Related papers: On spherical harmonics possessing octahedral symme…
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…
In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature…
Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the…
In this paper, we determine the spherical functions of positive type on the inductive limit space of square complex matrices.
We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with Semi-Dihedral groups $SD_{8n}$. The dimensions of these symmetry classes of tensors are also computed.
We interpret an open orbit in a 32-dimensional representation space of Spin(9,1) x SL(2,R) as a substitute for the non-existent group of invertible 2x2 matrices over the octonions and study various natural homogeneous subspaces. The…
The recently established existence of spherical harmonic functions, $Y_\ell^{m}(\theta,\phi)$ for half-odd-integer values of $\ell$ and $m$, allows for the introduction into quantum chemistry of explicit electron spin-coordinates; i.e.…
In this paper we study the recurrence relations in the spin-weighted spheroidal harmonics (SWSHs) through super-symmetric quantum mechanics. We use the shape invariance property to solve the spin-weighted spheroidal wave equations. The…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We describe some classes of PDE that display hidden symmetry, with reduced equations having additional symmetry operators compared to the initial equations. Relations between the concepts of hidden and conditional symmetry, and between…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…
The 8 $\times$ 8 matrix representation of SO(8) Symmetry has been defined by using the direct product of Pauli matrices and Gamma matrices. These 8 $\times$ 8 matrices are being used to describe the rotations in SO(8) symmetry. The…
We find that, in presence of the Snyder geometry, the quantization of d isotropic harmonic oscillators can be solved exactly.
We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…
The influence of the orbital symmetry on the ellipticity of the high-order harmonics is investigated. It is found that the ellipticity maps have distinct shapes for the molecular orbital with different symmetry. Our analysis shows that the…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
We show that 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode, induces energy level splitting, and is equivalent to an external magnetic field…