On regularity of solutions to some problems of mathematical physics
On regularization of variational problems in first-order field theory
On sectioning multiples of the nontrivial line bundle over Grassmannians
Let () denote the Grassmann manifold of linear -spaces (resp. oriented -spaces) in , and suppose . As an easy consequence of the Steenrod obstruction theory, one sees that -fold Whitney sum of the nontrivial line bundle over always has a nowhere vanishing section. The author deals with the following question: What is the least () such that the vector bundle admits a nowhere vanishing section ? Obviously, , and for the special case in which , it is known that . Using results...
On sectioning tangent bundles and other vector bundles
This paper has two parts. Part one is mainly intended as a general introduction to the problem of sectioning vector bundles (in particular tangent bundles of smooth manifolds) by everywhere linearly independent sections, giving a survey of some ideas, methods and results.Part two then records some recent progress in sectioning tangent bundles of several families of specific manifolds.
On separation and approximation of real functions defined on a Choquet simplex
On sets of small measure
On simplicial red refinement in three and higher dimensions
We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to the original...
On singularities of almost periodic functions
On some boundary value problems for systems of nonlinear ordinary differential equations
On some problems concerning the convergence spaces and groups
On some qualitative methods for systems of ordinary diferential equations in the large
On some rational fibrations with nonvanishing Massey products over homogeneous spaces
The main result of this brief note asserts, incorrectly, that there exists a rational fibration whose total space admits nonzero Massey products. The methods used would be appropriate for showing results of this kind, if the circumstances were to allow for it. Unfortunately the author makes a simple, but nonetheless fatal, computational error in his calculation that ostensibly shows the existence of a nonzero Massey product (p. 249, 1.13: . In fact, for any rational fibration the total space...
On some recent results on the numerical problems in semiconductor device simulation
On some relations between curvature and metric tensors in Riemannian spaces
The paper generalizes results of H. H. Hacisalihoglu and A. Kh. Amirov [Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 295-296 (1996; Zbl 0895.53038) and Sib. Mat. Zh. 39, No. 4, 1005-1012 (1998; Zbl 0913.53019)] on the existence and uniqueness of a Riemannian metric on a domain in given prescribed values for some of the components of the Riemann curvature tensor and initial values of the metric and its partial derivatives. The authors establish the construction (existence and uniqueness) of a...
On some results concerning -spaces
On some results concerning topological spaces and their continuous mappings
On some semilinear Volterra diffusion equations arising in ecology
On some singular boundary value problems for ordinary differential equations
On some spaces of functions and distributions
On some stability problems