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## Displaying 1 – 15 of 15

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### A rainbow inverse problem

ESAIM: Proceedings

We consider the radiative transfer equation (RTE) with reflection in a three-dimensional domain, infinite in two dimensions, and prove an existence result. Then, we study the inverse problem of retrieving the optical parameters from boundary measurements, with help of existing results by Choulli and Stefanov. This theoretical analysis is the framework of an attempt to model the color of the skin. For this purpose, a code has been developed to solve...

### Applied Mathematics and the Imaging of the Brain

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

### Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.

### Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.

### Energy Functionals in Scattering Theory

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

### Erratum to Fourier diffraction theorem for the tensor fields

Applications of Mathematics

### Introduction to magnetic resonance imaging for mathematicians

Annales de l’institut Fourier

The basic concepts and models used in the study of nuclear magnetic resonance are introduced. A simple imaging experiment is described, as well as, the reduction of the problem of selective excitation to a classical problem in inverse scattering.

### Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data

Applications of Mathematics

We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...

### Multiscale analysis of wave propagation in random media. Application to correlation-based imaging

Séminaire Laurent Schwartz — EDP et applications

We consider sensor array imaging with the purpose to image reflectors embedded in a medium. Array imaging consists in two steps. In the first step waves emitted by an array of sources probe the medium to be imaged and are recorded by an array of receivers. In the second step the recorded signals are processed to form an image of the medium. Array imaging in a scattering medium is limited because coherent signals recorded at the receiver array and coming from a reflector to be imaged are weak and...

### Numerical linear algebra for nonlinear microwave imaging.

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

### On the mathematical basis of the linear sampling method.

Georgian Mathematical Journal

### Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We deal with an inverse scattering problem whose aim is to determine the thickness variation of a dielectric thin coating located on a conducting structure of unknown shape. The inverse scattering problem is solved through the application of the Generalized Impedance Boundary Conditions (GIBCs) which contain the thickness, curvature as well as material properties of the coating and they have been obtained in the previous work [B. Aslanyürek, H. Haddar and H.Şahintürk, Wave Motion 48 (2011) 681–700]...

### Recovering quantum graphs from their Bloch spectrum

Annales de l’institut Fourier

We define the Bloch spectrum of a quantum graph to be the map that assigns to each element in the deRham cohomology the spectrum of an associated magnetic Schrödinger operator. We show that the Bloch spectrum determines the Albanese torus, the block structure and the planarity of the graph. It determines a geometric dual of a planar graph. This enables us to show that the Bloch spectrum indentifies and completely determines planar $3$-connected quantum graphs.

### The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation.

Electronic Journal of Differential Equations (EJDE) [electronic only]

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