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.     

Allocation of jobs and identical resources with two pooling centers

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.      

S)-(+)-2-(p-tolylsulfinyl)-2-buten-4-olide: an enantiomerically pure Michael acceptor for asymmetric synthesis of 3-substituted 4-butanolides. (—)-podorhizon.

A short, reliable, and practical synthesis of ($\text{S}$)-(+)-2-($\text{p}$-tolylsulfinyl)-2-buten-4-olide has been developed, and the utility of this Michael acceptor for highly enantiocontrolled synthesis of 3-substituted 4-butanolides has been demonstrated.     

The pzc of mercury in the presence of humic acids and their complexes with aluminium

Variation of the lifetime of a mercury drop with potential was used to determine the pzc of mercury in the presence of soil humic acids and their aluminium complexes. In all cases there was an overall net shift in the pzc in the cathodic direction. Variation in the extent of the shift with pH and concentration indicated greater adsorption of negatively charged species. The shift was smaller in the presence of aluminium humates, probably due to a decrease in the negative charge of the humic acid molecules after complexing. The use of electroanalytical techniques for metal speciation studies in soils and natural water, if humic materials are known to be present, might therefore be limited.     

The Structure of Silylated Amides: N-Methyl-N-Trimethylsilyltrifluoroacetamide,a Reassignment of structure

The ²⁹Si and ¹⁴N nmr spectra of some bissilylamides and monosilylamides are reported. The results are compared with those for model silylesters, amines and imines. The compound of formula CF₃CONCH₃Si(CH₃)₃ (MSTFA) is shown to exist as a tautemeric mixture of a silylamide and a silylimidate. This assignment is confirmed by ¹³C nmr. A rationale is proposed for the structure directing effect of substituents on the amide carbon atom.     

Hydro­gen‐bonded supramolecular lattice of the 1:3:4 complex between [5,10,15,20‐meso‐tetrakis(4‐hydroxy­phenyl)­porphyrinato‐κ4N]­zinc(II), dibenzo‐24‐crown‐8 and methanol

The title compound, [5,10,15,20‐meso‐tetrakis(4‐hydroxy­phenyl)­porphyrinato‐κ⁴N]­zinc(II) tris(dibenzo‐24‐crown‐8) methanol tetrasolvate, [Zn(C₄₄H₂₈N₄O₄)]·3C₂₄H₃₂O₈·4CH₄O, was synthesized and its molecular structure precisely charac­terized by low‐temperature single‐crystal analysis. All the components are involved in hydrogen bonding with each other, thus forming an extensively hydrogen‐bonded supramolecular lattice. The functionalized porphyrin moiety coordinates both equatorially and axially to the neighboring species.     

A titration study on alumina-coated rutile pigments

A series of potentiometric titrations was carried out on alumina coated rutile pigments. The point of intersection of the adsorption isotherms obtained at three ionic strengths was independent of the titration speed, hence these experiments are considered to give a reliable estimate of the i. e. p. of the sample. The adsorption isotherms are, however, irreversible and the uptake of protons and hydroxyl ions is dependent upon titration speed. The irreversibility of the isotherms appears to be related to the slow drift in the pH of the pigment suspension that takes place during the titration. This pH drift is due to 1) a partial dissolution of the alumina coating and 2) a slow movement of protons into and out of the coating on the pigment.     

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.