直面危机

中国企业面临着前所未有的成本上升压力。这次的成本上升和以前有什么不同？企业和企业的CFO如何面对和化解成本压力？本期的两位客座总编辑汤谷良先生和萧枭先生分别从理论和实务的角度给出了答案。     

批判性思维和创造性思维的理解和培养

批判性思维和创造性思维是数学学习中重要的思维方式和方法,本文探讨批判性思维和创造性思维在高中数学教学中的理解和应用.高三复习不仅是关于知识点的回顾和复习,更是关于如何运用思维方法解决问题的实践和创新,培养和提升学生的批判性思维、创造性思维能力非常重要,本文结合一个具体案例,展示批判性思维和创新性思维在解决问题中的应用,并探讨如何将批判性思维和创造性思维融入到数学教学中,提高学生的学习效果和思维能力.     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

初中数学公式和定理的教学方法初探

数学最核心的基础知识包括公式和定理.同时,这些知识也总结和体现了数量关系和空间形式中存在的最基本规律.公式和定理的广泛应用不仅贯串数学学习和现实生活,还是数学论证和推理所必不可少的理论基础.通过论证和推理,可以总结出包含在其中的数学思想和方法.这对于数学能力的提升也非常关键.本文参考苏科版本初中数学学习教材,结合具体的教学情况,分析研究数学公式和定理的有效教学方法.     

基于产品生命周期的闭环供应链定价和协调策略研究

研究产品生命周期条件下一个制造商、一个零售商组成的闭环供应链的定价和协调策略:制造商第一周期只生产新品,从第二周期开始生产再制造品,并负责回收。建立了两周期、多周期和无限周期下的分散决策模型和多周期下的集中决策模型,得到最优定价和生产策略。结果表明:两周期中,制造商和零售商应根据不同的成本节约额制定不同的批发价、零售价和生产量。多周期中,当成本节约额比较小时,除第一和最后一个周期外,制造商和零售商应采取相同的定价和生产策略;当成本节约额比较大时,除第一和最后两个周期外,制造商和零售商应采取相同的定价和生产策略。无限周期中,除第一周期以外,制造商和零售商都应该采取相同的定价和生产策略。在有限周期情况下,制造商和零售商应通过在前期制定比较低的批发价和零售价,以提高生产量和销售量,使得后期的回收量增大,达到降低成本的目的。通过引入收益共享契约制定合适的批发价和销售收入及再制造收益共享比率可以协调整个闭环供应链。算例验证了上述结论。     

公债市场波动、消费动态与经济增长——基于递归效用与习惯形成的分析

本文在考虑公债市场波动的经济增长模型中引入递归效用和习惯形成,建立基于递归效用和习惯形成的随机经济增长模型,求得均衡时的最优消费和政府债券需求,讨论递归效用和习惯形成对最优消费和政府债券需求的影响,推导出消费的动态路径和经济增长路径,研究递归效用和习惯形成对消费动态路径和经济增长路径的影响.     

四阶奇异边值问题的正解

研究了一类四阶奇异边值问题正解的存在性,在f和g满足比超线性和次线性条件更广泛的极限条件下,利用锥压缩和拉伸不动点定理获得了正解的存在性结果,推广和包含了一些已知结果.     

基于VAR模型的河南省经济增长与对外贸易关系研究

采用河南省GDP、进口和出口贸易的统计数据,在构建稳定的VAR模型基础上,通过脉冲响应函数分析、方差分解分析,分析了GDP、进口和出口贸易之间的关系.结果表明:GDP的波动对进口和出口贸易的影响是迅速和显著的,而进口和出口贸易的波动对GDP的影响是缓慢和滞后的,进口和出口贸易对河南经济的拉动作用不明显,但相对而言,出口较进口对河南省GDP有更大的拉动作用.     

高中数学探究性教学中教师教学行为的实践

进行数学探究的目的主要是为学生引入一种新的学习方式,使学生经历提出概念和结论的过程,体验数学创造的研究过程,形成勇于质疑和善于反思的习惯,培养学生发现问题、提出问题和解决问题的能力,提高学生的创新精神和探究能力．因此,教师在备课时应成为探究素材和问题的设计者、发现者和创造者,     

借助于复变数解析函数求一些三角级数的和

把求三角级数的和转化为求复数域内相应幂级数的和,所要求的余弦级数的和与正弦级数的和分别等于幂级数和的实部与虚部系数.     

