In this paper we present a simple method for handling projections on the hemisphere. The proposed method defines a coordinate system on the hemisphere surface that effectively converts the hemisphere to an infinite plane tangent to the top of the hemisphere, which is called the gradient space. Using this coordinate system, projections onto the hemisphere are replaced by simple perspective proje...

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the c...

A new modification of the method of Mode Expansion in Time Domain is proposed for studying transient signals propagation in conical lines (including multi-connected ones) with inhomogeneous and time-dependent medium. The method is based on expanding the fields in spherical coordinate system into series of angular dependent modes with mode amplitudes being governed by a system of coupled evoluti...

During visually guided movement, visual coordinates of target location must be transformed into coordinates appropriate for movement. To investigate the representation of this visuomotor coordinate transformation, we examined changes in pointing behavior induced by a local visuomotor remapping. The visual feedback of finger position was limited to one location within the workspace, at which a d...

The present study introduces a new approach to determining optimal electrode positions in transcranial direct current stimulation (tDCS). Electric field and 3D conduction current density were analyzed using 3D finite element method (FEM) formulated for a dc conduction problem. The electrode positions for minimal current injection were optimized by changing the Cartesian coordinate system into t...

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...

Juan Antonio Rubio Aniceto Belmonte Adolfo Comerón, MEMBER SPIE Universidad Politécnica de Cataluña Department of Signal Theory and Communications Campus Nord UPC—Edif. D3 Jordi Girona 1-3 08034 Barcelona Spain E-mail: [email protected] Abstract. A new method to overcome some limitations in the simulation of the propagation of waves originating from a point source through a very long path in a t...

Since parametric and implicit forms have complementary advantages with respect to certain geometric operations, it can be useful to convert from one form to the other. In this paper, a new method for converting between parametric and implicit forms based on polar/spherical coordinate representations is introduced. c © 2001 Academic Press

It is shown that the SO(3) isometries of the Euclidean Taub-NUT space combine a linear three-dimensional representation with one induced by a SO(2) subgroup, giving the transformation law of the fourth coordinate under rotations. This explains the special form of the angular momentum operator on this manifold which leads to a new type of spherical harmonics and spinors.

We give a conceptual proof that the Poincaré series of the coordinate algebra of a Kleinian singularity and of a Fuchsian singularity of genus 0 is the quotient of the characteristic polynomials of two Coxeter elements. These Coxeter elements are interpreted geometrically, using triangulated categories and spherical twist functors.