Scaling by Binormalization

We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices.     

Flame Temperature Effect on the Structure of SiC Nanoparticles Grown by Laser Pyrolysis

Small SiC nanoparticles (10 nm diameter) have been grown in a flow reactor by CO₂ laser pyrolysis from a C₂H₂ and SiH₄ mixture. The laser radiation is strongly absorbed by SiH₄ vibration. The energy is transferred to the reactive medium and leads to the dissociation of molecules and the subsequent growth of the nanoparticles. The reaction happens with a flame. The purpose of the experiments reported in this paper is to limit the size of the growing particles to the nanometric scale for which specific properties are expected to appear. Therefore the effects of experimental parameters on the structure and chemical composition of nanoparticles have been investigated. For a given reactive mixture and gas velocity, the flame temperature is governed by the laser power. In this study, the temperature was varied from 875°C to 1100°C. The chemical analysis of the products indicate that their composition is a function of the temperature. For the same C/Si atomic ratio in the gaseous phase, the C/Si ratio in the powder increases from 0.7 at 875°C up to 1.02 at 1100°C, indicating a growth mechanism limited by C₂H₂ dissociation. As expected, X-ray diffraction has shown an improved crystallisation with increasing temperature. Transmission electron microscopy observations have revealed the formation of 10 nm grains for all values of laser power (or flame temperature). These grains appear amorphous at low temperature, whereas they contain an increasing number of nanocrystals (2 nm diameter) when the temperature increases. These results pave the way to a better control of the structure and chemical composition of laser synthesised SiC nanoparticles in the 10 nm range.     

Interactions of surface states of copper with transition metals and cesium

The pseudopotential augmented-plane-wave method was used to study the surface structure of thin copper films with monolayers of Co, Ni, and Cs. Local densities of electron states, distributions of charge densities in the layers, and electron energy spectra are analyzed. The effect of adsorbates on the electronic properties of the Cu(001) surface and work function are discussed. Satisfactory agreement with available experimental data has been obtained.     

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.     

Collisional Relaxation of Luminescence Anisotropy in Rarefied Gases in the Condensed Phase

The orientational relaxation of optically induced anisotropy in rarefied gases and at a damped rotation has been investigated. It has been found that the anisotropy relaxation in rarefied gases is described by a reduced kinetic equation depending only on free rotation integrals. The behavior of the integral anisotropy of luminescence for free symmetric and asymmetric top molecules has been elucidated. The law of luminescence depolarization has been obtained for asymmetric top molecules in the Gordon J-diffusion model. It represents the sum of two Stern–Volmer-type dependences, whose relative contribution is determined by the orientation of the dipole moments of transitions with absorption and emission of light in the molecular coordinate system and by the principal moments of inertia of the molecular top. It has been established that in the limit of a strongly damped rotation, kinetic equations of the general form reduce to equations of rotational diffusion. A number of modified diffusion equations correctly describing the contribution of inertial effects to the orientational relaxation of anisotropy have been obtained.     

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     

A new algorithm for fixed design regression and denoising

In this paper, we present a new algorithm to estimate a regression function in a fixed design regression model, by piecewise (standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty term is chosen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising and of compression.