Re-writing $f(x, y)$ as $g(x)h(y)$
How can I separate a separable function
Pausing a long running program in the terminal? Is there a keyboard key combination that I can use to pause a program running in the terminal? In case it matters, I don't intend to run anything else inside that terminal while the program is paused. I just want to pause the program execution, and resume it later. How can I do this? Is there a way of finding a formula for $\sum\limits_{k=1}^n k^k$? Maybe I'm missing something really obvious, but I've looked around a bit on the Internet and I haven't been able to find anything.  So, what I'm looking for is a formula in closed form to generate the sequence $1,5,32,288,3413,\dots$ How to get the last date of a particular month with JodaTime? In  (2014) the human race seemed to be facing pretty poor odds until they discovered a convenient wormhole placed by an unknown entity expressed as "they". Later in the movie, we discover that       "they" are actually the human race in the future, reaching back in  time to save itself.   The end of the movie gets a little wild on the physics end, and I'm happy to take that ending as is - no need for it to make sense - but one very basic detail does bother me:  How could the human race have gone back in time to save itself from circumstances that would have caused us to go extinct without our own help (the convenient wormhole)? Sell your home and invest in growth stock mutual fund I purchased a home and I made an agreement with a guy who is living in that home and paying me monthly rent. Since I live with my brother I don't have to live in my purchased home.  The rent I'm getting is only 10% of total cost of home while stock fund industry (mutual fund) is paying 20% minimum i.e. I'm getting 10% loss every year and that is a big amount.  I'm not really sure if my home also increase it's value by 10% every year. But I don't think it will be.  Now I'm thinking of selling that home and investing all of my money in a growth mutual fund. Any advice? Edge won't connect to internet, Skype for business won't screen-share, Windows Store won't update apps after Windows 10 version 1809 installed I just installed Ubuntu and it is great.  However, I installed in beside the Windows Vista OS.  I now want to remove Windows in an effort to improve performance.  What is the easiest way to do this? How to create tagged PDF such that they will be:   good enough for PDF/UA "reflowable" on smaller screens and ebook readers   Any syntax &amp; any engine are of interest, but I'm most interested in using LaTeX with [Xe|pdf]latex engines. Why do we need sigma-algebras to define probability spaces? We have a random experiment with different outcomes forming the sample space $\Omega,$ on which we look with interest at certain patterns, called events $\mathscr{F}.$ Sigma-algebras (or sigma-fields) are made up of events to which a probability measure $\mathbb{P}$ can be assigned. Certain properties are fulfilled, including the inclusion of the null set $\varnothing$ and the entire sample space, and an algebra that describes unions and intersections with Venn diagrams.  Probability is defined as a function between the $\sigma$-algebra and the interval $[0,1]$.  Altogether, the triple $(\Omega, \mathscr{F}, \mathbb{P})$ forms a probability space.  Could someone explain in plain English why the probability edifice would collapse if we didn't have a $\sigma$-algebra? They are just wedged in the middle with that impossibly calligraphic "F". I trust they are necessary; I see that an event is different from an outcome, but what would go awry without a $\sigma$-algebras?     The question is: In what type of probability problems the definition of a probability space including a $\sigma$-algebra becomes a necessity?       provides a plain English accessible explanation. The idea is a spinning pointer rotating counterclockwise on a circle of unit perimeter:       We begin by constructing a spinner, which consists of a circle of unit   circumference and a pointer as shown in [the] Figure. We pick a point   on the circle and label it $0$, and then label every other point on the   circle with the distance, say $x$, from $0$ to that point, measured   counterclockwise. The  experiment  consists  of spinning the pointer and    recording the label of the point at the tip of the pointer. We let the random   variable $X$ denote the value of this outcome.  The sample space is   clearly the interval $[0,1)$.  We would like to construct a   probability model in which each outcome is equally likely to occur. If   we proceed as we did [...] for experiments with a finite number of   possible outcomes,  then we must assign the probability $0$ to each   outcome,  since otherwise,  the  sum  of  the  probabilities,  over    all  of  the  possible  outcomes,  would not equal 1.  (In fact,   summing an uncountable number of real numbers is a tricky business;    in  particular,  in  order  for  such  a  sum  to  have  any  meaning,   at  most countably many of the summands can be different than $0$.)    However, if all of the assigned probabilities are $0$, then the sum is   $0$, not $1$, as it should be.   So if we assigned to each point any probability, and given that there is an (uncountably) infinity number of points, their sum would add up to $&gt; 1$. I've searched for multiple forums for this questions and have seen different answers but so far, nothing have worked yet even from the ones I've seen here.  