Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials

Let C-n(lambda)(x), n = 0, 1,..., lambda > -1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal. in (-1, 1) with respect to the weight function (1 - x(2))(lambda-1/2). Denote by X-nk(lambda), k = 1,....,n, the zeros of C-n(lambda)(x) enumerated in decreasing order. In this short note, we prove that, for any n is an element of N, the product (lambda + 1)(3/2)x(n1)(lambda) is a convex function of lambda if lambda greater than or equal to 0. The result is applied to obtain some inequalities for the largest zeros of C-n(lambda)(x). If X-nk(alpha), k = 1,...,n, are the zeros of Laguerre polynomial L-n(alpha)(x), also enumerated in decreasing order, we prove that x(n1)(lambda)/(alpha + 1) is a convex function of alpha for alpha > - 1. (C) 2002 Published by Elsevier B.V. B.V.

Stand-alone posterior ressection of lumbar hemivertebrae: case report

Background: In this case report we presented the stand-alone posterior approach for hemivertebra resection with unilateral laminar hooks.Case report: The patient was male and five years old. The coronal and sagital X-Rays images showed a failure of vertebral formation, segmented hemivertebra of third lumbar vertebra. The segmented hemivertebra caused a thoracolumbar scoliosis from T12 to L4 (rightside convexity), of 30 degrees (Cobb angle). The patient was submitted to a hemivertebra resection from posterior approach with two unilateral laminars hooks stabilization (superior lamina in L2 and inferior lamina of L4) in association to a compression system and autologus bone graft. The coronal X-Ray image after surgery showed a partial improvement to 25 degrees (Cobb angle) between L2 and L4. After three years of follow up it was not observed system failure (hook pull-out), maintance of curve (25 degrees of Cobb angle) and correction of trunk inbalance.Conclusion: The hemivertebra resection with posterior approach is safe, with satisfactory correction of scoliosis curve, which means is a good choice for congenital scoliosis surgical treatment.

Transmission system expansion planning by an extended genetic algorithm

The paper presents an extended genetic algorithm for solving the optimal transmission network expansion planning problem. Two main improvements have been introduced in the genetic algorithm: (a) initial population obtained by conventional optimisation based methods; (b) mutation approach inspired in the simulated annealing technique, the proposed method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Excellent performance is reported in the test results section of the paper for a difficult large-scale real-life problem: a substantial reduction in investment costs has been obtained with regard to previous solutions obtained via conventional optimisation methods and simulated annealing algorithms; statistical comparison procedures have been employed in benchmarking different versions of the genetic algorithm and simulated annealing methods.

Alterações da margem palpebral associadas ao ectrópio

OBJETIVO: Investigar alterações da margem palpebral em portadores de ectrópio. MÉTODOS: Foi feito estudo observacional, do qual participaram 53 portadores de ectrópio palpebral e 25 portadores de dermatocálase (grupo controle), estudando-se, a partir de imagens digitais, a posição dos cílios e a presença de inflamações na margem palpebral. Os dados foram submetidos a análise estatística. RESULTADOS: Os portadores de ectrópio apresentaram com maior freqüência diminuição do número de cílios, perda da convexidade, triquíase e distiquíase quando comparados aos indivíduos do grupo controle. CONCLUSÃO: O portador de ectrópio possui alterações da margem palpebral provavelmente decorrentes do processo inflamatório crônico que ocorre na região.

