一类时变仿射非线性系统的完全线性化

本文用微分几何方法讨论时变仿射非线性系统的完全线性化问题 ,即同时线性化状态方程和输出方程 ,给出了一类时变仿射非线性系统完全线性化的充分条件     

一类时变仿射非线性系统的完全线性化

本用微分几何方法讨论时变仿射非线性系统的完全线性化问题,即同时线性化状态方程和输出方程,给出了一类时变仿射非线性系统完全线性化的充分条件。     

Wintner定理的推广与全局光滑线性化

微分方程光滑线性化的研究,目前仅限于原点近傍的小邻域,本文给出了一个全局光滑线性化的结论.全局拓扑线性化或全局光滑线性化的先决条件是任一解的存在区间为全实轴.因此,本文也讨论了Wintner定理的推广问题.     

动态补偿线性化

本文讨论仿射非线性系统带有动态补偿的线性化问题.我们对单重及多重动态补偿,分别给出动态反馈线性化的充要条件.这里给出的结果可以看作对原有的状态反馈线性化结果的一个推广.     

对带有盒约束的二次整数规划的一种线性化方法

本文主要讨论了二次整数规划问题的线性化方法.在目标函数为二次函数的情况下,我们讨论了带有二次约束的整数规划问题的线性化方法,并将文献中对二次0-1问题的研究拓展为对带有盒约束的二次整数规划问题的研究.最终将带有盒约束的二次整数规划问题转化为线性混合本文主要讨论了二次整数规划问题的线性化方法.在目标函数为二次函数的情况下,我们讨论了带有二次约束的整数规划问题的线性化方法,并将文献中对二次0-1问题的研究拓展为对带有盒约束的二次整数规划问题的研究.最终将带有盒约束的二次整数规划问题转化为线性混合0-1整数规划问题,然后利用Ilog-cplex或Excel软件中的规划求解工具进行求解,从而解决原二次整数规划.     

平面向量场在双曲奇点附近的光滑线性化

利用正则型方面的有关理论,讨论了平面向量场在双曲奇点附近的光滑线性化问题,对几类平面向量场给出了可以线性化的条件.     

三维空间中一类双曲向量场的光滑线性化

讨论了R~3中Poincare型双曲向量场的光滑线性化问题,具体地给出了当特征值之间存在共振关系时,向量场的非线性部分满足可以线性化的充分条件.     

带有平面边界凸曲面的无穷小刚性对偶问题的可解性

本文重新讨论了一类带有平面边界的凸曲面的无穷小刚性问题.找到该线性化等距嵌入系统和齐次线性化Gauss-Codazzi系统之间的对偶关系.主要找到了齐次线性等距嵌入系统的对偶问题及对偶边界条件,并证明了其具有非平凡解,再次验证了该类凸曲面具有无穷小非刚性.     

时变仿射非线性系统的动态补偿线性化

用微分几何方法讨论了时变仿射非线性系统的动态补偿线性化问题，给出了系统动态的反馈线性化的条件，它是状态反馈线性化的推广。     

半线性多调和方程解的分支

该文主要讨论一类多调和方程,通过研究此方程对应的线性化问题本征谱,得到了方程的全局分支结果.所讨论的方法主要依赖于P.M.Fitzpatrick,J.Pejsachowicz和P.J.Rabier C~2 Fredholm算子的度理论思想.     

多项式变换及其在卷积计算中的应用

其中_q表示整数k模q的最小非负剩余.这种卷积的计算,在通用计算机及专门结构的数字处理装置中有广泛的应用,特别可用于图象处理方面.直接计算(1),需要p~2q~2次     

线性目标函数下的 greedy-结构

有限集合E的一个子集类■2~E,如果对任意的 Y∈■及 X■Y,总有 X∈■,我们则称(E,■)为一独立系统.1971年 J.Edmonds 指出,独立系统(E,■)对任意线性目标函数其greedy基恒为最优基的充分必要条件是■满足交换公理,即对任意的 X,Y∈■,及|Y|>|X|,则存在 y∈Y\X,使 X∪{y}∈■.这时(E,■)是一拟阵.     

