关于迭代函数方程f~2(x)=af(x) bx的通解

设λ的二次三项式λ２－ａλ－ｂ的两个零点为λ１＝ｒ，λ２＝ｓ（ａ及ｂ为实数）．对０＜ｒ＜ｓ，ｒ＜０＜ｓ≠－ｒ及ｒ＝ｓ≠０这三种情形，Ｊ．Ｍａｔｋｏｗｓｋｉ与ＷｅｉｎｉａｎＺｈａｎｇ在“Ｍｅｔｈｏｄｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｓｆｏｒｆｕｎｃｔｉｏｎａｌｅｑｕａｔｉｏｎｓｉｎｐｏｌｙｎｏｍｉａｌｆｏｒｍ”一文中给出了迭代函数方程ｆ２（ｘ）＝ａｆ（ｘ）＋ｂｘ，对任ｘ∈Ｒ；ｆ∈Ｃ０（Ｒ，Ｒ）（１）的通解，并证明了当ｒ及ｓ非实数时方程（１）无解．对ｒ＝－ｓ≠０的情形，Ｍ．Ｋｕｃｚｍａ已给出了方程（１）的通解．本文则对ｒ＜ｓ＜０及ｒｓ＝０这两种情形给出了方程（１）的通解．此外，本文还给出了ｒ＜０＜ｓ≠－ｒ时关于方程（１）的通解的一个简洁的证明     

差异张量平行和半平行的仿射超曲面

本文用活动标架法证明了：若 Ｍｎ（ｎ≥２）是 ｎ＋１维仿射空间 Ａｎ＋１中非退化的仿射超曲面,（１）若■Ｋ＝０（即差异张量平行）,则Ｍ是仿射球,且Ｊ＝０和Ｇ是一个Ｅｉｎｓｔｅｉｎ度量,这里Ｊ是Ｍ的 Ｐｉｃｋ不变量,Ｇ是Ｂｌａｓｃｈｋｅ度量;（２）Ｒ·Ｋ＝０（即差异张量半平行）当且仅当Ｓ＝０（Ｍ为虚仿射球）,或者Ｋ＝０（Ｍ为非退化的二次超曲面）,这里 Ｒ为诱导仿射联络 ■的黎曼曲率算子．     

ON THE ｛2｝－INVERSE AND SOME ORDERING PROPERTIES OF NONNEGATIVE DEFINITE MATRICES

ＥＲＫＫＩＰ．ＬＩＳＫＩ（ＤｅｐｅｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＴａｍｐｅｒｓ，Ｆｉｎｌａｎｄ）ＷＡＮＧＳＯＮＧＧＵＩ（王松桂）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｂｅｉ...     

A REMARK ON _1 SUBSPACES OF L_1 (μ,X)

ＡＲＥＭＡＲＫＯＮ　_1　ＳＵＢＳＰＡＣＥＳＯＦＬΦ_１（μ，Ｘ）ＤｉｎｇＧｕａｎｇｇｕｉ（定光桂）；ＨｕａｎｇＳｅｎｚｈｏｎｇ（黄森忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｋａｉＵｎｉｖｅｒｓｉｔｙ，Ｔｉａｎｊｉｎ３０００７１，...     

R~(2,1)中类时Weingarten曲面的Bcklund变换

本文利用平行变换，得到３维Ｍｉｎｋｏｗｓｋｉ空间Ｒ２，１中的Ｋ－２ｍＨ＋ｍ２－ｌ２＝０（Ｈ２＞ Ｋ，０≤ｍ＜ｌ）类时Ｗｅｉｎｇａｒｔｅｎ曲面的Ｂａｃｋｌｕｎｄ定理．     

U1－sr条件

本文讨论Ｕ１－ｓｒ条件，这一条件有益于计算环的Ｋ１群．得到主要结果为；（１）完全确定满足Ｕ１－ｓｒ条件的半局部环：（２）给出使ＥｎｄＲ（Ｍ）满足Ｕ１－ｓｒ条件的一个刻划；（３）引进比Ｕ１－ｓｒ更强的一个条件ＳＵ１－ｓｒ，利用上述结果证明了：若Ｒ∈ＳＵ１－ｓｒ，则Ｍｎ（Ｒ）∈Ｕ１－ｓｒ；（４）证明了对于满足ＳＵ１－ｓｒ的环Ｒ，Ｋ１Ｒ＝ＧＬ１（Ｒ）ａｂ．     

ON LOWNER-ORDERING ANTITONICITY OF MATRIX INVERSION

ＯＮＬＯＷＮＥＲ－ＯＲＤＥＲＩＮＧＡＮＴＩＴＯＮＩＣＩＴＹＯＦＭＡＴＲＩＸＩＮＶＥＲＳＩＯＮ￥ＥＲＫＫＩＰ．ＬＩＳＫＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｔａｌＳｃｉｅｎｃｅｓ，ＵｎｉｖｅｒｓｉｔｖｏｆＴａｍｐｅｒｅ，Ｆｉｎｌａｎｄ）Ａｂｓｔ...     

