Enthalpies of sorption of linear hydrocarbons (C2–C8) and chloroderivatives of methane and ethylene on the surface of hydrotalcite

Differential molar adsorption enthalpies (DMAE) were determined by gas chromatographic measurements of specific retention volume of vapors on the surface of two forms of Mg–Al hydrotalcite. A linear dependence of the DMAE on the number of the carbon atoms in hydrocarbons was observed for both form of hydrotalcite. The dependence of the differential molar adsorption enthalpies on the number of chlorine atoms in organic molecules is discussed. A linear dependence of DMAE on the molecular weight of chloroderivatives of methane and ethylene on the basic form in an order monochloromethane < dichloromethane < trichloromethane or vinylidene chloride < 1,1-dichloroethylene < trichloroethylene was found.     

Diffraction of transverse horizontal waves in Fibonacci piezoelectric superlattices

The transfer matrix and global matrix techniques are used in the analysis of diffraction of transverse horizontal waves in piezoelectric superlattices. The system is composed of a set of different piezoelectric layers with quasiperiodic structure according to the Fibonacci sequence. The diffraction spectrum of different configurations of piezoelectric Fibonacci structures is studied. Numerical results for the diffraction spectrum for the piezoelectric Fibonacci superlattice are obtained and a comparison between the results of the transfer and global matrix methods is given, exhibiting the advantage of the latter.     

Young's inequality in trace-class operators

 If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥₁ denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality. Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003 Mathematics Subject Classification (2000): 47A63, 15A60     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Two-dimensional gas motion in nuclear-pumped laser cells at low energy deposits into the gas

The distribution of the two-dimensional gas velocity inside ion-irradiated laser cells is considered for low ion energy deposits into the gas. It is shown that, if the energy deposit is smoothly nonuniform, the twodimensional motion has two quasi-one-dimensional components: the longitudinal gas velocity is practically uniform across the cell and depends on the transversely averaged energy deposit, while the transverse velocity component depends on the difference between the local energy deposit and energy deposit averaged over the transverse direction.     

Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation.     

Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.