超线性Hammerstein型积分方程的多重解(英)

本文利用Frechet空间理论讨论了定义在无穷大区间上超线性Hammerstein型积分方程的多重解的存在性．     

具有势函数V（r）＝A_1r~（－10）－A_2r~（－6）的分子晶体的Hami

采用连续分数法得到了具有分子晶体中的分子之间的相互作用势为Ｖ（ｒ）＝Ａ１ｒ－１０－Ａ２ｒ－６（Ａ１，Ａ２＞０）的分子晶体的Ｈａｍｉｌｔｏｎｉａｎ算子的精确的能量本征值（即分子晶体的束缚能的精确值）。     

关于“Sawyer权对和Muckenhoupt猜想”

关于“Ｓａｗｙｅｒ权对和Ｍｕｃｋｅｎｈｏｕｐｔ猜想”李兴民（曲阜师范大学数学系，山东２７３１６５）１９８４年，Ｍｕｃｋｅｎｈｏｕｐｔ￣［３］提出了有关算子Ｈ的两个著名猜想：〈Ⅰ〉对１＜ｐ＜∞，非负权对（ｕ，ｖ）使的充分必要条件是（ｕ，ｖ）∈Ｓ＿ｐ且（...     

多圆柱上的完全准凸映射

在C~n中有界凸Reinhardt域上讨论了一类介于凸映射类与星形映射类之间的“完全准凸映射类”.特别地,在C~n中的多圆柱上给出了完全准凸映射的分解定理,得到了多圆柱上判别凸映射的一个改进的充分条件.     

Inverse-Definiteness of the Fourth-Order Symmetric Differential Operator （Ⅰ）

Abstract   We give a linear symmetric differential operator L defined by

On Weak Regular ^＊-semigroups

In this paper, a special kind of partial algebras called projective partial groupoids is defined.It is proved that the inverse image of all projections of a fundamental weak regular ^*-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular ^*-semigroup has a projective partial groupoid structure. Moreover, a weak regular ^*-product which connects a fundamental weak regular ^*-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular ^*-product is in fact a weak regular ^*-semigroup and any weak regular ^*-semigroup is constructed in this way.     

Rescaling Symmetry Flow of the Kadomtsev--Petviashvili Hierarchy

We present a new symmetry flow of the Kadomtsev-Petviashvili (KP) hierarchy, which origins from the rescaling of whole “multi-time“ valuables. This flow describes the deformation of solutions of the KP hierarchy with respect to a noncommutative parameter. It is shown that the introduced rescaling symmetry flow does not commute with the ordinary evolution flows of the KP hierarchy, but commutes with the evolution flows with respect to slow-variables.     

On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders

Abstract Let Ω R~m(m≥1)be a bounded domain with piecewise smooth boundary Ω.Let t and r bepositive integers with t>r+1. We consider the eigenvalue problems(1.1)and(12),and obtain Theorem 1and Theorem 2, which generalize the results in[1,2.5].     

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     

Classification of Hardy Submodules and Characteristic Space Theory（A Brief and Selective Survey）

This paper is a brief and selective survey on classification of Hardy Submodules over the polydisk. The survey reports some progress in classification of Hardy submodules.