Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We  obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.

The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.

In a previous conference honouring Hermann Grassmann’s profound intellectual contributions (Schubring 1996), I cast him as a central figure in the historical development of a universal geometric calculus for mathematics and physics (Hestenes 1996). Sixteen years later I am here to report that impressive new applications in this tradition are rapidly developing in computer science and robotics a...

Over the last century, linear algebra theory and matrix computations became irreplaceable, not only for high-tech industries, but also in every corner of our computerised society. Most of the time, any given problem (linear or not) is reduced to finding the solution of a linear system. Thus, the possibility of solving large linear systems in a reasonable amount of time using parallel algorithms...

Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates are easy to derive for a wide class of mixture models. However, the likelihood of a mixture model is non-convex, so EM has no known global convergence guarant...

let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

microalloyed cast steels are a group of microalloyed steels in which reliable mechanical properties could be achieved by heat treatment. in this work, the heat treatment processes were carried out on the cast specimens as the step samples by different thicknesses and zr content. the results show that after homogenization, variations in thickness have no effect on the hardness. also, after hea...