Given 0 < s ≤ 1 and à an s-convex function, s − à -sequence spaces are introduced. Several quasi-Banach sequence spaces are thus characterized as a particular case of s − Ã-spaces. For these spaces, new measures of noncompactness are also defi ned, related to the Hausdorff measure of noncompactness. As an application, compact sets in s − Ã-interpolation spaces of a quasi-Banach couple are studied.
This paper is devoted to the study of the stability of the compactness property of bilinear operators acting on the products of interpolated Banach spaces. We prove one-sided compactness results for bilinear operators on products of Banach spaces generated by abstract methods of interpolation, in the sense of Aronszajn and Gagliardo. To get these results, we prove a key one-sided bilinear interpolation theorem on compactness for bilinear operators on couples satisfying an extra approximation property. We give applications to general cases, including Peetre’s method and the general real interpolation methods.
The baking temperature (Tb) of an epoxy resin was optimized in order to decrease the dynamic interfacial tension, identifying the lowest wettability conditions for liquids flowing at a high rate. The dependence of dynamic interfacial tension on Tb was evaluated for the diglycidyl ether of bisphenol A. This resin was used to coat a sucking rod at the oil field of Bacia de Sergipe/Alagoas, Brazil in order to reduce blockage occurrences, maintenance stops, and the pumping capacity required. The samples were baked for 24 h between 100 and 180°C. Their color and absorption spectra showed progressive dependence of Tb, indicating a migration from polymerization, through polymer network degradation, until carbonization. Spectrofluorimetry showed an initial increase in the energy gap between absorption and emission followed by a decrease that was attributed to changes of the chemical environment isotropy. Fourier transform infrared spectroscopy showed that the maximum polymerization occurred at 140°C. Dynamic interfacial tension was evaluated by fluorescence depolarization of induced flowing liquids, using polarized laser-induced fluorescence within induced liquid flows and was clearly dependent on Tb. The lowest dynamic wettability was at 120°C, just before full polymerization, which was attributed to two competing effects as Tb increased: polymerization and progressive yielding of compounds from the epoxy degradation. This points to the need to review the standard application procedures of these resins.
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