海洋动力学中二维黏性原始方程组解对热源的收敛性

考虑了在一个柱形区域上的海洋动力学中二维黏性方程组解的收敛性.在此模型中存在一个关键的参数就是热源,众多周知,它的存在可能会使流体内层之间出现共振从而导致不稳定.因此,通过推导方程组的先验界,得到了方程组的解对热源自身的收敛性.     

一类非线性方程组的求解

对于一个给定的非线性方程组,通过一系列的变化,可以将其构造成一个函数,从而把非线性方程组的求解问题转换为求函数极小值问题.通过利用正交表的数据分析方法,给出了求函数极小值进而求解非线性方程组的方法,这种方法得到的解比已有的更精确,且大大缩减了复杂方程组的计算量,用时少,不需要初始值.最后,采用Matlab软件,验证了其可行性和有效性.     

解非线性约束方程的拉格朗日全局投影方法

基于最优化方法求解约束非线性方程组的一个突出困难是计算 得到的仅是该优化问题的稳定点或局部极小点,而非方程组的解点.由此引出的问题是如何从一个稳定点出发得到一个相对于方程组解更好的点. 该文采用投影型算法,推广了Nazareth-Qi$^{[8,9]}$ 求解无约束非线性方程组的拉格朗日全局算法(Lagrangian Global-LG)于约束方程上; 理论上证明了从优化问题的稳定点出发,投影LG方法可寻找到一个更好的点. 数值试验证明了LG方法的有效性.     

磁流体动力学截断方程组的动力学行为研究

本文研究了平面正方形区域上不可压缩的磁流体动力学方程组的动力学行为问题.利用模式截断的方法,获得了一个全新的十模类Lorenz方程组,求得了此方程组的平衡点,分析了其稳定性等动力学行为,证明了该类Lorenz方程组混沌吸引子的存在性,并对其动力学行为进行了数值模拟.     

一类复差分方程组的亚纯解(英文)

本文研究了一类复差分方程组的增长性的问题.利用亚纯函数的Nevanlinna值分布理论,得到了有关复差分方程组的亚纯解的一个重要结果,将复差分方程的某些结果推广到复差分方程组中.     

二阶锥权互补问题的非精确非内点连续化算法

基于二阶锥权互补函数,将二阶锥权互补问题转化为一个方程组,运用非精确非内点连续化算法求解该方程组.该算法能以任意点作为初始点,且每次迭代时至多求解一个方程组.为节省算法求解方程组时的计算时间和内存,将非精确牛顿法引入到算法中.在适当假设下,证明了该算法是全局与局部二阶收敛的.最后数值实验表明了算法的良好性能.     

一类定常对流运动方程组不稳定性

本文证明了粘性不可压缩流体定常对流运动完备方程组是一个不稳定方程组,并给出了不唯一性的例证.     

非光滑非线性互补问题的牛顿法

研究了非光滑的非线性互补问题. 首先将非光滑的非线性互补问题转化为一个非光滑方程组,然后用牛顿法求解这个非光滑方程组. 在该牛顿法中,每次迭代只需一个原始函数B-微分中的一个元素. 最后证明了该牛顿法的超线性收敛性.     

一类非线性偏微分方程组的直接解法

根据Hopf-Cole变换法和试探函数法的基本思想,引入一个变换,并把它应用于求解(2+1)维破裂孤子方程组、(2+1)维Nizhnik-Novikov-Vesslov方程组和(2+1)维Broer-Kaup方程组,得到了这三个方程组的许多新的解析解,包括孤波解和奇异行波解.该方法也适用于其它方程组.     

一类复函数方程组的亚纯解

本文研究了一类复函数方程组的亚纯解的存在性问题.利用亚纯函数的Nevanlinna值分布理论,得到了有关方程组的亚纯解变成了有理解的一个主要结论,将复函数方程的某些结果推广至复函数方程组中.     

用非线性方程组求解等式约束非线性规划问题的降维算法

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.     

Metric nonlinear connections

For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange metric. For the particular case when the system of SODE and the metric structure are Lagrangian, we prove that the canonical nonlinear connection of the Lagrange space is the only nonlinear connection which is metric and compatible with the symplectic structure of the Lagrange space. For this particular case, the metric tensor determines the symmetric part of the canonical nonlinear connection, while the symplectic structure determines the skew-symmetric part of the nonlinear connection.     

