# User talk:Juan Marquez

Welcome!

Hello, and welcome to Wikipedia. Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

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Also, I moved Juan Marquez to User:Juan Marquez. Please do not write about yourself in the main namespace. jni 18:23, 6 Apr 2005 (UTC)

## Your edits to 3-manifold

Hi Juan,

I haven't had a chance to think about your email, and I don't know when I can get to that. But your research sounds very interesting. I don't think it has been done before, but it sounds like the kind of thing that may have, so I wouldn't take my word for it. --C S 18:46, 30 September 2005 (UTC)

Thank you for your edits to mathematical analysis. I have a few general comments. First, is that links should be singular, and it is good if one checks where the links point. Thus, [[sequence]]s is preferred to [[sequences]] and [[series (mathematics)|series]] is preferrred to [[series]].

Also, it is good if you use an edit summary, it is a way of documenting what you changed and very helpful for others checking your contributions or looking at the page history. Thank you, and I hope you like it here. Oleg Alexandrov (talk) 00:15, 29 December 2005 (UTC)

## RF

In topology,

Let $M$ be a manifold. By a round function we mean a function $M\to{\mathbb{R}}$ whose critical points form connected components, each of which is homeomorphic to the circle.

## Title

In calculus, by a round function we mean a scalar function $M\to{\mathbb{R}}$ over be a manifold $M$ whose critical points form one or several connected components, each homeomorphic to the circle $S^1$, called critical loops.

## Zum beispiel

For example, let $M$ be the torus. Let $K=(0,2\pi)\times(0,2\pi)$. Then we know that a map $X\colon K\to{\mathbb{R}}^3$ given by

$X(\theta,\phi)=((2+\cos\theta)\cos\phi,(2+\cos\theta)\sin\phi,\sin\theta)\,$

$K(\theta,\phi)= \begin{bmatrix} (2+\cos\theta)\cos\phi\\ (2+\cos\theta)\sin\phi\\ \sin\theta \end{bmatrix}$

is a parametrization for almost all of $M$. Now, via the projection $\pi_3\colon{\mathbb{R}}^3\to{\mathbb{R}}$ we get the restriction $G=\pi_3|_M\colon M\to{\mathbb{R}}, (\theta,\phi)\mapsto\sin\theta$ whose critical sets are determined by

$\nabla G(\theta,\phi)=({{\partial}G\over {\partial}\theta},{{\partial}G\over {\partial}\phi})(\theta,\phi)=(0,0),$

if and only if $\theta={\pi\over 2},\ {3\pi\over 2}$.

These two values for $\theta$ give the critical sets

$X({\pi/2},\phi)=(2\cos\phi,2\sin\phi,1)$
$X({3\pi/2},\phi)=(2\cos\phi,2\sin\phi,-1)$

which represent two extremal circles over the torus $M$.

Observe that the Hessian for this function is

${\rm Hess}(G)=$$\begin{bmatrix} -\sin\theta & 0 \\ 0 & 0 \end{bmatrix}$

which clearly it reveals itself as of ${\rm rank Hess}(G)=1$ at the tagged circles, making the critical point degenerate, that is, showing that the critical points are not isolated.

## Reference

Siersma and Khimshiasvili, On minimal round functions, preprint [1]

## Schwarzschild coordinates

Good catch, thanks for noticing this! ---CH 23:27, 8 May 2006 (UTC)

Hi. Just a comment. One should not use links in section headings, so ==As a functor== better be ==As a functor==. I fixed that one but I thought I would let you know. You can reply here if you have comments. Thanks. Oleg Alexandrov (talk) 03:41, 1 July 2006 (UTC)

And one should not leave too much space between sections either, looks bad. :) Oleg Alexandrov (talk) 03:41, 1 July 2006 (UTC)

## Area of a circle

The area of a circle is the area of the enclosed region. Stating flat out that "a circle has not area" is confusing and at variance with established practice. Disk might more properly describe the enclosed region, but that's a distinction that most people (and most mathematicians) don't bother to make. EdC 06:59, 29 October 2006 (UTC)

## Totopo

If you are going to cancel a redirect, you need to replace it with an article, not just a one-line comment that Totopo is not a Tortilla chip. A better idea would be to add something to the tortilla chip article explaining the difference, there is room for expanision and more people will see it that way, few people are going to search for totopo. And , yes, there are round as well as triangular tortilla chips. Tubezone 04:27, 24 November 2006 (UTC)

Si, entiendo que totopos no son iguales de los tortilla chips, no tuve dudas de eso. La problema es el nuevo articulo que ud hizo falta explicacion de caracteristicas del producto, una oracion que dice que los dos no son iguales no es suficiente. Ellos van a borrar por rapido por razon de faltar contexto si el articulo queda en su condicion del presente. Ud. no hace pruebas matematicas asi, ¿verdad? Tubezone 04:58, 24 November 2006 (UTC)
I don't get who is going to erase
and in math there are some short powerful proofs. Gimme a few hours to expand totopo, thanx--kiddo 05:03, 24 November 2006 (UTC)
Estoy de acuerdo, escriba lo que ud quiere, yo regresare a la pagina a hacer correciones gramaticas si ud hace errores ;-) Tubezone 05:08, 24 November 2006 (UTC)

## Graf

—The preceding unsigned comment was added by Juan Marquez (talk • contribs) 23:46, 8 December 2006 (UTC).

