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.     

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.     

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.     

Ferromagnetism in colloidal Mn2+ -doped ZnO nanocrystals

High-temperature hydrolysis of Zn(II) and Mn(II) alkoxides in a high boiling point solvent in the presence of surfactants was used to prepare surfactant-coated Zn(1-x)Mn(x)O nanocrystals with average size of 5.5 nm and x = 0.04 +/- 0.03. The magnetic properties of the nanocrystals were measured both for isolated particles diluted in a hydrocarbon matrix and for a nanocrystal powder. Nanocrystals of manganese oxide and ZnO coated with manganese oxide were prepared for comparison to the Zn(1-x)Mn(x)O nanocrystals. We find that the manganese ions primarily substitute zinc ions in the hexagonal ZnO lattice, and part of them are ferromagnetically coupled up to room temperature even in isolated noninteracting nanocrystals. The rest of the ions are magnetically disordered or uncoupled. Surprisingly, these small Zn(1-x)Mn(x)O nanocrystals poses relatively large low-temperature magnetic coercivity and relatively high blocking temperature in the isolated form, which indicate large magnetic anisotropy. In the nanocrystal powder the coercive field decreased significantly. This study highlights the advantages of working with noninteracting single domain particles of these intriguing materials.     

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.     

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.     

Synthesis, binding affinity, and relaxivity of target-specific MRI contrast agents

Although magnetic resonance imaging (MRI) is one of the most important imaging modalities of the central nervous system (CNS), one of the main drawbacks of MRI is its limited specificity. This can potentially be partially alleviated by target-specific contrast agents. In the present paper we describe a simple high yield synthesis of two such gadolinium-based spiperone targeted MRI contrast agents, 1a and 1b. The R₁ relaxivities of 1a and 1b were evaluated and found to be 5.94 and 8.31 mM⁻¹ s⁻¹, respectively at 9.4T, while their R₂ relaxivities at the same magnetic field were found to be 18.05 and 22.60 mM⁻¹ s⁻¹, respectively. In addition and very importantly compound 1a, which is a gadolinium-based, spiperone-targeted MRI contrast agent, was found to preserve some of the spiperone affinity toward the dopamine D2 receptor. Compounds 1a and 1b thus represent potential agents for in vitro dopamine receptor imaging using MRI in experimental models. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Nonsteady-state flow in gas chromatography during fast changes in inlet pressure

The steady-state assumption for describing the flow in a capillary gas chromatography column fails when changes in inlet pressure are introduced at a fast rate. To accommodate the possibility of nonsteady-state conditions, or a transient behavior, a second-order nonlinear differential equation for the pressure is suggested. Good agreement between the new theoretical model and representative experimental results is shown when the inlet pressure is increased at a rate of several hundred kPa per minute; in contrast, predictions from traditional steady-state calculations are relatively poor.