A NICE PROPERTY OF OPERATORS DEFINED ON c_o

ＡＮＩＣＥＰＲＯＰＥＲＴＹＯＦＯＰＥＲＡＴＯＲＳＤＥＦＩＮＥＤＯＮｃ＿ｏＣ．Ｓｗａｒｔｚ（ＮｅｗＭｅｘｉｃｏＳｔａｔｅＵｎｉｖｒｓｉｔｙ，ＬａｓＣｒｕｃｅｓ，Ｕ．Ｓ．Ａ．）Ｍｉｎ－ＨｙｕｎｇＣｈｏ（Ｋｕｍ－ＯｈＵｎｉｖｅｒｓｔｙｏｆＴｅｃｈｎｏｌｏｇ...     

MARKOV DECISION PROGRAMMING WITH CONSTRAINTS

ＭＡＲＫＯＶＤＥＣＩＳＩＯＮＰＲＯＧＲＡＭＭＩＮＧＷＩＴＨＣＯＮＳＴＲＡＩＮＴＳＬＩＵＪＩＡＮＹＯＮＧ（刘建庸）；ＬＩＵＫＥ（刘克）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，...     

A KINETIC APPROACH TO SCALAR MULTI-DIMENSIONAL CONSERVATION LAWS

ＡＫＩＮＥＴＩＣＡＰＰＲＯＡＣＨＴＯＳＣＡＬＡＲＭＵＬＴＩ－ＤＩＭＥＮＳＩＯＮＡＬＣＯＮＳＥＲＶＡＴＩＯＮＬＡＷＳ￥ＨａＪｉａｘｉｎ（胡家信）（ＹｏｕｎｇＳｃｉｅｎｔｉｓｔｓＬａｂｏｒａｔｏｒｙｏｆＷｕｈａｎＩｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，Ａｃａｄ...     

右对称环

本文在左对称环的基础上提出了右对称环的概念,分别给出了是右对称环但不是左对称环和是左对称环但不是右对称环的例子．证明了（1）如果R是Armendariz环,则R是右对称环的充要条件R[x]是右对称环;（2）如果R是约化环,则R[x]/（x^n）是右对称环,其中（xn）是由xn生成的理想．     

环的几种内射性的关系

我们研究了关于广义自内射环(P-内射环,GP-内射环,AP-内射环,单内射环,n-内射环)的一些关系.     

On CS Rings and QF Rings

In this paper, we shall discuss the conditions for a right SC right CS ring to be a QF ring. In particular, we prove that if R is a right SI right CS ring satisfying the reflexive orthogonal condition (*) and if every CS right R-module is -CS, then R is a QF ring.AMS Subject Classification (1991): 16L30 16L60     

Strong Cleanness of Matrix Rings Over Commutative Rings

Let R be a commutative local ring. It is proved that R is Henselian if and only if each R-algebra which is a direct limit of module finite R-algebras is strongly clean. So, the matrix ring 𝕄 _n (R) is strongly clean for each integer n > 0 if R is Henselian and we show that the converse holds if either the residue class field of R is algebraically closed or R is an integrally closed domain or R is a valuation ring. It is also shown that each R-algebra which is locally a direct limit of module-finite algebras, is strongly clean if R is a π-regular commutative ring.     

Ideal-Symmetric and Semiprime Rings

Lambek extended the usual commutative ideal theory to ideals in noncommutative rings, calling an ideal A of a ring R symmetric if rst ∈ A implies rts ∈ A for r, s, t ∈ R. R is usually called symmetric if 0 is a symmetric ideal. This naturally gives rise to extending the study of symmetric ring property to the lattice of ideals. In the process, we introduce the concept of an ideal-symmetric ring. We first characterize the class of ideal-symmetric rings and show that this ideal-symmetric property is Morita invariant. We provide a method of constructing an ideal-symmetric ring (but not semiprime) from any given semiprime ring, noting that semiprime rings are ideal-symmetric. We investigate the structure of minimal ideal-symmetric rings completely, finding two kinds of basic forms of finite ideal-symmetric rings. It is also shown that the ideal-symmetric property can go up to right quotient rings in relation with regular elements. The polynomial ring R[x] over an ideal-symmetric ring R need not be ideal-symmetric, but it is shown that the factor ring R[x]/xⁿR[x] is ideal-symmetric over a semiprime ring R.     

Armendariz group rings

For a torsion or torsion-free group G and a field F, we characterize the group algebra FG that is Armendariz. Armendariz property for a group ring over a general ring R is also studied and related to those of Abelian group rings and the quaternion ring over R.     

Symplectic algebras and poisson algebras

Abstract

A ring R is called left P-injective if for every a ∈ R, aR = r(l(a)) where l( ? ) and r( ? ) denote left and right annihilators respectively. The ring R is called left GP-injective if for any 0 ≠ a ∈ R, there exists n > 0 such that a ⁿ  ≠ 0 and a ⁿ R = r(l(a ⁿ )). As a response to an open question on GP -injective rings, an example of a left GP-injective ring which is not left P-injective is given. It is also proved here that a ring R is left FP -injective if and only if every matrix ring 𝕄 _n (R) is left GP-injective.     

关于C-环

主要讨论了 C-环的结构以及它与其它环类之间的重要关系 ,从而较深刻地刻划这种环     

具有一对零态射的Morita Context 环(Ⅱ)

设(A,B,V,W,ψ,φ)是一个Morita Context,具有一对零态射ψ=0,φ=0,C= (A V W B)是对应的Morita Context环.本文给出了C与A,B,V,W之间关于环的π-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系.