Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

Structural evolution up to 1100 degrees C of xerogels prepared from TEOS sonohydrolysis and liquid phase exchanged by acetone

Silica xerogels were prepared from sonohydrolysis of tetraethoxysilane and exchange of the liquid phase of the wet gel by acetone. Monolithic xerogels were obtained by slow evaporation of acetone. The structural characteristics of the xerogels were studied as a function of temperature up to 1100 degrees C by means of bulk and skeletal density measurements, linear shrinkage measurements and thermal analyses (DTA, TG and DL). The results were correlated with the evolution in the UV-Vis absorption. Particularly, the initial pore structure of the dried acetone-exchanged xerogel was studied by small-angle X-ray scattering and nitrogen adsorption. The acetone-exchanged xerogels exhibit greater porosity in the mesopore region presenting greater mean pore size (similar to 4 nm) when compared to non-exchanged xerogels. The porosity of the xerogels is practically stable in the temperature range between 200 degrees C and 800 degrees C. Evolution in the structure of the solid particles (silica network) is the predominant process upon heating up to about 400 degrees C and pore elimination is the predominant process above 900 degrees C. At 1000 degrees C the xerogels are still monolithic and retain about 5 vol.% pores. The xerogels exhibited foaming phenomenon after hold for 10 h at 1100 degrees C. This temperature is even higher than that found for foaming of non-exchanged xerogels. (c) 2005 Elsevier B.V. All rights reserved.

Formulário do perfil psicossocial do paciente anoftálmico com indicação de prótese ocular

The patient with anophthalmia may present feelings of inferiority and rejection. Knowing his/her needs and expectations contribute to a better technical intervention. Purpose: To elaborate a questionnaire of the psychosocial profile of the patient with anophthalmia with indication of ocular prosthesis. Methods: An exploratory research was used to elaborate the questionnaire, by means of a guided interview followed by writing down what was said by the interviewees, who were adult patients of the Bucco-Maxillo-Facial Prosthesis Center of FOSJC - UNESP. The guided interview was made up of 14 items directly related to the future outline of the profile. Each item of the interview resulted in questions of the questionnaire, which was pretested twice before reaching its final version. Results: The patients reported, in the exploratory research, unpleasant feelings with the loss of the eye; relationship shyness; expectations regarding surgery and prosthesis use; a wish to receive explanations and to hold their opinion about the treatment. The questionnaire of the psychosocial profile of the patient with anophthalmia with indication of ocular prosthesis is, therefore, made of 43 questions divided into 5 blocks in order to aid the comprehension of the inquired aspects and to facilitate both the computation of data and discussion, and also to improve the selection of questions according to the objective of the researcher or professional. Conclusions: It was concluded that the questionnaire was viable, can be used in full or by selecting blocks and provide a panorama of the patient's history related to the problem he/she faces, from the loss of the ocular globe to the confection of the prosthesis.

Diabetes and pregnancy: An update of the problem

Pregnancies complicated by diabetes account for about 7% of all pregnancies attended by the Brazilian Unified Healthcare System (SUS) and are one of the main causes of maternal/perinatal morbidity and mortality in Brazil. Considering the importance of this topic, this article presents an update of diabetes classification, diagnostic criteria, maternal/perinatal outcomes, and both clinical and obstetric prenatal care. Even though there is no consensus about screening and diagnostic standards, the investigation of hyperglycemia in all risk pregnancies is recommended. The importance of adequate metabolic control is emphasized in order to improve maternal and neonatal outcomes. Finally, the development of educational programs is encouraged, viewing not only good gestational outcome but also long-term changes in the lifestyle of these women. © by São Paulo State University.

The Latin American development problem

Includes bibliography

Gorlin syndrome: Importance of clinical signs and danger of delayed diagnosis A case report with eight years follow-up

Nevoid basal cell carcinoma (NBCCS) or Gorlin-Goltz syndrome (GS) is a multidisciplinary problem, the early diagnosis of which allows secondary prophylaxis that follows an appropriate regimen to delay progression of the syndrome. The aim of this study was to present a case of delayed diagnosis of GS in a young patient who received multidisciplinary treatment 5 years after onset. The patient presented for evaluation with painless swelling of the left maxilla. Histological examination confirmed the diagnosis of a keratocyst odontogenic tumor (KOT) that was enucleated. On presentation, the patient’s symptoms and clinical signs were not related to complications of GS, and the possibility of GS was initially rejected, as he did not have a family history of the syndrome. Four years after the first surgery to remove the lesion, the patient came to our clinic with a brown, pigmented lesion. Computed tomography revealed ectopic lamellar calcification of the falx cerebri, which was the conclusive factor for the diagnosis of GS. It is important that clinicians recognize the clinical signs of GS, which mainly manifests itself as multiple basal cell carcinomas in the skin.

Processing optimized for symmetry in the problem of evasive maneuvers

The increasing number of space debris in operating regions around the earth constitutes a real threat to space missions. The goal of the research is to establish appropriate scientific-technological conditions to prevent the destruction and/or impracticability of spacecraft in imminent collision in these regions. A definitive solution to this problem has not yet been reached with the degree of precision that the dynamics of spatial objects (vehicle and debris) requires mainly due to the fact that collisions occur in chains and fragmentation of these objects in the space environment. This fact threatens the space missions on time and with no prospects for a solution in the near future. We present an optimization process in finding the initial conditions (CIC) to collisions, considering the symmetry of the distributions of maximum relative positions between spatial objects with respect to the spherical angles. For this, we used the equations of the dynamics on the Clohessy-Witshire, representing a limit of validation that is highly computationally costly. We simulate different maximum relative positions values of the corresponding initial conditions given in terms of spherical angles. Our results showed that there are symmetries that significantly reduce operating costs, such that the search of the CIC is advantageously carried out up to 4 times the initial processing routine. Knowledge of CIC allows the propulsion system operating vehicle implement evasive maneuvers before impending collisions with space debris.

