关于一类Lagrange函数族的存在条件

研究力学系统的Lagrange函数族,根据从第一积分直接构造Lagrange函数的方法,提出一类Lagrange函数族的结构,导出这类Lagrange函数族的存在条件和直接构造方法.举例说明所得结果的应用.     

基于一种可扩展函数族的聚类算法

提出了可扩展函数族概念，将无关联的或者有依赖关系的多个函数，按照参数和自变最的特征集成一个函数族，可以通过增加或删除函数对函数族进行扩展。利用此函数族概念，设计了两种聚类算法，对其聚类性能作了分析。实验结果表明，用函数族方法进行聚类，在可伸缩性、增量数据处理和复杂数据类型处理等方面都表现出很好的性能，而且具有线性的时间复杂度。     

从第一积分构造Lagrange函数的直接方法

提出力学系统Lagrange函数和第一积分之间存在一种新关联,在此基础上给出变分法逆问题的一种新的直接解法.证明系统Lagrange函数可以由带修正因子的第一积分构成,导出修正因子应满足的偏微分方程,运用此解法构建不同系统的Lagrange函数和函数族,并讨论新解法的特点.     

非标准H∞控制问题的降价控制器

研究了具有无穷远零点的非标准H∞控制问题的降价控制器及无穷远零点所对应的特征 空间与H∞控制器族之间的关系.当广义对象满足一定条件时,可通过选取控制器族中的自 由参量函数,构造低于广义对象阶次的降价H∞控制器;还讨论了降价H∞控制器的参量化问 题,从而得到了两个降价的H∞控制器族.     

鲁棒镇定区间系统族的一个充分条件

讨论了区间系统族的鲁棒镇定问题,给出存在控制器鲁棒镇定区间系统族的一个充分条 件,并且当这个条件成立时,得到了鲁棒镇定区间系统族的控制器的参数化公式.     

基于完全非线性函数的最优跳频序列族构造

基于完全非线性函数,构造了一类新的跳频序列族.根据完全非线性函数的性质,证明了这些跳频序列具有良好的汉明自相关和汉明互相关特性.利用不同的完全非线性函数,可以得到不同的并且具有最优汉明相关性能的跳频序列族.     

决策支持系统中经纬织网预测模型的研究

通过对连锁营销企业经济指标的分析,预测连锁营销企业经济指标尝试用未知原函数的插值方法进行解决。对经济指标值在时间序列的串行基础上进行年、月并联分解,改变原有时间自然延续的单一曲线属性,形成多条年、月并联曲线族,以月函数族作为织网基点线,求出预测年函数具体形式,逐步向前推进,从而得到需要预测的函数族,达到大面积多角度预测经济指标目的。     

基于DCR假设的KDM-CCA安全性

加密方案的KDM（Key-Dependent Message）安全性定义依赖于某一特定的函数族[F]。通过引入一类新的函数族,证明了在两个用户的情形下,Cramer和Shoup提出了基于DCR（Decisional Composite Residuosity）假设的方案（以下称为CS-DCR方案）,关于这类新函数族具有KDM-CCA安全性。由于CS-DCR方案本身非常得高效,因此,获得了兼有高效性和（相应）KDM-CCA安全性的加密方案。     

具有多线性相关系数扰动的有理函数的严格正实不变性判据及其应用

传递函数的严格正实不变性分析,由于它在绝对稳定性分析中的重要作用,引起了人们的 重视.该文考虑在多线性相关系数摄动下,有理函数族的严格正实不变性的判别问题.利用 严格正实函数所具有的相位条件和映射定理.证明了在参数空间中判别该有理函数族保持严 格正实不变性的顶点检验条件,并将这一结果应用于带参数不确定性的鲁里叶系统的绝对稳 定性分析中.     

小波阈值降噪中阈值函数族的一般构造方法

针对小波阈值降噪方法中阈值函数的通用性问题,提出阈值函数的一般构造方法,应用于小波阈值滤波的算法设计。确定阈值函数目标曲线;通过对满足构造条件的典型函数曲线进行平移、旋转、缩放等操作,形成一个具有不同阈值,并以不同速率逼近目标函数的函数族;针对信号特点,选择不同的阈值函数进行降噪。仿真和实测信号实验表明,该方法的降噪特性在信噪比增益（SNR）和最小均方误差（MSE）上优于传统的软硬阈值函数和改进阈值函数,并在敏感度和平滑度上取得了较好的平衡。     

On the dynamics of a gyrostat on Lagrangian equilibria in the three body problem

In this paper, we consider the noncanonical Hamiltonian dynamics of a gyrostat in the three-body problem. By means of geometric-mechanics methods, we study the approximate Poisson dynamics that arises when we develop the potential of the system in series of Legendre and truncate this in an arbitrary order k. After reduction of the dynamics by means of the two symmetries of the system, the existence and number of equilibria that we denominate of Lagrangian type in analogy with classic results on the topic, are considered. Necessary and sufficient conditions are established for their existence in an approximate dynamics of order k, and explicit expressions of these equilibria are given; this being useful for the subsequent study of the stability of these equilibria. The number of Lagrangian equilibria is thoroughly studied in approximate dynamics of orders zero and one. The main result of this work indicates that the number of Lagrangian equilibria in an approximate dynamics of order k for k≥1 is independent of the order of truncation of the potential, if the gyrostat S ₀ is almost spherical. In relation to the stability of these equilibria, necessary and sufficient conditions are given for linear stability of Lagrangian equilibria when the gyrostat is almost spherical. The rotational Poisson dynamics of the gyrostat placed at an Lagrangian equilibrium is explored and the study of nonlinear stability conditions is considered. In this way, we generalize the classical results on equilibria of the three-body problem and many results provided by other authors using more classical techniques for the case of rigid bodies.     

