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.

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.

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.

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.

Integrable approximation to the overlap of resonances

We study the interaction of resonances with the same order in families of integrable Hamiltonian systems. This can occur when the unperturbed Hamiltonian is at least cubic in the actions. An integrable perturbation coupling the action-angle variables leads to the disappearance of an island through the coalescence of stable and unstable periodic orbits and originates a complex orbit plus an isolated cubic resonance. The chaotic layer that appears when a general term is added to the Hamiltonian survives even after the disappearance of the unstable periodic orbit. © 1992.

Interaction potential between vortex lines for uniaxial superconductors in the London approximation

Two distinct expressions of the interaction potential between arbitrarily oriented curved vortex lines with respect to the crystal c axis are derived within the London approximation. One of these expressions is used to compute the eigenvalues of the elasticity matrix. We examine the elastic properties of the vortex chain lattice, recently proposed, concerning shearing deformation.

Nonforward parton distributions of the pion within an effective single instanton approximation

We develop a relativistic quark model for pion structure, which incorporates the nontrivial structure of the vacuum of quantum chromodynamics as modelled by instantons. Pions are bound states of quarks and the strong quark-pion vertex is determined from an instanton induced effective Lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark mass, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data. © 2000 Elsevier Science B.V.

Off-Diagonal Quark Distributions in Pions in the Effective Single-Instanton Approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables. © 2000 MAIK Nauka/Interperiodica.

Classes of exact wave functions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

The construction of two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions was discussed. The extension of solutions by introduction of a time-dependent mass was elaborated. The possibility of existence of a generalized Lewis-Riesenfeld invariant connected with such solutions was also analyzed.

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.

Análise da incerteza na representação de classes de cobertura do solo urbano resultantes da aplicação de uma rede neural artificial

The great diversity of materials that characterizes the urban environment determines a structure of mixed classes in a classification of multiespectral images. In that sense, it is important to define an appropriate classification system using a non parametric classifier, that allows incorporating non spectral (such as texture) data to the process. They also allow analyzing the uncertainty associated to each class from the output alues of the network calculated in relation to each class. Considering these properties, an experiment was carried out. This experiment consisted in the application of an Artificial Neural Network aiming at the classification of the urban land cover of Presidente Prudente and the analysis of the uncertainty in the representation of the mapped thematic classes. The results showed that it is possible to discriminate the variations in the urban land cover through the application of an Artificial Neural Network. It was also possible to visualize the spatial variation of the uncertainty in the attribution of classes of urban land cover from the generated representations. The class characterized by a defined pattern as intermediary related to the impermeability of the urban soil presented larger ambiguity degree and, therefore, larger mixture.

Destroying horseshoes via heterodimensional cycles: Generating bifurcations inside homoclinic classes

In this paper, we propose a model for the destruction of three-dimensional horseshoes via heterodimensional cycles. This model yields some new dynamical features. Among other things, it provides examples of homoclinic classes properly contained in other classes and it is a model of a new sort of heteroclinic bifurcations we call generating. © 2008 Cambridge University Press.

Lê cycles and Milnor classes

The purpose of this work is to establish a link between the theory of Chern classes for singular varieties and the geometry of the varieties in question. Namely, we show that if Z is a hypersurface in a compact complex manifold, defined by the complex analytic space of zeroes of a reduced non-zero holomorphic section of a very ample line bundle, then its Milnor classes, regarded as elements in the Chow group of Z, determine the global Lê cycles of Z; and vice versa: The Lê cycles determine the Milnor classes. Morally this implies, among other things, that the Milnor classes determine the topology of the local Milnor fibres at each point of Z, and the geometry of the local Milnor fibres determines the corresponding Milnor classes. © 2013 Springer-Verlag Berlin Heidelberg.