It was my initial status, so I wanted to reduce Windows 10 storage (dev/sda3) and merge that unallocated space to my Ubuntu  There are unallocated space left to Ubuntu space.  But when I try to expand Ubuntu storage to left side, it fails.  How can I solve this?
Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?
Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$ In general, the group $\mathbb Z_{mn}$ under addition $\bmod mn$ is isomorphic to the direct product $\mathbb Z_m \times \mathbb Z_n$ if and only if $\gcd(m,n)=1.$ This is easy to see since $\mathbb Z_{mn}$ is generated by the element $(1,1)$, and if $\gcd(m,n)=1$, then this will only be zero if it is multiplied by itself $mn$ times (resulting in the cyclic group).   However I'm interested in constructing an isomorphism between the two groups as an explicit expression. I've been playing around a bit with some examples, one of which is the function $\phi : \mathbb Z_2 \times \mathbb Z_3 \to \mathbb Z_6$ where $\phi(a,b) = 3a + 4b \pmod 6$, which gives us the desired isomorphism. I'm interested here in the relationship between the integers $2$, $3$, and the coefficients $3, 4$ of $a$ and $b$. After playing around in Wolfram|Mathematica, I managed to obtain the following isomorphisms $\phi_{m,n} : \mathbb Z_m \times \mathbb Z_n \to \mathbb Z_{mn}$ for coprime $m,n$ in $\{1, 2, \dots, 10\}$.   First of all, the following results seem to hold in general.  $$\phi_{1, n}(a, b) = a + b \qquad \text{for all $n$}$$  $$\phi_{m, 1}(a, b) = a + b \qquad \text{for all $m$}$$  $$\phi_{2, n}(a, b) = na + (n + 1)b \qquad \text{for all $n$}$$ $$\phi_{m, n}(a, b) = K a + L b \iff \phi_{n,m}(a, b) = L a + K b \qquad \text{for all $m, n$}$$  Beyond this point, I could not spot a general pattern. The isomorphisms I obtained are:  $$\phi_{3, 4}(a, b) = 4a + 9b$$ $$\phi_{3, 5}(a, b) = 10a + 6b$$ $$\phi_{3, 7}(a, b) = 7a + 15b$$ $$\phi_{3, 8}(a, b) = 16a + 9b$$ $$\phi_{3, 10}(a, b) = 10a + 21b$$ $$\phi_{4, 5}(a, b) = 5a + 16b$$ $$\phi_{4, 7}(a, b) = 21a + 8b$$ $$\phi_{4, 9}(a, b) = 9a + 28b$$ $$\phi_{5, 6}(a, b) = 6a + 25b$$ $$\phi_{5, 7}(a, b) = 21a + 15b$$ $$\phi_{5, 8}(a, b) = 16a + 25b$$ $$\phi_{5, 9}(a, b) = 36a + 10b$$ $$\phi_{6, 7}(a, b) = 7a + 36b$$ $$\phi_{7, 8}(a, b) = 8a + 49b$$ $$\phi_{7, 9}(a, b) = 36a + 28b$$ $$\phi_{7, 10}(a, b) = 50a + 21b$$ $$\phi_{8, 9}(a, b) = 9a + 64b$$ $$\phi_{9, 10}(a, b) = 10a + 81b$$ If you want to try and generate a few yourself, here is the Mathematica function I implemented. I'm sure it can be optimised, but for the first 10 coprime integers it sufficed.  isomorphism[{m_, n_}] :=       Module[{x = Null},       For[i = 1, i &lt; m*n,           i++, (If[#[[2]] == Table[i, {i, 0, m*n - 1}],           x = ToString[#[[1]][[1]]] &lt;&gt; "a+" &lt;&gt; ToString[#[[1]][[2]]] &lt;&gt;          "b"; Break[]] &amp;) /@       Table[{{i, j},       Mod[i #[[1]] + j #[[2]], m*n] &amp; /@       Table[{Mod[i, m], Mod[i, n]}, {i, 0, m*n - 1}]}, {i, 1,      m*n}, {j, 1, m*n}][[i]]]; x];   I'd appreciate if anyone can help me find the pattern to determine $\phi_{m, n}$ in general. Direction of friction for object that rolls with slipping How to run a script without closing the terminal? I have a script in file bla.sh and it is executable. When I click on it, the script is executed and the window is closed. I'd like the window to stay open.  Something like command cmd /k** command in Windows.  P.S. I don't want to use pause, but I want to able to write more commands after the script was executed. How did Sauron remain in control of the Nazgûl? Commutator of a group number of ways to make $2.00 All Stack Exchange data dumps The original ClearBits link to the September 2011 data dump has broken. How can I access it and other previous data dumps? The Internet Archive only has . Is it possible to migrate programs from 32 bit Windows to a new 64 bit Windows machine (both Windows 7)? I've got a Windows 7 Pro 32 bit PC. Getting a new Windows 7 Home 64 bit.  Is there anything I can use to transfer my  programs (the ones that don't come in a 64 bit flavor)  to the new PC? There is a related  that doesn't address the programs part. What kind of questions can I expect to see on a qualifying exam? In mathematics, there are certain open questions which are the subject of current research (think of the newest papers in the top journals).  