Mathematics

Manolis Lyviakis

12:00 PM

my thought is for example $C^n $ and a A= line in $C^n$ so $C^n - A$ but the zero polynomial is zero everywhere.

Akiva Weinberger

What's the difference of two algebraic sets?

AbhigyanC

Hello everyone! I need a little help (and further links) with a certain question: Why are there 24 hours in a day? I have a basic idea that the number of factors of a number expressed as a fraction of the number is large, but I'm looking for some further reading here... Can someone help out?

Everywhere I look this up, I'm getting historical answers... I'm looking for a mathematical one... Can anyone please enlighten me? :)

Akiva Weinberger

12 is just a very nice number I guess

The only numbers coprime to 12 are 1,5,7,11

(The only numbers between 1 and 12 inclusive, I mean)

AbhigyanC

@AkivaWeinberger Yeah, that's true in a way... It has a lot of factors (1,2,3,4,6) which is more than what 10 has (1,2,5)

Akiva Weinberger

I wonder if Native American civilizations also divided the day into the same number

AbhigyanC

12:08 PM

@AkivaWeinberger Exactly!

@AkivaWeinberger Not quite... This system, AFAIK, was used by the Egyptians and Indians

Check this out for History -> nist.gov/pml/walk-through-time-early-clocks

nist.gov/pml/walk-through-time-ancient-calendars

But I'm here for the math XD

Akiva Weinberger

I'm trying to look up Mesoamerican timekeeping, and I'm only getting calendars (and units larger than a day)

mick

0

Q: Formal group law and koenigs function conjecture !?

Let $f(x,y)$ be a symmetric real function and a formal group law. $G(x + y) = f(G(x),G(y)) $ Consider the equation $$ h(2x) = f(h(x),h(x)) = A(h(x)) $$ This equation has many solutions. Compute a solution to that equation with the fixpoint at $0$ and its koenigs function, and call the soluti...

Any ideas ?

Secret

hmm... what is:

💥(conjecture)

mick

Wiki koenigs if necc

Secret

Actually, I need a new operator, 💥 is too powerful to be useful

meanwhile, my complex analysis sucks too much to answer that question

I have not even wrap my head around branch cuts yet

Akiva Weinberger

12:19 PM

Highly composite number

A highly composite number, also known as an anti-prime, is a positive integer with more divisors than any smaller positive integer has. The term was coined by Ramanujan (1915). However, Jean-Pierre Kahane has suggested that the concept might have been known to Plato, who set 5040 as the ideal number of citizens in a city as 5040 has more divisors than any numbers less than it.The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as two highly composite numbers (1 and...

@AbhigyanC ^This may be of interest

AbhigyanC

Wow!!! Thanks @AkivaWeinberger

Secret

Define 🌀 to be the cyclone operator such that given any two objects M, N under the ordering induced by 💥, the follow is true

AbhigyanC

Exactly what I was looking for!

Secret

$$M < 🌀(N)$$

Akiva Weinberger

See also this concept:

Superior highly composite number

In mathematics, a superior highly composite number is a natural number which has more divisors than any other number scaled relative to some positive power of the number itself. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer. The first 10 superior highly composite numbers and their factorization are listed. For a superior highly composite number n there exists a positive real number ε such that for all natural numbers k smaller than n we have ...

@AbhigyanC

which is the same thing but with "superior" added onto it

AbhigyanC

12:23 PM

@AkivaWeinberger 'Superior' thank you XD

Secret

Thus while 💥(composite number) cannot fit within this chat, the following is true:

🌀🌀(composite number) = 🌀(highly composite number) = superior highly composite number

Due to the nature of 💥, the image of 🌀 is unstable, i.e. it changes depends on context

Now with the cyclone operator, I should be able to do explosive generalisation in a more controlled fashion

Some identities:

🌀💥=💥
💥🌀=family of higher cyclone operators

AbhigyanC

@Secret What are you doing??

Secret

Trying to upgrade my notions that I previously used in this chat. Akiva had already covered your query

AbhigyanC

Okay... Go ahead

abenthy

4:25 PM

Whats the real Lie algebra of $\text{SL}_2(\mathbb{C})$ considered as a real Lie group?

