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Databases : Springer ✕Index Type : ESCI ✕
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On the Method of Lyapunov Functionals for a Linear First-Order Volterra Integrodifferential Equation with Delay on the Semiaxis

Samandar İSKANDAROV

Sufficient conditions are established to ensure the estimation, boundedness, power-law absolute integrability on the semiaxis, the tendency to zero under the tendency to infinity of the independent variable of all solutions of the linear Volterra integrodifferential equation of the first order with delay. For this purpose, a generalized Lyapunov functional is constructed. An illustrative example is presented. Keyword: absolute integrability; argument lag; boundedness; estimation; generalized method of Lyapunov functionals; tending to zero of solutions; Volterra integrodifferential equation of ...More

Article 2023 Fen Fakültesi Moscow University Mathematics Bulletin78 ( 3 ) 18 Views
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A Singularly Perturbed System of Parabolic Equations

Asan ÖMÜRALİEV | Peyil Esengul Kızı

The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains boundary layer functions.

Article 2021 Fen Fakültesi Lobachevskii Journal of Mathematics42 ( 15 ) 77 Views
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Dynamics of Microbiological Diversity of Soils in the Chu Valley during Land Use Change in Pastures

Nurzat TOTUBAYEVA

Soil microflora is one of the first to feel a negative impact and can serve as a biological indicator of changes in the soil structure and the degree of impact on the soil ecosystem. In 2020, studies were carried out at two sites located in the Shamshy Gorge in the Chui region of the Kyrgyz Republic. One of the plots was withdrawn from pasture use for one year in 2020 and two years in 2019 as compared to the actively used control option. The microbiological diversity was studied with conventional methods of microbiology. The micromycetes of the studied soils were represented in the dominance o ...More

Article 2022 Mühendislik Fakültesi Arid Ecosystems12 ( 2 ) 68 Views
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About Power Absolute Integrated of the Solution of Volterra System of Linear Second Kind Integral Equations on Half-axis

Samandar İSKANDAROV

Sufficient conditions are established such as the sign of the functions of absolute and quadratic integrability on the half-axis of the components of the solution of a linear system of Volterra-type integral equations of the second kind in the new formulation, namely, without the assumption that the components of the free term possess the properties under study. To achieve the intended goals, the matrix method of weight functions, the matrix method of cutting functions, the matrix method of partial cutting of the author, and the method of integral inequalities of Ya. V. Bykov are developed. Th ...More

Article 2021 Fen Fakültesi Lobachevskii Journal of Mathematics42 ( 3 ) 98 Views
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One Class of Linear Fredholm Operator Equations of the Third Kind

Avıt ASANOV | Kalıskan MATANOVA

In this paper, we are applied a new approach to prove that the solution of the linear Fredholm operator equation of the third kind given on a segment and having a finite number of multipoint singularities is equivalent to the solution of the linear Fredholm operator equation of the second kind with additional conditions. We are showed an example of solving the system of linear integral Fredholm equations of the third kind based on the equivalence of the above equations.

Article 2021 Fen Fakültesi Lobachevskii Journal of Mathematics42 ( 3 ) 66 Views
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Specific Asymptotic Stability of Solutions to a Linear Homogeneous Volterra Integro-Differential Equation of the Fourth Order

Samandar İSKANDAROV

Sufficient conditions for the asymptotic stability of solutions to a fourth-order linear homogeneous Volterra integro-differential equation are established in the case where any nonzero solution to the corresponding linear homogeneous differential equation of the fourth order is not asymptotically stable. An illustrative example is given.

Article 2021 Fen Fakültesi Moscow University Mathematics Bulletin76 ( 1 ) 96 Views
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Solving a System of Linear Algebraic Equations with a Tridiagonal Matrix: A New Look at Cramer's Rule

Anarkül URDALETOVA

To numerically solve a system of linear algebraic equations with a tridiagonal matrix, a recursive version of Cramer's rule is proposed. This method requires no additional restrictions on the matrix of the system similar to those formulated for the double-sweep method. The results of numerical experiments on a large set of test problems are presented. A comparative analysis of the efficiency of the method and corresponding algorithms is given.

Article 2021 Fen Fakültesi Numerical Analysis and Applications14 ( 3 ) 60 Views
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A System of Singularly Perturbed Parabolic Equations with a Power Boundary Layer

Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı

The work is devoted to the construction of the asymptotics of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains, along with parabolic boundary layer functions, and power boundary layer functions.

Article 2020 Fen Fakültesi Lobachevskii Journal of Mathematics41 ( 1 ) 65 Views
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