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Jun
5
answered Piecewise smooth, non-orientable, closed-surface: a contradiction in terms, or am I going mad?
Jun
5
comment On natural solutions of the equation $y^{3}-3^{x}=100$
I have some idea how to prove that no other solutions exist but it's clear that there is a solution $y=7$, $x=5$ because $243+100=343$.
Jun
2
comment Finding the Zeros of a Matrix-Vector Equation
The original equation is just one single scalar equation, isn't it? So it's far from being able to uniquely determine $Z$ which has $N(N+1)/2$ entries.
Jun
1
comment Understanding a famous riddle
Hi @Chandru, why did you delete the question on $SL(2,Z)$ and $A_5$? I just wrote a complicated answer, constructing the homomorphism etc. ;-) and I couldn't post it. That sucks.
May
29
comment Poisson process traffic question
OK, if there are 2/3 of a car and not a vehicle, then you just change the numbers correspondingly. At least some work. ;-)
May
29
comment How do I construct this quasicyclic group?
Right, @Arturo, as long as you want to map particular elements of the groups in the sequence to the elements in the limiting group. While the question defines $\phi$ to allow such things, I think that what the question asks for doesn't require to map the individual elements. And the symbol of isomorphism, with the simple $\infty$ on the left hand side, doesn't really indicate that they're constructing any "special" limit.
May
29
comment Showing a (relatively simple) set of polynomial zeros in projective space is irreducible
Excellent, it's you et al. whom I meant. ;-) Is that right that the result from $C$ directly extends to all fields of characteristic $0$?
May
29
answered How can I estimate or calculate the area of a circular segment?
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.