Mathematics - 2021-03-30 (page 3 of 3)

leslie townes

18:02

i'm thinking of fencing her into a portion of the backyard

Ted Shifrin

Um, not really funny.

Karim Mansour

Hi everyone

Hi @TedShifrin

Simone

Hello karim

Karim Mansour

Hi @Simone

any cool mathematics being discussed?

Matthew Christopher Bartsh

@leslietownes I have been hearing a lot that my idea for pronouncing 111,111two as 'li ri mi four two one' and 100,000two as 'li' despite being valid and clever is not an 'interesting mathematical idea'. So I asked at Academia whether positional notation is an interesting mathematical idea and the answer was, to my surprise, 'no, I'm not interested in the alphabet either; I'd be interested in a novel' or words to that effect.

@leslietownes Here's the comment and it's got three upvotes:
@MatthewChristopherBartsh I'm not a mathematician but to be blunt with you, no. How does that help me gain new insight into the world? It's not maths, it's more like semantics and most (all?) mathematicians have much bigger fish to fry. It's like asking if I find the alphabet interesting. I'd much rather read a novel. – astronat 4 hours ago

Vrouvrou

18:17

hello Ted Shifrin

hello everyone

Matthew Christopher Bartsh

Hello Vrouv

Vrouvrou

hi

Matthew Christopher Bartsh

Are you Dutch?

Vrouvrou

no no

Matthew Christopher Bartsh

ha ha

Simone

18:19

Hello

Matthew Christopher Bartsh

Hello Simone

Nike Dattani

This question might be easy for anyone with enough experience in differential equations:

1

Q: How to solve general wave equation and dispersion relation using Fourier series?

In this paper (open access), the authors used Fourier series with most general wave equation to find the dispersion relation. I am presenting some main equations as snippets to depict their solution. We want to solve for $u(x,t)$ in the following wave equation (Eq. (1) in the paper): \begin{equat...

Matthew Christopher Bartsh

@NikeDattani and everyone I keep forgetting to ask this. What are these math questions you guys keep asking each other?

robjohn

@copper.hat continuous on a compact set implies...

Matthew Christopher Bartsh

Are they puzzles, homework, research, ...something else?

robjohn

18:24

@MatthewChristopherBartsh they could be almost anything. Hopefully, they are helpful to someone.

Ted Shifrin

@robjohn I said Stone-Weierstrass twice :)

anakhro

Might be a stupid question, but are there vector fields on R^2 whose flows do not commute?

Ted Shifrin

Of course.

user2103480

@MatthewChristopherBartsh hard

Ted Shifrin

Is Lie bracket always $0$, @anakhro?

Matthew Christopher Bartsh

18:26

@robjohn I don't follow. I am not a mathematician. Please explain like to a five year old.

Karim Mansour

@TedShifrin I want to send you a preprint of my work not to check or anything but as a friend to be happy with :)

is that ok?

anakhro

@TedShifrin I wouldn't suppose so, but I am trying to come up with examples and I am drawing blanks.

Ted Shifrin

Sure, thanks, Karim.

robjohn

@TedShifrin I wasn't sure of the space asked about.

@MatthewChristopherBartsh what was confusing: "almost anything" or "helpful to someone"?

Ted Shifrin

Take $X=\partial/\partial x$ and $Y= f(x)\partial/\partial y$.

Matthew Christopher Bartsh

18:28

@user2 What is hard?

anakhro

OH MY I AM STUPID

user2103480

@MatthewChristopherBartsh the questions

anakhro

You are right, Ted.

Matthew Christopher Bartsh

ha ha

Ted Shifrin

twiddles thumbs and bypasses smacks

Matthew Christopher Bartsh

18:29

@robjohn Both.

leslie townes

i pride myself on respectability but i just spilled mustard on myself. i did this to myself. i asked for pastrami with coleslaw and extra mustard.

Ted Shifrin

I'll eat it for you if it's too messy.

leslie townes

it's fine, i just had to change shirts. it's delicious.

copper.hat

@robjohn Thanks. I should not ask questions prior to large intake of caffeine.

leslie townes

now my cat's in here trying to find the extra mustard.

copper.hat

18:33

There is a slow mathematical knowledge rebirth every morning, some less successful than others.

Ted Shifrin

The cat probably prefers pastrami.

leslie townes

she's sensing the pastrami-adjacent locations. you're onto something.

thinking like a cat.

