12:03 AM
Hi

1 hour later…
1:26 AM
@schn: Of course you're right that there's an error there. Stop trusting answers in books!

1:42 AM
@TedShifrin It’s quite an error!
@TedShifrin thanks for checking though

2:01 AM
If $H$ and $N$ are subgroups which intersect trivially and $N$ is normal, can you say anything about $H$?

the map H -> G/N is injective but not sure what else you'd be looking for

yeah so H is (isomorphic to) a subgroup of G/N

I'm trying to prove there are no simple groups of order 90. I've shown that, if there does exist such a group, then it is isomorphic to a subgroup of $S_6$ and that it's intersection with $A_6$ is either itself or the trivial group. I'm trying to rule out the possibility that the intersection is trivial and arrive at the fact that the group would be a subgroup of $A_6$. Then I can show that $A_6$ has no subgroup of order 90 and I'm good.
I think showing $H\rightarrow G/N$ will work, though, because that gives an injective map to the cyclic group of two elements.

2:25 AM
An isomorphism means a bijection right? So the function needs to be both an injection or surjection
After spending an hour drawing on python ... I am back to math stuffs. It was the snowman's right arm. I'll do the left one later

Yeah, isomorphism implies bijection. However, bijection does not imply isomorphism.

I'm just trying to prove uncountable linear orders are not isomorphic
I think it is true since if a linear order is uncountable then there are many elements that may not be uniquely mapped. All it takes is either injection or surjection to fail
And its easier to do the injection fails part... But it seems that I can't write it in a more abstract tone :(

2 hours later…
4:57 AM
@YOUSEFY The Gödel sentence is pretty much built to be unprovable, the author is just wondering whether there are many naturally arising statements of mathematical interest which are also true but unprovable

5:21 AM
Quadratically-constrained quadratic programs (QCQPs) $\subset$ second-order cone programs (SOCPs) $\subset$ semidefinite programs (SDPs), right?

1 hour later…
6:35 AM
I've got a question about Fourier Series (in complex space). If I want to approximate a periodic function, does that function need to contain its own center of mass?
I know that with real-valued Fourier Series the endpoints of one period need to be equal to the average value of the function along that period. So if I want to do a Fourier transform on f(x) where x is on [0,L], then f(0)=f(L)="average value of f on [0,L]"
So does this mean that a periodic function through complex space needs to intersect its own center of mass in order for it to be able to undergo a Fourier transform?

@AlessandroCodenotti Thank you
I have a question: Suppose given you sum and product of two integer positive numbers a and b greater than one. Now, can you know a and b? The answer is given here:
https://math.stackexchange.com/questions/171407/finding-two-numbers-given-their-sum-and-their-product
But, now suppose the a and b are positive real numbers, does this make difference?

2 hours later…
8:41 AM
0

Vector of differences. Suppose $x$ is an $n$ -vector. The associated vector of differences is the $(n-1)$ -vector $d$ given by $d=\left(x_{2}-x_{1}, x_{3}-x_{2}, \ldots, x_{n}-x_{n-1}\right) .$ Express $d$ in terms of $x$ using vector operations $(e . g .,$ slicing notation, sum, difference, line...

9:28 AM
anybody knows about hamiltonian graphs ?
ok , so i learned that " the line graph of euler graph is hamiltonian "
does this argument also folows "that line graph of hamiltonian is euler "
hello ?

10:05 AM
Hi. Fix $n\in\mathbb{N}$ and let $A\subseteq \{1,\dots,n\}$ be a random set. Is it true that $E\left[\frac{1}{|A|}\sum_{i\in A}|X_i| \Bigg| |A| > 0\right] \leq \max_{i=1,\dots,n} E\left[|X_i| \Bigg| i\in A \right]$ if $A$ and $X_i$ are dependent? If $A$ were fixed, the answer would be yes, but now I can't see it.

10:55 AM
@Mathein went to the first ant lecture, it was only elementary nt
lol

2 hours later…
12:58 PM
Shameless "check-my-result"
Does this look fine?
I couldn't find a nice reference for these kinds of things...

1:13 PM
Nver mind, I don't think it makes sense

1:48 PM
hi guys!
is anyone here? :)

2:37 PM
No. see this example in this site "https://math.stackexchange.com/questions/2519390/if-the-graph-g-has-an-eulerian-circuit-prove-that-its-line-graph-has-a-hamilt"
The idea is that if you have a counterexample that shows that a hamiltonian G doesn't correspond to Eulerian graph in line graph G', or NOT-hamiltonian G doesn't correspond to NOT-Eulerian graph in line graph G', then you just prove that the converse doesn't follow.

2:56 PM
Given n and h, where n = a * b and h is the following equation: h is congruent to ca + rb mod n, where c and r are positive integer and a and b are PRIMES. Now, Is there any way to find a and b, given n and h?
suppose for example: n=6 and h is congruent to 10a + 20b mod 6, then how can you find a and b? I don't want to factor 6

3:17 PM
Hello
Hey can anyone tell me the difference between the first and the second principle of finite induction?
Is there anyone online who's not asleep?

I wish i knew :D

Hmmm

Could you help with my question?

I apologize for being off topic but can anyone see my dp bcoz it appears broken to me
Cap7 let me have a look at the question

and thank you!
I have no clue on how to solve that

3:28 PM
I can understand that the X has a value between the given range I'm not sure how the result is formulated.
But still I may try to make some guesses and hope it may be helpful.

neither do I

It seems that you want to continue this series, is it so?

yes

If yes then I can give you some kind of idea
Ok
Are you sure you want the successive range of X and the corresponding result?

what do you mean?

