General ω-hyperstructures and certain applications of those

The aim of this paper is to investigate general hyperstructures construction of which is based on ideas of A. D. Nezhad and R. S. Hashemi. Concept of general hyperstructures considered by the above mentioned authors is generalized on the case of hyperstructures with hyperoperations of countable arity. Speci cations of treated concepts to examples from various elds of the mathematical sturctures theory are also included.

Algebraic Spaces and Set Decompositions

The contribution is growing up from certain parts of scientific work by professor Boruvka in several ways. Main focus is on the decomposition theory, especially algebraized decompositions of groups. Professor Boruvka in his excellent and well-known book [3] has developed the decomposition (partition) theory, where the fundamental role belongs to so called generating decompositions. Furthermore, the contribution is also devoted to hypergroups, to algebraic spaces called also quasi-automata or automata without outputs. There is attempt to develop more fresh view point on this topic

Term Functions and Fundamental Relation of Fuzzy Hyperalgebras

We introduce and study term functions over fuzzy hyperalgebras. We start from this idea that the set of nonzero fuzzy subsets of a fuzzy hyperalgebra can be organized naturally as a universal algebra, and constructing the term functions over this algebra. We present the form of generated subfuzzy hyperalgebra of a given fuzzy hyperalgebra as a generalization of universal algebras and multialgebras. Finally, we characterize the form of the fundamental relation of a fuzzy hyperalgebra

Series of Semihypergroups of Time-Varying Articial Neurons and Related Hyperstructures

Detailed analysis of the function of multilayer perceptron (MLP) and its neurons together with the use of time-varying neurons allowed the authors to find an analogy with the use of structures of linear differential operators. This procedure allowed the construction of a group and a hypergroup of articial neurons. In this article, focusing on semihyperstructures and using the above described procedure, the authors bring new insights into structures and hyperstructures of articial neurons and their possible symmetric relations

SMARANDACHE LOOPS

The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absent. This is in marked contrast with group theory where books are abundantly available for all levels: as graduate texts and as advanced research books