We describe the basic Dolbeault cohomology algebra of canonical foliation on a class complex manifolds with torus symmetry group. This includes moment-angle manifolds, LVM- and LVMB-manifolds and, in most generality, maximal holomorphic action. also provide DGA model for ordinary algebra. The Hodge decomposition is proved by reducing to transversely Kähler (equivalently, polytopal) case using f...

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.

This research suggests a new type of inte1,ligent system based on new approaches to generation and selection of family of fuzzy logics. It is based on new generalizedl strategy of designing of fuzzy intelligent systems. Family of fuzzy logics can be generated by T-norms axiomatic system to choose the logic, that is the most suitable to expert way of thinking. Then the selected fuzzy logic is te...

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

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...

To any cleft Hopf Galois object, i.e., any algebra H obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle α, we attach two “universal algebras” AH and U α H . The algebra A α H is obtained by twisting the multiplication of H with the most general two-cocycle σ formally cohomologous to α. The cocycle σ takes values in the field of rational functions on H. By construct...