A symmetry  of a graph X is a permutation of the vertices that also happens to be a permutation of the induced edges. In particular, the distances between vertices are preserved by a symmetry. Show that the set of symmetries of X is a permutation group of V(X).  Compute the cycle index of the group for the Petersen graph.  Please help. How do you show that something is a permutation group? I have never calculated the cycle index for a graph before and we don't have any examples like this in our notes. How do I do it for a graph?
A symmetry of graph $X$ is a permutation of the vertices that also happens to be a permutation of the induced edges. In particular, the distances between vertices are preserved by a symmetry. Show that the set of symmetries of $X$ is a permutation group of $\operatorname{V}(X)$. Compute the cycle index of the group for the Petersen graph.   Alright I am super confused. I have no idea how to even start. Can someone point me in the right direction. How do I show that something is a permutation group? How do I compute the cycle index of a graph?
Windows Update not working on Windows 2012 R2 Standard I recently inherited the management of a Windows 2012 server at a remote site.    I checked Windows Update and it has not been updating since March.  When I tell Windows to check for updates, it acts like it is checking, but it seems to say that for hours.   If I attempt to restart the windows update service, it seems to never be able to shut down.  My only remedy seems to be rebooting to get back to the point where I can tell Windows Update to check for new updates.    The last successful check for updates says March 20.  The last time updates were installed says March 17 (failed).  The update history shows that one update failed for March 17, a printer driver update, but the history shows 13 failed updates for Feb 17.  Not sure what else to try. Why didn't Doc remember Marty's outfit? In Back to the Future 3, Doc (from 1955) sends Marty back in time wearing a cowboy outfit.  But then, Doc (from 1885) doesn't remember that it was him who offered this outfit to Marty.   Does this mean there are two different Docs (from differing timelines) or is it the same Doc but he somehow forgot the outfit. Can a person negotiate with banks on CD interest rates? I use a brick and mortar bank for some of my savings. I’d love to get a CD interest rate closer to what Ally or other online banks offer.   Are brick and mortar banks will to negotiate with customers on interest rates? For instance, if I went into a branch and said I’m moving my money to Ally unless the bank matches Ally’s rates, do I have any chance of getting them to? Can I visit other Schengen countries on a long-term Schengen visa or residency permit? I have requested for a French long term (Type D) student visa from a consulate in India. It's a national Type D visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from a consulate in France? Removing leading zeroes from a field in a SQL statement I am working on a SQL query that reads from a SQLServer database to produce an extract file. One of the  requirements to remove the leading zeroes from a particular field, which is a simple VARCHAR(10) field. So, for example, if the field contains '00001A', the SELECT statement needs to return the data as '1A'.  Is there a way in SQL to easily remove the leading zeroes in this way? I know there is an RTRIM function, but this seems only to remove spaces. How to assign symbols to functions I'm using Ubuntu 16.04.3 LTS, on a 64-bit system.   There are two available updates in "Updates" section of the Ubuntu Software, named OS Updates and Software respectively:      I usually update through Software Updater utility, (and occasionally used sudo apt update and sudo apt upgrade as recommended by some software installation tutorials)- anything that I think is required. So why is Ubuntu Software showing these updates? Should I install them?  As far as I know, these types of updates, if you look at the list, aren't ever available in the Software Updater. I recieve the below error when I am trying to call a Custom Lightning Component in a Visualforce page that is used in Communities.    Unrecognized Content-Security-Policy directive 'reflected-xss'.   logo180.png Failed to load resource: the server responded with a status of 404 (Not Found)   CommunityHomePage:1 Uncaught SyntaxError: Unexpected token w in JSON at position 0     at JSON.parse ()     at XMLHttpRequest.xhr.onreadystatechange (lightning/lightning.out.delegate.js?v=ZCuyRUYzK_kAf4cKCIeS2A:143)   My Component  &lt;aura:component controller="LeadController" implements="forceCommunity:availableForAllPageTypes"&gt;     &lt;aura:attribute name="theLead"          type="Lead"          default="{ 'sobjectType': 'Lead',                    'Rating__c': 2,                    'Company': '',                    'FirstName': '',                    'LastName': '',                    'Email': '' }"/&gt;     &lt;form&gt;          &lt;ui:inputText value="{!v.theLead.Company}" label="Company" class="input"/&gt;         &lt;ui:inputText value="{!v.theLead.FirstName}" label="First" class="input"/&gt;         &lt;ui:inputText value="{!v.theLead.LastName}" label="Last" class="input" /&gt;         &lt;ui:inputEmail value="{!v.theLead.Email}" label="Email" class="input" /&gt;         &lt;ui:button label="Save" press="{!c.save}"/&gt;     &lt;/form&gt; &lt;/aura:component&gt;   My Lightning App is   &lt;aura:application access="GLOBAL" extends="ltng:outApp" implements="forceCommunity:availableForAllPageTypes"&gt;     &lt;aura:dependency resource="c:CommunityChatter"/&gt; &lt;/aura:application&gt;   My VF Page is  &lt;apex:page standardController="Lead"&gt;     &lt;apex:includeScript value="{!