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Dependence of eigenvalues of a class of fourth-order Sturm–Liouville problems on the boundary

Suqin Ge, Wanyi Wang, Jianqing Suo, S. Ge, more

Applied Mathematics and Computation > 2013 > 220 > Complete > 268-276

In this paper, we consider the dependence of eigenvalues of a class of fourth-order Sturm–Liouville problems on the boundary. We show that the eigenvalues depend not only continuously but smoothly on boundary points, and that the derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. In addition, we prove that as the length of the interval shrinks...

article

Fisher information of a vector potential for time‐dependent Feinberg–Horodecki equation

Clement A. Onate, Michael C. Onyeaju

International Journal of Quantum Chemistry > 121 > 6 > n/a - n/a

The time‐dependent Feinberg–Horodecki equation in the presence of a special Mie‐type pseudoharmonic potential was solved and the quantized momentum with the corresponding wave functions were obtained with the supersymmetric approach. The Fisher information for both the time and the momentum space were calculated via expectation values of time and momentum. The effect of the dissociation energy, the...

article

Asymptotics for 2‐D wave equations with Wentzell boundary conditions in the square

Chan Li, Kun‐Peng Jin

Mathematical Methods in the Applied Sciences > 44 > 1 > 265 - 273

This paper concerns the asymptotics of the linear wave equation with frictional damping only on Wentzell boundary in the square. After reformulating the model into an abstract Cauchy problem, we show that the spectrum for the corresponding operator matrix has no purely imaginary values. Moreover, by analyzing a family of eigenvalues for the operator matrix, we prove that there exists a solution of...

article

The score test for the two‐sample occupancy model

N. Karavarsamis, G. Guillera‐Arroita, R.M. Huggins, B.J.T. Morgan

Australian & New Zealand Journal of Statistics > 62 > 1 > 95 - 115

The score test statistic from the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the likelihood‐ratio test and the Wald test. However, several authors have noted that under the alternative hypothesis this no longer holds and in particular the score...

article

Control problems for energy harvester model and interpolation in Hardy space

Marianna A. Shubov

Mathematische Nachrichten > 293 > 3 > 585 - 610

Three control problems for the system of two coupled differential equations governing the dynamics of an energy harvesting model are studied. The system consists of the equation of an Euler–Bernoulli beam model and the equation representing the Kirchhoff's electric circuit law. Both equations contain coupling terms representing the inverse and direct piezoelectric effects. The system is reformulated...

article

On the Riesz basis property of the root functions of a discontinuous boundary problem

Olgun Cabri

Mathematical Methods in the Applied Sciences > 42 > 18 > 6733 - 6740

In this paper, we consider the nonself‐adjoint discontinuous Sturm Liouville operator with periodic (antiperiodic) boundary condition and compatibility conditions. Asymptotic formulas of eigenvalues and eigenfunctions of the operator are obtained. Using these accurate asymptotic formulas for eigenvalues and eigenfunctions, we prove the basisness of the root functions of the boundary value problem.

article

On k-Circulant Matrices Involving the Pell Numbers

Biljana Radičić

Results in Mathematics > 2019 > 74 > 4 > 1-13

Let k be a nonzero complex number. In this paper, we consider a k-circulant matrix whose first row is $$(P_{1},P_{2},\dots ,P_{n})$$ (P1,P2,⋯,Pn) , where $$P_{n}$$ Pn is the nth Pell number, and obtain the formulae for the eigenvalues of such matrix improving the result which can be obtained from the result of Theorem 7 (Yazlik and Taskara in J Inequal Appl 2013:394, 2013). The obtained formulae...

article

Spectral analysis of an impulsive quantum difference operator

Martin Bohner, Serifenur Cebesoy

Mathematical Methods in the Applied Sciences > 42 > 16 > 5331 - 5339

This paper studies spectral analysis and symmetries of quantum difference equations of second order together with an impulsive condition. By determining a transfer matrix, we investigate the locations of the eigenvalues and spectral singularities of an operator corresponding to the q‐difference equation.

