丛上的相交数与Euler数

本文主要研究了带边流形上丛截面的相交数．应用作倍流形上的向量场的延拓，我们得到了带边流形上的Euler数用相交数的表示．     

ON WEYL MODULES OVER AFFINE LIE ALGEBRAS IN PRIME CHARACTERISTIC

We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.     

关于Euler相关数对

本文研究Euler函数问题.利用初等方法,获得了t≥3时Euler的所有数对(t是正整数),并推广了[2]的结果.     

ON THE APPROXIMAMATION OF DIFFERENTIABLE FUNCTIONS BY EULER MEANS

Let f∈C_(2π)~r.Denote by _n(f,x)the n-th Euler mean of f(x).This paper gives theasympto ic representations of the deviation _n(f,x)-f(x)and the quantity | _a(f,x)-f(x)|.Additionally,some applications of these asymptotic representations are obtained.     

NOTES ON NILPOTENCY OF NIL SUBRINGS OF ENDOMORPHISM RINGS OF MODULES

Abstract

A family K of right R-modules is called a natural class if K is closed under submodules, direct sums, infective hulls, and isomorphic copies. The main result of this note is the following: Let K be a natural class on Mod-R and M ε K. If M satisfies a.c.c. (or d.c.c.) on the set of submodules {N ? M: M/N ε K}, then each nil subring of End(M_R ) is nilpotent.     

广义n-表现模

本文研究了模的投射维数与环的总体维数的计算问题.利用n-表现模的性质,得到了广义n-表现模的结构定理和右n-凝聚环的总体维数的计算方法,推广了已有的维数计算方法.     

ON WEIGHT MODULES OF ALGEBRAS OF TWISTED DIFFERENTIAL OPERATORS ON THE PROJECTIVE SPACE

We classify blocks of categories of weight and generalized weight modules of algebras of twisted differential operators on ? ⁿ . Necessary and sufficient conditions for these blocks to be tame and proofs that some of the blocks are Koszul are provided. We also establish equivalences of categories between these blocks and categories of bounded and generalized bounded weight Open image in new window -modules in the cases of nonintegral and singular central character.     

ON (m,n)-INJECTIVITY OF MODULES

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-injective if every right R-homomorphism from an n-generated submodule of R^m to M extends to one from R^m to M. This definition unifies several definitions on generalizations of injectivity of modules. The aim of this paper is to investigate properties of the (m, n)-injective modules. Various results are developed, many extending known results.     

ON THE FINITENESS PROPERTIES OF THE GENERALIZED LOCAL COHOMOLOGY MODULES

Abstract

The question, posed in Crawley and Jónsson (Crawley, P., Jónsson, B. (1964). Refinements for infinite direct decompositions of algebraic systems. Pacific J. Math. 14:797–855), whether the finite exchange property implies the unrestricted exchange property for any modules, is still open. In this note we obtain the equivalence of the finite exchange property and the unrestricted exchange property for the class of modules whose endomorphism rings are Abelian.     

ON X-EXTENDING AND X-CONTINUOUS MODULES

Let X be a left R-module. We characterize when the direct sum of two X-extending modules is X-extending via essential injectivity and pseudo injectivity of modules. As a corollary, we show that if extending modules M ₁ and M ₂ are relatively essentially injective and M ₁ is pseudo-M ₂-injective (or M ₂ is pseudo-M ₁-injective) then M ₁ ⊕ M ₂ is extending. Also we characterize when the direct sum of two CESS-modules is CESS. Some characterizations of almost Noetherian rings are also given by relative (quasi-) continuity of left R-modules.     

CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ ( m ) ) and e r ∞ (△ ( m ) ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.     

关于拟圆性质的评注

设D是扩充复平面R-2中的单连通Jordan真子域,D*=R-2\D-是D的外部.本文肯定并证明 了K.Hag在1999年提出的如下两个悬而未决的问题:(1)D是Cigar域当且仅当D是OLC域; (2)D是Turning域当且仅当D*是Cigar域.     

VARIATIONS ON A THEME BY EULER

1.IntroductionAHallliltolliansystemofdifferentialequationsonRZnisgivedbyP~~H,(P,q),q=HP(P,q),(1)wherep=(pl,'.,P.),q=(ql,',q.)eR"arethegeneralizedcoordinatesandmolllentarespectivelyandH(P,q)istheellergyofthesystem.Thesystem(1)canberewrittenasthecompactf…     

关于拟圆性质的评注

设D是扩充复平面(R)2中的单连通Jordan真子域,D*=(R)2\(D)是D的外部.本文肯定并证明了K.Hag在1999年提出的如下两个悬而未决的问题(1)D是Cigar域当且仅当D是OLC域;(2)D是Turning域当且仅当D*是Cigar域.     

