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Volume 524, Nº 1 (2025)
MATHEMATICS
TRACES OF THE SOLUTION OF A GENERAL LINEAR DIFFERENTIAL EQUATION IN THE DOMAIN
Resumo
Conditions on the solution traces of a general differential equation on the boundary of the domain are obtained, allowing one to assert the existence and uniqueness of this solution based on the traces of the solution and the right-hand side of the equation. For the case of a general equation with constant coefficients, the conditions obtained on the traces of the solution have the form of a generalized moment problem.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):3-10
3-10
ON COMPLEXITY OF TOTAL DERIVABILITY PROBLEM IN NONCONTRACTING AND CONTEXT-FREE GRAMMARS
Resumo
In this paper we study the problem of total derivability in context-free, noncontracting, and context-sensitive grammars. Given a grammar and a terminal word, one has to determine whether there exists a derivation of this word which uses each production no less than a given number of times. It is proved that the problem of total derivability of the emptyword in a context-free grammar is NP-complete. For noncontracting and context-sensitive grammars it is polynomially decidable for words of length 1, and it is NP-complete for every fixed word of length at least 2. Analagous results are obtained for another variant of the problem of total derivability when restrictions are placed on the amount of uses of nonterminals in the derivation.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):11-18
11-18
INTEGRAL REPRESENTATIONS FOR THE ARGUMENT OF THE GAMMA FUNCTION OF A COMPLEX VARIABLE
Resumo
New analytical representations of the argument of the gamma function at points of the complex plane have been found. For this value, integral formulas of two types have been obtained. Characteristic examples are analyzed.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):19–24
19–24
LINEAR FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND WITH CONSTRAINTS ON THE SOLUTION
Resumo
A linear integral equation of the first kind is considered in with an approximately specified righthand side. The desired solution satisfies the specified convex constraints. An iteration sequence is constructed, the limit of which is an approximate solution satisfying the imposed constraints. The approximate solution converges strongly to the exact solution if the error in the right-hand side of the equation tends to zero (in the norms of the corresponding Hilbert spaces). The proposed iteration process is numerically tested in a model problem for a linear integral equation of the first kind, the solution of which satisfies the linear constraints.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):25-33
25-33
ON THE PROPERTIES OF THE FUNDAMENTAL SOLUTION OF A ONE-DIMENSIONAL WAVE INTEGRO-DIFFERENTIAL OPERATOR WITH A FRACTIONAL-EXPONENTIAL MEMORY FUNCTION
Resumo
The properties of the fundamental solution of the linear Volterra integro-differential operator, which is a one-dimensional wave linear differential operator with partial derivatives, perturbed the Volterra integral operator of convolution, are investigated. The kernel function of the integral operator is the sum of fractional exponential functions (Rabotnov functions) with positive coefficients. For linear Volterra integro-differential operators with second-order partial derivatives, the concept of hyperbolicity with respect to a cone is introduced. It is established that hyperbolicity with respect to a cone is equivalent to the localization of the support of the fundamental solution of a second-order linear Volterra integro-differential operator in the conjugate cone. Hyperbolicity relative to the cone is established for one-dimensionalwave integrodifferential operator with a fractional-exponential memory function.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):34-39
34-39
RELATIVELY OPERATOR LIPSCHITZ FUNCTIONS OF DISSIPATIVE OPERATORS
Resumo
In this note we study the behaviour of functions of maximal dissipative operators under relatively bounded and relatively trace class perturbations. We introduce the class of analytic relatively operator Lipschitz functions.We obtain a formula for the derivative in the strong operator topology in the parameter of functions of one-parametric families of dissipative operators.We also establish a trace formula for the difference of a function of a perturbed operator and the function of the initial operator. It turns out that the corresponding spectral shift function is integrable with weight (1+|x|)−1. Moreover, the maximal class of functions, for which the trace formula holds for all pairs of maximal dissipative operators under relatively trace class perturbations coincides with the class of analytic relatively operator Lipschitz functions.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):40-46
40-46
A METHOD FOR DECISION ANALYSIS UNDER UNCERTAINTY WITH A QUALITATIVE ASSESSMENT OF PREFERENCES AND PROBABILITIES
Resumo
In this paper, we consider decision analysis problems in which the preferences of the decision maker are measured on an ordinal scale and the possibilities of realization of an uncertain factor are given as a qualitative probability, either complete or partial.We use this qualitative information to determine preference and indifference relations on the set of decision strategies, suggest a simple decision rule for the comparison of strategies and illustrate this development by several examples.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):47-50
47-50
ON THE STABILITY OF HYPERBOLIC EQUATIONS WITH UNBOUNDED TIME DELAY TERM
Resumo
In this paper, we establish a stability theorem for the initial value problem of hyperbolic equations with an unbounded time delay term in a Hilbert space.We also present a second order of accuracy difference scheme for approximating the solution to this problem and prove a corresponding stability theorem for the proposed difference scheme.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;524(1):51-55
51-55
56-60