Connection coefficients and zeros of orthogonal polynomials

We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

ANOTHER QUADRATURE RULE OF HIGHEST ALGEBRAIC DEGREE OF PRECISION

We consider certain quadrature rules of highest algebraic degree of precision that involve strong Stieltjes distributions (i.e., strong distributions on the positive real axis). The behavior of the parameters of these quadrature rules, when the distributions are strong c-inversive Stieltjes distributions, is given. A quadrature rule whose parameters have explicit expressions for their determination is presented. An application of this quadrature rule for the evaluation of a certain type of integrals is also given.

Number of larval instars of the ant Pachycondyla (=Neoponera) villosa (Formicidae: Ponerinae) determined by the rule of Dyar

In this work we present the number of larval instars in the Ponerinae ant Pachycondyla (=Neoponera) villosa. The analysis of maximal head capsule width measurement of 147 larvae was made. Four larval instars were measured: 1st instar the cephalic capsule varied from 0.18mm to 0.22mm; 2nd instar from 0.23mm to 0.27mm; 3rd instar from 0.30mm to 0.33mm and the 4th instar varied from 0.35mm to 0.38mm. The mean growth rate was 1.2375 according to the rule of Dyar. We also reviewed the number of larval instars for 35 ant species.

Polinômios algébricos e trigonométricos com zeros reais

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

Regra de Sinais de Descartes para polinômios ortogonais

Pós-graduação em Matematica Aplicada e Computacional - FCT

Ensino e aprendizagem de matemática: o uso de recursos manipulativos em sala de aula

In this work, we understand the importance of the use of manipulative resources for learning mathematics. For both we developed a qualitative phenomenological approach. Performing a case study with nine 7th grade students of the Elementary School, we used the abacus of the integers to examine in what way the use of Abacus contributes to students learning. The choice of material was made according to the focus of research, understanding the signs rule. In the analysis and interpretation of data, highlight lines of students, subject of the research, units of meaning that allow us to say that the material using awakened interest in students Who actively participated in the research and enabled them to understand the rule of signs, to operate with integers enabled them to understand the rule of signs, to operate with integers

A Modified Technique of Rat Tail Suspension for Longer Periods of Observation

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

Alternative Treatment Modalities for Immature Intruded Permanent Incisors: Report of 2 Cases

Intrusion of permanent teeth is one of the most severe types of traumatic injuries. Different treatment strategies have been proposed, and the best approach for each case depends on the stage of root development, severity of the intrusive luxation, presence of alveolar fracture and number of intruded teeth. The purpose of this paper is to describe the treatment management of 2 cases of severely intruded immature permanent maxillary central incisors in 71/2- and 8-year-old children. In case 1, the traumatized tooth was treated by surgical repositioning, while in case 2 watchful waiting for spontaneous re-eruption was the treatment of choice. Treatment strategies were successful in both cases, as demonstrated by the continuation of root development, maintenance of pulp vitality, and absence of signs of per/apical pathosis during the follow-up period. Regardless of the treatment strategy, traumatically intruded teeth should undergo periodical clinical and radiographic surveillance on a long-term basis to allow early detection of possible complications. (Pediotr Dent 2009;31:340-5) Received March 11, 2008 vertical bar Last Revision June 25, 2008 vertical bar Revision Accepted July 16, 2008

Evaluation of different occlusal splints and counselling in the management of myofascial pain dysfunction

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effects of isoflavone on the learning and memory of women in menopause: a double-blind placebo-controlled study

Hormone decline is common to all women during aging and, associated with other factors, leads to cognitive impairment. Its replacement enhances cognitive performance, but not all women present a clinical and family or personal history that justifies its use, mainly women with a history of cancer. The aim of this study was to determine whether a daily oral dose of 80 mg of isoflavone extract for 4 months can produce benefits in women with low hormone levels, contributing to improvement in cognitive aspects. The sample comprised 50- to 65-year-old women whose menstruation had ceased at least 1 year before and who had not undergone hormone replacement. The volunteers were allocated to two groups of 19 individuals each, i.e., isoflavone and placebo. There was a weak correlation between menopause duration and low performance in the capacity to manipulate information (central executive). We observed an increase in the capacity to integrate information in the group treated with isoflavone, but no improvement in the capacity to form new memories. We did not observe differences between groups in terms of signs and symptoms suggestive of depression according to the Geriatric Depression Scale. Our results point to a possible beneficial effect of isoflavone on some abilities of the central executive. These effects could also contribute to minimizing the impact of memory impairment. Further research based on controlled clinical trials is necessary to reach consistent conclusions.

Is The amphibian tree of life really fatally flawed?

