This article will be devoted to generalisations of Fermat’s equation x + y = z. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would be chosen. We discuss the reduction of the resolution of such equations to the determination of rationa...

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

A 2D analytical method for magnetic vector potential calculation in inner rotor surface mounted and surface inset permanent magnet machines considering slotting effects, magnetization orientation and winding layout has been proposed in this paper. The analytical method is based on the resolution of Laplace and Poisson equations as well as Maxwell equation in quasi- Cartesian coordinate by using...

In this paper, we present a framework for getting a series of vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution. PACS numbers: 04.20-q, 0...

We introduce a new zooming algorithm curvature interpolation method(CIM) based on partial differential equation, which produce high resolution(HR) color image by solving a linearized curvature equation. Partial Differential Equations (PDEs) have become an important tool for interpolation methods in image processing and analysis. CIM first evaluates the curvature of the low-resolution image, aft...

We describe a space and time adaptive numerical method based on wavelet orthonormal bases for solving partial diierential equations. The multiresolution structure of wavelet orthonormal bases provides a simple way to adapt computational reenements to the local regularity of the solution 11] 16]. High resolution computations are performed only in regions where singularities or sharp transitions ...

this work reports the results of the application of the second-order maccormack method for numerical solution of‎ the conservative form of two-dimensional non-hydrostatic and fully compressible navier-stokes equations governing an inviscid and adiabatic atmosphere‎. various aspects of the computational approach such as discretization of the governing equations for the interior and boundary poin...

Let p be an odd prime and a, b positive integers. In this note we prove that the problem of the determination of the integer solutions to the equation y2 = x(x + 2apb)(x − 2apb) can be easily reduced to the resolution of the unit equation u+ √ 2v = 1 over Q( √ 2, √ p). The solutions of the latter equation are given by Wildanger’s algorithm.

Beams of microscopic particles penetrating scattering background matter play an important role in several applications. The parameter choices made here are motivated by the problem of electron-beam cancer therapy planning. Mathematically, a steady particle beam penetrating matter, or a configuration of several such beams, is modeled by a boundary value problem for a Boltzmann equation. Grid-bas...