By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, Kloop, Bruck-loop or Kikkawa-loop if and only if its Smarandache automorphism group is trivial and the loop is itself is a Smarandache; AIPL, CI...

In this paper a question posed in [1 J and concerning the Smarandache friendly prime pairs is analysed. Introduction In [1] the Smarandache friendly prime pairs are defmed as those prime pairs (p,q) such that:

These Smarandache spaces are right theories for objectives by logic. However, the mathematical combinatorics is a combinatorial theory for branches in classical mathematics motivated by a combinatorial speculation. Both of them are unifying theories for sciences and contribute more and more to mathematics in the 21st century. In this paper, I introduce these two subjects and mainly concentrate ...

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 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...

Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive use of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement of the artistic sphere through non-artistic elements. But especially the counter-time, counter-sense c...

The main purpose of this paper is using the elementary methods to study the properties of the function E(n, r) and O(n, r), and get two calculating formulaes for them.

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...