单位圆内亚纯函数的不同指数的充满足圆

对任一正数λ和τ（τ在λ和l 1之间），可构造单位圆内一λ级亚纯函数，具有一个τ级充满圆序列，但没有大于τ级的充满圆序列。     

Meixner functions for derivation of the unit hydrograph

The Meixner functions are utilized to relate the effective rainfall, the direct runoff and the unit hydrograph through linkage equations. The linkage equations are then employed to derive the unit hydrograph for given rainfall-runoff data on a small agricultural watershed. These functions are tested with regard to their ability to reproduce and predict the direct runoff hydrograph. The Meixner functions are found to be an effective analytical tool for hydrograph synthesis. Further, they compare well with the least squares and linear programming methods of the unit hydrograph derivation.     

Methodological Development of the Conditional Sampling Method. Part II: Quality Control Criteria of Relaxed Eddy Accumulation Flux Measurements

Determination of biosphere–atmosphere exchanges requires accurate quantification of the turbulent fluxes of energy and of a wide variety of trace gases. Relaxed Eddy Accumulation (REA) is a method that has received increasing attention in recent years, because it does not require any rapid sensor for the scalar measurements as the Eddy Correlation method (EC) does. As in all micrometeorological studies, REA measurements in the atmospheric surface layer are valid under some restrictive conditions so as to be representative of a specific ecosystem. These conditions are the homogeneity of the underlying surface, stationary and horizontally homogeneous turbulence. For most experiments these conditions are not fully satisfied. Data uncertainties can also be related to not fulfilling the method principles or to the technical characteristics of the REA system itself. In order to assess REA measurement quality, a methodological approach of data analysis is developed in this study. This methodological analysis is based on the establishment of criteria for data quality control. A set of them, deduced from the mean and turbulent flow, are called ‘Dynamic criteria’ and are designated to control the stationarity and homogeneity of the w function and the validation of Taylor’s hypothesis. A second set (‘REA operational criteria’) is designed to check the sampling process and, more precisely, the homogeneity of the negative and positive selection process throughout the sampling period. A third set of criteria (‘Chemical scalar criteria’) concerns the scalar measurements. Results of the criteria application to data measured at two different experimental sites are also presented. Cut-off limits of criteria are defined based on their statistical distribution and shown to be specific for each site. Strictness of each criterion, defined by the percentage of flagged samples, is analysed in conjunction with the meteorological conditions and atmospheric stability. It is found that flagged samples mainly correspond to neutral and stable nocturnal conditions. During daytime, nearly free convection conditions can also yield poor quality data.     

Planetary theories with the aid of the expansions of elliptic functions

For coplanar circular orbits, the mutual perturbations between two bodies can be expressed in term of the argument of Jacobian elliptic functions instead of the difference of the mean longitudes. For a given pair of planets, such a change of time variable improves the convergence of the developments. At the first order of planetary masses an integration of Lagrange's equations for the osculating elements is performed. When compared to classical developments the results are reduced by an important factor. The method is then extended to the mutual perturbations of Jupiter and Saturn, at any order of planetary masses, either with Fourier series with two arguments, or with one argument solely, taking advantage of the close commensurability of the mean motions.     

Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L ₄, L ₅. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date.     

参考经验模态分解-独立分量分析及其在GPS多路径误差处理中的应用

多路径误差在绝大部分应用中,其测站间相关性很弱,不能通过差分观测得到有效削弱,成为高精度GPS动态变形监测中的主要误差源。针对GPS多路径误差的特点,结合具有良好多尺度分解能力的经验模式分解方法(EMD)和具有良好盲分离能力的独立分量分析(ICA)方法,提出带参考信号的EMD-ICA方法来削弱多路径效应的影响。应用实例的结果证明了该方法的有效性。     

利用经验模态分解和主成分分析的SAR图像相干斑抑制

对SAR图像应用对数加性噪声模型,将经验模态分解(Empirical mode decomposition, EMD)与主成分分析(Principal Component Analysis, PCA)相结合,提出了一种基于PCA的EMD相干斑抑制算法。根据对数SAR图像中相干斑噪声的统计特性和高斯白噪声经EMD分解后的能量分布模型,近似估算SAR图像经EMD分解后各层内蕴模态函数中所含噪声的能量;将内蕴模态函数利用PCA进行分解,根据PCA对含噪信号的分解特性和内蕴模态函数中噪声能量所占的比例,选择合适的成分分量重构内蕴模态函数,以进一步去除噪声保留有用的细节信息。仿真实验结果表明,本文方法在有效抑制相干斑噪声的同时可以较好地保持边缘纹理细节的清晰。     

