On isomorphic factorizations of circulant graphs

We investigate the conjecture that every circulant graph X admits a k‐isofactorization for every k dividing |E(X)|. We obtain partial results with an emphasis on small values of k. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406–414, 2006     

Corn stover fractions and bioenergy

Information is presented on structure, composition, and response to enzymes of corn stover related to barriers for bioconversion to ethanol. Aromatic compounds occurred in most tissue cell walls. Ferulic acid esterase treatment before cellulase treatment significantly improved dry weight loss and release of phenolic acids and sugars in most fractions over cellulase alone. Leaf fractions were considerably higher in dry weight loss and released sugars with esterase treatment, but stem pith cells gave up the most phenolic acids. Results help identify plant fractions more appropriate for coproducts and bioconversion and those more suitable as residues for soil erosion control.     

Importance of the Debye interaction in organic solutions: Henry's law constants for polar liquids in nonpolar solvents and vice versa

Henry's law constants have been determined for -butyrolactone (BL), ethyl acetate (EA), and 2-methyl-3-pentanol (MEP) in mixtures of iso-octane (ISO) and toluene (TOL), for BL, EA, TOL, and ISO in cinnamaldehyde (CIN) and for TOL and ISO in each other and in BL. From these data and published vapor pressures, the activity coefficients at infinite dilution and the standard molar Gibbs free energy of transfer, G ₂ ⁰ of the solutes from dilute solution in ISO to dilute solution in each solvent medium have been calculated. The different behavior patterns of BL and EA are attributed to differences in their abilities to exist in different conformations possessing different dipole moments. For polar solutes, G ₂ ⁰ decreases with increasing polarizability of the solvent and with increasing dipole moment of the solute, suggesting increased contributions from dipole-induced dipole (Debye) interactions. The sigmoidal plot of G ₂ ⁰ against the change in pair potential energy calculated from the classical expressions suggests that G ₂ ⁰ seriously underestimates the strength of the Debye interactions in comparison with the London interactions.     

Gradient expansion of the atomic kinetic energy functional

It is demonstrated that the ground-state atomic kinetic energy functional T[?], where ? is the electron density, can be computed to surprising accuracy from the truncated gradient expansion: T[?] = + T₂[?] + T₄[?], with T_o[?] = $\text{3}\text{10}$(3π²)$\text{2}\text{3}$ ∫ ?$\text{5}\text{3}$ d_τ, T₂ [?] = $\text{1}\text{72}$ ∫ (??)²?^?1 d_τ, and T₄ [?] given by the formula of Hodges. Calculations of T₀, T₂ and T₄ are reported for He with ? both the Hartree—Fock and a very accurate density, and for Ne, Ar and Kr with ? the Hartree—Fock density. For Kr, T₀ + T₂ + T₄ is within 0.3% of the exact Hartree—Fock T, with T₂/T₀ = 0.05, T₄/T₂ = 0.17.     

Total synthesis of (-)-reveromycin a

The asymmetric total synthesis of (-)-reveromycin A is described. The key steps involved a Lewis acid catalyzed inverse electron demand hetero-Diels-Alder reaction followed by hydroboration/oxidation to afford the spiroketal core 4 in a highly stereoselective manner and introduction of the C18 hemisuccinate by high-pressure acylation.     

A Branched Pore Model Analysis for the Adsorption of Acid Dyes on Activated Carbon

A new branched-pore adsorption model has been developed using an external mass transfer coefficient, K _f, an effective diffusivity, D _eff, a lumped micropore diffusion rate parameter, K _b, and the fraction of macropores, f, to describe sorption kinetic data from initial adsorbent-adsorbate contact to the long-term adsorption phase. This model has been applied to an environmental pollution problem—the removal of two dyes, Acid Blue 80 (AB80) and Acid Red 114 (AR114), by sorption on activated carbon. A computer program has been used to generate theoretical concentration-time curves and the four mass transfer kinetic parameters adjusted so that the model achieves a close fit to the experimental data. The best fit values of the parameters have been determined for different initial dye concentrations and carbon masses. Since the model is specifically applicable to fixed constant values of these four parameters, a further and key application of this project is to see if single constant values of these parameters can be used to describe all the experimental concentration-time decay curves for one dye-carbon system.The error analysis and best fit approach to modeling the decay curves for both dye systems show that the correlation between experimental and theoretical data is good for the fixed values of the four fitted parameters. A significantly better fit of the model predictions is obtained when K _f, K _b and f are maintained constant but D _eff is varied. This indicates that the surface diffusivity may vary as a function of surface coverage.     

