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Set-Theoretical Solutions of the $$n$$ -Simplex Equation Sib. Adv. Math. Pub Date : 2024-03-11 V. G. Bardakov, B. B. Chuzhinov, I. A. Emelyanenkov, M. E. Ivanov, T. A. Kozlovskaya, V. E. Leshkov
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Negative Numberings in Admissible Sets. II Sib. Adv. Math. Pub Date : 2024-03-11 I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov
Abstract We describe constructions that are used in the proof of the main result of the first part of the article. They are based on automorphisms and properties of the Cantor space.
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Lipschitz Images of Open Sets on Sub-Lorentzian Structures Sib. Adv. Math. Pub Date : 2024-03-11 M. B. Karmanova
Abstract We prove a sub-Lorentzian analog of the area formula for intrinsically Lipschitz mappings of open subsets of Carnot groups of arbitrary depth with a sub-Lorentzian structure introduced on the image space.
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Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind Sib. Adv. Math. Pub Date : 2024-03-01
Abstract We consider the problem on optimal quadrature formulas for curvilinear integrals of the first kind that are exact for constant functions. This problem is reduced to the minimization problem for a quadratic form in many variables whose matrix is symmetric and positive definite. We prove that the objective quadratic function attains its minimum at a single point of the corresponding multi-dimensional
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Sharply Transitive Representations of the Algebra $$sl_3(\mathbb{R})$$ Sib. Adv. Math. Pub Date : 2023-12-14 M. V. Neshchadim, A. A. Simonov
Abstract We consider local sharply transitive representations of the algebra \(sl_3(\mathbb {R}) \) in the space of local vector fields with analytic coefficients in \( \mathbb {R}^{8}\) that are defined in a neighborhood of the origin. We find a system of differential equations that describes such representations.
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Rayleigh–Ritz Operator in Inverse Problems for Higher Order Multilinear Nonautonomous Evolution Equations Sib. Adv. Math. Pub Date : 2023-12-14 A. V. Lakeyev, Yu. E. Linke, V. A. Rusanov
Abstract We study solvability questions for the problem on realization of operator functions for an invariant polylinear regulator of a higher-order differential system in an infinite-dimensional separable Hilbert space. This is a nonstationary coefficient-operator inverse problem for multilinear evolution equations whose dynamic order is higher than one (notice that nonautomonous hyperbolic systems
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Negative Numberings in Admissible Sets. I Sib. Adv. Math. Pub Date : 2023-12-14 I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faĭzrakhmanov
Abstract We construct an admissible set \(\mathbb {A}\) such that the family of all \( \mathbb {A}\)-computably enumerable sets possesses a negative computable \(\mathbb {A}\) -numbering but lacks positive computable \(\mathbb {A}\) -numberings. We also discuss the question on existence of minimal negative \(\mathbb {A} \)-numberings.
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An Approach to Constructing Explicit Estimators in Nonlinear Regression Sib. Adv. Math. Pub Date : 2023-12-14 Yu. Yu. Linke, I. S. Borisov
Abstract We consider the problem of constructing explicit consistent estimators of finite-dimensional parameters of nonlinear regression models using various nonparametric kernel estimators.
