Asymptotic Correction of More Sturm–Liouville Eigenvalue Estimates

The asymptotic correction technique of Paine, de Hoog and Anderssen can dramatically improve the accuracy of finite difference or finite element eigenvalues at negligible extra cost if closed form expressions are available for the errors in a simpler related problem. This paper gives closed form expressions for the errors in the eigenvalues of certain Sturm–Liouville problems obtained by various methods, thereby increasing the range of problems for which asymptotic correction can achieve maximum efficiency. It also investigates implementation of the method for more general problems.     

系综分布和它的小涨落近似

由“从正则分布出发，在小涨落近似下得出的能量涨落分布公式”求得的能量涨落的二次矩与直接由正则分布求得的二次矩完全相同，但分别由二求得的高次矩并不完全相同。     

高等师范学校物理专业课程结构改革研究

为解决高等师范院校物理专业学生的知识结构和实际能力与社会需要明显不相适应的矛盾，我们对四年制物理专业的课程结构进行了全面改革。改革后，毕业生不仅能胜任普通中学或职业中学（职业中专）的教学，而且有能力参与厂矿企业的技术工作，具有更广泛的适应性和更强的竞争力。     

Third harmonics of cosmic ray intensity on quiet days at Deep River Neutron Monitoring Station

The cosmic ray (CR) intensity data recorded in Deep River Neutron Monitoring Station have been investigated on quietest days (QD) for third harmonics of daily variation during solar cycles 21 and 22. It has been observed that in spite of abrupt change in the amplitude and phase of tri-diurnal anisotropy in CR intensity, the amplitude is quite significant throughout the period of investigation with larger amplitude during the years 1980 and 1985. Thus, tri-diurnal anisotropy clearly shows 11-year variation at the mid latitude neutron monitoring station.      

On the successive supersymmetric rank‐1 decomposition of higher‐order supersymmetric tensors

In this paper, a successive supersymmetric rank‐1 decomposition of a real higher‐order supersymmetric tensor is considered. To obtain such a decomposition, we design a greedy method based on iteratively computing the best supersymmetric rank‐1 approximation of the residual tensors. We further show that a supersymmetric canonical decomposition could be obtained when the method is applied to an orthogonally diagonalizable supersymmetric tensor, and in particular, when the order is 2, this method generates the eigenvalue decomposition for symmetric matrices. Details of the algorithm designed and the numerical results are reported in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

On K1 and K2 of Algebraic Surfaces

In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH ^r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH ^r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH ³ (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix.     

对G.Ladas的一个开问题的解答

本文获得了一个高阶非线性差分方程具有无界正解的充分条件，所得结果解决了G.Ladas提出的一个开问题。     

对2005年高考试题中关于螺旋测微计实验试题的解析与拓展

解析了2005年普通高等学校全国联考(理综卷)中考察螺旋测微计原理的实验填空题,并给出了3方面的拓展:不常见的游标卡尺、圆弧游标、具有游标的螺旋测微计.     

浅析用图像法处理实验数据

指出了图像法在解决物理问题中的优势及应注意的问题,并对用图像法处理实验数据的考题进行了归类．     

齐次~Morrey-Herz 空间上分数次积分算子高阶交换子的有界性

在齐次Morrey-Herz空间上建立了高阶交换子~$T^{m}_{b,l}$ 和 ~$M^{m}_{b,l}$的有界性，其中~$T^{m}_{b,l}$ 和 ~$M^{m}_{b,l}$ 是由分数次积分算子和分数次极大算子分别与~BMO($R^{n}$)函数生成的高阶交换子.