Related papers: Quaternions in mathematical physics (1): Alphabeti…
This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract…
For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…
In this study, we introduce a new class of quaternions associated with the well-known modified third-order Jacobsthal numbers. There are many studies about the quaternions with special integer sequences and their generalizations. All of…
Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…
We present a unifying framework for understanding several different versions of the Hopf fibration, and use this framework to reconcile two methods of representing rotations of 3-space by unitary matrices--the mathematician's convention…
In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…
We introduce notions of bi-unitary, bi*-unitary and bi**-unitary harmonic numbers, along with their preliminary study.
This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…
This document is a pedagogical introduction to statistics for particle physics. Emphasis is placed on the terminology, concepts, and methods being used at the Large Hadron Collider. The document addresses both the statistical tests applied…
In this study, we introduce a new classes of quaternion numbers. We show that this new classes quaternion numbers include all of quaternion numbers such as Fibonacci, Lucas, Pell, Jacobsthal, Pell-Lucas, Jacobsthal-Lucas quaternions have…
In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary…
In light of a new experiment which claims an identification of tetraneutron [3], we discuss the results of experimental search of trineutron and tetraneutron in different nuclear reactions. A summary of theoretical studies for trineutron…
This paper gives a rather arbitrary choice of formulas for ($q$-)hypergeometric orthogonal polynomials which the author missed while consulting Chapters 9 and 14 in the book "Hypergeometric orthogonal polynomials and their $q$-analogues" by…
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
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…
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
In this paper I explore the set of quaternion algebras over field. Quaternion algebra E(C,-1,-1) is isomorphic to tensor product of complex field C and quaternion algebra H=E(R,-1,-1). Considered two sets of quaternion functions, which…
Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is…