On the lattice rest of a convex body in , III
On the length of some curves in the unit sphere
On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution
We consider n × n real symmetric and hermitian random matrices Hₙ that are sums of a non-random matrix and of mₙ rank-one matrices determined by i.i.d. isotropic random vectors with log-concave probability law and real amplitudes. This is an analog of the setting of Marchenko and Pastur [Mat. Sb. 72 (1967)]. We prove that if mₙ/n → c ∈ [0,∞) as n → ∞, and the distribution of eigenvalues of and the distribution of amplitudes converge weakly, then the distribution of eigenvalues of Hₙ converges...
On the lower bound of packing density for convex bodies in the plane.
On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)
Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function f with a convex body K instead of the whole space as the range of definition. In the present paper, we trace the consequences of an infinite extension of f outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the lower semicontinuous...
On the maximal operator associated to a convex body in Rn.
On the Maximum of the Minimum of a Sum.
On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space
The measurable sets of pairs of intersecting non-isotropic straight lines of type and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.
On the measurability of sets of pairs of straight lines in the simply isotropic space
We study the measurability of sets of pairs of straight lines with respect to the group of motions in the simply isotropic space by solving PDEs. Also some Crofton type formulas are obtained for the corresponding densities.
On the Minimal Convex Annulus of a Planar Convex Body.
On the Modality of Convex Polygons.
On the monotone upper bound problem.
On the monotonicity of the volume of hyperbolic convex polyhedra.
On the multiplicity points of monotone operators on separable Banach spaces. II.
On the multiplicity points of monotone operators on separable Banach spaces
On the Non-Existence of Certain Nearly Regular Planar Maps with Two Exceptional Faces
On the notion of the combinatorial -parametric property for polyhedra.
On the Number of Convex Lattice Polytopes.
On the Number of Critical Free Contacts of a Convex Polygonal Object Moving in Two-Dimensional Polygonal Space.
On the number of facets of three-dimensional Dirichlet stereohedra. II: Non-cubic groups.