Eigenfunctions of total angular momentum for a charged vector field interacting with a magnetic monopole are constructed and their properties studied. In general, these eigenfunctions can be obtained by applying vector operators to the monopole spherical harmonics in a manner similar to that often used for the construction of the ordinary vector spherical harmonics. This construction fails for ...

Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in spherical harmonics, basis functions with global support. For various reasons, however, inclined orbits are favorable. These leave a “polar gap”: an antipoda...

The spherical harmonics Y l m form a basis of the vector space V (of dimensions 2l + 1) of the eigen functions of the Laplacian on the sphere, with eigen value λl = −l (l+ 1). Here we show the existence of an other basis Φj for V, where Φj(X) ≡ (X · Nj), the l power of the scalar product of the current point with a specific null vector Nj . This very simple formulation makes calculations very e...

background: in nuclear medicine application often it is required to use computational methods for evaluation of organ absorbed dose. monte carlo simulation and phantoms have been used in many works before. the shape, size and volume in organs are varied, and this variation will produce error in dose calculation if no correction is applied. materials and methods: a computational framework for co...

Boltzmann’s Equation describes a myriad of phenomena from gas and fluid flow to electrons in semiconductors and hence plays an essential role in todays physics. However, calculating a solution to this seven-dimensional partial differential equation is very difficult. The high dimensionality of the equation poses a problem for its solution as traversal mechanisms for these high dimensions are no...

The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic pieces, which also determines the irreducible pieces under the action of SO(m) × Sp(2n). In the second part of the paper, this decomposition is used to describe al...