状态空间约束下一个最大值原理互补松驰强形式的分析

分析了约束条件不显式地包含控制变量时的有界状态变量约束条件下,一种应用最大值原理求解最优控制问题的方法所要求的互补松驰条件的强形式.在最优轨线从约束条件起作用到不起作用的连接点,该强形式条件不是总成立的,此时应使用互补松驰条件的一般形式来求解.算例分析证明了上述结论.     

分段函数的分段教学──出租车计价问题的数学思考

教学实践表明,函数是中学生感到最难学的数学内容之一,特别是分段函数的教学更是如此,所以在实际教学中教师应采取逐步渗透、螺旋上升的方法,分段而有循环地安排函数知识,实现分层的目标.……     

一类二阶奇异微分方程正解的存在唯一性

利用上下解方法,不动点理论研究奇异微分方程u" f(t,u)=0,t∈(0,1)在边界条件au(0)-βu'(0)=0,γu(1) δu'(1)=0下C[0,1]正解和C1[0,1]正解的存在性与唯一性.其中非线性项f(t,u)关于u是减的,仅满足较弱的要求.     

拟线性双曲抛物耦合组强适定非线性初边值问题

本文用叠代方法得到强适定双曲抛物耦合系统非线性初始边值问题局部解的存在唯一性。     

A difference scheme for solving the Timoshenko beam equations with tip body

In this article, a Timoshenko beam with tip body and boundary damping is considered. A linearized three-level difference scheme of the Timoshenko beam equations on uniform meshes is derived by the method of reduction of order. The unique solvability, unconditional stability and convergence of the difference scheme are proved. The convergence order in maximum norm is of order two in both space and time. A numerical example is presented to demonstrate the theoretical results.     

有相似产品信息情形下的可靠性评定方法

两个具有局部相同组成部分的相似设备为模型,建立有相关信息情形下进行可靠性评估的指数模型,并给出了指数模型中的参数估计方法,在此基础上建立了相似设备到目标设备信息的融合算法,进而提出了一种具有相似产品信息情形下的可靠性评定方法.     

话说“设而不求”

<正>"设而不求"是一种简化解题过程的技巧.下面就通过实例解说设而不求法,旨在帮助同学们摆脱因长期形成的思维定势,提高解题的准确性.     

求数列通项的两个途径

<正>求数列的通项在数列中是一个最重要的课题,07年高考十九份试卷中,一半以上均有直接求数列通项的题目,求通项的解题方法和技巧很多,但总的思路有两种:其一是找出α_n与α_n-1的关系求通项,其二是找出S_n与S_n-1的关系求S_n,再由α_n=S_n—S_n-1得通项.     

Procreating tiles of double commutative-step digraphs

Double commutative-step digraph generalizes the double-loop digraph. A double commutative-step digraph can be represented by an L-shaped tile, which periodically tessellates the plane. Given an initial tile L（l, h, x, y）, Aguil5 et al. define a discrete iteration L（p） = L（l ＋ 2p, h ＋ 2p, x ＋ p, y ＋ p）, p = 0, 1, 2,..., over L-shapes （equivalently over double commutative-step digraphs）, and obtain an orbit generated by L（l, h, x,y）, which is said to be a procreating k-tight tile if L（p）（p = 0, 1, 2, ~ ~ ~ ） are all k-tight tiles. They classify the set of L-shaped tiles by its behavior under the above-mentioned discrete dynamics and obtain some procreating tiles of double commutative-step digraphs. In this work, with an approach proposed by Li and Xu et al., we define some new discrete iteration over L-shapes and classify the set of tiles by the procreating condition. We also propose some approaches to find infinite families of realizable k-tight tiles starting from any realizable k-tight L-shaped tile L（l, h, x, y）, 0 ≤ y - x ≤ 2k ＋ 2. As an example, we present an infinite family of 3-tight optimal double-loop networks to illustrate our approaches.