tres discos que descomponen al plano proyectivo y tres toros que descomponen al fibrado trivial

lets look this $\sum$ from afar

## Area of a circle

Hello. I reverted your edits to circle. While you are technically correct that "a 1-manifold has no area" this is not how the phrase "area of a circle" is interpreted in english, even among mathematicians. Since a 1-manifold cannot have area, it is obvious that the phrase "area of a circle" must refer to the area enclosed by the circle. I note that this has been pointed out to you before on this page. Sincerely, Doctormatt 02:52, 10 January 2007 (UTC)

## Circle

I reverted your edits to circle. Similar to the instance above, I feel the less technical "interior and exterior" is better than your "bounded and unbounded" change, especially since this is the introductory paragraph, and not meant for those who care about topological issues. Also, your links to bounded and unbounded were not helpful. Try them out: bounded is a disambiguation page which is not helpful to the casual reader, and unbounded only talks about unbounded functions, not regions. Feel free to discuss your changes before introducing them in the future. Cheers, Doctormatt 06:23, 24 January 2007 (UTC)

No, I think you are wrong (especially about the links!). Interior and exterior are perfectly precise words in this context; they are not "wrong words" as you say. I feel your attempt to "correct the way ... people see and think about" mathematics by trying to confuse them with the introductory paragraph of a common term like circle is misguided. Cheers, Doctormatt 03:44, 25 January 2007 (UTC)
Think globaly and act localy. The little context (therein circle) is anyway about topology... and for interior and exterior there are only one possible meaning. And about the links, it just that we have to begin something like bounded and unbounded sets, as we do in math... greets, mathematician--kiddo 20:13, 25 January 2007 (UTC)
I don't know what you mean by "little context (therein circle)". Interior and exterior are terms used in standard english in the way that the article currently uses them. They are accurate terms, used in everyday, precise, non-mathematics-specific discussions. They do not have "only one possible meaning" , and the intro paragraph makes this clear, e.g. "Usually...the interior of the circle is called a disk". As for the links, I suggest writing articles for bounded and unbounded sets and then using them in the intro paragraph of an article about a general term like circle. Also, you added your response to the talk page for circle; this is out of context (i.e., our earlier discussion is not there), and makes no sense there: could you remove it? thanks, mathematician -- Doctormatt 21:24, 25 January 2007 (UTC)
I give up. I don't wish to discuss this any more with you. I will not monitor circle any further: do what you like with it. Cheers, Doctormatt 01:35, 26 January 2007 (UTC)

## Curso de astro general

La primera mitad de este semestre estare dando el curso de astronomia general, es el miercoles a las 7 am (horrible horario), en el V9. Veremos algo de mecanica celeste. —Preceding unsigned comment added by 189.169.58.13 (talk) 02:14, 11 February 2008 (UTC)

## Covariance and contravariance

I will relent on my insistence that elements of V are covariant and those of V* are contravariant. The incorrect terminology appears to be too entrenched, perhaps owing to physicists' rather sloppy identification of vectors in coordinates (which do transform contravariantly) with the vectors themselves (which transform covariantly). Personally, I think the entire terminology should be avoided to begin with, but people still insist on using it in articles whereever tensors are presented. Regretably the EOM link does little to rectify the problem. Silly rabbit (talk) 03:53, 10 March 2008 (UTC)

Did I say that Misner et al were wrong? Checking their book, they are careful to refer to covariant and contravariant components of tensors. The components modifier does make a difference here, and there is some discussion of this at the article Einstein summation convention. Anyway, I would appreciate a more carefully though out rebuttal than a snarky "I don't think so" response on my talk page. Silly rabbit (talk) 04:48, 10 March 2008 (UTC)
You are welcome to peruse my on-site credentials (see my contributions.) In particular, I am the primary author of the wikipedia articles on Spinors, the Exterior algebra, the Connection form, the Torsion tensor, and the Frenet-Serret formulas. I think I can claim at least a third of the articles Cartan connection, Ehresmann connection, Connection (mathematics), Curvature form. Beyond that, I have edited many many mathematics articles here. I will not, however, reveal my real-life identity to satisfy you. Silly rabbit (talk) 05:04, 10 March 2008 (UTC)
I have removed the offending sentence altogether. I deem that it is misleading at best and unintelligible at worst to refer to an element of a vector space V as co(ntra)variant without further qualification. In any event, it is not the vectors that are co(ntra)variant, but the system of quantities that one obtains by expressing a vector in a basis. Such language should be avoided unless bases are explicitly invoked, and in that case it should be done with more precision and care. siℓℓy rabbit (talk) 16:40, 14 October 2008 (UTC)

## An insult

My comments in talk:homeomorphism were not an insult, and I'm sorry that you took them as such. They were simply an observation. Everything that I wrote was true! We have a saying in English "The truth hurts". You had made one post that was an insult, and one post that repeated what I had already said with less detail and with less clarity. It's okay to tell someone to check that the inverse images of open sets are open, but how do you know that the person will understand how to construct open sets in a product space? If someone's asking you to explain why a map is continuous then you can bet that they won't know what a product topology is. Once again, I did not intend to insult you, I was simply replying with factual observations to your pluerile posts. Bueno, oye, parece que eres un hombre símpatico y por eso deberíamos olvidar lo que ha pasado. Trabajamos en la misma asignatura y deberíamos estar amigos. Pase un buen día. Dharma6662000 (talk) 02:48, 26 August 2008 (UTC)

D'accord, but, do you think that someone who can not understand homeomorphism well is going to understand Whitney C∞-topology which is not even here? i mean less detail meanwhile and more explains after another question is method to achieve -the guy- understands better, saludos my-friend.--kmath (talk) 03:06, 26 August 2008 (UTC)

## links to be used

A.Malyarenko notes —Preceding unsigned comment added by 148.202.11.53 (talk) 20:14, 27 August 2009 (UTC)

Juan Marquez

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