This is a duplicate of a question I've already asked, but got no answer to. I would appreciated any help.
So far, I understand that I have to look at each Jordan block. How do I prove that for a Jordan block with a value of x, $J_n(x)$, the Jordan decomposition of $(J_n(x))^2$ is $J_n(x^2)$ ? I have a feeling this will lead me to the solution. Thanks for your time.
Disable the default app key (super+num) functionality on Ubuntu 17.10 and later I like to switch workspaces via Super+Number. But unfortunately the default behavior in Ubuntu for Super+Number is to select applications from the dock.   Is it possible to disable that functionality? I've tried overriding the keyboard shortcuts but it doesn't appear to be working. allow you to create code which defines the methods of classes that implement it. You cannot however add any code to those methods.    allow you to do the same thing, along with adding code to the method.   Now if you can achieve the same goal with abstract classes, why do we even need the concept of interfaces?   I've been told that it has to do with OO theory from C++ to Java, which is what PHP's OO stuff is based on. Is the concept useful in Java but not in PHP? Is it just a way to keep from having placeholders littered in the abstract class? Am I missing something? Dual boot UEFI Windows 7 and Ubuntu 12.04 (both 64 bits). W7 entry doesn't appear in GRUB Counting nodes in a tree in Java First of all, I swear this is not homework, it's a question I was asked in an interview. I think I made a mess of it (though I did realise the solution requires recursion). Here is the question:  Implement the count() method which returns the number of nodes in a tree. If a node doesn't have either a left or right child, the relevant getXXChild() method will return null  class Tree {    Tree getRightChild() {     // Assume this is already implemented   }    Tree getLeftChild() {     // Assume this is already implemented   }    int count() {     // Implement me   } }   My reason for asking the question is simply curious to see the correct solution, and thereby measure how bad mine was.  Cheers, Tony Understanding the "Birthday Problem" What is the optimum pattern to place crops in Minecraft? What factors affect soil hydration and crop growth time? What is the most efficient layout of dirt and water to grow crops? Can the manual and tome magic items that increase stats be used multiple times by bypassing the century wait time via the spell Sequester? Assume we have a Wizard who is at least level 13 and can reliably cast  many times (either through acquired spell scrolls, or has acquired enough material components for it to be a non-issue), has a safe place (through the spell ) to be under the influence of Sequester for many centuries, and has access to the Manual of Bodily Health, Manual of Gainful Exercise, Manual of Quickness of Action, Tome of Clear Thought, Tome of Leadership and Influence, and Tome of Understanding.  Per the item descriptions in the DMG:     ...your [STAT] score increases by 2, as does your maximum for that score. The manual then loses its magic, but regains it in a century.   Now, normally this would be a once-in-a-lifetime use, or maybe twice (due to the lifespan of the races), but if a wizard used Sequester on themself, many years can pass without growing older:     ...[willing target creature] falls into a state of suspended animation. Time ceases to flow for it, and it doesn't grow older. You can set a condition for the spell to end [before the spell is dispelled by the caster].   So, assuming that time continues to flow for the magic items, but not for the sequestered wizard, can they study these books and take the necessary long rests, Sequester for a hundred years,  “wake” from the Sequester, and then repeat an arbitrary-but-finite number of times for an arbitrarily high (but finite) improvement to their stats?  To end the cycle and escape the demiplane, the wizard would simply Plane Shift out:     ...You can specify a target destination in general terms ... and you appear in or near that destination. What is the difference between old style and new style classes in Python? What is the difference between old style and new style classes in Python?  