A notion of robustness and stability of manifolds

Starting from the notion of thickness of Parks we define a notion of robustness for arbitrary subsets of Rk and we investigate its relationship with the notion of positive reach of Federer. We prove that if a set M is robust, then its boundary ∂M is of positive reach and conversely (under very mild restrictions) if ∂M is of positive reach, then M is robust. We then prove that a closed non-empty robust set in Rk (different from Rk) is a codimension zero submanifold of class C¹ with boundary. As a partial converse we show that any compact codimension zero submanifold with boundary of class C² is robust. Using the notion of robustness we prove a kind of stability theorem for codimension zero compact submanifolds with boundary: two such submanifolds, whose boundaries are close enough (in the sense of Hausdorff distance), are diffeomorphic.     

Evaluation of a total reflection set-up by an interface geometric model

We have studied the total reflection regime through a model represented by a region separating two dielectric bulk media with well-defined refraction indexes. This region is considered to be an interface in which the following hypotheses are established: – Refraction index linear variation with the transition from one medium to the other. – The thickness depends on the optical phenomenon supposedly produced in the interface. The results we obtained were in close agreement with those obtained by authors who have studied this regime through a fundamentally different treatment.     

Vasserstein distances in two-state systems

We present formulas for the Vasserstein distance between two statistical mechanical states of a two-state system. For example, in a ferromagnetic spin-1/2 Ising model the Vasserstein distance is half the difference in the magnetizations.     

地图中道路自动识别的方法

提出了一种基于统计特征的道路自动识别方法，给出了道路的统计模型并进行了分析．该算法对１：５００００的实际地图进行识别，识别速度快，正确率高，取得了满意的结果．     

一个几何不等式的高维推广与加强

将平面上的一个几何不等式推广到ｎ维欧氏空间Ｅｎ中去，并给出它的加强形式．     

XANES and EXAFS in Cu-Ti and Ni-Zr glasses

X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) measurements have been done at the K-edge of Cu in Cu-Ti glasses and on the K-edges of Ni and Zr in Ni-Zr glasses using a synchrotron radiation source. The results are discussed in terms of the shape shift and intensity of the absorption edge as well as the principal absorption maximum. The values of bondlength calculated by the one-electron multiple scattering XANES theory as well as the graphical analysis EXAFS technique show good agreement.     

Partitions of point processes: Multivariate poisson approximations

This study shows that when a point process is partitioned into certain uniformly sparse subprocesses, then the subprocesses are asymptotically multivariate Poisson or compound Poisson. Bounds are given for the total-variation distance between the subprocesses and their limits. Several partitioning rules are considered including independent, Markovian, and batch assignments of points.     

爆炸冲击作用导致岩体损伤的模型试验研究

岩土体开挖与围岩保护是岩土工程中两项重要内容,但在具体工程中普遍存在开挖和保护岩体的相互矛盾。本文针对以上矛盾来研究爆炸冲击作用导致岩体损伤及其力学特性的演化。文中采用实验室控制条件下的模型实验方法,在爆前及爆后对试件分别进行取芯检测,通过对芯样的各项力学性能指标的测量,研究爆破冲击载荷在预留岩体不同位置所造成损伤程度大小,同时还对现场采集的岩样进行了同样的试验研究。文中最后给出了利用试验所得出的各项结果来计算损伤变量值的方法,并且利用该方法计算得到了岩体在经过爆炸冲击载荷作用后的损伤值。该研究对于高陡边坡的爆破以及支护设计具有一定的意义。     

On One Generalization of Newton's Law of Gravitation

A statement is formulated which leads to the general formula for the force of interaction between two bodies. The distance between their centers of inertia varies with time. According to the third Kepler's law, the well-known Newton's law of gravitation follows from the formula. Some examples are presented and discussed     

微弯光纤传感器的光线寻迹法分析

采用光线寻迹法分析微弯光纤传感器，指出其微弯临界周期即为光线以最大入射角在光纤内传播的空间重复距离，结论与耦合模理论分析及实验结果一致。