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Articles 1 - 17 of 17
Full-Text Articles in Physical Sciences and Mathematics
Some Properties Of The Quartic Numerical Range For 4x4 Operator Matrices, Hakimboy Latipov
Some Properties Of The Quartic Numerical Range For 4x4 Operator Matrices, Hakimboy Latipov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In the present paper we consider self-adjoint 4x4 operator matrices A. For some special cases the alternative formulas for the calculating the quartic numerical range of 4x4 operator matrices A are derived. Using the obtained alternative formula for the quartic numerical range of A we estimate the lower and upper bound of A.
On The Negative Order Loaded Modified Korteweg–De Vries Equation, Praveen Agarwal, Bakhrom Abdullaev, Iroda Baltaeva, Shoira Atanazarova
On The Negative Order Loaded Modified Korteweg–De Vries Equation, Praveen Agarwal, Bakhrom Abdullaev, Iroda Baltaeva, Shoira Atanazarova
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this study, we establish the integration of the negative order loaded modified Korteweg-de Vries equation using the inverse scattering transform method. The main result is included in deriving the evolution equations for scattering data of the Dirac operator which is associated with the considered problem. Moreover, it was described the process of the construction of one-soliton solution of the negative order loaded modified Korteweg-de Vries equation.
Integration Of The Negative Order Korteweg-De Vries Equation With Self-Consistent Source, Michal Fečkan, Gayrat Urazboev, Iroda Baltaeva, Oxunjon Ismoilov
Integration Of The Negative Order Korteweg-De Vries Equation With Self-Consistent Source, Michal Fečkan, Gayrat Urazboev, Iroda Baltaeva, Oxunjon Ismoilov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper, we show that the negative-order Korteweg-de Vries equation with a self-consistent source can be solved by the inverse scattering method. The evolution of the spectral data of the Sturm-Liouville operator with the potential associated with the solution of the negative order Korteweg-de Vries equation with a self-consistent source is determined. The results obtained make it possible to apply the method of the inverse scattering problem to solve the problem under consideration.
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Turkish Journal of Mathematics
In this work, we are interested in a boundary value problem (BVP) generated by a Klein -Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example.
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
Turkish Journal of Mathematics
In this paper, we study two classes of operator-differential equations of the third order with a multiple characteristic, considered on the whole axis. We introduce the concept of a smooth regular solution of order 1 and obtain sufficient conditions for the "smoothly" regular solvability of these equations.
A Class Of Finsler Measure Spaces Of Constant Weighted Ricci Curvature, Songting Yin, Xiaohuan Mo, Ling Zhu
A Class Of Finsler Measure Spaces Of Constant Weighted Ricci Curvature, Songting Yin, Xiaohuan Mo, Ling Zhu
Turkish Journal of Mathematics
The weight Ricci curvature plays an important role in studying global Finsler geometry. In this paper, we study a class of Finsler measure spaces of constant weighted Ricci curvature. We explicitly construct new families of such complete Finsler measure spaces. In particular, we find an eigenfunction and its eigenvalue for such spaces, generalizing a result previously only known in the case of Gaussian shrinking soliton. Finally, we give necessary and sufficient conditions on the coordinate functions for these spaces to be Euclidean measure spaces.
Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung
Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung
Turkish Journal of Mathematics
Main purpose of this paper is to obtain fundamental relationships for the integrals and the matrix Wiener transforms on Hilbert space. Using some technics and properties of matrices of real numbers, we state some algebraic structure of matrices. We then establish evaluation formulas with examples. Furthermore, we define the matrix Wiener transform, and investigate some properties of the matrix Wiener transform. Finally, we establish relationships for the matrix Wiener transform.
On The Spectral And Scattering Properties Of Eigenparameter Dependent Discrete Impulsive Sturm-Liouville Equations, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram, Güher Gülçehre Özbey
On The Spectral And Scattering Properties Of Eigenparameter Dependent Discrete Impulsive Sturm-Liouville Equations, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram, Güher Gülçehre Özbey
Turkish Journal of Mathematics
This work develops scattering and spectral analysis of a discrete impulsive Sturm-Liouville equation with spectral parameter in boundary condition. Giving the Jost solution and scattering solutions of this problem, we find scattering function of the problem. Discussing the properties of scattering function, scattering solutions, and asymptotic behavior of the Jost solution, we find the Green function, resolvent operator, continuous and point spectrum of the problem. Finally, we give an example in which the main results are made explicit.
