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Diffusion Instability Domains for Systems of Parabolic Equations Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 S. V. Revina
We consider a system of two reaction-diffusion equations in a bounded domain of the \( m \)-dimensional space with Neumann boundary conditions on the boundary for which the reaction terms \( f(u,v) \) and \( g(u,v) \) depend on two parameters \( a \) and \( b \). Assume that the system has a spatially homogeneous solution \( (u_{0},v_{0}) \), with \( f_{u}(u_{0},v_{0})>0 \) and \( -g_{v}(u_{0},v_{
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On the Qualitative Properties of a Solution to a System of Infinite Nonlinear Algebraic Equations Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 M. H. Avetisyan, Kh. A. Khachatryan
We study and solve some class of infinite systems of algebraic equations with monotone nonlinearity and Toeplitz-type matrices. Such systems for the specific representations of nonlinearities arise in the discrete problems of dynamic theory of clopen \( p \)-adic strings for a scalar field of tachyons, the mathematical theory of spatio-temporal spread of an epidemic, radiation transfer theory in inhomogeneous
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On the Optimal Recovery of One Family of Operators on a Class of Functions from Approximate Information about Its Spectrum Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 E. V. Abramova, E. O. Sivkova
We find explicit expressions for optimal recovery methods in the problem of recovering the values of continuous linear operators on a Sobolev function class from the following information: The Fourier transform of functions is known approximately on some measurable subset of the finite-dimensional space on which the functions are defined. As corollaries, we obtain optimal methods for recovering the
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Riordan Arrays and Difference Equations of Subdiagonal Lattice Paths Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 S. Chandragiri
We study lattice paths by combinatorial methods on the positive lattice. We give some identity that produces the functional equations and generating functions to counting the lattice paths on or below the main diagonal. Also, we consider the subdiagonal lattice paths in relation to lower triangular arrays. This presents a Riordan array in conjunction with the columns of the matrix of the coefficients
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Optimal Recovery of a Family of Operators from Inaccurate Measurements on a Compact Set Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 E. O. Sivkova
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The Scale-Dependent Deformation Model of a Layered Rectangle Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 A. O. Vatulyan, S. A. Nesterov
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Light 3-Paths in 3-Polytopes without Adjacent Triangles Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 O. V. Borodin, A. O. Ivanova
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Birman–Hilden Bundles. II Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 A. V. Malyutin
We study the structure of self-homeomorphism groups of fibered manifolds. A fibered topological space is a Birman–Hilden space whenever in each isotopic pair of its fiber-preserving (taking each fiber to a fiber) self-homeomorphisms the homeomorphisms are also fiber-isotopic (isotopic through fiber-preserving homeomorphisms). We prove in particular that the Birman–Hilden class contains all compact
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Algebras of Binary Formulas for Weakly Circularly Minimal Theories with Trivial Definable Closure Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 B. Sh. Kulpeshov
We describe the algebras of binary formulas for countably categorical weakly circularly minimal theories with 1-transitive nonprimitive automorphism group and trivial definable closure having convexity rank 1. We find some criterion for commutativity of the algebras.
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Quasidenseness in $ ��^{��} $ and Projective Parallelotopes Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 A. E. Gutman, I. A. Emelianenkov
We establish two new criteria for the closedness of Archimedean cones in countable-dimensional locally convex spaces in terms of projective parallelotopes and projective automorphisms. We also answer some open questions about quasidenseness and quasi-interior.
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Novikov $ ��_{2} $ -Graded Algebras with an Associative 0-Component Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 A. S. Panasenko, V. N. Zhelyabin
In 1974 Kharchenko proved that if a \( 0 \)-component of an \( n \)-graded associative algebra is PI then this algebra is PI. In the Novikov algebras of characteristic 0 the existence of a polynomial identity is equivalent to the solvability of the commutator ideal. We study a \( _{2} \)-graded Novikov algebra \( N=A+M \) and prove that if the characteristic of the basic field is not 2 or 3 and its
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Homogenization of the Scalar Boundary Value Problem in a Thin Periodically Broken Cylinder Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 S. A. Nazarov, A. S. Slutskii
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Estimates for the Norm of the Hardy Operator in Operator Ideals Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 E. N. Lomakina, M. G. Nasyrova
We find the conditions for a compact Hardy operator in Lorentz spaces to belong to the operator ideals generated by sequences of \( s \)-numbers. We obtain some estimates of the norms of the Hardy operator in these ideals in terms of integral expressions depending on the weight functions of the operator.
