Why do more sentences start with 'data' as a plural, than when it is within the sentence?
Is the word "data" now considered singular? If so, what about "datum"?
Is there a way to locate diagrams and move them wherever you want in QGIS 1.7.4/ 1.8.0? I created a pie chart under the tab "diagram". I can mark those diagrams with a green box and move them via the label-tool, but they won't change their position in the end. When I create diagrams with the "diagram overlay" tab they cannot even be marked.  Also, what is the difference between "diagram" and "diagram overlay"? Why does `Position` by default return a list of lists of positions instead of a simple list of positions? Question about arithmetic–geometric mean We have two sequences: $$a_{n+1}=\sqrt{a_nb_n}$$ $$b_{n+1}=\frac{a_n+b_n}{2}$$ I need to prove that those are making Cantor's Lemma.(At the end I shold get that: $\lim_{n\to \infty}a_n=\lim_{n\to \infty}b_n$ by Cantor's Lemma)  Any ideas how?  Thank you. Does QGIS support true circular curves? Disable COPY drag and drop in Windows Explorer in Windows 7 If a black body is a perfect absorber, why does it emit anything? I'm trying to start understanding quantum mechanics, and the first thing I've come across that needs to be understood are black bodies. But I've hit a roadblock at the very first paragraphs. :( According to :     A black body (also, blackbody) is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.   OK, that's nice. It's an object that absorbs (takes in itself and stores/annihilates forever) any electromagnetic radiation that happens to hit it. An object that always looks totally black, no matter under what light you view it. Good. But then it follows with:     A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation.   Say what? Which part of "absorbs" does this go with? How can it absorb anything if it just spits it right back out, even if modified? That's not a black body, that's a pretty white body if you ask me. Or a colored one, depending on how it transforms the incoming waves.  What am I missing here? Suppose that $f : \mathbb{C} \to \mathbb{C}$ is entire. Let $\Omega = \{ z : \frac{1}{2} &lt; |z| &lt; 2\}$. Furthermore, suppose that $ \mathcal{F} = \{f(kz) : k \in \mathbb{C}\}$ is a normal family of analytic functions defined on $\Omega$; the family $\mathcal{F}$ is normal on $\Omega$ iff each sequence from $\mathcal{F}$ has a subsequence converging uniformly on compact subsets of $\Omega$. Prove that $f$ is a polynomial.  I'm studying for my qualifying exam in complex analysis, and this question appears on an old exam. Usually, when I want to show that some entire $f$ is a polynomial, I just try to show that there exists some $N$ so that $f^{(k)}(0) = 0$, all $k \ge N$, but I'm having trouble getting that strategy to work here. I've been looking at the sequence $f(\frac{z}{n})$ trying to make something work, but have not had any success.   I would prefer to receive a hint or two, and then I'll try to post my own solution. Thanks in advance! How do I batch convert many Word documents and have them saved as [originalfilename].pdf? PermGen elimination in JDK 8 String manipulation with & or + in VB.NET What is the reasoning that leads one to postulate this second form for the relativistic particle action? The action for the free relativistic particle with worldline $\gamma : I\subset \mathbb{R}\to M$ is  $$S[\gamma]=-m\int d\lambda\sqrt{-\dot{\gamma}^a(\lambda)\dot{\gamma}_a(\lambda)}\tag{1} $$  Now, one may postulate a second action  $$S'[\gamma,\eta]=\frac{1}{2}\int d\lambda \bigg(\eta(\lambda)^{-1}\dot{\gamma}^a(\lambda)\dot{\gamma}_a(\lambda)-\eta(\lambda)m^2\bigg).\tag{2}$$  These are classically equivalent actions.  My question is: usually what we have is (1) and we have a problem both with the square root and with the massless limit. Given this, how could we think about postulating (2)? In other words, how can we reach (2)?  Usually some people answer this by saying: "it doesn't matter, actions are postulated, you postulate it, compute the equations, prove it works and its over".  Now I beg to differ. I want to know how could someone reason exactly in order to know what to postulate.   I am perfectly comfortable with computing the equations of motion. I want to know is how given (1) we would have the idea to postulate (2).  Is it some special case of some general procedure that deals with constraints? Backtrack, Wi-Fi not working I've installed Backtrack 5R3 KDE, and I realized that my wireless is not working, but wired is working fine.  Here's the lshw output:     *-network         description: Ethernet interface         product: RTL8101E/RTL8102E PCI Express Fast Ethernet controller         vendor: Realtek Semiconductor Co., Ltd.         physical id: 0         bus info: pci@0000:02:00.0         logical name: eth0         version: 05         serial: 04:7d:7b:b7:46:f8         size: 100MB/s         capacity: 100MB/s         width: 64 bits         clock: 33MHz         capabilities: pm msi pciexpress msix vpd bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd autonegotiation         configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl_nic/rtl8105e-1.fw ip=192.168.2.2 latency=0 link=yes multicast=yes port=MII speed=100MB/s         resources: irq:42 ioport:2000(size=256) memory:f0404000-f0404fff memory:f0400000-f0403fff   lspci output:      00:00.0 Host bridge: Intel Corporation 2nd Generation Core Processor Family DRAM Controller (rev 09) 00:02.0 VGA compatible controller: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller (rev 09) 00:14.0 USB Controller: Intel Corporation Panther Point USB xHCI Host Controller (rev 04) 00:16.0 Communication controller: Intel Corporation Panther Point MEI Controller #1 (rev 04) 00:1a.0 USB Controller: Intel Corporation Panther Point USB Enhanced Host Controller #2 (rev 04) 00:1b.0 Audio device: Intel Corporation Panther Point High Definition Audio Controller (rev 04) 00:1c.0 PCI bridge: Intel Corporation Panther Point PCI Express Root Port 1 (rev c4) 00:1c.1 PCI bridge: Intel Corporation Panther Point PCI Express Root Port 2 (rev c4) 00:1d.0 USB Controller: Intel Corporation Panther Point USB Enhanced Host Controller #1 (rev 04) 00:1f.0 ISA bridge: Intel Corporation Panther Point LPC Controller (rev 04) 00:1f.2 SATA controller: Intel Corporation Panther Point 6 port SATA AHCI Controller (rev 04) 00:1f.3 SMBus: Intel Corporation Panther Point SMBus Controller (rev 04) 02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101E/RTL8102E PCI Express Fast Ethernet controller (rev 05) Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$. Let $a \in \mathbb {Z}$, $n &gt; 1$ a natural number with $\gcd(a, n) = 1$, and let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove that $r \mid \phi(n)$.  