Error bounds for rational quadrature formulae of analytic functions

We study the error of rational quadrature rules when functions which are analytic on a neighborhood of the set of integration are considered. A computable upper bound of the error is presented which is valid for a broad range of rational quadrature formulae and a comparison is made with the exact error for a number of numerical examples.This work was supported by the Dirección General de Investigación (DGI), Ministerio de Ciencia y Tecnología, under grants BFM2003-06335-C03-02 and BFM2002-04315- C02-01.     

Formamidines and triazenes as precursors for the preparation of rhenium imido-complexes

Summary The rhenium(V) imido-complexes [Re(NR)Cl₃(PPh₃)₂] have been obtained by heating the rhenium(V) derivative [ReOCl₃(PPh₃)₂] with RNHCHNR R = Ph (1a), p-MeC₆H₄ (1b), p-ClC₆H₄ (1c) andp-FC₆H₄ (1d) in THF under reflux. [Re(NR)Cl₃(PPh₃)₂] (R =p-MeQ₆H₄) has also been obtained by heating the rhenium(III)-triazenido complex [ReCl₂(RN N NR)(PPh₃)₂] in CCl₄ under reflux.     

Carbon-13 NMR spectra of Δ4(20).11- taxadiene derivatives

The ¹³C NMR spectra of a series of some Δ^4(20),11-taxadiene derivatives are reported. A detailed analysis of their assignments is presented.     

A Flory–Huggins thermodynamic approach for predicting sorption equilibrium in ternary polymer systems

The Flory–Huggins theory as modified by Pouchlý has been applied to calculate preferential (λ) and total (Y) sorption coefficients for a ternary polymer system. The ternary interaction function (?₁?₂?₃G_T(u₁, ?₃)) is described as the product of three independent binary functions. This expression allows prediction of λ and Y from binary interaction parameters χ, χ, g, g, and g₁₂(?₁₀). Three ternary polymer systems are used to check the validity of the expression. Moreover for polymer systems in which the parameters g and/or g are unknown, a procedure to evaluate them has been developed and verified on systems for which sufficient experimental information is available.     

{2,6‐Bis­[(di­methyl­amino)­methyl]pyridine‐κ3N}(2,2‐methyl­enediphenolato‐κ2O,O′)­dioxouranium(VI) acetone solvate

In the title compound, [UO₂(C₁₃H₁₀O₂)(C₁₁H₁₉N₃)]·C₃H₆O, the U atom is in a pentagonal–bipyramidal environment, with the three N atoms of the 2,6‐bis­[(di­methyl­amino)­methyl]­pyridine ligand and the two O atoms of the dianionic 2,2′‐methyl­ene­diphenolate ligand in the equatorial plane. The geometry is compared with that of previously reported 1:2 uranyl–diphenoxide complexes.     

Riccati equations and Lie series

Lie series and a special matrix notation for first-order differential operators are used to show that the Lie group properties of matrix Riccati equations arise in a natural way. The Lie series notation makes it evident that the solutions of a matrix Riccati equation are curves in a group of nonlinear transformations that is a generalization of the linear fractional transformations familiar from the classical complex analysis. It is easy to obtain a linear representation of the Lie algebra of the nonlinear group of transformations and then this linearization leads directly to the standard linearization of the matrix Riccati equations. We note that the matrix Riccati equations considered here are of the general rectangular type.     

Spectral density of surface states: Clean W(001) surface

The transfer matrix approach is applied to calculate the spectral density of electronic states for the W(001) surface. We use a tight-binding hamiltonian with a nine function basis: 6s, 6p and 5d. Results for $\text{k}$ points along the Σ and ? symmetry lines are presented for occupied states. Both surface and bulk features of the spectral density are in good agreement with angularly resolved photoemission spectra.     

Electro-oxidation of hispanolone and anti-inflammatory properties of the obtained derivatives

The electrochemical oxidation ((+)Pt-Ni(-)/NH(4)Br/MeOH) of the natural product hispanolone (1a) produced, in high yield (>95%), spiro-tetracyclic compounds 7a-7d as a result of the intramolecular addition of the C-9 hydroxyl group into the C-16 position with the simultaneous addition of a CH(3)O group at the C-15 position of the hispanolone furan moiety. After the electrochemical oxidation, an acid-catalyzed slow secondary reaction occurred producing the previously undescribed alpha-butenolide derivative, iso-Leopersin G (9). An anti-inflammatory study with the electro-synthesized compounds showed that 1a has higher anti-inflammatory properties with very low cytotoxicity (e.g., the inhibition of TPA-induced ear edema assay IC(50) = 1.05 microM/ear, positive control indomethacin IC(50) = 0.27 microM/ear).