虚拟压缩恢复基本原理及应用实例解析

概述了虚拟压缩恢复基本原理及其在地球科学特别是边值问题中的应用。作为新的应用实例，论证了Runge定理、Runge-Krarup定理和Keldysh-Lavrentiev定理均是虚拟压缩恢复原理的推论。     

Optical theorem for electromagnetic scattering by a three-dimensional scatterer in the presence of a lossless half space

The classical optical theorem for a scatterer in free space is useful in computing the total extinction cross section when the scattering amplitude in the forward scattering direction is known. In this letter, the classical optical theorem is extended to the case of a scatterer in the presence of a lossless half space. The extended optical theorem is derived based on energy conservation concepts, and the method of stationary phase is employed to obtain the final form. It is found that the total extinction cross section is related to the scattering amplitudes in the specular directions for reflected and transmitted fields. Numerical results are presented to illustrate use of the theorem for evaluating the energy conservation properties of an electromagnetic simulation.     

不确定系统的稳定性

本文研究不确定系统(1)″解的稳定性、定常系统(1)′稳定区间的存在性以及线性系统(4)解的有界性、周期解的存在性等问题;利用区间分析的方法给出系统(1)″稳定判别定理2、定理3和定常系统(1)′稳定区间的存在定理4、非线性系统(14)解的有界性、定理5周期解的存在定理6。     

The success rate and precision of GPS ambiguities

 An application of a theorem on the optimality of integer least-squares (LS) is described. This theorem states that the integer LS estimator maximizes the ambiguity success rate within the class of admissible integer estimators. This theorem is used to show how the probability of correct integer estimation depends on changes in the second moment of the ambiguity `float' solution. The distribution of the `float' solution is considered to be a member of the broad family of elliptically contoured distributions. Eigenvalue-based bounds for the ambiguity success rate are obtained. Received: 11 January 1999 / Accepted: 2 November 1999     

关于处处没有导数的连续函数求分数阶导数的例子

范德瓦尔登给出了一个著名的处处没有导数的连续函数的例子,本文求出了这个函数的分数阶导数。     

一元Laplace分布的L1—范估计的无偏性

根据Laplace分布的概率密度函数公式，推导了了中位数的概率密度，在此基础上证明了L1－范估计的无偏性。     

立体视觉系统检校中引入制约条件的推演

将需检校的立体视觉系统对室外大型控制场拍摄多方位立体像对时，引入像对间相互关系作为制约条件，是使成果稳定而高质的必要措施。本文介绍了所引入的制约条件的推演过程。     

Local Degrees of Freedom of Airborne Array Radar Clutter for STAP

In this letter, the local degree-of-freedom (LDOF) theorem for reduced-dimension space-time adaptive processing (STAP) methods is presented, and a rigorous proof is provided. LDOF is more valuable for practical STAP methods than conventional full degrees of freedom. The effectiveness of the LDOF theorem is verified, and the influences of some operations in practice on the LDOF are analyzed by simulations.     

ADJUSTMENT OF THE SECONDARY TRIANGULATION OF SOUTH AFRICA

Abstract

The Secondary Triangulation of South Africa consists of a uniform network of triangles of from 5- to 10-mile sides, enmeshed in the Geodetic and Primary Triangulations. As a rule the Primary Triangulation is rigorously adjusted by least squares, and the Secondary made to conform to it by an approximately rigorous method which was introduced into the Trigonometrical Survey in 1920 by the late Dr van der Sterr.     

一类拟线性抛物型方程T—周期古典解

利用构造性方法证明了拟线性抛物型方程边值问题的T—周期古典解的存在性，同时证明了T—周期古典解的比较原理和唯一性定理。     

关于阵列的一点注记

本文对于阵列代数中的一个基本定理(阵列与矩阵乘积定理)用归纳方法给出较简的证明,此外,并建立k阶阵列与张量的一个关系。     

改进的ARCE方法及其在单频 GPS快速定位中的应用

基于TIKHONOV正则化原理，设计了一种正则化矩阵的构造方法，将ARCE(ambiguity resolution using constraint equation)方法进行了改进。通过新的正则化矩阵的作用，减弱了GPS快速定位中少数历元情形下法矩阵的病态性，得到了比较准确的模糊度浮动解，大大减小了模糊度的搜索范围，利用ARCE方法固定模糊度的成功率高。并结合一个算例，验证了本文改进方法的效果。     

