喜迎2006新年

在公元2006年到来之际，谨拟有关“2006” 五题，喜庆新年，以飨读者. 题1 .口2006. a，!2二，。。+1一兰(，任N+)，试求二1 口” 解由题意有内 l2 一一，a3一一一乙x， X a2 l 2一内 反4= l 一一，“.‘，a2006- j X 倪z .aZoo6一Zx· X 题2 +a3+a;+ {a。}是公差为l …+a:。。 =3962 的等差数列，al+自 ，试证:a:十a、+吼 +…十a 100 证明 =2006. 由题意有a。一a，+l，a、~a3+i …，al。。=aog+1， :’(al十1)+aZ十(a3+1)十a、十 …+(a99十1)+a，。。 =3962+50=4012. a:+a、+a6+…+al。。一2006. 题3已知a，b，。是不为。的实数，且a+ b…     

2006年高考数学模拟试题

一、选择题(本大题共12小题,每小题5分,共60分.在每小题给出的四个选项中,只有一个选项符合题目要求.)1.设f:x→|x|是集合A到集合B的映射,若A={-1,0,1},-1 B,则A∩B只可能是()(A){0}.(B){1}.(C){0,1}.(D){-1,0,1}.2.如果tan(α β)=43,tan(β-π4)=21,那么tan(α 4π)的值是()(     

2006江苏高考数学试卷分析

江苏省2006年高考数学试题延续2005年试题的风格,保持了一定的稳定,坚持重点内容重点考,在“知识的交汇处命题”有新的突破,注重创新意识,不少题目较新,不落俗套.一、命题特点1.今年试卷在试题结构进行了微调,选择题、填空题、解答题三种题型题量由“12+6+5”调整为今年的“10+6+5”,同时减少了客观题(选择题)的分值,增加了主观题分值.2.试卷比较注重基础知识与基本方法,以中档试题为主,知识覆盖面比较宽,10个选择题前几道题易于下手,涉及到三角与函数、统计、不等式、集合、概率与立体几何、解析几何等内容,大多数考生都可以完成.3.试卷所…     

中国数学会2006年学术会议计划

学术会议名称 时间 地点 承办单位 联系人 联系电话 I助ernational Conferenee onRecentDeveloPmentS in DifferentialE晚uations aod APPlicationB 微分方程及应用最新进展 国际学术会议 7月 17日一21日 广州大学 国际学术 交流中心 广州大学 120人 周展 庚建设 02压39366038 zzbou@gZhu.edu.cn 02压31877026 第九届全国泛函微分方程 会议 7月 24日一28日 黑龙江大学 黑龙江大学 150人 任洪善 俞元洪 0451一86608331 renhsh15加80@to〔n.eom 010-84845366 yu84845366@126，com 第五届全国现代科学计算 研讨会、第八届西北地区 计算数…     

2006江苏高考数学试卷分析

江苏省2006年高考数学试题延续2005年试题的风格,保持了一定的稳定,坚持重点内容重点考,在“知识的交汇处命题“有新的突破,注重创新意识,不少题目较新,不落俗套.……     

2006江苏高考数学试卷分析

江苏省2006年高考数学试题延续2005年试题的风格,保持了一定的稳定,坚持重点内容重点考,在“知识的交汇处命题“有新的突破,注重创新意识,不少题目较新,不落俗套.……     

2006年中考模拟试卷

(考试时间:120分钟,满分:120分)一、细心填一填(本大题共有10小题,每小题3分,共30分,请把结果直接填在题中的横线上,只要你理解概念,仔细运算,相信你一定会填对的!)1.-5的相反数是2.观察下列等式:12 2×1=1×(1 2),22 2×2=2×(2 2),32 2×3=3×(3 2),……,则第n个等式可表示为3.三刀最多能把一个西瓜切成块4.若点(-2,1)在双曲线y=xk上,则双曲线的解析式为5.直线y=(k-1)x k 2经过一、二、四象限,则k的取值范围是6.等边△ABC的内切圆面积为4π,则等边△ABC的周长为7.方程组2mm- 23nn==53的解为第8题图8.如图,在△ABC中,∠C=900,AC=3,D…     