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Reconstruction of Parameters of a Set of Radiant Points from Their Images Sib. Adv. Math. Pub Date : 2023-12-14 E. Yu. Derevtsov
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The Generating Function is Rational for the Number of Rooted Forests in a Circulant Graph Sib. Adv. Math. Pub Date : 2023-12-14 U. P. Kamalov, A. B. Kutbaev, A. D. Mednykh
Abstract We consider the generating function \(\Phi \) for the number \(f_{\Gamma }(n) \) of rooted spanning forests in the circulant graph \(\Gamma \), where \(\Phi (x)= \sum _{n=1}^{\infty } f_{\Gamma }(n) x^n\) and either \(\Gamma =C_n(s_1,s_2,\dots ,s_k) \) or \(\Gamma =C_{2n}(s_1,s_2,\dots ,s_k,n) \). We show that \(\Phi \) is a rational function with integer coefficients that satisfies the condition
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To the Segal Chronometric Theory Sib. Adv. Math. Pub Date : 2023-09-01 V. N. Berestovskiĭ
Abstract The author expounds or proves some results connected with Segal’s chronometric theory. He gives short proofs of results about linear representation of the group of nondegenerate complex \((2\times 2) \)-matrices on the Minkowski space-time and on the universal covering of the Lie group of unitary \((2\times 2)\)-matrices, i.e., on the Einstein Universe, as well as about the Cayley transform
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Positive Reducibilities, Extreme Numberings, and Completeness Sib. Adv. Math. Pub Date : 2023-09-01 M. Kh. Faĭzrahmanov
Abstract In the present article, we study universal, minimal, and complete numberings of families of arithmetic sets. We show that, for every \(m\in {\mathbb N}\) and every nontrivial \( \Sigma ^0_{m+2}\)-computable family \(\mathcal S \), there exists a \(\Sigma ^0_{m+2} \)-computable numbering that is not universal with respect to positive reducibilities and is complete with respect to each element
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An Extension of a Theorem of Neumann Sib. Adv. Math. Pub Date : 2023-09-01 V. G. Durnev, A. I. Zetkina
Abstract In the present article, we prove that every countable infinite group \(G \) is embeddable into a countable infinite simple group \(\overline {G}\) such that every equation of the form $$ w(x_1,\dots ,x_n) = g $$ is solvable in \(\overline {G} \), where \(w \) is a nontrivial reduced group word in variables \(x_1,\dots ,x_n \) and \(g\in G \).
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On Location of the Matrix Spectrum with Respect to a Parabola Sib. Adv. Math. Pub Date : 2023-09-01 G. V. Demidenko, V. S. Prokhorov
Abstract In the present article, we consider the problem on location of the matrix spectrum with respect to a parabola. In terms of solvability of a matrix Lyapunov type equation, we prove theorems on location of the matrix spectrum in certain domains \({\cal P}_i \) (bounded by a parabola) and \({\cal P}_e \) (lying outside the closure of \({\cal P}_i \)). A solution to the matrix equation is constructed
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Exponential Inequalities for the Tail Probabilities of the Number of Cycles in Generalized Random Graphs Sib. Adv. Math. Pub Date : 2023-09-01 A. A. Bystrov, N. V. Volodko
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On a Boundary Value Problem for a Pseudohyperbolic Equation Sib. Adv. Math. Pub Date : 2023-09-01 V. V. Shemetova
Abstract In the present article, we consider a mixed boundary value problem in a quarter-space for a pseudohyperbolic equation. We find conditions on the right-hand side of the equation that guarantee existence of solutions of this problem in Sobolev spaces with exponential weight.
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The Area of Surfaces on Sub-Lorentzian Structures of Depth Two Sib. Adv. Math. Pub Date : 2023-09-01 M. B. Karmanova
Abstract For contact mappings of Carnot groups of depth two whose image is endowed with a sub-Lorentzian structure, we prove local properties of the surfaces-images and explicitly deduce a sub-Lorentzian analog of the area formula. The result in particular also holds for Lipschitz mappings in the sub-Riemannian sense.
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Exponential Stability and Estimates of Solutions to Systems of Functional Differential Equations Sib. Adv. Math. Pub Date : 2023-09-01 T. L. Sabatulina, V. V. Malygina
Abstract For systems of linear autonomous delay differential equations, we develop a method for studying stability, which consists in constructing an auxiliary system whose asymptotic properties are close to those of the original system. Alongside new signs of stability, we find sharp estimates for the rate at which solutions tend to zero. The effectiveness of the results obtained is illustrated by
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Identities and $$n$$ -Ary Kulakov Algebras Sib. Adv. Math. Pub Date : 2023-05-25 M. V. Neshchadim, A. A. Simonov
Abstract In the present article, we develop algebraic methods in the theory of physical structures. This theory is targeted at classification of fundamental physical laws. Axiomatic approach naturally leads to introduction of new algebraic systems which are called \(n \)-ary Kulakov algebras. The article is devoted to introduction and study of such systems.
