Quaternionic polynomials are generated by quaternionic variables and the quaternionic product. This paper proposes the generating ideal of quaternionic polynomials in tensor algebra, finds the Gröbner base of the ideal in the case of pure imaginary quaternionic variables, and describes the normal forms of such quaternionic polynomials explicitly.

Quaternionic vector mKDV equations are derived from the Cartan structure equation in the symmetric space n =Sp(n+ 1)/Sp(1)×Sp(n). The derivation of the soliton hierarchy utilizes a moving parallel frame and a Cartan connection 1-form ω related to the Cartan geometry on n modelled on (spn+1, sp1 × spn). The integrability structure is shown to be geometrically encoded by a Poisson– Nijenhuis stru...

The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n− 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be the...

The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n − 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be th...

In this paper, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. Due to quaternions noncommutativity, two quaternionic extensions are presented: the right-multiplication quaternionic OMP, that can be used to process right-multiplication linear combinations of quaternion...

Let L2(R,H) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ∈L2(R,H). We consider perturbation problems wavelet frame {Φm,n,a0,b0,m,n∈Z} about translation parameter b0 and dilation a0. particular, we also research stability irregular {SmΦ(Smx−nb),m,n∈Z} for sampling.

We define a quaternionic extension of the Szegedy walk on a graph and study its right spectral properties. The condition for the transition matrix of the quaternionic Szegedy walk on a graph to be quaternionic unitary is given. In order to derive the spectral mapping theorem for the quaternionic Szegedy walk, we derive a quaternionic extension of the determinant expression of the second weighte...

We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternio...

A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal deformations sending the standard flat torsion-free quaternionic contac...

In this article, we examine the relationship between Darboux frames along parameter curves and frame of base curve ruled surface. We derive equations quaternionic shape operators, which can rotate tangent vectors around normal vector, find corresponding rotation matrices. Using these Gauss curvature mean explore how properties are found by use Frenet instead generator vectors. provide illustrat...