Weighted weak semivalues

We introduce two new value solutions: weak semivalues and weighted weak semivalues. They are subfamilies of probabilistic values, and they appear by adding the axioms of balanced contributions and weighted balanced contributions respectively. We show that the effect of the introduction of these axioms is the appearance of consistency in the beliefs of players about the game. Received: March 1998/revised version: October 1998     

Nanopore Size Growth and Ultrafiltration Performance of SnO2 Ceramic Membranes Prepared by Sol-Gel Route

Supported ceramic membranes have been produced by the sol-casting procedure from aqueous colloidal suspensions prepared by the sol-gel route. Coatings on a tubular alumina support have been successfully performed leading to crack free layers. Samples have been sintered at 400, 500 and 600°C, and the effect of heating treatment on the nanostructure and on the ultrafiltration properties are analyzed. The characterization has been done by high resolution scanning electron microscopy, nitrogen adsorption-desorption isotherms, water permeation and cut-off determination using polyethylene glycol standard solutions. The micrographs have revealed that grains and pore size increase with the temperature, whereas their shape remains invariant. This results is in agreements with N₂ adsorption-desorption analyses, which have revealed that the mean pore size diameter increases from 4 to 10 nm as the sintering temperature increases from 400 to 600°C, while the total porosity remains constant. Furthermore, the tortuosity, calculated from water permeability, is essentially invariant with the sintering temperatures. The membranes cut-off, determined with a retention rate equal to 95%, are 3500, 6500 and 9000 g·mol^–1 for 400, 500 and 600°C, respectively, showing that the permeation properties of SnO₂ ultrafiltration membranes can easily be controlled by sintering condition.     

Characterization of Natural Chromite Samples from Ophiolite Complexes in the Philippines by 57Fe Mössbauer Spectroscopy

Mössbauer spectroscopy was applied to natural chromite samples from ophiolite complexes in the Philippines. Chemical and structural characterization of the chromite samples was also carried out using X-ray absorption fine structure (XAFS), X-ray diffraction (XRD) and X-ray fluorescence spectrometry (XRF). The Mössbauer spectra of the samples consisted of quadrupole doublets ascribable to Fe³⁺ in octahedral site, Fe³⁺ in tetrahedral site, and Fe²⁺ in tetrahedral site. The relative percentage of Fe³⁺ and Fe²⁺ ions suggested that these Philippine samples were formed under relatively high oxygen fugacity.     

Triangulations with Very Few Geometric Bistellar Neighbors

We are interested in a notion of elementary change between triangulations of a point configuration, the so-called bistellar flips , introduced by Gel'fand, Kapranov, and Zelevinski. We construct sequences of triangulations of point configurations in dimension 3 with n ² +2n+2 vertices and only 4n-3 geometric bistellar flips (for every even integer n ), and of point configurations in dimension 4 with arbitrarily many vertices and a bounded number of flips. This drastically improves previous examples and seems to be evidence against the conjecture that any two triangulations of a point configuration can be joined by a sequence of flips. Received June 4, 1998, and in revised form October 10, 1998.     

Wiener-Hopf factorization for a class of oscillatory symbols

Two classes of 2×2 matrix symbols involving oscillatory functions are considered, one of which consists of triangular matrices. An equivalence theorem is obtained, concerning the solution of Riemann-Hilbert problems associated with each of them. Conditions for existence of canonical generalized factorization are established, as well as boundedness conditions for the factors. Explicit formulas are derived for the factors, showing in particular that only one of the columns needs to be calculated. The results are applied to solving a corona problem.     

On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

Combining Steric and Electrostatic Stabilization Using Hydrophilic MacroRAFT Agents in an Ab Initio Emulsion Polymerization of Styrene

Hydrophilic (co)polymers carrying a thiocarbonyl thio end group such as poly(dimethylaminoethyl methacrylate), poly(ethylene oxide), and poly(ethylene oxide)‐block‐poly(dimethylaminoethyl methacrylate) have been evaluated as precursors of stabilizers in batch ab initio emulsion polymerization of styrene under acidic conditions to form electrosterically stabilized polystyrene latex particles. As a mixture of P(DMAEMA/H⁺Cl⁻)‐RAFT and PEO‐RAFT failed to give satisfactory results, PEO‐RAFT was used as a control agent for the RAFT polymerization of DMAEMA, and the resulting block copolymer was successfully used in ab initio styrene emulsion polymerization.

     

Dissolution and Doping of Polyaniline Emeraldine Base in Imidazolium Ionic Liquids Investigated by Spectroscopic Techniques

Polyaniline is a model molecular system in the study of conductive polymers. Ionic liquids, on the other hand, are becoming more and more a very convenient alternative for conventional organic solvents. The dissolution of polyaniline‐emeraldine base (PANI‐EB) in imidazolium ILs leads to its doping, as indicated by optical and resonance Raman spectroscopies. In this study, it is proposed that the interaction of PANI‐EB and imidazolium ILs involves the specific interaction of the quinoid moiety of the former with the imidazolium ring of the latter, an interpretation that is also based on N K‐edge XANES measurements of neat PANI‐EB, neat ILs, and of their solutions.

     

Finite-element method simulation of rotating disk flow: effect of the transport of a chemical species

Electrochemical cells containing an iron rotating disk electrode which is dissolved in the electrolyte, an 1 M H₂SO₄ solution present a current instability in the plateau region, where the current is controlled by the mass transport. Dissolution of the electrode gives rise to a thin concentration boundary layer, due to a Schmidt number Sc = 2000. This boundary layer, together with the potential applied to the electrode, leads to an increase in the fluid viscosity and in a decrease in the diffusion coefficient, coupling the concentration and the chemical species field. Since the current is proportional to the concentration gradient at the interface, an instability of the coupled fields at Reynolds numbers attained in experimental conditions could be responsible for the current instability. Mangiavacchi [1] performed a linear stability analysis of the problem and showed that this is indeed the case. In this paper we review the main results of the stability analysis and present the main features of the FEM code recently developed in our group, to proceed with the investigation of the current instability observed in electrochemical cells. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lagrangean Structure and Propagation of Singularities in Multidimensional Compressible Flow

We study the propagation of singularities in solutions of the Navier–Stokes equations of compressible, barotropic fluid flow in two and three space dimensions. The solutions considered are in a fairly broad regularity class for which initial densities are nonnegative and essentially bounded, initial energies are small, and initial velocities are in certain fractional Sobolev spaces. We show that, if the initial density is bounded below away from zero in an open set V, then each point of V determines a unique integral curve of the velocity field and that this system of integral curves defines a locally bi-Hölder homeomorphism of V onto its image at each positive time. This “Lagrangean structure” is then applied to show that, if the initial density has a limit at a point of such a set V from a given side of a continuous hypersurface in V, then at each later time both the density and the divergence of the velocity have limits at the transported point from the corresponding side of the transported hypersurface, which is also a continuous manifold. If the limits from both sides exist, then the Rankine–Hugoniot conditions hold in a strict pointwise sense, showing that the jump in the divergence of the velocity is proportional to the jump in the pressure. This leads to a derivation of an explicit representation for the strength of the jump in the logarithm of the density, from which it follows that discontinuities persist for all time, convecting along fluid particle paths, and in the case that the pressure is strictly increasing in density, having strengths which decay exponentially in time.