Mathematics - 2012-10-27 (page 2 of 2)

@Charlie hm... what a strange library?! But... we have special books that could be given only for one time during all study in university. What happened?

Charlie

@Nimza oh... i'm just not 100% good...

Nimza

eh :(

Charlie

7:29 PM

@Nimza what about you?

Nimza

Maybe somebody here knows about Cartan theorem (1951) in complex analysis?

Charlie

hmm i don't, sorry

Nimza

@Charlie nothing interesting. I didn't have a time for a walk for a month yet :( Work-study-work-study e.t.c.

Charlie

@Nimza know how that feels...

...

sometimes i stay mesmerized when i realize that i'm studying math

it's so incredible!

Gustavo Bandeira

8:08 PM

@Charlie Same here.

Charlie

@GustavoBandeira :)

Gustavo Bandeira

Geometria Analítica do Paulo Boulos, conhece?

Charlie

@GustavoBandeira não...

Gustavo Bandeira

Fui na faculdade hoje, me recomendaram.

Charlie

@GustavoBandeira bacana!

@gustavo have you been studying calculus?

Gustavo Bandeira

8:15 PM

@Charlie Yep. =)

Charlie

@GustavoBandeira what are you studying?

Gustavo Bandeira

Calculus, Geometry and I'll start on Physics.

jdoe

I just did such acool theorem sum of 1/primes = infinity

Gustavo Bandeira

Following the university curricula.

Charlie

hmm

what part of calculus are you?

@jdoe I read:"I just did alcohol theorem..." :P

Gustavo Bandeira

8:17 PM

I'm almost finishing the chapter on limits and entering derivatives.

Charlie

@GustavoBandeira preety cool!are you understanding everything?

Gustavo Bandeira

Yep.

Charlie

@GustavoBandeira good , good.hey , are you bold now?

Gustavo Bandeira

Yes

Almost bold. :P

Charlie

hehe

Gustavo Bandeira

8:21 PM

I'm gonna use it as the MSE pic

Charlie

@GustavoBandeira nice!

jdoe

so greaking cool

Nimza

Do you have a favourite function in mathematics?)

Charlie

hmmm

jdoe

favorite function.. Riemann Zeta Function

Charlie

8:26 PM

@Nimza i like trigonometric functions.

@jdoe :)

Nimza

@jdoe nice choice)))

Charlie

@TessaDangerBamkin wassupa?

Tessa Danger Bamkin

so i have a question for you genii

Charlie

say

Tessa Danger Bamkin

writing about AI and found this on an essay "I think there is a mathematical theorem stating that meaningful strings in a structured language have unique interpretations if their lengths exceed some rather small bound. I don't know how to formulate such a theorem. " anyone know what thisis?

Nimza

8:27 PM

@Charlie why?

Tessa Danger Bamkin

for all you cryptographers out there

Charlie

@Nimza why what?

jdoe

@TessaDangerBamkin, sounsds like Kolmogorov complexity

well it doesn't really

Nimza

@Charlie why trigonometric functions?)

Charlie

@Nimza they are cool! I like them.Like the curves, sometimes, the awckward things

Nimza

8:29 PM

@Charlie and what about their analitic continuations in $\mathbb{C}$? Complex cosinus is really cute :)

Charlie

@Nimza :D

i love curves!

Tessa Danger Bamkin

hm im not sure thats right @jdoe looked it up and from what i can read it seems like its more abuot the decriptive length being related to the length of a string and not the amount of interpretations of a natural language

Nimza

I love surfaces :)

Charlie

@Nimza Nice!

@Nimza what's your favorite?

Nimza

@Charlie I think $w^4 = z^4 - 1$. I've plotted it two weeks ago. I have a nice gif animation, I can send it to your mail

Charlie

8:38 PM

@Nimza awesome!do it!

@Nimza my mail is in my profile

Nimza

@Charlie I can't see it :(

ok

@Nimza got it?

aha'

hi

Hi!

