A census of maximum uniquely hamiltonian graphs

We show that there are 2^[n/2]-4 largest graphs of order n ≥ 7 having exactly one hamiltonian cycle. a recursive procedure for constructing these graphs is described.     

Substituent effects on methane activation and elimination by high-valent Zr complexes

A computational study of substituent effects on methane activation and elimination by high-valent zirconium complexes is reported. Substituent (Z) effects (in a structural, electronic, and enthalpic sense) are substantially less important for the imido (L_nZr(DOUBLE BOND)NZ) and imidolike TS than the amido (L_nM(SINGLE BOND)NHZ). For the microscopic reverse reaction, methane CH activation, it suggests that tailoring imido reactivity through electronic modification of nitrogen substituents will be difficult. Analysis of the earliest part of the reaction coordinate for methane elimination entails structural deformation of the Zr—amido to assume an appropriate geometry for elimination, which, in some cases, is directly reflected in substantially higher elimination barriers. Lower elimination barriers correlate with stronger agostic bonding, providing further support for the crucial importance of agostic bonding in facilitating alpha-elimination processes for high-valent transition-metal complexes. © 1996 John Wiley & Sons, Inc.     

The time evolution of the pair distribution function of polymeric systems

Summary The stress tensor of a polymeric system, solution or melt, is the sum of single molecule terms which may be expressed as integrals involving the distribution function in the phase space of a single molecule and intermolecular terms which involve the distribution function in the configuration space of pairs of molecules. The evaluation of the single molecule terms is usually based on the solution of the diffusion equation in the configuration space of a single molecule. In the present development, an analogous diffusion equation in the configuration space of a pair of molecules is developed. The development is based on a generalization of the time-smoothing ideas introduced by Kirkwood. Expressions are obtained for the various friction coefficients as time correlation functions.     

Development of a novel single sensor multiplexed marker assay

There is an increasing desire to measure multiple analytes simultaneously for disease management and detection. However, in the case of invasive devices, it would be better to obtain one small sample and immediately be able to detect the analytes rapidly, as in the case of self-monitoring blood glucose, without the need for additional steps, arrays, or reagents. Electrochemical impedance spectroscopy is used to measure the interaction between ultralow levels of analyte and molecular recognition element in a label-free and rapid manner. Gold nanoparticles were attached to antibodies against interleukin-12 and tumor necrosis factor-α, typical inflammatory markers found with near overlapping responses, on an impedance spectroscopy based biosensor. Cross-reactivity and specificity of tuned antibodies were verified using ELISA. Impedance frequency was quantified by concentration gradients of marker against the device. The natural impedance frequency for interleukin-12 (5.00 Hz) was tuned to a lower frequency four Hertz away from one another for better signal processing. This was accomplished without significantly altering the lower limits of detection (<4 pg ml(-1) and ～60 pg ml(-1) for interleukin-12 and tumor necrosis factor-α, respectively), no cross-reactivity and specificity as determined by ELISAs. With modeling the nanoscale effects and further development, a larger tuning will be possible for making a better multiplexed sensor. Although interleukin-12 and TNF-α equivalent circuit calculations were modeled here, a sensor with the potential to measure multiple markers at once might offer a solution on the sensor front for simplified management of conditions such as diabetes, where both glucose and hemoglobin A1c values could be obtained.     

Size of the freeze-out source in high energy heavy ion collisions

Based on a hydro-inspired azimuthally symmetric emission function, we analyze the HBT radius Rs and the single-particle transverse momentum spectra in Au+Au collisions measured by the STAR Collaboration at SNN = 200 GeV. The results show that consistent assumptions about transverse density (and/or flow profile) in the calculation of the HBT radius Rs and single-particle spectral analyses play an important role for understanding the size of the freeze-out source.     

Theory of the ionization of ethane

Ab initio molecular orbital studies on C₂H₆ ⁺ support an assignment of ² A _1g (D _3d point group symmetry) for the ground state of this cation. This differs from the prediction of Koopmans' theorem which suggests a ² E_g state for vertical ionization. Approximate force constants and vibrational frequencies are calculated for the ethane cation in the ² A _1g state and are found to be consistent with the vibrational progression observed in the experimental photoelectron spectrum.