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On the $ K $ -functionals of Absolutely Calderón Elements of the Banach Pair $ (l_{1},c_{0}) $ Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 V. I. Dmitriev, E. V. Zhuravleva, O. Yu. Mikhailova, I. N. Burilich
We characterize the absolutely Calderón elements of the canonical pair \( (l_{1},c_{0}) \) of sequence spaces in terms of the Peetre \( K \)-functional. This result has been known to the first author since rather long ago but the proof appears here. Also, we formulate a few unsolved problems.
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Geodesics and Shortest Arcs of Some Sub-Riemannian Metrics on the Lie Groups $ \operatorname{SU}(1,1)\times �� $ and $ \operatorname{SO}_{0}(2,1)\times �� $ with Three-Dimensional Generating Distributions Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 I. A. Zubareva
We find geodesics, shortest arcs, cut loci, and first conjugate loci for some left-invariant sub-Riemannian metrics on the Lie groups \( \operatorname{SU}(1,1)\times \) and \( \operatorname{SO}_{0}(2,1)\times \).
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A Family with a Single Minimal but Not Least Numbering Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 M. Kh. Faizrahmanov
We prove the existence of a family of computably enumerable sets that, up to equivalence, has a unique computable minimal but not least numbering.
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Craig’s Interpolation Property in Pretabular Logics Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 L. L. Maksimova, V. F. Yun
All pretabular extensions of the minimal logic were described and the tabularity problem was solved earlier. As turned out, in total, there are seven pretabular logics over the minimal logic. It was proved that four of them have Craig’s interpolation property (CIP) and two do not. In the present article, we solve the problem of CIP in the seventh logic. We prove that it has Craig’s interpolation property
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Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral Sib. Math. J. (IF 0.5) Pub Date : 2024-03-25 V. N. Dubinin
We show that changing the level curve of a harmonic function with the classical Hadamard variation with a small parameter entails a change in the Dirichlet integral of the function which is quadratic in the parameter. As a corollary, we supplement the well-known theorem of Teichmüller about the sum of moduli of doubly connected domains into which an annulus is subdivided by a continuum that differs
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On the Relation between Denjoy–Khintchine and $ \operatorname{HK}_{r} $ -Integrals Sib. Math. J. (IF 0.5) Pub Date : 2024-03-01
Abstract We locate Musial and Sagher’s concept of \( \operatorname{HK}_{r} \) -integration within the approximate Henstock–Kurzweil integral theory. If we restrict the \( \operatorname{HK}_{r} \) -integral by the requirement that the indefinite \( \operatorname{HK}_{r} \) -integral is continuous, then it becomes included in the classical Denjoy–Khintchine integral. We provide a direct argument demonstrating
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On the Spectral Properties of Selfadjoint Partial Integral Operators with a Nondegenerate Kernel Sib. Math. J. (IF 0.5) Pub Date : 2024-03-01
Abstract We consider bounded selfadjoint linear integral operators \( T_{1} \) and \( T_{2} \) in the Hilbert space \( L_{2}([a,b]\times[c,d]) \) which are usually called partial integral operators. We assume that \( T_{1} \) acts on a function \( f(x,y) \) in the first argument and performs integration in \( x \) , while \( T_{2} \) acts on \( f(x,y) \) in the second argument and performs integration
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Hilbert–Pólya Operators in Krein Spaces Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 V. V. Kapustin
We construct some class of selfadjoint operators in the Krein spaces consisting of functions on the straight line \( \{\operatorname{Re}s=\frac{1}{2}\} \). Each of these operators is a rank-one perturbation of a selfadjoint operator in the corresponding Hilbert space and has eigenvalues complex numbers of the form \( \frac{1}{s(1-s)} \), where \( s \) ranges over the set of nontrivial zeros of the
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On the Levi Class of the Quasivariety of Right-Orderable Groups Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 A. V. Zenkov
We show that the Levi class of the quasivariety of right-orderable groups strictly includes this quasivariety.
