Lorentz transformation for timelike and spacelike points
A question about causality and Quantum Field Theory from improper Lorentz transformation
What should I do, as my submitted paper is still under review after 1 year? How to use Parameterized MessageFormat with non-Value attributes of JSF components Exact Sequences of Modules and Rank Suppose that:  $0 \rightarrow M_{1} \rightarrow M \rightarrow M_{2} \rightarrow 0$  Is an exact sequence of $R$-modules (for $R$ commutative integral domain). Show that $\mathrm{rk}(M) = \mathrm{rk}(M_{1})+\mathrm{rk}(M_{2})$    I have shown the inequality $\mathrm{rk}(M) \geq \mathrm{rk}(M_{1})+\mathrm{rk}(M_{2})$, however for the opposite direction I'm lost. I tried to take $N$ as a linear independent subset and tried to decompose it into $N_{1}$ (the elements in $\mathrm{Ker}(g)$) and $N_{2}$ (the elements not in $\mathrm{Ker}(g)$), but I haven't got far, since $N_{1}$ gives us a linearly independent set in $M_{1}$, however $N_{2}$ can give us a linearly dependent set in $M_{2}$.   We define $\mathrm{rk}(M)$ in this case as the supremum over all cardinalities of the linearly independent subsets of $M$ (where the only finite linear combination equaling $0$ implies trivial coefficients for $r \in R$).  Would this be the proper way to show the result? I think I'm missing something important. Why isn't Arthur woken up by the kick? How to add flavouring ingredients to steamed or boiled veggies? Downgrading MacBook Pro 16” to Mojave Did anyone succeed in installing Mojave on the MacBook Pro 16”? It ships with Catalina but my corporate requires Mojave to connect to the corporate network.  I  but once I select booting from the Mojave external drive I get a “forbidden” icon and the system shuts down. Non academic career options for PhD in Math I am thinking of getting my M.S. in Computer Science. I chose C.S. because I enjoy programming and because its a solid choice, career wise.  Low unemployment, good pay, all that jazz.  But my real passions has always been math and lately I have been thinking about swapping and going for my graduate degree in Math. If I went the math route I would probably go full PhD (since I don't think there is much you can do with just a Masters in math).  But as much as I love math, I can't see myself being a math teacher. I would want to work in research or industry, applying math to solve real world problems.    What kind of non-academic jobs are there for someone with a PhD in math (or what is the best resource to see what jobs are out there)? Case field mapping with custom object fields? Is it possible to create a "weak reference" in javascript? Is there any way in javascript to create a "weak reference" to another object?   Can anyone think of a way to implement this  behavior in javascript? Which movie/TV show has an evil cyborg harvesting eyes from androids in a hidden town? I watched it maybe more than 8 to 12 years ago, but as far as I remember there was this place where androids (or maybe they were cyborgs) lived. (I think it was more like a hidden town). This guy finds them by accident (or at least I remember it that way) and tries to help them. I don't remember seeing any aliens or spaceships or anything like that. It was live-action, and I think US-based.  So, what I remember:   The bad guy is a human who has one red flashy robotic eye (not like terminators, it looks like a square eye patch above one of his eyes that functions like a second eye), he is collecting eyes from these androids/cyborgs. He also kills some of these androids/cyborgs but not all of them, some of them he just collects their eyes and doesn't kill (or get to kill). There was this woman who was a sexbot or something, she tried to give pleasure to the bad guy at some point, yet the bad guy added one of her eyes to his collection instead, but didn't/wasn't able to kill her. Towards the end she says something like "I used to give pleasure, now I only want to give pain" The human guy who found them tried to help them defend themselves from the bad guys, but they were in bad shape, many of them needed repair. To repair some of them, they needed spare parts they didn't seem to have, but one of the android/cyborg dudes said something like "we don't really bury our dead" and he brought a box of spare parts (or maybe android/cyborg body parts), they used these parts to repair some of the androids/cyborgs. There was this android/cyborg guy who was an assassin or something, but lost his fingers or hands, they couldn't find any hands compatible to his, but he said something like "I can still feel my trigger finger, just attach the weapons to my hands".   I remember it as a great movie/tv show, but I can't find anything about it. Can someone help me?  Please and thank you in advance... How do you override page.tpl.php in Omega 4? I am using the  base theme, and am trying to override page.tpl.php.    This file is in the base theme in sites/all/themes/omega/templates/system.  When I copy it into my theme, edit it, clear caches, I don't see my changes?  Why can't I override this template? I have always recommended pressing ALT+F2 and typing for example gksu nautilus or gksudo nautilus both are equivalent; to run graphical programs with root privileges.  However, I have just installed raring on a test system and this no longer works.  