Secret

4:50 PM

Take 3 on infinity:

Let $X$ be an object, $M$ be an object of type $\text{Fin}$, $S$ be an abstract operator that capture a notion of size, $f$ be an operator that scales the notion of size as defined by $S$. Then $X$ is potentially infinite if:

$$S.(X,X)\neq S.(X,f.M)$$

$f.M$ is interpreted to be all possible strings consists of $M$, as sufficiently many scaling operators that changes the notion of size given by $S$. Thus if $S$ is denoted by doubling the number of elements in the set and $M$ is a set, then $f.M$ includes all $2^nM$ for all $n \in \Bbb{N}$, as well things like $2^n MM, 2^nM2^mM^2$ and so on

The basic idea is that potential infinity, when explosively generalised, is an abstract mathematical object that is boundness in the most general sense, that is given any fixed non infinite object and its scaled version such that it stays non infinite, it never contain said object

Now, $X$ is actually infinite if in addition it satisfies:

$$S.(X,f.X)$$ is not of type $\text{Fin}$

Thus 💥(Infinity) is charaterised by unboundedness by finite objects and scale invariance

For comparison, the class $S$ such that the elements satisfy the relation $x_{i+1}=x_i+1$ does not biject with any finite natural number, and e.g. $n\aleph_0=\aleph_0$ for natural number $n$

9 hours ago, by Akiva Weinberger

In other words, "what are near-counterexamples"

Thus, an object that can model a notion of the "edge of infinity" will look something like this:

The object Y can be bounded by at least one object K of type Fin, however, of the all possible f.Y, in a partial ordering, as we transverse up through any chain, the K that can successfully bound Y will started to become increasingly larger, eventually after some finite object, said representative of f.Y can no longer be bounded

For a real value function example, it is any function in the 1st quadrant such that its x asymptote is positive, in other words, finite time blowup functions

Manolis Lyviakis

5:20 PM

i want to prove that the set $C^n -V$ where V is an algebraic proper subset of $C^n$ cant be algebraic

this means there doesnt exist Ideal $I$ of $C[x_1,...x_n]$such that generates $C^n -V$

ahorn

5:40 PM

What is the word for 'percentile' when there are $n$ bins?

Paul Plummer

7:05 PM

n-quantitles @ahorn

@ManolisLyviakis Is there way to write C^n in terms of the ideal which defines V anc C^n\V

Mike Miller

@PaulPlummer Thanks for the information! It doesn't surprise me: the Smith theory argument is inaccessible.

I don't know an obstruction in the smooth case either, though, but it seems implicit in your statement that one exists.

In the future it will be easier to get in touch with me via my email, smmiller@ucla.

MatheinBoulomenos

7:23 PM

@MikeMiller are math blogs citable?

Mike Miller

I guess? I wouldn't try to get it in a published paper.

MatheinBoulomenos

I got a mail from a student who said that my blog helped him a lot for his thesis, so he's asking me how to cite it

Mike Miller

Just find the relevant fact elsewhere; I doubt the full details first appeared in a blog.

MatheinBoulomenos

yeah, that's true

Mike Miller

Oh, for a student? Seems fine.

They're probably writing a paper for a class.

MatheinBoulomenos

7:28 PM

tbh, I wouldn't exactly recommend them to cite me, since I worked the stuff out on my own (though it's probably all well-known), so I don't know if my notation and terminology is standard

Paul Plummer

Ah, okay, I can email instead. I had been reading some stuff/slides by Kathryn Mann, which I can't find right now and there where some results which imply Diff(M) can't contain high rank lattice subgroups and things like that. Are you saying that p-group paper is inaccessible(Some parts definitely looked complicated, but assuming fixed points didn't look to bad, assuiming some smith theory) @MikeMiller

MatheinBoulomenos

thanks @MikeMiller

Mike Miller

7:48 PM

Sorry, @Paul, I didn't look at the paper. I mean that Smith theory is about fixed points of finite group actions, so the torsion-free assumption renders it useless to us.

Leaky Nun

8:02 PM

@MatheinBoulomenos Can one prove that the free commutative ring over a set is an integral domain (if one doesn't know that multivariable polynomials exist)?

i.e. just using the universal properties?

mick

8:14 PM

1

Q: Formal group law and koenigs function conjecture !?

Let $f(x,y)$ be a symmetric real function and a formal group law. $G(x + y) = f(G(x),G(y)) $ Consider the equation $$ h(2x) = f(h(x),h(x)) = A(h(x)) $$ This equation has many solutions. Compute a solution to that equation with the fixpoint at $0$ and its koenigs function, and call the soluti...

real-analysis dynamical-systems functional-equations complex-dynamics formal-groups

Any ideas ?

Alek Murt

8:50 PM

Hey guys, if $\Omega$ is a compact set, then $C_0^{\infty}(\Omega) \subset H^2(\Omega)$?

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$Mathematics$ Mathematics