I have also heard that some graduate programs ask questions such as these on their qualifying exam.  How common is this practice?  What kinds of questions can I expect to see on a qualifying exam?  I know that a qualifying exam typically tests the knowledge gained in graduate school, but I'm not sure to what extent this knowledge is tested?  How "advanced" should I expect these questions to be? Why is January month 0 in Java Calendar? In java.util.Calendar, January is defined as month 0, not month 1. Is there any specific reason to that ?  I have seen many people getting confused about that... What is the probability that the selected function maps prime numbers to prime numbers? Let $X = \{1, 2, 3, . . . , 25\}$. If a student selects a function randomly from the set of all functions from $X$ onto $X$, then what is the probability that the selected function maps prime numbers to prime numbers ? No idea how to proceed, please guide. Is this defined by the language? Is there a defined maximum? Is it different in different browsers? I have ran into some issues when it went down to install Steam on Debian. The console as well as Apper comes up with missing dependencies  and the package isn't going to install. Usually \label does not create any white spaces. However, It creates an white space when \label is used after \phantomsubcaption from subcaption package.   Why? How can I get rid of this white space?   Here is a MWE:  \documentclass{article} \usepackage{subcaption}  \begin{document}  \section{a} a\label{sec:a}b% no white space between `a' and `b'  \begin{figure}   \centering   {a\phantomsubcaption\label{fig:a}}%   {b\phantomsubcaption\label{fig:b}}   \caption{With label}% undesired white space between `a' and `b' \end{figure}  \begin{figure}   \centering   {a\phantomsubcaption}%   {b\phantomsubcaption}   \caption{Without label}% no white space between `a' and `b' \end{figure}  \end{document} How does a magnet work? I just bought a house. Now I'm getting ads in the mail every day or two trying to get me to sign up to pay my mortgage bi-weekly (every two weeks) or weekly instead of monthly. In their words I could cut seven years and thousands of dollars off what I pay in long term. It seems like I would be paying the exact same amount of money, also.  I know "if something sounds too good to be true then probably it is". But I cannot figure out why in this case. What is the catch? Or is this something I should be signing up for ASAP? After discussion with colleagues regarding the use of the 'var' keyword in C# 3 I wondered what people's opinions were on the appropriate uses of type inference via var?  For example I rather lazily used var in questionable circumstances, e.g.:-  foreach(var item in someList) { // ... } // Type of 'item' not clear. var something = someObject.SomeProperty; // Type of 'something' not clear. var something = someMethod(); // Type of 'something' not clear.   More legitimate uses of var are as follows:-  var l = new List&lt;string&gt;(); // Obvious what l will be. var s = new SomeClass(); // Obvious what s will be.   Interestingly LINQ seems to be a bit of a grey area, e.g.:-  var results = from r in dataContext.SomeTable               select r; // Not *entirely clear* what results will be here.   It's clear what results will be in that it will be a type which implements IEnumerable, however it isn't entirely obvious in the same way a var declaring a new object is.  It's even worse when it comes to LINQ to objects, e.g.:-  var results = from item in someList               where item != 3               select item;   This is no better than the equivilent foreach(var item in someList) { // ... } equivilent.  There is a real concern about type safety here - for example if we were to place the results of that query into an overloaded method that accepted IEnumerable&lt;int&gt; and IEnumerable&lt;double&gt; the caller might inadvertently pass in the wrong type.  var does maintain strong typing but the question is really whether it's dangerous for the type to not be immediately apparent on definition, something which is magnified when overloads mean compiler errors might not be issued when you unintentionally pass the wrong type to a method. Add days to JavaScript Date Is $\cot(z)-\frac1z$ bounded on a given circle? Getting hybrid graphics to work nvidia-prime GT650M