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Estimates of Alexandrov’s $ n $ -Width of the Compact Set of $ C^{\infty} $ -Smooth Functions on a Finite Segment Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 V. N. Belykh
We obtain two-sided estimates for Alexandrov’s \( n \)-width of the compact set of infinitely smooth functions boundedly embedded into the space of continuous functions on a finite segment.
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Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5 Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 S. V. Pchelintsev
We construct an additive basis for a relatively free alternative algebra of Lie-nilpotent degree 5, describe the associative center and core of this algebra, and find the T-generators of the full center. Also, we give some asymptotic estimate for the codimension of the T-ideal generated by a commutator of degree 5 in a free alternative algebra, and find a finite-dimensional superalgebra that generates
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Topological Properties of Mappings with Finite Distortion on Carnot Groups Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 D. V. Isangulova
We prove that every mapping with finite distortion on a Carnot group is open and discrete provided that it is quasilight and the distortion coefficient is integrable. Also, we estimate the Hausdorff dimension of the preimages of points for mappings on a Carnot group with a bounded multiplicity function and summable distortion coefficient. Furthermore, we give some example showing that the obtained
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The Injectivity Radius and Shortest Arcs of the Oblate Ellipsoid of Revolution Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 V. N. Berestovskii, A. Mustafa
We found the geodesics, shortest arcs, cut loci, and injectivity radius of any oblate ellipsoid of revolution in three-dimensional Euclidean space.
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On the Approximative Properties of Fourier Series in Laguerre–Sobolev Polynomials Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 R. M. Gadzhimirzaev
Considering the approximation of a function \( f \) from a Sobolev space by the partial sums of Fourier series in a system of Sobolev orthogonal polynomials generated by classical Laguerre polynomials, we obtain an estimate for the convergence rate of the partial sums to \( f \).
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Admissible Inference Rules of Modal WCP-Logics Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 V. V. Rimatskiy
We study admissible rules for the extensions of the modal logics S4 and GL with the weak co-covering property and describe some explicit independent basis for the admissible rules of these logics. The resulting basis consists of an infinite sequence of rules in compact and simple form.
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Two Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov
We construct two new infinite series of irreducible components of the moduli space of semistable nonlocally free reflexive rank 2 sheaves on the three-dimensional complex projective space. In the first series the sheaves have an even first Chern class, and in the second series they have an odd one, while the second and third Chern classes can be expressed as polynomials of a special form in three integer
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Kolmogorov Equations for Degenerate Ornstein–Uhlenbeck Operators Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 V. I. Bogachev, S. V. Shaposhnikov
We consider Kolmogorov operators with constant diffusion matrices and linear drifts, i.e., Ornstein–Uhlenbeck operators, and show that all solutions to the corresponding stationary Fokker–Planck–Kolmogorov equations (including signed solutions) are invariant measures for the generated semigroups. This also gives a relatively explicit description of all solutions.
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Birman–Hilden Bundles. I Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 A. V. Malyutin
A topological fibered space is a Birman–Hilden space whenever in each isotopic pair of its fiber-preserving (taking each fiber to a fiber) self-homeomorphisms the homeomorphisms are also fiber-isotopic (isotopic through fiber-preserving homeomorphisms). We present a series of sufficient conditions for a fiber bundle over the circle to be a Birman–Hilden space.
