The Experts below are selected from a list of 237 Experts worldwide ranked by ideXlab platform
Zinovii Nytrebych - One of the best experts on this subject based on the ideXlab platform.
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The conditions of existence of a solution of the degenerate two-point in time problem for PDE
Asian-European Journal of Mathematics, 2019Co-Authors: Zinovii Nytrebych, Oksana MalanchukAbstract:The problem with local nonhomogeneous two-point in time conditions for homogeneous PDE of the second order in time and, generally, infinite order in spatial variables is investigated. This problem is degenerated namely its Characteristic Determinant is identically zero. The condition of existence of a solution of the degenerate problem is established. Also, we proposed the differential-symbol method of constructing the solution of the problem in the classes of entire functions. Some examples of solving the degenerate two-point in time problems are presented.
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The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem
Demonstratio Mathematica, 2019Co-Authors: Zinovii Nytrebych, Oksana MalanchukAbstract:Abstract The solvability of the problem with local nonhomogeneous two-point in time conditions for a homogeneous PDE of the second order in time and infinite order in spatial variable in the case when the set of zeroes of the Characteristic Determinant is not empty and does not coincide with C is investigated. The existence of a solution of the problem in which the right-hand sides of the two-point conditions are quasi-polynomials is proved. We propose the differential-symbol method of constructing the solutions of the problem.
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On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time
Journal of Mathematical Sciences, 2019Co-Authors: Zinovii Nytrebych, О. М. MalanchukAbstract:We study the problem for a homogeneous partial differential equation of the second order with respect to time with given homogeneous two-point conditions in this variable and, in general, of the infinite order in the other (space) variable. It is proved that the analyzed problem possesses solely the trivial solution if the Characteristic Determinant is not identically equal to zero. In the case where the set of zeros of the Characteristic Determinant of this problem is nonempty, we propose a method for the construction of nontrivial solutions of the problem.
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Homogeneous Problem with Two-point Conditions in Time for Some Equations of Mathematical Physics
Azerbaijan Journal of Mathematics, 2017Co-Authors: Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro PukachAbstract:We study the problem for homogeneous partial differential equations in two variables which are of second order with respect to time variable and of finite order with respect to another (spatial) variable, with homogeneous two-point conditions in time. We propose a method for the construction of nontrivial solutions of this problem when its Characteristic Determinant is nontrivial and the set of its zeroes is not empty. We apply this method to the construction of non-zero solutions of homogeneous two-point problems for some equations of mathematical physics.
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Homogeneous Problem with two-point in time Conditions for Some Equations of Mathematical Physics
Azerbaijan Journal of Mathematics, 2017Co-Authors: Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro PukachAbstract:We study the problem for homogeneous partial differential equations of two variables of the second order with respect to the time variable in which there given homogeneous two-point conditions, and finite order with respect to another (spatial) variable. We propose a method of construction nontrivial solutions of the problem when the Characteristic Determinant of the problem is nontrivial and the set of its zeroes is not empty. We applied this method to the construction of non-zero solutions of homogeneous two-point problems for some equations of mathematical physics.
Oksana Malanchuk - One of the best experts on this subject based on the ideXlab platform.
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The conditions of existence of a solution of the degenerate two-point in time problem for PDE
Asian-European Journal of Mathematics, 2019Co-Authors: Zinovii Nytrebych, Oksana MalanchukAbstract:The problem with local nonhomogeneous two-point in time conditions for homogeneous PDE of the second order in time and, generally, infinite order in spatial variables is investigated. This problem is degenerated namely its Characteristic Determinant is identically zero. The condition of existence of a solution of the degenerate problem is established. Also, we proposed the differential-symbol method of constructing the solution of the problem in the classes of entire functions. Some examples of solving the degenerate two-point in time problems are presented.
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The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem
Demonstratio Mathematica, 2019Co-Authors: Zinovii Nytrebych, Oksana MalanchukAbstract:Abstract The solvability of the problem with local nonhomogeneous two-point in time conditions for a homogeneous PDE of the second order in time and infinite order in spatial variable in the case when the set of zeroes of the Characteristic Determinant is not empty and does not coincide with C is investigated. The existence of a solution of the problem in which the right-hand sides of the two-point conditions are quasi-polynomials is proved. We propose the differential-symbol method of constructing the solutions of the problem.
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Homogeneous Problem with Two-point Conditions in Time for Some Equations of Mathematical Physics
Azerbaijan Journal of Mathematics, 2017Co-Authors: Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro PukachAbstract:We study the problem for homogeneous partial differential equations in two variables which are of second order with respect to time variable and of finite order with respect to another (spatial) variable, with homogeneous two-point conditions in time. We propose a method for the construction of nontrivial solutions of this problem when its Characteristic Determinant is nontrivial and the set of its zeroes is not empty. We apply this method to the construction of non-zero solutions of homogeneous two-point problems for some equations of mathematical physics.
