MS Access SQL multiple rows into one row with new columns
Access: Making a Pivot Table with Multiple, Same Values as Columns
Strip whitespace from jsp output How can I strip out extra whitespace from jsp pages' output?  Is there a switch I can flip on my web.xml?  Is there a Tomcat specific setting? This is a follow-on from my  about samples from a distribution.  Suppose $X_1 \ldots X_{n-1}, X_n$ are random variables all following some fixed distribution $D$. How do I prove that $P(X_n &gt; X_1 \wedge \ldots \wedge X_n &gt; X_{n-1}) = \frac{1}{n}$ (this is true intuitively and experimentally). Inequality involving $\limsup$ and $\liminf$: $ \liminf(a_{n+1}/a_n) \le \liminf((a_n)^{(1/n)}) \le \limsup((a_n)^{(1/n)}) \le \limsup(a_{n+1}/a_n)$ Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$ I am confused by expressions like $\mathbb{R}/\mathbb{Z}$, especially if I see something of the sort $SL(2,\mathbb{R})/SO(2,\mathbb{R})$. I don't know what to make of it. I understand what a quotient of a group for an equivalence looks like, but I can't get my head around expressions like above.   Is a quotient like this always a group and what do elements in the set $SL(2,\mathbb{R})/SO(2,\mathbb{R})$ look like? How to determine equality for two JavaScript objects? n-dimensional vector space isomorphic to the n-th product of a field as abelian groups Let $V$ be a finite dimensional vector space (of dimension n) over a field $F$. I need to show that $V$ is isomorphic to $F^n$ as abelian groups. However, I don't really understand what does "isomorphic as abelian groups" mean, my (poor) attempt to solve this was:  Let $f:V\to F^n$, $f((v_1,v_2,\ldots,v_n)):=v_1+\ldots+v_n$, clearly $f$ is a group homomorphism, but it is not biyective since, for example, in the case where $dim(V)=2$ and $F=\mathbb{R}$ we have $f((2,-2))=0=f((3,-3))$, I've also tried it by defining $f$ to be the product of a vector's entries but obviously it didn't work so I'm stuck!   I think this should be an easy problem but since I don't quite understand it, it's giving me problems. Thank you for your help. Getting the default text editor used in system I have used select-editor and I note that I am using /usr/bin/nano. Is this the default text editor I am using?  When I open text files, It opens with gedit  What command in terminal must be specified to get the default text editor that I am using, and have it returned to e in terminal? I know that atan2 gives me the absolute angle of any vector. But it doesn't give a value from 0 to 360 degrees. Instead, it gives a value (if I'm not mistaken), between 0 and 180, or between 0 and -180. For example, instead of giving angle 270, it will say -90.  This is a little confusing for me. Let me try to describe how I think this works, and please tell me if I'm correct. Actually, I'll draw it.    Is this correct? I'm having a little trouble understanding this. Thanks We hold an L1 visa (Citizens of India) and are planning a cruise to the Bahamas this summer. Are there any Visa requirements to enter Bahamas. I am looking for a proof possibly using the sandwich theorem and/or Bernoulli's inequality for proving the following statement:  If $x&gt;0$ then $x^{1/n}$ tends to $1$. Trichromelibrary was suddenly downloading from Google Play Store From nowhere, my friend got a notification that com.google.android.trichromelibrary was downloading together with a progress bar.  Why? Dirichlet's problem in the unit disk is to construct the harmonic function from the given continuous function on the boundary circle. It is solved by the convolution with the Poisson kernel, and we know that the constructed function has uniform limit which is the given continuous function as $r\to 1$, and we can complexify the solution by taking the Schwarz integral formula. Now (in this very particular case) does the imaginary part has a uniform limit? If it does, why don't we prove the uniqueness of the solution by a simple application of the Cauchy integral formula? Here is the proof that I reckon to be reasonable(which is what I expose here to be criticised)  We construct the Schwarz integral, or $\frac{1}{2\pi}\int _{0}^{2\pi}\frac{\exp(it)+z}{\exp{(it)}-z}u(\exp{(it)})\mathrm{d}t$. This function is an analytic function in the interior unit disk, and is continuous in the closed unit disk(its closure). Let this analytic function denoted by $f$, and another analytic function that has the same uniform limit function on the circle be $v$. Then $u-v$ is an complex analytic function in the interior of the unit disk, continuous on the closure, with boundary value identically zero. An application of Cauchy's integral formula gives rise to the conclusion that $u-v$ in identically zero on the entire disk.   