We study characteristic schemes for a model problem for the Fermi pencil beam equation. The objective is twofold: (i) To design eecient and accurate numerical schemes based on the principle of solving a particle transport problem, exactly, on each collision free spatial segment combined with a projection on each collision site, from a pre collision angle and energy coordinates (AE) to a post co...

In a recent paper [10], M.E. Kahoui and M. Ouali have proved that over an algebraically closed field k of characteristic zero, residual coordinates in k[X][Z1,…,Zn] are one-stable coordinates. this we extend their result to the case arbitrary characteristic. fact, show holds when k[X] is replaced by any one-dimensional seminormal domain R which affine k. For our proof, S. Maubach [11] giving cr...

Fermi-normal (FN) coordinates provide a standardized way to describe the effects of gravitation from the point of view of an inertial observer. These coordinates have always been introduced via perturbation expansions and were usually limited to distances much less than the characteristic length scale set by the curvature of spacetime. For a plane gravitational wave this scale is given by its w...

There is usually a pattern of veins on an insect wing. This pattern is species-specific and is used taxonomically. For example, the coordinates of some characteristic points on the wing are used to compare vein patterns. The characteristic points are often vein junctions or vein ends. A tool is presented that enables automatic identification of vein junctions. An image of an insect wing is used...

Optimum laminate configuration for minimum weight of filament–wound laminated conical shells subject to buckling load constraint is investigated. In the case of a laminated conical shell the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and its weight. These effects complicate the optimization problem consider...

Transversal vibrations of an axially moving string under boundary damping are investigated. Mathematically, it represents a homogenous linear partial differential equation subject to nonhomogeneous boundary conditions. The string is moving with a relatively (low) constant speed, which is considered to be positive.  The string is kept fixed at the first end, while the other end is tied with the ...

Let S be an orientable, finite type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on was first defined and topologized by the author. In this article, we give explicit description topology using coordinates. More precisely, given every point in space, find continuous coordinates quotient a suitable open neighborhood about subgroup ma...

The characteristic function (chf) of a lognormal process is derived using saddle point method . Relations are established between the polar coordinates of the saddle point and variance and mean parameters. The characteristic function and cumulants are then decomposed into a primary and a secondary component. The sum rules for the variance and means of a sum of lognormals and the computation of ...

The problem of normalization of circuit regime parameters, choice of characteristic regimes and scale values is considered. Disadvantages of traditional normalization are shown. The method of projective coordinates reveals the characteristic regimes and proves the normalized expressions. The examples of recalculation of regime parameters are given for comparable circuits. The obtained results a...

A hypersurface of order (n+ 1)(ph − 1) in projective space of dimension n of prime characteristic p has an invariant monomial. This implies that a hypersurface of order (n+1)(ph−1)−1 determines an invariant point. A hypersurface of order d < n+ 1 in a projective space of dimension n of characteristic two has an invariant set of subspaces of dimension d− 1 determined by one linear condition on t...