On Rings With Conditions On Nonperiodic Elements

We study commutativity of rings R with the property that for each nonperiodic element x of R there exists a positive integer K = K(x) such that x^k is central for all k≥K.     

On recurrence

Summary LetT be a non-singular ergodic automorphism of a Lebesgue space (X,L,) and letf: X be a measurable function. We define the notion of recurrence of such a functionf and introduce the recurrence setR(f)={:f– is recurrent}. If , then R()={0}, but in general recurrence sets can be very complicated. We prove various conditions for a number to lie in R(f) and, more generally, forR(f) to be non-empty. The results in this paper have applications to the theory of random walks with stationary increments.     

On formalisms

Extreme attacks on formalisms overestimate the expressive power of natural language and underestimate the power of formal languages. An overemphasis on the role of human intuition leads to an underemphasis of the value of flexible formalisms in protecting ourselves from human errors. When one uses a computer to solve problems, one builds a theory, a model of the real world, and one should use the mixture of formal and natural language that is most appropriate for the problems to be solved.Dedicated to Peter Naur on the occasion of his 60th birthday     

On BO-algebras

In this paper, we introduce the notion of a BO-algebra, and we prove that every BO-algebra is 0-commutative, and we show that BO-algebras, 0-commutative B-algebras, BM-algebras, p-semisimple BCI-algebras and abelian groups are logically equivalent.     

On G-Compactifications

The semilattice of G-compactifications of a G-Tikhonov space X is studied. The question of what sets containing X and contained in the maximal G-compactification β _G X must be contained also in all other G-compactifications of X is considered. Conditions for β _G X to be the completion of the G-space X with respect to a natural uniformity (proximity) on X are obtained. Sufficient conditions for the existence of a smallest (minimal, unique) G-compactification of X are given.     

关于UR-环

A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relations of these rings are studied and several properties of clean rings and （S, 2）-rings are extended. PAng extensions of UR-rings are also investigated.     

关于超格

首先给出了超格的最小元、最大元及有界超格的定义,并举例说明了这种定义的合理性.其次,进一步研究了超格的理想.     

On zero-trees

Consider an integer-valued function on the edge-set of the complete graph K_m+1. The weight of an edge-subset is defined to be the sum of the associated weights. It is proved that there exists a spanning tree with weight 0 modulo m.     

On S-Stability

We prove in this paper that no consistent and well-defined Runge-Kutta method is S-stable and point out the errors of the theorems on S-stability in [1].     

On UJ-rings

UJ-rings are studied, i.e., ring in which all units can be presented in a form 1+x, for some x∈J(R). The behavior of UJ-rings under various algebraic construction is investigated. In particular, it is shown that the problem of lifting the UJ property from a ring R to the polynomial ring R[x] is equivalent to the Köthe’s problem for 𝔽₂-algebras.     

关于C-环

主要讨论了 C-环的结构以及它与其它环类之间的重要关系 ,从而较深刻地刻划这种环     

On self-complementation

We prove that, with very few exceptions, every graph of order n, n ? 0, 1(mod 4) and size at most n ? 1, is contained in a self-complementary graph of order n. We study a similar problem for digraphs.     

On spinors

For a 2^n-dimensional complex Hermitian vector space S, we prove that any unitary basis of S can be explained as an augmented spinor structure on S. By using this explanation, a SpinC（2n）- action on S is equivalent to an action on a subset of augmented spinor structures. The latter action is a little easy to be understood, and is shown in the last part of this paper. Such kind of understanding could be of use to the discussions of Hermitian manifolds and spin manifolds, especially could help to find connections and elliptical operators.