We briefly review and illustrate our procedure to ‘decouple’ by transformation of generators: either a Hopf algebra H from a Hmodule algebra A1 in their cross-product A1>⊳H; or two (or more) H-module algebras A1,A2. These transformations are based on the existence of an algebra map A1>⊳H → A1. Preprint 02-64 Dip. Matematica e Applicazioni, Università di Napoli DSF/29-2002 ∗Contribution to the P...

In cite{beh}, the authors claimed by a counterexample that the cross product definition in cite{molo} is not correct and thus the proposed technique is false. In this note, we show that this assertion is ‎incorrect.

The fundamental group of a hyperbolic manifold acts on the limit set, giving rise to a cross-product C∗-algebra. We construct nontrivial K-cycles for the cross-product algebra, thereby extending some results of Connes and Sullivan to higher dimensions. We also show how the Patterson-Sullivan measure on the limit set can be interpreted as a center-valued KMS state.

This contribution describes a new approach for solving linear system of algebraic equations and differential equations using Laplace transform by the extended-cross product. It will be shown that a solution of a linear system of equations Ax=0 or Ax=b is equivalent to the extended cross-product if the projective extension of the Euclidean system and the principle of duality are used. Using the ...

The paper explores the application of Web 2.0 technologies to support product development efforts in a global, virtual and cross-functional setting. It analyses the dichotomy between the prevailing hierarchical structure of CAD/PLM/PDM systems and the principles of the Social Web under the light of the emerging product development trends. Further it introduces the concept of Engineering 2.0, in...

Serological cross-reactivity between the products of the H-2K and H-2D genes has been demonstrated by a design in which antibody was produced against determinants controlled by one locus (e .g . H-2K(k)), and then tested against the product of the opposite locus (e .g . H-2D(d)). A total of 13 out of 18 such test combinations exhibited H-2K-H-2D cross-reactivity. The presence or absence of cros...

Nowadays many companies develop and maintain families of systems, termed product lines (PL), rather than individual systems. Furthermore, due to increase in market competition and the dynamic nature of companies’ emergence, several PLs may exist under the same roof. These PLs may be independently developed taking into consideration different sets of products and requirements. Thus the developed...