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 ...

A simple path cover of a graph G is a collection ψ of paths in G such that every edge of G is in exactly one path in ψ and any two paths in ψ have at most one vertex in common. More generally, for any integer k ≥ 1, a Smarandache path k-cover of a graph G is a collection ψ of paths in G such that each edge of G is in at least one path of ψ and two paths of ψ have at most k vertices in common. T...

in this note we review a simple criterion, due to ekedahl, for superspecial curves defined over finite fields.using this we generalize and give some simple proofs for some well-known superspecial curves.

might hold (the authors of [6] claim that (4) has been tested by Ibstedt in the range x S 5 . 106 in [4J. Although I have read [4J carefully, I found no trace of the aforementioned computation!). In this note, we show that -I x is indeed the correct order of magnitude of ogx A(x). For any positive real number x let 7I"(x) be the number of prime numbers less then or equal to x, B(x) = xA(x) = 2:...

The aim of this paper is to present a study about recent progressions in the neutrosophic algebraic structures. Also, it lists most interesting open questions structures such as rings, refined and n-refined rings. On other hand, on rings complex numbers has been presented, with many Smarandache-Kandasamy problems properties these numbers, especially ones.

Given a positive integer n, let P(n) denote the largest prime factor of nand S(n) denote the smallest integer m such that n divides m! This paper extends earlier work [1] on the average value of the Smarandache function S(n) and is based on a recent asymptotic result [2]: (W J I{n ~ N:P(n) < S(n)}j = 01 • I ~ln(N)J for any positive integer j due to Ford. We first prove: Theorem 1.

Kashihara[2] defined the Pseudo-Smarandache function Z by m(m+l) } Properties of this function have been studied in [1], [2] etc. 1. By answering a question by C. Ashbacher, Maohua Le proved that S(Z(n»-Z(S(n» changes signs infmitely often. Put d s,z (n) = I S(Z(n»-Z(S(s» I We will prove first that lim inf d s,z (n) ~ 1 (1) n-oo and (2) n-+oo p(p+l) Indeed, let n = , where p is an odd prime. Th...

Florentin Smarandache and Ştefan Vlăduţescu the authors and coordinators of the book “Communication Neutrosophic Routes”, published by Education Publishing, Ohio, USA, on 2014, are two remarcable professors, with many researches in neutrosophical, communication, mathematic, literature domains, social sciences. Logic is a fundamental component of advanced computer classes. Reference is constantl...