Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

Lower bound for the convergence rate of nonstationary Jacobi-like iteration

Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix A is an H-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with 〈A〉 as the coefficient matrix, where 〈A〉 is a comparison matrix of A.     

Three-body problem in the theory of the dielectric constant

We study the corrections to the Clausius-Mossotti formula for the dielectric constant of a disordered system of polarizable spherical particles. Previously we have derived an exact cluster expansion for the correction terms. Here we study the three-body correction in detail. We derive an explicit expression for the integrand of the three-body cluster integral for a system of polarizable point dipoles.     

A quasilinearization method for a class of integro-differential equations with mixed nonlinearities

We develop an extended form of the quasilinearization method for an initial value problem involving a nonlinear integro-differential equation with mixed nonlinearities, occurring in distributed-infective and distributed-contact models. In fact, a monotone sequence of iterates converging uniformly and quadratically to a solution of the problem is obtained. Some interesting observations are presented.     

Properties of<Emphasis Type="Italic">B</Emphasis><Subscript>c</Subscript> meson

The mass spectrum ofcb meson is investigated with an effective quark-antiquark potential of the form -α_c/r +Ar ^νwith ν varying from 0.5 to 2.0. TheS andP-wave masses, pseudoscalar decay constant, weak decay partial widths in spectator model and the lifetime ofB _cmeson are computed. The properties calculated here are found to be in good agreement with other theoretical and experimental values at potential index,ν = 1     

BOUNDEDNESS AND CONVERGENCE FOR THE NON-LINARD TYPE DIFFERENTIAL EQUATION

In this article, the author studies the boundedness and convergence for the non-Lienard type differential equation (x|·)=a(y)-f(x) (y|·)=b(y)β(x)-g(x) e(t) where a(y),b(y),f(x),g(x),β(x) are real continuous functions in y∈R or x∈R,β(x)≥0 for all x and e(t) is a real continuous function on R = {t: t≥0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.     

线性常微分方程的保线性变换及其应用

研究了线性常微分方程的保线性变换，得到任意两个二阶线性常微分方程等价的条件，并用于求解一类二阶线性变系数齐次常微分方程．对数学物理方法教学中怎样通过适当的变换把给定的二阶线性变系数齐次常微分方程化为可解的方程给出了合理解释。     

几种模糊传递关系的收敛性

本文对几种模糊传递关系进行比较 ,从一个侧面说明了用于构造偏好关系的模糊关系应是互逆关系 .文中证明了对任意的 n阶互逆传递模糊关系 R,必有 Rn=Rn+1 .     

Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

In this work we study connections between various asymptotic properties of the nonlinear filter. It is assumed that the signal has a unique invariant probability measure. The key property of interest is expressed in terms of a relationship between the observation σ field and the tail σ field of the signal, in the stationary filtering problem. This property can be viewed as the permissibility of the interchange of the order of the operations of maximum and countable intersection for certain σ-fields. Under suitable conditions, it is shown that the above property is equivalent to various desirable properties of the filter such as

(a) uniqueness of invariant measure for the signal,

(b) uniqueness of invariant measure for the pair (signal, filter),

(c) a finite memory property of the filter,

(d) a property of finite time dependence between the signal and observation σ fields and

(e) asymptotic stability of the filter.

Previous works on the asymptotic stability of the filter for a variety of filtering models then identify a rich class of filtering problems for which the above equivalent properties hold.     

一类非线性椭圆问题的schwarz算法

其中考虑下述泛函最小问题:求u∈W01,α(Ω),使F(u)=