@RyanUnger indeed.

Balarka are you interested in Number theory?

yo

I'm new to ODEs

I'm learning them on my own for some research I'm doing.

I've got this equation

$$x' + c x^a = d$$

this is a nonlinear ODE right?

Is there a name for this type of equation?

Abel equation I think

@Lozansky super, i'll check it out

thanks!

@RTn Sure but I don't know much

I think that one is actually called a Chini equation? A generalization of Abel equations.

Though don't take my word for it. I'm not sure.

What's everyones wood cutting level?

I have cut down thin pine trees with a hacksaw when I was a kid. Beyond that, fairly low.

What's my math level?

@Rithaniel hmmm...

It looks like that one involves another term that's dependent on the independent variable

Ah, so what you have is a special case. The same one as in that question, even.

well no, mine doesn't have the $a(t)$ term

but yes

for the rest

i mean, i guess if a(t) is constant

then it's the same

I am looking for anyone who is well versed in solving Pell's equations of the form X^2-DY^2=C by using automorphisms

what is going on?

Yeah, just looking at the answer mathphysicist provides, just set $f(t)=-c$

automorphisms of $\Bbb Q(\sqrt{D})$ ?

I am the 🐐

how many sylow $3$ subgroups of $G$ with $|G|=36$?...$4$?

At using the Socratic method

@igjognummeg Kind of

what do you mean? lol

why has my life become a constant futile search for a lighter that has any fluid left in it

@ÍgjøgnumMeg depressed much?

Sad

THe principle of existence "Life sucks and then you die!"

@ÍgjøgnumMeg I can lend you one virtually

@Balarka pls

Dont be sad.. It is all a part of life

chat.stackexchange.com/users/103383

I am a mix of order and Randomness. WHAT AM I

Sheogorath

George, you are George

gar fatche vai

That's why I always keep matchsticks with me. Old school.

@BalarkaSen Do you know about automorphisms and Pell's equations

Nope

I actually didn't know you smoked, ÍgjøgnumMeg

I am change !!!!

I'm a hot mess

@Ultradark -_-

Anyone here? Need help with automorphisms and Pell's equations

how many of you smoke here?

Automorphisms of what?

All change is a mix of order and Randomness!!

@ÍgjøgnumMeg Go sit in an icebath.. you will be a cold mess

lol

@ÍgjøgnumMeg I am talking about this: math.stackexchange.com/questions/1719280/…

balarka, how many sylow 3 subgroups of group of order 36. 4?

That means I am also related to calculus

1 or 4, @SubhasisBiswas

Just use Sylow's first theorem

ahem

Subhasis: I have one word for you and Barlaka : JSR

@SubhasisBiswas: I have one word for you and Barlaka : JSR

How do I invite an user to chat here? It is pretty confusing

java specification requirements?

No..

tui o bangali?

It is more political.. famous in your state

:-D

@RTn so you mean automorphisms of quadratic forms

@ÍgjøgnumMeg yes sir

@BalarkaSen what are some theorems regarding normality of a subgroup

That's a very broad question lmao

in this particular context

Is know ledge infinite

@SubhasisBiswas @BalarkaSen ki hocche

e.g. if a p-Sylow subgroup is unique then it is normal

@BalarkaSen wish I could crack a "that's what she said" joke...

@ÍgjøgnumMeg ummmmmmmmm.........................................

@RTn bal chera hocche. Ek haat boro boro bal

@SubhasisBiswas ?

Leave no leaf unturned. Leave no pebble not skipped

@SubhasisBiswas Joi Shri Ram

@ÍgjøgnumMeg don't worry. That's a prayer.

Any subgroup of order N is normal if it's unique of that order.

@Rithaniel that's a very good one

i will try to prove it.

@RTn facebook.com/subhasis.biswas.944 add me

I am going to be the second PhD out of all my 15 cousins

@SubhasisBiswas I dont have facebook

@RTn nerd alert

@Ultradark Good for you, but your phd is just a degree, remember that

@RTn that's a very good point

Go on

@SubhasisBiswas kid, I have better work to do than to see gossip on facebook

@Ultradark Which is your dissertation topic?

lmao

@RTn actually I have only one friend there. I added him from this site too. So we are on the same boat kind of

@Rithaniel what do I need to know first to prove this?

@SubhasisBiswas so you are preparing for your phd exam?

phd entrance I meant

Can anyone here guide me how to invite a user to chat?

@RTn No. Masters. Getting my basics solid. Still I am not confident. Apparently talentlessness is killing me

conjugation of a group by an element in that group is an automorphism of the group and isomorphisms preserve subgroup structure.

@SubhasisBiswas Jadavpur?

