Mixed Norm Inequalities for Directional Operators Associated to Potentials

We study mixed norm inequalities for directional operators which appear applying the method of rotations to homogeneous operators with variable kernel and with the homogeneity of Riesz potentials. The results are sharp for a range of values of the parameter and for all its values when the inequalities are restricted to radial functions.     

Egalitarian solutions in the core

In this paper we define the Lorenz stable set, a subset of the core consisting of the allocations that are not Lorenz dominated by any other allocation of the core. We introduce the leximin stable allocation, which is derived from the application of the Rawlsian criterion on the core. We also define and axiomatize the egalitarian core, a set of core allocations for which no transfer from a rich player to a poor player is possible without violating the core restrictions. We find an inclusive relation of the leximin stable allocation and of the Lorenz stable set into the egalitarian core. Received: October 1999/Final version: July 2001     

Novel Cobalt (II) Phthalocyanine‐Containing Polyimides: Synthesis,Characterization, Thermal and Optical Properties

Summary: A novel class of polymer has been prepared by reaction of a copolyimide containing carboxylic acid groups, and a cobalt phthalocyanine peripherally substituted with a reactive hydroxyl group. The incorporation of the phthalocyanine ring was achieved by esterification of the carboxylic acid groups of the polyimide with the free hydroxyl group of the phthalocyanine. In this work, a limited number of phthalocyanine rings have been introduced in order to avoid extensive modification of the copolyimide properties. The extent of modification (percentage of esterified carboxylic groups) was estimated to be about 18%. The resulting material showed good thermal stability and a high glass transition temperature (above 300 °C). The incorporation of the bulky phthalocyanine ring brought about a light decrease of thermal properties, relative to those of the initial polyimide. The presence of phthalocyanine was confirmed by the absorption band at 670 nm showing in the visible region for the modified polyimide. The novel copolyimide also exhibited a remarkable emission peak at 430 nm, when excited at 350 nm, corresponding to the emission of the cobalt phthalocyanine moiety.

Schematic representation of the PI‐CoPc molecule and the chemical structure of the repeat unit.     

Phase Diagram for a System of Polydisperse Components Consisting of the Precursor of an Epoxy/Diamine Thermoset and a Thermoplastic: Analysis Based on a Lattice Theory Model

Summary: The miscibility of a thermoplastic modifier with the precursors of an epoxy/diamine thermoset without chemical reaction was studied thermodynamically. The experimental cloud point curve showed a UCST behavior. A model based on the Flory‐Huggins lattice theory and on the Koningsveld approach was used for the thermodynamic analysis, in which the polydispersity of components was taken into account and the interaction parameter was considered depending on the temperature and composition. A phase diagram for the unreacted system was obtained. Calculations of species distributions in both separated phases were realized for different compositions of the modifier. Finally, the miscibility of our system was compared with that of the same system without diamine, obtaining a greater miscibility in the system with diamine.

Phase diagram for the system formed by the precursors of an epoxy thermoset without chemical reaction modified with different amounts of polystyrene.     

An application of some high order operator splitting methods to systems of stiff differential equations

In this work we compare operator splitting methods of high order that are applied to problems with stiff matrices. In order to efficiently solve the resultant subproblems is possible to use implicit Runge-Kutta methods. We apply an alternative extrapolation technique that works well for the tested problems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow patterns and interfacial velocities near a moving contact line

Experimental data on velocity fields and flow patterns near a moving contact line is shown to be at variance with existing hydrodynamic theories. The discrepancy points to a new hydrodynamic paradox and suggests that the hydrodynamic approach may be incomplete and further parameters or forces affecting the surfaces may have to be included. A contact line is the line of intersection of three phases: (1) a solid, (2) a liquid, and (3) a fluid (liquid or gas) phase. A moving contact line develops when the contact line moves along the solid surface. A flat plate moved up and down, inside and out of a liquid pool defines a simple, reliable experimental model to characterize dynamic contact lines. Highlighted are three important conclusions from the experimental results that should be prominent in the development of new theoretical models for this flow. First, the velocity along the streamline configuring the liquid–fluid interface is remarkably constant within a distance of a couple of millimeters from the contact line. Second, the relative velocity of the liquid–fluid interface, defined as the ratio of the velocity along the interface to the velocity of the solid surface, is independent of the solid surface velocity. Third, the relative interface velocity is a function of the dynamic contact angle.     

A numerical approximation to the elastic properties of sphere-reinforced composites

Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50%. The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost. Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin. The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the “exact” solution to the problem, in agreement with the results of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites. They were used to assess the accuracy of three classical analytical models: the Mori-Tanaka mean-field analysis, the generalized self-consistent method, and Torquato's third-order approximation.     

Investigation of rat bone fracture healing using pulsed 1.5 MHz, 30 mW/cm burst ultrasound – Axial distance dependency

This study investigated the effect of LIPUS on fracture healing when fractures were exposed to ultrasound at three axial distances: z = 0 mm, 60 mm, and 130 mm. We applied LIPUS to rat fracture at these three axial distances mimicking the exposure condition of human fractures at different depths under the soft tissue. Measurement of LIPUS shows pressure variations in near field (nearby transducer); uniform profile was found beyond it (far field). We asked whether different positions of the fracture within the ultrasound field cause inconsistent biological effect during the healing process. Closed femoral fractured Sprague–Dawley rats were randomized into control, near-field (0 mm), mid-near field (60 mm) or far-field (130 mm) groups. Daily LIPUS treatment (plane, but apodized source, see details in the text; 2.2 cm in diameter; 1.5 MHz sine waves repeating at 1 kHz PRF; spatial average temporal average intensity, I_SATA = 30 mW/cm²) was given to fracture site at the three axial distances. Weekly radiographs and endpoint microCT, histomorphometry, and mechanical tests were performed. The results showed that the 130 mm group had the highest tissue mineral density; and significantly higher mechanical properties than control at week 4. The 60 mm and 0 mm groups had significantly higher (i.e. p < 0.05) woven bone percentage than control group in radiological, microCT and histomorphometry measurements. In general, LIPUS at far field augmented callus mineralization and mechanical properties; while near field and mid-near field enhanced woven bone formation. Our results indicated the therapeutic effect of LIPUS is dependent on the axial distance of the ultrasound beam. Therefore, the depth of fracture under the soft tissue affects the biological effect of LIPUS. Clinicians have to be aware of the fracture depth when LIPUS is applied transcutaneously.     

On dimers and complexes of tetracene and the Kasha's molecular excitonic model

Aggregation processes that occur in a solution of 3.4 × 10^?5 M tetracene in decalin at 213 K and in a 1.3 × 10^?4 M solution of anthracene in methylcyclohexane at 135 K show that they are second‐order kinetic processes responsible for generating the corresponding dimeric structures of these acenes. The UV–Vis absorption spectra of these dimeric structures show the presence of isosbestic points. We also show that the rate constants of these processes appear to depend on the viscosity of the solvent employed. Excitonic interactions involved in these dimers are described in the light of Kasha's model. We also show that a solution of 6.7 × 10^?5 of tetracene in toluene at 173 K exhibits aggregation but following a first order kinetics and that the corresponding absorption spectra describing the process at 173 K show no isosbestic points. Consequently, it is concluded that in this solvent, the tetracene does not dimerize, but it forms a complex with toluene. The strong similarity between the first band of the tetracene dimer and the tetracene/toluene complex may give rise to a strong controversy over the excitonic model to be considered. Copyright © 2014 John Wiley & Sons, Ltd.