I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thinplate spline smoothing problem, and are optimal in the sense that the truncation is designed to result in the minimum possible pe...

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

Thin plate splines provide smooth interpolation of the given data in two or more dimensions. These are analogous to cubic splines in one dimension. The main objectives of this report is to provide an implementation of the thin plate spine interpolation of data using various efficient methods and to investigate the possibility of using thin plate splines in adaptive optics. In this report, we co...

We investigate the global bifurcations and multipulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations. We analyze directly the nonautonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that the multipulse chao...

The paper deals with Div-Curl approximation problem by weighted thin plate splines. The weighted thin plate splines are an extension of the well known thin plate splines and are radial basis functions which allow the approximation and interpolation of a scalar functions from a given scattered data. We show how the weighted thin plate splines may also be used for the approximation and interpolat...

The floating thin plate is amongst the best studied problems in hydroelasticity. The time-harmonic linear wave response of a floating thin plate can be determined straightforwardly by a number of different methods.. Since the problem is linear, the time-dependent response of the thin plate can in theory be written as an expansion in these timeharmonic solutions. However, the theory for this exp...

The multi-pulse heteroclinic orbits with a Melnikov method and chaotic dynamics in a parametrically and externally excited thin plate are studied in this paper for the first time. The thin plate is subjected to transversal and in-plane excitations, simultaneously. The formulas of the thin plate are derived from the von Kármán equation and Galerkin’s method. The method of multiple scales is used...

In this paper, we prove that the inverse problems for 2D elasticity and for the thin plate with boundary data (finite or full measurements) are equivalent. Having proved this equivalence, we can solve inverse problems for the plate equation with boundary data by solving the corresponding inverse problems for 2D elasticity, and vice versa. For example, we can derive bounds on the volume fraction...