On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

Proteína c reactiva ultrasensible (PCR-h) en el dolor torácico de probabilidad intermedia para síndrome coronario agudo

INTRODUCCION: El dolor torácico es una de las principales causas de consulta en los servicios de urgencias y cardiología, se convierte en un reto clasificar a los pacientes empleando una herramienta diagnóstica lo suficientemente sensible y especifica para establecer riesgo y pronóstico, la estrecha relación existente entre enfermedad aterosclerótica e inflamación ha dirigido su atención al papel de marcadores plasmáticos de inflamación como predictores de riesgo de eventos cardiovasculares. La Proteína C reactiva (PCR) ha sido ampliamente estudiada en pacientes con factores de riesgo cardiovascular y Eventos coronarios Agudos, pero se desconoce el comportamiento en pacientes con dolor torácico de probabilidad intermedia. OBJETIVOS: Determinar la utilidad y comportamiento de la Proteína C reactiva en pacientes con dolor torácico de probabilidad Intermedia para síndrome coronario. MATERIALES Y METODOS: Este estudio fue realizado entre junio 2008 y febrero de 2009 en una institución de referencia en cardiológica ( Fundación Cardio Infantil, Bogotá-Colombia), Se Estudiaron pacientes con EKG normal o no diagnostico y marcadores de injuria miocardica negativos. Los pacientes continuaron su estudio según las recomendaciones y guías internacionales para dolor torácico. Nosotros realizamos dos tomas de PCR, Una PCR antes de 12 horas de iniciado el dolor torácico y otra PCR después de las 18 Hrs de iniciado el dolor torácico, se realizo la deferencia entre estas dos PCR (PCR 18 hrs vs PCR basal) Con estos 3 resultados se hizo el análisis estadístico para hallar sensibilidad, especificidad, valor predictivo positivo, valor predictivo negativo, comparándolo contra las pruebas de provocación de isquemia y cateterismo. RESULTADOS: Un total de 203 pacientes fueron analizaron. Con un promedio de edad fue de 60.8 ± 11 años, Los dos géneros tuvieron una distribución sin diferencia significativas. Los factores de riesgo asociados fueron: Hipertensión arterial 76%(n=155), Dislipidemia 68.1%(n=139), Diabetes Mellitus 20.6%(n=42), Obesidad 7.4%(n=15) y tabaquismo 9.3%(n=19). El total de cateterismos realizados fueron 66 pruebas: Normal el 27%(n=18), lesiones no significativas el 25.8%(n=17) y lesiones Obstructivas 47%(n=31). La PCR tuvo una utilidad diagnostica baja, la PCR a las 18 horas es la mejor prueba diagnóstica , con un mejor comportamiento del área de la curva ROC 0.74 (IC , 0.64-0.83), con sensibilidad del 16.13% (IC 95%, 1.57-30.69), especificidad del 98.26%( IC 955, 96.01-100), un valor predictivo negativo de 86.67%(IC 95%, 81.64-91.69). En el seguimiento a los 30 días no encontró nuevas hospitalizaciones de causa cardiovascular. CONCLUSIONES: Nuestro estudio muestra una utilidad diagnostico baja de la PCR en el dolor torácico de probabilidad intermedia para enfermedad coronaria, el mejor comportamiento diagnostico se encontró en la PCR a las 18 hrs con una alta especificidad y un alto Valor predictivo negativo para un valor de PCR > de 3mg/dl, siendo menor la utilidad de la PCR basal y diferencia de la PCR. diferencia de la PCR. Estos hallazgos no se correlacionaron con estudios previos. No se pudo establecer un punto de Corte de la PCR diferente a los ya existentes debido a la variabilidad de la PCR entre la población de estudio. Las limitaciones encontradas en nuestro estudio hacen necesaria la realización de un estudio multicéntrico.

