Mathematics - 2021-09-22 (page 2 of 2)

Gyromagnetic

19:03

Hi!

I need to solve a rather complicated integral... and Im curious if its ok to just post a question about it in the stack exchange

or will people get salty?

leslie townes

people are more likely to get salty when one asks for something to be solved without saying anything about what they've tried or not tried. it's sometimes also helpful to provide context about where it's coming from, for example, so a person doesn't give an answer using methods that you don't 'have access to' in a classroom setting.

if there's some obvious thing to try that doesn't work, it's sometimes helpful to point that out too, so you don't get junk comments/answers from people who haven't thought all the way through

Xander Henderson

@Gyromagnetic I'll get peppery.

copper.hat

i will get salty anyway.

Xander Henderson

@copper.hat You were born salty, near as I can tell.

copper.hat

@XanderHenderson definitely :-). i mean its like 70f here. i'm dying in the heat.

Xander Henderson

19:17

List of copper salts

Copper is a chemical element with the symbol Cu (from Latin: cuprum) and the atomic number of 29. It is easily recognisable, due to its distinct red-orange color. Copper also has a range of different organic and inorganic salts, having varying oxidation states ranging from (0,I) to (III). These salts (mostly the (II) salts) are often blue to green in color, rather than the orange color copper is known for. Despite being considered a semi-noble metal, copper is one of the most common salt-forming transition metals, along with iron. == Copper(0,I) salts == == Copper(I) salts == == Coppe...

copper.hat

@XanderHenderson my family used to call me tin hat (so the aliens could notread my mind) and i pointed out that copper is a better conductor, hence the name.

english is so not continuous.

Ted Shifrin

@copper.hat 90's here. East Bay is frequently in the 70's!

copper.hat

a lot of old buildings had copper roofs which turned a nice colour.

@TedShifrin i'm just kidding, i was expecting Xander to reply with something like 100 or more

Ted Shifrin

I'm getting tired of these epsilonic edits after 8+ years. Here is the latest. For an "s" this comes to the front page. growls in @Xander's direction.

copper.hat

my daughter is in LA at the moment. not exactly sure what she is up to.

Ted Shifrin

19:23

Lots of great food in LA?

copper.hat

i believe my son is in santa cruz, but the last confirmed sighting was last friday.

i suspect my daughter is indulging in boba & the like.

Ted Shifrin

Let him enjoy his college experience. Geez.

leslie townes

90s here also. good day for boba.

Ted Shifrin

Well, that wasn't what I had in mind for great food.

copper.hat

i know. i am just concerned.

Xander Henderson

19:24

@copper.hat It is fall here, more or less. It is 74°F outside of my office.

copper.hat

she has my credit card, i told her to use it.

Ted Shifrin

I guess boyfriends murdering longtime girlfriends are making everyone nervous if a child or relative falls out of touch for an hour.

Xander Henderson

82°F at home.

copper.hat

@XanderHenderson that is pleasant. my last AZ visit was something like 110+

Ted Shifrin

I think @Xander is up in elevation.

Xander Henderson

19:25

@copper.hat It almost never gets quite that hot here. I think we topped out at 107°F this summer.

copper.hat

@TedShifrin i'm not worried about him in that regard, 6'3", black belt

Xander Henderson

By my office is at 5700 ft.

Ted Shifrin

@copper.hat I'd be afraid of him.

copper.hat

@XanderHenderson i like the heat when i am doing nothing. i went for a run a while ago and the heat kills me. i like altitude.

he's a gentle guy.

quite unlike his father

Ted Shifrin

@copper.hat You like altitude or, rather, attitude?

copper.hat

19:27

both :-).

Xander Henderson

The altitude is nice. I went hiking this weekend. The weather at 8k+ ft was wonderful (despite the rain).

Ted Shifrin

I miss being able to do a little hiking :(

Gyromagnetic

0

Q: Trouble with a complicated integral

I am a physicist trying to calculate the lineshape $f_2(\nu)$ for the oscillations given in a new dark matter model; the entire problem at the end can be reduced to calculating a convolution, $f_2(\nu) = \int_{-\infty}^{+\infty} f_1(\phi)f_1(\nu + \phi)d\phi$, where $f_1(\nu) = \alpha e^{-\beta \...

let the salt flow

copper.hat

its been a few years since i was above 10k' (outside of an aircraft) :-(

yup, my hip precludes hiking unfortunately.