增长曲线模型中UMRE估计和UMRU估计的存在性

对于一般的增长曲线模型,在一般的矩阵损失和二次损失下,用统一的方法分别给出了回归系数矩阵的任一指定可估函数存在一致最小风险同变（ＵＭＲＥ）估计（分别在仿真变换群和转换变换群下）和一致最小风险无编（ＵＭＲＵ）估计的充要条件,以及所有可估函数恒存在ＵＭＲＥ估计和ＵＭＲＵ估计的允要条件。最后将结果应用于一些特殊模型。     

Necessary Optimality Conditions and New Optimization Methods for Cubic Polynomial Optimization Problems with Mixed Variables

Multivariate cubic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot of practical applications in real world. In this paper, some necessary local optimality conditions and some necessary global optimality conditions for cubic polynomial optimization problems with mixed variables are established. Then some local optimization methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization methods for cubic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local optimality conditions and necessary global optimality conditions. A global optimization method is proposed for cubic polynomial optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical examples are also given to illustrate that these approaches are very efficient.     

On Optimality Conditions for Generalized Semi-Infinite Programming Problems

Generalized semi-infinite optimization problems (GSIP) are considered. We generalize the well-known optimality conditions for minimizers of order one in standard semi-infinite programming to the GSIP case. We give necessary and sufficient conditions for local minimizers of order one without the assumption of local reduction. The necessary conditions are derived along the same lines as the first-order necessary conditions for GSIP in a recent paper of Jongen, Rückmann, and Stein (Ref. 1) by assuming the so-called extended Mangasarian–Fromovitz constraint qualification. Using the ideas of a recent paper of Rückmann and Shapiro, we give short proofs of necessary and sufficient optimality conditions for minimizers of order one under the additional assumption of the Mangasarian–Fromovitz constraint qualification at all local minimizers of the so-called lower-level problem.     

Role of copositivity in optimality criteria for nonconvex optimization problems

Second-order necessary and sufficient conditions for local optimality in constrained optimization problems are discussed. For global optimality, a criterion recently developed by Hiriart-Urruty and Lemarechal is thoroughly examined in the case of concave quadratic problems and reformulated into copositivity conditions.     

Local Perturbations of the Schrödinger Operator on the Axis

We present necessary and sufficient conditions for the existence of eigenvalues of the Schrödinger operator on an axis under small local perturbations. In the case where the eigenvalues exist, we construct their asymptotic approximations.     

Local sidon sets and uniform convergence of fourier series

For compact groups several necessary and sufficient conditions for a set to be local Sidon are given; these conditions are expressed in functional-analytic terms. An immediate corollary is the existence of a large class of compact groupsG, including all the connected non-Abelian Lie groups, which support functions not inA(G) but having Fourier series that are both unformly and absolutely convergent. This has been shown for the special case ofSU(2) by Mayer. Also several necessary and sufficient conditions for a set to be local Λ (p) are given.     

On the Construction of Optimal Monotone Cubic Spline Interpolations

In this paper we derive necessary optimality conditions for an interpolating spline function which minimizes the Holladay approximation of the energy functional and which stays monotone if the given interpolation data are monotone. To this end optimal control theory for state-restricted optimal control problems is applied. The necessary conditions yield a complete characterization of the optimal spline. In the case of two or three interpolation knots, which we call thelocalcase, the optimality conditions are treated analytically. They reduce to polynomial equations which can very easily be solved numerically. These results are used for the construction of a numerical algorithm for the optimal monotone spline in the general (global) case via Newton's method. Here, the local optimal spline serves as a favourable initial estimation for the additional grid points of the optimal spline. Some numerical examples are presented which are constructed by FORTRAN and MATLAB programs.     

Local Perturbations of the Schrödinger Operator on the Plane

We obtain necessary and sufficient conditions for the appearance of a small eigenvalue of the Schrödinger operator on the plane under local operatorial excitations. In the case where the small eigenvalue exists, we construct its asymptotic behavior. We present examples.