I want to extract a single file from a tar to a different directory.  I've tried this:  tar xvf file.tar -C /home/dir/ filename   or this:  tar -x filename -f file.tar -C /home/dir   But got these errors respectively:  x filename, 14826 bytes, 29 media blocks. File -C not present in the archive. File /home/dir not present in the archive.   and:  tar: /dev/rmt0: A file or directory in the path name does not exist.   The first extracted the file but in the same directory, not to the folder I wanted. Overriding "+=" in Python? (__iadd__() method) Where are the default settings saved for the Command prompt defaults? So I'm at that step where I am finally ready to Render my first big project. Aaaaaand it's been stuck on the first 4 tiles for the last 2 hours?   I am using a MacBook Pro Processor: 2.5 GHz Intel Core i5 Memory: 4 GB 1600 MHz DDR3 Graphics: intel HD Graphics 4000 1024 MB  (I include these because I have no idea what affects a computers ability to render but I assume it's one of them, most liekly the graphics card).  So anyways here are the pictures, as you can see I played with changing the resolution, the sample size and the max steps to see if I got different results but it just keeps getting stuck at those 1st four tiles. I've rendered a few other small projects successfully but this was my first time changing some values. I assume i've managed to accidentally change the wrong values and thats causing some conflict thats either stopping the render itself or is making it just too much for my computer.  My goal was the render this particular picture at a good enough resolution and clarity that it could then be made into a poster. So i wanted the resolution to be good and the sampling to be high.       Since writing this there has been no change to any of the numbers at the top of the render result (the time left, etc) The default font is too small on my screen at the resolution I have it, so I like to reset the font to size 12, but it appears I have to do this everytime I launch the program.  How do I make it remember my preferences? I have been thinking on and off about a problem for some time now. It is inspired by an exam problem which I solved but I wanted to find an alternative solution. The object was to prove that some sequence of functions converges weakly to zero in $L^2$.   I managed to show (with some help) that the limit $f$ (of a subsequence) satisfies $\int_0^x f \ dm=0$ for all $x&gt;0 $. From this I want to conclude that $f=0$ a.e. I can do this with the fundamental theorem of calculus in its Lebesgue version but there ought to be a more elementary proof.  Can someone here help me out? Spacial curvature and expanding space If we take the analogy that in an empty space the space is just a flat sheet then if there is a single planet or a star then the flat sheet will curve below the planet leaving a curvature shaped like a hemisphere below the object, my question is, Does this curvature change as space expands? Multiple domains for different products? I have a website with software applications. Is it good for SEO to choose one keyword rich domain name for each of our software products or should we stick to a single domain?  From a user's perspective I think it would be easier to remember a domain that is keyword rich as the user will instantly know what this product is for.  But I have read articles that the latest trend in SEO is to stick to one domain for all of your products and invest on this single domain website.  Is that true? What do you advise? Should I register a separate domain for each of our products or should I use only one single domain?  Should I do a 301 redirect with a .htaccess to a single domain? And what about the sitemaps? Should I register all sites in Google Webmaster Tools and post a separate sitemap for each one of them? should my main site sitemap include all pages or should separate domains have their own sitemaps? Make flash drive bootable with MULTIPLE Windows Installers I have seen many ways to make a USB an installer for about any Windows OS. But how can I (using grub or something like that) make it bootable to all editions on Windows XP and 7?   I have tried Googling it and researching, I've even tried to do it, But I dont understand much about GRUB or linux at all.  Please keep in mind that I am not very good with linux, so please use as many details as possible. Does "notified by [date]" include the end date? I have read the Rules of a competition. The text of the Rules include a sentence as follows:     As per stated in the Rules the entrants will be notified by May 30th 2010.   Does the sentence above mean that May 30th is included in the term of notification or not? Down vote changed to up vote caused reputation meter to pass daily maximum I just experienced a minor visual bug.  I had an answer that earned 2 down votes and 22+ upvotes, earning me the daily maximum of +200. Upon making some edits to the answer at the behest of the comments, one of the users who down voted changed their vote. Now my reputation meter shows that I gained +202 for the day.    This correctly did NOT affect my reputation, as I still only gained 200, so it is merely a minor display bug.  This appears in the achievements drop down and my reputation tab on my profile.