Composition of ?-stable vector functions

The class of functions that are ?-stable at some point is a generalization of the class of C ^1,1 functions. In this paper we prove that the class of vector functions that are ?-stable at some point is closed under composition.     

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.     

Effects of melting and ordering on the isosteric heat and monolayer density of argon adsorption on graphite

The aim of this paper is to study the effects of temperature on the state of the adsorbed argon on an uniform graphite surface. We applied the kinetic Monte Carlo scheme to simulate adsorption over a very wide range of temperature, which allows us to model the vapor–solid, the vapor–liquid and the order–disorder transition of the monolayer. The main distinction of our methodology is that it accounts for the lattice constant change with loading in the case of formation of an ordered molecular layer by appropriately changing the simulation box size. To do this we enforced the equality of the tangential pressures obtained by the virial and thermodynamic routes, which corresponds to the minimum Helmholtz free energy of a system at a given number of molecules and volume. This criterion is a consequence of the Gibbs–Duhem equation. A significant result obtained by application of the new simulation method was a sharp contraction of the monolayer just after its completion and the onset of the second layer. It manifests itself in an additional heat release. We re-determined the 2D-melting and 2D-critical temperatures of the molecular layer of argon. We also analyzed the order–disorder transition above the 2D-melting and showed that it could occur at some temperatures above the 2D-critical temperature. In this case, a hexagonal lattice appears at a sufficiently large tangential pressure. The effects of loading on the lattice constant, the 2D-critical temperature of the order–disorder transition and the differential heat of adsorption are thoroughly discussed.     

On sequences of solutions for discrete anisotropic equations

Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for an anisotropic problem with a parameter is established. More precisely, a concrete interval of positive parameters, for which the treated problem admits infinitely many solutions, is determined without symmetry assumptions on the nonlinear data. Our goal was achieved by requiring an appropriate behavior of the nonlinear terms at zero, without any additional conditions.