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.     

Reactions of N-silylphosphoranimines with alcohols: synthesis and structure of cyclotriphosphazenes with nongeminal methyl and phenyl substituents

The reactions of Me(3)SiN=P(OR")RR'(R" = Ph, CH(2)CF(3); R, R' = Me, Ph) with alcohols were investigated. With nonequivalent amounts of CF(3)CH(2)OH, the reactions produced high yields of the cyclic phosphazene (Me(2)PN)(3) and both the cis and trans isomers of nongeminally substituted [(Ph)(Me)PN](3). The isomers of this new cyclic phosphazene were separated by column chromatography and characterized by NMR and IR spectroscopy, elemental analysis, and X-ray crystallography. Crystals of the cis isomer 6a have a monoclinic crystal system, while the trans isomer 6b has a triclinic crystal system with two different molecules in an asymmetric unit. The bond lengths and bond angles are very similar to those of the simpler cyclic trimers (Me(2)PN)(3) and (Ph(2)PN)(3.) A likely pathway for the formation of these compounds is discussed.     

Palm Raceme as a Promising Biomass Precursor for Activated Carbon to Promote Lipase Activity with the Aid of Eutectic Solvents

This study concerns the role of activated carbon (AC) from palm raceme as a support material for the enhancement of lipase-catalyzed reactions in an aqueous solution, with deep eutectic solvent (DES) as a co-solvent. The effects of carbonization temperature, impregnation ratio, and carbonization time on lipase activity were studied. The activities of Amano lipase from Burkholderia cepacia (AML) and lipase from the porcine pancreas (PPL) were used to investigate the optimum conditions for AC preparation. The results showed that AC has more interaction with PPL and effectively provides greater enzymatic activity compared with AML. The optimum treatment conditions of AC samples that yield the highest enzymatic activity were 0.5 (NaOH (g)/palm raceme (g)), 150 min, and a carbonization temperature of 400 °C. DES was prepared from alanine/sodium hydroxide and used with AC for the further enhancement of enzymatic activity. Kinetic studies demonstrated that the activity of PPL was enhanced with the immobilization of AC in a DES medium.     

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.     

Condition Monitoring of Ground Anchorages by Dynamic Impulses: GRANIT System

The GRANIT system operates by applying an impulse of known force by means of an impact device that is attached to the tendon of the anchorage. The vibration response signals resulting from this impulse are complex in nature and require analysis to be undertaken in order to extract information from the vibrational response signatures that is relevant to the condition of the anchorage. In the system, the complicated relationship that exists between characteristics of an anchorage and its response to an impulse is identified and learned by a novel artificial intelligence network based on artificial intelligence techniques.The results presented in this paper demonstrate the potential of the GRANIT system to diagnose the integrity of ground anchorages at a site near Stone, England, by using a trained neural network capable of diagnosing the post-tension level of the anchorage. This neural network was used for the diagnosis of load in a second ground anchorage adjacent to the original anchorage used for the training of the neural network. Further tests were taken with a different anchor head configuration of the anchorage and a different relationship between the signature response of the anchorage to an applied impulse and its post-tension level was found.Problems encountered during the diagnosis of this second set of test signatures by the trained neural network are investigated with the use of a lumped parameter dynamic model. This model is able to identify the parameters in the anchorage system that affect this change in response signature. The results from the investigation lead to a new form of classification for the installed anchorages, based on their anchor head configuration.Laboratory strand anchorage tests were undertaken in order to compare with and validate the results obtained from the field tests and the lumped parameter dynamic model.     

High precision measurement of the superallowed 0+ --> 0+ beta decay of 22Mg

The half-life, 3.8755(12) s, and superallowed branching ratio, 0.5315(12), for 22Mg beta decay have been measured with high precision. The latter depended on gamma-ray intensities being measured with an HPGe detector calibrated for relative efficiencies to an unprecedented 0.15%. Previous precise measurements of 0+ --> 0+ transitions have been restricted to the nine that populate stable daughter nuclei. No more such cases exist, and any improvement in a critical Cabibbo-Kobayashi-Maskawa unitarity test must depend on precise measurements of more exotic nuclei. With this branching-ratio measurement, we show those to be possible for T(z)=-1 parents. We obtain a corrected Ft value of 3071(9) s, in good agreement with expectations.     

Outer space formation of a laser host glass

Classical crystallization calculations were performed to determine the possibility of forming a particular type of laser glass with the avoidance of devitrification in an outer space laboratory. Although the laser glass in question readily crystallizes in an earth environment, it is demonstrated that under the homogeneous nucleating conditions obtainable in a zero gravity laboratory this laser glass may be easily quenched to a virtually crystal-free product. Use of this material as a host in a neodymium glass laser would result in a more than 10% increase in efficiency when compared to laser glass rods of similar composition currently commercially available.