Hello I have problems with exercise For a positive integer $n&gt; 1$ let us denote by $Z_n$ the cyclic group of order $n$ a) Prove that all homomorphs of group $f: Z_{10}  \longrightarrow Z_9$ it is trivial. B) Find all homomorphisms of group $f: Z_{10}  \longrightarrow Z_8$ My atemp: a) We have $f: Z_{10}  \longrightarrow Z_9$ is homomorphism and we have $f(x) =1$ but I don't know how to better justify. b)How do I find all homomorphisms Thanks
All group homomorphism from $ \mathbb{Z} _m $ to $ \mathbb{Z}_n $  How could I find every group homomorphism?
Mixed DML operation error I am facing Mixed DML error in the following case:  static testmethod void method1() {     User u1 = DataFactory.createUser('testUser','test@user.com','permissionSetAPIname');        Obj1 rec1 = DataFactory.createrec1('Record1');     insert rec1;      Obj2 rec2 = DataFactory.createrec2('Rec2',rec1,system.today()-10, system.today()+10 );     insert rec2;       Obj3 rec3 = DataFactory.createrec3(rec2,'Tester',u1,'US');     insert Role;      test.starttest();         //testing code      test.stoptest();  }   However the following is working fine  static testmethod void method1() {      User u1 = new User(Alias = 'testRole',                   Email             = 'role@test.com',                   EmailEncodingKey  = 'UTF-8',                   LastName          = 'user',                   FirstName         = 'test',                   LanguageLocaleKey = 'en_US',                   LocaleSidKey      = 'en_US',                   ProfileId         = [select Id from Profile where Name = 'Basic User' limit 1].Id,                   TimeZoneSidKey    = 'America/Chicago',                   Username          = 'stakeholder@test' + Math.round(Math.random() * 10000) + '.com',                   UserRoleId        = null,                   Country           = 'Great Britain');     insert u1;         Obj1 rec1 = DataFactory.createrec1('Record1');     insert rec1;      Obj2 rec2 = DataFactory.createrec2('Rec2',rec1,system.today()-10, system.today()+10 );     insert rec2;       Obj3 rec3 = DataFactory.createrec3(rec2,'Tester',u1,'US');     insert Role;      test.starttest();         //testing code      test.stoptest();  }   Please explain the difference. As my understanding is that transaction remains the same in both the cases. Create taxonomy terms on the fly Close and flag links do nothing on mobile site This morning (it's about six AM here) I find that I can no longer submit close votes; the link just jumps to the beginning of the page.  I'm on iOS, using a third-party browser called Grazing, but a brief check with Mobile Safari shows the same problem there.   Here on Meta, where my score is much lower, I only get a "delete" link on my own question, and that works fine. (Oops :-))   Update: As per comments, this affects the "flag" link, too, which doesn't even scroll to the top of the page. Update 2: Latest comment suggests this affects Android, too. Update 3: This also affects desktop computers when viewing mobile (when you click "mobile" in the footer) Update 4:  mentions Windows 8, too; simply deleting platform-specific tags Is hyperref really the best way to add metadata to a TeX file? So I know one of hyperref's features is that it can add metadata to you PDFs. This is a nice feature and if you're putting stuff online, it's good to include metadata.  But is the hyperref package really the best way to do it? I mean, if you're using hyperref anyway, that's fine. But if you don't want hyperrefs in your document, it seems weird to include the package, and then turn off pretty much all its functionality. And given that hyperref is a shorthand for "package conflict nightmare", is seems insane that you should have to deal with it just for the sake of some metadata.  So I have two questions.   Is there a good reason that hyperref includes this functionality which is apparently unrelated to its primary purpose? Is there a better (smaller, less conflicty, easier...) option to include metadata in my PDFs? Fade in each element - one after another I am trying to find a way to load a JSON page to display my content, which I currently have. But I am trying to fade in each element one after another? Is anyone familiar with a way to do that?  Fade in each element with a slight delay?  Here is an example of my code, I am using the jquery framework.  CODE: Dynamic grid with Atlas generation How can I run Maniac Mansion through ScummVM? Day of the Tentacle Remastered Edition includes Maniac Mansion as a .  The game appears to be exactly the same as the old DOS release (albeit, the enhanced version).  If possible, how can I run this game through ScummVM?  Pointing ScummVM at my installed game doesn't work.  