Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

Photoluminescence characterization of silicon nanostructures embedded in silicon oxide

This paper describes a simple method to analyze the photoluminescent characteristics of materials based on embedded light-emitting nanoclusters. Photoluminescence spectra of deposited silicon sub-oxide layers with the same composition and different thicknesses have been obtained. A saturation of the total luminescence intensity is observed with increase in thickness. By analyzing the photoluminescence spectra several optical and structural parameters can be evaluated. We thus propose a model in which the absorption of light from a nanostructure layer implies the possibility of subsequent luminescence and affects the underlying layers as well. By fitting the data to the developed model, two fundamental parameters are extracted: nanostructures absorption probability, which is independent of the emission energy and the spectra of emission probability of an excited nanostructure which fits a Gaussian shape.     

The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.     

Manufacture of xylose-based fermentation media from corncobs by posthydrolysis of autohydrolysis liquors

Milled corncob samples were mixed with water and heated to obtain a liquid phase containing oligosaccharides, sugars, and acetic acid as main reaction products (autohydrolysis reaction). To hydrolyze the sugar oligomers to the correspondent monomers, sulfuric acid was added to the autohydrolysis liquors to reach 0.5–2 wt% of solution, and the reaction media were heated at 101.5–135°C. With this operational procedure, sugar solutions suitable as fermentation media (containing xylose as the major component) were obtained. The kinetics of the posthydrolysis step was characterized on the basis of experimental data concerning the time courses of the concentrations of xylooligosaccharides, xylose, furfural, and acetic acid. The concentrations of other reaction byproducts (glucose or arabinose) were also measured.     

Kinetics of the formation of Fe2B layers in gray cast iron: Effects of boron concentration and boride incubation time

The growth kinetics of Fe₂B layers formed at the surface of gray cast iron were evaluated in this study. The pack-boriding process was applied to produce the Fe₂B phase at the material surface, and the variables included three temperatures (1173, 1223 and 1273 K) and four exposure times (2, 4, 6 and 8 h). Taking into account the growth fronts obtained at the surface of the material and the mass balance equation at the Fe₂B/substrate interface, the boron diffusion coefficient on the borided phase was estimated for the range of treatment temperatures. Likewise the parabolic growth constant, the instantaneous velocity of the Fe₂B/substrate interface, and the weight gain in the borided samples were established as a function of the parameters τ(t) and α(C), which are related to the boride incubation time (t₀(T)) and boron concentration at the Fe₂B phase, respectively. Observation of the growth kinetics of the Fe₂B layers in gray cast irons suggest an optimum value of boron concentration that is in good agreement with the set of boriding experimental conditions used in this work.     

The elimination kinetics of secondary Alkyl Bromides in the gas phase

Elimination kinetics of 2-bromohexane and 2-bromo-4-methylpentane in the gas phase were examined over the temperature range of 310–360°C and pressure range of 46–213 torr. The reactionsin seasoned, static reaction vessels, and in the presence of the free radical inhibitor cyclohexene, are homogeneous, unimolecular, and follow first order rate laws. The overall rate coefficients are described by the following Arrhenius equations: For 2-bromohexane, log??₁(s^?1) = (13.08 ± 0.70) ? (185.7 ± 8.2) kJ mol^?1 (2.303RT)^?1; for 2-bromo-4-methylpentane, log??₁(s^?1) = (13.08 ± 0.33) ? (183.4 ± 3.8) kJ mol^?1 (2.303RT)^?1. The electron releasing effect of alkyl groups influences the overall elimination rates. The olefin products isomerize in the presence of HBr gas until an equilibrium mixture is reached.     

An experimental investigation of how accurate,simply supported boundary conditions can be achieved in compression testing of panels

How accurate, simply supported boundary conditions can be obtained experimentally in the testing of rectangular panels subjected to uniaxial compression has been investigated. Experimental buckling loads are obtained using the Southwell method and are compared with theoretical predictions. Several support arrangements are examined and compared to the idealized support conditions.