三角形垂心的性质及其应用

三角形垂心的性质及其应用海南省农垦中学方亚斌我们知道．对任意ＡＢＣ．三条高线ＡＤ、ＢＥ、ＣＦ（Ｄ、Ｅ、Ｆ分别为垂足）交于一点Ｈ关于垂心Ｈ．有下述一些重要性质：（１）四点Ａ、Ｂ、Ｃ、Ｈ构成一垂心组．即Ａ、Ｂ、Ｃ、Ｈ四点中．任意一点都是其余三点连线所成三...     

G-旋模型场代数中的对偶定理

设Ｇ是有限群，　Ｈ是Ｇ的子群，Ｄ（Ｇ）为Ｇ的Ｄｏｕｂｌｅ代数，　Ｆ是　Ｇ－旋模型所对应的场代数．　本文考虑Ｄ（Ｇ）的Ｈｏｐｆ子代数Ｄ（Ｈ），证明了Ｆ的Ｄ（Ｈ）不变子空间ＡＨ是Ｃ＊－代数．Ｄ（Ｈ）存在Ｃ＊－表示，使得Ｄ（Ｈ）和ＡＨ互为换位子．     

On Theorem of the “Mountain Impasse” Type

ＬｅｔＦ（ｕ），Ｇ（ｕ）ｂｅＣ１－ｆｕｎｃｔｉｏｎａｌｓｏｎａＨｉｌｂｅｒｔｓｐａｃｅＨａｎｄｓｕｐｕ∈ＨＦ（ｕ）＝∞．ＬｅｔＫｂｅａｃｏｍｐａｃｔｍｅｔｒｉｃｓｐａｃｅａｎｄｌｅｔＫｂｅａｎｏｎ－ｅｍｐｔｙｃｌｏｓｅｄｓｕｂｓｅｔ≠Ｋ，ｐ∈Ｃ（Ｋ；Ｈ）．ＤｅｎｏｔｅＦＲ＝｛ｕ∈Ｈ｜Ｆ（ｕ）Ｒ｝；　　　　　　ΦＲ＝｛ｐ∈Ｃ（Ｋ；ＦＲ）｜ｐ＝ｐｏｎＫ｝；ｃ（Ｒ）＝ｉｎｆｐ∈ΦＲｍａｘξ∈ＫＧ（ｐ（ξ））；ｃ０＝ｍａｘξ∈ＫＧ（ｐ（ξ））；Φ∞＝｛ｐ∈Ｃ（Ｋ；Ｈ）｜ｐ＝ｐｏｎＫ｝；…     

ESTIMATES OF EIGENVALUES FOR UNIFORMLY ELLIPTIC OPERATOR OF SECOND ORDER

ＥＳＴＩＭＡＴＥＳＯＦＥＩＧＥＮＶＡＬＵＥＳＦＯＲＵＮＩＦＯＲＭＬＹＥＬＬＩＰＴＩＣＯＰＥＲＡＴＯＲＯＦＳＥＣＯＮＤＯＲＤＥＲＱＩＡＮＣＨＵＮＬＩＮ（钱椿林）ＣＨＥＮＺＵＣＨＩ（陈祖墀）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｔｎａｔｉｃｓ，Ｕｎｉｖｅｒ...     

具有扩散和群体防卫的简单食物链的Hopf分支

具有扩散和群体防卫的简单食物链的Ｈｏｐｆ分支李云（武汉水运工程学院基础部，武汉４３００６３）ＴＨＥＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＦＯＲＳＩＭＰＬＥＦＯＯＤＣＨＡＩＮＷＩＴＨＤＩＦＦＵＳＩＯＮＡＮＤＧＲＯＵＰＤＥＦＥＮＣＥ￥ＬＩＹＵＮ（Ｄｅｐａｒｔｍｅ...     

A COMPLETE SOLUTION OF HOSOYA'S MYSTERY

ＺＨＡＮＧＦＵＪＩ（张福基）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉａｍｅｎ３６１００５，Ｃｈｉｎａ）ＣＨＥＮＲＯＮＧＳＩ（陈荣斯）（ＣｏｌｌｅｇｅｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，Ｆｕｚｈｏ...     

CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS WITH VARIABLE DELAY

Ｃｏｎｓｉｄｅｒｔｈｅｄｉｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｗｉｔｈａｖａｒｉａｂｌｅｄｅｌａｙｘｎ－ｘｎ－１＝Ｆ（ｘｎ，ｘｒ（ｎ），ｎ＝ｎ０，ｎ０＋１，…（１）ｗｈｅｒｅ（Ｈ１）：Ｆ∈Ｃ（Ｒ×Ｒ，Ｒ），Ｆ（ｕ，ｖ）ｉｓｄｅｃｒｅａｓｉｎｇｗｉｔｈｒｅｓ...     

On Bahadur asymptotic efficiency in a semiparametric regression model

ＯＮＢＡＨＡＤＵＲＡＳＹＭＰＴＯＴＩＣＥＦＦＩＣＩＥＮＣＹＩＮＡＳＥＭＩＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＭＯＤＥＬＬＩＡＮＧＨＵＡ（梁华）;ＣＨＥＮＧＰＩＮＧ（成平）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ,ｔｈｅＣｈｉｎｅｓｅＡ...     

THE CONVERGENCE OF GLOWINSKI'S ALGORITHM FOR ELLIPTIC PROBLEMS

ＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＧＬＯＷＩＮＳＫＩ＇ＳＡＬＧＯＲＩＴＨＭＦＯＲＥＬＬＩＰＴＩＣＰＲＯＢＬＥＭＳＣＨＵＤＥＬＩＮ（储德林）；ＨＵＸＩＡＮＣＨＥＮＧ（胡显承）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇ－Ｈｕ...     

