I cannot start up QGIS and get an error message
QGIS installation error
Arithmetic of continued fractions, does it exist? I'm interested in the arithmmetic of continued fractions and specially in multiplication. Consider  $$ f(x)=\cfrac{f_{0}(x)}{1-\cfrac{f_{1}(x)}{1+f_{1}(x)-\cfrac{f_{2}(x)}{1+f_{2}(x)-\cfrac{f_{3}(x)}{1+f_{3}(x)-\cdots}}}} $$   and   $$ g(x)=\cfrac{g_{0}(x)}{1-\cfrac{g_{1}(x)}{1+g_{1}(x)-\cfrac{g_{2}(x)}{1+g_{2}(x)-\cfrac{g_{3}(x)}{1+g_{3}(x)-\cdots}}}} $$   Are there arithmetic rules (algorithms) for the multiplication of continued fractions? Specifically, is it possible to obtain a continued fraction $h(x)=f(x)\cdot g(x)$ where   $$ h(x)=\cfrac{h_{0}(x)}{1-\cfrac{h_{1}(x)}{1+h_{1}(x)-\cfrac{h_{2}(x)}{1+h_{2}(x)-\cfrac{h_{3}(x)}{1+h_{3}(x)-\cdots}}}} $$   I've found , but I'd like more. Does anyone here knows of papers, algorithms, etc?  Thanks.    Update 1: Another . Aligning numbers by decimal points in table columns How to modify a text file? I'm using Python, and would like to insert a string into a text file without deleting or copying the file. How can I do that? Is list::size() really O(n)? Recently, I noticed some people mentioning that std::list::size() has a linear complexity. According to  , this is in fact implementation dependent as the standard doesn't say what the complexity has to be. The comment  says:     Actually, it depends on which STL you   are using. Microsoft Visual Studio V6   implements size() as {return (_Size);   } whereas gcc (at least in versions   3.3.2 and 4.1.0) do it as { return std::distance(begin(), end()); } The   first has constant speed, the second   has o(N) speed    So my guess is that for the VC++ crowd size() has constant complexity as Dinkumware probably won't have changed that fact since VC6. Am I right there? What does it look like currently in gcc? If it is really O(n), why did the developers choose to do so? Number formation from given digits I was asked this question in a recent interview. You are given two digits $0$ and $9$. Using only these two digits you must form the least positive number that is a multiple of a given '$n$' . The value of $n$ will be provided before hand. For example if we are given $n$ as $7$ then the answer will be $9009$ .  I tried using some basic divisibility principles but was not able to come up with a correct solution and code it up. Probably I need some help in number theory What does a de Broglie wave look like? What does a  wave look like? Are de Broglie waves transverse or longitudinal?   Can they be polarized?    What about the de Broglie wave of a ground state neutral spin-zero Helium 4 atom?   What experimental evidence do we have that supports the detailed nature of a de Broglie wave?     I have always assumed that de Broglie waves were mathematically  identical to electromagnetic waves, but I just realized there is no basis for this assumption, and in fact it must be false, unless there is an analogue to both the magnetic and the electric components of the electromagnetic wave.  So what does a de Broglie wave "look like"? When given $p = 5, q = 11, N = 55$ and $e = 17$, I'm trying to compute the RSA private key $d$.  I can calculate $\varphi(N) = 40$, but my lecturer then says to use the extended Euclidean algorithm to compute $d$. That's where I get stuck.    Here's my work so far:  First I use the Euclid algorithm to calculate:  40 = 2(17) + 6  17 = 2(6) + 5 6 = 1(5) + 1 = gcd   So I know the GCD is 1. Applying the 'extended' section of the algorithm:  6 = 40-2(17) 5 = 17-2(6) 1 = 6-1(5) 1 = 6-1(17-2(6)) 3(6) = 1 (17) 3(40 - 2(17)) - 1(17) 3(40) - 3(17)   I know the answer is $33$, but I have no idea how to get there using the extended Euclidean algorithm. I can't figure out why I'm getting $3(40) - 3(17)$ when I know the answer should contain $33$. I would like to know how I can get the value of a node with the following paths:   config/global/resources/default_setup/connection/host config/global/resources/default_setup/connection/username config/global/resources/default_setup/connection/password config/global/resources/default_setup/connection/dbname   from the following XML:  &lt;?xml version="1.0"?