Spectroscopic studies of the Eu3+ and Er3+ ions in the fluorozirconate LaZr2F11 matrix

An investigation by optical spectroscopy of the Eu3 + and Er3 + active ions in the crystallized fluorozirconate matrix LaZr2F11 is presented. The D-5(1) --> F-7(0-5) emission lines of Eu3 + are used to extract the F-7(0-5) energy scheme and the observed extinctions permit the deduction of irreducible representations (IRREPS) associated with corresponding sub-levels in the D-2 symmetry. The crystal field analysis was carried out on a 387 x 387 basis set, comprising the F-7, D-5(1,2,3) F-5(1,2), (5)G(1,2,3) and P-3(1,2,3,4,5,6) terms of the Eu-3 (+) 4f(6) configuration. The deviation and rms are 6.8 and 7.9 cm (-1), respectively for 38 levels and ten parameters. The experimental crystal field parameters are in good agreement with the ab-initio ones. Moreover, the relative intensities of the D-5(0) --> F-7(2,3,4) emissions are well reproduced by an 'ab-initio' calculation, except for three lines. The Er3 + ions introduced in LaZr2F11, microcrystals also lie in an unique crystallographic site. A total of 31 energy levels were recorded and the crystal field analysis led to 6.6 and 7.8 cm (-1) for the deviation and rms, respectively, for nine variable parameters taken into account. The experimental CF parameters for Er3 + and Eu3 + are very similar, which seems to show that the host lattice contracts around the smaller Er3 + ion. The informations given by both Eu3 + and Eu3 + optical probes in LaZr2F11 are very consistent with the structure previously determined for the isotypic PrZr2F11 fluoride. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Companion orthogonal polynomials: some applications

In this paper the recurrence relations of symmetric orthogonal polynomials whose measures are related to each other in a certain way are considered. Many of the relations satisfied by the coefficients of the recurrence relations are exposed. The results are applied to obtain, for example, information regarding certain Sobolev orthogonal polynomials and regarding the measures of certain orthogonal polynomial sequences with twin periodic recurrence coefficients. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S-3(omega, beta, b) of strong distribution functions defined on the interval [beta(2)/b, b], 0 < beta < b <= infinity, where 2 omega epsilon Z. The classification is such that the distribution function psi epsilon S-3(omega, beta, b) has a (reciprocal) symmetry, depending on omega, about the point beta. We consider properties of the L-orthogonal polynomials associated with psi epsilon S-3(omega, beta, b). Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some omega epsilon S-3(1/2, beta, b). (c) 2004 Elsevier B.V. All rights reserved.

Occurrence of biflagellate spermatozoa in Cetopsidae, Aspredinidae, and Nematogenyidae (Teleostei : Ostariophysi : Siluriformes)

In the present study spermiogenesis was investigated in Cetopsis coecutiens (Cetopsidae), and Bunocephalus amazonicus (Aspredinidae), while spermatozoa ultrastructure was investigated in C. coecutiens, B. amazonicus, and Nematogenys inermis (Nematogenyidae). Aspredinidae and Cetopsidae share a spermatogenesis of the semicystic type, and a particular type of spermiogenesis process not reported in any fish group. In the three species analyzed, spermatozoa are biflagellate with flagella having the classical axoneme formulae (9 + 2). The analysis of thirteen characters showed the presence of eight characters shared by Cetopsidae and Aspredinidae, and six characters shared by Cetopsidae and Nematogenyidae, which may suggest that these three families may be more related than actually hypothesized, comprising a very primitive siluriform lineage originated after Diplomystidae.

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

Companion orthogonal polynomials

We give some properties relating the recurrence relations of orthogonal polynomials associated with any two symmetric distributions d phi(1)(x) and d phi(2)(x) such that d phi(2)(x) = (I + kx(2))d phi(1)(x). AS applications of these properties, recurrence relations for many interesting systems of orthogonal polynomials are obtained.

The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings

We carry out a numerical and analytic analysis of the Yang-Lee zeros of the ID Blume-Capel model with periodic boundary conditions and its generalization on Feynman diagrams for which we include sums over all connected and nonconnected rings for a given number of spins. In both cases, for a specific range of the parameters, the zeros originally on the unit circle are shown to depart from it as we increase the temperature beyond some limit. The curve of zeros can bifurcate- and become two disjoint arcs as in the 2D case. We also show that in the thermodynamic limit the zeros of both Blume-Capel models on the static (connected ring) and on the dynamical (Feynman diagrams) lattice tend to overlap. In the special case of the 1D Ising model on Feynman diagrams we can prove for arbitrary number of spins that the Yang-Lee zeros must be on the unit circle. The proof is based on a property of the zeros of Legendre polynomials.

Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

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

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Isolation and characterization of Wharton's jelly-derived multipotent mesenchymal stromal cells obtained from bovine umbilical cord and maintained in a defined serum-free three-dimensional system

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

Reproductive biology in the primitive relic Angiosperm Drimys brasiliensis (Winteraceae)

From field observations on Drimys brasiliensis, principally in the Botucatu region of São Paulo State, Brazil, new data on the reproductive biology, the rhythm of growth, and the development of lateral cymose inflorescences, flowers and fruits are presented. Pollination accelerates the rate of flower-development for about 4-6 days. Pollination experiments show that D. brasiliensis is not self-sterile; because of mechanical devices the sticky pollen grains do not normally come into contact with the stigmata unless an animal pollen vector is involved. The pollinators are diurnal Coleoptera, Diptera and Thysanoptera which eat from the pollen, lick from the stigmatic exudates and (in case of the flies) probably also from the staminal glands. Fruit- and seedeaters are birds which seem to be the main dispersal agents. Establishment of new individuals normally is through seedlings, but also by vegetative propagation through plagiotropous branches which may root and separate from the mother plant. The morphological, developmental and reproductive aspects in D. brasiliensis are discussed in a wider context, compared with data from other Magnoliidae, and related to aspects of early Angiosperm evolution. © 1980 Springer-Verlag.

Projective Fourier duality and Weyl quantization

The Weyl-Wigner correspondence prescription, which makes great use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. Both an Abelian and a symmetric projective Kac algebra are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Absorption and fluorescence of Er3+-doped LiYF4: Measurements and simulation

Er3+:LiYF4 single crystal has been studied by absorption and fluorescence spectroscopy in the IR-visible-UV (0-44000 cm-1) region from 4.2 K to room temperature. Polarized spectra were recorded in order to assign numerous Stark levels of electronic transitions mentioned but not attributed before in the related literature and to discuss the irreducible representations (irreps) of the 4I15/2 sublevels. A parametric hamiltonian, including free ion (Eν, α, β, γ, Tλ, ζ, Mk and Pi) and crystal field parameters (B2 0, B4 0, B4 4, B6 0 and B6 4) in an approximate D2d symmetry for the rare earth site in this scheelite type structure, was used to simulate 109 energy positions of the Er ion with a r.m.s. standard deviation of 14.6 cm-1. A comparison with previously published results for Nd3+ in the same matrix is done. © 1998 Elsevier Science S.A.