Crescimento facial espontâneo Padrão II: estudo cefalométrico longitudinal

OBJETIVO: o presente estudo cefalométrico longitudinal investigou as alterações espontâneas ocorridas em crianças com má oclusão Classe II, divisão 1, Padrão II. MÉTODOS: foram selecionadas 40 crianças, 20 meninos e 20 meninas, distribuídas na faixa etária compreendida entre 6 e 14 anos de idade. Para avaliar o comportamento das bases apicais, dos incisivos e do tecido mole, as seguintes grandezas cefalométricas foram mensuradas: SN.Ba, SNA, SNB, SND, SN.Pog, ANB, NAP, SN.PP, SN.GoGn, SN.Gn, Ar.Go.Gn, 1.PP, 1.NA, 1.SN, IMPA e ANL. As seguintes grandezas alcançaram significância estatística com o crescimento: SNB, SND,SN.Pog,ANB,NAP,SN.GoGn,SN.Gn,Ar.Go.Gn e IMPA. RESULTADOS: os resultados demonstraram que as principais alterações quantitativas registradas estavam relacionadas com o crescimento mandibular,independentemente do gênero. A mandíbula deslocou-se para frente, com tendência de rotação no sentido anti-horário e com conseqüente redução nos ângulos de convexidade facial. No entanto, as oscilações quantitativas nas grandezas cefalométricas não foram suficientes para mudar a morfologia dentofacial ao longo do período de acompanhamento. CONCLUSÃO: conclui-se, portanto, que a morfologia facial é definida precocemente e é mantida, configurando o determinismo genético na determinação do arcabouço esquelético.

KT-invexity in optimal control problems

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

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Avaliação tomográfica dos pedículos vertebrais no tratamento cirúrgico dos pacientes com escoliose idiopática do adolescente

OBJETIVO: Determinar através de cortes tomográficos e reconstrução tridimensional a incidência de mal posicionamento de parafusos em pacientes submetidos ao tratamento cirúrgico da Escoliose idiopática do adolescente. MÉTODOS: Foram analisados exames tomográficos de 8 pacientes, tratados cirurgicamente no Hospital de Base de São José do Rio Preto-SP, realizada instrumentação posterior partindo de T2 /T4 a L4/L5 totalizando 164 parafusos. RESULTADOS: 32,9% (n=54) apresentavam posicionamento com risco potencial,ou seja desvio acima de 2 milímetros, sendo 20,1% (n=33) com invasão lateral, 9,1% (n=15) com invasão medial, 3,6 %(n=6) com invasão anterior. Dos parafusos que ofereciam risco potencial a relação com aspecto da curva foi de 46% (n=25) na concavidade, 35% (n=19) na convexidade e 19% (n=10) em vértebras adjacentes a curva. CONCLUSÃO: Os limites de penetração aceitáveis, assim como os métodos de mensuração ainda não foram padronizados, a técnica free hand' mostrou-se segura, apesar da violação dos pedículos. A tomografia computadorizada pré-operatória, auxilia no planejamento cirúrgico e na redução das complicações.

Cephalometric evaluation of skeletal alterations induced by Herbst appliance during mixed dentition

OBJECTIVE: The present prospective clinical study was designed in order to evaluate horizontal and vertical skeletal alterations induced by the use of Herbst appliance in individuals with Class II, division 1 malocclusion during mixed dentition stage. METHODS: The sampling consisted of 15 pre-pubertal individuals (12 boys and 3 girls; initial age 9 years and 6 months), who were treated with Herbst appliance for a period of 7 months. The effects of the treatment were compared to a group of 15 individuals with Class II, division 1 malocclusion (8 boys and 7 girls, initial age averaged 9 years and 1 month), orthodontically untreated, who were followed up for a period of 12 months. Statistical analysis was performed with Student's t-test with significance level at 5%. RESULTS: It was showed that the treatment with Herbst appliance in mixed dentition stage has restricted maxilla growth. Mandibular and palatal planes have not undergone significant alteration; however, anterior and posterior facial heights have increased significantly. Facial convexity and maxillomandibular relationship were altered positively. Mandible has positioned significantly forward and its effective length increased 2.5 times more than the increase observed in control group. CONCLUSION: It was possible to conclude that Herbst appliance was able to provide satisfactory results in individuals during mixed dentition stage.

