Том 221, № 6 (2017)

We prove vanishing theorems for projective and holomorphically projective diffeomorphisms of Riemannian and Kähler complete manifolds. In the proof, we use the wellknown Liouville type theorems on harmonic, subharmonic and superharmonic functions on complete Riemannian manifolds. Bibliography: 31 titles.

We study some inverse problems of mathematical physics in classes of entire functions. We investigate some questions of construction of solutions and source functions in described classes for the Maxwell system, Lamé system and for integral Volterra equation of the first kind. Bibliography: 9 titles.

E. Rips constructed a series of groups such that their group rings have zero divisors. such groups can serve as counterexamples to Kaplansky’s problem on zero divisors. The problem is to find such a group without torsion. We study simplest groups of this series, classify such groups, describe the structure, and show that all such groups have 2-torsion.

We consider nearly Kähler structures on a 6-dimensional sphere as sections of the twistor bundle over the sphere and prove that for any point of the space of twistor bundle there is a one-parameter family of nearly Kähler structures passing through the point. We study some properties of such one-parameter families.

We study mappings inducing bounded composition operators on weighted Sobolev spaces on Carnot groups. We give an analytical description of such mappings in terms of the integrability of weighted distortion function. Bibliography: 17 titles.

We prove that a computable ordinal α is autostable relative to strong constructivizations if and only if α < ω^ω+1. We obtain an estimate of the algorithmic complexity for the class of strongly constructivizable linear orderings that are autostable relative to strong constructivizations.

We study the problem of parametric identification of an object described by a system of linear difference equations by a set of observations of solutions provided that there are additive deterministic disturbances in the observations. The disturbances are also described by linear difference equations of a given order with uncertain initial conditions and coefficients. We obtain necessary and sufficient conditions for local co-identifiability of coefficients of the equations of object and disturbances.

We study the influence of nonclassical boundary conditions on the accuracy of approximation of a smooth function by a quintic spline of class C⁴ on a uniform mesh of a segment. We give an asymptotic analysis and compare different boundary conditions.