Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Thermodynamic Complexation of Dopamine with Zinc(II) in Media with Different Dielectric Constants

The complexation of zinc(II) with dopamine has been investigated by spectrophotometric measurements in mixed solvent system at an ionic strength of 0.2 mol•dm－3 sodium chloride, employed at at (15±0.1), (25±0.1), (35±0.1) ℃ at inin a pH range of ca. 6 to ca. 7 with a high ratio of ligand to metal. The effect of solvent systems on protonation and complexation are was was discussed. Linear relationships are werewere observed by plotting lg K versus 1/D, where K and D show stability and dielectric constants, respectively.     

Self-assembled functional organic monolayers on oxide-free copper

The preparation and characterization of self-assembled monolayers on copper with n-alkyl and functional thiols was investigated. Well-ordered monolayers were obtained, while the copper remained oxide-free. Direct attachment of N-succinimidyl mercaptoundecanoate (NHS-MUA) onto the copper surface allowed for the successful attachment of biomolecules, such as β-d-glucosamine, the tripeptide glutathione, and biotin. Notably, the copper surfaces remained oxide-free even after two reaction steps. All monolayers were characterized by static water contact angle measurements, X-ray photoelectron spectroscopy, and infrared reflection absorption spectroscopy. In addition, the biotinylated copper surfaces were employed in the immobilization of biomolecules such as streptavidin.     

Double diffraction dissociation and test of pomeron factorization at the CERN ISR

We report the observation of double diffraction dissociation in the process p + p → (pπ⁺π^?) + X at √s of 45 GeV and momentum transfer in the ?t range 0.15?0.53 GeV² at the CERN ISR. The relative rates for elastic, single and double dissociation reactions measured here are found to agree with the prediction of Pomeron factorization.