Chain sequences and symmetric generalized orthogonal polynomials

in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Spin tunneling in magnetic molecules: Quantitative estimates for Fe8 clusters

Spin tunneling in the particular case of the magnetic molecular cluster octanuclear iron(III), Fe8, is treated by an effective Hamiltonian that allows for an angle-based description of the process. The presence of an external magnetic field along the easy axis is also taken into account in this description. Analytic expressions for the energy levels and barriers are obtained from a harmonic approximation of the potential function which give results in good agreement with the experimental results. The energy splittings due to spin tunneling is treated in an adapted WKB approach and it is shown that the present description can give results to a reliable degree of accuracy. (c) 2007 Elsevier B.V. All rights reserved.

REGULATION OF BOVINE ENDOMETRIAL SECRETION OF PROSTAGLANDINS AND SYNTHESIS OF 2',5'-OLIGOADENYLATE SYNTHETASE BY INTERFERON-ALPHA MOLECULES

Experiments were performed to (1) verify the inhibitory effect of bovine trophoblast protein-1 (bTP-1) on uterine prostaglandin synthesis, (2) evaluate whether other interferon-alpha (IFN-alpha) molecules also inhibit prostaglandin secretion, and (3) test whether the enzyme 2',5'-oligoadenylate synthetase (2-5A synthetase) can be induced in endometrium by interferon-alpha. In experiment 1, all interferon molecules (bTP-1, oTP-1, bIFN-alpha and hIFN-alpha) equally inhibited secretion of PGF and PGE2 from endometrial explant cultures obtained at day 17 of the estrous cycle. In experiment 2, endometrial explants obtained from day 17 of the cycle were cultured with and without bovine serum albumin (BSA; 50-mu-g/ml) and bIFN-alpha (0, 0.84, 4.2, and 42 nM). Addition of BSA to the culture medium greatly enhanced the accumulation of PGF into the medium. The bIFN-alpha inhibited accumulation of PGF and PGE2 in both the presence or absence of BSA by 12 h. All three concentrations of bIFN-alpha were equally effective in inhibiting prostaglandin accumulation. Additionally, all concentrations of bIFN-alpha increased the amounts of 2-5A synthetase in endometrium. In conclusion, these results confirm the inhibitory effect of bTP-1 on PGF release from endometrium and demonstrate that bTP-1 can also inhibit PGE2 secretion. Furthermore, other interferon-alpha molecules, including bIFN-alpha, hIFN-alpha, and oTP-1, also reduced PGF and PGE2 secretion in culture. It is likely, therefore, that conceptus and other interferon-alpha molecules exert similar effects on endometrium in vitro and that the antiluteolytic effects of bIFN-alpha in vivo are mediated in part by changes in endometrial prostaglandin synthesis.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Hormonal therapy in the senescence: Prostatic microenvironment structure and adhesion molecules

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

Morse basis expansion applied to diatomic molecules

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

On the periodic solutions of the static, spherically symmetric Einstein-Yang-Mills equations

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

On the interaction of small molecules with hemoproteins: Sperm whale myoglobin

The spin label TEMPO does not show a binding to myoglobin molecule in solution. This is probably due to the fact that this protein does not have a hydrophobic pocket large enough to accommodate the TEMPO molecule. In the crystal the spin label is bound and two kinds of spectra are observed: one isotropic and the other anisotropic. The anisotropic site is probably an intermolecular one. The correlation time for the label in the crystal is very sensitive to temperature showing a transition near 30 °C. This change can be explained as a result of the conformational change observed for myoglobin near this temperature: the motion of the spin label becomes more restricted below this temperature. Change in hydration is the probable cause of this structural change. The changes in the EPR spectra of the anisotropic label suggest that it is bound near the first layers of protein in the crystal. © 1985 Societá Italiana di Fisica.

Interaction between Li+ and C60 molecules

MNDO calculations with complete geometry optimization were used to calculate the interaction between Li+ and C60, C- 60 and C2- 60 molecules. In order to determine the more stable configuration, Li+ was approximated to the C60 molecule or to their reduced forms from 10 Å up to the geometric center of the molecule. From the simulations we determine that Li+ remains close to the surface at 5 Å from the geometric center of the C60 molecules. © 1995.

Associated symmetric quadrature rules

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained through this relation are also considered.

Spherically symmetric scalar field in general relativity

We analyze the presence of a scalar field around a spherically symmetric distribution of an ordinary matter, obtaining an exact solution for a given scalar field distribution.

Duality-symmetric eleven-dimensional supergravity and its coupling to M-branes

The standard eleven-dimensional supergravity action depends on a three-form gauge field and does not allow direct coupling to five-branes. Using previously developed methods, we construct a covariant eleven-dimensional supergravity action depending on a three-form and six-form gauge field in a duality-symmetric manner. This action is coupled to both the M-theory two-brane and five-brane, and corresponding equations of motion are obtained. Consistent coupling relates D = 11 duality properties with self-duality properties of the M5-brane. From this duality-symmetric formulation, one derives an action describing coupling of the M-branes to standard D = 11 supergravity. © 1998 Elsevier Science B.V.

Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds

We reexamine the two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. The appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime.

Inversely symmetric interpolatory quadrature rules

We consider interpolatory quadrature rules with nodes and weights satisfying symmetric properties in terms of the division operator. Information concerning these quadrature rules is obtained using a transformation that exists between these rules and classical symmetric interpolatory quadrature rules. In particular, we study those interpolatory quadrature rules with two fixed nodes. We obtain specific examples of such quadrature rules.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.