Discontinuities in integral-transform solutions

Reconstructing Discontinuities Using Complex Geometrical Optics Solutions

In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions inside a domain filled with known conductivity from local boundary measurements. Computational results dem...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

Experimental evidence for excess entropy discontinuities in glass-forming solutions.

Glass transition temperatures T(g) are investigated in aqueous binary and multi-component solutions consisting of citric acid, calcium nitrate (Ca(NO(3))(2)), malonic acid, raffinose, and ammonium bisulfate (NH(4)HSO(4)) using a differential scanning calorimeter. Based on measured glass transition temperatures of binary aqueous mixtures and fitted binary coefficients, the T(g) of multi-componen...

Complex Geometrical Optics Solutions and Reconstruction of Discontinuities

In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions inside of a domain filled with known conductivity from local boundary measurements. Computational results ...

Integral Transform Technique for Meson Wave Functions

In a recent paper [1] we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for non-diagonal correlators obtained in [2]. Here, we test our approach using an exactly solvable toy model as an illustrating example. We demonstrate the validity of the method and suggest a pure algebr...