Small Transitive Families of Subspaces

A family of subspaces of a complex separable Hilbert space is transitive if every bounded operator which leaves each of its members invariant is scalar. This article surveys some results concerning transitive families of small cardinality, and adds some new ones. The minimum cardinality of a transitive family in finite dimensions (greater than 2) is 4. In infinite dimensions a transitive pair of linear manifolds exists but the minimum cardinality of a transitive family of dense operator ranges or norm-closed subspaces is not known. However, a transitive family of dense operator ranges with 5 elements can be found, and so can a transitive family of norm-closed subspaces with 4 elements. In finite dimensions (> 1) three nest algebras (corresponding to maximal nests) can intersect in the scalar operators, but two cannot. It is not known if this is the case in infinite dimensions for maximal nests of type ω + 1. Four such nest algebras can intersect in the scalar operators. Received June 15, 2002, Accepted November 27, 2002     

Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions：Further Results

The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained.     

一类非线性算子的带误差的Ishikawa迭代程序及其稳定性

建立了任意实Banach空间中带误差的Ishikawa迭代程序逼近Lipschitz强伪压缩算子的不动点的一般性定理,指出已被广泛广泛研究的Ishikawa迭代序列的稳定性问题仅是带误差的Ishikawa迭代程序的特例,作为直接的应用,用不同于通常的方法证得任意实Banach空间中的Ishikawa迭代序列关于Lipschitz强伪压缩算子是稳定的,这些推广或发展了近期许多相应的结果。     

UNILATERAL EIGENVALUE PROBLEMS FOR NONLINEARLY ELASTIC PLATES： AN APPROACH VIA PSEUDO-MONOTONE OPERATORS

gi.TheTOpologicalDegreeforGeneralizedMonotoneOperatorsMonotoneoperatortheoryisoftenanefficienttoolforprovingtheexistenceofsolutionstononlinearProblems.Inparticular,thepseudo-monotoneoperatorsintroducedbyBrezis[2]areveryusefulforstudyingnonlinearellipticproblems.Weconsiderherethefollowingclassesofmappingsofgeneralizedmonotonetype.(QM)=theclassofquasi-mollotoneoperators,(S )=theclassofoperatorsoftype(S ),(PM)=theclassofpseudthmonotoneoperators,(LS)=theclassofLeray-Schauderoperators(compac…     

θ(t)-Caldern-Zygmund算子在群上的Hardy空间H~p(G)中的有界性

设Ｇ为局部域Ｋ上的２ｎ＋１维Ｈｅｉｓｅｎｂｅｒｇ群,文献［１］给出了一类Ｈａｒｄｙ空间 Ｈ~ｐ（Ｇ）,（０＜Ｐ≤１）,本文讨论了θ（ｔ）－Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ算子在Ｈ~ｐ（Ｇ）（０＜Ｐ≤１）中的有界性。     

混合单调算子的某些不动点定理与锥上的正不动点

给出在半序距离空间以迭代而得到的某些不动点定理的混合单调算子和在锥上某些非零不动点定理。     

S3亚椭圆算子的谱

本文研究了与紧流形S3上的与Hopf纤维丛相联系的亚椭圆算子的 谱.利用球调和函数的直和分解,得到了亚椭圆算子的谱和每个特征值所对应的特征空间及其维数.     

四川省入境旅游需求组合预测研究

通过对四川省入境旅游人数的准确预测,可以加强政府部门对旅游行业的把控,引导旅游市场资源的合理利用与配置提供了技术支持.建立了4种预测模型,对四川省入境旅游人数进行预测.比较两个误差指标值,表明组合预测方法能够有效地提高预测精度.     

Meyer-K(o)nig-Zeller 算子加权逼近的收敛阶

利用加权Ditzin-Totik 光滑模ω2φλ(f;t)w,借助Peetre K-泛函研究了Meyer-K(o)nig-Zeller算子,给出其特征刻画.