When should I use one or the other? Who would get the longest road? Imagine the following setup. There are 3 (or more) players with an equally long road. What would happen if the longest road was broken? How is it decided who obtains the longest road from there on? Recently I have been working on a mini-game that gives a few players custom spawn eggs. I want the mob to simply have a name and be on a team. I'm attempting to use this command:   /give @p[x=-102,y=48,z=81,distance=..1] shulker_spawn_egg{Team:PurpleTeam,CustomName:"\"Purple Turret\""}   It does give the player a spawn egg, but the resulting shulker spawn does not have a team or a name. Any ideas why this isn't working? What is wrong with code snippets/blocks on Stack Overflow? I wasn't following Meta Stack Overflow too closely so maybe something was changed that I'm not aware of. But each time I paste a snippet from a Python console I'm getting wrong formatting. What I'm doing wrong? It seems that &gt;&gt;&gt; is confusing for Stack Overflow. I've tried to escape it with backslashes, and it was working fine in preview but doesn't work after the question is rendered.  I was able to observe that problem on: recent Chrome (Windows, Mac), Safari 4 (Mac).  Here is  I wasn't able to make right.  Funny, I think the snippets are rendered just fine on Meta Stack Overflow. Here is one:  &gt;&gt;&gt; def throw(): raise Exception()  ...  &gt;&gt;&gt; a=1 &gt;&gt;&gt; a=throw() Traceback (most recent call last):   File "&lt;stdin&gt;", line 1, in &lt;module&gt;   File "&lt;stdin&gt;", line 1, in throw Exception &gt;&gt;&gt; a 1 Assume I wield a Whip in one hand and a dagger in the other.  If a creature moves from 5ft to 10ft it has technically moved out of my reach (dagger), but at the same time it is still inside my reach (whip). When does it provoke opportunity attacks from me?  I am fully aware that this would not enable me to make off-hand attacks since the whip is not a light weapon, just to cut that issue out of the question. Writing C# debug output to .txt file What is the result of measuring $\sigma_x$ on the state $|01\rangle+|10\rangle$? I confused about how to calculate the probabilities and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be projected onto an eigenstate of the observable. given $|\psi\rangle = \frac{1}{\sqrt2} (|01⟩ + |10⟩)$ as the state and $\sigma_x = \left[\begin{matrix}0&amp;1\\1&amp;0\\\end{matrix}\right]$ as the observable. if the probability is 1/2, how to calculate them actually? What is the state after measurement? Why don't researchers request payment for refereeing? Page layout assignments with XML metadata API How do I define page layout assignments for different record types via metadata XML files? What are the advantages of Light Application objects I was hoping that the introduction of "Light Application object" would do something about the data storage of junction objects, but it doesn't seem to do anything about it.  The  seems limited to why I would use a "Light Application object", what are the advantages? Browsing  I came across this:  The conjugacy class of an element $g\in A_{n}$:  splits if the cycle decomposition of $g\in A_{n}$ comprises cycles of distinct odd length. Note that the fixed points are here treated as cycles of length $1$, so it cannot have more than one fixed point; and does not split if the cycle decomposition of $g$ contains an even cycle or contains two cycles of the same length.   Anybody with a proof? I am a new Ubuntu user running Ubuntu 13.04.  I've been trying to install and use a DeDRM tool, but I've been having problems doing so. I was following some directions that said I needed a version of Python 2.7, but not anything Python 3.0 or later (because 3.0 versions are missing some necessary libraries?). I tried to install Python 2.7.5.6, but it didn't work. I thought it was probably because I had the later version of Python, so I went through terminal and removed Python 3.3, so I could install the earlier version of Python.  Now that I've uninstalled Python 3.3, a lot of applications no longer work, including the terminal and the Ubuntu Software Center. I have no idea how to fix this problem now. I've just upgraded to Windows 10 from Windows 8.1 on my partitioned laptop that has Ubuntu 14.04 installed. Grub no longer appeared on boot so I ran boot-repair from an Ubuntu liveUSB. This didn't seem to have any effect. I've checked and secure boot is still disabled. Log from boot-repair:  So what's next?  Update: I've attempted to use chroot to update grub from my Ubuntu partition. update-grub runs successfully finding both linux and windows boot manager but the process still doesn't have any effect. grub-install complains that it cannot find EFI directory (but I have mounted everything correctly).  Update2: Just discovered that running efibootmgr after chroot into ubuntu shows ubuntu as not being in the boot order at all. I manually changed the order and rebooted to discover that the bootorder was reset. I run in windows: bcdedit /set {bootmgr} path \EFI\ubuntu\shimx64.efi But this has no effect either even after reporting 'Operation Successful'.