| Perfectly Matched Layers (PML) are derived for cylindrical and spherical FDTD grids. The formulation relies on the complex coordinate stretching approach. 2D cylindrical and 3D spherical staggered-grid FDTD codes are written based on the time-domain versions of the equations. Numerical simulations validate the formulation by showing very good agreement between the PML-FDTD results and the fre...

A new type of 3D-QSAR descriptors is introduced. For each molecule under consideration an internal coordinate system is defined relative to molecular points, such as positions of atoms in the molecule or centers of mass or certain substructures. From the origin of this system distances to the solvent accessible surface are calculated at defined spherical coordinate angles, theta and phi. The di...

A new family of exact solutions of the scalar Helmholtz equation is presented. The 0, 0 order of this family represents a new mathematical model for the fundamental mode of a propagating Gaussian beam. The family consists of nonseparable functions in the oblate spheroidal coordinate system and can easily by transformed into a different set of solutions in the prolate spheroidal coordinate syste...

The proposed method for watermark insertion in 3D polygon mesh is based on its geometrical properties. In this method selected vertices (geometrical attribute) are shifted from its original position. The changes in position of vertices w.r.t. original position is considered as watermark. The selection of vertices for shifting from their original position is dependent on the number normalization...

Antenna measurement data is collected over a surface as a function of position relative to the antenna. The data collection coordinate system directly affects how data is mapped to the surface: planar, cylindrical, spherical or other types. Far-field measurements are usually mapped or converted to spherical surfaces from which directivity, polarization and patterns are calculated and projected....

We study the cone of effective divisors and the total coordinate ring of wonderful varieties, with applications to their automorphism group. We show that the total coordinate ring of any spherical variety is obtained from that of the associated wonderful variety by a base change of invariant subrings.