The best student in a school or university
Is there a word in English to qualify the highest-ranked student in a class in a year?  We are talking here about higher education, especially in the context of curricula that keep a given set of students over the course of several years, being ranked at the end of each year, possibly with competitive admission for the following year. The ranking is a weighted average of all marks obtained over the year.  I am looking for a single word, or expression, to quickly designate the one student with the highest ranking. If there is no such thing in English, then let's try to get the most concise and idiomatic definition.  In all cases, it is not emotionally connoted, i.e. not pejorative nor bragging.  For French speakers: I am looking for the translation of “major de promotion”.    EDIT: additional, not as much of a pure “word request” question: is this anything you should mention on a curriculum vitæ in the English-speaking world? If so, please mention whether the given word is appropriate for such a use&nbsp;&nbsp;:)
contractive property A topological property $\mathcal{R}$ is contractive if $(X,\tau)$ has property $\mathcal{R}$ and if $\tau^{\prime} \subset \tau$, then (A, $\tau^{\prime}$) has property $\mathcal{R}$.  A topological space is $T_B$ if each compact subset  is closed.  A topological space is called a US-space provided that each convergent sequence has a unique limit.  A topological space is called a C- C-space provided that  the  compact subsets  are precisely the closed sets.     Is property C-C , US contractive,  hereditary?      Is property $T_B$  contractive? If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian? I know that any group satisfying $x^2=1$ for all $x$ is abelian. Is the same true if $x^3=1$? I don't think it is, but I can't find a basic counterexample. Suppose a vibrating fork exerts force to the air particles to compress which leads to the increase of internal energy (heat).This heat or energy given by the fork is given to the next layer of air and in this way, this energy makes sound. But if it was so, it will be isothermal. And Laplace told it was adiabatic. How can it be? I am confused. The heat energy infact is the energy given by the fork. If it is adiabatic, how can the air pass this energy ? Broken image link on the new Stack Exchange blog Before I jump on to the problem, let me first congratulate  and his team for the newly re-designed Stack Exchange blog. I like it very much, great job! While searching on Google, I stumbled upon  blog post of Jeff Atwood and found few broken images. There are currently four images are broken on this post, Here is one of them:    Upon doing an inspect element on one of the broken image (same goes for all other broken images on the post), I found out that it is currently pointing to: https://blog.stackoverflow.com/wp-content/uploads/stackexchange-genuine-example11.png The newly re-designed Stack Exchange blog is now moved to a new location:  and the old blog URL i.e.  has the correct mapping of URL redirection (also called URL forwarding) and works perfectly. But, the problem lies in the latter part i.e. /wp-content/uploads/ directory structure does not exist anymore at the new blog location. I read the Jon Chan's  post (nice writeup! btw) where he talks about his custom Python script. Here is the relevant excerpt taken from that post:  I wrote a Python script to go through all the imported posts, looked for references to WordPress hosted content, download all the static assets into images/wordpress in the repo, and changed all the links to relative paths on Jekyll. Worked surprisingly well.  In other words, all of the old /wp-content/uploads/ static assets is now resides under the /images/wordpress/ directory at the new blog location. So, Jon's find and replace script should have worked (which it did for the most of the part) as intended to be but apparently it did not catch few of them. At least on  blog post and few other like ,  or . We could possibly have more but these are the ones I have found so far. I believe it's a minor bug somewhere in the script and could be fixed with few lines of code tweaking. Also, the static content link mapping problem would not have occurred at all if the directory name was unchanged as the URL redirection (as stated above) would have taken care of it. But, there must a reason for this