Gyromagnetic

@xan

Ted Shifrin

19:28

Yup, my back/hips too at this stage.

Gyromagnetic

@XanderHenderson pepper's also good

Ted Shifrin

@Gyromagnetic Well, my guess is that there's no elementary expression. But the problem doesn't make sense. You have $\phi$ ranging over all $\Bbb R$, so square roots won't be defined and integrals won't even converge. Care to revise?

copper.hat

i generally don't bother with new questions any more.

Ted Shifrin

LOL

copper.hat

too much work chasing elaboration

Ted Shifrin

19:30

how 'bout ones 8 years old where an "s" has been added to the text?

copper.hat

:-)

leslie townes

at least it appears he's editing his own answer. for some reason that makes it less obnoxious to me.

maybe he has a job interview on friday and he's getting everything on the web just right

Ted Shifrin

@leslie I agree that I occasionally go back to an old answer and try to improve it, but generally I try to improve the exposition or mathematics if I'm going to disturb it.

leslie townes

he may not be aware that a one-character edit bumps the answer. if you filter what you look at by topic or other things you may miss how often it happens on the main page.

Ted Shifrin

Yeah, that's true.

leslie townes

19:35

i don't know why i'm playing public defender here. the power washers are on their lunch break. i should be productive.

this reminds me i should edit my linkedin profile to remove my essay about how hollywood is run by the CIA. it didn't get me any likes. the truth hurts i guess.

Ted Shifrin

You can add an essay about how a certain group of politicians is about to make the whole country and economy implode. In addition to my usual complaints.

Gyromagnetic

@TedShifrin would it be different if phi was only positive :)? might've screwed up, in principle because of physics-related arguments one can say that phi cant be negative

Ted Shifrin

Yeah, if $\phi$ is positive (or is bounded below), then the integral converges. But, regardless, I highly doubt an explicit antiderivative can be calculated. And I don't offhand see any obvious complex analysis approach to it.

But, more seriously, you need $\phi\ge\delta$ for the square roots to make sense.

leslie townes

if the economy implodes i may move some of my lesliecoin holdings into the stock market. but for now, lesliecoin is the way to go.

Ted Shifrin

I should have bought $10 of lesliecoin.

o.9

19:43

I lost all of my non-lesliecoin holdings

should I be concerned?

or is leslie coin headed to the moon?

Xander Henderson

@TedShifrin A decade ago, I had a student tell me that I should invest in bitcoin (this particular student had some integer > 1 number of bitcoins). I said "that looks like a speculative bubble and/or scam" (when 1 bitcoin was on the order of $50).

o.9

you were right tho

Xander Henderson

I'm still waiting for it to collapse completely.

o.9

kappa

Gyromagnetic

@TedShifrin alright, yeah... I can see this now. Thanks a lot, you really helped me :) hahaha

o.9

19:47

is lesliecoin an eco friendly coin?

leslie townes

yes. transactions on the lesliecoin block chain are actually powered by carbon capture technology.

the more you buy, the healthier everybody gets.

Ted Shifrin

19:59

Especially leslie.

3

leslie townes

20:16

math.stackexchange.com/questions/4257615/… seems hopeless, note that n is apparently very large. i wonder what the motivation is.

just looking for roots of a high degree polynomial, looks like. i wonder if the a_i are 'choice.'

Xander Henderson

20:33

@leslietownes Oh, I saw that question a few minutes ago. I think I had a very similar reaction to yours.

Mohcine

please, Let P=Dt Q+I with Q=(q_{ji}) is generator matrix, I is an in finite dimensional identity matrix, and $P=(p_{ji})$. I would like to show that P is positive matrix, which means all the entries of P are nonnegative. given that $(1+q_{ii}Dt)>0$ and all the elements $q_{ii}$ are finite. but I m stuck here $p_{ji}=\Delta tq_{ji}+1$

Mohcine

21:05

$p_{ji}=\Delta t\,q_{ji}+\delta_{ji}=\begin{cases} \Delta t\, q_{ii}+1>0 & j=i\\ \Delta t\,q_{ji} & j\neq i\end{cases}$

Ted Shifrin

22:02

@Mohcine What does "generator matrix" mean? Obviously, you need all the entries of $Q$ to be nonnegative if that's what you mean by positive matrix. For small enough $\Delta t$, it will be positive in other ways, but you need to know your own definitions.

