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theory of functions of a complex variable
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  复变函数论
     In this article,principle of compactness and theory normal family in the theory of functions of a complex variable are popularized to the family of solution of Бичазе equation.
     本文将复变函数论中的致密性原理和正规族理论推广到Бичaзе方程的解族中去.
短句来源
  复变函数理论
     Exact Solution of Navier-Stokes Equations——The Theory of Functions of a Complex Variable under Dirac- Pauli Representation and Its Application in Fluid Dynamics (Ⅱ)
     Navier-Stokes方程的精确解——Dirac-Pauli表象的复变函数理论及其在流体力学中的应用(Ⅱ)
短句来源
     Chaplygin Equation in Three-Dimensional Non-Constant Isentropic Flow——The Theory of Functions of a Complex Variable under Dirac-Pauli Represen tation and Its Application in Fluid Dynamics(Ⅲ)
     三维非定常等熵流中的Chaplygin方程——Dirac-Pauli表象的复变函数理论及其在流体力学中的应用(Ⅲ)
短句来源
     We apply the theory of functions of a complex variable under Dirac-Pauli representation and the Legendre transformation, transform these equations of two problems from physical space into velocity space, and obtain two general Chaplygin equations in this paper.
     我们应用Dirac-Pauli表象的复变函数理论并采用Legendre变换,将此两类问题的方程组变换到速度空间,从而得到了两种推广的Chaplygin方程。
短句来源
     The Theory of Functions of a Complex Variable under Dirac-Pauli Representation and Its Application in Fluid Dynamics (I)
     Dirac-Pauli表象的复变函数理论及其在流体力学中的应用(Ⅰ)
短句来源
     In Ref. [1] -we applied the theory of functions of a complex variable under Dirac-Pauli representation,introduced the Kaluza "Ghost" coordinate, and turned Navier-Stokes equations of viscofluid dynamics of homogeneous and incompressible fluid into nonlinear equation with only a pair of complex unknown functions.
     在文[1]中我们应用Dirac-Pauli表象的复变函数理论并引入Kaluza“鬼”坐标,将不可压缩粘流动力学的Navier-Stokes方程化成只有一对复未知函数的非线性方程。
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  “theory of functions of a complex variable”译为未确定词的双语例句
     Discussion of Several Problems in "Theory of Functions of a Complex Variable"
     对《复变函数论》书中几个问题的商榷
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     The Application of the Theory of Functions of a Complex Variable to Algebra
     复变函数论在代数学上的一个应用
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  theory of functions of a complex variable
This result can be regarded as a natural four-dimensional generalization of the method used to solve two-dimensional static problems in the theory of functions of a complex variable.
      
Theory of functions of a complex variable applied to like-charged-particle flow formation under the action of a magnetic field
      
We consider some conventional problems of the theory of functions of a complex variable such that their extremal configurations have the n-fold symmetry.
      
The theory of functions of a complex variable is used to construct an approximate solution for the stationary oscillations of an elliptical cylinder with longitudinal elliptical cavities.
      
The problem of finding the optimum shape of the holes in a perforated plate weakened by a triangular or square lattice of holes and subject to bending is considered by methods based on the theory of functions of a complex variable.
      
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It is proved, for the two-dimensional question, that the general expression of total intensity △T has the same form as the vertical intensity Z. There is a possibility to consider the anomaly curves △T as Z. Therefore by use of the Cauch-Riemann's condition in the theory of function of a complex variable we may from anomaly curves △T calculate its so called "negative harmonic conjugate function" () which is corresponding to the anomaly curves H. It is indicated that interpretation...

It is proved, for the two-dimensional question, that the general expression of total intensity △T has the same form as the vertical intensity Z. There is a possibility to consider the anomaly curves △T as Z. Therefore by use of the Cauch-Riemann's condition in the theory of function of a complex variable we may from anomaly curves △T calculate its so called "negative harmonic conjugate function" () which is corresponding to the anomaly curves H. It is indicated that interpretation of the magnetic data may be facilitated by ussing () together with its original function △T. Two examples of application are given: 1) the calculation of the magnetic moment and its inclination for two-dimensional bodies from △T and AT; 2) downward analytical continuation of △T by use of values of △T and △T on the horizon of observation.

本文对于二度问题证明了总磁場强度△T与垂直磁場强度Z的一般表达式具有相同的形式,因此可以把△T异常曲线看成Z异常曲线,利用复变函数理论中的柯西-黎曼条件我们就可根据△T异常曲线计算出与H异常曲线相当的所谓△T的“负共轭调和函数”△T,文中指出了同时利用△T及其原函数△T将有助于磁测资料的解释工作,还举出了两个应用的例子:1)根据△T与△T计算二度体的磁矩及其倾角;2)利用观测水平上的△T及△T值将△T向下解析延拓。

In this paper, several critical moments in the development of the theory of functions in the nineteenth century are pointed out. In particular, the contributions made by Gauss, Cauchy, Weierstrass and Riemann on the foundations of the theory of functions of a complex variable are discussed.

本文指出了十九世纪函数论发展中的几个关键时刻,特别讨论了Gauss,Cauchy,Weierstrass和Riemann在建立单复变函数理论基础方面的贡献。

This work is the continuation of the discussion of Ref.[l]. In Ref. [1] -we applied the theory of functions of a complex variable under Dirac-Pauli representation,introduced the Kaluza "Ghost" coordinate, and turned Navier-Stokes equations of viscofluid dynamics of homogeneous and incompressible fluid into nonlinear equation with only a pair of complex unknown functions. In this paper we again combine the complex independent variable except time, and cause it to decrease in a pair...

This work is the continuation of the discussion of Ref.[l]. In Ref. [1] -we applied the theory of functions of a complex variable under Dirac-Pauli representation,introduced the Kaluza "Ghost" coordinate, and turned Navier-Stokes equations of viscofluid dynamics of homogeneous and incompressible fluid into nonlinear equation with only a pair of complex unknown functions. In this paper we again combine the complex independent variable except time, and cause it to decrease in a pair to the number of complex independent variables. Lastly, we turn Navier-Stokes equations into classical Burgers equation. The Cole-Hopf transformation join up with Burgers equation and the diffusion equation is Backlund transformation in fact, and the diffusion equation has the general solution as everyone knows. Thus, we obtain the exact solution of Navier-Stokes equations by Backlund transformation.

本文是文[1]的继续。在文[1]中我们应用Dirac-Pauli表象的复变函数理论并引入Kaluza“鬼”坐标,将不可压缩粘流动力学的Navier-Stokes方程化成只有一对复未知函数的非线性方程。在本文中,我们将除时间之外的复自变量进行重新组合,从而成对地减少了复自变量的数目。最后,我们将Navier-Stokes方程化成经典的Burgers方程。联结Burgers方程与扩散方程的Cole-Hopf变换实际上是Backlund变换,而扩散方程众所周知是具有通解的。于是,我们利用Backlund变换求得了Navier-Stokes方程的精确解。

 
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