半群和线性时滞偏微分方程

证明了一类线性时滞偏微分方程的mild解与相应的抽象柯西问题的mild解一一对应,并且给出了此类线性时滞偏微分方程的mild解存在唯一的充要条件.     

基于直线特征的有理函数模型定位精度改善方法

探讨了利用已知直线特征进行有理函数模型定位误差在物方进行补偿的方法.推导了在两种物方补偿模型(平移加主因子比例和一阶仿射变换模型)下,基于已知直线特征进行补偿模型参数解算的数学模型.给出了利用已知直线特征进行有理函数模型定位误差补偿的解算方案.实验表明:基于线特征的补偿方法是可行的,并且平移加主因子比例模型的精度好于基于控制点的方法,也好于一阶仿射变换模型的补偿效果;但对于一阶仿射变换模型,该方法的补偿效果要比基于控制点的方法差.     

动中通系统中陀螺信号小波滤波算法

在动中通系统中,陀螺检测的载体扰动信号的精度直接关系到整个系统的精度和性能。针对陀螺噪声信号的特点,提出了一种将3σ模平方阈值和平移不变小波变换(translation invariant discrete wavelet transform, TIDWT)相结合的滤波算法,能够有效地抑制陀螺噪声信号和由小波变换产生的失真现象。仿真和实验结果表明,该滤波算法效果优于传统的小波滤波算法。     

基于Parseval框架的多小波子空间抽样定理

研究了基于Parseval框架的多小波子空间中的抽样定理.通过满足一定条件,给出抽样定理在多小波子空间中成立的等价条件.所得结果不仅推广了单小波子空间的抽样定理,而且抽样公式在L2(R)收敛意义下成立.     

Sobolev空间的伪平移框架

根据Sobolev空间Hs(R)(s0)中平移框架的等价条件,验证了生成子不能同时具有很好的时-频局部性质.并通过引入伪框架的定义,成功地克服了平移框架的上述缺点.     

偏微分演化方程的代数动力学解法中无穷小时间平移算子的等价构造

我们给出了王顺金等提出的偏微分演化方程的代数动力学解法中关于时间平移的无穷小算子L的等价构造形式,我们的形式只涉及简单的偏导数运算,避免了在运用王-张时间平移算子进行计算的时候出现的大量的δ函数的导数.我们给出了两种表示的等价性,即王顺金等价性定理的证明.作为应用,利用我们给出的无穷小算子L的构造,处理了非线性对流方程,Burgers方程,非线性Schrdinger方程,KdV方程以及sine-Gordon方程等几个典型方程,并计算到至少二阶展开项,这些例子包括了实场量和复场量情形以及对时间的一阶导数和二阶导数情形.     

Detection of the translational oscillations of the Earth＇s solid inner core based on the international superconducting gravimeter observations

Based on the 21 series of the high precision tidal gravity observations recorded using superconducting gravimeters (SG) at 14 stations distributed globally (in to-tally about 86 years), the translational oscillations of the Earth抯 solid inner core (ESIC) is detected in this paper. All observations are divided into two groups with G-Ⅰ group (8 relatively longer observational series) and G-Ⅱ group (13 relatively shorter observational series). The detailed correc-tions to minute original observations for each station are carried out, the error data due to the earthquakes, power supply impulses and some perturbations as change in at-mospheric pressure and so on are carefully deleted for the first step, the gravity residuals are obtained after removing further synthetic tidal gravity signals. The Fast Fourier Transform analysis is carried out for each residual series, the estimations of the product spectral densities in the sub-tidal band are obtained by using a multi-station staking technique. The 8 common peaks are found after further removing the remaining frequency dependent pressure signals. The eigen-periods, quality factors and resonant strengths for these peaks are simulated. The numerical results show that the discrepancies of the eigenperiods for 3 of 8 peaks, compared to those of theoretical computation given by Smith, are only 0.4%, -0.4% and 1.0%. This coincidence signifies that the dynamical phenomenon of the Earths solid inner core can be detected by using high precision ground gravity observations. The reliability of the numerical computation is also checked, the spectral peak splitting phenomenon induced by Earths rotation and ellipticity is preliminary discussed in this paper.     

数字分析仪曲线平滑的数学原理

本文给出了用积分微分光滑曲线的方法。解答了实际使用者提出的问题。特点是计算方便,精度较高。     

高维空间中几类可嵌入连续流或半流的自映射

给出了高维空间中几类可嵌入连续流和半流的自映射的特征。