Chain sequences and symmetric generalized orthogonal polynomials

in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Patterns of distribution of the hermit crab Loxopagurus loxochelis (Moreira, 1901) (Decapoda, Diogenidae) in two coastal areas of southern Brazil

The present study determined the distribution pattern of the hermit crab Loxopagurus loxochelis by a comparison of catch, depth and environmental factors at two separate bays (Caraguatatuba and Ubatuba) of Sao Paulo State, Brazil. The influence of these parameters on the distribution of males, non- ovigerous females and ovigerous females was also evaluated. Crabs were collected monthly, over a period of one year (from July/2002 to June/2003), in seven depths, from 5 to 35 m. Abiotic factors were monitored as follows: superficial and bottom salinity (psu), superficial and bottom temperature (C), organic matter content (%) and sediment composition (%). In total, 366 hermit crabs were sampled in Caraguatatuba and 126 in Ubatuba. The highest frequency of occurrence was verified at 20 m during winter (July) in Caraguatatuba and 25 m during summer (January) in Ubatuba. The highest occurrences were recorded in the regions with bottom salinities ranging from 34 to 36 psu, bottom temperatures from 18 to 24 C and, low percentages of organic matter, gravel and mud; and large proportion of sand in the substrate. There was no significant correlation between the total frequency of organisms and the environmental factors analyzed in both regions. This evidence suggests that other variables as biotic interactions can influence the pattern of distribution of L. loxochelis in the analyzed region, which is considered the limit of the northern distribution of this species.

Continuity of care and readmission in two service systems: a comparative Victorian and Groningen case-register study

Objective: We compared service consumption, continuity of care and risk of readmission in a record linkage follow-up study of cohorts of patients with schizophrenia and related disorders in Victoria (Australia) and in Groningen (The Netherlands). These areas are interesting to compare because mental health care is in a different stage of deiustitutionalization. More beds are available in Groningen and more community resources are available in Victoria. Method: The cohorts were followed for 4 years, since discharge from inpatient services using record linkage data available in the psychiatric case-registers in both areas. Survival analysis was used to study continuity of care and risk of readmission. Results: Available indicators showed a higher level of continuity of care in Victoria. While the relative risk of readmission was the same in both areas and not affected by aftercare contact after discharge, the number of days spent in hospital was much higher in the Groningen register area. Conclusion: These findings provide further support for earlier reports that the risk of readmission is predominantly affected by attributes of mental illness. However, the duration of admissions, is strongly affected by service system variables, including the provision of continuity of care.

Reducing the number of membership functions in linguistic variables

Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations Research

Bancroftian filariasis in two urban areas of Recife, Brasil: the role of individual risk factors

Bancroftian filariasis is spreading in towns of endemic areas as in Recife, northeastern Brazil, where it is a major public health problem. This paper deals with the prevalence of microfilaraemia and filarial disease in two urban areas of Recife, studying their association with individual characteristics and variables related to the exposure to the vectors. The parasitologic survey was performed through a "door-to-door" census and microfilaraemia was examined by the thick-drop technique using 45µl of peripheral blood collected between 20:00 and 24:00 o' clock. 2,863 individuals aged between 5 and 65 years were interviewed and submitted to clinical examination. Males aged between 15 and 44 years old presented the greatest risk of being microfilaraemic. Microfilaraemia was also significantly associated with no use of bednet to sleep. The risk of being microfilaraemic was greater among those who had lived in the studied areas for more than 5 years. The overall disease prevalence was 6.3%. Males presented the greatest risk of developing acute disease. The risk of developing chronic manifestations was also greater among males and increased with age. We found no association between time of residence, bednet use, microfilaraemia and acute and chronic disease. We may conclude that in endemic areas there are subgroups of individuals who has a higher risk of being microfilariae carriers due to different behaviours in relation to vector contact.

Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

Psychiatric morbidity and quality of life of primary care attenders in two cities in Brazil

Objective: To identify the associations among quality of life (QoL), social determinants and psychological distress in primary care in two cities in Brazil. Methods: A cross-sectional study with 1,466 patients from 2009 to 2010. The statistical analysis used the t-test to compare the variables of interest to the study. Results: The prevalence of Common Mental Disorders (CMD3), severe forms of Common Mental Disorders (CMD5), anxiety and depression were 20.5%, 32%, 37% and 25.1% respectively. Thes presence of psychological distress is associated with worse QoL among the patients studied, especially those older than 40 years of age. In cases of CMD3, those with higher income and educational levels presented higher QoL in the psychical and psychological domains. For the cases of probable anxiety, those with higher educational levels presented lower scores on the physical and social relationship scores. Conclusion: Psychological distress can be associated with a worse QoL among those studied and can be influenced by socioeconomic conditions. Therefore, it is important to structure patient-centered help, which should also include patients’ social contexts.

Lipid profile and cardiovascular risk in two Amazonian populations

OBJECTIVE: To compare the lipid profiles and coronary heart disease risks of 2 Brazilian Amazonian populations as follows: a riverside population (village of Vigia) and an urban population (city of Belém in the state of Pará). METHODS: Fifty individuals controlled for age and sex were assessed in each region, and the major risk factors for coronary heart disease were analyzed. RESULTS: According to the National Cholesterol Education Program (NCEP III) and using the Framingham score, both populations had the same absolute risk of events (Vigia = 5.4 ± 1 vs Belém = 5.7 ± 1), although the population of Vigia had a lower consumption of saturated fat (P<0.0001), a greater consumption of mono- and polyunsaturated fat (P<0.03), in addition to lower values for body mass index (25.4± 0.6 vs 27.6 ± 0.7 kg/m², P<0.02), of biceps skin fold (18.6 ± 1.1 vs 27.5 ± 1.3 mm, P<0.0001), of triceps skin fold (28.7 ± 1.2 vs 37.3 ± 1.7 mm, P<0.002), and of total cholesterol (205 ± 5 vs 223 ± 6 mg/dL, P< 0.03) and triglycerides (119 ± 9 vs 177 ± 18 mg/dL, P<0.005). Both populations did not differ in regard to HDL-C (46 ± 1 vs 46 ± 1 mg/dL), LDL-C (135 ± 4 vs 144 ± 5 mg/dL) and blood pressure (SBP 124 ± 3 vs 128 ± 3 mmHg; DBP 80 ± 2 vs 82 ± 2 mmHg). CONCLUSION: The riverside and urban populations of Amazonia had similar cardiovascular risks. However, the marked difference in the variables studied suggests that different strategies of prevention should be applied.

Seasonal variation in natural populations of Drosophila spp. (Diptera) in two woodlands in the State of São Paulo, Brazil

The composition and the seasonality of the natural populations of Drosophila species in relation to the climatic variables temperature and rainfall were analyzed from September 1998 through October 1999 by monthly collections, in two woodlands in the Northwest of the State of São Paulo, Brazil. The diversity dominance component curves were inclined, reflecting low diversity and high dominance of few species. Among the 25 species recorded, Drosophila sturtevanti Duda, 1927 was the most frequent and abundant. On the opposite to data in literature, D. paranaensis Barros, 1950 abundance and frequency were greater than those from D. mercatorum Patterson & Wheeler, 1942. A positive correlation between abundance and rainfall was observed for D. nebulosa Sturtevant, 1916. These data are indicative of changes in the populations structure due to new adaptive strategies arised in response to environmental modifications.

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

Sex difference and the role of leptin in the association between high-sensitivity C-reactive protein and adiposity in two different populations.

Elevated high-sensitivity C-reactive protein (hs-CRP) concentration is associated with an increased risk of cardiovascular disease but this association seems to be largely mediated via conventional cardiovascular risk factors. In particular, the association between hs-CRP and obesity has been extensively demonstrated and correlations are stronger in women than men. We used fractional polynomials-a method that allows flexible modeling of non linear relations-to investigate the dose/response mathematical relationship between hs-CRP and several indicators of adiposity in Caucasians (Switzerland) and Africans (Seychelles) surveyed in two population-based studies. This relationship was non-linear exhibiting a steeper slope for low levels of hs-CRP and a higher level in women. The observed sex difference in the relationship between hs-CRP and adiposity almost disappeared upon adjustment for leptin, suggesting that these sex differences might be partially mediated, by leptin. All these relationship were similar in Caucasians and Africans. This is the first report on a non-linear relation, stratified by gender, between hs-CRP and adiposity.