In recent years some attempts have been done to relate the RBF with wavelets [1,2] in handling high dimensional multiscale problems. To the author’s knowledge, however, the orthonormal and bi-orthogonal RBF wavelets are still missing in the literature. By using the nonsingular general solution and singular fundamental solution of differential operator [3], recently the present author made some ...

to date, a number of numerical methods, including the popular finite-difference time domain (fdtd) technique, have been proposed to simulate ground-penetrating radar (gpr) responses. despite having a number of advantages, the finite-difference method also has pitfalls such as being very time consuming in simulating the most common case of media with high dielectric permittivity, causing the for...

Since radial positive definite functions on R remain positive definite when restricted to the sphere, it is natural to ask for properties of the zonal series expansion of such functions which relate to properties of the Fourier-Bessel transform of the radial function. We show that the decay of the Gegenbauer coefficients is determined by the behavior of the Fourier-Bessel transform at the origi...

We define the radiation fields of solutions to critical semilinear wave equations in R3 and use them to define the scattering operator. We also prove a support theorem for the radiation fields with radial initial data. This extends the well known support theorem for the Radon transform to this setting and can also be interpreted as a Paley-Wiener theorem for the distorted nonlinear Fourier tran...

This paper presents the application of radial basis neural networks to the development of a novel method for the condition monitoring and fault diagnosis of synchronous generators. In the proposed scheme, flux linkage analysis is used to reach a decision. Probabilistic neural network (PNN) and discrete wavelet transform (DWT) are used in design of fault diagnosis system. PNN as main part of thi...

A new feature detection technique is presented that utilises local radial symmetry to identify regions of interest within a scene. This transform is significantly faster than existing techniques using radial symmetry and offers the possibility of real-time implementation on a standard processor. The new transform is shown to perform well on a wide variety of images and its performance is tested...