3:37 PM
Like continue the table.
Do you want me to continue the table?
Hey Cap7 are you there?

there is no need for that
if x = 32 i just need to know how the result is 3 for example

so far i've failed

It seems like this is not definite function or formula to find the result for any value of X. It just seems to follow a pattern.
Yes
There can't be
I'm pretty sure

yeah, you are right
but there must be a way to express the pattern

3:43 PM
Hey by the way can you see my dp or it it appears like a broken file?

broken file

Oh
Nevertheless I can give you a continuation of the pattern.

okay..

Here you go
I tried to express it in the most mathematical way I could
Do upvote it ^_^

okay
thank you

3:59 PM
Hey do you study in school or in university/college?

no, not really
i'm stuck at work with this problem

Ok bye ◉‿◉

Bye

4:14 PM
Cap7 You know calculus
?

4:28 PM
Is this correct?
I guess it holds only for N>1

Which chapter is it from?

It's from chapter 1010011010

Good, it makes sense.

I'm on the fence about the second factor, one moment...

Jokes aside, just tell me..

4:41 PM
No I really just conjectured this, though it is an educated guess

5:16 PM
Hello
someone help me
how to study this sequence
$\prod_{m=1}^n \cos(m x)$

5:48 PM
0

There is a commutative ring $R$ with $1$ the elements of which correspond one-to-one with the context-free grammars of a single string $s \in \Sigma^*$. In $R$, $+$ is symmetric difference and $\cdot$ is intersection. If you look at a CF grammar, say $g = \{S \to AAA, A \to aa\}$, for a string ...

@Ultradark I'm looking ath the SGP from a ring-theoretical persepective

2 hours later…
7:30 PM
-1

How can I solve the functional equation to find all involutions whose reciprocals are non trivial involutions? I think this functional equation can be expressed as: $$f(x)=\frac{1}{f(x)},$$ with the conditions that $f(f(x))=x$ and $\frac{1}{f(f(x))}=\frac{1}{x}.$ $f(x)=\frac{1}{x}$ does not ...

2 hours later…
9:07 PM
hey guys
how do we know that each unitary representation is equivalent to $\phi\colon G\to U_n(\mathbb C)$?
I'm confused, because say we have a unitary representation $\rho$, then all we know it's unitary w.r.t. some specific inner product
I don't see how that would translate to the standard inner product if we consider matrix representations

9:36 PM
@ShaVuklia we can always choose an orthonormal basis for a vector space with a specified inner product
by applying the Gram-Schmidt algorithm to any basis

10:10 PM
Are Pure-Tine ODEs the only first order ODEs where the arbitrary constant can appear as its own term?
Or is there some $y' = f(x, y)$ where $y$ appears explicitly and the solution is $y = g(x) + C$?

@user10478 pure-tine -> pure-time?

yeah

@user10478: For starters, how many times can you solve $y'=f(x,y)$ and get an explicit solution $y=g(x)$ rather than an implicit solution $g(x,y)=c$?
I don't know who time is here. Are you thinking of $x$ as time? And by "pure-time" you mean that $f(x,y) = f(x)$?

Sure, by pure-time ODE I just meant an ODE where $y$ doesn't appear except as $y'$.

Pure-time apparently means (for first-order odes) y’=f(x)

10:21 PM
So if you expect precisely an additive constant of integration as you wrote, then I would expect you're right, but I've never thought about this before.
I guess it's clear. If the $+C$ appears additively, then we know that $y'$ MUST depend just on $x$ (differentiate your expression).

To say that another way: you’d need need g’(x)=f(x,g(x)+C) for all C
But it seems like the only way for that to be true is if f(x,y) doesn’t depend on y in the first place

It seems?
Since $C$ is arbitrary, $f(x,y) = f(x,0)$ depends only on $x$.

yeah, that settles it

Hmm, I'm not sure if I understand that argument of differentiating. If the solution was instead $y = Cg(x)$, it would differentiate to $y' = Cg'(x)$, but there are ODEs where $y$ appears explicitly with the solution $y = Cg(x)$, i.e., $y' = y$.

No, you start with the solution $y=g(x)+C$. Differentiate that!!
That was the point I made ages ago.

10:28 PM
Sure, I get $y' = g'(x)$

So?

I'm just not seeing how this shows that there are no other ODEs with explicit $y$ and the solution $y = g(x) + C$

Is the question : why doesn’t that same argument apply to y=Cg(x)?

That's where my analogy of $y = Cg(x)$ comes in.
Yeah

In that instance, you’d need C g’(x) = f(x, C g(x))
But now both sides depend on C, so that argument can’t apply as before

10:32 PM
Because we showed that if $y=g(x)+C$ is the general solution, then $y'$ depends only on $x$.
Trying to eliminate all other function types will never work :P

The point is that differentiation eliminates the C dependence of y=g(x)+C but not the C dependence of y=Cg(x)
So the analogy doesn’t hold up

10:46 PM
Hmm, I'm still not quite sure what the differentiation shows. The same general solution can belong to more than one ODE, can't it?

How does one find $g(t)$?

Like, if I tell you my bank account balance as a function of time, there are an infinite number of ways you could separate that between interest as a function of time and deposits as a function of time, correct?
You couldn't give me back the ODE accurately describing my interest (coefficient of the dependent variable) and deposits (forcing term) just from the balance as a function of time, I believe.