Nonlinear PDEs and measure-valued branching type processes

We deal with the probabilistic approach to a nonlinear operator Λ of the form , in connection with the works of M. Nagasawa, N. Ikeda, S. Watanabe, and M.L. Silverstein on the discrete branching processes. Instead of the Laplace operator we may consider the generator of a right (Markov) process, called base process, with a general (not necessarily locally compact) state space. It turns out that solutions of the nonlinear equation Λu=0 are produced by the harmonic functions with respect to the (linear) generator of a discrete branching type process. The consideration of the general state space allows to take as base process a measure-valued superprocess (in the sense of E.B. Dynkin). The probabilistic counterpart is a Markov process which is a combination between a continuous branching process (e.g., associated with a nonlinear operator of the form Δu−uα, 1<α?2) and a discrete branching type one, on a space of configurations of finite measures. Our approach uses probabilistic and analytic potential theoretical tools, like the potential kernel of a continuous additive functional and the subordination operators.     

Synthesis and characterization of indium oxide-hematite magnetic ceramic solid solution

Indium oxide-doped hematite xIn₂O_3*(1-x)??-Fe₂O₃ (molar concentration x = 0.1?C0.7) solid solutions were synthesized using mechanochemical activation by ball milling. XRD patterns yield the dependence of lattice parameters and grain size as function of milling time. After 12 h of milling, the completion of In^3?+? substitution of Fe^3?+? in hematite lattice occurs for x = 0.1. For x = 0.3, 0.5 and 0.7, the substitutions between In^3?+? and Fe^3?+? into hematite and respectively, In₂O₃ lattices occur simultaneously. The lattice parameters of ??-Fe₂O₃ (a and c) and In₂O₃ (a) vary with milling time. For x = 0.1, Mössbauer spectra were fitted with one, two, or three sextets versus milling time, corresponding to gradual substitution of In^3?+? for Fe^3?+? in hematite lattice. For x = 0.3, Mössbauer spectra after milling were fitted with three sextets and two quadrupole-split doublets, representing In^3?+? substitution of Fe^3?+? in hematite lattice and Fe^3?+? substitution of In^3?+? in two different sites of In₂O₃ lattice. For x = 0.5 and 0.7, Mössbauer spectra fitting required two sextets and one quadrupole-split doublet, representing coexistence of In^3?+? substitution of Fe^3?+? in hematite lattice and Fe^3?+? substitution of In^3?+? in indium oxide lattice. The recoilless fraction studied versus milling time for each molar concentration exhibited low values, consistent with the occurrence of nanoparticles in the system. SEM/EDS measurements revealed that the mechanochemical activation by ball milling produced xIn₂O_3*(1-x)??-Fe₂O₃ solid solution system with a wide range of particle size distribution, from nanometer to micrometer, but with a uniform distribution of Fe, In, and O elements.     

Modeling and optimization of a propeller-type tribocharger for granular materials

Electrostatic separation has already proved to be an effective means for the recycling of granular plastics from industrial wastes. The aim of the present work was to optimize the operation of a novel device that could ensure effective triboelectric charging of such materials prior to their selective sorting in a high-intensity electric field. The experiments were performed on two sorts of mm-size granular materials Acrylonitrile Butadiene Styrene and High Impact Polystyrene, originating from the processing of waste electric and electronic equipment. The samples were introduced in a Polyvinyl Chloride cylinder, where a co-axial propeller entrained the plastic granules into a helical motion that favored their triboelectric charging by combining the mechanical and aerodynamical effects. The experimental design methodology was employed for the modeling and optimization of the tribocharging process.     