8:41 PM

hi-hi

Charlie

@Nimza did you send??

Nimza

@Charlie yup

check your mail

Charlie

@Nimza That's awesome!!!

Nimza

does it roll?

Charlie

@Nimza yes, it does!

Nimza

8:45 PM

nice)

green points are branching points

Charlie

looks like a beating heart

Nimza

aha

Charlie

@Nimza there's a heart shape

Nimza

yup, I know one)

Charlie

it's fascinating!

it's breathing :P

Nimza

8:50 PM

a lot of fascinating sets is provided by reach sets of dynamical systems. Did you see some?

jdoe

can you show me one example what you mean

is julia set one?

Charlie

@Nimza no :(

Nimza

@jdoe are you talking about heart shape? then no)

$user image$

aha, that's nice :)

8:51 PM

@jdoe sweet!

it's from iterating z^2 + c in the complex plane

Nimza

:)

jdoe

it's very beautiful, but the mathematics is soo hard

youare' brave :P

I like things simple, but tough stuff can be very cool too

Charlie

@jdoe i'm mathsochist

jdoe

8:53 PM

haha

Nimza

I didn't see :(

jdoe

she is being lewd

maybe

Nimza

talking about dynamical systems. that's a reach tube for one linear system cs5711.userapi.com/u2054176/140900259/y_57ffdf0a.jpg

jdoe

thhat's interesting

Nimza

:) aha. nonlinear systems are unimaginable at all!

Minimal surfaces are very beautiful too

Charlie

8:57 PM

:-)

Nimza

bugman123.com/MinimalSurfaces/index.html

Jonas Teuwen

@Nimza 8-(.

jdoe

brilliant website

Nimza

@JonasTeuwen I think they should introduce VIP-readers notion :)

Charlie

Really cool!

Jonas Teuwen

9:00 PM

I got that, otherwise only 10 books!

Nimza

oho

@JonasTeuwen in that sense in live in soviet russia still: anybody can take no more than 30 books, the equal rights)))

jdoe

can someone help me here ? math.stackexchange.com/questions/220791/…

I tried to apply it to d/dx sin(sin(x)) and got cos(x) cos(sin(x))

but that looks wrwong

wait a second, it' s actually correct

Charlie

@jdoe that's right

jdoe

well I'm confused because of this then math.stackexchange.com/questions/222297/…

according to that, shouldn't we have d/dx sin(sin(x)) = 2 cos(x) sin(x)?

certainly cos(x) cos(sin(x)) is not equal to 2 cos(x) sin(x)

Nimza

there are no composition in the linked topic

jdoe

9:13 PM

OH!

Charlie

@jdoe read the question again

jdoe

sin(x)^2 should mean the same as (sin(x))^2

that way sin^2(x) can be reserved for iterated sin

Nimza

but what about traditions?)

@jdoe I don't know a good notation for compositional powers, but maybe $f^{\circ n}$ is ok?

jdoe

that's fine but it's not necessary to write the circ

unless there's multiple operations exponentiation might be over

Nimza

yup :)

Bitrex

9:21 PM

I accomplished precisely nothing today, I learned absolutely nothing, I actually think I've forgotten a few things over the course of the day

I had a negative productivity day

Nimza

@jdoe do you know a functional transform $f \mapsto \sum\limits_{k=0}^{\infty} \frac{f^{\circ k}}{k!}$

jdoe

no

Nimza

heh) looks nice

jdoe

looks like some weird fake version of maclaurin series

Nimza

hm) yup, it is exponent $e(f(\cdot))$ if we consider composition as multiplication and usual addition. I don't know if it makes some productive sense

jdoe

9:25 PM

composition as multiplication?

shouldn't you write f^{\times k} then?

