MathOverflow

Let $\ 0<\Lambda_1\le\ldots\le\Lambda_n\ $ be a finite non-decreasing sequence of positive reals, of length $\ n>0.\ $ Let
$$ D:=\sum_{k=1}^n \Lambda_k $$
The question is about the conditions whichallows to shift the interval $\ [0;\Lambda_k)\ $ over arbitrary$\ x\in[0;D)\ $ by applying a permutation$\ \pi:\{1\ldots n\}\rightarrow\{1\ldots n\}\ $ to the members$\ [0;\Lambda_k)\ $ of partition $\ [0;D)...

I have noticed a recurring approximation strategy that has worked well for several special functions. The basic idea is:
Normalize the function to remove dominant asymptotic behaviour (for example, logarithmic singularities).Choose a simple ansatz (often a power law). The ansatz parameters are determined from analytically derived anchor conditions, including endpoint values...

For $U\subseteq\mathbb{R}^n$ open, Peetre's theorem completely determines the "local and linear" operators on $C^\infty_c(U)$ (that is, the $D$s which linear in the usual sense and additionally satisfy $\mathrm{supp}(f)\supseteq\mathrm{supp}(Df)$. Peetre...

It is known (P. Chojecki, 2026) that there are only finitely many natural numbers $n$ which do not have a
representation $n = x^2 + y^2 - z^2$with $x^2 \le n$, $y^2 \le n$, and $z^2 \le n$.
$n=6563$ is the largest known such example.