Factors which affect the catalytic activity of iron(III) meso tetrakis(2,6-dichlorophenyl)porphyrin chloride in homogeneous system

An optimization study of the reaction conditions of Fe(TDCPP)Cl when it is used as catalyst in the hydroxylation of cyclohexane by iodosylbenzene (PhIO) has been carried out, It was found that Fe(TDCPP)Cl follows the classical PhIO mechanism described for Fe(TPP)Cl, which involves the monomeric active species Fe-IV(O)P-+. (I). In the optimized condition ([Fe(TDCPP) = 3.0 X 10(-4) mol l(-1) in 1,2-dichloroethane (DCE); ultrasound stirring at 0 degrees C; PhIO/FeP molar ratio = 100), this FeP led to a yield of cyclohexanol (C-ol) of 96% and a turnover number of 96, Therefore, Fe(TDCPP)Cl may be considered a good biomimetic model and a very stable, resistant and selective catalyst, which yields C-ol as the sole product. DCE showed to be a better solvent than dichloromethane (DCM), 1 DCE:1 MeOH mixture or acetonitrile (ACN). Since the Fe-IV(O)P-+. is capable of abstracting hydrogen atom from DCM, MeOH or ACN, the solvent competes with the substrate. Presence of O-2 lowers the yield of C-ol, as it can further oxidize this alcohol to carboxylic acid in the presence of radicals, Presence of H2O also causes a decrease in the yield, since it converts the active species I into Fe-IV(OH)P, which cannot oxidize cyclohexane. Addition of excess imidazole or OH- to the system results in a decrease in the yield of C-ol, due to the formation of the hexacoordinated complexes Fe(TDCPP)Im(2)(+) (low-spin, beta(2) = 2.5 X 10(8) mol(-2) l(2)) and Fe(TDCPP)(OH)(2)(-) (high-spin, beta(2) = 6.3 X 10(7) mol(-2) l(2)), the formation of both Fe(TDCPP)Im(2)(+) and Fe(TDCPP)(OH)(2)(-) complexes were confirmed by EPR studies. The catalytic activities of Fe(TDCPP)C and Fe(TFPP)Cl were compared, the unusually high yields of C-ol with Fe(TFPP)Cl obtained when ultrasound, DCM and O-2 atmosphere were used, suggest that a parallel mechanism involving the mu-oxo dimer form, O-2 and radicals may also be occurring with this FeP, besides the PhIO mechanism.

Szego type polynomials and para-orthogonal polynomials

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

Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Squeezed states, generalized Hermite polynomials and pseudo-diffusion equation

We show that the wavefunctions 〈pq; λ|n〈, of the harmonic oscillator in the squeezed state representation, have the generalized Hermite polynomials as their natural orthogonal polynomials. These wavefunctions lead to generalized Poisson Distribution Pn(pq;λ), which satisfy an interesting pseudo-diffusion equation: ∂Pnp,q;λ) ∂λ= 1 4 [ ∂2 ∂p2-( 1 λ2) ∂2 ∂q2]P2(p,q;λ), in which the squeeze parameter λ plays the role of time. Th entropies Sn(λ) have minima at the unsqueezed states (λ=1), which means that squeezing or stretching decreases the correlation between momentum p and position q. © 1992.

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.

Pre-weighted homogeneous map germs finite determinacy and topological triviality

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather's groups A or K.) and show that any G-pre-weighted homogeneous map germ is G-finitely determined. We also give an explicit order, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.

Nonnegative trigonometric polynomials

An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szego are obtained explicitly. Associated cosine polynomials k n (θ) are constructed in such a way that { k n (θ) } are summability kernels. Thus, the L p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. © 2002 Springer-Verlag New York Inc.

Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials

Connection between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), are looked at. The results are applied to obtain information regarding Sobolev orthogonal polynomials associated with certain pairs of measures.

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.

A tool to simplify the management of homogeneous and heterogeneous grids

To simplify computer management, several system administrators are adopting advanced techniques to manage software configuration on grids, but the tight coupling between hardware and software makes every PC an individual managed entity, lowering the scalability and increasing the costs to manage hundreds or thousands of PCs. This paper discusses the feasibility of a distributed virtual machine environment, named Flexlab: a new approach for computer management that combines virtualization and distributed system architectures as the basis of a management system. Flexlab is able to extend the coverage of a computer management solution beyond client operating system limitations and also offers a convenient hardware abstraction, decoupling software and hardware, simplifying computer management. The results obtained in this work indicate that FlexLab is able to overcome the limitations imposed by the coupling between software and hardware, simplifying the management of homogeneous and heterogeneous grids. © 2009 IEEE.

Monte Carlo and analytical calculation of lateral deflection of proton beams in homogeneous targets

Proton radiation therapy is a precise form of radiation therapy, but the avoidance of damage to critical normal tissues and the prevention of geographical tumor misses require accurate knowledge of the dose delivered to the patient and the verification of his position demand a precise imaging technique. In proton therapy facilities, the X-ray Computed Tomography (xCT) is the preferred technique for the planning treatment of patients. This situation has been changing nowadays with the development of proton accelerators for health care and the increase in the number of treated patients. In fact, protons could be more efficient than xCT for this task. One essential difficulty in pCT image reconstruction systems came from the scattering of the protons inside the target due to the numerous small-angle deflections by nuclear Coulomb fields. The purpose of this study is the comparison of an analytical formulation for the determination of beam lateral deflection, based on Molière's theory and Rutherford scattering with Monte Carlo calculations by SRIM 2008 and MCNPX codes. © 2010 American Institute of Physics.

Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)