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complex variable
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  复变
     The complex variable equation of Ln z~(1/n)=1/n Lnz1nhas been proved true, and erroneous conclusion in the old textbook has been corrected.
     证明了复变等式Ln z~(1/n)=1/n Lnz的成立,纠正了原有教材中的错误结论。
短句来源
     Based on the path-integral method and the Plana summation formula in the theory of complex variable function,the Casimir effect of Maxwell-Chern-Simons field under square boundary conditions in the (2+1)-dimensional space-time has been calculated.
     利用路径积分方法与复变函数论中Plana求和公式,计算了(2+1)维空间中正方形边界下Maxwel-Chern-Simons场的Casimir效应。
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     Application of MATLAB in Complex Variable Function & Integral Transform
     MATLAB在《复变函数与积分变换》中的应用
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     The computing formulae for strain field and displacement field near crack tip of Type Ⅰ and Type Ⅱ anisotropic composite plate were derived by using the complex variable function method.
     采用复变函数方法推出了各向异性复合材料板的Ⅰ型、Ⅱ型裂纹尖端附近的应变场与位移场的计算公式。
短句来源
     Complex Variable Function Method for Hole Shape Optimization in an Elastic Plane
     弹性平面孔洞形状优化复变函数方法
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  复变量
     (3) Extend the recurrence relations of Thiele type GVRI to the case of complex variable Thiele-Werner type GVRI (See Theorem 6.7-Theorem 6.12).
     (3) 推广Thiele型向量连分式的递推关系到Thiele-Werner型向量连分式结构中,建立起复数域复变量情形下向量有理插值的递推算法(定理6.7-定理6.12)。
短句来源
     Study of the Complex Variable Method for Sensitivities Calculation in MDO of Flying Vehicles
     飞行器MDO中灵敏度计算的复变量方法研究
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     Equation in Complex Variable of Axisymmetrical Deformation Problems for a General Shell of Revolution
     一般旋转壳在轴对称变形下的复变量方程
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     Calculation of the Spencc Function for a Complex Variable
     复变量Spence函数的数值计算
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     The Solution of the Characteristic Impedance of an Arbitrarily Shaped TEM Transmission Line by Using Complex Variable Boundary Element Method (CVBEM)
     用复变量边界元法求解任意截面TEM传输线的特性阻抗
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  复变数
     Hardy-Littlewood Theorem in Bergman Space of Several Complex Variable
     多复变数Bergman空间中的Hardy-Littlewood定理
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     define a new space H~(p,a) in one complex variable, characterize the properties of function, and give two guesses.
     在单复变数中,定义了一种新的空间,即H~P空间的子空间H~(P,α)空间,对其函数进行了简单的刻划,并提出了两个猜想。
短句来源
     The paper also extends the corresponding results of one complex variable random Dirichlet Series and lower bitangent Laplace Stieltjes transform.
     建立了该级数所定义的随机解析函数的θ线性下级与下型的存在定理 ,推广了单复变数的随机Dirichlet级数与下侧二重Laplace -Stieltjes积分的有关结果 .
短句来源
     A holomorphic function of bicomplex number corresponds to a holomorphic mapping on C2 which satisfies the complex Cauchy-Riemann equations. It is known that the holomorphic solutions of complex Cauchy-Riemann equations are essentially the direct product of two holomorphic functions of one complex variable. In this short note, we prove that in the complex Banach space, the holomorphic solutions of the Cauchy-Riemann equations have the same property.
     二重复数是复数的一种推广,在其上的全纯映照族对应于C2上满足复Cauchy-Riemann方程的全纯映照族.可以证明,这样的映照族本质上是由二个单复变数的全纯函数的直乘积所组成的族.本文证明:即使在Banach空间中,Cauchy-Riemann方程的全纯解,具有同样的性质.
短句来源
     The study of analytic function spaces of one complex variable has a long time, and obtains a lot of complete results.
     单复变数解析函数空间H~p、D~P等的研究已有很久的历史,并且也得到了许多比较完美的结果。
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  “complex variable”译为未确定词的双语例句
     There was strong correlation between C_0+C_2 and AUC_0-12h,and the correlation between C_2 and AUC_0-4h or AUC_0-12h was both more excellent than C_0.In regression models for calculating AUC_0-12h,C_0+C_2 single complex variable was the best,SE and R-sq were 501.02 and 94.7,respectively.
     C0+C2与AUC0-12h相关较为强烈,C2与AUC0-4h和AUC0-12h的相关性高于C0。
短句来源
     Neighborhoods and partial sums of the function f(z)=z~(-p)+∑∞m=na_mz~(m-p). and neighborhoods of the function z~(-p)+∑∞m=n|a_m|z~(m-p)are studied,the method used is function of the complex variable.
     研究了函数f(z)=z-p+∑∞m=pamzm-p的邻域及部分和,并研究了函数f(z)=z-p+∑∞m=1|am|zm的邻域。
短句来源
     In this paper two theorem for the variance of from of analitic function are given from the unique theorem of analytic function,and a simple method about changing function of complex variable from form f(x+iy)=u (x,y) +iv(x,y) into f(z) is given.
     由解析函数唯一性定理推出了两个可应用于解析函数变形的定理,并给出了将复交函数由形式f(X+iy)=u(x,y)+iv(x,y)变到形式f(z)的简捷方法.
短句来源
     (2) Establish the interrelation between the forward recurrence relation and backward recurrence relation of complex variable Thiele-type GVRI (See Theorem 6.3, Theorem 6.6).
     (2) 建立起Thiele型向量有理插值j阶渐进分式递推关系与后向三项递推关系的紧密联系(定理6.3,定理6.6);
短句来源
     The results achieved mainly include three aspects:(1) Obtain the stepwise rational interpolation sequence of complex variable Thiele-type GVRI by forward the recursive approach (See Theorem 6.2, Theorem 6.4, Theorem 6.5).
     (1) 得到Thiele型向量连分式在复数域情形下的逐次渐进有理插值函数的递推算法(定理6.2,定理6.4,定理6.5);
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  complex variable
The characteristic polynomials of the fractional-order systems are pseudo-polynomials whose powers of the complex variable are non-integers.
      
