Hypertopologies on function spaces

The aim of this paper is to continue Naimpally’s seminal papers [16], [17], [18], i.e. we investigate topological properties of spaces which force the coincidence of convergences of functions associated with different hyperspace topologies. For example a metric spaceX is locally compact iff the topological convergence and the convergence induced by the Fell topology coincide onC(X,IR). Moreover, the proximal topology on the space of functions, not necessarily continuous, is studied in great detail.     

Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity conditions for the traction and displace- ment along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.     

Lorentz Geometry of 2-Step Nilpotent Lie Groups

We study the geometry of 2-step nilpotent Lie groups endowed with left-invariant Lorentz metrics. After integrating explicitly the geodesic equations, we discuss the problem of the existence of translated geodesics in those groups. A good part of the paper focuses on the existence of closed timelike geodesics in compact Lorentz 2-step nilmanifolds. Other related results, corollaries, and examples are also presented.     

Closed characteristics on non-degenerate star-shaped hypersurfaces in R2n

In this paper, firstly we establish the relation theorem between the Maslov-type index and the index defined by C. Viterbo for star-shaped Hamiltonian systems. Then we extend the iteration formula of C. Viterbo for non-degenerate star-shaped Hamiltonian systems to the general case. Finally we prove that there exist at least two geometrically distinct closed characteristics on any non-degenerate star-shaped compact smooth hypersurface on R2n with n ＞ 1. Here we call a hypersurface non-degenerate, if all the closed characteristics on the given hypersurface together with all of their iterations are non-degenerate as periodic solutions of the corresponding Hamiltonian system. We also study the ellipticity of closed characteristics when n=2.     

Intersection Theorems with a Continuum of Intersection Points

In all existing intersection theorems, conditions are given under which a certain subset of a collection of sets has a nonempty intersection. In this paper, conditions are formulated under which the intersection is a continuum of points satisfying some interesting topological properties. In this sense, the intersection theorems considered in this paper belong to a new class. The intersection theorems are formulated on the unit cube and it is shown that both the vector of zeroes and the vector of ones lie in the same component of the intersection. An interesting application concerns the model of an economy with price rigidities. Using the intersection theorems of this paper, it is easily shown that there exists a continuum of zero points in such a model. The intersection theorems treated give a generalization of the well-known lemmas of Knaster, Kuratowski, and Mazurkiewicz (Ref. 1), Scarf (Ref. 2), Shapley (Ref. 3), and Ichiishi (Ref. 4). Moreover, the results can be used to sharpen the usual formulation of the Scarf lemma on the cube.     

闭合宇宙的应力能量张量

本文在Ｆｒｉｅｄｍａｎｎ－Ｒｏｂｅｒｔｓｏｎ－Ｗａｌｋｅｒ模型下考察了闭合宇宙的应力能量张量，并用应力分析和能量条件对闭合宇宙临界相进行了讨论。     

Expansions of ordered fields without definable gaps

In this paper we are concerned with definably, with or without parameters, (Dedekind) complete expansions of ordered fields, i. e. those with no definable gaps. We present several axiomatizations, like being definably connected, in each of the two cases. As a corollary, when parameters are allowed, expansions of ordered fields are o‐minimal if and only if all their definable subsets are finite disjoint unions of definably connected (definable) subsets. We pay attention to how simply (in terms of the quantifier complexity and/or usage of parameters) a definable gap in an expansion is so. Next we prove that over parametrically definably complete expansions of ordered fields, all one‐to‐one definable (with parameters) continuous functions are monotone and open. Moreover, in both parameter and parameter‐free cases again, definably complete expansions of ordered fields satisfy definable versions of the Heine‐Borel and Extreme Value theorems and also Bounded Intersection Property for definable families of closed bounded subsets.     

Ideals and atoms of <Emphasis Type="Italic">BZ</Emphasis>-algebras

Ideals and atoms are studied by various authors from different point of views. In different algebras there are studied different ideals, but obtained results are similar. Below we present a new method of study of ideals in BZ-algebras. Using this method we describe the connection between ideals of various types. Supported by Natural Science Foundation of China (Grant No. 60775038).     

On Real Closed Regular Rings

The aim of this paper is to investigate some properties of real closed regular rings, in particular, the role played by real place in a real closed regular ring.2000 Mathematics Subject Classification: 13J25This work was supported by NSF of Jiangxi Province, China.