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.     

Three-dimensional trajectory study of the I + HI → IH + I, H + I2 reactions

The quasiclassical trajectory calculation of the I + HI collision is performed in order to study the exchange and endothermic reaction channels. The rate constant of the exchange reaction I′ + HI → HI′ + I is found to be equal to 7.7 × 10¹¹ cm³/mol s at room temperature of 300 K. The study of the endothermic reaction I + HI → H + I₂ shows that it takes place only in configurations with large bend angles. Due to the non-collinear character of this reaction its threshold (2 eV) exceeds significantly the threshold of the minimal energy (collinear) reaction path (1.55 eV).     

At Least n – 1 Intersection Points in a Connected Family of n Unit Circles in the Plane

Let C be a family of n different unit circles in the plane. We show that C determines at least n - c intersection points, where c is the number of connected components in ∪_{C ∈ C}C. This proves a conjecture of A. Bezdek.     

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.     

Predictable projections for point process filtrations

Summary We consider a point process with the Polish phase space (X,X) and a system of -fields (x),xX, generated by on certain sets (x)X. We define predictability for random processes indexed byX and for random measures onX and prove the existence and uniqueness of predictable and dual predictable projections under a regularity condition on . ForX= ₂ ⁺ and under monotonicity assumptions on the sets x we will identify the predictable projections of some simple processes as regular versions of certain martingales.     

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.