不连续不可逆二维映象的动力学特性

总结两个保守映象不可逆地分段连续链接(称为类耗散系统)以及一个保守映象与一个耗散映象不可逆地分段连续链接(称为半耗散系统)情况下得到的五项共同动力学特征：不连续边界象集构成的随机网成为唯一的混沌轨道；由于某些相点具有两个逆象而导致的相空间塌缩(类耗散)；由于系统的不连续不可逆性质而出现的胖分形禁区网；在具有吸引子共存时占据不连续边界象集随机网和胖分形禁区网区域的点滴状吸引域以及由此导致的吸引子不可预言性；即使在传统强耗散存在的情况下点滴状吸引域仍由类耗散机制主宰.以一个累积-触发电路为例，说明这五项系统动 关键词： 随机网 禁区网 点滴状吸引域     

Kolmogorov Width of Classes of Smooth Functions on the Sphere

Let ^d−1{(x₁,…,x_d) ^d:x²₁+···+x²_d=1} be the unit sphere of the d-dimensional Euclidean space ^d. For r>0, we denote by B^r_p (1p∞) the class of functions f on ^d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on ^d−1, and P^λ_k(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of B^r_p in L^q( ^d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces X_N of L^q( ^d−1).The main result in this paper is that for r2(d−1)²,where A_NB_N means that there exists a positive constant C, independent of N, such that C⁻¹A_NB_NCA_N.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions.     

On the stability of Riemannian manifold with parallel spinors

Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor. We also prove a rigidity result for special holonomy metrics. In the case of SU(m) holonomy, the rigidity result implies that scalar flat deformations of Calabi-Yau metric must be Calabi-Yau. Finally we explore the connection with a positive mass theorem of [D03], which presents another approach to proving these stability and rigidity results. Dedicated to Jeff Cheeger for his sixtieth birthday     

Analysis on Shack–Hartmann wave-front sensor with Fourier optics

In Shack–Hartmann wavefront sensor (SHWS), the behavior of the irradiance pattern produced by the micro-lens array is important for an accurate centroid estimation. In this paper, the behavior of a micro-lens array in SHWS is analyzed using Fourier optics, and reveals that in addition to the main, expected spots, secondary spots with smaller intensities also appeared as a result of diffraction by the small dimensions of the micro-lens and interference from the different micro-lenses. This result is confirmed by comparing with a irradiance pattern taken from an actual SHWS. The additional error in centroid estimation caused by these secondary spots is discussed and relationship to the parameters of the micro-lens of SHWS is analyzed.     

成分和厚度的依赖

通过调整Mn的成分，系统地研究了Ni81Fe19/Ni100-xMnx双层膜的磁学性质，特别是交换偏置场(Hex)的变化.当Ni100-xMnx中Mn的原子百分比在534%到600%之间时，对于150nm的Ni81Fe19，得到了最大的交换偏置场175kA/m，同时由于Mn对Ni81Fe19层的扩散所造成的磁矩的降低小于20%；高角x射线衍射证明Ni100-xMnx的晶格常数随着Mn成分的改变而变化，Mn含量越多，其晶格常数越大；制备态Ni100-xMnx膜晶格常数与θ相NiMn膜晶格常数的接近程度与NiMn膜θ相形成的容易程度相对应.也研究了交换偏置场随着Ni１００-xMnx厚度的变化，第一次得到了当Ni100-xMnx中Mn的原子百分比为706%时，Ni81Fe19(150nm)/Ni100-xMnx(90nm)双层膜在经过240℃，5h退火后，可以有80kA/m的交换偏置场，此时铁磁层磁矩的大小几乎不变. 关键词： Ni81Fe19/Ni100-xMnx 交换偏置场     

多结超导环在外磁场中的行为

分析和计算了双结超导环在无偏置电流时的磁通、环流、自由能与外磁场的关系.发现双结环与单结环在磁场中的行为有所不同.当两个结的Ic相等时，双结环在1＜β=2πLIcΦ0＜2时，若无偏置电流，总磁通Φ、环流I与外磁通Φe的关系仍然是非回滞的曲线.仅当β≥2时，曲线才出现回滞.另外双结环有两支解，并且每支解的周期为2Φ0. 关键词： 双结环 双支解 2Φ0周期 回滞     

Giant Magneto-Impedance of Co50Ni22Ga28 Alloy with High Chemical Ordering

The microstructure of CosoNi22Ga28 ribbon with the L10 structure is examined. The band-like morphology is observed. These bands with the width in a range of 40-200 nm appear along the transverse direction of the ribbon. The giant magnetoimpedance （GMI） effect in this alloy is measured. The results show that Co5oNi22Ga28 exhibits a sharp peak of the GAI effect. The maximum GAH ratio up to 360% is detected. The GMI effect measured versus temperature shows large jumps of the magnetoimpedance amplitude at the reversal martensitic transformation temperature 240℃ and Curie temperature 375℃C respectively. The jump ratios of the magnetoimpedance amplitude examined at these temperatures are about 5 and 10, respectively.     

关于实Hilbert环

通过引进“强实Hilbert环”这一概念,本文证明了,一个环A是强实Hilbert环,当且仅当多项式环A[X]是实Hilbert环,当且仅当A[X]的每个实极大理想在A上的局限是实极大的,从而文献[1]中两个主要结果被否定.此外,本文还研究了所谓的“严格的实Hilbert环”,这类环对于半代数零点定理等方面的探讨更具应用意义.     

处理原子-辐射场相互作用系统的变分方法

用Heisenberg-Weyl(简H-W)群直积SU(2)群上的相干态表述了原子-辐射场相互作用系统的非平衡态统计力学.引入一个新定义的含时分布函数,将非平衡态下密度矩阵所满足的von Neumann方程转化成可分离变量的偏微分方程,给出了方程的形式解,算符的平均值表示.本文还就便于作微扰展开的相互作用绘景作了讨论.