区间周期系统的平稳振荡

本文给出了区间周期系统平稳振荡的概念，建立了区间矩阵稳定性与区间周期系统平稳振荡之间的关系，推广和改进了文[1]的结果．     

Principal and nonprincipal solutions of impulsive dynamic equations with applications

In this paper, we introduce the concept of principal and nonprincipal solutions for second order impulsive dynamic equations on time scales. Polya and Trench Factorizations play an important role in this article. Firstly we establish these factorizations. Using these factorizations, we establish some new oscillation criteria for second impulsive dynamic equations on time scales.     

脉冲中向量中立型抛物偏微分方程的H-振动性

研究一类脉冲向量中立型抛物偏微分方程的振动性,借助Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲中立型微分不等式不存在最终正解的问题,建立了该类方程在Dirichlet边值条件下所有解H-振动的若干充分判据,这里H是R~M中的单位向量.     

Relative oscillation of linear Hamiltonian differential systems

We discuss the concept of relative oscillation for linear Hamiltonian differential systems. We prove a statement which enables to study this oscillation using the criteria of the classical oscillation theory. We also discuss some other aspects of the problem.     

Optimal control of water level oscillations in surge tank of hydropower station with long headrace tunnel under combined operating conditions

This paper aims to realize the optimal control of water level oscillations in surge tank of hydropower station with long headrace tunnel under combined operating conditions. Firstly, the definitions of four typical combined operating conditions are presented, and the optimal control objectives of water level oscillations in surge tank under combined operating conditions are proposed. Then, the concept of the most favorable superimposition time of water level oscillation is proposed, and the analytical solutions of the most favorable superimposition time are derived and verified. Finally, for the superimposition operating condition, the attenuation of the water level oscillation under the most favorable superimposition time is analyzed, a novel control strategy of the load adjustments of the units is proposed, and an application example for the proposed load adjustment mode is presented. The results indicate that the optimal control of the water level oscillations in surge tank under combined operating conditions depends on the selection of the superimposition time and the optimization of the mode of the load adjustments under the superimposition operating condition. The most favorable superimposition time can minimize the extreme water levels in surge tank under the superimposition operating condition, and the analytical solutions under the four typical combined operating conditions are highly accurate. The cascaded load adjustment mode proposed in this paper can realize the ideal attenuation of water level oscillations under superimposition operating conditions, and can obviously improve the flexibility of the unit operations.     

Unsaturated solutions for partial difference equations with forcing terms

The concept of unsaturated infinite double sequence is introduced by making use of frequency measures. Unsaturated solutions are then studied for a partial difference equation. Conditions for all solutions to be unsaturated are obtained. Since unsaturated solutions are oscillatory, our results yield oscillation criteria.     

非线性脉冲向量双曲型微分方程解的H-振动性

研究一类具脉冲时滞的非线性双曲型向量泛函微分方程解的H-振动性.方法是采用由Domslak引进的H-振动性的概念,将向量微分方程解的振动问题转化为纯量微分不等式正解和负解的不存在性问题.得到了解的H-振动性的若干判别准则.     

关于泛函微分系统的平稳振荡

该文对高维泛函微分系统引进S-稳定的概念,得到了较一般的关于高维泛函微分系统存在平稳振荡的充分条件.作为结果的应用,给出了一些泛函微分系统存在平稳振荡的简明判别准则.     

Fluctuations in a SIS epidemic model with variable size population

In an epidemiological model, time spent in one compartment is often modeled by a delay in the model. In general the presence of delay in differential equations can change the stability of an equilibrium to instability and causes the appearance of oscillatory solutions.In this paper we consider a SIS epidemiological model with demographic effects: birth, mortality and mortality caused by infection. The delay is the period of infection. We define the concept of oscillation in the sense that solutions of the model studied fluctuate around a steady state. Our goal is to show that in this model, there are oscillating solutions for certain parameters values. We determine a large set of initial data for which solutions of this model are slowly oscillating.     

