Constrained minimax approximation and optimal preconditioned for Toeplitz matrices

A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented.     

Ion-selective electrodes in organic analysis-determination of xanthate

A PVC membrane xanthate-selective electrode has been developed for the direct determination of xanthates of primary and secondary alcohols. The xanthate electrode is highly selective and exhibits a Nernstian response in the range 5.0 x 10(-2)-7.1 x 10(-5)M xanthate with a slope of 58.6 mV per concentration decade. The electrode has a wide working pH range (5.0-11.5), a fast response time (less than 30 sec) and is stable for at least two months.     

SSZ-53 and SSZ-59: two novel extra-large pore zeolites

The syntheses, structure solutions, and physicochemical and catalytic characterizations of the novel zeolites SSZ-53 and SSZ-59 are described. SSZ-53 and SSZ-59 were synthesized under hydrothermal conditions with the [1-(4-fluorophenyl)cyclopentylmethyl]trimethyl ammonium cation and 1-[1-(4-chlorophenyl)cyclopentylmethyl]-1-methyl azocanium cation, respectively, as structure-directing agents. The framework topology of SSZ-53 was solved with the FOCUS method, and the structure of SSZ-59 was determined by model building. Rietveld refinement of synchrotron X-ray powder diffraction data confirms each proposed model. SSZ-53 and SSZ-59 each possess a one-dimensional channel system delimited by 14-membered rings. Results from transmission electron microscopy, electron diffraction, catalytic experiments (spaciousness index and constraint index tests), and argon and hydrocarbon adsorption experiments are consistent with the proposed structures.     

Thermodynamics of electrolyte solutions. The system HCl + CaCl2 + H2O at 298.15°K

Activity coefficients of hydrochloric acid have been determined from electromotive-force measurements of cells containing mixtures of hydrochloric acid and calcium chloride at constant total ionic strengthsI=0.1, 0.5, 1.0, 2.0, and 3.0 mole-kg^–1 at 298.15°K. Interpretations based on Scatchard's and Pitzer's equations indicate that Pitzer's equations probably provide a more convenient guide to the thermodynamic properties of the mixed-electrolyte solutions. Activity coefficients for calcium chloride were derived from these equations.     

Comparison of gas chromatographic and high-performance liquid chromatographic assays for the determination of debrisoquine and its 4-hydroxy metabolite in human fluids

A comparison of an established gas chromatographic assay for 4-hydroxydebrisoquine and debrisoquine and a modified high-performance liquid chromatographic assay was made. Both assays used guanoxan as the internal standard and required derivatization of all three compounds with acetylacetone at 96 degrees C for 2.5 h and subsequent ethereal extraction and cleaning steps before chromatographic analysis. For detailed pharmacokinetic studies the gas chromatographic assay was more sensitive in the measurement of low concentrations in plasma, but the liquid chromatographic assay was adequate for phenotyping the 4-hydroxylation of debrisoquine in a population. In the latter assay a mobile phase consisting of 70% methanol in water at pH 3.5 (adjusted with orthophosphoric acid containing 10 mM 1-pentanesulphonic acid was employed (flow-rate 1.5 ml/min) with a pre-column (C8) linked to a reversed-phase muBondapak C18 cartridge in a Z-module. The eluate was detected at 248 nm. With this assay it was observed that the buccal absorption of debrisoquine and 4-hydroxy-debrisoquine was affected by the pH of the buccal medium. This indicates that urinary pH may influence the excretion of both substances at high pH. The debrisoquine-to-4-hydroxydebrisoquine ratio may be dose-dependent.