Normal Vietoris Implies Compactness: A Short Proof

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.     

On the evaluation of the nonisothermal kinetic parameters of (GeS2)0.3(Sb2S3)0.7 crystallization using the IKP method

The isoconversional method suggested by Friedman and the invariant kinetic parameters method (IKP) were used in order to examine the kinetics of the nonisothermal crystallization of (GeS₂)_0.3(Sb₂S₃)_0.7. The objective of the paper is to show the usefulness of the IKP method both for determining the activation parameters as well as the model of the investigated process. It was shown that the kinetic triplet [(E, A, f(α), where E is the activation energy, A is the preexponential factor, and f(α) is the differential function of conversion], which results through the application of the IKP method, depends on the set of kinetic models considered. For different sets of kinetic models, proportional values of f(α) are obtained. A criterion for the selection of this set, the use of which lead to the true kinetic triplet corresponding to the analyzed process (E = 163.2 kJ mol^?1; A = 2.47 × 10¹² min^?1 and the Avrami‐Erofeev model, A_m, for m = 2.5–2.6 was suggested. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 309–315, 2004     

Wave processes in media with hysteretic nonlinearity: Part 2

Nonlinear processes caused by the propagation of low-frequency and high-frequency acoustic pulses in an unbounded medium and the propagation of continuous waves in a ring resonator are theoretically studied on the basis of two hysteretic equations of state for media with imperfect elasticity. The profiles and parameters of pulses, the resonance curve and the Q factor of the resonator, and the ratio of the nonlinear resonance frequency shift to the nonlinear damping decrement are determined. For nonlinear wave processes in such media, the distinctive features that allow one to choose an appropriate hysteretic equation of state for analytically describing the experimental data are revealed.     

Bounded imaginary powers of differential operators on manifolds with conical singularities

 We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L _p -spaces over B, 1<p<∞. Under suitable ellipticity assumptions we can define a family of complex powers A ^z , zℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations. Received: 12 June 2001; in final form: 3 June 2002 / Published online: 1 April 2003 Mathematics Subject Classification (2000): 35J70, 47A10, 35K57     

Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations

We discuss the calculation of homotopy indices on closed convex sets in a Banach space and then use these ideas to prove the existence of multiple solutions of nonlinear elliptic equations. We obtain more information on the solutions than in earlier work. A key idea is to calculate the homotopy index of the stable and mountain pass solutions and the connections joining them. Dedicated to the memory of Jean Leray     

Stark structure of the Yb3+ ion levels in (YbxY1?x)2Ti2O7 and the crystal field in rare-earth titanates with a pyrochlore structure

The absorption spectra of Yb₂Ti₂O₇ single crystals and the luminescence and luminescence excitation spectra of Y₂Ti₂O₇: Yb (1%) polycrystals were studied in the temperature range 4.2–300 K. The spectra were analyzed in terms of the crystal-field theory and the exchange-charge model. Based on the set of crystal-field parameters found for Yb₂Ti₂O₇, analogous sets of parameters were determined for other rare-earth titanates and proved to be in reasonable agreement with all available experimental data. __________ Translated from Fizika Tverdogo Tela, Vol. 47, No. 8, 2005, pp. 1376–1380. Original Russian Text Copyright ? 2005 by Klimin, Popova, Chukalina, Malkin, Zakirov, Antic-Fidancev, Goldner, Aschehoug, Dhalenne.     

An aqueous route to organically functionalized silica diatom skeletons

Diatomaceous earth was functionalized by grafting organotrialkoxysilane precursors onto the surface of the porous silica cell walls of this biomineral. Vinyl- and mercapto-containing structures were prepared in aqueous media without disruption of the diatomic architecture. Successful grafting of the organic moieties was confirmed using solid state ²⁹Si MAS NMR spectroscopy, and the presence of the intact diatom framework by scanning electron microscopy. The sorption properties of mercaptopropyl-functionalized diatoms towards heavy metals was studied by measuring the accessibility and diffusion rates of mercury(II) species to the binding sites (-SH) by the means of electrochemical methods.     

Reactivity of a Ti–45.9Al–8Nb alloy in air at 700–900°C

A Ti–45.9Al–8Nb (at%) alloy with a lamellar structure (γ+α₂) was oxidised in air at 700, 800, 850 and 900°C in isothermal and thermal cycling conditions. The reaction progress was followed by thermogravimetric measurements. In isothermal conditions the oxidation kinetics followed approximately a parabolic rate law and the rate constants ranged from about 10^–12 kg² m^–4 s^–1 at 700°C to 10^–10 kg² m^–4 s^–1 at 900°C. The oxide scales were built of Al₂O₃ and TiO₂, the former being the main component of the outermost layer. The oxidation behaviour of Ti–45.9Al–8Nb was referred to a commercial titanium alloy, WT4 (Ti–6Al–1Mn), and selected oxidation-resistant alloys.