Wiens (2007, Q. Rev. Biol. 82, 55-56) recently published a severe critique of Frost et al.'s (2006, Bull. Am. Mus. Nat. Hist. 297, 1-370) monographic study of amphibian systematics, concluding that it is a disaster and recommending that readers simply ignore this study. Beyond the hyperbole, Wiens raised four general objections that he regarded as fatal flaws: (1) the sampling design was insufficient for the generic changes made and taxonomic changes were made without including all type species; (2) the nuclear gene most commonly used in amphibian phylogenetics, RAG-1, was not included, nor were the morphological characters that had justified the older taxonomy; (3) the analytical method employed is questionable because equally weighted parsimony assumes that all characters are evolving at equal rates; and (4) the results were at times clearly erroneous, as evidenced by the inferred non-monophyly of marsupial frogs. In this paper we respond to these criticisms. In brief: (1) the study of Frost et al. did not exist in a vacuum and we discussed our evidence and evidence previously obtained by others that documented the non-monophyletic taxa that we corrected. Beyond that, we agree that all type species should ideally be included, but inclusion of all potentially relevant type species is not feasible in a study of the magnitude of Frost et al. and we contend that this should not prevent progress in the formulation of phylogenetic hypotheses or their application outside of systematics. (2) Rhodopsin, a gene included by Frost et al. is the nuclear gene that is most commonly used in amphibian systematics, not RAG-1. Regardless, ignoring a study because of the absence of a single locus strikes us as unsound practice. With respect to previously hypothesized morphological synapomorphies, Frost et al. provided a lengthy review of the published evidence for all groups, and this was used to inform taxonomic decisions. We noted that confirming and reconciling all morphological transformation series published among previous studies needed to be done, and we included evidence from the only published data set at that time to explicitly code morphological characters (including a number of traditionally applied synapomorphies from adult morphology) across the bulk of the diversity of amphibians (Haas, 2003, Cladistics 19, 23-90). Moreover, the phylogenetic results of the Frost et al. study were largely consistent with previous morphological and molecular studies and where they differed, this was discussed with reference to the weight of evidence. (3) The claim that equally weighted parsimony assumes that all characters are evolving at equal rates has been shown to be false in both analytical and simulation studies. (4) The claimed strong support for marsupial frog monophyly is questionable. Several studies have also found marsupial frogs to be non-monophyletic. Wiens et al. (2005, Syst. Biol. 54, 719-748) recovered marsupial frogs as monophyletic, but that result was strongly supported only by Bayesian clade confidence values (which are known to overestimate support) and bootstrap support in his parsimony analysis was < 50%. Further, in a more recent parsimony analysis of an expanded data set that included RAG-1 and the three traditional morphological synapomorphies of marsupial frogs, Wiens et al. (2006, Am. Nat. 168, 579-596) also found them to be non-monophyletic.Although we attempted to apply the rule of monophyly to the naming of taxonomic groups, our phylogenetic results are largely consistent with conventional views even if not wth the taxonomy current at the time of our writing. Most of our taxonomic changes addressed examples of non-monophyly that had previously been known or suspected (e.g., the non-monophyly of traditional Hyperoliidae, Microhylidae, Hemiphractinae, Leptodactylidae, Phrynobatrachus, Ranidae, Rana, Bufo; and the placement of Brachycephalus within Eleutherodactylus, and Lineatriton within Pseudoeurycea), and it is troubling that Wiens and others, as evidenced by recent publications, continue to perpetuate recognition of non-monophyletic taxonomic groups that so profoundly misrepresent what is known about amphibian phylogeny. (C) The Willi Hennig Society 2007.

Recognition of altered segments in Brazilian Sign Language

The purpose of this study was to verify discriminative control by segments of signs in adolescents with deafness who use Brazilian Sign Language (BSL). Four adolescent with bilateral deafness, with 3 years of BSL teaching, saw a video presenting a children's tale in BSL. After showing accurate understanding of the story, participants saw another video of the same story with 12 signs altered in one of their segments (hand configuration, place of articulation, or movement). They apparently did not detect the alterations. However, when the signs were presented in isolation in a matching-to-sample test, they virtually always selected the picture corresponding to the unaltered signs. Three participants selected an unfamiliar picture in 50% or more trials with an altered sign as a sample, showing that they could detect the majority of the altered signs.

A CHEBYSHEV-TYPE QUADRATURE RULE WITH SOME INTERESTING PROPERTIES

We give here an n-point Chebyshev-type rule of algebraic degree of precision n - 1, but having nodes that can be given explicitly. This quadrature rule also turns out to be one with an ''almost'' highest algebraic degree of precision.