Ted Shifrin

I have had numerous kitties.

leslie townes

olivia likes to sleep in the sun. and when the sun moves and she can't sleep in it anymore, she moves to her heated bed. it heats up when weight is placed upon it. technology evolved far enough along to give cats what they need.

copper.hat

I dislike when an animal is obviously smarter than me.

Ted Shifrin

18:36

A lot of jealousy in this room.

Vrouvrou

If $A\cap B\neq \emptyset$ how to prove that $d(A,B)=0$

if someone have an idea please tell me

copper.hat

$d(x,x) = 0$ usually?

my level of question.

Vrouvrou

yes

copper.hat

That is the essence of the proof.

Ted Shifrin

I think we need to start a triage system in this room.

copper.hat

18:40

i can triage my own questions...

Vrouvrou

je m'excuse Ted Shifrin

Ted Shifrin

LOL ... That was not directed at you, @Vrouvrou. I was referring to copper's "my level of question." :)

Vrouvrou

ah ok

I don't understand how to use $A\cap B\neq \emptyset$

Ted Shifrin

@Karim: Thanks for the preprint. I just glanced at it. My immediate comment is that all your definitions in the preliminaries are very elementary, but I have no idea what the twisted Chow group or regulators are. You need to rewrite the preliminaries section.

anakhro

It means they share a point, @Vrouvrou. What is your definition of distance between A and B?

copper.hat

18:44

Let $x \in A \cap B$ then $0 \le d(A,B) \le d(x,x)$.

Vrouvrou

$d(A,B)=\inf\{d(x,y), x\in A, y\in B\}$

anakhro

@copper.hat it might be your level of question, but helping them arrive at the answer themselves rather than just giving them the answer is ideal.

Ted Shifrin

Also, @Karim, your example before definition 1.6 is wrong unless $X$ is a hypersurface and the last term has a typo in it. The first term needs to be the ideal sheaf (twisted). I think you guys need to proofread carefully.

copper.hat

suitably chastised

Ted Shifrin

warms up the smacking glove :D

geocalc33

18:46

hello

leslie townes

i once received $e^{1/e} + \pi/2$ smacks. afterward, i had a better understanding of myself and where i had misstepped.

Vrouvrou

@copper.hat $d(A,B)\leq d(x,x)$ because it is the inf ?

anakhro

@Vrouvrou Do a simple example to get a rough idea of how it works. Consider subsets A=[-1,1] and B={0} in R. They have a non-empty intersection. Try applying your definition of d(A,B).

Ted Shifrin

I don't remember ever doing $e^{1/e}$. Did someone else usurp? :D

copper.hat

@Vrouvrou Then you must have $d(A,B) \le d(a,b)$ for all $a\in A, b \in B$.

So pick suitable $a,b$

Karim Mansour

18:47

@TedShifrin Yeah. I will define Twisted chow groups are defined as the triple they are the triple $(\sigma, || ||_{L_i}, Z_i)$ where $\sigma$ is rational function over line bundle L and $|| ||_{L_i}$ is a flat metric

copper.hat

sounds like a hungry rock group.

Ted Shifrin

I'm just saying that giving first-grade definitions and then writing fancy-level paper is wrong. But note the serious error I pointed out.

Karim Mansour

@TedShifrin Yeah this is very early stage of the first result. Yeah I agree with you.

Ted Shifrin

I will try to read through the hard stuff later.

After you give me the definitions I need :D

Karim Mansour

Okay

copper.hat

18:49

@anakhro to be fair to me, there is some history...

leslie townes

i have all of twisted chow groups' records. including their split 7" with banach limits.

copper.hat

ahhh, the complete set

Ted Shifrin

@copper: Yes, I am fully aware.

Karim Mansour

@TedShifrin the next result will be proving surjectivity result for product of two elliptic curves, four elliptic curves, and elliptic surfaces.

anakhro

@copper.hat history of what?

leslie townes

18:54

i just ate some snack crackers. i'm going to upload a photo of the back of the snack crackers. please provide a detailed exposition of the nutrition i will aquire from the crackers. i will include highlights and arrows toward nutritional information that matters the most to me.

Ted Shifrin

Forget the snack crackers. I want the pastrami.

leslie townes

the important thing here is, you do detailed work for me.

it's nothing without the coleslaw and extra mustard.

my best friend lives in beverly hills, i used to love visiting her because we'd go to a deli where i could get the aforementioned sandwich. now it's all gone to hell.

