5 problems

Data augmented bootstrap (DAB) uses Euclidean structures, the Kolmogorov metric, and Gaussian universality to obtain coverage guarantees through distributional approximation. Non-E…

Let $S^2$ be the unit round sphere, and let $\gamma$ be a smooth Jordan curve in $S^2$. Its diameter is the supremum of the round distances between points of $\gamma$; assume that…

Let $\mathcal{F}_k$ denote the mass center system defined for $k\in[0,\infty)$ on material vector systems in $\mathbb{H}^1$ or $\mathbb{E}^1$. Uniqueness conjecture. There exists n…

Linearity conjecture. Superintegrable systems in two-dimensional non-Euclidean space can be reduced to linear equations by means of their hidden symmetries.

Let $n\ge 3$, and let a flexible polyhedron lie either in Lobachevsky space $\Lambda^n$ or in the open hemisphere $S^n_+$. Its generalized oriented volume is defined in the relevan…