First authorb paper out in the wild. It's challenging as an independent researcher, but it can be done. This has been a long time coming. Maybe more in the future https://zenodo.org/records/11214976 #paper#math#matheducation#proofs
Should show up in a couple other locations as well hopefully (pending reviews)
(1/2) Hands-On Mathematical Optimization with Python 🚀
The Hands-On Mathematical Optimization with Python book by Krzysztof Postek, Alessandro Zocca, Joaquim Gromicho, and Jeffrey Kantor provides the foundation for mathematical optimization. As the name implies, the book is hands-on with Python examples, mainly using Pyomo.
(2/2) The book covers different optimization methods, such as:
✅ Mathematical Optimization
✅ Linear Optimization
✅ Network Optimization
✅ Convex Optimization
✅ Stochastic Optimization
@lisyarus oh I like how you solve the problem in 4 lines while I'm taking the most batshit insane path (though you don't provide the speed conversion formula)
You may be interested in the expm1 trick to avoid writing the unintuitive swapped form a=lerp(b,a,x)
> 1 / speed is the time in which position becomes closer to target by a factor of e = 2.71828
The wiki page you link proposes a another reading when using the time constant (T=1/speed); something along 63.2%; this may help?
@bug Yep, I was planning to mention expm1 (which is also more precise) but decided the post is already too long :)
The thing wiki mentions is actually the same as in my article: if you divide a thing by e = 2.71828, you get 0.3678 of the thing, or 36.78%, meaning you got closer to zero by 100 - 36.78 = 63.21%
Im currently working on trajectory systems and forgot what tan() does and I kinda am embarrassed about that. Also I'm awful at trigonometry apparently. Haven't thought about it in a couple decades!
Hi all, I've started the arxiv submission process of my first author paper in the general math category, but it needs an endorser. Apparently the endorser must be someone who has published 2 papers earlier than 2 months ago and less than 5 years ago, in the general math category. Please let me know if you can. Thanks in advance! #math#arxiv#papers
I just realized that all perfect squares mod 9 can only be 0, 1, 4, 7, but I can't find an easier proof than by exhaustion (square all numbers 0 to 8, mod 9). Is there a more elegant proof of this?
mod 11 has a wider choice (0, 1, 3, 4, 5, 9), but I wonder how good of a “perfect square detector” they can be together. Of course if either proof (by 9s and by 11s) fails, it's not a perfect square, but how many “not perfect square” are perfect squares both mod 9 and mod 11?
I have a question about the aperiodic spectre tile (or the hat/turtle).
I know that the proof of aperiodicity works by showing that the tiles must fit together in a hierarchical structure that eventually repeats itself at a larger scale. But the larger units aren't literally scaled copies of the spectre. I also know that there is some freedom as to how you draw the edges of the spectre.
Is there a way you can draw the edges that allows you to literally use spectres to cover a larger copy of themselves? If so, is this way of doing it unique?
@OscarCunningham I'm pretty sure you can transform the hats' HTPF metatile system into a form where each higher-order metatile exactly covers a set of metatiles of the next order down. (Use the 'converged' metatile shapes; use a non-overlapping version of the expansion rules; do some horrible limiting thing that fractalises all the metatile edges.)
But then you still have four different fractally-shaped metatiles, and no way to decompose those into individual hats that are all congruent.
@OscarCunningham in fact, here's the paper I vaguely remembered seeing but couldn't put my hands on yesterday, which does pretty much what I said. https://arxiv.org/abs/2305.05639, diagrams on pages 7 and 8.
I said this to a room full of people years ago and it turned out to be controversial, so what the heck I'll post it here:
Science results and math theorems should not be named after people, and we should undertake to rename any that currently are. We should prioritize renaming results or theorems named after white men and other privileged categories of people, with special attention to cases where a privileged person accepted or was assigned credit for work a less-privileged person did.