A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.     

曲面平滑的自适应几何扩散

1.引 言 本文的目的是用求解偏微分方程（PDE）的方法来消除离散三角形曲面的噪声,所使用的方程是热传导方程到曲面的推广.热传导方程应用于图像处理已有二十余年的历史,有关参考文献相当丰富（见[1,11,12,19]）.众所周知,对于给定的初始图像ρ0,热传导方程　　在τ时刻的解与用Gauss滤波器Gσ（x）=　（当标准差σ=2τ,时）和ρ0作卷积的结果相同.容易看出Gρ和ρ0的卷积运算相当于对ρ0做加权平均,当标准离差σ变大时,该加权平均在一个较大的范围实现,这解释了热传导方程的滤波作用.近来热传导方程已推广到空间曲面[4,5]以及高维空间中的二维流形（见[3]）,对     

Some formulae for the q-Bernoulli and Euler polynomials of higher order

The purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli numbers of higher order, which is an answer to a part of the problem in a previous publication (see Indian J. Pure Appl. Math. 32 (2001) 1565-1570).     

Coupled intervals in the discrete calculus of variations: necessity and sufficiency

In this work we study nonnegativity and positivity of a discrete quadratic functional with separately varying endpoints. We introduce a notion of an interval coupled with 0, and hence, extend the notion of conjugate interval to 0 from the case of fixed to variable endpoint(s). We show that the nonnegativity of the discrete quadratic functional is equivalent to each of the following conditions: The nonexistence of intervals coupled with 0, the existence of a solution to Riccati matrix equation and its boundary conditions. Natural strengthening of each of these conditions yields a characterization of the positivity of the discrete quadratic functional. Since the quadratic functional under consideration could be a second variation of a discrete calculus of variations problem with varying endpoints, we apply our results to obtain necessary and sufficient optimality conditions for such problems. This paper generalizes our recent work in [R. Hilscher, V. Zeidan, Comput. Math. Appl., to appear], where the right endpoint is fixed.     

具有模糊数的模糊多目标群体决策优选模型与方法

多目标群体决策问题是运筹学的一个重要研究领域，目前已经提出了一些有效的决策方法。但对目标值和权重均为模糊数的模糊多目标群体决策问题却研究不多，本对此类模糊多目标群体决策问题进行了探讨，利用相对正理想方案与相对负理想方案概念定义了相对差异距离，进而建立了模糊多目标群体决策优选模型与方法，并通过战役决心方案的评价说明了该方法是可行、有效的，可作为军事决策与决策支持系统的备选方法。     

N指标d维广义Wiener过程象集的m项代数和的几个性质

设珮犠（狋）：犚犖＋ →犚犱是犖指标犱维广义Ｗｉｅｎｅｒ过程，对任意紧集犈１，…，犈犿犚犖＞ ，该文研究了犿项代数和珮犠（犈１）…珮犠（犈犿）的Ｈａｕｓｄｏｒｆｆ维数，Ｐａｃｋｉｎｇ维数和正的Ｌｅｂｅｓｇｕｅ测度及内点的存在性． 其结果包含并推广了布朗单的结果．     

Two-component model of solar plages

By use of the 2-m Mcmath-Pierce telescope at Kitt Peak, the high-quality spectra of a plage with moderate brightness near the center of solar disk were obtained. The data include seven spectral lines, which are Hα, Hβ, CaII H and K lines and the infrared triplet. With the consideration of fine structures of solar plages, a two-component atmospheric model is constructed by keeping the cool component to be the quiet atmosphere. Three cases of the hot component are given for different filling factors where the temperature and density distribution are adjusted in order to reproduce the seven observed spectral profiles. We also briefly discuss the influence of the column density at the base of the corona, m0, and the macro-turbulent velocity on the required filling factor and computed profiles. The two-component model is compared with precious one-component semi-empirical models. The limitation of the model is pointed out and further improvement is indicated.     

分子聚集理论在医药学研究中的应用

本文利用聚集型状态方程，克拉贝龙方程以及临界条件推出聚集活性参量方程．分析结果表明，医药的药理活性是可以用聚集活性参量予以定量表征．本文给出了某些医药的主要的药物成分，如氧化亚氮 乙醚、氯仿和水杨酸甲酯等嘛醉剂），一氧化氮（硝酸甘油）、乙醇胺（医药活性剂）和多巴胺（神经递质）的生物活性数据．实践经验表明，这些化学品分别在生命体的心血管系统、神经系统和免疫系统中起着重要的药理功能作用．这表明，本文研究的内容在医药学研究领域有其重要意义．     

Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.