一类三阶时滞微分方程解的渐进稳定性

本文研究了三阶非线性时滞微分方程解的渐近稳定性.利用Lyapunov泛函,得到了微分方程的零解是渐进稳定的,这一结果推广了文献[2]的结果.     

On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method

Radial basis function method is an effective tool for solving differential equations in engineering and sciences. Many radial basis functions contain a shape parameter c which is directly connected to the accuracy of the method. Rippa [1] proposed an algorithm for selecting good value of shape parameter c in RBF-interpolation. Based on this idea, we extended the proposed algorithm for selecting a good value of shape parameter c in solving time-dependent partial differential equations.     

A complex multi-attribute large-group PLS decision-making method in the interval-valued intuitionistic fuzzy environment

In the complex multi-attribute large-group decision-making (CMALGDM) problems in interval-valued intuitionistic fuzzy (IVIF) environment, attributes of the alternatives are often stratified and correlated. This paper proposes a decision-making method for these problems based on partial least squares (PLS) path modelling, which not only fully exploits the decision information of decision makers (DMs), but also effectively addresses the relativity problem in the decision attributes and objectively assigned weights to the primary decision attributes (i.e., “latent variables for decision making”). The method can be outlined in three steps. First, a two-stage method is proposed to transform the interval-valued intuitionistic fuzzy number (IVIFN) samples into single-valued samples. In this step, an improved C-OWA operator is first given to transform the IVIFN samples into intuitionistic fuzzy number (IFN) samples, which makes the preference information of the DMs more objectively aggregated. Then a proposed membership-based method is applied to reduce the information loss and transform the IFN samples into single-valued samples. Second, the estimated values and weights of the “latent variables for decision-making” are obtained by means of the PLS path modelling algorithm. Finally, a multi-alternative sorting method is devised in accordance with the estimated values and weights. An example is provided to illustrate the proposed technique and evaluate its feasibility and validity.     

Computing economies of vertical integration,economies of scope and economies of scale using partial frontier nonparametric methods

So far, in the nonparametric literature only full frontier nonparametric methods have been applied to search for economies of scope and scale, particularly the data envelopment analysis method (DEA). However, these methods present some drawbacks that might lead to biased results. This paper proposes a methodology based on more robust partial frontier nonparametric methods to look for scope and scale economies. Through this methodology it is possible to assess the robustness of these economies, and in particular to assess the influence that extreme data or outliers might have on them. The influence of the imposition of convexity on the production set of firms was also investigated. This methodology was applied to the water utilities that operated in Portugal between 2002 and 2008. There is evidence of economies of vertical integration and economies of scale in drinking water supply utilities and in water and wastewater utilities operating mainly in the retail segment. Economies of scale were found in water and wastewater utilities operating exclusively in the wholesale, and in some of these utilities diseconomies of scope were also found. The proposed methodology also allowed us to conclude that the existence of some smaller utilities makes the minimum optimal scales go down.     

Exponential stability of uniform Euler–Bernoulli beams with non-collocated boundary controllers

We study the stability of a robot system composed of two Euler–Bernoulli beams with non-collocated controllers. By the detailed spectral analysis, we prove that the asymptotical spectra of the system are distributed in the complex left-half plane and there is a sequence of the generalized eigenfunctions that forms a Riesz basis in the energy space. Since there exist at most finitely many spectral points of the system in the right half-plane, to obtain the exponential stability, we show that one can choose suitable feedback gains such that all eigenvalues of the system are located in the left half-plane. Hence the Riesz basis property ensures that the system is exponentially stable. Finally we give some simulation for spectra of the system.     

Analyticity and exponential stability of semigroups for the elastic systems with structural damping in Banach spaces

In this paper, we consider a second order evolution equation in a Banach space, which can model an elastic system with structural damping. New forms of the corresponding first order evolution equation are introduced, and their well-posed property is proved by means of the operator semigroup theory. We give sufficient conditions for analyticity and exponential stability of the associated semigroups.     

A delay-dependent model with HIV drug resistance during therapy

The use of combination antiretroviral therapy has proven remarkably effective in controlling HIV disease progression and prolonging survival. However, the emergence of drug resistance can occur. It is necessary that we gain a greater understanding of the evolution of drug resistance. Here, we consider an HIV viral dynamical model with general form of target cell density, drug resistance and intracellular delay incorporating antiretroviral therapy. The model includes two strains: wild-type and drug-resistant. The basic reproductive ratio for each strain is obtained for the existence of steady states. Qualitative analysis of the model such as the well-posedness of the solutions and the equilibrium stability is provided. Global asymptotic stability of the disease-free and drug-resistant steady states is shown by constructing Lyapunov functions. Furthermore, sufficient conditions related to the properties of the target cell density are obtained for the local asymptotic stability of the positive steady state. Numerical simulations are conducted to study the impact of target cell density and intracellular delay focusing on the stability of the positive steady state. The occurrence of Hopf bifurcation of periodic solutions is shown to depend on the target cell density.     

Long time behavior for nonlocal stochastic Kuramoto–Sivashinsky equations

In this paper, we consider a class of nonlocal stochastic Kuramoto–Sivashinsky equations driven by additive noises. Under some appropriate conditions, we investigate long time behavior, i.e., stability and growth bounds of the solutions to the equation. Finally, several examples are given to illustrate our results.