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Известия Иркутского государственного университета: Серия "Математика"
Scopus
ISSN 1997-7670 · Irkutsk State University · 480 articles in the index
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Journal Article
Decidability of Multi-agent Logic of Computation Trees $\mathcal{CTLK}^{Rel}$
We continue to explore the multi-agent logic of computational trees relative to the relational Kripke semantics of possible worlds: we investigate the question of logical solvability, the complexity of model construction, feasibility testing, and correctness. For the semantics introduced earlier…
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Journal Article
Evgeniy Konstantinovich Leinartas (1954–2024)
The article is devoted to the scientific and pedagogical activity of Doctor of Physical and Mathematical Sciences, Professor of the Department of Function Theory at Siberian Federal University Evgeniy Konstantinovich Leinartas (1954–2024).
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Journal Article
On the Collocation Method in Constructing a Solution to the Bending Equation for a Long Rectangular Nanoplate
Within the framework of the theory of microstructural deformation, a new approach is proposed for constructing a solution to the bending equation of a long rectangular nanoplate that is under the influence of a transverse load. The proposed approach is based on the collocation method using a system…
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Journal Article
On the Cardinality of the Lattice of Closed Classes\\of Polynomials in $k$-Valued Logic for Composite Numbers $k$
Closed classes under superposition are examined in $k$-valued logic. E.~Post established that the lattice (on inclusion) of all closed classes in two-valued logic is countable. Besides, each closed class has a finite basis in two-valued logic. Yu.\,I.~Yanov and A.\,A.~ Muchnick proved that the…
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Journal Article
Composite-type Differential Equations with Degeneration
The paper is devoted to the study of the solvability of boundary value problems for fourth-order linear composite-type differential equations. A distinctive feature of the considered equations is that the operator coefficient at the highest derivative with respect to the time (distinguished)…
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Journal Article
On the Establishment of the Order of Smoothness of the Minimal Concave Continuation of a Real Discrete Function Defined on the Vertices of a Parallelepiped
In this paper, we study the order of differentiability of the minimal concave continuation to an n-dimensional coordinate parallelepiped of a real discrete function defined on the vertices of this arbitrary n-dimensional coordinate parallelepiped. As a result of the study, the order of…
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Journal Article
Shunkov Groups with Additional Finiteness Conditions, Containing Dihedral Subgroups
In this paper, Shunkov groups are studied in the context of the well-known question of B. Amberg and L. S. Kazarin about the structure of groups containing direct products of a finite number of dihedral groups. To do this, two additional finiteness conditions are imposed on the Shunkov group: it is…
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Journal Article
System of Kaup Equations with a Loaded Term in the Class of Periodic Functions
In this paper, a system of nonlinear Kaup equations with a loaded additional term in the class of periodic functions with respect to the spatial variable is considered. The invariance of the spectrum is proved and an analog of the Dubrovin system is derived for the evolution of the spectral…
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Journal Article
Noncommutative Products on Categories and Chu Construction
The category of Chu spaces is constructed from a given symmetric monoidal closed category $K$ and a fixed object in it. If the object is not fixed, we obtain the category $Chu(K)$, whose objects are Chu spaces and whose morphisms are defined in a more general way. E.E. Skurikhin defined and studied…
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Journal Article
$N$-recognizability of Groups $ Alt_p\times Alt_5$,\\ Where $p>1361$ Is a Prime Number
$N$-recognizability of Groups $ Alt_p\times Alt_5$, Where $p>1361$ Is a Prime Number} Given a finite group $L$, let $N(L)$ denote the set of its conjugacy class sizes. Let $X$ and $Y$ be sets of natural numbers, $G$ be a finite group such that $N(G)=X\times Y$. In the article \cite{Gor24} the…
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Journal Article
On an Asymptotic Property of Dirichlet Kernels
The main object of our study is the Dirichlet kernel. The properties of this trigonometric polynomial — the sum of cosines of multiple arcs — are of undoubted interest in the theory of trigonometric series. For example, the results on the asymptotic behavior of the Lebesgue constants, which are the…
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Journal Article
Algebras of Binary Formulas for Weakly Circularly Minimal Theories with Trivial Definable Closure: Monotonic-to-right Case
This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. We consider the binary level of these structures forming algebras of binary isolating formulas, which are based on families of labels and compositions of related formulas…
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Journal Article
Concatenations of Linear Orderings and Their Rigidity Characteristics
Among algebraic operations the operation of concatenation for families of words and for orderings is broadly used in various fields of theoretical and applied mathematics, and informatics. It allows to structure to group and to modify information relative required sequences. Degrees of rigidity are…
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Journal Article
The Collection Formula and Regular $p$-Groups
For any elements $x,y$ of a group $G$ and for any positive integer $n$, we obtain the collection formula for the $n$-th power of the product $xy$ when all commutators in $G$ that have more than 3 occurrences of the element $y$ are equal to 1. Suppose $n=p$ is a prime number, and any commutator…
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Journal Article
Kernel Determination Inverse Problem in the Moore–Gibson–Thompson Equation
We investigate an inverse problem of determining the kernel function 𝑔(𝑡) in the third-order Moore–Gibson–Thompson (MGT) equation. First, the solution to the direct initial–boundary value problem for a homogeneous MGT equation is constructed using the Fourier spectral method. Then, based on this…
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Journal Article
A Mixed Problem for the Negative Order Nonlinear Modified Korteweg–de Vries Equation with a Special Term
In this paper, a mixed problem for the negative order nonlinear modified Korteweg–de Vries (mKdV) equation with a special free term is considered. It is shown that the mixed problem for the negative order nonlinear mKdV equation with a special free term can be integrated using the inverse spectral…
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Journal Article
Existence and Uniqueness Theorem for a Weak Solution to the Initial-Boundary Value Problem for the Kelvin–Voigt Mathematical Model of the Motion of a Mixture of Fluids
Equations describing three-dimensional unsteady motions of Kelvin–Voigt mixture of viscous incompressible liquids are considered. The theorem of existence and uniqueness of a weak solution of an initial boundary value problem corresponding to flows in a limited domain is proved. To prove the…
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Journal Article
Gradient Projection Method and Stochastic Search for Some Optimal Control Models with Spin Chains. I
This article (I) considers optimal control models for both transferring an excitation from the first spin to the last spin in a chain of 𝑁 spins and keeping an excitation initially given at the last spin. Each model employs an external controlled parabolic magnetic field represented by two control…
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Journal Article
Tensor Representation of a Numerical Method for Solving the Plateau Problem
This paper proposes an operator approach for solving computational problems on irregular meshes in the form of triangulations. The proposed method is based on organizing the computational process as a sequence of operations on multidimensional tensors that represent all the processed data…
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Journal Article
The Problem of Optimizing a Set of Quadratic Criteria Relative to a Linear Multi-Step Control System
A linear-quadratic problem of optimal control in a discrete-time formulation and multi-objective setting is considered: a linear system, a set of quadratic objective functions in state and control variables, multi-objective optimization, and Pareto-optimal solutions. Based on a linear scalarization…