Mathematics

« first day (3455 days earlier) ← previous day next day → last day (1549 days later) »

1:32 AM

If $\ast$ is a binary operation on a set $S$, we say a subset $X \subseteq S$ is closed under $\ast$ if $x, y \in X \implies x\ast y \in X$.

Is there a name for a subset $X$ for which $x\ast y \in X \implies x, y \in X$?

Thorgott

1:45 AM

Reminds me of prime ideals, but I don't know any general terminology

Lucas Henrique

2:00 AM

yeah

maybe there's something like this in more general algebra?

Bob

will things like general algebra be useful outside of academia?

Lucas Henrique

Applied category theory

Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer science, physics (in particular quantum mechanics), control theory, natural language processing, probability theory and causality. The application of category theory in these domains can take different forms. In some cases the formalization of the domain into the language of category theory is the goal, the idea here being that this would elucidate the important structure and properties of the domain. In other cases the formalization is used...

Thorgott

is it useful to know which regular n-gons can be constructed with ruler and compass

Shine On You Crazy Diamond

2:16 AM

Not really, but the constructibility and field extension approach is very elegant proof

This site is somethin else

yutsumura.com/group-of-order-18-is-solvable

Renaming BananaCats to AfterPaper, and the design is totally changing

I'm going to make a general math tool, but aimed at higher math

such as group theory

Ultradark

@shi hi

Ultradark

2:39 AM

A lamination of a surface is a partition of a closed subset of the surface into smooth curves. It may or may not be possible to fill the gaps in a lamination to make a foliation.

How does one determine whether it's possible or not to fill the gaps in a lamination to make a foliation?

12 hours later…

sevdaicmis

2:56 PM

hi, i and one of my friends willing to use these se chatrooms for studying like some people do

but he don't have an account, even he creates one now it'll take some to reach 100 points

do you know any other mathjax enabled chat systems/projects? i took a look at google for such projects but didn't succeed to find a suitable one

maybe i'll write one, eventually

1010011010

3:11 PM

Howdy everybody

For my research I'm using an argument containing the general form of the Heaviside cover-up method. One of the guys had the following expression for it:

$$
\frac{{{\prod}_{i=1}}^A(x-a_i)}{{{\prod}_{i=1}}^B (x-b_i)} &= \delta_{A,B} + {{\sum}_{i=1}}^B \frac{1}{x-b_i} \left[{{\prod}_{j=1}}^A (b_i-a_j)\right]\left[{{\prod}_{\substack{j\neq i\\1}}}^B \frac{1}{b_i-b_j}\right].
$$

For the case $B\geq A$.

I'm interested also in the case where a part of the $x-b_i$ have power $2$

So I've been looking at that case, and it appears this just spawns more terms, and an additional summation within each term

Now I'm considering the complicated case where I admit that it would be nice to have some verification,

So I got something like this for the extra terms:
$$
\sum_{i=1}^{C} \frac1{x-c_i} \left[\prod_{j=1, j\neq i}^{C} \frac1{c_{ij}^2\right]\left[\prod_{j=1}^{B}\frac1{c_i-b_j}\right}\left[-\sum_1^B \frac1{c_i-b_j} + \sum_{1}^C \frac{2(-1)^j}{c_{ij}}\right]
$$

For the case without numerators, though this one is pretty much subject to changes of the poles

So I'm treating the denominators as the part that matters

Is there any reference for this stuff?

3 hours later…