These studies contain either exact solutions obtained with the aid of the apparatus of functions of a complex variable or solutions in the linearized formulation.
      
An application of methods of the theory of functions of a complex variable leads to an effective solution of the problem.
      
Here and in [1], we use and generalize the representation of the linearized conservation laws across the shock front as the conditions of a boundary-value problem for an analytic function of a complex variable as obtained in [4, 5].
      
The solution to such a problem for homogeneous anisotropic layers of different thickness by means of a special complex variable representation and linear conjugation was given in [3] by Prusov and the author of the present paper.
      
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The method of functions of complex variable is used in solving the problem of small amplitude surface waves on water generated by a vibrating side wall, the general formula for the complex velocity is given, and three different types of wall vibrations are discussed in some detail.Two different methods were used for the measurements and recording of surface waves. The experimental results in the case of small amplitude agree well with theory. Some observation and recording were made with large amplitudes....

The method of functions of complex variable is used in solving the problem of small amplitude surface waves on water generated by a vibrating side wall, the general formula for the complex velocity is given, and three different types of wall vibrations are discussed in some detail.Two different methods were used for the measurements and recording of surface waves. The experimental results in the case of small amplitude agree well with theory. Some observation and recording were made with large amplitudes. Second subharmonic vibrations were observed in the surface waves when the driving frequency is above a certain critical value. This phenomenon is yet to be accounted for theoretically.

侧壁振动所产生的小振幅表面波的理论问题是一个求解具有混合边界条件的Laplace方程的问题.我们在引入一新的变量后,将它化为一Dirichlet问题,及使用复变函数方法求解,得到计算表面波复速势的普遍式.使用它得到了侧壁的三种典型振动的复速度、自由面的鉛直位移,无限远的波幅及辐射功率等.在实验中,装置了两种测量表面波的设备,证明了小振幅波的理论结果并观测了大振幅表面波的一些现象.发现在壁的恒定振幅下,侧壁振动频率有一临界值,超过它表面波的频率成为侧壁振动频率的一半,我们称这种波为半频波.关于半频波还需要可靠的理论解释.

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...

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。

On the basis of the author's former paper, in this paper the forced vibrations of rectangular orthotropic plates taking into account the shear deformation and rotatory inertia are discussed. At first, the normal modes of free vibrations are obtained. Next, using the E. C. assumption about the internal frietion and the complex variable method, the forced vibrations of rectangular plates with simply supported edges under various harmonic disturbances are solved. At last, as an example, the result is applied...

On the basis of the author's former paper, in this paper the forced vibrations of rectangular orthotropic plates taking into account the shear deformation and rotatory inertia are discussed. At first, the normal modes of free vibrations are obtained. Next, using the E. C. assumption about the internal frietion and the complex variable method, the forced vibrations of rectangular plates with simply supported edges under various harmonic disturbances are solved. At last, as an example, the result is applied to the vibrations of the ship's double bottom.

本文是作者在上一篇文章的基础上进一步讨论了矩形正交异性板在虑及剪切变形和剖面转动惯量影响下的强迫振动。文章首先讨论了固有振形的计算,然后用E.C.索洛金的非弹性阻尼假设和复变数方法求解了四周简支板在各种谐和干扰作用下的强迫振动。最后举了一个在船上应用的例题。

 
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