Karim Mansour

I decided I will read GH very very carefully.

they seem to have few things about elliptic surfaces.

I think I will not work as TA in the fall next fall want to focus more.

leslie townes

that's a good move. if you have the opportunity, take time away from teaching or teaching-adjacent activities and figure stuff out.

Karim Mansour

@leslietownes Yeah. TA sucks a lot of my time and I really want to read GH and Andreas Gathman very carefully for my project.

leslie townes

19:03

good. i think that my thesis would have been better if i hadn't been teaching every semester while i was writing it. and before it.

my teaching would have been better too.

Karim Mansour

I won teaching award so I don't need anymore teaching experience. Though I will miss it . I will come back to teaching anyway once I am done with the main ideas and figured out things for my thesis.

leslie townes

congratulations! i taught so much that every semester the department had to apply to the college, or university, or somewhere, to get me an exemption from the maximum teaching requirements. i needed the money. i didn't have grant money. i had to do it. i did win an award once, but relatively early on. it was useless when i needed to graduate.

Karim Mansour

Thanks. :) @leslietownes I am assuming you did your PhD in Berkeley ?

you mentioned before that you didn't have a semester with Borcherds so I am assuming you studied in Berkeley?

leslie townes

i spent a semester grading homework for an algebra class taught by dr. borcherds. i did get a ph.d. there.

Karim Mansour

I want to ask because I am curious how postdoc positions etc

that is cool

leslie townes

19:09

i did not do a postdoc at berkeley. my impression is that the hiring process was driven by particular subfields. but that is a vague impression.

Karim Mansour

I see. I really want to come to California once I am done with my PhD.

I like the cold weather here but prefer warm climate

leslie townes

come to california even if you aren't done with your phd, it

is nice here.

i came from northern california where it is colder and foggier than most people imagine california to be. but now i live in southern california where it is palm trees and surfing every day of the year.

come and join us

Karim Mansour

Yeah I will definitely will come hopefully getting some postdoc position in CA. My uncle lives there too he has his own business.

it is not as cold as Edmonton here in the winter it is crazy haha

though super nice in the summer.

leslie townes

i know some very good good sushi restaurants. if you eat sushi, which maybe you don't. keep in touch.

also some dumpling restaurants. i'm a huge fan of japanese and chinese or taiwanese or korean cooking.

i spend all my money at those restaurants.

Ted Shifrin

The best Chinese food in LA is now way in the eastern suburbs, though.

leslie townes

19:14

near where i live!!!

it's fine!

Ted Shifrin

I have a Chinese friend who lives in Long Beach and drives out to Rowland Heights ...

copper.hat

@anakhro with the op that you were chastising me about...

Ted Shifrin

I miss the Bay Area. Chinese food here in SD is at best B level.

Karim Mansour

@leslietownes I love Sushi. I will definitely PM you when I come to California.

leslie townes

for chinese-adjacent food i mostly eat/ate at din tai fung which has locations in orange county and torrance.

anakhro

19:16

I don't think any history should make you give up basic tenets of pedagogy, @copper.hat :)

copper.hat

its been a while, but Chinese food in China is a lot different than Chinese food in the USA.

Karim Mansour

I love Asian food in general

Ted Shifrin

@anakhro: I support copper in this particular matter.

leslie townes

i also love southern california specific food. fish tacos, all kinds of anarchy happening in burritos. i'm there for that.

copper.hat

@anakhro i am optimising, which is reasonable after then $n$th attempt.

Ted Shifrin

19:17

I've eaten at Din Tai Fung in Burbank, Costa Mesa, and San Diego. I don't find it to be the holy grail that everyone else does. Good, but not what the press says.

copper.hat

i love mx food.

The Chinese food I enjoyed the most was in Hainan.

leslie townes

there was a chinese place i used to love in oakland, but it closed. the owner fired the chef. and three weeks later, nobody wanted to eat there. i couldn't repair the interpersonal situation.

copper.hat

China ruined Chinese food for me, by way of comparison

Karim Mansour

Did you go to China recently @copper.hat ?

copper.hat

@KarimMansour Unfortunately it was many decades ago.

Ted Shifrin

19:20

@copper I very much regret that I didn't take the time to visit China when Chern was still alive.

leslie townes

my wife went to china for an academic conference and came back with crazy hives. i couldn't tell if it was from eating stealth shellfish (which don't work well with my wife), or being bitten by a mosquito or something, or i don't know what.

it was a problem for a while.

copper.hat

@TedShifrin I think the China of today is vastly different place than when I visited.

