Existence of analytic function from A to B .
Non constant analytic function from $\{z\in\mathbb{C}:z\neq 0\}$ to $\{z\in\mathbb{C}:|z|>1\}.$
Extract all the polygon coordinates from a SpatialPolygonsDataframe? I want to do something relatively simply but it seems to be very difficult to do, though I am very new to using R for spatial data so apologies if I've missed something obvious.  I have a list containing 161 shapefiles of bird distributions in the world, they are each in the format of a SpatialPolygonsDataFrame. I also have world climate data in a raster stack format for 8 variables. Both sets of files are in the same projection (lat and long WGS84). I want to create new columns for the climate data with 1's where the species polygon overlaps with the climate data and 0 where it doesn't. I tried various functions to do this, quite a few initial options didn't work, the best option appeared to be:  pnt.in.poly(XY coordinates of climate data points, XY coordinates of species polygon)   I changed my raster of climate data into points to get the XY coordinates. I unified the polygons for each species shapefile and then used:  species@polygons[[1]]@Polygons[[1]]@cords   to get the coordinates for my species polygons as a matrix. However, I discovered that:  species@polygons[[1]]@Polygons[[1]]@coords    wasn't actually getting all the coordinates of the polygons only some of them.  I tried using fortify from the ggplot package, and it gives me a dataframe with coordinates but some of them are for holes in the polygons. I ran that with the pnt.in.poly function excluding the holes but it took an hour to run and when I looked at the output maps after it matched for some of the range but not all of it- there were holes in the distribution where there shouldn't be holes.   I also tried this method that I found somewhere else:  lonlat &lt;- lapply(slot(species, "polygons"), function(x) lapply(slot(x,"Polygons"), function(y) slot(y, "coords")))    which gives me a list with 436 items- but I'm still not sure how to get the coordinates into a matrix form that will work in pnt.in.poly.  I'm sure this should be easier to do! Does anyone know a better way? How does the SQL injection from the "Bobby Tables" XKCD comic work? Just looking at:   (Source: )  What does this SQL do:  Robert'); DROP TABLE STUDENTS; --   I know both ' and -- are for comments, but doesn't the word DROP get commented as well since it is part of the same line? Explanation behind Second Derivative of a Parametric Equation Formula I am looking to find out how the second derivative formula works.  I can blindly apply it but I don't have a grasp of what is going on or why. The first derivitive has the formula $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$. I told this was because if you divide them you cancel out the dts and get dy/dx. The second derivative has the formula $\frac{d^2y}{dx^2} = \frac{d}{dx} \left(\frac{dy}{dx}\right) = \frac{ \frac{d}{dt}\left(\frac{dy}{dx}\right) }{\frac{dx}{dt}}$. Is this something that can be explained with only a knowledge of calculus or is this something I would have to take on faith until I learn more. Any help would be greatly appreciated. What is the difference between '/' and '//' when used for division? Change date format [YYYYMMDD] to [MM/DD/YYYY] Are there rules for disassembling a slain creature, especially dragon? If $I_n=\int _0^{\pi }\sin^{2n}\theta \:d\theta $, show that $I_n=\frac{\left(2n-1\right)}{2n}I_{n-1}$, and hence $I_n=\frac{\left(2n\right)!}{\left(2^nn!\right)2}\pi $  Hence calculate $\int _0^{\pi }\:\sin^4t\cos^6t\:dt$  I knew how to prove that $I_n=\frac{\left(2n-1\right)}{2n}I_{n-1}$, but I am not very good at English, what does it mean Hence $I_n=\frac{\left(2n\right)!}{\left(2^nn!\right)2}\pi $ do we need to prove this part as well or is it just a hint to use? and for the other calculation to find $\int _0^{\pi }\:\sin^4t\cos^6t\:dt$ is there something in the first part that I can do to help me solve this question because otherwise it becomes very long and it's part of the question. How would gravity change on a planet rotating around itself very fast? Let's take a planet identical to Earth, but with rotation speed multiplied by ten thousand. What would happen with the gravity if it was spinning madly around itself? Would the centrifugal force make objects seem lighter than on normal Earth? Would the people on that planet be able to jump higher? Where do deleted items go on the hard drive? Is "connected, simply connected" Redundant? Here are my definitions of &quot;connected&quot; and &quot;simply connected.&quot;  A topological space $X$ is connected if and only if it is not the union of two nonempty disjoint open sets. A topological space $X$ is simply connected if and only if it is path-connected and has trivial fundamental group (i.e. $\pi_1(X)\simeq\{\mathrm{e}\}$ and $|\pi_0(X)|=1$).  It is a classic and elementary exercise in topology to show that, if a space is path-connected, then it is connected. Thus, if a space is simply connected, then it is connected. Yet, despite this implication, I've read several cases where the words &quot;connected, simply connected&quot; appear together. For example, in Kobayashi and Nomizu's Foundations of Differential Geometry, Volume 1, page 252, the following is written: &quot;Let $M$ be a connected, simply connected analytic manifold with an analytic linear connection.&quot; In  and  (Links to Journal Storage, also known as JSTOR), they use &quot;connected, simply connected&quot; on their first page. The first of these takes it a step further, referring to &quot;closed, compact, connected, simply connected $4$-manifolds,&quot; where a closed manifold (unfortunate terminology) is defined as a compact manifold without boundary. My question is simple: Why use the words &quot;connected, simply connected&quot; when being simply connected implies connectedness? Thank you. Got a bunch of .mp4 videos (info shows H.264 Video + AAC Audio) that are chapters of a larger video.  