I burnt Ubuntu 12.04 to a CD since that was the max it could hold. I've used the disc four times before, therefore it's not invalid.
I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:
Choosing OpenLayers or Leaflet? I was debating with one of my collegues on OpenLayers v/s Leaflet. I made a point that OpenLayers is much better API if we wish to build a project, where you need direct connectivity to the Geoserver and PostGIS.  Then I found , which looks pretty new but has the features of connectivity with the Geoserver and PostGIS.  So my project details are as follows,   Use the map interface to fetch Feature Info Create a customized tool that takes the lat/lon from user as to where he/she clicks on the map and then fetches the Climate Data from the raster (which is handled by a py script on the server) Allows user to upload excel, which is sent to the py script, which returns a GeoJSON, which creates Vector Features on the map Allow user to create vector polygons, which will fetch the Features it intersects from the WFS Layer. Fetches Layer from the PostGIS Datastore on GeoServer and displays the layers on the map.   So now I am confused on which is better and why using OpenLayers over Leaflet makes more sense or not? transforming ordinary generating function into exponential generating function Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials? Let $ A, B $ be two square matrices of order $n$. Do $ AB $ and $ BA $ have same minimal and characteristic polynomials?   I have a proof only if $ A$ or $ B $ is invertible. Is it true for all cases? Evaluate $\int \cos(3x) \sin(2x) \, dx$. Evaluate the indefinite integral    \begin{align} \int \cos(3x) \sin(2x) \, dx \end{align}   Please see my work attempt as my answer below. Future humans build using dirt, go to war over small amounts of it I am looking for a short story that I read in the 1970s (It may have been published in the 60s) about humans using the Earth's dirt to make stuff; as a result the Earth has shrunk and is smaller than the moon; also how nations go to war over a country's amount of dirt; Microcosmic God was in the same book.  Bought book through a science fiction book club; a collection of short stories. How do I learn to become a good GM? I have played and tried to GM games since I was in elementary school, beginning with games like Shadowrun, Earthdawn, and Champions. Recently, I've gotten dack into gaming with a variety of other games (newer Shadowrun and Earthdawn, plus TOON! and Outbreak:Undead).  I've found examples of actual play and advice on how to actually GM a game in games to be lacking. I can only help but feel I am not alone as someone who isn't already a LITERAL dungeon MASTER.  I fully realize that there are an unlimited number of GM styles, personalities, etc. I do not think I am a very good GM though. No one else wants to be the GM, and few care enough to learn the complex rules that I often have to assist with and explain AS WE PLAY. Being left with the responsibility is quite overwhelming unless I create dynamic encounters or make it all up on the spot. I'm often left having no idea what to do.  Examples of Why I Think I Need Help  This question isn't about these examples so please don't dig into them in the answers - they're here to explain the basic things that leave me feeling like I don't know how to proceed as a GM.  I've read preparation is important, but last time I tried to make a story, the players immediately killed the primary character (a friendly person.) within about 2 minutes of starting the game. While I realize now that I let the dice take control over the story, it was rather difficult to continue a story that relied on this friendly character, with the players making enemies with the character's faction. It is still discouraging when my only other attempt at a prepared story ended with the players wanting to go in a complete opposite direction of where I planned. Both times, the hours of work I put into it were completely wasted, leaving me as ignorant as I always was before.  My group often wants to play Shadowrun, Earthdawn, or L5R- but I feel as though I am a horrible GM. The last time we played Shadowrun, I was bored out of my mind as we rolled hundreds of dice to do an obvious straight-forward "kick down the door" mission.   If I make security as I believe it should or as the forum threads describe their security or a few example missions I can scrounge up (examples of stories, not actual gameplay), my players literally feel completely hopeless as to how to achieve their mission without total failure.   One time when I was a teenager, I had players blow up at me saying "We have no idea what would work. You're telling us that our character's experience or the ally operative says that would get us killed, but what else can we do?" Since there are no examples of what players can do - I am left with the same feeling as the players. As an adult, I've had a similar occurrence where a player said to me, "I don't know what to do. I don't think we can even begin this mission." I had to make something up and just go with it, creating an NPC group (that fit in with the story) that goes in before the players to do something stupid so they don't have to. Mainly because I ALSO didn't know how to accomplish the mission, so I acted as the players would using my NPC group. Extremely boring and IMO a failed dungeon run.  I've had successful stories, but I've had more boring encounters than successful ones. Seeing as how roleplaying takes endless hours to complete a story, I do not see benefit in an activity that wastes more time than is enjoyable.  How Do You Learn To GM?  Where are the resources? Books, blogs, gameplay examples? Am I missing them? How did YOU learn to be a good GM? Or do you feel as bad at this as I do, even when it's a successful, fun encounter? Finding an isomorphic subring of matrices I'm struggling a fair amount with this exercise:     Find a subring of $M(2,\mathbb{Q})$ which is isomorphic to a) $\mathbb{Q}$ x $ \mathbb{Q}$ b) $\mathbb{Q}$ c) $\mathbb{Q}[x]$/$x^2$   Now I know a subring must be a subgroup, must contain the elements $0,1$ and must be closed under multiplication. As we are looking for isomorphisms then they must also be ring homomorphisms and must be bijective.  