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Том 230, № 1 (2018)
- Год: 2018
- Статей: 18
- URL: https://journals.rcsi.science/1072-3374/issue/view/14898
Article
Liouville-Type Theorems for Theories of Riemannian Almost Product Structures and Submersions
Аннотация
We prove Liouville type theorems, i.e., non-existence theorems for special classes of Riemannian almost product structures and submersions, that generalize well-known similar results of the theory of compact Riemannian manifolds.
1-9
10-13
14-24
Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative
Аннотация
We consider a class of quasielliptic operators in Rn and establish the isomorphism property in special weighted Sobolev spaces. In more general weighted spaces, we obtain the unique solvability conditions for quasielliptic equations and prove estimates for solutions. Based on the obtained results, we study the solvability of the initial problem for equations that are not solvable with respect to the higher order derivative.
25-35
Sufficient Condition for Consistency of Infinite Systems
Аннотация
Based on the theory of double series, we obtain a sufficient condition for the existence of strictly partial solutions to infinite systems of linear algebraic equations. We prove series expansion theorems for infinite determinants of Gaussian infinite matrices. Examples of application of the proposed condition are given.
36-45
Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback
Аннотация
We construct a discretization of the phase portrait of a 3-dimensional dynamical system of biochemical kinetics with piecewise linear right-hand sides. We describe geometry of the phase portrait and construct an invariant piecewise linear surface bounded by a stable cycle of this system composed of eight linear segments.
46-54
Solution of Boundary Value Problems in Cylinders with Two-Layer Film Inclusions
Аннотация
We consider the class of boundary value problems for elliptic, parabolic, and hyperbolic equations in cylinders separated by a two-layer film into two half-cylinders. We prove the existence and uniqueness theorem and express the solutions in terms of solutions to analogous classical problems in cylinders without films.
55-59
Groups with Almost Regular and Almost Perfect Involutions
Аннотация
We establish the solubility of a group with Sylow 2-subgroup of the least order in the centralizer of an almost regular involution. We also study the structure of a group G with an almost perfect and almost regular involution a.
60-66
Linear Inverse Problems for Ultraparabolic Equations: The Case of Unknown Coefficient of Spatial Type
Аннотация
We study the solvability of linear inverse problems for ultraparabolic equations with an unknown coefficient depending only on the spatial variables. The feature of such problems is special overdetermination conditions. We use the method based on reducing the inverse problem to a nonlocal boundary-value problem for ultraparabolic equations.
67-78
Prym Differentials on Variable Tori
Аннотация
We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.
79-94
Conditions of Asymptotic Normality of One-Step M-Estimators
Аннотация
In the case of independent identically distributed observations, we study the asymptotic properties of one-step M-estimators served as explicit approximations of consistent M-estimators. We find rather general conditions for the asymptotic normality of one-step M-estimators. We consider Fisher’s approximations of consistent maximum likelihood estimators and find general conditions guaranteeing the asymptotic normality of the Fisher estimators even in the case where maximum likelihood estimators do not necessarily exist or are not necessarily consistent.
95-111
112-117
A Priori Tame Estimates in Sobolev Spaces for the Plasma–Vacuum Interface Problem
Аннотация
We study the free boundary problem for the plasma–vacuum interface in the case where the plasma density is strictly positive up to the boundary. For the linearized problem we derive the so-called tame estimates which can be used for proving the existence of solutions to the nonlinear problem by the Nash-Moser method.
118-140
n-Algebraic Complete Algebras, Pseudodirect Products, and the Algebraic Closure Operator on Subsets of Universal Algebras
Аннотация
We introduce the notions of n-algebraic complete algebras and n-algebraic completeness, which makes it possible to find algebraic closures of subsets of universal algebras. We clarify how the n-algebraic completeness of an algebra is connected with the pseudodirect product of algebras.
141-145
Strong Solutions to Nonlinear Degenerate Fractional Order Evolution Equations
Аннотация
We obtain conditions for the existence and uniqueness of a strong solution to the initial problem for a degenerate evolution equation that is not solvable with respect to the fractional order derivative. The obtained results are used to study the initial- boundary value problem governing the fractional model of a viscoelastic Kelvin–Voigt fluid.
146-158
Optimal Control Problem for Two-Layer Elastic Body with Crack
Аннотация
We establish the unique solvability of the equilibrium problem for a two-layer body. One layer contains a crack, whereas the second one is glued along its edge to the first layer in such a way that to cover one of the crack ends. In the case, where the second layer is a rigid plate, we show that the problem with a rigid patch is the limit of problems with elastic patches as the rigidity parameter tends to infinity. We also study the optimal control problem with the exterior forces acting on both layers taken for the control function.
159-166
167-174
Pseudodifferential Equations on Manifolds with Complicated Boundary Singularities
Аннотация
We consider model pseudodifferential equations in canonical multidimensional domains with boundary singularities presented by the union of cones or a cone of lower dimension. We study the solvability of these equations by using the wave factorization concept.
175-183