By Noether's Theorem we know that any conserved quantity can be associated with a continuous symmetry. I was reading Kepler's Problem and I saw that there can be conserved quantities like Laplace-Runge-Lenz vector which might not be obvious to figure out. So my questions are,   Are there any techniques to find all of the conserved quantities? How many conserved quantities can a system with $n$ degrees of freedom necessarily have?   Comments on the questions:   Suppose by observations I found some conserved quantities, how can I be sure that I have found all the conserved quantities?  Is there any necessary upper bound?
I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's equations. These equations are invariant under many transformations (Lorentz transformation, rotations, spatial and temporal translations, etc. By the way is there a way, maybe from group theory, to find all the possible transformations that leaves the equation(s) invariant?) which imply as many conserved quantities thanks to Noether's theorem. In wikipedia I can see an equation that seems to give all the conserved quantities () but it involves the Lagrangian and I'm not sure whether the formula is valid for all systems whose Lagrangian is possible to obtain.
Does a bad grade in one course (with otherwise OK record) affect graduate admissions? I'm currently an M. Phil student in Math and I failed a course last semester because I was not able to hand in a home work assignment (which was worth 40% of my grade) on time (I was 30 minutes late).   Apart from that I'd say I'm a fairly decent student, I got an upper second class honours bachelors degree, I have a B+ and A's for all my other courses in my current programme and I'm almost finished with my first paper to be published.   I've however been deeply worried about this failure as it would reflect poorly on my transcript if I were to apply to a Ph.D or another Master's programme.   Will my failing grade affect my chances of getting into a competitive programme or greatly lower my chances of getting a scholarship? Improve the editing flow with predefined options for "Edit Summary" Remove specific duplicates (all but latest) When removing duplicate rows, using the below query from  tutorial, how would I go about forcing which of the found duplicates to remove?  DELETE FROM dbo.ATTENDANCE      WHERE AUTOID NOT IN (SELECT MIN(AUTOID) _ FROM dbo.ATTENDANCE      GROUP BY EMPLOYEE_ID,ATTENDANCE_DATE)    And this works great. The reason why I am using this one is because the only unique id available is one in the IDENTITY column. And to determine if there are duplicate rows I have to look at a combination of multiple columns.    But if I have a set of duplicate rows how do I / how does SQL Server decide which to remove? And how would I force it to remove all but the one with the highest IDENTITY value?  EMPLOYEE_ID     ATTENDANCE_DATE     AUTOID A001            2011-01-01          1 A001            2011-01-01          2   If I would run the query now it happens to remove the second one, with AUTOID 2. But I am trying to remove all but this one (because this is the one latest added). First Bash Script Problem How to delay or slowly loop commands? When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module? Assume that $M$ and $N$ are two finitely generated $R$-modules. Then $\operatorname{Hom}_{R}(M,N)$ is a finitely generated $\mathbb Z$-module and/or $R$-module (in this case, assume that $R$ is commutative)?   Note that $R$ is not Noetherian ring. Is there any counterexample (for any cases)? I recently re-watched Contact for the first time since my childhood, and while I thoroughly enjoyed it, I realized that there was something I'd never understood: why couldn't they corroborate Ellie's account of her journey?  As far as I could tell, the pod fell harmlessly through the machine.  That is, it didn't break anything, and the machine wasn't destroyed.  I don't recall any dialogue about circuits being fried or the system shutting down, so presumably it wouldn't be hard to simply hoist the pod up and go again.  I imagine the energy draw was substantial on the local Japanese power grid, but given the amount of effort and money already invested in the machine, surely "Round 2" wasn't out of the question?  I mean, they almost certainly expected that this machine would get more than one good use out of it, anyway!  So given Ellie's vehement insistence that the machine had worked, the public nature of the controversy surrounding her testimony, and the government's (secret) findings that her device had recorded 18 hours of static, why wasn't it the obvious choice to have someone else suiting up the next day, ready to drop through the machine and corroborate her story? When computing the covariance matrix of a sample, is one then guaranteed to get a symmetric and positive-definite matrix?  Currently my problem has a sample of 4600 observation vectors and 24 dimensions. Would the One Ring even work for anyone but Sauron? "Speak to" vs. "Speak with" What are the differences between these two phrasal verbs and what are the best situations to use each? Public-key cryptographic systems are often implemented on top of an existing problem. For example, RSA is built on top of integers and the difficulty of factoring. ECDSA/ECIES are built on top of elliptic curves and the difficulty of the discrete logarithm.  My question is, what are, mathematically speaking, the exact primitives needed to implement public-key based signature and encryption cryptography in a generic way? Prove that if the positve term series $\sum^{\infty}_{n=1}a_n$ is convergent, also $\sum^{\infty}_{n=1}\sqrt{a_na_{n+1}}$ is convergent.  Prove that if the positive term series $\sum^{\infty}_{n=1}a_n$ and $\sum^{\infty}_{n=1}b_n$ are convergent, also $\sum^{\infty}_{n=1}a_nb_n$ is convergent.  I've tried to solve it using comparison test, but no results. Group of order $pqr$, $p < q < r$ primes $$ \sum_{n=1}^{\infty} \frac{(\sin n+2)^n}{n3^n}$$  Does it converge or diverge?   Can we have a rigorous proof that is not probabilistic?   For reference, this question is supposedly a mix of real analysis and calculus. Is there a noun for something that is "out of place" in space, like an anachronism is "out of place" in time? E.g., an old-timey barber shop in a chic neighborhood. I searched it a while and found some articles regarding Xperia Mini X10 also on XDA but I couldn't understand them easily. So I want help from you geeks who can give me the lighted way with simple steps to root my phone.    I want a step by step guide about to root this model. I'm a not much familiar with this technology so please guide me through some detailed answer. Windows Batch recursive delete old files How to divide the money based on the below conditions? Rep value on the new flair is not updated There is an update issue with the new flairs. Yesterday I replaced all my flair snippets with the new ones, but the rep value on the "default theme" has not been updated. Here is a screeny:    The other themes show the correct value whereas the default one does not. Showing that $\frac{\sqrt[n]{n!}}{n}$ $\rightarrow \frac{1}{e}$