I'd like to merge them, but not sure which is the best way.  I don't have Quicktime Pro, but I'll get it if that's the best way to do this.  Edit: Just to clariify this is Mac OSX 10.6 I'm on. I have a beamer frame with about 150 slides on it.  I want article and handout mode to only show frame 92.    Reading section 8.6.2 of the beamer manual it seems like I should be able to do something like  \begin{frame}&lt;handout:92&gt; ... \end{frame}   but that seems to have no effect--all 150 slides are set in handout mode, overlaying (making the result unreadable).  I have gotten the effect I want by taking all commands within the frame that have an overlay specification and adding "| handout:0" to make them not appear in handout mode.  Annoying, but works.  But for my 150-slide frame the different slides are generated by a PGF \foreach loop so I can't code slide 92 differently from the rest.  But can I do this at the frame's overlay specification?  It seems that the frame's overlay spec really acts differently from other commands.  If I only do  \begin{frame}&lt;92&gt;...\end{frame}   then I get only slide 92 in beamer mode but all slides in article or handout mode. I'm about to fly from Istanbul to Seoul and I have a useful amount of Turkish Lira (TRY) left but I don't have any South Korean Won (KRW) to pay for the metro to my hostel when I get there.  Several times in the past I've ended up being stuck with currencies that are very difficult to exchange in the country I've arrived in.  Can I buy KRW at the airport in Istanbul?  (I've also asked , since Stack Exchange questions are meant more for the long tail than just for the original asker.) Lebesgue integration: $f = g$ a.e. $ \Rightarrow \int_\Omega f = \int_\Omega g$ Let $f,g : \Omega \subseteq \mathbb R^n \rightarrow [0,+\infty]$ be measurable functions with $f(x) = g(x)$ a.e. . Then I have to show that $\int_\Omega  f = \int_\Omega g$.  I may not assume that $\int_\Omega (f+g) = \int_\Omega f + \int_\Omega g$.   This task is from Tao Proposition 19.2.6. Why does evolution not make our life longer? Why does evolution not make life longer for humans or any other species?  Wouldn't evolution favour a long life? When looking at my Apache2 access logs, I occasionally see GET requests asking my server for a page on a completely different server. For example:  xx.xx.xx.xx - - [18/Jan/2012:07:12:10 -0500] "GET http://someotherserver.com/?sometimesmorestuff=likethis HTTP/1.1" 200 389 "-" "Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.8.1.12) Gecko/20080201 Firefox/2.0.0.12"   I remembered reading something about that in the past, but at the time I had never seen that on my server, so I didn't worry about it.   Now that I am seeing it on my server, I just ran a test and it appears that my site does indeed serve requests for content from other servers. This seems like a bad thing. So, two questions:  A) Is this something I should be worrying about?  B) How can I fix it?  I've tried a little Googling, but I don't even know what this sort of thing is called, and that makes it difficult. How do I redirect command output to a file? preventDefault when clicking bounty "cancel" link When you click "start a bounty" then "cancel," href="#" exiles you to the top of the page and you lose your spot near the end of the question's comments. Clicking anywhere else on the page simply closes the bounty popup; clicking "cancel" ought to do the same.  In case that wasn't clear:    Dramatization aside, it's a nuisance. Can the click event on that anchor be preventDefaulted? UK Visa Refusal: Provenance of funds/parking I have applied recently for a general visitor visa to the UK to spend 10 days during Christmas with my British unmarried partner and it has been turned down.   The Entry Clearance Officer stated on his refusal notice the following:     I note that you have never previously travelled to the UK or any country with similar immigration requirements and you therefore do not have a history of travel and compliance to consider.      You have submitted an employment letter to confirm your occupation in KSA but I am required to also assess your personal, domestic and economic circumstances in determining whether you are genuine visitor travelling to the UK for the period and purpose you state.      You claim an income of SAR ........ per month which equal ........ GBP and from the evidence submitted this appears to be your sole source of income.   I note that this monthly income is reflected on your bank statements. However, the bank statement you have presented show a recent large deposit that are in excess of your stated income and inconsistent with the account history. You haven't provided evidence toward the origin of this recent deposit and in the absence of reasonable evidence I am not satisfied that these bank statements accurately reflect your personal circumstances.      In view of the above, I am not satisfied you have demonstrated that your circumstances are as you claim and therefore I am not satisfied that you're travelling to the UK for the period and purpose you stated. 41(i)and(ii).   Its true that I have deposited that sum of money right before I apply and it was a commission I received from work earlier this month.   So, could you please give me your advice on the above as I am planning to apply again soon. and how to avoid my application being refused again? Can't do reviews after failing 1 audit