基于公式真度的公式集约简

基于经典命题逻辑的真度理论,讨论了经典命题逻辑系统当中公式集的约简问题。提出了真度约简及α-真度约简的概念,为公式集的约简提供了一种可行的操作方法。     

A characterization of

This work is devoted to the relationship between topological properties of a space and those of (= the space of continuous real-valued functions on , with the topology of pointwise convergence). The emphasis is on -compactness of and on location of in . In particular, -compact cosmic spaces are characterized in this way.

     

最佳跳频序列族的设计与分析

本文提出了基于ｐ元广义ＧＭＷ序列和ｐ元Ｋａｓａｍｉ序列构造跳频序列族的方法,证明了基于广义ＧＭＷ序列所构造的跳频序列族具有最佳Ｈａｍｍｉｎｇ相关特性,而基于Ｋａｓａｍｉ序列所构造的跳频序列族不具有最佳Ｈａｍｍｉｎｇ相关特性。     

Bent函数的一般构造法

本文用概率方法给出小项表示的布尔函数谱的性质,据此得到了Ｂｅｎｔ函数的特征矩阵的等价刻画,原则上给出了Ｂｅｎｔ函数的一般构造法,并为Ｂｅｎｔ函数的计数问题提供了一个模型。文中还提出了Ｂｅｎｔ矩阵的概念,考察了Ｂｅｎｔ矩阵的性质,并借助Ｂｅｎｔ矩阵得到由已知Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数的方法。     

Rate of Convergence for the Empirical Distribution Function and the Empirical Characteristic Function of Mixing Processes

Ｒａｔｅ　ｏｆ　Ｃｏｎｖｅｒｇｅｎｃｅ　ｆｏｒ　ｔｈｅ　Ｅｍｐｉｒｉｃａｌ　Ｄｉｓｔｒｉｂｕｔｉｏｎ　Ｆｕｎｃｔｉｏｎ　ａｎｄ　ｔｈｅ　Ｅｍｐｉｒｉｃａｌ　Ｃｈａｒａｃｔｅｒｉｓｔｉｃ　Ｆｕｎｃｔｉｏｎ　ｏｆ　Ｍｉｘｉｎｇ　ＰｒｏｃｅｓｓｅｓＨｕＳｈ...     

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.     

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.