article

Difference equations with a point interaction

Elgiz Bairamov, Serifenur Cebesoy, Ibrahim Erdal

Mathematical Methods in the Applied Sciences > 42 > 16 > 5498 - 5508

In this paper, we consider an impulsive second‐order difference equation on the whole axis. We determine eigenvalues, spectral singularities, continuous spectrum corresponding to this difference equation with an impulsive condition by using the asymptotic properties of Jost functions, and uniqueness theorems of analytic functions. Finally, we demonstrate that the impulsive difference equation has...

article

Nearness results for real tridiagonal 2‐Toeplitz matrices

Natália Bebiano, Susana Furtado

Numerical Linear Algebra with Applications > 26 > 5 > n/a - n/a

In this article, we extend the results for Toeplitz matrices obtained by Noschese, Pasquini, and Reichel. We study the distance d, measured in the Frobenius norm, of a real tridiagonal 2‐Toeplitz matrix T to the closure

N_{T}^{R}

of the set formed by the real irreducible tridiagonal normal matrices. The matrices in

N_{T}^{R}

, whose distance to T is d, are characterized, and the location of their eigenvalues...

article

Exclusion sets in Dashnic–Zusmanovich localization sets

Jianxing Zhao, Lili She

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-10

A new eigenvalue localization set is given by excluding some proper subsets that do not contain any eigenvalues of matrices from Dashnic–Zusmanovich localization sets. As an application, a sufficient condition for non-singularity of matrices is obtained. In order to locate all eigenvalues of matrices precisely, another set including two positive integers s and k is presented. By adjusting the parameters...

article

Integration of a Linear Equation with Differential Operator, Corresponding to the Main Diagonal in the Space of Independent Variables, and Coefficients, Constant on the Diagonal

A. A. Kulzhumiyeva, Zh. A. Sartabanov

Russian Mathematics > 2019 > 63 > 6 > 29-41

We consider an n-th order linear equation with differential operator corresponding to the direction of the main diagonal in the space of independent variables; its coefficients. in general, are variable but constant on the diagonal. We establish conditions on variable eigenvalues which give a possibility to apply some known methods of the theory of for ODEs, when integrating the equation. On this...

article

Copositive and Positive Quadratic Forms on Matrices

Mohammad Al-khlyleh, Mowaffaq Hajja

Results in Mathematics > 2019 > 74 > 4 > 1-10

A real symmetric quadratic form $$f = f(Z_1,\ldots ,Z_n)$$ f=f(Z1,…,Zn) in the n non-commuting indeterminates $$Z_1,\ldots ,Z_n$$ Z1,…,Zn is said to be d-positive (respectively, d-copositive) if for all real symmetric (respectively, positive semidefinite) $$(d \times d)$$ (d×d) -matrices $$A_1,\ldots ,A_n$$ A1,…,An , the matrix $$f(A_1,\ldots ,A_n)$$ f(A1,…,An) is positive semidefinite. When $$d=1$$...

article

Natural Transverse Oscillations of a Rotating Rod of Variable Cross Section

L. D. Akulenko, A. A. Gavrikov, S. V. Nesterov

Mechanics of Solids > 2018 > 53 > 5 > 510-519

The problem of natural oscillations of a rotating rod of variable cross section is considered. It is believed that the rod is rigidly attached at one end to a rotor with a constant speed orthogonal to the axis of rotation, the other end is assumed to be free. Flexural movements occur in the plane of rotation or perpendicular to it. To determine the natural oscillations, the Euler rod oscillation model...

article

Classical Sobolev Orthogonal Polynomials: Eigenvalue Problem

Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar

Results in Mathematics > 2019 > 74 > 4 > 1-12

We consider the discrete Sobolev inner product $$\begin{aligned} ~~(f,g)_S=\!\int f(x)g(x)d\mu +Mf^{(j)}(c)g^{(j)}(c), ~~~ j\in \mathbb {N}\cup \{0\}, ~~~ c\in \mathbb {R}, ~~~ M>0, \end{aligned}$$ (f,g)S=∫f(x)g(x)dμ+Mf(j)(c)g(j)(c),j∈N∪{0},c∈R,M>0, where $$\mu $$ μ is a classical continuous measure with support on the real line (Jacobi, Laguerre or Hermite). The orthonormal polynomials with...

article

Properties of the Fourth-Order Boundary Value Problem with Transmission Conditions

Şerife Faydaoğlu

Iranian Journal of Science and Technology, Transactions A: Science > 2019 > 43 > 5 > 2515-2522

