On many‐sorted algebraic closure operators

A theorem of Birkhoff‐Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many‐sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many‐sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimality and duality in multiobjective fractional programming involving ρ-semilocally type I-preinvex and related functions

Optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and a duality result is proved using concepts of generalized ρ-semilocally type I-preinvex functions.     

Use of the Apparent Content Curves for the spectrophotometric identification of substances: identification of amphetamines

The possibility of identification of substances which have similar spectral behaviour by means of Apparent Content Curves has been studied. This study is carried out with absorption, excitation and emission spectra of several amphetamines of widespread pharmaceutical use. Results obtained show that amphetamine, phenylpropanolamine, pseudoephedrine, phenylephrine, epinephrine, dopamine and methoxyamphetamine can be identified with a probability of >95%.     

Limonene concentration in lemon (Citrus volkameriana) peel oil as a function of ripeness

The dependence of the limonene content of lemon (Citrus volkameriana) peel oil on the degree of ripeness of the fruit has been studied by using steam distillation and cold pressing to extract the oils from lemon fruit peel at different stages of maturation (green, greenish-yellow, and yellow-orange peel coloration). Samples of essential oils were analyzed by high resolution GC and GC-MS, using tetradecane as internal standard for quantitation. Forty components were detected; thirty eight were positively identified by comparison of their mass spectra (El, 70 eV) and Kováts retention indexes (determined using a non-logarithmic scale on capillary columns coated with both polar (DB-Wax) and non-polar (DB-1) stationary phases) with those of standards and with data reported in the literature. The limonene concentration reached a maximum level of 79.4% when the fruit was in the intermediate maturation stage characterized by greenish-yellow coloration.     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

The effect of simultaneous temperature, pressure and stress on the experimental annealing of spontaneous fission tracks in apatite: a brief overview

Tracks made in minerals by the electronic stopping of uranium fission fragments provide a modern geological dating tool, and are believed also to yield specific information on the low-temperature thermal history of rocks. Experimental work showing that the damaged crystal lattice along a fission track recovers primarily as a function of temperature ignored the fact that the basic theory of atomic diffusion requires an exponential decrease in the intrinsic diffusion coefficient with increasing pressure. Here, fission track recovery was experimentally investigated in basic apatite under the simultaneous influences of temperature, pressure and stress. We show that track fading is a complex recovery mechanism responding to several environmental physical parameters simultaneously. In particular a strong decrease in the track recovery rate was observed as a function of increasing pressure. And a nearly temperature-independent recovery was observed in samples under stress.     

Bounds for non‐periodic mixtures of infinitely many materials

We prove bounds on the homogenized coefficients for general non‐periodic mixtures of an arbitrary number of isotropic materials, in the heat conduction framework. The component materials and their proportions are given through the Young measure associated to the sequence of coefficient functions. Upper and lower bounds inequalities are deduced in terms of algebraic relations between this Young measure and the eigenvalues of the H‐limit matrix. The proofs employ arguments of compensated compactness and fine properties of Young measures. When restricted to the periodic case, we recover known bounds. Copyright © 2005 John Wiley & Sons, Ltd.