A note on spectrum distribution of constraint preconditioned generalized saddle point matrices

In this note, results concerning the eigenvalue distribution and form of the eigenvectors of the constraint preconditioned generalized saddle point matrix and its minimal polynomial are given. These results extend previous ones that appeared in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

包络半群与拓扑动力学中的接近关系

运用包络半群的理论，对接近关系中一个重要定理给出了一个简单证明．作为这一定理的应用，我们得到接近关系可乘性的一个结果．并且对另一种接近关系，也得到一个结果．这两个定理减弱了Ｃｌａｙ在这一领域中两个定理的条件．     

Minimal Surfaces Obtained by Ribaucour Transformations

We consider Ribaucour transformations between minimal surfaces and we relate such transformations to generating planar embedded ends. Applying Ribaucour transformations to Enneper's surface and to the catenoid, we obtain new families of complete, minimal surfaces, of genus zero, immersed in R ³, with infinitely many embedded planar ends or with any finite number of such ends. Moreover, each surface has one or two nonplanar ends. A particular family is obtained from the catenoid, for each pair (n,m), nm, such that n m0 is an irreducible rational number. For any such pair, we get a 1-parameter family of finite total curvature, complete minimal surfaces with n+2 ends, n embedded planar ends and two nonplanar ends of geometric index m, whose total curvature is –4(n+m). The analytic interpretation of a Ribaucour transformation as a Bäcklund type transformation and a superposition formula for the nonlinear differential equation = e^-2 is included.     

Minimal Length Elements of Thompson's Group F

Elements of the group are represented by pairs of binary trees and the structure of the trees gives insight into the properties of the elements of the group. The review section presents this representation and reviews the known relationship between elements of F and binary trees. In the main section we give a method of determining the minimal lengths of elements of Thompson's group F in the two generator presentation

Linear maps preserving ideals of -algebras

We show that unital self-adjoint linear bijections of matrix algebras, type factors and abelian -algebras preserving maximal left ideals are isomorphisms and we show that a unital continuous linear map of a -algebra that maps the minimal left ideal into itself is the identity map.     

Evolution Equations for Special Lagrangian 3-Folds in C3

This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C ^m . The previous paper (Math. Ann. 320 (2001), 757–797), defined the idea of evolution data, which includes an (m – 1)-submanifold P in R ⁿ , and constructed a family of special Lagrangian m-folds N in C ^m , which are swept out by the image of P under a 1-parameter family of affine maps _t : R ⁿ C ^m , satisfying a first-order o.d.e. in t. In this paper we use the same idea to construct special Lagrangian 3-folds in C³. We find a one-to-one correspondence between sets of evolution data with m = 3 and homogeneous symplectic 2-manifolds P. This enables us to write down several interesting sets of evolution data, and so to construct corresponding families of special Lagrangian 3-folds in C³.Our main results are a number of new families of special Lagrangian 3-foldsin C³, which we write very explicitly in parametric form. Generically these are nonsingular as immersed 3-submanifolds, and diffeomorphic to R³ or ¹× R². Some of the 3-folds are singular, and we describe their singularities, which we believe are of a new kind.We hope these 3-folds will be helpful in understanding singularities ofcompact special Lagrangian 3-folds in Calabi–Yau 3-folds. This will beimportant in resolving the SYZ conjecture in Mirror Symmetry.     

Generalized Bicyclic Semigroups and Jones Semigroups

In this paper, we consider the generalized bicyclic semigroups B_n = a, b | aⁿb = 1 and the Jones semigroups A_n = a, b | aⁿ⁺¹b = a. They are the generalizations of the bicyclic semigroup B = a, b | ab = 1 and its analogous semigroup A = a, b | a²b = a discovered by P.R., Jones in 1987. The word problem for these kinds of semigroups is solved. It is proved that, for n 2, B_n are bisimple right inverse but not inverse semigroups and that the semigroup C = a, b | a²b = a, ab² = b is the smallest idempotent-free homomorphic image of A_n. Moreover, we also prove that A_n and A_m are mutually embeddable but not isomorphic with each other if n m. As a consequence, different kind of -nontrivial [0-]simple semigroups without idempotents are discussed.AMS 1991 Subject Classification: primary 20M10 secondary 20M05.Supported by NNSF of China (19671063) and KSRF of Sichuan Education Committee ([1999]127).     

CP~n中具有循环调和序列的平坦极小环面

研究具有循环调和序列的平坦极小浸入ψ:T2→CPn。证明了存在T2的一个有限覆盖p:T2→T2和一个全迷向的平坦极小浸入φ:T2→CPn使得ψ。p=A。φ,其中A:CPn→CPn:[v]→[vA]是线性全纯同胚。     

极大代数上线性系统的3维最小实现的研究

研究了极大代数上线性系统的3维最小实现问题,给出了特征方程为λ<'3> c<,0>λ<'0>=c<,2>λ<'2> c<,1>λ,当c<,1>=c<'2><,2>,c<,0>=C<,1>C<,2>时,无穷序列{g<,2>}<,0><'∞>存在3维最小实现的充要条件.     

晶体学与准晶体学点群的母子群关系

依据群论，得出了准晶体学点群的直积或半直积推导算式；依据结晶学理论，绘出了五角、八角、十角和十二角晶系各点群的极赤投影图.据此推导出了每一个准晶体学点群的全部最大子群，从而推导并绘制出了三维晶体学和准晶体学点群之间的母子群关系(60个点群的“家谱”).该“家谱”以最大子群链的图解形式直观地给出了每个点群的最小母群和最大子群. 关键词： 准晶体 晶体 点群 最大子群 最小母群 群链