The Szeg\"o curve and Laguerre polynomials with large negative parameters

We study the asymptotic zero distribution of the rescaled Laguerre polynomials, $\displaystyle L_n^{(\alpha_n)}(nz)$, with the parameter $\alpha_n$ varying in such a way that $\displaystyle \lim_{n\rightarrow \infty}\alpha_n/n=-1$. The connection with the so-called Szeg\"{o} curve will be showed

Climate Change Impacts on Maize and Dry Bean Yields of smallholder farmers in Honduras

The rotation maize and dry bean provides the main food supply of smallholder farmers in Honduras. Crop model assessment of climate change impacts (2070?2099 compared to a 1961?1990 baseline) on a maize?dry bean rotation for several sites across a range of climatic zones and elevations in Honduras. Low productivity systems, together with an uncertain future climate, pose a high level of risk for food security. The cropping systems simulation dynamic model CropSyst was calibrated and validated upon field trail site at Zamorano, then run with baseline and future climate scenarios based upon general circulation models (GCM) and the ClimGen synthetic daily weather generator. Results indicate large uncertainty in crop production from various GCM simulations and future emissions scenarios, but generally reduced yields at low elevations by 0 % to 22 % in suitable areas for crop production and increased yield at the cooler, on the hillsides, where farming needs to reduce soil erosion with conservation techniques. Further studies are needed to investigate strategies to reduce impacts and to explore adaptation tactics

A Declarative Semantics for CLP with Qualification and Proximity

Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this paper we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and proof-theoretical characterizations of least program models as well as an implementation-independent notion of goal solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10

Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

9 pages, no figures.-- MSC2000 code: 33C45.MR#: MR2431543 (2009g:41009)Zbl#: Zbl 1155.33006We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same $n$th root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e−φ(x), giving a unified treatment for the so-called Freud (i.e., when φ has polynomial growth at infinity) and Erdös (when φ grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.Research by first two authors (C.D.M. and R.O.) was partially supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología of Spain, under grants MTM2005-08571 and MTM2007-68114. Research by third author (H.P.) was partially supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología of Spain, under grant MTM2006-13000-C03-02, by Comunidad de Madrid-Universidad Carlos III de Madrid, under grants CCG06-UC3M/EST-0690 and CCG07-UC3M/ESP-3339, by Centro de Investigación Matemática de Canarias (CIMAC) and by Vicerrectorado de Investigación de La Universidad de La Laguna: Convocatoria 2005 de Ayudas a Profesores Invitados.Publicad