&gt; &lt;config&gt;     &lt;global&gt;         &lt;install&gt;             &lt;date&gt;&lt;![CDATA[Tue, 11 Dec 2012 12:31:25 +0000]]&gt;&lt;/date&gt;         &lt;/install&gt;         &lt;crypt&gt;             &lt;key&gt;&lt;![CDATA[70e75d7969b900b696785f2f81ecb430]]&gt;&lt;/key&gt;         &lt;/crypt&gt;         &lt;disable_local_modules&gt;false&lt;/disable_local_modules&gt;         &lt;resources&gt;             &lt;db&gt;                 &lt;table_prefix&gt;&lt;![CDATA[]]&gt;&lt;/table_prefix&gt;             &lt;/db&gt;             &lt;default_setup&gt;                 &lt;connection&gt;                     &lt;host&gt;&lt;![CDATA[localhost]]&gt;&lt;/host&gt;                     &lt;username&gt;&lt;![CDATA[root]]&gt;&lt;/username&gt;                     &lt;password&gt;&lt;![CDATA[pass123]]&gt;&lt;/password&gt;                     &lt;dbname&gt;&lt;![CDATA[testdb]]&gt;&lt;/dbname&gt;                     &lt;initStatements&gt;&lt;![CDATA[SET NAMES utf8]]&gt;&lt;/initStatements&gt;                     &lt;model&gt;&lt;![CDATA[mysql4]]&gt;&lt;/model&gt;                     &lt;type&gt;&lt;![CDATA[pdo_mysql]]&gt;&lt;/type&gt;                     &lt;pdoType&gt;&lt;![CDATA[]]&gt;&lt;/pdoType&gt;                     &lt;active&gt;1&lt;/active&gt;                 &lt;/connection&gt;             &lt;/default_setup&gt;         &lt;/resources&gt;         &lt;session_save&gt;&lt;![CDATA[files]]&gt;&lt;/session_save&gt;     &lt;/global&gt;     &lt;admin&gt;         &lt;routers&gt;             &lt;adminhtml&gt;                 &lt;args&gt;                     &lt;frontName&gt;&lt;![CDATA[admin]]&gt;&lt;/frontName&gt;                 &lt;/args&gt;             &lt;/adminhtml&gt;         &lt;/routers&gt;     &lt;/admin&gt; &lt;/config&gt;   Also I want to assign that value to the variable for further use. Let me know your idea. Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$ I'm not sure how to go about this. Does it involve using MVT?  I got as far as saying $e = \frac{e^x - e^y}{x-y}$. I want to display from cache for a long time and I want a slightly different behavior on page render vs loading the page from cache.  Is there an easy way I can determine this with JavaScript? I wonder a generalization of Jensen's inequality: let $\mathbf{X,Y}$ be two positive definite matrices, can we obtain the following Jensen like inequality $$(1-\lambda)\mathbf{X}^{-1}+\lambda\mathbf{Y}^{-1} \succeq((1-\lambda)\mathbf{X}+\lambda\mathbf{Y})^{-1}$$ for any $\lambda \in (0,1)$, where the notation $\mathbf{A}\succeq \mathbf{B}$ represents matrix $(\mathbf{A-B})$ positive semi-definite. $\sum \cos$ when angles are in arithmetic progression Possible Duplicate:          Prove $$\cos(\alpha) + \cos(\alpha + \beta) + \cos(\alpha + 2\beta) + \dots + \cos[\alpha + (n-1)\beta] = \frac{\cos(\alpha + \frac{n-1}{2}\beta) \cdot \sin\frac{n\beta}{2}}{\sin\frac{\beta}{2}} $$ How do I install a .deb file via the command line? Do numbers exist independently from observers? Are there any rules related to the creation of a ?   I am aware of the creation method for the amulet. But I'm asking about creating the actual construct. Reference for creative set criterion theorem How to prevent alt-f1 from selecting Dash How to quit Skype on Android? Code for looping through all excel files in a specified folder, and pulling data from specific cells I'm considering buying a solid state drive for my Unibody White MacBook 2010. The trouble is, I have no idea what to look for. What kind of connector am I looking for? (SATA?) What size? I'm told to get the kind that Apple uses so that I don't void my AppleCare warranty. What model/brand(s) would that be?