On the calculation of inner products of Schur functions

Two methods for calculating inner products of Schur functions in terms of outer products and plethysms are given and they are easy to implement on a machine. One of these is derived from a recent analysis of the SO(8) proton-neutron pairing model of atomic nuclei. The two methods allow for generation of inner products for the Schur functions of degree up to 20 and even beyond.

Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Influence of the iron source on the solar photo-Fenton degradation of different classes of organic compounds

In this work the influence of two different iron sources, Fe(NO3)(3) and complexed ferrioxalate (FeOx), on the degradation efficiency of 4-chlorophenol (4CP), malachite green, formaldehyde, dichloroacetic acid (DCA) and the commercial products of the herbicides diuron and tebuthiuron was studied. The oxidation of 4CP, DCA, diuron and tebuthiuron shows a strong dependence on the iron source. While the 4CP degradation is favored by the use of Fe(NO3)(3), the degradation of DCA and the herbicides diuron and tebuthiuron is most efficient when ferrioxalate is used. on the other hand, the degradation of malachite green and formaldehyde is not very influenced by the iron source showing only a slight improvement when ferrioxalate is used. In the case of formaldehyde, DCA, diuron and tebuthiuron, despite of the additional carbon introduced by the use of ferrioxalate, higher mineralization percentages were observed, confirming the beneficial effect of ferrioxalate on the degradation of these compounds. The degradation of tebuthiuron was studied in detail using a shallow pond type solar flow reactor of 4.5 L capacity and 4.5 cm solution depth. Solar irradiation of tebuthiuron at a flow rate of 9 L h(-1), in the presence of 10.0 mmol L-1 H2O2 and 1.0 mmol L-1 ferrioxalate resulted in complete conversion of this herbicide and 70% total organic carbon removal. (c) 2005 Elsevier Ltd. All rights reserved.

Integration of polyharmonic functions

The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.

On some classes of exactly-solvable Klein-Gordon equations

In this work we discuss some exactly solvable Klein-Gordon equations. We basically discuss the existence of classes of potentials with different nonrelativistic limits, but which shares the intermediate effective Schroedinger differential equation. We comment about the possible use of relativistic exact solutions as approximations for nonrelativistic inexact potentials. (c) 2005 Elsevier B.V. All rights reserved.

Analytic element modelling for strip aquifers

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

Documenting the advantages and limitations of different classes of molecular markers in a well-established phylogeographic context: lessons from the Iberian endemic Golden-striped salamander, Chioglossa lusitanica (Caudata: Salamandridae)

Previous analyses of mitochondrial (mt)DNA and allozymes covering the range of the Iberian endemic golden-striped salamander, Chioglossa lusitanica, suggested a Pleistocene split of the historical species distribution into two population units (north and south of the Mondego river), postglacial expansion into the northernmost extant range, and secondary contact with neutral diffusion of genes close to the Mondego river. We extended analysis of molecular variation over the species range using seven microsatellite loci and the nuclear P-fibrinogen intron 7 (beta-fibint7). Both microsatellites and beta-fibint7 showed moderate to high levels of population structure, concordant with patterns detected with mtDNA and allozymes; and a general pattern of isolation-by-distance, contrasting the marked differentiation of two population groups suggested by mtDNA and allozymes. Bayesian multilocus analyses showed contrasting results as populations north and south of the Douro river were clearly differentiated based on microsatellites, whereas allozymes revealed differentiation north and south of the Mondego river. Additionally, decreased microsatellite variability in the north supported the hypothesis of postglacial colonization of this region. The well-documented evolutionary history of C. lusitanica, provides an excellent framework within which the advantages and limitations of different classes of markers can be evaluated in defining patterns of population substructure and inferring evolutionary processes across distinct spatio-temporal scales. The present study serves as a cautionary note for investigations that rely on a single type of molecular marker, especially when the organism under study exhibits a widespread distribution and complex natural history. (C) 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 95, 371-387.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polyno-mial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high. © 2001 American Society of Animal Science. All rights reserved.

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

Quantum propagator for some classes of three-dimensional three-body systems

In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and masses, by using the Feynman path integral formalism. Finally, the energy spectrum and the eigenfunctions are recovered from the propagators. © 2005 Elsevier Inc. All rights reserved.

Early impairment of cognitive functions in Parkinson's disease

Background: Impairment in non-motor functions such as disturbances of some executive functions are also common events in Parkinson's disease patients. Objective: To verify the performance of Parkinson's disease patients in activities requiring visuoconstructive and visuospatial skills. Method: Thirty elderly patients with mild or moderate stages of Parkinson's disease were studied. The assessment of the clinical condition was based on the unified Parkinson's disease rating scale (56.28; SD=33.48), Hoehn and Yahr (2.2; SD=0.83), Schwab and England (78.93%), clock drawing test (7.36; SD=2.51), and mini-mental state examination (26.48; SD=10.11). Pearson's correlation and stepwise multiple regression were used for statistical analyses. Results: The patients presented deterioration in visuospatial and visuoconstructive skills. Conclusion: The clock drawing test proved to be a useful predictive tool for identifying early cognitive impairment in these individuals.

The fat body of termites: Functions and stored materials

The functions of the fat body in the different castes of termites, and accumulation of energy reserves, proteins and urates within this organ, are reviewed. The termite fat body is involved in multiple metabolic activities, including recycling of nitrogen. Termite fat body showed three different types of cells: adipocytes, urocytes and mycetocytes, the latter restricted to the species Mastotermes darwiniensis. Adipocytes synthesize and store lipids, glycogen and several proteins. These cells also elaborate important peptides, including some that act in immune processes. Urocytes are responsible for the storage of spherocrystals of urates, which vary quantitatively among the termite castes. The different metabolic functions of the fat body in the several castes and stages of termites are associated with specific adipocyte morphologies. The synthesis and storage of different compounds modify the structure of the fat body; this differentiation is coordinated by hormones involved with molting and reproductive cycles. © 2013 Elsevier Ltd.