Failed to fetch update on Ubuntu 14.04 LTS (Trusty Tahr)
Trouble downloading packages list due to a "Hash sum mismatch" error
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: I was reviewing  for , and noticed that nobody voted to close it, even though the page reports a duplicate.      Why does this happen? CSS technique for a horizontal line with words in the middle Let $V$ be spherically symmetric and $W$ i.i.d. Gaussian. Then $E[V|V+W=t]=g(\|t\|)$ A random vector $V \in \mathbb{R}^n$ is said to be spherically symmetric. If for every orthogonal matrix  $A$   the distribution of $AV$ is the same as the distribution of $V$.   My question: Let $W$ be  i.i.d. zero mean Gaussian random variable.     Can we show that  for a spherically symmetric $V$ the conditional expectation  \begin{align} E[V|V+W=t]=   g(\|t\|).  \end{align}  That is the conditional expectation is only a function of the magnitude.   My attempt:  \begin{align} E[V|V+W=t]= \int  V  \frac{f_W(t-v)}{f_{V+W}(t)} dP_V(v)= \frac{\int  v  f_W(t-v) dP_V(v)}{f_{V+W}(t)}= \frac{E[ V  f_W(t-V) ]}{f_{V+W}(t)} \end{align}  Therefore, we can show that the two functions in the above ratio only depend on $\|t\|$.   Observe that we can write $t= \|t\| u_t$  where $u_t$ is a unit vector. Then, for any orthogonal matrix $A$ \begin{align} f_{V+W}(t)=f_{V+W}(\|t\|, u_t)&amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-AV  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|tA^{-1}-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t A^T-V  \|^2}{2}} ]\\ &amp;= f_{V+W}(tA^T)\\ &amp;= f_{V+W}(\|t\|,  u_t A^T) \end{align}  Since, $A$ was arbitrary  we have that $f_{V+W}(t)=h(\|t\|)$(i.e., only depends on the magnitute).  Now I am not sure how to show that $E[ V  f_W(t-V) ]$ only depends on $\|t\|$? What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $ Could someone advise me on how to determine all entire functions $f$ such that $|f'(z)| \leq |f(z)|, \forall z\ ?$  Hints will suffice, thank you. Does "no larger than" imply shapability? I try to get rounded corners on a UIImage, what I read so far, the easiest way is to use a mask images. For this I used code from TheElements iPhone Example and some image resize code I found. My problem is that resizedImage is always nil and I don't find the error...  - (UIImage *)imageByScalingProportionallyToSize:(CGSize)targetSize {     CGSize imageSize = [self size];     float width = imageSize.width;     float height = imageSize.height;      // scaleFactor will be the fraction that we'll     // use to adjust the size. For example, if we shrink     // an image by half, scaleFactor will be 0.5. the     // scaledWidth and scaledHeight will be the original,     // multiplied by the scaleFactor.     //     // IMPORTANT: the "targetHeight" is the size of the space     // we're drawing into. The "scaledHeight" is the height that     // the image actually is drawn at, once we take into     // account the ideal of maintaining proportions      float scaleFactor = 0.0;      float scaledWidth = targetSize.width;     float scaledHeight = targetSize.height;      CGPoint thumbnailPoint = CGPointMake(0,0);      // since not all images are square, we want to scale     // proportionately. To do this, we find the longest     // edge and use that as a guide.      if ( CGSizeEqualToSize(imageSize, targetSize) == NO )     {          // use the longeset edge as a guide. if the         // image is wider than tall, we'll figure out         // the scale factor by dividing it by the         // intended width. Otherwise, we'll use the         // height.          