As in the title: &quot;This needs reviewed.&quot; vs &quot;This needs to be reviewed.&quot; Are either of these grammatically incorrect ? And/or is one preferable to the other ? I'm not quite sure what area this falls under, so I'm having a hard time finding the correct references elsewhere. Sources preferred if possible please. Thank you
I'm from Central Pennsylvania, and apparently, we have a strange language construct in this area. I was recently talking about how "my car needs washed" to a friend from NJ, and she told me that my sentence was grammatically incorrect.   I realize she's right, and I realize my options are "my car needs to be washed" or "my car needs washing". But I'm not clear on the precise rule being invoked.
What does "had had" mean? How does this differ from "had"? For example, what is the difference between the following two sentences:     I had a bad day      I had had a bad day What are the best books to study Neural Networks from a purely mathematical perspective? I am looking for a book that goes through the mathematical aspects of neural networks, from simple forward passage of multilayer perceptron in matrix form or differentiation of activation functions, to back propagation in CNN or RNN (to mention some of the topics).  Do you know any book that goes in depth into this theory? I've had a look at a couple (such as Pattern Recognition and Machine Learning by Bishop or Deep Learning by Goodfellow, Bengio and Courville) but still have not found a rigorous one (with exercises would be a plus). Do you have any suggestions? Easiest way to solve $y''+y=\frac{1}{\cos x}$ Shrink exFAT partition Is there any way to shrink an exFAT partition?   The windows disk manager has the "Shrink" option greyed out. We all know that Superman changes in the phone booth. But where does he put his regular clothes while he's on a mission? He doesn't throw it out, because he changes back. But we don't see him carrying a bag of dirty laundry while he's on a mission.  ("In his right hand, Superman has Lois Lane, and in his left hand he seems to be holding... boxers??)  And I can't imagine he leaves it in the phone booth.  So where does Superman leave his regular clothes after he changes? Computing the inverse of a permutation I didn't understand the permutation and of course, I got this question wrong.     Compute the inverse of the following permutation:   $$ \begin{pmatrix}  1&amp;2&amp;3&amp;4&amp;5&amp;6\\ 2&amp;5&amp;4&amp;1&amp;6&amp;3 \end{pmatrix} $$   Could you please help me with this question and provide an explanation?  Furthermore, is it possible to compute the direct permutation, not the inverse one? If yes, how?  Thank you in advance! Embed LaTeX math equations into Microsoft Word Let's say I have a (comparatively) lovely-looking document in LaTeX, full of lovingly typeset, (relatively) complex equations. Now, let's say some barbarians come along one day and decide that the document has to be put into Microsoft Word (2007). ...after the usual mourning period associated with such events, let's say I value my job (more specifically, the bread it provides) enough to get all the text and tables formatted and references organised into the Word document. –...related questions  and – Now I'm looking at the equations with fear and dread. One option of course is to just lift screenshots from the original document, but this is painstaking if I need to refer to parts of the equation in the text. Also, I might need to edit equations on the fly. Anyone know of a free application which allows embedding LaTeX math into MS Word? I've looked at  and  which do roughly what I want... they build LaTeX images from source and embed them into the Word document, allowing to edit the source later... but both are commerical. ...any help in these troubling times will be greatly appreciated. EDIT: Just a note that  offers a 30-day free trial and is working out really nicely... but still, it's not free. Might be a good solution for those with short-term needs, or money. Proof that no polynomial with integer coefficients can only produce primes Doing a discrete math review and am trying to solve problem 1.6 in the text found here:  - I believe I've gotten parts (a) and (b) correctly, but (c) is a bit tricky for me. Would appreciate a review of a/b and a hint for c if possible. Restatement here:  For n = 40, the value of polynomial $p(n)::=n^2 + n + 41$ is not prime, as noted in Section 1.1. But we could have predicted based on general principles that no nonconstant polynomial can generate only prime numbers.  In particular, let $q(n)$ be a polynomial with integer coefﬁcients, and let $c::=q(0)$ be the constant term of q.  (a) Verify that $q(cm)$ is a multiple of c for all $m \in Z$  Proof: Since q is a polynomial, it will be of the form: $q(x) = a_nx^n+a_{n-1}x^{n-1} + ... + a_1x + c$  If $x = cm$, then notice that cm will be inside every term of the polynomial, and since the final term is c, c can be factored out of every term. Hence, q(cm) is a multiple of c for all $m \in Z$.  b) Show that if q is nonconstant and c > 1, then as n ranges over the nonnegative integers, $N$, there are infinitely many $q(n) \in Z$ that are not primes.  Proof: Continuing from the result found in (a), it is easy to see that for all $m \in Z$, there will be an infinite number of multiples of c that will be generated by q. Since c > 1, these multiples are guaranteed not to be prime.  c) Conclude that for every nonconstant polynomial, q, there must be an $n \in N$ such that $q(n)$ is not prime. Hint: Only one easy case remains.  c = 0 is trivially easy to prove using the (b) above.  