On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds.
On an ODE problem for equisingularities
A type of ODE is studied. The results are applied to algebraic geometry. An unsolved ODE problem is proposed.
On Asplund functions
A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.
On -stability and -determinacy
On Cohomology of Singularities of C°° Mapping.
On collective compactness of derivatives
On conability of singlevalued mappings
On conjugacy of diffeomorphisms infinitely tangent to the identity. II.
On differential equations and inclusions with mean derivatives on a compact manifold
We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds
We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.
On Finite Ck Left Determinacy.
On Finite Determinacy of Formal Vector Fields.
On generalized “ham sandwich” theorems
In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let be subsets with finite Lebesgue measure. Then, for any sequence of -linearly independent polynomials in the polynomial ring there are real numbers , not all zero, such that the real affine variety simultaneously bisects each of subsets , . Then some its applications are studied.
On Hadamard differentiability
On higher order point singularities of some geometric object fields
On hypersurface singularities which are stems
On inverses of -convex mappings
In the first part of this paper, we prove that in a sense the class of bi-Lipschitz -convex mappings, whose inverses are locally -convex, is stable under finite-dimensional -convex perturbations. In the second part, we construct two -convex mappings from onto , which are both bi-Lipschitz and their inverses are nowhere locally -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at . These mappings show that for (locally) -convex mappings...
On lens spaces which are isospectral but not isometric
On linear functions on the sphere
On Lipschitz and d.c. surfaces of finite codimension in a Banach space
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated -ideals are studied. These -ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.