gksu and gksudo are not installed as part of a default raring install; though they are in the repositories. In 12.04 at least gksudo was just a symbolic link to gksu  The reasons I have always done this are because while it is often safe to use sudo under some circumstances it can cause problems with graphical applications because gksu has you running the program as root while with sudo you are running as yourself but with elevated privileges.  This can mean you inadvertently change the owner of critical system files.  This can cause problems.  This reasoning is explained better here:         Why was command removed from a fresh install and what should we be using instead? Which standard objects don't support triggers? List all sites in multisite I want to list all sites in the multi site network in alphabetical order? Right now, the code lists by registered date  &lt;?php // Query for getting blogs             $blogs = $wpdb-&gt;get_results( $wpdb-&gt;prepare("SELECT blog_id, domain, path FROM $wpdb-&gt;blogs WHERE site_id = %d AND public = '1' AND archived = '0' AND mature = '0' AND spam = '0' AND deleted = '0' ORDER BY registered DESC", $wpdb-&gt;siteid), ARRAY_A );              // put it in array               foreach ( (array) $blogs as $details ) {$blog_list[ $details['blog_id'] ] = $details;}             unset( $blogs );             $blogs = $blog_list;              // if is valid array             if (is_array( $blogs ) ){                     echo '&lt;ul&gt;';                     $array= array();                     // reorder                     $array= array_slice( $blogs, 0, count( $blogs ) );                     for($i=0;$i&lt;count($array);$i++){                     // get data for each id                     $blog = get_blog_details( $array[$i]['blog_id'] );                     // print it                     echo '&lt;li&gt;&lt;a href="'.$blog-&gt;siteurl.'"&gt;'.$blog-&gt;blogname.'&lt;/a&gt;&lt;/li&gt;';                     }                     echo '&lt;/ul&gt;';             }             ?&gt; A generic question across most board games: once a player has taken their turn (taken their finger off the piece they are playing), should they be allowed to change their mind?  Similarly, if a player forgets to take a privilege, such as an occupied building in Puerto Rico giving an extra worker, or plantation, if they remember a few moves later, should they be allowed to take the privilege?  Very few rules explicitly express how these events should be dealt with, so they are generally left up to the group. However, my group's rules will change depending on the personality of the players playing (not all members are available each time we play). I would like to make this consistent, and would appreciate feedback on how others deal with this scenario. Why is it called the Millennium Falcon? I'm particularly interested in how the "Millennium" part pertains to the ship itself. It wouldn't hurt to explain the "Falcon" part either though. Can you prove that if $p$ is a prime greater than $5$, then the sum of the squares of the quadratic nonresidues modulo $p$ is divisible by $p$?  Note that I have just proved that the sum of the quadratic residues modulo $p$ is divisible by $p$ for $p$ greater than $3$. What does "isomorphic" mean in linear algebra? Enumerate or list all variables in a program of [your favorite language here] A friend asked me last week how to enumerate or list all variables within a program/function/etc. for the purposes of debugging (essentially getting a snapshot of everything so you can see what variables are set to, or if they are set at all). I looked around a bit and found a relatively good way for Python:   #!/usr/bin/python                                                                                                                                                                                                                            foo1 = "Hello world" foo2 = "bar" foo3 = {"1":"a",         "2":"b"} foo4 = "1+1"  for name in dir():     myvalue = eval(name)     print name, "is", type(name), "and is equal to ", myvalue   which will output something like:   __builtins__ is &lt;type 'str'&gt; and is equal to  &lt;module '__builtin__' (built-in)&gt; __doc__ is &lt;type 'str'&gt; and is equal to  None __file__ is &lt;type 'str'&gt; and is equal to  ./foo.py __name__ is &lt;type 'str'&gt; and is equal to  __main__ foo1 is &lt;type 'str'&gt; and is equal to  Hello world foo2 is &lt;type 'str'&gt; and is equal to  bar foo3 is &lt;type 'str'&gt; and is equal to  {'1': 'a', '2': 'b'} foo4 is &lt;type 'str'&gt; and is equal to  1+1   I have so far found a partial way in PHP (courtesy of ) but it only lists all variables and their types, not the contents:   &lt;?php // create a few variables $bar = 'foo'; $foo ='bar'; // create a new array object $arrayObj = new ArrayObject(get_defined_vars()); // loop over the array object and echo variables and values for($iterator = $arrayObj-&gt;getIterator(); $iterator-&gt;valid(); $iterator-&gt;next())         {         echo $iterator-&gt;key() . ' =&gt; ' . $iterator-&gt;current() . '&lt;br /&gt;';         } ?&gt;   So I put it to you: how do you list all variables and their contents in your favorite language?    Edit by : I propose this question follows the spirit of a little "". If you do not agree, just edit and remove the tag and the link. Shuffle an array with python, randomize array item order with python What's the easiest way to shuffle an array with python?