Multinomial permutations on a circle

Multinomial permutations on a circle are considered in the framework of combinatorics. Different cases are presented and shown to agree with previously derived formula for the number of cyclic necklaces. Two applied examples are discussed with a view to illustrate the implications of derived formulas. Copyright © 2006 John Wiley & Sons, Ltd.     

Electrical Conductance Studies in Aqueous Solutions with Ascorbate Ions

Conductivity measurements in dilute aqueous solutions of L-ascorbic acid, sodium-L-ascorbate, magnesium-L-ascorbate, calcium-L-ascorbate and ferrous-L-ascorbate were performed in the (288.15 to 323.15) K temperature range. The limiting molar conductances of the ascorbic anion, λ^∘(HAsc⁻, T), and the dissociation constants of ascorbic acid, K(T), were derived by the use of the Debye-Hückel equation for the activity coefficients and the Onsager and Quint and Viallard conductivity equations.     

Discrimination of guests encapsulation in large hexameric molecular capsules in solution: pyrogallol[4]arene versus resorcin[4]arene capsules

NMR experiments demonstrate that, although 2b and 3b form hexameric capsules in chloroform solutions and despite the very similar building units of these hexamers, 3b encapsulates only the noncharged trialkylamines while 2b can encapsulate both the noncharged trialkylamines and the respective ammonium salts obtained by the addition of DCl. In fact, it was found that protonation that forms in situ the ammonium salt ejects the guest from the hexameric capsule of 3b. This is a general observation as it was found for guests containing alkyl chains of four, five, six, and eight carbons.     

Conductivity Studies of Dilute Aqueous Solutions of Oxalic Acid and Neutral Oxalates of Sodium, Potassium, Cesium, and Ammonium from 5 to 35°C

Conductivity measurements of oxalic acid and neutral oxalates (disodium oxalate, dipotassium oxalate, dicesium, and diammonium oxalate) were performed on dilute aqueous solutions, c < 3 × 10^–3 mol-dm^–3, from 5 to 35°C. These data and those available from the literature were analyzed in terms of dissociation steps of oxalic acid, the Onsager conductivity equation for neutral oxalates, the Quint–Viallard conductivity equation for the acid, and the Debye–Hückel equation for activity coefficients, to give the limiting equivalent conductances of bioxalate anion ;(HC₂O₄ ^–) and oxalate anion (1/2C₂O₄ ^2–) and the corresponding dissociation constants K ₁ and K ₂.     

Thomas–Fermi theory from a perturbative treatment of the hydrogenic limit energy density functional: A possible link to local density functional theory

A perturbation expansion which connects the hydrogenic limit energy density functional to the Thomas–Fermi functional is discussed. This perturbation series, where the Coulomb energy density functional is treated as the perturbation to the hydrogenic limit functional, is, in fact, the q = (N/Z) expansion of Thomas–Fermi theory. A truncated form of the first-order correction to the functional provides further insight into the model which treats the ground state energy as a local functional of the electron density.     

Thermally activated conduction in molecular junctions

We report temperature dependence measurements on the conductance of individual molecular wires. The results show for the first time in a molecular junction the theoretically predicted transition from coherent superexchange tunneling conductance to an activated hopping mechanism as temperature is increased.     

Electrical Conductance Studies in Aqueous Solutions of Glutaric Acid,Disodium Glutarate and Sodium Hydrogen Glutarate

Conductivity measurements of glutaric acid and disodium glutarate in dilute aqueous solutions were performed in the 288.15 to 323.15 K temperature range. The limiting equivalent conductances of glutarate anions, λ ^o(HGlut⁻,T) and λ ^o(1/2Glut²⁻,T), and the dissociation constants of glutaric acid, K ₁(T) and K ₂(T), were derived by the use of the Onsager and the Quint and Viallard conductivity equations. The applied molecular model was successfully confirmed by analyzing the conductivities of sodium hydrogen glutarate at 298.15 K.     

Infrared intensities of liquids XXV: Dielectric constants, molar polarizabilities and integrated intensities of liquid toluene at 25 °C between 4800 and 400 cm

The main purpose of this paper is to present accurate infrared integrated intensities of liquid toluene, C₆H₅CH₃, at 25 °C. Also presented are the decadic molar absorption coefficients, E_m, the real and imaginary dielectric constants, ε′ and ε″, and the real and imaginary molar polarizabilities, ^′_m and ^″_m. Integrated intensities were determined as C_j, the area under bands in the spectrum, for all bands between 4800 and 440 cm⁻¹. The contributions from the different bands were separated by fitting the spectrum with classical damped harmonic oscillator bands. The uncertainties in the integrated intensities of most bands are estimated to be 5–10%, with the uncertainties in very weak bands and in shoulders possibly up to 100%. The intensity that should be assigned to the fundamentals is more difficult to estimate due to Fermi resonance with overtone and combination bands, and a best estimate is given. The integrated intensities of the fundamental vibrations and the corresponding transition dipole moments are summarized and are compared with literature values for the gas.