$Site.BaseUrl}/lightning/lightning.out.js"/&gt;     &lt;script&gt;         $Lightning.use("c:MyLightApp", function() {             $Lightning.createComponent(                 "c:CommunityChatter",                 {},                 "theLead",                 function(cmp) {                     console.log("Component created!");                     console.log(cmp);                 });             });     &lt;/script&gt;      &lt;div id="theLead"&gt;&lt;/div&gt; &lt;/apex:page&gt; Double calculation producing odd result How to switch between tty and xorg session How can I take a screenshot with Selenium WebDriver? In programming terminology, what do you call the difference between these instructions: What happens when many neurons have same weights? Does it make any sense to have two (or more) neurons in a neural network with the same weights? (intuitively it makes no sense, since all the neurons would behave the same way).   Please consider both the input and hidden layers. What if the weights are equal 0? What's a good word for a person, or a state, when a person is constantly waiting for life to get good, but does nothing to actually make it happen I've written a song about people who constantly wait for something good to happen to them and am looking for a word to describe this state/paradox/condition.   The song is about people who expect life to get better for no reason, talk about moving to a bigger city or a different place as if that would magically make them rich, famous and happy, and keep talking about how they are going to do this or that, but never do it. I was under the impression that there's a psychological term for this state, but can't google it up, so I probably made it up.  This is essentially a song about myself, I keep talking about how I love to make music, or shoot videos, but I never actually produce anything, yet it's the only thing I can think of. When it comes to the moment to take action – I just stay at home watching tv shows.  I know it's a broad question and list of topics, but I guess I'm looking for a word that describes this state – of doing NOTHING. pgfplots: Clipping Everything Outside a Specific Area I want to add information to each column of a histogram. every node near coord is probably the best approach. It works well with bar plots but not with the histogram:  \documentclass{article}  \usepackage{pgfplots} \pgfplotsset{compat=newest} \usetikzlibrary{pgfplots.statistics}  \begin{document}  \begin{tikzpicture} \begin{axis}[ ybar interval, xticklabel=\pgfmathprintnumber\tick--\pgfmathprintnumber\nexttick, % Code to generate labels nodes near coords={ \pgfmathprintnumber{\pgfkeysvalueof{/data point/y}} }, every node near coord/.style={ anchor=south,xshift=9mm, }, % ] \addplot+[hist={bins=3}] table[row sep=\\,y index=0] { data\\ 1\\ 2\\ 1\\ 5\\ 4\\ 10\\ 7\\ 10\\ 9\\ 8\\ 9\\ 9\\ }; \end{axis} \end{tikzpicture}  \end{document}   I used every node near coord/.style to shift the labels.  The problem is that I have four labels for three columns/bars:    I addition I would like to center the labels. A workaround will be a manual adjustment (every node near coord/.style) just like in the shown example.  Update  Maybe clipping is a possibility. Is there a way to clip the labels (in this case the 7 in the right) away?  Like this: How do I uninstall xcode 5 command line tools? Lenovo Yoga 13 Realtek wireless driver This question is here so we can offer users who are looking for information on how to make one or more common or basic redirects in Apache using the htaccess file. All future questions pertaining to finding information that is that is covered by the question should be closed as a duplication of this question. .  Whats the point in this question? The idea while not perfect is catch the most commonly asked questions regarding redirects using the  htaccess on the Apache platform either on  some type of lamp or a live server. The type of answers should be generally those that you could imagine are used by 100,000’s of sites world-wide and are constantly asked here at Pro Webmasters repeatedly over and over in various forms.  A few examples of the type of answers we are looking for:   How can I redirect non-www to www? How can I redirect a sub domain to the main domain? How can I redirect a sub folder from domain to a root or a subdomain?  How can I redirect an old URL to a new URL?   A few examples of the types of answers that we are not looking for:   Answers that do not involve a redirect. Any answers relating to NGinx, IIS or any other non-Apache platform. Answers that involve custom and complex string or query removals.   Resources for Advanced to Complex Mod_Rewrite Rules:      Please note: that this question is still in construction and may need some refining either by myself or a real moderator of Pro Webmasters, if you have any concerns or questions . Solve $x^2+5x+6 \equiv 0 \pmod{\!11\cdot 17}$ Solve $x^2+5x+6 \equiv 187 \mod 187$ Solution $$x^2+5x+6 \equiv 187 \mod 187$$ $$ (x+\frac{5}{2})^2 \equiv \frac{1}{4}$$ $$ 4(x+\frac{5}{2})^2 \equiv 1$$ $$ y:= x+\frac{5}{2} $$ $$ 4y^2 \equiv 1 \mod 11 \wedge 4y^2 \equiv 1 \mod 17  $$ $$ ( 2y \equiv 1 \mod 11 \vee 2y \equiv 10 \mod 11 ) \wedge ( 2y \equiv 1 \mod 17  \vee 2y \equiv 13 \mod 17)  $$ $$ ( y \equiv 6 \mod 11 \vee y \equiv 5 \mod 11 ) \wedge ( y \equiv 9 \mod 17  \vee y \equiv 15 \mod 17)  $$ Combining that from CRT I got: $$ y \in \left\{49, 60,83,94 \right\} $$ and for example: $$ x+\frac{5}{2}  \equiv 94 \mod 187$$ $$ 2x  \equiv 183 \mod 187$$ some calculus and get... $$x \equiv 185 $$ And the same thing for each other case. Question Is there any faster (or smarter) way to solve equations like that? How to get past a forgotten iPhone passcode?