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2: Paper Source PDF document

Paper's Title:

Numerical Studies on Dynamical Systems Method for Solving Ill-posed Problems with Noise

Author(s):

N. H. Sweilam and A. M. Nagy

Mathematics Department, Faculty of Science,
Cairo University,
Giza, Egypt.
n_sweilam@yahoo.com

Mathematics Department, Faculty of Science,
Benha University,
Benha, Egypt.
abdelhameed_nagy@yahoo.com


Abstract:

In this paper, we apply the dynamical systems method proposed by A. G. RAMM, and the the variational regularization method to obtain numerical solution to some ill-posed problems with noise. The results obtained are compared to exact solutions. It is found that the dynamical systems method is preferable because it is easier to apply, highly stable, robust, and it always converges to the solution even for large size models.



1: Paper Source PDF document

Paper's Title:

C*-algebras Associated Noncommutative Circle and Their K-theory

Author(s):

Saleh Omran

Taif University,
Faculty of Science,
Taif,
KSA

South Valley University,
Faculty of Science,
Math. Dep.
Qena,
Egypt

salehomran@yahoo.com

Abstract:

In this article we investigate the universal C*-algebras associated to certain 1 - dimensional simplicial flag complexes which describe the noncommutative circle. We denote it by S1nc. We examine the K-theory of this algebra and the subalgebras S1nc/Ik, Ik . Where Ik, for each k, is the ideal in S1nc generated by all products of generators hs containing at least k+1 pairwise different generators. Moreover we prove that such algebra divided by the ideal I2 is commutative.



1: Paper Source PDF document

Paper's Title:

Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated f-divergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.


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