How many and which distinct groups of order 20 that are not isomorphic?  Why are they not isomorphic?  I have the $Z_{20}, Z_2+Z_{10}, D_{10}$.  There are more than 4.  I don't know the limit.
Find four groups of order 20 not isomorphic to each other and prove why they aren't isomorphic.   So far I thought of $\mathbb Z_{20}$, $\mathbb Z_2 \oplus\mathbb Z_{10}$, and $D_{10}$ (dihedral group), but I can't find another one. Would $U(50)$ work? I know it has order 20 and is cyclic but I'm not exactly sure how to move from there. Can someone to point me on the right direction?
Retrieving date in sql server, CURRENT_TIMESTAMP vs GetDate() Using SQL Server - which is the fastest or best practice method to use for date retrieval? Is there a difference? Word for killing off or attempting to kill off an entire bloodline? I would like to know if there is a word or phrase for a systematic campaign to annihilate every descendant of a particular ancestor.   We have the word 'genocide' for killing off an entire race, and plenty of words for killing people based on how they are related to you (fratricide, filicide, et. al.), but looking over the  and the , I couldn't find a term for systematically killing an entire bloodline.   My question is prompted by a US news story about the horrific murder of 8 members of the same family, but those murders are not an example of what I'm thinking of because the children of the victims were left alive, so the motive for the killings was not to kill off the bloodline. The sense that some group had coordinated an attack against just one family is what made me wonder what the "not an entire race, just one bloodline" version of 'genocide' would be called.   Searching the Internet for "kill off" and bloodline sends me straight into the land of vampires, Illuminati, reptilian overlords, and, naturally, Priory of Sion nonsense so I haven't had much luck finding a thread to pull.   It may be that there is no word for it in the sense of murdering a human bloodline, because we just don't attempt kill off our royals down to the last heir often enough to coin a term for it. Maybe there is a scientific term for culling a line from a test population as part of biological research? Suppose $a_n>0$ and $\sum_{n=1}^{\infty}{a_n}$ diverges. Determine convergence of $\sum_{n=1}^{\infty}{\frac{a_n}{s_n^2}}$, where $s_n=\sum^n a_n$. \colorbox height too long \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{xcolor} \usepackage{minted} \usepackage{parskip}  \definecolor{codegray}{gray}{0.9} \newcommand{\code}[1]{\colorbox{codegray}{\texttt{#1}}}  \begin{document}  \code{test code}\\ anotherline  \end{document}   This is working good on sharelatex.com and looks like I expect and want it:   but on my local project using this command gives me this:   any idea what could be causing this colorbox height going to the next line? How to customize the Ubuntu Live CD? How do I update the GUI from another thread? Which is the simplest way to update a Label from another Thread?   I have a Form running on thread1, and from that I'm starting another thread (thread2).  While thread2 is processing some files I would like to update a Label on the Form with the current status of thread2's work.   How could I do that? I have ubuntu 12.04 (original) installed on a server.  How do I upgrade this to 12.04.03? $|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. I'm trying to show that $(a_n)$ is convergent by showing that $(a_n)$ is Cauchy.  let $|a_2 - a_1 |  =x$.   $|a_3-a_2| \leq \frac{1}{2}x$  $|a_4-a_3| \leq \frac{1}{2}|a_3-a_2|\leq \frac{1}{4}x$  In general, for every $n$:  $|a_{n+1}-a_n| \le \frac {1}{2^{n-1}}x$  Let $\epsilon &gt;0$  for every $m,n &gt; 0 $, say $m&gt;n$ the following holds:  $$|a_m-a_n| = |a_m-a_{m-1} + a_{m-1} - a_{m-2} \dots a_{n+1}- a_n| \le$$  $$|a_m-a_{m-1}| + |a_{m-1} - a_{m-2}| + \dots |a_{n+1}-a_n| \leq \frac{x}{2^{m-2}} + \frac{x}{2^{m-3}} + \dots + \frac{x }{2^{n-1}}$$.  I can say that for big enough $n,m$, $|a_m-a_n|&lt;\epsilon$ and therefore, this sequence is Cauchy? It sounds not good enough to me yet I don't know what else to do here. If $x$ and $y$ are irrational, is $x + y$ irrational? Is $x - y$ irrational? I'd like to create a popup list on one of my Visualforce pages, for a user to select from a list of OrgWideEmailAddress records.  My goal is to limit the list to only those records that they're allowed to use.  I'm going to save the selection for use in later automatic emails.  Based on what I've read, I won't be able to send emails to certain OrgWideEmailAddresses:   The address hasn't been verified yet.  