ERGODIC THEOREMS FOR NON-LIPSCHITZIAN SEMIGROUPS WITHOUT CONVEXITY

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图中推广的正交因子分解

设G是一个图,具有顶点集合V(G)和边集合E(G).设g和f是定义在V(G)上的整数值函数,使对每个x∈V(G),有g(x)≤f(x).图G的一个(g,f)-因子是G的一个支撑子图H,使对每个x∈V(G),有g(x)≤d_H(x)≤f(x).G的一个(g,f)-因子分解是E(G)的边不相交的(g,g)-因子的一个划分.设F={F-1,F_2,…,F_m}为G的一个因子分解,H是G的一个有mr条边的子图.如果每个F_i恰好与H有r条公共边,1≤i≤m,则称Fr-正交于H.本文证明每个(mg+kr,mf-kr)-图含有一个子图R,使R有(g,f)-因子分解r-正交于任意给定的有kr条边的子图,其中m,k和r为正整数且k相似文献   

Agreeable domains

An integral domain D with quotient field K is defined to be agreeable if for each fractional ideal F of D[X] with F C K[X] there exists 0 = s ε D with sF C D[X]. D is agreeable ? D satisfies property (*) (for 0 ^ f(X) G K[X], there exists 0 = s ε D so that f(X)g(X) ε D[X] for g(X) ε K[X] implies that sg(X) ε D[X]) &; D[X] is an almost principal domain, i.e., for each nonzero ideal I of D[X] with IK[X] = K[X], there exists f(X) ε I and 0 = s ε D with sI C (f(X)). If D is Noetherian or integrally closed, then D is agreeable. A number of other characterizations of agreeable domains are given as are a number of stability properties. For example, if D is agreeable, so is ?^αD_{P α} and for a pair of domains D?D′ with a [DD:′]≠0, D is agreeable?D′ is agreeable. Results on agreeable domains are used to give an alternative treatment of Querre's characterization of divisorial ideals in integrally closed polynomial rings. Finally, the various characterizations of D being agreeable are considered for polynomial rings in several variables.     

伪压缩族公共不动点的复合隐格式迭代逼近问题

设H是一实Hillber空间,K是H之一非空间凸子集,设{Ti}Ni=1是N个Lipschitz伪压缩映象使得F=∩Ni=1F(Ti)≠0,其中F(Ti)={x∈K:Tix=x}并且{αn}n∞=1,{βn}∞n=1[0,1]是满足如下条件的实序列(i)∑∞n=1(1-αn)2= ∞;(ii)limn→∞(1-αn)=0;(iii)∑∞n=1(1-βn)< ∞;(iv)(1-αn)L2<1,n1;(v)αn(1-βn)2 αn[βn L(1-βn)]2<1,其中L1是{Ti}iN=1的公共Lipschitz常数,对于x0∈K,设{xn}n∞=1是由下列定义的复合隐格式迭代xn=αnxn-1 (1-αn)Tnyn,yn=βnxn (1-βn)Tnxn,其中Tn=TnmodN,则(i)limn→∞‖xn-p‖存在,对于所有的p∈F;(ii)limn→∞d(xn,f)存在,其中d(xn,F)=infp∈F‖xn-p‖;(iii)liminfn→∞‖xn-Tnxn‖=0.本文的结果推广并且改进H-K.Xu和R.G.Ori在2001年的结果和Osilike在2004年的结果,并且在这篇文章中,主要的证明方法也不同与H-K.Xu和Osilike的方法.     

An intersection theorem for multivalued maps

LetE be a Banach space and letV, W ? E be two closed subspaces such thatE=V ⊕ W. LetF, G: E-· E be two multivalued maps. The problem we are concerned with is to give conditions onF andG ensuring the nonemptiness ofF(V) ∩ G(W).     

