JournalTOCs

Siberian Mathematical Journal
Journal Prestige (SJR): 0.675

Citation Impact (citeScore): 1
Number of Followers: 0

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-9260 - ISSN (Online) 0037-4466
Published by Springer-Verlag

[2469 journals]

On Some Classes of Inverse Problems of Recovering the Heat Transfer
Coefficient in Stratified Media
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  Abstract: Abstract We consider the well-posedness, in Sobolev spaces, of the inverse problem of recovering the heat transfer coefficient at the interface in the transmission condition of the imperfect contact type. The existence and uniqueness theorem are exhibited. The method is constructive and the approach allows us to develop some numerical methods for solving the problem. The proof relies on a priori estimates and the fixed-point theorem.
  PubDate: 2022-03-01
On Nonconstant Pre-Lie Bimodules over $ M_{2}(F) $
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  Abstract: Abstract We describe the unital finite-dimensional simple nonconstant bimodules $ {\mathcal{W}} $ over the matrix algebra $ M_{2}(F) $ over a field $ F $ of characteristic $ 0 $ ; i.e., the left action of the idempotents of $ M_{2}(F) $ is diagonalizable and $ {\mathcal{W}} $ does not contain constant bichains. Also, we construct an example of a nondiagonal bimodule and a series of constant right-symmetric bimodules over $ M_{2}(F) $ .
  PubDate: 2022-03-01
Algorithms for Recognizing Restricted Interpolation over the Modal
Logic S4
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  Abstract: Abstract We consider the restricted interpolation property IPR in modal logics. Earlier, the decidability of IPR over the modal logic S4 was proved and a finite list was found that contains all logics that can possess IPR over S4. However, this list contains some undue logics. The present article gives examples of the logics.
  PubDate: 2022-03-01
Essentially Invertible Measurable Operators Affiliated to a Semifinite
von Neumann Algebra and Commutators
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  Abstract: Abstract Suppose that a von Neumann operator algebra $ {\mathcal{M}} $ acts on a Hilbert space $ {\mathcal{H}} $ and $ \tau $ is a faithful normal semifinite trace on $ {\mathcal{M}} $ . If Hermitian operators $ X,Y\in S({\mathcal{M}},\tau) $ are such that $ -X\leq Y\leq X $ and $ Y $ is $ \tau $ -essentially invertible then so is $ X $ . Let $ 0<p\leq 1 $ . If a $ p $ -hyponormal operator $ A\in S({\mathcal{M}},\tau) $ is right $ \tau $ -essentially invertible then $ A $ is $ \tau $ -essentially invertible. If a $ p $ -hyponormal operator $ A\in{\mathcal{B}}({\mathcal{H}}) $ is right invertible then $ A $ is invertible in $ {\mathcal{B}}({\mathcal{H}}) $ . If a hyponormal operator $ A\in S({\mathcal{M}},\tau) $ has a right inverse in $ S({\mathcal{M}},\tau) $ then $ A $ is invertible in $ S({\mathcal{M}},\tau) $ . If $ A,T\in{\mathcal{M}} $ and $ \mu_{t}(A^{n})^{\frac{1}{n}}\to 0 $ as $ n\to\infty $ for every $ t>0 $ then $ AT $ ( $ TA $ ) has no right (left) $ \tau $ -essential inverse in $ S({\mathcal{M}},\tau) $ . Suppose that $ {\mathcal{H}} $ is separable and $ \dim{\mathcal{H}}=\infty $
  PubDate: 2022-03-01
Identities and Quasi-Identities of Pointed Algebras
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  Abstract: Abstract Each pointed enrichment of an algebra can be regarded as the same algebra with an additional finite set of constant operations. An algebra is pointed whenever it is a pointed enrichment of some algebra. We show that each pointed enrichment of a finite algebra in a finitely axiomatizable residually very finite variety admits a finite basis of identities. We also prove that every pointed enrichment of a finite algebra in a directly representable quasivariety admits a finite basis of quasi-identities. We give some applications of these results and examples.
  PubDate: 2022-03-01
On the Moment Problem in the Spaces of Ultradifferentiable Functions of
Mean Type
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  Abstract: Abstract We consider a version of the classical moment problem in the Beurling and Roumieu spaces of ultradifferentiable functions of mean type on the real axis. We obtain the necessary and sufficient conditions for the weights $ \omega $ and $ \sigma $ under which, for each number sequence in the space generated by $ \sigma $ , there is an $ \omega $ -ultradifferentiable function whose derivatives at zero coincide with the elements of the sequence.
  PubDate: 2022-03-01
About Exact Two-Sided Estimates for Stable Solutions to Autonomous
Functional Differential Equations
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  Abstract: Abstract Considering some linear autonomous differential equation with distributed delay that has a positive fundamental solution, we develop a method for obtaining effective exponential stability tests and two-sided estimates of the fundamental solution in the form of two exponential functions with exponents and coefficients determined exactly. A few examples illustrate the use of the method.
