求解非线性系统的有效集信赖域方法

该文给出了一个求解非线性系统的信赖域方法.主要思想是通过引入松弛变量,将问题等价地转化为带非负约束的最优化问题.作者利用有效集策略,在每次迭代中只需求解一个低维的信赖域子问题,该信赖域子问题是通过截断共轭梯度法来近似求解的.在较弱的条件下,获得了一个更一般的收敛性结果.     

The first initial-boundary value problem for fully nonlinear parabolic equations generated by functions of the eigenvalues of the Hessian

For a class of elliptic Hessian operators raised by Caffarelli-Nirenberg-Spruck, the corresponding parabolic Monge-Ampère equation was studied, the existence and uniqueness of the admissible solution to the first initial-boundary value problem for the equation were established, which extended a result of Ivochkina-Ladyzhenskaya.     

A Necessary and Sufficient Condition for Admissibility of Nonnegative Quadratic Estimator

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一类一般形式的抛物型Monge-Ampbre方程

对于Caffarelli-Nirenberg-Spruck提出的一种更一般形式的椭圆型Monge-AmpéFe算子det(D2u+σ),讨论与之对应的～种抛物型Monge-Ampére方程第一初边值同题.在一定的结构性条件下,利用连续性方法证明了其古典解的存在惟-性.     

The interference characteristics of platform and towed body noise in shallow water for active/passive towed array sonar

The interference characteristics of towed platform noise resulted from propeller and towed body for active/passive towed array is analyzed. It is shown that, in shallow water environment, the direct wave and bottom/sea surface reflected wave will seriously affect the performance of sonar system. The formula for calculating the direction of arrival (DOA) of interference in terms of various parameters, such as array depth, length of tow cable, is derived. The effect of interference noise for the detection performance of sonar system is described. The results of system simulation provide the method for reducing the effect of these kind of interferences.     

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subd-ifferential characterizations of optimal value functions are given. Using these properties, we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.     

环形斑光束在非线性克尔介质中的自聚焦效应

通过数值求解非线性Schrödinger方程,详细讨论了环形斑光束在非线性克尔介质中的传输特性.当入射光超过一定的功率时,光束产生多级自聚焦现象,自聚焦焦点出现在离轴的环上;自聚焦阈值与环形光束的半径有关;传输过程中光斑存在横向分裂现象,并且分裂与聚焦交替进行;当两个半径不同的同轴环状光束同时在非线性介质中传输时产生耦合效应,耦合效应使其自聚焦增强.     

Rheological Investigations in Understanding Shear‐Enhanced Crystallization of Isotactic Poly(propylene)/Multi‐Walled Carbon Nanotube Composites

A novel experimental technique to follow the crystallization processes of poly(propylene)/MWCNT composites that experience a steady shear deformation using dynamic melt rheometry is described. The effects of heterogeneous nucleation, temperature, and preshear on the crystallization behaviors were determined. A quantitative evaluation of crystallization kinetics difference between quiescent and preshear conditions could be achieved. By combining rheology with POM, we demonstrate that two different crystallization processes account for the shear‐enhanced crystallization at low and high temperatures, respectively.