Which of these sentences sounds correct?  These dynamics are used to explain the convergence toward an equilibrium state. These dynamics are used to explain the convergence towards an equilibrium state.  I have been reading a lot of posts, but I still have doubts. Need your suggestions :).
Which one should should I use? For some reason I have always used "towards", but I see some people saying "toward", like :     A great deal of his work in economic   theory has been directed toward   strengthening the foundations of our   understanding of central banking and   social insurance--indeed, one of my   most advanced macroeconomic classes   was nothing but a set of changes rung   upon a particular model that Peter   Diamond had advanced at...   Is there a difference between the two? When should they be used?
What does it mean to "align" partitions? I am familiar with what partitions are, but I saw , and realised I didn't know what "aligned partitions" are.  So what does it mean to "align" partitions? What are the benefits, and the downsides? Evaluating $\int_0^\infty \frac{dx}{1+x^4}$. Can anyone give me a hint to evaluate this integral?  $$\int_0^\infty \frac{dx}{1+x^4}$$  I know it will involve the gamma function, but how? How to remove the WordPress version from some .css/.js files I know that I can use the following function to remove the version from all .css and .js files:  add_filter( 'style_loader_src', 'sdt_remove_ver_css_js', 9999 ); add_filter( 'script_loader_src', 'sdt_remove_ver_css_js', 9999 ); function sdt_remove_ver_css_js( $src ) {     if ( strpos( $src, 'ver=' ) )         $src = remove_query_arg( 'ver', $src );     return $src; }   But I have some files, for instance style.css, in the case of which I want to add a version in the following way:  function css_versioning() {     wp_enqueue_style( 'style',         get_stylesheet_directory_uri() . '/style.css' ,         false,         filemtime( get_stylesheet_directory() . '/style.css' ),         'all' ); }   But the previous function removes also this version. So the question is how to make the two work together? How to make a font with Adobe Illustrator? I have recently created my own font/typeface with Adobe Illustrator, and I would like to use it as a real font (e.g I would like to use it as I type something).   Is this possible in Adobe Illustrator or would I need a different software?   If so what program would be good for creating a font? Saving Arduino sensor data to a text file How can I save data retrieved from a sensor to a text file on the computer? Height of colorbox Is there anything like GF(6)? After running Win 7 for some unknown period of time, the taskbar icon highlight starts to stick (video demo here: ). If I restart or kill explorer.exe and relaunch, it goes away.  Any idea what might be causing this? Let $E|F$ be an algebraic field extension and a ring $K$ such that $F\subseteq K\subseteq E$. It is true that $K$ is a field? How do I check if an object has a specific property in JavaScript? Optimization used in latex In my scene I have a camera sitting at the origin. I would like to contraint it so that it always looks at the center of a given object. But the camera should not change its position.  I found some answers using a "TrackTo" or "LockedTrack" constraint but could not manage to make it work.  Could I probably use a Driver for this and if yes, how can I adjust it?  Thanks in advance! I obtained a licence key for Windows 8 through DreamSpark. Is there a way to download a Windows 8 ISO image like you could for Windows 7? I am on a non-Windows machine, so I cannot use the Secure Download Manager to download Windows 8 directly using DreamSpark. We just got a new laptop (ASUS) though we did have a mac.  We are trying to log onto Mojang to download Minecraft and it keeps saying, "The username and password are not recognized."   We have done all the usual procedures; we have reset the password, we are using the email, not the username to sign in, and it looks like the minecraft login servers are working etc. etc.  We quit Minecraft on the old computer and shut off that computer thinking that was the issue.   Still, we can't get onto Mojang.  We are accessing mincraft through firefox and trying to download it to the new computer but we can't get into the account to do that!  What in the world could be the issue? DNS subdomain (child) NS records If we have example.com we would setup things something like this: $ORIGIN example.com. @  1D  IN  SOA ns1.example.com. hostmaster.example.com. (                   2002022401 ; serial                   3H ; refresh                   15 ; retry                   1w ; expire                   3h ; nxdomain ttl                  )           IN  NS     ns1.example.com.           IN  NS     ns2.example.com.  since in the parent zone .com. there is already NS record for the example.com. child zone and A glue record for the ns1.example.com. for what purpose do we state NS records again in the child zone? and also, do we need to state A record for the name servers in the child zone itself? When should I upgrade my camera body? How to show that $L^p$ spaces are nested? Suppose $1&lt;p_1&lt;p_2&lt;\infty$, then show $L^{p_1}[a,b] \supset L^{p_2}[a,b]$.  I was able to show $\|f\|_{p_1} \le \|f\|_{p_2} (b-a)^{1/p_1 - 1/p_2}$ but I'm not sure how to proceed from here. PHB says 'once per turn,' so, it would seem that a Rogue with Sentinel, for example, could "consistently" deal Sneak attack twice per round (whether the enemy triggers an OA or the melee weapon attack provided by the Feat).  So, can rogues deal sneak attack damage with any weapon attack outside their turn? (obv. one that meets the standard requirements--finesse, adv or adj ally) How to duplicate sys.stdout to a log file? Edit: Since it appears that there's either no solution, or I'm doing something so non-standard that nobody knows - I'll revise my question to also ask: What is the best way to accomplish logging when a python app is making a lot of system calls?  My app has two modes.  In interactive mode, I want all output to go to the screen as well as to a log file, including output from any system calls.  In daemon mode, all output goes to the log.  Daemon mode works great using os.dup2().  I can't find a way to "tee" all output to a log in interactive mode, without modifying each and every system call.    In other words, I want the functionality of the command line 'tee' for any output generated by a python app, including system call output.  To clarify:   To redirect all output I do something like this, and it works great:  # open our log file so = se = open("%s.log" % self.name, 'w', 0)  # re-open stdout without buffering sys.stdout = os.fdopen(sys.stdout.fileno(), 'w', 0)  # redirect stdout and stderr to the log file opened above os.dup2(so.fileno(), sys.stdout.fileno()) os.dup2(se.fileno(), sys.stderr.fileno())   The nice thing about this is that it requires no special print calls from the rest of the code.  The code also runs some shell commands, so it's nice not having to deal with each of their output individually as well.  Simply, I want to do the same, except duplicating instead of redirecting.  At first thought, I thought that simply reversing the dup2's should work.  Why doesn't it?  Here's my test:   import os, sys  ### my broken solution: so = se = open("a.log", 'w', 0) sys.stdout = os.fdopen(sys.stdout.fileno(), 'w', 0)  os.dup2(sys.stdout.fileno(), so.fileno()) os.dup2(sys.stderr.fileno(), se.fileno()) ###  print("foo bar")  os.spawnve("P_WAIT", "/bin/ls", ["/bin/ls"], {}) os.execve("/bin/ls", ["/bin/ls"], os.environ)   The file "a.log" should be identical to what was displayed on the screen. UK PLAB Visa Refusal due to unexplained bank deposits