Principles of Extremum and Application to some Problems of Analysis

AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.

Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

* This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.

Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55

Design, Synthesis And Biological Evaluation Of Hybrid Bioisoster Derivatives Of N-acylhydrazone And Furoxan Groups With Potential And Selective Anti-trypanosoma Cruzi Activity.

Hybrid bioisoster derivatives from N-acylhydrazones and furoxan groups were designed with the objective of obtaining at least a dual mechanism of action: cruzain inhibition and nitric oxide (NO) releasing activity. Fifteen designed compounds were synthesized varying the substitution in N-acylhydrazone and in furoxan group as well. They had its anti-Trypanosoma cruzi activity in amastigotes forms, NO releasing potential and inhibitory cruzain activity evaluated. The two most active compounds (6, 14) both in the parasite amastigotes and in the enzyme contain the nitro group in para position of the aromatic ring. The permeability screening in Caco-2 cell and cytotoxicity assay in human cells were performed for those most active compounds and both showed to be less cytotoxic than the reference drug, benznidazole. Compound 6 was the most promising, since besides activity it showed good permeability and selectivity index, higher than the reference drug. Thereby the compound 6 was considered as a possible candidate for additional studies.

Synthesis And Antiproliferative Activity Of 8-hydroxyquinoline Derivatives Containing A 1,2,3-triazole Moiety.

Twelve novel 8-hydroxyquinoline derivatives were synthesized with good yields by performing copper-catalyzed Huisgen 1,3-dipolar cycloaddition (click reaction) between an 8-O-alkylated-quinoline containing a terminal alkyne and various aromatic or protected sugar azides. These compounds were evaluated in vitro for their antiproliferative activity on various cancer cell types. Protected sugar derivative 16 was the most active compound in the series, exhibiting potent antiproliferative activity and high selectivity toward ovarian cancer cells (OVCAR-03, GI50 < 0.25 μg mL(-1)); this derivative was more active than the reference drug doxorubicin (OVCAR-03, GI50 = 0.43 μg mL(-1)). In structure-activity relationship (SAR) studies, the physico-chemical parameters of the compounds were evaluated and docking calculations were performed for the α-glucosidase active site to predict the possible mechanism of action of this series of compounds.

Design And Synthesis Of N-acylated Aza-goniothalamin Derivatives And Evaluation Of Their In Vitro And In Vivo Antitumor Activity.

Herein we describe the synthesis of a focused library of compounds based on the structure of goniothalamin (1) and the evaluation of the potential antitumor activity of the compounds. N-Acylation of aza-goniothalamin (2) restored the in vitro antiproliferative activity of this family of compounds. 1-(E)-But-2-enoyl-6-styryl-5,6-dihydropyridin-2(1H)-one (18) displayed enhanced antiproliferative activity. Both goniothalamin (1) and derivative 18 led to reactive oxygen species generation in PC-3 cells, which was probably a signal for caspase-dependent apoptosis. Treatment with derivative 18 promoted Annexin V/7-aminoactinomycin D double staining, which indicated apoptosis, and also led to G2 /M cell-cycle arrest. In vivo studies in Ehrlich ascitic and solid tumor models confirmed the antitumor activity of goniothalamin (1), without signs of toxicity. However, derivative 18 exhibited an unexpectedly lower in vivo antitumor activity, despite the treatments being administered at the same site of inoculation. Contrary to its in vitro profile, aza-goniothalamin (2) inhibited Ehrlich tumor growth, both on the ascitic and solid forms. Our findings highlight the importance of in vivo studies in the search for new candidates for cancer treatment.

Esi(+)-ms And Gc-ms Study Of The Hydrolysis Of N-azobenzyl Derivatives Of Chitosan.

