Measure of stability for a finite cooperative game with a parametric optimality principle (from Pareto to Nash)

A finite cooperative game in normal form is considered. Its optimality principle is specified with the help of a parameter such that Pareto optimality and Nash equilibrium correspond to two extreme parameter values. The limiting level of perturbations in the coefficients of payoff functions that do not give rise to new efficient situations is studied.     

Ekeland's variational principle, minimax theorems and existence of nonconvex equilibria in complete metric spaces

In this paper, we introduce the concept of τ-function which generalizes the concept of w-distance studied in the literature. We establish a generalized Ekeland's variational principle in the setting of lower semicontinuous from above and τ-functions. As applications of our Ekeland's variational principle, we derive generalized Caristi's (common) fixed point theorems, a generalized Takahashi's nonconvex minimization theorem, a nonconvex minimax theorem, a nonconvex equilibrium theorem and a generalized flower petal theorem for lower semicontinuous from above functions or lower semicontinuous functions in the complete metric spaces. We also prove that these theorems also imply our Ekeland's variational principle.     

An existence result for generalized vector equilibrium problems without pseudomonotonicity

In this work, we introduce and study a class of generalized vector equilibrium problems for multifunctions which includes a number of generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. By using the KKM–Fan theorem and Nadler’s result, we prove an existence theorem for solutions for this class of generalized vector equilibrium problems in Banach spaces. Applications to generalized vector variational-like inequalities are given.     

TWO DIFFERENTIAL INFECTIVITY EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE

This paper considers two differential infectivity（DI） epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely., a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity,O is globally stable and the disease always dies out. If σ〉1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover,when σ〈 1 ,the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.     

Ar辅助确定Al等离子体电子温度

用Ar气作保护气时 ,Nd :YAG脉冲激光烧蚀Al靶 ,将诱发Ar气电离 ,并产生丰富的Ar离子谱线辐射。文章根据Ar离子谱线辐射信息 ,分析了ArⅡ 385 0 5 7,ArⅡ 386 85 3,ArⅡ 4 0 4 2 91 ,ArⅡ 4 0 7 2 0 1nm等 4条谱线的时间分辨行为 ,计算了Al等离子体的电子温度。结果发现 :Al等离子体的电子温度约 1 5 0 0 0～2 2 0 0 0K ,随延迟时间的增加 ,电子温度单调衰减     

Statistical Theory of Equilibrium Fluctuations

An analysis of the BBGKY hierarchy shows that the fluctuation theory for hydrodynamic variables (i.e., the fluid density, velocity, and temperature) must be constructed based on the hydrodynamic equations. We show that fluctuations in the hydrodynamic variables uniquely determine the fluctuations in all other thermodynamic parameters of a fluid (such as the pressure, entropy, and intrinsic energy). We find the spectral structure of fluctuation waves of the hydrodynamic variables, calculate their amplitudes, and derive the dispersion equation establishing the relation between the phase velocity of the fluctuation wave propagation and its frequency. We explain the effects of the flicker noise generation and of the stability loss on the first-order phase equilibrium lines. We also analyze the fluctuation decay process and show that this process gives rise to the effect of the Mandelstam–Brillouin scattering. We compare the obtained results with the existing fluctuation theories.     

具有外部输入和偏差的细胞神经网络的完全稳定性

本文证明了对于由两个细胞组成的细胞神经网络，外部输入和偏差不影响网络的稳定平衡点的存在性和完全稳定性．     

Comments on purification in continuum games

It is pointed out that Corollary 1 in a recent paper by Khan et al. (Int J Game Theory 34:91–104, 2006), presented there as an extension of the Dvoretzky–Wald–Wolfowitz theorem, is a special case of Lyapunov’s theorem for Young measures (Balder in Rend Instit Mat Univ Trieste 31 Suppl. 1:1–69) It is also pointed out that Theorems 1–4 in Khan et al. (Int J Game Theory 34:91–104, 2006) follow from a single strong purification per se result that is already contained, as an implementation of that Lyapunov theorem for Young measures, in the proof of Theorem 2.2.1 in Balder (J Econ Theory 102:437–470, 2002).     

Analytical ultracentrifugation of gels

Analytical ultracentrifugation is a powerful tool for the determination of thermodynamic, elastic and molecular parameters and structural properties of gels. Although gelling systems are an important class of mixtures, only a few researchers have studied their properties by means of analytical ultracentrifugation. This might be due to the extreme experimental difficulties concerning the detection of the polymer concentration in turbid gels, adhesion problems, etc. Nevertheless, the potential benefit of such experiments has led to several investigations in this field during recent years. These resulted in the introduction of a theoretical treatment of the sedimentation of even multicomponent gels and an improved experimental set-up which allows the characterization of a gel/solvent system in a limited concentration range in a single sedimentation equilibrium experiment. For microgels prepared and crosslinked in emulsions, an interesting rapid sedimentation velocity technique is available for their characterization. This review article describes the capabilities of the experimental method and what has been achieved with it in the past. Furthermore, it gives an outlook on applications which may be possible in the future.Dedicated to Prof. Dr. W. Borchard on occasion of his 60th birthday     

THE EQUILIBRIUM PROBLEM AND CAPACITY FOR JUMP MARKOV PROCESSES

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