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Том 231, № 2 (2018)
- Год: 2018
- Статей: 13
- URL: https://journals.rcsi.science/1072-3374/issue/view/14920
Article
111-123
Exact Solutions of the Precursor Film Equation
Аннотация
We find and analyze exact solutions to equations with logarithmic nonlinearity. To construct the soltuions, we use the classical group analysis methods, as well as the method of invariant manifolds and the Lagrangian coordinate method. Bibliography: 23 titles. Illustrations: 5 figures.
124-142
143-152
One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations
Аннотация
We consider a class of nonlinear convolution type integral equations with a noncompact Hammerstein operator on the half-line and on the whole line. Under certain conditions on nonlinearity, we prove the existence of a one-parameter family of positive solutions and study the asymptotic behavior of the solutions at infinity. The results are illustrated by examples of the equations under consideration.
153-167
168-180
Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components
Аннотация
We study the boundary values of conformal mappings of plane finitely connected domains. We present a complete exposition of a theorem giving an exhaustive description of the boundary values of such mappings in terms of conformal moduli (extremal lengths) of pairs of boundary components of a domain of connectedness at most 3. Bibliography: 12 titles.
181-188
Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space
Аннотация
We give a definition of a conformally connected space with an angular metric of an arbitrary signature. We present basic formulas and classes of such spaces. We obtain the decomposition of the main tensor of a conformally connected torsion free space into irreducible gauge invariant summands and prove that all affine connections obtained from the Levi–Civita connection via the normalization transformation have the same Weyl conformal tensor. We describe all conformal torsion free connections on hypersurfaces of a projective space and give some examples. We construct a global conformal connection on a hyperquadric of the projective space.
189-205
Two-Step Estimation in a Heteroscedastic Linear Regression Model
Аннотация
We study the problem of estimating a parameter in some heteroscedastic linear regression model in the case where the regressors consist of all order statistics based on the sample of identically distributed not necessarily independent observations with finite second moment. It is assumed that the random errors depend on the parameter and distributions of the corresponding regressors. We propose a two-step procedure for finding explicit asymptotically normal estimators.
206-217
Stationary Distribution of a Stochastic Process
Аннотация
We find a stationary distribution of a stochastic process with delay at the origin. The trajectories of the process have linear growth and random jumps at random times. We use known results for regenerative processes and factorization technique for the study in boundary crossing problems for random walks.
218-226
Local Solvability of Initial-Boundary Value Problem for One-Dimensional Equations of Polytropic Flows of Viscous Compressible Multifluids
Аннотация
We consider the initial-boundary value problem governing unsteady polytropic motions of viscous compressible multifluids. We prove the existence and uniqueness of a strong solution to the problem. Bibliography: 11 titles.
227-242
Asymptotic Behavior of the Spectrum of a Multipoint Differential Operator with an Integrable Potential
Аннотация
We consider the boundary value problem for a differential operator with an integrable potential and study the asymptotic behavior of solutions for large values of the spectral parameter. We derive an equation for eigenvalues and obtain asymptotics of eigenfunctions of the operator.
243-254
255-266
Exact Asymptotics of the Solution to a Difference Equation of General Type
Аннотация
An asymptotic expansion for the solution to a nonhomogeneous difference equation of general type is obtained. The influence of the roots of the characteristic equation is taken into account. The asymptotic behavior of the remainder is established, depending on the asymptotics of the nonhomogeneous term of the equation.
267-277