Class Of Binary Operations Research Articles

Generating quasi-t-subnorms on preordered sets via Adjunctions and Left Galois Connections

In this paper, we investigate several classes of binary operations within the preordered framework. First, we give the definition of quasi-t-subnorm on preordered sets. Subsequently, we research two classes of quasi-t-subnorms by means of Adjunctions and Left Galois Connections respectively. Meanwhile, we introduce new preorders differing from the inclusion order on powersets. Importantly, quasi-t-subnorms can be defined on powersets with preorders. Then we get a class of extensive binary operations via Adjunctions between preordered sets and the preordered sets consisting of powersets, which generalizes the previous results. The relationship between related binary operations is explored at last.

Binary operations for homotopy groups with coefficients

We define and study binary operations for homotopy groups with coefficients, and give conditions to prove that certain binary operations are the homomorphic image of the generalized Whitehead product. This allows carrying over properties of the generalized Whitehead product to these operations. We discuss two classes of binary operations, i.e., the Whitehead products and the torsion products. We also introduce a new class of operations called Ext operations and determine some of its properties. Then we compare the torsion product to the Whitehead product in a special case, and prove that the smash product of two Moore spaces has the homotopy type of a wedge of two Moore spaces.

Relation between neutral element and annihilator in absorption equation

The absorption identities in algebra give a relationship between two associative and commutative binary operators join and meet. We generalize these operators into a new class of binary operators and study their structures in the context of absorption equation and show that the study of absorption equation involving triangular norms, triangular conorms, uninorms and nullnorms in the literature are special cases of our study.

De Rham systems and the solution of a class of functional equations

The main objective of this paper is to solve the functional equation $$N(f_0 (x)) = f_1 (N(x))$$ with strong negationN as unknown function. From the solution of a system of functional equations studied by De Rham in 1956, we obtain the unique solution of our equation and, from a convenient dense set in [0, 1], a description of the key function is attained. As application, we present a class of binary operations on [0, 1] which is stable byN-duality if, and only if,N is the solution of the above equation.

Duality for a class of binary operations on [0, 1

Abstract In this paper we study a duality relation for pairs of a class of binary operations on [0, 1]. From the solution of a functional equation system solved by De Rham in 1956 we obtain several results. Finally by using a dense set in [0, 1] a description of the key function in this work is obtained.