三角形一个重要公式及其应用

在三角形中，我们把角的顶点与其对边上一点的连线称作这个角的分角线．下面给出分角线长的一种公式．定理　如图１，Ｄ是△ＡＢＣ的边ＢＣ上一点，设ＡＢ、ＡＣ分别为ｃ、ｂ，∠ＢＡＤ＝α，∠ＣＡＤ＝β，图１则　　　　ＡＤ＝ｂｃｓｉｎ（α＋β）ｃｓｉｎα＋ｂｓｉｎβ．（１）当ＡＤ是∠Ａ的平分线时，　　　ＡＤ＝２ｂｃｃｏｓＡ２ｂ＋ｃ；（２）当ＡＤ是中线时，　　ＡＤ＝ｂｓｉｎ（α＋β）２ｓｉｎα＝ｃｓｉｎ（α＋β）２ｓｉｎβ；（３）当ＡＤ是高线时，　　　ＡＤ＝ｃｃｏｓα＝ｂｃｏｓβ＝ｂｃｓｉｎＡａ．（４）证明　在…     

WELL-BEHAVED BASIS AND LR ARRAYS

ＷＥＬＬ－ＢＥＨＡＶＥＤＢＡＳＩＳＡＮＤＬＲＡＲＲＡＹＳＬＩＮＤＯＮＧＤＡＩ（林东岱）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

On Unitary Equivalence of Analytic Toeplitz Operators

ＯｎＵｎｉｔａｒｙＥｑｕｉｖａｌｅｎｃｅｏｆＡｎａｌｙｔｉｃＴｏｅｐｌｉｔｚＯｐｅｒａｔｏｒｓＤｉｎｇＸｕａｎｈａｏ（丁宣浩）（ＤａｘｉａｎＴｅａｃｈｅｒ＇ｓＣｏｌｅｇｅ，Ｄａｘｉａｎ，Ｓｉｃｈｕａｎ，６３５０００）ＡｂｓｔｒａｃｔＩｎｔｈｉｓｐａｐ...     

A Degenerate Stefan Problem with Two Free Boundaries

ＡＤｅｇｅｎｅｒａｔｅＳｔｅｆａｎＰｒｏｂｌｅｍｗｉｔｈＴｗｏＦｒｅｅＢｏｕｎｄａｒｉｅｓ￥（李辉来）ＬｉＨｕｉｌａｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）Ａｂｓｔｒａｃｔ...     

An Outline of Dai Xu‘s Mathematical Achievements

ＡｎＯｕｔｌｉｎｅｏｆＤａｉＸｕ＇ｓＭａｔｈｅｍａｔｉｃａｌＡｃｈｉｅｖｅｍｅｎｔｓＷａｎｇＲｏｎｇｂｉｎ（王荣彬）ＷａｎｇＲｏｎｇｂｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＵｎｉｖ．Ｘｉ＇ａｎ７１００６９）Ａｂｓｔｒ...     

PARTIAL FERRERS MATRICES

ＰＡＲＴＩＡＬＦＥＲＲＥＲＳＭＡＴＲＩＣＥＳ￥ＲＩＣＨＡＲＤＡ；ＢＲＵＡＬＤＩ＆ＬＩＱＩＡＯ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＷｉｓｃｏｎｓｉｎ，Ｍａｄｉｓｏｎ，Ｗｉｓｃｏｎｓｉｎ５３７０６，Ｕ．Ｓ．Ａ．）（Ｄ...     

Sub－product Clases of l－Groups

Ｓｕｂ┐ｐｒｏｄｕｃｔＣｌａｓｅｓｏｆｌ┐ＧｒｏｕｐｓＴｏｎｇＤａｏｒｏｎｇ（仝道荣）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｈａｉＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，２１００２４）ＡｂｓｔｒａｃｔＡｃｌａｓｓｏｆｌ－ｇｒｏｕｐｓｉｓ...     

Olesky D.D.和Driessche P.Van Den问题（1）的回答

ＯｌｅｓｋｙＤ．Ｄ．和ＤｒｉｅｓｓｃｈｅＰ．ＶａｎＤｅｎ问题（１）的回答永学荣，梁义（新疆大学数学系乌鲁木齐８３００４６）关键词：ＬＵ分解；广义逆；广义Ｓｃｈｕｒ补ＡＭＳ（１９９１）主题分类：１５Ａ０９，１５Ａ２３．１９８７年，在加拿大的Ｖｉｃｔｏｒ...     

