Clifford's geometric algebra has enjoyed phenomenal development over the last 60 years by mathematicians, theoretical physicists, engineers, and computer scientists in robotics, artificial intelligence data analysis, introducing a myriad of different often confusing notations. The Euclidean 3-space, natural generalization both well-known Gibbs-Heaviside vector Hamilton's quaternions, is used he...

In this note, we describe the Gel’fand-Tsetlin procedure for the construction of an orthogonal basis in spaces of Hermitean monogenic polynomials of a fixed bidegree. The algorithm is based on the Cauchy-Kowalewski extension theorem and the Fischer decomposition in Hermitean Clifford analysis.

In this contribution we construct an orthogonal basis of Hermitean monogenic polynomials for the specific case of two complex variables. The approach combines group representation theory, see [5], with a Fischer decomposition for the kernels of each of the considered Dirac operators, see [4], and a Cauchy-Kovalevskaya extension principle, see [3].

THE CAUCHY DOUBLE ALTERNANT AND DIVIDED DIFFERENCES WENCHANG CHU Dedicated to my friend Pier Vittorio Ceccherini for his 65th birthday Abstract. As an extension of Cauchy’s double alternant, a general determinant evaluation formula is established. Several interesting determinant identities are derived as consequences by means of divided differences.

We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the strongly dispersive ones with focus on the “KdV-KdV” system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical K...

Let h ∼ i be arbitrary. It is well known that k ≡ ∅. We show that there exists a Riemannian, finite, everywhere regular and continuous pseudo-Cauchy, canonically linear matrix. Recently, there has been much interest in the extension of subrings. Therefore here, splitting is trivially a concern.

This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace’s equation in domains with C boundary. It is an extension of an earlier result of [19] for domains of class C. Our estimate is established by using a global Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Further...

The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying ...

We consider QED in a constant axial vector background. Lorentz invariance violation(LIV) occurs through radiative corrections. A detailed study of the phenomenology of the model is carried out, clarifying important issues related to the various regularizations employed . In this context, the physical meaning of the cutoffs induced by LIV is emphasized. Finally, finite temperature radiative corr...