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In this paper we examine spatio-temporal pattern formation in reaction-diffusion systems on the surface of the unit sphere in 3D. We first generalise the usual linear stability analysis for a two-chemical system to this geometrical context. Noting the limitations of this approach (in terms of rigorous prediction of spatially heterogeneous steady-states)(More)
Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in two-and three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton(More)
We study a subspace of bivariate trigonometric polynomials for interpolating functions on the sphere. We give an explicit construction for a system of interpolation nodes, and the corresponding basis for this space, that allows a (discrete) fast Fourier transform–type formula for the interpolant. We prove that the uniform norm of our interpolation operator(More)
AIM This study evaluates erosive potential of commonly used beverages, medicated syrup, and their effects on dental enamel with and without restoration in vitro. MATERIALS AND METHODS Test medias used in this study included carbonated beverage, noncarbonated beverage, high-energy sports drink medicated cough syrup, distilled water as the control. A total(More)