数学年刊第18卷B辑第2期(1997)目次和提要

数学年刊第１８卷Ｂ辑第２期（１９９７）目次和提要椭圆型方程内边界问题应隆安给了一个新的方法研究二阶椭圆方程内边界问题奇点附近解的正则性．对于一般的主部非对称的、具有间断的分片光滑系数的方程，证明了Ｈ１的解可以分解成两部分，一部分是对应的分片常数系数的...     

二阶差分方程非振动解的渐近性态

把二阶线性差分方程（１．１）看成非振动方程（１．２）的扰动,其中是向前差分算子,是实数序列．假设（１．２）非振动,则（１．２）有一个主解及副解．本文给出充分条件或必要条件使（１．１）也有一个主解ｘｎ和一个副解ｘｎ满足且这种渐近表示式以三种不同形式给出．     

复合材料稳态热传导问题多尺度计算的一个数学模型

本文给出小周期复合材料稳态热传导问题的一种多尺度渐近展开方法，区别于传统方法中一次项和二次项系数都用解Hper^1（Q）周期边值问题得到，新展式构造时一次项系数仍通过解关于单胞Hper^1（Q）周期边值问题求得，而二次项系数用齐次边值问题求得，所构造渐近解属于H^1（n）．对光滑凸区域Ω，渐近解在H^1（Ω）空间仍具有较好的收敛性．优点为数值方法求解时，解一个齐次边界问题要比解一个Hper^1（Q）周期边值问题简单．     

高维空间中反应对流方程的柯西问题

该文由两部分组成；第一部分利用补偿列紧理论研究（１．１），（１．２）的广义解存在性；第二部分利用粘性消失法研究了（１．１），（１．２）的全局Ｗ１，∞解的存在性．     

高阶非线性差分方程的振动性

本文研究了差分方程△ｄｘ（ｎ）＋ｐ（ｎ）△（ｄ－１）ｘ（ｎ）＋Ｈ（ｎ，ｘ（ｎ））＝０，（１．１）△ｄｘ（ｎ）＋ｐ（ｎ）△（ｄ－１）ｘ（ｎ，ｘ（ｎ））＝Ｑ（ｎ）．（１．２）在一定的条件下，证明了方程（１．１）与（１．２）在振动性方面的等价问题．对于方程（１．１）或（１．２），在ｎ是偶数时的每一个有界解是振动的，在ｎ是奇数时，每一个有界解是振动的或当→∞时单调趋于零的充要性定理也建立了．     

不等式“有解”与“恒成立”

不等式历来是高考和竞赛命题的热点．不等式“有解”与“恒成立”是容易混淆的问题．下面给出一组命题,说明两者之间的区别．Ⅰ　ａ＞ｆ（ｘ）恒成立　　ａ＞ｆｍａｘ（ｘ）;Ⅱ　ａ＜ｆ（ｘ）恒成立　　ａ＜ｆｍｉｎ（ｘ）;Ⅲ　ａ＞ｆ（ｘ）有解　　ａ＞ｆｍｉｎ（ｘ）;Ⅳ　ａ＜ｆ（ｘ）有解　　ａ＜ｆｍａｘ（ｘ）．例１　不等式ｋｘ２＋ｋ－２＜０有解,求ｋ的范围．解　ｋｘ２＋ｋ－２＜０有解　ｋ（ｘ２＋１）＜２有解ｋ＜２ｘ２＋１有解　ｋ＜［２ｘ２＋１］ｍａｘ＝２　（应用命题Ⅳ）∴　　　　ｋ∈（－∞,２）．…     

A-调和方程很弱解的正则性

本文证明了二阶拟线性偏微分方程很弱解的正则性．若ｕ是（１）的一个很弱解并属于一个合适的包含Ｗ１,ｐ　ｌｏｃ（ ）的空间,则ｕ属于 （ ）,即ｕ是（１）通常意义下的弱解．变分积分弱极值的同样结果被得到．     

卡斯方程唯一解的简洁初等证明

卡斯方程唯一解的简洁初等证明王云葵（广西灌阳县高级中学５４１６００）１８７５年，卡斯（Ｅ．Ｌｕｃａｓ）问丢番图，方程：是否仅有平凡解（ｘ，ｙ）＝（１，１）及非平凡解（ｘ，ｙ）＝（２４，７０）．为研究方便，我们称以上方程为卡斯方程．１９１９年沃森（Ｗ...     

数学软件在中学数学教育中的应用(8)

解数学题是每个中学教师必须具备的能力．无论是课堂上的例题、练习题、习题、还是课外作业题、测验题、考试题、竞赛题的选取和解答,均占用了教师大量时间．如何使教师从中解放出来？学会用数学软件来解数学题,就可以做到“事半功倍”．以后的续篇将分专题加以阐述,本文的主题是用数学软件解有关因式分解的数学问题．下面用例子说明用数学软件（Ｍａｔｈｃａｄ７．０）解有关因式分解的数学问题的两个基本方法．例１　分解因式　（ａ＋ｂ－２ａｂ）（ａ＋ｂ－２）＋（１－ａｂ）２ｆａｃｔｏｒ→（ａ－１）２（ｂ－１）２．上面的结果可…     

97小学数学竞赛试题选解(三)

９７小学数学竞赛试题选解（三）合川市教科所何剑秋１、计算（１＋１２）×（１＋１４）×（１＋１６）×…×（１＋１１０）×（１－１３）×（１－１５）×…×（１－１９）＝．解原式＝３２×５４×７６×９８×１１１０×２３×４５×６７×８９＝１１１０２、计算（...     

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 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.     

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.     

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     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.