一道以群的定义为背景的高考试题赏析

每一年的高考数学试卷中都有一些以高等数学背景立意的好题目,如2006年四川卷理科第16题,是一道以近世代数中群的定义为背景立意的填空题,这样的试题能够有效考查学生的学习能力、思维能力和数学创新意识,这为高校选拔学习潜质好的学生创造了条件.……     

负数的自述

我是负数,你以前虽然见过我,但我们还不很熟悉.下面就听听我的自述,我们会成为好朋友的.一、我的出现是实际生活的需要.数的扩充都是由于实际的需要而产生的,负数的引入也不例外,它是由于表示具有相反意义的量的需要而产生的.小学学过的自然数和分数只能表示相反意义的量中的一个量,不能满足实际需要,为了更好的记数而引入一种     

“1”的自述

我是数字1,大家对我似乎很熟悉,其实却不然,为了以后我们能够成为好朋友,也为了同学们能学好数学,下面请听我的自我介绍:一、我是最小的正整数,我的绝对值还是我;我的相反数是-1,-1的绝对值也是我;我的任何次幂都是我1n=1;我的算术根还是我n1=1;一个数与它倒数的积也等于我,怎么样,牛吧?其实这也不算什么,下面还有更牛的呢.     

分配格上上标准特征向量的求法

本文研究了分配格(L,∧,∨,0,1)上方阵A的上特征向量的性质.利用矩阵的伴随有向图,得到格上方阵A的上标准特征向量的一种实用的新方法.     

抓机会用“嫁接”

把要繁殖的植物的枝或芽接到另一种植物体上使它们结合在一起,成为一个独立生长的植株……叫做嫁接,嫁接能够保持植物原有的某些特性,是常用的改良品种的方法.把“嫁接”的思想应用于数学,常常可以收到意想不到的效果.     

食饵具脉冲扰动与捕食者具连续收获的时滞捕食-食饵模型

本文讨论了与生物资源管理相关的食饵具脉冲扰动与捕食者具连续收获的时滞捕食-食饵模型,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件.也证明了系统的所有解的一致完全有界.我们的结论为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲时滞微分方程的理论.     

例谈备课中新课程的导入与设问环节

备课是教师的一项基本功,是教师对教材进行再创造的过程,是集教学内容,教学方式,教学艺术于一体的一项关键设计.备课质量的高低,不仅影响着教学计划的实施和教育方针的落实,更潜在地制约着课堂教学的效率.     

手机套餐问题的一个数学模型

随着信息时代的到来,手机在人们日常工作、社交、经营等社会活动中的作用越来越重要.近年来我国通信业务量飞速增长,手机的功劳更是功不可没.手机资费问题也越来越受到人们的关注,并且对原有的各种资费方案越来越质疑.2007年1月以来上海、北京、广东等地相继推出的手机"套餐"琳琅满目,让人眼花缭乱,人们不能理性分辨手机"套餐"究竟优惠在何处.……     

赏析2011年湖北高考理科立几题

2011年高考已经落幕,笔者有意关注了湖北数学试卷,解读理科数学试卷,两道立体几何试题给我留下了很深的印象.小题的背景和问题设置让人耳目一新;大题的解法入口宽,方法多,涉及的知识面广,打破了单纯考查立体几何的常规,建立了立体几何与函数、三角、向量、解几的密切联系.这两道试题充分体现了源于教材,略高于教     

如何分遗产

古罗马一位寡妇，遵照丈夫的遗嘱，把丈夫遗留下来的3500元遗产同她即将出生的孩子一起分配。如果生的是儿子，那么，按照罗马的法律，做母亲的应分得儿子份额的一半；如果生的是女儿，做母亲的就应分得女儿份额的两倍。可发生的事情是：生了一对双胞胎——一男一女。     

Banach 空间上算子的几种不可约性

本文根据Cowen-Douglas 算子的定义引入两类与强不可约算子有紧密联系的算子类— B_n 算子与B 算子. 说明了在可分Banach 空间上存在B_n 算子与B 算子. 文章详细讨论了几种具有不可约性的算子类之间的关系并得到了一个关系图. 本文还给出这些算子类的一些性质, 包括算子的(拟) 相似不变性等.     

Rate of approximation for functions with derivatives of bounded variation

We estimate pointwise convergence rates of approximation for functions with derivatives of bounded variation and for functions which are exponentially bounded and have derivatives locally of bounded variation. The approximation is made through the operation of a sequence of integral operators with not necessarily positive kernel functions. The general result is then applied to deduce estimates for Beta operators, Hermite-Fejér operators, Picard operators, Gauss-Weierstrass operators, Baskakov operators, Mirakjan-Szász operators, Bleimann-Butzer-Hahn operators, Phillips operators, and Post-Widder operators.     

Disturbing Fuzzy Propositional Logic and its Operators

In this paper, the concept of disturbing fuzzy propositional logic is introduced, and the operators of disturbing fuzzy propositions is defined. Then the 1-dimensional truth value of fuzzy logic operators is extended to be two-dimensional operators, which include disturbing fuzzy negation operators, implication operators, “and” and “or” operators and continuous operators. The properties of these logic operators are studied.     

Dirichlet空间上Toeplitz算子与Berezin型变换相关的一些性质

本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2T_uv-T_uT_v-T_vT_u 的紧性, 其中函数u,v ∈ L^2,1.     

Fixed points of generalized e-concave (generalized e-convex) operators and their applications

In this paper, we present the definitions of generalized e-concave operators and generalized e-convex operators, which are the generalizations of e-concave operators and e-convex operators, respectively. Without compactness or continuity assumption of generalized e-concave operators and generalized e-convex operators, we have proved the existence, uniqueness and monotone iterative techniques of their fixed points. Our results are even new to e-concave operators and e-convex operators. Finally, we apply the results to the singular boundary value problems for second order differential equations.     

一类新型非正规算子的谱分析

本文引入了一类新型非正规算子,即具复谱的u-标算子.证明了该类算子具有Jordan型分解,讨论了u-标算子与标型谱算子的关系,并通过例子说明了该类算子的构造.     

Boundedness of sublinear operators in weighted grand Morrey spaces

The boundedness of sublinear integral operators in grand Morrey spaces defined by means of measures generated by the Muckenhoupt weights is established. The operators under consideration involve operators of Harmonic Analysis such as Hardy–Littlewood and fractional maximal operators, Calderoń–Zygmund operators, potential operators etc.     

Banach格上的b-几乎Dunford-Pettis算子

首先给出了Banah格上的b-几乎Dunford-Pettis算子的定义;其次,研究了b-几乎Dunford-Pettis算子的相关性质,如b-几乎Dunford-Pettis算子的等价刻画,构成空间的性质,以及控制性;最后,研究了b-几乎DunfordPettis算子与相关算子(b-弱紧算子,弱紧算子,几乎Dunford-Pettis算子)间的关系.     

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.     

Two classes of operators with irreducibility and the small and compact perturbations of them

This paper gives the concepts of finite dimensional irreducible operators((FDI) operators)and infinite dimensional irreducible operators((IDI) operators). Discusses the relationships of(FDI)operators,(IDI) operators and strongly irreducible operators((SI) operators) and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an(FDI) operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in(Σ FDI)(X) with respect to the strong-operator topology and every compact operator K can be approximated by operators in(Σ FDI)(X) with respect to the norm topology on a Banach space X with a Schauder basis, where(ΣFDI)(X) := {T∈B(X) : T=Σki=1Ti, Ti ∈(FDI), k ∈ N}.