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 Solubility of the Chloromethanes in Water

Summary.  There are more than 150 papers that report on the solubility of the four chloromethanes in water. Volume 62 of the Solubility Data Series compiles and evaluates the papers concerned with the liquid–liquid solubility of the chloromethanes with water. A similar evaluation has not been carried out for the vapor–liquid solubility at a partial pressure up to the saturation vapor pressure of the four chloromethanes. This paper uses the liquid–liquid evaluated solubility values to calculate vapor–liquid Henry’s constants. They are compared with a compilation of Henry’s constants with good agreements between the calculated constants and the median of the compiled constants. It is believed that the calculated constants are a reliable set of values to use for the vapor–liquid solubility of the chloromethanes in water. E-mail: hlclever@worldnet.att.net Received October 11, 2002; accepted October 22, 2002 Published online April 24, 2003 RID="a" ID="a" Dedicated to Prof. Dr. Heinz Gamsj?ger on the occasion of his 70^th birthday     

Thermal and viscosity characterization of two asphalt emulsions

Journal of Thermal Analysis and Calorimetry - Asphalt emulsion is a versatile product that can be used for different waterproofing applications in civil construction and highway constructions....     

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.     

Studying Dynamical Principles of Human Locomotion using Inverse Optimal Control

Human movement, as for example human gait, can be considered as an optimal realization of some given task. However, the criterion for which the naturally performed human motion is optimal, is generally not known. In this article we formulate an inverse optimal control problem to study the relevance of four different optimization criteria in human locomotion. As a walking model we use an actuated three dimensional spring loaded inverted pendulum (3D-SLIP), which is able to mirror the typical shape of the center of mass trajectory in human gait. Using a direct all-at-once approach, the weighting of the optimization criteria and the position of the footsteps are optimized in such a way, that the center of mass trajectory of the resulting optimal state fits real motion capture data as good as possible. Numerical experiments show, that whereas the so called capture point seems to have a great impact on human walking, minimization of the vertical center of mass movement does not show any relevance at all. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stepwise Halide‐Triggered Double and Triple Catenation of Self‐Assembled Coordination Cages

A simple self‐assembled [Pd₂ L ₄] coordination cage consisting of four carbazole‐based ligands was found to dimerize into the interpenetrated double cage [3 X@Pd₄ L ₈] upon the addition of 1.5 equivalents of halide anions (X=Cl^?, Br^?). The halide anions serve as templates, as they are sandwiched by four Pd^II cations and occupy the three pockets of the entangled cage structure. The subsequent addition of larger amounts of the same halide triggers another structural conversion, now yielding a triply catenated link structure in which each Pd^II node is trans‐coordinated by two pyridine donors and two halide ligands. This simple system demonstrates how molecular complexity can increase upon a gradual change of the relative concentrations of reaction partners that are able to serve different structural roles.