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On the Separability of Abelian Subgroups of the Fundamental Groups of Graphs of Groups. II Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 E. V. Sokolov
Consider the fundamental group \( {\mathfrak{G}} \) of an arbitrary graph of groups and some root class \( {\mathcal{C}} \) of groups, i.e., a class containing a nontrivial group and closed under subgroups, extensions, and unrestricted direct products of the form \( \prod_{y\in Y}X_{y} \), where \( X,Y\in{\mathcal{C}} \) and \( X_{y} \) is an isomorphic copy of \( X \) for each \( y\in Y \). We provide
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Oriented Rotatability Exponents of Solutions to Homogeneous Autonomous Linear Differential Systems Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 A. Kh. Stash
We fully study the oriented rotatability exponents of solutions to homogeneous autonomous linear differential systems and establish that the strong and weak oriented rotatability exponents coincide for each solution to an autonomous system of differential equations. We also show that the spectrum of this exponent (i.e., the set of values of nonzero solutions) is naturally determined by the number-theoretic
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A Spectral Criterion for Power-Law Convergence Rate in the Ergodic Theorem for $ {��}^{d} $ and $ {��}^{d} $ Actions Sib. Math. J. (IF 0.5) Pub Date : 2024-02-07 A. G. Kachurovskii, I. V. Podvigin, V. È. Todikov, A. Zh. Khakimbaev
We prove the equivalence of the power-law convergence rate in the \( L_{2} \)-norm of ergodic averages for \( {}^{d} \) and \( {}^{d} \) actions and the same power-law estimate for the spectral measure of symmetric \( d \)-dimensional parallelepipeds: for the degrees that are roots of some special symmetric polynomial in \( d \) variables. Particularly, all possible range of power-law rates is
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Boolean Valued Analysis of Banach Spaces Sib. Math. J. (IF 0.5) Pub Date : 2024-01-01
Abstract We implement the Boolean valued analysis of Banach spaces. The realizations of Banach spaces in a Boolean valued universe are lattice normed spaces. We present the basic techniques of studying these objects as well as the Boolean valued approach to injective Banach lattices.
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Admissibility and Unification in the Modal Logics Related to S4.2 Sib. Math. J. (IF 0.5) Pub Date : 2024-01-01
Abstract We study unification and admissibility for an infinite class of modal logics. Conditions superimposed to these logics are to be decidable, Kripke complete, and generated by the classes of rooted frames possessing the greatest clusters of states (in particular, these logics extend modal logic S4.2). Given such logic \( L \) and each formula \( \alpha \) unifiable in \( L \) , we construct a unifier
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The Riesz–Zygmund Sums of Fourier–Chebyshev Rational Integral Operators and Their Approximation Properties Sib. Math. J. (IF 0.5) Pub Date : 2024-01-01
Abstract Studying the approximation properties of a certain Riesz–Zygmund sum of Fourier–Chebyshev rational integral operators with constraints on the number of geometrically distinct poles, we obtain an integral expression of the operators. We find upper bounds for pointwise and uniform approximations to the function \( |x|^{s} \) with \( s\in(0,2) \) on the segment \( [-1,1] \) , an asymptotic expression
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The Quasi-Two-Dimensional Coefficient Inverse Problem for the Wave Equation in a Weakly Horizontally Inhomogeneous Medium with Memory Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 Z. A. Akhmatov, Zh. D. Totieva
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On the Virtual Potency of Automorphism Groups and Split Extensions Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 D. N. Azarov
We obtain some sufficient conditions for potency and virtual potency for automorphism groups and the split extensions of some groups. In particular, considering a finitely generated group \( G \) residually \( p \)-finite for every prime \( p \), we prove that each split extension of \( G \) by a torsion-free potent group is a potent group, and if the abelianization rank of \( G \) is at most 2 then
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$ BV $ -Spaces and the Bounded Composition Operators of $ BV $ -Functions on Carnot Groups Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 D. A. Sboev
Under study are the homeomorphisms that induce the bounded composition operators of \( BV \)-functions on Carnot groups. We characterize continuous \( BV_{\operatorname{loc}} \)-mappings on Carnot groups in terms of the variation on integral lines and estimate the variation of the \( BV \)-derivative of the composition of a \( C^{1} \)-function and a continuous \( BV_{\operatorname{loc}} \)-mapping
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On the Irreducible Carpets of Additive Subgroups of Type $ F_{4} $ Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 A. O. Likhacheva
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On the Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean $ d $ -Space Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 V. A. Alexandrov
We study the existence of the two affine-equivalent bar-and-joint frameworks in Euclidean \( d \)-space which have some prescribed combinatorial structure and edge lengths. We show that the existence problem is always solvable theoretically and explain why to propose a practical algorithm for solving the problem is impossible.
