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reuns

 Discussion on question by Anixx: Does…

Imported from a comment discussion on math.stackexchange.com/q...
reuns
Mar 3, 2023 21:38
"pointwise-defined function" --> what does it mean. You are eluding that I asked "from what space to what space".
reuns
Mar 3, 2023 21:38
That's why I wrote the first comment above. Why don't you try to answer it instead of eluding?
reuns
Mar 3, 2023 21:38
Why don't you see that if $\bar{\delta}(x)$ means $\delta(f(x))|f'(x)|$ with $f(x)=x$ then $\bar{\delta}(x)=\delta(x)$ and your "is it a function" question doesn't make sense?
reuns
Mar 3, 2023 21:38
Function from what space to what space? It is unclear what you mean with $\bar{\delta}(x)$.
 

 Discussion on question by Mathlearner…

Imported from a comment discussion on math.stackexchange.com/q...
reuns
Nov 28, 2021 11:59
$G$ doesn't act on $\Bbb{Z}_p$ in a natural way (except if you have an homomorphism from $G$ to the $p-1$-th roots of unity) why do you think it does. $T_p$ is an abelian group and a free $\Bbb{Z}_p$-module by definition. No idea what you mean for the number of variables. For an elliptic curve it is $GL_2$, for a dimension 2 abelian variety it is $GL_4$.
reuns
Nov 28, 2021 11:59
$G$ doesn't act on $T_p$, it acts on $T_p/p^n T_p$ or $C[p^n]$. You are confusing with $Gal(\Bbb{Q}_p(C[p^\infty])/\Bbb{Q}_p)$. In general $G$ is not abelian, that's the answer, period.
reuns
Nov 28, 2021 11:59
$Gal(\mathbb{Q}_p(C[p^n])/\Bbb{Q}_p)$ doesn't have to be abelian. It is naturally a subgroup of $GL_2(\Bbb{Z}/p^n\Bbb{Z})$.
reuns
Nov 28, 2021 11:59
Still unclear. Please define $R_G$ and what is supposed to be a $\Bbb{Z}_p$-module.
reuns
Nov 28, 2021 11:59
Take any faithful representation ($K$ or $\Bbb{Z}_p[G]$ or whatever) and check if the elements of the group commute. $G$ acts on $K$ or $\Bbb{Z}_p[G]$ in the natural way.
reuns
Nov 28, 2021 11:59
I don't understand your question. Please clarify $G,R_G$, what is supposed to be a $\Bbb{Z}_p$-module, $r$, and so on.
 

 The Biosphere

General discussion for biology.stackexchange.com
reuns
Sep 20, 2021 16:20
Thank you, I am new in biology ! In maths it is very different, giving (alternative) answers in comments often happens, and they are not deleted, but when I have the answer I know I do and I post it. In biology I know I have some part of the answer, that's very different. The problem is to not engage with a new user in a friendly manner, you are engaging in a very harsh way, deleting comments I needed 30 minutes to write each time (because I am studying biology, I don't have infuse knowledge).
2
reuns
Sep 18, 2021 11:18
Hi, some moderator deleted several of my comments because "we shouldn't write an answer as comments". He just deleted them, I can't find them back, so I can't write an answer. And presumably if they look like answers then they contain interesting content...

This is really not an acceptable way to interact with new users, like me. I don't know why he wanted to be so harsh/insulting with me, but please explain to him the problem with his behavior.

I can't even find his user id since he deleted the comments where I intereacted with him. There https://biology.stackexchange.com/questions/10452…
2
 

 Math Mods' Office

For informal chat with the site moderators about moderation, s...
1
reuns
May 16, 2021 11:37
The main problem is that he is repeatedly asking almost identical questions and his many users makes it impossible to refer to previous questions/answers/comments. Note he may recently have stopped sending 10 "please answer" comments.
reuns
May 16, 2021 11:33
Hi, maybe you already know but all these users are the same (19 in < 3 months)
https://math.stackexchange.com/questions/4065715/if-xi-is-the-riemann-xi-function-then-value-of-xi1-2
https://math.stackexchange.com/questions/4065510/xis-xi0-prod-rho-1-fracs-rho
https://math.stackexchange.com/questions/4054635/jensens-formula-application-fz-has-no-zeros-on-z-r-r1
https://math.stackexchange.com/questions/4116671/lim-r-to-1-frac12-pi-int-pi-pi-logfrei-thetad-theta-wh
https://math.stackexchange.com/questions/4039899/evaluate-oint-z-1-frac-log-1-zzdz
2
reuns
Mar 21, 2021 17:03
Please someone explain to @amWhy how being friendly etc. I'm tired of someone just giving lessons and voting to close and delete everything, eventually on topics for which he has 0 clues, until he proves the opposite (if he is capable of constructive mathematical comments I will be glad to read those).
 

