分式Brown运动的局部时:白噪声分析法

本文利用白噪声分析的方法,讨论了分式布朗运动的局部时,即将其看作一个Hida分布.进一步,给出分式布朗运动的局部时的混沌分解以及局部时平方可积性.     

广义随机Solow经济增长模型

本文在文[1]的基础上进一步拓广了随机Solow经济增长模型．利用白噪声分析理论建立的广义随机Solow经济增长模型，将随机Solow模型推广到包含广义白噪声泛函及具有非可料扩散系数的情形，并且借助U—泛函方法表明了Picard迭代法在此仍十分有效．     

The mechanochemical stochastic processes of molecular motors

In this article, we develop a rigorous mathematical foundation of microscopic motors. The main characteristic is the combination of Brownian and Poisson noises.     

重正化核的Poisson随机积分表示

本文考虑具有有限矩的1维无穷可分分布的正交多项式的母函数,通过“一步提升”原则得到的重正化核的显式表示,建立重正化核运算与Poisson随机积分之间的关系.     

-function of an operator: A white noise approach

Let be the canonical framework of white noise analysis over the Gel'fand triple and be the space of continuous linear operators from to . Let be a self-adjoint operator in with spectral representation . In this paper, it is proved that under appropriate conditions upon , there exists a unique linear mapping such that for each . The mapping is then naturally used to define as , where is the Dirac -function. Finally, properties of the mapping are investigated and several results are obtained.

     

Unitarity of Generalized Fourier–Gauss Transforms

Abstract

A generalized Fourier–Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.     

An Itô Formula of Generalized Functionals and Local Time for Fractional Brownian Sheet

Abstract

By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameters H ₁, H ₂ ∈ (0,1). As an application, we give the integral representations for two versions of local times of a fractional Brownian sheet, respectively.     

White Noise Approach Construction of Ф4 4 Quantum to The Fields （Ⅱ）

In this paper a complete proof for the existence of generalized operators satisfying abstract 02 dynamical equations of quantum motions δ^2/δt^2Ф（t, x） ＋ （ △- m^2）Ф（t, x） = -λ ：Ф^3（t, x）, subject to a suitable initial condition, is given under the framework of white noise analysis. Also some important commutation relations related to Ф44 quantum fields are discussed and proved in detail.     

On the averaged quantum dynamics by white-noise hamiltonians with and without dissipation

Exact results are derived on the averaged dynamics of a class of random quantum-dynamical systems in continuous space. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic, time-independent and quadratic, the Weyl-Wigner symbol of the other part is a homogeneous Gaussian random field which is delta correlated in time, but smoothly correlated in position and momentum. The averaged dynamics of the resulting white-noise system is shown to be a monotone mixing increasing quantum-dynamical semigroup. Its generator is computed explicitly. Typically, in the course of time the mean energy of such a system grows linearly to infinity. In the second part of the paper an extended model is studied, which, in addition, accounts for dissipation by coupling the white-noise system linearly to a quantum-mechanical harmonic heat bath. It is demonstrated that, under suitable assumptions on the spectral density of the heat bath, the mean energy then saturates for long times.     

基于CdSe/ZnS量子点光转化层的高稳定性白光LED器件

采用一步法合成了510,550和630 nm三种峰值的高稳定性、高量子效率核壳结构CdSe/ZnS量子点材料,其量子产率分别达到82%,98%,97%。将该量子点材料取代传统的荧光粉材料,与硅胶均匀混合后作为光转换层涂覆到蓝色InGaN LED芯片上,制备了白光LED器件。通过依次添加不同颜色量子点制备的量子点光转换层,考察了510,550和630 nm三色CdSe/ZnS量子点在硅胶中的不同配比对白光LED器件性能的影响,研究了不同颜色量子点之间的能量转换机制,利用量子点对白光光谱及其色坐标的影响机制,得到优化的白光器件结果及其三色量子点的配比,结果表明,当绿色、黄绿色、红色三种量子点之间的配比为24∶7∶10时,得到高稳定性、高效率的正白光器件特性,在电流20～200 mA范围内,色温变化为4 607～5 920 K,色坐标变化为（0.355 1,0.348 3）～（0.323 4,0.336 1）,显色指数变化为77.6～84.2,器件最高功率效率达到31.69 lm W-1@20 mA。另外,为了进一步考察器件性能稳定的原因,研究了时间、温度以及UV处理对CdSe/ZnS QDs/硅胶混合光转换材料稳定性的影响,结果表明,器件的高稳定性可归因于所采用的一步法合成的核壳结构量子点材料本身的稳定性,研究的优化器件结果是一种低能耗的优质白光光源,可使人们真实地感知物体的原貌,在正白光光源领域具有很好的应用前景。