Utilidad de la patología placentaria en el diagnóstico de sepsis temprana en recién nacidos pretermino

Antecedentes : la incidencia de sepsis neonatal tempana en prematuros es del 40% en nuestro medio, con mortalidad entre el 15-50% de los casos, el cual aumenta exponencialmente con la prematurez y se relaciona con secuelas neurológicas y pulmonares. Hasta la fecha no se han dado conclusiones definitivas en cuanto a la mejor prueba diagnóstica en este tópico, por lo anterior es de vital importancia encontrar el mejor método para su detección precoz. Objetivo: evaluar la utilidad de la histopatología placentaria en el diagnóstico de sepsis neonatal temprana de los recién nacidos menores de 36 semanas de edad gestacional, de la Fundación Santa Fe de Bogotá. Metodología: estudio de prueba diagnóstica donde se describieron los resultados obtenidos del análisis de la histopatología placentaria de los recién nacidos pretermino con sospecha de sepsis temprana comparados con el diagnostico de sepsis temprana probada. Resultados : se analizaron 114 pacientes con factores de riesgo para sepsis temprana de los cuales 74 tuvieron diagnóstico de sepsis probable confirmándose en cinco casos, encontrándose así para la histopatología placentaria sensibilidad del 100% IC 95% (90%-100%), especificidad 78.9% (IC 95% 70.7-87.0), índice de validez 79.8% (IC 95% 72%-87.6%), VPP 17.7 (IC 95%: 1.89%-33.8%) y VPN 100% (IC:98.7%-100%). Conclusión La corioamnionitis histológica es un biomarcador relevante en el diagnóstico oportuno de sepsis temprana probada en recién nacidos pretermino, ofreciendo una opción de ayuda diagnostica, no invasiva, con resultados definitivos en 24 horas.

Analisis de la politica exterior china para Africa Subsahariana en materia politica y energetica. Una aproximacion a la relacion sino sudanesa. Periodo 1996 - 2005

Este trabajo explica las razones por las cuales China se estrecha sus vinculos con Afirca. El tema principal es el inicio de la relacion sino-sudanesa y la evolucion de esta hasta el fin de la guerra civil en Sudan.

On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

Non-display uses of digital works: Google Books and beyond

With the advent of mass digitization projects, such as the Google Book Search, a peculiar shift has occurred in the way that copyright works are dealt with. Contrary to what has so far been the case, works are turned into machine-readable data to be automatically processed for various purposes without the expression of works being displayed to the public. In the Google Book Settlement Agreement, this new kind of usage is referred to as ‘non-display uses’ of digital works. The legitimacy of these uses has not yet been tested by Courts and does not comfortably fit in the current copyright doctrine, plainly because the works are not used as works but as something else, namely as data. Since non-display uses may prove to be a very lucrative market in the near future, with the potential to affect the way people use copyright works, we examine non-display uses under the prism of copyright principles to determine the boundaries of their legitimacy. Through this examination, we provide a categorization of the activities carried out under the heading of ‘non-display uses’, we examine their lawfulness under the current copyright doctrine and approach the phenomenon from the spectrum of data protection law that could apply, by analogy, to the use of copyright works as processable data.

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

In silico screening of HIV-1 non-nucleoside reverse transcriptase and protease inhibitors

Two targets, reverse transcriptase (RT) and protease from HIV-1, were used during the past two decades to the discovery of non-nucleoside reverse transcriptase inhibitors (NNRTI) and protease inhibitors (PI) that belong to the arsenal of the antiretroviral therapy. Herein these enzymes were chosen as templates for conducting a computer-aided ligand design. Ligand and structure-based drug designs were the starting points to select compounds from a database bearing more than five million compounds by means of cheminformatic tools. New promising lead structures are retrieved from the database, which are open to acquisition and test. Classes of molecules already described as NNRTI or PI in the literature also came out and were useful to prove the reliability of the workflow, and thus validating the work carried out so far. (c) 2007 Elsevier Masson SAS. All rights reserved.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.

New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

In this paper, a general class of Halanay-type non-autonomous functional differential inequalities is considered. A new concept of stability, namely global generalized exponential stability, is proposed. We first prove some new generalizations of the Halanay inequality. We then derive explicit criteria for global generalized exponential stability of nonlinear non-autonomous time-delay systems based on our new generalized Halanay inequalities. Numerical examples and simulations are provided to illustrate the effectiveness of the obtained results.

Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.