Euler's generalization of Fermat's Little Theorem: If $n \in \mathbb {N}$ and $m \in \mathbb{Z}$ such that $\gcd(m, n) = 1$, then $m^{\phi(n)} \equiv 1\bmod(n)$.  By Euler's generalization I would have $a^{\phi(n)} \equiv 1\bmod{n}$.  Then I could say $a^r \equiv a^{\phi(n)} \equiv 1 \bmod{n}$. At this point I can see that $r$ clearly must be some multiple of $\phi(n)$.  If I want to show that $r \mid \phi(n)$, then I can show that $\phi(n) = rk$, for some $k \in \mathbb {Z}$.  However, I am a bit stuck about how to make this last step showing that  $\phi(n) = rk$, where $k \in \mathbb {Z}$. Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle I need to evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle.    Attempt: Let $\gamma(t) = e^{it} $ where $t \in [0,2 \pi]$. How can I get rid of the absolute values in the differential? I need help to solve following problem from Rudin's Mathematical analysis book:    Convergence of the series $\sum a_n$  implies the convergence of $\sum \dfrac{\sqrt {a_n}}{n}$, if $a_n&gt;0$  I tried to construct a suitable convergence sequence $b_n$ such that $\sum b_n$ converges and $a_n \leq b_n$ but, I am not able to find such sequence $b_n$ .  Thanks for the help and sugestions. Unable to upgrade Windows 10 edition from Home to Pro I have a Lenovo laptop which upgraded from Windows 8.1 Home to Windows 10 Home.  I have a (legitimate) Windows 10 Pro key which I ran through the "Change Product Key" wizard.  After a reboot I get an error which states "We couldn't upgrade your edition" and asks me to try again or seek help from my system administrator (me!) or Microsoft.  There is nothing in the event logs except Info entries in the Setup log stating it failed to change the installed state to Pro Edition with a hex error code (I don't have access to the laptop right now, I will update later with the full log details)  Googling the hex error code led me to a Windows 7 KB Article regarding Windows Update failure due to locked files. The article stepped through using MSCONFIG to perform a clean boot which I did, but still got the error.  Any pointers on how to upgrade this laptop? Or will I have to get the sledgehammer out and do a clean install? 1N5819-E3/73  1N5819-E3/53 1N5819-E3/54   the first one is 4x cheaper than the last, why ?  aren't they all the same ? Are there instances where citing Wikipedia is allowed? For example, suppose you're writing an article about triangles, and you want to include a short proof of Pythagoras' theorem, but you can't quite remember how to derive it, so you pop over to:  and check the proof there. It works mathematically, makes sense and is as far as you can tell, correct, so you include it. Now the proof on Wikipedia doesn't have a citation because probably someone has been taught it and copied it over to Wikipedia, but it's still correct. The only thing you could cite for the proof would be Wikipedia, would a citation be ok or should it just be copied down without a citation?  Edit: Ok, there have been many responses. Most with a firm "no", but some giving the reason: "Just get the proof from a book" since it's so common, but suppose then it wasn't a common proof of something. Maybe it's not very well known or something but suppose there is a small Wikipedia page with the correct mathematical proof. How much effort are people going to go to to find a proof in a book when there's a (correct (which we know, becuase it's maths and we can check it)) proof on Wikipedia? Why is it so bad to say: "I found this proof on Wikipedia, and the maths checks out so it doesn't matter who wrote it, it is correct, but that's where I found it." Or if you do find it somewhere else why not say: "Proof taken from Wikipedia and verified by the proof shown in "Triangles and their properties, Nature, 2014, p113 etc..." Are static class instances unique to a request or a server in ASP.NET? On an ASP.NET website, are static classes unique to each web request, or are they instantiated whenever needed and GCed whenever the GC decides to disposed of them?  The reason I ask is because I've written some static classes before in C# and the behavior is different than I would have expected. I would have expected static classes to be unique to each request, but it doesn't seem like that is the case.  If they are not unique to each request, is there a way to allow them to be?  UPDATE: The answer driis gave me was exactly what I needed. I was already using a singleton class, however it was using a static instance and therefore was being shared between requests even if the users were different which in this case was a bad thing. Using HttpContext.Current.Items solves my problem perfectly. For anyone who stumbles upon this question in the future, here is my implementation, simplified and shortened so that it easy to understand the pattern:  using System.Collections; using System.Web;  public class GloballyAccessibleClass {     private GloballyAccessibleClass() { }      public static GloballyAccessibleClass Instance     {         get         {             IDictionary items = HttpContext.Current.Items;             if(!items.Contains("TheInstance"))             {                 items["TheInstance"] = new GloballyAccessibleClass();             }             return items["TheInstance"] as GloballyAccessibleClass;         }     } } Please Join Us in Welcoming Our New Meta Stack Exchange Moderators!