We show that a regular von Neumann Q-m-convex Fréchet algebra is of finite dimension. We also show that a regular von Neumann m-convex Fréchet algebra is a projective limit of finite dimensional algebras. Finally, we prove that a bilateral Q-F-algebra is a regular von Neumann algebra if and only if it is isomorphic to a finite product of algebras which are also fields.

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Let M be a factor von Neumann algebra. It is shown that every nonlinear *-Lie higher derivation D={Æn}nÎN on M is additive. In particular, if M is infinite type I factor, a concrete characterization of D is given.

This paper deals with the solution of a class of Volterra integral equations in the sense of the conformable fractional derivative. For this goal, the well-organized Neumann method is developed and some theorems related to existence, uniqueness, and sufficient condition of convergence are presented. Some illustrative examples are provided to demonstrate the efficiency of the method in solving conformable fractional Volterra integral equations.

This research paper investigates the numerical analysis of the damped wave equation (DWE), focusing on the properties of numerical solutions achieved via semi-discrete approximation (SDA) and fully-discrete approximation (FDA) finite element methods (FEMs). This study established the existence of SDA and FDA solutions. Theoretical results are validated with numerical examples conducted in one, two, and three dimensions, demonstrating the accuracy and effectiveness of the proposed approaches.

In this article we study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras with some other known Banach algebras and with each other. In particular we show that the class of topologically von Neumann regular Banach algebras contains all C*-algebras, group algebras of compact abelian groups and certain weakly amenable Banach algebras while it excludes measure algebras of certain locally compact Abelian groups. Moreover we show that in a unital amenable Banach algebra principal regularity implies topological regularity. Finally we use topological regularity to obtain some information about hereditary C*-subalgebras of a given C*-algebra.