Determining radii of meromorphy via orthogonal polynomials on the unit circle

19 pages, no figures.-- MSC2000 codes: 30E10, 42C05, 41A20, 30D30.MR#: MR2016676 (2004k:30087)Zbl#: Zbl 1051.30033Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szegö functions.The research of D.B.R. and G.L.L. was supported, in part, by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under grant BFM 2000-0206-C04-01 and the research of G.L.L. was also supported by Ministerio da Ciencia e do Ensino Superior, under Grant PRAXIS XXI BCC-22201/99, and by INTAS under Grant 2000-272. The research of E.B.S. was supported, in part, by V.S. National Science Foundation Grant DMS-0296026.Publicad

Past and present potential distribution of the Iberian Abies species: A phytogeographic approach using pollen data and species distribution models

This is the accepted version of the following article: Alba-Sánchez, F., López-Sáez, J. A., Pando, B. B.-d., Linares, J. C., Nieto-Lugilde, D. and López-Merino, L. (2010), Past and present potential distribution of the Iberian Abies species: a phytogeographic approach using fossil pollen data and species distribution models. Diversity and Distributions, 16: 214–228, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/j.1472-4642.2010.00636.x/abstract.Aim - Quaternary palaeopalynological records collected throughout the Iberian Peninsula and species distribution models (SDMs) were integrated to gain a better understanding of the historical biogeography of the Iberian Abies species (i.e. Abies pinsapo and Abies alba). We hypothesize that SDMs and Abies palaeorecords are closely correlated, assuming a certain stasis in climatic and topographic ecological niche dimensions. In addition, the modelling results were used to assign the fossil records to A. alba or A. pinsapo, to identify environmental variables affecting their distribution, and to evaluate the ecological segregation between the two taxa. Location - The Iberian Peninsula. Methods - For the estimation of past Abies distributions, a hindcasting process was used. Abies pinsapo and A. alba were modelled individually, first calibrating the model for their current distributions in relation to the present climate, and then projecting it into the past—the last glacial maximum (LGM) and the Middle Holocene periods—in relation to palaeoclimate simulations. The resulting models were compared with Iberian-wide fossil pollen records to detect areas of overlap. Results - The overlap observed between past Abies refugia—inferred from fossil pollen records—and the SDMs helped to construct the Quaternary distribution of the Iberian Abies species. SDMs yielded two well-differentiated potential distributions: A. pinsapo throughout the Baetic mountain Range and A. alba along the Pyrenees and Cantabrian Range. These results propose that the two taxa remained isolated throughout the Quaternary, indicating a significant geographical and ecological segregation. In addition, no significant differences were detected comparing the three projections (present-day, Mid-Holocene and LGM), suggesting a relative climate stasis in the refuge areas during the Quaternary. Main conclusions - Our results confirm that SDM projections can provide a useful complement to palaeoecological studies, offering a less subjective and spatially explicit hypothesis concerning past geographic patterns of Iberian Abies species. The integration of ecological-niche characteristics from known occurrences of Abies species in conjunction with palaeoecological studies could constitute a suitable tool to define appropriate areas in which to focus proactive conservation strategies.The Andalusian Innovation, Science, and Industry Regional Ministry and the National Plan of the Spanish Government

Feature Selection for Big Visual Data: Overview and Challenges

International Conference Image Analysis and Recognition (ICIAR 2018, Póvoa de Varzim, Portugal

Asymptotics of orthogonal polynomials inside the unit circle and Szegö-Padé approximants

11 pages, no figures.-- MSC2000 codes: 42C05, 41A21.MR#: MR1858277 (2002h:42043)Zbl#: Zbl 1009.42016We study the asymptotic behavior of orthogonal polynomials inside the unit circle for a subclass of measures that satisfy Szegö's condition. We give a connection between such behavior and a Montessus de Ballore-type theorem for Szegö–Padé rational approximants of the corresponding Szegö function.The research of the second author (G.L.L.) was partially supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01. The research of the third author (E.B.S.) was supported, partly by NSF research Grant DMS-9801677.Publicad

Equilibrium currents in a Corbino graphene ring

We address the description of a graphene Corbino disk in the context of a tight binding approach that includes both kinetic and Rashba spin-orbit coupling due to an external out-of-plane electric field. Persistent equilibrium currents are induced by an external magnetic field breaking time reversal symmetry. By direct diagonalization, we compute the spectrum and focus on the dispersion near the $K$ points at the Fermi level. The dispersion keenly reproduces that of a continuum model in spite of the complexity of the boundary conditions. We validate the assumptions of the continuum model in terms of predominant zig-zag boundaries conditions and weak sub-band coupling. The wave functions displaying the lowest transverse modes are obtained, showing the predominance of edge states with charge density at the zig-zag edges. The persistent charge currents, nevertheless, do not follow the traditional argument of current cancellation from levels below the Fermi level, and thus they depart in the tight-binding from those found in the continuum model.Comment: 8 pages, 6 figure

Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.Comment: 3 pages, 1 figur