复连通曲面体高维积分的Monte Carlo 法

本文讨论了用Monte Carlo法求积分区域为复连通曲面体的高维积分,即用Monte Carlo法估计下面形式的高维积分：I＝∫G-s∪j=1Gj…,xn)dx1dx2…,dxn,其中n为积分维数,Gj包含G（j=1,2…,s）体积示知和G,Gj(j=1,2,…,s)体积都未知情形得出估计法、收敛性定理和具体算法,另外,也对求复连通曲面体的重心问题进行分析,得出估计法和收敛性定理。     

Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems

In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions.     

模糊概率随机变量

研究了第二类模糊随机变量——具有清晰事件、模糊概率的随机变量的数学描述。在区间概率的基础上,利用模糊分解定理给出了概率模糊数集是可行的条件,进一步给出了具有模糊概率的随机变量及模糊概率随机变量的模糊分布函数和模糊分布列的定义和性质。提出并证明了具有模糊概率运算封闭性的模糊概率分解定理。研究了模糊概率随机变量的模糊数学期望和模糊方差的定义和性质。所有关于模糊概率随机变量的数学描述都具有模糊概率运算的封闭性,这为完善模糊概率的运算方法打下了基础。     

Interpolation of Herz Spaces and Applications

C. Herz introduced in [Hr] some new spaces to study properties of functions. An Interesting account, with many applications, of some particular cases of the generalized Herz spaces is given in [BS]. In this paper we first identify the duals of the generalized Herz spaces. Then, we characterize their intermediate spaces when the complex method of interpolation for families of spaces Is used. Applications are given that show the bounded ness of many operators on the generalized Herz spaces.     

乙肝表面抗原检测方法的优化研究

本文应用概率论知识对乙肝表面抗原检测方法进行了探讨 ,建立了相应的数学模型 ,优化了检测模式     

一类零点为次线性的椭圆方程的可解性

该文考虑-Δu =g(x) |u|q- 2 u λ|u|p- 2 u f(x) ,x∈Ω,u| Ω =0 ,g,f∈ L∞ (Ω ) ,1 相似文献   

集值序上鞅

本文研究了连续时间的集值序上鞅．在一定的条件下首先证明了集值序上鞅有（Ｋ－Ｍ）Ｒｉｅｓｚ分解;然后证明了集值序上鞅的Ｄｏｏｂ－停时定理．     

连续时间集值(上、下)鞅Doob-停时定理

本文首先给出了Ｊ_L意义下的集值鞅的正则性,然后证明了几种连续时间集值（上、下）鞅Ｄｏｏｂ－停时定理．     

A Penalized Matrix Normal Mixture Model for Clustering Matrix Data

Along with advances in technology, matrix data, such as medical/industrial images, have emerged in many practical fields. These data usually have high dimensions and are not easy to cluster due to their intrinsic correlated structure among rows and columns. Most approaches convert matrix data to multi dimensional vectors and apply conventional clustering methods to them, and thus, suffer from an extreme high-dimensionality problem as well as a lack of interpretability of the correlated structure among row/column variables. Recently, a regularized model was proposed for clustering matrix-valued data by imposing a sparsity structure for the mean signal of each cluster. We extend their approach by regularizing further on the covariance to cope better with the curse of dimensionality for large size images. A penalized matrix normal mixture model with lasso-type penalty terms in both mean and covariance matrices is proposed, and then an expectation maximization algorithm is developed to estimate the parameters. The proposed method has the competence of both parsimonious modeling and reflecting the proper conditional correlation structure. The estimators are consistent, and their limiting distributions are derived. We applied the proposed method to simulated data as well as real datasets and measured its clustering performance with the clustering accuracy (ACC) and the adjusted rand index (ARI). The experiment results show that the proposed method performed better with higher ACC and ARI than those of conventional methods.     

Picture change and calculations of expectation values in approximate relativistic theories

The effect of the so-called picture change on expectation values of one-electron operators in approximate two(one)-component relativistic theories is discussed. This effect is expected to be particularly large for operators which assume large values in the vicinity of heavy nuclei. The numerical results illustrating the picture change effect on electric field gradients at nuclei have been obtained in the spin-free Pauli and Douglas–Kroll approximations. It has been found that the picture change effect lowers the electric field gradient at I in HI by about 1 a.u. Very large picture change effect (−8 a.u.) has been calculated for HAt. It is concluded that in accurate calculations of expectation values of operators involving high inverse powers of the electron–nucleus distance the picture change, which accompanies the transformation of the Dirac (Dirac–Coulomb) equation to approximate two(one)-component relativistic Hamiltonians, must be taken into account. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 159–174, 1998