What value should be used for scale while calculating slope percent in QGIS?    Some documents suggest is as 111120 and some as 365130.  I am using ESPG 4326 projection and do I need to convert this value to some other value using lat like given in this link:
I used an SRTM DEM to create a hillshade in QGIS 2.2.0. However, the resultant hillshade seems to be vertically exaggerated. Also, changing the settings for scale and z-factor does not have any effect on the resultant hillshade. I have tried both options in QGIS, Analysis-> DEM (Terrain models) and Terrain analysis -> Hillshade. Both methods gave the same results.  Is this an isolated incident, a bug, or am I missing something?
Absolutely continuity and Lipschitz-like continuity I'm trying to figure out if the following is true or false:  Let $\mu$ and $\nu$ be finite measures on Borel subsets of $[0,1]$,and $\nu \ll \mu$ ($\nu$ is absolutely cts with respect to $\mu$). Does there exist always a $C \in \mathbb{R}$ such that $\forall A \subseteq [0,1]$ that is Borel, we have $\nu(A)$ $\lt$ $C \mu (A)$.  The Radon-Nykodym theorem seems to almost suggest that is true, if I knew it was bounded, then I could say $\nu (A) \le \int_{A} g \ d\mu \le \int_{A} C \ d\mu \le C\mu (A)$, where $C$ is the bound. However, I don't know if it is bounded and in fact, I could take an unbounded function that is still integrable on $[0,1]$, such as $\frac{1}{\sqrt x}$.  I can't even be sure if it is true or false.   Thank you! Formatting section titles Forgive the stupid simplicity of this question, and please feel free to refer me to an older answer. I'm not quite familiar enough with LaTeX terminology to have found it.  All I want to do is set a different default format for my section titles. Instead of just being bolded and slightly larger than the main text, I'd like them to be of normal weight, the same size as the main text, and all caps.   I'm using the article class. I got the following problem: Right now I am checking my equations, which are usually written in align. This looks great in most of the cases, but sometimes the pagebreaks are weird, ie there is a lot of vertical whitespace left (like 2.5cm) at the end of a page. I made the following MWE to illustrate this.  \documentclass[a4paper, 12pt, headsepline]{scrreprt} \usepackage[onehalfspacing]{setspace} \usepackage{amsmath, amssymb, mathtools} \usepackage{mathptmx} \usepackage[a4paper]{geometry} \geometry{left=2cm,right=5cm,top=2cm,bottom=2cm} % \usepackage{lipsum} %\lipsum \usepackage[pangram]{blindtext}  \begin{document} \Blindtext[1][3]%1 paragraph, 3 pangrams \begin{align} X_{t+1} &amp;=  \frac{X_{t+1}+X_{t+1}}{Y_t}  \label{eq:1}  \intertext{Solving...:} \notag  X_{t}  &amp;=  \frac{X_{t+1}+X_{t+1}}{Y_{t+1}} \notag \\ \intertext{Solving further...:} \notag  % ===PAGEBREAK HERE: 2nd page begins=== &amp;= \frac{X_{t+1}+X_{t+1}}{Y_t} +  \frac{X_{t+1}+X_{t+1}}{Y_t}  \notag \\ &amp;= \frac{X_{t+1}+X_{t+1}}{Y_t}...  \notag \\ \intertext{Solving further...:} &amp; = \frac{X_{t+1}+X_{t+1}}{Y_t}  \notag \end{align}  \end{document}   In the MWE, the first 'Solving further' should be on the first page instead (to save space and it would also look better I guess?). The position where I would like the pagebreak to be is also marked as a comment in the MWE.  My question is first on a general basis: Which is the best environment to achieve multiple line equations, which can be aligned as in align, and to save space at the same time? Or to be more precise: If possible, I'd like to stick with align and adapt the pagebreaks only if necessary.  Thanks! How do I backup ssh keys? I am planning to do a fresh install of ubuntu 11.10 in my system. Before that i have setuped key based ssh authentication in this machine. Is it possible to take backup of those ssh keys, so that i  can use that in my new installation. Or else i must setup keybased ssh authentication again? If i can take backup, what are the files i need to copy? Can someone explain it in detail pls. Thanks in advance. Let $A$ and $B$ be two fixed points on a fixed straight line. Two circles touch this line at $A$ and $B$ respectively and tangent to each other at $M$. When the circles vary, what does the locus of $M$ form? Float/double precision in debug/release modes Do C#/.NET floating point operations differ in precision between debug mode and release mode? What is the speed of sound in space? What is an SE "day"? When does each day start? When does a day start on the Stack Exchange network? Some badges (Enthusiast, , ) and voting limits are bound by and relate heavily to the concept of a day. Do days correspond to calendar days? What time zone is used?  