Spontaneous Generation of Modular Invariants

It is possible to compute and its modular equations with no perception of its related classical group structure except at . We start by taking, for prime, an unknown ``-Newtonian' polynomial equation with arbitrary coefficients (based only on Newton's polygon requirements at for and ). We then ask which choice of coefficients of leads to some consistent Laurent series solution , (where . It is conjectured that if the same Laurent series works for -Newtonian polynomials of two or more primes , then there is only a bounded number of choices for the Laurent series (to within an additive constant). These choices are essentially from the set of ``replicable functions,' which include more classical modular invariants, particularly . A demonstration for orders and is done by computation. More remarkably, if the same series works for the -Newtonian polygons of 15 special ``Fricke-Monster' values of , then is (essentially) determined uniquely. Computationally, this process stands alone, and, in a sense, modular invariants arise ``spontaneously.'

     

Gas chromatographic quantitation of methoxyphenamine and three of its metabolites in plasma

Sensitive gas chromatographic procedures for the determination of methoxyphenamine and three of its metabolites in plasma have been developed. The metabolites were measured using an electron-capture detector. This simple procedure is based on the precipitation of protein from a 1-ml plasma sample with 10% trichloroacetic acid, followed by aqueous derivatization with pentafluorobenzoyl chloride at pH 9.2 and a single-step cyclohexane extraction. The lower limit of detection for the N-desmethyl, O-desmethyl and aromatic 5-hydroxy metabolites of methoxyphenamine were 1.6, 3.1 and 2.2 ng ml-1, respectively, with coefficients of variation less than 10%. The poor electron-capture response of fluorinated derivatives of methoxyphenamine necessitated the use of nitrogen-phosphorus detection. Extractive derivatization with pentafluorobenzoyl chloride, without the need for protein precipitation, enabled quantitation of methoxyphenamine down to 3.8 ng ml-1 from a 2-ml aliquot of plasma. In a pilot study involving healthy volunteers who received a single oral dose of methoxyphenamine hydrochloride plasma concentration could be followed in all three subjects for at least 24, 32, 12 and 4 h for methoxyphenamine and the O-desmethyl, 5-hydroxy and N-desmethyl metabolites, respectively.     

Film-Pore Diffusion Control for the Batch Sorption of Cadmium Ions from Effluent onto Bone Char

The sorption equilibrium and kinetics of cadmium ions from aqueous solution onto bone char have been studied. Equilibrium isotherms for the sorption system were correlated by Langmuir and bi-Langmuir equations. The application of the bi-Langmuir equation was developed because the mechanistic analysis in this research indicated that cadmium removal occurs ion exchange and physical adsorption onto different surface sites. The bi-Langmuir equation provides a better fit to the experimental data. In addition, the removal rates of cadmium ions based on the Langmuir models have been investigated. The effective diffusivity was calculated using the effects of initial metal ion concentration and bone char mass. Two mass-transport models based on film-pore diffusion control have been applied to analyze the concentration decay curves. The film and pore diffusion coefficients using an analytical equation are equal to 1.26x10(-3) cm/s and 5.06x10(-7) cm(2)/s, respectively. The pore diffusion coefficient obtained from the numerical method is 4.89x10(-7) cm(2)/s. A sensitivity analysis showed that the film-pore diffusion model and constant effective diffusivity could be used to describe the mass-transport mechanism of the sorption system with a high degree of correlation. Copyright 2001 Academic Press.     

Standard enthalpy of solution of ammonium nitrate in water at 298 K

We have made calorimetric measurements of the enthalpy of solution of NH₄NO₃(c, IV) in water at 298 K, where (c, IV) indicates the crystal form of amomonium nitrate that is stable from 256 to 305 K. Results of our measurements have been combined with enthalpy of dilution values from Parker to obtain the standard enthalpy of solution of NH₄NO₃ (c, IV) in water at 298.15 K to be ΔH^o = 25.41 kJ mol^?1.