The Australian Journal of Mathematical Analysis and Applications
In this paper, we introduce para-chaotic tuples of operators and we give some relations between para-chaoticity and Hypercyclicity Criterion for a tuple of operators.
Application of Jacobi polynomials to approximate solution of a singular integral equation with Cauchy kernel
Abstract In this paper, exact solution of the characteristic equation with Cauchy kernel on the interval [−1, 1] is presented. Next, Jacobi polynomials are used to derive approximate solutions of the characteristic and general Cauchy-type singular integral equations. Moreover, estimations of errors of the approximated solutions are presented and proved.
Robust solutions of inverse problems in electromagnetic non-destructive evaluation
Non-destructive testing (NDT) is the application of physical measurement technology based on energy interaction with the material and its nonconformities. The material's response is sensed by transducers and sensors which?in most cases?scan the component and document the results in inspection images. However, NDT measures a physically defined quantity or even an intrinsic property. The difference between non-destructive evaluation (NDE) and NDT is in the interpretation of the inspection data. NDE has to discuss the inspection results in terms of quality elements and characteristics which are relevant to describe the fitness of the material for use. In the case of macroscopic defects these are the kind of defect (cracklike, globular) and its size and orientation to the main stress directions; in the case of material property determination the parameters are mainly mechanical properties. Therefore, in NDE one has to solve inverse problems. The solution of inverse problems based on mathematical procedures such as integral equations is a strong developing discipline and most of the articles prepared for this special issue of the journal have the objective of discussing the latest state of the art in that field. However, practical NDE needs robust and quick solutions which are to be applied mainly online. Therefore, we present here inversion procedures based on multiple linear regression algorithms applied to inspection data. We describe the calibration procedure to fit the free parameters of the model functions and give examples of practical applications in industry.