Polynomial P= Q² + R²
Prove that a positive polynomial function can be written as the squares of two polynomial functions
How to calculate the difference between two dates using PHP? Transfering money from NRE to saving account is taxable or not Newton's Law of Universal Gravitation tells us that the potential energy of object in a gravitational field is $$U ~=~ -\frac{GMm}{r}.\tag{1}$$  The experimentally verified near-Earth gravitational potential is  $$U ~=~ mgh.\tag{2}$$  The near-Earth potential should be an approximation for the general potential energy when $r\approx r_{\text{Earth}}$, but the problem I'm having is that they scale differently with distance.  $(1)$ scales as $\frac 1r$.  So the greater the distance from the Earth, the less potential energy an object should have.  But $(2)$ scales proportionally to distance.  So the greater the distance from the Earth, the more potential energy an object should have.  How is this reconcilable? I have a table to store StudentID, SubjectID, ObtainedMarks. Now I have to create a pivot table to show studentID and obtainedMarks in different subject. Number of subject may differ. I could generate pivot table for fixed subjectID like    SELECT * FROM (SELECT StudentID, SubjectID, ObtainedMarks from [Exam].[ObtainedMarkEntry]) as InvoiceResult PIVOT (     sum(ObtainedMarks) for [SubjectID] in  ([1],[2],[3],[4]) )as finalResult   This works but problem is 1,2,3 is not static it should come from same table   So I did something like   declare @minvalue int, @maxvalue int declare @myArray varchar(max) set @MyArray=''  select RowID=IDENTITY(int, 1,1), SubjectID into #tempSubject from [Exam].[ObtainedMarkEntry] select * from #tempSubject set @minvalue = (select min(RowID) from #tempSubject) set @maxvalue = (select max(RowID) from #tempSubject) while (@minvalue&lt;=@maxvalue) begin     declare @sid nvarchar(10)     set @sid=(select SubjectID from #tempSubject where RowID=@minvalue)     set @myArray= @myArray + '[' + @sid + '], '      set @minvalue= @minvalue+1 end set @myArray= SUBSTRING(@myArray,0,len(@myArray)) drop table #tempSubject  declare @q as nvarchar(max) SELECT * FROM (SELECT StudentID, SubjectID, ObtainedMarks  from [Exam].[ObtainedMarkEntry]) as InvoiceResult PIVOT (     sum(ObtainedMarks) for [SubjectID] in  (@myArray) )as finalResult   Now I am getting error at in(@myArray) can't I assign variable in this section. In Mootools, I'd just run if ($('target')) { ... }.  Does if ($('#target')) { ... } in jQuery work the same way? Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$ Suppose $m,n&gt;0$, $U$ an open subset of $\mathbb{R}^{m+n}$ and let $f: U \to \mathbb{R}^n$ be continuously differentiable.  Is it possible for $f$ to be injective?    My thinking is that continuous differentiability+injectivity suggests that this is sort of getting at a converse to the Inverse Function Theorem.  We know the Jacobian is not invertible at any point in $U$, and the question is asking if this implies that $f$ cannot be invertible in any neighborhood contained in $U$. referring to Eqn. 1a) and 1b) in a sentence as eqn. (1) Linear regression with non-symmetric cost function? I want to predict some value $Y(x)$ and I am trying to get some prediction $\hat Y(x)$ that optimizes between being as low as possible, but still being larger than $Y(x)$. In other words: $$\text{cost}\left\{ Y(x) \gtrsim \hat Y(x) \right\}  &gt;&gt; \text{cost}\left\{ \hat Y(x) \gtrsim Y(x) \right\}  $$  I think a simple linear regression should do totally fine. So I somewhat know how to implement this manually, but I guess I'm not the first one with this kind of problem. Are there any packages/libraries (preferably python) out there doing what I want to do? What's the keyword I need to look for?  What if I knew a function $Y_0(x) &gt; 0$ where $Y(x) &gt; Y_0(x)$. What's the best way to implement these restrictions? Why are two universal objects isomorphic? Browsing some , it is claimed that two universal objects are isomorphic because they admit the identity morphism on themselves. But from two identity morphisms, how would you get an isomorphism between the two? When there is a Personal Hotspot network available, it displays a chain link icon instead of the usual lock icon in the list of available networks on iOS and OS X.    