I'm experimenting with the idea of making a "portfolio" animation that shows some simple scenes and adds text and screenshots of blender's UI so people can see how the animation was made.  The problem I'm having is I tried to incorporate the video from one of my animations by linking the scene into the blend file.  When I add the scene to the VSE, it shows up rendered using the aspect ratio of the VSE scene (16:9), not the aspect ratio of the original animation (1:1).    When I browse the properties of the linked scene I can see it is a 384x384 render.    I tried fiddling with "cropping" the strip, but you can't crop by a negative amount.  Size effects just resize the incorrect image.  I know I can work around this by rendering the second scene to files and adding those files as an image sequence, but I'd like to build this portfolio scene to render without needing those temporary files.
When you add an image strip to the Video Sequence Editor, it stretches/shrinks your image to fit the full output frame.  How can I add an image at its original resolution?  For example, if I add a 60x60 pixel image, it should appear very small in the final 1080p render.
In Walter Rudin's Principles of mathematical analysis Exercise 5.21, it is proved that for any closed subset $E\subseteq \mathbb{R}$, there exists a smooth function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$.   Since $E^c$ is open in $\mathbb{R}$, $E^c$ is a countable disjoint union of open intervals $(a_i,b_i)$. On an interval $(a,b)$, if we let $f(x)=\exp(\frac{1}{(x-a)(x-b)})$, $x\in(a,b)$; $f(x)=0$, $x\notin(a,b)$, ($f(x)=\exp(\frac{1}{(x-a)})$ or $f(x)=\exp(\frac{1}{(x-b)})$ on $(a,\infty)$ and $(-\infty,b)$ resp.), then $f$ is smooth. Hence we can get a smooth function on $\mathbb{R}$ such that $E$ is the zero point sets of $f$.  (1). How about a closed subset $E$ of $\mathbb{R}^n$? is it true that for any closed subset $E\subseteq \mathbb{R}^n$, there exists a smooth function $f$ on $\mathbb{R}^n$ such that $E=\{x\in \mathbb{R}^n\mid f(x)=0\}$?  An open set in $\mathbb{R}^n$ cannot be written as a disjoint union of countable open balls hence the proof above is not valid. The partition of unity only claims that for an  open set $U$, there exists open $V$ in $U$ such that $\bar V\subseteq U$ and a smooth function $f$ on $\mathbb{R}^n$ such that $supp f\subseteq U$, $f|_V=1$.   (2). The taylor series of $f(x)=\exp(\frac{1}{(x-a)(x-b)})$ does not converge around points $a,b$ hence $f$ is not analytic at $a,b$. Is it true that for any closed subset $E\subseteq \mathbb{R}$, there exists an analytic function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$? The  tag doesn't appear to be very useful.  It's used in a variety of ways (for reading, writing, showing, transforming, compiling, translating, obfuscating, obtaining, ... source code) on 1747 questions right now, and doesn't appear to be adding any classification value to the site.  Can we get rid of it? In the review page, it shows stats of recent reviewers. But it is showing wrong stats. Because today (on Monday) it shows week count 53 (on Meta Stack Overflow) which is impossible as there is a limit of 20 reviews per day.    PS: This bug   and . But the bug has occurred again. Which is correct: I'll be moving next month or I'll be shifting next month? For changing one's home from one place to another, I've heard people in western part of the world using the sentence:      I'll be moving next month.   In India, even in the English news channels, I've heard many people using the phrase:     I'll be shifting next month.   Which one is the correct usage? Or are both of them correct and the difference in usage is regional? How do I change my profile picture, or avatar? Where does the image come from? How do I change my profile picture, or avatar? How do I change my profile picture on all SE sites at once? How can I use different avatars on different SE sites? How do avatars work? How do the SE sites know when I changed my Gravatar? Why do SE sites show a different Gravatar identicon than other sites where I use the same email address? How can I use a Gravatar image after logging in to facebook.stackoverflow.com? I changed my picture but am still seeing the old one    See also: This is in very common use on the internet. I just read this:     "[The] hotel employee walks in, I say "uh, puppy" and she just NOPEd the [heck] out of the room."   This is often done by adding 'd to the word. "media change: please insert the disc labeled" when trying to install Ruby on Rails Difference between phrase and idiom What is the difference between a phrase and an idiom? How much time is too much time playing educational computer games? I recently bought an iPad primarily for my 3-year-old daughter. I put nothing on it but educational apps and children's books. No YouTube, no Internet, no (non-educational) games. I've decided to let her use it as much as she wants, for now, and see how it goes. That was a few weeks ago.  So far she's been using the iPad maybe 2 to 5 hours each day. She still enjoys other activities -- playing outside, playing with dolls and blocks, interacting with friends, being read to, etc. And I think she might be learning a thing or two from the apps. Still, several hours a day seems like a lot. How do I know if it's too much?  I've searched the web, and there's lots of info on limiting TV time and video games, but I can't find any recommendations on limiting use if it's only educational games.  