Lipscomb's space

It is known that Lipscomb's space can be imbedded in Hilbert's space . Let be the imbedded version of endowed with the -induced topology. We show how to construct as the attractor of an iterated function system containing an infinite number of affine transformations of . In this way we answer an open question of J.C. Perry.

     

Vapour pressure and excess Gibbs energy of binary 1,2-dichloroethane + cyclohexanone,chloroform + cyclopentanone and chloroform + cyclohexanone mixtures at temperatures from 298.15 to 318.15 K

The vapour pressures of the binary systems 1,2-dichloroethane + cyclohexanone, chloroform + cyclopentanone and chloroform + cyclohexanone mixtures were measured at temperatures between 298.15 and 318.15 K. The vapour pressures vs. liquid phase composition data for three isotherms have been used to calculate the activity coefficients of the two components and the excess molar Gibbs energies, G^E, for these mixtures, using Barker's method. Redlich–Kister, Wilson, NRTL and UNIQUAC equations, taking into account the vapour phase imperfection in terms of the 2-nd virial coefficient, have represented the G^E values. No significant difference between G^E values obtained with these equations has been observed. Our data on vapour–liquid equilibria (VLE) and excess properties of the studied systems are examined in terms of the DISQUAC and modified UNIFAC (Dortmund) predictive group contributions models.     

Comparative study on different carbon nanotube materials in terms of transparent conductive coatings

We compared conductive transparent carbon nanotube coatings on glass substrates made of differently produced single-wall (SWNT), double-wall, and multiwall carbon nanotubes. The airbrushing approach and the vacuum filtration method were utilized for the fabrication of carbon nanotube films. The optoelectronic performance of the carbon nanotube film was found to strongly depend on many effects including the ratio of metallic-to-semiconducting tubes, dispersion, length, diameter, chirality, wall number, structural defects, and the properties of substrates. The electronic transportability and optical properties of the SWNT network can be significantly altered by chemical doping with thionyl chloride. Hall effect measurements revealed that all of these thin carbon nanotube films are of p-type probably due to the acid reflux-based purification and atmospheric impurities. The competition between variable-range hoping and fluctuation-assisted tunneling in the functionized carbon nanotube system could lead to a crossover behavior in the temperature dependence of the network resistance.     

Arithmetic differential equations on $$GL_n$$, II: arithmetic Lie–Cartan theory

Motivated by the search of a concept of linearity in the theory of arithmetic differential equations (Buium in Arithmetic differential equations. Math. surveys and monographs, vol 118. American Mathematical Society, Providence, 2005), we introduce here an arithmetic analogue of Lie algebras, of Chern connections, and of Maurer–Cartan connections. Our arithmetic analogues of Chern connections are certain remarkable lifts of Frobenius on the p-adic completion of \(GL_n\) which are uniquely determined by certain compatibilities with the “outer” involutions defined by symmetric (respectively, antisymmetric) matrices. The Christoffel symbols of our arithmetic Chern connections will involve a matrix analogue of the Legendre symbol. The analogues of Maurer–Cartan connections can then be viewed as families of “linear” flows attached to each of our Chern connections. We will also investigate the compatibility of lifts of Frobenius with the inner automorphisms of \(GL_n\); in particular, we will prove the existence and uniqueness of certain arithmetic analogues of “isospectral flows” on the space of matrices.     

Arithmetic differential equations on $$GL_n$$, III Galois groups

Differential equations have arithmetic analogues (Buium in Arithmetic differential equations, Mathematical Surveys and Monographs, vol 118. American Mathematical Society, Providence 2005) in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations, and the present paper is concerned with the “linear” ones. The equations themselves were introduced in a previous paper (Buium and Dupuy, in Arithmetic differential equations on \(GL_{n}\), II: arithmetic Lie–Cartan theory, arXiv:1308.0744). In the present paper we deal with the solutions of these equations as well as with the Galois groups attached to the solutions.     

Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

^** Email: todor{at}math.ethz.ch^*** Corresponding author. Email: schwab{at}math.ethz.ch A scalar, elliptic boundary-value problem in divergence formwith stochastic diffusion coefficient a(x, ) in a bounded domainD ^d is reformulated as a deterministic, infinite-dimensional,parametric problem by separation of deterministic (x D) andstochastic ( ) variables in a(x, ) via Karhúnen–Loèveor Legendre expansions of the diffusion coefficient. Deterministic,approximate solvers are obtained by projection of this probleminto a product probability space of finite dimension M and sparsediscretizations of the resulting M-dimensional parametric problem.Both Galerkin and collocation approximations are considered.Under regularity assumptions on the fluctuation of a(x, ) inthe deterministic variable x, the convergence rate of the deterministicsolution algorithm is analysed in terms of the number N of deterministicproblems to be solved as both the chaos dimension M and themultiresolution level of the sparse discretization resp. thepolynomial degree of the chaos expansion increase simultaneously.     

The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit

We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term in the asymptotic formula of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.In memory of Walter Philipp     

Asymptotic behaviour of families of real curves

We consider the family of fibres of a polynomial function f on a smooth noncompact algebraic real surface and we characterise the regular fibres of f which are atypical due to their asymptotic behaviour at infinity. We compare to the similar problem in the complex case. Received: 5 May 1998 / Revised version: 20 March 1999     

Bioglass thin films for biomimetic implants

Pulsed laser deposition (PLD) method was used to obtain bioglass (BG) thin film coatings on titanium substrates. An UV excimer laser KrF* (λ = 248 nm, τ = 25 ns) was used for the multi-pulse irradiation of the BG targets with 57 or 61 wt.% SiO₂ content (and Na₂O-K₂O-CaO-MgO-P₂O₅ oxides). The depositions were performed in oxygen atmosphere at 13 Pa and for substrates temperature of 400 °C. The PLD films displayed typical BG of 2-5 μm particulates nucleated on the film surface or embedded in. The PLD films stoichiometry was found to be the same as the targets. XRD spectra have shown, the glass coatings obtained, had an amorphous structure. One set of samples, deposited in the same conditions, were dipped in simulated body fluids (SBFs) and subsequently extracted one by one after several time intervals 1, 3, 7, 14 and 21 days. After washing in deionized water and drying, the surface morphology of the samples and theirs composition were investigated by scanning electron microscopy (SEM), X-ray diffraction (XRD), IR spectroscopy (FTIR) and energy dispersive X-ray analysis (EDX). After 3-7 days the Si content substantially decreases in the coatings and PO₄³⁻ maxima start to increase in FTIR spectra. The XRD spectra also confirm this evolution. After 14-21 days the XRD peaks show a crystallized fraction of the carbonated hydroxyapatite (HAP). The SEM micrographs show also significant changes of the films surface morphology. The coalescence of the BG droplets can be seen. The dissolution and growth processes could be assigned to the ionic exchange between BG and SBFs.     

Enhanced quantum well infrared photodetector focal plane arrays for space applications

A 30 months European Space Agency project started in March 2008, whose overall purpose is to expand and assess the performance of broadband (11–15 μm) quantum detectors for spectro-imaging applications: Dispersive Spectrometers and Fourier Transform Spectrometers. We present here the technical requirements, the development approach chosen as well as preliminary experimental results. Our approach is fully compatible with the final array format (1024 × 256, pitch 50–60 μm). We expect the requested uniformity, operability and SNR levels to be achieved at temperatures close to the goal values. The performance level will be demonstrated on 256 × 256, 50 μm pitch arrays. Also, operability and uniformity issues will be addressed on large mechanical 1024 × 256 hybrid arrays.