When I press Ctrl +  F12 to render animation Blender outputs images to folder. That's nice. But it fails to do that when I press  F12. It's very annoying when - for example - I want to manually re-render couple of frames that were broken for some reason when rendering full animation. Sure, I can manually save them, but I have to input frame name and that makes it error-prone and annoying. Sure I can change animation range to do this, but that's also annoying. I know I can write a script to render whatever frames I want, but that's also a bit of work that I hope could be avoided.
Every time I render an image and try to save it, it just disappears. How do you exactly save a render? I am using a mac.
Asymptotic expansion for Fresnel Integrals Which is the most portable of sed, awk, perl and sh? Why shouldn't I use "Hungarian Notation"? Is there a nice solution to get a "presenter mode" for Latex presentations? How do I find this conditional expectation? Some text lines are italicized with no spaces between words Is the $\sum\sin(n)/n$ convergent or divergent? Possible Duplicate:          So, in my calculus class (one I'm teaching, not taking), the sum $\sum_{n=1}^\infty \frac{\sin(n)}{n}$ has come up a few times.  Unfortunately, as someone not exactly an expert in the convergence of sums, it seems to resist the few techniques I know.  Certain none of the usual first year calculus tricks (integral test, alternating series test, ratio test, etc.) work, and the only more tricky technique, partial summation, I can think of doesn't seem to work either (one would need that $\sum_{n=1}^N\sin(n)$ is bounded, which I believe is false).  It seems like it should converge, since it switches sign quite often, but on the other hand, the harmonic series can mess with your intuition, so I don't have much trust in that.  So, I ask to you:     Does this series converge? My linear algebra professor proved that      Diagonalizable matrices with complex values are dense in set of $n \times n$ complex matrices.   He defined a metric (I believe) that was somehow related to the usual metric on $\mathbb{R}^{n^2}$.  Then somehow proved that diagonalizable matrices were dense because for any matrix $A$ if $\det(A - \lambda I) = 0$ on an open subset, then $\det(A - \lambda I)$ was the zero polynomial.  I Googled around a bit and found some stuff talking about the Zariski topology, and I am not sure this is what I want. Most of what I have found on this topology is much more general than what he was doing.  Does anyone know any resources that would explain how to go about proving this statement?  Edit: I found out how to prove this the way my professor did.  We define the norm of a matrix by $$ |A| = \max\{|Ax| : |x| = 1 \}.$$ Now we have a distance $d(A, B) &lt; \epsilon$. You can prove that if $(A - B)_{ij} &lt; \epsilon/n$, then $|A - B| &lt; \epsilon$.  Let $p(x)$ be the characteristic polynomial of $A$, an $n \times n$ matrix.  $$p(x) = \prod_1^n (x - x_i) = x^n + (-1)\sigma_1 x^{n - 1} + \cdots + (-1)^n\sigma_n$$ where $\sigma_1, \ldots, \sigma_n$ are the elementary symmetric polynomials of $x_1, \ldots, x_n$ which are the eigenvalues.  The discriminant of the characteristic polynomial is a symmetric polynomial, therefore it can be written in terms of the elementary symmetric polynomials, which in turn can be written in terms of the entries of the matrix.  But since the discriminant is a polynomial, it only has finitely many roots. Therefore for $\epsilon &gt; 0$, by changing the entries of the matrix less than $\epsilon / n$ we can find a new matrix $B$ such that $|B - A| &lt; \epsilon$ and the discriminant is not zero.   The discriminant being not zero means $B$ has distinct eigenvalues, thus has a basis of eigenvectors. Therefore, it is diagonalizable.  Thus the set of diagonalizable matrices is dense in the set of matrices with respect to that metric. When we implement the Always Encrypted feature in SQL Server 2016, do the .mdf files, .ldf files and .bak files get encrypted as well?  I would like to know if the data/log/backup files gets encrypted or not. Can low-gravity planets sustain a breathable atmosphere? If astronauts could deliver a large quantity of breathable air to somewhere with lower gravity, such as Earth's moon, would the air form an atmosphere, or would it float away and disappear? Is there a minimum amount of gravity necessary to trap a breathable atmosphere on a planet? What is the "correct" way of embedding text into math mode? Lets say I have something like:   \[ Let x = number of cats \]   (This is a contrived example, but pretend we are actually inside a long align environment block...) "Let" and "number of cats" need to be written like normal text, while x= needs to be math type text.  