Solution properties of the de Branges differential recurrence equation

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system Λn/k(t) which (by Todorov and Wilf) was realized to be directly connected with de Branges', Tn/k(t)=-kΛn/k(t), and the positivity results in both proofs Tn/k(t)<=0 are essentially the same. In this paper we study differential recurrence equations equivalent to de Branges' original ones and show that many solutions of these differential recurrence equations don't change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.

Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen

Die q-Analysis ist eine spezielle Diskretisierung der Analysis auf einem Gitter, welches eine geometrische Folge darstellt, und findet insbesondere in der Quantenphysik eine breite Anwendung, ist aber auch in der Theorie der q-orthogonalen Polynome und speziellen Funktionen von großer Bedeutung. Die betrachteten mathematischen Objekte aus der q-Welt weisen meist eine recht komplizierte Struktur auf und es liegt daher nahe, sie mit Computeralgebrasystemen zu behandeln. In der vorliegenden Dissertation werden Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen vorgestellt. Alle Algorithmen sind in dem Maple-Package qFPS, welches integraler Bestandteil der Arbeit ist, implementiert. Nachdem in den ersten beiden Kapiteln Grundlagen geschaffen werden, werden im dritten Kapitel Algorithmen präsentiert, mit denen man zu einer q-holonomen Funktion q-holonome Rekursionsgleichungen durch Kenntnis derer q-Shifts aufstellen kann. Operationen mit q-holonomen Rekursionen werden ebenfalls behandelt. Im vierten Kapitel werden effiziente Methoden zur Bestimmung polynomialer, rationaler und q-hypergeometrischer Lösungen von q-holonomen Rekursionen beschrieben. Das fünfte Kapitel beschäftigt sich mit q-hypergeometrischen Potenzreihen bzgl. spezieller Polynombasen. Wir formulieren einen neuen Algorithmus, der zu einer q-holonomen Rekursionsgleichung einer q-hypergeometrischen Reihe mit nichttrivialem Entwicklungspunkt die entsprechende q-holonome Rekursionsgleichung für die Koeffizienten ermittelt. Ferner können wir einen neuen Algorithmus angeben, der umgekehrt zu einer q-holonomen Rekursionsgleichung für die Koeffizienten eine q-holonome Rekursionsgleichung der Reihe bestimmt und der nützlich ist, um q-holonome Rekursionen für bestimmte verallgemeinerte q-hypergeometrische Funktionen aufzustellen. Mit Formulierung des q-Taylorsatzes haben wir schließlich alle Zutaten zusammen, um das Hauptergebnis dieser Arbeit, das q-Analogon des FPS-Algorithmus zu erhalten. Wolfram Koepfs FPS-Algorithmus aus dem Jahre 1992 bestimmt zu einer gegebenen holonomen Funktion die entsprechende hypergeometrische Reihe. Wir erweitern den Algorithmus dahingehend, dass sogar Linearkombinationen q-hypergeometrischer Potenzreihen bestimmt werden können. ________________________________________________________________________________________________________________

NLO QCD Corrections to the Polarized Photo- and Hadroproduction of Heavy Quarks

The complete details of our calculation of the NLO QCD corrections to heavy flavor photo- and hadroproduction with longitudinally polarized initial states are presented. The main motivation for investigating these processes is the determination of the polarized gluon density at the COMPASS and RHIC experiments, respectively, in the near future. All methods used in the computation are extensively documented, providing a self-contained introduction to this type of calculations. Some employed tools also may be of general interest, e.g., the series expansion of hypergeometric functions. The relevant parton level results are collected and plotted in the form of scaling functions. However, the simplification of the obtained gluon-gluon virtual contributions has not been completed yet. Thus NLO phenomenological predictions are only given in the case of photoproduction. The theoretical uncertainties of these predictions, in particular with respect to the heavy quark mass, are carefully considered. Also it is shown that transverse momentum cuts can considerably enhance the measured production asymmetries. Finally unpolarized heavy quark production is reviewed in order to derive conditions for a successful interpretation of future spin-dependent experimental data.

Processes of task performance as measured by the assessment of motor and process skills (AMPS): a predictor of work-related outcomes for adults with schizophrenia?

Objective: To determine whether the processes of task performance as measured by the Assessment of Motor and Process Skills (AMPS) would discriminate between the employment levels of adults with schizophrenia. Participants: Twenty adults with schizophrenia who were engaged either in competitive employment, supported employment, prevocational training, or nonvocational activities, participated in this exploratory study. Methods: Each participant completed the AMPS, the Positive and Negative Syndrome Scale (PANSS), the Addiction Severity Index (ASI), and theWorker Role Interview (WRI) to gather data about their occupational performance, symptoms, drug / alcohol use, and psychosocial / environmental factors that might influence their work related outcomes. Results: Analysis revealed a moderate correlation between the level of employment and the global scores of the process skills scale in the AMPS. Conclusions: This should be seen as preliminary evidence that beyond the basic cognitive functions, processes of task performance may also be a predictor of work related outcomes for this population. The results also highlighted the importance of considering personal causation and worker roles when assessing the work capacities of these clients. Finally, findings supported the four levels of employment used in this study, which appeared to form a continuum from nonvocational activities, prevocational training, supported employment, through to competitive employment.

