User talk:Cosmia Nebula

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Fixed Point Combinator

"However this is a value in the lambda calculus domain, it may not correspond to any value in the domain of the function, so in a practical sense it is not necessarily a fixed point of the function, and only in the lambda calculus domain is it a fixed point of the equation."

I try to keep my sentences short, for ease of reading, but your version reads better. Grammar is not my strong point ;)

Thepigdog (talk) 14:04, 26 January 2014 (UTC)

Fagnano's problem

Hi there!

Could you provide/add a source for your addition at Fagnano's problem.--Kmhkmh (talk) 19:28, 22 November 2015 (UTC)

That's how I solved it when I was in Physics Olympiad competition. I can't find a source for it anywhere online. Cosmia Nebula (talk) 03:17, 23 November 2015 (UTC)

Well it doesn't have to be an online source (though that would be nice) any good offline works too. If the physics olympiad publishes problems and solutions somewhere (and this approach is included in there), that could be cited.

Sources issues aside, there is one aspect I didn't quite understand myself and that is how angle equalities are concluded (i don't see right now on what entities Lami's theorem is applied) and how the right angles are derived from them.--Kmhkmh (talk) 17:35, 29 November 2015 (UTC)

No. It's basically something that only exists in our heads. We solved some other perimeter-minimizing problems this way too, such as. If you know of any journal that accepts such kind of publications I can probably write it up and submit it myself.

If you look at a point on the rubber band at point c, then there are three forces: $F_{cb},F_{ca},F_{c}$. $F_{cb},$ and $F_{ca}$ are tensions in the rubber band, thus they are equal. $F_{c}$ is the normal force exerted by the frame. Since the frame is slippery, the normal force must be perpendicular to the frame, then we have

$F_{cb}cos\angle bcA=F_{ca}cos\angle acB$

$F_{cb}=F_{ca}$

$\angle bcA=\angle bcA$

and similarly for other two triangles. I used Lami's theorem because it's easier to quote it than to explain how three forces are in equilibrium. Cosmia Nebula (talk) 23:30, 29 November 2015 (UTC)

Now that I think about it, this question can also be solved using Fermat's Principle. Imagine the triangle is made of mirrors, and a light bounces through the three mirrors. At any point of reflection, if the angles of reflection are not equal, then the reflection point can be moved to equalize the angles and thus reduce the perimeter. Thus the minimal triangle must have three pairs of angles of reflection equal.Cosmia Nebula (talk) 23:48, 29 November 2015 (UTC)

Thanks, I think I get it now. Maybe the wording in article can a bit tweaked and extended. The problem for me for example was that I did not understand the intended order of conclusions/implications. For instance I didn't realize that the right angle of the force to the triangle side was already is given for physics reasons rather than derived geometrically. Originally I thought you argument about the angles was intended to establish that right angle (rather than just the orthic triangle through its properties).--Kmhkmh (talk) 00:49, 2 December 2015 (UTC)

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SwisterTwister talk 05:45, 25 November 2015 (UTC)

Might be of interest

You might find the following dispute interesting: Talk:Pythagorean_theorem#explicit_sources_needed?. Feel free to comment there.--Kmhkmh (talk) 06:31, 16 December 2015 (UTC)

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Reference errors on 10 July

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Coreflexive relation

In this edit summary you direct readers to a talk page with no discussion of a merge. Was there in fact discussion somewhere? --JBL (talk) 16:52, 8 October 2016 (UTC)

There was no discussion whatsoever because no one was interested. I added that edit summary because that's what Wikipedia:Merging#How to merge told me to do. User:Cosmia Nebula (talk) 16:59, 8 October 2016 (UTC)

Coreflexive relation

Hi, I saw that you performed (on 8 Oct 2016) a merge as result of which Coreflexive relation became a redirect to Binary relation#Relations over a set. I think meanwhile it is better to redirect to reflexive relation, as this article is more particular, and adding details about coreflexivity is more appropriate there. - Since I'm not familiar with the merging procedure, I don't dare to change just the contents of Coreflexive relation; it seems that this might cause the edit history to get lost if not done carefully. Can you give me some advice on how to proceed best? Many thanks in advance! Best regards - Jochen Burghardt (talk) 19:51, 31 May 2018 (UTC)

Hi Jochen Burghardt,

There is no reason not to change the redirect target, and I agree with you about what the better place for it to point is, so I will go ahead and change it.

