Generalizing Mutational Equations for Uniqueness of Some Nonlocal 1st-Order Geometric Evolutions

The mutational equations of Aubin extend ordinary differential equations to metric spaces (with compact balls). In first-order geometric evolutions, however, the topological boundary need not be continuous in the sense of Painlevé–Kuratowski. So this paper suggests a generalization of Aubin’s mutational equations that extends classical notions of dynamical systems and functional analysis beyond the traditional border of vector spaces: Distribution-like solutions are introduced in a set just supplied with a countable family of (possibly non-symmetric) distance functions. Moreover their existence is proved by means of Euler approximations and a form of “weak” sequential compactness (although no continuous linear forms are available beyond topological vector spaces). This general framework is applied to a first-order geometric example, i.e. compact subsets of ℝ ^N evolving according to the nonlocal properties of both the current set and its proximal normal cones. Here neither regularity assumptions about the boundaries nor the inclusion principle are required. In particular, we specify sufficient conditions for the uniqueness of these solutions.      

一个创新网络动态性的仿真模型

提出了一个关于创新网络动态性研究的仿真模型,模型较为全面地考察了网络的形成过程和不同的角色在创新和网络中的作用,研究结论指出:网络的形成是由于创新主体为适应创新的复杂性而寻求资源互补效应的动态相互作用的结果,中小型企业的个体在网络演化的早期和中期起了重要的作用,合作体的作用主要发挥在中后期.     

Mazur-Ulam定理的一个注记

本文的主要结论是给出了一个更广泛形式的Mazur-Ulam定理.讨论的对象是实的赋准范空间,满等距算子被减弱成其像空间构成一个加法子群的算子.最后给出的推论推广了Skof的一个结果.     

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. For this, we show that the geometric nonlinearities arising from the multiplicative decomposition of the strain can be controlled via polyconvexity and a priori stress bounds in terms of the energy density. While temporal oscillations are controlled via energy dissipation, the spatial compactness is obtained via regularizing terms involving gradients of the internal variables. Dedicated to Sir John Ball on the occasion of his 60th birthday.     

一种机器人支撑臂的力学分析与距离选优

采用Adams虚拟样机仿真技术对一种机器人的主要构件进行建模,分析了模型前后支撑臂的受力情况;分别建立了7种前后两臂之间不同距离的模型,通过数据对比,优选出使电机功率输出最小的两臂间距离.     

A molecular orbital explanation for the B?N bond shortening in H3BNH3 on going from the gaseous to the solid state

A simple molecular orbital model has been applied to explanation of the B? N bond shortening in H₃BNH₃ on going from the gaseous to the solid state. In this model, the shortening is attributed to the bond order increase that is caused by the fact that each atom in the crystal experiences different external electrostatic potential to each other and thus the orbital energy level of each atom is changed. To illustrate this model, Effective Fragment Potential (EFP) method has been applied to the system consisting of a H₃BNH₃ molecule and 30 dipole moments whose magnitudes are determined by Lorentz's local field theory. This EFP computation has brought significant B? N bond shortening (1.668 → 1.623 Å), which is about 50% of the actual shortening. The factor of the remaining discrepancy has been analyzed by Morokuma decomposition under EFP and localized orbital analysis. These analyses have revealed that the remaining discrepancy is almost compensated by incorporating the dihydrogen bonds (B? H···H? N) that are formed by the orbital interaction between the bonding orbital of the B? H and the antibonding orbital of the N? H. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

On the performance of the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not.     

基于KMV模型的我国上市公司信用风险研究

在KM V框架的基础上对股权价值计算方法进行了改进,通过改进后的方法,计算出1999年至2006年各年所有上市公司的违约距离、理论违约率、企业价值、股权价值等指标数据.从分析的结果来看,上市公司规模对信用风险有一定影响,上市公司规模越大,信用风险越小,公司规模越小,信用风险越大.从违约风险的变化情况看,2003—2006年上市公司的违约距离呈下降态势,说明近年来上市公司的违约风险加大.对比沪深300上市公司股改前和股改后信用状况,发现股改前后信用状况有显著不同,股改后上市公司的违约风险变大.通过违约距离的敏感性分析,认为股权价值波动率对违约距离最敏感.     

A continuity theorem for Stinespring's dilation

We show a continuity theorem for Stinespring's dilation: two completely positive maps between arbitrary C^∗-algebras are close in cb-norm if and only if we can find corresponding dilations that are close in operator norm. The proof establishes the equivalence of the cb-norm distance and the Bures distance for completely positive maps. We briefly discuss applications to quantum information theory.     

有机低维结构EL器件的特性

近年来，有机电发光器件已经有了很大进展，寿命也已突破万小时，尽管如此，如何更进一步提高发光效率仍是人们所关注的热点。通过与无机半导体低维结构特性的类比，指出对某些有机材料体系,低维结构同样可以改善器件的性能。