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Finite Time Stabilization to Zero and Exponential Stability of Quasilinear Hyperbolic Systems Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 N. A. Lyul’ko
We consider the asymptotic properties of solutions to the mixed problems for the quasilinear nonautonomous first-order hyperbolic systems with two variables in the case of smoothing boundary conditions. We prove that all smooth solutions to the problem for a decoupled hyperbolic system stabilize to zero in finite time independently of the initial data. If the hyperbolic system is coupled then we show
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Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 V. V. Aseev
We fully describe the form of the graphical limit of a sequence of \( K \)-quasimeromorphic mappings of a domain \( D \) in \( \overline{R^{n}} \) which take each of its values at \( N \) distinct points at most. For the family of all \( K \)-quasimeromorphic mappings of \( \overline{R^{n}} \) onto itself taking each value at \( N \) points at most we establish the presence of a common estimate for
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On Locally Finite Subgroups in $ \operatorname{Lim}(N) $ Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 N. M. Suchkov, A. A. Shlepkin
Let \( G \) be the group of all limited permutations of the naturals \( N \). We prove that every countable locally finite group is isomorphic to a subgroup in \( G \).
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The Myshkis 3/2 Theorem and Its Generalizations Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 V. V. Malygina
We discuss the well-known Myshkis result on the stability of nonautonomous first-order delay differential equations, providing an extension to the general differential equations with aftereffect, and make comparison with available results.
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Classes of Noncontact Mappings of Carnot Groups and Metric Properties Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 M. B. Karmanova
We study the metric properties of level surfaces for classes of smooth noncontact mappings from arbitrary Carnot groups into two-step ones with some constraints on the dimensions of horizontal subbundles and the subbundles corresponding to degree 2 fields. We calculate the Hausdorff dimension of the level surfaces with respect to the sub-Riemannian quasimetric and derive an analytical relation between
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Openness and Discreteness of Mappings of Finite Distortion on Carnot Groups Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 S. G. Basalaev, S. K. Vodopyanov
We prove that a mapping of finite distortion \( f:\Omega\to 𝔾 \) in a domain \( \Omega \) of an \( H \)-type Carnot group \( 𝔾 \) is continuous, open, and discrete provided that the distortion function \( K(x) \) of \( f \) belongs to \( L_{p,\operatorname{loc}}(\Omega) \) for some \( p>\nu-1 \). In fact, the proof is suitable for each Carnot group provided it has a \( \nu \)-harmonic function of
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$ E $ -Rings and Quotient Divisible Abelian Groups Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 M. N. Zonov, E. A. Timoshenko
Under study are the relations between \( E \)-rings and quotient divisible abelian groups. We obtain a criterion for the quotient divisibility of the additive group of an \( E \)-ring and give a negative solution to the Bowshell and Schultz problem about the quasidecompositions of \( E \)-rings.
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On the Existence of Radially Symmetric Solutions for the $ p $ -Laplace Equation with Strong Gradient Nonlinearities Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 Ar. S. Tersenov
We consider the Dirichlet problem for the \( p \)-Laplace equation in presence of a gradient not satisfying the Bernstein–Nagumo type condition. We define some class of gradient nonlinearities, for which we prove the existence of a radially symmetric solution with a Hölder continuous derivative.
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The Minimal Number of Generating Involutions Whose Product Is 1 for the Groups $ PSL_{3}(2^{m}) $ and $ PSU_{3}(q^{2}) $ Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 R. I. Gvozdev, Ya. N. Nuzhin
Considering the groups \( PSL_{3}(2^{m}) \) and \( PSU_{3}(q^{2}) \), we find the minimal number of generating involutions whose product is 1. This number is 7 for \( PSU_{3}(3^{2}) \) and 5 or 6 in the remaining cases.
