Levy area for the free Brownian motion: existence and non-existence

This note extends the work of Capitaine (J. Funct. Anal. 179 (1) (2001) 153) on the Levy area process for the free Brownian motion in two directions. First, we reprove that a Levy area for the Free Brownian motion exists in the Von Neumann tensor product, by exhibiting a non-commutative Burkholder-Davis-Gundy type inequality. Then, we show that there does not exist a Levy area in the projective tensor product.     

Rough隶属函数关于集合并与交的一种高精度计算方法

近些年来，许多处理近似问题的方法陆续被提出，其中利用Rough集理论计算两个集合的并和交的Rough隶属函数方法是被用较多的一种方法，但毕竟该方法精度较差。为此，介绍了一种精度较高的计算两个集合的并和交的Rough隶属函数方法，它克服了前者利用Rough集理论计算Rough隶属函数的复杂性，而迎来了简单和高精度的特点。     

Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold

We determine the limit of the bottom of spectrum of Schrödinger operators with variable coefficients on Wiener spaces and path spaces over finite-dimensional compact Riemannian manifolds in the semi-classical limit. These are extensions of the results in [S. Aida, Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space, J. Funct. Anal. 203 (2) (2003) 401-424]. The problem on path spaces over Riemannian manifolds is considered as a problem on Wiener spaces by using Ito's map. However the coefficient operator is not a bounded linear operator and the dependence on the path is not continuous in the uniform convergence topology if the Riemannian curvature tensor on the underling manifold is not equal to 0. The difficulties are solved by using unitary transformations of the Schrödinger operators by approximate ground state functions and estimates in the rough path analysis.     

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.     

A stratospheric chemical reaction controlling climatic change

It has been established from geological studies that change in the atmospheric content of carbon dioxide gas commenced about one hundred million years ago. The likely origin of this change is advanced as being the onset of the Brewer circulation caused by the rise in terrain induced by tectonic plate movement. It is demonstrated that tectonic plate movement can be affected by impacts from external bodies which penetrate the crust of the Earth. The consequences of the change in atmospheric concentration of carbon dioxide are proposed as first, extinctions and reductions in animal numbers, including primates, as a result of changes in body chemistry of these animals and second, a change in the rate of weathering of rocks giving rise to changes in the availability of chemicals such as calcium and potassium which are essential for plant and animal life. This latter change contributing to the extinctions and reductions in animal numbers. It is shown that the change in weathering can account for the rise to dominance of angiosperm plants. It is concluded that there were several simultaneous evolutionary environments on Earth which were a function of altitude which gave rise to a vertical variation in atmospheric content of carbon dioxide. This variation disappeared with rise of terrain and the onset of the Brewer circulation. Such changes are advanced and being much more important than any changes in temperature caused by greenhouse effects since the disappearance of atmospheric variations in carbon dioxide allowed animal migration. It is demonstrated that the conditions of extinction could be reintroduced by human activities.     

Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies

The scattering cross sections for arbitrarily shaped dielectric objects with rough surface are determined for optical and infrared frequencies using the Kirchhoff approximation. The formula of the coherent scattering cross section is derived, and numerical method of incoherent scattering cross section is given. As a specific example, the infrared laser scattering cross sections of rough spheres are calculated at 1.06 m.     

基于模糊不变子群的上、下近似

研究群中集合的粗糙近似问题。利用分解定理和表现定理,定义了群中集合关于模糊不变子群的上、下近似,并给出了近似算子的性质。证明了子群的上、下近似在同态映射下的不变性质。     

基于优势关系下不协调目标信息系统的分布约简

在基于优势关系下的不协调目标信息系统中引入了分布约简和最大分布约简的概念,并讨论了二者之间的关系,而且得到了分布和最大分布约简的判定定理以及辨识矩阵,建立了不协调目标信息系统的分布和最大分布约简的具体方法,同时通过实例验证了该方法的有效性,从而进一步丰富了粗糙集理论。     

粗糙线性空间

将粗糙集思想引入到线性空间。提出线性空间中子集的上近似和下近似的概念,给出上、下粗线性子空间与上、下粗不变子空间的概念,讨论粗糙集线性空间的有关性质。