In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.

We introduce several color image restoration algorithms based on the Mumford-Shah model and nonlocal image information. The standard Ambrosio-Tortorelli and Shah models are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, textures are not local in nature and require semi-local/non-local information to be denoised effic...

In this paper a novel region-merging image segmentation approach is presented. This approach is based on a two-step procedure: a distance metric is learned from some features on the image, then a piecewise approximation function for the Mumford-Shah model is optimized by this metric. The global optimum of the approximation function is inductively achieved under high polynomial terms of the Maha...

We use a probabilistic approach to produce sharp asymptotic estimates as n → ∞ for the Laplace transform of Pn, where P is a fixed complex polynomial. As a consequence we obtain a new elementary proof of a result of Askey-Gillis-Ismail-Offer-Rashed, [1, 3] in the combinatorial theory of derangements.

D.E. Segall, Alejandro Strachan, Sohrab Ismail-Beigi, William A. Goddard III, and T.A. Arias Department of Physics, Massachusetts Institute of Technology, Cambridge MA 02139 2 Materials and Process Simulation Center, Beckman Institute (139-74) California Institute of Technology, Pasadena, CA 91125 Department of Physics, University of California at Berkeley, Berkeley, CA 94720 Laboratory of Atom...

In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through particular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, BleimannButzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.

Effects of green tea on ACE gene expression in rat liver in CCl4-induced cirrhosis Syed Muhammad SHAHID*, Rozeena SHAIKH, Sana SHAMIM, Muhammad ISMAIL, Tabassum MAHBOOB The Karachi Institute of Biotechnology & Genetic Engineering, University of Karachi, Karachi, Pakistan Department of Biochemistry, University of Karachi, Karachi, Pakistan Institute of Biotechnology & Genetic Engineering, Islama...

Multimodality imaging in transcatheter aortic valve implantation (TAVI): comparison between cardiovascular magnetic resonance, cardiac computed tomography and echocardiography Jabbour Andrew, Francois Okoroafor, Bradley Park, Isabelle Roussin, Francisco Alpendurada, Tevfik Ismail, Maria N Paes, Simon Davies, Michael J Mullen, Nicola Delahunty, Sanjay Prasad, Michael Rubens, Neil Moat, Raad Mohi...

In the paper, three basic properties of the logarithmically N alternating monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are obtained in [W. E. Clark and M. E. H. Ismail, Inequalities involving gamma and psi functions, Anal. Appl. (Singap.) 1 (2003), no. 1, 129–140.], are generalized to the logarithmically N -a...

1 Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R. v. Ferrata 1, 27100 Pavia. Italy. ([email protected]). 2 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie. Bôıte courrier 187, 75252 Paris Cedex 05. France. ([email protected]). 3 Laboratoire de Mathématiques, Université Paris-Sud. Bâtiment 425, 91405 Orsay. France. ([email protected]...