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.     

The growth of crystals in solution

The crystallization of sparingly soluble salts from their aqueous supersaturated solutions is discussed from the standpoint of two important applications; scale formation and biological mineralization. Theories of crystal growth are outlined and the importance of kinetic factors in determining the nature of the growing phases is discussed. The kinetic factors can be studied by using a highly reproducible seeded growth technique and under certain conditions secondary nucleation can also be induced on the surface of the inoculating seed crystals. The kinetics of crystallization of the alkaline earth surfaces and the calcium phosphates is discussed. In the latter systems, temperature, supersaturation, surface concentration, pH, ionic strength and the presence of foreign ions are important in determining the nature of the phase which grows on the added seed crystals. The mechanism of the retardation of crystal growth by added crystallization inhibitors is illustrated by the influence of organic phosphonate molecules upon the precipitation of calcium carbonate.     

Linear crystallization and induction-period studies of the growth of calcium sulphate dihydrate crystals

The linear crystallization of well-formed crystallites of calcium sulphate dihydrate from supersaturated solutions has been studied by a microscopic method at temperatures ranging from 25 degrees to 55 degrees . The activation energy is 16 +/- 1.5 kcal/mole for the fast-growing faces. Induction periods in the crystallization of calcium sulphate dihydrate have been determined as a function of solution concentration at temperatures of 25 degrees and 90 degrees .     

Ion association in calcium phosphate solutions at 37°C

Ion association in the system Ca(OH)₂–H₃PO₄–KCl–H₂O at 37°C has been studied potentiometrically over a range of pH from 3 to 9. The experimental conditions were optimized for the accurate determination of the association constants for the formation of the ion pairs CaH₂PO ₄ ⁺ , CaHPO₄ and CaPO ₄ ^– which were found to be 27.9±0.1, 591±2, and (1.35±0.02)×10⁶ L-mol^–1, respectively.     

THE SURFACE,INTERFACIAL AND ELECTROKINETIC PROPERTIES OF BIOMINERALS

ABSTRACT

The apolar (Lifshitz van der Waals) component (γ ^LW _S) and the polar [electron-acceptor (γ ⁺ _S) and electron-donor (γ ^? _S)] parameters of the surface tension of biominerals and surfaces of dental hard tissues have been measured, as well as their ζpotentials. The interfacial tensions between their surfaces and aqueous solutions, determined using van Oss-Chaudhury-Good equations, are comparable with the interfacial free energy values obtained from the kinetics of crystallization and dissolution using a constant composition technique. The electron-donor (γ ^? _S) parameters indicate that most of these minerals have a moderate to high hydrophobicity. The interfacial tension values are consistent with the order of the solubilities of these minerals.     

Application of the extended DLVO theory—the stability of alatrofloxacin mesylate solutions

Electrophoretic mobility and contact angle measurements have been made on alatrofloxacin mesylate and its formulations which were protected from or exposed to light, and its degradation product compound (F). In aqueous solution, the light-protected alatrofloxacin mesylate had a zeta-potential of +19 mV, a negligible electron-acceptor (γ_i⁺) surface tension parameter and an electron-donor surface tension parameter γ_i⁻=32.5 mJ m⁻², which was higher than that of water. This caused the particles to be very hydrophilic and to form very stable suspensions in aqueous solution due, mainly, to a net Lewis acid–base (polar) repulsion. After the suspensions were exposed to light, the zeta-potential of the degradation product increassed to +37.8 mV, but the electron-donor surface tension parameter decreased to γ_i⁻=8 mJ m⁻², making the molecules or particles very hydrophobic and causing them to flocculate. The energies of attraction in the latter case were mainly hydrophobic (90%) with about 10% resulting from van der Waals forces.     

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.     

Modulation of calcium oxalate crystallization by linear aspartic acid-rich peptides

Calcium oxalate monohydrate (COM) kidney stone formation is prevented in most humans by urinary crystallization inhibitors. Urinary osteopontin (OPN) is a prototype of the aspartic acid-rich proteins (AARP) that modulate biomineralization. Synthetic poly(aspartic acids) that resemble functional domains of AARPs provide surrogate molecules for exploring the role of AARPs in biomineralization. Effects of linear aspartic acid-rich peptides on COM growth kinetics and morphology were evaluated by the combination of constant composition (CC) analysis and atomic force microscopy (AFM). A spacer amino acid (either glycine or serine) was incorporated during synthesis after each group of 3 aspartic acids (DDD) in the 27-mer peptide sequences. Kinetic CC studies revealed that the DDD peptide with serine spacers (DDDS) was more than 30 times more effective in inhibiting COM crystal growth than the DDD peptide with glycine spacers (DDDG). AFM revealed changes in morphology on (010) and (-101) COM faces that were generally similar to those previously described for OPN and citrate, respectively. At comparable peptide levels, the effects of step pinning and reduced growth rate caused by DDDS were remarkably greater. In CC nucleation studies, DDDS caused a greater prolongation of induction periods than DDDG. Thus, nucleation studies link changes in interfacial energy caused by peptide adsorption to COM to the CC growth and AFM results. These studies indicate that, in addition to the number of acidic residues, the contributions of other amino acids to the conformation of DDD peptides are also important determinants of the inhibition of COM nucleation and growth.