Simple Lie Algebras and Complete Lie Algebras

ＳｉｍｐｌｅＬｉｅＡｌｇｅｂｒａｓａｎｄＣｏｍｐｌｅｔｅＬｉｅＡｌｇｅｂｒａｓ＊）ＹａｎｇＱｉ（杨奇）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ，Ｔｉａｎｊｉｎ，３０００７２）ＭｅｎｇＤａｏｊｉ（孟道骥）（Ｄ...     

On Reducing Handle Additions

ＯｎＲｅｄｕｃｉｎｇＨａｎｄｌｅＡｄｄｉｔｉｏｎｓＬｅｉＦｅｎｇｃｈｕｎ（雷逢春）ａｎｄＱｉｕＲｕｉｆｅｎｇ（邱瑞锋）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）Ａｂｓｔｒａｃｔ...     

On strongly (<Emphasis Type="Italic">P</Emphasis>)-cyclic acts

By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong (P)-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.     

On uniform acts over semigroups

The paper is devoted to the investigation of uniform acts over semigroups perceived as an overclass of subdirectly irreducible acts. We establish conditions for a uniform act to be subdirectly irreducible. In particular, we prove that uniform acts with two zeros are subdirectly irreducible. Ultimately we investigate monoids which are uniform as right acts over themselves and we describe regular monoids with this property.     

L－逆左系对幺半群的刻画

正则左Ｓ-系是ｖｏｎ Ｎｅｕｍａｎｎ正则半群的自然推广，逆左Ｓ-系是逆半群的自然推广．作为左逆半群的自然推广，本文引入了Ｌ-逆左系的概念，并用来刻画了几类幺半群，如左逆幺半群，逆幺半群，ａｄｅｑｕａｔｅ幺半群等．     

C(P)系对幺半群的刻画

设S是幺半群.本文介绍并研究了正则右系的一个推广.一个右S-系A称为C(P)系,如果A的所有循环子系满足条件(P).本文证明了右C(P)系形成了右S-系的一个新的类,同时,C(P)性质为幺半群同调分类研究提供了新思路.     

右消去幺半群、左正则带和左正则型A幺半群

本文利用右消去幺半群,左正则带建立了真左正则型A幺半群．在证明了任一左正则型A幺半群均有P－覆盖后,给出P－覆盖的结构．     

On left C-wrpp semigroups

It is known that a C–rpp semigroup can be described as a strong semilattice of left cancellative monoids. In this paper, we introduce the class of left C–wrpp semigroups which includes the class of left C–rpp semigroups as a subclass. We shall particularly show that the semi-spined product of a left regular band and a C–wrpp semigroup forms a curler which is a left C–wrpp semigroup and vice versa. Results obtained by Fountain and Tang on C–rpp semigroups are extended and strengthened.     

关于所有强平坦右S-系是正则系的幺半群(英)

本论文考虑了所有强平坦右S-系是正则系的幺半群的刻画,证明了所有强平坦右S-系是正则S-系当且仅当S是右PSF幺半群并且S的每一个左coilpasible子幺半群包含左零元．该结果对Kilp和Knauer在文献[7]中的问题给出了一个新的回答．     

Endomorphism monoids of free acts and O-wreath products of monoids

Monoids and acts which may have zero elements are considered. In Section 1 we construct a O-wreath product of monoids. In 2 we prove the theorem that the endomorphism monoid of a free act over a monoid with zero can be represented as a O-wreath product. Considering monoids with tero we are interested in their annihilator properties. In 3 we give necessary and sufficient conditions for a O-wreath product of monoids to be a right (left) Baer (Rickart) monoid. In 4 we obtain as a consequence corresponding conditions for the endomorphism monoid of a free act over a monoid with zero.     

When Torsion Free Acts are Principally Weakly Flat

A necessary and sufficient condition for principal weak flatness of all right torsion free acts over a monoid is found. It is shown that the corresponding class of monoids is a proper subclass of left PP monoids.