Homogenization in a thin domain with an oscillatory boundary

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type R(epsilon) = {(x(1), x(2)) is an element of R(2) vertical bar x(1) is an element of (0, 1), 0 < x(2) < epsilon G(x(1), x(1)/epsilon)} where the function G(x, y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter epsilon. (C) 2011 Elsevier Masson SAS. All rights reserved.

Doença granulomatosa crônica: diagnóstico no primeiro episódio infeccioso

OBJETIVO: Relatar caso ilustrativo de doença granulomatosa crônica cujo diagnóstico ocorreu durante o aparecimento do primeiro episódio infeccioso, colaborando com a iniciativa do Brazilian Group for Immunodeficiency para a sensibilização do pediatra geral em relação ao diagnóstico precoce das imunodeficiências primárias, o que está associado a melhor qualidade de vida e maior sobrevida desses indivíduos. DESCRIÇÃO DE CASO: Paciente do sexo masculino, 39 dias de vida, admitido em pronto-socorro pediátrico por febre alta há cinco dias e irritabilidade. No dia seguinte, observou-se abscesso cervical, isolando-se Staphylococcus aureus comunitário. Durante a internação, ocorreram outros abscessos superficiais e em cadeias ganglionares profundas, além de resposta lenta aos antimicrobianos. Solicitou-se investigação para imunodeficiências, que confirmou a hipótese de doença granulomatosa crônica por quantificação dos ânions superóxido e teste de redução do nitrobluetetrazolio. Paciente foi encaminhado a serviço especializado, no qual identificou-se doador de medula óssea compatível, realizando-se o transplante seis meses após o diagnóstico. Quatro meses após o transplante, ocorreu normalização do burst oxidativo, indicando sucesso. COMENTÁRIOS: O paciente mostrou apresentação típica da doença, o que permitiu seu diagnóstico por pediatras gerais já na primeira infecção, tendo como consequência o acompanhamento por especialistas em imunodeficiências primárias, a introdução da profilaxia antimicrobiana e a procura bem sucedida de doador de medula HLA-compatível.

A dimensão criadora no trabalho docente: subsídios para a formação de professores alfabetizadores

Este artigo tem como objetivo evidenciar a dimensão criadora dos saberes docentes mobilizados por uma professora alfabetizadora, a partir da concepção de saberes docentes desenvolvida pela teoria histórico-cultural. A pesquisa realizou-se em escola pública, no estado de Rondônia, por meio de uma abordagem etnográfica. O trabalho traz para a análise duas cenas recortadas do cotidiano escolar para exemplificar como os saberes docentes são alterados e recriados no enfrentamento dos desafios impostos pela prática pedagógica. Os resultados permitem compreender que a prática docente no cotidiano não se caracteriza apenas como reprodução de modelos ou propostas utilizadas por outros profissionais. Ao contrário, no encontro de uma professora e uma turma de alunos há sempre certa originalidade que demanda a criação de formas específicas de intervenção para aquele grupo, nas condições do contexto. Acompanhar o trabalho da professora durante o período de pesquisa permitiu compreender que há inúmeras possibilidades de condução do trabalho pedagógico e as razões que motivam as escolhas dos professores e das professoras estão fundamentadas em saberes construídos ao longo de suas experiências de formação e atuação. Considera-se, portanto, que as práticas pedagógicas precisam ser conhecidas e estudadas para que se possa compreendê-las, mais do que avaliá-las, tendo-se em vista a contribuição desses estudos para a formação docente.

