Hill-Type Formula and Krein-Type Trace Formula for Hamiltonian Systems

In this paper, we give a survey on the Hill-type formula and its applications.Moreover, we generalize the Hill-type formula for linear Hamiltonian systems and Sturm-Liouville systems with any self-adjoint boundary conditions, which include the standard Neumann, Dirichlet and periodic boundary conditions. The Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions. Further, based on the Hill-type formula, we derive the Krein-type trace formula. As applications, we give nontrivial estimations for the eigenvalue problem and the relative Morse index.     

New discrimination method combining hit quality index based spectral matching and voting

A new discrimination method, called hit quality index (HQI)-voting, that uses the HQI for discriminant analysis has been developed. HQI indicates the degree of spectral matching between two spectra as known. In this method, a library sample yielding the highest HQI value for an unknown sample was initially searched and a group containing this sample was chosen as the group for the unknown sample. When overall spectral features of two groups are quite close to each other, many library samples with similar HQI values could be available for an unknown sample. In this situation, the simultaneous consideration of multiple votes (several library samples with close HQI values) for final decision would be more robust. In order to evaluate the discrimination performance of HQI-voting, three different near-infrared (NIR) spectroscopic datasets composed of two sample groups were used: (1) domestic and imported sesame samples, (2) domestic and imported Angelica gigas samples, and (3) diesel and light gas oil (LGO) samples. For the purpose of comparison, principal component analysis–linear discriminant analysis (PCA–LDA), partial least squares–discriminant analysis (PLS–DA) as well as k-nearest neighbor (k-NN) were also performed using the same datasets and the resulting accuracies were compared. The discrimination performances improved with the use of HQI-voting in comparison with those resulted from PCA–LDA and PLS–DA. The overall results support that HQI-voting is a comparable discrimination method to that of existing factor-based multivariate methods.     

Magnetically Enhanced 15 kHz Glow Discharge of Methane

This work deals with the luminous chemical vapour deposition (plasma polymerization) of hydrocarbon polymeric thin films in a magnetic field enhanced discharge of methane. The films were deposited on 4″ <111> single crystal silicon substrates. We investigated the influence of the different glow discharge parameters (e.g. pressure, flow rate, power input, etc.) on the deposition rate of methane and the refractive index of the resulting polymeric films, as well as the distribution of these parameters across the wafer. We used a Shinko Seiki Plasma Polymerization equipment with a bell jar reactor comprising two electrodes connected to a symmetric AC power supply of 15 kHz. Two magnetrons were formed by placing two circular shaped concentric magnetic poles behind each electrode. The substrates were attached on both sides of a rotating wheel held at a floating potential in the middle of the two electrodes. This equipment allowed us to vary a single parameter and keep the other parameters constant over the whole process. We measured the thickness and the refractive index and their distribution over the wafer. The effect of the system pressure, decoupled from the effect of flow rate, is explained by the characteristic nature of luminous gas phase and by the polymerization/deposition mechanism of luminous chemical vapour deposition.     

电离层与卫星通信

利用电子流体动力学方程和麦克斯韦方程组推导了等离子体的特征频率、折射率，并讨论了电磁波在等离子体中传播的基本条件，从而得出了卫星通信的基本电磁学条件．     

Desorption induced by hot electrons: wave packet calculation of CO on Cu surfaces

A quantum mechanical photodesorption model, valid for metallic substrates and sub-picosecond laser pulses, is presented. It takes into consideration the photodesorption coordinate and models the metal hot-electron mediated desorption by a three electronic states: an ionic state of the adsorbate and two effective states representing the continuum of the metal. This multiple-state picture allows the sharing of the flow of energy injected by the laser between the adsorbate and the substrate. For the first time, the present modeling introduces the hot electrons of the metal through an optical potential based on the kinetic model developed earlier by the authors. This potential, and the resulting desorption yield, depend on the laser fluence. For CO on Cu(1 0 0) or Cu(1 1 1), the results are in fair agreement with the experimental findings.     

利用全反射原理测定水的折射率

介绍一种利用全反射原理测定水的折射率的方法。实验中利用He-Ne激光束在水底产生点光源,根据全反射原理对水底的暗影和水深进行测量,求出水的折射率。     

Optical functions of InGaP/GaAs epitaxial layers from 0.01 to 5.5 eV

In_0.49Ga_0.51P films, both undoped and doped n- and p-type (up to 10¹⁸ cm^-3), were grown lattice matched on GaAs substrates, with different miscut angles, by Metal-Organic Vapour Phase Epitaxy (MOVPE) at different temperatures. The shift of the fundamental gap E₀, caused by “ordering effect” was measured as a function of temperature by photoluminescence. The complex refractive index = n + ik and the dielectric function = ɛ ₁ + iɛ ₂ at room temperature were determined from 0.01 to 5.5 eV by using complementary data from fast-Fourier-transform far-infrared (FFT-FIR), dispersive, and ellipsometric spectroscopies. The effect of the native oxide was accounted for and the self-consistency of the optical functions was checked in the framework of the Kramers-Kronig causality relations. In the restrahlen region the dielectric function was well fitted by classical Lorentz oscillators; in the transparent region below E₀, the refractive index was modelled by a Sellmeier dispersion relation; in the interband region the dielectric function was well reproduced by analytical lineshapes associated to seven critical points. Thus parametrized analytical expressions were obtained for the optical functions all over the spectral range, without discontinuities, to be used in the modelling and characterization of multi-layer structures, also on opaque substrates. Received 13 December 2001 Published online 25 June 2002     

Effect of concentration and particle size on nonlinearity of Au nano-fluid prepared by γ (Co) radiation

Nonlinear properties of Au nano-fluid prepared by γ-radiation method at different concentrations were investigated. Measurements of nonlinear refractive index and nonlinear absorption coefficient were carried out using a single beam Z-scan technique. A green CW laser beam operated at 532 nm was used as excitation source. The Au nano-fluid shows a good third order nonlinear response. The sign of the nonlinear refractive index is found to be negative and the magnitude is in the order of 10⁻⁷ cm²/W. This nonlinear effect increases as the concentration increases from 3.119 × 10⁻⁴ to 2.354 × 10⁻³ M which correspond to particle sizes of 4.0-30.5 nm, respectively. A good linear relationship was obtained between nonlinear refractive index and concentration. However the relationship between nonlinear refractive index and particle size was nonlinear behavior.     

Pd deposits on Ni(111): a theoretical study

The ASED-MO method has been used to gather electronic and energetic information on Pd deposits on Ni(111) and Pd atom inclusion in the first Ni layer since these model catalysts exhibit a striking catalytic efficiency towards butadiene hydrogenation. The electronic structure of Pd atoms is strongly altered compared with pure Pd. A Pd(4d)→Pd(5s) electronic transfer occurs in the case of the deposit when a slight similar transfer and a charge transfer from Pd to surrounding Ni takes place in the case of the inclusion. Those results are consistent with XPS experimental data. A low density of states, near the Fermi level, is also observed. The optimal geometrical situation for Pd deposits is found to be 2D-aggregates (in pseudoepitaxy or pseudomorphy with the underlying Ni surface, depending on the aggregate size). Small aggregates (part of the first Ni layer) are found to be the most stable in the case of a Pd inclusion in the Ni with a Pd---Pd distance of 2.64 Å, in agreement with available EXAFS experimental data.