一类广义时变时滞神经网络的动态分析

讨论了一类广义时变时滞递归神经网络的平衡点的存在性、唯一性和全局指数稳定性。这个神经网络模型包括时滞Hopfield神经网络,时滞Cellular神经网络,时滞Cohen-Grossberg神经网络作为特例。基于微分不等式技术,利用Brouwer不动点定理并构造合适的Lyapunov函数,得到了保证递归神经网络的平衡点存在、唯一、全局指数稳定的新的充分条件。新的充分条件不要求激励函数的可微性、有界性和单调性,同时减少了对限制条件的要求。两个仿真例子表明了所得结果的有效性。     

浅谈解的存在唯一性定理在《偏微分方程数值解》中的应用

从一个新的角度讨论常微分方程中解的存在唯一性定理在偏微分方程数值解法中的重要应用。给出一类伪双曲型偏微分方程的新的分裂混合有限元数值格式,将该格式转化成常微分方程系统,利用解的存在唯一性定理证明该系统是存在唯一解的。通过简短的讨论、概述明确解的存在唯一定理在偏微分方程数值解中的应用方法．并希望能够在教学科研未来的发展中有新的观念。     

The contact problem in Lagrangian systems subject to bilateral and unilateral constraints,with or without sliding Coulomb’s friction: a tutorial

This work deals with the existence and uniqueness of the acceleration and contact forces for Lagrangian systems subject to bilateral and/or unilateral constraints with or without sliding Coulomb’s friction. Sliding friction is known to yield singularities in the system, such as Painlevé’s paradox. Our work aims at providing sufficient conditions on the parameters of the system so that singularities are avoided (i.e., the contact problem is at least solvable). To this end, the frictional problem is treated as a perturbation of the frictionless case. We provide explicit criteria, in the form of calculable upper bounds on the friction coefficients, under which the frictional contact problem is guaranteed to remain well-posed. Complementarity problems, variational inequalities, quadratic programs and inclusions in normal cones are central tools.     

Global stability analysis of a class of delayed cellular neural networks

Employing Brouwer’s fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis, the authors study further global exponential stability and the existence of periodic solutions of a class of cellular neural networks with delays (DCNNs) in this paper. A family of sufficient conditions is given for checking global exponential stability and the existence of periodic solutions of DCNNs. The results extend and improve the earlier publications.     

Schnorr方案推广及其在格密码学中的应用

Schnorr身份认证方案是密码学中的经典方案,可以推广到很多其他数学问题(如离散对数问题)上,从而构造出在标准模式中安全的身份认证方案,并且可以通过Fiat-Shamir转换工具,将其转换为在随机谕示模式中安全的数字签名方案。但将上述转换方法用于基于格的密码学中时会出现一些特殊现象(如方案中止现象)。为此,通过矩阵表示方法分析Schnorr方案的构造方法,得出其构造方法成立的充要条件,从而使其可在更大范围内构造出安全的类Schnorr方案。根据类Schnorr方案,分析基于格的身份认证方案中的方案中止现象,并通过数学方法证明,对于某些身份认证方案(如∑-身份认证方案),其中的方案中止现象不可避免,该结论为深入研究基于格的密码学提供了参考依据。     

航天TT&C调度的拉格朗日松弛策略

根据航天遥测、跟踪和指挥(TT&C)调度的测控需求,建立航天测控调度问题的0-1整数规划模型,运用 、 和 3种策略对模型中的约束进行松弛,通过次梯度优化算法求得每种松弛问题的上界。利用2个场景验证上界(目标函数值)的有效性,调度结果表明,3种松弛策略中以次梯度优化算法得到的上界差别最小。     

Hierarchical control for large-scale systems with general multiple linear-quadratic structure

A class of large-scale linear control systems, where the overall objective function is a nonlinear function of multiple quadratic performance indices, is investigated in this paper. This type of large-scale control problem with a general multiple linear-quadratic structure is nonseparable in the sense of conventional hierarchical control. Hierarchical control is extended in this paper to large-scale nonseparable control problems, where multiobjective optimization is used as a separation strategy. The large-scale general multiple linear-quadratic control problem is embedded, under certain conditions, into a family of the weighted Lagrangian formulation. The weighted Lagrangian formulation is separable with respect to subsystems and can be effectively solved using the interaction prediction approach at the two lower levels in the proposed three-level solution structure. At the third level, the weighting vector for the weighted Lagrangian formulation is adjusted iteratively to search the optimal weighting vector with which the optimal control of the original large-scale nonseparable control problem is attained. One feature of this hierarchical control scheme is a derived analytical solution for the large-scale general multiple linear-quadratic control.     

Improved Lagrangian bounds and heuristics for the generalized assignment problem

Modified Lagrangian bounds are proposed for the generalized assignment problem. The approach is based on a double decomposable structure of the formulation. A family of greedy heuristics is considered to get Lagrangian based feasible solutions. Numerical results for problem instances with number of agents close to number of tasks are provided.