Strong limit point criteria for a class of singular discrete linear Hamiltonian systems

This paper is concerned with the limit point case for a class of singular discrete linear Hamiltonian systems. The limit point case is divided into the strong and the weak limit point cases. Several sufficient conditions for the strong limit point case are established. In consequence, two criteria of the strong limit point case for second-order formally self-adjoint vector difference equations are obtained.     

每个点都是链回归点的树映射

设f是端点数为n的树T上的连续自映射且T上的每一点都是f的链回归点.本文证明了: (1)如果T的某个端点是f的不动点,那么,T上的每个点都是f的周期为r≤n-1的周期点,或存在自然数r ≤ n-1,使得fr含有湍流; (2)如果f的不动点都在T的内部,那么,T上的每个点都是f的周期为r≤n的周期点,或存在自然数r≤n,使得,fr含有湍流.     

拟二次系统的广义焦点量与极限环分枝

本文给出了拟二次系统的前18个奇点量和可积性条件,由此统一解决了几类实平面微分自治系统的初奇点、高次奇点以及无穷远点的中心焦点判定与极限环分枝问题.     

On farthest points of sets

For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.     

一阶自回归模型参数变点的假设检验

本文讨论一阶自回归模型自回归参数$\phi$的变点问题. 对于一阶自回归模型, 在模型的白噪声序列的方差$\sigma^2$已知和未知的条件下, 利用最大似然方法, 我们分别讨论了模型自回归参数$\phi$的Abrupt Change-Point 和Gradual Change-Point的检测问题.     

向量值映射锥鞍点存在定理

本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理.     

On the stability of the vertical rotation of a solid suspended on a rod

The problem of the motion of a dynamically symmetric solid suspended from a fixed point by a weightless rod and two ball and socket joints one of which is fixed at the fixed point O', and the other is on the body axis of symmetry at the point O is considered. The question of the stability of the uniform body rotation when points O' and O, and the body centre of inertia C lie on the same vertical, and at the same time point O may be either above or below point O', and point C either above or below point O, is discussed. An analysis of the necessary and sufficient conditions for stability is given. The set of all the system's parameters is reduced to three independent dimensionless parameters L, Ω and β, and in the plane (L, Ω), for fixed values of β, the regions for which the unperturbed rotation is steady, or steady to a first approximation, or non-steady are indicated. The regions for which the body rotation is steady to a first approximation when the point O is situated higher than the point O', and the point C lies higher or lower than the point O are determined.

The sufficient conditions for the vertical rotation of a dynamically symmetric body suspended on a filament were obtained in /1/ and investigated for the cases where in non-perturbed motion the point C is below point O, when points C and O coincide, and when the length of the filament is zero (Lagrange gyroscope). In /2/ an analysis is given of the sufficient conditions for stability obtained in /1/, and also the necessary conditions for the cases where in a non-perturbed motion point C is located above point O.     

求解互补约束优化问题的乘子松弛法

利用互补问题的Lagrange函数, 给出了互补约束优化问题\,(MPCC)\,的一种新松弛问题. 在较弱的条件下, 新松弛问题满足线性独立约束规范. 在此基础上, 提出了求解互补约束优化问题的乘子松弛法. 在MPCC-LICQ条件下, 松弛问题稳定点的任何聚点都是MPCC的M-稳定点. 无需二阶必要条件, 只在ULSC条件下, 就可保证聚点是MPCC的B-稳定点. 另外, 给出了算法收敛于B-稳定点的新条件.     

Generalized singular point quantity and integrability of degenerate resonant singular point

In this paper, integrability and generalized complex resonant center condition of degenerate resonant singular point for a class of complex polynomial differential system were studied. The concept of generalized singular point quantity of degenerate resonant singular point was proposed and the construction of that was studied. Two methods of computing generalized singular point quantities were given. Furthermore, the sufficient and necessary condition of integrability of degenerate resonant singular point was discussed for the first time.     

The generalized center problem of degenerate resonant singular point

In this paper, generalized center condition and integrability of degenerate resonant singular point for a class of complex polynomial differential system were studied. The method was based on a homeomorphic transformation of the degenerate singular point into elementary singular point, which allows us to compute the generalized singular point quantities and determine the generalized center condition for the origin. In the end, we obtained the necessary and sufficient conditions of generalized complex center of degenerate resonant singular point.