change. Upon investigating further, I found out that the issue with broken images does not end here. They will still appear as broken even if Jon's script replaces the path to the correct one. Because the images have not been uploaded (or copied) to the blog's new /images/wordpress/ directory at all. They are missing! For example, try clicking on the following link: ## I replaced old dir. path /wp-content/uploads/ to the new /images/wordpress/  So, in a nutshell, in order to fix this broken images link problem, we need to make sure that not only they are pointing to new path i.e. /images/wordpress/ but also do exists (i.e. uploaded) at the blog's new location. Please fix this at your earliest. Windows Batch recursive delete old files How can I retrieve data within my widget I have a Widget which I am creating but my quesiton is how do I access my custom table which I created via my plugin. I am attempting to fill the dropdown from the table called tfp which contains the column liters which I wish to popluate the values into the drop down   class my_plugin extends WP_Widget {  // constructor function my_plugin() {         parent::WP_Widget(false, $name = __('Thomsons Fuels Widget', 'wp_widget_plugin') );  }  // widget form creation function form($instance) {  //Check values if( $instance) {  $title = esc_attr($instance['title']);  $dropdown= esc_attr($instance['dropdown']);  $textarea = $instance['textarea'];  } else {  $title = '';  $textarea = ''; } ?&gt;   &lt;p&gt; &lt;label for="&lt;?php echo $this-&gt;get_field_id('dropdown'); ?&gt;"&gt; &lt;?php _e('Liters',   'wp_widget_plugin'); ?&gt;&lt;/label&gt; &lt;select&gt; &lt;option value="volvo"&gt;Volvo&lt;/option&gt; &lt;/select&gt;  &lt;/p&gt;   How I created the table in the plugin   global $wpdb; global $custom_table_example_db_version;  $table_name = $wpdb-&gt;prefix . 'tfp'; // do not forget about tables prefix  // sql to create your table // NOTICE that: // 1. each field MUST be in separate line // 2. There must be two spaces between PRIMARY KEY and its name //    Like this: PRIMARY KEY[space][space](id) // otherwise dbDelta will not work $sql = "CREATE TABLE " . $table_name . " (   id int(11) NOT NULL AUTO_INCREMENT,   liters VARCHAR(100) NOT NULL,   price VARCHAR(100) NOT NULL,      postcodearea varchar(20) NULL,         dft varchar(20) NULL,   PRIMARY KEY  (id) );";  // we do not execute sql directly // we are calling dbDelta which cant migrate database require_once(ABSPATH . 'wp-admin/includes/upgrade.php'); dbDelta($sql);  // save current database version for later use (on upgrade) add_option('custom_table_example_db_version', $custom_table_example_db_version); Why do damaged hard drives freeze the entire system? How long does the Truffle take to move in after building the mushroom biome? I currently find myself in a pickle because even after I've built the mushroom biome and met all other requirements, the Truffle NPC won't move in.   I've defeated not only the Wall of Flesh but Ocram already. Created a surface mushroom biome. Built a house made out of mushrooms with mushroom furniture.   I have no idea how long it takes for the NPC to move in or if I'm wrong in any of the steps. Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$ I'm working on this problem already, the domain and co-domain are the set of Rational Numbers. we see that setting $x = 1$ and $y = n$, we obtain $f(n + 1) = f(n) + 1$  But I'm trying to prove that $f(n) = n + 1$ for all $n$, the case when $n = 1, 2$ is obviously true, how do I approach this via induction? No cycle containing edges $e$ and $g$ implies there is a vertex $u$ so that every path sharing one end with $e$ and another with $g$ contains $u$ There is a proof in my textbook for the following claim, which doesn't make a whole lot of sense to me.  My annotations are in bold.  Could someone perhaps elaborate on what's going on?  Claim.  If there does not exist a cycle containing edges $e$ and $g$ then there exists a vertex $u \in V (G)$ such that every path in $G$ sharing one end with e and another with $g$ contains $u$.  Proof: The claim trivially holds if $e$ or $g$ is a loop OK, so we assume that neither is. Let $P$ with vertex set $v_1, v_2, . . . , v_k,$ in order, be a path with $e$ joining $v_1$ to $v_2$ and $g$ joining $v_{k−1}$ and $v_k$. Let $f_i \in E(P_i)$ be the edge with ends $v_i$ and $v_{i+1}$. Let $j$ be chosen minimum so that no cycle in $G$ contains $e$ and $f_j$ We can do this because we know that at least the edge $g$ will not create a cycle by assumption, right?. We will show that $u = v_j$ satisfies the claim.  