Preparation and characterization of polyvinyl alcohol—chitosan biocompatible magnetic microparticles

This work addresses the obtaining of biocompatible magnetic polyvinyl alcohol—chitosan microspheres, specifically tailored/functionalised to bind directly blood toxins using an emulsion crosslinking preparation method. The following synthesis parameters were studied: water to oil phase ratio, polyvinyl alcohol molecular weight, chitosan to polyvinyl alcohol weight ratio, surfactant composition and concentration of the crosslinking agent. These parameters were optimized for producing a high yield of colloidally stable and uniformly sized particles with significant magnetization of saturation, bearing surface amino groups that can be further used to bind blood toxins directly. The particles were characterized regarding their size distribution and surface charge (laser diffraction analysis), morphology (transmission electron microscopy), magnetic properties, chemical composition (Fourier transform infrared spectroscopy) and concentration of the surface amino groups (conductometric titration).     

Effective communication,critical aspects and compositionality in algebra

This paper contains a discussion of how the concept of critical aspects and the principle of compositionality can provide a powerful tool to analyse and understand the communications that occur in the classroom. It is grounded in data collected in a longitudinal study. The content chosen is algebra. It is argued that the critical aspects and the principle of compositionality should be considered as a methodological principle that describes how communication in the classroom should be designed. Here, I present the power of using variation theory whose main purpose is to generate an understanding of critical aspects and compositionality in practice.     

Computing the Longest Previous Factor

The Longest Previous Factor   array gives, for each position i$i$ in a string y$y$, the length of the longest factor (substring) of y$y$ that occurs both at i$i$ and to the left of i$i$ in y$y$. The Longest Previous Factor array is central in many text compression techniques as well as in the most efficient algorithms for detecting motifs and repetitions occurring in a text. Computing the Longest Previous Factor array requires usually the Suffix Array and the Longest Common Prefix array. We give the first time–space optimal algorithm that computes the Longest Previous Factor array, given the Suffix Array and the Longest Common Prefix array. We also give the first linear-time algorithm that computes the permutation that applied to the Longest Common Prefix array produces the Longest Previous Factor array.     

Numerical modeling of the trajectories of plastic granules in a tribo-aero-electrostatic separator

A tribo-aero-electrostatic separator has been recently patented for the selective sorting of granular plastics mixtures generated during the recycling of waste electrical and electronic equipments (WEEE). The plastics are tribo-charged in a parallelepiped fluidized bed device, two opposite walls of which being the electrodes that generate the electric field that performs the separation. In two previous papers, different sets of operating parameters of this separator have been studied by hundreds of experiments, in order to improve the efficiency of the process and the purity of the products. The aim of the present paper is to complement these studies by establishing a model for computing the trajectory of plastics granules in such separator. The distribution of electric field and the profile of the airflow between electrodes were expressed using simple analytical formulas, which were introduced in the system of differential equations that served for the calculation of granule trajectories under the action of the various electric and mechanical forces. The computations were performed for various operating parameters: applied-voltage, granule size, charge density. The model can guide the design of industrial tribo-aero-electrostatic separators and the choice of the optimum values of the operating variables of such equipment.     

Correlations between the electric charging properties and the optically determined structure of non-woven fabrics

The aim of this paper is to determine the degree of correlation between the electrostatic potential distribution on the surface of non-woven fabrics and the material structure as obtained by optical means. The potential distribution on the material surface was monitored for several samples of two types of fabrics that were electrically charged using corona discharge. The results show that the charge distribution on the samples surface significantly correlates with the spreading and the third centered moment of the gray-scale pictures of the samples.     

Metal-ferroelectric-metal current-voltage characteristics: A charge flow balance through interfaces approach

A model for current voltage characteristics of a thin film metal-ferroelectric-metalstructure is constructed by combining the electrostatics of a polarized ferroelectric filmwith the balanced flow of charge through its interfaces. Using a set of fittingparameters, good agreement with several sets of experimental data is obtained fordifferent system temperatures. The influence of model parameters on the current-voltagecharacteristic is discussed. Best fit values of some of these parameters correlate wellwith ab initio calculations in the literature, supporting the idea of low dielectricpermittivity of the interface transition layers in the ferroelectric.