An Improved Upper Bound for Leo Moser's Worm Problem

   Abstract. A worm ω is a continuous rectifiable arc of unit length in the Cartesian plane. Let W denote the class of all worms. A planar region C is called a cover for W if it contains a copy of every worm in W . That is, C will cover or contain any member ω of W after an appropriate translation and/ or rotation of ω is completed (no reflections). The open problem of determining a cover C of smallest area is attributed to Leo Moser [7], [8]. This paper reduces the smallest known upper bound for this area from 0.275237 [10] to 0.260437.     

Photochemical electron transfer reactions of tirapazamine

The absorption and fluorescence spectra of 3-aminobenzo-1,2,4-triazine di-N-oxide (tirapazamine) have been recorded and exhibit a dependence on solvent that correlates with the Dimroth ET30 parameter. Time-dependent density functional theory calculations reveal that the transition of tirapazamine in the visible region is pi-->pi* in nature. The fluorescence lifetime is 98+/-2 ps in water. The fluorescence quantum yield is approximately 0.002 in water. The fluorescence of tirapazamine is efficiently quenched by electron donors via an electron-transfer process. Linear Stern-Volmer fluorescence quenching plots are observed with sodium azide, potassium thiocyanate, guanosine monophosphate and tryptophan (Trp) methyl ester hydrochloride. Guanosine monophosphate, tyrosine (Tyr) methyl ester hydrochloride and Trp methyl ester hydrochloride appear to quench the fluorescence at a rate greater than diffusion control implying that these substrates complex with tirapazamine in its ground state. This complexation was detected by absorption spectroscopy.     

A review of spin Hamiltonian forms for various point-group site symmetries

A review has been made of the spin Hamiltonian forms for all the 32 point groups, including linear magnetic field-dependent terms in spin operators $\hat O_1^m $ , $\hat O_3^m $ , $\hat O_5^m $ , $\hat O_1^m $ , $\hat O_3^m $ , and $\hat O_5^m $ . All spin operators, as well as their matrix elements, to be used in constructing spin Hamiltonian matrices, have been listed. The various point group aggregates for distinct spin-Hamiltonian forms have been classified. In addition, descent of symmetry point groups, useful for studying structural phase transitions, have been indicated.     

Determination of vanillin and related flavor compounds in natural vanilla extracts and vanilla-flavored foods by thin layer chromatography and automated multiple development

Summary Thin layer chromatography on silica gel high performance layers and automated multiple development was used to separate the polar aromatic flavor compounds vanillin, ethyl vanillin, 4-hydroxybenzaldehyde, 4-hydroxybenzoic acid, 4-hydroxybenzyl alcohol, vanillic acid, coumarin, piperonal, anisic acid, and anisaldehyde commonly found in extracts of natural and artificial vanilla flavors. The ratio of 4-hydroxybenzoic acid, 4-hydroxybenzaldehyde and vanillic acid to vanillin in natural vanilla extracts was used to confirm the authenticity of extracts purchased in the United States of America and the United Kingdom. Natural vanilla extracts purchased in Mexico and Puerto Rico were identified as counterfeit products based on changes in the above ratio and the presence of synthetic flavor compounds such as ethyl vanillin and coumarin. It is also demonstrated that the proposed method is suitable for the determination of natural and synthetic vanilla flavors in solvent extracts from food, beverage and confectionery products. The main advantage of thin layer chromatography for the analysis of vanilla extracts and food stuffs flavored with vanilla is its high sample throughput since sample preparation requirements are minimal and multiple samples can be separated simultaneously.     

Factors affecting the rates of addition of free radicals to alkenes-determination of absolute rate coefficients using the persistent aminoxyl method

The rate of coupling of alkyl radicals with the persistent aminoxyl radical 1,1,3,3-tetramethylisoindolin-N-oxyl (1) has been used as a kinetic probe to determine absolute rate coefficients for the addition of alkyl radicals to methyl acrylate. The results are discussed in terms of the role of the structure and functionalization of the attacking radical on the rates of addition, particularly as they affect steric, polar, and enthalpic factors. The aminoxyl method is assessed against other methods for determining free radical addition rate coefficients.     