(g,f) -因子和可扩图

设G是一个图,并设g和f是定义在V(G)上的整值函数使得对所有的点x∈ V(G)均有g(x)≤ f(x).称一个图G是(g,f,H) -可扩的,如果在删除了任意一个同构于H的子图中所有点后,剩下G的子图有一个(g,f) -因子.该文给出了(g,f,H) -可扩图的特征.进一步,研究了(g,f,H) -可扩(H=nK₁)的性质.     

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.     

自相似集的Hausdorff测度与连续性

对集合F Rn,以dim F和Hdim F(F)分别表示F的Hausdorff维数和dim F维Hausdorff测度.设T=T(f1,...,fm)为Rn中的自相似集,即由相似压缩组成的迭代函数系统{f1...,fm)的吸引子.假如fi(T)∩fj(T)= (i≠j),那么,对任意ε>0,存在δ>0,若D=D(g1,...,gm)为Rn中的自相似集并且sup{||fk(x)-gk(x)||:||x||≤1,1≤k≤m}<δ,则1HdimT(T)-Hdim D(D)|<ε.     

COMPENSATED COMPACTNESS AND THE STRATIFIED LIE GROUP

In this paper we prove that the Jacobian J(F) of a map F( f1, , fl) from Ginto Rl maps the product of Lebesgue space Lp1 × × Lpl into local Hardy space hγ(G),where Q/(Q+1)<γ≤ 1, and Q is the homogeneous dimension of the stratified Lie group G .     

有限个非扩张非自映像隐迭代格式的逼近

假设E为一致凸Banach空间,K为E的非空闭凸子集且为E的非扩张收缩,P为非扩张收缩映像.{Ti:i=1,2,…,N}:K→E为非扩张映像且F(T)=∩ from i=1 to N F(Ti)≠■.定义{xn}如下:x0∈K,xn=P(αnxn-1+(1-αn)TnP[βnxn-1+(1-βn)Tnxn]),n≥1,这里{αn},{βn}为[δ,1-δ]中的实序列,其中δ∈(0,1).若{Ti:i=1,2,…,N}满足条件(B),则{xn}强收敛于x*∈F(T).     

具误差隐格式迭代逼近严格伪压缩映像族公共不动点 (英)

设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设K是实Banach空间E中非空闭凸集，{Ti}i=1^N是N个具公共不动点集F的严格伪压缩映像，{αn}包括于[0,1]是实数例，{un}包括于K是序列，且满足下面条件（i）0〈α≤αn≤1;（ii）∑n=1∞（1-αn）=＋∞.（iii）∑n=1∞ ‖un‖〈＋∞.设x0∈K,{xn}由正式定义xn=αnxn-1＋（1-αn）Tnxn＋un-1,n≥1,其中Tn=Tnmodn，则下面结论（i）limn→∞‖xn-p‖存在，对所有p∈F；（ii）limn→∞d（xn,F）存在，当d（xn,F）=infp∈F‖xn-p‖；（iii）lim infn→∞‖xn-Tnxn‖=0.文中另一个结果是，如果{xn}包括于[1-2^-n,1]，则{xn}收敛，文中结果改进与扩展了Osilike（2004）最近的结果，证明方法也不同。     

On principal invariant subspaces

Let F and G be closed subspaces of the complex Hilbert space H, and U and V be closed subspaces of F and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which (U, V) is a pair of (strictly, non-degenerate) principal invariant subspaces for (F, G).     

逼近非扩张非自映像不动点（英文）

设E是一致凸Banach空间,K是E中非空闭凸集且是一个非扩张收缩核,T：K→E是具非空不动点集F（T）：={x∈K：Tx=x}的非扩张映像.设{α_n},{β_n},{γ_n},{α′_n},{β′_n},{γ′_n}是[0,1]中实数列满足α_n＋β_n＋γ_n=α′_n＋γ′_n＋γ′_n=1,对任意初值x_1∈K,定义{x_n}如下（ⅰ）如果对偶空间E＊具有Kadec-Klee性质,那么{x_n}弱收敛于T的某不动点x＊∈F（T）;（ⅱ）若T满足（A）条件,那么{x_n}强收敛于T的某不动点x＊∈F（T）.     

