I want to install my first Ubuntu version on my laptop, but I have a big question about that.   I am looking for the 16.04 LTS but I see there is different versions of Ubuntu Desktops (Unity, Gnome, Mate...) and I don't know what version of these is the most appropriate for my laptop. It is an i5 with 8GB of ram and a 240GB SSD, with a 4-cell battery. I am worried about the battery life, and if it works slow or not.  Could you help me with this decision? Is it any big difference between these versions?  Sorry if it's a very common question, I cannot find another question which resolve my doubt.  Thanks
For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?
We consider $g : (t,u,v)\in \mathbb{R}^3 \mapsto (t^2,u^2,v^2,\sqrt{2}uv, \sqrt{2}tv,\sqrt{2}tu)\in\mathbb{R}^6$. I have to prove that $g(\mathbb{S}^2)$ is a submanifold of $\mathbb{R}^6$.  $dg_{(t,u,v)}=\begin{pmatrix}2t&amp;0&amp;0\\  0&amp;2u&amp;0\\  0&amp;0&amp;2v\\  0&amp;\sqrt{2}v&amp;\sqrt{2}u\\ \sqrt{2}v&amp;0&amp;\sqrt{2}t\\ \sqrt{2}u&amp;\sqrt{2}t&amp;0\\ \end{pmatrix} $  So it proves that $g$ is an immersion (the rank is $3$ clearly) for $(\mathbb{R}^3-\{(0,0,0)\})$.  Now how to prove that $\mathbb{S}^2$ is homeomorphic to $g(\mathbb{S}^2)$ ? I must prove that $g$ is injective  ?  Thanks in advance ! Proving the inequality $\frac{n^k}{k^k}\leq\binom{n}{k}\leq\frac{n^k}{k!}$ involving binomial coefficient. What is the best way of proving inequalities including binomial coefficients in general? Lets look at this example:     $$\frac{n^k}{k^k}\leq\binom{n}{k}\leq\frac{n^k}{k!}$$   What I started with is:  $$\binom{n}{k}\frac{1}{n^k}\leq\frac{1}{k!}$$ $$\frac{n!}{k!(n-k)!}\frac{1}{n^k}\leq\frac{1}{k!}$$ $$\frac{(n-1)!}{(n-k)!n^{k-1}}\leq1$$ This is where I got stuck. How can I prove that is is lower than or equal to 1? Could you give me a hint? Discontinuous derivative. Could someone give an example of a ‘very’ discontinuous derivative? I myself can only come up with examples where the derivative is discontinuous at only one point. I am assuming the function is real-valued and defined on a bounded interval. How to stop iPhone users from sending iMessages and send SMS instead I used to have an iPhone, but I changed to an android (shock, horror!). Unfortunately Apple refuses to let me go and whenever friends message me the messages get sent as iMessages (unless they remember to specifically chnge the format). I never get these messages. They never get resent as SMSs automatically as is supposed to happen. How can I get my phone number deleted from the iMessage list. I've turned off iMessage on the old iPhone. Does there currently exist a free online service that accepts a file, hashes it, takes an authoritatively chosen timestamp (from one or more time services), signs these and sends this signed message back? E.g. a digital notary, but only with regards to the timestamp and not the validity of the content as legal notaries might be obligated to guarantee.  Such a service might have an extremely simple API: Simply wget http://service/&lt;checksum&gt; and receive a signed message containing one or more timestamps and the checksum. The emphasis would be on the type of authority who might make such a service.  Edit: Although the original question did not emphasise the following, the Bitcoin-based timestamping services provided below do not rely on one authority, but rather the entire Bitcoin network. They can be seen as tamper-proof and verifiable without the help of the service that helped you sign it! Let $A,B$ be two sets. The  states that if there is an injection $f\colon A\to B$ and an injection $g\colon B\to A$, then there exists a bijection $h\colon A\to B$.  I was wondering whether the following statements are true (maybe by using the AC if necessary):   Suppose $f \colon A\to B$ and $g\colon B\to A$ are both surjective, does this imply that there is a bijection between $A$ and $B$. Suppose either $f\colon A\to B$ or $g\colon  A\to B$ is surjective and the other one injective, does this imply that there is a bijection between $A$ and $B$. PlotLegends disappearing with list of functions Proper use of the IDisposable interface I know from reading  that the "primary" use of the IDisposable interface is to clean up unmanaged resources.  To me, "unmanaged" means things like database connections, sockets, window handles, etc.  But, I've seen code where the Dispose() method is implemented to free managed resources, which seems redundant to me, since the garbage collector should take care of that for you.  For example:  public class MyCollection : IDisposable {     private List&lt;String&gt; _theList = new List&lt;String&gt;();     private Dictionary&lt;String, Point&gt; _theDict = new Dictionary&lt;String, Point&gt;();      // Die, clear it up! (free unmanaged resources)     public void Dispose()     {         _theList.clear();         _theDict.clear();         _theList = null;         _theDict = null;     }   My question is, does this make the garbage collector free memory used by MyCollection any faster than it normally would?  edit:  So far people have posted some good examples of using IDisposable to clean up unmanaged resources such as database connections and bitmaps.  