Radiating and non-radiating sources in elasticity

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.Comment: 17 page

An iterative contractive framework for probe methods: LASSO

We present a new iterative approach called Line Adaptation for the Singular Sources Objective (LASSO) to object or shape reconstruction based on the singular sources method (or probe method) for the reconstruction of scatterers from the far-field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far-field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces that touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown, and its feasibility is demonstrated using a numerical study with several examples

Boundary-integral approach to the numerical solution of the Cauchy problem for the Laplace equation

We present a survey of a direct method of boundary integral equations for the numerical solution of the Cauchy problem for the Laplace equation in doubly connected domains. The domain of solution is located between two closed boundary surfaces (curves in the case of two-dimensional domains). This Cauchy problem is reduced to finding the values of a harmonic function and its normal derivative on one of the two closed parts of the boundary according to the information about these quantities on the other boundary surface. This is an ill-posed problem in which the presence of noise in the input data may completely destroy the procedure of finding the approximate solution. We describe and present the results for a procedure of regularization aimed at the stable determination of the required quantities based on the representation of the solution to the Cauchy problem in the form a single-layer potential. For given data, this representation yields a system of boundary integral equations with two unknown densities. We establish the existence and uniqueness of these densities and propose a method for the numerical discretization in two- and three-dimensional domains. We also consider the cases of simply connected domains of the solution and unbounded domains. Numerical examples are presented both for two- and three-dimensional domains. These numerical results demonstrate that the proposed method gives good accuracy with relatively small amount of computations

Gender and Age Distribution of Thyroid Nodules using Imaging Diagnostic and Management Modalities in Albania; Our data

Purpose: The purpose of this study was to evaluate gender and age distribution and the importance of imaging modalities in the evaluation and management of thyroid nodular disease in Albania nowadays. Material and method: The study analyzed the results of 310 patients (N=257 women; N=53 men), assessed at U. O. Clinic, American Hospital and Hygiea Hospital, Tirana, Albania during one year period; May 2015 – May 2016. The average age in the sample was 45.6 years. Thyroid nodules were found in 221 cases (185 females and 36 males). The patients had a standard ultrasound (US) of the thyroid; scintigraphy (SC) and ultrasound-guide fine needle aspiration biopsy (US-FNAB) when indicated. Results: The study shows that nodular disease of the thyroid was found in 84 % of women patients, and in 16 % of men patients. The largest presence of nodules was at the age group of 41-49 years. Moreover, this survey showed that ultrasound can help to distinguish nodules that are definitely benign and those with suspicious features that may require further investigation under FNAB. Some statistically significant connections were found between ultrasound characteristics and FNAB. Conclusion: Females were vast majority of patients as in regards of gender with 84 % of total sample population in the study of 310 subjects. And group age of 41-49 years old were more affected. Ultrasound and other imaging modalities are reliable methods for diagnosis and management of thyroid nodules, including patients' selection to undergo through FNAB. SC was indicated to evaluate the functional features of a nodule, especially in the presence of a low TSH value. In Albania these modalities are now used by many trained medical staff thus offering quality medical service to our patients over all. Keywords: Thyroid nodule, malignant, ultrasound, FNAB DOI: 10.7176/ALST/92-04 Publication date: February 28th 202