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Mar
23
asked Fubini-Study norm of homogeneus polynomials
Mar
1
comment Smoothly Equivalent Curves
I don't know what kind of regularity do you assume for curves; but if one of the two is only continuous and the other one is $\mathcal{C}^1$ they cannot be smoothly equivalent, otherwise the former would be $\mathcal{C}^1$ as well.
Feb
20
comment If $\{f_1,…,f_n\}$ generate $R$ then does $\{f_1^N,…,f_n^N\}$
@user26857 Thanks! I'm sorry for the sloppiness in the example, I just tried to rapidly concretize a stomach feeling...
Feb
19
comment If $\{f_1,…,f_n\}$ generate $R$ then does $\{f_1^N,…,f_n^N\}$
But if the ring does not have a unity I think the statement is false. Indeed one can consider the ring of even integers, which is generated by $2$ but not by $4$. Right?
Feb
15
comment Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
@Mary Star I edited the answer to extend the hint.
Feb
15
revised Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
I extended the hint, as requested by the OP.
Feb
14
comment Show that the space $C^{0, \gamma}(U)$ is complete
All your last 10 questions (not to go too far in the past) received an upvoted answer, none of them got accepted. Would you mind either accepting them or let the answerers know how they can improve on their work? Thanks for your cooperation.
Feb
11
comment Function for encryption/decryption - What is $n \phi(n)$?
All your last 10 questions (not to go too far in the past) received an upvoted answer, none of them got accepted. Would you mind either accepting them or let the answerers know how they can improve on their work? Thanks for your cooperation.
Feb
11
comment the continuity of argmin on convex funtion
In your setting, without the additional assumption that $g(y_1,y_2,\lambda)$ is strictly convex, I don't even see why $\mathrm{argmin}$ should be a well defined function. In general it is defined to be the set of points where the argument achieves a minimum. If you could provide some more background perhaps I could be more helpful. And, as a side remark, if you enclose your latex code in dollar symbols $ it is going to look at it's supposed to.
Feb
10
comment Approximate Laplace Operator with Central Difference in Polar Coordinates
I'm unfortunately not familiar with the approximation method of central difference and I still have to read something about it. But if our Laplacian acts on $f(r,\phi)$, the term that seems to generate confusion is just $\frac{1}{r}\partial_r r \partial_r f(r,\phi) = \partial_r\partial_r f(r,\phi) + \frac{1}{r}\partial_r f(r,\phi)$. And, approximating: $ \partial_r(f(r_j,\phi))= \frac{f(r_{j-1},\phi) -f(r_{j+1},\phi)}{2\Delta r}$. Does this make any sense to you?
Feb
10
comment Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
@Marystar Did you find the answer useful? If so please reward the time I invested thinking of your problem, and help to keep the website clean, by accepting the answer. Otherwise please let me know how can I improve my answer.
Feb
10
answered Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
Feb
10
comment Differentiable function with a set of critical points of second category.
If anybody else has to check it, a set of second category is defined to be not Meagre.
Feb
10
comment Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
@MaryStar This is correct, but, as Giuseppe pointed out, this is not equivalent to show what you wrote in the question. Do you see what is the behavior of your function making it (or not) integrable?
Feb
10
comment Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
You may want to check again the definition of $L^1$-space: en.wikipedia.org/wiki/Lp_space#Lp_spaces
Feb
10
comment the continuity of argmin on convex funtion
This is clearly going to depend on the regularity of $f$, respectively $g$. A first rough result would be that if $f$ is $\lambda$-continuous in a an open set $U$, and it is strictly convex for any $\lambda \in U$, then $x'$ is $\lambda$-continuous in $U$; if it wasn't we would have a value of $\lambda$ for which $f$ has two different minimums.On the other hand if $f$ is not $\lambda$-continuous $x'$ doesn't have to be too. But I guess you are looking for something a bit more refined, right? Do you have any specific statement in mind?
Feb
7
comment Duhamel's principle in constructing heat kernel
Nice question! I checked the computation and it seems right to me, but I didn't find an elementary way to prove the equality, even though I understand what you mean by "I have a feeling there is a simple substitution that I am missing". I'll try to think about it again.
Feb
4
comment Integration proof without using primitive function
By change of variables this is equivalent to the divergence of $\int_1^\infty \frac{1}{y} dy$, which is bounded from below by $\sum_{n=1}^\infty \frac{1}{n+1} =\infty$.
Feb
3
comment using logarithms to solve the following equation to find x
@JackYoon Ehm... ...ehm... ...oops... ...mmh... :(
Feb
3
comment using logarithms to solve the following equation to find x
Observe that $27= 9^2$.