A systematic analysis of the localization of objects in extra-personal space requires a three-dimensional method of documenting location. In auditory localization studies the location of a sound source is often reduced to a directional vector with constant magnitude with respect to the observer, data being plotted on a unit sphere with the observer at the origin. This is an attractive form of d...

We present a new mechanical design for a compact three degrees-of-freedom joint mechanism. This joint design is ideal for use in robotic devices, especially hyper-redundant or snake-like robots. This joint exhibits an unprecedented range of motion: the origin of a coordinate frame attached to the output link of the joint can move on a spherical cone whose apex angle is 120 and this coordinate f...

We describe numerical techniques used in our construction of a 4th order in time evolution for the full Einstein equations, and assess the accuracy of some representative solutions. The scheme employs several novel geometric and numerical techniques, including a geometrically invariant coordinate gauge, which leads to a characteristic-transport formulation of the underlying hyperbolic system, c...

We study integrable and superintegrable systems with magnetic field possessing quadratic integrals of motion on the three-dimensional Euclidean space. In contrast case without vector potential, corresponding may no longer be connected to separation variables in Hamilton-Jacobi equation can have more general leading order terms. focus two cases extending physically relevant cylindrical- spherica...

Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤ 4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identificiation of circle families on ...

A solar eclipse is an unusual natural occurrence. Muslims used the phenomenon of a as season for prayer, which was only carried out during from early in until end. Although there no statistically significant difference estimating eclipse, seasons change, becomes increasingly important. Lots alternatives can be reference determination eclipse. Among commonly calculation spherical astronomy. Desp...

This new alternate approach to data processing for analyses that traditionally employed grid-based counting methods is necessary because it removes a user-imposed coordinate system that not only limits an analysis but also may introduce errors. We have modified the widely used "binomial" analysis for APT data by replacing grid-based counting with coordinate-independent nearest neighbour identif...

The consideration of the N-body gravitational problem equations can give to us some class of boundary-value problems defined on the " beem's " construction. One can considere it as weak or so-called finite element method's approximation with the linear function's basis. So there are time and coordinate dependent beems as distances between points and unknown coordinate functions which are define...

The human brain may be considered as a genus-0 shape, topologically equivalent to a sphere. Various methods have been used in the past to transform the brain surface to that of a sphere using harmonic energy minimization methods used for cortical surface matching. However, very few methods have studied volumetric parameterization of the brain using a spherical embedding. Volumetric parameteriza...

Aspects of continuous and discrete harmonic analysis on the circle are generalized to star graphs, and through spherical coordinates to the two sphere. The resulting function theory is used to analyze trapezoidal rule integration on the two sphere. 2000 Mathematics Subject Classification 65D30, 65T99, 34B45