Stochastic model of dissociation-recombination kinetics in micelles

The small number of reagents solubilized in a micelle prohibits the use of conventional reaction kinetics. In order to describe the kinetics of the reaction A + B ? AB proceeding in a micellar phase, a stochastic model is evaluated. The deviation of these results from those obtained by conventional kinetics may be as high as 20%.     

The magnetizability of excited-state hydrogen: temperature-independent paramagnetism in the B1Σ+u state

Components, of the magnetizability tensor for the B¹Σ⁺_u and a ³Σ⁺_g states ot the hydrogen molecule have been calculated for fixed bond lengths near equilibrium. Explicitly correlated “generalised James-Coolidge” type wavefunctions were used. It is found thilt in the B 1Σ⁺_u state the molecular magnetizability is a positive quantity.     

Homogeneity and the disjoint arcs property

Some previous results of the author towards a classification of homogeneous metric continua are improved. The disjoint arcs property is fully revealed in this context. In particular, closed -manifolds, , are characterized as those homogeneous continua which do not have the disjoint arcs property.

     

Displacement exponent for loop-erased random walk on the Sierpiński gasket

We prove that loop-erased random walks on the finite pre-Sierpiński gaskets can be extended to a loop-erased random walk on the infinite pre-Sierpiński gasket by using the ‘erasing-larger-loops-first’ method, and obtain the asymptotic behavior of the walk as the number of steps increases, in particular, the displacement exponent and a law of the iterated logarithm.     

The effect of the gas atmosphere on the phase transformation in the solid solution of MoO3 in V2O5

The nature of the structure transformation occurring under the influence of oxidizing or reducing gas atmosphere in powdered oxide (V₂O₅)_0.93 (MoO₃)_0.07 has been investigated. The formation of an intermediate compound in the inner parts of the catalyst grains during the oxidation and in the subsurface layers during the reduction has been observed.     

Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpinski gasket

In this note we investigate the asymptotic behavior of spectra of Schrödinger operators with continuous potential on the Sierpinski gasket . In particular, using the existence of localized eigenfunctions for the Laplacian on we show that the eigenvalues of the Schrödinger operator break into clusters around certain eigenvalues of the Laplacian. Moreover, we prove that the characteristic measure of these clusters converges to a measure. Results similar to ours were first observed by A. Weinstein and V. Guillemin for Schrödinger operators on compact Riemannian manifolds.

     

Critical point approaches to Gradient-Type systems on the Sierpi\'{n}ski Gasket

We investigate the existence of multiple solutions for parametric quasi-linear systems of the gradient-type on the Sierpi\''{n}ski gasket. We give some new criteria to guarantee that the systems have at least three weak solutions by using a variational method and some critical points theorems due to Ricceri. We extend and improve some recent results. Finally, we give two examples to illustrate the main results.     

Some remarks on James-Schreier spaces

The James-Schreier spaces Vp, where 1?p<∞, were recently introduced by Bird and Laustsen (in press) [5] as an amalgamation of James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. The purpose of this note is to answer some questions left open in Bird and Laustsen (in press) [5]. Specifically, we prove that (i) the standard Schauder basis for the first James-Schreier space V₁ is shrinking, and (ii) any two Schreier or James-Schreier spaces with distinct indices are non-isomorphic. The former of these results implies that V₁ does not have Pe?czyński's property (u) and hence does not embed in any Banach space with an unconditional Schauder basis.