  PubDate: 2022-03-01
Functional and Analytical Properties of a Class of Mappings of
Quasiconformal Analysis on Carnot Groups
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  Abstract: Abstract This article addresses the conceptual questions of quasiconformal analysis on Carnot groups. We prove the equivalence of the three classes of homeomorphisms: the mappings of the first class induce bounded composition operators from a weighted Sobolev space into an unweighted one; the mappings of the second class are characterized by way of estimating the capacity of the preimage of a condenser in terms of the weighted capacity of the condenser in the image; the mappings of the third class are described via a pointwise relation between the norm of the matrix of the differential, the Jacobian, and the weight function. We obtain a new proof of the absolute continuity of mappings.
  PubDate: 2022-03-01
On the Sharp Baer–Suzuki Theorem for the $ \pi $ -Radical: Sporadic
Groups
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  Abstract: Abstract Let $ \pi $ be a proper subset of the set of all primes and $ { \pi \geq 2} $ . Denote the smallest prime not in $ \pi $ by $ r $ and let $ m=r $ if $ r=2,3 $ , and $ m=r-1 $ if $ r\geq 5 $ . We study the following conjecture: A conjugacy class $ D $ of a finite group $ G $ lies in the $ \pi $ -radical $ \mathrm{O}_{\pi}(G) $ of $ G $ if and only if every $ m $ elements of $ D $ generate a $ \pi $ -subgroup. We confirm this conjecture for the groups $ G $ whose every nonabelian composition factor is isomorphic to a sporadic or alternating group.
  PubDate: 2022-03-01
The Jacobian Problem for One Class of Nonpolynomial Mappings
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  Abstract: Abstract The Jacobian conjecture in its classical form reads: If $ f:{{ð•‰}}^{n}\rightarrow{{ð•‰}}^{n} $ (or $ {{ð”º}}^{n}\rightarrow{{ð”º}}^{n} $ ) is a polynomial mapping with the Jacobian determinant $ J_{f}\neq 0 $ , then $ f $ is injective. This conjecture was first stated by Keller in 1939 for $ n=2 $ and disproved in the two-dimensional real case by Pinchuk in 1994. Since then the conjecture is formulated in modified form: If $ J_{f}\equiv\operatorname{const}\neq 0 $ for a polynomial mapping $ f $ , then $ f $ is injective. In 1998, this conjecture was included in the list of 18 mathematical problems of the forthcoming century. In this paper we describe a broad subclass of polynomial mappings where the classical conjecture is true; and we transfer these results to nonpolynomial mappings with $ J_{f}\neq 0 $ .
  PubDate: 2022-03-01
On Possible Estimates of the Rate of Pointwise Convergence in the Birkhoff
Ergodic Theorem
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  Abstract: Abstract We study the separation from zero of a sequence $ \phi $ to obtain the estimates of the form $ {\phi(n)/n} $ for the rate of pointwise convergence of ergodic averages. Each of these $ \phi $ is shown to be separated from zero for mixings which is not always so for weak mixings. Moreover, for the characteristic function of a nontrivial set, it is shown that there exists a measure preserving transformation with arbitrarily slow decay of ergodic averages.
  PubDate: 2022-03-01
Values of the Permanent Function on Multidimensional $ (0,1) $ -Matrices
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  Abstract: Abstract We study the range of the permanent function for the multidimensional matrices of 0 and 1. The main result is a multidimensional version for the Brualdi–Newman upper bound on the consecutive values of the permanent (1965). Moreover, we deduce a formula for the permanent of the multidimensional (0,1)-matrices through the number of partial zero diagonals. Using the formula, we evaluate the permanents of the $ (0,1) $ -matrices with a few zeros and estimate the permanents of the matrices whose all zero entries are located in several orthogonal hyperplanes. We consider some divisibility properties of the permanent and illustrate the results by studying the values of the permanent for the $ 3 $ -dimensional $ (0,1) $ -matrices of order $ 3 $ .
  PubDate: 2022-03-01
On $ C $ - $ {\mathcal{H}} $ -Permutable Subgroups of Finite Groups
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  Abstract: Abstract Let $ \sigma=\{\sigma_{i}\mid i\in I\} $ be some partition of the set of all primes $ {ð•‡} $ , let $ G $ be a finite group, and $ \sigma(G)=\{\sigma_{i}\mid\sigma_{i}\cap\pi(G)\neq\varnothing\} $ . A set $ {\mathcal{H}} $ of subgroups of $ G $ is a complete Hall $ \sigma $ -set of $ G $ if every nonidentity member of $ {\mathcal{H}} $ is a Hall $ \sigma_{i} $ -subgroup of $ G $ for some $ i\in I $ and $ {\mathcal{H}} $ includes exactly one Hall $ \sigma_{i} $ -subgroup of $ G $ for every $ \sigma_{i}\in\sigma(G) $ . Let $ {\mathcal{H}} $ be a complete Hall $ \sigma $ -set of $ G $ and let $ C $ be a nonempty subset of $ G $ . We say that a subgroup $ H $ of $ G $ is $ C $ - $ {\mathcal{H}} $ -permutable if for all $ A\in{\mathcal{H}} $ there exists some $ x\in C $ such that $ H^{x}A=AH^{x} $ . We investigate the structure of $ G $ by assuming that some subgroups of $ G $ are $ C $ - $ {\mathcal{H}} $ -permutable. Some known results are generalized.