Related How do I backup my Stackexchange favorites for offline use? Show that any prime ideal from such a ring is maximal. Are there any way to execute a query inside the string value (like eval) in PostgreSQL? I needed some simple string encryption, so I wrote the following code (with a great deal of "inspiration" from ):      // create and initialize a crypto algorithm     private static SymmetricAlgorithm getAlgorithm(string password) {         SymmetricAlgorithm algorithm = Rijndael.Create();         Rfc2898DeriveBytes rdb = new Rfc2898DeriveBytes(             password, new byte[] {             0x53,0x6f,0x64,0x69,0x75,0x6d,0x20,             // salty goodness             0x43,0x68,0x6c,0x6f,0x72,0x69,0x64,0x65         }         );         algorithm.Padding = PaddingMode.ISO10126;         algorithm.Key = rdb.GetBytes(32);         algorithm.IV = rdb.GetBytes(16);         return algorithm;     }      /*       * encryptString      * provides simple encryption of a string, with a given password      */     public static string encryptString(string clearText, string password) {         SymmetricAlgorithm algorithm = getAlgorithm(password);         byte[] clearBytes = System.Text.Encoding.Unicode.GetBytes(clearText);         MemoryStream ms = new MemoryStream();         CryptoStream cs = new CryptoStream(ms, algorithm.CreateEncryptor(), CryptoStreamMode.Write);         cs.Write(clearBytes, 0, clearBytes.Length);         cs.Close();         return Convert.ToBase64String(ms.ToArray());     }      /*      * decryptString      * provides simple decryption of a string, with a given password      */     public static string decryptString(string cipherText, string password) {         SymmetricAlgorithm algorithm = getAlgorithm(password);         byte[] cipherBytes = Convert.FromBase64String(cipherText);         MemoryStream ms = new MemoryStream();         CryptoStream cs = new CryptoStream(ms, algorithm.CreateDecryptor(), CryptoStreamMode.Write);         cs.Write(cipherBytes, 0, cipherBytes.Length);         cs.Close();                     return System.Text.Encoding.Unicode.GetString(ms.ToArray());     }   The code appears to work fine, except that when decrypting data with an incorrect key, I get a CryptographicException - "Padding is invalid and cannot be removed" - on the cs.Close() line in decryptString.   example code:      string password1 = "password";     string password2 = "letmein";     string startClearText = "The quick brown fox jumps over the lazy dog";     string cipherText = encryptString(startClearText, password1);     string endClearText = decryptString(cipherText, password2);     // exception thrown   My question is, is this to be expected? I would have thought that decrypting with the wrong password would just result in nonsense output, rather than an exception. How to find all subgroups of a direct product? I am wondering how do we find all subgroups of a direct product? Is there a method to find it?  For example, how can we find all the subgroups of $\mathbb{Z}_2\times\mathbb{Z}_2$?  There is the answer: $\{(0, 0), (1, 0)\}, \{(0, 0), (0, 1)\}, \{(0, 0), (1, 1)\}$, and the improper and trivial subgroup. But I do not know the method how to find it.   All I can think about is the following: since the order of $\mathbb{Z}_2\times\mathbb{Z}_2$ is $4$, the order of a subgroup of it can be $1,2$ or $4$.   If order is $1$, then it is trivial, and if order is $4$, it is proper. Then, the order of a subgroup is $2$. We know all the elements of   $\mathbb{Z}_2\times\mathbb{Z}_2$, so we try all the pairs.   Is that the method?   But what if we are given a bigger order product, such as $\mathbb{Z}_2\times\mathbb{Z}_8\times\mathbb{Z}_3\times\mathbb{Z}_9$? It looks very long to try all possibilities.   Can anyone help?  Thanks Difference between might and could I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude.  This appears to be the opposite of this question ().  I have already looked into the haversine formula and think it's approximation of the world is probably close enough.  I am assuming that I need to solve the haversine formula for my unknown lat/long, is this correct? Are there any good websites that talk about this sort of thing? It seems like it would be common, but my googling has only turned up questions similar to the one above.  What I am really looking for is just a formula for this. I'd like to give it a starting lat/lng, a bearing, and a distance (miles or kilometers) and I would like to get out of it a lat/lng pair that represent where one would have ended up had they traveled along that route. PHP: running scheduled jobs (cron jobs) I have a site on my webhotel I would like to run some scheduled tasks on. What methods of achieving this would you recommend?  What I’ve thought out so far is having a script included in the top of every page and then let this script check whether it’s time to run this job or not.  This is just a quick example of what I was thinking about:  if ($alreadyDone == 0 &amp;&amp; time() &gt; $timeToRunMaintainance) {    runTask();    $timeToRunMaintainance = time() + $interval; }    Anything else I should take into consideration or is there a better method than this? Is it appropriate to ask questions about software licenses/licensing on ? Or is the appropriate place  ? Or is there no appropriate site currently and we should suggest such a site on ? I'm trying to prove that the rationals are not the countable intersection of open sets, but I still can't understand why   $$\bigcap_{n \in \mathbf{N}} \left\{\left(q - \frac 1n, q + \frac 1n\right) : q \in \mathbf{Q}\right\}$$   isn't a counter-example. Any ideas? Thanks! Merging folders with mv? Should the number "0" be pronounced "zero" or "oh"?