Below is the question and the answer is "what."     Xerosis is a technical medical term for ___ most people refer to as dry skin.    From my instinct, I understood why "what" should be an answer. The problem is I can't explain why "which" can't be an answer.   If I chose "which" for this question, then "which" indicated the word "term," but it couldn't be like that. I need an explanation based on grammar.
Most of the time one or the other feels better, but every so often, "which" vs. "what" trips me up.   So, what's the exact difference and when should you use one or the other?
Apply function conditionally What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass? This is a variation of the  questioned some time ago.  For a complex Hilbert space $H$ let $T: H \rightarrow H$ be a bounded operator. We call that $T$ is a trace-class operator if the following sum  $$\sum_{i}{\langle |T|e_{i}, e_{i} \rangle} &lt; \infty$$  converges, where $|T| = (T T^{*})^{\frac{1}{2}}$ is the absolute value of the operator.  Assume that  $$\sum_{i}{\langle Te_{i}, e_{i} \rangle}$$  converges for any basis in the space $H$. How to prove that if the aformentioned property holds then the operator is a trace class operator?  The progress on the problem is the following: Given an arbitrary bounded operator $T: H \rightarrow H$, one can use the following decomposition $$T = \big( \frac{T + T^{*}}{2} \big) ^{*} + i \big( \frac{T^{*} - T}{2i} \big) ^{*}$$  The latter line gives the decomposition $$T = A + i B$$ where $A, B$ are normal operators.  For the normal operators we can apply the spectral theorem that proposes that $T$ is unitary equivalent to  $$(UT U^{-1})(f(x)) = g(x) f(x)$$  where  $$U: H \rightarrow L^{2}(X, \mu)$$ $$g \in L^{\infty}(X, \mu)$$  Though this decomposition classify the operator in a broad sence, i see no direct way to conclude the statement. Are the any hints that may extend the previous argument? If not, are there any ways to conclude the statement? What is the best way to check whether a given object is of a given type? How about checking whether the object inherits from a given type?  Let's say I have an object o. How do I check whether it's a str? Classification of automorphisms of projective space Let $k$ be a field, n a positive integer.  Vakil's notes, 17.4.B: Show that all the automorphisms of the projective scheme $P_k^n$ correspond to $(n+1)\times(n+1)$ invertible matrices over k, modulo scalars.   His hint is to show that $f^\star \mathcal{O}(1) \cong \mathcal{O}(1).$ (f is the automorphism. I don't if $\mathcal{O}(1)$ is the conventional notation; if it's unclear, it's an invertible sheaf over $P_k^n$) I can show what he wants assuming this, but can someone help me find a clean way to show this? Server 2008 Net Send or Msg? I have a Windows 2008 server running as a domain controller. The details are as follows:  Domain: corp Server Name: oxygen   The workstations are all running Windows XP SP3 and have fixed IP addresses.  I am trying to use the net send functionality to be able to send simple messages to either individual machines/users and also to all machines. This is so I can send a message to a user to alert them about something, or likewise alert everyone of something such as the server being rebooted.  Is this possible using Windows Server 2008? If so, what would the command be? I have a trained logistic regression model that I am applying to a testing data set. The dependent variable is binary (boolean). For each sample in the testing data set, I apply the logistic regression model to generates a % probability that the dependent variable will be true. Then I record whether the acutal value was true or false. I'm trying to calculate an $R^2$ or Adjusted $R^2$ figure as in a linear regression model.  This gives me a record for each sample in the testing set like:  prob_value_is_true         acutal_value    .34                          0    .45                          1    .11                          0    .84                          0     ....                        ....             I am wondering how to test the accuracy of the model. My first attempt was to use a contingency table and say "if prob_value_is_true > 0.80, guess that the actual value is true" and then measure the ratio of correct to incorrect classifications. But I don't like that, because it feels more like I'm just evaluating the 0.80 as a boundary, not the accuracy of the model as a whole and at all prob_value_is_true values.  Then I tried to just look at each prob_value_is_true discrete value, as an example, looking at all samples where prob_value_is_true=0.34 and measuring the % of those samples where the acutal value is true (in this case, perfect accuracy would be if the % of samples that was true = 34%). I might create a model accuracy score by summing the difference at each discrete value of prob_value_is_true. But sample sizes are a huge concern here, especially for the extremes (nearing 0% or 100%), such that the averages of the acutal values are not accurate, so using them to measure the model accuracy doesn't seem right.  I even tried creating huge ranges to ensure sufficient sample sizes (0-.25, .25-.50, .50-.75, .75-1.0), but how to measure "goodness" of that % of actual value stumps me. Say all samples where prob_value_is_true is between 0.25 and 0.50 have an average acutal_value of 0.45. Is that good since its in the range? Bad since its not near 37.5% (the center of the range)?  So I'm stuck at what seems like should be an easy question, and hoping someone can point me to a resource or method to calculate an accuracy stastic for a logistic regression model. How do you debug PHP scripts? I am currently looking at the various libraries that I can use to show a map in my custom Android App. I have found several like Mapsforge, OSMDroid, ArcGIS runtime for Android, Google Maps for Android and so on. I'm sure that I am missing a few.   Is there a comparison chart somewhere about the differences in functionalities and pros and cons of each one?   