I've seen this:  \[ \mbox{Let } x = \mbox{ number of cats} \]   and this:  \[ \textrm{Let } x = \textrm{ number of cats} \]   They seem to produce equivalent output, but I'm not sure which is the "correct" one. Also, they are not ideal in that the extra space needs to be placed inside the text mode block, otherwise it is ignored as math mode and butts the text right up against the math.  Ideally there would be some command which allowed embedding text into an equation, which correctly inserted leading and trailing space around the block as required without adding space inside the text block.  How does one do that "correctly"? Similar to '', is it also ok to add an example?   I was going to  but I noticed that one answer had most of the things I needed to say, except perhaps that the questioner didn't perhaps understand the answer and  I feel that an example may help. Why do the Localization of a Ring This question may be a bit vague, but neverthless, i would like to see an answer. Wikipedia tells me that:   In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring.   It is clear that for integral domains, we have the Field of Fractions, and we work on it. It's obvious that a Field has multiplicative inverses. Now if we consider any arbitrary ring $R$, by the definition of localization, it means that we are adding multiplicative inverses to $R$ thereby wanting $R$ to be a division ring or a field. My question, why is it so important to look at this concept of Localization. Or how would the theory look like if we never had the concept of Localization. Why can't the Klein-Gordon equation with a Couloumb potential describe the hydrogen atom?  Why can the first order Dirac equation explain it? What are the failures? In some papers or documents, "linear times series" seems to refer to a time series that can be modeled as a linear AR (auto-regressive) model.   In other places, "linear time series" seems to refer to a time series with a linear trend.   When someone just drops "linear time series" out of the blue without any context, what do they mean usually? Where does the term "fun fact" originate?-- namely, not with the compositional meaning but rather with the idiomatic usage to introduce some sort of unusual, esoteric, absurd or otherwise "controversial" fact? How to see this improper integral diverges? $$\int^\infty_1\frac{1}{x^{1+1/x}}dx$$  I'm preparing for exams. I would also like to know what are some commonly used methods to show an improper integral diverges? Including +/- signs to battery in Circuitikz I'm attempting to draw a battery (using the battery1 component) that includes positive and negative signs at the appropriate ends. A  that was answered here (using version 2.4) shows exactly what I mean:    Only, of course, I want to be using a battery1 symbol instead. So, I have my code as follows:  \usepackage[americanvoltages,fulldiodes,siunitx]{circuitikz} \begin{document} \begin{circuitikz}     \draw (0,0) to [battery1=\SI{9}{V}] (3,0)                 to [pC,v=$v_C$] (6,0); \end{circuitikz} \end{document}   And I end up with this:    Notice the lack of +/- signs (I know how circuits work so I don't need to be actually shown these signs, but for the sake of copying my class notes diagrams I want these signs to be included in my latex diagram).  In either case, I think it may have something to do with the version of Circuitikz I'm using because I'm using the latest version (I believe, 0.3.0) but in the previous question linked above, they were using 2.4 and it worked out for them.  I would really like to find a way to add +/- without having to manually add it with Tikz or something, i.e. just have it naturally part of the component without having to add nodes or extra Tikz code etc. If that's not possible, then I'll have to settle for that as a last result.   Thank you for your help!  EDIT: I should also mention that I've tried using battery1, v=$9V$ instead of battery1=\SI{9}{V} and to no avail (the +/- signs still don't show up). How do I turn on workspaces? (Why do I only have one workspace?) It appears that Unity on Raring only comes with a single virtual desktop (aka workspaces) by default, and CCSM's Wall plugin has no way to add more. Is this configurable at all? Exclude property from serialization via custom attribute (json.net)