The goal of this paper is to classify linear operators with octonionic coefficients and octonionic variables. While building up to the octonions we also classify linear operators over the quaternions and show how to relate the linear operators over the quaternions and octonions to matrices. We also construct a basis...
This paper is included in the Proceedings, Part 1, of the International Conference on Computational Science 2009 (ICCS 2009) held in Baton Rouge, LA, USA, May 25-27, 2009.
We present a methodology for creating a simulated foam microstructure for use in forward simulations of wave equations to quantitatively analyze the expected scattering phenomenon primarily responsible for the attenuation of interrogating signals in Sprayed-On Foam Insulation (SOFI). Our approach builds off of the popular use of Voronoi Tessalations for...
Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our...
A mixed initial and boundary value problem is considered for
a partial differential equation of the form Muₜ(x, t)+Lu(x, t)=0,
where M and L are elliptic differential operators of orders 2 m
and 2l, respectively, with m ≤ l. The existence and uniqueness
of a strong solution of this equation...
We are concerned here with well-posed problems for the partial differential equation uₜ(x, t) + yMuₜ(x, t) + Lu(x, t) = f(x, t) containing the elliptic differential operator M of order 2m and the differential operator L of order ≤2m. Hilbert space methods are used to formulate and solve an...
An existence theory is developed for a semilinear evolution equation in Banach space which is modeled on boundary value problems for partial differential equations of Sobolev type. The operators are assumed to be measurable and to satisfy coercive estimates which are not necessarily uniform in their time dependence, and to...