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A Priori Estimates and Fredholm Criteria for a Class of Regular Hypoelliptic Operators Sib. Adv. Math. Pub Date : 2023-05-25 A. G. Tumanyan
Abstract We study the Fredholm property of regular hypoelliptic operators with special variable coefficients. In this paper, necessary and sufficient conditions are obtained for a priori estimates for differential operators acting in multianisotropic Sobolev spaces. Fredholm criteria are obtained for a wide class of regular hypoelliptic operators in multianisotropic weighted spaces in \(\mathbb {R}^n
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On Boundary Value Problems in a Quarter-Plane for a Pseudohyperbolic Equation Sib. Adv. Math. Pub Date : 2023-05-25 L. N. Bondar’, V. V. Shemetova
Abstract We consider a mixed boundary value problem in a quarter-plane for a pseudohyperbolic equation and assume that the Lopatinskiĭ condition is satisfied. We find conditions on the right-hand side of the equation that guarantee existence of solutions of this problem in Sobolev spaces with exponential weight.
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Maximal Ideal Spaces of Invariant Function Algebras on Compact Groups Sib. Adv. Math. Pub Date : 2023-05-25 V. M. Gichev
Abstract Let \(G \) be a compact group and \(A \) be a closed subalgebra of \(C(G) \) which is invariant under the left and right shifts in \(G \). We consider maximal ideal spaces (spectra) \(\mathord {\mathcal {M}}_A\) of these algebras. They can be defined as closed sub-bialgebras of \(C(G)\). There is a natural semigroup structure in \(\mathord {\mathcal {M}}_{A} \) that admits an involutive anti-automorphism
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Sub-Riemannian Properties of the Level Sets of Noncontact Mappings of Heisenberg Groups Sib. Adv. Math. Pub Date : 2023-03-24 M. B. Karmanova
Abstract We consider a model example of noncontact mappings of Heisenberg groups where the dimension of the source space is greater than the dimension of the target space. We derive metric properties of level surfaces and prove an analog of the coarea formula.
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On Locally Boundedly Exactly Doubly Transitive Lie Groups of Transformations of the Space with a Subgroup of Parallel Translations Sib. Adv. Math. Pub Date : 2023-03-24 V. A. Kyrov
Abstract The paper solves the problem of extending the group of parallel translations of the three-dimensional space to a locally boundedly exactly doubly transitive group of transformations for the case of a decomposable Lie algebra. The Lie algebra of the desired Lie group of transformations is representable as the semidirect sum of a commutative three-dimensional ideal and a three-dimensional Lie
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On Distance-Regular Graphs of Diameter $$3 $$ With Eigenvalue $$0 $$ Sib. Adv. Math. Pub Date : 2023-03-24 A. A. Makhnev, I. N. Belousov
Abstract For a distance-regular graph \(\Gamma \) of diameter \(3 \), the graph \(\Gamma _i \) can be strongly regular only if either \(i=2 \) or \(i=3\). For the case in which \(\Gamma _2 \) is strongly regular, Koolen and his coauthors found parameters of \( \Gamma _2\) in terms of the intersection array of \(\Gamma \) (these parameters were obtained independently by Makhnev and Paduchikh). In this
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Semantic Programming and Polynomially Computable Representations Sib. Adv. Math. Pub Date : 2023-03-24 A. V. Nechesov
Abstract In the present article, we consider the question on existence of polynomially computable representations for basic syntactic constructions of the first-order logic and for objects of semantic programming (such as \(L\)-programs and \(L \)-formulas). We prove that the sets of linear or tree-like derivations in the first-order predicate calculus admits a polynomially computable representation
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Contributions to Automatic Continuity of $$(\sigma , \tau ) $$ -Derivations on Banach Algebras Sib. Adv. Math. Pub Date : 2023-03-24 A. Hosseini