地貌及等高线表示的分解定理与表现定理

随着计算机制图和GIS的迅速发展，对于有着广泛应用的地貌形态特征问题，提出了进一步加以科学、系统、深入定量研究的迫切要求，以便获得更科学、合理的应用。作为一个系列研究的开始，首先要解决用2维空间的等高线表示3维空问地貌形态的科学性这一问题。为此，文中引入了地貌截影及截地貌的概念，通过地貌分解定理与表现定理的证明，以及等高线、地貌截影和截地貌三者之间的等价关系的论述，最终从数学上解决了上述基本问题，为今后的深入研究奠定了基础。     

Coerciveness of the linear gravimetric boundary-value problem and a geometrical interpretation

In this paper the linear gravimetric boundary-value problem is discussed in the sense of the so-called weak solution. For this purpose a Sobolev weight space was constructed for an unbounded domain representing the exterior of the Earth and quantitative estimates were deduced for the trace theorem and equivalent norms. In the generalized formulation of the problem a special decomposition of the Laplace operator was used to express the oblique derivative in the boundary condition which has to be met by the solution. The relation to the classical formulation was also shown. The main result concerns the coerciveness (ellipticity) of a bilinear form associated with the problem under consideration. The Lax-Milgram theorem was used to decide about the existence, uniqueness and stability of the weak solution of the problem. Finally, a clear geometrical interpretation was found for a constant in the coerciveness inequality, and the convergence of approximation solutions constructed by means of the Galerkin method was proved. Received: 21 June 1996 / Accepted: 14 April 1997     

水面油膜微波辐射特性的研究

用36GHz和9.2GHz微波辐射计测量了不同厚度的水面油膜的亮度温度,应用并矢格林函数及起伏逸散定理进行了理论模式的数值计算,同实验取得了基本一致的结果。     

Analytic tools for investigating the structure of network reliability measures with regard to observation correlations

A global measure of observation correlations in a network is proposed, together with the auxiliary indices related to non-diagonal elements of the correlation matrix. Based on the above global measure, a specific representation of the correlation matrix is presented, being the result of rigorously proven theorem formulated within the present research. According to the theorem, each positive definite correlation matrix can be expressed by a scale factor and a so-called internal weight matrix. Such a representation made it possible to investigate the structure of the basic reliability measures with regard to observation correlations. Numerical examples carried out for two test networks illustrate the structure of those measures that proved to be dependent on global correlation index. Also, the levels of global correlation are proposed. It is shown that one can readily find an approximate value of the global correlation index, and hence the correlation level, for the expected values of auxiliary indices being the only knowledge about a correlation matrix of interest. The paper is an extended continuation of the previous study of authors that was confined to the elementary case termed uniform correlation. The extension covers arbitrary correlation matrices and a structure of correlation effect.     

关于地球自由摆动中分解定理的讨论

实际地球是一个非旋转对称的椭球体,甚至是梨形椭球体.因此,三轴整体地球自转动力学的理论研究是有一定意义的.主要将研究三轴刚体地球自转的自由摆动,对有关学者提出的分解定理进行重新探讨,指出了其中可能存在的一些问题.     

不依赖假设检验的整周模糊度确认

扼要分析了现行整周模糊度确认方法 ,进而提出并证明了一条缩小整周模糊度搜索空间的定理。根据此定理 ,提出了一种不依赖假设检验的整周模糊度确认方法。该方法不仅可以加快整周模糊度的搜索速度 ,而且在次小残差二次型和最小残差二次型之比较小的情况下也能固定整周模糊度 ,并给出一个固定正确性的数字指标     

SDINS/GPS in-flight alignment using GPS carrier phase rate

The alignments of the strapdown inertial navigation system (SDINS) utilizing GPS carrier phase rate measurements is introduced. In this paper, a measurement model of GPS carrier phase rate under two antenna configurations is derived in order to be used for the SDINS alignment process. For in-flight alignment, the performance of the proposed SDINS/GPS integration method is analyzed using the covariance analysis and the overall performance is briefly confirmed by the navigation result of a van test. Furthermore, we find that during in-flight alignment the proposed SDINS/GPS integrated system using GPS carrier phase rate measurements can be implemented in real time because the integer ambiguity problem resulting from carrier phase measurements is avoided.     

等价观测与GPS差分法定位

本文首先利用空间和投影算子的概念证明了等价观测中的部分等价性定理，然后从该定理出发讨论了各种GPS差分定位法的等价性问题并给出了其相应的等价条件。