树的最大特征值的上界的一个注记

设T是一个树,V是T的顶点集．记dv是υ∈V的度,△是T的最大顶点度．设υ∈V且dw=1．记k=ew+1,这里ew是w的excentricity．设δj′= max{dυ:dist(υ,w)=j},j=1,2,…,k-2,我们证明和这里μ1(T)和λ1(T)分别是T的Laplacian矩阵和邻接矩阵的最大特征值．特别地,记δo′=2．     

乘方的指数与其幂的位数的关系

为了探究乘方的指数与其幂的位数的关系,定义了几个有关的新概念,并且证明了两个关于乘方以及进制进位的定理,由此建立起关于乘方以及进制进位的理论体系,其中包括进位理论中判定乘方的指数与其幂的位数是否存在周期规律的判别法,以及进位规律的求解法和四条相关的性质.     

一类具有转向点的三阶微分方程的边值问题的解的高阶渐近展开

利用上下解方法,研究如下一类具有转向点的三阶微分方程的边值问题{ε~2y″′=f(t,y,ε)y″ g(t,y,ε)y′ h(t,y,ε),a相似文献   

自由群的直积的检验元素的注记

本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.     

与一类算术函数关联的矩阵的行列式的下界

设f为一个算术函数,S={x 1,…,x n}为一个n元正整数集合.称S为gcd-封闭的, 如果对于任意1 i,j n,均有(x i,x j)∈S.以 ={y 1,…,y m}表示包含S的最小gcd-封闭的正整数集合. 设(f(x i,x j))表示一个n×n矩阵, 其(i,j)项为f在x i与x j的最大公因子(x i,x j)处的值. 设(f[x i,x j])表示一个n×n矩阵, 其(i,j)项为f在x i与x j的最小公倍数[x i.xj]处的值. 本文证明了: (i) 如果f∈C s ={f:(f*μ)(d)>0, x∈S,d|x},这里f*μ表示f与μ的Dirichlet乘积,μ表示M bius函数,那么 并且(1)取等号当且仅当S=;(ii)如果f为乘法函数,并且 ∈Cs,那么 并且(2)取等号当且仅当S= .不等式(1)和(2)分别改进了Bourque与Ligh在1993年和1995年所得到的结果.     

数的蒙蔽与形的误导

数与形是一个数学问题的两个层面,数能精细,形可直观,但同学们也须注意,如果你在解题时,出现了疏漏,数也可能出现貌似精细的蒙蔽,形也可以导致似乎明了的误导.本文通过两个典型例子,提醒同学们在学习     

函数的对称性和周期性的关系

“函数”一章的内容贯穿于高中数学的始终,历来是数学高考考查的一个难点和热点,要求学生熟练掌握函数的性质．但在学习这一章过程中,许多同学被函数的若干性质弄的头昏脑涨．事实上,只要把握其中的关系,也就不困难了．     

一个问题的争论引发的思考

最近在网上看到这样一个题目：“王师傅是卖鱼的,一斤鱼进价45元,现亏本大甩卖,顾客35元买了一公斤,给了王师傅100元假钱,王师傅没零钱,于是找邻居换了100元.事后邻居存钱过程中发现钱是假的,被银行没收了,王师傅又赔了邻居100,请问王师傅一共亏了多少？”笔者把题目抛给办公室的老师们：谢老师：“55＋65＋100.”     

由自然数的因子构成的半群

本文首先介绍了半群、群的定义,研究了自然数n取何值时,通过定义相应的代数运算,使得它的因子集构成半群、群,从而为半群的代数理论提供了一个有趣的实例.     

基于Spearman的rho的Copula参数模型的选择

从Spearman的rho与Kendall的tau的关系入手,讨论了一类二元Copula参数模型的选择问题.由于这类二元Copula参数模型的Spearman的rho与Kendall的tau存在某种函数关系,模型选择问题转化为了曲线拟合检验问题.对于正态Copula、Frank-Copula,FGM-Copula、B11-Copula等这类Copula参数模型,说明了两种情况下进行模型选择的方法,并对中国股市的上证指数与深证综指作了实证分析,结果表明两者存在着较强的正相关性,相关性模型选取B11-Copula参数模型最合适.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

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

正August 10-14,2015Beijin,China The 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     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.