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.     

Preliminary results of a non-spherical aerosol method for the retrieval of the atmospheric aerosol optical properties

There is experimental evidence that the non-sphericity of certain atmospheric particles can cause scattering properties different from those predicted by standard Mie theory. Numerous studies indicate the need to consider the presence of non-spherical particles in modeling the optical properties of atmospheric aerosols. On the other hand, natural aerosols show a great variety of shapes, making difficult a realistic choice of a particle shape (or shape mixture) model. In this paper, we test a parameterization of the particle shape in the retrieval of size distribution, phase function, single scattering albedo and asymmetry parameter from direct and sky-radiance measurements. For this purpose we have substituted the Kernel based on the Mie theory included in the model SKYRAD.PACK by one derived for non-spherical particles. The method is applied under different atmospheric conditions, including Saharan dust outbreak, polluted and local mineral episodes. We compare the results with those obtained by the well known spheroids algorithm used in the AERONET network.     

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.     

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.     

Correct structures of Diels-Alder adducts from the natural cyclolignan thuriferic acid and its 8-epimer

A detailed analysis of one- and two-dimensional ¹H and ¹³C NMR data for the endo and the exo adducts, obtained by Diels-Alder reaction of thuriferic and epithuriferic acids with cyclopentadiene is described. The unequivocal spectral data assignment of the endo and exo structures was complemented with molecular modelling studies and confirmed through X-ray diffraction studies.