A Class of Trees and its Wiener Index

In this paper, we will consider the Wiener index for a class of trees that is connected to partitions of integers. Our main theorem is the fact that every integer is the Wiener index of a member of this class. As a consequence, this proves a conjecture of Lepović and Gutman. The paper also contains extremal and average results on the Wiener index of the studied class.This work was supported by Austrian Science Fund project no. S-8307-MAT.     

Effect of isomorphic atom substitution on the refractive index and oscillator parameters of TlInS2xSe2(1‐x) (0.25 ≤ x ≤ 1) layered mixed crystals

The optical properties of TlInS_2xSe_2(1‐x)mixed crystals (0.25 ≤ x ≤ 1) have been studied at room temperature through the transmittance and reflectivity measurements in the wavelength range of 400–1100 nm. The spectral dependence of the refractive index for all compositions of studied crystals were obtained. The dispersion of the refractive index is discussed in terms of the Wemple–DiDomenico single‐effective‐oscillator model. The compositional dependencies of refractive index dispersion parameters: oscillator energy, dispersion energy and zero‐frequency refractive index were revealed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lefschetz fixed point formula for symplectomorphisms

Consider a compact Kähler manifold endowed with a prequantum bundle. Following the geometric quantization scheme, the associated quantum spaces are the spaces of holomorphic sections of the tensor powers of the prequantum bundle. In this paper we construct an asymptotic representation of the prequantum bundle automorphism group in these quantum spaces. We estimate the characters of these representations under some transversality assumption. The formula obtained generalizes in some sense the Lefschetz fixed point formula for the automorphisms of the prequantum bundle preserving its holomorphic structure. Our results will be applied in two forthcoming papers to the quantum representation of the mapping class group.     

Theoretical studies on the optical absorption coefficients and refractive index changes in parabolic quantum dots in the presence of electric and magnetic fields

The optical absorption coefficients and the changes in the refractive index in GaAs/AlGaAs parabolic quantum dots(QDs) with applied electric and magnetic fields are studied in detail. Analytical expressions for the linear and nonlinear intersubband absorption coefficients and refractive index changes are obtained by using a compact density matrix approach and an iterative procedure. Finally, the calculated results show the incident optical intensity, the frequencies of the confined potential of the QDs and the applied electric and magnetic fields have a great influence on the optical absorption coefficients and refractive index changes in this system.     

Effect of magnetic fields on the linear and nonlinear intersubband optical absorption coefficients and refractive index changes in square and graded quantum wells

In this study, both the intersubband optical absorption coefficients and the refractive index changes as dependent on the magnetic field are calculated in square and graded quantum wells. Our results show that the position and the magnitude of the linear and total absorption coefficients and refractive index changes depend on the magnetic field strength and the shape of potential. The incident optical intensity has a great effect on the total absorption and refractive index changes.     

硝酸酯热分解的机理分析

使用加速量热仪研究硝酸正丙酯（NPN）、硝酸异丙酯（IPN）和硝酸异辛酯（EHN）的热分解过程。分析了在绝热条件下热分解反应动力学, 根据实验数据计算出表观活化能、指前因子和反应热等参数。根据NPN、IPN和EHN热分解的起始温度和反应热数据,给出了三种硝酸酯在75℃时的反应风险指数,分析得到三种物质的热失稳风险度。分别在B3LYP/6-31+G(2df,2p)和B3P86/6-31+G(2df,2p)的理论水平下,计算得到NPN、IPN和EHN的O-NO2键离解能(BDE)。由NPN、IPN和EHN的O-NO2键离解能在很大程度上符合由加速量热仪测试得到的活化能,推知三种硝酸酯的热分解反应只是单分子O-NO2键的均裂反应。     

High-resolution liquid refractive-index sensor using reflective arrayed-waveguide grating

A high-resolution sensor for measuring the refractive index of liquids using a reflective arrayed-waveguide grating (AWG) is proposed. The refractive index of a liquid placed in the groove of the arrayed region is measured via the shift of the maximum intensity in the imaging plane of the AWG owing to the phase change in the region. The refractive index can be monitored in real time by measuring the power ratio between two output waveguides of the AWG with a narrow-band source. A mathematical model based on Fourier optics and wave optics is established. A fitting formula for the relationship between the power ratio and the refractive index of liquid is derived. The results of the study show that the proposed method can eliminate the effects of instability of the light source and the inner loss of the system and provide a refractive index resolution of 10⁻⁷.     

Fabrication of long-period gratings with a mercury-arc lamp

Long-period gratings (LPGs) were fabricated in hydrogen-loaded standard single-mode fibers by use of a broadband UV mercury-arc lamp. Several kinds of LPGs with loss of ∼50% were fabricated in 40 min. With this technology, LPGs can be mass produced at very low cost.     

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.     

Electron beam evaporated LaF3 thin films prepared by different temperatures and deposition rates

LaF₃ thin films were prepared by electron beam evaporation with different temperatures and deposition rates. Microstructure properties including crystalline structure and surface roughness were investigated by X-ray diffraction (XRD) and optical profilograph. X-ray photoelectron spectroscopy (XPS) was employed to study the chemical composition of the films. Optical properties (transmittance and refractive index) and laser induce damage threshold (LIDT) at 355 nm of the films were also characterized. The effects of deposition rate and substrate temperature on microstructure, optical properties and LIDT of LaF₃ thin films were discussed, respectively.