Relevant: A quick search for currency regex brings up . The problem I have in choosing one is that regex is difficult to verify without testing all the edge cases. Does anyone have a regex for U.S. currency that has been thoroughly tested? My only requirement is that the matched string is U.S. currency and parses to System.Decimal:  [ws][sign][digits,]digits[.fractional-digits][ws]   Elements in square brackets ([ and ]) are optional.  The following table describes each element.   ELEMENT             DESCRIPTION ws                  Optional white space. sign                An optional sign. digits              A sequence of digits ranging from 0 to 9. ,                   A culture-specific thousands separator symbol. .                   A culture-specific decimal point symbol. fractional-digits   A sequence of digits ranging from 0 to 9. Proving $v(s,p)=2^{p-1}(2s-1)$ is a bijection of natural numbers and $f(s)=2s-1$ is a bijection between natural numbers and odd numbers. How do I prove this function is bijective? $$ v(s,p)=2^{p-1}(2s-1). $$ The domain is natural numbers and the codomain is also the natural numbers.  And this one: $$ f(s)=2s-1. $$ The domain is the natural numbers, and the codomain is the odd numbers in the natural numbers.  With this one I would do this to show it's injective: $$ \begin{align} v(s)&amp;=v(s_1)\\ \implies 2s-1&amp;=2s_1-1\\ \implies (2s_1)/2&amp;=(2s_2)/2\\ \implies s=s_1 \end{align} $$ So it's injective since if $v(s)=v(s_1)$ then $s=s_1$.  And to show it's surjective $f(s)=y$: $$ \begin{align} y&amp;=2s-1\\ \implies s&amp;=(y+1)/2 \end{align} $$ Then the function must be surjective since every $y$ is the same as the codomain for $f$.  Am I correct? From :   (formal) showing great care and effort in your work synonym: diligent  (formal) working very hard and taking great care that everything is done as well as it can be synonym: diligent  (formal) showing care and effort in your work or duties  These definitions look alike. What they have in common is that these words mean to take care and to put effort into your work. All words are formal. None of these seems to be a proper term in a specific field, e.g. medical, law. I also looked at  to get more details. This adds the connotation of steady and earnest to diligent and unremitting attention and persistent application to assiduous. But in the end, these additional information are again describing an equal thing, i.e., continuously doing your work. The entry on sedulous doesn't add any more content; it refers to diligent and again describes the word with perseverance. From this point (checking dictionaries only), I don't see any difference at all. I continued with a corpora search. From : Diligent is most used in combination with work, effort, research, study but also student, people.  She's a diligent student. His diligent research identified the value of ...  Assiduous is also most used with work, effort, research but not with student, people. Merriam-Webster's Learner's Dictionary entry on  lists student as example though.  He's assiduous in his work. With assiduous attention to detail ...  Sedulous is most used, um, to little results.  has even less content. Merriam-Webster's example is, once again, a student. So, diligent is used most often, followed by assiduous and sedulous is quite rare. All words are formal. All words seem to be usable as an attribute to a person (e.g., student) but also specifying the intense care and effort on work, e.g., a research. I don't see any significant difference in these words, besides frequency. When is a student diligent, assiduous or sedulous? And when is a research diligent, assiduous or sedulous? Or simply: What are the subtle distinctions which aren't represented by dictionaries? Rails: What's a good way to validate links (URLs)? An integer is a $n$'th power if that holds true for all moduli. I have not been able to solve this problem. Any insights would be appreciated!   Let $x, n > 1$ be integers. Suppose that for each $k > 1$ there exists an integer $a_{k}$ such that $x − a_k^n$ is divisible by $k$. Prove that $x = A^{n}$ for some integer $A$. It is very easy to put a tilde over the symbol in math mode. Simply type $\tilde{a}$. But how to put a tilde under the symbol in math mode? What does "Baking" mean? I want to make some cool items for Dota 2 and I'm reading a guide. There are some tips about baking  etc. but I can't use them, because I don't even know what baking means. Can somebody explain this, please?  Thanks for all answers. How to remove a vector QgsVectorLayer from QGIS python plugin I managed to add QgsVectorLayer in QGIS through a python plugin, for example:  vl = self.iface.addVectorLayer(uri.uri(), layerName, self.dbConn.getProviderName())   But how can I remove it? 2.5 GB usable out of 4 GB of ram Batch fit images into ratio with blurred background I need to resize a lot of images into a 4:3 ratio with the desired effect.  Is there a way to do this using photoshop actions? (the background can be scaled or two copies moved to the sides, either way works)     image credits: sftp: upload all files, directories and sub-directories contained in a folder On machine A I have the folder /home/a/  On machine B I have the folder /home/b/  I wish transfer all files, directories and sub-directories of /home/a in /home/b with sftp On machine A I tried the commands: sftp fibon82@machineB.com put /home/a/* /home/b/  but it doesn't work, i get the error message: &quot;skipping non-regular file /home/a/a1&quot;... [a1 is a sub-directory of a] How could I modify the put instruction? Thanks! :) EDIT: I solved using scp: scp -r /home/a/ fibon82@machineB.com:/home/b/