The Coset Group and Com ove Group

§１．　ＢａｓｉｃＤｅｆｉｎｉｔｉｏｎｓＬｅｔＸａｎｄＹｂｅｓｅｔｓ，ｆｏｒａｇｉｖｉｎｇｍａｐｐｉｎｇｆ：Ｘ→Ｙ，ｘ｜→ｙ＝ｆ（ｘ），ａｍａｐｐｉｎｇｆｏｎｐｏｗｅｒｓｅｔｃａｎｂｅｃｏｎｄｕｃｔｅｄｂｙｆ：ｆ：Ｐ（Ｘ）→Ｐ（Ｙ），Ａ｜→Ｂ＝ｆ（Ａ）＝｛ｙ｜ｘ∈Ａ，ｙ＝ｆ（ｘ）｝．　　Ｎｏｔｅｔｈａｔａｂｉｎａｒｙｏｐｅｒａｔｉｏｎｉｓａｓｐｅｃｉａｌｍａｐｐｉｎｇｏｎｓｅｔｓ．ＧｉｖｅｎａｂｉｎａｒｙｏｐｅｒａｔｉｏｎｏｎｓｅｔＸｓｕｃｈｔｈａｔ：：Ｘ×Ｘ→Ｘ，　（ｘ，ｙ）｜→ｘ…     

关于Thue方程的解数

设ｍ是正整数，ｆ（Ｘ，Ｙ）＝ａ０Ｘｎ＋ａ１Ｘ（ｎ－１）Ｙ＋．．．＋ａｎＹｎ∈Ｚ［Ｘ，Ｙ］是Ｑ上不可约化的叫ｎ（ｎ≥３）次齐次多项式。本文证明了：当ｇｃｄ（ｍ，ａ０）＝１，ｎ≥４００且ｍ≥１０（３５）时，方程｜ｆ（ｘ，ｙ）｜＝ｍ，ｘ，ｙ∈ｚ，ｇｃｄ（ｘ，ｙ）＝１，至多有６ｎｖ（ｍ）组解（ｘ，ｙ），其中ｖ（ｍ）是同余式Ｆ（ｚ）＝ｆ（ｚ，１）≡０（ｍｏｄｍ）的解数。特别是当ｇｃｄ（ｍ，ＤＦ）＝１时，该方程至多有６ｎ（ω（ｍ）＋１）组解（ｘ，ｙ），其中ＤＦ是多项式Ｆ的判别式，ω（ｍ）是ｍ的不同素因数的个数．     

求双曲线的渐近线的策略和公式

求双曲线的渐近线的策略和公式罗万才（湖南湘潭师范４１１２０４）双曲线ｍ２ｘｗ—ｎ２ｙ２＝ｋ（ｋ≠０）与其渐近线。ｍ２ｘ２—ｎ２ｙ２＝０的方程结构相近，仅是常数项不同（＊）．由此联想问题：（１）双曲线Ｌ：ｆ（ｘ，ｙ）＝Ａｘ２＋Ｂｘｙ＋Ｃｙ２＋ＤＸ＋Ｅｙ...     

Lax定理在局部凸空间中的推广

本文给出Ｌａｘ定理在局部凸空间中的几个推广，特别地，我们获得Ｌａｘ定理的如下推广：设Ｘ和Ｙ为自反Ｆｒｅｃｈｅｔ空间，其拓扑分别由半范序列ｑ１≤ｑ２≤…和半范序列ｐ１≤Ｐ２≤…所给出．设Ａ：Ｙ→Ｘ′为连续线性算子，则存在连续线性算子Ｇ：Ｙ′→Ｘ使满足：（Ｇｇ，Ａｙ）＝（ｇ，ｙ），ｇ∈Ｙ′，Ｖ∈Ｙ当且仅当：对于ｎ，存在ｃｎ＞０，使ｓｕｐ｛１（Ａｙ，ｘ）｜：ｑｎ（ｘ）≤１｝≤ｃｎｐｍ．（ｙ），ｙ∈Ｙ且Ａ的值域在互Ｘ′中具拓扑补，这里，Ｘ′和Ｙ′分别记Ｘ和Ｙ的强对偶．     

