Localized linear polynomial operators and quadrature formulas on the sphere

The purpose of this paper is to construct universal, auto--adaptive, localized, linear, polynomial (-valued) operators based on scattered data on the (hyper--)sphere \SS^q ($q\ge 2$). The approximation and localization properties of our operators are studied theoretically in deterministic as well as probabilistic settings. Numerical experiments are presented to demonstrate their superiority over traditional least squares and discrete Fourier projection polynomial approximations. An essential ingredient in our construction is the construction of quadrature formulas based on scattered data, exact for integrating spherical polynomials of (moderately) high degree. Our formulas are based on scattered sites; i.e., in contrast to such well known formulas as Driscoll--Healy formulas, we need not choose the location of the sites in any particular manner. While the previous attempts to construct such formulas have yielded formulas exact for spherical polynomials of degree at most 18, we are able to construct formulas exact for spherical polynomials of degree 178.Comment: 24 pages 2 figures, accepted for publication in SIAM J. Numer. Ana

Role of the Mean-field in Bloch Oscillations of a Bose-Einstein Condensate in an Optical Lattice and Harmonic Trap

Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses the dispersion of the condensate in momentum space. When the mean field becomes large, soliton and vortex structures appear in the condensate wavefunction.Comment: BEC simulation, 7 figure

Detubularized isolated ureterosigmoidostomy in a complicated common cloaca: A case report

Urinary incontinence in a child secondary to a severe congenital anatomical disorder or due to complication of a previous surgery can be difficult to manage. Decisions can be especially hard when a redo procedure is being considered. We present one such case where a 6 year old girl previously operated for cloaca was brought with incontinence and after much consideration of options available, underwent a modified ureterosigmoidostomy to aid in her continence. The modification used was detubularized isolated ureterosigmoidostomy, described by Atta et al in 1996

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Theory of random matrices with strong level confinement: orthogonal polynomial approach

Strongly non-Gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in presence and absence of hard edge in their energy spectra. Employing a theory of polynomials orthogonal with respect to exponential weights we calculate with asymptotic accuracy the two-point kernel over all distance scale, and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the endpoints of spectrum. We also obtain exact expressions for density of levels, one- and two-point Green's functions, and prove that new universal local relationship exists for suitably normalized and rescaled connected two-point Green's function. Connection between structure of Szeg\"o function entering strong polynomial asymptotics and mean-field equation is traced.Comment: 12 pages (latex), to appear in Physical Review

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

THE DOUBLE-DOUBLE BEND ACHROMAT (DDBA) LATTICE MODIFICATION FOR THE DIAMOND STORAGE RING

Abstract We present an overview of the status of the DDBA project, the various accelerator physics and engineering studies that have been carried out, and plans for the implementation of one or two DDBA cells in Diamond

Gendered vulnerabilities to climate change: insights from the semi-arid regions of Africa and Asia

Emerging and on-going research indicates that vulnerabilities to impacts of climate change are gendered. Still, policy approaches aimed at strengthening local communities’ adaptive capacity largely fail to recognize the gendered nature of everyday realities and experiences. This paper interrogates some of the emerging evidence in selected semi-arid countries of Africa and Asia from a gender perspective, using water scarcity as an illustrative example. It emphasizes the importance of moving beyond the counting of numbers of men and women to unpacking relations of power, of inclusion and exclusion in decision-making, and challenging cultural beliefs that have denied equal opportunities and rights to differently positioned people, especially those at the bottom of economic and social hierarchies. Such an approach would make policy and practice more relevant to people’s differentiated needs and responses