In the last 30 days

• Open/close Injectivity sets for the Radon transform over a sphere

  V V Volchkov 1999 Izv. Math. 63 481 Tag this article

  Article References Full text PDF (380 KB)

  This paper contains a solution of the problem of describing the kernel of the Radon transform over a sphere with respect to sets with spherical symmetry. This solution enabled us, in particular, to characterize all injectivity sets of this type. The technique used in the proofs enabled us to obtain other exact results concerning spherical means, namely, new two-radii theorems and a uniqueness theorem.

• Open/close Homogenization of a mixed boundary-value problem in a domain with anisotropic fractal perforation

  Sergei A Nazarov and Andrey S Slutskii 2010 Izv. Math. 74 379 Tag this article

  Article References Full text PDF (495 KB)

  We carry out a homogenization of a mixed boundary-value problem for a scalar elliptic equation in a rectangle with anisotropic fractal perforation, namely, the (small) size of holes is preserved in one direction, whereas it is reduced in the other when moving away from the base of the rectangle. Neumann conditions are imposed on the boundaries of the holes. A specific feature of the asymptotic constructions is the presence of several boundary layers. Explicit formulae are obtained for the homogenized differential operator and asymptotically exact error estimates are derived, and the smallness of the majorant is related to the smoothness property of the right-hand side with respect to the slow variable in the scale of Sobolev-Slobodetskii spaces.

• Open/close On the topology of wave fronts in spaces of low dimension

  Vyacheslav D Sedykh 2012 Izv. Math. 76 375 Tag this article

  Article References Full text PDF (688 KB)

  We calculate the adjacency indices of the singularities of generic wave fronts in spaces of dimension . As a corollary, we find new conditions for the coexistence of singularities of wave fronts.

• Open/close On the spectrum of a two-dimensional periodic operator with a small localized perturbation

  Denis I Borisov 2011 Izv. Math. 75 471 Tag this article

  Article References Full text PDF (485 KB)

  We consider a two-dimensional periodic self-adjoint second-order differential operator on the plane with a small localized perturbation. The perturbation is given by an arbitrary (not necessarily symmetric) operator. It is localized in the sense that it acts on a pair of weighted Sobolev spaces and sends functions of sufficiently rapid growth to functions of sufficiently rapid decay. By studying the spectrum of the perturbed operator, we establish that the essential spectrum is stable, the residual spectrum is absent, and the set of isolated eigenvalues is discrete. We obtain necessary and sufficient conditions for the existence of new eigenvalues arising from the ends of lacunae in the essential spectrum. In the case when such eigenvalues exist, we construct the first terms of asymptotic expansions of these eigenvalues and the corresponding eigenfunctions.

• Open/close Cohomology of real three-dimensional triquadrics

  Vyacheslav A Krasnov 2012 Izv. Math. 76 113 Tag this article

  Article References Full text PDF (445 KB)

  We consider non-singular intersections of three real five-dimensional quadrics. They are referred to for brevity as real three-dimensional triquadrics. We calculate the dimensions of the cohomology spaces of triquadrics with coefficients in the field of two elements.

• Open/close Chattering regimes and Lagrangian manifolds in problems with phase constraints

  Vladimir F Borisov et al 2012 Izv. Math. 76 1 Tag this article

  Article References Full text PDF (466 KB)

  Given a class of optimal control problems with a phase constraint, we construct a Lagrangian manifold containing extremals with countably many tangencies to the boundary of that constraint. The construction proceeds by resolving the singularities of the Hamiltonian system of the problem at the accumulation point of the points of contact of extremals with that boundary.