If there isn't one, we could make this question community wiki, to serve alongside  &amp; . Tags in spoilers are always visible, even if you don't put your mouse on the spoiler (on  for example). See the screenshot:      Looks a bit strange on this site too:        that needs ! How to redirect with "www" URL's to without "www" URL's or vice-versa? I am using ASP.NET 2.0 C#. I want to redirect all request for my web app with "www" to without "www"  www.example.com to example.com  Or  example.com to www.example.com  Stackoverflow.com is already doing this, I know there is a premade mechanism in PHP (.htaccess) file. But how to do it in asp.net ?  Thanks Adapt Ubuntu to a high-DPI resolution screen How can I adapt Ubuntu to a high resolution display?  I have a display with 3200x1600px on only 11'' and everything looks really tiny. Is adding a time dummy the same as estimating by within-time fixed effects? Writing to NTFS drive in Linux How to fix "error: unknown filesystem. grub rescue> I get this error:  Error: unknown filesystem. grub rescue&gt;   I'm not exactly sure what I did. I believe I installed Ubuntu over Windows on my Acer netbook. I then tried to install , but it wouldn't start installing.  I turned the netbook off and back on. Now I get the error.  I have read a lot of other questions like this, but in my case I cannot boot a CD. If I put a Ubuntu CD or a Linux Mint CD into my external CD/DVD drive and change my BIOS to boot the CD-ROM first, it just gives me the same error screen.  Update copied from comment dated 2012-05-26 02:54:29Z  Here are some results from my commands:   grub rescue&gt;ls (hd0) (hd0,msdos5) (hd0,msdos1)  grub rescue&gt;ls (hd0,msdos5) unknown filesystem  grub rescue&gt;ls (hd0,msdos1) unknown filesystem  grub rescue&gt;ls (hd0) unknown filesystem Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf   implies that $X$ is separable.   My attempt:  Let $d$ be the metric that induces the topology $\mathcal{T}$.   For every $n \geq 1$, consider the open cover: $$\{B_X(x,1/n)\mid x \in X\}$$  Because the space is Lindelöf, this implies that for every $n \geq 1$, there is a countable (or finite) subcover given by $$\mathcal{B}_n:= \{B_X(x,1/n) \mid x \in I_n, |I_n| \leq |\mathbb{N}|\}$$  Now, define $D:= \bigcup_{n\geq 1} I_n$. Let $y \in X$. Let $\epsilon &gt; 0$. Choose $m$ a positive integer so large that $1/m &lt; \epsilon$.  Because $y\in X =\bigcup\mathcal{B}_m$, it follows that there exists $x \in D$ such that $y \in B_X(x,1/m)$, meaning that $d(x,y) &lt; 1/m &lt; \epsilon$, such that $x \in B_X(y, \epsilon) \cap D$. Hence, $y \in \overline{D}$ and it follows that $D$ is a dense countable set in $X$, such that $X$ is separable.  Is this correct? There are n letters addressed to n eople at different addresses. The n addresses are typed on n envelopes.  A disgruntled secretary shuffles the letters and puts them in the envelopes in random order, one letter per envelope.  Find the probability that at least one letter is put in a correctly addressed envelope. [Hint: use the inclusion-exclusion formula.] What is the probability approximately, for large n ?    My attempt at a solution:  P(all correct) = $\frac{1}{n!}$  P(n-1 correct) = ${n \choose n-1} \frac{1}{n!} = \frac{1}{1!(n-1)!}$  ${n \choose n-1}$ ways of selecting n-1 correct letters.  P(n-2 correct) = ${n \choose n-2} \frac{1}{n!} = \frac{1}{2!(n-2)!}$  ...  P(n-n correct) = ${n \choose n-n} \frac{1}{n!} = \frac{1}{n!(n-n)!} = \frac{1}{n!}$  This all looks ok to me, but I tested this for a case of 4 people, (I think the theoretical value should be $\frac{9}{24}$ but obviously that is not what I got. Can someone correct my logic please? Also, with regards to the hint about inclusion/exclusion - where would that come in?  I read about derangements on Wikipedia but it did not make total sense to me (the derivation).  I would appreciate any advice whatsoever including references to other material. How do I find the package that provides a file? Simple enough question: is there some shell command (or GUI method) I can use that, given the path to a file on my system, tells me what package put it there? Assuming the file did in fact come from a package, that is.  Bonus question: what if it's a file that isn't installed on my system? Is there, say, a website that will let me look up a file and see what packages, if any, provide it? Why can't I have a non-integral static const member in a class? I noticed C++ will not compile the following:  class No_Good {   static double const d = 1.0; };   However it will happily allow a variation where the double is changed to an int, unsigned, or any integral type:  class Happy_Times {   static unsigned const u = 1; };   My solution was to alter it to read:  class Now_Good {   static double d() { return 1.0; } };   and figure that the compiler will be smart enough to inline where necessary... but it left me curious.  Why would the C++ designer(s) allow me to static const an int or unsigned, but not a double?  Edit: I am using visual studio 7.1 (.net 2003) on Windows XP.  Edit2:  Question has been answered, but for completion, the error I was seeing:  error C2864: 'd' : only const static integral data members can be initialized inside a class or struct If each suit is represented then we will have two cards from one suit and one card each from the remaining suits. So I am counting the ways this can happen like so -  ${52 \choose 1}$ ways of selecting the first card.  ${12 \choose 1}$ ways of selecting a card from the same suit as the first.  ${13 \choose 1}$ ways of selecting a card for each of the 3 remaining suits.  So I have -  $${52 \choose 1}{12 \choose 1}{13 \choose 1}{13 \choose 1}{13 \choose 1}$$  Then I have the sample space as $52 P 5$ as we are counting with regard to order on the numerator so we need to do the same for the denominator.  So I have $$\frac{{52 \choose 1}{12 \choose 1}{13 \choose 1}{13 \choose 1}{13 \choose 1}}{52P5}$$  Does that look correct?