Influence of intentional ankylosis of deciduous canines to reinforce the anchorage for maxillary protraction

INTRODUÇÃO: nesse estudo cefalométrico retrospectivo, analisou-se a influência da anquilose intencional de caninos decíduos em pacientes com má oclusão de Classe III e mordida cruzada anterior, nos estágios de dentição decídua e mista precoce, tratados com expansão ortopédica da maxila, seguida de tração reversa. MÉTODOS: foram utilizadas telerradiografias em norma lateral de 40 pacientes, divididos em 2 grupos pareados por idade e sexo. O Grupo Anquilose foi constituído de 20 pacientes (10 meninos e 10 meninas) tratados com anquilose induzida e que apresentavam as idades médias inicial e final, respectivamente, de 7a 4m e 8a 3m, e o tempo médio de tração reversa de 11 meses. O Grupo Controle, composto de 20 pacientes (10 meninos e 10 meninas) tratados sem anquilose induzida e que apresentavam as idades médias inicial de 7a 8m e final de 8a 7m, e tempo médio de tração reversa de 11 meses. Foram empregadas as análises de Variância a dois critérios e de Covariância para comparar as variáveis cefalométricas inicial e final e as alterações de tratamento entre os grupos. RESULTADOS: segundo os resultados, as variáveis que evidenciaram as mudanças de tratamento significativas entre os grupos confirmaram que o procedimento de anquilose intencional potencializou a resposta sagital das bases apicais (Pg-NPerp) e aumentou os ângulos de convexidade facial (NAP e ANB). CONCLUSÃO: o protocolo envolvendo a anquilose intencional de caninos decíduos potencializou a resposta sagital das bases apicais.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Parallel simulated annealing applied to long term transmission network expansion planning

The simulated annealing optimization technique has been successfully applied to a number of electrical engineering problems, including transmission system expansion planning. The method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Moreover, it has the ability to provide solutions arbitrarily close to an optimum (i.e. it is asymptotically convergent) as the cooling process slows down. The drawback of the approach is the computational burden: finding optimal solutions may be extremely expensive in some cases. This paper presents a Parallel Simulated Annealing, PSA, algorithm for solving the long term transmission network expansion planning problem. A strategy that does not affect the basic convergence properties of the Sequential Simulated Annealing algorithm have been implementeded and tested. The paper investigates the conditions under which the parallel algorithm is most efficient. The parallel implementations have been tested on three example networks: a small 6-bus network, and two complex real-life networks. Excellent results are reported in the test section of the paper: in addition to reductions in computing times, the Parallel Simulated Annealing algorithm proposed in the paper has shown significant improvements in solution quality for the largest of the test networks.

Nonsmooth continuous-time optimization problems: Sufficient conditions

We discuss sufficient conditions of optimality for nonsmooth continuous-time nonlinear optimization problems under generalized convexity assumptions. These include both first-order and second-order criteria. (C) 1998 Academic Press.

Optimal control problems with nonsmooth mixed constraints

In this paper we present a weak maximum principle for optimal control problems involving mixed constraints and pointwise set control constraints. Notably such result holds for problems with possibly nonsmooth mixed constraints. Although the setback of such result resides on a convexity assumption on the extended velocity set, we show that if the number of mixed constraints is one, such convexity assumption may be removed when an interiority assumption holds. © 2008 IEEE.

Changes on facial profile in the mixed dentition, from natural growth and induced by Balters' bionator appliance

Objective: The purpose of this study was to evaluate the facial profile changes induced by Balters' bionator appliance in Class II division 1 patients, at mixed dentition stage. Methods: The sample consisted of 28 prepubertal individuals at stages 1 and 2 of skeletal maturation (CVM), which were divided in two groups. The experimental group consisted of 14 individuals (7 boys and 7 girls, initial mean age of 8y12m) which were treated with Balters' bionator appliance for 14.7 months. The effects of treatment were compared to a control group of 14 subjects (7 boys and 7 girls, initial mean age of 8y5m) with Class II malocclusion, division 1, not orthodontically treated, which were followed up for 15.4 months. The statistical analysis was performed using Student's t test, at a significance level of 5%. Results: The results showed that the Balters' bionator appliance promoted a significant increase on the mentolabial angle, in addition to demonstrating a tendency to reduce the facial skeletal convexity, to restrict the maxillary growth and to increase the nasolabial angle and the lower anterior facial height. Conclusion: It can be concluded that the Balters' bionator appliance improved the facial profile of children treated at mixed dentition stage. © 2013 Dental Press Journal of Orthodontics.