Abstract The main purpose of this paper is to investigate the automatic continuity of \((\sigma , \tau \))-derivations on Banach algebras and to present several results in this regard. For instance, we prove the following theorem: Let \( \mathcal {A}\) and \(\mathcal {B} \) be two Banach algebras such that \(\mathcal {A} \) has the Cohen’s factorization property and \(\bigcap _{\varphi \in \Phi _B}
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Determination of a Non-Stationary Adsorption Coefficient Analytical in Part of Spatial Variables Sib. Adv. Math. Pub Date : 2023-03-24 D. K. Durdiev, Zh. D. Totieva
Abstract The multidimensional adsorption coefficient inverse problem is considered for a second order hyperbolic equation. It is supposed that this coefficient is continuous with respect to the variables \(t, x \) and analytic in the other spatial variables. For solving this equation, the scale method of Banach spaces of analytic functions is applied. The problem are reduced to a system of nonlinear
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On Numberings for Classes of Families of Total Functions Sib. Adv. Math. Pub Date : 2022-12-16 M. Kh. Faĭzrahmanov
Abstract In the present article, we study computable numberings and the Rogers semilattices for classes of families of everywhere defined (total) computable functions. We prove that the isomorphism type of the Rogers semilattice for a finite class \(\mathfrak F \) of computable families of total functions depends only on the order with respect to inclusion on the class \(\mathfrak F \) itself and the
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On a Class of Nonlinear Integro-Differential Equations Sib. Adv. Math. Pub Date : 2022-12-16 Kh. A. Khachatryan, H. S. Petrosyan
Abstract We investigate a class of higher-order nonlinear integro-differential equations with noncompact monotone Hammerstein operator on the positive half-line. An existence theorem is proved for a nonnegative nontrivial solution in a certain Sobolev space. The asymptotic behavior of the solution at infinity is studied. At the end, we give specific examples of such equations.
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Kernel Estimators for the Mean Function of a Stochastic Process under Sparse Design Conditions Sib. Adv. Math. Pub Date : 2022-12-16 Yu. Yu. Linke
Abstract The problem of nonparametric estimation of the mean function for a continuous random process is considered, when the noisy values of each of its independent trajectories are observed in some random time points — design elements. Under broad conditions on the dependence of design elements, uniformly consistent estimates are constructed for the mean function in the case of one of the versions
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The Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with a Loaded Term Sib. Adv. Math. Pub Date : 2022-12-16 U. B. Muminov, A. B. Khasanov
Abstract The method of inverse spectral problems is applied for integrating the defocusing nonlinear Scrödinger (DNS) equation with loaded terms in the class of infinite-gap periodic functions. We describe the evolution of the spectral data for a periodic Dirac operator whose coefficient is a solution to the DNS equation with loaded terms. We prove the following assertions. (1) It the initial function
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Some Questions on Polynomially Computable Representations for Generating Grammars and Backus–Naur Forms Sib. Adv. Math. Pub Date : 2022-12-16 A. V. Nechesov
Abstract In the present article, we consider the question on modeling Backus–Naur forms (BNF-systems) and generating grammars in GNF-systems. GNF-systems serve as the base for construction of monotone operators whose least fixed points are polynomially computable. We obtain our results by construction of GNF-systems and application of a generalized polynomial analog of Gandy’s fixed point theorem.
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A Sharp Constant in the Estimation of the Error of the Approximation of Classes of Differentiable Functions by the Second-Order Cesáro Means Sib. Adv. Math. Pub Date : 2022-09-02 O. G. Rovenskaya
Abstract We consider the problem of finding a sharp constant in the approximation of continuous functions by linear methods. The best constant is obtained for the approximation by the second-order Cesàro means of classes of Lipschitz continuous periodic functions.