All the best, JBL (talk) 21:11, 31 May 2018 (UTC)

Whoops, never mind, Cosmia Nebula got there just before me! --JBL (talk) 21:12, 31 May 2018 (UTC)

@Cosmia Nebula and Joel B. Lewis: Thanks for your advice and your help! - Jochen Burghardt (talk) 15:22, 1 June 2018 (UTC)

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Your GA nomination of Distance geometry

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Your GA nomination of Distance geometry

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Your GA nomination of Distance geometry

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GA Nomination on Anania Shirakatsi

Hi, just wondering what happened with the review of Anania Shirakatsi. I think it should be a GA and you seem like the right man for the job. Thanks. Thatoneweirdwikier (talk) 20:04, 21 October 2019 (UTC)

Teahouse talkback: you've got messages!

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IP block appeal key

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Proposed deletion of "Udwadia–Kalaba equation"

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Copyright problem on Viola–Jones object detection framework

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A barnstar for you!

The Original Barnstar

Hello Cosmia Nebula, I am a scientist using Bregman divergences in my publications and wanted to appreciate a specific figure of yours (see at the end). I have some further results that are based on this figure and want to cite the original source for this kind of depiction of a Bregman divergence. If you are the sole creator of this idea (not just the specific figure), I will be very grateful for a way to cite you. Thanks a lot for your help! Greetings, Sebastian Gruber The respective figure: https://en.wikipedia.org/wiki/Bregman_divergence#/media/File:Bregman_divergence_diagram_used_in_proof_of_squared_generalized_Euclidean_distances.png Sebastian Gruber 96 (talk) 15:56, 6 January 2023 (UTC)

It's my original design. I was inspired by pictorial proofs of integration by parts.

You may credit me as Cosmia Nebula from Wikipedia. pony in a strange land (talk) 19:31, 11 January 2023 (UTC)

Myhill–Nerode theorem

Hi! Thanks for adding the new proof to Myhill–Nerode theorem. I tried to match it with the textbook Hopcroft+Ullman 1979 (Thm.3.9, p.65), but I failed (even the theorem is stated slightly different). So I'd like to ask you to provide a source for your version of the proof. Best regards - Jochen Burghardt (talk) 10:08, 24 February 2023 (UTC)

The statement and proof are a combination of Theorem 3.9 and 3.10. The proof is simplified to use less of the formal notations of DFA, but the idea is exactly the same as those presented in Hopcraft and Ullman 1979. pony in a strange land (talk) 18:32, 24 February 2023 (UTC)

After careful reading I noted that I missed the statement of Theorem 3.9(2). Well it is simple enough to incorporate into the proof. I think it's a bit obscure but if you think it's important enough I can add it and the proof to Wikipedia. pony in a strange land (talk) 18:37, 24 February 2023 (UTC)

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CS1 error on Neural scaling law

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Nomination of Artificial intelligence in mathematics for deletion

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Your draft article, Draft:Reparametrization trick

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Proof of Carathéodory's theorem

Hi, Cosmia Nebula, do you have a source I can cite for the proof on the page of the Carathéodory theorem you added. I would be very grateful :) Tealoni (talk) 14:17, 4 August 2023 (UTC)

Which one? (there are several: https://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_theorem ) pony in a strange land (talk) 19:58, 4 August 2023 (UTC)

Sorry, I thought I already replied, I was looking for the a source of the proof for the convex hull Carathéodory theorem (Carathéodory's theorem (convex hull)). Tealoni (talk) 13:17, 9 August 2023 (UTC)

Leonard, I. Ed; Lewis, J. E. (2016). "3.3 Convex Hulls". Geometry of convex sets. Hoboken, New Jersey: Wiley Blackwell. ISBN 978-1-119-02266-4.

added to the page too. pony in a strange land (talk) 16:02, 9 August 2023 (UTC)

Thank you !! Tealoni (talk) 17:01, 9 August 2023 (UTC)

Woody Bledsoe

I have not reverted your editing, but I do think what you have inserted is WP:OR. You said it is literally just rephrasing the relevant parts of the paper itself, but that's the point - you as a wikipedia editor are summarising his work, rather than including what secondary sources say about it. I would urge you to find a source for what you are wanting to include. Melcous (talk) 09:32, 29 October 2023 (UTC)

The source is the paper itself. To find a secondary source would be simply looking for a secondary source that rephrases the paper, and then I rephrase the rephrasing -- I can't copy paste it, of course, since *that* would be copyright violation. The paper is already quite clear. I would be pretty alright with just the key parts of the paper without rephrasing -- but *that* would be copyright violation (I have done it before and got that deleted).

