As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to...
The proposed cyclic universes model based on the split division algebras accounts for the inflation, the Big Bang, gravity, dark energy, dark matter, the standard model, and the masses of all elementary particles. The...
In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2...
In this paper, for rings R, we introduce complex rings C(R), quaternion rings H(R), and octonion rings O(R), which are extension rings of R; R C(R) H(R) O(R). Our main purpose of this paper is to sho...
Supported by the National Natural Science Foundation of China(11171298);the Zhejiang Natural Science Foundation of China(Y6110425)
The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the ...
This work was supported by the NNSF of China(11071230),RFDP(20123402110068).
The octonions are distinguished in the M-theory in which Universe is the usual Minkowski space R4 times a G2 manifold of very small diameter with G2 being the automorphism group of the octonions.The multidimensional o...
Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. A...
Research supported by the NNSF (19631080);973 Project of China (1999075105);NSF of Guangdong (030497,020586);NSF of Guangzhou (232)
The three-line theorem on the octonions is obtained, which generalizes the result of J. Peetre and P. Sj?lin from the associative Clifford algebra to non-associative octonion algebra.