Nimza

aha

jdoe

e.g. f^(*2)(x) = f(x)f(x) whereas f^(o2)(x) = f(f(x))

Nimza

yup)

in economics the similar thing is made in study of informational goods

jdoe

what's an informational good? that sounds interesting

Nimza

for example some information considered as goods. In IT it makes sense

jdoe

9:27 PM

cool, I didn't know that sort of stuff was taken into account

Nimza

do you know Leontieff model of production?

jdoe

no

Nimza

:(

there exists a modification of such model for informational goods.

jdoe

so for informational goods, how do you handle the fact that one can copy information infinitely many times at almost zero cost?

Nimza

it is the most interesting thing!)))

jdoe

9:29 PM

:D

Nimza

we make a switch from usual addition and multiplication operations to a structure (idempotent semiring) with usual multiplication but with idempotent addition $a \oplus b = \max(a,b)$

jdoe

I see!

Nimza

we can define matrices powers in this semiring) find eigenvectors e.t.c.

jdoe

cool

Nimza

and the most interesting thing!

What do you think there arises instead of Fourier transform?

jdoe

9:34 PM

Well I don't actually what the fourier transform is used for

Nimza

ah :(

jdoe

in economics

Nimza

in advanced economics I think anything is used) I work mainly with Radon transform over hypersurfaces (within economics!)

jdoe

so what is the fourier transform used for in the normal economics?

Nimza

@jdoe I don't know if it has a clear economical interpretation, but it helps to receive some results (like a tool)

jdoe

9:39 PM

ah right, that's how it is elsewhere

Nimza

:)

jdoe

but then when you're using these idempotent semirings what tool is used?

Nimza

instead of Fourier? Fenhel transform: $f^{*}(y) = \sup_{x} ( x \cdot y - f(x) )$

render)

jdoe

y isn't in the RHS?

Nimza

in the RHS $y$ is multiplied by $x$ (scalar multiplication)

jdoe

9:43 PM

ah!

this looks a lot simpler than the fourier transform!

Nimza

:)

idempotent analysis is a lot simpler I think

jdoe

nice

Nimza

for example if matrix power series is convergent it's sum is defined only by first $n$ members

jdoe

that sounds like a pretty fun theory

Nimza

aha and it has very interesting applications

finding arbitration chains in cross-courses of currency matrix

jdoe

9:46 PM

what is an arbitration chain?

Nimza

do you know what is a cross-course matrix?

jdoe

no

Nimza

a matrix A such that $A[i,j]$ is a number of units of $i$-th currency to be exchanged on unit of $j$-th currency

jdoe

hmm

Nimza

ok?

jdoe

9:49 PM

I'm not sure what that matrix means

it's a bit different than just exchange rates between different currencies?

Nimza

that is :D it's my bad english

jdoe

ahh

okay,

but is it symmetric?

Nimza

no

jdoe

you can change your money back and forth to get more and more each time?

Nimza

hm, not so easy

~30 roubles = 1 $ then 1 rouble = 1/30 $ - there are no symmetry

jdoe

9:51 PM

ohhh

ok!

Nimza

but there may be chains $i_1, i_2, \ldots, i_k$, $i_1 = i_k$ that provide you possibility to gain money)

jdoe

can there be chains where it does end up with more than you started?

ok

wait a second

when you say "currency"

does it mean just dollars, roubles, pounds?

or could it also be also goods?

(like some kind of information)

Nimza

here it means dollars, roubles e.t.c.

jdoe

okay

Nimza

so idempotent analysis provides you possibility to find such chains or to say if they exist

that problem was actual when Europe was introducing the common currency

jdoe

9:56 PM

that's neat!

Nimza

I'm going to bed, good night! :)

skullpatrol

later

jdoe

good night, thanks for telling me about this!!

skullpatrol

10:15 PM

hi @PeterTamaroff

Peter Tamaroff

@skullpatrol Hey

skullpatrol

hi @IanMateus

Peter Tamaroff

@skullpatrol What are you up to today?

skullpatrol

@PeterTamaroff Chillin'... how about you?