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Unsaturated Algorithms for the Numerical Solution of Elliptic Boundary Value Problems in Smooth Axisymmetric Domains Sib. Adv. Math. Pub Date : 2022-09-02 V. N. Belykh
Abstract A fundamentally new, unsaturated, method is constructed for the numerical solution of the Laplace equation in a smooth axisymmetric domain of rather general shape. An essential feature of this method is lack of the leading error term \(O(m^{-r}) \), where \(r \) is a fixed integer with \(r>2 \). As a result, the method automatically adjusts to the excess (extraordinary) smoothness of solutions
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A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time Sib. Adv. Math. Pub Date : 2022-09-02 A. G. Kachurovskii, I. V. Podvigin, A. A. Svishchev
Abstract We consider monotone pointwise estimates for the rates of convergence in the Birkhoff ergodic theorem with continuous time. For an ergodic semiflow in a Lebesgue space, we prove that such estimates hold either on a null measure set or on a full measure set. It is shown that monotone estimates that hold almost everywhere always exist. We study the lattice of such estimates and also consider
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Minimal Surfaces Over Carnot Manifolds Sib. Adv. Math. Pub Date : 2022-09-02 M. B. Karmanova
Abstract We consider minimal graph-surfaces constructed from contact mappings of Carnot manifolds with values in Carnot–Carathéodory spaces. We establish basic properties of these graph-surfaces and distinguish the case in which the image space is endowed with the structure of a group. It turns out that, in the non-holonomic case, the problem is well posed if certain requirements on the preimage are
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Solution to the Dirichlet Problem for the Polyharmonic Equation in the Ball Sib. Adv. Math. Pub Date : 2022-09-02 V. V. Karachik
Abstract We give a representation of the solution to the Dirichlet problem for the inhomogeneous polyharmonic equation in the unit ball in terms of solutions to the Dirichlet problem for the Laplace equation.
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On Universal Functions in Hereditarily Finite Superstructures Sib. Adv. Math. Pub Date : 2022-06-18 A. N. Khisamiev
Abstract We obtain the necessary and sufficient condition for existence of a universal \(\Sigma \)-function in the hereditarily finite superstructure over a structure. We apply this condition to various well-known classes of structures.
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Completely Reducible Factors of Harmonic Polynomials of Three Variables Sib. Adv. Math. Pub Date : 2022-06-18 V. M. Gichev
Abstract We describe the divisors of complex valued homogeneous harmonic polynomials which are products of linear forms on \(\mathbb R^{3}\), and characterize homogeneous polynomials \(p\) that admit a couple of linear forms \(\ell _{1}\) and \(\ell _{2} \) such that \(\ell _{1}^{m}p \) and \(\ell _{2}^{m}p \) are harmonic for some \(m\in \mathbb N \). The latter gives an example of a pair of spherical
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On the Boundedness of Integral Operators in Morrey-Type Spaces with Variable Exponents Sib. Adv. Math. Pub Date : 2022-06-18 N. A. Bokayev, Zh. M. Onerbek
Abstract We consider the global Morrey-type spaces \({GM}_{p(\cdot ),\theta (\cdot ),w(\cdot )}(\Omega )\) with variable exponents \(p(x) \), \(\theta (x)\), and \(w(x,r) \) defining these spaces. In the case of unbounded sets \(\Omega \subset {\mathbb {R}}^{n}\), we prove the boundedness of the Hardy–Littlewood maximal operator and potential-type operator in these spaces. We prove Spanne-type results
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Exponential Inequalities for the Distribution Tails of the Number of Cycles in the Erdös-Rényi Random Graphs Sib. Adv. Math. Pub Date : 2022-06-18 A. A. Bystrov, N. V. Volodko
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Integration of the Loaded KdV Equation with a Self-Consistent Source of Integral Type in the Class of Rapidly Decreasing Complex-Valued Functions Sib. Adv. Math. Pub Date : 2022-06-18 U. A. Hoitmetov
Abstract We apply the inverse scattering method to integrating the loaded Korteweg–de Vries equation with a self-consistent source of integral type in the class of rapidly decreasing complex-valued functions.