 Cafe and Tavern on the math.se

A place to socialize, have fun, share humor and war stories, a...
reuns
May 1, 2021 23:19
Imagine the OP searching for patterns in weird sequences/formulas when there is essentially nothing to find? This is numerology.
reuns
May 1, 2021 23:17
Well find a better name for the tag and tell me. I like the name numerology, it is fun and easy to remember, and the tag description can explain what it means in this context.
reuns
May 1, 2021 23:12
This is exactly numerology: I have a weird formula that doesn't mean anything but I like it and I run a script for a few minutes then I go on a math website to tell "look how my formula is nice". That said sometimes the answers are interesting.
reuns
May 1, 2021 23:11
3
Q: Positive integer solutions to $pxy+x+y=p\#$

David Jones Let $p$ be prime and $p{\#}$ the product of all primes not larger than $p$. Are there any positive integers $x$ and $y$ such that $pxy+x+y=p{\#}$. It appears there are no solutions. There are no solutions with $p<200$. Can it be shown that this is the case for all primes $p$? My thoughts: Let $n...

number-theory prime-numbers diophantine-equations prime-factorization
reuns
May 1, 2021 23:10
I don't see what you mean, there are many such questions everyday.
https://math.stackexchange.com/questions/4122803/how-to-prove-that-1x2x3x4x-nx-will-never-sum-to-a-prime-number-exce/4122915#4122915
reuns
May 1, 2021 23:07
I like the name but I mean creating a tag for those kind of questions without much mathematical content other than "please run a script to find a counter-example, or tell me that you know some genial theorem proving I'm wrong" (or right)
reuns
May 1, 2021 23:06
I don't see what you mean, those questions are never closed, deleted, and they are often promoted.
reuns
May 1, 2021 23:02
Hi does anyone like the idea of creating a "numerology" tag for all those relatively low quality questions claiming that some weird invented sequence without much mathematical content doesn't contain primes, 0, or whatever, after running a short script for 10 minutes?
Most of the answers are counter-examples, but sometimes there are nice proofs that the claim is wrong using complicated/interesting theorems.
 

 2021 MathOverflow Moderator Election …

Open Discussion for mathoverflow.net/election/2
reuns
Apr 11, 2021 16:06
The comment feed is often cleared by a moderator with the "moved to chat" message.
reuns
Apr 11, 2021 16:05
Thanks, I read your interesting clues. On MSE it is easier to get an idea of what moderation accounts for, because we are often seeing practical cases needing moderation, in contrary to MO.
reuns
Apr 10, 2021 12:26
Hi, I won't vote because I realize I don't know what is the MO moderators todo list: I am wondering what is the level needed to be moderator on MO, and if in most cases no super-high level is needed and if the community is moderating itself (as it seems to be) then why not just ask to the MSE moderators to deal with MO once a month?
 

 Discussion on answer by Ian: Why is c…

Imported from a comment discussion on math.stackexchange.com/q...
reuns
Apr 10, 2021 14:43
I explained : in signal/image processing we look at $h$ fixed, not $h \to 0$. And the forward difference is just the central difference shifted, so all we have to do is take the phase in account. In this context, it wasn't really possible to see what you meant with "second order" and "higher order methods" (the vocabulary of numerical analysis for approximating integrals and differential equations)
reuns
Apr 10, 2021 14:43
No ok I got it. I didn't except it changed something assuming it is $C^3$ (and you should see that your answer is really impossible to understand alone)
reuns
Apr 10, 2021 14:43
??? Come on do the calculation rigorously, both $|f'(x) - \frac{f(x+h)-f(x-h)}{2h}|$ and $|f'(x) - \frac{f(x+2h)-f(x)}{2h}|$ are $< h \sup_y |f''(y)|$. The only difference is that in the 1st case we can bound with $h \sup_{|y-x| < h} |f''(y)|$ while in the second it is $h \sup_{|y-x-h| < h} |f''(y)|$
reuns
Apr 10, 2021 14:43
Ok I just understood, you are looking at the error as $h \to 0$. But then $|f'(x) - \frac{f(x+2h)-f(x)}{2h}| < h^2 \sup_x |f''(x)|$ is very close to $|f'(x) - \frac{f(x+h)-f(x-h)}{2h}|$, it doesn't change the order of the error. And in real life $h$ is fixed, so we look at the total error $\int_a^b |f'(x) - \frac{f(x+h)-f(x-h)}{2h}|^2 dx$ with respect to the frequency. And the derivative filter is $\delta'$ because $(f \ast \delta)' = f' \ast \delta = f \ast \delta'$ (there is some time reversal in the convolution)
reuns
Apr 10, 2021 14:43
The central difference with $h$ is almost the same as the forward difference with $2h$ : it doesn't change the order of the error
reuns
Apr 10, 2021 14:43
I don't see what you mean with "second order" or with "for smooth $f$, the central difference scheme is second order in $h$". Theoretically, for analyzing a discrete filter replacing $\delta'$ the true derivative filter, we look at its frequency response and compare it to $i \omega$
reuns
Apr 10, 2021 14:43
A typical derivative filter with greater length is $[-\frac{1}{3},-\frac{2}{3},\frac{2}{3},\frac{1}{3}]$.
reuns
Apr 10, 2021 14:43
I don't see what you mean.
 

