Which one is the best answer and why?
What’s the rule for using “who” and “whom” correctly?
Hi I would like to know whether the trace of the inverse of a symmetric positive definite matrix $\mathrm{trace}(S^{-1})$ is convex.  Actually I know that the trace of a symmetric positive definite matrix $S\in M_{m,m}$ is convex since we can find $B\in M_{n,m}$ such that $S=B^T\times B$ then we can write the trace as the sum of scalar quadratic forms, i.e. $\mathrm{trace}(S)=\mathrm{trace}(B^T\times B)=\sum_{j=1}^mb_j^T\times b_j$ where $b_j$ is the $j^{th}$ column of $B$.  for instance if we have  $trace([\begin{array}{cc} 1 &amp; 2  \\ 3 &amp; 4  \\ \end{array}] \times [\begin{array}{cc} 1 &amp; 3  \\ 2 &amp; 4  \\ \end{array}])= [\begin{array}{cc} 1 &amp; 2  \\ \end{array}]\times [\begin{array}{c} 1   \\ 2   \\ \end{array}]+ [\begin{array}{cc} 3 &amp; 4  \\ \end{array}]\times [\begin{array}{c} 3   \\ 4   \\ \end{array}]=30$  And so I wonder if $\mathrm{trace}(S^{-1})$ is convex too.. Zero visibility while editing a message in a chat room Why is it impossible, without attempting I/O, to detect that TCP socket was gracefully closed by peer? As a follow up to a , I wonder why it is impossible in Java, without attempting reading/writing on a TCP socket, to detect that the socket has been gracefully closed by the peer? This seems to be the case regardless of whether one uses the pre-NIO Socket or the NIO SocketChannel.  When a peer gracefully closes a TCP connection, the TCP stacks on both sides of the connection know about the fact. The server-side (the one that initiates the shutdown) ends up in state FIN_WAIT2, whereas the client-side (the one that does not explicitly respond to the shutdown) ends up in state CLOSE_WAIT. Why isn't there a method in Socket or SocketChannel that can query the TCP stack to see whether the underlying TCP connection has been terminated? Is it that the TCP stack doesn't provide such status information? Or is it a design decision to avoid a costly call into the kernel?  With the help of the users who have already posted some answers to this question, I think I see where the issue might be coming from. The side that doesn't explicitly close the connection ends up in TCP state CLOSE_WAIT meaning that the connection is in the process of shutting down and waits for the side to issue its own CLOSE operation. I suppose it's fair enough that isConnected returns true and isClosed returns false, but why isn't there something like isClosing?  Below are the test classes that use pre-NIO sockets. But identical results are obtained using NIO.  import java.net.ServerSocket; import java.net.Socket;  public class MyServer {   public static void main(String[] args) throws Exception {     final ServerSocket ss = new ServerSocket(12345);     final Socket cs = ss.accept();     System.out.println("Accepted connection");     Thread.sleep(5000);     cs.close();     System.out.println("Closed connection");     ss.close();     Thread.sleep(100000);   } }   import java.net.Socket;  public class MyClient {   public static void main(String[] args) throws Exception {     final Socket s = new Socket("localhost", 12345);     for (int i = 0; i &lt; 10; i++) {       System.out.println("connected: " + s.isConnected() +          ", closed: " + s.isClosed());       Thread.sleep(1000);     }     Thread.sleep(100000);   } }   When the test client connects to the test server the output remains unchanged even after the server initiates the shutdown of the connection:  connected: true, closed: false connected: true, closed: false ... Show that if $fd'=f'd $ and the pairs $f, d $ and $f',d' $ are coprime, then $f=f' $ and $d=d' $. Show that if $fd'=f'd $ and the pair $f, d $ are coprime, that is gcd($d,f $)=1, as is the pair $f',d' $, then $f=f' $ and $d=d' $.  This should be simple, but I couldn't verify it. Thanks in advance! Shortest path from points in one layer to points in another layer via roads in QGIS Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction? WebView loading Url Do's and Don't's of Undergraduate Research I was fortunate enough to get a position as a researcher for the Mayo Clinic's SURF Program this year. My PI's lab focus is on the the immune system's role in CNS axonal and neuronal injury, specifically through the lens of how innate and adaptive immune effectors interact w/ infected neurons.  Although I do research under a professor at my college and I volunteered for a state university lab during the previous summer, this is my first REU/SURF opportunity, and I REALLY want to make a good impression. Here are my questions:  What are the do's and don't's in terms of being a skilled and efficient researcher?  Since I am still an undergrad, I know that I will be a less useful asset to the lab than a grad student or post-doc, but what can I do as an undergrad to not burden my colleagues and PI?  Thank you all for your help! Wishing you all the very best! What are the technical advantages and disadvantages of mirrorless? The main doubt one can have about mirrorless is, I think that they do not provide ttl viewfinder. Is this a big disadvantage? In what way is it worst (or best) than classical reflex system?  What are the others advantages and disadvantages of a mirrorless compared to a reflex?  