Karim Mansour

I see. I have never been to China. I would love to visit one day. I think it is probably very different now than it was years ago @copper.hat

Ted Shifrin

I suspect you're right. But I know a lot of famous geometers who used to visit ... and I should have done it.

copper.hat

I had some street Mandarin which helped.

Ted Shifrin

19:22

Now even driving for a half hour hurts my neck badly, so I'm not sure about a 3-hour plane ride, let alone a day plane ride.

leslie townes

i want to visit china, japan, and korea. i have friends there but no free time. i have not been on vacation in five years.

copper.hat

Sorry to hear it, and can appreciate the issue.

Karim Mansour

sorry to hear that Ted

copper.hat

Traveling for a week or two to a place is just a tease.

Karim Mansour

I really want to visit China and Japan. The other day I saw a video of Canadian exchange student in Japan it was amazing.

leslie townes

19:23

ted, i drove to my office yesterday, first time in over a year. because of a recent cold, my neck hurt when i went to check any mirrors. it was nearly unmanageable.

copper.hat

For me it is about meeting people and sometimes the geography.

leslie townes

i also own a very small car, prius C, i'm over six foot tall, i want to click the driver's seat back far further than it will let me go. my spine tingles after 20 minutes

i had to drive to palm springs once. i was numb when i got there

Ted Shifrin

That doesn't sound good at all, @Leslie. I am a runt, so that is not my particular problem :P

copper.hat

on my last flight back from ireland last november i was prepared for a long haul, but it turned out i knew the pilot and got bumped to 1st. nice to lie flat.

leslie townes

i remember test driving the car and thinking "well it is only $18k off the lot.."

anakhro

19:26

@copper.hat Ignoring would be optimizing. Fostering poor learning makes them come back for more.

copper.hat

@anakhro i am not young enough to know everything.

do not judge until you are in the cockpit

Ted Shifrin

@anakhro I think you should drop this.

anakhro

I already am familiar with the struggles of teaching and helping others.

Ted Shifrin

We cannot have an open and forthright discussion of the matter in the public room.

copper.hat

much appreciated.

leslie townes

19:29

first class is something else. i was bumped there from denmark to san francisco once. the person next to me said "are you supposed to be here?" and i acted up like "do you think i'm not supposed to be here?" then i realized we were both strangers in first class just trying to understand this new world where people brought you wines. we still email from time to time.

Vrouvrou

I understand @copper.hat thank you very much

Ted Shifrin

The only time I got bumped to first class was a hysterical situation. I had been in line for 3+ hours at DeGaulle to fly back to Boston. TWA had three departing flights within one hour, and we were all crammed like sardines in one tiny room. I got to the gate literally 5 minutes before takeoff and was scolded for arriving so late. I threw my best French and best subjunctives at the person, ended up in Business Class, and then got pushed into first class.

leslie townes

you locked it in with the subjunctives.

Ted Shifrin

I sure hope so. But I was so angry ... 3 f***ing hours in line.

copper.hat

it was funny, the stewardess came by and asked if i would like some wine, and, thinking of the little plastic bottles of vinegar i replied white. she said, umm, what sort of white. ended up getting a bottle of a nice Portuguese something or other. different experience.

Ted Shifrin

19:33

Speaking of lines in Paris ... salut, @Astyx.

That was 1980 ... long before airport security, pandemics, etc.

copper.hat

sadly, since 9/11 no cockpit visits

at least in the air

Astyx

Salut

Ted Shifrin

I remember a few puddle-jumper flights (e.g., Charlotte, NC to Athens, GA) where the pilot was pretty much in the same room with the 8 of us.

leslie townes

my bump up was post-shoe bomber but after shoe bomber doing whatever it is he did. it was a mixed rules situation

copper.hat

i was on the no fly list for a while.

i live in the tail of some odd distribution

leslie townes

19:36

did you visit a pub somewhere where there was a contribution pot for something that styled itself "the REAL IRA?" that tripped up some of my cousins.

they were mostly trying to keep people from not annoying them.

copper.hat

there could be many reasons. anyway, i got it sorted out pretty quickly surprisingly. even with my fbi file.

geocalc33

0

Q: Bounded vector field in a square region (soft question)

Given a system of integral curves how does one find the associated system of differential equations and the vector field corresponding to these integral curves?

ordinary-differential-equations

leslie townes

i probably have one of those. my dad dated someone related to the rosenbergs.

geocalc, my view is similar to the commenters, more info is needed. i do not think the commenters are trying to be difficult with you.

anakhro

@TedShifrin does it matter to the Lie bracket if the flows are not parametrized by arc length?

geocalc33

@leslietownes it's a question I asked 3 years ago when I didn't know as much as I do now

anakhro

19:47

For example, I am thinking about a "flow parallelogram". If I flow "time 1" down one vector field, and then the other, and vice versa---doesn't this depend on the parametrization of the integral curves (the time 1 part).

