@XanderHenderson I meant like nowadays not ancient ones

But yeah Googling says it could be any kosher animal

"In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex."

That sounds annoying

yep

Concave means $-x^2$, right?

right

@Semiclassical just sing yourself to sleep at night that $x^2$ is convex and lies above its tangent lines to never forget

And convex is $x^2$

that's what i did

i hate the up down terminology

so bad

concave and convex are terrible terms

concave and convex lenses are easy to remember

functions, not so easy

For functions, yeah

For shapes they make sense

Concave things have caves

convex lenses are convex sets

@Semiclassical You can also remember that a function is convex iff its epigraph is convex

The most annoying thing is when you need to optimize a multidimensional function that's neither concave nor convex

which is kinda what machine learning is doing

i was about to say

@Semiclassical now since everyone knows ancient greek, you know that epi=above, maybe

at least I imagine that's what it means

tbh I mostly just remember epicycles

epimorphism = above morphism?

ah!

epigraph in the literature sense

it comes above the paragraph

Epigenetics

@Semiclassical there, now you can never forget.

I think epiphenomenon is also a word?

anything is a word if you get one more person to say it

Epic?

@XanderHenderson acceptable start? i.gyazo.com/632784f234a76d5d2ec53c1af26becc0.png

@EricSilva Someone a while ago was trying to popularize the word "oxt", meaning the one after the next. Like oxt week isn't next week but the week after that

Don't make the next right, make the oxt right

ugh

That sort of thing

that's awful

Completely made up but apparently he got his friends to use it

just say ubernachstes

the germans already have a word for it

sneezes

@0celo7 is it obvious that $a\leq b$ and $a\leq c$ implies $a\leq (b+c)/2$? I guess it is, since that'd lie between b and c

@Semiclassical well just set $\mu=0$ and $\nu=1$

right

There's no good symbol to express the idea that $b$ is between $a$ and $c$

besides $a<b<c$ you mean?

oh, but you don't know $a<c$

$b\in\{x\in\Bbb R:x>b\land x<c\}$

But it might be $c<b<a$

Yeah

$a\lesseqgtr b\lesseqgtr c$

you actually run into that in E&M sometimes

Oh wow that's a thing

@Semiclassical for spherical harmonic expaaaaaaaaansioooooons

\lessgtr $\lessgtr$ \lesseqgtr $\lesseqgtr$

yuuuup

Tthe hell

Is that meant for this purpose?

@AkivaWeinberger when you take a course on scattering theory you'll see.

I'll see the $\lessgtr$ symbol?

expansions in spherical harmonics get written in terms of $r_{\pm}$ as the greater/lesser of $a,b$

@AkivaWeinberger yes

@0celo7 Burninate it with fire!

I mean it kinda looks like $a\lesseqgtr b$ means that $a$ is either less than, equal to, or greater than $b$

which is always true

it makes the formulas waaay more readable

@AkivaWeinberger $i$ is either less than, equal to, or greater than $-i$? :P

@Semiclassical yes

by the well-ordering theorem

okay, good to know

"There exists a total order on $X$"

sorry

theorem

not principle

(which actually needs choice, by the way, you can't define a total order on $\mathcal P(\Bbb R)$ in ZF)

me no brain today

(With choice you can even define a well-order of course)

@AkivaWeinberger The well-order theorem is equivalent to choice

Right, I don't think the total-order theorem is though

Okay this is very simple: The axiom of choice is obviously true, the well-order theorem is clearly nonsensical bullshit, and noöne even knows what the fuck is going on with Zorn's lemma

Nice umlaut, though I still maintain that noone, noöne, and no-one are all evil corruptions of no one

that isn't a umlaut

Er, not umlaut

The other one

Dieresis

it is a dieresis

Sniped and countersniped

the net outcome is a draw :\

@Semiclassical i.gyazo.com/7c61d67721982ba0f88958eda0d69ce7.png

OK but how is the symbol used in scattering theory

Don't know what it's about but it's got a cool-looking picture

scattering theory is a hypermasculine branch of physics in which we destroy things with particles

I guess waves get all whiny when you put shit in the way

@0celo7 Shouldn't "We thus obtain" be indented?

