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

Alessandro Codenotti

19:03

Hi @Dami

Oskar Tegby

19:19

Anyone down for a question?

r9m

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?

r9m

19:37

@Delonixregia perhaps we have complex entries?

Jasper Loy

@r9m Hiiii

Delonix regia

@r9m It makes sense, thanks!

Drew Brady

Anyone happen to have Donald Cohn's measure theory?

r9m

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

Jasper Loy

@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.

Drew Brady

19:42

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.

Jasper Loy

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

r9m

@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

Jasper Loy

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

Drew Brady

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

r9m

@JasperLoy I see! :) :)

Jasper Loy

19:45

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

r9m

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

Drew Brady

It should be an easy application of dominated convergence.

Jasper Loy

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

r9m

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

Drew Brady

Section 2.4: Limit Theorems, Problem 9

Makes a reference to Example 2.4.6 as well

r9m

19:46

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

Drew Brady

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

r9m

@DrewBrady lemme check ..

Drew Brady

*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).

Jasper Loy

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

Drew Brady

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

Jasper Loy

19:49

Yeah, most books are best at the latest editions.

I know of one exception.

Drew Brady

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

famesyasd

new books are generally better than the old ones

Jasper Loy

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

Drew Brady

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

Jasper Loy

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

Drew Brady

19:51

@r9m any luck locating it?

Jasper Loy

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

Manolis Lyviakis

hey !!!

Jasper Loy

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

r9m

@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 $||\dot{||γ(t_0)||}$

Drew Brady

20:00

@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.

r9m

@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 $t_n \to \infty$

Drew Brady

well let's just forget about all of that.

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

r9m

@DrewBrady yes yes ..

Drew Brady

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

r9m

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

Drew Brady

20:04

We already have f is measurable.

r9m

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

Drew Brady

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}.

r9m

yes ..

Drew Brady

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.

r9m

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

Drew Brady

20:17

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)

r9m

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

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

Jasper Loy

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

r9m

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

Jasper Loy

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

r9m

20:32

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

Manolis Lyviakis

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

Jasper Loy

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

r9m

@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

Semiclassical

tbf, books take a while

Jasper Loy

20:34

@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.

r9m

@JasperLoy I see .. sounds fun! :)

Jasper Loy

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.

r9m

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 //

Jasper Loy

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

Semiclassical

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

r9m

20:39

@Semiclassical LOL

Jasper Loy

Yes, and there is also the jejunum.

Semiclassical

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

Jasper Loy

Will you be taking any professor position anywhere @Semiclassical?

Semiclassical

Doubtful

I could maybe see myself ending up at an undergraduate college

Jasper Loy

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

Semiclassical

20:42

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

Jasper Loy

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

Semiclassical

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

Jasper Loy

I am also trying to win the lottery.

Semiclassical

that seems problematic

Nick

21:11

@micsthepick now, you've got me confused. Is it zero or two?

micsthepick

it is 2

it is also not the matrix I was looking for

famesyasd

I have finally proved the associativtiy of composition for functions

Nice-o!

Nick

21:52

@famesyasd nice!

associativity :)

fo(goh) is (fog)oh

am I right?

or is that distributivity?

lol

Mary Star

22:05

We have the letters 'WINPRESENT'. I want to calculate the rearrangements of these letters that contain either the word 'WIN' or the word 'PRESENT' or both of them.

I have done the following:

The subword 'WIN' is contained in $8!$ rearrangements. Since at 'PRESENT' we have twice the letter E we get $\frac{8!}{2}$ rearrangements. The subword 'PRESENT' is contained in $4!$ rearrangements. We have calculated twice 'WINPRESENT' and twice 'PRESENTWIN'.

So the total amount of rearrangements that contain either the word 'WIN' or the word 'PRESENT' or both of them is equal to $\frac{8!}{2}+4!-2$,…

Wilson

23:19

I would like to hire someone to teach me how to do this:
https://math.stackexchange.com/a/2895836/389017
By *teach*, I mean:
1) Write out step-by-step instructions
2) Instructions to be in terms that I can understand (grade 10 math), with no mathematical notation (I don’t know how to read that stuff)
3) Preferably, the instructions would be tailored to Excel.

What kind of service can you recommend in this scenario?
You might be thinking: "Just go back to school and learn math!" Well, that's not exactly practical for a one-time, somewhat time-sensitive problem like this. I simply need to up…

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$Mathematics$ Mathematics