Representações sociais, relações de gênero e programas de assistência e educação à saúde da mulher no climatério em Natal/RN

Climacteric is the name of the period of the human life that it is going from the 40 years old, approximately, until the 65 years old. Though, for besides a biological phase of the woman's life, the climacteric is an object of the social world that is rendered to different apprehensions and readings on the symbolic plan. In this study, it was looked for to know the social representations, that health' professionals acting in the programs of the climacteric and the users of those same services, build in respect of that purpose. Besides, it tried to be seen that the social hegemonic representation that guides the actions and the agents' attitudes in the practices of attendance and education for the woman's health in the climacteric in the extent of the investigated institutions. The data were collected through interviews, questionnaire, focal discussion group and direct observation. The observation field was constituted by the three institutions that develop the attendance and education for the woman's health in the climacteric phase, in the city of Natal. A gender perspective was also been adopted, sought to evidence as the cognitive structures that assure the masculine power reproduction, pronounce to the social representations to build a sense to the investigated purpose. It was verified that the social representations of the climacteric are built mainly around the semantic fields old age and disease. For the health professionals, the meaning of the simbol old age carries the marks of the indentified system of the middle class employed, but also, of the feminine habitus that guides them to have an ethical and aesthetic apprehension of their own body. The climacteric, in that way, is seen as a difficult phase , a painful event that scares . For the women attended by those professionals, the sign old age means feeling emphasis from the biological climacteric aspects, in other words, the sensations and signs that forbid the body to accomplish certain linked basic life functions. Along the whole course of this thesis, it was verified that the climacteric is a complex phenomenon that needs to be faced as such. While cultural phenomenon, it is urgent to look for means to help to combat the centrality of the professional representations that face the climacteric as old age and disease, particularly in the field of health

Convolutions and zeros of orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Non-planar double-box, massive and massless pentabox Feynman integrals in the negative-dimensional approach

The negative-dimensional integration method is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass, and in the case all of them are massless. Our results are given in terms of hypergeometric functions of Mandelstam variables and also for arbitrary exponents of propagators and dimension D.

epsilon-Expansion for nonplanar six-propagators double boxes

We present calculations for a nonplanar double box with four massless, massive external, and internal legs propagators. The results are expressed for arbitrary exponents of propagators and dimension in terms of Lauricella's hypergeometric functions of three variables and hypergeometric-like multiple series.

Two-Point Function at Two Loops via Triangle Diagram Insertion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Expressed sequence tags from Atta laevigata and identification of candidate genes for the control of pest leaf-cutting ants.

Leafcutters are the highest evolved within Neotropical ants in the tribe Attini and model systems for studying caste formation, labor division and symbiosis with microorganisms. Some species of leafcutters are agricultural pests controlled by chemicals which affect other animals and accumulate in the environment. Aiming to provide genetic basis for the study of leafcutters and for the development of more specific and environmentally friendly methods for the control of pest leafcutters, we generated expressed sequence tag data from Atta laevigata, one of the pest ants with broad geographic distribution in South America. Results: The analysis of the expressed sequence tags allowed us to characterize 2,006 unique sequences in Atta laevigata. Sixteen of these genes had a high number of transcripts and are likely positively selected for high level of gene expression, being responsible for three basic biological functions: energy conservation through redox reactions in mitochondria; cytoskeleton and muscle structuring; regulation of gene expression and metabolism. Based on leafcutters lifestyle and reports of genes involved in key processes of other social insects, we identified 146 sequences potential targets for controlling pest leafcutters. The targets are responsible for antixenobiosis, development and longevity, immunity, resistance to pathogens, pheromone function, cell signaling, behavior, polysaccharide metabolism and arginine kynase activity. Conclusion: The generation and analysis of expressed sequence tags from Atta laevigata have provided important genetic basis for future studies on the biology of leaf-cutting ants and may contribute to the development of a more specific and environmentally friendly method for the control of agricultural pest leafcutters.

National public investment systems in Barbados, Guyana, Jamaica and Trinidad and Tabago

Includes bibliography

Policy and programme evaluation in the English-speaking Caribbean: conceptual and practical issues

Includes bibliography

The British Virgin Islands national integrated development strategy

Includes bibliography

Long-term planning: institutional action and restructuring in the Caribbean

Includes bibliography

Analogia entre propriedades de alguns polinômios ortogonais em uma e em várias variáveis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)