Rithaniel

22:31

So, I'm grading other graduate students this semester, but some of the attempted arguments I'm seeing are so nonsensical that I'm bewildered. I had someone try to say that $(AB)^T=B^TA^T$ because their domains and codomains matched

No other reason given

It's making me wish that I had hair so that I could pull it out

Semiclassical

I’d suggest substituting grass for hair but the grounds workers probably wouldn’t like that

Ted Shifrin

Is that something that really requires a proof at the graduate level? What course is this?

Rithaniel

It's linear algebra (a breadth course, so all grad students end up taking it or a similar course, regardless of focus), and I've seen the same question in undergraduate classes, yeah

Ted Shifrin

But a graduate-level linear algebra that is not at an advanced level? Interesting.

Rithaniel

I'd agree with you. It should be a trivial problem

Ted Shifrin

22:41

My favorite proof is to use Ted's favorite formula $x\cdot Ay = A^\top x\cdot y$.

Rithaniel

There's also a mix of different problems on the homeworks. Some are "so easy that they should be free" and some are more complicated

Ted Shifrin

That's really the "right" definition of transpose, anyhow. Especially if you're going to work in infinite dimensions.

It's always difficult for students in such a situation to know what is "obvious" and what "needs proof."

Rithaniel

Yeah, that's the definition they're supposed to use. Most students are just making the mistake of treating the transpose as if they transformation were a matrix

Ted Shifrin

Ah, so they aren't allowed to switch rows and columns? So this might be in an infinite-dimensional inner product space?

Rithaniel

Yep, that's the thing, but it's still easy. All you gotta do is manipulate the inner product

Ted Shifrin

22:44

Yes, of course I know.

Rithaniel

(I know you know, you're Ted)

Ted Shifrin

But I'm just wondering if the professor made it clear what was expected and what was not allowed.

Rithaniel

Well, I'm not auditing the class, so I can't say for sure

Ted Shifrin

It would be nice if the homework assignment made such things clear. Oh well. I always had issues with this teaching proof-y courses. What can we assume in homework or on an exam, what can we not assume?

Obviously, if I ask you to regurgitate a proof of something in the book or done in class, you can't just say, "It's in the book" or "we did this in class." But if it's a different result, then it's fair game to use what we've proved in class. Pretty subtle, actually.

Rithaniel

Yeah, I get that. I tend to go a little bit overboard when I write proofs, myself, to avoid getting caught on that. But now that I'm grading, when I see a proof that goes a little overboard, there's a voice at the back of my brain saying "Oh no . . ."

Ted Shifrin

22:49

LOL ...

leslie townes

23:06

far better to just use the fact without proof than offer 'domains and codomains match' as an 'explanation', imvho.

if you're gonna go overboard, style it out with confidence and do not offer explanations. don't make me question whether the understanding is all a house of cards

love_sodam

23:27

@Thorgott Why it factor through $(U-B,U-B)$? how about the inclusion map $(U,U-B)\to (U,U-y)$?

Thorgott

read what I said again

love_sodam

ah you're talking about the map $(U,U-y)\to (U,U-B)$ hmm..

Thorgott

not "the", any map

love_sodam

yes any map

Same argument shows $(M,M-B)$ and $(M,M-y)$ are not homotopy equivalent?

Thorgott

23:52

yes

if you're dealing with pairs, it is very often the case that you have inclusions inducing isomorphisms on homology that are not homotopy equivalences

love_sodam

But $U-y$ and $U-B$ are homotopy equivalent isn't it?

Derivative

Which integers m do you think can be written as m = s(n)
for some n? (In mathematical language, when is m in the range of the function
s?)If m is in the range of s,how many different n have m = s(n)?Is the number
finite or infinite?

(From Stopple analytic number theory)

$s(n)$ is the sum of the proper divisors of n

Is this just me or this question is insanely hard? I have that the image is infinite, but nothing else

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