I tried to come up with a random subring and attempt to prove it is an isomorphism. E.g $\left\{\left.\begin{matrix}  a &amp; b \\ c &amp; 0  \end{matrix}\right|a,b,c \in \mathbb{Q}\right\}$ is a subgroup of $M(2,\mathbb{Q})$ and then try and show it's an isomorphism. However I'm stuck here as I don't actually know how to go about finding these specific isomorphisms and I completely lose what I'm doing. Any help would be great. Sometimes I need to upload, embed, or display inline an image in a question or answer. How can I do that? If I have a native C++ windows program (i.e. the entry point is WinMain) how do I view output from console functions like std::cout? What are recursive triggers? How can recursive triggers be controlled? What are recursive triggers? How can we control them, or prevent infinite recursion?  Are these any risks inherent in them, and any limits that we should be aware of?  Please explain with an example. Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$ I think I have heard that the following is true before, but I don't know how to prove it:     Let $A$ be a matrix with real entries. Then the minimal polynomial of $A$ over $\mathbb{C}$ is the same as the minimal polynomial of $A$ over $\mathbb{R}$.   Is this true? Would anyone be willing to provide a proof?    Attempt at a proof:  Let $M(t)$ be the minimal polynomial over the reals, and $P(t)$ over the complex numbers. We can look at $M$ as a polynomial over $\Bbb C$, in which case it will fulfil $M(A)=0$, and therefore $P(t)$ divides it. In addition, we can look at $P(t)$ as the sum of two polynomials: $R(t)+iK(t)$. Plugging $A$ we get that $R(A)+iK(A)=P(A)=0$, but this forces both $R(A)=0$ and $K(A)=0$. Looking at both $K$ and $R$ as real polynomials, we get that $M(t)$ divides them both, and therefore divides $R+iK=P$.   Now $M$ and $P$ are monic polynomials, and they divide each other, therefore $M=P$.  Does this look to be correct?    More generally, one might prove the following     Let $A$ be any square matrix with entries in a field$~K$, and let $F$ be an extension field of$~K$. Then the minimal polynomial of$~A$ over$~F$ is the same as the minimal polynomial of $A$ over$~K$. I was wondering if having less than 5-10GB of free space on an SSD would affect performance. Is it specific to SSD or is it more of an operating system aspect?  For example, on an Intel X-25 G2 that has TRIM support (on Windows 7). Countdowntimer in minutes and seconds Proper fstab entry to mount a samba share on boot? What do they do with all the plates and cups in Star Trek? Whenever someone in Star Trek creates food or drink in the replicator it is generated in the bowl, plate, or cup. It seems like after a few months they would have piles of used dishes from replicator food while making more for every meal. What do they do with all the dishes? Is it possible to install an app and exclude some of its requested permissions? Occasionally I want to install an application which requires certain permissions that I feel it really shouldn't need. Can I install the app without giving it these permissions? For example, GPS location, , internet connection, etc.  Is it possible to change the permissions of an application once it is installed? Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$ For $a\ge 0$ let's define $$I(a)=\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right)dx.$$ Find explicit formula for $I(a)$.   My attempt: Let  $$\begin{align*} f_n(x) &amp;= \frac{\ln\left(1-2 \left(a+\frac{1}{n}\right)\cos x+\left(a+\frac{1}{n}\right)^2\right)-\ln\left(1-2a\cos x+a^2\right)}{\frac{1}{n}}\\ &amp;=\frac{\ln\left(\displaystyle\frac{1-2 \left(a+\frac{1}{n}\right)\cos x+\left(a+\frac{1}{n}\right)^2}{1-2a\cos x+a^2}\right)}{\frac{1}{n}}\\ &amp;=\frac{\ln\left(1+\dfrac{1}{n}\left(\displaystyle\frac{2a-2\cos x+\frac{1}{n}}{1-2a\cos x+a^2}\right)\right)}{\frac{1}{n}}. \end{align*}$$ Now it is easy to see that $f_n(x) \to \frac{2a-2\cos x}{1-2a\cos x+a^2}$ as $n \to \infty$. $|f_n(x)|\le \frac{2a+2}{(1-a)^2}$ RHS is integrable so $\lim_{n\to\infty}\int_0^\pi f_n(x)dx = \int_0^\pi \frac{2a-2\cos x}{1-2a\cos x+a^2} dx=I'(a)$. But  $$\int_0^\pi \frac{2a-2\cos x}{1-2a\cos x+a^2}=\int_0^\pi\left(1-\frac{(1-a)^2}{1-2a\cos x+a^2}\right)dx.$$ Consider $$\int_0^\pi\frac{dx}{1-2a\cos x+a^2}=\int_0^\infty\frac{\frac{dy}{1+t^2}}{1-2a\frac{1-t^2}{1+t^2}+a^2}=\int_0^\infty\frac{dt}{1+t^2-2a(1-t^2)+a^2(1+t^2)}=\int_0^\infty\frac{dt}{(1-a)^2+\left((1+a)t\right)^2}\stackrel{(*)}{=}\frac{1}{(1-a)^2}\int_0^\infty\frac{dt}{1+\left(\frac{1+a}{1-a}t\right)^2}=\frac{1}{(1-a)(1+a)}\int_0^\infty\frac{du}{1+u^2}=\frac{1}{(1-a)(1+a)}\frac{\pi}{2}.$$ So $$I'(a)=\frac{\pi}{2}\left(2-\frac{1-a}{1+a}\right)\Rightarrow I(a)=\frac{\pi}{2}\left(3a-2\ln\left(a+1\right)\right).$$  It looks too easy, is there any crucial lack?  $(*)$ — we have to check $a=1$ here by hand and actually consider $[0,1), (1,\infty)$ but result on these two intervals may differ only by constant - it may be important but in my opinion not crucial for this proof. My university's thesis guidelines require that each bibliographic entry appear in whole on a single page, rather than being split across two. How can I prevent (La)TeX breaking a paragraph across a page boundary? I have an excel file with 2 attribute columns, 1-feature info 2-Number of color (RGB) that the current feature should be symbolize. This file file can be joined with the layer using the "feature info" field which is unique (join by attribute table). So i have as attribute the color number attribute for every polygon feature.  How can  i use this this information to symbolize every feature with their attributed color already imported from the excel sheet?