In order to approximate the integral I( f ) = ∫ b a f (x)dx, where f is a sufficiently smooth function, models for quadrature rules are developed using a given panel of n (n ≥ 2) equally spaced points. These models arise from the undetermined coefficients method, using a Newton’s basis for polynomials. Although part of the final product is algebraically equivalent to the well known closed Newto...

The solution of an integral equation arising in a covariance factorization problem is obtained by a Newton-Raphson iteration that is almost always globally convergent. Interpretations of the iterates are given, and the result is shown to specialize to known algorithms when the covariance is stationary with a rational Fourier transform.

We express the cohomology of the basic Newton stratum of some unitary Shimura varieties associated to division algebras in terms of automorphic representations of the group in the Shimura datum. 2010 Mathematics Subject Classification: Primary 11G18 ; Secondary 11F70, 11F72.

Let L be a quadratic imaginary field, inert at the rational prime p. Fix an integer n ≥ 3, and let M be the moduli space (in characteristic p) of principally polarized abelian varieties of dimension n equipped with an action by OL of signature (1, n−1). We show that each Newton stratum of M, other than the supersingular stratum, is irreducible.

The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in I1 provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an approximation result. An application to error localization in spectral factorization is s...

Pseudo-absences, pseudo-models and pseudo-niches: pitfalls of model selection based on the area under the curve Duncan Golicher a b , Andrew Ford b , Luis Cayuela c & Adrian Newton b a El Colegio de la Frontera Sur, Conservación de la Biodiversidad, San Cristóbal de las Casas, Mexico b Applied Sciences, Bournemouth University, Bournemouth, UK c Área de Biodiversidad y Conservación, Universidad ...

In the Laurent expansion ζ(s, a) = 1 s− 1 + ∞ ∑ k=0 (−1)γk(a) k! (s− 1) , 0 < a ≤ 1, of the Riemann-Hurwitz zeta function, the coefficients γk(a) are known as Stieltjes, or generalized Euler, constants. [When a = 1, ζ(s, 1) = ζ(s) (the Riemann zeta function), and γk(1) = γk.] We present a new approach to high-precision approximation of γk(a). Plots of our results reveal much structure in the gr...

We show how ideas originating in the theory of dynamical systems inspire a new approach to numerical integration of functions. Any Lebesgue integral can be approximated by a sequence of integrals with respect to equidistributions, i.e. evenly weighted discrete probability measures concentrated on an equidistributed set. We prove that, in the case where the integrand is real analytic, suitable l...

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically com...