Hardy-Hilbert不等式与Mulholland不等式的一个联系

本文引入单参数λ,利用β函数,建立Hardy-Hilbert不等式与Mulholland不等式的一个具有最佳常数因子的联系式．作为应用,给出它的等价形式及一些特殊结果．     

Inelastic partial cross sections for scattering of HF by neon

An analytic expression of the potential energy surface (PES) of the ground state of the Ne-HF complex is obtained by utilizing nonlinear least square method to fit the intermolecular interaction energies [Zhang Y. Guizhou Science, 2003, 21(3): 9–13 (in Chinese)], which have been computed using the augmented correlation-consistent polarized quadruple zeta basis set aug-cc-pVQZ at the theoretical level of CCSD (T). On the basis of the PES, the partial cross sections (PCSs) at the incident energies of 60, 75, 100 and 150 meV for collisions between Ne atoms and HF molecules are calculated using the quantum close coupling approach. The effects of the long-range attractive and the short-range anisotropic interactions on the inelastic PCSs are discussed in detail. The results show: (1) The long-range attractive well of the EPS makes the significant contribution to the lower excitation PCSs, especially the tail maximum for j = 0→j′ = 1 transitions, whereas no contribution is to the j′⩾3 inelastic transitions. (2) The short-range (the repulsive and attractive) interaction makes the significant contribution to the lower excitation PCSs, especially the main peak for j = 0→j′ = 1, 2. As for the transitions of j′⩾3, the short-range interaction plays a key role in the inelastic excitation. (3) Although the positions of the maximums and minimums of the inelastic PCSs are different at the collision energies, they correspond to almost the same impact parameter. Supported by the National Natural Science Foundation of China (Grant Nos. 10676025 and 10574096)     

Existence of solutions for a nonlinear system with a parameter

In this paper, the existence of solutions for a system of nonlinear equations is considered. n² nonzero real solutions are obtained by using the critical point theory. Additionally, the Dirichlet boundary value problems of even order difference equations and partial difference equations are investigated.     

Evaluation of natural recharge of Chingshui geothermal reservoir using tritium as a tracer

Naturally existing tritium in groundwater was applied as a tracer to evaluate the natural recharge of the Chingshui geothermal reservoir. The residence time (or, age) of Chingshui geothermal water was first determined with tritium data at 15.2 and 11.3 year using the plug flow and dispersive model, respectively. The annual natural recharge was then estimated by combining the use of the residence time and the fluid-in-place of the Chingshui geothermal reservoir. The natural recharge for Chingshui geothermal reservoir was estimated at 5.0 × 10⁵ and 6.7 × 10⁵ m³ year^?1 using the plug flow and dispersive model, respectively. Chingshui geothermal water is largely from a fractured zone in the Jentse Member of the Miocene Lushan Formation. The dispersive model more adequately represents the fracture flow system than the simple plug flow model.     

The attractor of the dissipative coupled fractional Schrödinger equations

In the present paper, we consider the dissipative coupled fractional Schrödinger equations. The global well‐posedness by the contraction mapping principle is obtained. We study the long time behavior of solutions for the Cauchy problem. We prove the existence of global attractor. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of particle size on the photochromic response of PWA/SiO2 nanocomposite

A series of photochromic phosphotungstic acid (PWA)/SiO₂ composites were synthesized using the sol-gel method. Depending on the feeding schedule of PWA during synthesis, the size of the formed PWA/SiO₂ particles varied considerably from as small as 1.2 nm to ca. 10 nm. With decreasing silica particle size, the total contact area/interaction between SiO₂ and PWA increases, as revealed by FT-IR and solid-state ²⁹Si-NMR analyses. Particularly, when the size of PWA/SiO₂ is ~1 nm, crystallization of PWA is inhibited, and PWA presents as amorphous molecular entities distributing uniformly in the SiO₂ host, which is in evidence in the XRD spectroscopy and HR-TEM imaging. In contrast, substantial crystallization of PWA takes place when PWA/SiO₂ particles are as large as 10 nm, in which case less amount of surface free Si-OH is available for PWA to make bonds with. Photochromism occurs activated by ultraviolet light irradiation. The rate of coloration/bleaching is found to depend strongly on the particle size of PWA/SiO₂; specifically, the rate increases twice when the particle size is reduced from 10 nm to 1.2 nm.     

Crystal growth,spectroscopic characterization and laser performance of Nd:Lu<Subscript>0.33</Subscript>Y<Subscript>0.36</Subscript>Gd<Subscript>0.3</Subscript>VO<Subscript>4</Subscript> crystal

A new three-matrix mixed vanadate crystal Nd:Lu_0.33Y_0.36Gd_0.3VO₄ (Nd:LuYGdVO₄) crystal was grown by the Czochralski method. Room temperature absorption and fluorescence spectra of the Nd:LuYGdVO₄ crystals were measured and the spectroscopic parameters were calculated by the Judd-Ofelt theory. The intensity parameters of the Nd:LuYGdVO₄ crystal were Ω₂ = 9.736 × 10⁻²⁰ cm², Ω₄ = 4.179 × 10⁻²⁰ cm², Ω₆ = 8.020 × 10⁻²⁰ cm² and the stimulate emission cross section was 5.3 × 10⁻¹⁹ cm². Diodepumped actively Q-switched and passively Q-switched Nd:LuYGdVO₄ and Nd:Lu_0.14Y_0.86VO₄ lasers at 1.06 μm were demonstrated. The results indicate that, for both actively and passively Q-switched lasers, the Nd:LuYGdVO₄ lasers can generate shorter pulse width with higher peak power than the Nd:Lu_0.14Y_0.86VO₄ lasers at the same cavity conditions.     

Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers

We propose and experimentally demonstrate a novel subwavelength grating coupler on silicon-on-insulator, for coupling to optical fibers with a wide optical bandwidth. Theoretical analysis and design optimization of the coupler are described. About 73?nm 1?dB bandwidth was experimentally demonstrated with -5.6 dB coupling efficiency. Better than -3.4 dB efficiency with 86?nm 1?dB bandwidth is predicted for these structures with optimized buried oxide thickness.