整体观视角下高中数学教学的建构与思考——兼谈“双曲线的标准方程”的教学北大核心

1引言《现代汉语词典》(第7版)中关于“整体”的解释为:“整个集体或整个事物的全部(对各个成员或各个部分而言)”[1].在哲学范畴,联系是唯物辩证法的起点,生活中所有事物都是紧密联系的.数学是研究数量关系和空间形式的一门科学,对现实世界的抽象是数学的来源.关于数学的整体性,有不少经典的表述,如著名数学家约瑟夫·傅里叶曾说:“Mathematics compares the most diverse phenomena,and discovers the most secret analogies which unite them.”(数学能从事物的个性之中寻求事物的共性特征.)普遍联系的原理走向具体化与深层次的体现之一就是系统观的形成,而系统论最本质的特征就是整体性.     

Variable time-period optical switching:a novel OBS implementation

In this paper, we proposed a novel optical switching method based on optical burst switching (OBS), we call it variable time-period optical switching (VTPOS). It can both support circuit services and other immerged packet services. It has better usability of bandwidth, shorter offset and latency time than others of unidirectional transport signaling mechanisms for OBS. It supports deflection switching for improve blocking performance without the need of schedule buffer. It introduces a time pointer and phase indicator that made synchronous more precisely and requires less guard time, it also classifies the different services classes with a relative QoS model.     

Gauss Sum of Index Four

Let p be a prime number, q = pf and m| q - 1. For a multiplicative character χ of Fq with order m, the Gauss sum G(χ) over Fq is defined by G(χ)=∑(X()Fq)χ(x)ζTP(x),ζp=e2πi/p,(1)where T is the mapping for Fq/Fp.     

Gauss Sum of Index Four

Let p be a prime number, q=p^f and m|q-1. For a multiplicative character x of Fq with order m, the Gauss sum G(x) over Fq is defined by     

仓库容量有限条件下的一类存贮管理模型

建立了一类仓库容量有限条件下存贮管理决策模型 ,给出最优存贮策略 .     

正三角形和正四面体的优美定值

用解析法可以得到正三角形的一个优美定值如下： 定理1 若正三角形的边长为a，以其中心为圆心的圆半径为r．则该圆上任意一点与该正三角形各顶点连线段长度的平方和及四次方和均是定值．     

Nilsson平均场加邻近轨道对力模型对超铀区和稀土区核素的描述

利用严格可解的平均场加邻近轨道对力模型, 在区分质子和中子及冻结质子对激发两种情况下对超铀区核素^226—234Th, ^230—239U, ^236—243Pu, 及稀土区核素^160—170Er, ^166—176Yb, ^172—180Hf的结合能, 对激发能, 奇偶能差及偶偶核最低激发态转动惯量进行了计算并与实验结果进行了比较.     

Synchronization of Chaotic Storage-Ring Free-Electron Laser by Bi-Directional Coupling Scheme with the Coupling Strength Varied Periodically

We analyse the chaotic dynamics of storage-ring free-electron lasers and report a bi-directional coupled scheme with the coupling strength varied periodically to synchronize two chaotic storage-ring free-electron lasers. The period is the same as the period of system＇s external modulation. ,The possibility of synchronization is proven according to the Lyapunov stability theory. The results of numerical simulation are obtained. Both the numerical simulation and theoretic analysis show that two storage-ring free-electron lasers can be controlled in the synchronization in a short time with this method.     

稀土掺杂硼铝硅酸盐玻璃结构的NMR研究

采用魔角核磁共振（MAS NMR）研究了稀土掺杂B2O3-Al2O3-SiO2玻璃的结构及其组成和热处理等因素对玻璃结构的影响。研究发现，在B2O3-Al2O3-SiO2玻璃结构中，硼的配位主要是三角体[BO3]和[BO4]，铝的配位主要是[AlO4]，[AlO5]和少量的[AlO6]。随着B2O3-Al2O3-SiO2玻璃中BaO含量的增加，[BO3]逐渐向[BO4]转变，[AlO5]和[AlO5]也转变为[AlO4]。此外，由于稀土离子比钡离子更高的离子场强，其能够积聚硼氧结构使得其形成了巨大的网络结构。随着稀土掺量的增加，玻璃结构中的硅氧配位逐渐以Q4（3T）为主。热处理对玻璃结构中的硼氧和铝氧配位影响很小。     

“9”与两位数相乘的兴趣

当用“9”这个较为特殊的数去乘一个两位数时,采用排积法,不仅速度快,乘积结果准确,而且饶有兴趣。 “9”乘一个两位数,除了乘“11”而外,乘积都是一个三位数。我们拟3个排积法口诀;