The algebraic hyperstructure of elementary particles in physical theory

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Algebraic hyperstructure theory has a multiplicity of applications to other disciplines. The main purpose of this paper is to provide examples of hyperstructures associated with elementary particles in physical theory.Comment: 13 page

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Approximate Hamiltonian Symmetry Groups and Recursion Operators for Perturbed Evolution Equations

The method of approximate transformation groups, which was proposed b

The Perspective of Creativity in the Process of Learning Mathematics

Mathematical creativity is often considered as a mysterious phenomenon. Most mathematicians seem to be not interested in analyzing their own thinking processes and do not describe how they work or conceive their theories. One of the goals of this paper, which is based on research findings from contemporary literature, presents some definitions and characteristics of mathematical creativity and also describes and analyzes mathematicians’ thinking processes during creating mathematics. For this purpose, a four-stage model is considered consisting of: preparation, incubation, illumination and verification. Referring to literature, it is evident that there is not a specific conventional definition of mathematical creativity. According to some of definitions, a creative act in mathematics could consist of: creating a new fruitful mathematical concept; discovering an unknown relation; and reorganizing the structure of a mathematical theory. The challenges in the identification and development of mathematical creativity are due to the large variety in definitions and characteristics of mathematical creativity. Understanding, intuition, insight and generalization are some of moving powers of mathematical creativity. Fallibility is one of the characteristics of creative mathematical activities which should be appreciated since this existing chance of fallibility could lead to major success achievements of human. Hence, considering all above mentioned, learning-teaching mathematics should be so that it provides environment that fosters ability to make connections among concepts and processes and also provides opportunities to generalize