关于二次规划问题分段线性同伦算法的改进

本文利用Ｃｈｏｌｅｓｋｙ分解，Ｇａｕｓｓ消去等技术和定义适当的同伦映射，将关于二次规划问题的分段线性同伦算法加以改进，改进后的算法，对于严格凸二次规划来说，计算效率与Ｇｏｌｄｆａｒｂ－Ｉｄｎａｎｉ的对偶法相当。     

Asymptotic behavior of continuous stochastic games

Summary The aim of this paper is to analyze the asymptotic behavior of the value functions of a continuous stochastic game as the number of stages grows to infinity or the discount factor approaches 1. After the setup of the problem we prove that, in both cases, the extrema of the value functions converge to the same limits. The convergence of the value functions is then obtained from the unicity of the solution of a functional problem and it is thus possible to design hypotheses that assure the convergence to a constant. This allows to assign a value to an undiscounted infinite-stage stochastic game in several senses and to show that optimal strategies are available for both players. Furthermore the boundedness of the remainders of the value function after removing the principal terms is analyzed, with appropriate hypotheses, and related to the existence of solutions of a Howard's type functional equation. This allows to show that for an infinite-stage undiscounted stochastic game optimal stationary strategies exist at least if this functional equation has some solution.     

Projection conditions on the vorticity in viscous incompressible flows

The problem of establishing appropriate conditions for the vorticity transport equation is considered. It is shown that, in viscous incompressible flows, the boundary conditions on the velocity imply conditions of an integral type on the vorticity. These conditions determine a projection of the vorticity field on the linear manifold of the harmonic vector fields. Some computational consequences of the above result in two-dimensional calculations by means of the nonprimitive variables, stream function and vorticity, are examined. As an example of the application of the discrete analogue of the projection conditions, numerical solutions of the driven cavity problem are reported.     

On the global attractivity for a logistic equation with piecewise constant arguments

In this paper, we consider the following logistic equation with piecewise constant arguments:

     

Haar wavelets of higher order on fractals and regularity of functions

Wavelets of Haar type of higher order m on self-similar fractals were introduced by the author in J. Fourier Anal. Appl. 4 (1998) 329-340. These are piecewise polynomials of degree m instead of piecewise constants. It was shown that for certain totally disconnected fractals, spaces of functions defined on the fractal may be characterized by means of the magnitude of the wavelet coefficients of the functions. In this paper, the study of these wavelets is continued. It is shown that also in the case when the fractals are not totally disconnected, the wavelets can be used to study regularity properties of functions. In particular, the self-similar sets considered can be, e.g., an interval in or a cube in . It turns out that it is natural to use Haar wavelets of higher order also in these classical cases, and many of the results in the paper are new also for these sets.     

Consistent Lyapunov exponent Estimation for one-dimensional dynamical systems

Summary  The author proves the consistency of a nearest neighbor estimator of the Lyapunov exponent for a general class of one-dimensional ergodic dynamical systems. The author shows that this estimator has good practical properties on a set of simulations.     

“最小键级原理”的从头算证实———苯和苯胺类硝基衍生物

感度是爆炸物对外界刺激的敏感程度 ,是火药、炸药和起爆药的基本属性 .在外界撞击作用下炸药发生爆炸的难易程度即该炸药的撞击感度 .感度通常依靠实测 ,从理论上加以判别是人们追求的目标 ,故研究炸药感度与结构的关系一直是该领域的热点 .根据撞击引起热解、热解引起爆炸、撞击感度主要与热解引发步骤相关联等思想 ,我们建议了“最小键级原理 (PSBO)”[1- 4] :对系列结构相似爆炸物 ,其热解引发键键级 (或重叠布居 )越小 ,则撞击感度越大 ;热解引发键键级越大 ,则撞击感度越小 .该判据已在多系列炸药中获得证实和应用[1- 4] .“热解引…     

Extending hysteresis operators to spaces of piecewise continuous functions

We consider continuous-time hysteresis operators, defined to be causal and rate independent operators mapping input signals to output signals . We show how a hysteresis operator defined on the set of continuous piecewise monotone functions can be naturally extended to piecewise continuous piecewise monotone functions. We prove that the extension is also a hysteresis operator and that a number of important properties of the original operator are inherited by the extension. Moreover, we define the concept of a discrete-time hysteresis operator and we show that discretizing continuous-time hysteresis operators using standard sampling and hold operations leads to discrete-time hysteresis operators. We apply the concepts and results described above in the context of sampled-data feedback control of linear systems with input hysteresis.