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12:26 AM
@vzn nvm lol. dumb comment on my part.
 
12:38 AM
!!
If u have two points on a straight line(with known equation)
can we obtain the points in between those two points which lies on the straight line
I thought of taking convex combinations but that will include points other than the straight line too
 
@BAYMAX Are you talking about the perpendicular bisector?
 
no actually
 
oh on the straight line...
 
we have a straight line and we know its equation
and we have two points on it like two different points on the straight lines(we know them too)
Now I am trying to find the points on the straightline between those two points
 
@Baymax: Convex linear combinations won't include points off the line!!
If I take $tx+(1-t)y$, as $t$ varies, I get the line through $x$ and $y$. When $t\in [0,1]$, I get the line segment.
 
12:45 AM
suppose we have straight line $y = x + 1$
 
I meant vectors $x$ and $y$, of course.
 
and now we have two points on the straight line $(2,3)$ and $(4,5)$
say
now if I take the convex combination
that is $(2t + (1-t)4 , 3t + (1-t)5)$
will include all the points on the straight line $y = x+1$ in between the points $(2,3)$ and $4,5$
 
I think it's easier to think about vectors
 
is that correct?
 
Read what I wrote above.
 
12:48 AM
yup
I wan tthe points in between two points
 
So read what I said (again!).
 
yes I got it that if we treat them as vectors it is nice to see that convex combination would include every point in between two points
 
Read the second sentence?
To get the line segment joining $x$ and $y$ ....
 
yes i have t overy $t$ in between $[0,1]$
*to vary
 
OK ... so then that's it.
 
12:53 AM
I am trying to code this, I want the points actually
 
I don't understand what that means.
 
6 mins ago, by BAYMAX
that is $(2t + (1-t)4 , 3t + (1-t)5)$
i am thinking why this is not working
 
@BAYMAX: Those are the points. Introduce a variable t, introduce a step size and multiply it by the pt1 and pt2 (a la Ted's equation)
 
for $t \in [0,1]$
 
this will give you "approximately" all the points in the system...
 
12:54 AM
And how exactly is it not working?
 
ya that works!!
 
i'm probably being way too informal with "approximately" but i'm too lazy to adjust it.
 
Well, that was a waste of time :D
 
let me try that now!! thanks!!
 
LOL
 
12:56 AM
@TedShifrin which1
 
Por que no los dos?
 
All this ... since you were convinced it was wrong and it was right all along.
 
atleast it is was math!
nothing would be a waste of time till it is a math discussion!
here
 
believe in yourself.
ugh, i'm going through a circuit book and all the equations have the messiest numbers.
 
Numbers are just numbers if you're using a calculator or computer.
 
1:03 AM
i could just whip at a calculator, but using a calculator feels so wrong.
 
Nah.
Even I am not so ridiculous as to say that.
 
I need to bring my TI-89.
My phone runs out of battery and I don't like having the computer in front of me lol.
 
Or you need an auxiliary battery to plug your phone into ... those things come in handy.
 
@TedShifrin I'm considering that, I have been preparing for extended periods w/o internet connection.
but i wouldn't use it for just the phone... But also the computer too.
I think it would be cool if I could go out door climbing and then like bring my computer/tablets and work on math/CS outdoors. At least try it once.
I got an app to download documentation for programming languages for offline use and math books are self contained usually.
 
i use google as calculator
hehe
 
1:07 AM
regardless, i've been trying to use StackOverflow less because some of the answers are questionable and I've been trying to force myself to just use the reference material.
 
Dair, for once be an un-nerd and go appreciate nature for nature :P
 
@TedShifrin Don't worry, I do this, although I climb far more often indoors. :P
 
And I presume you're not referring just to "climbing the walls."
 
hehe..@Dair you do coding?
 
wait lol, I was referring to climbing walls... what did you think I was referring to?
@BAYMAX Like every day lol.
 
1:14 AM
I meant the phrase "climbing the walls," not the actual physical climbing, Dair.
 
ohh like which programming language?
 
@TedShifrin Ohhh I literally meant climbing, like up walls.
@BAYMAX I have most experience with Python, but I am currently doing a decent amount with Rust.
 
I've never heard of Rust.
demonic @Alessandro !
 
@TedShifrin It's a fairly new language.
 
wow, really past your bedtime
 
1:17 AM
i tend to not remember programming languages well anymore tho.
I just say: This is how I wanna write it. The compiler fails and then I strangle the compiler until it complies with my vision.
 
So you put "computer strangler" on your resumé as your chief skill.
 
i tabbed in and read that first as "complete stranger"
 
I can't help it you flunked reading, Semiclassic.
 
a rare occurence when your initial reading of a phrase is -less- weird than the reality
 
@TedShifrin It's closer to "compiler strangler" but yeah... :P
It would definitely show I have a quirky personality.
 
1:24 AM
Let $U$ be a domain in $\Bbb C$ and $K$ be a compact subset, $p \in [1,\infty)$ why does there exists a constant $C_K$ such that $\|f\|_{L^\infty(K)} \leq C_K \|f\|_{L^p(U)}$ uniformly for all $f$ holomorphic on $U$?
 
