Removing old kernels
How do I remove old kernel versions to clean up the boot menu?
Ubuntu/Kubuntu 16.04.1 installation in VirtualBox I'm trying to install Kubuntu 16.04.1 on a virtual machine (I'm using VirtualBox). When I boot from the disk image Ubuntu begins to load and then I get this screen:   It looks like it's loading but the display is not working properly (the pink blob is my mouse pointer, only very large and pink).  I also tried installing Ubuntu 16.04.1 and I get a very similar result:   Am I missing something in VirtualBox? Thanks! Existence of a local geodesic frame Let $(M,g)$ be a Riemannian manifold of dimension $n$ with Riemannian connection $\nabla,$ and let $p \in M.$ Show that there exists a neighborhood $U \subset M$ of $p$ and $n$ (smooth) vector fields $E_1,...,E_n \in \chi (U),$ orthonormal at each point of $U,$ s.t. at $p,$ $\nabla_{E_i}E_j(p)=0.$  What I've found so far;  Let $V$ be a normal neighborhood at $p.$ Let $(W,x(x_1,...,x_n))$ be a local coordinate system at $p$ s.t. $x(W) \subset V.$  Let $\{X_i:=\frac{\partial}{\partial x_i}\}$ be the standard basis of $T_pM.$ By Gram-Schmidt, there exists an orthonormal basis $\{E_i\}$ of $T_pM.$ Consider the orthonormal frame $E_i(t),$ by parallel transporting $\{E_i(0)=E_i\}$ along a  a geodesic $\gamma :I \to M$ starting at $\gamma(0)=p$ and ending in $\gamma(1)=q,$ where $q \in V.$ This gives us an orthonormal frame at each point of $V.$ To satisfy the second condition, let $E_i(t)=\sum_{l}a_{li}X_l$ and  $E_j(t)=\sum_{s}b_{sj}(t)X_s.$ Then   $$\nabla_{E_i}E_j=\sum_{k}(\sum_{l,s} a_{li}(t)b_{sj}(t)\Gamma^k_{ls}+E_i(b_{kj}))X_k,$$  where $\Gamma^k_{is}$ are Christoffel symbols.   To have $\nabla_{E_i}E_j(p)=0,$ we must have $\sum_{l,s}a_{li}(0)b_{sj}(0)\Gamma^k_{ls}+E_i(b_{kj})(p)=0$ for each $k.$      How can I conclude the argument? Can I travel in UK before switching to a study visa? As I read in general visitor visa Terms &amp; Condition, I would only be granted to stay up to 6 months in UK. However I am planning to apply for General Student Visa to further my studies. Would it be possible for me to enter UK as visitor for first 6 months/less before I apply for student visa in the same year if I want to travel and study on the same year? Turning a cipher into a hashing function This is theoretical question. I'd like to know if it's possible (and what are eventually the consequences), not that I'm going to do it in one of my projects. ;)  The first hashing functions created were based on a symmetric cipher (just like the first Unix crypt was based on DES). The idea was simple. Use the password as key to encode a constant.  I'd like to know if it's still possible to convert any modern symmetric cipher into a hashing function (and second question: into a cryptographic hashing function). Is it possible (easier) to guess the key, when you have an encoded and decoded messages? Inclusion of Fields whose order is a prime power Blue was correct, I need to fix my understanding of this:     Finite fields have cardinality of a prime order because they have a prime subfield that has finite characteristic.    I do not completely understand why finite field of each characteristic is unique. Perhaps we look at a polynomial and express the finite field as a splitting field? And we use uniqueness of splitting fields?  Then, why is it that  $\mathbb F_{p^m} \subseteq \mathbb F_{p^n}$ if and only if $m$ divides $n$? Unable to SSH to my virtual machine via Windows Power Shell ISE "The train will leave" vs. "is going to leave" vs. "leaves" vs. "is leaving" As much as I have tried, it doesn't seem possible to use separate labels when using a casesconstruction (from the amsmath package).  Ideally, I would like to be able to write something like  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x)=\begin{cases}   1&amp;x\geq0\label{positive}\\   0&amp;x&lt;0\label{negative} \end{cases} \end{equation} \end{document}   and later refer to both cases at different places. What would be the best way to achieve this result? Laptop power supplies, does current matter? I have two laptops (same manufacture), with the same type of power connector.  However, the power supplies/transformers are slightly different.    The output on the first laptop's power supply is 15.6&nbsp;V at 8.0&nbsp;A. The output on the second laptop's power supply is 15.6&nbsp;V at 5&nbsp;A.  Clearly the voltages are the same, but the currents are different. I assume the second laptop's power supply can not be used on the first, because it can't supply enough power to the laptop.   However, can the first laptop's power supply be safely used on the second laptop? Issue in evaluating the performance of my "clustering algorithm" using NMI, ARI when the "ground truth" is available? $1+x+\ldots+x^n$ perfect square Let $p$ be the polynomial $p(x)=1+x+\ldots+x^n$. For which couples $(a, n)\in\mathbb{N}^2$, $p(a)$ is a perfect square? I'm particularly interested in $p(3)$. These are my current disk partitions. /yedek is for some personal backup files. As you can see there is only Ubuntu on my PC. I will install Windows, too. Because of this I want to shrink /dev/sda3 . It currently 546GB and I want to split it: 300GB for / and 246GB for Windows (NTFS) is OK for me.  I'm using GParted for the first time. How can I shrink /?  I don't want to lose any datas from Ubuntu. Which $n$ can be expressed as $x^2 − y^2$? Which $n$ can be expressed as $x^2 − y^2$?  Attempt: Any number which is odd or or which is a multiple of 4. What are some alternatives to "hover" on touch-based devices? Came up recently in a 37signals podcast:    The straightforward, "brute-force" solution is to just use the first touch on a UI object as the hover.    It works. But are there other, more elegant solutions? For instance, could the hardware ever be made to support actual finger hovering? parsing XML file gets UnicodeEncodeError (ElementTree) / ValueError (lxml) Extracting one band from three band raster in ArcMap? Is is possible to restore the MFT of a NTFS partition after a format? Ubuntu stuck/freeze on install I've been trying to replace my current Windows 10 installation with Ubuntu 16.04. My computer is a Lenovo Thinkpad T470. I've formatted my 15GB USB-dongle. Downloaded the software Rufus, and burned the ISO onto the USB. I've tried the settings "MBR Partition for BIOS or UEFI", "MBR Partition for UEFI" and "GPT partition for UEFI". I've tried using memtest86+ to test if I have any memory errors, I have not. I've tried disabling Secure boot, and Fast startup. I've tried using other software than Rufus, and I've tried entering the "nomodeset" in the boot options, as well "acpi=off", nothing works.   When I boot from my USB. I choose "Install Ubuntu" from the grub menu. And then select my language in the installer. It is from this point on, it gets problematic. Sometimes when I try to connect to my WIFI, it connects successfully, but when I press the "continue" button, the installer freezes and nothing happens. Sometimes I get past this point, but it then freezes later on in the installation progress - typically right when I press the "Install now" button.   It should also be mentioned that, if I press the "Quit" button in the install. I get to a black screen with a lot of text saying something like squashfs error.   Can someone please help me? When I tried booting memtest86+ it only worked when I changed my boot mode from UEFI to Legacy. Could this be it? Are there any downsides to installing an operating system in legacy?   If anyone has any other suggestions, it would be greatly appreciated!  Thank you :-) A smooth vector field on $S^2$ vanishing at a single point Is it true that for algebraic sets $V,W$ we have $I(V \times W ) =I(V) + I(W)$?