相关论文: Kolmogorov widths of a finite-dimensional balls in…

In this paper, we prove a family of sharp geometric inequalities for free boundary hypersurfaces in a ball in space forms.

For rescaled additive functionals of the sine-process, upper bounds are obtained for their speed of convergence to the Gaussian distribution with respect to the Kolmogorov-Smirnov metric. Under scaling with coefficient $R$ the…

We determine the finite groups whose real irreducible representations have different degrees.

The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…

We obtain Calder{\'o}n-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous coefficients. We then derive the well-posedness of the martingale problem associated to related degenerate operators, and therefore…

The structure of integral manifolds in the Kovalevskaya problem of the motion of a heavy rigid body about a fixed point is considered. An analytic description of a bifurcation set is obtained, and bifurcation diagrams are constructed. The…

We discuss the polynomial representation for long knots and elaborate on how to obtain them with a bound on degrees of the defining polynomials, for any knot-type.

We prove a version of the Aleksandrov-Fenchel inequality for mixed volumes of coconvex bodies. This version is motivated by an inequality from commutative algebra relating intersection multiplicities of ideals.

We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p…

In this note, we first bound the intersection number of the regular simplicial partitions.

We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…

We prove the local boundedness of the solutions to degenerate second order partial differential equations of Kolmogorov type with measurable coefficients in divergence form, under minimal integrability assumption on the lower order…

The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of…

In this paper, we derive formulas for the analytical calculation of the moments of the distance between two uniformly and independently distributed random points in an $n$-sided regular polygon. A number of closed form expressions is…

In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.

We prove that Hofer's distance between two diameters of the open 2-disk admits an upper bound in terms of the Maslov index of their intersection points.

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…

Busemann's intersection inequality gives an upper bound for the volume of the intersection body of a star body in terms of the volume of the body itself. Koldobsky, Paouris, and Zymonopoulou asked if there is a similar result for…

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

Under correlation-type conditions, we derive upper bounds of order $\frac{1}{\sqrt{n}}$ for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law.