A finite presentation of the rational Urysohn space

We give a new construction of the rational Urysohn space UQ, which yields a finite presentation of UQ. This may be viewed as an extension of the finite presentation of the generic partial order.     

An augmented Lagrangian approach with a variable transformation in nonlinear programming

Tangent cone and (regular) normal cone of a closed set under an invertible variable transformation around a given point are investigated, which lead to the concepts of θ⁻¹-tangent cone of a set and θ⁻¹-subderivative of a function. When the notion of θ⁻¹-subderivative is applied to perturbation functions, a class of augmented Lagrangians involving an invertible mapping of perturbation variables are obtained, in which dualizing parameterization and augmenting functions are not necessarily convex in perturbation variables. A necessary and sufficient condition for the exact penalty representation under the proposed augmented Lagrangian scheme is obtained. For an augmenting function with an Euclidean norm, a sufficient condition (resp., a sufficient and necessary condition) for an arbitrary vector (resp., 0) to support an exact penalty representation is given in terms of θ⁻¹-subderivatives. An example of the variable transformation applied to constrained optimization problems is given, which yields several exact penalization results in the literature.     

On the equivalence of a theorem of Kisynski and the Hille-Yosida generation theorem

We show that a theorem of Kisynski on the generation of Banach-algebra homomorphisms of certain convolution algebras is equivalent to the Hille-Yosida theorem on the generation of operator-valued one-parameter semigroups.

     

关于G－分次环与G－集的Smash积的几个结果

设Ｇ为任意群，本文借助于环的矩阵表示给出了Ｇ－分次环与任意可迁Ｇ－集的Ｓｍａｓｈ积是素环或单环的刻画。     

Simple Coherent State and New Form for Inhomogeneous Differential Realization of OSP(2,1) Superalgebra

The simple coherent state of the OSP(2,1) superalgebra is constructed and its properties are discussed in detail. The matrix elements of the OSP(2,1) generators in the coherent state space are calculated. The new form for inhomogeneous differential realization of the OSP(2,1) superalgebra is given.     

BAYESIAN ANALYSIS, LIKELIHOOD RATIO AND INFORMATION

ＢＡＹＥＳＩＡＮＡＮＡＬＹＳＩＳ，ＬＩＫＥＬＩＨＯＯＤＲＡＴＩＯＡＮＤＩＮＦＯＲＭＡＴＩＯＮ￥ＺＨＡＮＧＹＡＯＴＩＮＧＡＮＤＤＵＪＩＮＧＳＯＮＧＡｂｓｔｒａｃｔ：Ｗｅｐｒｅｓｅｎｔａｎｅｗｓｃｈｅｍｅｆｏｒｕｎｃｅｒｔａｉｎｒｅａｓｏｎｉｎｇｂａｓｅ...     

A matrix description of a wild category

A bocsA of representation wild type over an algebraically closed fieldk and its representation categoryR A are concretely described by using matrix method. It is proved thatA has almost split sequences and strong homogeneous property in the case chk=0. Thus there exists neither proper projective nor proper injective object inR A. And for each indecomposable object M inR A, there exists a proper almost split sequence, which is given explicitly. Project supported by the National Natural Science Foundation of China(Grant Nos. 19331013; 19671013).     

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

1.IntroductionandDefinitionsTheinducedrepresentationofgroupC*-algebrasfirstwasalgebraicallyintroducedbyfueffelin[3].P.Greenin[6]similiaxlyintroducedtheoneforcovariantdynamicsystem.TheinducedrepresentationofcrossedproductsbycoactionswasintroducedbyK.Mansfieldin[9].Using[8]wecanobtaintheinducedrepresentationofgrollpoidC*-algebrasin[1Ol.TherichapplicationofthesecanbefoundamongmanypapersrelativetotheC*-analysisofgroupoidandgroup.TheC*-groupoiddynamicsystemanditsreducedcrossedprod-uctwereintro…     

Soap films spanning rectangular prisms

In this paper, we consider soap films spanning rectangular prisms with regular n-gon bases. As the number of edges n varies, we show that there are significant changes in the qualitative properties of the spanning soap films as well as a change in the number of spanning soap films whose existence we can prove: We can find two nontrivial soap films for n = 3, 4, 5 but only one for n ≥ 6. We also prove some results concerning the interval of aspect ratios through which the soap films exist: The interval is finite if n = 3, 4, 5 and infinite if n ≥ 6. Furthermore, for n > 6, we have that the spanning soap film converges to a soap film spanning the vertical lines through the vertices of a regular n-gon as the aspect ratio goes to infinity. We can also make sense of the case n = ∞. Here, we discover some interesting singly and triply periodic soap films spanning singly and doubly periodic sets of vertical lines or spanning singly periodic sets of vertical line segments connected by pairs of parallel, horizontal lines. Finally, for n = 3, 4, 5, 6, we can derive parameterizations for the spanning soap films, and these parameterizations are explicit up to knowing the aspect ratio.      

Equivariant cobordism of Grassmann and flag manifolds

We consider certain natural (ℤ₂)ⁿ actions on real Grassmann and flag manifolds andS ¹ actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly.