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article

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

Online Voltage Control of DC Microgrids with Different Loading Conditions Using Particle Swarm Optimization

Hossam Aboelsoud, Naoya Ikeda, Takao Tsuji, Masahide Hojo, more

IEEJ Transactions on Electrical and Electronic Engineering > 17 > 6 > 780 - 791

This paper presents a contemplate study on online voltage control strategy with different loading conditions in a DC microgrid using particle swarm optimization (PSO). DC microgrids consist of many converters and it is an important issue to stabilize network voltage by properly designing their controllers. Conventional feedback controls have been often used as a primary control for voltage stabilization...

article

Eigenvalues and $[a, b]$ ‐factors in regular graphs

Suil O

Journal of Graph Theory > 100 > 3 > 458 - 469

For positive integers,

r \geq 3

,

h \geq 1

, and

k \geq 1

, Bollobás, Saito, and Wormald proved some sufficient conditions for an

h

‐edge‐connected

r

‐regular graph to have a

k

‐factor in 1985. Lu gave an upper bound for the third largest eigenvalue in a connected

r

‐regular graph to have a

k

‐factor in 2010. Gu found an upper bound for certain eigenvalues in an

h

‐edge‐connected

r

‐regular graph to have a...

article

Power considerations for generalized estimating equations analyses of four‐level cluster randomized trials

Xueqi Wang, Elizabeth L. Turner, John S. Preisser, Fan Li

Biometrical Journal > 64 > 4 > 663 - 680

In this article, we develop methods for sample size and power calculations in four‐level intervention studies when intervention assignment is carried out at any level, with a particular focus on cluster randomized trials (CRTs). CRTs involving four levels are becoming popular in healthcare research, where the effects are measured, for example, from evaluations (level 1) within participants (level...

article

SIMPLE: Statistical inference on membership profiles in large networks

Jianqing Fan, Yingying Fan, Xiao Han, Jinchi Lv

Journal of the Royal Statistical Society: Series B (Statistical Methodology) > 84 > 2 > 630 - 653

Network data are prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the statistical uncertainty associated with the identification of latent links still remains largely unexplored. In this paper, we propose the method of statistical inference...

article

Computing eigenvalues of quasi‐rational Bernstein–Vandermonde matrices to high relative accuracy

Zhao Yang, Xiao‐Xiao Ma

Numerical Linear Algebra with Applications > 29 > 3 > n/a - n/a

In this article, we consider how to accurately solve the eigenvalue problem for a class of quasi‐rational Bernstein–Vandermonde (q‐RBV) matrices. This class of matrices belongs to generalized sign regular matrices with signature

(1, \dots, 1, - 1)

. An algorithm is developed to accurately compute the parameter matrix for q‐RBV matrices. Based on the parameter matrix, all the eigenvalues of q‐RBV matrices have...

article

Eigenvalues of Schrödinger operators on finite and infinite intervals

Evgeny L. Korotyaev

Mathematische Nachrichten > 294 > 11 > 2188 - 2199

We consider a Sturm–Liouville operator with an integrable potential q on the unit interval

I = [0, 1]

. We consider a Schrödinger operator with a real compactly supported potential on the half line and on the line, where this potential coincides with q on the unit interval and vanishes outside I. We determine the relationships between eigenvalues of such operators and obtain estimates of eigenvalues in...

article

Multispan bridges with distributed deck and pier mass and pier‐flexure‐deck‐torsion coupling under transverse excitation—Analytical solution, parametric studies, design implications

Michael N. Fardis

Earthquake Engineering & Structural Dynamics > 50 > 14 > 3713 - 3740

An “exact” analytical dynamic model is developed for symmetric bridges with two to five spans under transverse earthquake. It considers the mass as distributed along the deck and the piers and accounts for coupling of deck torsion with pier bending in vertical planes normal to the deck's axis. The characteristic equation is formulated in terms of (up to) seven dimensionless parameters which fully...

article

Shape sensitivity analysis for electromagnetic cavities

Pier Domenico Lamberti, Michele Zaccaron

Mathematical Methods in the Applied Sciences > 44 > 13 > 10477 - 10500

We study the dependence of the eigenvalues of time‐harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of the elementary symmetric functions of the eigenvalues splitting a multiple eigenvalue, as well as a Rellich‐Nagy‐type result describing the corresponding bifurcation...

article

A Comparative Study of Fluid Flow in Hemodialyzer using Differential Transform Method

Pradeep Kumar Singh, Pankaj Sharma

Macromolecular Symposia > 397 > 1 > n/a - n/a

In this paper, a series‐based method called differential transform method (DTM) is used (which is relatively simple and high accurate) for solving the differential equations in biofluid problems. Diffusion equation governed during laminar flow of blood in hemodialysis is solved under the view of this method. The problem formulation of the present paper is modeled under the situation where patients...

article

A general semianalytical method for computing the propagation characteristics of radially inhomogeneous cylindrical dielectric waveguides

Qianru Weng, Sichen Pan, Chujie Lu

Microwave and Optical Technology Letters > 63 > 6 > 1657 - 1663

A general and simple semianalytical method based on the Galerkin procedure is introduced in this letter for wave propagation problems related to radially inhomogeneous cylindrical dielectric waveguides with arbitrary permittivity profiles. The complicated wave propagation problem in an inhomogeneous waveguide is transformed into a simple problem of solving an equivalent matrix in terms of the Galerkin...

article

Active fault tolerant control based on eigenstructure assignment applied to a 3‐DOF helicopter

Jorge A. Brizuela‐Mendoza, Felipe D. J. Sorcia‐Vázquez, Jesse Y. Rumbo‐Morales, Ricardo E. Lozoya‐Ponce, more

Asian Journal of Control > 23 > 2 > 673 - 684

In this paper an active fault tolerant control (AFTC) has been designed and applied to a 3‐DOF helicopter mathematical model. The main contribution corresponds to an AFTC design based on eigenstructure assignment aiming at reconfiguring the controller gain after actuator fault occurrences, modelled as additive faults. The reconfigured controller gain is computed ensuring the best approximation acquired...

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...

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Search results

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

Online Voltage Control of DC Microgrids with Different Loading Conditions Using Particle Swarm Optimization

Eigenvalues and $[a, b]$ ‐factors in regular graphs

Power considerations for generalized estimating equations analyses of four‐level cluster randomized trials

SIMPLE: Statistical inference on membership profiles in large networks

Computing eigenvalues of quasi‐rational Bernstein–Vandermonde matrices to high relative accuracy

Eigenvalues of Schrödinger operators on finite and infinite intervals

Multispan bridges with distributed deck and pier mass and pier‐flexure‐deck‐torsion coupling under transverse excitation—Analytical solution, parametric studies, design implications

Shape sensitivity analysis for electromagnetic cavities

A Comparative Study of Fluid Flow in Hemodialyzer using Differential Transform Method

A general semianalytical method for computing the propagation characteristics of radially inhomogeneous cylindrical dielectric waveguides

Active fault tolerant control based on eigenstructure assignment applied to a 3‐DOF helicopter

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

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