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We propose a new integral equation formulation to characterize and compute transmission eigenvalues in electromagnetic scattering. As opposed to the approach that was recently developed by Cakoni, Haddar and Meng (2015) which relies on a two‐by‐two system of boundary integral equations, our analysis is based on only one integral equation in terms of the electric‐to‐magnetic boundary trace operator that results in a simplification of the theory and in a considerable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further, we use the numerical algorithm for analytic nonlinear eigenvalue problems that was recently proposed by Beyn (2012) for the numerical computation of the transmission eigenvalues via this new integral equation. [ABSTRACT FROM AUTHOR]

A new second order Newton method for reconstructing the shape of a sound soft scatterer from the measured far-field pattern for scattering of time harmonic plane waves is presented. This method extends a hybrid between regularized Newton iterations and decomposition methods that has been suggested and analyzed in a number of papers by Kress and Serranho [Inverse Problems 19: 91–104, 2003, Inverse Problems 21: 773–784, 2005, J. Comput. Appl. Math. 204: 418–427, 2007, Inverse Problems 22: 663–680, 2006, Inverse Problems and Imaging 1: 691–712, 2007] and has some features in common with the second degree method for ill-posed nonlinear problems as considered by Hettlich and Rundell [SIAM J.Numer. Anal. 37: 587–620, 2000]. The main idea of our iterative method is to use Huygen's principle, i.e., represent the scattered field as a single-layer potential. Given an approximation for the boundary of the scatterer, this leads to an ill-posed integral equation of the first kind that is solved via Tikhonov regularization. Then, in a second order Taylor expansion, the sound soft boundary condition is employed to update the boundary approximation. In an iterative procedure, these two steps are alternated until some stopping criterium is satisfied. We describe the method in detail and illustrate its feasibility through examples with exact and noisy data. [ABSTRACT FROM AUTHOR]

We consider the problem of determining the shape and location of cracks from Cauchy data on the boundary of semi-infinite domains modeling the reconstruction of cracks within a heat conducting medium from temperature and heat flux measurements. Our reconstructions are based on a pair of nonlinear integral equations for the unknown crack and the unknown flux jump on the crack that are linear with respect to the flux and nonlinear with respect to the crack. We propose two different iteration methods employing the following idea: Given an approximate reconstruction for the crack we first solve one of the equations for the flux and subsequently linearize the other equation for updating the crack. The foundations for this approach for solving the inverse problem in semi-infinite domains are provided and numerical experiments exhibit the feasibility of both methods and their stability with respect to noisy data. [ABSTRACT FROM AUTHOR]

The problem to determine the location and shape of a perfect conductor within a conducting homogeneous host medium from measured current and voltages on the accessible exterior boundary of the host medium can be modelled by an inverse Dirichlet boundary value problem for the Laplace equation. For this, recently Kress and Rundell suggested a novel inverse algorithm based on nonlinear integral equations arising from the reciprocity gap principle. The present paper extends this approach to the problem to recover the location and shape of a rigid body immersed in a fluid from the measured velocity and traction at the exterior boundary of the fluid, that is, to an inverse boundary value problem for the Stokes equation. The mathematical foundation of this extension is provided and numerical examples illustrate the feasibility of the method. [ABSTRACT FROM AUTHOR]

Akduman, Haddar and Kress [1, 12, 15] proposed a conformal mapping approach for solving inverse boundary value problems for the two-dimensional Laplace equation in a doubly connected domain D with interior boundary curve Γ0 and exterior boundary curve Γ1. The inverse problem consists of reconstructing the interior boundary Γ0 from the Cauchy data on Γ1 of a harmonic function satisfying a homogeneous Dirichlet or Neumann boundary condition on the unknown interior boundary curve Γ0. The reconstruction method consists of two parts: In the first step, by successive approximations a nonlocal and nonlinear ordinary differential equation is solved to determine the boundary values of a holomorphic function Ψ on the outer boundary circle C1 of an annulus B. Then in the second step via regularizing a Laurent expansion in the sense of Tikhonov an ill-posed Cauchy problem is solved to determine Ψ in the annulus and the unknown Γ0 as the image Ψ(C0) of the interior boundary circle C0 of B. The present paper extends this approach to the case of a homogeneous impedance boundary condition. The analysis and the numerical implementation of the method differ from the limiting cases of the Dirichlet and Neumann conditions since the impedance problem in the annulus B that is associated with the impedance problem in the original domain D depends on the conformal map Ψ. [ABSTRACT FROM AUTHOR]

