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 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 Number of Critical Free Contacts of a Convex Polygonal Object Moving in Two-Dimensional Polygonal Space.
On the Number of Guard Edges of a Polygon.
On the number of minimal pairs of compact convex sets that are not translates of one another
Let [A,B] be the family of pairs of compact convex sets equivalent to (A,B). We prove that the cardinality of the set of minimal pairs in [A,B] that are not translates of one another is either 1 or greater than ℵ₀.
On the Openness of Continuous Averagings.
On the Openness of the Barycentre Map.
On the points of multiplicity of monotone operators
On the radius of a set in a Hilbert space
On the radius of convergence of an entire function in a normed space
On the rank of a topological convexity
On the reduction of pairs of bounded closed convex sets
Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The second theorem...