关于图中子图的（n,k）—正交因子分解

设G是一个具有顶点集V(G)和边集E(G)的图. 设g和f是定义在V(G)上的两个整数值函数,使得g(x)f(x)对所有的点x∈V(G)都成立.如果G是一个(mg+n,mf-n)-图,1n<m2k,且g(x)2k-1对所有的点x∈V(G)都成立,则对任意给定具有|E(H)|=nk边的G的子图H,存在G的一个子图G′使G′有一个(g,f)-因子分解(n,k)-正交H.     

Endomorphism Rings of Faithfully Flat Abelian Groups

We discuss faithfully flat abelian groups in conjunction with the following: A class C of abelian groups with full A-socle is A-balanced closed if it is closed with respect to finite direct sums and subgroups with full A-socle, ker ? ε C for all ? ε Horn (G, H) and G, H ε C, and A is projective with respect to all exact sequences of elements of C. A self-small group A admits an A-balanced closed class C which contains ⊕_IA for all index-sets I exactly if it is faithfully flat as an E(A)-module. We show that Corner's as well as Dugas' and Göbel's realization theorems yield abelian groups that are faithfully flat as E(A)-modules. Several applications of these results are given, some of which yield an answer to part a of Fuchs' Problem 84 and a partial respond to part c of the same problem.     

Quadratic maps and Bockstein closed group extensions

Let be a central extension of the form where and are elementary abelian -groups. Associated to there is a quadratic map , given by the -power map, which uniquely determines the extension. This quadratic map also determines the extension class of the extension in and an ideal in which is generated by the components of . We say that is Bockstein closed if is an ideal closed under the Bockstein operator.

We find a direct condition on the quadratic map that characterizes when the extension is Bockstein closed. Using this characterization, we show for example that quadratic maps induced from the fundamental quadratic map given by yield Bockstein closed extensions.

On the other hand, it is well known that an extension is Bockstein closed if and only if it lifts to an extension for some -lattice . In this situation, one may write for a ``binding matrix' with entries in . We find a direct way to calculate the module structure of in terms of . Using this, we study extensions where the lattice is diagonalizable/triangulable and find interesting equivalent conditions to these properties.

     

关于单李超三系的分类(英文)

本文证明了特征零代数闭域上的单李超三系可分为两部分:一是将单李超代数视为李超三系;二是单李超代数的对合自同构的(-1)-特征子空间.这些推广了Lister和Meyberg给出的关于单李三系分类的相应结果.     

On extensions of the generalized quadratic functions from “large” subsets of semigroups

Let $$(G,+)$$ be a commutative semigroup, $$\tau $$ be an endomorphism of G and involution, D be a nonempty subset of G, and $$(H,+)$$ be an abelian group, uniquely divisible by 2. Motivated by the extension problem of J. Aczél and the stability problem of S.M. Ulam, we show that if the set D is “sufficiently large”, then each function $$g{:} D\rightarrow H$$ such that $$g(x+y)+g(x+\tau (y))=2g(x)+2g(y)$$ for $$x,y\in D$$ with $$x+y,x+\tau (y)\in D$$ can be extended to a unique solution $$f{:} G\rightarrow H$$ of the functional equation $$f(x+y)+f(x+\tau (y))=2f(x)+2f(y)$$.     

Stability Results for Ekeland's ε Variational Principle for Set-Valued Mappings

In this paper, we define the Mosco convergence and Kuratowski-Painleve (P.K.) convergence for set-valued mapping sequence F n . Under some conditions, we derive the following result If a set-valued mapping sequence F n , which are nonempty, compact valued, upper semicontinuous and uniformly bounded below, Mosco (or P.K.) converges to a set-valued mapping F , which is upper semicontinuous, nonempty, compact valued, then Q l >0, u >0, $\varepsilon / \lambda - {\rm ext}\, F := \{ \bar x \in X : (F(x) - \bar y + \varepsilon / \lambda \Vert x - \bar x \Vert e)$