What do I need to do to play this version of Maniac Mansion? How to prove $B-A \succeq 0 \Leftrightarrow$ ellipsoid $x^TBx \leq 1$ contains $x^TAx \leq 1$? Assume $A \in \textbf{S}^n_{++}$, an ellipsoid centered at the origin given by $$\mathcal{E}_A = \{x\mid x^TA^{-1}x \leq 1\}$$ Then we have $\mathcal{E}_A \subseteq \mathcal{E}_B $ if and only if $B-A \succeq 0$. This is the proposition in the Boyd &amp; Vandenberghe's  (pages 45-46). The authors gave only the result, without proof. How to prove it? Why am I getting "size mismatch" errors from the Iceland mirror? After installing Ubuntu 12.04 (clean install) I fetch a bunch of program via synaptic (installed specially), all programs worked except Gimp 2.8. So I tried purging Gimp, install again (no luck). Checked broken packages and reinstalled them. When using the Software center I get this MSG:  Failed to fetch http://is.archive.ubuntu.com/ubuntu/pool/main/o/openexr/libopenexr6_1.6.1-4.1_amd64.deb Size mismatch   Tried also this:  sudo apt-get purge gimp* sudo add-apt-repository ppa:otto-kesselgulasch/gimp sudo apt-get update sudo apt-get install gimp   And get this MSG:  Failed to fetch http://is.archive.ubuntu.com/ubuntu/pool/main/o/openexr/libopenexr6_1.6.1-4.1_amd64.deb  Size mismatch E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?   I am wondering if the Icelandic Archive has an outdated version or something?   would really like to install Gimp 2.8 but Gimp 2.6 is OK to.   I am also wondering if I am doing something wrong? Equation left margin Pagination not working with custom loop I've got a custom loop that I'm using to display some Real Estate listings that will be available within 60 days. I'm calling it with the following function:   &lt;?php  $sixtydays = date('Y/m/d', strtotime('+60 days')); $paged = (get_query_var('paged')) ? get_query_var('paged') : 1; $query = new PostsOrderedByMetaQuery(array(   'post_type' =&gt; array('post', 'real-estate'),   'meta_key' =&gt; 'Time Available',   'meta_compare' =&gt; '&lt;=',   'meta_value' =&gt; $sixtydays,   'paged' =&gt; $paged,   'orderby_meta_key' =&gt; 'Price',   'orderby_order'    =&gt; 'ASC' )); ?&gt; &lt;?php while ($query-&gt;have_posts()) : $query-&gt;the_post(); ?&gt;   While the loop works great, I can't get it to paginate. It shows the first 10 (my default) posts but doesn't show the pagination. The only way to display all posts is to show them on one page by adding 'posts_per_page' =&gt; -1, I have similar loops on other pages that have no problem paginating. The only difference with this one is that there are two meta keys that are filtering the posts.   I'm using WP Page Navi for this and the rest of my pages. I'm closing the loop and adding the pagination using the following code:   &lt;?php endwhile; // End the loop. Whew. ?&gt; &lt;?php wp_pagenavi(); ?&gt; &lt;?php wp_reset_query(); ?&gt;   How can I go about fixing this? $d_1(x_1,y_1)$ and  $d_2(x_2,y_2)$ are metric on $X$ and $d(x,y)$ is defined as: $$d(x,y)= \sqrt{d_1(x_1,y_1)^2+d_2(x_2,y_2)^2}.$$ I am trying to show this is a metric. Can you give me some clue about proving the triangle inequality for $d$ ? Thank you for your help. How do I use the conditional (ternary) operator? Shape of the universe? Package Listings Warning: Text dropped after begin of listing when calling function I'm trying to this:  \newcommand{\code}[1] {\begin{lstlisting} {#1} \end{lstlisting} }   But I keep getting this error:  Package Listings Warning: Text dropped after begin of listing   I'm calling \usepackage and all so, do any of you knows how to solve this? Chat arrangement question: Left or right? I'm building a small chat. Now I see but in other chats (whatsapp, facebook mobile chat, sms ...) that the arrangement is always the same:  Left: the chat partner. right: myself      Why is that? I'd like to declare some new operators using \DeclareMathOperator and some of the names are already taken by other commands (that I do not want to use). Is there an equivalent to the \renewcommand command for \DeclareMathOperator or a different way to overwrite the commands using \DeclareMathOperator? How to turn off the iOS-style character picker menu Inductive proof of the closed formula for the Fibonacci sequence Fibonacci numbers $f(n)$ are defined recursively:  $f(n) = f(n-1) +f(n-2)$ for $n &gt; 2$ and $f(1) = 1$, $f(2) = 1$. They also admit a simple closed form: $$\sqrt 5 f( n ) = \left(\dfrac{1+ \sqrt 5}{2}\right)^n- \left(\dfrac{1 - \sqrt 5}{2}\right)^n \tag1$$  How to prove (1) using induction?  Remarks One could get (1) by the general method of solving recurrences: look for solutions of the form $f(n)=r^n$, then fit them to the initial values. But there should be a more concrete proof for this specific sequence, using the principle of mathematical induction. The phrase "let alone" I notice that "let alone" is used in sentences that have a comma. The structure of the sentence is what comes before the comma is some kind of negative statement. Right after the comma is "let alone," followed by the rest of the sentence.  What does "let alone" mean here? Does it mean the same thing as "or even?" Can someone explain this phrase and sentences that have it?