Certain multidimensional integral transformations (I)

Certain Nonlinear Transformations

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).

Multidimensional generalized fuzzy integral

In this paper, we study multidimensional integrals. We introduce a generalized fuzzy integral and we present a Fubini-like theorem for this generalized fuzzy integral. As this research was partly motivated by the definition of citation indices, we also describe how such multidimensional integrals can be used to define such indices. © 2008 Elsevier B.V. All rights reserved.

Univalence of Certain Integral Operators

We study some integral operators and determine conditions for the univalence of these integral operators.

On Certain Integral Tensor Categories and Integral Tqfts

We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over rings of algebra integers. We show how to obtain TQFTs defined over algebra integers from these categories.