Like it should need that...

Ted Shifrin

20:19

@anakhro This question makes no sense.

anakhro

Normally when people discuss the Lie bracket, they draw a little flow parallelogram which does not meet up (or does).

Like as a visualization.

Ted Shifrin

Look ip definitions.

anakhro

with a hand wavy "flow a little down one, then flow down the other, and vice versa"

Ted Shifrin

I am acquainted with the picture, but you need to review the definition of flow and see if your question makes any sense.

Thorgott

you can't reparametrize integral curves

that scales the derivative

Ted Shifrin

20:28

Follow anakhro's orders. Don’t give away answers.

Flows.

20:59

Sorry I ask a question from earlier without a typo this time: Partition the interval $[0,T]$ into subintervals $[t_{n},t_{n+1}]$ of length $h$. Then of course $ lim_{h\to 0} \sum_n \int_{t_{n}}^{t_{n+1}} g(t_{n}) = \int_0^T g(t) dt $. What happens to the integral if there is an extra weakly convergent function? i.e how do I handle $lim_{h\to 0} \sum_n \int_{t_{n}}^{t_{n+1}} f_h(t) g(t_{n}) dt $ for $f_h$ weakly converging in L^1

Astyx

If I have a differential operator that I express as a polynomial $P(\partial)$ in $\partial$, is there a common name for the differential operators $P^{(i)}(\partial)$ ? ($P^{(i)}$ is the i-th formal derivative of the polynomial $P$)

Astyx

21:24

I take that as a no

Ted Shifrin

Yes. No.

Astyx

Thanks.

Silvinha

22:42

@TedShifrin Hi. How are you? I would like to ask you for a favour if it is possible...
Would you delet a post for me? Please?

7

Q: How to prove that $\phi=f:S\rightarrow \mathbb{S}^2$ is a bijection without using $h$?

This question is already answered. However, I would like to understand in the proof provided two things: Why do I have to define the function $h$ and why I need do obtain $h'$? (I would like to understand this part in a step by step way) Is there any way to prove that $\phi=f:S\rightarrow \mathb...

differential-geometry differential-topology diffeomorphism

I really appreciate your help. Thanks.

Ted Shifrin

@Silvinha I am not that powerful. You can't delete it yourself? If not, maybe @robjohn can help.

Thorgott

why would you want that question deleted now

robjohn

@Silvinha Let me look...

Ted Shifrin

I think once it has an accepted answer, no one can touch it.

I suspect it was an exam question ... I answered a different version of the same question.

robjohn

@Silvinha I'm sorry, that question has an upvoted and even bountied answer.

Ted Shifrin

22:48

My suspicions loom ...

robjohn

@TedShifrin And I would not bet against you there.

Ted Shifrin

I used to be a much nicer person before cheating grew exponentially.

Well, my friends might dispute that.

And some in here might dispute that I have friends. 🤷‍♂️🤷‍♂️

robjohn

@TedShifrin do you weave doubt on your suspicions loom?

Ted Shifrin

LOL ... I can't even smack you for that one!

Silvinha

23:06

@TedShifrin Yes. ='/. The professor allowed us to search help anywhere. But I'm ashamed about the comment "12 hours" etc... lol

@robjohn ok

Ted Shifrin

You should be ashamed @Silvinha

Silvinha

@TedShifrin You're right! I don't disagree of you... However would you please, delet that comment?

Ted Shifrin

23:31

Can’t you edit and remove the sentence? I cannot edit anyone except my own.

leslie townes

it's a testatment to your advice that people just assume that you have super powers.

Ted Shifrin

Maybe I should work at Newsmax or OAN.

leslie townes

23:49

that's where i work. it's not a bad job if you don't mind being paid in camel cash.

Ted Shifrin

23:59

Camel manure...

Transcript for

$Mathematics$ Mathematics