Lipschitz classes on local fields

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).     

Ba(Zr0.3Ti0.7)O3 铁电薄膜的制备

介绍了用溶胶-凝胶法(sol-gel)在Pt/Ti/SiO2/Si衬底和石英衬底上制备Ba(Zr0.3Ti0.7)O3铁电薄膜的基本原理、工艺过程及工艺特点;Sol-gel制备的Ba(Zr0.3Ti0.7)O3铁电薄膜表面平整、厚度均匀.     

Generalized 3G theorem and application to relativistic stable process on non-smooth open sets

Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes.     

On multiple integrals of special form

Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.     

G-网络排队系统的研究新进展

在研究排队网络的文献中,G-网络(即推广的排队网络)最近受到了国际学者广泛的关注,它的研究在一定程度上丰富了排队网络的内容.正因为有很多学者投入到此项研究中,新的结果是层出不穷的.本文简短地介绍G-网络近年来的发展.     

Recent radiochemical studies of the fission process

This article summarizes the recent radiochemical investigations on mass, charge kinetic energy and fragment angular distributions in low energy fission of actinides.     

Optimal production and rationing decisions in supply chains with information sharing

This paper considers a two-echelon capacitated supply chain with two non-identical retailers and information sharing. We characterize the optimal inventory policies. We also study the benefits of the optimal stock rationing policy over the first come first served (FCFS) and the modified echelon-stock rationing (MESR) policies.     

Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

随机环境中分枝过程的等价定理

给定了随机环境中分枝过程(BPRE)的精确定义,讨论了有关的可测性问题和BPRE的基本性质．在此基础上,证明了BPRE的一个等价定理．     

Allocating unfunded liability in pension valuation under uncertainty

This paper studied the cost allocation for the unfunded liability in a defined benefit pension scheme incorporating the stochastic phenomenon of its returns. In the recent literature represented by Cairns and Parker [Insurance: Mathematics and Economics 21 (1997) 43], Haberman [Insurance: Mathematics and Economics 11 (1992) 179; Insurance: Mathematics and Economics 13 (1993) 45; Insurance: Mathematics and Economics 14 (1994) 219; Insurance: Mathematics and Economics 14 (1997) 127], Owadally and Haberman [North American Actuarial Journal 3 (1999) 105], the fund level is modeled based on the plan dynamics and the returns are generated through several stochastic processes to reflect the current realistic economic perspective to see how the contribution changed as the cost allocation period increased. In this study, we generalize the previous constant value assumption in cost amortization by modeling the returns and valuation rates simultaneously. Taylor series expansion is employed to approximate the unconditional and conditional moments of the plan contribution and fund level. Hence the stability of the plan contribution and the fund size under different allocation periods could be estimated, which provide valuable information adding to the previous works.