On Certain Weak Phase Transformations in Multilattices

On certain weak phase transformations in multilattices

This paper is dedicated to the memory of Clifford Truesdell, to whom I acknowledge my debt and gratitude. I present some recent results of mine on thermomechanics of crystalline solids, a research on which I began working during my stay at The Johns Hopkins University, 1977–1979. Then, in the last section, I mention some unusual merits of Truesdell, which I experienced in my scientific career a...

On certain semigroups of transformations that preserve double direction equivalence

Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E}It is known that TE(X) is a subsemigroup of TX. In this paper, we discussthe Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE(X).

Homomorphism Weak amenability of certain Banach algebras

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

Congruence Relations on Multilattices

On Certain Groups of Birational Contact Transformations*