The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact simply connected semisimple Lie group G. Such functions can always be restricted without loss of information to a fundamental region F̌ of the affine Weyl group. The members of each family satisfy basic orthogonality rel...

We use numerical simulations to study the effect of nonlinear MHD waves in a stratified, self-gravitating molecular cloud that is bounded by a hot and tenuous external medium. In a previous paper, we had shown the details of a standard model and studied the effect of varying the dimensionless amplitude ãd of sinusoidal driving. In this paper, we present the results of varying two other importan...

The numerical solution of acoustic wave propagation problems in planar domains with corners and cracks is considered. Since the exact solution of such problems is singular in the neighborhood of the geometric singularities the standard meshfree methods, based on global interpolation by analytic functions, show low accuracy. In order to circumvent this issue, a meshfree modification of the Metho...

In reasoning about time and duration, researchers often use Allen’s Interval Algebra. This algebra describes possible relations between 1-D intervals. An interval can precede the other one, follow the other one, start the other one, etc. This algebra describes the relationship between different intervals in terms of words from natural language. To give a natural language description of 2D image...

In this paper, the method of fundamental solutions (MFS) for solving the eigenfrequencies of multiply connected plates is proposed. The coefficients of influence matrices are easily determined when the fundamental solution is known. True and spurious eigensolutions appear at the same time. It is found that the spurious eigensolution using the MFS depends on the location of the inner boundary wh...

Previous work of the authors developed a theoretically well-founded scheme (FNS) for finding the minimiser of a class of cost functions. Various problems in video analysis, stereo vision, ellipse-fitting, etc, may be expressed in terms of finding such a minimiser. However, in common with many other approaches, it is necessary to correct the minimiser as a post-process if an ancillary constraint...

We present a meshless technique which can be seen as an alternative to the Method of Fundamental Solutions (MFS). It calculates homogeneous solutions of the Laplacian (i.e. harmonic functions) for given boundary data by a direct collocation technique on the boundary using kernels which are harmonic in two variables. In contrast to the MFS, there is no artifical boundary needed, and there is a f...