ON THE CHARACTERISTIC FUNCTION OF SEMI-HYPONORMAL OPERATOR

本文继[3]之后，研究拟亚正常算子和半亚正常算子的特征函数.设\[A = U|A{|_r}\]是\[H{\kern 1pt} {\kern 1pt} \] 上拟亚正常算子，\[U\]是酉算子，\[B = |A{|_ + } - |A{|_ - }\],作算子\[A\]的特征函数\[W(\lambda ,A) = I - {B^{\frac{1}{2}}}{(\lambda I - {A_ - })^{ - 1}}U{B^{\frac{1}{2}}}\] 定理1 设\[A = U|A{|_r}\]及\[{A^'} = {U^'}|{A^'}{|_r}\]为\[\varphi - \]拟亚正常算子而且都是简单的.又设 \[U\]与\[{U^'}|\]是酉算子.如果有酉算\[T\]将\[H\]映照成\[{H^'}\]而且\[|{A^'}{|_ \pm } = T|A{|_ \pm }{T^{ - 1}}\]，\[{U^'} = TU{T^{ - 1}}\]那末必有\[{\cal B}(A)\]到\[{\cal B}({A^'}){\kern 1pt} \]上的酉算子\[S{\kern 1pt} {\kern 1pt} \]使当\[\lambda \notin \sigma ({A_ - }) = \sigma (A_ - ^')\]时\[W(\lambda ,{A^'}) = SW(\lambda ,A){S^{ - 1}}\]反之亦真. 下面设\[A\]是半亚正常的.又设\[{\cal D}\]为一辅助的希尔伯特空间，\[K\]为\[{\cal D}\]到\[{\kern 1pt} H\]中的线 性算子使\[Q = |A{|_{\rm{r}}} - |A{|_l} = K{K^*}{\kern 1pt} {\kern 1pt} \]，当\[\lambda \in \rho (A)\]，\[|Z| \ne 1\]时作 \[Y(z,\lambda ) = I - {\kern 1pt} {\kern 1pt} z{K^*}{(I - z{U^*})^{ - 1}}{(A - \lambda I)^{ - 1}}K\] 定理2设\[A = U|A{|_r}{\kern 1pt} {\kern 1pt} {\kern 1pt} \]及\[{A^'} = {U^'}|{A^'}{|_r}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \]分别是\[H\]与\[{H^'}{\kern 1pt} {\kern 1pt} {\kern 1pt} \]中的半亚正常算子，\[U\]与 \[{U^'}\]是酉算子而且\[A\]与\[{A^'}\]都是简单的.如果存在\[{\cal D} \to {{\cal D}^'}{\kern 1pt} \]上的酉算子\[S\]使 \[{Y^'}(z,\lambda ) = SY(z,\lambda ){S^{ - 1}}\] 那末必有由\[H\]到\[{H^'}{\kern 1pt} {\kern 1pt} {\kern 1pt} \]上的酉算子\[T\]使(1)成立，反之亦真. 定理3 若\[K\]是希尔伯特-许密特算子则\[Y(z,\lambda )\]的行列式（当\[|Z| \ne 1\]时）存在， 且\[\det (Y(z,\lambda )) = \det ((I - z{U^*})(A - \lambda I){(I - z{U^*})^{ - 1}}{(A - \lambda I)^{ - 1}})\] 下面只考虑奇型积分模型这时\[W(\lambda ,A)\]成为乘法算子，\[(W(\lambda ,A)f)({e^{i\theta }}) = W({e^{i\theta }},\lambda )f({e^{i\theta }})\]其中\[W({e^{i\theta }},\lambda ) = I - \alpha ({e^{i\theta }}){(\lambda {e^{i\theta }}I - \beta ({e^{i\theta }}))^{ - 1}}\alpha ({e^{i\theta }})\] 我们又假设\[A\]是完全非正常的.记\[{Y_ \pm }({e^{i\theta }},\lambda )a = \mathop {\lim }\limits_{r \to 1 \pm 0} Y({e^{i\theta }},\lambda )a\] 定理4设\[\lambda \in \rho (A){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \]，\[a \in {\cal D}{\kern 1pt} {\kern 1pt} {\kern 1pt} \]为固定的，那末\[{Y_ \pm }({e^{i\theta }},\lambda )a\]为黎曼-希尔伯特问题 \[{Y_ - }({e^{i\theta }},\lambda )a = W({e^{i\theta }},\lambda ){Y_ + }({e^{i\theta }},\lambda )a\] 的解. 设\[{\cal L}({\cal D}{\kern 1pt} {\kern 1pt} {\kern 1pt} ){\kern 1pt} {\kern 1pt} {\kern 1pt} \]为\[{\cal D}{\kern 1pt} {\kern 1pt} {\kern 1pt} \]上线性有界算子全体所成的Banach空间，\[H_ \pm ^p({\cal L}{\kern 1pt} ({\cal D}{\kern 1pt} {\kern 1pt} ){\kern 1pt} {\kern 1pt} ){\kern 1pt} {\kern 1pt} \]为单位圆 外，内取值于\[{\cal L}({\cal D}{\kern 1pt} {\kern 1pt} {\kern 1pt} ){\kern 1pt} \]的某些解析函数所成的Hardy空间.设\[f({e^{i\theta }})\]是单位圆周上的函 数，如果有\[{u_ \pm } \in H_ \pm ^p({\cal L}{\kern 1pt} ({\cal D}{\kern 1pt} {\kern 1pt} ){\kern 1pt} {\kern 1pt} ){\kern 1pt} {\kern 1pt} (p > 2)\]使\[u_ - ^{ - 1}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \]存在\[{u_ - }{\kern 1pt} {\kern 1pt} {\kern 1pt} {({e^{i\theta }})^{ - 1}}{u_ + }{\kern 1pt} ({e^{i\theta }}) = f({e^{i\theta }})\]则称\[f\]是可分解的.     

伪投射模的特征

本文运用伪投射模刻划了半单环、左遗传环、完全环、半完全环、拟完全环和半局部环的性质和特征。     

关于最大特征指数的上稳定性与最小特征指数的下稳定性

<正> §1.引言 1952年(?)提出线性组特征指数稳定性定义和一些重要的结果,同一年(?)对一类非线组的特征指数分布作了较详细的研究.1955年(?)给出了一类非线性组之正则首次近似(对角型)的最大特征指数上稳定性的充要条件.本文将研究较广泛非线性组之首次近似最大特征指数的上稳定性、最小特征指数的下稳定性及解的渐近稳定性.