Related papers: Split octonions and Maxwell equations
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
There is a growing interest in the logical possibility that exceptional mathematical structures (exceptional Lie and superLie algebras, the exceptional Jordan algebra, etc.) could be linked to an ultimate "exceptional" formulation for a…
Electromagnetic splittings for mesons and baryons are calculated in a formalism where the constituent quarks are considered as dressed quasiparticles. The electromagnetic interaction, which contains coulomb, contact, and hyperfine terms, is…
In this paper, we present a formula describing the formation and decay of shock wave type solutions in some special cases.
These lecture notes for the course APM 351 at the University of Toronto are aimed at mathematicians and physicists alike. It is not meant as an introductory course to PDEs, but rather gives an overview of how to view and solve differential…
We solve the difference equation with linear coefficients by the Momentenansatz to obtain explicit formulas for orthogonal polynomials.
We present in this work the hamiltonian formulation of an octonionic extension for the Korteweg-de Vries equation. The formulation takes into account the non commmutativity and non associativity of the implicit algebra which defines the…
This is a complete classification of the complex forms of quaternionic symmetric spaces
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
We derive closed formulas for the number of $k$-coloured partitions and the number of plane partitions of $n$ in terms of the Bell polynomials.
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
In this note, the octonion multiplication table is recovered from a regular tesselation of the "equilateral" two dimensional torus by seven hexagons, also known as Heawood's map.
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We define a special matrix multiplication among a special subset of $2N\x 2N$ matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
Isospin splittings in baryons with two heavy quarks and a $u$ or $d$ quark are calculated using simple methods proposed previously by the authors. The results are $M(\Xi_{cc}^{++})-M(\Xi_{cc}^+) = 1.41 \pm 0.12^{+0.76}$ MeV, $M(\Xi_{bb}^0)…
A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a…