A categorical characterization of varieties

A simple, direct proof of the following characterization of varieties of (finitary) algebras is presented: a cocomplete category is equivalent to a variety iff it has an algebraic generator, i.e., a regular generator which is exactly projective and finitely generated. This improves somewhat a recent restatement, due to Pedicchio and Wood, of the classical characterization theorem of Lawvere. A bijective correspondence between algebraic theories and algebraic generators is established.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

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.     

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.