The birth and death processes are closely related to the orthogonal polynomials. The latter allows determining the stochastic matrix associated with these processes. Let us also note that these processes are stationary Markov processes whose state space is the nonnegative integers. Many authors treated the question of the existing relationship between the birth and death processes and the ortho...

The symmetric Al-Salam–Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christianse...

The symmetric Al-Salam and Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christi...

1 Department of Biochemistry, Pir Mehr Ali Shah Arid Agriculture University Rawalpindi, Pakistan. 2 Department of Plant Breeding and Genetics, Pir Mehr Ali Shah Arid Agriculture University Rawalpindi, Pakistan. 3 Department of Chemistry and Biochemistry, University of Agriculture Faisalabad, Pakistan. 4 Pakistan Museum of Natural History, Islamabad, Pakistan. 5 Pakistan Science Foundation, Isla...

Department of Oral Pathology and Microbiology, Manubhai Patel Dental College and Hospital, ORI, Vadodara, Gujarat, India Department of Pediatric and Preventive Dentistry, Manubhai Patel Dental College and Hospital, ORI, Vadodara, Gujarat, India Department of Oral Pathology and Microbiology, K M Shah Dental College and Hospital, Vadodara, Gujarat, India Department of Pedodontics and Preventive D...

Department of Oral and Maxillofacial Pathology, Bangalore Institute of Dental Sciences and Hospital, Bengaluru, Karnataka, India Department of Oral Pathology and Microbiology, Bangalore Institute of Dental Sciences, Bengaluru, Karnataka, India Department of Conservative Dentistry and Endodontics, K M Shah Dental College and Hospital, Vadodara, Gujarat, India Department of Pedodontics and Preven...

Shah et al have recently reported the first successful sequencing of the entire genome of a solid tumour (Shah et al, 2009). Philippe Bedard and Christos Sotiriou analyse their findings as well as the challenges of applying the study of cancer genomes to clinical cancer care.

In this work, we first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah paradigm from a curve evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Each gradient step ...

We propose a novel convex prior for multilabel optimization which allows to impose arbitrary distances between labels. Only symmetry, d(i, j) ≥ 0 and d(i, i) = 0 are required. In contrast to previous grid based approaches for the nonmetric case, the proposed prior is formulated in the continuous setting avoiding grid artifacts. In particular, the model is easy to implement, provides a convex re...

We give a sufficient condition for a first order infinitesimal deformation of a curve on a 3-fold to be obstructed. As application we construct generically non-reduced components of the Hilbert schemes of uniruled 3-folds and the Hom scheme from a general curve of genus five to a general cubic 3-fold.