The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave–current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91...

color halftoning, dithering, barycentric coordinates. Monochrome dither halftoning is a gray-scale image rendering procedure where gray-levels in an image are compared against a periodic threshold array, placing a Black dot in every location whose gray-level is smaller than the corresponding threshold value. Current generalizations to color printing result in Cartesian thresholding procedures, ...

The principle of equipartition of (kinetic) energy for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has ½kT of kinetic energy in a canonical ensemble. This principle is used in molecular dynamics simulations to initialize velocities, and to calculate statistical properties such as entropy. Internal coordinate molecular dynamics (ICMD) mod...

Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cart...

The unit vectors transformation between the Cartesian and novel similar oblate spheroidal coordinates, vice versa, is derived. It facilitates of vector fields these two types orthogonal coordinates can advantageously simplify solutions problems exhibiting geometry. Several examples demonstrate use derived relations. Generalized sine cosine applicable in coordinate system are introduced as well.

We show that using an adequate coordinate transformation the charged regular black hole solution given by Ayón-Beato and Garcia can be put in the Kerr-Schild form. Then we use this metric in Kerr-Schild Cartesian coordinates with a result given by Virbhadra and obtain the energy distribution associated with this.

The Skyrme-Hartree-Fock-Bogoliubov code HFBTHO using the axial (2D) Transformed Harmonic Oscillator basis is tested against the HFODD (3D Cartesian HO basis) and HFBRAD (radial coordinate) codes. Results of large-scale ground-state calculations are presented for the SLy4 and SkP interactions.

By embedding images as surfaces in a high dimensional coordinate space defined by each pixel’s Cartesian coordinates and color values, we directly define and employ cotangent-based, discrete differentialgeometry operators. These operators define discrete energies useful for image segmentation and colorization.

     This research has attempted to measure the parameters of barchan dunes as one of the desert landforms. This has been conducted by a field survey using cartographic techniques. In the field, two barchan dunes have completely been surveyed by total station equipment. Using the sample points a novel method has been devised to measure the barchans parameters. The method is mainly based on geom...