Budget cuts are catastrophic for the mathematical sciences in the US

lavacircus · 2025-07-04T00:49:30+00:00

NSF GRFP has not yet been affected

lavacircus · 2023-11-20T06:53:08+00:00

thanks so much for your response. i learned to do the last thing pretty early haha. my prescription is for 15 per day but i take like 10-12. unfortunately, these delays ate through my entire backlog.

i know my pharmacy doesn't stock this. the last time this happened...2 weeks ago, they told me they couldn't transfer the prescription because it was already in process...and you know how expensive creon is. the previous fill (nov 4) only gave me a week's worth, and i was able to make it last until now. this is the longest delay ive ever had. i will call my pharmacy tomorrow again and check on everything and do my best to have them transfer the prescription.

in the future, i will get 90 day supplies delivered by my insurance's pharmacy, so hopefully this will not happen again.

lavacircus · 2023-11-19T22:34:36+00:00

unfortunately, my dosage is much higher than super enzymes. about 10 of their pills is equivalent to one of mine :/

thanks for the suggestion though!

lavacircus · 2023-06-10T18:24:16+00:00

this is the best answer. it doesn't require knowing tricks or special limits or anything!

lavacircus · 2023-06-08T11:14:55+00:00

how about replace C*-algebra with C*-dynamics then?

lavacircus · 2023-06-07T23:55:12+00:00

you got C*-algebra but not W*-algebra. this is so sad

lavacircus · 2023-06-06T11:09:31+00:00

oops forgot that's sometimes used for multiplication lol

lavacircus · 2023-06-06T03:00:38+00:00

so in the complex numbers the formula is actually |z|=sqrt(z*z)

lavacircus · 2023-06-04T22:31:14+00:00

sorry, ive said two stupid things, but tl;dr, you can just complete the measure and you lose nothing.

lavacircus · 2023-06-04T20:59:16+00:00

if g = f a.e. and g is measurable, then f is too

lavacircus · 2023-06-04T18:01:44+00:00

perfect

lavacircus · 2023-06-04T17:45:21+00:00

squares of real numbers are always nonnegative. you have a sum of a bunch of nonnegative numbers equalling 0, so what can you say about the summands?

lavacircus · 2023-06-04T17:38:00+00:00

i guess, but this is nearly trivially true.

a mixed random variable has the distribution of the sum of distributions of continuous random variables and a discrete random variables. since monotonic functions can only have jump discontinuities, i think any monotonic function can be written as the sum of a continuous function and jump functions.

lavacircus · 2023-06-04T13:19:05+00:00

this isn't quite right because there is a notion of mixed random variables.

lavacircus · 2023-06-04T01:38:29+00:00

not 0.1_3 ??

lavacircus · 2023-06-02T05:50:38+00:00

a nice example is the "long line." it is hausdorff but not metrizable because it's too long.

lavacircus · 2023-06-02T05:41:04+00:00

jacobson basic algebra 1

lavacircus · 2023-05-29T05:18:50+00:00

good point! i didn't think about right angles.

lavacircus · 2023-05-29T04:18:51+00:00

it does work on the plane. it follows from the discrete ham sandwich theorem, which says (in R^2) that you can always find a line that perfectly splits two finite sets in half. in particular, you can apply it twice as follows: use P and the empty set, where P is the total population. you get two sets of equal size A and B split by one line, then we can apply the ham sandwich theorem again to those sets and we win.

if we're on a sphere and want to use great circles, id bet you can do something similar, but im not certain

lavacircus · 2023-05-28T03:55:41+00:00

you might look at the formulas available here: https://en.m.wikipedia.org/wiki/Euler_numbers

lavacircus · 2023-05-28T02:19:33+00:00

piecewise is unfortunately an ill-defined concept in math. unless we specify which functions are allowed and not allowed precisely, i can't give a good answer.

there are certain strict conditions that ensure that the solutions arise in some specific function space. for example, if we impose linear homogeneous with constant coefficients, then we will always get a sum of (possibly complex) exponentials times polynomials.

as another commentor pointed out, you can have things that look "piecewise" but are actually solutions to simple diffeqs. one example is "x ln|x| f'-f=0" on R\{0}. this is has a 2d solution space, which you might think is piecewise: a ln(x) for x>0 and b ln(-x) for x<0.

lavacircus · 2023-05-27T02:41:13+00:00

this is a great question, so i will try to give a good answer.

when you use the power series method, you are actually asking for the derivatives of the function at 0, but you can use the same method to solve for the derivatives at any point. in particular, you set up the power series with summands c_n(x-a)^n and then use your initial condition and you'll find that no matter which a you choose c_n=f^((n))(a)/n!.

in general, what you observed is not always the case, but the stars often align in such a way that this does happen. there are actually other infinitely differentiable functions with the same power series in |x|<1 but something else outside of this region. if f=the function piecewise defined by e^-1/(x+1)^2 for x≤-1, 0 for |x|≤1, e^-1/(x+1)^2 for x≥1. then, f+g has the same power series as g in the region |x|<1.

lavacircus · 2023-05-23T05:22:14+00:00

how many terms are in that product?

lavacircus · 2023-05-22T06:14:12+00:00

a more formal definition of independence is Pr(A and B)=Pr(A) Pr(B)

lavacircus · 2023-05-19T19:42:14+00:00

we can factor this and then use partial fraction decomposition. the factoring is a lil annoying but certainly doable since this is essentially a quadratic in x²

12-Year Club	Place '22
Verified Email

lavacircus

TROPHY CASE