Mathematics

@JasperLoy just kidding :-p

user19161

@robjohn Yes, I know.

@JasperLoy good afternoon

user19161

@robjohn You should be sleeping soon then!

@JasperLoy God... they'll give 20K to anyone!

user19161

7:01 AM

@robjohn Yes, even a banana!

@JasperLoy Congratulations on your bananahood! (and 20K)

I got my second gold badge and didn't even know it was coming. Evidently, 1000 upvotes on a tag (for at least 200 answers) is a gold badge. And here I was waiting on an Electorate badge.

user19161

@robjohn I already have Electorate and Fanatic!

user19161

I am now aiming for Copy Editor!

@JasperLoy I have Fanatic; I am almost to Electorate

@JasperLoy I am only half way to Copy Editor

κρανίοπεριπολία

7:18 AM

)8<

Badges?

►

Every answer is downvoted.

But I cannot understand the downvotes...

7:58 AM

@awllower Two each. It's weird

@robjohn Mehdi is now both here and in tagging chatroom. (Just in case you might have some idea what might go wrong with his posting questions problem.)

(Sorry for bothering you, but since you were chatting here anyway....)

@robjohn My sentiment is exactly!

@Mehdi: can you take a screenshot of the page?

He's away... :-(

@MartinSleziak but there will be an inbox message :-)

8:13 AM

Yes, I know.

But as he was in chat for a few minutes, I hoped this was going to be resolved quickly.

Now I can only hope that my answer does clarify the doubts.

Hello! I think that the following statement is not true, is it? If $M,N$ are smooth manifolds, $\{ U_\alpha \}$, $\{V_\alpha \}$ are their open coverings and for each $\alpha$ there is a diffeomorphism $f_\alpha \colon U_\alpha \to V_\alpha$ such that if $U_\alpha \cap U_\beta \equiv U_{\alpha \beta} \neq \varnothing$ then $f_\alpha = f_\beta$ on $U_{\alpha \beta}$. Then $f(x) = f_\alpha(x)$ for $x \in U_\alpha$ will be a diffeomorphism of $M$ and $N$

I found a strange thing: if I answer with few words, then probably it can earn 4 to 5 votes. But if I elaborate more, then oft it gets only 1 to 2 votes...
Shall I conclude that the number of votes is negatively related to my effort on elaboration?

Euclidean

How to show the third part of this question math.stackexchange.com/questions/301127/… ?

he-he, a nice way to present surfaces plots on paper cs309729.vk.me/v309729774/7044/azc4nN3xuxs.jpg

Euclidean

8:25 AM

Why are my professors so dumb. I asked him the above question and he said since f is lipschitz, it is a constant function :|

@Euclidean it is more interesting to ask them something to what you already know the answer)

Euclidean

hmm. Btw this site is the only beacon of light, when i get lost. Respect Math.StackExchange _/_

:) not the only, there is a mathoverflow site for research-level math)

@Nimza Cannot you obtain chart/atlas for $M$, from the manifold $N$? Lemma 1.23 in Lee's Smooth Manifolds suggests, that system of maps similar to this should uniquely define structure of smooth manifold.

(Disclaimer: I know very little about differential geometry; hopefully someone more experienced in it will come around.)

@MartinSleziak aha, I see. My $f_\alpha$'s are actually diffeomorphisms of charts

The only thing that I'm not sure about $f$ is the injectivity. If it is injective, then $f$ will be diffeomorphism

8:49 AM

Exercise 2.9 local diffeomorphism is diffeomorphism.

Something similar was asked in this question @Nimza

Oh, I see.

You know this and you are asking whether your conditions already imply that $f$ must be injective.

then the answer is "no", I think

because here we have the same requirements as in my post + bijectivity

But it would be good to find a counterexample.

9:07 AM

@robjohn He provided a screenshot. As I wasn't able to give him advice, I've posted a question on meta. (I am not sure whether this is possible, but if mods can change question owner, perhaps the question should belong to him.)

@MartinSleziak a dev might be able to, but not a mod

ok, it's probably not such a big deal - we should not bother the overlords with this

@Nimza Your requirements are a little stronger. You want the local maps to coincide on intersections. This condition is not in the definition of a local diffeomorphism.

