2n阶微分方程周期解的存在性

考虑微分方程u^（2a）＋△↓G（u）=M（u）解的存在性问题，运用同胚理论及不动点方法给出在M为有界全连续算子条件下此类方程解的存在性定理。     

基于空间算子代数的高效率机器人反向动力学建模方法

针对大规模多体系统动力学建模过程复杂及计算效率、精度不高的难题,在空间算子代数理论的基础上,通过旋量表达的有关力学量和运动量,将包含机构拓扑关系及运动、力递推关系的移位算子直接与Newton-Euler递推动力学计算相结合,实现了广义速度、广义加速度、广义力和广义质量沿着链正向或反向递推,避免了交叉运算和不必要的积分运算,得到了高效率、高精度的动力学建模方法.该方法形式简洁、物理意义明确,适于计算机编程和运算,具有重要的科学意义和工程应用价值,并通过算例验证了结果的正确性和有效性.     

多变量方程误差类系统的部分耦合迭代辨识方法

针对多变量方程误差滑动平均系统,利用最小二乘原理和迭代搜索原理,给出了增广随机梯度辨识方法、递推增广最小二乘辨识方法、梯度迭代辨识方法和最小二乘迭代辨识方法.针对多变量方程误差滑动平均系统和多变量方程误差自回归滑动平均系统,将多变量系统分解为一些子系统,利用耦合辨识概念,讨论了梯度迭代辨识方法、部分耦合（子系统）梯度迭代辨识方法、子系统最小二乘迭代方法和部分耦合子系统最小二乘迭代辨识方法.进一步结合数据滤波技术,研究了多变量方程误差自回归滑动平均系统的子系统梯度迭代辨识方法、部分耦合（子系统）梯度迭代辨识方法、部分耦合子系统最小二乘迭代辨识方法.文中给出了几个典型算法的计算步骤.     

宁夏区域太阳日辐射通量计算方法的研究

利用银川站过去5 a的太阳日辐射观测资料(1981~1985)与大气外太阳辐射、日照时数、日照长度间的相关关系,确定了区域系数as。通过对bs的取值进行敏感测试,可得到一组最佳推算太阳辐射通量的区域系数:as=0.3,bs=0.5。用此系数和太阳日辐射通量计算公式,推算了银川站1986、1987年太阳日辐射通量并用观测值进行验证,结果表明:两者之间有很好的线性相关,R2=0.94,验证了区域系数的可信度。通过对银川站2 a(1986,1987)资料的平均误差、平均偏差、平均绝对偏差和均方根偏差的计算表明,结果与国内相关报道基本一致。对宁夏永宁站1989~2000年的太阳日辐射通量用区域系数进行估算,并与银川站的实际观测资料比较,结果显示永宁站太阳日辐射通量估算值和银川站实测值间有很好的线性关系,12 a间的方差最小值R2=0.88。     

New analytical solution of the dispersion equation

The dispersion of pollutants from a point source is analytically investigated taking into consideration the vertical variation of both wind speed and eddy diffusivity. The deposition of the diffusing particles on the ground is taken into account throughout the boundary conditions. The concentration of pollutants under different atmospheric stabilities was found assuming that the vertical diffusion is limited by an elevated inversion layer. The decay distance of a pollutant along the wind direction for different atmospheric stabilities was derived. The resulting analytical formulae have been applied on a case study namely, the emission from the research reactor at Inshas. The results are discussed and presented in illustrative figures.     

正压原始方程的差分格式

本文把[1—3]中的数值方法应用于正压原始方程组,并给出了差分格式的严格的误差估计。特别分析了边界误差的影响,并构造了一些新的算法。     

非线性Schrödinger方程的一个线性化紧致差分格式

对非线性Schrödinger方程给出了一个线性化紧致差分格式,运用不动点定理和能量方法证明了格式的唯一可解性,还运用能量方法和数学归纳法,避开困难的先验估计,证明格式在空间方向和时间方向分别具有四阶和二阶精度,数值算例验证了格式的精度和数值稳定性.     

Sensitivity of lidar equation solution to boundary values and determination of the values

An analytical dependence of the optical depth solution to lidar equation on boundary values was con-firmed. According to the dependence this paper analyzed the sensitivity of lidar equation solutions obtained by forward and backward integration algorithms to the boundary values and quantitatively expounded an error limit to the boundary values under a given inversion accuracy. Furthermore, this paper presented a method for determination of the far-end boundary value in the case of inhomogeneous atmosphere, improving the accuracy of lidar equation solution.     

A new technique for the solution of diffusion equation systems for reacting pollutants

In this paper it is shown how equation systems describing the vertical diffusion of reacting pollutants can be efficiently solved without employing operator splitting. The proposed technique is based on a selfadaptive predictor-corrector method the idea being to replace each inversion of a (K·J)²-matrix by 2K-1 inversions of J²-matrices. As an application, simulation results for the transport and the chemical transformation of motorcar emissions are presented.     

基于PPP和双差网解法的GNSS水汽反演效果分析

基于2021年5—7月GPS卫星资料,采用精密单点定位(Precise Point Positioning,PPP)和双差网解两种算法进行了大气可降水量（Precipitable Water Vapor,PWV）反演,利用同址探空水汽资料,对比分析了PPP算法与双差网解法计算的PWV反演精度。结果表明,PPP算法和双差网解法反演出的PWV随时间变化的趋势基本一致。两种算法反演出的PWV结果合理,与探空PWV相比,采用PPP和双差网解两种算法反演的PWV相对偏差均小于2.4 mm、绝对偏差在4 mm以下,均方差约4 mm,与探空PWV相关系数均在0.87以上,均能较好地反映大气中水汽含量的变化情况,两种算法均具备较强的水汽反演能力,双差网解法反演的PWV在相关性、精度上略优于PPP算法。PPP算法可实现单站水汽高时间分辨率反演,对于获取台站高时效、高精度的大气水汽探测产品具备优势。     

大气红外间接遥测方程的估计解和验前限制

在线性估计调整方法中研究如何考虑验前信息的方法,是发展估计算法的重要途径.为此,在文中根据十五通道理论权重函数和五个不同估计方法所得到的模拟数值试验结果,从估计模式所涉及的信息形式、不同形式验前限制的效应以及估计解的实际可解性等对估计解的精度和验前限制的内在联系进行了数值分析,确认TPRD1的解和验前信息之间具有最佳的统计结构.     

An Efficient Accurate Direct Solution of Poisson’s Equation for Computation of Meteorological Parameters

Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.     

The solution of the vector radiative transfer equation using the discrete ordinates technique: Selected applications

The paper is devoted to the presentation of a newly developed radiative transfer code SCIAPOL_1.0 for a plane-parallel turbid slab illuminated by the monodirectional wide beam. The SCIAPOL_1.0 is based on the discrete-ordinates solution of the vector radiative transfer equation.The code is applied to a number of problems, including studies of the applicability of the scalar approximation for the calculation of light reflectance from aerosols, clouds, and molecular atmospheres. We also study the accuracy of the single scattering approximation as applied to the calculation of light reflection from molecular and cloudy atmospheres and propose new approximations for the calculation of the reflection function and the degree of light polarization under unpolarized light illumination conditions.