Reputation
5,381
Next privilege 10,000 Rep.
Access moderator tools
Badges
1 10 19
Impact
~91k people reached

May
29
answered Showing a (relatively simple) set of polynomial zeros in projective space is irreducible
May
29
comment Problem with an integration
Dear @Rodrigo, what I wrote was that the expressions you wrote are the simplest ways to write the same result if $A$ is a general function - so what you wrote is already a solution. One may write it both in terms of $E$, as an $xy$ integral, or in terms of $A$, as an $k_xk_y$ integral, just like you did. Do you want us to prove the identity on the first line assuming the definition of $E$ on the second line? It's simple - just substitute it and use the usual Fourier integral identities. At any rate, it's not clear what you want.
May
29
comment Problem with an integration
Dear Rodrigo, if by "performing', you mean just calculating it analytically, well, I am afraid that you will have to say what $A(k_x,k_y)$ is. For a general $A$, the formula above is clearly the simplest explicit way to write the same expression.
May
26
comment How do I construct this quasicyclic group?
Dear @Qiaochu, you would probably have to say much more to defend the idea that this "direct" adjective is more than just a meaningless complication in mathematical terminology. Is there also something that is called a limit of the sequence of groups? If not, I am afraid that the object described in the question is not a direct limit because it agrees neither in the detailed construction nor in the notation with the things you may find in definitions, e.g. on Wikipedia.
May
26
comment How do I construct this quasicyclic group?
Dear Kate, if two sequences are isomorphic one element after another, then all properties of these two sequences including the limit have to be isomorphic as well. "Isomorphic" really means "the same thing when it comes to any behavior of them".
May
26
answered How do I construct this quasicyclic group?
May
26
answered How can I calculate “most popular” more accurately?
May
26
comment Poisson process traffic question
I corrected the word "cars" to "vehicles" in the first sentence. Otherwise it was totally deliberate to avoid complicated and pre-cooked notions such as a binomial distribution - as well as Poisson distribution (mostly), in fact. The homework is also formulated in such an elementary language.
May
26
revised Poisson process traffic question
added 4 characters in body
May
26
answered Poisson process traffic question
May
25
comment Two introductory linear algebra problems
Dear user, it was a pleasure. I also had to do some hard work before I could see the relevance the exterior "square" of the exterior product, or $AB+CD+EF$. I still haven't managed to write down a sensible story in which the minors are all positive. Maybe if it is minors multiplied by $(-1)^{i+j}$ where $i,j$ are the indices of the omitted columns, it can be made positive.
May
25
comment Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
But if you combine the neighbors into pairs, you may get 0+0+0... = 0, or if you single out the first 1, you get 1-0-0-0=1... The right result $1/2$ is actually the arithmetic average of these guesses, but things are usually not that simple in general.
May
25
comment Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
Dear Gottfried, thanks for your interest in these matters. I would still warn you that it may be ill-advised to attribute a finite answer to any series with individual numbers. Those things may sense if there's some glimpse of a functional dependence of the terms, and even in that case one should avoid the ad hoc random clustering of the terms - this is how the convergent sums may be calculated, but that's exactly how the divergent things can't be treated. A simple example: $1-1+1-1+1-1...$ is equal to $1/2$ in any sensible definition.
May
25
comment The form of a solution in a linear system
You want to shift $\beta$ by a multiple of $1/11$, by $k/11$, that makes the absolute coefficients integer as well. $10k+7$ and $8k-1$ have to be a multiple of $11$. $k=7$ just does the job but that's not the only solution: $k=-4$ or any $11n-4$ does the job, too.
May
25
comment The form of a solution in a linear system
I see, that was my guess that this is what you wanted. Well, if you had your form only, you would first make the coefficients of $\alpha$ integer by writing $\alpha = 11\beta$ where $11$ was found as the smallest common multiple of the denominators. That would yield $(x,y,z) = (10\beta+7/11,8\beta-1/11,11\beta)$. Then you would shift $\beta$ in such a way that the absolute coefficients are also integer.
May
25
comment The form of a solution in a linear system
Apologies, I don't understand this question. What does it mean to "linearize the solution"?
May
25
answered The form of a solution in a linear system
May
25
answered Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
May
25
comment When $G'$/$G''$ and $G''$ both are cyclic groups
$G''=Z_p$, $G'=Z_p\times Z_q$, $G'/G'' = Z_q$. ;-)
May
25
revised Limits in Double Integration
texized formula, D in it remains incomprehsible though