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Problem of the statistical model in deep inelastic scattering phenomenology

Recent deep inelastic data leads to an up-down quark asymmetry of the nucleon sea. Explanations of the flavour asymmetry and the di-lepton production in proton-nucleus collisions call for a temperature T ≈ 100 MeV in a statistical model. This T may be conjectured as being due to the Fulling-Davies-Unruh effect. But it is not possible to fit the structure function itself.

Computational speed-up with a single qudit

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

SETTING UP AN EFFECTIVE URBAN BLACKBIRD ROOST CONTROL PROGRAM

The City of Denton is situated 35 miles north of north-central Texas. This area is within one of the major N-S corridors for migratory birds. It is also far enough south so that winters are generally mild and open. The average rainfall of 30 inches sustains good stands of pecan and several species of oak, which serve as excellent roost sites for blackbirds. For the past several years, summering flocks of blackbirds have chosen Denton as a roosting site. Interviews with oldtimers here indicate that flocks of birds have always been around. It is only in recent years that their numbers seem much greater and the resulting mess deeper. They also say that "in the old days" if flocks appeared and started creating a problem, they were simply shot with little fuss resulting. This method is not generally acceptable today.

Testing allele homogeneity: the problem of nested hypotheses

Background: The evaluation of associations between genotypes and diseases in a case-control framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic homogeneity is known to be valid only under Hardy-Weinberg equilibrium, a property that may not hold in practice. Results: We first describe the flaws of the traditional (chi-squared) tests for both allelic and genotypic homogeneity. Besides the known problem of the allelic procedure, we show that whenever these tests are used, an incoherence may arise: sometimes the genotypic homogeneity hypothesis is not rejected, but the allelic hypothesis is. As we argue, this is logically impossible. Some methods that were recently proposed implicitly rely on the idea that this does not happen. In an attempt to correct this incoherence, we describe an alternative frequentist approach that is appropriate even when Hardy-Weinberg equilibrium does not hold. It is then shown that the problem remains and is intrinsic of frequentist procedures. Finally, we introduce the Full Bayesian Significance Test to test both hypotheses and prove that the incoherence cannot happen with these new tests. To illustrate this, all five tests are applied to real and simulated datasets. Using the celebrated power analysis, we show that the Bayesian method is comparable to the frequentist one and has the advantage of being coherent. Conclusions: Contrary to more traditional approaches, the Full Bayesian Significance Test for association studies provides a simple, coherent and powerful tool for detecting associations.

Gender parity and drug use: are girls catching up with boys?

Objective: To evaluate the association between gender and use of alcohol, tobacco, and other drugs in adolescents aged 10 to 18 years in the municipalities of Jacare and Diadema, Sao Paulo, Brazil. Methods: A total of 971 adolescents completed the Drug Use Screening Inventory (DUSI). Results: In our sample, 55% of adolescents were male, 33.8% reported having made use in the previous month of alcohol, 13.5% of cigarettes, and 6.4% of illicit drugs. There was no significant difference between genders in the use of alcohol, tobacco, and illicit drugs in any of the analysis (p > 0.05). The use of alcohol, tobacco, and illicit drugs was associated with the city, age, educational level, school failure, and relationship with parents (p < 0.05). Conclusions: Substance abuse among adolescents in our sample seems to follow the recent global trend towards the equalization of drug use between genders. This result should be taken into account by public health professionals in developing policies for this problem. (C) 2012 Elsevier Editora Ltda. All rights reserved.

A knapsack problem as a tool to solve the production planning problem in small foundries

According to recent research carried out in the foundry sector, one of the most important concerns of the industries is to improve their production planning. A foundry production plan involves two dependent stages: (1) determining the alloys to be merged and (2) determining the lots that will be produced. The purpose of this study is to draw up plans of minimum production cost for the lot-sizing problem for small foundries. As suggested in the literature, the proposed heuristic addresses the problem stages in a hierarchical way. Firstly, the alloys are determined and, subsequently, the items that are produced from them. In this study, a knapsack problem as a tool to determine the items to be produced from furnace loading was proposed. Moreover, we proposed a genetic algorithm to explore some possible sets of alloys and to determine the production planning for a small foundry. Our method attempts to overcome the difficulties in finding good production planning presented by the method proposed in the literature. The computational experiments show that the proposed methods presented better results than the literature. Furthermore, the proposed methods do not need commercial software, which is favorable for small foundries. (C) 2010 Elsevier Ltd. All rights reserved.

Implant-Supported Prosthesis Misalignment Related to the Dental Arch: A 14-Year Clinical Follow-up

The purpose of this study was to warn the dental community about a possible problem in function with partial implant-supported prostheses used for long periods. The misalignment between natural teeth and the implant-supported prosthesis on teeth 11 and 12, observed in a 14-year clinical follow-up, illustrates the fact. The metal-ceramic crowns were placed in 1995 after a rigorous occlusal adjustment. Evaluations were made at 4, 6, 9, and 14 years, when it was noticed that the restorations were positioned palatally and extruded in comparison with the natural teeth. After 9 years, a greater discrepancy was noticed, with anterior occlusion and esthetic changes. The possible causes have been discussed: occlusal problems, parafunctional habits, and natural movement. The first 2 options were discarded after clinical analysis and diagnosis. Therefore, the natural movement probably deriving from an interaction of mechanical and genetic factors might have been the cause. The implants do not have periodontal ligaments but rather ankylosis, so they do not suffer those movements. This case emphasizes the need to inform patients that implants can last more than 10 years in function, but this is not the case with restorations, which lose function and esthetics and must be replaced.