when my daughter melted down at the duck pond last saturday and refused to walk i had to carry her back to the car. she's heavy enough that i can't just use my arms for that anymore. fireman's carry all the way.
i wonder if it is optimal for preventing spine damage. this is a mass transport problem.
Can anyone help explain why these people can use $L^1$ weak convergence to take limits in their integral. In short they have an integral $\int F(x) \rho_h(x) dx $, and they take the limit $h\to 0$ claiming it holds by weak $L^1$ convergence. Where $F$ is some function ( but it doesnt look like its in $L^\infty$...) Can I link the result?
i think flows is more concerned about the boundedness of the function than the convergence of the integral, but it still looks like it ought to be bounded because zeta is smooth
says the guy who has not picked up a pencil today and isn't planning to
If memory serves, ten years ago to the week (or so), I taught first semester freshman calculus for the first time. As many calculus instructors do, I decided I should ask some extra credit questions to get students to think more deeply about the material. The first one I asked was this:
1) Rec...
@Koro: Do you find it reasonable to think that there should be a function you can construct?
@Leslie: I left it to you to finish off with @Flows. Now that he understands (?) that the function is locally bounded along the diagonal in the appropriate coordinates.
No no. Jump discontinuities are at most countable but I suppose we can’t say the same for removable discontinuities because for them creating a bijection onto set of rationals may not be possible. For jump discontinuities, I can always chose a rational btw left hand limit and right hand limit and get a one one mapping to rationals
To avoid confusion: let me also state the definitions I’m using because some people use the word discontinuity of first kind also. By removable discontinuity at a point, I mean limit exists at that point but does not equal value of the function at the point
sorry @TedShifrin but the change of variable trick is only showing me that they are in $L^1(\mathbb{R}^d)$ ( if k \le d-1 ) wheres the $L^\infty $ coming from
Well, change of variables is an essential notion in lower and higher mathematics. One of the crucial technical lemmas in my Ph.D. thesis was exactly this sort of question, because I needed to know an integral converged along a set where the integrand blew up.
I understand copper’s comment now. The key is to prove/disprove whether removable discontinuities are isolated or not. If isolated then easily shown to be countable hence proving the non existence of this function. But I doubt the countability of removable discontinuities.
@TedShifrin ok ill have to think about it I guess ( just to confirm the strategy in this case you think is to change to polar coordinates then use the (already established) weak convergence of $\rho_h$, then reverse the change of variables)
Does anyone have this book? I talked to the author today and he claims that he solved a problem in which I am interested in but I am not really sure if this is the case. Also I'd only need three lines and not a whole book. (@Thorgott It is about the problem we and others here could not solve a while ago in nt.)
that reminds me, there were quite a few retirements in my department this last week, and ive always made out well when retiring profs just leave piles of books for anyone to take. i need to go hang out int the math building!
Yeah, I contributed some to our departmental library, but gave the rest to colleagues, grad students, and a few miscellaneous friends. MikeMiller got at least one from me.
I have a side question on style, I think. I see people writing \mathrm{d}x alot for integrals, does it make sense to do \frac{\mathrm{d}y}{\mathrm{d}x} for a derivative?
@TedShifrin Haha, I can explain. I asked for a very specific problem but the response I got was "You can see all the details for the case of $\Psi(x)$ worked out in my book 'A Primer of Analytic Number Theory', that should provide the hint you need." That doesn't sound very convincing, at least not for me.
well, i have it on my desk. it slipped out of a box of books when i was moving. i found it under a car seat about two weeks ago, and i couldn't remember what box it belonged in, so it's on my desk now.
@copper.hat I have a colleague who thinks i have it in for him, when I'm just being straight forward, direct and honestly responding in all our interactions.
the typesetting in these old princeton UP 'annals of mathematics studies' books is horrible. it's like a caveman etched each character into the page with a stick. great reminder of what led knuth to tex.
don't get the wrong idea, I'm usually good with people (this guy just has a stick up his arse becuase he used to be at the top of a heirachy, now is at the bottom, and can't stand it when someone he percieves as below him asks him for assistance)
I don't know much about Ghandi in general, but he wrote a fantastic letter to Hitler , in which he appealed to the furhers better nature and tried to get him to stop acting aggresivley, I think I like to err on that side of interacting with people :P
i used to have some rarities but most were lost in the move. i thought it was weird that the USPS lost the highest cash value books, because how would postal workers even know. it was just fate being unkind to me.
@copper.hat I'm still waiting on parts for my motorcycle to arrive from j a pan, I think I don't mind waiting for books I will have forgot I asked for too :P
i use qquad for spacing if i'm only doing one row, and don't really need columns as much as i need some space. like $$f(x) \to L, \qquad x \to \infty.$$
if you think you've seen people be stomped on for answering PSQs, see what they do on the tex stackexchange with people who post really kludgy answers.
the scientology-like slang abbreviation for questions on math.SE that do nothing but state a problem and do not provide context such as where the asker is coming from or what they have tried.
problem statement questions, for they contain only a statement of a problem.
even if someone isn't cheating it's thought to be abusive of the community and lowering of the quality of the site. there's a meta thread that goes into a whole schism about it.
i had exactly one take home final in graduate school. i went to get a burrito and found about half of my class working on it together, out in the open, at the restaurant.
it was a hard final too, a number of tricks. i identified them but gave up on several. the prof must have been shocked to see someone not finish several of the problems.
i always preferred in-class tests because although they do put pressure on test-taking skills, which can introduce unfairness, they also limit the difficulty of the exam.
and they equalize differentials between out-of-class time that people have to spend on stuff. i tended to take heavy courseloads or work part time, so being able to take something home wasn't a lot of extra time for me. if someone's only taking one hard class, they might have a solid week to spend on an exam.
it really depends on the field. sometimes people use scores, tests, quizzes, riddles as a simple gating mechanism. not because it's that important but because you need to get the numbers down before you engage in individualized review
when i first began TAing classes in grad school there was a movement to have at least half of all in-class time be collaborative group work. it was far from collaborative and barely resembled work. people who were lost got more lost. people who weren't were bored or felt put upon when someone had to share what their group had done.
ok, I think I hit another point of confusion. So I have $$\int{\frac{\partial}{\partial t} g(t)\frac1{g(t)}}\, \mathrm{d}t$$ (and I know the answer is $\ln|g(t)| + C$) I'm trying to get there using substitution (which I thought I had done, but misplaced my scrawls)...
so I start by channelling my inner Ted, and applying substitution: let $u = \frac1{g(t)}$
so then I can get to here with out too much hassle: $$\int{{\frac{\partial}{\partial t} g(t)}\cdot u^3} -du$$ because 1/g^2 = 1/1/u^2
If memory serves, ten years ago to the week (or so), I taught first semester freshman calculus for the first time. As many calculus instructors do, I decided I should ask some extra credit questions to get students to think more deeply about the material. The first one I asked was this:
1) Rec...