相依样本下条件密度双重核估计的强相合性

设（Ｘ１，Ｙ１），…，（Ｘｎ，Ｙｎ）是从取值于Ｒ＾ｐ×Ｒ＾ｑ的随机向量（Ｘ，Ｙ）中抽取的随机样本，在给定Ｘ＝ｘ的条件下Ｙ具有条件密度ｆ（ｙ│ｘ）。在本文中，我们考虑ｆ（ｙ│ｘ）的通常的和递归形式的双重核估计ｆｎ（ｙ│ｘ）＝ｎ∑ｉ＝１Ｋ１（Ｘｉ－ｘ／ａｎ）Ｋ２（Ｙｉ－６／ｂｎ）／〔ｂｎ＾ｑｎ∑ｊ＝１Ｋ１（Ｘｊ－ｘ／ａｎ）〕ｆｎ（ｙ│ｘ）＝ｎ∑ｉ－１Ｋ１（Ｘｉ－ｘ／ａｉ）Ｋ２（Ｙｉ－ｙ／ｂｉ）／ｎ∑ｊ     

用方程的观点求函数的值域

用方程的观点求函数的值域雷海勇（陕西麟游县中学７２１５００）定理已知函数ｙ＝ｆ（ｘ）（Ｘ∈Ａ）的值域为Ｃ，且关于Ｘ的方程ｆ（ｘ）－ｙ＝０在Ａ中至少有一解的ｙ的集合为Ｄ，那么Ｃ＝Ｄ．由证明较易，这里从略．此定理从根本上解释清了用判别式求函数值域出现问题...     

Some Properties of a Class Self—homomorphism of BCI—algebras

ＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ；，０）ｏｆｔｙｐｅ（２，０）ｓａｔｉｓｆｙｉｎｇｔｈｅａｘｉｏｍｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｘ＝ｙｆｏｒａｎｙｘ，ｙａｎｄｚｉｎＸ．ＦｏｒａｎｙＢＣＩ－ａｌｇｅｂｒａＸ，ｔｈｅｒｅｌａｔｉｏｎ≤ｄｅｆｉｎｅｄｂｙｘ≤ｙｉｆａｎｄｏｎｌｙｉｆｘｙ＝０ｉｓａｐａｒｔｉａｌｏｒｄｅｒｏｎＸ［１］．ＩｎａｎｙＢＣＩ－ａｌｇｅｂｒａＸ，…     

复合函数求导法则的又一证明

复合函数的求导法则是求导运算的重要法则;对于ｙ＝ｆ（ｕ）,ｕ＝ｇ（ｘ）,复合函数ｙ＝ｆ〔ｇ（ｘ）〕的求导法则的证明有一个很自然的想法：ΔｙΔｘ＝ΔｙΔｕ·ΔｕΔｘ,ｌｉｍΔｘ→０ΔｙΔｘ＝ｌｉｍΔｕ→０ΔｙΔｕ·ｌｉｍΔｘ→０ΔｕΔｘ;但是,当Δｘ→０时,Δｕ可能等于０,此时ΔｙΔｕ没有意义,所以上面很直接的想法行不通;一般的证明采取另外的方法［１］,［２］;本文仍从上面直观的想法出发,加以改进,得到了又一个证明;定理　若ｙ＝ｆ（ｕ）在ｕ可导,函数ｕ＝ｇ（ｘ）在ｘ可导,则复合函数ｙ＝ｆ〔ｇ（ｘ）…     

2001年普通高等学校春季招生考试(北京、内蒙古、安徽卷) 数学(理工农医类)试题及参考解答

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４个选项中,只有ｌ项是符合题目要求的． （１）集合Ｍ＝｛１,２,３,４,５｝的子集个数是（　）． （Ａ）３２（Ｂ）３１（Ｃ）１６（Ｄ）１５ （２）函数ｆ（ｘ）＝ａｘ（ａ＞０且ａ≠１）对于任意的实数ｘ,ｙ都有（　）． （Ａ）ｆ（ｘｙ）＝ｆ（ｘ）ｆ（ｙ） （Ｂ）ｆ（ｘｙ）＝ｆ（ｘ）＋ｆ（ｙ） （Ｃ）ｆ（ｘ＋ｙ＝ｆ（ｘ）ｆ（ｙ） （Ｄ）ｆ（ｘ＋ｙ）＝ｆ（ｘ）＋ｆ（ｙ） 辽ｄ）１１】日ｔｒｗ Ｍ 区） ”“’“““““厂用十１””’ Ｑ————丸Ｊ２…     

弱条件下同胚的ACL性质

假设Ｄ是Ｒｎ（ｎ２）中的区域，ｙ＝ｆ（ｘ）：ＤＲｎ是一个同胚．如果ｆ（ｘ）的模伸张Ｋ（ｘ，ｆ）适合条件Ａ，则ｆ（ｘ）是ＡＣＬ的．     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with