@Semi @Ted i tabbed im and read it as complete strangler so i’m meeting y’all in the middle
 
I want to live in an incomplete space ... just for you guys.
 
I am now a serial killer apparently.
The Complete Strangler
 
Is this a difficult result or something obvious? I can't tell
 
The Completely Stranger
 
1:26 AM
note to self: avoid the word "strangle"
 
I haven't seen that one, @Mathein, that I recall. I'm used to similar things that hinge on the Cauchy integral formula plus compactness fiddling.
 
cya. gonna get dinner.
 
@Semiclassic: Let's all read Camus now.
Damn, the website is malfunctioning again. I keep getting failed posts and failed attempts at reposts.
 
I've never read The Stranger. there was a Camus short story we read in high school but I forget the title
 
The other famous novel is the Myth of Sisyphus.
 
1:30 AM
I only read The Pest
 
La Peste = The Plague
 
oh I see
 
"One must imagine Sisyphus happy" is the only bit of that that I know
 
LOL @Mathein's translation.
 
I knew the German and the French title, but not the English one
 
1:30 AM
I presume the German one gave a hint :P
 
yeah it's just "Die Pest" lol
 
pest = cockroach or human who is very annoying :P
 
just checked, we read "The Guest" by Camus in high school
 
oh, I don't think I know that, @Semiclassic
 
@TedShifrin I see, someone who pesters
 
1:32 AM
In the human case, yes, @Mathein
I wonder if exiting and re-entering will fix my glitch
Nope.
In the human case, yes, @Mathein
Agh.
 
the inequality I posted seems really interesting. It means that for holomorphic functions $L^p$ convergence implies compact convergence, so we get that the holomorphic $L^p$ functions are a closed subspace of $L^p$
 
So, Mathein, I think the exercise I assigned was that $f$ uniformly bounded in $L^p$ on compact subsets implies a normal family.
($f$ holomorphic of course)
 
1:48 AM
In the really nice case that $K$ is a $C^2$-submanifold manifold with boundary, then it seems one might get something with Stokes and Cauchy's integral formula, but I have no idea in general. Cauchy's integral formula gives a contour integral and the $L^p(U)$-norm a surface integral, I'm not sure how to compare that without Stokes
 
You reduce to disks and use polar coordinates, usually.
 
2:05 AM
Okay, suppose that $U=B_{r}(0)$ is an open disk around $0$ and $K=\overline{K_{s}(0)}$ is a closed disk contained in it. Take $t$ with $s < t < r$, then for any $\xi \in K$ we have for $C$ the circle around $0$ in counterclockwise rotation once with radius $t$
$$f(\xi)= \frac{1}{2\pi i}\int_{C} \frac{f(z)}{z-\xi}\mathrm{d}z=\frac{1}{2\pi i}\int_0^{2\pi}\frac{f(t e^{ix})te^{ix}}{\xi-te^{ix}}\mathrm{d}x$$

$$\|f\|_{L^p(U)}^p=\int_{x+iy \in U}|f(x+iy)|^p \mathrm{d}x \mathrm{d}y=\int_{0}^{2 \pi} \int_{0}^r |f(re^{i \varphi})|^pr \mathrm{d}r \mathrm{d}\phi$$
I don't see it
maybe this is too hard for my algebra-brain and I should post it on main
 
Pig
3:01 AM
which inequality?
 
2 hours ago, by MatheinBoulomenos
Let $U$ be a domain in $\Bbb C$ and $K$ be a compact subset, $p \in [1,\infty)$ why does there exists a constant $C_K$ such that $\|f\|_{L^\infty(K)} \leq C_K \|f\|_{L^p(U)}$ uniformly for all $f$ holomorphic on $U$?
 
sniiped
 
3:23 AM
Hey there chat
 
@Daminark hi there!
 
How's everything going?
 
pretty well, thanks
I have semester break, so it's pretty chill
and for yourself?
 
Getting closer to the end of the quarter, so final exams looming overhead is less than fun for sure
But after that I have a week off between quarters
Yo Eric
 
 
1 hour later…
5:00 AM
cool!!
@Dair
Am into MATLAB though, still will ask you questions on codes!! hehe
 
 
1 hour later…
6:07 AM
@Rithaniel Ah, thanks; I see now. Of course, this does not disprove the hypothesis that I am going crazy as I had hoped...
 
 
1 hour later…
7:35 AM
Hi all! I am doing stupid mistakes. Maybe someone can help me. I have an equation:
$$ \cot(x \pi/2)+1/(6x)=0$$
I solve it numerically and get some $x_0\approx 1.096$
Then I want to transform the equation to some nicer $k\to x\pi/2$:
$$ \cot(k)+\pi/12k=0$$
I solve that numerically and get some $k_0\approx 2.06676$
Then I want to transform that back to $x$:
$$2k_0/\pi=1.316\ne1.096=x_0$$ ???
 
8:32 AM
Please ignore it, I found the mistake (the second solution is simply wrong).
 
