We express Maxwell’s equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equati...

We have investigated new Pauli Fibonacci and Lucas quaternions by taking the components of these as Gaussian numbers, respectively. calculated some basic identities for quaternions. Later, generating functions Binet formulas are obtained Furthermore, Honsberger’s identity, Catalan’s Cassini’s been given

A quick glance through the Mathematics section of the 2004 Stanford University Bulletin reveals five courses devoted to complex analysis, but no courses even mentioning quaternions. How is it that complex analysis, a subject that has suffered through hundreds of years of skepticism and distrust, came to be so widely accepted today, while quaternionic analysis, a modern subject immediately accep...

The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. This effect is equivalent to replacing ordinary products in the effective theory by the deformed star product. An immediate consequence of this is that all fields get complexified. The only possible noncommutative Yang-Mills theory is the one with U(N) ...

In this paper Fibonacci sequences of quaternions are introduced, generalizing Fibonacci sequences over commutative rings, and properties of such sequences are investigated. In particular we are concerned with two kinds of Fibonacci sequences of generalized quaternions over finite fields Fp, with p an odd prime, and their periods.

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's real quaternions. also characterize generalized identities which hold quaternions, and more generally, any division algebra .