An annulene-fused cyclopentadienide. A photochromic cyclopentadienodimethyldihydropyrene where the fused cyclopentadienide group resembles benzene in its effect on the dihydropyrene-metacyclophanediene valence isomerization

The synthesis of the green cyclopentadiene-fused dimethyldihydropyrene 12 was achieved in 36% yield in 7 steps from the parent dihydropyrene 3. Reaction of 12 with KH or LiCH(2)SiMe(3) gave the [14]annulene-fused cyclopentadienide anion quantitatively. In the (1)H NMR spectra, the internal methyl protons of 12 at delta -3.9, change dramatically on formation of anion 5, becoming deshielded to delta -1.82. This is caused by the reduction in diatropicity of the [14]annulene ring on fusion to the 6pi-cyclopentadienide ring. The anion is also a photochromic switch. Irradiation of the closed form 5 with visible light opens it to the open form 5', which reverts to the closed form 5 either with UV light or thermally. The switching behavior is between that of the parent 3/3' and the benzannelated system 4/4' and suggests that in its effect on the photoswitching, cyclopentadienide is behaving chemically similar to benzene.     

Characterisation of selected hypnotic drugs and their metabolites using electrospray ionisation with ion trap mass spectrometry and with quadrupole time-of-flight mass spectrometry and their determination by liquid chromatography-electrospray ionisation-ion trap mass spectrometry

The electrospray ionisation-ion trap mass spectrometry (ESI-MSⁿ) of selected hypnotic drugs, i.e. zopiclone, zolpidem, flunitrazepam and their metabolites have been investigated. Sequential product ion fragmentation experiments (MSⁿ) have been performed in order to elucidate the degradation pathways for the [M+H]⁺ ions and their predominant fragment ions. These MSⁿ experiments show certain characteristic fragmentations in that functional groups are generally cleaved from the ring systems as neutral molecules such as H₂O, CO, CO₂, NO₂, amines and HF. When an aromatic entity is present in a drug molecule together with a nitrogen-containing saturated ring structure as with zopiclone and its N-desmethyl metabolite fragmentation initially occurs at the latter ring with the former being resistant to fragmentation. The structures of fragment ions proposed for ESI-MSⁿ can be supported by electrospray ionisation-quadrupole time-of-flight mass spectrometry (ESI-QTOF-MS).These molecules can be identified and determined in mixtures at low ng/ml concentrations by the application of liquid chromatography (LC)-ESI-MSⁿ which can be used for their analysis in saliva samples.This paper includes a tabulation of mass losses/signals at low m/z values for these hypnotic drugs and many others in recent publications which will be of value in the characterisation of drug metabolites of unknown structure and also natural product pharmaceuticals isolated from plants, etc.     

Gradient expansion of the kinetic energy density functional: Local behavior of the kinetic energy density

Calculations with Hartree—Fock electron densities for the rare gas atoms He through Xe show that the gradient expansion for the kinetic energy functional, T[] = T₀[] + T₂[] + T₄[] + … = ∫t() dτ, approximates the kinetic energy by averaging over the shell structure present in the true local kinetic energy density, t(), and that the accuracy of the gradient expansion improves with increasing atomic number. Components of t(), t₀(), t₂() and t₄(), are exhibited and discussed. The defined function t() is everywhere positive.     

Inherent speedup limitations in multiple time step/particle mesh Ewald algorithms

Multiple time step (MTS) algorithms present an effective integration approach to reduce the computational cost of dynamics simulations. By using force splitting to allow larger time steps for the more slowly varying force components, computational savings can be realized. The Particle-Mesh-Ewald (PME) method has been independently devised to provide an effective and efficient treatment of the long-range electrostatics interactions. Here we examine the performance of a combined MTS/PME algorithm previously developed for AMBER on a large polymerase beta/DNA complex containing 40,673 atoms. Our goal is to carefully combine the robust features of the Langevin/MTS (LN) methodology implemented in CHARMM-which uses position rather than velocity Verlet with stochasticity to make possible outer time steps of 150 fs-with the PME formulation. The developed MTS/PME integrator removes fast terms from the reciprocal-space Ewald component by using switch functions. We analyze the advantages and limitations of the resulting scheme by comparing performance to the single time step leapfrog Verlet integrator currently used in AMBER by evaluating different time-step protocols using three assessors for accuracy, speedup, and stability, all applied to long (i.e., nanosecond) simulations to ensure proper energy conservation. We also examine the performance of the algorithm on a parallel, distributed shared-memory computer (SGI Origin 2000 with 8 300-MHz R12000 processors). Good energy conservation and stability behavior can be demonstrated, for Newtonian protocols with outer time steps of up to 8 fs and Langevin protocols with outer time steps of up to 16 fs. Still, we emphasize the inherent limitations imposed by the incorporation of MTS methods into the PME formulation that may not be widely appreciated. Namely, the limiting factor on the largest outer time-step size, and hence speedup, is an intramolecular cancellation error inherent to PME. This error stems from the excluded-nonbonded correction term contained in the reciprocal-space component. This cancellation error varies in time and introduces artificial frequencies to the governing dynamics motion. Unfortunately, we find that this numerical PME error cannot be easily eliminated by refining the PME parameters (grid resolution and/or order of interpolating polynomial). We suggest that methods other than PME for fast electrostatics may allow users to reap the full advantages from MTS algorithms.