随着基础教育课程改革的深入,基于"三教"理念的"情境―问题"教学成为培育学生数学核心素养的重要方式,而跨学科情境在此基础上能让学生从多学科的角度深入思考和深刻体验.立足双新课程,以"指数函数的概念"教学为例,设计五个环节,即创设情境、形成概念、回归情境、动手实践以及升华理解,以此拓展学生的视野,感受学科之间的联系,让学生在问题中思考,在情境中体验,在感悟中表达,进而学到"活知识"与"活技能".

作者在Henn定义的模糊用户均衡条件的基础上,建立了模糊路径选择模型.并运用β最短路对模糊路径选择模型进行了求解,最终给出了模糊用户均衡的一个启发式算法.

In this paper, based on the extreme eigenvalues of the matrices arisen from the given elasticity tensor, S-type upper bounds for the M-eigenvalues of elasticity tensors are established. Finally, S-type sufficient conditions are introduced for the strong ellipticity of elasticity tensors based on the S-type M-eigenvalue inclusion sets.

[目的]为了在不具有线性结构的T-凸空间中得到弱于H0-条件的GH0-条件下的KKM引理.[方法]利用非线性分析中关于度量以及从属于紧集的有限覆盖的单位分解构造辅助函数,并基于GH0-条件的特征,构造复合函数.[结果]在弱于H0-条件的GH0-条件下建立了T-凸度量空间和T-凸拓扑空间中的KKM引理.[结论]在空间结构和凸结构条件较弱的情形下推广了KKM引理.

Abstract In this paper, cone b-metric-like space is an extension of cone metric space, b-metric space and metric-like space. In this space, two functions have an unique common couple fixed point if they are w-compatible. Some examples are given to explain these new results.

为了解变时滞随机竞争型神经网络在固定时间的控制同步问题,运用Lyapunov稳定性理论、固定时间稳定性理论、随机微分方程理论、伊藤公式和一些不等式方法,在p-范数下得到了该神经网络新的固定时间同步的充分条件.

In this paper, we give a new Z-eigenvalue localization set for Z-eigenvalues of structured fourth order tensors. As applications, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative fourth order tensors is obtained and a new Z-eigenvalue based sufficient condition for the positive definiteness of fourth order tensors is also presented. Finally, numerical examples are given to verify the efficiency of our results.

研究了具有变时滞的高阶随机Hopfield神经网络在有限时间内的控制同步.通过李雅普诺夫函数,有限时间内稳定性理论,随机微分方程理论和一些不等式方法,基于p-范数得到了新的有限时间内同步的充分条件.本文结论是对之前相关结论的推广.

基于动力系统的理论和方法,构造出一个具有复杂混沌吸引子的非线性混沌自治三维系统.其与经典的混沌系统具有类似的结构与性态.采用理论分析和Matlab仿真相结合的方式研究,得到了系统在平衡点处不稳定的参数范围.通过分岔图和Lyapunov指数谱进一步揭示了系统丰富的动力学行为,Matlab模拟验证了计算理论的正确性.

In this paper,based on the fuzzy set theory,the concept of fuzzy relative weight is constructed by de-fining fuzzy correlation coefficient and fuzzy association degree.A novel pattern recognition algorithm is designed based on this,and the quality of agricultural land in Liupanshui City,Guizhou Province,is comprehensively e-valuated by the established algorithm.The results show that the model and method are feasible and effective,and they have a certain reference value.

In this paper,we study the exponential synchronization of stochastic perturbation fuzzy cellular neural networks with Leakage terms delay and impulsive effects.By the Lyapunov stability theory,the theory of stochastic differential equation,stochastic analysis methods,the It?' s formula and some inequality methods, some new and useful sufficient conditions on the exponential synchronization are obtained based on p-norm.The impulse effects in this paper is a general function, not a linear function. It is also found that stochastic perturbation term and Leakage time delays have an inhibitory effect on the synchronization of the system.

通过直觉模糊集决策方法和TOPSIS方法的组合使用,定义了直觉模糊集的正理想解和负理想解,构建了基于直觉模糊集的突发事件应急预案综合评价模型.并基于此模型对突发森林火灾扑救的应急预案进行综合评价,通过算例的计算表明了该模型和方法的有效性和可行性,对于模糊决策的理论和应用研究具有一定的参考价值和借鉴意义.

介绍了修正转移Laplace预条件子来解决对称复线性系统,这类系统常常是不定的、大型的,并且用迭代的方法来求解很困难。研究了预处理子的性质,表明预处理后的矩阵的特征值变得非常集中。数值例子阐述了预条件子的有效性。

Distribution center is an important pivot position at the logistics system. This paper presents the site selection's model of logistics distribution center based on decision matrix C, which adopts particle swarm optimization (PSO) to find the best combination of site selection by structuring the iteration of decision matrix. At the same time, simulation experiments are conducting for the site selection of logistics distribution center with 4 candidate centers and 10 distribution points, and the results show that PSO can get the best solution of distribution center in 90 % success rate of the best solution and the average research time of the approximate 3.5 s. From simulation experiment, PSO is efficient, accurate and suitable for the model optimization of distribution center, and therefore, it can be regarded as an effective method for the site selection's model of logistics distribution.

Exponential synchronization of neural networks with nonlinear impulsive γij∈ [0,2]effects and mixed time delays was discussed.By Lyapunov stability theory and inequality techniques,some new and useful sufficient conditions on the exponential synchronization were obtained based on p-norm.Compared with recently years of linear impulsive effects results about neural networks synchronization,our results remove the restrictions that the impulsive gain γij∈[0,2],so our results are more general.

In this paper, using mathematical software MATLAB to the Lorenz chaotic system, Rossler chaotic system for numerical calculation and simulation of some chaos phenomena, At the same time to simulate all kinds of unique properties of chaotic system, Such as chaotic attractor, cycle times, initial value sensitivity of phase dia-gram, the bifurcation diagram etc. Through the observation and analysis of the above features, Deepens our under-standing of chaos phenomenon.

By combining with the actual and related data of postgraduate education development in China,this paper selects indicators to build the graduate education quality evaluation index system.And based on TOPSISdecision method,we launch an evaluation research by a certain case.The analysis results show that the proposedmodel and the method are feasible,and are worth reference and promotion.

本文是对2014年高教社杯全国大学生数学建模竞赛 B 题问题1[1]的简单探究。关于平板折叠桌的设计问题，通过分析题目所给的折叠桌参数，建立了决策规划模型、线性规划模型、拟合模型和动态规划模型[2][3]，分别利用 MATLAB 软件和 LINGO 软件对上述模型进行了逐一求解，解决了题目提出的问题。