In this paper a problem posed in [1J and concerning the number of primes in the Smarandache Unary sequence is analysed. Introduction In [1] the Smarandache Unary sequence is defined as the sequence obtained concatenating Pn digits of 1, where Pn is the n-th prime number: 11,111,11111,1111111,11111111111,1111111111111,11111111111111111, ......... . In the same paper the following open question i...

SMARANDACHE TERMS AND FACTOR PARTITIONS (Amarnath Murthy ,S.E. (E & T), Well'Logging Services,Oil And Natural Gas Corporation Ltd. ,Sabarmati, Ahmedbad, India380005.) ABSTRACT: In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP) , as follows: Let U1, U2 , U3 , ... Ur be a set of r natural numbers and P1, P2, P3 , ... Pr be arbitrarily chosen distinct primes then F(u1 , U2 , U3 , ... u ...

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 nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equil...

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 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.

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.

This paper surveys the applications of Smarandache’s notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. In fact, many problems discussed in these papers are generalized in this paper. Topics covered in this paper include: (1)What is a Smarandache System? (2)Vertex-Edge Labeled Graphs with Applications: (i)Smarandachely k-constrained labeling of a grap...