Matrix-induced peak enhancement of pesticides in gas chromatogrtaphy: Is there a solution?

In this study, it is shown that calibration solution prepared in control matrix extrix extract can be used to compensate for matrix-induced chromatographic response enhancement observed for certain pesticedes. This phenomenon is characterized by enhanced chromatographic response for certain pesticides in the presence of matrix du to reduced analyte loss during injection. Unacceptably high recoveries are seen for affected pesticides when maatrix-free solutions are used for reference and calibration. The effects of matrix concentration on overall enhancement and linear response were determined. When used as reference standards for the determination of recovery, matrix-standard solutions were found to provide acceptable recoveries for pesticides subject to matrix-induced chromatographic response enhancement along with other pesticides. General guidelines are presented for using matrix-standard calibration solutions in pesticide residue analysis.     

Influence of solvent effects on retention in reversed-phase liquid chromatography and solid-phase extraction using a cyanopropylsiloxane-bonded,silica-based sorbent

Summary The solvation parameter model is used to characterize the retention properties of a cyanopropylsiloxane-bonded, silica-based sorbent with methanol, acetonitrile, tetrahydrofuran, and isopropanol in water as mobile phases. The system constants over the composition range 1 to 50% (v/v) organic solvent indicate that retention occurs because of the relative ease of cavity formation in the solvated stationary phase compared to the same process in the predominantly aqueous mobile phase as well as from more favorable stationary phase interactions with solutes containing - and n-electrons. The capacity of the solute for dipole-type interactions is not important whereas all hydrogen-bond-type interactions result in reduced retention. Graphing the system constants as a function of mobile phase composition provides a simple mechanism for interpreting the change in capacity of the chromatographic system for retention in terms of changes in the relative weighting of fundamental intermolecular interactions. A comparison is also made with the retention properties of an octadecylsiloxane-bonded, silica-based sorbent with 30% (v/v) methanol in water as the mobile phase and the extraction characteristics of a porous polymer sorbent with 1% (v/v) methanol, acetonitrile, tetrahydrofuran, and isopropanol in water as the sample processing solvent. Changes in sorbent selectivity due to selective uptake of the processing solvent are much smaller for the cyanopropylsiloxane-bonded sorbent than the results found for a porous polymer sorbent.     

Evaluation of the Linear-Elution-Strength Model for the Prediction of Retention and Selectivity in Isothermal Gas Chromatography

Linear-elution strength theory and temperature-programmed gas chromatography is evaluated as a rapid method for predicting isothermal retention factors and column selectivity. Retention times for a wide range of compounds are determined at the program rates of 3 and 12 °C/min for the temperature range 60 to 160 °C on three open-tubular columns (DB-1701, DB-210 and EC-Wax) and used to predict isothermal retention factors for each column over the temperature range 60 to 140 °C. The temperature-program predicted isothermal retention factors are compared with experimental values using linear regression and the solvation parameter model. It is shown that isothermal retention factors predicted by the linear-elution-strength model only approximately represents the experimental data. The model fails to predict the slight curvature that exists in most plots of the experimental retention factor (log k) as a function of temperature. In addition, regression of the temperature-program predicted isothermal retention factors against the experimental values indicates that the slopes and intercepts deviate significantly from their target values of one and zero, respectively, in a manner which is temperature dependent. The temperature-program predicted isothermal retention factors result in system constants for the solvation parameter model that are different to those obtained from the experimental retention factors. These results are interpreted as indicating that linear-elution-strength theory predicts retention factors that fail to accurately model stationary phase interactions over a wide temperature range. It is concluded that temperature-program methods using linear-elution-strength theory are unsuitable for constructing system maps for isothermal separations.     

Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.