紧支撑Gabor框架的稳定性

1引言自Duffin和Schaeffer提出了框架理论以来,框架理论在数学和信息科学等领域占有非常重要的地位,在小波分析和时频分析中起着举足轻重的作用.现在Gabor框架系统被广泛地应用在信息论,量子力学,信号处理和图象处理等方面.Gabor框架的稳定性是应用中所需要的,同时也是人们关心的问题.但是,一直以来对Gabor框架的稳定性的研究主要集中在L~2(R)上,即使在L~2(R~d)上的研究也主要针对单项指标扰动进行了研究.本文借助于文[2]中的定理3和定理4,文[3]中的定理2和文[5]中的定理2.1,分别对L~2(R~d)上紧支撑Gabor框架的窗函数、平移指标、旋转指标以及多项混合扰动的稳定性进行了讨论.     

Water-dispersible hydroxyapatite nanorods synthesized by a facile method

A simple and effective method, using calcium nitrate and triammonium phosphate as starting materials, for the preparation of water-dispersible hydroxyapatite nanorods (HAp) was reported. The process primarily involves the preparation of HAp with the addition of sodium citrate (NaC) and the exchange of absorbed ions (NaC) with sodium hexame taphosphate (NaP). The end products were investigated using various means in order to confirm the particles’ crystal phase and morphology and to understand how to improve their stability. The results demonstrate that the resulting HAp at 90 °C is rod-like with length of 300-400 nm and width of 40-60 nm. The zeta potential values of pure HAp, HAp-NaC, HAp-NaC/NaP are from −15.20, −30.89 to −44.84 mV. The settling time test shows the HAp-NaC/NaP could keep stable above 7 months without any creaming or visible sedimentation. The amount of NaC and the reaction temperature play significant roles in the whole process due to the formation of Ca containing precipitates.     

Periodic orbits around the collinear libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure

Periodic orbits belonging to the stromgren families A, B and C around the collinear libration points in the restricted three body problem have been studied when the smaller primary is a triaxial rigid body and more massive body is a source of radiation pressure. These families are determined in three different cases: (i) classical case, (ii) when bigger primary is a source of radiation pressure, (iii) when smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure. The Liapunov stability of each periodic solution has also been examined.      

Synthesis of PrBa2Cu4O8 by Solution Method under Ambient Oxygen Pressure

A highly homogeneous and nearly monophasic PrBa₂Cu₄O₈ compound has been synthesized at 1 atm of oxygen via a route employing polymeric ethylenediamine/citric acid precursors. The PrBa₂Cu₄O₈ compound with a trace amount of BaCuO₂ was synthesized for the first time by sintering the pellets at the temperature of 875 °C under ambient oxygen pressure. The temperature coefficient of the resistivity is positive below 190 K while above 190 K is negative. The superconducting transition was not detected down to 4.2 K. Samples were characterized by X-ray diffraction, scanning electron microscopy, thermal analysis, and transport and magnetic measurements.     

A study on stress intensity factors and singular stress fields of three-dimensional interface crack

By using the finite-part integral concepts and limit technique, the hypersingular integrodifferential equations of three-dimensional (3D) planar interface crack were obtained; then the dominant-part analysis of 2D hypersingular integral was further used to investigate the stress fields near the crack front theoretically, and the accurate formulae were obtained for the singular stress fields and the complex stress intensity factors. After that, a numerical method is proposed to solve the hypersingular integrodifferential equations of 3D planar interface crack, and the problem of elliptical planar crack is then considered to show the application of the method. The numerical results obtained are satisfactory. Project supported by the Foundation of Solid Mechanics Open Research Laboratory of State Education Commission at Tongji University and the National Natural Science Foundation.     

THE STABILITY OF LINEAR MULTISTEP METHODS FOR LINEAR SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS

1. IntroductionFor a large class of electrical ~ks containing IOssless transmission lines the describingequations can be reduced to a system of neutral differential equations.This paper deals with the numerical solution of initial value problems for syste…     

Thermal Decomposition of Triazine Herbicides. I. 1,2-(4-chloro-6-ethylamino-1,3,5-triazin-2-ylamino)-2-methylpropionitrile (cyanazine)

Cyanazine was taken as an example for investigations under the influence of different conditions on thermal decomposition of triazine herbicides. DSC measurements were carried out under atmospheric pressure and hermetically closed, under pressure 1.3 kPa. The influence of the pressure on the constant reaction rate of decomposition of cyanazine was discussed. It was also proved that the predicted reaction constant rates from isothermal and non-isothermal measurements are consistent. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium

In this paper, the temporal development of small disturbances in a pressure‐driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth‐order eigenvalue problem, which reduces to the well‐known Orr–Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The critical Reynolds number Re_c, the critical wave number α_c, and the critical wave speed c_c are obtained for a wide range of the porous medium shape factor parameter S. It is found that a decrease in porous medium permeability has a stabilizing effect on the fluid flow. Copyright © 2008 John Wiley & Sons, Ltd.     

Surface electronic properties of sulfur-treated GaAs determined by surface photovoltage measurement and its computer simulation

The Kelvin method together with the simulations of surface photovoltage has been used to determine the surface electronic properties, i.e. the surface band bending (qV_S), surface state density (N_SS0) and surface fixed charge (Q_Fx) of S₂Cl₂-treated GaAs (100) surfaces. The measured values of surface photovoltage (SPV) do not show saturation at high photon flux densities in contradiction to the simple theory of SPV. This behavior of SPV agrees very well with the rigorous computer simulations and can be explained in terms of the Dember effect. Moreover, the SPV values become insensitive to surface states at moderate photon flux densities. On this basis, the surface band bending of untreated (0.79 eV) and S₂Cl₂-treated (0.60 eV) GaAs surfaces was determined. The band diagrams summarizing the obtained results proved the influence on the potential variations not only from the ionized surface states and surface fixed charge but also from the surface dipole layer on the S₂Cl₂-treated GaAs surface. The dipole arises most probably due to the S-Ga bonding on the surface. The presented results offer an alternative explanation for increased PL commonly observed after the sulfidation in the absence of substantial reduction in the band bending.     

偏二甲肼渗透管标准物质的制备及其均匀性稳定性研究

以精馏和光解纯化工艺获得的高纯偏二甲肼为原料,制备了渗透率范围为0.5-30μg/min的偏二甲肼渗透管标准物质.经过均匀性、稳定性检验,结果表明:该标准物质均匀性、稳定性良好,为航天作业环境中各类快速检测仪的监控准确性提供了判定依据.