float widthFactor = targetSize.width / width;         float heightFactor = targetSize.height / height;          if ( widthFactor &lt; heightFactor )             scaleFactor = widthFactor;         else             scaleFactor = heightFactor;          // ex: 500 * 0.5 = 250 (newWidth)          scaledWidth = width * scaleFactor;         scaledHeight = height * scaleFactor;          // center the thumbnail in the frame. if         // wider than tall, we need to adjust the         // vertical drawing point (y axis)          if ( widthFactor &lt; heightFactor )             thumbnailPoint.y = (targetSize.height - scaledHeight) * 0.5;          else if ( widthFactor &gt; heightFactor )             thumbnailPoint.x = (targetSize.width - scaledWidth) * 0.5;     }       CGContextRef mainViewContentContext;     CGColorSpaceRef colorSpace;      colorSpace = CGColorSpaceCreateDeviceRGB();      // create a bitmap graphics context the size of the image     mainViewContentContext = CGBitmapContextCreate (NULL, targetSize.width, targetSize.height, 8, 0, colorSpace, kCGImageAlphaPremultipliedLast);      // free the rgb colorspace     CGColorSpaceRelease(colorSpace);          if (mainViewContentContext==NULL)         return NULL;      //CGContextSetFillColorWithColor(mainViewContentContext, [[UIColor whiteColor] CGColor]);     //CGContextFillRect(mainViewContentContext, CGRectMake(0, 0, targetSize.width, targetSize.height));      CGContextDrawImage(mainViewContentContext, CGRectMake(thumbnailPoint.x, thumbnailPoint.y, scaledWidth, scaledHeight), self.CGImage);      // Create CGImageRef of the main view bitmap content, and then     // release that bitmap context     CGImageRef mainViewContentBitmapContext = CGBitmapContextCreateImage(mainViewContentContext);     CGContextRelease(mainViewContentContext);      CGImageRef maskImage = [[UIImage imageNamed:@"Mask.png"] CGImage];      CGImageRef resizedImage = CGImageCreateWithMask(mainViewContentBitmapContext, maskImage);     CGImageRelease(mainViewContentBitmapContext);      // convert the finished resized image to a UIImage      UIImage *theImage = [UIImage imageWithCGImage:resizedImage];      // image is retained by the property setting above, so we can      // release the original     CGImageRelease(resizedImage);      // return the image     return theImage; } Is there a single word for "moving unhinderedly"? Cleaning unwanted overlapping duplicate meshes I have a model with hundreds of mesh objects. Unfortunately I clicked shift+D to duplicate many and did not notice. Later after working a while, I was rendering, and noticed there are double meshes overlapping each other.   How can I find all duplicate meshes and delete them. I could do it manually,  just clicking,  but it would take a long time and if I miss something i will not notice.   Is there any option,  or can anybody suggest to me,  how can I find all duplicate mesh and delete them.  Model with all double (duplicate) mesh  Final Result Is there some sort of classification of all minimal non-cyclic groups? Does there exist some sort of classification of all minimal non-cyclic groups (non-cyclic groups, such that all their proper subgroups are cyclic)  I know the following classes of such groups:  1) $C_p × C_p$, where $p$ is a prime  2) $Q_8$  3) $\langle a,b | a^p = b^{q^m} = 1, b^{−1}ab = a^{r}\rangle$, where $p$ and $q$ are distinct primes and $r ≡ 1 \pmod q$, $r^q ≡1 \pmod p$.  (These three classes completely cover the case, when our group is finite: )  4)$C_{p^{\infty}}$, where $p$ is a prime  5)$(\{ \frac{n}{p^m}| m, n \in \mathbb{Z} \}, +)$, where $p$ is a prime  (These two classes completely cover the case, when our group is infinite abelian: )  6)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{p}$ for a fixed prime $p$ (Tarski monster groups)  7)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{\infty}$ ().  However, I do not know, whether there exists anything, that does not fall into these classes. I only know, that if such groups exist, they have to be infinite non-abelian. Canon claims that EOS 6D has special capability to focus in low light, but it has only one cross-type sensor and overall only 11 focus points. Does only one cross-type focus point in the Canon EOS 6D affect its ability to focus in low light? Is it correct to assume that more cross-type focus points produce more accurate and sharper focus? Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$ In trying to understand why there are two sets of groups of order 4.  I know that there exists the Vierergruppe of $\mathbb{Z}_2 \times \mathbb{Z}_2$ and the group $\mathbb{Z}_4$ but I do not understand why they are not isomorphic Math mode macro in TeXstudio I want to set up a macro in TeXstudio for math mode which displays $*$ and places the cursor at position *. So far I have tried using $%|$ but upon triggering, this macro does not allow text insertion at the placeholder.  