Suppose not. Let $C$ be a cycle containing $e$ and $f_{j−1}$ What if $f_j = e$?  then what cycle? a single vertex? and let $P′$ be a path from an end of $e$ to an end of $f$ Not sure what the book meant by $f$ here, any guesses? avoiding $u$. Choose a subpath $Q$ of $P′$ with one end in $V (C)$ and another in ${v_{j+1}, v_{j+2}, . . . , v_k}$ as short as possible. Then $C \cup Q \cup P$ contains a cycle containing both $e$ and $f_j$, a contradiction. (The last statement requires some case checking.) This ending seems a bit abrupt and non-obvious to me  Thanks for the help How would I implement the quantum oracle in Deutsch's algorithm? It's $\mathbb{Z}\subseteq \mathbb{Z}[X]/(X^5-1)$ an integral extension? It's $\mathbb{Z}\subseteq \mathbb{Z}[X]/(X^5-1)$ an integral extension?  $\mathbb{Z}[X]/(X^5-1) \simeq \mathbb{Z}[x]$ where $x^5-1=0$.  So is an integral extension because $x$ is integral  over $\mathbb{Z}$. It's right? Which is the best way to put function plots into a LaTeX document? Help for Mathematics High school I'm looking for mathematics books, courses + exercises for high school level. My daughter was high school certificated but she has stopped her studies for 5 years. She would like to be involved in new educational program but she needs to restore her mathematic capabilities.  Could you help me to identify which mathematics books can help her?  Thanks a lot for your reply,  FR. I need scale up video from one DOS game using . But with  on left side and  filter on the other one.  Input (320x200)    Output (1280x800)    Here is a command, where's xBR processing whole screen...  ffmpeg     -i input.avi     -sws_flags neighbor     -vcodec libx264 -strict -2     -preset veryslow -qp 0     -filter:v "xbr=4"     output.mp4 Problem about angle in isosceles triangle $ABC$ is an isosceles triangle, $AB=AC$, and $\measuredangle A=20^{\circ}$. For point $M$ on $AB$ and $N$ on $AC$, we have $AM=NC=BC$. Compute the  $\measuredangle BMN$.  In a similar problem (with only one point on one side) the key step was to construct an equilateral triangle on the other side. I tried using that in this problem too, but I didn't manage to solve it. Explanation of C++ FAQ's unsafe macro? Why the value of $PATH is different for root and normal user? for normal user I get :     /usr/lib/lightdm/lightdm:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/home/monty/google_appengine   which is actually the content of /etc/environment  For root I get:     /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin   what's the reason behind this and which file contains this line? What is the Big-O time complexity of the following nested loops: for (int i = 0; i &lt; N; i++) {     for (int j = i + 1; j &lt; N; j++) {         System.out.println(&quot;i = &quot; + i + &quot; j = &quot; + j);     } }  Would it be O(N^2) still? Django templates offer the builtin tag cycle for alternating between several values at different points in a template (or for loop in a template) but this tag does not reset when it is accessed in a scope outside of the cycles definition.  I.e., if you have two or more lists in your template, the rows of all of which you'd like to use some css definitions odd and even, the first row of a list will pick up where the last left off, not with a fresh iteration from the choices (odd and even)  E.g., in the following code, if the first blog has an odd number of entries, then the first entry in a second blog will start as even, when I want it to start at odd.  {% for blog in blogs %}   {% for entry in blog.entries %}     &lt;div class="{% cycle 'odd' 'even' %}" id="{{entry.id}}"&gt;       {{entry.text}}     &lt;/div&gt;   {% endfor %} {% endfor %}   I've tried obviating this by patching with the resetcycle tag offered here:    to no avail.  (The code didn't work for me.)  I've also tried moving my inner loop into a custom tag, but this also did not work, perhaps because the compile/render cycle moves the loop back into the outer loop?  (Regardless of why, it didn't work for me.)  How can I accomplish this simple task!?  I'd prefer not to create a data structure in my view with this information pre-compiled; that seems unnecessary.  Thanks in advance.