MathOverflow

I am an independent researcher and have written a short heuristic note exploring the time-average of the 2-adic valuation (k(n) = v_2(3n+1)) in the Collatz conjecture.
The note starts from a base-6 modular analysis, computes heuristic averages of (k(n)) over selected residue classes modulo 6/8/12/20/60, introduces notions of non-locality and block structure, and reports limited numerical observations (up to (n \le...

Consider the Green function of the restricted fractional Laplacian $(-\Delta)^s+\alpha I$ in a unit ball $B$, $\alpha>0$ with $0$ exterior boundary condition. If $G_{\alpha}(x, y)$ is the Green function of the perturbed fractional Laplacian and ...

Let $\mathbf{Sch}_k$ denote the category of schemes over a commutative ring $k$. Is it true that $\mathbf{Sch}_k$ is well-copowered? In other words, for every $k$-scheme $X$, is the category of epimorphisms $X \to Y$ essentially small? Intuitively, this...

Christmas is just around the corner and I haven't bought all the gifts for my family yet ( yeah, �)My Dad has a PhD in Mathematics, he works in Graph theory and his thesis was about Quasiperiodic tilings.What do you think would make a good gift for him...