Infimum Properties Differ in the Weak Truth-table Degrees and the Turing Degrees

Abstract We prove that there are non-recursive r.e. sets A and C with A < _T C such that for every set . Both authors are supported by “863” and the National Science Foundation of China     

Isolated maximal d.r.e. degrees

There are very few results about maximal d.r.e. degrees as the construction is very hard to work with other requirements. In this paper we show that there exists an isolated maximal d.r.e. degree. In fact, we introduce a closely related notion called $(m,n)$-cupping degree and show that there exists an isolated $(2,\omega )$-cupping degree, and there exists a proper $(2,1)$-cupping degree. It helps understanding various degree structures in the Ershov Hierarchy.     

Z—P—S空间中一类新的不动点定理

利用概率度量空间中A—proper映射拓扑度的基本性质,在投影完备的Z—P—S空间中研究了非线性映射的不动点问题,得到了一些新的结果．     

Estimates of Disjoint Sequences in Banach Lattices and R.I. Function Spaces

We introduce UDS _p -property (resp. UDT _q -property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions     

The Index Set of Injectively Enumerable Classes of Recursively Enumerable Sets in ∑5-Complete

I introduce an effective enumeration of all effective enumerations of classes of r. e. sets and define with this the index set IE of injectively enumerable classes. It is easy to see that this set is ∑₅ in the Arithmetical Hierarchy and I describe a proof for the ∑₅-hardness of IE. Mathematics Subject Classification: 03D25, 03D45.     

Some New Types of KKM Theorem in H spaces with Applications

本文证明了Ｈ－空中的几个新型非空交定理．作为应用,文中得到了向量值极大极小定理和不动点定理,并研究了抽象经济平衡问题．     

Maximal independent sets in minimum colorings

Every graph G contains a minimum vertex-coloring with the property that at least one color class of the coloring is a maximal independent set (equivalently, a dominating set) in G. Among all such minimum vertex-colorings of the vertices of G, a coloring with the maximum number of color classes that are dominating sets in G is called a dominating-χ-coloring of G. The number of color classes that are dominating sets in a dominating-χ-coloring of G is defined to be the dominating-χ-color number of G. In this paper, we continue to investigate the dominating-χ-color number of a graph first defined and studied in [1].