The Sandor-Smarandache function, SS(n), is a recently introduced Smarandache-type arithmetic which involves binomial coefficients. It known that SS(n) does not possess many of the common properties classical functions theory numbers. Sandor gave expression when n ( ³ 3) an odd integer. found has simple form even and divisible by 3. In previous papers, some closed-form expressions have been deri...

In this paper three problems posed in [1J and concerning the Smarandache LeM sequence have been analysed. Introduction In [1] the Smarandache LCM . sequence is defined as the least common mUltiple (LCM) of (1,2,3, .,. ,n) : 1,2,6, 12,60,60,420,840,2520,2520,27720,27720,360360, 360360, 360360, 720720 ...... . In the same paper the following three problems are reported: 1. If a(n) is the n-th ter...

In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC-algebras, and then we determine the relationships between these hyper ideals. © 2011 Elsevier Ltd. All rights reserved.

A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a n-manifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equi...

A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This monograph concentrates on characterizing various multi-spaces including three parts altogether. The first part is on algebraic multi-spaces with st...

The study of primality for the Smarandache sequences represents a recent research direction on the Smarandache type notions. A few articles that were published recently deal with the primality of the direct and reverse Smarandache sequences. The primality of Smarandache symmetric sequences has not been studied yet. This article proposes some results concerning the non-primality of these symmetr...

In this paper some Smarandache conjectures and open questions will be analysed. The first three conjectures are related to prime numbers and formulated by F. Smarandache in [1].

By developing F. Smarandache thema on paradoxes in mathematics it is stated, firstly, ifin measurement (natural science) experiments the best solutions are found by using methods of modem data analysis theory, then some difficulties with the interpretation of the computation results are liable to occur; secondly, one is not capable to overcome these difficulties without a data analysis theory m...

A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a n-manifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equi...

The pair (GH , ·) is called a special loop if (G, ·) is a loop with an arbitrary subloop (H, ·) called its special subloop. A special loop (GH , ·) is called a second Smarandache Bol loop (S2ndBL) if and only if it obeys the second Smarandache Bol identity (xs · z)s = x(sz · s) for all x, z in G and s in H. The popularly known and well studied class of loops called Bol loops fall into this clas...