Mathematics - 2018-08-27 (page 3 of 3)

o/ Hello! @Jasper :)

Delonix regia

I am studying the Frobenius Norm and definitions state "defined as the square root of the sum of the absolute squares of its elements" (e.g. mathworld.wolfram.com/FrobeniusNorm.html). What I don't get is why would you take the absolute value if you are going to square it?

7:37 PM

@Delonixregia perhaps we have complex entries?

@r9m Hiiii

Delonix regia

@r9m It makes sense, thanks!

Anyone happen to have Donald Cohn's measure theory?

@JasperLoy Hi man! long time no see (I haven't visited the chat room in a while .. so faults on me I guess)

@DrewBrady As far as I know, this book is not commonly used.

@r9m I haven't had an account for months. I just created one a couple of days ago.

7:42 PM

I know, I just had a question about a particular problem in it that makes a page reference, so I figured I'd wait to see if someone had it so I didn't have to figure out how to copy 2 pages

have a question about it.

I only know of one other Cohn, and that is Paul Cohn, the great algebraist.

@JasperLoy what is bugging me is ... is it the same shade of blue that you used in your avatar as you had in past? XD

@r9m I don't know. This one is one of the selections in Paint in Windows 10. That's all. =)

Fair enough. Maybe someone else will have that book on hand!

@JasperLoy I see! :) :)

7:45 PM

@r9m Chris's Sis is seldom here these days, and also goes by strange and stranger usernames...

@DrewBrady I have access to springer links .. btw what is the problem about roughly speaking?

It should be an easy application of dominated convergence.

@r9m Most of us do know of Russian servers...

@JasperLoy Indeed .. last time I checked 'she' was waiting ..

Section 2.4: Limit Theorems, Problem 9

Makes a reference to Example 2.4.6 as well

7:46 PM

@JasperLoy lol .. I was trying to sound legal for a change :P

yeah you can always find it on linden, but didn't want people to have to go through too much work :-)

@DrewBrady lemme check ..

*libgen

and alright, thanks!

let me know once you've had a look at problem 9, section 2.4 and example 2.4.6 (just locate the example, don't need to read it).

@r9m I do buy the books after that. I use it only for evaluation.

oh, I should mention also that there are two editions of the book; I'm using the second edition.

7:49 PM

Yeah, most books are best at the latest editions.

I know of one exception.

sometimes the typesetting or formatting or organization craps out in a later edition.

famesyasd

new books are generally better than the old ones

The book on differential equations and dynamical systems by Hirsch and Smale is that exception.

but as a general rule, later = fewer errors, more refined presentation, possibly more modern material depending on the discipline.

There is more content covered in an earlier edition, and the latest one simplifies many things.

7:51 PM

@r9m any luck locating it?

@r9m I am also waiting for some things too, but I am not Waiting.

Manolis Lyviakis

hey !!!

@r9m Strange this is, a few people in this room have thought that Waiting and I are the same person. OMG.

@DrewBrady found it .. as in example call $h(x,t) := f_t(x)$ to be a map from $X \times [0, \infty) \to [0,\infty]$, basically what we have is every $t$-section of $h$ is integrable .. and we'd like to conclude $h$ can be extended to $X \times [0,\infty]$ ..

Manolis Lyviakis

$γ:I \to \mathbb{R^n}$ normal parametrized curve with $γ(t)\not= 0$ for every $t$. If there exists $t_0$ inside $I$ s.t $$||γ(t_0)||=inf{||γ(t_0)||:t \in I}$$. Prove that $γ(t_0)$ is normal to $||\dot{||γ(t_0)||}$

8:00 PM

@r9m isn't the result trivial

Like we know that f(x) = \lim_t->infty f_t(x)

Right?

So now just take any sequence (t_n) \uparrow +\infty.

@DrewBrady yes .. since $g$ bound is uniform for each $t$ section the a.e. poitwise limit $f$ defined is integrable as well .. first we need to check it suffices to consider any sequence $t_n \to \infty$

well let's just forget about all of that.

Let's take any (t_n) \uparrow +\infty.

@DrewBrady yes yes ..

Then f(x) = \lim_n f_{t_n}(x), agreed?

yes .. first we need to show $f$ is measurable in appropriate sense ..

8:04 PM

We already have f is measurable.

@JasperLoy may be you are .. maybe not .. who knows?!

Just hold on

Okay so f(x) = \lim_n f_{t_n}(x).

And f_{t_n} are measurable, and f as well.

Additionally, |f_{t_n}| <= g a.e., and g is integrable.

So dominated convergence immediately implies \int f_t_n -> \int f.

So lim_n \int f_{t_n} \to \int f.

Oh so, I guess the only thing to show is that lim_{t \to \infty} \int f_t = lim_{n} \int f_{t_n}.

yes ..

Ok, never mind, I see why this is not immediate now.

You do have to run the same approximation argument as in exercise 2.4.6.

*example 2.4.6.

anyone any ideas here .. I'm beat! :)

8:17 PM

r9m you should add the tag geometric measure theory to your problem.

you're more likely to get people who know something about it to read it then. (people who are watching that tag)

ya thanks! .. I was guessing more like integral-geometry ..

Hello! Prof. @TedShifrin :) How are you?

@r9m LOL, I am certainly not Waiting, because I hate computing integrals. =)

@JasperLoy ya .. perhaps that's what you'd like us to believe while you are using this account .. :P

@r9m Oh no, now I think maybe you are Waiting!

8:32 PM

@JasperLoy I am certainly not waiting .. I waited but then I left :P

Manolis Lyviakis

are the following different? $||γ(t_o)||'$ ,$||\dot{γ}(t_o)||$ ??

@r9m I see. What were you waiting for, by the way?

@JasperLoy 'her' book of course .. I have been eagerly waiting for last couple of years .. but now I have lost patience and I wait no more .. -_-

mercio

o..o

tbf, books take a while

8:34 PM

@r9m I am still waiting for her book. She said she would give me a copy, but I think it's best reserved for others who appreciate integrals more.

Maybe I will write my treatise on mathematics in a few decades, around ten volumes.

@JasperLoy I see .. sounds fun! :)

There will be no exercises in them, just exposition, which would make them useless to many people.

Somehow the Bourbaki dream is no longer what it was meant to be. In the end, only a few parts of mathematics are covered, and most are not covered at all.

I think Dieudonne's Treatise on Analysis is a more meaningful collection, but that is out of print.

but then again I'd hate it if it's a book written in hurry .. in which case I have often seen unreasonable exercises .. -_- but wait who am I kidding .. as if there'd be any 'reasonable' exercise in 'her' book if there were any //

I think the exercises in her book would be undoable for me.

Whenever I see the name Dieudonne I think of the word duodenum

8:39 PM

@Semiclassical LOL

Yes, and there is also the jejunum.

that's probably not a nice linkage, but there you are

Will you be taking any professor position anywhere @Semiclassical?

Doubtful

I could maybe see myself ending up at an undergraduate college

I won't be doing physics, so you won't be my instructor.

8:42 PM

but the route of doing postdocs in random places with the hope of eventually landing a tenure track position at a research university

is not one i'm interested in anymore

I see. I am also trying to think of what options I have when I am finally well.

Right now I probably just need to work on getting any job, though

having too much time on my hands is not doing me any good

I am also trying to win the lottery.