But suppose that _theList in the above code contained a million strings, and you wanted to free that memory now, rather than waiting for the garbage collector.  Would the above code accomplish that? The class will be over in 10 minutes. The class will be over after 10 minutes.  I know the first is correct but why? Zsh says "no matches found" when trying to download video with youtube-dl I downloaded youtube-dl using pip on CrunchBang (a Debian Wheezy distro). When I run   youtube-dl {video URL}   I get  zsh: no matches found: {video URL}   I guess it has something to do with zsh, because I found some users on Arch forums complaining about it. When I switched to bash it worked. I have a quick question about the refraction of light, and I'm sorry if it seems a bit simplistic or even stupid, but I'm still learning.  We know that when light passes through a denser medium, it slows down. However, is there a limit to that slowing down? If no, wouldn't it be possible, with some type of medium we make ourselves (like a crystal), to decrease the light's speed down to a point where we would be able to "see the photons moving forwards"?  I know it is way more complicated than that and that you can't see light unless some other light bounces off it, what I mean is slowing down light to an extreme and unusual speed). That sounds completely absurd but I can't seem to find what is wrong. Can anyone can explain it to me? :) Bottom of tool shelf grayed out Reprojecting raster from 0 360 to -180 180 with cutting 180 meridian using gdalwarp I have a geotiff raster image that has a coordinate system with longitudes from 0 to 360. The horizontal center of the image is 180 longitude. See image below:    I want to transform it to EPSG:4326 SRS with -180 180 longtitude range.  And I want the center of the image to be at Greenwich meridian (0). I guess this srs is very widely used. I expect the result look like this:    So I use a gdalwarp command to reproject:  gdalwarp -s_srs '+proj=latlong +datum=WGS84 +pm=180dW' -t_srs EPSG:4326 test_col.tif test_4326.tif   But I only get a tiff with bigger dimensions (more pixels) and EPSG:4326 metadata. The image itself looks the same, as the initial one. But I expect it to swap the hemispheres.  How do I gdalwarp an image to be strictly -180 180 EPSG:4326 with the center in 0 longitude?  This is gdalinfo of my initial file:  Origin = (-0.102272598067084,89.946211604095552) Pixel Size = (0.204545196134167,-0.204423208191126) Metadata:   AREA_OR_POINT=Area Image Structure Metadata:   INTERLEAVE=BAND Corner Coordinates: Upper Left  (  -0.1022726,  89.9462116) (  0d 6' 8.18"W, 89d56'46.36"N) Lower Left  (  -0.1022726, -89.9462116) (  0d 6' 8.18"W, 89d56'46.36"S) Upper Right (     359.897,      89.946) (359d53'50.18"E, 89d56'46.36"N) Lower Right (     359.897,     -89.946) (359d53'50.18"E, 89d56'46.36"S) Center      ( 179.8975000,  -0.0000000) (179d53'51.00"E,  0d 0' 0.00"S)   This is gdalinfo after gdalwarp     Origin = (-180.102727401932952,89.946211604095552) Pixel Size = (0.091397622896436,-0.091420837939082) Metadata:   AREA_OR_POINT=Area Image Structure Metadata:   INTERLEAVE=PIXEL Corner Coordinates: Upper Left  (-180.1027274,  89.9462116) (180d 6' 9.82"W, 89d56'46.36"N) Lower Left  (-180.1027274, -89.9699975) (180d 6' 9.82"W, 89d58'11.99"S) Upper Right ( 179.8211116,  89.9462116) (179d49'16.00"E, 89d56'46.36"N) Lower Right ( 179.8211116, -89.9699975) (179d49'16.00"E, 89d58'11.99"S) Center      (  -0.1408079,  -0.0118929) (  0d 8'26.91"W,  0d 0'42.81"S) Correct usage of "lest" Which of the followings is/are the correct usage of the word "lest"? How are these different from each other?   ...hesitant to speak out lest he be fired. ...hesitant to speak out lest he'd be fired. ...hesitant to speak out lest he would/will be fired.   P.S. I took point number 1 as the reference for this question from the definition of lest from the Merriam-Webster Dictionary. Can the sun damage the camera sensor? Under what conditions? I want to experiment taking photos in which the sun appears. I'm afraid of what might happen if I take one with a narrower angle (where sun would be bigger). Can the lens act as a magnifying glass and burn the CCD or CMOS sensor?  Under which circumstances (zoom, exposure, aperture, etc...), can the sensor be damaged by the sun? Randomize a List What is the best way to randomize the order of a generic list in C#? I've got a finite set of 75 numbers in a list I would like to assign a random order to, in order to draw them for a lottery type application. What do you call a person who does/thinks the opposite of the crowd for just that reason? I have 2 hard disks, on first I have installed win xp. I boot into xp and run setup of win7 and installed it on second hard disk. Now the problem is that win7 bootloader is installed on first harddisk, so if I remove the first harddisk, I cannot boot into win7.   How I can move / install bootloader of win7 on second hard disk? What exactly is tested when a fire extinguisher is tagged? I am just curious: the obvious is that the  pressure mass   can be inspected /measured to ensure that the device has not been discharged. Is there anything else that is measured \ checked? jQuery Event Handler created in loop