Multiparameter Polynomial Adaptive Stabilizers

In 1983 Morse proved, for unknown scalar one-dimensional linearsystems, the nonexistence of rational or polynomial universalstabilizers (UAS). In 1983, Nussbaum gave an example of an analyticUAS. In our paper, it is shown that there exist time-invariantpolynomial UAS's with multidimensional gain adaptation. Thedesign procedure is developed for linear, minimum-phase systemsof relative degree one. Convergence of the closed-loop systemis proved. Some numerical simulations are provided.     

A system for defining reference materials applicable to all food matrices

Recently the subcommittee on Food Definition of the AOAC INTERNATIONAL Task Force on Methods for Nutrition Labeling proposed a Food Matrix Organizational System [4] to systematically judge the applicability of collaboratively studied methods over a range of food matrices. This system describes a food matrix by its location in one of nine sectors in a triangle, with each point of the triangle defined as representing 100% and the opposite side representing 0% of the normalized contents of each of three major components of FAT, PROTEIN and CARBOHYDRATE. Foods falling within the same sector would be chemically similar and thus should behave in a similar analytical manner. This same scheme can be used to select one or two food matrices representing each sector, for development of a series of reference materials representing all foods. The list of 5250 foods contained in the USDA Nutrient Data Base for Standard Reference has been sorted and matched to this schematic to determine the scope of the selection process. In addition the list of foods in the USDA Data Base for Food Consumption Surveys has been examined. Results and progress of this selection process are reported.     

A two-chromophore model for two-photon circular dichroism

A discussion of two-photon circular dichroism due to dissymmetrically placed chromophores is presented. Using quantum electrodynamics, expressions are derived for the differential rates or absorption associated with an electronic transition which is electric dipole forbidden to a one-photon interaction. A complex field formulation enables effective interaction operators to be derived which are formally equivalent to those arising in the theory of induced circular dichroism. For non-equivalent chromophores, it is shown that a coupling mechanism provides the necessary chiral discrimination, whilst for equivalent chromophores there is an additional contribution from an interference term which becomes more important as the chromophore separation is decreased.     

Development of a screening method for cocaine and cocaine metabolites in urine using solvent microextraction in conjunction with gas chromatography

A simple, quick and inexpensive screening method for cocaine and cocaine metabolites has been developed. Drug extraction was achieved using the relatively new technique of solvent microextraction (SME). Complete analysis is achieved in 13 min, using, a 6-min extraction with a 2-microl drop followed by separation on a gas chromatograph. The developed procedure was tested as a screening method for cocaine and cocaine metabolites in spiked urine samples. Using SME, concentrations as low as 0.125 microg ml(-1) of cocaine, ecgonine methyl ester, cocaethylene and anhydroecgonine methyl ester were measurable with relative standard deviation values averaging 9.0%.     

ANION AND SOLVENT EFFECTS ON THE RATE OF REDUCTION OF TRIPLET EXCITED THIAZINE DYES BY FERROUS IONS

Abstract— The lifetimes of the triplet excited states of thionine and methylene blue were measured in aqueous and 50 v/v% aqueous acetonitrile solutions acidified with 0.01 N sulfuric or trifluoromethyl-sulfonic acid. The rate constants for reaction of the triplet excited dyes with ferrous ions were measured in the same solutions. The triplet lifetimes in the absence of added quenchers were insensitive to a change in acid from trifluoromethylsulfonic to sulfuric or to a change in solvent from water to 50v/v% aqueous acetonitrile (τ for triplet thionine ˜7.5 μs, τ for triplet methylene blue ˜4.5 μs). In contrast, the rate constant for reaction of the triplet dyes with ferrous ions increased by nearly a factor of 10 with a change in acid from trifluoromethylsulfonic to sulfuric. In solutions containing sulfate ions this reaction rate constant increased with increasing sulfate concentration and with a change in solvent from water to 50 v/v% aqueous acetonitrile. The results are discussed in terms of the possibility of association of the positively charged reactive ions with sulfate anions. Quenching of the triplet excited dyes by ferric ions or by ground state dye molecules was shown to be negligible at the concentration used for the ferrous ion quenching study.     

Absorption spectra and photochemistry of the toluene cation and benzyl radical in solid argon

Toluene diluted in argon subjected to continuous argon discharge radiation during condensation at 21 K revealed absorptions at 310.5 and 449.6 nm due to benzyl radical, and 317 nm due to a C₇7H₉ radical. A photosensitive 430 nm band, in agreement with photodissociation spectra of the toluene parent cation, is assigned to this species.     

Synthesis of δ-Lactones from Glutaraldehyde

A novel and general synthesis of δ-lactones from glutaraldehyde is described. The dialdehyde is first reacted with an alkyl or substituted alkyl Grignard reagent to afford a δ-hydroxyaldehyde in good yield. These aldehydes exist preferentially in the cyclic hemiacetal form (δ-lactols). Oxidation of the latter compounds to give δ-lactones is readily achieved with silver oxide or bromine. The δ-lactols and δ-lactones serve as intermediates for the total synthesis of steroids.     

Synthesis of alpha-kainic acid from a 7-azabicyclo[2.2.1]heptadiene by tandem radical addition-homoallylic radical rearrangement

Reductive radical addition of 2-iodoethanol to N-Boc 2-tosyl-7-azabicyclo[2.2.1]heptadiene gives N-Boc syn-7-(2-hydroxyethyl)-4-tosyl-2-azabicyclo[2.2.1]hept-5-ene, which is converted into the neuroexcitants 3-(carboxymethyl)pyrrolidine-2,4-dicarboxylic acid and alpha-kainic acid. [structure: see text]     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.