It's part of the q>2 case specifically

Who cares about whitespace, this isn't Python

if the $1<q\le 2$ case had more than one line, it would be nonindented

hmm

Just make sure your brackets and semicolons are done right

@AkivaWeinberger I'm trying to find an example for you but I'm failing

ah

well, maybe I misremembered this

you use $r_<$ and $r_>$, but not with the thing stacked

maybe there's some formula where it's stacked

$\begin{matrix}\rm stack\\\rm all\\\rm the\\\rm things\end{matrix}$

$$\frac{\hbar^2}{2m}\langle \mathbf x|\frac{1}{E-H_0+i\epsilon}|\mathbf{x}'\rangle=-ik\sum_l\sum_m Y^m_l(\hat{\mathbf r})(Y^m_l)^*(\hat{\mathbf r}')j_l(kr_<)h_l^{(1)}(kr_>)$$

You sure you didn't mean $\neq$? Easy typo to make

Rest of it seems fine though

lol

I'm trying to find an electrostatics example that isn't too tedious

@Semiclassical I'm slightly nervous that my inequality is not what I see in the original paper or the guy's student's notes

hrm

@AkivaWeinberger Ah, here: mathworld.wolfram.com/GreensFunctionPoissonsEquation.html

equation (6)

but it's not stacked there semi

hmm, point

one rather silly approach to finding examples: scholar.google.com/…

@Semiclassical It seems that the $q2^{q-2}$ just blows it up immensely

hmm

so it's not a very effective bound?

right.

then again, the original one is $(q-1)^{q-1}$, which is worse

if $q\gtrsim 2$ then maybe it's useful

but the student writes $2^{q-2}$, no $q$ in front

lol

@Semiclassical Oh I'm establishing some bound

it's actually the $1$ in front that's important

right

you want to show that $(1+t)^q$ can't be too much bigger than 1?

it's way bigger than $1$

huh

I actually want to estimate $|x+y|^p$

the exponents work out so that I get like $x+$ other terms I don't care about

but the coefficient in front of $x$ is important

the rest go in an error term

a big error term, but hey :)

I want a shirt that says "asymmetrical" down one side

ack! No!

ouch... :(

it hurts my head just to think about such a shirt

meh, that still would have 360 degree rotation symmetry :P

what doesn't have 360 degree rotational symmetry?

yes, that's the joke

oh

like I said, me no brain today

hi

Hi @LeakyNun and @0celo7 and @Semiclassical, the blue square is back.

there is no spoon, too

Is there a known name for an "algorithm" that given a number $n$ and a factor $f$ returns $m$ where $f$ is not a factor of $m$ and $n = f^k * m$?

the algorithm would be an integer factorization algorithm. i just wanted to check if it has a name

Yeah

Else you end up writing $\phi(g)(v)$ which is of course confusing

Oh I see your confusion

"You write $\phi_g$ instead of $\phi(g)$ and you write $\phi_g(v)$ or simply $\phi_gv$ for the action of $\phi_g$ on $v \in V$"

would be a way to break it down I suppose

Oh, thank you so much. now I see what is meant there :)

@LeylaAlkan And you should type the phi as \phi in LaTeX.

Hey @Daminark, sick, LOL

@LeylaAlkan And also the belongs to set symbol as \in

@BalarkaSen I see you are still the most starred user here, LOL

Hi @TedShifrin I sense your presence with the Force.

Who are you, Gasparo?

Well, Gasparo is the Italian version of ...

I am the Librarian ...

Hey there!

Hi Demonark

That notification sound is very scary in the middle of the night, esp when you are in a completely quiet room. @Gasparo I'll copied those in the pdf text directly and didn't change them much

@Gasparo Hey mr. blue square

@LeylaAlkan Ah OK, in which case there is no need to put the dollars sign for the LaTeX anymore, lol.

@Semiclassical Sorry, but that video is not available where I am, lol.

@Gasparo I'll be careful next time

So @Semiclassical I have been taking a look at a lot of physics books recently. In particular, the relatively recently published Course in Classical Physics 1,2,3,4 by Bettini and Theoretical Physics 1,2,3,4,5,6,7 by Nolting (8,9 to be translated soon) and Course of Theoretical Physics 1,2,3,4,5,6,7,8,9,10 by Landau, LOL

good lord

there's no way you're reading all of those