpou@targetserver   The question I want to ask is how to use the ssh -o ProxyCommand to command in a slightly cleaner way. I tried to put the second part of the command as the proxy command and I had a successful SSH connection, but I was unable to use the proxy after that.   I've also tried  but the command line hangs after connecting to targetserver.  How can I do that? Am I wrong to try to use ProxyCommand option for this task? Chosing a reference frame in which the Earth is at rest and doesn't rotate How do I disable negative scaling? By default blender allows you to scale past 0 - how do I prevent this?  i.e. it's common in other 3D modelling software to resize a set of vertices against an axis to align them - however this isn't possible when negative scaling is enabled. Possible Duplicate:          I have seen  in SQL. I wonder how would you approach the opposite problem: splitting coma delimited string into rows of data:  Lets say I have tables:  userTypedTags(userID,commaSeparatedTags) 'one entry per user tags(tagID,name)   And want to insert data into table  userTag(userID,tagID) 'multiple entries per user   Inspired by  question  EDIT  Thanks for the answers, actually more then one deserves to be accepted but I can only pick one, and the  with recursions seems pretty clean to me. It works on SQL Server 2005 and above.   For earlier version of SQL Server the solution  can be used.  For working with text data type  will be helpful. Thanks again. I wanted to use my android phone as a proxy server, meaning that I wanted to be able to use the IP on the phone as a proxy, so all request and response are received on the phone and forwarded back to the original requestor. How do I do this? iPad won't turn on after a complete battery drain My iPad mini retina is out of warranty,  I forgot to plug in my iPad after the critical battery warning and it went some minutes following the warning. I was not worried because same thing had happened a few times before and iPad was perfectly okay after charging it. However, this time I remember seeing a flash of blue screen immediately after it went black. Then, I plugged it in an waited for a while and tried starting it. Ever since, it fails to start hanging on the apple logo with white background screen.   I tried to connect to my Mac but nothing showed up in iTunes. I am worried now. Can I troubleshoot this or is it broken and needing repair?