A Smarandache system (Σ;R) is such a mathematical system with at leastone Smarandachely denied rule r in R such that it behaves in at least two different wayswithin the same set Σ, i.e., validated and invalided, or only invalided but in multiple dis-tinct ways. A map is a 2-cell decomposition of surface, which can be seen as a connectedgraphs in development from partition to per...

Two Divisibility Tests for Smarandache semigroups are given . Further, the notion of divisibility of elements in a semigroup is applied to characterize the Smarandache semigroups. Examples are provided for justification.

In this paper, we introduce special Smarandache curves according to Sabban frame on S and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results. Mathematics Subject Classification (2010): 53A04, 53C40.

In this paper we show that a commutative semisimple ring is always a Smarandache ring. We will also give a necessary and sufficient condition for group algebra to be a Smarandache ring. Examples are provided for justification.

Neutrosophy, the study of neutralities, is a new branch Philosophy that has applications in many different fields science. Inspired by idea Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) allowing partiality and indeterminacy to be included structures’ operations and/or axioms. The aim this paper combine concept Neutrosophy with hyperstructures theory. In regard, we introdu...

On a geometrical view, the conception of map geometries is introduced , which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surfaces. Some open problems related combinatorial maps with the Riemann geometry and Smarandache geometries are presented.

All kinds of things can be found among integer sequences, including the weird and nonsensical. Enter Smarandache sequences (S. sequences, for short), which are integer sequences due to Florentin Smarandache and his disciples. Some S. sequence are related to number-theoretic topics. Others, at first glance (second, third, ...) seem downright silly. An example is the progressive concatenation of ...

A Smarandache multi-space is a union of n spaces A 1 , A 2 , · · · , A n with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric space is introduced. Some characteristics of a multi-metric space are obtained and Banach's fixed-point theorem is generalized in this paper.