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Homogeneous Problem with two-point in time Conditions for Some Equations of Mathematical Physics
Azerbaijan Journal of Mathematics, 2017Co-Authors: Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro PukachAbstract:We study the problem for homogeneous partial differential equations of two variables of the second order with respect to the time variable in which there given homogeneous two-point conditions, and finite order with respect to another (spatial) variable. We propose a method of construction nontrivial solutions of the problem when the Characteristic Determinant of the problem is nontrivial and the set of its zeroes is not empty. We applied this method to the construction of non-zero solutions of homogeneous two-point problems for some equations of mathematical physics.
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Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables
Open Mathematics, 2017Co-Authors: Oksana Malanchuk, Zinovii NytrebychAbstract:Abstract We prove that homogeneous problem for PDE of second order in time variable, and generally infinite order in spatial variables with local two-point conditions with respect to time variable, has only trivial solution in the case when the Characteristic Determinant of the problem is nonzero. In another, opposite case, we prove the existence of nontrivial solutions of the problem, and we propose a differential-symbol method of constructing them.
A. M. Akhtyamov - One of the best experts on this subject based on the ideXlab platform.
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Various Spectral Problemswith the Same Characteristic Determinant
Differential Equations, 2020Co-Authors: A. M. AkhtyamovAbstract:We show that there exist whole classes of various boundary value problems having the same Characteristic Determinant, with the respective problems allowed to have differing orders of the differential equations and to be defined both on intervals and on geometric graphs.
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Degenerate Boundary Conditions for the Diffusion Operator on a Geometric Graph
Differential Equations, 2020Co-Authors: Victor Antonovich Sadovnichii, Ya. T. Sultanaev, A. M. AkhtyamovAbstract:We study boundary conditions for the diffusion operator defined on a star-shaped geometric graph consisting of three edges with a common vertex. We show that if the edge lengths are pairwise distinct, then there do not exist degenerate boundary conditions for the diffusion operator. If the edge lengths coincide and the potentials are symmetric, then the Characteristic Determinant of a boundary value problem for the diffusion operator cannot be a constant other than zero, and the set of boundary value problems for which the Characteristic Determinant is identically zero is infinite (a continuum). We show that, for the diffusion operator on the star-shaped graph, the set of boundary value problems whose spectrum fills the entire plane consists of eighteen classes, each of which contains eight to nine arbitrary constants. Recall that for the diffusion operator defined on an interval this set consists of two problems.
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Identification of Nonseparated Boundary Conditions
Journal of Mathematical Sciences, 2019Co-Authors: A. M. Akhtyamov, A. V. MouftakhovAbstract:We consider the problem of identification of nonseparated boundary conditions by five eigenvalues. Based on the Plucker conditions that appear in the problem of matrix recovery by its maximal-size minors, we construct the well-posedness set for this problem. We solve the problem of identification of the matrix of nonseparated boundary conditions in terms of the Characteristic Determinant of the corresponding spectral problem. The corresponding examples are presented.
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Degenerate Boundary Conditions on a Geometric Graph
Доклады Академии наук, 2019Co-Authors: Victor Antonovich Sadovnichii, Ya. T. Sultanaev, A. M. AkhtyamovAbstract:The boundary conditions of the Sturm-Liouville problem defined on a star-shaped geometric graph of three edges are studied. It is shown that if the lengths of the edges are different, then the Sturm-Liouville problem does not have degenerate boundary conditions. If the lengths of the edges and the potentials are the same, then the Characteristic Determinant of the Sturm-Liouville problem can not be equal to a constant different from zero. But the set of Sturm-Liouville problems for which the Characteristic Determinant is identically equal to zero is an infinite (continuum). In this way, in contrast to the Sturm-Liouville problem defined on an interval, the set of boundary-value problems on a star-shaped graph whose spectrum completely fills the entire plane is much richer. In the particular case when the minor A 124 for matrix of coefficients is nonzero, it does not consist of two problems, as in the case of the Sturm-Liouville problem given on an interval, but of 18 classes, each containing two to four arbitrary constants.
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Degenerate Boundary Conditions for the Sturm-Liouville Problem on a Geometric Graph
Differential Equations, 2019Co-Authors: Victor Antonovich Sadovnichii, Ya. T. Sultanaev, A. M. AkhtyamovAbstract:We study the boundary conditions of the Sturm-Liouville problem posed on a star-shaped geometric graph consisting of three edges with a common vertex. We show that the Sturm-Liouville problem has no degenerate boundary conditions in the case of pairwise distinct edge lengths. However, if the edge lengths coincide and all potentials are the same, then the Characteristic Determinant of the Sturm-Liouville problem cannot be a nonzero constant and the set of Sturm-Liouville problems whose Characteristic Determinant is identically zero and whose spectrum accordingly coincides with the entire plane is infinite (a continuum). It is shown that, for one special case of the boundary conditions, this set consists of eighteen classes, each having from two to four arbitrary constants, rather than of two problems as in the case of the Sturm-Liouville problem on an interval.
Nurlan S Imanbaev - One of the best experts on this subject based on the ideXlab platform.
