Path continuity of fractional Dirichlet functionals

We prove that the quasi continuous version of a functional in E^p_r is continuous along the sample paths of the Dirichlet process provided that p>2, 0<r?1 and pr>2, without assuming the Meyer equivalence. Parallel results for multi-parameter processes are also obtained. Moreover, for 1<p<2, we prove that a n parameter Dirichlet process does not touch a set of (p,2n)-zero capacity. As an example, we also study the quasi-everywhere existence of the local times of martingales on path space.     

单位球上不同Privalov空间之间的复合算子

利用η-Carleson测度给出了单位球上不同Privalov以及不同加权Bergman-Privalov空间之间的复合算子是度量有界或度量紧的充要条件,并给出了一些函数理论方面的刻画．     

“矩阵有理插值及其误差公式”一文的注

本文对文[1]中所给出的错误的误差公式做了修订,并给出了相应的证明。     

激发对相干态的等阶Y压缩效应

用数值计算法研究了激发对相干态|ζ;m〉＝a^+mb^+m|ζ〉的等阶Y压缩效应.结果表明:对于态a^+mb^+m|ζ〉,光场存在着等阶K(＝2,3,4,5,…)次方Y压缩效应,但是随着场模上光子增加数m的增大,等阶K次方Y压缩效应减弱.     

The complex correlation between current density and pore density based on non-SCR effects

The controllability of pore density and diameter is critical for emerging applications, e.g., non-lithographic photonic-crystal formation; however pore density and diameter could either increase or decrease self-orderedly with enhanced current density. In this letter, similar paradoxical phenomena were demonstrated; the etch rate as a function of field strength was evidenced and interpreted in light of current-burst-model. Based on a hybrid of SCR (space charge region) and breakdown effects, a semi-quantitative model was established in order to disentangle the paradox: such a model could also potentially serve as a design reference for various applications as far as breakdown comes into play. The paradox was finally found to be dominated by physics on patterned samples.     

Solutions of sturm-liouville boundary value problems for higher-order differential equations

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearityf in the equation depends on all lower derivatives, and the growth conditions imposed onf are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don’t apply the Green’s functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.     

指数型寿命数据中异常值的检验

本文讨论了在指数型寿命数据中,对同时存在的异常大数据和异常小数据的检验方法,给出了一个明确的判别标准,并以一例说明其应用。     

Mersenne数$M_p$都是孤立数

设p是素数,M_P=2~P-1.本文证明了M_P都是孤立数.     

Mode Coupling in Single-Mode Helical Fibres Under Perturbations

The mode coupling in a helical fibre with a circular cross-section undergoing perturbations is investigated in the Serret-Frenet frame. The coupled-mode equations have been derived and are compared with the conventional ones. Applying the coupled-mode equations to a helical fibre with an elliptical core deformation, we obtained, for the first time, a rigorous analysis of the transmission characteristics of the fibre. The numerical examples show that the mode ellipticity and elliptical birefringence increase as the core ellipticity increases and also vary as the pitch or the core offset change.     

ICP-AES中Ca、Al之间相互干扰的研究

本文在不同条件下比较详细地研究了Ca与Al在ICP-AES中的相互干扰,结果表明:这种干扰的垂直空间分布与其它元素的基体效应不同,特别在低观察区域Ca、Al之间呈现较为明显的相互抑制效应,说明Ca和Al之间产生了溶质挥发干扰。对分析条件特别是入射功率、载气流量及观察高度进行最优化可以使这种干扰减至最小。