The Union Internationale Contre le Cancer and American Joint Committee on Cancer classification propose that pN0-classified colorectal lymphadenectomy specimens will ordinarily include 12 or more tumor-negative lymph nodes. We performed a clinical trial to investigate whether a short-term preoperative radiotherapy (5×5 Gy) leads to a reduction of the number of lymph nodes in rectal cancer specimens after total and partial mesorectal excision (TME and PME, respectively). Within a 5-year period, 28 (15%) of 148 rectal cancer patients underwent hypofractionated preoperative radiotherapy in this monocenter study, whereas 120 patients (85%) underwent TME/PME surgery alone. The main criterion was the number of lymph nodes in TME/PME specimens. We used a stratified one-sided Wilcoxon–Mann–Whitney test to test for a significant difference in the number of lymph nodes, stratifying for tumor location and postoperative tumor stage. Patients who were suspected of having any alterations in the number of pelvic lymph nodes were excluded from the study. Fewer lymph nodes were detected in the TME/PME specimens of patients who received hypofractionated preoperative radiotherapy compared to patients who underwent TME/PME surgery alone (12 detectable lymph nodes vs 15; p=0.0005). Tumor location ( p=0.095) and tumor stage ( p=0.093) did not significantly influence the number of lymph nodes in this study. We conclude that a 5×5 Gy short-term preoperative radiotherapy leads to a reduction in the number of lymph nodes in TME/PME specimens. Because neoadjuvant therapy in rectal cancer for T2 and T3 tumors has advanced a new therapeutic standard procedure, in the future, less lymph nodes will be detected in TME/PME specimens. This might influence the required number of lymph nodes in current staging systems for rectal cancer in the future. [ABSTRACT FROM AUTHOR]

Background: Previous studies of anticipation in familial pancreatic cancer have been small and subject to ascertainment bias. Our aim was to determine evidence far anticipation in a large number of European families. Patients and methods: A total of 1223 individuals at risk from 106 families (264 affected individuals) were investigated. Generation G3 was defined as the latest generation that included any individual aged over 39 years; preceding, generations were then defined as G2 and G1. Results: With 80 afflicted child-parent pairs, the children died o median (interquartile range) of 10 (7, 14) years earlier. The median (interquartile range) age of death from pancreatic cancer was 70 (59, 77), 64 (57, 69), and 49 (44, 56) years far G1, G2, and G3, respectively. These indications of anticipation could be the result of bias. Truncation of Kaplan-Meier analysis to a 60 year period to correct far fallow up time bias and a matched test statistic indicated significant anticipation (p=0.002 and p<0.001). To minimise bias further, an iterative analysis to predict cancer numbers was developed. No single risk category could be applied that accurately predicted cancer cases in every generation. Using three risk categories (low with no pancreatic cancer in earlier generations, high with a single earlier generation, and very high where two preceding generations were affected), incidence was estimated without significant error. Anticipation was independent of smoking. Conclusion: This study provides the first strong evidence far anticipation in familial pancreatic cancer and must be considered in genetic counselling and the commencement of secondary screening far pancreatic cancer. [ABSTRACT FROM AUTHOR]

We describe a new method for solving an inverse Dirichlet problem for harmonic functions that arises in the mathematical modelling of electrostatic and thermal imaging methods. This method may be interpreted as a hybrid of a decomposition method, in the spirit of a method developed by Kirsch and Kress, and a regularized Newton method for solving a nonlinear ill-posed operator equation, in terms of the solution operator that maps the unknown boundary onto the solution of the direct problem. As opposed to the Newton iterations the new method does not require a forward solver. Its feasibility is demonstrated through numerical examples. [ABSTRACT FROM AUTHOR]

In a general Hilbert space of periodic functions numerical approximations with equidistant nodes for any bounded linear functional are given which are of minimal error norm in the class of approximations being exact for certain trigonometric polynomials. In examples optimal quadrature formulas with such side conditions are considered. [ABSTRACT FROM AUTHOR]

Optimal rules of numerical approximation of bounded linear functionals in a general Hilbert space of periodic functions are investigated by Davis' method. The weights and error norms for optimal rules with equidistant nodes for an arbitrary bounded linear functional are given explicitly in terms of a total orthonormal system in the Hilbert space. Further the optimal approximation rules are compared with the numerical approximations obtained by means of trigonometric interpolation. As examples the numerical integration and the numerical evaluation of conjugate harmonic functions are considered in two distinct Hardy spaces and also in Sobolev spaces. [ABSTRACT FROM AUTHOR]

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Copyright of Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)