A Computationally Efficient Modeling Code for Sh-Waves in Austenitic Welds Using an Explicit Space-Time Green-Function

For ultrasonic inspection of austenitic welds and cladded components horizontally polarized shear (SH) waves — as generated by electromagnetic acoustic transducers (EMATs) — have certain benefits compared with quasi-vertically polarized shear and quasi-pressure waves. SH-waves suffer the least distortion of all three wave modes when propagated through anisotropic weld material and no energy is lost through mode conversion at the steel/free surface or base metal/weld interfaces. To explain experimentally observed phenomena and to predict the cases where SH-waves might be best employed, modeling of the respective wave propagation effects is useful. In this contribution, a computationally efficient modeling code is presented for SH-waves propagating in transversely isotropic media, thus particularly applicable to ideally fiber-textured austenitic weld material. An explicit space-time domain far-field representation of Green’s dyadic function has been derived with respect to the wave type under concern, the fiber direction being included as a free parameter. The obtained relationships have been applied to the Generalized Point-Source-Synthesis method (GPSS [1,2]) to model radiation, propagation and scattering effects. The code thus improved — SH-GPSS— is characterized by a considerable reduction of computer run-time and is therefore particularly convenient in view of a respective extension to inhomogeneous weldments. Numerical results are presented for both continuous wave and time-dependent rf-impulse modeling for austenitic weld metal specimens, covering field profiles as well as wave front snapshots for a phased array EMAT-probe

Mixed spatially varying L2L^2-BV regularization of inverse ill-posed problems

Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers which allow the capturing of diverse properties of the exact solution (e.g. edges, discontinuities, borders, etc.). However, in some problems in which it is known that the regularity of the exact solution is heterogeneous and/or anisotropic, it is reasonable to think that a much better option could be the simultaneous use of two or more penalizers of different nature. Such is the case, for instance, in some image restoration problems in which preservation of edges, borders or discontinuities is an important matter. In this work we present some results on the simultaneous use of penalizers of $L^2$ and of bounded variation (BV) type. For particular cases, existence and uniqueness results are proved. Open problems are discussed and results to signal restoration problems are presented.Comment: 18 pages, 12 figure

Die problematiek verbonde aan die maatskaplike hantering van die gemolesteerde kind

Sexual moleslation is most certainly the phenomenon that evokes most repulsion in society at large, and in the helping professions. Since this phenomenon has been exposed by various sources, it is clear at present that professional institutions or people are still not successfully geared to render a non-fragmented service to the culprit, the victim and their various families. It would appear that, when services are rendered, the various professions involved in the case are not clear with regard to their various roles. Not only does a lack of knowledge exist regarding the phenomenon dealt with, hut also regarding the legal process that is mostly involved in these cases. Almost no identified resource exists in the community which one can approach for help without the emphasis on prosecution. This may enhance the possibility that cases still be kept secret. The question may be asked whether prosecution should be the way to handle sexual molestation, a process during which the involved child cannot he fully protected. Should other forms o f help-rendering not be considered

Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

The analysis of spectra of novae taken near maximum

A project to analyze ultraviolet spectra of novae obtained at or near maximum optical light is presented. These spectra are characterized by a relatively cool continuum with superimposed permitted emission lines from ions such as Fe II, Mg II, and Si II. Spectra obtained late in the outburst show only emission lines from highly ionized species and in many cases these are forbidden lines. The ultraviolet data will be used with calculations of spherical, expanding, stellar atmospheres for novae to determine elemental abundances by spectral line synthesis. This method is extremely sensitive to the abundances and completely independent of the nebular analyses usually used to obtain novae abundances

Existence, uniqueness and stability of solutions of generalized Tikhonov-Phillips functionals

The Tikhonov-Phillips method is widely used for regularizing ill-posed inverse problems mainly due to the simplicity of its formulation as an optimization problem. The use of different penalizers in the functionals associated to the corresponding optimization problems has originated a variety other methods which can be considered as "variants" of the traditional Tikhonov-Phillips method of order zero. Such is the case for instance of the Tikhonov-Phillips method of order one, the total variation regularization method, etc. In this article we find sufficient conditions on the penalizers in generalized Tikhonov-Phillips functionals which guarantee existence and uniqueness and stability of the minimizers. The particular cases in which the penalizers are given by the bounded variation norm, by powers of seminorms and by linear combinations of powers of seminorms associated to closed operators, are studied. Several examples are presented and a few results on image restoration are shown.Comment: 24 pages, 8 figure