Approximation Properties AP s and p-Nuclear Operators (the Case 0 < s ≤ 1)

We investigate Banach spaces possessing (or not possessing) the approximation properties AP _s, 0 < s ≤ 1, in connection with the following known question in the geometric theory of operators: under which conditions on Banach spaces X and Y and on positive numbers r and p does the p-nuclearity of the second adjoint of a continuous operator T from X to Y imply the p-nuclearity of T? Actually, we give necessary and sufficient conditions under which this question is answered affirmatively. In addition, the corresponding counterexamples are obtained in the maximally strong form. For instance, it is shown (and this statement is a significant strengthening of the previous results of that sort) that there exists a pair of separable Banach spaces Z and W such that the spaces Z ^** and W have Schauder bases, while for every p, 1 ≤ p < 2, there is a non-p-nuclear operator from W to Z with a p-nuclear second adjoint. Earlier, in similar examples, the corresponding spaces did not possess even the Grothendieck approximation property. The technique developed in this paper does not allow us to treat the case p > 2. That case will be studied in a forthcoming paper of the author. Bibliography: 11 titles.     

Effect of maltodextrins on the surface activity of small-molecule surfactants

We report on the effect of commercially important polysaccharides (maltodextrins with variable dextrose equivalent (Paselli SA-2, MD-6 and MD-10) on the surface activity at the air–water interface of small-molecule surfactants (sms), possessing different hydrophobic–lipophilic balance ((SSL (Na⁺), the main component is a sodium salt of stearol–lactoyl lactic acid, and PGE (080), polyglycerol ester of C18 fatty acid), and widely used in food products. A marked change of the surface activity of sms was found in the presence of maltodextrins by tensiometry. The combined data of laser multiangle light scattering and mixing calorimetry have suggested that this result is governed by specific complex formation between maltodextrins and sms in aqueous medium. Measurements have been made of the molar mass, the second virial coefficient and the enthalpy of intermolecular interactions in aqueous solutions. The implication of a degree of polymerization of maltodextrins in this phenomenon was shown. The interrelation between the molecular parameters of the formed complexes and their surface activity at the air–water interface has been revealed and discussed.     

Justification of Averaging Method for Multifrequency Impulsive Systems

We prove new theorems on the justification of the averaging method for multifrequency oscillation systems with pulse influence at fixed times.     

On Necessary and Sufficient Conditions for the Asymptotic Stability of Impulsive Systems

We prove that the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are also necessary conditions.     

Investigation and modelling of damping in a plate with a bonded porous layer

Behavior of a poro-elastic material bonded onto a vibrating plate is investigated in the low-frequency range. From the analysis of dissipation mechanisms, a model accounting for damping added by the porous layer on the plate is derived. This analysis is based on a 3-D finite element formulation including poro-elastic elements based on Biot displacement theory. First, dissipated powers related to thermal, viscous and viscoelastic dissipation are explicited. Then a generic configuration (simply-supported aluminium plate with a bonded porous layer and mechanical excitation) is studied. Thermal dissipation is found negligible. Viscous dissipation can be optimized as a function of airflow resistivity. It can be the major phenomenon within soft materials, but for most foams viscoelastic dissipation is dominant. Consequently an equivalent plate model is proposed. It includes shear in the porous layer and only viscoelasticity of the skeleton. Excellent agreement is found with the full numerical model.     

A study of the atmospheric lead pollution in Seville, Spain. Influence of meteorology and traffic, and relationship with other traffic-generated pollutants

A study of the atmospheric pollution by suspended particulate lead in the city of Seville, Spain, was carried out during the period between March 1983 and February 1984. The results obtained from seven sampling stations allowed us to study the site to site variations; there are two locations with average annual concentrations higher than 2 micrograms X m-3. In one station, the meteorological and traffic effects and relationship with other traffic-related pollutants, were investigated. The regression analyses performed on the average monthly data have shown an inverse correlation with wind speed and temperature and a direct correlation with carbon monoxide and smoke concentrations, but no significant correlation was found with the lead deposition levels.     

Elastoplastic torsion theory for whisker crystals

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 127–134, March–April, 1991.     

Reaction Medium and Kinetics of N-Vinylsuccinimide Copolymerization

Studies in the field of radical copolymerization of N-vinylsuccinimide were summarized, theeffect of the reaction medium on the process kinetics was examined. Factors governing the relative activity ofthe monomers were revealed, and ways to control the reactivity of N-vinylsuccinimide in binary copolymerizations were suggested.