一类模糊非线性方程组及解法

模糊非线性方程组 ,在模糊控制和现实生活中很普遍 .本文考虑一类模糊非线性方程组的性质 ,然后给出一种解法 .首先把模糊非线性方程组转变成非线性规划 ,再用非线性规划中的方法或软件来解 .     

Nonlinear Separation Approach to Constrained Extremum Problems

In this paper, by virtue of a nonlinear scalarization function, two nonlinear weak separation functions, a nonlinear regular weak separation function, and a nonlinear strong separation function are first introduced, respectively. Then, by the image space analysis, a global saddle-point condition for a nonlinear function is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Finally, some necessary and sufficient optimality conditions are obtained for constrained extremum problems.     

A class of asynchronous parallel nonlinear accelerated overrelaxation methods for the nonlinear complementarity problems

In accordance with the principle of using sufficiently the delayed information, and by making use of the nonlinear multisplitting and the nonlinear relaxation techniques, we present in this paper a class of asynchronous parallel nonlinear multisplitting accelerated overrelaxation (AOR) methods for solving the large sparse nonlinear complementarity problems on the high-speed MIMD multiprocessor systems. These new methods, in particular, include the so-called asynchronous parallel nonlinear multisplitting AOR-Newton method, the asynchronous parallel nonlinear multisplitting AOR-chord method and the asynchronous parallel nonlinear multisplitting AOR-Steffensen method. Under suitable constraints on the nonlinear multisplitting and the relaxation parameters, we establish the local convergence theory of this class of new methods when the Jacobi matrix of the involved nonlinear mapping at the solution point of the nonlinear complementarity problem is an H-matrix.     

Analysis of the nonlinear vibration of a two-mass–spring system with linear and nonlinear stiffness

An analytical approach is developed for areas of nonlinear science such as the nonlinear free vibration of a conservative, two-degree-of-freedom mass–spring system having linear and nonlinear stiffnesses. The main contribution of this research is twofold. First, it introduces the transformation of two nonlinear differential equations for a two-mass system using suitable intermediate variables into a single nonlinear differential equation and, more significantly, the treatment of a nonlinear differential system by linearization coupled with Newton’s method. Secondly, the major section is the solving of the governing nonlinear differential equation where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using a first-order variational approach. The aforementioned approach proposed by J.H. He, who actually developed the method, is exactly He’s variational method. This approach is an explicit method with high validity for resolving strong nonlinear oscillation system problems. Two examples of nonlinear two-degree-of-freedom mass–spring systems are analyzed, and verified with published results and exact solutions. The method can be easily extended to other nonlinear oscillations and so could be widely applicable in engineering and science.     

Nonlinear separation approach to inverse variational inequalities

In this paper, we employ the image space analysis to investigate an inverse variational inequality (for short, IVI) with a cone constraint. By virtue of the nonlinear scalarization function commonly known as the Gerstewitz function, three nonlinear weak separation functions, two nonlinear regular weak separation functions and a nonlinear strong separation function are first introduced. Then, by these nonlinear separation functions, theorems of the weak and strong alternative and some optimality conditions for IVI with a cone constraint are derived without any convexity. In particular, a global saddle-point condition for a nonlinear function is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Finally, two gap functions and an error bound for IVI with a cone constraint are obtained.     

Stability of Manifold-Valued Subdivision Schemes and Multiscale Transformations

Linear subdivision schemes can be adapted in various ways so as to operate in nonlinear geometries such as Lie groups or Riemannian manifolds. It is well known that along with a linear subdivision scheme a multiscale transformation is defined. Such transformations can also be defined in a nonlinear setting. We show the stability of such nonlinear multiscale transforms. To do this we introduce a new kind of proximity condition which bounds the difference of the differential of a nonlinear subdivision scheme and a linear one. It turns out that—unlike the generic nonlinear case and modulo some minor technical assumptions—in the manifold-valued setting, convergence implies stability of the nonlinear subdivision scheme and associated nonlinear multiscale transformations.     

Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.