含边界在内的一般极值的必要条件与拉格朗日乘数法

讨论包括定义域边界点在内的极值,称为一般极值.对可导的一元和多元函数给出了一般极值点的必要条件,这些必要条件与经典极值的必要条件是相容的.还利用一般极值的必要条件导出了条件极值的拉格朗日乘数法.     

封面故事

水是生命发生的必要条件.地球在太阳系所处的位置使得水的保持成为可能,而水能够以液态、固体和气态三种方式在地球上存在则让地球建立起有效的水循环.水能够孕育生命还得益于水的许多特殊性质,比如固体水,冰,就比水     

一类几何最值问题的解法(Ⅱ)

介绍了另一类几何问题取得最值的必要条件,并通过实例说明其应用.     

Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory

This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.     

向量组的极小生成组

分析了线性相关概念的教学难点.引入了向量组的生成组和极小生成组的概念.由此给出了线性相关和极大线性无关组的刻画.     

一类特殊Gabor框的存在性

通过Littlewood问题与一类Gabor框存在性的问题的等价性,借助对均匀分布在单位圆上的n个单位向量和为零的充分必要性论证,解决了n大于等于3时这类Gabor框的充分必要条件,并对此结果和已有结果进行了比较研究。更多还原     

管内变密度流体流动与换热的充分发展及解析解

本文提出了圆管内变密度流体流动与换热充分发展的概念和相关假设及其推论.在所提出的概念和假设基础上对理想气体在圆管内的流动与换热进行了解析求解,得到了充分发展时的无量纲速度抛物分布及无量纲温度分布.对圆管内密度随温度变化的氩气的流动与换热数值模拟所获得的无量纲速度分布及无量纲温度分布在入口段后与上述解析解非常吻合,从而验证了在本文的计算条件范围内,圆管内变密度流体充分发展流动与换热的概念及其解析解是合理的.     

一种求解非线性无约束优化问题的充分下降的共轭梯度法

共轭梯度法是一类具有广泛应用的求解大规模无约束优化问题的方法. 提出了一种新的非线性共轭梯度(CG)法,理论分析显示新算法在多种线搜索条件下具有充分下降性. 进一步证明了新CG算法的全局收敛性定理. 最后,进行了大量数值实验,其结果表明与传统的几类CG方法相比,新算法具有更为高效的计算性能.     

Consensus protocol for heterogeneous multi-agent systems: A Markov chain approach

This paper deals with the consensus problem for heterogeneous multi-agent systems. Different from most existing consensus protocols, we consider the consensus seeking of two types of agents, namely, active agents and passive agents. The objective is to directly control the active agents such that the states of all the agents would achieve consensus. In order to obtain a computational approach, we subtly introduce an appropriate Markov chain to cast the heterogeneous systems into a unified framework. Such a framework is helpful for tackling the constraints from passive agents. Furthermore, a sufficient and necessary condition is established to guarantee the consensus in heterogeneous multi-agent systems. Finally, simulation results are provided to verify the theoretical analysis and the effectiveness of the proposed protocol.     

The global dynamics of a class of vector fields in ℝ<Superscript>3</Superscript>

In this paper, we find a bridge connecting a class of vector fields in ℝ³ with the planar vector fields and give a criterion of the existence of closed orbits, heteroclinic orbits and homoclinic orbits of a class of vector fields in ℝ³. All the possible nonwandering sets of this class of vector fields fall into three classes: (i) singularities; (ii) closed orbits; (iii) graphs of unions of singularities and the trajectories connecting them. The necessary and sufficient conditions for the boundedness of the vector fields are also obtained.