非线性不适定问题一种双循环的牛顿型迭代格式

本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。     

伴随方法在热带气旋路径预测的统计动力预报方案(SD-90)中的应用的研究--Ⅰ:理论基础及数值试验

把变分同化中的伴随方法应用于热带气旋路径预测的统计动力预报方案(SD-90)中,利用前面时刻热带气旋中心位置的观测值,同时确定出初始速度和气压梯度力,然后进行预报.理想试验表明,热带气旋路径无明显转向时,该方案具有较高的预报精度;当热带气旋路径有明显转向时,随着同化时段内的热带气旋路径(作为观测值)趋向于转向处,该方案的预报误差会加大,其主要特征是预报路径的方向有较大偏差;当同化时段内的热带气旋路径(作为观测值)离开转向处时,该方案又趋向于有较高的预报精度.最后结合最优控制思想,对9807号台风进行了同化试验,试验结果表明,效果十分明显.     

New method to solve electromagnetic parabolic equation

This paper puts forward a new method to solve the electromagnetic parabolic equation （EMPE） by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convo- lution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing ana- lytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm.     

无线电掩星滑动频谱方法和后传播方法的分析比较

本文详细介绍了滑动频谱方法,并通过模拟仿真和实测资料处理与后传播方法进行比较. 通过对模拟仿真信号反演发现:后传播方法和滑动频谱方法均能削弱大气多路径的影响,后传播方法在一定程度上优于滑动频谱方法;在模拟信号的相位中加入高斯噪声对后传播方法影响不大,但对滑动频谱方法影响较大,尤其在边界层以下. 分别用后传播方法和滑动频谱方法对2007年第71天至73天共约4500个COSMIC掩星数据进行处理. 将折射率反演结果与ECMWF分析场资料进行统计比较,结果显示:滑动频谱方法反演的掩星廓线深度大于后传播方法;后 关键词： GPS/LEO掩星 多相位屏模型 后传播方法 滑动频谱方法     

Ocean internal waves interpreted as oscillation travelling waves in consideration of ocean dissipation

Most studies of the synthetic aperture radar remote sensing of ocean internal waves are based on the solitary wave solutions of the Korteweg-de Vries （KdV） equation, and the dissipative term in the KdV equation is not taken into account. However, the dissipative term is very important, both in the synthetic aperture radar images and in ocean models. In this paper, the traveling-wave structure to characterize the ocean internal wave phenomenon is modeled, the results of numerical experiments are advanced, and a theoretical hypothesis of the traveling wave to retrieve the ocean internal wave parameters in the synthetic aperture radar images is introduced.     

ON PSEUDO-RIEMANN-HILBERT PROBLEM FOR COMPLEX OVERDETERMIND PARTIAL DIFFERENTIAL SYSTEMS OF FIRST ORDER

Suppose G_j= {z_j||z_j|<1}, G_j= {z_j||z_j|=1},j= 1,2, G_(1 )= {z_1|ε< |z_1|<1},where εisa constant, 0 <ε<1 . We consider the pseudo-Riemann-Hilbert problem;We assume that(i) λis a H lder continuous function on G_1× G_2, and λ≠0; γis a real H lder continuous functionon G_1× G_2, and let H_β(γ) be its bound.(ii) f_j is continuous with respect to (z_1 ,z_2) ∈ _1z× _2 and is holomorphic with respect to W ∈B_R ={W||W|≤R, B is a positive constant}; f_i satisfies compatibility condition.(iii) and and continuous with respect to (z_1,z_2, W) ∈ _1× _2× B_R; f_1,f_2, and satisfyLipschitz condition with respect to W ∈B_R, and let L_R be the Lipschitz constant and K_R be their bound.     

二阶超复方程的广义解及拟Neumann问题

§1 引言对于一般形式的椭圆型方程组,在引进 Douglis 代数后,可以表示成 D_w+A_w+B_=C 的形式,这里 w、A、B、C 都是超复函数。关于一阶方程由于引进了 Pompieu 算子 J_G 以后对一系列性质与边值问题进行了研究,为了研究二阶及高阶椭圆型耦合方程组,必须引进对 J_G 的微分踅算,由于     

E_2类二阶椭圆型方程组的斜微商问题

本文考虑形如(?)复形式的二阶线性椭圆型方程组,其中h(z,ω,ω-(?),ω_z,)=r_1(z)ω_z~(?) r_2(Z)ω_2 r_3(z)ω_(z)~ r_4(z)(?)     

ON DISCONTINUOUS PERIODIC SOLUTION AND DISCONTINUOUS SOLITARY WAVE OF TWO-DIMENSION SHALLOW WATER EQUATION

In this papepr we discues discomunucus peridic solution and discontinuous solitarywave of the shallow water model of geophysical fiuid dynamics.When we consider theproperties of vajeciory necr non一epuiulmium nom point.i.e.singular we fund that if weintraduce the concept of gendralized solution smoothing continuous solution),then the system will produce discontinueus periodle solution and the condition ofdiscontinuous periodic solution can be obtahed When the system is dagenerated.we findthat the discontinucus solitary wave is existent in the system. In this paper we consider aserdes of problems and obtain analyvic expression of discontinuous solution.This result iscompared with squall lime in the anmosphere, and both of them have many thing in common.     

大气中非线性波动的非频散解——Ⅱ.非线性波速公式

本文的第二部分主要讨论非线性波速公式。由于非线性波动的波速公式与波形有关,为此文中引入了反映波形的无量纲量M。我们发现M可以表征波动非线性程度的大小,此即为M判据。文中还给出了非线性Rossby波与非线性重力惯性波的波速公式,对前者振幅大的波动相速度小,而对后者则相反。此外,文中还讨论了在求非线性波动的近似解时应用Taylor展开时所必须注意的问题。