UNIQUENESS AND NONUNIQUENESS RESULTS FOR A CERTAIN CLASS OF ALMOST PERIODIC DISTRIBUTIONS

We consider distributions u is an element of S'(R) of the form u(t) = Sigma(n is an element of N) a(n)e(i lambda nt), where (a(n))(n is an element of N) subset of C and Lambda = (lambda n)(n is an element of N) subset of R have the following properties: (a(n))(n is an element of N) is an element of s', that is, there is a q is an element of N such that (n(-q) a(n))(n is an element of N) is an element of l(1); for the real sequence., there are n(0) is an element of N, C > 0, and alpha > 0 such that n >= n(0) double right arrow vertical bar lambda(n)vertical bar >= Cn(alpha). Let I(epsilon) subset of R be an interval of length epsilon. We prove that for given Lambda, (1) if Lambda = O(n(alpha)) with alpha < 1, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (2) if Lambda = O(n) is uniformly discrete, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (3) if alpha > 1 and. is uniformly discrete, then for all epsilon > 0, u vertical bar I(epsilon) = 0 double right arrow u = 0. Since distributions of the above mentioned form are very common in engineering, as in the case of the modeling of ocean waves, signal processing, and vibrations of beams, plates, and shells, those uniqueness and nonuniqueness results have important consequences for identification problems in the applied sciences. We show an identification method and close this article with a simple example to show that the recovery of geometrical imperfections in a cylindrical shell is possible from a measurement of its dynamics.

SOME PROPERTIES OF THE MULTIPLICITY SEQUENCE FOR ARBITRARY IDEALS

In this work we prove that the Achilles-Manaresi multiplicity sequence, like the classical Hilbert-Samuel multiplicity, is additive with respect to the exact sequence of modules. We also prove the associativity formula for his mulitplicity sequence. As a consequence, we give new proofs for two results already known. First, the Achilles-Manaresi multiplicity sequence is an invariant up to reduction, a result first proved by Ciuperca. Second, I subset of J is a reduction of (J,M) if and only if c(0)(I(p), M(p)) = c(0)(J(p), M(p)) for all p is an element of Spec(A), a result first proved by Flenner and Manaresi.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

The Lobel-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree at least some k is an element of N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r( T, T') of trees T, T' from the above classes.

Topological instability and electronegativity effects on the glass-forming ability of metallic alloys

The glass-forming ability (GFA) of metallic alloys is associated with a topological instability criterion combined with a new parameter based on the average electronegativity difference of an element and its surrounding neighbours. In this model, we assume that during solidification the glassy phase competes directly with the supersaturated solid solution having the lowest topological instability factor for a given composition. This criterion is combined with the average electronegativity difference among the elements in the alloy, which reflects the strength of the liquid. The GFA is successfully correlated with this combined criterion in several binary glass-forming systems.

Knowledge transfer in product development processes: A case study in small and medium enterprises (SMEs) of the metal-mechanic sector from Sao Paulo, Brazil

This paper reports a research that evaluated the product development methodologies used in Brazilian small and medium-sized metal-mechanic enterprises (SMEs), in a specific region of Sao Paulo. The tool used for collecting the data was a questionnaire, which was developed and applied through interviews conducted by the researchers in 32 companies. The main focus of this paper can be condensed in the synthesis-question ""Is only the company responsible for the development?"" which was analyzed thoroughly. The results obtained from this analysis were evaluated directly (through the respective percentages of answers) and statistically (through the search of an index which demonstrates if two questions are related). The results point to a degree of maturity in SMEs, which allows product development to be conducted in cooperation networks. (C) 2007 Elsevier Ltd. All rights reserved.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

The existence of solutions for impulsive neutral functional differential equations

This work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed (not necessarily bounded) operators {A(t) : t is an element of 1}. (C) 2009 Elsevier Ltd. All rights reserved.

Evaluation of the poly-L-lactic acid implant for treatment of the nasolabial fold: 3-year follow-up evaluation

The search for an ideal filler for soft tissue augmentation still continues. Because aging changes are continuous, temporary fillers should be preferred against permanent ones. Since 1999, the poly-L-lactic acid filler (PLA) has been marketed in Europe as Newfill. As a synthetic biocompatible polymer, PLA originally was used in suture materials and screws. In 2004, the U.S. Food and Drug Administration approved PLA under the name of Sculptra for the treatment of human immunodeficiency virus-related facial lipoatrophy. This study aimed to evaluate a 3-year follow-up investigation into the effect of PLA implant injection for the treatment of sunken nasolabial folds. Between October 2003 and February 2004, 10 women with a median age of 54 years (range, 43-60 years) were injected with polylactic acid hydrogel (Newfill) in the nasolabial fold area for aesthetic reasons. All the patients underwent three injections: one injection per month for 3 months. Evaluation of the results based on clinical examination and photography was performed at each session, at 6 months, and then 36 months after the third session. Injectable PLA was able to correct nasolabial folds successfully with a more lasting result than absorbable fillers commonly used in clinical practice, such as hyaluronic acid and collagen. Careful and standardized photographic documentation is indispensable.