Oscillation behavior of solution of impulsive fractional differential equation

In this paper, we study the oscillation of impulsive Caputo fractional differential equation. Sufficient conditions for the asymptotic and oscillation of the equation are obtained by using the inequality principle and Bihari Lemma. An example is given to illustrate the results. This is the first time to study the oscillation of impulsive fractional differential equation with Caputo derivative.     

Oscillation results for fourth-order nonlinear dynamic equations

This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. A new oscillation result and an example are included.     

OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z of positive integers and for differential equations when the time scale is the set R of real numbers.     

Oscillation criteria for second-order dynamic equations on time scales

Erbe’s and Hassan’s contributions regarding oscillation criteria are interesting in the development of oscillation theory of dynamic equations on time scales. The objective of this paper is to amend these results.     

Free and forced finite amplitude oscillation of a spherical shell of radially isotropic elastic material

A spherical elastic shell with radial transverse isotropy is considered. The periods of finite amplitude radial oscillation of the shell have been obtained in two cases, namely (i) when both the surfaces of the shell are free from traction, and (ii) when the shell boundaries are uniformly loaded in such a way that the pressure difference between inner and outer surfaces is constant with respect to time. It is observed that for free oscillation to take place it is necessary to impose a new restriction on the strain energy function in addition to those already obtained for finite amplitude oscillation of an isotropic elastic shell. In the forced oscillation case however the required conditions are of the same form as in the corresponding case for isotropic media.     

A Multiobjective Hybrid Metaheuristic Approach for GIS-based Spatial Zoning Model

This paper presents a multiobjective hybrid metaheuristic approach for an intelligent spatial zoning model in order to draw territory line for geographical or spatial zone for the purpose of space control. The model employs a Geographic Information System (GIS) and uses multiobjective combinatorial optimization techniques as its components. The proposed hybrid metaheuristic consists of the symbiosis between tabu search and scatter search method and it is used heuristically to generate non-dominated alternatives. The approach works with a set of current solution, which through manipulation of weights are optimized towards the non-dominated frontier while at the same time, seek to disperse over the frontier by a strategic oscillation concept. The general procedure and its algorithms are given as well as its implementation in the GIS environment. The computation has resulted in tremendous improvements in spatial zoning.     

Principal and nonprincipal solutions of impulsive differential equations with applications

We introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results.     

OSCILLATION OF SECOND-ORDER NEUTRAL DYNAMIC FUNCTIONAL EQUATIONS

In this paper we establish some oscillation criteria for the second-order neutral dynamic delay equations on time scales. By using the generalized Riccati technique, new oscillation criteria are obtained.     

脉冲向量时滞抛物型方程的H-振动性

研究一类脉冲向量时滞抛物型偏微分方程的振动性,借助Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲时滞微分不等式不存在最终正解的问题,建立了该类方程在Robin边值条件下所有解H-振动的若干充分条件,这里H是RM中的单位向量.     

具连续分布变元的向量抛物型方程振动性的新准则(英文)

The oscillations of a class of vector parabolic partial differential equations with continuous distribution arguments are studied.By employing the concept of H-oscillation and the method of reducing dimension with inner product,the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional differential inequalities have not eventually positive solution.Some new sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Dirichlet boundary condition,where H is a unit vector of RM.     

Oscillation theorems for linear Hamiltonian systems with nonlinear dependence on the spectral parameter and the comparative index

We consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. In our consideration we do not impose any controllability and strict normality assumptions and omit the Legendre condition for the Hamiltonian. We adapt the theory developed by A.A. Abramov for the Hamiltonian spectral problems based on piecewise constant transformations of their conjoined bases using the notion of the comparative index. We introduce the concept of oscillation numbers which generalize the notion of proper focal points and prove the oscillation theorem relating the number of finite eigenvalues in the given interval with the values of the oscillation numbers at the end points of this interval.