Tame kernels of pure cubic fields

In this paper, we study the p-rank of the tame kernels of pure cubic fields. In particular, we prove that for a fixed positive integer m, there exist infinitely many pure cubic fields whose 3-rank of the tame kernel equal to m. As an application, we determine the 3-rank of their tame kernels for some special pure cubic fields.     

Invariant mean value property and harmonic functions

We give conditions on the functions and u on [image omitted] such that if u is given by the convolution of and u, then u is harmonic on [image omitted].     

Symmetry groups and Gauss kernels of Schrödinger equations

The relationship between symmetries and Gauss kernels for the Schrödinger equation iu_t=u_xx+f(x)u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schrödinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.     

Mean Shift跟踪算法中核函数参数的评估与分析

Mean Shift是一种基于特征的对目标实现快速跟踪的算法,传统的Mean Shift算法由于跟踪中物体的尺度变化会使跟踪偏离目标乃至跟踪失败,并且原有的自适应地对跟踪窗宽的调整,是基于对核窗宽的改变来得到的。在＂固定跟踪窗宽—改变核窗宽＂的基础上对目标进行跟踪,对目标空间定位精度进行了评估与分析,通过实验结果表明改变核函数参数能改善目标跟踪的精度。     

Carrier transport and bandgap shift in n-type degenerate ZnO thin films: The effect of band edge nonparabolicity

Contribution of band edge nonparabolicity to the charge carrier transport in degenerate n-type zinc oxide thin films has been investigated theoretically in order to understand the fundamental aspects of electron scattering in such thin films regardless of precise details of the preparation procedure. To conduct this, the theoretical evaluated results have been compared to the experimental values taken from literatures. The results indicate that the nonparabolicity (introducing through effective mass of charge carriers) has a strong effect on the total mobility of carriers in zinc oxide films so that a satisfactory agreement with experimental data is fulfilled. The dependence of nonparabolicity on bandgap shift is also discussed. Studying the optoelectronic properties of numerous moderately and heavily doped samples revealed that their optical bandgap has lower blueshift than the theoretical value obtained from the well-known Burstein–Moss effect. So, the observed bandgap shift was dependent on the carrier concentration and the total shift of bandgap was evaluated by combining the Burstein–Moss and bandgap narrowing effects. Two different cases were also examined; parabolic and nonparabolic (modified) Burstein–Moss effects. The results show that the modified Burstein–Moss effect leads to great agreement with experimental data.     

Viscosity solutions of a class of degenerate quasilinear parabolic equations with Dirichlet boundary condition

This paper is concerned with viscosity solutions for a class of degenerate quasilinear parabolic equations in a bounded domain with homogeneous Dirichlet boundary condition. The equation under consideration arises from a number of practical model problems including reaction–diffusion processes in a porous medium. The degeneracy of the problem appears on the boundary and possibly in the interior of the domain. The goal of this paper is to establish some comparison properties between viscosity upper and lower solutions and to show the existence of a continuous viscosity solution between them. An application of the above results is given to a porous-medium type of reaction–diffusion model which demonstrates some distinctive properties of the solution when compared with the corresponding semilinear problem.     

A hierarchical multiple kernel support vector machine for customer churn prediction using longitudinal behavioral data

The availability of abundant data posts a challenge to integrate static customer data and longitudinal behavioral data to improve performance in customer churn prediction. Usually, longitudinal behavioral data are transformed into static data before being included in a prediction model. In this study, a framework with ensemble techniques is presented for customer churn prediction directly using longitudinal behavioral data. A novel approach called the hierarchical multiple kernel support vector machine (H-MK-SVM) is formulated. A three phase training algorithm for the H-MK-SVM is developed, implemented and tested. The H-MK-SVM constructs a classification function by estimating the coefficients of both static and longitudinal behavioral variables in the training process without transformation of the longitudinal behavioral data. The training process of the H-MK-SVM is also a feature selection and time subsequence selection process because the sparse non-zero coefficients correspond to the variables selected. Computational experiments using three real-world databases were conducted. Computational results using multiple criteria measuring performance show that the H-MK-SVM directly using longitudinal behavioral data performs better than currently available classifiers.     

拟线性退化抛物方程Cauchy问题的解

对来自金融数学领域的方程_xxu+u_yu-_tu=c（x,y,t,u）,（x,y,t）∈Q_T=R²×[0,T)的Cauchy问题,给出了一种新的熵解的定义,得到了其适定性结果.可以证明所得到的解还是强解,即方程中所出现的各阶偏导数几乎处处连续.最后讨论了解的爆破性质以及与解的间断点相关的几何性质.     

基于非参数估计方法的沪铜期货价格研究

非参数估计方法是现代统计学的一个新发展方向,在各领域有重要的应用价值.本文针对非参数模型的三种估计方法,将其应用于沪铜期价与LME现价的相关关系分析,得到模型的拟合值和拟合曲线.最后,与最小二乘法的结果进行比较分析,证实了非参数估计在不同历史时期有预测精度高的优点.