My question is, how does OS X distinguish these networks? Is it specified in 802.11 how hotspots broadcast their SSID's differently? Fly and Two Trains Riddle Why would a JavaScript variable start with a dollar sign? Arrays in Unix Bourne Shell I am trying to use arrays in Bourne shell (/bin/sh). I found that the way to initialize array elements is:  arr=(1 2 3)   But it is encountering an error:  syntax error at line 8: `arr=' unexpected   Now the post where I found this syntax says it is for bash, but I could not find any separate syntax for Bourne shell. Does the syntax stand the same for /bin/sh as well? Suppose you have a physical . It is true that as amplitude increases, the period increases. Can we demonstrate this fact without explicitly finding the period (which is pretty involved and pretty messy) in:    an intuitive fashion,  rigorously? There are a variety of characters that are not legally encodeable in XML 1.0, e.g. U+0007 ('bell') and U+001B ('escape'). Most of the interesting ones are non-whitespace 'control' characters.    It's clear from (e.g.)  and others that it's  -- but can anyone illuminate me as to why the XML spec forbids these characters?   It seems like it could have been required that they be encoded in escapes, e.g. as &amp;#x0007; and &amp;#x001B; respectively, but perhaps there's a practical reason that the characters were forbidden rather than required to be escaped?  Answerers have suggested that there is some motivation towards avoiding transmission control characters, but Unicode includes many other control-like characters (consider U+200C "zero width non joiner"). I recognize there may be no good reason for this behavior, but I would still like to understand it better.  It's particularly frustrating because when those character values appear in other encodings data formats, I end up "double-escaping" new XML documents that need to encode this. Mention a specific potential adviser and project in the PhD statement of purpose I am writing my statement of purpose for my Ph.D. and I want to work in a specific field with a specific professor in the department that I am going to apply for and I have a very good experience in this field. I sent an email for that professor asking if he/she is accepting Ph.D. students and he/she did not respond. I built my whole statement of purpose based on my previous achievements and future plan for that specific area. I also mentioned that I am willing to work with that professor. My statement of purpose tells that I am very passionate about this field and I am only willing to work with that professor (if there were more than one professor working on the same area, I would mention all of them). if that professor doesn't accept new Ph.D. students, will I risk my admission to that school?   Will the committee response be something like this:  "the applicant really knows what he/she is going to do and there is a specific future plan and he/she also got a good experience in this field, but he/she sounds very strict to his plan and doesn't show any flexibility...REJECTED"? Do mankind and manmade activities/constructions have any effect on the rotation of the Earth? I have just started learning Japanese Mahjong and I am a bit lost as to why this hand failed.  I did several pons and chis over the course of a hand, having a total of three open melds (one set and two sequences).  Apart from these I had an incomplete bamboo sequence of II and III as well as a pair of dragons, therefore I was on a single wait for I or IV bamboo stick tile. When the IV tile appeared in one of the discards of other players, I was given a choice to do another chi and declare another open meld, but I couldn't win with a ron. Why was that?  Am I wrong that winning by ron guarantees a single needed yaku to win a hand, just like Closed Tsumo does?  After declaring the chi I was offered with, my hand was left with a single pair of tiles, one of which I had to discard.  Eventually the round finished with a draw.  Why couldn't I win this hand with a ron on the IV bamboo tile, and why was I given only the choice of chi instead? What is a NullPointerException, and how do I fix it? What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely? Why are POSIX Find Parameters Different from Other Program styles? Why is a parameter in the POSIX find command added with a single hyphen for multi-character parameter names, while most other programs use single hyphen to indicate multiple single-character flags, and double-hyphens to indicate single parameter names with multiple characters?  This seems inconsistent, and I'm curious as to  A. why it's really not inconsistent, or  B. the history of that decision.