The cubic spherical optimization problems

The cubic spherical optimization problems

In this paper, the cubic spherical optimization problems, including the cubic one-spherical/two-spherical/three-spherical optimization problems, are discussed. We first show that the two-spherical optimization problem is a special case of the three-spherical optimization problem. Then we show that the one-spherical optimization problem and the two-spherical optimization problem have the same op...

Spherical Harmonic Decomposition on a Cubic Grid

A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to the treatment of boundary conditions imposed at radii larger than the size of the grid, following Abrahams, Rezzola, Rupright et al. [1]. In the method describ...

Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems

In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...

Template-assisted assembly of the functionalized cubic and spherical microparticles.

The patterned template-assisted assembly of the cubic microparticles driven by the competing capillary, Columbic, and van der Waals forces had been studied in comparison with the traditional spherical colloidal microparticles. We observed that the spherical and cubic microparticles assembled with different probability in the channels of the hydrophobic-hydrophilic patterned substrates due to di...

Synthesis and Piezoelectric Response of Cubic and Spherical LiNbO3 Nanocrystals