In .NET Core C#, how do I parse this Date string: 'Jun 3, 2021 4:36:56 PM EDT'
Parse DateTime with time zone of form PST/CEST/UTC/etc
Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.   I saw some proof of $\frac d {dx} x^n=nx^{n-1}$ using binomial theorem, which is only available for $n \in\mathbb N$. Do anyone have the proof of $\frac d {dx} x^n=nx^{n-1}$ for all real $n$? Thank you. I wish to show that $\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$.    What I did so far was to show that $\mathbb{Q}(\sqrt2,\sqrt3) =\text{span}\{1,\sqrt2,\sqrt3,\sqrt6\}$.  Assuming they are isomorphic, denoting $f$ the isomorphism, then $f(1) = 1$, so $x^2-3$ has a root in $\mathbb{Q}(\sqrt2,\sqrt3)$ so $\sqrt 3\in\mathbb{Q}(\sqrt[4]2)$. ($\sqrt2 \in \mathbb{Q}(\sqrt[4]2)$, $\sqrt[4]2\cdot\sqrt[4]2=\sqrt2)$.   Thus under the assumption, $\mathbb{Q}(\sqrt2, \sqrt3)\subseteq \mathbb{Q}(\sqrt[4]2)$. As a vector spaces of the same dimension over $\mathbb{Q}$, it means that $\mathbb{Q}(\sqrt2, \sqrt3)= \mathbb{Q}(\sqrt[4]2)$.  Now all is left to do it to show a contradiction: $\sqrt[4]2\in\mathbb{Q}(\sqrt2,\sqrt3)$, then $\sqrt[4]2 = a+b\sqrt2+c\sqrt3+d\sqrt6$ so $2=(a+b\sqrt2+c\sqrt3+d\sqrt6)^4$, I believe that opening the expression, I would find out that it can't be an element of $\mathbb{Z}$. However this is a really inelegant way (if it really works), and I wish for a better way to do so.  An other approach: $\mathbb{Q}(\sqrt2,\sqrt3) = \mathbb{Q}(\sqrt2 + \sqrt3)$ by the irreducibility of $x^4-10x^2+1$ over $\mathbb{Q}$ (an some dimension theorem usage). Also, $x^4-10x^2+1$ splits in $\mathbb{Q(\sqrt2, \sqrt3)}$.   Is there a way to show that this polynomial doesn't split over $\mathbb{Q}(\sqrt[2]4)$? with different method then assuming that $\sqrt3\in\mathbb{Q}(\sqrt[4]2)$ and getting a contradiction? Maybe the fact that $\sqrt[4]2$ has complex roots might help? Is the following sentence correct English?      Have you the address?   The address in question is obvious to the person being asked.  It's normal to ask such a question as "Do you have the address?" or even "Have you got the address?" But is it acceptable to use just the verb have without do or got? If virtual particles sometimes add more mass/energy to a system then was inputed or comes out in the output, how do they not violate conservation of mass/energy. Can there be an option to allocate rep from any site account for offering a bounty? I think it would be useful if we had an option when deciding to open a bounty on a question that we could choose to allocate rep from one site even though the bounty is being offered on another site.  For instance I would like to use my rep from SO for putting a bounty on a question that resides on SF. I don't have enough rep on SF to make it enticing. So when you click on "start a bounty" you get sliders for each site that you can pull your rep from, maybe make it where you need to burn up all your rep for the site that your asking the question on and then allocate more rep from other ones, if you have it.  thanks devinb for clearing up my question with your comments! " transfer rep INTO a bounty. But you can't transfer rep across accounts. So, the rep you'd 'lose' from SO would never actually go into your SF account, it would go straight onto a bounty on whatever question." – devinb How to show $\lim_{n \to \infty} a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} = x/2$? One of the joys of high-school mathematics is summing a complicated series to get a “closed-form” expression. And of course many of us have tried summing the harmonic series $H_n =\sum \limits_{k \leq n} \frac{1}{k}$, and failed. But should we necessarily fail?      More precisely, is it known that $H_n$ cannot be written in terms of the elementary functions, say, the rational functions, $\exp(x)$ and $\ln x$? If so, how is such a theorem proved?    Note. When I started writing the question, I was going to ask if it is known that the harmonic function cannot be represented simply as a rational function? But this is easy to see, since $H_n$ grows like $\ln n+O(1)$, whereas no rational function grows logarithmically.  Added note: This  asks a similar question for “elementary integration”. I guess I am asking if there is an analogous theory of “elementary summation”. "Deleted by {owner}" vs "Deleted by owner" in self deleted answers Why isn't temperature frame dependent? In (non-relativistic) classical physics, if the temperature of an object is proportional to the average kinetic energy ${1 \over 2} m\overline {v^{2}}$of its particles (or molecules), then shouldn't that temperature depend on the frame of reference - since $\overline {v^{2}}$ will be different in different frames?  (I.e. In the lab frame  $K_l = {1 \over 2} m\overline {v^{2}} $, but in a frame moving with velocity $u$ relative to the lab frame, $K_u =  {1 \over 2} m \overline {(v+u)^{2}}$). What does "bad girls go backstage" mean? (sorry for my poor English)  I saw this phrase somewhere but I don't know what this means..     Good girls go to heaven, bad girls go backstage   What means 'bad girls go backstage'?   Maybe.. it's when good girls try to be good, but bad girls become famous?  Am I right? Any evidence that subdomain can help with domain authority and vice-versa? Define the sequence $aₙ=20+n²$ and $dₙ=\gcd(aₙ , aₙ₊₁)$ Find with proof the values dₙ takes. A concrete example of involution in group theory I am reading the textbook "Introduction to Modern Algebra, Joyce 2017" and in the Cyclic groups and subgroups section, there is a following sentence about involution.     An involution $a$ is an element of a group which is its own inverse, $a^{-1} = a$. Clearly, the order of an involution $a$ is $2$ unless $a = 1$, in which case the order of $a$ is $1$.    