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Full-Text Articles in Physical Sciences and Mathematics
Some Estimates On The Spin−Submanifolds, Serhan Eker
Some Estimates On The Spin−Submanifolds, Serhan Eker
Turkish Journal of Mathematics
In this paper, an optimal lower bound is given for the Submanifold Dirac operator in terms of the trace of an Energy−Momentum tensor, scalar curvature and mean curvature. In the equality case, it is proven that the submanifold is Einstein if the normal bundle is flat. Key words: Spin geometry, eigenvalues,
On The Eigenstructure Of The $Q$-Durrmeyer Operators, Övgü Gürel Yilmaz
On The Eigenstructure Of The $Q$-Durrmeyer Operators, Övgü Gürel Yilmaz
Turkish Journal of Mathematics
The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the $q$-Durrmeyer operators $D_{n,q}$ and the limit $q$-Durrmeyer operators $D_{\infty,q}$ introduced by V. Gupta in the case 0<$q$<1. All moments for $D_{n,q}$ and $D_{\infty,q}$ are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.
Mathematics Model Of Inheritance Three Different Traits In Genetics With Matrix Approach, Jufra Jufra, Asrul Sani, Sardin Sardin
Mathematics Model Of Inheritance Three Different Traits In Genetics With Matrix Approach, Jufra Jufra, Asrul Sani, Sardin Sardin
PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika
Mathematical models can solve problems to find out which individuals are superior from crosses in the field of genetics. The matrix form of the mathematical model using the concept of matrix diagonalization can solve these problems. The general definition of matrix diagonalization is with the diagonalized matrix elements obtained from the probability of crossing the average parent and the recessive parent. The mathematical model of a cross between the average parent and recessive parent can be formulated as . The behavior of the solution from the cross is in the form of an explicit equation which can be formulated as …
Discrete Impulsive Sturm-Liouville Equation With Hyperboliceigenparameter, Turhan Köprübaşi, Yelda Aygar Küçükevci̇li̇oğlu
Discrete Impulsive Sturm-Liouville Equation With Hyperboliceigenparameter, Turhan Köprübaşi, Yelda Aygar Küçükevci̇li̇oğlu
Turkish Journal of Mathematics
Let $L$ denote the selfadjoint difference operator of second order with boundary and impulsive conditions generated in $\ell _{2}\left( %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion \right) $ by \begin{equation*} a_{n-1}y_{n-1}+b_{n}y_{n}+a_{n}y_{n+1}=\left( 2\cosh z\right) y_{n}\text{ },% \text{ }n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion \setminus \left\{ k-1,k,k+1\right\} , \end{equation*}% \begin{equation*} \begin{array}{c} y_{0}=0\text{ }, \\ \left\{ \begin{array}{c} y_{k+1}=\theta _{1}y_{k-1} \\ \bigtriangleup y_{k+1}=\theta _{2}\bigtriangledown y_{k-1} \end{array}% \right. ,\text{ }\theta _{1},\theta _{2}\in %TCIMACRO{\U{211d}}% %BeginExpansion \mathbb{R}, %EndExpansion \end{array}% \end{equation*} where $\left\{ a_{n}\right\} _{n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion },$ $\left\{ b_{n}\right\} _{n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion }$ are real sequences and $\bigtriangleup ,\bigtriangledown $ are respectively forward …
Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy
Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy
Turkish Journal of Mathematics
In this paper, the main content is the consideration of the concepts of eigenvalues and spectral singularities of an operator generated by a discrete Dirac system in $\ell_{2}(\mathbb{Z},\mathbb{C}^{2})$ with an interior interaction point. Defining a transfer matrix $ M $ enables us to present a relationship between the $ M_{22} $ component of this matrix and Jost functions of mentioned Dirac operator so that its eigenvalues and spectral properties can be studied. Finally, some special cases are examined where the impulsive condition possesses certain symmetries.
General Characteristics Of A Fractal Sturm-Liouville Problem, Fatma Ayça Çeti̇nkaya, Alireza Khalili Golmankaneh
General Characteristics Of A Fractal Sturm-Liouville Problem, Fatma Ayça Çeti̇nkaya, Alireza Khalili Golmankaneh
Turkish Journal of Mathematics
In this paper, we consider a regular fractal Sturm-Liouville boundary value problem. We prove the self-adjointness of the differential operator which is generated by the $F^\alpha$-derivative introduced in [32]. We obtained the $F^\alpha$-analogue of Liouville's theorem, and we show some properties of eigenvalues and eigenfunctions. We present examples to demonstrate the efficiency and applicability of the obtained results. The findings of this paper can be regarded as a contribution to an emerging field.