  PubDate: 2022-03-01
Shunkov Groups Saturated by General Linear Groups of Degree 3
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  Abstract: Abstract Saturation and the related concept of a saturating set are among the finiteness conditions for infinite groups. Saturation is applied to studying periodic groups and Shunkov groups with saturating sets consisting of finite simple nonabelian groups. This article addresses periodic Shunkov groups with saturating sets consisting of groups of a larger class. We establish the structure of a periodic Shunkov group saturated by the general linear groups of degree 3 over finite fields of characteristic 2.
  PubDate: 2022-03-01
On Discrete Universality in the Selberg–Steuding Class
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  Abstract: Abstract Let $ {{\mathcal{S}}} $ be the class of Dirichlet series introduced by Selberg and modified by Steuding, and let $ \{\gamma_{k}:k\in{{ð•…}}\} $ be the sequence of the imaginary parts of the nontrivial zeros of the Riemann zeta-function. Using the modified Montgomery’s pair correlation conjecture, we prove a universality theorem for a function $ L(s) $ in $ {{\mathcal{S}}} $ on approximation of analytic functions by the shifts $ L(s+ih\gamma_{k}) $ , $ h>0 $ .
  PubDate: 2022-03-01
On $ p $ -Universal and $ p $ -Minimal Numberings
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  Abstract: Abstract We study the $ p $ -reducibility of numberings which was introduced and first studied by Degtev. $ p $ -Reducibility is an effectively bounded version of the $ e $ -reducibility of numberings. Also, we prove that for every set $ A $ there exists an $ A $ -computable family without universal numberings but admitting $ p $ -universal numberings and obtain a criterion for the existence of $ p $ -universal numberings of finite families of $ A $ -c.e. sets. Finally, we show that every $ A $ -computable family, with $ \varnothing^{\prime\prime}\leq_{T}A $ , has infinitely many pairwise non- $ p $ -equivalent $ p $ -minimal $ A $ -computable numberings.
  PubDate: 2022-03-01
On the Core and Shapley Value for Regular Polynomial Games
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  Abstract: Abstract Considering some classes of polynomial cooperative games, we describe the integral representation of the Shapley values and the support functions of their cores. Also, we analyze the relationship between the Shapley values and the polar forms of homogeneous polynomial games. The found formula for the support function of the core of a convex game is applied for the dual description of the Harsanyi sets of finite cooperative games. The main peculiarity of the proposed approach to the study of optimal solutions of game theory is a systematic use of the extensions of polynomial set functions to the corresponding measures on symmetric powers of the initial measure spaces.
  PubDate: 2022-01-01
  DOI: 10.1134/S0037446622010050
Maximal Solvable Extension of Naturally Graded Filiform $ n $ -Lie
Algebras
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  Abstract: Abstract We study naturally graded filiform $ n $ -Lie algebras. Among these algebras, we distinguish some algebra with the simplest structure that is an analog of the model filiform Lie algebra. We describe the derivations of the algebra and obtain the classification of solvable $ n $ -Lie algebras whose maximal hyponilpotent ideal coincides with the distinguished naturally graded filiform algebra. Furthermore, we show that these solvable $ n $ -Lie algebras possess outer derivations.
  PubDate: 2022-01-01
  DOI: 10.1134/S0037446622010013
On Uniqueness of a Cycle in One Circular Gene Network Model
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  Abstract: Abstract We obtain conditions for uniqueness of a cycle in the phase portrait of a piecewise linear dynamical system of the Elowitz–Leibler type which simulates the functioning of a simplest circular gene network. We describe the behavior of trajectories of this system in the invariant toric neighborhood of the cycle.
  PubDate: 2022-01-01
  DOI: 10.1134/S0037446622010062
Finite Groups with $ p $ -Nilpotent or $ \Phi $ -Simple Maximal
Subgroups
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  Abstract: Abstract Under study is the structure of a finite non- $ r $ -nilpotent group, with $ r\in\{2,3,5\} $ , in which any non- $ r $ -nilpotent maximal subgroup is a $ \Phi $ -simple group.
  PubDate: 2022-01-01
  DOI: 10.1134/S0037446622010025