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 ...

In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three–dimensional boundary value problems governed by elliptic systems of partial differential equations. In particular, we consider problems arising in linear elasticity in axisymmetric domains. The proposed algorithm exploits the block circulant structure of the coeffic...

The mean operator R0 and its dual R0 play an important role and have many applications, for example, in image processing of the so-called synthetic aperture radar (SAR) data [11, 12] or in the linearized inverse scattering problem in acoustics [6]. Our purpose in this work is to define and study integral transforms which generalize the operators R0 and R0. More precisely, we consider the follow...

We consider abstract differential equations of the form u′(t) = Au(t)+f(t) or u′′(t)=Au(t)+f(t) in Banach spaces X, where f(·), R→X is almost-periodic, while A is a linear operator, (A)⊂X →X. If the solution u(·) is likewise almost-periodic, R→X, we establish connections between their Bohr-transforms, û(λ) and f̂ (λ). 2000 Mathematics Subject Classification. 34C27, 34G10.

A nodal collocation method is proposed to compute the dominant Lambda modes of nuclear reactor core with a hexagonal geometry. This method is based on a triangular mesh and assumes that the neutronic flux can be approximated as a finite expansion in terms of Dubiner’s polynomials. The method transforms the initial differential eigenvalue problem into a generalized algebraic one, from which the ...

A general method is proposed for constructing templates of cells in differential interference contrast (DIC) microscopy. This takes account of the optics which generate DIC images, and is applicable to both transparent and semi-transparent cells of simple and complex shapes. Then, a template matching methodology is presented, which uses fast Fourier transforms to fit templates of a range of siz...

Our purpose here is to announce results in harmonic analysis related to a large class of hypoelliptic operators on arbitrary simply-connected nilpotent Lie groups. We find the asymptotic development of their fundamental solutions, both locally and at infinity, and study corresponding Riesz transforms and analogues of the Hardy-Littlewood-Sobolev theorem for fractional integration. Details will ...

On the other hand, whether the Christoffel symbol is the only connection which can be constructed from a symmetric second–rank tensor gμν remains an open question. In this note we exhibit a constructive demonstration of the uniqueness of the Christoffel symbol. Let us start by reviewing some simple results of tensor calculus. Let M be an n–dimensional differentiable manifold. Several geometric ...

In this paper we study the class of mixed-index time fractional differential equations in 1 which different components of the problem have different time fractional derivatives on the left hand 2 side. We prove a theorem on the solution of the linear system of equations, which collapses to the 3 well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the 4 ...

Ear modeling can significantly improve sound signal processing and the design of hearing devices. Ear models based on mechanics and neural phenomenology of the inner ear (cochlea) form a class of nonlinear nonlocal dispersive partial differential equations (PDEs). These PDEs capture the essential nonlinear phenomena in hearing, such as combination frequency generation, compression, and suppress...