The recently developed multiscale kernel of R. Opfer is applied to approximate numerical derivatives. The proposed method is truly mesh-free and can handle unstructured data with noise in any dimension. The method of Tikhonov and the method of L-curve are employed for regularization; no information about the noise level is required. An error analysis is provided in a general setting for all dim...

This paper introduces the mechanical behavior of precise straightening thin-walled members systematically. As a result of its cross section characteristics of the thin-walled members, traditional straightening theory does not work well in the straightening process of this kind of metal bar stock. Considering the stress evolvement of section during the straightening process, a model was built to...

The use of a 3D model helps to diagnosis and accurately locate a disease where it is neither available, nor can be exactly measured in a 2D image. Therefore, highly accurate software for a 3D model of vessel is required for an accurate diagnosis of patients. We have generated standard vessel because the shape of the arterial is different for each individual vessel, where the standard vessel can...

In epidemiological studies one is interested in investigating the probability of disease depending on risk factors and in particular in detecting interactions of risk factors. Within the setting of parametric logistic regression interactions can be modeled only in a clumsy and limited way. Modeling the risk function nonparametrically, estimating it e.g. by a smoothing (thin plate) spline is att...

The ionosphere is still considered one of the most significant error sources in precise Global Navigation Satellite Systems (GNSS) positioning. On the other hand, new satellite signals and data processing methods allow for a continuous increase in the accuracy of the available ionosphere models derived from GNSS observables. Therefore, many research groups around the world are conducting resear...

Radial basis functions are used in the recovery step of nite volume methods for the numerical solution of conservation laws. Being conditionally positive deenite such functions generate optimal recovery splines in the sense of Micchelli and Rivlin in associated native spaces. We analyse the solvability to the recovery problem of point functionals from cell average values with radial basis funct...

A very handy tool in the study of the asymptotic behavior of variational problems defined on Sobolev spaces is Fonseca, Müller and Pedregal’s equi-integrability Lemma [8] (see Theorem 2.1 below; see also earlier work by Acerbi and Fusco [2] and by Kristensen [11]), which allows to substitute a sequence (wj) with (∇wj) bounded in L by a sequence (zj) with (|∇zj | ) equi-integrable, such that the...

Thin plate splines are utilized in the construction of a non-oscillatory finite volume method for the inviscid Burgers' equation which is a prototype nonlinear conservation law. To capture the sharp features that occur during numerical simulation, the method is implemented on an adaptive triangulation. An a posteriori error indicator is used to detect regions where the solution varies rapidly.

We introduce an approach to elastic registration of tomographic images based on thin-plate splines. Central to this scheme is a well-de ned minimizing functional for which the solution can be stated analytically. In this work, we consider the integration of anisotropic landmark errors as well as additional attributes at landmarks. As attributes we use orientations at landmarks and we incorporat...