不确定离散时滞模糊系统的保性能控制

针对一类模糊模型表示的，具有范数有界时变参数不确定性离散时滞系统，研究了保性能控制器设计问题。首先推导了保性能控制器存在的充分条件，在此基础上通过求解等价的线性矩阵不等式给出了控制器的设计方法和参数表示。     

Kinetic Limit for a System of Coagulating Planar Brownian Particles

We study a model of mass-bearing coagulating planar Brownian particles. The coagulation occurs when two particles are within a distance of order ε. We assume that the initial number of particles N is of order |logε|. Under suitable assumptions of the initial distribution of particles and the microscopic coagulation propensities, we show that the macroscopic particle densities satisfy a Smoluchowski-type equation.     

积逻辑系统中的广义重言式

讨论积逻辑系统中的广义重言式理论 ,给出积逻辑系统中子代数和广义重言式的一系列性质。本文的主要结果表明 ,在几个重要的逻辑系统中 ,标准积逻辑系统具有最简单的广义重言式结构 ,而在推理过程中 ,它具有较差的真值传递性。     

Moment problem with contractive solutions: the regular case

An operator multivariate moment problem with contractive solutions having regular unitary dilation is characterized in terms of the initial data. This extends a recent result of Sebestyén and Popovici, but the ideas of our proof differ from those used by them. The connection between the operator multivariate moment problem and harmonizable multivariate discrete processes is mentioned.

     

On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

Polydisperse suspensions consist of particles differing in size or density that are dispersed in a viscous fluid. During sedimentation, the different particle species segregate and create areas of different composition. Spatially one-dimensional mathematical models of this process can be expressed as strongly coupled, nonlinear systems of first-order conservation laws. The solution of this system is the vector of volume fractions of each species as a function of depth and time, which will in general be discontinuous. It is well known that this system is strictly hyperbolic provided that the Masliyah–Lockett–Bassoon (MLB) flux vector is chosen, the particles have the same density, and the hindered-settling factor (a multiplicative algebraic expression appearing in the flux vector) does not depend on the particle size but is the same for all species. It is the purpose of this paper to prove that this hyperbolicity result remains valid in a fairly general class of cases where the hindered-settling factor does depend on particle size. This includes the common power-law type hindered-settling factor in which the exponent, sometimes called Richardson–Zaki exponent, is determined individually for each species, and is a decreasing function of particle size. The importance of this paper is two-fold: it proves stability for a class of polydisperse suspensions that was not covered in previous work, and it offers a new analysis of real data.     

Etude de phases quaternaires Winsor IV. Diagrammes de phases et propriétés electriques

A comparative study of phase diagram features and electrical properties of Winsor IV phases (so-called microemulsions) led to define two types of quaternary systems involving water, a hydrocarbon, and an ionic surfactant/alcohol combination defined byk, the surfactant/alcohol mass ratio. Systems of the first type exhibit a Winsor IV domain consisting of two disjointed areas corresponding to water-in-oil (w/o) and oil-in-water (o/w) monophasic fluid transparent isotropic media. The w/o and o/w areas are separated by a composition zone over which exist viscous turbid long-range organized structures related to the o/w w/o phase inversion mechanism. In that case, over the w/o area, the low frequency electrical conductivity and permittivity undergo non-monotonous changes as the composition varies. From conductivity maxima and minima, it is possible to define in the general case two lines ₁ and ₂ separating three adjacent sub-areas to which can be assigned compositions representing pre-micellar entities, inverted swollen spherical micelles and micelles clusters. For systems of the second type, the w/o and o/w sub-areas merge so as to form a unique monophasic area, which implies that the w/o o/w phase inversion occurs through a progressive diffuse mechanism. In that case the conductivity exhibits much higher values than in the preceding situation, and its variations with composition allow to define two linesC _d andC _m partitioning the Winsor IV domain into three adjacent areas. AboveC _d , that is for low and medium water contents, the conductivity variations with water content follow equations derived from the Percolation and Effective Medium theories, which indicates that the w/o swollen spherical micelles are submitted to attractive interactions. Below C_m, i. e. in the water rich region, the conductivity decrease with water content results from the progressive dilution of the external aqueous phase of the o/w Winsor IV media. BetweenC _d andC _m , the Winsor IV media exhibit an anomalous conductive behaviour which suggests that they are neither w/o nor o/w systems. This region can be considered as the diffuse phase inversion zone over which the systems are in a hybrid state that could be depicted tentatively as resulting from the formation of equilibrium bicontinuous structures.

     

Exploiting structure in piecewise-linear homotopy algorithms for solving equations

We consider the recent algorithms for computing fixed points or zeros of continuous functions fromR ⁿ to itself that are based on tracing piecewise-linear paths in triangulations. We investigate the possible savings that arise when these fixed-point algorithms with their usual triangulations are applied to computing zeros of functionsf with special structure:f is either piecewise-linear in certain variables, separable, or has Jacobian with small bandwidth. Each of these structures leads to a property we call modularity; the algorithmic path within a simplex can be continued into an adjacent simplex without a function evaluation or linear programming pivot. Modularity also arises without any special structure onf from the linearity of the function that is deformed tof. In the case thatf is separable we show that the path generated by Kojima's algorithm with the homotopyH ² coincides with the path generated by the standard restart algorithm of Merrill when the usual triangulations are employed. The extra function evaluations and linear programming steps required by the standard algorithm can be avoided by exploiting modularity.This research was performed while the author was visiting the Mathematics Research Center, University of Wisconsin-Madison, and was sponsored by the United States Army under Contract No. DAAG-29-75-C-0024 and by the National Science Foundation under Grant No. ENG76-08749.     

Symmetric homotopy construction

Homotopy continuation methods can be applied to compute all finite solutions to a given polynomial system. Computations will be performed more efficiently if the symmetric structure of the system can be exploited. This paper presents the construction of a symmetric homotopy. Using this homotopy, only the paths according to the generating solutions have to be traced during continuation.     

Branch-and-bound methods for solving systems of Lipschitzian equations and inequalities

In this note, we show how branch-and-bound methods previously proposed for solving broad classes of multiextremal global optimization problems can be applied for solving systems of Lipschitzian equations and inequalities over feasible sets defined by various types of constraints. Some computational results are given.This research was accomplished while the second author was a fellow of the Alexander von Humboldt Foundation at the University of Trier, Trier, West Germany.     

Decomposition of arborescent linear programs

We apply what we call sequential projection to reformulate certain linear programs as recursive optimization problems. We then apply the standard idea of approximating the return function at each stage of the recursion by using inner (or outer) linearization, and iteratively refining the approximation until the original linear program has been solved. The contribution of the paper lies in its unification of existing decomposition approaches and in showing that they can be generalized to apply to what we call arborescent linear programs.