The analytic torsion of a disc

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

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.

Path formulation for Z(2) circle plus Z(2)-equivariant bifurcation problems

M. Manoel and I. Stewart 0101) classify Z(2) circle plus Z(2)-equivariant bifurcation problems up to codimension 3 and 1 modal parameter, using the classical techniques of singularity theory of Golubistky and Schaeffer [8]. In this paper we classify these same problems using an alternative form: the path formulation (Theorem 6.1). One of the advantages of this method is that the calculates to obtain the normal forms are easier. Furthermore, in our classification we observe the presence of only one modal parameter in the generic core. It differs from the classical classification where the core has 2 modal parameters. We finish this work comparing our classification to the one obtained in [10].

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Reversible equivariant Hopf bifurcation

In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues of the linearization of the vector field at the equilibrium point. The eigenvalue movements near such a degeneracy typically follow one of three scenarios: splitting (from two pairs of imaginary eigenvalues to a quadruplet on the complex plane), passing (on the imaginary axis), or crossing (a quadruplet crossing the imaginary axis). We give a complete description of the behaviour of reversible periodic orbits in the vicinity of such a bifurcation point. For non-reversible periodic solutions. in the case of Hopf bifurcation with crossing eigenvalues. we obtain a generalization of the equivariant Hopf Theorem.

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

DIRAC CONFINEMENT BY A VARIATIONAL APPROACH

An analytical approximate method for the Dirac equation with confining power law scalar plus vector potentials, applicable to the problem of the relativistic quark confinement, is presented. The method consists in an improved version of a saddle-point variational approach and it is applied to the fundamental state of massless single quarks for some especial cases of physical interest. Our treatment emphasizes aspects such as the quantum-mechanical relativistic Virial theorem, the saddle-point character of the critical point of the expectation value of the total energy, as well as the Klein paradox and the behaviour of the saddle-point variational energies and wave functions.

New higher-derivative R-4 theorems for graviton scattering

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R-4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, partial derivative R-n(4) terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n <= 8, perturbative contributions to partial derivative R-n(4) terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On computing discriminants of subfields of Q(zeta(pr))

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(Q(zeta(n))/Q), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of Q(zeta(p)r), where p is an odd prime and r is a positive integer. (C) 2002 Elsevier B.V. (USA).

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

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.

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.