In this paper we verify two conjectures concerning extents of Smarandache factor partitions.

In this paper we completely determinate all the Smarandache friendly natural number pairs.

In this paper, under the Smarandache algorithm ,we construct a class of commutative multiplicative semigroups.

A Smarandache multi-space is a union of n spaces A 1 , A 2 , · · · , A n with some additional conditions holding. Combining classical of a group with Smarandache multi-spaces, the conception of a multi-group space is introduced in this paper, which is a generalization of the classical algebraic structures, such as the group, filed, body, · · ·, etc.. Similar to groups, some characteristics of a...

Received March 13, 2007 Abstract For any positive integer n, the Smarandache LCM dual function SL∗(n) is defined as the greatest positive integer k such that [1, 2, · · · , k] divides n. The main purpose of this paper is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL∗(n) and the mean value distribution property o...

Based on the concept of neutrosophic linguistic numbers (NLNs) in symbolic neutrosophic theory presented by Smarandache in 2015, the paper firstly proposes basic operational laws of NLNs and the expected value of a NLN to rank NLNs. Then, we propose the NLN weighted arithmetic average (NLNWAA) and NLN weighted geometric average (NLNWGA) operators and discuss their properties. Further, we establ...

A combinatorial map is a connected topological graph cellularly embeddedin a surface. This monograph concentrates on the automorphism groupof a map, which is related to the automorphism groups of a Klein surfaceand a Smarandache manifold, also applied to the enumeration of unrootedmaps on orientable and non-orientable surfaces. A number of results for theautomorphism groups ...

In this paper we prove Smarandache cube-partial-digital subsequence