A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies`s extension

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is the extended Skyrme-Faddeev model with a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled nonlinear partial differential equations in two variables by a successive over-relaxation method. We construct numerical solutions with the Hopf charge up to 4. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms.

Exact vortex solutions in a CP(N) Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP(N) which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP(1). We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x(1) + i x(2)) and (x(3) + x(0)) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.

Cutpoint selection for discretizing a continuous covariate for generalized estimating equations

We consider consider the problem of dichotomizing a continuous covariate when performing a regression analysis based on a generalized estimation approach. The problem involves estimation of the cutpoint for the covariate and testing the hypothesis that the binary covariate constructed from the continuous covariate has a significant impact on the outcome. Due to the multiple testing used to find the optimal cutpoint, we need to make an adjustment to the usual significance test to preserve the type-I error rates. We illustrate the techniques on one data set of patients given unrelated hematopoietic stem cell transplantation. Here the question is whether the CD34 cell dose given to patient affects the outcome of the transplant and what is the smallest cell dose which is needed for good outcomes. (C) 2010 Elsevier BM. All rights reserved.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

Synthesis, characterization and adsorption properties of porous mixed valent diruthenium(II,III)-terephthalate and diruthenium(II,III)-adipate polymers

Two porous mixed valent diruthenium(II,III)-dicarboxylate compounds have been prepared and characterized by spectroscopic methods, X-ray diffraction and thermogravimetry. Crystalline solids of [Ru(2)(tere)(2)Cl] center dot 3.5H(2)O (tere=terephthalate) and [Ru(2)(adip)(2)Cl] center dot 1.5H(2)O (adip=adipate) consist of extended chains in which polymeric layers of multiply metal-metal bonded [Ru(2)](5+) cores are bridged by dicarboxylate ligands in paddlewheel type geometries. Units of [Ru(2)(dicarboxylate)(2)](n)(+) are linked by axial bridging chloride ions generating three-dimensional networks. The polymers loose non-bonded water molecules at low temperatures but do not undergo thermal decomposition below 280-300 degrees C. Both of compounds exhibit high BET surface areas, [Ru(2)(tere)(2)Cl]: 235 m(2) g(-1) and [Ru(2)(adip)(2)Cl]: 281 m(2) g(-1), and occlude similar numbers of mol of N(2) per mol of metal. The terephthalate ligand generated an organized structure with supermicropores (total pore size of 0.24 cm(3) g(-1)) while the adipate ligand led to a mesoporous structure (total pore sizes of 0.47 cm(3) g(-1)) for the corresponding diruthenium(II,III)-dicarboxylate polymers. (c) 2008 Elsevier B.V. All rights reserved.

Specific detection of Lettuce mosaic virus isolates belonging to the Most type

Lettuce mosaic virus (LMV)-Most isolates can infect and are seed-borne in cultivars containing the mol gene. A reverse transcription and polymerase chain reaction (RT-PCR)-based test was developed for the specific detection of LMV-Most isolates. Based on the complete genome sequences of three LMV isolates belonging respectively to the Most type, the Common type and neither of these two types, three different assays were compared: (i) presence of a diagnostic restriction site in the region of the genome encoding the variable N-terminus of the capsid protein, in the 3' end of the genome, (ii) RT-PCR using primers designed to amplify a cDNA corresponding to a portion of the P1 coding region, in the 5' end of the genome and (iii) RT-PCR using primers designed to amplify a central region of the genome. The assays were performed against a collection of 21 isolates from different geographical origins and representing the molecular variability of LMV. RT-PCR of the central region of the genome was preferred because its results are expected to be less affected by natural recombination between LMV isolates, and it allows sensitive detection of LMV-Most in situations of single as well as mixed contamination. (C) 2004 Elsevier B.V. All rights reserved.

Biomass and Stand Characteristics of a Highly Productive Mixed Douglas-Fir and Western Hemlock Plantation in Coastal Washington

Aboveground biomass predictive equations were developed for a highly productive 47-year-old mixed Douglas-fir and western hemlock stand in southwest Washington State to characterize the preharvest stand attributes for the Fall River Long-Term Site Productivity Study. The equations were developed using detailed biomass data taken from 31 Douglas-fir and 11 western hemlock trees within the original stand. The stand had an average of 615 live trees per hectare, with an average dbh of 35.6 cm (39.1 cm for Douglas-fir and 33.3 cm for western hemlock) and an average total tree height of 31.6 m (32.8 m for Douglas-fir and 30.2 m for western hemlock). Equations developed were of the form In Y = b(1) + b(2) In dbh, where Y = biomass in kg, dbh = diameter in cm at 1.3 m height, b(1) = intercept, and b(2) = slope of equation. Each tree part was estimated separately and also combined into total aboveground biomass. The total aboveground biomass estimation equations were In Y = -0.9950 + 2.0765 In dbh for Douglas-fir, and In Y = -1.6612 + 2.2321 In dbh for western hemlock. The estimate of the aboveground live-free biomass was of 395 Mg ha(-1) (235 Mg ha(-1) for Douglas-fir and 160 Mg ha(-1) for western hemlock), with 9.5, 29.3, 12.9, 308, and 32.7 Mg ha(-1) in the foliage, live branches, dead branches, stem wood, and stem hark, respectively. When compared with biomass estimates from six other studies, ranging in age from 22 to 110 years and from 96.3 to 636 Mg ha(-1), the biomass of the Fall River site was relatively high for its age, indicating very high productivity.

Detection of mixed microbial biofilms on central venous catheters removed from Intensive care Unit Patients

Cateteres venosos centrais inseridos em pacientes internados em unidade de terapia intensiva foram avaliados por métodos microbiológicos (cultura semi-quantitativa) e microscopia eletrônica de varredura a fim de detectar adesão microbiana e correlacionar com a cultura de sangue. Durante o período de estudo, foram avaliados 59 pacientes com cateter venoso central. A idade dos pacientes, sexo, sítio de inserção e tempo de permanência do cateter foram anotados. O cateter era de poliuretano não tunelizado e de único lúmen. O sangue para cultura foi coletado no momento da remoção do cateter. de 63 pontas de cateteres, 30 (47,6%) foram colonizadas e a infecção encontrada em 5 (23,8%) cateteres. A infecção foi mais prevalente em 26 pacientes (41,3%) com cateteres inseridos em veia subclávia do que nos 3 (3,2%) inseridos em veia jugular. A infecção foi observada com mais freqüência em cateteres com tempo de permanência maior do que sete dias. Os microrganismos isolados incluíram 32 estafilococos coagulase-negativa (29,7%), 61 bactérias Gram-negativas (52,9%), 9 estafilcocos coagulase-positiva (8,3%) e 3 leveduras (2,7%). Como agentes causais de infecções em unidade de terapia intensiva foram isolados E. aerogenes, P. aeruginosa, A. baumannii. Os antimicrobianos com maior atividade in vitro contra as bactérias Gram-negativas foram o imipenem e contra as Gram-positivas vancomicina, cefepime, penicilina, rifampicina e tetraciclina. As análises por microscopia eletrônica de varredura revelaram biofilmes sobre a superfície de todos os cateteres examinados.

Confinement of spin-0 and spin-1/2 particles in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V-v = V-s + constant. These isospectral problems are solved in the case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfunctions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subjected to the same potentials.

Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V(v) + V(s) = constant. These intrinsically relativistic and isospectral problems are solved in the case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.

Antimicrobial activity of disinfectant agents incorporated into type IV dental stone

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

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

On exact boundary controllability for linearly coupled wave equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Type-II Backlund transformations via gauge transformations

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