Математика и физика. Mathematics & Physics. 2018 11 (6)
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Jacobian Conjecture for Mappings of a Special Type in C²
(Сибирский федеральный университет. Siberian Federal University, 2018-12)We show that a polynomial mapping of the type (x!F[x+f(a(x)+b(y))]; y!G[y+g(c(x)+d(y))]), where (a; b; c; d; f; g; F;G) are polynomials with non-zero Jacobian is a composition of no more than 3 linear or triangular ... -
Optimal Formulas of Numerical Integration with Derivatives in Sobolev Space
(Сибирский федеральный университет. Siberian Federal University, 2018-12)The problem of construction of optimal quadrature formulas in the sense of Sard in the space L(m) 2 (0; 1) is considered in the paper . The quadrature sum consists of values of the integrand at internal nodes and values ... -
Global Solvability of the One-dimensional Inverse Problem for the Integro-differential Equation of Acoustics
(Сибирский федеральный университет. Siberian Federal University, 2018-12)The hyperbolic integro–differential acoustic equation is considered. Direct problem is to find the acoustic pressure from the initial - boundary value problem for this equation with point source located on the boundary ... -
Study of the Non-isothermal Coupled Problem with Mixed Boundary Conditions in a Thin Domain with Friction Law
(Сибирский федеральный университет. Siberian Federal University, 2018-12)This paper deals with the asymptotic behavior of a coupled system involving of an incompressible Bing- ham fluid and the equation of the heat energy, in a three-dimensional bounded domain with Tresca free boundary friction ... -
Construction of Szeg˝o and Poisson Kernels in Convex Domains
(Сибирский федеральный университет. Siberian Federal University, 2018-12)In this paper, we construct Szeg˝o and Poisson kernels in convex domains in Cn and study their properties -
Permanents as formulas of summation over an algebra with a unique n-ary operation
(Сибирский федеральный университет. Siberian Federal University, 2018-12)We give a new general definition for permanents over an algebra with a unique n-ary operation and study their properties. In particular, it is shown that properties of these permanents coincide with the basic properties ... -
Multidimensional Free Interpolation Framework for High-precision Modeling of Slant Total Electron Contents in Mid-latitude and Equatorial Regions
(Сибирский федеральный университет. Siberian Federal University, 2018-12)Standard models of ionospheric delays have errors of order 1–8 TECU (standard total electron content units). On the basis of the free interpolation framework we propose a new simple model of the slant TEC distributions ... -
The Calculation of Magnetoresistance Coefficient for Multilayer Magnetic Structures
(Сибирский федеральный университет. Siberian Federal University, 2018-12)We performed a simulations of magnetic properties for the multilayer structures Fe/Cr/Fe and Co/Cu/Co using the Monte Carlo methods and the anisotropic Heisenberg model. The calculation of magnetoresistance coefficient ... -
Theoretical Study of Atomic Structure of Solid Solution Al₁₋ ₓScₓNin
(Сибирский федеральный университет. Siberian Federal University, 2018-12)The features of atomic structure of Al₁₋ ₓScₓNin the whole Sc concentration were studied using ab initio DFT approach. The possible segregation of AlN and ScN phases in a solid solution was investigated and results were ... -
Decomposition of Functions of Finite Analytical Complexity
(Сибирский федеральный университет. Siberian Federal University, 2018-12)Functions of two variables can be obtained from functions of one variable by substitutions and additions. Each composition scheme corresponds to a class of functions of two variables, such that they can be represented ... -
Singular Points of Complex Algebraic Hypersurfaces
(Сибирский федеральный университет. Siberian Federal University, 2018-12)We consider a complex hypersurface V given by an algebraic equation in k unknowns, where the set A Zk of monomial exponents is fixed, and all the coefficients are variable. In other words, we consider a family of ... -
Coefficient Multipliers for the Privalov class in a Disk
(Сибирский федеральный университет. Siberian Federal University, 2018-12)We obtain exact estimates of the growth and the Taylor coefficients of analytic functions from the Privalov classes in the unit disk. Also we describe coefficient multipliers from the Privalov classes into the Hardy classes. -
The Cauchy Problem for Multidimensional Difference Equations and the Preservation of the Hierarchy of Generating Functions of its Solutions
(Сибирский федеральный университет. Siberian Federal University, 2018-12)We study the dependence of the properties of the generating function of the solution of the Cauchy problem on the properties of the generating function of the initial data for a difference equation with constant coefficients ... -
Self-assembly of Three Nanoparticles in Structures with a Predetermined Geometry Controlled by Quasiresonant Laser Fied
(Сибирский федеральный университет. Siberian Federal University, 2018-12)In the paper a dynamic model of self-assembly of nanoparticles under laser field is proposed for research the possibility of a step-by-step assembly of a structure consisting of three particles with different form. The ... -
Existence and Uniqueness of the Solution for Volterra-Fredholm Integro-Differential Equations
(Сибирский федеральный университет. Siberian Federal University, 2018-12)In this article, modified Adomian decomposition method is successfully applies to find the approximate so- lutions of Volterra-Fredholm integro-differential equations. Moreover, we prove the existence and unique- ness ... -
Prym Differentials and Teichm¨uller Spaces
(Сибирский федеральный университет. Siberian Federal University, 2018-12)In this article we study multiplicative meromorphic functions and differentials on Riemann surfaces of finite type. We proved an analogue of P. Appell’s formula on decomposition of multiplicative functions with poles of ...