Математика и физика. Mathematics & Physics. 2022 15 (2)
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Analytic Solvability of the H¨ormander Problem and the Borel Transformation of Multiple Laurent Series
(Сибирский федеральный университет. Siberian Federal University, 2022)In this paper, the initial-boundary value problem of Hormander is formulated in the class of functions representable by Laurent series supported in rational cones. Using the Borel transformation of Laurent series we ... -
Some Systems of Transcendental Equations
(Сибирский федеральный университет. Siberian Federal University, 2022)Several examples of transcendental systems of equations are considered. Since the number of roots of such systems, as a rule, is infinite, it is necessary to study power sums of the roots of negative degree. Formulas for ... -
Morera’s Boundary Theorem in Siegel Domain of the First Kind
(Сибирский федеральный университет. Siberian Federal University, 2022)The paper considers the realization of the matrix unit polydisk in the form of a Siegel domain of the first kind and proves the boundary analogue of Morera’s theorem -
A Note on Explicit Formulas for Bernoulli Polynomials
(Сибирский федеральный университет. Siberian Federal University, 2022)For r 2 { 1; - 1; 1 2 } , we prove several explicit formulas for the n-th Bernoulli polynomial Bn (x), in which Bn (x) is equal to a linear combination of the polynomials xn, (x + r)n ; : : : ; (x + rm)n, where m ... -
Convolutional Integro-Differential Equations in Banach Spaces With a Noetherian Operator in the Main Part
(Сибирский федеральный университет. Siberian Federal University, 2022)An initial-value problem for an integro-differential equation of convolution type with a finite index operator for the higher order derivative in Banach spaces is considered. The equations under consideration model the ... -
Some Observations on Koide Formula
(Сибирский федеральный университет. Siberian Federal University, 2022)The Koide parameter for leptons and quarks is discussed. A probabilistic approach is used to verify if the results obtained in the various cases are purely coincident -
Algorithm of the Regularization Method for a Singularly Perturbed Integro-differential Equation with a Rapidly Decreasing Kernel and Rapidly Oscillating Inhomogeneity
(Сибирский федеральный университет. Siberian Federal University, 2022)In this paper, we consider a singularly perturbed integro-differential equation with a rapidly oscillating right-hand side, which includes an integral operator with a rapidly varying kernel. The main goal of this work ... -
A Problem with Wear Involving Thermo-Electro-viscoelastic Materials
(Сибирский федеральный университет. Siberian Federal University, 2022)In this paper, we consider a mathematical model of a contact problem in thermo-electro- viscoelasticity. The body is in contact with an obstacle. The contact is frictional and bilateral with a moving rigid foundation ... -
An Analogue of the Hartogs Lemma for R-Analytic Functions
(Сибирский федеральный университет. Siberian Federal University, 2022)The paper is devoted to the problem of R-analytic continuation of functions of several real variables which admit R-analytic continuation along parallel sections. We prove an analogue of the well-known Hartogs lemma for ... -
On the Cauchy Problem for the Biharmonic Equation
(Сибирский федеральный университет. Siberian Federal University, 2022)The work is devoted to the study of continuation and stability estimation of the solution of the Cauchy problem for the biharmonic equation in the domain G from its known values on the smooth part of the boundary @G. The ... -
On Ground States for the SOS Model with Competing Interactions
(Сибирский федеральный университет. Siberian Federal University, 2022)We study periodic and weakly periodic ground states for the SOS model with competing interactions on the Cayley tree of order two and three. Further, we study non periodic ground states for the SOS model with competing ... -
Inverse Scattering and Loaded Modified Korteweg-de Vries Equation
(Сибирский федеральный университет. Siberian Federal University, 2022)The Cauchy problem for the loaded modified Korteweg-de Vries equation in the class of "rapidly decreasing" functions is considered in this paper. The main result of this work is a theorem on the evolution of the scattering ...