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Paper's Title:
On Opial's Inequality for Functions of n-Independent Variables
Author(s):
S. A. A. El-Marouf and S. A. AL-Oufi
Department of Mathematics,
Faculty of Science,
Minoufiya University,
Shebin El-Koom,
Egypt
Department of Mathematics,
Faculty of Science, Taibah University,
Madenahmonwarah,
Kingdom of Saudia Arabia
Abstract:
In this paper, we introduce Opial inequalities for functions of n-independent variables. Also, we discuss some different forms of Opial inequality containing functions of n independent variables and their partial derivatives with respect to independent variables.
Paper's Title:
Stability of the D-Bar Reconstruction Method for Complex Conductivities
Author(s):
1S. El Kontar, 1T. El Arwadi, 1H. Chrayteh, 2J.-M. Sac-Épée
1Department of Mathematics and
Computer Science,
Faculty of Science, Beirut Arab University,
P.O. Box: 11-5020, Beirut,
Lebanon.
E-mail: srs915@student.bau.edu.lb
2Institut Élie Cartan de
Lorraine,
Université de Lorraine - Metz,
France.
Abstract:
In 2000, Francini solved the inverse conductivity problem for twice-differentiable conductivities and permittivities. This solution was considered to be the first approach using D-bar methods with complex conductivities. In 2012, based on Francini's work, Hamilton introduced a reconstruction method of the conductivity distribution with complex values. The method consists of six steps. A voltage potential is applied on the boundary. Solving a D-Bar equation gives the complex conductivity. In this paper, the stability of the D-Bar equation is studied via two approximations, texp and tB, for the scattering transform. The study is based on rewriting the reconstruction method in terms of continuous operators. The conductivity is considered to be non smooth.
Paper's Title:
Action of Differential Operators On Chirpsconstruct On L∞
Author(s):
Taoufik El Bouayachi and Naji Yebari
Laboratoire de Mathematiques et
applications,
Faculty of sciences and techniques, Tangier,
Morocco.
E-mail:
figo407@gmail.com,
yebarinaji@gmail.com
Abstract:
We will study in this work the action of differential operators on L∞ chirps and we will give a new definition of logarithmic chirp. Finally we will study the action of singular integral operators on chirps by wavelet characterization and Kernel method.
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