@MartinSleziak but if they don't coincide I don't see a way how to define global diffeomorphism

I think that they coincide, because in this exercise our local diffeomorphisms are of the form $F|_{U}$

Oh, yes. You're right.

Google returns a few hits for "local diffeomorphism" "not bijective".

For nonconnected manifold it $M$ it is easy to find such example

Aha, so I have to require bijectivity

thank you

9:18 AM

Surjectivity is clear, so id toes not matter whether you ask for injecitve or bijective map.

right

9:38 AM

Greetings

user19161

10:07 AM

Wow, I woke up from my nap to find that my rep has increased by 50, amazing...

Gustavo Bandeira

@JasperLoy XD

@JasperLoy: is rep important to you?

10:23 AM

@Chris'ssisterandpals Its like money.

@JayeshBadwaik idempotent money

@JayeshBadwaik: really?

@JayeshBadwaik: there are many brilliant persons that don't need the other's appreciation.

@Chris'ssisterandpals reputation gives you new abilities

@Chris'ssisterandpals yes, you need enough of it to wield the powers you so desire. Anything above is not really necessary. If you want to see MSE succeed well, it is imperative that you get 30k to be able to become a moderator to contribute or 10k to be able to close questions and so on.

@Chris'ssisterandpals yes, but a lack of appreciation for your efforts is a good sign that you might be on the wrong path. Its not black and white, and history is littered with counterexamples. But there has to be a method in the madness, reputation is a good method for that.

@Nimza hehe, right. :-)

@JayeshBadwaik have you ever printed an animation framewise?

10:30 AM

@Nimza exorbitantly expensive it would be!

I did draw a very simple one on my notebook once.

Is there some easy way to divide it on vertical blocks for printing?

I'm wondering of some markers

if there are only sixteen, you can manually crop stuff out.

that might work much better, rough hack, but does the job well enough.

yup, but it is just for example)

Ahh, I see.

@JayeshBadwaik: I was only referring to MSE rep.

10:33 AM

@Chris'ssisterandpals I was talking about MSE rep only too.

@JayeshBadwaik The ideal for me is the possibility to manually put vertical markers on positions of sheets break

@Nimza Hmm. I am not sure. I suspect you are getting them premade from someone else I would have told you to generate them better. I don't know. There are software algorithms which can do the job though. Especially if you have different colored graph and borders, edge detection can come to the rescue as usual, but you might have to write stuff on your own. If you have like a thousands of those, then it might be worth it (to write the code for your purposes.)

Ah, right. I will generate vertical 4-tuples then and print them

@JayeshBadwaik: but would you like to be a moderator?

@Chris'ssisterandpals No.

10:41 AM

I see.

Naah, I do not think I am good enough for being a moderator now. There are two factors:
1. I must be good enough for being a moderator.
2. Their must be a requirement (too many cooks spoil the broth.)

@JayeshBadwaik: I think you're good. You need some more rep. :D

@Chris'ssisterandpals Thanks. :-) I need to learn a lot more math too though. I think I currently understand like 5-10% of MSE questions. I need to get to around 20-30% to be of any decent use in general.

@JayeshBadwaik: I see. Btw, I'm almost out of math and glad for that. There are many other interesting activities out there. Sometimes I think that I better go jogging than solving weird calculus problems. :D

@Chris'ssisterandpals Hehe. Good for you. :-) On a more frank note, it was kind of expected given how hard you were working for last so many months. Do not be hasty in making decisions, relax and then come back and see if you still like the math you did, and may be next time you can take it up in a more gradual fashion.

10:51 AM

Life is really beautiful (without math). Yeah, I need a break.

anon

jogging and weird calculus problems are not mutually exclusive.

@anon: true!

@JayeshBadwaik: this seems an interesting site too: fitness.stackexchange.com

:D

3

Q: Drink beer after gym?

I know that it's better don't drink beer before gym. But after gym? Here they claim the following: Carbon dioxide in beer helps quench the thirst more quickly, while beer's carbohydrates replace calories lost during physical exertion. Based on the studies, the researchers have recommende...