We investigate the fourth-order eigenvalue problem with transmission conditions. We apply the Fourier method for solving of this problem arising in finding of transverse vibration of a string. We derive the eigenvalues and eigenfunctions of Sturm–Liouville problems and their properties. We obtain a solution of the considered equation subject to initial, boundary and transmission conditions at the...

article

Riesz basis of exponential family for a hyperbolic system

Abdelkader Intissar, Aref Jeribi, Ines Walha

Journal of Applied Analysis > 2019 > Vol. 25, nr 1 > 13--23

This paper studies a linear hyperbolic system with boundary conditions thatwas first studied under someweaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. It is shown that the associated linear system is the infinitesimal generator of a C₀-semigroup; its spectrum consists of zeros of a sine-type function,...

article

Space of 2D elastic materials: a geometric journey

B. Desmorat, N. Auffray

Continuum Mechanics and Thermodynamics > 2019 > 31 > 4 > 1205-1229

In this paper, we describe geometrically the domain of elastic materials in terms of invariants of the integrity basis (including the positive definiteness condition) and prove a theoretical link between those polynomial invariants and the Kelvin invariants of the elasticity tensor, to finally introduce the concept of design transformation which leads to subsets of elastic materials having identical...

article

Operator-based approach to $${\mathcal {P}}{\mathcal {T}}$$ P T -symmetric problems on a wedge-shaped contour

Florian Leben, Carsten Trunk

Quantum Studies: Mathematics and Foundations > 2019 > 6 > 3 > 315-333

We consider a second-order differential equation $$\begin{aligned} -y''(z)-(iz)^{N+2}y(z)=\lambda y(z), \quad z\in \varGamma \end{aligned}$$ - y ′ ′ ( z ) - ( i z ) N + 2 y ( z ) = λ y ( z ) , z ∈ Γ with an eigenvalue parameter $$\lambda \in {\mathbb {C}}$$ λ ∈ C . In $${\mathcal {P}}{\mathcal {T}}$$ P T quantum mechanics z runs through a complex contour...

article

The first negative eigenvalue of Yoshida lifts

Soumya Das, Ritwik Pal

Research in Number Theory > 2019 > 5 > 3 > 1-9

We prove that for any given $$\epsilon >0$$ ϵ>0 , the first negative eigenvalue of the Yoshida lift F of a pair of elliptic cusp forms f, g having square-free levels (where g has weight 2 and satisfies $$(\log Q_{g})^2 \ll \log Q_f$$ (logQg)2≪logQf ), occurs before $$c_{\epsilon } \cdot Q_F^{1/2-2 \theta + \epsilon }$$ cϵ·QF1/2-2θ+ϵ ; where $$Q_F,Q_f,Q_g$$ QF,Qf,Qg are the analytic conductors...

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Search results

Dependence of eigenvalues of a class of fourth-order Sturm–Liouville problems on the boundary

Fisher information of a vector potential for time‐dependent Feinberg–Horodecki equation

Asymptotics for 2‐D wave equations with Wentzell boundary conditions in the square

The score test for the two‐sample occupancy model

Control problems for energy harvester model and interpolation in Hardy space

On the Riesz basis property of the root functions of a discontinuous boundary problem

On k-Circulant Matrices Involving the Pell Numbers

Spectral analysis of an impulsive quantum difference operator

Difference equations with a point interaction

Nearness results for real tridiagonal 2‐Toeplitz matrices

Exclusion sets in Dashnic–Zusmanovich localization sets

Integration of a Linear Equation with Differential Operator, Corresponding to the Main Diagonal in the Space of Independent Variables, and Coefficients, Constant on the Diagonal

Copositive and Positive Quadratic Forms on Matrices

Natural Transverse Oscillations of a Rotating Rod of Variable Cross Section

Classical Sobolev Orthogonal Polynomials: Eigenvalue Problem

Properties of the Fourth-Order Boundary Value Problem with Transmission Conditions

Riesz basis of exponential family for a hyperbolic system

Space of 2D elastic materials: a geometric journey

Operator-based approach to $${\mathcal {P}}{\mathcal {T}}$$ P T -symmetric problems on a wedge-shaped contour

The first negative eigenvalue of Yoshida lifts

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