On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

Teacher knowledge and classroom practice : examining the connection

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Give or take: thoughts on museum collections as working tools and their connection with human beings

This paper proposes a look at museums from the perspective of sociomuseology, an area of research and practice under development in countries such as Portugal, Brazil and Spain. Sociomuseology was born from the Latin new museology tradition and is closely connected with the International Movement for a New Museology (MINOM/ICOM). The Lusofona University in Lisbon offers MA and PhD programmes in Sociomuseology. The University supports a research centre in Sociomuseology and publishes the journals Cadernos de Sociomuseologia, in Portuguese, and Sociomuseology, in English (for more information see http://tercud.ulusofona.pt.). Sociomuseology concerns the study of the social role of museums and of the continuous changes in society that frame their trajectories. The practice of sociomuseologists is based on their work with the different dimensions of social and community development from ecomuseums to networking and other ways of organizing social action in the 21st century in which heritage plays a strategic role.

The role of pediatrician in hearing loss: from detection to connection

This paper presents a study investigating how informed pediatricians are about hearing loss and their ability to assist and refer parents of children with hearing loss.

The importance of parental involvement in language acquisition and activities and techniques to enhance the home-school connection

This study discusses the importance of parental involvement in children’s language development, and the related project offers parents books and activities to assist them in developing their children’s linguistic skills.

Stratospheric influence on baroclinic lifecycles and its connection to the Arctic Oscillation

Using an idealized primitive equation model, we investigate how stratospheric conditions alter the development of baroclinic instability in the troposphere. Starting from the lifecycle paradigm of Thorncroft et al., we consider the evolution of baroclinic lifecycles resulting from the addition of a stratospheric jet to the LC1 initial condition. We find that the addition of the stratospheric jet yields a net surface geopotential height anomaly that strongly resembles the Arctic Oscillation. With the additional modification of the tropospheric winds to resemble the high-AO climatology, the surface response is amplified by a factor 10 and, though dominated by the tropospheric changes, shows similar sensitivity to the stratospheric conditions.

Danish razors and Swedish rocks: Cosmology and the Bronze Age landscape

A recent study has suggested that the decorated Bronze Age metalwork of South Scandinavia depicted the path of the sun through the sky during the day and through the sea at night. At different stages in its journey it was accompanied by a horse or a ship. Similar images are found in prehistoric rock art, and this paper argues that, whilst there are important differences between the images in these two media, they also signal some of the same ideas.

The NAO troposphere–stratosphere connection

Using monthly mean data, daily data, and theoretical arguments, relationships between surface pressure variations associated with the North Atlantic Oscillation (NAO), tropopause height, and the strength of the stratospheric vortex are established. An increase in the NAO index leads to a stronger stratospheric vortex, about 4 days later, as a result of increased equatorward refraction of upward-propagating Rossby waves. At tropopause level the effects of the enhanced NAO index and stratospheric polar vortex are opposite, resulting in a lower tropopause over Iceland and a higher tropopause over the Arctic. The raising of the Arctic tropopause leads to a stretching and spinup of the tropospheric column and is therefore associated with a lowering of the surface pressure near the North Pole. For monthly mean data it is found that a standard deviation increase in the NAO index is associated with a 10% increase in the strength of the stratospheric vortex, as measured by potential vorticity at 500 K. A simple theoretical model predicts that this is associated with about 300-m elevation of the Arctic tropopause, as is observed, and a 5-hPa lowering of the surface pressure at the North Pole. The effects of the spinup of the tropospheric column may project on the NAO pattern so that the stratosphere acts as an integrator of the NAO index.

Tweaking the gain on platelet regulation: The tachykinin connection

Soluble factors such as ADP and thromboxane (TX) A(2) that are secreted or released by platelets at sites of tissue injury, mediate autocrine and paracrine regulation of platelet function, resulting in rapid localised thrombus formation. The suppression of platelet function, particularly through targeting such secondary regulatory mechanisms, that serve to 'fine-tune' the platelet response, has proven effective in the prevention of inappropriate platelet activation that results in thrombosis. The most commonly used anti-platelet approaches (ADP receptor antagonism or inhibition of TXA(2) synthesis), however, lack efficacy in many patients, suggesting the existence of additional uncharacterised mechanisms for the regulation of platelet function. Recent data, which form a focus of this review, have identified peripheral tachykinin peptide family members, such as substance P and the newly identified endokinins, as physiologically important positive feedback regulators of platelet function. The actions of tachykinins that are released from platelets during activation are mediated by the neurokinin-1 receptor. Initial analysis of the role of this receptor in platelet thrombus formation, and thrombosis in the mouse, indicate this to be a promising new target for the development of anti-thrombotic drugs. (C) 2008 Elsevier Ireland Ltd. All rights reserved.