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the asymptotic expansion
相关语句
  函数的渐近展开
     When parameters of the input of a large scale system deviate, its approximate reduced order model can be obtained by using the asymptotic expansion of the input function.
     当大系统的输入函数的初始参数发生偏离时,其最优简化模型的近似模型可以利用输入函数的渐近展开得到。
短句来源
     We have dealt with integral evaluation of a general exponential integrand by use of the tech- nique of steepest descent,and interpreted that it can be related with usual stationary phase and saddle point method. Its application to the asymptotic expansion of the Γ function and the analysis of Fresnel diffraction by a straightedge barrier indicate that the approximation is widely valid because the ealculation results are good.
     我们用最陡下降法处理一类指数型被积函数的积分的估值问题,解释了它与稳定相分析及鞍点法之间的联系.把这种方法用于Γ函数的渐近展开和直边阻挡物的菲涅耳衍射得出很好的结果,说明这是一种有效的近似方法.
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  “the asymptotic expansion”译为未确定词的双语例句
     This paper discusses the first step of the asymptotic expansion of the weak nonlinear equation y ″+y ′=-ε(λ 1 sin y ′+λ 2e y ) using the method of two variables, and obtains the following result: y=a cos( t+β ). where a and β are determined by a =- λ 1∑∞n=1(-1) n+1 na 2n+1 (n!)
     用两尺度法探讨了弱非线性振动系统y″ +y′=-ε(λ1 siny′ +λ2 ey)的一阶一致有效展开式 ,得到结果y=acos(t+ β) ,其中a和β由a =-λ1 ∑∞n =1(-1) n + 1 na2n + 1(n !)
短句来源
     On Series of the Asymptotic Expansion for n∫ π/2 0 sin nx d x(n→∞)
     关于n~(1/2)∫_0~(π/2)(sin~nxdx(n→∞))渐近级数展开计算
短句来源
     On the Asymptotic Expansion Formula of ln2
     关于ln2的渐近展开公式
短句来源
     A New Method of Deriving the Asymptotic Expansion of the Integral ∫f(x, {λx} )dx and Its Remainder Estimates
     关于积分∫f(x,{λx})dx渐近展开的一种新推导及余项估计
短句来源
     The asymptotic expansion as follows n∫ π/2 0 sin nx d x~π2∞i=0a in i is set up by using the result in reference where a l is inferred from the recursive formula as follows: li=0a ib l-i =(-1) l1/2(1/2-1)…(1/2-l+1)l!
     运用文献[1]的结果建立了如下的渐进展开式:n∫π/20sinnxdx~π2∞i=0aini其中,al由下面的递推公式所决定:li=0aibl-i=(-1)l1/2(1/2-1)…(1/2-l+1)l!
短句来源
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  相似匹配句对
     The Asymptotic Expansion of C-semigroups
     C-半群的渐近展开
短句来源
     THE ASYMPTOTIC EXPANSION OF INTEGRAL
     积分的渐近展开式
短句来源
     ASYMPTOTIC EXPANSION FOR T DISTRIBUTION DENSITY
     t-分布密度函数的渐近展开
短句来源
     Asymptotic Expansion of Cubic Spline
     三次样条函数的逐项渐近展开
短句来源
     ASYMPTOTIC EXPANSION OF THE TENSION SPLINE FUNCTION
     关于张力样条函数的渐近展开
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  the asymptotic expansion
A method is proposed which permits constructing the asymptotic expansion of any order in the small parameter ε, which characterizes the viscosity and thermal conductivity coefficients.
      
The fourth term of the asymptotic expansion of the tangential-velocity component is obtained.
      
The second and third terms in the asymptotic expansion of the stream function in the nonsimilar problem of the development of a two-dimensional turbulent jet in an unbounded space are found in final form.
      
In the articles published on the Blasius problem [1-3] the solutions are investigated either by some numerical method or by joining the series solution for small values of the argument with the asymptotic expansion for large values.
      
The first two terms of the asymptotic expansion with respect to the small Reynolds number are obtained for the mean Sherwood and Nusselt numbers.
      
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In this paper, we suggest one method of finding the Green tensor functions in whole space, which are defined in formula (3). Some times it is also called the elementary solution of the corresponding differential equation. All this method is based on Fourier transform. Owing to complexity, we are obliged to make some simplifications. Magneto-gyrotropic media and electric-gyrotropic media are considered separately. For magneto-gyrotropic medium, such as ferrite, μ, is a tensor while s remains scalar. Conversely,...

In this paper, we suggest one method of finding the Green tensor functions in whole space, which are defined in formula (3). Some times it is also called the elementary solution of the corresponding differential equation. All this method is based on Fourier transform. Owing to complexity, we are obliged to make some simplifications. Magneto-gyrotropic media and electric-gyrotropic media are considered separately. For magneto-gyrotropic medium, such as ferrite, μ, is a tensor while s remains scalar. Conversely, for electric-gyrotropic medium, such as plasma, e is tensor and μ remains scalar. Taking advantage of the smallness of matrix μp (defined in (15)) we make an expansion in power series of μp, and carry out the calculations in first order approximation. The concrete results are expressed in formulae (23)、(25)、(28)、(32) and (33). The physical meaning of Γ and the effective region of the asymptotic expansions are discussed.

本文提出一个方法,来推求在(3)式中所定义的、在全空间中的格林张量函数。它有时亦称为对应微分方程的基本解。这个方法是以富氏变换为基础。由于问题的复杂性,我们不得不作某些近似。首先,把各向异性介质分为两类,一类是磁迴旋介质,另一类是电迴旋介质。对于磁迴旋介质,如铁氧体,取为张量而ε为标量。而对电迴旋介质,如等离子体,取为张量而μ为标量。其次,由于矩障非常小(在(15)式中定义),我们可以把解展为的冪级数,并计算出一级近似。具体结果在式(23)、(25)、(28)、(32)和(33)中表示。最后对Г函数的物理意义和它的渐近展开式的有效范围作了讨论。

In this paper the existence and uniqueness of the solution of the boundary value problem for the ordinary differential equation (u—scalar function) and the asymptotic expansion of the solution with respect to the small parameter were discussed, taking the smoothing of discontinuous solutions of Riemann problem for quasilinear hyperbolic differential equations as a background. The asymptotic expansion of the solution of the equation for the given initial values was also given in passing.

本文以准线性双曲型方程Riemann问题间断解展平为背景,讨论了常微分方程边值问题 e d~2u/dξ~2=F(ξ,u)du/dξ (u——数值函数)u(-∞,∈)=u~-(∈),u(∞,∈)=u~+(∈)解的存在性、唯一性和解对小参数∈的渐近展开,顺便,也给出了方程满足初值条件 l(ξ_0,∈)=a(∈),u'(ξ_0,∈)=b(∈)/∈的解之渐近展开式。

Taking the problem of smoothing the discontinuous self-similar solutions of the system of hyperbolic equations as a research background, in the paper is discussed the asymptotic expansion of the solution of the equation of second order with a small paramater εu″=F(ξ, u)u′which satisfies the boundary value conditions u(-∞)=u~-(ε), u(+∞)=u~+(ε). This paper is the continuation of the paper [2].

本文以拟线性双曲型方程组自模间断解的展平问题为背景,讨论了带小参数ε的二阶方程式满足边值条件的解之渐近展开,是文献的续篇。

 
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