The tight upper bound on the state complexity of the reverse of R-trivial and J -trivial regular languages of the state complexity n is 2n−1. The witness is ternary for R-trivial regular languages and (n− 1)ary for J -trivial regular languages. In this paper, we prove that the bound can be met neither by a binary R-trivial regular language nor by a J -trivial regular language over an (n − 2)-el...

In 1995, Camillo and Yu showed that an exchange ring has stable range 1 if and only if every regular element is unit regular. An element m in a module RM is called regular if (mλ)m = m for some λ ∈ hom(M,R). In this paper we define stable modules and show that if M has the finite exchange property then M is stable if and only if, for every regular element m ∈ M, (mγ)m = m where γ : M → R is epi...

The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.’ In this paper is presented a ‘Regular Boundary Element Method’ as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular int...

Regular convergence, together with other types of have been studied since the 1970s for discrete approximations linear operators. In this paper, we consider eigenvalue approximation a compact operator $T$ that can be written as an problem holomorphic Fredholm function $F(\eta) = T-\frac{1}{\eta} I$. Focusing on finite element methods (conforming, discontinuous Galerkin, non-conforming, etc.), s...

In 1954 Zelinsky [16] proved that every element in the ring of linear transformations of a vector space V over a division ring D is a sum of two units unless dim V = 1 and D = Z2. Because EndD(V ) is a (von-Neumann) regular ring, Zelinsky’s result generated quite a bit of interest in regular rings that have the property that every element is a sum of (two) units. Clearly, a ring R, having Z2 as...

Inclines are additively idempotent semirings in which products are less than or equal to either factor. Necessary and sufficient conditions for an element in an incline to be regular are obtained. It is proved that every regular incline is a distributive lattice. The existence of the Moore-Penrose inverse of an element in an incline with involution is discussed. Characterizations of the set of ...

Matroids are a modern type of synthetic geometry in which the behavior of points, lines, planes, and higher-dimensional spaces are governed by combinatorial axioms. In this paper we describe our work on two well-known classification problems in matroid theory: determine all binary matroids M such that for every element e, either deleting the element ( ) or contracting the element ( ) is regular...

‎we characterize those groups $g$ and vector spaces $v$ such that $v$ is a faithful irreducible $g$-module and such that each $v$ in $v$ is centralized by a $g$-conjugate of a fixed non-identity element of the fitting subgroup $f(g)$ of $g$‎. ‎we also determine those $v$ and $g$ for which $v$ is a faithful quasi-primitive $g$-module and $f(g)$ has no regular orbit‎. ‎we do use these to show in ...