Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.     

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.     

Simultaneous Determination of Carbamate and Organophosphorus Pesticides in Honeybees by Liquid Chromatography-Mass Spectrometry

Summary The potential of liquid chromatography-mass spectrometry (LC-MS) has been studied for the simultaneous determination of sixteen carbamate and organophosphorus pesticides in honeybees using a traditional sample preparation protocol based on acetone extraction and dichloromethane partitioning. The performances of both atmospheric pressure chemical ionization (APCI) and electrospray (ES) interfaces were compared. APCI offered better sensitivity and specificity for a higher range of pesticides. Limits of quantification were from 0.01 to 0.17 mg kg^–1, at which recoveries obtained were between 64 and 93%, except for pirimicarb that was at 13%, with relative standard deviations ranging from 7 to 20%. Fenitrothion, fenoxycarb, methiocarb and phoxim were found in bees from Valencian Community beehives at concentrations between 0.03 and 3.75 mg kg^–1.     

Pattern forming precipitation in gels due to coupling of chemical reactions with diffusion

Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses.     

Design and application of double amplified recirculating ring structure for hybrid fibre buses

The design of a double-parallel amplified recirculating optical delay line utilizing an erbium-doped fibre amplifier for a fibre optical bus is described. This structure is used for amplifying, equalizing and filtering multicarrier signals coming from optoelectronic units attached to fibre couplers. The use of this structure for a hybrid multimode-singlemode fibre bus that includes optoelectronic units for sensors is also demonstrated.     

Addendum to “examples of semiperfect rings”

We fill a gap in [4], and provide a rigorous example of a local ringR whose Jacobson radical is locally nilpotent, butM ₂(R) is not strongly π-regular. The online version of the original article can be found at The work of the first author was partially supported by the DGICYT (Spain), through the grant PB92-0586, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya.     

Necessary conditions and duality for inexact nonlinear semi-infinite programming problems

First order necessary conditions and duality results for general inexact nonlinear programming problems formulated in nonreflexive spaces are obtained. The Dubovitskii–Milyutin approach is the main tool used. Particular cases of linear and convex programs are also analyzed and some comments about a comparison of the obtained results with those existing in the literature are given.