let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure μ on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg μ-entropy values of the ergodic, properly nonsingular G-actions are bounded away from zero. We show that this is also a sufficient condit...

The boundary knot method is a recent truly meshfree boundary-type radial basis function (RBF) collocation scheme, where the nonsingular general solution is used instead of the singular fundamental solution to evaluate the homogeneous solution, while the dual reciprocity method is employed to the approximation of particular solution. Despite the fact that there are not nonsingular RBF general so...

Let M = [ttUiSi /_i be completely nonnegative (CNN), i.e., every minor of Mis nonnegative. Two methods for reducing the eigenvalue problem for M to that of a CNN, tridiagonal matrix, T = [?,-,] (r,-,= 0 when |i — j\ > 1), are presented in this paper. In the particular case that M is nonsingular it is shown for one of the methods that there exists a CNN nonsingular 5 such that SM = TS.

The aim of this paper is to show that any two knots can be realized as an attractor and repeller pair for some nonsingular Smale flow on S with any linking number. We view this as progress, albeit limited, to the conjecture that all two component links can be realized as an attractor-repeller pair in a nonsingular Smale flow on S with just one other basic set of saddle type.