Performance of various similarity functions for nondimensional wind and temperature profiles in the surface layer in stable conditions

The linear functions for non-dimensional wind and temperature profiles are commonly used to describe the surface layer fluxes in atmospheric models. However, their applicability is limited to smaller values of the stability parameter z/L (where z is the height above ground and L is the Obukhov length) i.e. z/L < 1.0. These linear functions have been modified (Webb 1970, Quart. J. Roy. Meteor. Soc. 96, 67–90; Clarke 1970, Quart. J. Roy. Meteor. Soc. 96, 91–114; Hicks 1976, Quart. J. Roy. Meteor. Soc. 102, 535–551; Beljaars and Holtslag 1991, J. Appl. Meteorol. 30, 327–341; Cheng and Brutsaert 2005, Boundary-Layer Meteorol. 114, 519–538) over the years for calculating fluxes when z/L > 1.0 under strongly stable conditions. In view of this, the objective of the present study is to analyze the performance of these similarity functions to compute surface fluxes in stable conditions.The meteorological observations from the Cooperative Atmosphere-Surface Exchange Study (CASES-99) experiment are utilized for computing the surface fluxes in stable conditions. The computed fluxes are found to be reasonably close to those observed. The ratio of observed to computed fluxes reveals that the computed fluxes are close to the observations for all the similarity functions for z/L < 1.0 whereas the computed values show relatively a large scatter from observations for z/L > 1.0. The computed values of u and heat flux do not show significant differences from those observed at 99% confidence limit. The performance of all the similarity functions considered here is found to be comparable to each other in strongly stable conditions.     

Gap Filling and Quality Assessment of CO2 and Water Vapour Fluxes above an Urban Area with Radial Basis Function Neural Networks

Vertical turbulent fluxes of water vapour, carbon dioxide, and sensible heat were measured from 16 August to the 28 September 2006 near the city centre of Münster in north-west Germany. In comparison to results of measurements above homogeneous ecosystem sites, the CO₂ fluxes above the urban investigation area showed more peaks and higher variances during the course of a day, probably caused by traffic and other varying, anthropogenic sources. The main goal of this study is the introduction and establishment of a new gap filling procedure using radial basis function (RBF) neural networks, which is also applicable under complex environmental conditions. We applied adapted RBF neural networks within a combined modular expert system of neural networks as an innovative approach to fill data gaps in micrometeorological flux time series. We found that RBF networks are superior to multi-layer perceptron (MLP) neural networks in the reproduction of the highly variable turbulent fluxes. In addition, we enhanced the methodology in the field of quality assessment for eddy covariance data. An RBF neural network mapping system was used to identify conditions of a turbulence regime that allows reliable quantification of turbulent fluxes through finding an acceptable minimum of the friction velocity. For the data analysed in this study, the minimum acceptable friction velocity was found to be 0.15 m s⁻¹. The obtained CO₂ fluxes, measured on a tower at 65 m a.g.l., reached average values of 12 μmol m⁻² s⁻¹ and fell to nighttime minimum values of 3 μmol m ⁻² s⁻¹. Mean daily CO₂ emissions of 21 g CO₂ m⁻²d ⁻¹ were obtained during our 6-week experiment. Hence, the city centre of Münster appeared to be a significant source of CO₂. The half-hourly average values of water vapour fluxes ranged between 0.062 and 0.989 mmol m⁻² s⁻¹and showed lower variances than the simultaneously measured fluxes of CO₂.     

Analysis of the three-dimensional stellar velocity field using vector spherical functions

We apply vector spherical functions to problems of stellar kinematics. Using these functions allows all of the systematic components in the stellar velocity field to be revealed without being attached to a specific physical model. Comparison of the theoretical decomposition coefficients of the equations for a particular kinematical model with observational data can provide precise information about whether the model is compatible with the observations and can reveal systematic components that are not described by this model. The formalism of vector spherical functions is particularly well suited for analyzing the present and future (e.g., GAIA) catalogs containing all three velocity vector components: the propermotions in both coordinates and the radial velocity. We show that there are systematic components in the proper motions of Hipparcos stars that cannot be interpreted in terms of the linear Ogorodnikov-Milne model. The same result is also confirmed by an analysis of the radial velocities for these stars.