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On a Problem that Does not Have Basis Property of Root Vectors, Associated with a Perturbed Regular Operator of Multiple Differentiation
Journal of Siberian Federal University. Mathematics & Physics, 2020Co-Authors: Nurlan S ImanbaevAbstract:A spectral problem for a multiple differentiation operator with integral perturbation of boundary value conditions which are regular but not strongly regular is considered in the paper. The feature of the problem is the absence of the basis property of the system of root vectors. A Characteristic Determinant of the spectral problem is constructed. It is shown that absence of the basis property of the system of root functions of the problem is unstable with respect to the integral perturbation of the boundary value condition
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a regular differential operator with perturbed boundary condition
Mathematical Notes, 2017Co-Authors: Makhmud A Sadybekov, Nurlan S ImanbaevAbstract:The operator ℒ0 generated by a linear ordinary differential expression of nth order and regular boundary conditions of general form is considered on a closed interval. The Characteristic Determinant of the spectral problem for the operator ℒ1, where ℒ1 is an operator with the integral perturbation of one of its boundary conditions, is constructed, assuming that the unperturbed operator ℒ0 possesses a system of eigenfunctions and associated functions generating an unconditional basis in L 2(0, 1). Using the obtained formula, we derive conclusions about the stability or instability of the unconditional basis properties of the system of eigenfunctions and associated functions of the problem under an integral perturbation of the boundary condition. The Samarskii–Ionkin problem with integral perturbation of its boundary condition is used as an example of the application of the formula.
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About Characteristic Determinant of one boundary value problem not having the basis property
2017Co-Authors: Nurlan S Imanbaev, Makhmud A SadybekovAbstract:In this paper we consider a spectral problem of one boundary value problem for a two-fold differentiation operator with an integral perturbation of boundary conditions of one type which are regular, but not strongly regular. The unperturbed problem has an asymptotically simple spectrum, and its system of eigenfunctions does not form a basis in L2. We construct a Characteristic Determinant of the spectral problem with an integral perturbation of boundary conditions. We show that a set of kernels of the integral perturbation, under which absence of basis properties of the system of root functions persists, is dense in L2.
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Characteristic Determinant of the spectral problem for the ordinary differential operator with the boundary load
2014Co-Authors: Nurlan S Imanbaev, Makhmud A SadybekovAbstract:In this paper, we consider a linear operator, generated by the ordinary differential expression with the boundary load and strongly regular boundary conditions of the general form. We prove the possibility of constructing the Characteristic Determinant of the spectral problem.
Yiuwing Mai - One of the best experts on this subject based on the ideXlab platform.
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specimen design for ifss measurement in fiber pullout test
Key Engineering Materials, 2006Co-Authors: Ying Dai, Yiuwing MaiAbstract:Since stress singularity was found at the interface end in current specimen of pullout test, interface shear strength (IFSS) obtained from the tests loses its rationality [2]. But a useful conclusion [2] is that when the wedge angle of the matrix is less than a critical angle, the singularity of stress field at the interface end of the specimen in micro-debond test nearly disappears. Following this conclusion, a conic specimen shown in Fig. 1 is presented, in which the wedge angle of the specimen is designed to be less than a critical angle in order to prevent the singular stress field occurred at the interface end. The conic specimen is designed for pullout test to avoid disadvantages inherent in the micro-debond test [3]. An axisymmetric model of fiber/matrix system with arbitrary wedge angles at the interface end is used for the determination of critical wedge angle. With the aid of asymptotic analysis and variable separation, eigenvalue, λ, could be determined by a Characteristic Determinant. For a given fiber-matrix system, a curve representing the relationship between the stress singularity index and wedge angle could be obtained by solving the Characteristic Determinant. We define the critical wedge angle, θcr, as the corresponding singularity index of – 0.005. The design of a conic pullout specimen is also discussed. FEM analysis is adopted to calculate the distribution of interfacial stresses near the interface end with different wedge angle. The results verify the rationality of the principle of the design of conic pullout specimen for IFSS measurement.
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stress singularity analysis of interface end and specimen design for fiber pullout test
Composite Technologies for 2020#R##N#Proceedings of the Fourth Asian–Australasian Conference on Composite Materials (ACCM 4), 2004Co-Authors: Ying Dai, Yiuwing MaiAbstract:ABSTRACT Since stress singularity was found at the interface end in current specimen of pullout test, interface shear strength (IFSS) obtained from the tests loses its rationality [2]. But a useful conclusion [2] is that when the wedge angle of the matrix is less than a critical angle, the singularity of stress field at the interface end of the specimen in micro-debond test nearly disappears. Following this conclusion, a conic specimen shown in Figure 1 is presented, in which the wedge angle of the specimen is designed to be less than a critical angle in order to prevent the singular stress field occurred at the interface end. The conic specimen is designed for pullout test to avoid disadvantages inherent in the micro-debond test [3]. An axisymmetric model of fiber/matrix system with arbitrary wedge angles at the interface end is used for the determination of critical wedge angle. With the aid of asymptotic analysis and variable separation, eigenvalue, λ, could be determined by a Characteristic Determinant. For a given fiber-matrix system, a curve representing the relationship between the stress singularity index and wedge angle could be obtained by solving the Characteristic Determinant. We define the critical wedge angle, Ocr, as that for a singularity index of −0.005. The design of a conic pullout specimen is also discussed.