Teaching Theory of Programming: Methodology and Basic Notions

Basic notions and properties of ordered semihyperrings

In this paper, we introduce the concept of semihyperring $(R,+,cdot)$ together with a suitable partial order $le$. Moreover, we introduce and study hyperideals in ordered semihyperrings. Simple ordered semihyperrings are defined and its characterizations are obtained. Finally, we study some properties of quasi-simple and $B$-simple ordered semihyperrings.

Topology in Fuzzy Class Theory: Basic Notions

In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fu...

Superradiance Theory and X-ray Lasers : Basic Notions and Models

The essential characterist ics of superradiance are described by using two simple models, the Dicke model and the semi-classical model. The main extensions to r e a l i s t i c si tuations are also presented and the possibil ity of superradiance theory being a s tar t ing point of a general approach of X-ray coherent emission is discussed. Coherent light production generally originates from sti...

History and Basic Notions

This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the cent...

THEORY OF FINANCIAL RISK: Basic notions in probability