2006年北京市中考数学试卷

一、选择题(共11个小题,共44分)1.5的倒数是()A.15B.-15C.5D.-52.在“北京2008”奥运会国家体育场的“鸟巢”钢结构工程施工建设中,首次使用了我国科研人员自主研制的强度为460000000帕的钢材.将460000000用科学记数法表示为()A.4.6×108B.4.6×109C.0.46×109D.46×1073.下列运算中,正确的是()A.9=±3B.(a2)3=a6C.3a·2a=6aD.3-2=-64.点P(3,-4)关于原点对称的点的坐标是()A.(3,4)B.(-3,4)C.(4,-3)D.(-4,3)5.在下列图形中,既是中心对称图形,又是轴对称图形,且对称轴只有两条的是()A.等腰梯形B.平行四边形C.菱形D.正方形6.一次函数y…     

Call for nominations for 1994 elections

Mathematical Programming -     

Criterion for complete determinacy for concave-convexlike games

Translated from Matematicheskie Zametki, Vol. 49, No. 3, pp. 73–76, March, 1991.     

Algorithms for Computing Characters for Symmetric Spaces

Symmetric spaces or more general symmetric k-varieties can be defined as the homogeneous spaces G _k /K _k , where G is a reductive algebraic group defined over a field k of characteristic not 2, K the fixed point group of an involution θ of G and G _k resp. K _k the sets k-rational points of G resp. K. These symmetric spaces have a fine structure of root systems, characters, Weyl groups etc., similar to the underlying algebraic group G. The relationship between the fine structure of the symmetric space and the group plays an important role in the study of these symmetric spaces and their applications. To develop a computer algebra package for symmetric spaces one needs explicit formulas expressing the fine structure of the symmetric space and group in terms of each other. In this paper we consider the case that k is algebraically closed and give explicit algorithmic formulas for expressing the characters of the weight lattice of the symmetric space in terms of the characters of the weight lattice of the group. These algorithms can easily be implemented in a computer algebra package. The root system of the symmetric space can be described as the image of the root system of the group under a projection π derived from an involution θ on . This implies that . Using these formulas for the characters of each of these lattices we show that in fact . A.G. Helminck is partially supported by N.S.F. Grant DMS-0532140.     

Continuity Adjustment for Control Charts for Attributes

A unified approach is proposed for making a continuity adjustment on some control charts for attributes, e.g., np-chart and c-chart. through adding a uniform (0,1) random observation to the conventional sample statistic (e.g., npi and ci). The adjusted sample statistic then has a continuous distribution. Consequently, given any Type I risk a (the probability that the sample statistic is on or beyond the control limits), control charts achieving the exact value of a can be readily constructed. Guidelines are given for when to use the continuity adjustment control chart, the conventional Shewhart control chart (with ±3 standard deviations control limits), and the control chart based on the exact distribution of the sample statistic before adjustment.     

多产品公司创建平台邀请竞争对手进行联合销售的策略研究

由于资金分配或生产规模的限制,多产品公司的某类产品与专门销售此类产品的专业产品公司相比,会有一定的不足.以两个产品公司为对象,研究了两个竞争性公司的联合销售模式,即多产品公司投资建设平台,邀请销售单一产品的专业公司在平台上共同销售某类产品.运用主从博弈建立联合销售的基础模型,探讨不同销售模式下的相关投资,并利用数值计算进行决策分析.研究表明,通过创建平台进行联合销售,一方面,消除了消费者的额外购物成本;另一方面,在平台进行联合销售使得两个公司由单纯的竞争关系转化为相互补充,不仅能够吸引更多有不同产品需求的客户,而且能够在一定程度上提高两个产品公司的利润.     

Appropriate problems for learning and for performing—an issue for teacher training

Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities).     

Challenges for mathematical and statistical modelling for metrology

There are challenges in disseminating information concerning mathematical and statistical modelling for metrology. We specify these challenges and consider ways they are being met. In addition to journal papers, the value of supporting software and other aspects are indicated. Relevant work in the UK Software Support for Metrology programme is outlined. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimates for the classical parametrix for the Laplacian

We consider the integral operators which were used classically to give a parametrix and remainder for the Laplacian on a Riemannian manifold. Their kernels are defined in terms of the distance function. These operators are shown to be bounded operators on the L₂ Hilbert spaces of differential forms, under the hypotheses that the manifold be complete and of finite volume, and that it satisfy curvature bounds. Furthermore, the remainder is shown to be compact.