Another question being if the boundary function has finite jump discontinuities, what is the behaviour of the convolution with the Poisson kernel near the discontinuous points? Plotting function defined with Lua doesn't do anything Suppose $K \subset L$ is a finite field extension of degree $m$. Is it true that there exists some natural $n$ such that $L$ is isomorphic to a subfield of $M^{n\times n}(K)$, the ring of $n\times n$ matrices with entries in $K$? What is the smallest dimension (as a function of $m$) for which an isomorphism exists?  The example I had in mind was the 2-dimensional extension $\mathbb{R} \subset \mathbb{C}$ with $\mathbb{C}$ being isomorphic to $\{ \begin{pmatrix}a&amp;-b\\b&amp;a\end{pmatrix} : a, b \in \mathbb{R}\}$. ASP.NET MVC custom routing for search Here is my scenario.  For the example lets say that I need to return a list of cars based on a search criteria.  I would like to have a single View to display the results since the output will be the same, but I need several ways of getting there.  For instance, I may have a Form with a textbox to search by year.  I may have another separate page that contains a hyperlink for all red, Toyota cars.  How do I handle these multiple scenarios in the same View and Controller.  My dilemma is that the search could contain several options… year, make, model, etc but I don’t know where to put them.  What is the best approach for this?  Should I define the parameters in the routing or go with query strings, etc? How To Group Records By Value In A Specific Field? I have a List of records of type abc__c. abc__c is a custom object. The record has a field called code__c. What I am trying to accompolish is to group the records in the list based on the code__c.  For example the list might have :  Code__c     abc__c record 30       (Record 1) 40       (Record 2) 40       (Record 3) 50       (Record 4) 30       (Record 5)   I want to group these records based on Code__c in a Map. There could be any number of code__c which is populated dynamically. It is not static. how can I loop through the list and store the records as a list for a particular code__c(Id) in Map? How to add a list of vectors (lists) to a directed graph as an edge weight? Suspected adware infection of Mac Homology of $S^1 \times (S^1 \vee S^1)$ I'm trying to solve question 2.2.9(b) in Hatcher's Algebraic Topology.   Question: Calculate the homology groups of $X=S^1 \times (S^1 \vee S^1)$.  My attempt: I try to use the Mayer-Vietoris sequence.   Let $A=S^1 \times (S^1 \vee \text{small bit}) =S^1\times S^1$ and $B=S^1 \times ( \text{small bit} \vee S^1)=S^1 \times S^1$. (Unsure how to express this, but hopefully this is clear enough.)   Then $A\cap B=S^1\times \{\text{point}\}=S^1$ and $A\cup B=X$.  The Mayer-Vietoris sequence then gives us an exact sequence in reduced homology as follows:  $$0 \to \mathbb{Z}^2 \to \tilde{H}_2(X) \to \mathbb{Z} \to \mathbb{Z}^2 \to \tilde{H}_1(X) \to 0.$$  Is it possible from this exact sequence to determine the homology groups, in some algebraic fashion? Or do I need to determine what the maps are? How do I determine the maps? Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite. I have seen another post for this same question but it never got an answer. Since I am fairly new, I can't comment on other's posts, therefore I am creating a new one. The question states:  If a, b, and c are positive integers, prove that if $(a + b + c) | (a*b*c)$, then $a+b+c$ is composite.  I do not really know how to approach this.  The link to the post with the same question is: