according to my input formatting code, combined with Knuth's algorithm X, as implemented in github.com/water-vapor/DancingLinksAlgorithmX , I've managed to determine that 3D T tetrominoes may tile a 6 by 6 by 2 area.
(this is news to me, because as of yet, I've struggled to find such a solution by intuitive brute forcing, however I could find a solution for 6 by 6 by 4.
@Mrcrg sry i fell asleep. yeah, you can make a 3-4 sentence summary of what you know (I am reading paper A and I saw this class of analytic functions holder at the boundary. I also saw it in paper B, its a banach subspace of C, but I want to learn more, for example D. I tried these notes/books (X,Y,Z) on Banach spaces of analytic functions but they don't have this space. Any good references?) and that should be enough.
@Asinomás I would have rejected as well but I feel reject and edit was abused. If amWhy's edit was suggested edit, I would have rejected that as well, on the basis of the mathjax typo introduced (now fixed).
i thought i found a nice convex question but they are asking silly things like the circumference of a convex set. that's for manifold people
why complicate life?
one of the references in my daughter's final year report had an author of the name s. shit. nothing wrong with that, of course, but just required a double take.
i always strive to raise the tone of conversation.
Hey, easy question. If M and N are finite-dimensional vector spaces over D, E (division rings). How can i show that if End_D(M) ~= End_E(N) then M ~= N and D ~= E
I'm trying to find the value of $$\lim_{a\to \infty}\int_0^1 a^x x^a \,dx$$
My attempt:
Let $\epsilon >0$ be given.
$ x\mapsto a^{x}$ is continuous at $ 1$ so there is a $d_a\in ( 0,1)$ such that $|a^{x} -a|< \epsilon $ for all $ x\in [d_a,1]$. WLOG, let $d_a<1/2$.
$ |\int _{0}^{1} x^{a} a^{x} \...
her mother was called a "bad mom" this morning for giving her two saltines. dad had given her three at dinner yesterday, when mom wasn't there. "you weren't there" also came up.
breakfast is usually a toasted waffle with a light coating of almond butter and some fruit and a glass of water.
it's just easier to give her the saltines.
she had a pretty bad meltdown last night. my wife had to go to the doctor and they took forever to see her. so i'd stupidly told her that mom would be home before bedtime and that didn't happen.
not fixing the semi ambiguous hers although i would do that if i were billing for this in a legal document.
I just indicated in chat that one should set it up with the vertex at the origin and use spherical coordinates. It's not pretty, but I thought about it enough to decide it's eminently doable. Perhaps grotesque, too, but no pretense of surface integrals.
A doctor wrote to me to ask for differential geometric help with something called tortuosity in vessels inside the eye. They have some weird software that numerically computes it without divulging any of the "ingredients." It integrates $\kappa^2\,ds$ and divides by the length. He gets numbers and wants to compare different eyes.
I told him that mathematically, even with some constraints, it's just an ill-posed question. How can software compute that thing without being able to tell you the length itself?
@robjohn Can you tell this person that it is beyond bad form to delete questions once you've been told the answer? Granted, I didn't post an answer, but the question and comments might be helpful to others.
i remember using it in some analysis contexts where people are bothered less by arbitrary choices, but even there you're sometimes expressing something relating to all roots of a polynomial, not just one of them, and singling out any particular one of them for special indexing feels weird
i certainly prefer that notation being adopted once to seeing long expressions with exp(2pi i k/n) in them, which they love to do in some parts of signals processing