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 effect of high electric fields on the structure and dielectric properties of the B2 phase

Dielectric studies are presented of a banana-shaped compound that exhibits the antiferroelectric B₂ phase. Upon application and subsequent removal of strong electric fields the textures and dielectric properties of the phase drastically change. Most notable is the huge increase of the low frequency permittivity. This behaviour would suggest the induction of ferroelectricity by the electric field.     

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.     

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.     

Optimized Method for the Determination of Prednisolone, Zn-Bacitracin and Phenylephrine in Local Pharmaceutical Preparations by Micellar Electrokinetic Capillary Chromatography

Summary A new, rapid and simple method is described and applied to resolve and quantify mixtures of prednisolone, Zn-bacitracin and phenylephrine. The determination was accomplished by MEKC. The separation was carried out at 25 °C and 30 kV, using a 5 mM phosphate-5 mM borate buffer (pH=8.2), 40 mM SDS as background electrolyte. Under these conditions, the run time was 6.6 min and the limits of quantification were about 1.0 mg L^–1 for every component. Repeatability and reproducibility studies were achieved showing no significant differences at 95% confidence level. The MEKC method has been applied for quantifying these compounds in different commercials pharmaceuticals products, without separations steps.     

Determination of styrene in olive oil by an automatic purge-and-trap system coupled to gas chromatography-mass spectrometry

Summary A new gas chromatographic method using an automatic purge-and-trap system coupled to a GC with mass selective detection to analyze styrene at the parts-per-trillions (ng kg^–1) level is described. The method shows a good sensitivity and the detection limit is 10 ng kg^–1 with a relative standard deviation (RSD) of 4.7% for 164 ng kg^–1 styrene in olive oil. This analytical method has been successfully applied to the analysis of styrene in extra-virgin olive oil from the European market.