Peter Tamaroff

@skullpatrol Think I'll start with some algebra in a while

skullpatrol

10:30 PM

@PeterTamaroff I was pondering the converse of the reflexive property of equality...

Peter Tamaroff

@skullpatrol Converse?

skullpatrol

@PeterTamaroff Yes.

Peter Tamaroff

@skullpatrol Explain.

skullpatrol

The reflexive property of equality states: If a is a real number, then a=a.

Peter Tamaroff

@skullpatrol Ok, so?

skullpatrol

10:33 PM

@PeterTamaroff The converse would be If a=a, then a is a real number.

Peter Tamaroff

@skullpatrol Well, no.

You define equality over something. Before you state $a=a$ you must say what $a$ is.

skullpatrol

So we can not say a=a iff a is a real number?

Peter Tamaroff

@skullpatrol Man, equality is something very broad.

skullpatrol

or a is a real number iff a=a?

Peter Tamaroff

@skullpatrol No. $A=A$ is a definition.

For functions, for real numbers, for matrices, for topologies, whatever. We define what we mean when we say two things are equal. Or maybe better, equivalent.

@BenjaLim Duuuuuuude

BenjaLim

10:42 PM

@PeterTamaroff yes

Peter Tamaroff

@BenjaLim No.

BenjaLim

anything?

skullpatrol

@PeterTamaroff Yes, stated as: If we know what we are talking about, then what we are talking about is what we are talking about.

Peter Tamaroff

@BenjaLim "Hello"

@skullpatrol I don't know where you want to get at.

skullpatrol

14 mins ago, by skullpatrol

@PeterTamaroff I was pondering the converse of the reflexive property of equality...

@PeterTamaroff So it is not true.

Peter Tamaroff

10:46 PM

@skullpatrol It is not true.

skullpatrol

Thank you.

Peter Tamaroff

11:18 PM

@BillDubuque

user45170

11:41 PM

One short question: Is it legitimate to write [0;1,1,1,...,n] for a infinte continued fraction? Because I am not sure wheter [0;1,1,1,...,n] is finite if and only if n=1, but for different n is infinite

Argon

@user45170 I think that that fact that you have $,\cdots, n$ would imply that it is finite.

Peter Tamaroff

@user45170 You mean $[0;1,1,1\dots,1,\dots]$?

That'd be better.

Or just $[0;\bar 1]$

@user45170 If and only if?

What do you mean by $ [0;1,1,1,...,n] $?

Argon

$[1;1,1,\cdots] = \varphi$ Yay!

Peter Tamaroff

@Argon \cdots makes it look odd.

Argon

@PeterTamaroff Which dots to use?

$[1;1,1,\ddots]$ :)

Peter Tamaroff

11:44 PM

@Argon Just $\dots$

\dots?

@Argon Yeah

Cool

\cdots fit better with say $1\cdot 2 \cdot \;\cdots\;\cdot n$

user45170

I dont want to check $[0;\bar 1]$, because it is clear that this is finite. I am interested in [0;1,1,1,...,n]. The infinite item should be n>1, every other item =1

Argon

11:46 PM

@PeterTamaroff Or better yet $1+2+\cdots+n$

Peter Tamaroff

@Argon Yes.

@user45170 What does $[0;1,1,1,...,n].$ mean? What do you want to symbolize with the three dots?

user45170

They should be symbolized as infnite dots. I have this sequence, here: $x_{n+1}=1/(1+x_n)$ for a random starting point x_0 > 0 and thought it might be possible to write it as an infinite continued fraction

Argon

@user45170 Sure :)

Do you know what it converges to?

user45170

Well that's the problem. If the starting point x_0=1 it converges to 0.618..., but I am not sure if it converges for a different starting point

Argon

I am terrible with proofs of stuff like this (Pedro is great, though)

But intuitively, I think that it should not matter what value you choose as $x_0$

Peter Tamaroff

11:52 PM

@user45170 Of course.

@user45170 You have some steps to carry out, but it isn't that hard.