LIMITATIONS ON PRESCRIBING THE HOPF DIFFERENTIAL FOR MINIMAL SURFACES IN H3

ABSTRACT

The Hopf map from minimal surfaces in H ³ to holomorphic quadratic differentials on H ² is considered. Whether or not a given quadratic differential is in the image of this map is determined by the global existence/non-existence of solutions to a certain quasi-linear PDE. It is shown that this map is not surjective.     

The zero curvature equation for rigid CR-manifolds

In this paper, we present the general analytic solution to the zero curvature equation for rigid three-dimensional CR-manifolds. The solutions are uniquely determined by one function and four real parameters.     

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.     

Multiscale geometric modeling of macromolecules II: Lagrangian representation

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics, and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X‐ray, NMR, and cryo‐electron microscopy, and theoretical/mathematical models, such as molecular dynamics, the Poisson–Boltzmann equation, and the Nernst–Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger's functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent–solute interaction, and ion channel dynamics, whereas our coarse resolution representations highlight the compatibility of protein‐ligand bindings and possibility of protein–protein interactions. © 2013 Wiley Periodicals, Inc.     

复射影空间CP~((n+p)/2)中具有2-调和的一般子流形

本文研究了复射影空间中具有2-调和的一般子流形问题.利用活动标架法,获得了这类子流形成为极小子流形的Pinching定理和Simons型积分不等式,此外还得到关于2-调和伪脐一般子流形的一个刚性定理,推广了复射影空间中具有2-调和全实子流形的一些相应结果.     

计算富勒烯结构的新方法:曲率定理*

介绍了利用曲率定理计算富勒烯结构的方法,证明了富勒烯结构中五元环数恒为12,与传统的欧拉定理法进行了对比,凸显了曲率定理法在研究多面体结构时直观形象的特点,强调了数学方法对解决化学问题和认识化学模型的重要性。     

基于Demons算法改进的图像去噪模型研究

在Demons算法的基础上, 将扩散过程看作图像配准, 建立一种新的基于图像配准的Demons 去噪模型. 实验表明, 该模型去噪效果优于经典的Perona-Malik模型, 排除了模型的病态性. 考虑到新模型在图像去噪过程中仅靠梯度信息表示图像的局部特征还不完善, 故将水平集曲率作为控制图像结构的驱动力因素引入到此模型中, 提出了一种新的梯度和曲率双重驱动力的图像去噪模型. 分析和仿真结果表明, 两种新模型都可有效抑制噪声, 清晰度也有明显的提高, 其中双重驱动力的图像去噪模型去噪效果更具优越性.     

基于支座反力影响线曲率差分的等截面连续梁损伤识别方法

为了实现仅采用损伤状态信息对等截面连续梁进行损伤识别,通过推导三跨不等跨连续梁在移动荷载作用下的支座反力影响线,发现支座反力影响线求曲率并作差分后的曲线在损伤位置会发生突变,基于该现象提出了一种损伤定位方法,进一步建立了损伤程度计算方法,可对损伤程度进行较精确的定量。通过一三跨连续梁和一四跨连续梁工程实例的仿真分析,证明了支座反力影响线曲率差分指标损伤定位和相应的损伤程度定量方法对等截面连续梁损伤识别具有可行性。     

基于高斯曲率极值点的桥梁结构损伤识别方法

目前中小桥梁日常安全巡检存在对检查人员依赖性高、缺乏可量化的科学依据等不足.针对这些问题,本文提出了一种利用高斯曲率极值点对结构进行损伤识别的方法.将桥面视为受弯弹性薄板,根据弹性薄板的弯曲理论得到了在荷载作用下结构刚度变化与桥面弯曲程度(高斯曲率)的理论关系,并由此推导了高斯曲率对结构刚度损伤的敏感程度公式.通过有限...