I don't see any fields in the schema that appear to show verification state. The address is only available to profiles that the user isn't a member of.  I don't see where the profile list is stored for each record.   Some of my problem could just be due to not understanding the standard objects so well, and perhaps there's a way to get at this through UserInfo, or by making my query on the User object which may have a child relationship to OrgWideEmailAddress since it's listed in the schema viewer of the Force.com IDE.  Here's the test code I'm working with:  for (OrgWideEmailAddress addr : [SELECT DisplayName, Address          FROM OrgWideEmailAddress ORDER BY DisplayName]) {     System.debug( addr.DisplayName + ' &lt;' + addr.Address + '&gt;'); }   I tried creating a new Messaging.SingleEmailMessage and then calling setOrgWideEmailAddressId() on it with each OrgWideEmailAddress Id, in hopes that invalid Ids would throw an exception, but to no avail.  My goal is to modify the test code to provide just the subset of records that the current user will be able to use. Why my DCIM folder is empty seen in the computer but not empty in the phone I am using HuaWeiNova device, and I tried to access it with aft-mtp-cli. $ aft-mtp-cli $ ls DCIM/  I got folders listed here: |-photos |-Camera ....  When I tried to list or download my photos in the Camera/ folder, I got nothing. Only the empty folders are listed and the folders that contains files are not shown at all. I am quite sure my photos are stored in the Camera folder in my cell phone. How come I could not access my photos with my computer ? What does var prime = num != 1; mean? Modifying Score text in Locate Widget of Flexviewer 2.4? I want to add text where it says "score" to make it more clear that this is an address matching score.    I am using the LocateWidget_US.xml and do not think I can do it here.  I think the place to do it may be in the LocateWidget.mxml in this line????   locateResult.content = getDefaultString("resultScoreText") + " " +   (addrCandidate.score % 1 == 0 ? addrCandidate.score : addrCandidate.score.toFixed(1)); Knots in Smoothing Splines In , there's this line under the section describing Smoothing Spline's tuning parameter $\lambda$:       In fitting a smoothing spline, we do not need to select the number or   location of knots - there will be a knot at each training observation,   $x_1,...,x_n$.   But, in my opinion wouldn't that be overfitting?     Reason for such a claim: If there are more points which act as knots in the Spline fit, then the range for each slot for fitting is very small. Thus each change in the data, is recognized and imititated in the fit. Thus fitting the changes, which are random, and do not mean anything. Thus overfitting.    Possibilities: We know that cubic splines and Smoothing splines are different. The basic differences are:     Smoothing splines try to minimize the function $$\sum_{i=1}^n(y_i-g(x_i))^2+\lambda\int g''(t)^2dt$$ Smoothing splines shrink the parameters.   Moreover, Smoothing Splines are basically natural cubic splines, and thus they're smooth too.  So, how can these differences( and properties) save the Smoothing Spline from overfitting? Is there anything else that I'm missing here? Sums in math mode: how to display index under the sigma sign? I have a fraction with sums above and under the line. How can I convince LaTeX to write the indices of the sums under the sigma instead of next to it?  \begin{displaymath}   \frac{\sum_{s \in S} s^2}{\sum_{p \in P} p^2} \end{displaymath} Understanding psql prompts How to quit Skype on Android? Best way to save data in a Java application? Where can I find people for hire with LaTeX skills and designer skills? The description of the  says:     Your Intelligence score is 19 while you wear this headband. It has no   effect on you if your Intelligence is already 19 or higher.   The  spell description says that my Intelligence score becomes 1 on a failed save:     [...] On a failed save, the creature's Intelligence and Charisma   scores become 1. The creature can't cast spells, activate magic items,   understand language, or communicate in any intelligible way. [...]   If I am affected by Feeblemind and I am wearing the Headband of Intellect, would I have an Intelligence score of 19 or 1?   Also, what about the other effects like not being able to cast, activate magic items, understand languages or communicate in any way? Those seem Intelligence-related, but are mentioned additionally to the reduction.   If the Intelligence score becomes 19, are the other effects still active?