@RTn Symplectic geometry and lagrangian submanifoldz

@ultradark I have no clue what that is.. but i think you will have no clue in my domain and my dissertation.. I wish I had the time to do a phd in mathematics :-(

@Rithaniel I have done this very sort of thing with $a$ where $a$ is the only element of order $m$

@RTn what is your specialization ?

@RTn what is your domain of knowledge

Ah yeah, I recall a question like that.

@Rithaniel wonderful question it was.

it has to be an abelian group (i think) to be an automorphism

@RTn dhur. Durgapur Govt college. puro baler

Am an electronics engineer dissertation about ultra low power frequency synthesizers for duty cycled IoT radios

But I am trying to learn math in my spare time

For conjugation to be an automorphism?

@Ultradark As I said, what is important is what you do with your PhD. We can be just the run of the mill PhD or try to break new ground. It is hard to break out, but at the end we can say we at least tried, if not successful.

@Rithaniel no. that's not required.

Okay, then I don't follow what you're saying.

Define $\phi(x) =x^m$

show that phi is an automorphism

where the group is abelian

another question I recall. If $a$ is the only element of order $m$, then $a\in Z(G)$.

@SubhasisBiswas Rithaniel is saying for $h\in G$ consider the function $\varphi_h:G\to G$, $g\mapsto hgh^{-1}$.

@RyanUnger Yes. I know that

He claims this is an automorphism

Which it is, always

@RTn my PhD will build the foundations for the work I really want to do

@RyanUnger @Ultradark can you guys help me with the automorphisms of quadratic forms

sorry no

@Ultradark very good

@RyanUnger, I was thinking about the question I last sent. That proof is also along the line of conjugation.

is this a different question

@Ultradark you work at the uni maryland?

No I thought about attending though

@RyanUnger okay. If $a$ is an unique element of order $m$, then $a \in Z(G)$. So, $a$ commutes with every element of $G$. And $a, a^2, ..., a^m \in Z(G)$. All of them commute with each $g \in G$. So, the subgroup of order $m$ generated by $a$ must be normal

@RTn Brian swingle is at U Maryland. Heard of him?

I don't know if that's correct

@Ultradark no sorry.. I studied in europe.

@RTn, where did you study?

where do you live anyway

@SubhasisBiswas Switzerland

@SubhasisBiswas If $a$ does not commute with $h$, then $\varphi_h(a)\ne a$ and also has order $|a|$.

@RyanUnger I was talking about a different question (which is actually a follow up). If there is an unique element of order $m$ in a group $G$, then $G$ has at least one normal subgroup of order $m$.

@RyanUnger yes, due to associative property

Sure $\langle a\rangle$ has order $m$ and is central, hence normal

conjugate of an element $a$ by some other element also has the same order as $a$.

@Ultradark are you good at Pell's equations? I have a few doubts and want to get it solved..

@RyanUnger is my proof correct?

Looks so

@RTn bishaaaaaaaaaaaaaal borolok to :P

@RTn , don't you miss your country?

@SubhasisBiswas I am not bengali.. ami bola na..

wtf mate.

this is very confusing

@SubhasisBiswas I need not be bengali to know certain things

how come do you even know these "certain things" :p

what makes you interested in this

@SubhasisBiswas curiosity..

:O

so what kind of equation is it?

One question; so it's pretty obvious that 0 is an essential singularity of $e^\frac{1}{z}$. But , how do I know that 0 is also an essential singualirity of e.g. $\frac{e^\frac{1}{z}-1}{z-1}$. I've been told it's pretty trivial.

a vector field $F$ on $T^2$ flows across $T^2.$ I'm fairly interested in perturbing $F$ so that I can achieve different directional flows on $T^2$ and analyze properties of groups of these flows on higher dimensional tori. Specifically I want to decompose $F$ into two flows $\Phi$ and $M$ and vary a velocity parameter so that these different flows can be properly analyzed

Hey!! The inequality $-|x|\leq x\le |x|$ is correct, isn't it?

$F_{\Phi}+F_M=F_{net}$

and stability analysis on $F_{net}$ would be cool too

@MaryStar looks okay to me, what are you using it for?

I am trying to show an inequality and I want to apply this inequality. @Ultradark

Nice @MaryStar good luck with that inequality

Thank you!! :-) @Ultradark

Are there two different real sets with the same number of elements, the same standard deviation and the same mean?

I cannot find such sets, could you?

If I had to write a paper I would write it on: Piecewise isomorphic flows and holographic code perturbations of simplicial structures and their adjoint relation to manifold approximations of positive gaussian curvature

and then I would not publish it

o/

@Danu is your profile profile picture related to homotopy theory?

@Ultradark It's the hopf fibration, it's a picture of a generator of $\pi_3 S^2$

oh yeah duh, lol I didn't expand the image

fibrations are pretty cool not gonna lie. question: I'm not sure I unerstand the fibration of

keplers curve

longitudinal fibration