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Almost Convergent 0-1-Sequences and Primes Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 N. N. Avdeev
We study 0-1-sequences and establish the connection between the values of the upper and lower Sucheston functional on such sequence and the set of all possible divisors of the elements in the sequence support. If the union of the sets of all simple divisors of the elements in a 0-1-sequence support is finite then the sequence is almost convergent to zero. We study the 0-1-sequences whose support consists
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Regularization of a Distribution Holomorphic in a Parameter Sib. Math. J. (IF 0.5) Pub Date : 2023-11-24 A. L. Pavlov
We give sufficient conditions for regularizing a distribution of the form \( a(\sigma,\lambda)f(\lambda) \), where \( f(\lambda) \) is a distribution holomorphic in the parameter \( \lambda \), while \( a(\sigma,\lambda) \) is an infinitely differentiable function of \( \sigma \) outside some closed set \( N \) with power singularities of derivatives on \( N \) and holomorphic in \( \lambda \).
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Locally Convex Spaces with All Archimedean Cones Closed Sib. Math. J. (IF 0.5) Pub Date : 2023-09-26 A. E. Gutman, I. A. Emelianenkov
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On the Existence of Hereditarily $ G $ -Permutable Subgroups in Exceptional Groups $ G $ of Lie Type Sib. Math. J. (IF 0.5) Pub Date : 2023-09-26 A. A. Galt, V. N. Tyutyanov
A subgroup \( A \) of a group \( G \) is \( G \)-permutable in \( G \) if for every subgroup \( B\leq G \) there exists \( x\in G \) such that \( AB^{x}=B^{x}A \). A subgroup \( A \) is hereditarily \( G \)-permutable in \( G \) if \( A \) is \( E \)-permutable in every subgroup \( E \) of \( G \) which includes \( A \). The Kourovka Notebook has Problem 17.112(b): Which finite nonabelian simple groups
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Continuity of the Mappings with Finite Distortion of the Sobolev Class $ W^{1}_{\nu,\operatorname{loc}} $ on Carnot Groups Sib. Math. J. (IF 0.5) Pub Date : 2023-09-26 S. K. Vodopyanov
We prove the continuity of the mappings with finite distortion of the Sobolev class \( W^{1}_{\nu,\operatorname{loc}} \) on Carnot groups and establish that these mappings are \( \mathcal{P} \)-differentiable almost everywhere and have the Luzin \( \mathcal{N} \)-property.
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On Well-Posedness of the Cauchy Problem for Pseudohyperbolic Equations in Weighted Sobolev Spaces Sib. Math. J. (IF 0.5) Pub Date : 2023-09-26 L. N. Bondar, G. V. Demidenko
We consider a class of strictly pseudohyperbolic equations and establish some solvability conditions of the Cauchy problem in the class of weighted Sobolev spaces. We also prove the uniqueness of solutions and obtain some estimates.
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On Some Properties of Semi-Hamiltonian Systems Arising in the Problem of Integrable Geodesic Flows on the Two-Dimensional Torus Sib. Math. J. (IF 0.5) Pub Date : 2023-09-26 S. V. Agapov, Zh. Sh. Fakhriddinov
Bialy and Mironov demonstrated in a recent series of works that the search for polynomial first integrals of a geodesic flow on the 2-torus reduces to the search for solutions to a system of quasilinear equations which is semi-Hamiltonian. We study the various properties of this system.
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Infinitesimal Sliding Bendings of Compact Surfaces and Euler’s Conjecture Sib. Math. J. (IF 0.5) Pub Date : 2023-09-26 I. Kh. Sabitov
We give some historical information about Euler’s conjecture on the rigidity of compact surfaces as well as the available results related to its proof. We thoroughly describe an approach to the conjecture by infinitesimal bendings in the case when the deformation of the surface is considered in the class of sliding bendings. We prove that Euler’s conjecture is true for the surfaces of revolution of
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Harnack’s Inequality for Harmonic Functions on Stratified Sets Sib. Math. J. (IF 0.5) Pub Date : 2023-09-26 N S. Dairbekov, O. M. Penkin, D. V. Savasteev