New N-p-chloro-, N-p-bromo-, and N-p-nitrophenylazobenzylchitosan derivatives, as well as the corresponding azophenyl and azophenyl-p-sulfonic acids, were synthesized by coupling N-benzylvchitosan with aryl diazonium salts. The synthesized molecules were analyzed by UV-Vis, FT-IR, 1H-NMR and 15N-NMR spectroscopy. The capacity of copper chelation by these materials was studied by AAS. Chitosan and the derivatives were subjected to hydrolysis and the products were analyzed by ESI(+)-MS and GC-MS, confirming the formation of N-benzyl chitosan. Furthermore, the MS results indicate that a nucleophilic aromatic substitution (SnAr) reaction occurs under hydrolysis conditions, yielding chloroaniline from N-p-bromo-, and N-p-nitrophenylazo-benzylchitosan as well as bromoaniline from N-p-chloro-, and N-p-nitrophenylazobenzyl-chitosan.

Inequalities in the distribution of dental caries among 12-year-old Brazilian schoolchildren

We assessed the inequality in the distribution of dental caries and the association between indicators of socioeconomic status and caries experience in a representative sample of schoolchildren. This study followed a cross-sectional design, with a sample of 792 schoolchildren aged 12 years, representative of this age group in Santa Maria, RS, Brazil. Guardians answered questions on socioeconomic status and a dental examination provided information on the dental caries experience (DMF-T). Inequality in dental caries distribution was measured by the Gini coefficient and the Significant Caries Index (SiC). The assessment of association used Poisson regression models. Socioeconomic factors were associated with prevalence of dental caries for the whole sample and also for individuals with a high-caries level. Children from low-income households had the highest prevalence of dental caries. The Gini coefficient was 0.7 and the SiC Index 2.5. The percentage of caries prevalence was 39.3% (95% CI: 35.8%-42.8%) and the mean for DMF-T was 0.9 (± SD 1.5). Inequalities in the distribution of dental caries were observed and socioeconomic factors were found to be strong predictors of the prevalence of oral disease in children of this age group.

Antioxidant and antimicrobial properties of 2-(4,5-dihydro-1H-pyrazol-1-yl)-pyrimidine and 1-carboxamidino-1H-pyrazole derivatives

Five previously synthesized 4-trifluoromethyl-2-(5-aryl-3-styryl-1H-pyrazol-1yl)-pyrimidines and six 5-aryl-3-styryl-1-carboxamidino-1H-pyrazole derivatives were screened for their antioxidant proprieties. The antioxidant activities were evaluated by using the DPPH and the HRP/luminol/H2O2 chemiluminescence assay systems and for their antimicrobial activity (MIC). The results were good for those series in some concentration in comparison with the standards.

Inequalities in access and utilization of dental services: a cross-sectional study in an area covered by the Family Health Strategy

This cross-sectional study aimed to investigate the presence of inequalities in the access and use of dental services for people living in the coverage area of the Family Health Strategy (FHS) in Ponta Grossa, Paraná State, Brazil, and to assess individual determinants related to them. The sample consisted of 747 individuals who answered a pre-tested questionnaire. Data analysis was performed by chi-square test and Poisson regression analysis, obtaining explanatory models for recent use and, by limiting the analysis to those who sought dental care, for effective access. Results showed that 41% of the sample had recent dental visits. The lowest visit rates were observed among preschoolers and elderly people. The subjects who most identified the FHS as a regular source of dental care were children. Besides age, better socioeconomic conditions and the presence of a regular source of dental care were positively associated to recent dental visits. We identified inequalities in use and access to dental care, reinforcing the need to promote incentives to improve access for underserved populations.

Social inequalities in health among the elderly

The aim of the present study was to assess social inequalities in health status, health behavior and the use of health services based on education level. A population-based cross-sectional study was carried out involving 1,518 elderly residents of Campinas, São Paulo State, Brazil. Significant demographic and social differences were found between schooling strata. Elderly individuals with a higher degree of schooling are in greater proportion alcohol drinkers, physically active, have healthier diets and a lower prevalence of hypertension, diabetes, dizziness, headaches, back pain, visual impairment and denture use, and better self-rated health. But, there were no differences in the use of health services in the previous two weeks, in hospitalizations or surgeries in the previous year, nor in medicine intake over the previous three days. Among elderly people with hypertension and diabetes, there were no differences in the regular use of health services and medication. The results demonstrate social inequalities in different health indicators, along with equity in access to some health service components.

