In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras. Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras. In the following we study the relation between module amenability, weak module amenability and module approximate amenability of Banach algebra. The notation of amenability of Banach algebras was introduced by B. Johnson in [7]. A Banach algebra A is amenable if every bounded derivation from A into any dual Banach A-bimodule is inner, equivalently if H(A; X) = 0 for any Banach A-bimodule X, where H(A; X) is the first Hochschild co-homology group of A with coefficient in X. Also, a Banach algebra A is weakly amenable if H(A; A) = 0. Bade, Curtis and Dales introduced the notion of weak amenability on Banach algebras in [4]. They considered this concept only for commutative Banach algebras. After that Johnson defined the weak amenability for arbitrary Banach algebras.

Let S be a semitopological semigroup. The wap- compact-ification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the Lmc- compactification of semigroup S is a universal semigroup compactification of S, which are denoted by Swap and SLmc respectively. In this paper, an internal construction of the wap-compactification of a semitopological semigroup is constructed as a space of z-filters. Also we obtain the cardinality of Swap and show that if Swap is the one point compactification then (SLmc - S) * SLmc is dense in SLmc - S.

In this paper, weakly supercyclicity and weakly hypercyclicity of composition operators on some Hilbert spaces of analytic functions, especially on some weighted Hardy spaces are investigated.

Decomposer functional equations were introduced by the author and have been completely solved on arbitrary groups. Their solutions are as decomposer functions and play important role regarding to decomposition (factorization) of groups by their two subsets. In this paper, we introduce an important class of strong decomposer functions, namely parter (or cyclic decomposer) functions. As some important applications of this topic, we characterize all periodic, coperiodic functions in arbitrary groups and give general solution of their functional equations: f (bx)=f (x), f (xb)=f (x), f (bx)=bf (x) and f (xb)=f (x) b. Moreover, we characterize all parter functions in arbitrary groups and completely solve the decomposer equation with the condition which its -range is a cyclic subgroup of G. Finally, we give some functional characterization for related projections and b-parts functions and also, we introduce some uniqueness conditions for b-parts of real numbers.

We will present an approach to deal with a problem of existence of (not) weakly invertible functions in various spaces of analytic functions in the unit ball and polydisk based on estimates for integral operators acting between functional classes of different dimensions.

In this paper, we have analyzed the effect of time periodic temperature modulation on convective stability in anisotropic porous cavity. The cavity is heated from below and cooled from above. A weakly non-linear stability analysis is done to find Nusselt number governing the heat transport. The infinitely small disturbances are expanded in terms of power series of amplitude of modulation. Analytically the nonautonomous Ginzburg- landau amplitude equation is obtained for the stationary mode of convection. The effects of various parameters like Vadasz number, mechanical and thermal anisotropic parameters, amplitude of oscillations, frequency of modulation and aspect ratio of the cavity on heat transport is studied and plotted graphically. It is observed that the heat transport can also be controlled by suitably adjusting the external and internal parameters of the system.

We show that every semi-artinian module which is contained in a direct sum of finitely presented modules in s [M], is weakly co-semisimple if and only if it is regular in s [M]. As a consequence, we observe that every semi-artinian ring is regular in the sense of von Neumann if and only if its simple modules are FP-injective.

This article is a continuation of E. Momtahan’s work in which he studied the literature via countable injectivity. Along this line, N0-Ikeda-Nakayama rings have been studied and among other things, new characterizations of basically disconnected and extremally disconnected spaces have been given. Furthermore we will observe that a boolean ring is N0-self-injective if and only if it is an N0-IN ring.