The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...

Given a partial action α of a group G on an associative algebra A, we consider the crossed product A α G. Using the algebras of multipliers, we generalize a result of Exel (1997) on the associativity of A α G obtained in the context of C∗-algebras. In particular, we prove that A αG is associative, provided that A is semiprime. We also give a criterion for the existence of a global extension of ...

Frédéric Grosshans, Thomas Lawson, François Morain, and Benjamin Smith Laboratoire Aimé Cotton, CNRS, Univ. Paris-Sud, ENS Cachan, Université Paris-Saclay, 91405 Orsay, France LTCI — Télécom ParisTech, 23 avenue d’Italie, 75013, Paris, France École Polytechnique/LIX and Institut national de recherche en informatique et en automatique (INRIA) INRIA and École Polytechnique/LIX (Dated: November 16...

In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout work, assume that is commutative ring with identity and left unitary R- module. A proper submodule called (for short Q-rad-semiprime), if for , ,and then . Where intersection all submodules

In this work we consider a certain class of Volterra integral equations possessing an infinite set of solutions. We investigate the application of Euler’s method together with the use of extrapolation procedures. Several examples are considered illustrating our results as well as the use of graded meshes and the application of higher order methods. keywords Volterra integral equations; weakly s...

The role of Ca(2+) in the induction of neural correlates of memory has frequently been described in binary terms despite the fact that many forms of memory are graded in their strength and/or persistence. We find that Ca(2+) dynamics encode the magnitude of sensorimotor adaptation of the electromotor output in a weakly electric fish. The neural correlate of this memory is a synaptically induced...

Let A be a uniformly complete almost f -algebra and a natural number p ∈ {3, 4, . . . }. Then Πp(A) = {a1 . . . ap; ak ∈ A, k = 1, . . . , p} is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σp(A) = {a; 0 ≤ a ∈ A} as positive cone.