This paper introduces a no vel quaternion{valued MLP{ type net w ork called the Quaternionic Spinor MLP (QSMLP). In con trast to another recently proposed Quaternionic MLP it uses spinors in its propagation function. This allows very eÆciently the processing of 3D vector data, whic his demonstrated by experiments. The QSMLP is pro ven to be a universal approximator and a learning algorithm for ...

We present a novel full-rate full-diversity orthogonal space-time block code for QPSK modulation and 4 transmit antennas based on quaternionic algebra. The code does not result in constellation expansion unlike other full-rate full-diversity codes in the literature. The quaternionic structure of the code is exploited to reduce the complexity of maximum likelihood (ML) coherent decoding from a s...

The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by inhomogeneous Dirac and Schrödinger equations. Mixing of hyper-complex components of wavefunctions occurs through their interaction with potentials dissipative into ...

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...

Colour image representation using real quaternions has shown to be very useful for linear and morphological colour filtering. This paper deals with the extension of first derivatives-based structure tensor for various quaternionic colour image representations. Classical corner and edge features are obtained from eigenvalues of the quaternionic colour structure tensors. We study the properties o...

By considering the three-dimensional incompressible Euler equations, a 4-vector ζ is constructed out of a combination of scalar and vector products of the vorticity ω and the vortex stretching vector ω · ∇u = Sω. The evolution equation for ζ can then be cast naturally into a quaternionic Riccati equation. This is easily transformed into a quaternionic zero-eigenvalue Schrödinger equation whose ...

A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in [11]. Several results of the theory recall the classical complex analysis, whereas other results reflect the peculiarity of the quaternionic structure. The recent [1] identified a larger class of domains, on which the study of regular functions is most natural and not limited to t...

In this paper, we obtain analogues of Jørgensen’s inequality for non-elementary groups of isometries of quaternionic hyperbolic n-space generated by two elements, one of which is loxodromic. Our result gives some improvement over earlier results of Kim [10] and Markham [15]. These results also apply to complex hyperbolic space and give improvements on results of Jiang, Kamiya and Parker [7]. As...

The aim of this paper is to present the basics of a mathematical theory of a new Fourier transform of colour images from the point of view of Clifford analysis. Quaternionic-valued signals have long been used as a model for colour images and Fourier transforms for such signals have been studied in [3], [?], [6], [?], [7]. In this paper we use a version of the Fourier kernel markedly from those ...

The classical matrix groups are of fundamental importance in many parts of geometry and algebra. Some of them, like Sp.n/, are most conceptually defined as groups of quaternionic matrices. But, the quaternions not being commutative, we must reconsider some aspects of linear algebra. In particular, it is not clear how to define the determinant of a quaternionic matrix. Over the years, many peopl...