Parabolic Omori–Yau Maximum Principle for Mean Curvature Flow and Some Applications

We derive a parabolic version of Omori–Yau maximum principle for a proper mean curvature flow when the ambient space has lower bound on \(\ell \)-sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in euclidean spaces with uniformly bounded second fundamental forms. This generalizes the result of Wang (Math Res Lett 10:287–299, 2003) for compact immersions. We also prove a Omori–Yau maximum principle for properly immersed self-shrinkers, which improves a result in Chen et al. (Ann Glob Anal Geom 46:259–279, 2014).     

面向信息化战争的广义兰切斯特战争模型

21世纪是一个信息化时代,为了更好的面向信息化战争.通过对传统的兰切斯特微分方程进行改进,考虑了信息化的诸多因素,引入了战场情报感知系数和信息优势系数.构建了数学模型,并对其进行差分处理求解,比较分析了交战双方对战场感知系数变化和信息优势系数变化情况下,对战争的影响.以海湾战争为例,检验了模型的可行性.     

Distortion theorems for normalized biholomorphic quasi-convex mappings

In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball B ⁿ respectively.     

Characterization of multispherical and block structures of Euclidean distance matrices

This paper presents some new characterizations of Euclidean distance matrices (EDMs) of special structures. More specifically, we discuss multispherical and block-structured EDMs, each of which can be viewed as a generalization of spherical EDM. We focus on a well-known inequality that characterizes spherical EDMs and extend it to the sets of multispherical and block-structured EDMs. Some related results are also presented.     

风险规避和最优套期保值比率

在一般的期望效用框架下,研究投资者的风险厌恶态度对于其套期保值策略的影响.首先,给出了投资者采用不同套期保值策略时,效用函数应该满足的条件;其次,讨论了期望效用框架下,Rubinstein整体风险厌恶度量与经典的Arrow Pratt局部风险厌恶度量和更强的Ross的风险度量之间的关系,提出了一组条件,使得在该组条件下,风险厌恶的人际间比较可以用Rubinstein整体风险厌恶度量来刻画;最后,在现货和期货服从正态分布的假设下,使用之前提出的条件,研究投资者风险厌恶程度对于其持有的最优套期保值比率的影响.     

A class of differential equations of PI-type with the quasi-Painlevé property

We present a certain class of second order nonlinear differential equations containing the first Painlevé equation (PI). Each equation in it admits the quasi-Painlevé property, namely every movable singularity of a general solution is at most an algebraic branch point. For these equations we show some basic properties.     

低速轴流涡轮非定常数值模拟的非线性谐波法

本文介绍了旋转机械非定常数值模拟的非线性谐波方法,并对某低速轴流涡轮的流场进行了数值模拟,获得了该涡轮通道内的非定常流场结构.在与实验结果及定常计算结果对比确认的基础上,分析了该涡轮动静叶间干涉与非定常流动特性,并比较了谐波阶数和工质的压缩性对计算结果的影响.研究结果表明,非线性谐波方法可有效地模拟动静非定常干涉.     

温跃层及其变化对被动声纳检测概率的影响

根据被动声纳工作原理,构建被动声纳探测水下目标物概率数学模型。利用声学调查实测数据,综合考虑传播损失、环境噪声、和水文环境分布及季节变化,研究温跃层垂直分布及季节变化对声纳检测概率的影响。结果表明:温跃层对被动声纳影响巨大,逆温跃层环境中,声纳检测概率从海表向下逐渐减小;正温跃层对声纳总的影响与逆温跃层相反,在正温跃层上界,检测概率从表层向下先减小后增大;逆温跃层对被动声纳检测概率的影响随目标物与声纳距离的增大而增大,正温跃层影响相反。     

Fault-Tolerant Quantum Anonymous Voting Protocol

In this paper, we propose a new fault-tolerant quantum anonymous voting protocol, which is designed to be robust against the collective-phasing noise and the collective-rotation noise. In the proposed protocol, the scrutineer, Charlie, prepares the photons sequence, which is used not only as the quantum ballot ticket, but also to authenticate the voter’s (i.e., Alice) identity. Especially it can realize the detection of Alice’s identity during the voting process. At the same time, the proposed protocol solves the problem of non-reusability of the quantum anonymous voting. Compared with other quantum anonymous voting protocols, our quantum anonymous voting protocol is more secure and practical.