The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops) that are not universal have been found to be isotopic invariant relative to a special type of isotopism or the other. Presently, there are two outstanding open...

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...

The family of Metallic Means comprises every quadratic irrational number that is the positive solution of algebraic equations of the types r--nx-l =0 and r--x-n =0 , where n is a natural number. The most prominent member of this family is the Golden Mean, then it comes the Silver Mean, the Bronze Mean, the NIckel Mean, the Copper Mean, etc. All of them are closely related to quasi-periodic dyna...

Every quasigroup (L, ·) belongs to a set of 6 quasigroups, called parastrophes denoted by (L, πi), i ∈ {1, 2, 3, 4, 5, 6}. It is shown that (L, πi) is a Smarandache quasigroup with associative subquasigroup (S, πi) ∀ i ∈ {1, 2, 3, 4, 5, 6} if and only if for any of some four j ∈ {1, 2, 3, 4, 5, 6}, (S, πj) is an isotope of (S, πi) or (S, πk) for one k ∈ {1, 2, 3, 4, 5, 6} such that i 6= j 6= k....

Different from the system in classical mathematics, a Smarandache system is a contradictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple distinct ways. Such systems exist extensively in the world, particularly, in our daily life. In this paper, we discuss such a kind of Smarandache system...

The spatial prediction of land cover at the field scale in winter appears useful for the issue of bare soils reduction in agricultural intensive regions. High variability of the factors that motivate the land cover changes between each winter involves integration of uncertainty in the modelling process. Fusion process with Dempster-Shafer Theory (DST) presents some limits in generating errors i...

The aim of this article is to establish the complexity order of the Erdos function average. This will be studied based on some recent results about the Smarandache function.

The objective of this paper is to present an approach for target tracking, which incorporates the advanced concept of generalized data (kinematics and attribute) association to improve track maintenance performance in complicated situations (closely spaced targets), when kinematics data are insufficient for correct decision making. It uses Global Nearest Neighbour-like approach and Munkres algo...

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...

A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This monograph concentrates on characterizing various multi-spaces including three parts altogether. The first part is on algebraic multi-spaces with st...