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.     

Stable heteroleptic complexes of divalent lanthanides with bulky pyrazolylborate ligands--iodides, hydrocarbyls and triethylborohydrides

The reaction of YbI(2) with KTp(Me2) gives (Tp(Me2))YbI(THF)(2) (1-Yb) as a thermally unstable product. Use of the more hindered KTp(tBu,Me) gave (Tp(tBu,Me))LnI(THF)(n) (Ln = Sm, n = 2, 2-Sm; Ln = Yb, n = 1, 2-Yb). The crystal structures of both these compounds are reported. Adducts with neutral ligands such as pyridines and isonitriles can be prepared and the crystal structures of [(Tp(tBu,Me))YbIL(n)] (L = CN(t)Bu, n = 1; L = 3,5-lutidine, n = 2) are described. 2-Sm can be oxidized using AgBPh(4) to give [(Tp(tBu,Me))SmI(THF)(2)]BPh(4). Compounds 2-Sm and 2-Yb are useful starting materials for the preparation of heteroleptic compounds by metathesis with appropriate potassium reagents. The preparations and characterization of the hydrocarbyls (Tp(tBu,Me))Ln{CH(SiMe(3))(2)} (Ln = Sm, 5-Sm; Yb, 5-Yb) and [(Tp(tBu,Me))Ln{CH(2)(SiMe(3))}(THF)] (Ln = Yb, 6a-Yb) and the triethylborohydrides [(Tp(tBu,Me))Ln(HBEt(3))(THF)(n)] (Ln = Sm, n = 0, 7-Sm; Yb, n = 1, 7-Yb) are reported, as well as the crystal structures of 5-Sm and 5-Yb, and the THF adducts 6a-Yb and [(Tp(tBu,Me))Sm{CH(SiMe(3))(2)}(THF)], 5a-Sm.     

Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field

In this paper, the effects of a magnetic field on natural convection flow in filled long enclosures with Cu/water nanofluid have been analyzed by lattice Boltzmann method. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³–10⁵, the volumetric fraction of nanoparticles between 0 and 6 %, the aspect ratio of the enclosure between A = 0.5 and 2. The Hartmann number has been varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered at inclination angles of θ = 0°, 30°, 60° and 90°. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and the aspect ratios. Heat transfer decreases with the growth of the aspect ratio but this growth causes the effect of the nanoparticles to increase. The magnetic field augments the effect of the nanoparticles at high Rayleigh numbers (Ra = 10⁵). The effect of the nanoparticles rises for high Hartmann numbers when the aspect ratio increases. The rise in the magnetic field inclination improves heat transfer at aspect ratio of A = 0.5.     

Facile pyrazolylborate ligand degradation at lanthanide centers: X-ray crystal structures of pyrazolylborinate-bridged bimetallics

Adventitious hydrolysis of a number of different complexes with the molecular formula Ln(Tp(Me2))(2)X [Tp(Me2) = (HB(dmpz)(3)), where X is a basic anionic ligand] in various solvents, yielded crystals of highly insoluble dimers of the general formula [Ln(Tp(Me2))(mu-BOp(Me2))](2) (1) [Ln = La, Ce, Sm; BOp(Me2) = (HBO(dmpz)(2))(2)(-); dmpzH = 3,5-dimethylpyrazole]. The results of several single-crystal X-ray determinations are reported. One metal nitrogen distance, that lying across from the two negatively charged bridging oxygen atoms, is 0.06 A longer than the others, suggesting an unusual trans influence at a lanthanide center. The formation of 1 is proposed to involve the intermediacy of Ln(Tp(Me2))(2)OH formed by protonolysis with adventitious water.     

Synthesis and Molecular Structures of Hydrotris(dimethylpyrazolyl)borate Complexes of the Lanthanides

The reaction of lanthanide triflates with 2 equiv of potassium hydrotris(dimethylpyrazolyl)borate (Tp(Me)()2) gives good yields of complexes of composition Ln(Tp(Me)()2)(2)OTf. For La (2), Ce (3), Pr (4), and Nd (5) the complexes are seven-coordinate in the solid state with the triflate group coordinated to the metal in unidentate fashion. Complex 5 crystallizes in the monoclinic space group P2(1)/c with a = 17.629(3) ?, b = 12.740(2) ?, c = 18.163(3) ?, beta = 107.35(1) degrees, V = 3893(1) ?(3), Z = 4, and R(w) = 0.0458. For the complexes of Y (1), Sm (6), Eu (7), Gd (8), Dy (9), Ho (10), and Yb (11), the smaller size of the metal ion leads to ejection of the triflate from the coordination sphere and the complexes are ionic in the solid state with a six-coordinate metal center. Complex 11 crystallizes in the monoclinic space group C2/m with a = 16.593(7) ?, b = 13.671(5) ?, c = 8.746(2) ?, beta = 91.66(3) degrees, V = 1983(1) ?(3), Z = 2, and R(w) = 0.0416. In solution, however, complex 6 adopts a seven-coordinate molecular structure with the triflate ion within the first coordination sphere.