I was trying to come up with a concrete example, but I am having difficulties. Maybe when $a = \frac{1}{2}, \frac{1}{2}^2 = 1$? I also searched the  for a concrete example, but wasn't able to find anything.  Can someone provide an example with numbers for me please? I want to understand why the author writes "clearly" that the order of an involution $a$ is $2$. Thank you During the First Wizarding War, why didn't Dumbledore just hunt Voldemort down, as he had done with Grindelwald?  By 'hunting down', I mean finding, defeating and imprisoning him, exactly as in Gridelwald's case, and not, say killing him, something which Dumbledore would not do, as the answers to a previous question (as to him not hunting down Death Eaters) show.  Dumbledore knew that Voldemort had delved into the Dark Arts deeper than anyone else in history and hence "had powers he will never have". But he must have also known well that he could have defeated Voldemort at a direct confrontation, given that he had defeated Grindelwald earlier even against the Elder Wand, and now had that same wand at his disposal. He is seen confident about this throughout the series.  At the Battle of the Department of Mysteries, he did not go beyond outweighing Voldemort and forcing him to flee, probably because, by then, he had reasons to suspect that there was more to Voldemort's survival than his physical body, and thus, destroying that body which had Harry's blood without permanently disposing him off would not have been wise.  But why did he not do that at the First Wizarding War? Is it just that they could not track him down, or did he suspect even then that Voldemort had more sinister things about his soul? is there any canon confirmation of the latter suspicion? How to repair a corrupted Excel file I'm trying to restore some files for a friend who messed up a USB stick by pulling it out of the computer too soon. By searching invisible partitions I was able to restore the files. All files are intact, except 1 excel file that seems to be corrupted.  I've googled about ways to repair an Excel file, because the default repair options in Excel 2003-2010 do not work for this file. I've came across a numerous  third-party apps, of which the  one seemes to be able to do the job: Recovery Toolbox for Excel.  Of-course, this and all other apps I found require a purchase to actually repair the file. It seems a bit silly to pay 30 dollars for a one time thing, and something that is not for myself. So, I would like to keep that as a last-resort option.  Is there anything I can try to fix this? I've attached a screenshot of how the file looks when I open it on my OSX when converted to a HTML file (to view the code), for  the option that it could be a character set problem. $SU(3)$ irreducible representations with tensor method I am dealing with the tensor product representation of $SU(3)$ and I have some problems in understanding some decomposition.  1) Let's find the irreducible representation of $3\otimes\bar{3}$  we have that this representation trasforms like   $${T^\prime}^i_j=U^i_k {U^{\dagger}}^l_j T^k_l $$  hence I observe that  $$Tr(T)=\delta^j_iT^i_j$$ is an invariant and so  $$T^i_j=\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)+\frac{1}{3}\delta^j_iT^i_j$$  allows me to write $$3\otimes\bar{3}=8\oplus1$$ Here comes my questions: I have heard that this $8$ representation is an "$8_{MA}$" where MA is for "mixed-antisymmetric". The meaning of "mixed-antisymmetric" shold be: "the tensor $\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)$ should be antisymmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes". What does this mean? I see only 2 index in that tensor.  2) Consider this representation: $$3\otimes3\otimes3=3\otimes(6\oplus\bar{3})=3\otimes6_S\oplus3\otimes\bar{3}=3\otimes 6_S\oplus8_{MA}\oplus1$$  and now on my notes I have $$3\otimes6_S=10_S\oplus8_{MS}$$  Where "MS" is for "mixed symmetric": symmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes.  I could not demonstrate this last decomposition using tensor method. I started noticeing that: $$3\otimes6_S=q^iS^{k,l}$$ where $S^{k,l}$ is a symmetric tensor But then I am not able to proceed in demonstrating the above decomposition (note: I would like to demonstrate this decomposition using only tensor properties, not Young tableaux). I tried to look on Georgi, Hamermesh, Zee and somewhere online but I have not found any good reference which explains well this representatin decomposition...  EDIT: the demonstration should not include the use of Young diagrams...my professor started the demonstration by writing $\epsilon_{\rho,i,k}q^i S^{k,l}=T'^l_\rho=8_{MS}$ and then stopped the demonstration. XGBoost Loss function Approximation With Taylor Expansion How can I tell what RAM will fit my computer? If I want to add more RAM to my computer, how can I buy something compatible? What kinds are there? How do I determine which kind my computer will accept and how much I can add? How to prove that limit doesn't exist using epsilon-delta definition? It is easy to prove the limit exists, all we have to show is there exists a relationship between $\delta$ and $\epsilon$. But how are we supposed to prove limit doesn't exists? The problem is when we are proving for a limit we already know what the limit is and with that, algebra is all that's needed.   Please show through an example (you may show that $\lim_{x\rightarrow0} \frac{1}{x}$ doesn't exist)  If possible please use the explanation scheme that is used by this answer How can I distinguish between words which have the -ing in a sentence that are nouns, verbs, or adjectives?    For example sometimes -ing come with word to give us a noun, and sometimes a verb or an adjective.       That interesting snake.   That crawling snake.   That barking dog keeps everyone awake.     Is there any rule to determine whether a word with -ing is a noun, verb, or adjective?