A Study Of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter, Turhan Köprübaşi
A Study Of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter, Turhan Köprübaşi
Turkish Journal of Mathematics
Let $L$ denote the discrete Dirac operator generated in $\ell _{2}\left( %TCIMACRO{\U{2115} }% %BeginExpansion \mathbb{N} %EndExpansion ,% %TCIMACRO{\U{2102} }% %BeginExpansion \mathbb{C} %EndExpansion ^{2}\right) $ by the difference operators of first order% \begin{equation*} \left\{ \begin{array}{cc} {\bigtriangleup y_{n}^{\left( 2\right) }+p_{n}y_{n}^{\left( 1\right) }=\lambda y_{n}^{(1)}} & \\ {\bigtriangleup y_{n-1}^{\left( 1\right) }+q_{n}y_{n}^{\left( 2\right) }=\lambda y_{n}^{(2)}}, \end{array} \text{ }n\in \mathbb{N} \setminus \left\{ k-1,k,k+1\right\} \right. \end{equation*} with boundary and impulsive conditions% \begin{equation*} \begin{array}{c} y_{0}^{(1)}=0\text{ }, \\ \\ \left( \begin{array}{c} y_{k+1}^{(1)} \\ y_{k+2}^{(2)}% \end{array}% \right) =\theta \left( \begin{array}{c} y_{k-1}^{(2)} \\ y_{k-2}^{(1)}% \end{array}% \right) ;\text{ }\theta =\left( \begin{array}{cc} \theta _{1} & \theta _{2} \\ \theta _{3} & \theta _{4}% …
Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri
Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri
Turkish Journal of Mathematics
In this paper, fractional Sturm--Liouville problems of high-order are studied. A simple and efficient approach is presented to determine more eigenvalues and eigenfunctions than other approaches. Existence and uniqueness of solutions of a fractional high-order differential equation with initial conditions is addressed as well as the convergence of the proposed approach. This class of eigenvalue problems is important in finding solutions to linear fractional partial differential equations (LFPDE). This method is illustrated by three examples to signify the efficiency and reliability of the proposed numerical approach.
On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov
On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov
Turkish Journal of Mathematics
In this paper, we study the magnetic Schrödinger operator in a three-dimensional layer. We obtain an estimate for the number of eigenvalues of this operator lying to the left of the essential spectrum threshold. We show that the magnetic Schrödinger operator to the left of the continuous spectrum threshold can have only a finite number of eigenvalues of infinite multiplicity.
Eigenvalue Problems For An Elliptic Equation With Two Singular Coefficients, Asror M. Shokirov
Eigenvalue Problems For An Elliptic Equation With Two Singular Coefficients, Asror M. Shokirov
Scientific Bulletin. Physical and Mathematical Research
For the elliptic type of differential equation with two singular coefficients, the quadratic values of the Dirixle and Dirixle-Neumann problems were found in the quarter in that work. The field and boundary conditions for solving these problems are described in the polar coordinate system. The result is a rectangle in the polar coordinate system. Then, we used the method of separating variables in the right rectangle, that is, divided the variables by the equation and divided the problem into two distinct values for ordinary differential equations. The first of the ordinary differential equations is the substitution of , where the …
A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova
A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova
Scientific journal of the Fergana State University
In the article a generalised spectral problem with the second kind integral condition for the linear ordinary differential equation with discontinuous coefficient is investigated. Eigenvalues and eigenfunctions of the considered problem are found out.
A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova
A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova
Scientific journal of the Fergana State University
In the article a generalised spectral problem with the second kind integral condition for the linear ordinary differential equation with discontinuous coefficient is investigated. Eigenvalues and eigenfunctions of the considered problem are found out.
A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova
A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova
Scientific journal of the Fergana State University
In the article a generalised spectral problem with the second kind integral condition for the linear ordinary differential equation with discontinuous coefficient is investigated. Eigenvalues and eigenfunctions of the considered problem are found out.
Spectrum And Scattering Function Of The Impulsive Discrete Dirac Systems, Elgiz Bairamov, Şeyda Solmaz
Spectrum And Scattering Function Of The Impulsive Discrete Dirac Systems, Elgiz Bairamov, Şeyda Solmaz
Turkish Journal of Mathematics
In this paper, we investigate analytical and asymptotic properties of the Jost solution and Jost function of the impulsive discrete Dirac equations. We also study eigenvalues and spectral singularities of these equations. Then we obtain characteristic properties of the scattering function of the impulsive discrete Dirac systems. Therefore, we find the Jost function, point spectrum, and scattering function of the unperturbed impulsive equations.
On The Solution Of An Inverse Sturm-Liouville Problem With A Delay And Eigenparameter-Dependent Boundary Conditions, Seyfollah Mosazadeh
On The Solution Of An Inverse Sturm-Liouville Problem With A Delay And Eigenparameter-Dependent Boundary Conditions, Seyfollah Mosazadeh
Turkish Journal of Mathematics
In this paper, a boundary value problem consisting of a delay differential equation of the Sturm-Liouville type with eigenparameter-dependent boundary conditions is investigated. The asymptotic behavior of eigenvalues is studied and the parameter of delay is determined by eigenvalues. Then we obtain the connection between the potential function and the canonical form of the characteristic function.
Solving An Initial Boundary Value Problem On Thesemiinfinite Interval, Feri̇he Atalan, Gusein Sh. Guseinov
Solving An Initial Boundary Value Problem On Thesemiinfinite Interval, Feri̇he Atalan, Gusein Sh. Guseinov
Turkish Journal of Mathematics
We explore the sign properties of eigenvalues and the basis properties of eigenvectors for a special quadratic matrix polynomial and use the results obtained to solve the corresponding linear system of differential equations on the half line subject to an initial condition at $t=0$ and a condition at $t=\infty$.
Spectral Problems For Operator Pencils In Non-Separated Root Zones, Mahi̇r Hasanov
Spectral Problems For Operator Pencils In Non-Separated Root Zones, Mahi̇r Hasanov
Turkish Journal of Mathematics
Variational principles for real eigenvalues of self-adjoint operator pencils in non-separated root zones are studied.
On The Expansions In Eigenfunctions Of Hill's Operator, Fi̇li̇z Aras, Gusei̇n Sh Gusei̇nov
On The Expansions In Eigenfunctions Of Hill's Operator, Fi̇li̇z Aras, Gusei̇n Sh Gusei̇nov
Turkish Journal of Mathematics
In this paper we show how one can deduce the Titchmarsh expansion formula in eigenfunctions of Hill's operator from the Gel'fand expansion formula.