We have encapsulated the concept of matrix multiplication into a system of cubic equations. We discuss the properties of this system and the symmetry group of the set of solutions. Using solutions of these equations, we propose new algorithms for matrix multiplication, with explicit inequalities that bound the error. Also we calculate exactly the “hidden coefficient” in the Big-Oh notation for ...

The electromagnetic field inside a cubic cavity filled up with a linear magnetodielectric medium and in the presence of external charges is quantized by modelling the magnetodielectric medium with two independent quantum fields. Electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. Maxwell and constitu...

Starting from the Maxwell’s equations and without resort to the paraxial approximation, we derive equations describing stationary (1+1)-dimensional beams propagating at an arbitrary direction in an optical crystal with cubic symmetry and purely quadratic (χ) nonlinearity. The equations are derived separately for beams with the TE and TM polarizations. In both cases, they contain χ and cubic (χ)...

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the to...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

Ab initio calculations at 0 K have been used to predict the effect of nickel on the phase stability of the body-centred-cubic (bcc), face-centred-cubic (fcc) and hexagonal-close-packed (hcp) phases of iron. We have calculated the relative stability of hcp-Fe in the ferromagnetic and two antiferromagnetic structures (afmI and afmII) and find the afmII structure to be the more stable at low press...