图论中若干重要定理的历史注记

考察了图论中若干重要定理的历史背景,这些定理包括图论基本定理,矩阵-树定理,门格尔定理,霍尔定理,柯尼希定理,塔特定理,彼得森定理,库拉托夫斯基定理,布鲁克斯定理和维津定理.     

积分型中值定理的推广及统一表示

通过减弱连续的条件,推广了一类积分型中值定理,在适当的条件下,用一个式子将Lagrange中值定理、Cauchy微分中值定理、积分型Cauchy中值定理、积分中值定理、积分第一中值定理、Lagrange型积分中值定理、Cauchy型积分中值定理及推广的积分第一中值定理这8个中值定理统一起来.     

无穷区间上的中值定理

本文将微积分学中的几个中值定理(Rolle定理、Lagrange中值定理、Cauchy中值定理、积分中值定理和推广积分中值定理)全部扩展到无穷区间上去,得到若干个无穷区间上的中值定理,其中值点均在无穷开区间内存在,从而使微积分学的中值定理理论更完善、应用更广泛。     

托勒密定理与西姆松线定理的等价性及折射定律的一个初等证明

托勒密定理与西姆松线定理是两个有名的经典定理,蔡聪明在[1]中对托勒密定理及其有关性质做了细致的综述,但从西姆松线定理与托勒密定理的关系入手,更容易看清这两个经典定理的实质.     

微分中值定理的预备定理

罗尔定理是证明拉格朗日中值定理与柯西中值定理的预备定理。以罗尔定理为基础,通过引进适当的满足罗尔定理的辅助函数便能证明拉格朗日中值定理与柯西中值定理。然而教学中学生总感到老师给出的辅助函数不好想,很难。辅助函数的引入多年来一直成为教学上的一个难点。     

一个一般的多值随机算子的随机不动点定理

近年来,由于理论和应用上的需要,随机不动点定理的研究获得了很大进展.许多重要的不动点定理的随机类比已相继得到证明。本文的定理2.1是一个一般的随机不动点定理,它推广了重要的 Chuong 的结果.利用这个定理,结合非随机不动点定理立即可以得到许多非随机不动点定理的随机类比.例如,[1,2,4,6]中的结果都是本定理的特例。     

发现法讲授中值定理的一种尝试

微分学中值定理通常包括费尔马定理、罗尔定理、拉格朗日定理、柯西定理、泰勒定理。用启发式讲授这些定理的方案很多。笔者设计一种用发现法讲述这组定理的一种方案。最近的教法研讨会上,笔者介绍这种方案,同行们希     

关于“拉特马吼级数表示的函数”一文中一个定理的简单证明和推广

王斯雷在[1]中建立了下述定理1。但是他的证明似乎太长,本文指出,这个定理只需用初等微积分的方法就可以很简单地证明出来。用新证明的类似方法我们还可以得到定理2及定理3。定理2将原定理中F(x)连续的条件减弱为近似连续,定理3又在定理2的基础上把定理1进一步推广。定理1.设F(x)是[0,1]上的连续函数,级数     

微积分中值定理间的关系

直观地阐述从微分中值定理到积分中值定理,乃至第二积分中值定理的演绎过程,指出积分中值定理的实质仍是微分中值定理,并在经典积分中值定理的条件下,得到更强的结论。     

多项式簇的稳定性分析

本文利用值映射的概念在系数空间里讨论了多项式簇的Hurwitz稳定性的鲁棒性,给出了判别多项式簇是Hurwitz稳定的原象定理,同时应用这个定理证明了边界定理,棱边定理,Харитонов定理和菱形簇定理.     

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.