Higher-Order Sturm-Liouville Problems With The Same Eigenvalues, Hanif Mirzaei
Higher-Order Sturm-Liouville Problems With The Same Eigenvalues, Hanif Mirzaei
Turkish Journal of Mathematics
In this paper, we consider self-adjoint Sturm?Liouville problem (SLP) of higher-order. We define an equivalence relation between second- and higher-order SLP. Using the Darboux lemma and equivalence relation we obtain the closed form of a family of SLP which have the same eigenvalues. Also, some spectral properties of this family of Sturm?Liouville problems are investigated.
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Turkish Journal of Mathematics
In this manuscript,we study nonself-adjoint second-order differential operators with finite number of constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied for recovering differential operator from the potential from spectra of two boundary value problems with one common boundary condition.The uniqueness theorem is proved for this inverse problem.
On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Sh.S. Lakaev, Z.E. Muminov
On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Sh.S. Lakaev, Z.E. Muminov
Scientific Journal of Samarkand University
On the d- dimensional lattice 2 , 1 , d d Z the discrete Schrödinger operator H with non- local potential constructed via the Dirac delta function and shift operator is considered. The existence of negative eigenvalues on the parameters of the operator is explicity derived.
Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal
Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal
Turkish Journal of Mathematics
The Schrödinger equation for the eigenvalues of the infinitely deep square well potential is solved within the class of generalised functions. It is found that the ground state consists of a step function like eigenfunction with the eigenvalue zero.
Quadraticeigenparameter-Dependent Quantum Difference Equations, Yelda Aygar Küçükevci̇li̇oğlu
Quadraticeigenparameter-Dependent Quantum Difference Equations, Yelda Aygar Küçükevci̇li̇oğlu
Turkish Journal of Mathematics
The main aim of this paper is to construct quantum extension of the discrete Sturm--Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. We present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral singularities with finite multiplicities.
Fourth-Order Birkhoff Regular Problems With Eigenvalue Parameter Dependent Boundary Conditions, Bertin Zinsou
Fourth-Order Birkhoff Regular Problems With Eigenvalue Parameter Dependent Boundary Conditions, Bertin Zinsou
Turkish Journal of Mathematics
A regular fourth-order differential equation that depends quadratically on the eigenvalue parameter $\lambda$ is considered with classes of separable boundary conditions independent of $\lambda$ or depending on $\lambda$ linearly. Conditions are given for the problems to be Birkhoff regular.
Universal Inequalities And Bounds For Weighted Eigenvalues Of The Schrödinger Operator On The Heisenberg Group, Hejun Sun
Turkish Journal of Mathematics
For a bounded domain \Omega in the Heisenberg group H^n, we investigate the Dirichlet weighted eigenvalue problem of the Schrödinger operator - \Delta_{H^n} +V, where \Delta_{H^n} is the Kohn Laplacian and V is a nonnegative potential. We establish a Yang-type inequality for eigenvalues of this problem. It contains the sharpest result for \Delta_{H^n} in [17] of Soufi, Harrel II and Ilias. Some estimates for upper bounds of higher order eigenvalues and the gaps of any two consecutive eigenvalues are also derived. Our results are related to some previous results for the Laplacian \Delta and the Schrödinger operator -\Delta+V on a …
Determination Of A Fractional-Linear Pencil Of Sturm-Liouville Operators By Two Of Its Spectra, R. T. Pashayev
Determination Of A Fractional-Linear Pencil Of Sturm-Liouville Operators By Two Of Its Spectra, R. T. Pashayev
Turkish Journal of Mathematics
In this paper we consider the Sturm-Liouville equations on a finite interval which is fractional-linear in the spectral parameter. The inverse spectral problem consisting of the recovering of the operator from the two spectra is investigated and a uniqueness theorem for solution of the inverse problem is proved.
On The Spectral Properties Of The Regular Sturm-Liouville Problem With The Lag Argument For Which Its Boundary Conditions Depends On The Spectral Parameter, Mehmet Bayramoğlu, Kevser Özden Köklü, Oya Baykal
On The Spectral Properties Of The Regular Sturm-Liouville Problem With The Lag Argument For Which Its Boundary Conditions Depends On The Spectral Parameter, Mehmet Bayramoğlu, Kevser Özden Köklü, Oya Baykal
Turkish Journal of Mathematics
In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y''(t) + \lambda^2 y(t) + M(t)y (t - \Delta(t)) = 0 and the spectral parameter in the boundary conditions \lambda y(0) +y'(0) = 0 \lambda^{2}y(\pi) + y'(\pi) = 0 y(t - \Delta(t)) = y(0)\varphi(t - \Delta(t)), t - \Delta(t) < 0 has been founded in a finite interval, where M(t) and \Delta(t) \geq 0 are continuous functions on [0, \pi], \lambda > 0 is a real parameter, \varphi(t) is an initial function which is satisfied with the condition \varphi(0) = 1 and continuous in the initial set.