具有中心幂等元的L-弱正则半群

本文定义了具有中心幂等元的(L)-弱正则半群,研究了这类半群的代数结构.利用半群上的右同余(L)+和左同余R+,证明了半群S是一个具有中心幂等元的(L)-弱正则半群,当且仅当S是H-左可消幺半群的强半格.这推广了Clifford半群的相应结果.     

一个解非线性方程组新的非单调自适应信赖域法

本文利用函数平均权重的非单调技术以及自适应信赖域方法,提出一个解非线性方程组的非单调自适应信赖域法.并在适当假设条件下,讨论了算法的全局收敛性.数值试验表明了算法是有效的.     

On the global optimality of generalized trust region subproblems

Quadratically constrained quadratic programming is an important class of optimization problems. We consider the case with one quadratic constraint. Since both the objective function and its constraint can be neither convex nor concave, it is also known as the ‘generalized trust region subproblem.’ The theory and algorithms for this problem have been well studied under the Slater condition. In this article, we analyse the duality property between the primal problem and its Lagrangian dual problem, and discuss the attainability of the optimal primal solution without the Slater condition. The relations between the Lagrangian dual and semidefinite programming dual is also given.     

A non-monotone trust region algorithm for unconstrained optimization with dynamic reference iteration updates using filter

We present a non-monotone trust region algorithm for unconstrained optimization. Using the filter technique of Fletcher and Leyffer, we introduce a new filter acceptance criterion and use it to define reference iterations dynamically. In contrast with the early filter criteria, the new criterion ensures that the size of the filter is finite. We also show a correlation between problem dimension and the filter size. We prove the global convergence of the proposed algorithm to first- and second-order critical points under suitable assumptions. It is significant that the global convergence analysis does not require the common assumption of monotonicity of the sequence of objective function values in reference iterations, as assumed by the standard non-monotone trust region algorithms. Numerical experiments on the CUTEr problems indicate that the new algorithm is competitive compared to some representative non-monotone trust region algorithms.     

A BFGS trust-region method with a new nonmonotone technique for nonlinear equations

In this paper, we consider a trust-region method for solving nonlinear equations which employs a new nonmonotone technique. A strong nonmonotone strategy and a weaker nonmonotone strategy can be obtained by choosing the parameter adaptively. Thus, the disadvantages of the traditional nonmonotone strategy can be avoided. It does not need to compute the Jacobian matrix at every iteration, so that the workload and time are decreased. Theoretical analysis indicates that the new algorithm preserves the global convergence under classical assumptions. Moreover, superlinear and quadratic convergence are established under suitable conditions. Numerical experiments show the efficiency and effectiveness of the proposed method for solving nonlinear equations.     

菲涅尔双棱镜干涉实验中双棱镜两种放置方法的讨论

在菲涅尔双棱镜干涉实验中,双棱镜有两种不同的放置方法,分析了这两种放置方法中两虚光源的距离、干涉区域范围、干涉条纹间距、干涉条纹数目应相同,因而得到双棱镜的两种放置方法是等价的结论。     

特定边界跟踪中角点检测研究

针对边界跟踪算法中在角点附近丢失边界信息的问题,对待检测边界中角点的判别和检测方法进行了研究。分析了边界搜索中所扩展的邻域的半径和角点位置的关系,提出了角点存在判据,给出了角点存在区间。提出了寻区间法角点检测算法,用5个已知边界点之间的关系,判断出角点存在的邻域,通过选取合适的邻域半径,使角点存在区间向角点收敛。对测试图像和人侧面轮廓图像的边界利用所提出的算法进行跟踪,测试图像的边界点从19个增长为37个,人侧面轮廓图像边界点从13个增长为21个,新算法准确地检测到轮廓角点和后续种子点,使边界跟踪能够反映所有的边界信息。     

A localised dynamic closure model for Euler turbulence

ABSTRACT

In this work, we present a localised form of the dynamic eddy viscosity model for computationally efficient and accurate simulation of the turbulent flows governed by Euler equations. In our framework, we determine the dynamic model coefficient locally using the information from neighbouring grid points through a test filtering process. We then develop an optimised Gaussian filtering kernel, using a consistent definition with respect to the test filtering ratio, which gives full attenuation at the grid cut-off wave number. A systematic a-posteriori analysis of our model is performed by solving two 3D test problems: (i) incompressible Taylor–Green vortex flow and (ii) compressible shear layer turbulence induced by Kelvin–Helmholtz instability to show the wide range of applicability of the proposed localised dynamic model. We demonstrate that the proposed dynamic model is robust and provides a better estimation of the inertial range turbulence dynamics than other numerical models tested in this study.     

基于实测地应力深埋巷道塑性区定量分析

深埋巷道大变形、强流变的破坏特征源于其高地应力的作用,准确分析已开掘巷道塑性区分布对巷道围岩变形影响、开掘方案选择及后续类似条件巷道布置意义深远。在围岩力学参数测试、地应力场测试的基础上,采用弹塑性理论、M-C准则、修正的“当量半径”理论简化计算了直墙半圆拱形断面布置下深埋巷道的围岩塑性区大小,分析了巷道围岩塑性区受采动应力、侧压系数单独及耦合作用影响规律。在侧压系数为0.5、垂直压力为35MPa时底板塑性区最大,其值为2.65m,建议加强巷道底板的支护与维护,并给出了塑性区控制方案。研究结果可为后续类似条件下巷道开掘方案优选、支护设计及围岩稳定性判定提供一定的借鉴。     

中部地区上市公司融资效率差异化实证分析

在对衡量融资效率的若干财务指标进行了主成分分析的基础上,对中部六省(湖北、安徽、湖南、河南、江西和山西)上市公司的融资效率差异化进行了实证分析,得出六省融资效率普遍偏低、差异化不明显,但行业间存在着明显差异;然后,通过逐步回归法,得到影响融资效率的相关因素,如融资结构、净利润、公司规模、主营业务收入等,并对这些因素进行了回归分析,得出其与融资效率关系;最后,给出提高中部六省上市公司融资效率的对策建议。