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Multiply Transitive Lie Group of Transformations as a Physical Structure Sib. Adv. Math. Pub Date : 2022-06-18 V. A. Kyrov
Abstract We establish a connection between physical structures and Lie groups and prove that each physical structure of rank \((n+1,2)\), \(n\in \mathbb {N} \), on a smooth manifold is isotopic to an almost \(n \)-transitive Lie group of transformations. We also prove that each almost \(n\)-transitive Lie group of transformations is isotopic to a physical structure of rank \((n+1,2) \).
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Inversion of Series of Resolvents for Closed Operators and Some Applications Sib. Adv. Math. Pub Date : 2022-06-18 A. R. Mirotin
Abstract We consider an operator represented by the sum of a series in the values of the resolvent of a densely defined closed operator in a complex Banach space. We describe the left inverse for this operator, apply this result to regularization of equations of the first kind, and consider several examples.
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On Linearly Unstable Steady States of an MHD Model of an Incompressible Polymeric Fluid in the Case of Absolute Conductivity Sib. Adv. Math. Pub Date : 2022-03-17 A. M. Blokhin, D. L. Tkachev
Abstract We study linear stability of steady states for a certain generalization (namely, nonisothermal flows under the influence of magnetic field) of the Pokrovskiĭ–Vinogradov basic rheological model which describes flows of solutions and melts of incompressible viscoelastic polymeric media. We prove that the linear problem describing magnetohydrodynamic (MHD) flow of polymers in an infinite plane
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On the Accuracy of Approximation of a Binomial Distribution by a Poisson Law Sib. Adv. Math. Pub Date : 2022-03-17 S. V. Nagaev
Abstract We deduce a number of new estimates for the proximity of a binomial distribution to the corresponding Poisson distribution in the uniform metric and propose a combined approach to estimate this uniform distance when, for small \(n\) and large \(p \), the estimation is performed by computer calculating and the estimates obtained in the paper are used for the remaining values of \(n \) and \(p
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The Extended Large Deviation Principle for the Trajectories of a Compound Renewal Process Sib. Adv. Math. Pub Date : 2022-03-17 A. A. Mogul’skiĭ
Abstract We study a homogeneous compound renewal process (c.r.p.) \(Z(t) \). It is assumed that the elements of the sequence that rules the process satisfy Cramér’s moment condition \([{\bf C}_0] \). We consider the family of processes $$ z_T(t):=\frac 1xZ(tT),\enspace \enspace 0\le t\le 1,$$ where \(x=x_T\sim T \) as \(T\to \infty \). Conditions are proposed under which the extended large deviation
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Boundary Value Problems for One Pseudohyperbolic Equation in a Quarter-Plane Sib. Adv. Math. Pub Date : 2022-03-17 L. N. Bondar’, G. V. Demidenko
Abstract We consider mixed boundary value problems for one pseudohyperbolic equation in a quarter plane. We assume that the boundary value problems satisfy the Lopatinskiĭ condition. We prove theorems on unique solvability in anisotropic Sobolev spaces with exponential weight and establish some estimates for the solutions.
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Two-Sided Estimates of the Norm for a Class of Matrix Operators Sib. Adv. Math. Pub Date : 2022-03-17 A. A. Kalybay
Abstract For \( 1
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On Splitting of the Normalizer of a Maximal Torus in $$E_7(q) $$ and $$E_8(q) $$ Sib. Adv. Math. Pub Date : 2021-12-24 A. A. Galt, A. M. Staroletov
Abstract Let \(G \) be a finite group of Lie type \(E_7 \) or \(E_8\) over a field \(\mathbb {F}_q \) and let \(W \) be the Weyl group of \(G \). In the present article, we find all maximal tori \(T \) of the group \(G \) that admit complements in the algebraic normalizer \(N(G,T) \). For every group under consideration except for the simply connected group \(E_7(q)\), we prove the following assertion:
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On Decidable Categoricity for Almost Prime Models of the Signature of Graphs Sib. Adv. Math. Pub Date : 2021-12-24 M. I. Marchuk
Abstract We study the degrees of decidable categoricity for almost prime models and their relationship with the degrees of the sets of complete formulas. We show that a result of Goncharov, Harizanov, and Miller for models of infinite signature is valid for models of the signature of graphs.