I assume the "easy" case is referring to c = 1, but in this case I'm not sure how to continue, since the result of (a) and (b) don't apply: I can't use them since adding 1 to any even number may make it prime. If the result of the terms not including c is odd, then adding 1 to that result makes it even and it is not prime. However, if the terms add up to an even number, I don't see a way of using the knowledge I have so far to prove conclusively that that number + 1 will NOT in fact be prime. How to Avoid Precision Errors While Creating Numpy Arrays? Let $a$ and $b$ be natural numbers with $ab&gt;2$. Suppose that the sum of their highest common factor and least common multiple is divisible by $a+b$. Prove that the quotient is at most $\frac{a+b}4$. When is this quotient exactly equal to $\frac{a+b}4$. sed - replace string with file contents I have two files: file1 and file2.  file1 has the following contents:  ---   host: "localhost"   port: 3000   reporter_type: "zookeeper"   zk_hosts:      - "localhost:2181"   file2 contains an IP address (1.1.1.1)  What I want to do is replace localhost with 1.1.1.1, so that the end result is:  ---   host: "1.1.1.1"   port: 3000   reporter_type: "zookeeper"   zk_hosts:      - "1.1.1.1:2181"   I have tried:  sed -i -e "/localhost/r file2" -e "/localhost/d" file1 sed '/localhost/r file2' file1 |sed '/localhost/d' sed -e '/localhost/r file2' -e "s///" file1   But I either get the whole line replaced, or the IP going to the line after the one I need to modify. Nested sequence of non-empty compact subsets - intersection differs from empty set I have the following proposition:  "If $(S_n)$ is a sequence of compact subsets of a metric space such that  $S_1 \supseteq S_2 \supseteq ... \supseteq S_n$  Then $\bigcap^\infty_{i=1} S_i$ $\neq$ $\emptyset$"  My lecture notes provide the following proof, whose last step I don't understand:    Proof: Assume by way of contradiction that $\bigcap^\infty_{i=1} S_i$ = $\emptyset$. Let $V_n := (S_n)^c$ for each $n$. The class $\mathbb{C} :=\{V_n: n \in \mathbb{N} \}$ is an open covering of $S_1$. Since $S_1$ is compact, $\exists I$ finite, $I \subset \mathbb{N}$, s.t $\{V_i: i \in I \}$ covers $S_1$. Let $n:=max(I)$. The class $\{V_1, ..., V_n \}$ also covers $S_1$ and we get the following contradiction   $\emptyset = \bigcap^n_{i=1} S_i = S_n$    So, I don't get the part from "Let $n:=max(I)$..." onwards, especially the contradiction. I have tried applying DeMorgan's Law and the only way the last equalities makes sense is if the union of $\{V_1, ..., V_n \}$ equals the whole metric space, a property I haven't been able to understand from the steps of the proof. This is a corollary to the finite intersection property, so it must have a connection but again I can't quite get it.  Thanks in advance Execution order of event receivers and workflow on a list Where is the line drawn with domain names which include a trademark? A search on google for "iphone developer" turns up loads of websites which have "iphone" in them, a trademarked name by Apple.  So I'm led to believe that having a domain such as iphonedeveloper.com is ok? Well, you're still using Apple's trademark, but it would be hard to brand yourself otherwise. You're an IPHONE DEVELOPER... right?  Well, what if I want to provide a website where users pay to get a list of the best offers from Ebay? I might have a domain like ebaydeals.com (I don't... i'm just speculating!).  Now I've heard that places like Ebay are really hot on the trigger and fire out emails to people who register domains like that straight away. But whats the difference?  In both cases I'm making money from the trademark, effectively, so is it just down to how lenient the company who owns the trademark is? Or are there rules? Is there a specific "line" you don't cross?  Thanks In both the movies and comics Cap gains his peak human strength via the supersoldier serum and a does of vita rays, resulting in the rapid development of his super buff body:     While the most obvious real world analogue would be the use of steroids, these would still require that the person taking them train extensively and significantly increase their protein intake in order to gain muscle mass. While there are frequent scenes of Steve training in both mediums I've yet to see any scenes of him eating a 12-egg omelette or downing protein shakes. Are there any in-world explanations that would account for the increased muscle mass? Extra-dimensional energy conversion? Use Outgoing SSH to receive incoming SSH My ISP does not allow me to have a static IP address. As such I am unable to remotely SSH in my home machine. Is there a way I could SSH from my home machine to a server and SSH into the server from my remote laptop and bridge the two connections?  Cheers! Suppose that $(U,V)$ has the following joint pdf: $$f_{U,V}(u,v)=\exp(-\theta u-\theta^{-1}v)$$ , where $u\geq0$, $v\geq0$, $\theta&gt;0$. Define $X=UV$ and $Y=U/V$. Find the marginal pdf of $X$ and $Y$.  With transformation, I got $U=\sqrt{XY}$ and $V=\sqrt{X/Y}$ and the absolute value of Jacob is $1/2Y$. Then, the joint pdf of $(X,Y)$ is  $$f_{X,Y}(x,y)=\exp(-\theta \sqrt{XY}-\theta^{-1}\sqrt{X/Y})1/2Y, X,Y&gt;0.$$  But I am not sure how to get the marginal pdf?  Thank you! How to convert decimal to hexadecimal in JavaScript Can every even integer be expressed as the difference of two primes? If so, is there any elementary proof? Reverse Cauchy Schwarz for integrals Let $f,g$ be two continuous positive functions over $[a,b]$ Let $m_1$ and $M_1$ be the minimum and maximum of $f$ Let $m_2$ and $M_2$ be the minimum and maximum of $g$ Prove that $$\sqrt{\int_a^bf^2 \int_a^b g^2}\leq \frac{1}{2}\left(\sqrt{\frac{M_1M_2}{m_1m_2}}+\sqrt{\frac{m_1m_2}{M_1M_2}}\right)\int_a^bfg$$  I can't make any significant progress on this one... Thanks for any hint.