A new higher-order method of moment (MoM) technique is presented for volume-surface integral equations (VSIE) for electromagnetic modeling of composite metallic and dielectric objects. The higher-order MoM scheme comprises higher-order hierarchical Legendre basis functions and an accurate representation of the object by higher-order curvilinear elements. Due to the orthogonal nature of the basi...

I perform the factorization(s) of the Wheeler-DeWitt equation for the FRW minisuperspace universes of arbitrary Hartle-Hawking factor ordering introducing by this means a new, Darboux-type, free parameter in “quantum” cosmology. This parameter can be thought of as giving the time scale of a force due to a cosmological field. Mathematically speaking, the parameter is a Riccati integration consta...

in a domain Ω ⊂ IR accompanied with homogeneous Neumann boundary conditions and an initial condition. Equation (1.1) is useful in image processing for selective smoothing of images and shapes. Numerical experiments in processing of 2D and 3D images are presented in [10]. Here, we present analysis of a special semidiscrete scheme for solving (1.1). Equation (1.1) is a degenerate parabolic equati...

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F . This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, ...

This paper studies a two-variable zeta function ZK(w, s) attached to an algebraic number field K, introduced by van der Geer and Schoof [11], which is based on an analogue of the RiemannRoch theorem for number fields using Arakelov divisors. When w = 1 this function becomes the completed Dedekind zeta function ζ̂K(s) of the field K. The function is an meromorphic function of two complex variable...

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. T...