let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

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 studythe...

Using the helicity amplitude technique, we derive differential decay widths and angular distributions for cascade $D\to K_{1}(1270,1400)\ell^+\nu_{\ell}\to (K\pi\pi)\ell^+\nu_{\ell} (\ell=e,\mu)$, in which electron muon mass is explicitly included. a set of phenomenological results K_1$ form factors, calculate partial branching fractions $D^0\to K_1^-\ell^+\nu_{\ell}$ $D^+\to K_1^0\ell^+\nu_{\e...

electrosensory lateral line lobe (ELL) of mormyrid electric fish. The mormyrid ELL is one member of a group of cerebellum-like sensory structures found in fish, amphibians and mammals (Fig. 1). These structures possess a molecular layer, an underlying sensory input layer and an intervening layer of large cells. The large cells have apical dendrites that receive input from parallel fibers, and b...

The ``Brownian bees'' model describes a system of $N$-independent branching Brownian particles. At each event the particle farthest from origin is removed so that number particles remains constant at all times. Berestycki et al. [arXiv:2006.06486] proved $N\ensuremath{\rightarrow}\ensuremath{\infty}$ coarse-grained spatial density this lives in spherically symmetric domain and described by solu...