We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle. We find the suffi...

Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter–antimatter symmetry and some new ways to understand the baryo–genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the ...

Little work has been completed which addresses the logical composition and use of ternary relationships in entity-relationship modeling. Many modeling notations and most CASE tools do not allow for ternary relationships. Alternative methods and substitutes for ternary relationship structures do not necessarily reflect the original logic, semantics or constraints of a given situation. Furthermor...

Copper, cadmium, and phthalic acid (H2Lp) adsorption by ferrihydrite was examined for binary and ternary systems. In binary systems adsorption was well reproduced using the diffuse layer model (DLM), and H2Lp adsorption was analogous to that of inorganic diprotic acids in terms of the relationship between the adsorption constants and acidity constants. In ternary systems H2Lp caused both the en...

We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern xyzxzyx. In fact, we • characterize all the (two-way) infinite ternary square-free words avoiding letter pattern xyzxzyx • characterize the lexicographically least (one-way) infinite ternary square-free w...

A cyclotomic polynomial Φn(x) is said to be ternary if n = pqr with p, q and r distinct odd prime factors. Ternary cyclotomic polynomials are the simplest ones for which the behaviour of the coefficients is not completely understood. Eli Leher showed in 2007 that neighboring ternary cyclotomic coefficients differ by at most four. We show that, in fact, they differ by at most one. Consequently, ...

In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties. In particular we also investigate the maximal ideals of the ternary semiring Z0 .

With the larger penetration of variable renewable energy resources, the role of energy storage in the power system is becoming increasingly important. The flexibility of operation of hydro and pumped-storage power plants and the variety of ancillary services that they provide to the grid enable better utilization of variable renewable resources and more efficient and reliable operation of the e...

|We introduce the notions of fuzzy ternary subsemiring, fuzzy ideal and quasi-ideal in ternary semirings and study some properties of these two ideals. We also study the properties of fuzzy ideal and fuzzy quasi-ideal of ternary semirings.

For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called “proper”. It is known that the Boolean semiring, the semiring of natural numbers, the ring of integers, all finite commutative positively ordered semirings and all fields are proper. The semiring S is Noetherian...