In this paper, we present a new definition, referred to as the Francois sequence, related to
the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo …

This study considers high-dimensional neural networks based on hypercomplex numbers
that form a four-dimensional algebra over the field of real numbers, such as quaternion …

This paper aims to establish a framework for extreme learning machines (ELMs) on general
hypercomplex algebras. Hypercomplex neural networks are machine learning models that …

In this paper, the real, complex octonion algebra and their properties are defined. The
electromagnetic and gravito-electromagnetic equations with monopoles in terms of S and S …

In this paper, after presenting the biquaternion formalism, a new formulation is proposed for
the massive gravi-electromagnetism with monopole terms. By combining the generalized …

Extending the biquaternionic generalization of the Maxwell type equations of compressible
fluids, an effort has been introduced for the reformulation of analogous multifluid plasma …

In this paper, the conic sedenionic formulation is presented for the unification of generalized
field equations of dyons (electromagnetic theory) and gravito-dyons (linear gravity) …

The paper aims to adopt the complex quaternion and octonion to formulate the field
equations for electromagnetic and gravitational fields. Applying the octonionic …

We present a generalization of the equations of hydrodynamics based on the
noncommutative algebra of space-time sedeons. It is shown that for vortex-less flow the …

We develop a quaternionic electrodynamics and show that it naturally supports the
existence of magnetic monopoles. We obtained the field equations, the continuity equation …