Periodontal outcomes and social, racial and gender inequalities in Brazil: a systematic review of the literature between 1999 and 2008

The objective of this study was to review the Brazilian epidemiologic literature on periodontal outcomes and socio-demographic factors, assessing bibliographic and methodological characteristics of this scientific production, as well as the consistency and statistical significance of the examined associations. A systematic review was carried out in six bibliographic sources. The review was limited to the period between 1999 and 2008, without any other type of restriction. Among the 410 papers identified, 29 were included in the review. An increasing number of articles, specifically in the last four years of study, was observed. However, there is a concentration of studies in the South and Southeast regions of Brazil, and many of them are not closely connected to theoretical formulations in the field. In spite of these shortcomings, the review findings corroborate the idea that poor socioeconomic conditions are associated with periodontal outcomes, as demonstrated primarily by income and schooling indicators.

Color/race inequalities in oral health among Brazilian adolescents

This study assessed oral health outcomes (perceived dental treatment need, untreated dental caries, gingival bleeding, periodontal pockets, and pain in teeth and gums), in relation to color/race inequalities among adolescents in each Brazilian region. The database included dental examination and interview of 16,833 15-19-year-old adolescents, surveyed by the Brazilian health authority, from May 2002 to October 2003, in accordance with international diagnostic criteria standardized by the World Health Organization. Prevalence ratios estimated by Poisson regression, and controlled by socioeconomic status and access to fluoridated piped water, assessed oral health differentials among color/race groups and country's regions. Except for periodontal pockets, prevalence figures were higher in the North and Northeast: perceived dental treatment needs, untreated dental caries, gingival bleeding at probing and pain in teeth and gums varied between 80-83%, 75-76%, 38-43%, and 17-18%, respectively, in these regions. Adolescents living in the Southeast - the richest Brazilian region - presented a better general profile of oral health than their counterparts living in the remaining regions; they had a lower prevalence of untreated dental caries (54%) and unfavorable gingival status (29%). However, the Southeast presented color/race inequalities in all oral health outcomes, with a poorer profile systematically affecting browns or blacks, depending on the oral health condition under consideration. These results reinforce the need for expanding the amplitude of health initiatives aimed at adolescent oral health. Socially appropriate health programs should concurrently aim at the reduction of levels of oral disease and its inequalities.

Gender and schooling inequalities in risk and protective factors for chronic diseases among Brazilian adults, through telephone survey

OBJECTIVES: To assess risk and protective factors for chronic noncommunicable diseases (CNCD) and to identify social inequalities in their distribution among Brazilian adults. METHODS: The data used were collected in 2007 through VIGITEL, an ongoing population-based telephone survey. This surveillance system was implemented in all of the Brazilian State capitals, over 54,000 interviews were analyzed. Age-adjusted prevalence ratios for trends at different schooling levels were calculated using Poisson regression with linear models. RESULTS: These analyses have shown differences in the prevalence of risk and protective factors for CNCD by gender and schooling. Among men, the prevalence ratios of overweight, consumption of meat with visible fat, and dyslipidemia were higher among men with more schooling, while tobacco use, sedentary lifestyle, and high-blood pressure were lower. Among women, tobacco use, overweight, obesity, high-blood pressure and diabetes were lower among men with more schooling, and consumption of meat with visible fat and sedentary lifestyles were higher. As for protective factors, fruit and vegetables intake and physical activity were higher in both men and women with more schooling. CONCLUSION: Gender and schooling influence on risk and protective factors for CNCD, being the values less favorable for men. vigitel is a useful tool for monitoring these factors amongst the Brazilian population.