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On the Wigner Law for Generalizided Random Graphs Sib. Adv. Math. Pub Date : 2021-12-24 A. N. Tikhomirov
Abstract We prove the Wigner law for conjugacy matrices of generalized non-oriented weighted random graphs under some simple conditions on probabilities of the graph edges.
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On Boundary Value Problems for Fractional-Order Differential Equations Sib. Adv. Math. Pub Date : 2021-12-24 M. Kh. Beshtokov, F. A. Erzhibova
Abstract The article is devoted to the study of boundary value problems for a fractional-order convection-diffusion equation with memory effect. We construct two-layer monotone schemes with weights of the second order accuracy with respect to the time and space variables. We prove the uniqueness and stability for the solution with respect to the initial data and right-hand side and also the convergence
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Finite Homogeneous Subspaces of Euclidean Spaces Sib. Adv. Math. Pub Date : 2021-09-10 Berestovskiĭ, V. N., Nikonorov, Yu. G.
Abstract The paper is devoted to the study of the metric properties of regular and semiregular polyhedra in Euclidean spaces. In the first part, we prove that every regular polytope of dimension greater or equal than 4, and different from 120-cell in \(\mathbb {E}^4 \) is such that the set of its vertices is a Clifford–Wolf homogeneous finite metric space. The second part of the paper is devoted to
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The Large Deviation Principle for Finite-Dimensional Distributions of Multidimensional Renewal Processes Sib. Adv. Math. Pub Date : 2021-09-10 Mogul’skiĭ, A. A., Prokopenko, E. I.
Abstract We study two types of multidimensional compound renewal processes (c.r.p.). We assume that the elements of the sequences that control the processes satisfy Cramér’s moment condition. Wide conditions are proposed under which the large deviation principle holds for finite-dimensional distributions of the processes.
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On Orlicz–Sobolev Classes on Quotient Spaces Sib. Adv. Math. Pub Date : 2021-09-10 Sevost’yanov, E. A.
Abstract We study the quotient spaces of the unit ball by some group of Möbius transformations. For mappings of such spaces, we obtain a bound for the distortion of a modulus of a family of spheres. As an application, we prove theorems on the local and boundary behavior of Orlicz–Sobolev classes on the quotient spaces.
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On the Discriminant of a Quadratic Field with Intermediate Fractions of Negative Norm Sib. Adv. Math. Pub Date : 2021-09-10 A. A. Korobov, O. A. Korobov
Abstract We investigate the Diophantine equation of the form \(x^2-dy^2=4t \), with $$ d=k^2\big (-m+(k^2m-2)u\big )^2-4\big (m+(k^2m-1)u\big ), $$ where \(k\) and \(m \) are odd and \(u \) is even, and \(4t \) is a sufficiently small natural number. We obtain a complete description of the set of solutions to such an equation.
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Asymptotic Properties of Solutions to Differential Equations of Neutral Type Sib. Adv. Math. Pub Date : 2021-06-06 A. S. Balandin, V. V. Malygina
Abstract We consider an important class of differential-difference equations of neutral type and study asymptotic properties of their solutions. We find necessary and sufficient conditions for exponential stability and represent them in geometric terms as a domain in the space of parameters. We analyze the behavior of the solutions on the boundary of the domain where stability is lost by various reasons
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The Block Structure of the Images of Regular Unipotent Elements from Subsystem Symplectic Subgroups of Rank $$2 $$ in Irreducible Representations of Symplectic Groups. III Sib. Adv. Math. Pub Date : 2021-06-06 T. S. Busel, I. D. Suprunenko
Abstract This is the final part of the paper on the dimensions of Jordan blocks in the images of regular unipotent elements from subsystem subgroups of type \(C_2 \) in \(p\)-restricted irreducible representations of groups of type \(C_n\) in characteristic \(p\geq 11 \) with locally small highest weights. Here the case where \(n>3 \) and the restriction of a representation considered to a canonical