 Discussion on answer by reuns: quater…

Imported from a comment discussion on math.stackexchange.com/q...
reuns
Mar 13, 2021 14:04
$End_\Bbb{C}(\Bbb{H})$ means that we assume some complex vector space structure on $\Bbb{H}$. And you can check that the natural ones (ie. compatible with the canonical real vector space structure) all give $\Bbb{H}\cong \Bbb{C}^2$, independently of left right, or the swapping of $i,j$, or the basis.
reuns
Mar 13, 2021 14:04
It is the one inherited from the isomorphism to $M_2(\Bbb{C})$ :) Or $(u\otimes a)(v\otimes b)=uv\otimes ab$
reuns
Mar 13, 2021 14:04
Yes, that's why my answer takes only 3 lines. $\frac{a}2 I-i\frac{a}2 J = \pmatrix{a&0\\0&0}$, following the same idea it is clear that it is surjective.
reuns
Mar 13, 2021 14:04
You didn't mention the ring (complex algebra) structure on $\Bbb{H\otimes_R C}$ I am quite sure this is the least obvious part.
reuns
Mar 13, 2021 14:04
Yes but no, for $\Bbb{H}$ then $a,b,c,d$ are real numbers, in $\Bbb{H\otimes_RC}$ they are complex numbers, so $\{aI+bJ+cK+dL,a,b,c,d\in \Bbb{C}\}$ is the whole of $M_2(\Bbb{C})$. That what we wanted to prove: the isomorphism between $\Bbb{H\otimes_RC}$ and $M_2(\Bbb{C})$.
reuns
Mar 13, 2021 14:04
$End_\Bbb{C}(\Bbb{C}^2)=M_2(\Bbb{C})$, the $2\times 2$ complex matrices.
 

 Discussion on question by Ashyln Broo…

Imported from a comment discussion on math.stackexchange.com/q...
reuns
Mar 8, 2021 23:06
Did you read my comment?
reuns
Mar 8, 2021 23:06
I don't understand your question. What does it mean $I$ integrable? Everything you need is proven in the Balazard papers, why don't you follow them. $\frac{\log|\zeta(\frac{1}{2}+it)|}{\frac{1}{4}+t^2}dt$ is locally integrable (because $\zeta$ is meromorphic), if it is integrable then $I=\lim_{\epsilon\to 0}I_\epsilon$ trivially. Is it integrable?
 

 Discussion on answer by reuns: Is the…

Imported from a comment discussion on math.stackexchange.com/q...
reuns
Mar 2, 2021 12:58
No. You really need to learn about this topic: analyticity / analytic continuation (not continuity). $\log F(s)$ can be continued analytically along a curve iff $F$ is analytic with no zeros/poles on that curve. This is because $\log F(s)$ is the primitive of $F'(s)/F(s)$.
reuns
Mar 2, 2021 12:58
It is not, this is what I am doing in my answer. We start with $\log \zeta(s)$ analytic on $\Re(s) > 1$ then we continue analytically along horizontal lines.
reuns
Mar 2, 2021 12:58
The word is branch point and branch cut. I explained everything in my answer. What is unclear to you.
reuns
Mar 2, 2021 12:58
See my edit ${}{}$
reuns
Mar 2, 2021 12:58
It is as if you didn't care of my answer.
reuns
Mar 2, 2021 12:58
$\Im \log$ and $arg$ are the same thing, this is not the point, for a function with zeros and poles there are many ways to define $\Im \log F(s)$, adding or substracting $2 k\pi$ differently at every $s$. Gram points don't have anything to do in my answer.
reuns
Mar 2, 2021 12:58
$\log \zeta(s)$ has a branch analytic on any simply connected domain not containing a zero/pole. When removing the horizontal 'lines' $(-\infty,1]$ and $(i\Im(\rho)-\infty,i\Im(\rho)+1]$ I get a simply connected domain where $\log \zeta(s)$ is analytic. This function has some jumps on vertical lines on $\Re(s)\le 1$.
reuns
Mar 2, 2021 12:58
@StevenClark It is a bit frustrating that you don't reply when I am asking if those few complex analysis prerequisites are clear to you. To understand what mathematica is doing you should show us a ComplexPlot (modulus/phase) of $\log \zeta(s)$ on $\Re(s)\in (-1,3),\Im(s)\in (-50,50)$