Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001     

On a bifurcation governed by hysteresis nonlinearity

We consider autonomous systems with a nonlinear part depending on a parameter and study Hopf bifurcations at infinity. The nonlinear part consists of the nonlinear functional term and the Prandtl--Ishlinskii hysteresis term. The linear part of the system has a special form such that the close-loop system can be considered as a hysteresis perturbation of a quasilinear Hamiltonian system. The Hamiltonian system has a continuum of arbitrarily large cycles for each value of the parameter. We present sufficient conditions for the existence of bifurcation points for the non-Hamiltonian system with hysteresis. These bifurcation points are determined by simple characteristics of the hysteresis nonlinearity.     

Synthesis and characterisation of cadmium titanium oxide thin films by sol-gel technique

Crack free, dense and transparent CdTiO₃ thin films have been prepared by sol-gel technique using titanium butoxide and cadmium acetate. The formation of the CdTiO₃ phase started from 500°C annealing temperature onwards. The complete orthorhombic structure of CdTiO₃ was formed on Silicon (100) substrate at an annealing temperature of 600°C for 5 h. As the annealing temperature increased from 600 to 700°C, we have observed the cadmium silicate phase at the interface of Si and CdTiO₃ phase. Structural, morphological and elemental evolution of these CdTiO₃ thin films produced by sol-gel synthesis were characterised by grazing incidence X-ray diffraction (GIXRD), tapping mode atomic force microscopy (TMAFM), scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) respectively.     

C60激发三重态被哌嗪猝灭特性研究

本文使用激光诱导瞬态吸收光谱装置,研究了C60激发三重态在乙腈/甲苯混合溶剂中的光物理性质,得到了3C60的激发态寿命、自猝灭速率常数和时间分辩的瞬态吸收光谱.此外,实验中引入了哌嗪作为激发三重态猝灭剂.我们发现哌嗪能有效的猝灭3C60,猝灭速率常数kq接近扩散控制极限.改变混合溶剂的比例,相应的猝灭速率常数值也发生变化,即kq随混合溶剂极性的增加而增加,随溶剂粘度的增加而减小.稳态光解实验反映了反应物向产物转化过程中在紫外-可见波段吸收强度的变化.     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

Laser induced copper electroless plating on polyimide with Q-switch Nd:YAG laser

The results of laser induced deposition of copper on polyimide substrate from copper electrolyte solution are reported. Unlike most work reported in the literatures where CW Ar⁺ lasers were used, a second harmonic (532 nm wavelength) Q-switch Nd:YAG laser was used for our experiments. The deposition process was conducted by laser-catalyzing of the polyimide surface and subsequent photothermal-accelerated reduction of copper-complex ions in an alkaline reducing environment. The characteristics of the deposited copper line were investigated in terms of laser beam scanning speed, and the number of scans. The surface morphology and chemical composition of the deposited copper were analyzed using field emission scanning electron microscope (FESEM) and energy dispersive spectrometer (EDX). The optimum processing conditions have been identified. The copper deposit was found to adhere well to the substrate.     

In situ neutron diffraction study (300-1273 K) of non-stoichiometric strontium ferrite SrFeOx

The high-temperature cubic phase of non-stoichiometric strontium ferrite SrFeO_x (2.5≤x≤3.0) has been studied by in situ neutron powder diffraction in air over the temperature range 300-1273 K. The composition of SrFeO_x changes within the range 2.56≤x≤2.81 from 1273 to 673 K, respectively.Rietveld refinements of the diffraction patterns show that the high-temperature cubic phase of SrFeO_x is consistent with a face-centred Fm3c structure. This structure leads to agreement with previous density measurements. This cell allows the high-temperature structure of SrFeO_x to be described in terms of a solid solution of the composition end members. Cubic SrFeO_x at high temperature is found to closely obey Vegard's law. The density of cubic SrFeO_x is also found to exhibit a linear relationship with composition.     

Spatial design matrices and associated quadratic forms: structure and properties

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling intrinsically stationary and isotropic spatial processes. We give concise structural formulae for these matrices, and simple generating functions for them. The generating functions provide formulae for the cumulants of the quadratic forms of interest when the process is Gaussian, second-order stationary and isotropic. We use these to study the statistical properties of the associated quadratic forms, in particular those of the classical variogram estimator, under several assumptions about the actual variogram.     

Vibrational dynamics of fullerene molecules adsorbed on metal surfaces studied with synchrotron infrared radiation

Infrared (IR) spectroscopy of chemisorbed C₆₀ on Ag (111), Au (110) and Cu (100) reveals that a non-IR-active mode becomes active upon adsorption, and that its frequency shifts proportionally with the charge transferred from the metal to the molecule by about 5 cm^-1 per electron. The temperature dependence of the frequency and the width of this IR feature have also been followed for C₆₀/Cu (100) and were found to agree well with a weak anharmonic coupling (dephasing) to a low-frequency mode, which we suggest to be the frustrated translational mode of the adsorbed molecules. Additionally, the adsorption is accompanied by a broadband reflectance change, which is interpreted as due to the scattering of conduction electrons of the metal surface by the adsorbate. The reflectance change allows determination of the friction coefficient of the C₆₀ molecules, which results in rather small values (∼2×10⁹ s^-1 for Ag and Au, and ∼1.6×10⁹ s^-1for Cu), consistent with a marked metallic character of the adsorbed molecules. Pre-dosing of alkali atoms onto the metal substrates drastically changes the IR spectra recorded during subsequent C₆₀ deposition: anti-absorption bands, as well as an increase of the broadband reflectance, occur and are interpreted as due to strong electron–phonon coupling with induced surface states. Received: 6 June 2001 / Accepted: 23 October 2001 / Published online: 3 April 2002