DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

Historically,decay rates have been used to provide quantitative and qualitative information on the solutions to hyperbolic conservation laws.Quantitative results include the establishment of convergence rates for approximating procedures and numerical schemes.Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time.This work presents two decay estimates on the positive waves for systems of hyperbolic and genuinely nonlinear balance laws satisfying a dissipative mechanism.The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7,17,24].     

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.     

Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation

The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian func-tionals. The multi-symplectic discretization of each formulation is exemplified by the multi-symplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.     

On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated（m-NA） random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.     

A NOTE ON OSCILLATION MODULUS OF PL-PROCESS AND ITS APPLICATIONS UNDER RANDOM CENSORSHIP

The strong limit results of oscillation modulus of PL-process are established in this paper when the density function is not continuous function for censored data. The rates of convergence of oscillation modulus of PL-process are sharp under week condition. These results can be used to derive laws of the iterated logarithm of random bandwidth kernel estimator and nearest neighborhood estimator of density under continuous conditions of density function being not assumed.     

$B$值独立随机元序列加权和的完全收敛性和强大数律

In this paper, we obtain theorems of complete convergence and strong laws of large numbers for weighted sums of sequences of independent random elements in a Banach space of type p （1 ≤ p ≤ 2）. The results improve and extend the corresponding results on real random variables obtained by [1] and [2].     

ON THE ZERO-ONE LAWS FOR THE ERGODIC QUASI-INVARIANT MEASURES

Many zero-one laws for the quasi-additive functional and quasi-additive operator are proved. The results may be especially applied to the abstract Wiener measure space. As an application, we give a generalization of a remarkable result of the σ-additivity of a Gaussian cylinder probability due to L. Gross.     

Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations

The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.     

\rho混合随机变量的强大数律

In this paper we present some results for the general strong laws of large numbers of ■-mixing random variables by a maximal inequality of Utev and Peligrad.These results extend and improve the related known works in the literature.     

The Strong Law of Large Numbers for ■-Mixing Random Variables

In this paper we present some results for the general strong laws of large numbers of ■-mixing random variables by a maximal inequality of Utev and Peligrad.These results extend and improve the related known works in the literature.     

On Geometric-Stable Laws, a Related Property of Stable Processes, and Stable Densities of Exponent One

Klebanov et al. (1985, Theory Probab. Appl., 29, 791-794) introduced a class of probability laws termed by them "geometrically-infinitely-divisible" laws, and studied in detail the sub-class of "geometrically-strictly-stable" laws. In Section 2 of the present paper, the larger sub-class of "geometric-stable" laws is (defined and) studied. In Section 3, a characterization of stable processes involving (stochastic integrals and) geometric-stable laws is presented. In Section 4, the asymptotic behaviour of stable densities of exponent one (and || < 1) is studied using only real analysis methods. In an Appendix, "geometric domains of attraction" to geometric-stable laws are investigated, motivated by the work of Mohan et al. (1993, Sankhy Ser. A, 55, 171-179).     

DEGENERATIONS OF 7-DIMENSIONAL NILPOTENT LIE ALGEBRAS

ABSTRACT

We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimension.     

Relaxation WENO schemes for multidimensional hyperbolic systems of conservation laws

We present a class of high‐order weighted essentially nonoscillatory (WENO) reconstructions based on relaxation approximation of hyperbolic systems of conservation laws. The main advantage of combining the WENO schemes with relaxation approximation is the fact that the presented schemes avoid solution of the Riemann problems due to the relaxation approach and high‐resolution is obtained by applying the WENO approach. The emphasis is on a fifth‐order scheme and its performance for solving a wide class of systems of conservation laws. To show the effectiveness of these methods, we present numerical results for different test problems on multidimensional hyperbolic systems of conservation laws. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

带有微结构的连续统中新的能量守恒定律和C-D不等式

对带有微结构的连续统中现有的基本定律、均衡方程和Clausius-Duhem不等式进行了系统的再研究,发现所有的能量均衡方程和相关的C-D不等式都是不完整的.本文对现有的结果进行了评注,并提出新的能量均衡方程和相关的C-D不等式.     

函数S-粗集对偶与F-粗边际规律

函数单向S粗集对偶(dual offunction one direction singular rough sets)是函数S粗集的基本形式之一,函数单向S-粗集对偶具有动态特性与规律(函数)特性.函数S粗集(function singular rough sets)是把函数概念引入到S粗集内(singular rough sets)改进S粗集得到的把导数概念与函数单向S粗集对偶交叉、渗透给出粗边际规律F-粗边际规律概念;给出粗边际规律F-粗边际规律特征;给出F-粗边际规律与粗边际规律的关系;给出F-粗边际规律在经济信息系统中的应用     

Rates of convergence for the laws of large numbers for independent Banach-valued random variables

In this paper, results of Lai, Heyde, and Rohatgi concerning the convergence rates for the laws of large numbers are extended for the case of independent random variables taking values in a separable Banach space.     

General max-stable laws

We review the work on max-stable laws and their max domains of attraction introduced by Pancheva (Lect Notes Math 1155:284–309, 1984). We introduce the concept of general max domain of strict attraction of the general max-stable laws, a subclass of the general max domain of attraction and prove new results. Some interesting examples also are discussed.      

中国海洋产业结构时空分异研究

利用偏离-份额分析法,从海洋三次产业和海洋产业部门两个层次对中国沿海地区海洋产业结构时间和空间分异特征进行定量研究.结果表明:中国沿海地区海洋产业结构存在明显的时空分异特征;上海、天津、山东、浙江、广东5省市偏离总量、份额分量、结构分量和竞争力分量都较其他省市优势明显,对全国海洋经济发展的贡献较大;优势海洋产业部门主要分布在山东、广东、浙江、上海4省市.     

Conservation laws for nonlinear telegraph equations

A complete conservation law classification is given for nonlinear telegraph (NLT) systems with respect to multipliers that are functions of independent and dependent variables. It turns out that a very large class of NLT systems admits four nontrivial local conservation laws. The results of this work are summarized in tables which display all multipliers, fluxes and densities for the corresponding conservation laws. A physical example is considered for possible applications.     

Some results on increments of the partially observed empirical process

The author investigates the almost sure behaviour of the increments of the partially observed, uniform empirical process. Some functional laws of the iterated logarithm are obtained for this process. As an application, new laws of the iterated logarithm are established for kernel density estimators.