THE STABILITY OF A KIND OF DISCRETE-TIME HOPFIELD NEURAL NETWORKS WITH ASYMPTOTICAL WEIGHTED MATRICES

In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale's invariance principle in difference equation is applied.     

Spectral Fluctuations of Schrödinger Operators Generated by Critical Points of the Potential

Starting from the spectrum of Schrödinger operators on ${\mathbb R}^nStarting from the spectrum of Schr?dinger operators on , we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed.     

具有常数输入的SEIR模型的稳定性分析

讨论了易感者类和潜伏者类均为常数输入,潜伏期、染病期和恢复期均具有传染力,且传染率为一般传染率的SEIR传染病模型.利用Hurwitz判据证明了地方病平衡点的局部渐近稳定性,进一步利用复合矩阵理论得到了地方病平衡点全局渐近稳定的充分条件.     

Phase equilibriums,self-assembly and interactions in two-, three- and four medium-chain length component systems

The Scandinavian surface (surfactant) and colloid science owes much of its success to Per Ekwall and Björn Lindman. In this review the main topics shared by their research groups at Åbo Akademi University in Finland and at Lund University in Sweden are described. The nature of surface active substances (cosolvents, co-surfactants and surfactants) and microemulsions are evaluated. It is shown that the properties of medium-chain length surfactants differ dramatically from long-chain surfactants. The phase equilibriums of binary systems are related to the phase equilibriums of ternary and quaternary systems referred to as microemulsions or more recently also as nanoemulsions. A distinction is made between hydrotrope liquids, detergentless microemulsions, surfactant mixture systems and microemulsions. Three component systems are assembled to “true” quaternary microemulsions. An exceptionally comprehensive network of thermodynamic parameters describing molecular site exchange and micelle formation are derived and related mutually. Gibbs free energy, enthalpy, entropy, volume, heat capacity, expansivity and compressibility can be used to illustrate the degree of aggregation cooperativity and to evaluate whether micelle formation is of a first-, second- or intermediate order phase transition. Theoretical simulations and experimental results show that the associate structures of medium-chain length surfactants are quite open and may be deformed due to small aggregation numbers. The self-assembly occurs over a number of distinct steps at a series of experimentally detectable critical concentrations. Despite the low aggregation tendency their phase behavior equals those of long-chain homologs in surfactant mixture and microemulsion systems. A number of models describing the self-assembly are reviewed. Nuclear magnetic resonance (shift, relaxation rate and diffusion), Laser Raman and infrared spectroscopies were chosen as key instruments for molecular interaction characterization since they were used in the collaboration between the research groups in Åbo and in Lund. A new method is introduced in order to evaluate the traditional procedure for extracting limiting parameters which also enables an illustration of the degree of cooperativity. The focus is laid mainly on aqueous, alcoholic, saline and, to a limited extent oil phases of one-, two-, three- and four component systems of water–sodium carboxylates–alcohol–oil. The extensive thermodynamic characterization of these liquid phases and liquid crystalline phases is left out due to space restrictions.     

Excited-state inter- and intramolecular proton transfer in methyl 3-hydroxy-2-quinoxalinate: effects of solvent and acid or base concentrations

Absorption, fluorescence excitation and fluorescence spectroscopy, combined with time-dependent spectroscopy and semi-empirical (AM1) and density functional theory using Gaussian 98 program calculations have been used to study the effects of solvent and acid or base concentration on the spectral characteristics of methyl 3-hydroxy-2-quinoxalinate (M3HQ). M3HQ is present as enol in less polar solvents and as keto in polar media. In non-polar solvents, large Stokes shifted fluorescence band is assigned to the phototautomer, formed by the excited-state intramolecular proton transfer, whereas fluorescence is only observed from keto in the polar solvents. In aqueous and polar solvents the monocation (MC5/MC6) is formed by protonating the carbonyl oxygen atom in the ground (S₀) and the first excited singlet states (S₁). Dication is formed by protonating one of N- atom of MC5/MC6. Monoanion is formed by deprotonating the phenolic proton of enol in the basic solution. pK_a values for different prototropic equilibriums were determined in S₀ and S₁ states and discussed.     

Competitive facility location models

Two classes of competitive facility location models are considered, in which several persons (players) sequentially or simultaneously open facilities for serving clients. The first class consists of discrete two-level programming models. The second class consists of game models with several independent players pursuing selfish goals. For the first class, its relationship with pseudo-Boolean functions is established and a novel method for constructing a family of upper and lower bounds on the optimum is proposed. For the second class, the tight PLS-completeness of the problem of finding Nash equilibriums is proved.