一类高维Riccati方程的解

研究了一类具有指数型二分性的高维Riccati方程存在有界解、周期解的充分条件,得到一些结论。     

Improved asymptotic analysis of the average number of steps performed by the self-dual simplex algorithm

In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. Consider a problem ofn variables withm constraints. Smale established that for every number of constraintsm, there is a constantc(m) such that the number of pivot steps of the self-dual algorithm,(m, n), is less thanc(m)(lnn) ^m(m+1) . We improve upon this estimate by showing that(m, n) is bounded by a function ofm only. The symmetry of the function inm andn implies that(m, n) is in fact bounded by a function of the smaller ofm andn. Parts of this research were done while the author was visiting Stanford University, XEROX- PARC, Carnegie-Mellon University and Northwestern University and was supported in part by the National Science Foundation under Grants MCS-8300984, ECS-8218181 and ECS-8121741.     

粗化过程中颗粒界面形状演化的三维多相场法研究

利用多相场模型对液-固两相体系中固相颗粒的粗化过程进行了三维模拟,对粗化过程中的界面形状分布进行了统计分析,研究了不同固相体积分数下颗粒连接状态对界面形状演化及粗化速率的影响.模拟结果表明:当颗粒间存在大量连接时,粗化速率随固相分数的变化速率比颗粒无连接时变缓,且随着粗化进行,高曲率的双曲形界面所占比例不断降低,低曲率的椭球形界面所占比例逐渐增多;无论固相颗粒间是否发生连接,界面形状演化经历一定阶段后,三维界面形状分布均呈现自相似性,但随着固相体积分数的增加,界面形状分布呈现自相似性所需的时间延长.     

常曲率空间中有限点集的两类几何不等式

应用距离几何的理论与方法,研究了n维常曲率空间中有限点集的一些几何度量之间关系,建立了常曲率空间中有限点集的两类几何不等式,推广了已有的结果.     

变量有广义界线性规划的直接对偶单纯形法

本文讨论变量有广义界线性规划问题借助标准形线性规划同单纯形法技术，建立问题的一个直接对偶单纯形法。分析了方法的性质，给出了初始对偶可行基的计算方法，并用实例说明方法的具体操作。     

与"求线性规划问题可行基的一种方法"的再商榷

再次说明文[1]提出的方法不能直接使用，仍须按文[2]的修正结果实行才是正确的。同时指出最近提出的某些算法的不实之处，以飨读者，避免误导。     

基于量纲分析和达西定律的地下化学爆炸气体泄漏规律

针对周围是均匀岩石介质的地下化学爆炸,研究爆炸后爆室内气体的泄漏规律.利用量纲分析,得到影响气体泄漏时间的主要物理量,包括气体动力学粘度、爆室内超压、围岩孔隙率及围岩厚度的平方与渗透率的比值等,并初步给出它们之间的函数关系.然后基于达西定律,推导计算气体泄漏时间的解析公式.得到的气体泄漏时间计算公式与通过量纲分析得到的定性函数关系式完全相符,二者从不同的角度对同一问题给出了相容的结果.可为地下化学爆炸气体泄漏的理论分析和规律性研究提供研究思路和工具,为地下爆炸有关的工程估算提供参考依据.     

基于数字非线性锁相环的相干态相位估计

基于量子理论获取相位参数的导航机制,理论上可以突破经典物理极限对导航精度的限制.利用量子零拍探测对相干态光场相位进行测量时,通常需要相位与之正交的本振光才能使测量精度达到量子标准极限.由于导航信号相位的高非线性特点,想要利用传统的线性锁相环获取完全满足条件的本振光具有一定的难度.为此,本文设计了一种基于容积准则的非线性锁相环,实现了在非正交本振光的条件下对相干态相位进行精确测量的功能.首先,利用相干态的Wigner函数推导了其相位在量子零拍探测的输出结果,设计了量子相位估计的非线性数字锁相环框架.然后基于正交单纯形容积准则设计了非线性滤波算法实现锁相环功能,该锁相环通过对本振相位进行多次状态更新,最终实现非线性迭代估计.实验结果表明,本文方法突破了本振光相位需与相干态相位正交的局限性,避免了传统量子锁相环方法引入的线性化误差,实现了对相干态相位的准确、稳定估计.     

Efficient algorithms for three‐dimensional axial and planar random assignment problems

Beautiful formulas are known for the expected cost of random two‐dimensional assignment problems, but in higher dimensions even the scaling is not known. In three dimensions and above, the problem has natural “Axial” and “Planar” versions, both of which are NP‐hard. For 3‐dimensional Axial random assignment instances of size n, the cost scales as Ω(1/ n), and a main result of the present paper is a linear‐time algorithm that, with high probability, finds a solution of cost O(n^–1+o(1)). For 3‐dimensional Planar assignment, the lower bound is Ω(n), and we give a new efficient matching‐based algorithm that with high probability returns a solution with cost O(n log n). © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 160–196, 2015     

Symmetry Reductions,Group‐Invariant Solutions,and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

Nonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α₁, α₂, α₃, and α₄, on the soliton's amplitude, width, and velocity are discussed. It is seen that α₁, α₂, α₃, and α₄ have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.