Spectral methods for pantograph-type differential and integral equations with multiple delays

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.      

A combination of energy method and spectral analysis for study of equations of gas motion

There have been extensive studies on the large time behavior of solutions to systems on gas motions, such as the Navier-Stokes equations and the Boltzmann equation. Recently, an approach is introduced by combining the energy method and the spectral analysis to the study of the optimal rates of convergence to the asymptotic profiles. In this paper, we will first illustrate this method by using some simple model and then we will present some recent results on the Navier-Stokes equations and the Boltzmann equation. Precisely, we prove the stability of the non-trivial steady state for the Navier-Stokes equations with potential forces and also obtain the optimal rate of convergence of solutions toward the steady state. The same issue was also studied for the Boltzmann equation in the presence of the general time-space dependent forces. It is expected that this approach can also be applied to other dissipative systems in fluid dynamics and kinetic models such as the model system of radiating gas and the Vlasov-Poisson-Boltzmann system.      

胭脂红荧光光谱机理研究

胭脂红是食品添加剂中最常用的一种食用色素之一,国家标准对其在食品中添加的剂量有明确的规定,研究其荧光光谱特性具有一定的实际意义。文章分别从理论与实验上对220～400 nm不同激发波长下胭脂红标准溶液的荧光光谱进行了分析,结果表明,胭脂红可以产生较强的荧光,分别在420,530,635,687 nm波长处产生了4个荧光峰,各荧光峰的最佳激发波长也不尽相同,文章给出了相应的荧光光谱图。经研究认为胭脂红荧光是由—OH中的n电子的n→π*跃迁和奈环中的π电子的π→π*跃迁这两类跃迁而产生的,其中420 nm处的荧光峰是由n→π*跃迁产生的, 而530, 635和687 nm这3个波长处的荧光峰是由π→π*跃迁而产生的, 同时其4个波长处的荧光相对强度随激发波长的变化相对改变不同,文章分别从微观机理上给出了一定的解释。研究胭脂红的荧光光谱及其特性可为其他偶氮类色素的荧光光谱研究提供参考,同时能为食品安全检测提供新的方法与途径。     

New Exact Solutions and Evolution of Solitons in Background Waves for (2+1)-Dimensional Modified Dispersive Water-Wave System

With the help of the conditional similarity reduction method, some new exact solutions of the (2+1)-dimensional modified dispersive water-wave system (MDWW) are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.     

A new method for high-energy pulsed Gamma measurement within intense background x-rays

The accelerator-generating 6.13~MeV pulsed Gamma by ¹⁹F(p, αγ )¹⁶⁰ reaction usually synchronizes with an intense bremsstrahlung x-ray which has a maximum energy of 1~MeV. This paper proposes a new method, named the scattering and absorbing method, to diagnose the 6.13~MeV Gamma. This method includes two parts: the detector and a scatterer placed in front of the detector. The detector converts the Gamma to electrons and then collects the electrons by a scintillator. In order to restrain the interference of the low-energy background, the scintillator collects the electrons at a small angle. The scintillator is wrapped with electro-absorbing material to absorb the low-energy electrons generated by background x-rays. The theoretical sensitivity ratio of 6.13~MeV Gamma to 1~MeV x-rays is greater than 150. The scatterer is a pretreatment tool to scatter some background x-rays away from the radial beam before they enter the detector. By varying the length, the scatterer can reduce the background x-rays to an acceptable level for the detector.     

宽光谱Czerny-Turner光谱仪中的彗差与分辨率

小型光谱仪较多地采用Czerny-Turner(切尼—特纳)光路结构,其设计应遵循Shafer消彗差原理消除中心波长处的初级彗差并尽量平直整个谱面以提高分辨率。但常规设计并未考虑非中心波长处彗差和分辨率的变化情况。在对两种典型切尼—特纳光路结构进行初级彗差分析的基础上,指出交叉型光路结构宽光谱范围内的分辨率呈“V”形,而M型光路结构分辨率在全光谱范围内变化较小,近似呈“一”形,即后者宽光谱范围内的分辨率一致性远好于前者。针对于此,该文设计了光谱范围为400～600 nm的2种光路,并对其进行了理论计算和对比实验,实验结果表明,两者边缘波长处分辨率分别比中心波长处分辨率低3.7倍和1.2倍,与理论计算结果基本一致。     

通过确定初始电离位点预测吲哚类生物碱质谱的特征裂解规律

确定初始电离位点是EI源质谱解析中一个至关重要的环节. 本文提出了一种确定初始电离位点的新方法. 该法通过计算和分析分子离子自旋密度, 进而比较从中性分子到分子离子的电荷变化和键长变化, 从而确定初始电离位点. 对简单吲哚类生物碱质谱的特征裂解机理进行了预测, 结果与标准物质的质谱吻合. 在此基础上, 与传统的根据基团电离能确定电离位点的方法进行了比较. 结果表明, 该法优于电离能方法. 此法不仅可用于预测以α-裂解为主导的吲哚生物碱和其它含氮化合物的质谱裂解规律, 还为揭示其它小分子化合物以及气相多肽离子的裂解机理奠定了基础.     

计算Pascal矩阵谱半径和相应特征向量的一个快速算法

研究Pascal矩阵谱半径及其对应特征向量的数值求解算法问题,利用幂法和Pascal矩阵的性质给出了一个有效的迭代求解算法,该算法每一步迭代只用到浮点数的加法运算。同时数值实验显示,该算法具有较高的精度和较快的收敛速度。     

运动壁面槽道流动的直接数值模拟

采用谱方法,在曲线坐标系下对不可压缩Newton流体的N-S方程进行求解,采用定义在物理空间中的流动物理量以避免使用协变、逆变形式的控制方程．在计算空间采用Fourier-Chebyshev谱方法进行空间离散,时间推进采用高精度时间分裂法．为了减小时间分裂带来的误差,采用了高精度的压力边界条件．与其他求解协变、逆变形式控制方程的谱方法相比,该方法在保持谱精度的同时减小了计算量．首先通过静止波形壁面和行波壁面槽道湍流的直接数值模拟,对该数值方法进行了验证;其次,作为初步应用,利用该方法研究了槽道湍流中周期振动凹坑所产生的流动结构．     

New accurate data for the spectrum of neutral silver

High resolution spectra of neutral silver have been recorded by Fourier Transform Spectrometry in the region 2 000-8 280 ?(50 000-12 000 cm^-1) with silver-neon and silver-argon hollow cathode lamps as sources. This work represents order-of-magnitude improvements, compared to previous work on Ag I, in accuracy of transition wavelengths and wavenumbers, and energy level values. 35 classified Ag I transitions are given, and the wavenumber uncertainty for the strongest lines is less than 0.002 cm^-1. Improved values for 28 energy levels are presented. Received 31 January 2000 and Received in final form 13 June 2000