矩母函数:拟对称概率测度

本文用凸函数的方法研究了概率测度的矩母函数和由C.J.Stone提出的拟对称性,并刻画了Martin边界的法向量.拟对称性在随机游动的比例极限定理中是一个重要的概念.这些结果可应用于Levy过程的研究.     

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.     

Martin Boundaries of Elliptic Skew Products, Semismall Perturbations, and Fundamental Solutions of Parabolic Equations

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations.     

The interlace polynomial of a graph

Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers.     

Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M_∂D×[0,T)), where M_∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D).     

Wiener's test for space-time random walks and its applications

This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.

     

The Synthesis of 1,3-Bis(Phenylseleno)-2-Propanol

A general and efficient synthetic method of 1,3-bis(phenylseleno)-2-propanol by reducing diphenyl diselenides with sodium borohydride in basic environment and then reacting with epichlorohydrin are described.     

The Surface Analysis Working Group at the Consultative Committee for Amount of Substance,Metrology in Chemistry and Biology: A successful initiative by Martin Seah

Dr Martin Seah, NPL, was the initiator, founder, and first chairman of the Surface Analysis Working Group (SAWG) at the Consultative Committee for Amount of Substance, Metrology in Chemistry and Biology (CCQM) at the Bureau International des Poids et Mesures (BIPM), the international organization established by the Metre Convention. This tribute letter summarizes his achievements during his chairmanship and his long-running impact on the successful work of the group after his retirement.     

Structural characterization and biological activity of galactoglucan from Castanea mollissima Blume

Abstract

A galactoglucan (HCPA) was extracted from C. mollissima Blume fruits using hot water, which was composed of glucose and galactose, with a molecular weight of 5.5?kDa. Methylation and 1?D, 2?D NMR spectroscopy analysis showed that HCPA contained [→4)-α-D-Glcp(1→], [→4,6)-α-D-Glcp(1→], [→4)-β-D-Galp(1→] and [α-D-Glcp(1→] motifs in a molar ratio of approximately 6.11:1.08:1.00:1.03. HCPA showed a spherical-like structure as detected by scanning electron microscope (SEM). HCPA biological activity was investigated in vitro. The results showed that HCPA inhibited the proliferation of HeLa, MCF-7 and MGC-803 cells, induced HeLa cells apoptosis and arrested cell cycle in G2/M phase of HeLa cells. HCPA also enhanced the viability and phagocytic ability of RAW 264.7 cells and stimulated the production of NO, TNF-α and IL-6. The results demonstrated that HCPA had a potent antitumor and immunomodulating effects in vitro, suggesting its potential use as functional food and drug products.     

A stable manifold MCMC method for high dimensions

We combine two important recent advancements of MCMC algorithms: first, methods utilizing the intrinsic manifold structure of the parameter space; then, algorithms effective for targets in infinite-dimensions with the critical property that their mixing time is robust to mesh refinement.