Have mirrorless a chance to replace reflex (at least for non pros) in the future? Determine number of real roots of $f(x)=x^{5}+x^{3}-2x+1$.   I used Descartes's rule of sign to determine the number of positive and negative roots; there is only 1 negative (hence minimum 1 real root) and two positive roots. These 2 positive roots can be anything- a complex pair, or two real roots- but what about the other 2 roots? Is there any flaw in my understanding of rule of signs? How can I find the exact number of real roots?  Thanks in advance. Turning off "Update page numbers only" in Word When I update the fields document-wide (Ctrl + A, then F9) in a Word document that has a table of contents, a dialog appears asking if I want to update page numbers only, or update the entire table. I never want to update page numbers only if the document headings have changed, nor will I ever.  (Apparently this is given as an option in case someone has manually changed an automatically generated ToC, which is almost always a really bad idea.)   Unfortunately, "Update page numbers only" is the default selection in the dialog, which means that I have to select the other option every time. I update the fields all the time when I'm working in a document that has figures and cross-references, so this is an annoying extra step I'd really like to get rid of.   Is there any way to tell Word to stop asking me this stupid unnecessary question? How Triangle Law and Parallelogram law of addition of Vectors are different?Ain't they.  Please don't tell me the things written in book......give me the appropriate reason.And how do i distinguish between the two while adding vectors,what am i trying to say is i get really confused where to use parallelogram law and where triangle law  P.s:my basics are really weak though!May be the question might not be right How can I see the source of built-in JavaScript functions? "Series" – a noun of multitude similar to "lot", "majority", "percentage", "proportion"– verb agreement According to Garner's fourth edition  Though serving as a plural when the need arises, series is ordinarily a singular noun. But it is also a noun of multitude, so that phrases such as a series of things take a plural verb. However, the collocation there {has been - is} a series has predominated in print sources. Common nouns of multitude: lot, majority, mass, minority, multitude, percentage, proportion, variety.  However,  reads  When it has the singular sense of &quot;one set,&quot; it takes a singular verb, even when series is followed by of and a plural noun: A series of lectures is scheduled.  Are these dissimilar usages stylic advice? Secondly, the inversion after there also chooses singular elsewhere; why is it so?  When the verb precedes the noun percentage, a singular verb is required. That is, a higher percentage of them are, but there is a higher percentage of them. Is it possible to schedule my laptop to mute and unmute at a specific time? I always used to wake up to my favorite radio station on my alarm clock. However, I have moved and can no longer get that radio station over the air. To solve this problem, I would like to stream the station on my laptop, but have it muted overnight, then set it to unmute at a specific time in the morning, so that it will act as an alarm clock. Is there a way to schedule my laptop (Windows 7 64-bit) to unmute at a specific time? In Age of Ultron, Thor seems to know something he possibly shouldn't? Sorry for the cryptic title, but I realise the film has only just been released in the UK and Europe and is yet to be released in the US.  I'll hide all substantial parts of my question, just in case. I don't want to spoil anything.     At the end of Age of Ultron, Thor states that 4 infinity stones have now shown up in the last few years.   So,     By my count we have the Tesseract, from several of the first few films. The Aether, from Thor 2. The Chitauri Scepter, again from several films. And finally, we have The Orb, from Guardians.    Now, to my knowledge     Thor, and indeed none of the Avengers, should know about The Orb. I don't remember Thor visiting the Collector between GoTG and the AoU. So, how did Thor know that The Orb had appeared? Or is he referencing a different infinity stone?   I'm looking for an in universe answer, ideally. True displacement in EEVEE? I have a Blender 2.8 scene with animated true displacement. It is created using material nodes and works fine in Cycles. However, EEVEE doesn't displace my meshes truly, only normals are changed. Is it possible and how to solve the problem now or in the future? How to enable default file manager(nautilus) to handle desktop icons Radius of convergence of entire function Let $f$ be an entire function on the complex plane.      Is the radius of convergence of $f$ around any point $z_0$ infinite? If so, why?   Thank you. Where is composition tab in QGIS Composer to change page size? I am trying to change the page size in the QGIS 3.0 Composer but I am not able to see the Composition tab.  I have right clicked an empty space in the toolbar but did not see anything about composition.  I am using Windows 7.  I tried looking at the QGIS docs but they are still in testing.