Calling this as WP:OR is silly. pony in a strange land (talk) 09:35, 29 October 2023 (UTC)

Stolz sectors

Hi, I would like to ask if the section #Stolz sector you added to the article Abel's theorem is original research or not. Jayy V (talk) 22:34, 21 December 2023 (UTC)

Just expand $|1-x-iy|\leq M(1-|x+iy|)$ and solve for $y^{2}$. It is just quadratic equation, middle school algebra. pony in a strange land (talk) 22:38, 21 December 2023 (UTC)

Yes of course - it's whether it is important enough to be in the article that I'm thinking about; it seems to me that a polar equation would be much more useful than a cartesian one (because we care about the Stolz angle), which is presumably also why I don't see the cartesian equation anywhere in the literature. Jayy V (talk) 16:42, 22 December 2023 (UTC)

The cartesian equations are quite useful for plotting on a computer.

You are free to convert it to polar coordinates and add those to the article. pony in a strange land (talk) 17:18, 22 December 2023 (UTC)

I have sent you a note about a page you started

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I have sent you a note about a page you started

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Higher order terms in Stirling's formula

Hello Cosmia Nebula. Thanks for adding the extra details to the Stirling's_approximation#Higher orders section in response to my earlier query. It's a neat way to do it. I think the source of my confusion was actually the in an earlier formula. I think we should have

$x^{-x}e^{x}\Gamma (x)=x^{-x}e^{x}\int _{0}^{\infty }s^{x}e^{-s}ds=x\int _{-\infty }^{\infty }e^{x\left(t+1-e^{t}\right)}e^{t}dt$

The point is I think there is an extra $xe^{t}$ coming from the change of variables $s=xe^{t}$. For the subsequent change of variables, $t+1-e^{t}=-{\frac {1}{2}}\tau ^{2}$, I obtain the same power series that you write using the Lagrange_inversion_theorem but the change of measure term is $e^{t}{\frac {dt}{d\tau }}d\tau$ rather than just ${\frac {dt}{d\tau }}d\tau$. In this case, it seems that $e^{t}{\frac {dt}{d\tau }}={\frac {dt}{d\tau }}+\tau$ (from the relationship between t and $\tau$) so that the resulting power series differ only in the first order term - which then integrates to zero by symmetry!

I didn't notice this at first and thought incorrectly that my calculation differed from yours at higher orders (it doesn't). If you agree that I haven't made a mistake with these calculations, it might still be worth us updating the presentation since this method looks like it could be used more generally. However the symmetry that renders the $e^{t}$ factor irrelevant is probably not general.

Also, if you have a reference for this calculation, I think it would be worth adding - I really struggled to find such a concise explanation for this either in the literature or elsewhere online.

ColmConnaughton (talk) 17:42, 12 April 2024 (UTC)

$\int _{\mathbb {R} }e^{x(1+t-e^{t})}dt{\overset {t\mapsto \ln t}{=}}e^{x}\int _{0}^{\infty }t^{x-1}e^{-xt}dt{\overset {t\mapsto t/x}{=}}x^{-x}e^{x}\int _{0}^{\infty }e^{-t}t^{x-1}dt=x^{-x}e^{x}\Gamma (x)$

I have no reference for this calculation. pony in a strange land (talk) 19:27, 12 April 2024 (UTC)

Is Da Vinci relevant for diffraction?

Concerning your recent addition to Diffraction, I don't think it will be very clear to general readers as the book is behind a paywall. Did he, in some earlier year (please include what) describe it enough that he should have first credit? Similar to standard, a cursory mention is not enough. Therefore please either expand that sentence so it is clearer or remove it. Thanks. Ldm1954 (talk) 22:53, 25 April 2024 (UTC)

idk, I just found the reference in Born and Wolf's Optics, 60th anniversary edition, section 8.1. I can't find any good reference on it either.

I guess removing it is fine. pony in a strange land (talk) 22:56, 25 April 2024 (UTC)