查询词典 analytic continuation

In this paper, taking the downward continuation of potential field as an inverse problem of upward continuation, we obtain a convolution type linear integral equation for downward continuation. Making use of the orthogonal symmetry characteristic of Fourier transform matrix, and combining the principles of singular value decomposition of matrix and generalized inverse, we proposed a stable generalized inverse method for downward continuation of potential field, called wavenumber domain generalized inverse algorithm, which doesn't need the computation for inverse matrix. It resolves the instability of potential field downward continuation of large depth.

本文通过把位场向下延拓视为向上延拓的反问题，得到向下延拓的褶积型线性积分方程，再利用Fourier变换矩阵的正交对称特性，并结合矩阵的奇异值分解和广义逆原理，提出了一种稳定的不需要进行求逆运算的位场向下延拓广义逆方法——波数域广义逆算法，解决了位场大深度向下延拓的不稳定性问题。

However, after I came to understand distance education more deeply, I find that network distance continuation education has many advantages. Firstly, it breaks through the limitation of time and distance. It enables the students all over the country to get instructed from those top level teachers, take the most advanced teaching method, and enjoy richer education information resource. Secondly, it profits in extending the teaching scope, providing more education chances and more flexible way of learning, which make it possible to let more people accept education. Thirdly, the modern network distance continuation, which is based on information, offers a good space-time platform for a lifelong learning. At last, the modern network distance continuation makes students to focus on self study, which help them to fully develop their proactivity, intuitivity and creativity. For the four reasons mentioned above, finally, I chose network distance continuation education as the way of my further education.

但是，经过深入了解之后，发现远程网络继续教育是有很多的优势的，第一，它可以突破时空的限制，使全国各地的学生都能接受一流水平教师的教导，接受最先进的教学方法，享有更丰富的教学信息资源；第二，有利于扩大教学规模，提供更多的学习机会和更灵活的学习方式，使更多的人可以接受教育；第三，以基于信息技术的现代远程网络继续教育，为终生学习的实现提供了时空平台，为人们提供更多开展的实施终身学习的机会；第四，现代远程网络继续教育以学习者自学为主，充分发挥学习者自主学习的主动性、积极性及创造性，综合以上四点，我最终选择远程网络继续教育作为我继续学习的途径。

Weierstrass took the concept of "analytic Gebilde" as basic constitution to analytic continuation in order to access to integer analytic function by local ones.

魏尔斯特拉斯以"解析映射"概念为基本构成，进行解析延拓，从而实现由局部获得整体解析函数。

The content of this course is: analytic function (the definition of analytic function, elementary functions, etc.), conformal mapping (the definition if conformal mapping, fractional linear functions, elementary mappings, etc.), complex integration (Cauchy's integral formula, Cauchy's theorem, etc.), Series (Laurent Series, singularities, local property, etc.), residues and its applications (the Residues Theorem, integration by residues, the Argument Principle, the Maximum Principle, Schwarz's Lemma, etc.), analytic continuation and harmonic functions, etc.

本课程内容主要包括：解析函数(解析函数的定义、初等函数等)、共形映射(共形映射的定义、分式线性变换及初等映射等)、复积分(Cauchy 积分公式、 Cauchy 定理等)、级数(Laurent 级数、孤立奇点、局部映射等)、留数及其应用(留数定理、利用留数计算积分、幅角原理、最大模原理、 Schwarz 引理等)、解析开拓和调和函数等内容。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

The computation implies that the influence of truncation error of up/downwards continuation is about 0.001 m2·s-2, the maximum error is only 0.11 m2·s-2, which can be ignored in CHAMP gravity field recovery. The influence of the reference gravity field error of up/downwards continuation is less than 0.1 m2·s-2 in general, but the maximum error can reach 1.3 m2·s-2. To reduce this error, a high-precision gravity field model should be used in the up/downwards continuation.

计算表明：延拓误差中的截断误差部分影响量级约0.001 m2·s-2，最大误差仅为0.11 m2·s-2，可完全忽略；延拓误差中的参考重力场模型误差影响随参考场选取的不同而有所差异，整体而言小于0.1 m2·s-2，但最大误差可达1.3 m2·s-2，采用高精度的参考重力场模型能大大减小延拓误差影响。

In this paper, an iterative approach to potential field continuation from curved surface to plane is proposed. The continuation of potential field data from a curved surface to a plane can be viewed as an inverse problem of upward continuation of plane potential field data, getting a linear integral equation. Through viewing the potential field data on the curved surface as the data on the average elevation plane of the curved surface, then using the wavenumber domain generalized inverse algorithm to downward continue the data from the average elevation plane to a given plane, and a topography correction based on the change of curved surface relative to its average elevation is implemented to the downward continued data on the given plane, finally the downward continued data plane is upward continued to the curved surface.

本文提出一种位场数据曲化平的迭代方法，即通过把位场数据曲化平视为平面位场数据向上延拓的反问题，得到曲化平的线性积分方程，再把曲面上位场数据视为曲面平均高程面上的位场数据，利用向下延拓的波数域广义逆算法把平均高程面上的位场数据向下延拓到设定平面上，再根据曲面和其平均高程面的相对起伏对设定平面上的向下延拓数据进行起伏校正，最后再把所得平面上的位场数据向上延拓得到曲面上的位场数据，并进行迭代。

Farewell and Sleepless Night is the continuation of Why Does Sunset Make Us So Beautiful . This continuation is not referring to the form but to the relation of subject and object. Either surrealism or pictorialization is retreating from this continuation. From the unconscious split of subject and object to the hint of objectification, the pure object finally surfaced. This is a significant change of Deng Jianjin.

再见和不眠夜》是《夕阳为什么让我们如此美丽》的延续，这种延续不是指形式，而是指主客体的关系，无论是超现实还是图像化都在这种延续中隐退，从无意识的主客体分裂到客体化的暗示，纯粹的客体终于浮出水面，这在邓箭今是一个很大的转变。

Plane analytic geometry is a important content in the mathematics curriculum of high school, which embodies powerful function of analytic method and algebraic method in the depicting curve. It reflects important idea of the combination of number and figure. Learning the course is very important for students to improve mathematics thought ability. Teachers and students are engaged in teaching and learning by the textbook, so it is necessary to analyse plane analytic geometry textbook.

平面解析几何是高中数学课程中的重要内容之一，它体现了解析方法和代数方法在刻画平面曲线方面的强大作用，反映了数形结合的重要思想，学习这部分内容对提高学生的数学思维能力具有十分重要的价值，师生正是通过教材这一载体从事教学和学习活动的，因此，很有必要对平面解析几何教材进行分析。

In this paper, we treat the composition operators on several analytic function spaces. The study of analytic composition operators links analytic-function theory and operator theory.

本文主要从事解析函数空间上的复合算子的研究而未涉及可测函数空间上的复合算子。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。