In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

in this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.

Belief in God and belief in the science of evolution are not mutually exclusive concepts. Thousands of scientists who believe in God are able to separately study and teach evolution. As scientists and parents, we owe it to our children to ensure that public school science curricula teach the science of evolution and not promote a particular religious faith or belief system.

Cystic fibrosis (CF) is an inherited disease that primarily affects the lungs and the digestive system, however, it also affects a number of other organs and systems. More than 90% of mortality of  CF patients is due to lung complications.  Healthy lungs are important for a long life for people with CF, We will discuss two important topics for maintaining respiratory health. Chronic use of drug...

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.