Convergence of row sequences of simultaneous Pad\'{e}-Faber approximants

We consider row sequences of vector valued Pad\'{e}-Faber approximants (simultaneous Pad\'{e}-Faber approximants) and prove a Montessus de Ballore type theorem.Comment: This paper is accepted and will be published in Journal "Mathematical Notes" V. 103, 201

... nuvens apenas ... peça para televisão

Escrita em inglês, outubro-novembro de 1976. Primeira exibição em televisão na BBC2, 17 de abril de 1977. Publicada pela primeira vez por Faber and Faber, Londres, 1977, no livro Ends and Odds (“Impasses e Ímpares” ou “Resíduos e Refugos”). Tradução de Maria Helena Kopschitz com sugestões de Haroldo de Campos

Virasoro constraints and the Chern classes of the Hodge bundle

We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds CP^1 and CP^2 (or more generally, smooth projective curves and smooth simply-connected projective surfaces). We obtain predictions involving intersections of psi and lambda classes on the compactification of M_{g,n}. In particular, we show that the Virasoro conjecture for CP^2 implies the numerical part of Faber's conjecture on the tautological Chow ring of M_g.Comment: 12 pages, latex2

Improved Cosmological Constraints from Gravitational Lens Statistics

We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital Sky Survey (SDSS) data on the local velocity dispersion distribution function of E/S0 galaxies, $\phi(\sigma)$, to derive lens statistics constraints on $\Omega_\Lambda$ and $\Omega_m$. Previous studies of this kind relied on a combination of the E/S0 galaxy luminosity function and the Faber-Jackson relation to characterize the lens galaxy population. However, ignoring dispersion in the Faber-Jackson relation leads to a biased estimate of $\phi(\sigma)$ and therefore biased and overconfident constraints on the cosmological parameters. The measured velocity dispersion function from a large sample of E/S0 galaxies provides a more reliable method for probing cosmology with strong lens statistics. Our new constraints are in good agreement with recent results from the redshift-magnitude relation of Type Ia supernovae. Adopting the traditional assumption that the E/S0 velocity function is constant in comoving units, we find a maximum likelihood estimate of $\Omega_\Lambda = 0.74$--0.78 for a spatially flat unvierse (where the range reflects uncertainty in the number of E/S0 lenses in the CLASS sample), and a 95% confidence upper bound of $\Omega_\Lambda<0.86$. If $\phi(\sigma)$ instead evolves in accord with extended Press-Schechter theory, then the maximum likelihood estimate for $\Omega_\Lambda$ becomes 0.72--0.78, with the 95% confidence upper bound $\Omega_\Lambda<0.89$. Even without assuming flatness, lensing provides independent confirmation of the evidence from Type Ia supernovae for a nonzero dark energy component in the universe.Comment: 35 pages, 15 figures, to be published in Ap

Bounds for Faber coefficients of functions univalent in an ellipse

Let [omega] be a bounded, simply connected domain in C with [partial][omega] analytic. Assume that 0ϵ[omega]. Let S([omega]) denote the class of functions F(z) which are analytic and univalent in [omega] with F(0) = 0 and F[superscript]\u27(0) = 1. Let [phi][subscript]n(z)\[subscript]spn=0[infinity] be the Faber polynomials associated with [omega]. If F(z)ϵ S([omega]) then F(z) can be expanded in a Faber series of the form F(z) = [sigma][limits][subscript]spn=0[infinity]A[subscript]n[phi][subscript]n(z), zϵ[omega].LetE = \x+iy:x[superscript]2[over](5/4)[superscript]2 + y[superscript]2[over](3/4)[superscript]2 \u3c 1.;In Chapter 2, we obtain sharp bounds for the Faber coefficients A[subscript]0, A[subscript]1 and A[subscript]2 of functions F(z) in S(E) and in certain related classes. In addition. we find sharp bounds for certain linear combinations of the Faber coefficients for the same class of functions;In Chapter 3, we obtain global sharp bounds for the Faber coefficients of functions F(z) in certain related classes and subclasses of S(E)

Decedent Estates—Settlement for After-born Children

In Re Faber\u27s Estate, 305 N. Y. 200, 11I N. E. 2d 883 (1953)

Decedent Estates—Settlement for After-born Children

In Re Faber\u27s Estate, 305 N. Y. 200, 11I N. E. 2d 883 (1953)