COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Support vector machines for detecting age-related changes in running kinematics

Age-related changes in running kinematics have been reported in the literature using classical inferential statistics. However, this approach has been hampered by the increased number of biomechanical gait variables reported and subsequently the lack of differences presented in these studies. Data mining techniques have been applied in recent biomedical studies to solve this problem using a more general approach. In the present work, we re-analyzed lower extremity running kinematic data of 17 young and 17 elderly male runners using the Support Vector Machine (SVM) classification approach. In total, 31 kinematic variables were extracted to train the classification algorithm and test the generalized performance. The results revealed different accuracy rates across three different kernel methods adopted in the classifier, with the linear kernel performing the best. A subsequent forward feature selection algorithm demonstrated that with only six features, the linear kernel SVM achieved 100% classification performance rate, showing that these features provided powerful combined information to distinguish age groups. The results of the present work demonstrate potential in applying this approach to improve knowledge about the age-related differences in running gait biomechanics and encourages the use of the SVM in other clinical contexts. (C) 2010 Elsevier Ltd. All rights reserved.

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

Habitat suitability of Anopheles vector species and association with human malaria in the Atlantic Forest in south-eastern Brazil

Every year, autochthonous cases of Plasmodium vivax malaria occur in low-endemicity areas of Vale do Ribeira in the south-eastern part of the Atlantic Forest, state of São Paulo, where Anopheles cruzii and Anopheles bellator are considered the primary vectors. However, other species in the subgenus Nyssorhynchus of Anopheles (e.g., Anopheles marajoara) are abundant and may participate in the dynamics of malarial transmission in that region. The objectives of the present study were to assess the spatial distribution of An. cruzii, An. bellator and An. marajoara and to associate the presence of these species with malaria cases in the municipalities of the Vale do Ribeira. Potential habitat suitability modelling was applied to determine both the spatial distribution of An. cruzii, An. bellator and An. marajoara and to establish the density of each species. Poisson regression was utilized to associate malaria cases with estimated vector densities. As a result, An. cruzii was correlated with the forested slopes of the Serra do Mar, An. bellator with the coastal plain and An. marajoara with the deforested areas. Moreover, both An. marajoara and An. cruzii were positively associated with malaria cases. Considering that An. marajoara was demonstrated to be a primary vector of human Plasmodium in the rural areas of the state of Amapá, more attention should be given to the species in the deforested areas of the Atlantic Forest, where it might be a secondary vector.

Prevalência de hipertensão arterial em militares jovens e fatores associados

OBJETIVO: Estimar a prevalência de hipertensão arterial entre militares jovens e fatores associados. MÉTODOS: Estudo transversal realizado com amostra de 380 militares do sexo masculino de 19 e 35 anos de idade em uma unidade da Força Aérea Brasileira em São Paulo, SP, entre 2000 e 2001. Os pontos de corte para hipertensão foram: >140mmHg para pressão sistólica e > 90mmHg para pressão diastólica. As variáveis estudadas incluíram fatores de risco e de proteção para hipertensão, como características comportamentais e nutricionais. Para análise das associações, utilizou-se regressão linear generalizada múltipla, com família binomial e ligação logarítmica, obtendo-se razões de prevalências com intervalo de 90% de confiança e seleção hierarquizada das variáveis. RESULTADOS: A prevalência de hipertensão arterial foi de 22% (IC 90%: 21;29). No modelo final da regressão múltipla verificou-se prevalência de hipertensão 68% maior entre os ex-fumantes em relação aos não fumantes (IC 90%: 1,13;2,50). Entre os indivíduos com sobrepeso (índice de massa corporal - IMC de 25 a 29kg/m2) e com obesidade (IMC>29kg/m2) as prevalências foram, respectivamente, 75% (IC 90%: 1,23;2,50) e 178% (IC 90%: 1,82;4,25) maiores do que entre os eutróficos. Entre os que praticavam atividade física regular, comparado aos que não praticavam, a prevalência foi 52% menor (IC 90%: 0,30;0,90). CONCLUSÕES: Ser ex-fumante e ter sobrepeso ou obesidade foram situações de risco para hipertensão, enquanto que a prática regular de atividade física foi fator de proteção em militares jovens.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Spin alignment measurements of the K*(0)(892) and phi(1020) vector mesons in heavy ion collisions at root S(NN)=200 GeV

We present the first spin alignment measurements for the K*(0)(892) and phi(1020) vector mesons produced at midrapidity with transverse momenta up to 5 GeV/c at root s(NN) = 200 GeV at RHIC. The diagonal spin-density matrix elements with respect to the reaction plane in Au+Au collisions are rho(00) = 0.32 +/- 0.04 (stat) +/- 0.09 (syst) for the K*(0) (0.8 < p(T) < 5.0 GeV/c) and rho(00) = 0.34 +/- 0.02 (stat) +/- 0.03 (syst) for the phi (0.4 < p(T) < 5.0 GeV/c) and are constant with transverse momentum and collision centrality. The data are consistent with the unpolarized expectation of 1/3 and thus no evidence is found for the transfer of the orbital angular momentum of the colliding system to the vector-meson spins. Spin alignments for K(*0) and phi in Au+Au collisions were also measured with respect to the particle's production plane. The phi result, rho(00) = 0.41 +/- 0.02 (stat) +/- 0.04 (syst), is consistent with that in p+p collisions, rho(00) = 0.39 +/- 0.03 (stat) +/- 0.06 (syst), also measured in this work. The measurements thus constrain the possible size of polarization phenomena in the production dynamics of vector mesons.

Comparative Study of the Changes in Partial Pressure of Plasma Carbon Dioxide During Carbon Dioxide Insufflation into the Intraperitoneal and Preperitoneal Spaces

Background: We aimed to compare plasma concentrations of carbon dioxide (CO(2)) in dogs that underwent intra- and preperitoneal CO(2) insufflation. Materials and Methods: Thirty dogs were studied. Ten formed a control group, 10 underwent intraperitoneal CO(2) insufflation, and 10 underwent preperitoneal CO(2) insufflation. General anesthesia with controlled ventilation was standardized for all dogs. After stabilizing the anesthesia, blood samples were collected at predetermined times and were sent for immediate gasometric analysis. Analysis of variance was used for comparing variables. Results: The plasma CO(2) concentration in the intraperitoneal insufflation group increased significantly more than in the preperitoneal insufflation group and was significantly greater than in the control group (P < 0.05). The pH values in the intraperitoneal group were lower than in the preperitoneal group (P < 0.05). Conclusion: The data from this study suggest that a greater plasma concentration of CO(2) is achieved by insufflation at constant pressure into the intraperitoneal space than into the preperitoneal space.