 
3 hours later…
11:26 AM
Hi all! Here it says, in the red part, that $\forall i,m,n=1, 2, 3$

$\delta_{i2}\delta_{m1}=0 $ and $\delta_{i3}\delta_{n1}=0 $

But for $\delta_{i2}\delta_{m1}=0 $, when plugging values $i=2$ and $m=1$, we get $\delta_{22}\delta_{11}=1.1=1 $
Similarly for $\delta_{i3}\delta_{n1}=0 $, when plugging values $i=3$ and $n=1$, we get $\delta_{33}\delta_{11}=1.1=1 $

So, $\delta_{i1}\delta_{i1}+\delta_{i2}\delta_{m1}+\delta_{i3}\delta_{n1}=\delta_{ii}+\delta_{i2}\delta_{m1}+\delta_{i3}\delta_{n1}= \delta_{11}+\delta_{22}+\delta_{33}+\delta_{22}\delta_{11}+\delta_{33}\delta_{11}=1+1+1+1+1=5 $
 
 
3 hours later…
2:41 PM
1
Q: Upper Derivatives and Chebyshev's Inequality

user193319Recall Chebyshev's Inequality: Let $f$ be a nonnegative measurable function on $E$. Then for any $\lambda > 0$, $$m \{x \in E \mid f(x) \ge \lambda \} \le \frac{1}{\lambda } \int_{E} f$$ Here is a theorem in my book: Let $f$ be an increasing function on the closed, bounded interval $[...

 
3:12 PM
99.9% of the universe we don't know what it is
$\mathfrak{c}$ many of the number universe we don't know what it is
Indescribably indescribable unknown unknown in this whole world we don't know we don't know what even it is
> Unknown: the ultimate frontier and the ultimate answer to life, the universe and everything
 
3:28 PM
This is a stupid question, but why does the standard deviation formula sometimes have n and sometimes have n-1? What’s the formula if you have the sum of variable squared?
 
 
2 hours later…
5:22 PM
Is it true that if we have measurable function $f : X \rightarrow \mathbb{C}$ Let $A \subset X$ then it is true that if we have $u(A_c) c \leq \int{ f d\mu}_{A_c}$ such that $A_c := \{ x \in A : f(x) = c\}$
 
Pig
5:49 PM
@Piomicron it should be n-1 - otherwise it's a biased estimator
 
 
2 hours later…
7:35 PM
are there patterns that can't be studied using mathematics
 
@Ultradark Empirical patterns (things that fall under the domain of science), subjective patterns (things that fall under the domain of art)
though in both cases people can use math as a tool for it
less so for art but it does happen
 
okay
What tools can one use to analyze diffraction patterns?
Fourier analysis comes to mind
 
 
1 hour later…
8:54 PM
Hi @Ted
 
hi, demonic @Alessandro
wie geht's?
 
Very well, thanks, what about you?
 
Doing fine, thanks :)
 
For an invertible $n \times n$ matrix $A$, I found a polynomial $q$ such that $q(A) = A^{-1}$, but is $q$ unique..?
 
That's a nice question, @JoeShmo.
What do you think?
 
8:57 PM
I think not
 
Have you an example?
 
because I need $\{I, A, A^2, \ldots, A^{n^2 - 1}\}$ to be linearly independent, which I think is false in general
I have not
 
oh, you don't need that, do you?
You should be able to get a polynomial of degree at most $n-1$.
 
yes
I did
 
But if $Ap(A) = I = Aq(A)$, what do we infer?
 
9:00 PM
well thats how I got to needing $\{I, A, A^2, \ldots, A^{n^2 - 1}\}$ to be linearly independent
so $A^{-1}$ is unique
 
how?
But doesn't Cayley-Hamilton tell you they can't be?
 
so now $A^{k-1} + c_{k-1}A^{k-2} + \ldots + c_1 I = A^{-1}$
where $m_A(A) = A^k + c_{k-1} A^{k-1} + \ldots + c_1 A + c_0 I = 0$
(Just pointing out where the off-by-one coefficients are coming from)
$c_0 \ne 0$..
so now $A^{k-1} + c_{k-1}A^{k-2} + \ldots + c_1 I = q(A) = A^{-1} = p(A) = b_lA^{l} + b_{l-1}A^{k-l} + \ldots + b_0 I$
 
Anyhow, your independence thing never holds.
 
I know
 
Once you know Cayley-Hamilton, you know it cannot.
 
9:06 PM
$I_{n \times n}$ is a counter example
 
So we conclude that $p(A)=q(A)$, of course, but that doesn't mean that $p(X)=q(X)$. What can we conclude, @JoeShmo?
 
precisely.. to conclude the latter is where I wanted to use linear independence, but that's false..
 
Right.
Hint: Think about $p-q$.
 
ah
minimal polynomial
would be lesser
dur
thanks @TedShifrin
 
you're most welcome
 
9:15 PM
Would be of lesser degree*, btw. I didn't English properly there.
As opposed to this ^ statement. This is proper English.
 

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