This paper presents a new approach of constructing special ruled surfaces and aims to study their developability minimalist conditions. Our concept opens opportunities for application in engineering, surface modeling, architectural design. The principle our is introduce the original definitions Smarandache according Darboux frame curve lying on an arbitrary regular <math xmlns="http://www.w3.or...

A Smarandache multi-space is a union of n spaces A1, A2, · · · , An with some additional conditions holding. Combining Smarandache multispaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. Some characteristics of a multi-vector space are obtained in this paper.

This function generalizes many particular functions. For f( k) = k! one gets the Smarandache function, while for f(k) = k(k: 1) one has the Pseudo-Smarandache function Z (see [1], [4-5]). In the above paper [3] we have defined also dual arithmetic functions as follows: Let 9 : N* -+ N* be a function having the property that for each n 2:: 1 there exists at least a k 2:: 1 such that g(k)ln. Let ...

Felice Russo _\/tcr()J7 7ecil17()/o!!:1' 110/\' '.-1 re~~CIl7() (-1(1) IW(1' In this note v.e report the results regarding ,he check of the third Smarandache conjecture on primes [1 J.[2] for P ~ 2 and 2 ~ k ~ 10, In the range analysed the conjecture is true, n \loreover. according to experimental data obtained. it seems likely that the conjecture is true for all primes and for all positi\'e va...

In this paper we analyze and study the Smarandache idempotents (S-idempotents) in the ring Zn and in the group ring ZnG of a finite group G over the finite ring Zn. We have shown the existance of Smarandache idempotents (S-idempotents) in the ring Zn when n = 2 p (or 3p), where p is a prime > 2 (or p a prime > 3). Also we have shown the existance of Smarandache idempotents (S-idempotents) in th...

The aim of this article is to propose a Java concurrent program for the Smarandache fimction based on the equation sept' ..... p:.) = max{s(p~' ), ... ,S(p:·)}. Some results concerning the theoretical complexity of this program are proposed. Fmally, the experimental results of the sequential and Java programs are given in order to demonstrate the efficiency of the conament implementation. 1. IN...

A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space ...