EDIT: The method above works fine if the macro shortcut is set to the default Shift+F1. However, changing the shortcut to another combination, as I would like to do, seems to be the cause of the problem. How to prove that $a \cdot b$ is not divisible by 5 for $\frac{1}{1} + \frac{1}{2} + ... + \frac{1}{99} + \frac{1}{100} = \frac{a}{b}$? When does the Death Saving Throw happen with respect to sources of automatic ongoing damage? If a character is knocked unconscious with 0HP with a source of automatically dealt damage, for example, into a fire, and takes damage from it each turn, does the automatic Death Saving Throw failure from taking damage at 0hp happen before or after the player's regular Death Saving Throw roll?  If the unconscious PC takes the auto-fail first then they effectively only get 1 Death Saving Throw to survive, because they'd autofail and roll a failure the first turn, then autofail again and die the next turn.   If they get to roll first, then they only effectively get two death saving throws before they die. CSOM: Identify "columns" created by user rather than built-in When iterating the fields of a list how do you know which columns are yours and which are built-in ?  I know a solution for "classic" SDK using SPField.SourceId  but I can't find one for CSOM.  I thought UserCreated was the way to go for but   So how do you tell apart theirs and mine ? Using a combination of Hidden CanBeDeleted FromBaseType ? Checking for a list of special internalNames ?          ClientContext context = new ClientContext(siteUrl);         context.Credentials = creds;         Web web = context.Web;         var list = web.Lists.GetByTitle(listName);          context.Load(list.Fields);         context.ExecuteQuery();          foreach (Field field in list.Fields)         {         bool thisColumnWasCreatedByUser =                        field .FromBaseType == false &amp;&amp;                     //this.InternalName != "Title" &amp;&amp; // builtin but I'd rather keep it                     field .InternalName != "_dlc_DocId" &amp;&amp; // probably safe                     field .InternalName != "_dlc_DocIdUrl" &amp;&amp;                     field .InternalName != "_dlc_DocIdPersistId" &amp;&amp;                     field .InternalName != "Combine" &amp;&amp; // sucks                     field .InternalName != "RepairDocument" // sucks too         }   EDIT  Mixing suggestions by Viraj Gorajia and Dikesh Gandhi, my current solution is  bool thisColumnWasCreatedByUser =  field .FromBaseType == false &amp;&amp; (!field .SchemaXml.Contains(" SourceID=\"http")) &amp;&amp; // remove "Title", "Combine", "RepairDocument"  (!field .EntityPropertyName.StartsWith("OData__")) // field .Sealed == true could be working too but I don't know if it could exclude valid results I have written an essay last year, as a personal exercise. I now have a course at uni on the topic and could basically just hand in this essay now, the topic fits perfectly. I have also never submitted this essay to any other course or so.  Could I just hand in this essay, or would I violate some rules with that? Is this maybe already self-plagiarism? Do the topologies with the same convergent sequences coincide? Do the same sequential convergence in two topologies the result are the same topologies? Let $X$ be topological  space with topologies $\tau$, $\tau'$. Let $(x_{n})\in X$ and $x\in X$ and $(x_{n})\rightarrow x$ with $\tau$ if and only if $(x_{n})\rightarrow x$ with $\tau'$. Do the two topologies on $X$ coincide? Detail in bijection between Inn(G) and G/Z(G)? Is one preposition enough for multiple months? A colleague of mine has written her thesis and requested me to read and correct its grammar. I have seen some sentences like     The maximum deviation of the concentration values were obtained in the growing season, especially in May, in July, in August and in September.   As you see there is one 'in' for each month. I think that one preposition would be enough for all:     The maximum deviation of the concentration values were obtained in the growing season, especially in May, July, August and September.   Which one is more suitable?