不等式x~3 y~3 z~3≥3xyz的几何证法

我们先证ｘ２＋ｙ２≥２ｘｙ（ｘ、ｙ∈Ｒ＋,当ｘ＝ｙ时,等号成立）证明　如图１,设正方形ＡＢＣＤ的边长为ｘ,正方形ＢＥＦＪ的边长为ｙ,在ＡＢ上取ＡＨ＝ｙ,则ＨＢ＝ｘ－ｙ,故ＨＥ＝ＨＢ＋ＢＥ＝ｘ－ｙ＋ｙ＝ｘ,∴　Ｓ矩ＡＨＰＤ＝Ｓ矩ＨＥＦＫ＝ｘｙ．由图１显然有　Ｓ正ＡＢＣＤ＋Ｓ正ＢＥＦＪ≥Ｓ矩ＡＨＰＤ＋Ｓ矩ＨＥＦＫ,即　　　ｘ２＋ｙ２≥２ｘｙ（当且仅当ｘ＝ｙ时,等号成立）再证　ｘ３＋ｙ３＋ｚ３≥３ｘｙｚ（ｘ、ｙ、ｚ∈Ｒ＋,当且仅当ｘ＝ｙ＝ｚ时,等号成立）证明　如图２,设三个正方体ＶＡＢ、ＶＣＤ、ＶＥＦ…     

A question in the theory of saturated formations of finite soluble groups

This paper examines the following question. If and are saturated formations then is defined to be the class of all soluble groups whose belong to . In general is a formation, but need not be a saturated formation. Here the smallest saturated formation containing is studied.     

THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES

Let X be a comPlex Banach space and let D be the open unit disc in the complex plane.We shall denote by H"(D, X) the Banach space consisting of all uniformly bounded X-vaued analytic functions defined on D equipped with the norm llflloo = suP lIf(z)Il. Az eDcomplex Banach space X is said to have the analytic Radon-NikOdym property if eachelemellt f E Hoo(D,X) has radial limits almost everywhere on the torus T = {e": 0 E[0, 2x]} (see [1]), this means that for almost all 0 C [0,27l, 9W…     

The Löwenheim—Skolem—Mal'tsev Theorem for ℍ\mathbb{F}-Structures

We deal with the problem asking whether hereditarily finite superstructures have elementary extensions of the form . In so doing, we settle the question whether a theory for some hereditarily finite superstructure have models of arbitrarily large cardinality. A Hanf number is shown to exist, and we provide an exact bound for the countable case.     

PRODUCTS OF CIRCULANT GRAPHS

ABSTRACT

Graph products of circulants are studied. It is shown that if G and H are circulants and gcd(v(G), v(H)) = 1, then every B-product of G and H is again a circulant. We prove that if m ≠ 2, then the generalised prism K₂ ^mxC_n is a circulant iff n is odd. A similar result is deduced for the conjunction. We also prove that C_p x C_q is a circulant iff p and q are relatively prime. We close by showing that the composition of two circulants is again a circulant and explicitly describe the resultant circulant's jump sequence in terms of the constituent circulants' jump sequences.     

Cartan型模李超代数W的二阶上同调群H2(W,F)

本文研究了有限维广义Witt李超代数W的二阶上同调群H2(W,F),其中F是一个特征P＞2的代数封闭域.通过计算W到W*的导子,得到H2(W,F)是平凡的.应用此结果,我们可得W的中心扩张是平凡的.     

关于亚纯函数理论中与极点无涉的基本不等式

<正> 关于奈望利纳(Nevanlinna)氏第二基本不等式曾有引入纪(导)数而作之种种不同的推广,在这些推广式中,极点的密指量每见出现且有特殊作用,因之能否将此量消去是一问题.米约(Milloux)氏及熊庆来教授由不同途径各获得与极点无涉之一不等式此二结果形状互异而各有特点.熊庆来教授指出这两个结果尚可推广到更普遍的境地,我们由此方向探研得如下两个定理,为熊、米二氏者之推广.     

一类矩阵方程的公共解

By applying the GSVD of matrix pairs,we discuss common solutions of the matrix equations AXC = E, BXD = F, AXD = G, BXC = H, under consistent and nonconsistent case respectively. We also discuss common symmetric solutions of the matrix equations AXA^T = E, BXB^T = F, AXB^T = G, BXA^T = H under consistent and nonconsistent case respectively. The necessary and sufficient conditions for the existence and the expressions of solutions of these matrix equations are provided.     

Subdifferentials of compactly lipschitzian vector-valued functions

Summary We introduce the concept of compactly lipschitzian functions taking values in a topological vector space F. We show that if F is finite dimensional the Lipschitz functions are compactly lipschitizian. We define the notions of generalized directional derivatives and subdifferentials for such functionsf taking values in an ordered topological vector space. It is shown that this notion of subdifferential coincides with the one of F. H. Clarke whenf is Lispchits and F=. Some formulas for this subdifferential concerning the cases of finite sum, composition, pointwise supremum and continuous sum are studied.     

SPECTRAL GAP SOLUTIONS OF THE DISSIPATIVE KIRCHHOFF EQUATION

§1. Introduction This paper is devoted to the question of the global solvability of the dissipative Kirch-ho? equation ?t u ? m 2 | x u|2dx x u δ?tu = 0 (x ∈?, t > 0), …