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high order derivatives
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  高阶导数
     The local great-gain control system is a feedback system with high order derivatives. It can be used to restrain the perturbance, nonlinearity and parameter variation.
     局部高放系统是用高阶导数组成的反馈回路抑制干扰,非线性及变参数的影响,从而使低阶导数和位置反馈回路的性能得到改进,局部高放回路增益易调高。
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     Block θ-method has good stability, and doesn't use the high order derivatives, so it is a kind of potential methods.
     块θ-方法有较好的稳定性,又不使用高阶导数,是一个很有潜力的方法。
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     Both the derivative and high order derivatives of F(s) are very useful for finding the function \%F(s)\% and its inverse transformation, so, it is indispensable to cerify the existence and derivability of the laplace transformation of \%f(t)\% and try to find a rule of operation for it.
     而 F ( s)的导数及 F( s)的高阶导数在求 F ( s)及其逆变换时是很有用的 ,因此 ,弄清函数 f ( t)的 Laplace变换存在性、可导性及其运算规律是非常必要的 .
短句来源
     The Local Great-gain Hierarchical Decentrilezed control problem was disscused. The Local Great-gain Control is a feedback system with high order derivatives. It can realize decouple system.
     讨论了分散递阶系统的局部高增益控制问题,它是用高阶导数反馈组成局部高增益回路实现解耦,提高鲁棒性从而提高系统的可靠性和精度,为分散递阶控制提供了新方法.文中在状态空间进行了一般理论分析,给出了实际例题并给出了实现无穷增益的条件(简称为K∞控制).
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     This decomposition yields, for an appropriate gauge fixing, a Skyrme Faddeev like Wilsonian action and confirms the presence of high order derivatives of a color unit vector at the classical level.
     在一定的规范条件下 ,该分解可以导出类似于Skyrme Faddeev形式的Wilson作用量并在经典层次上肯定了色单位矢量场的高阶导数的存在 .
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  高阶微商
     On the differences in determining the time and vertical velocity characteristic scales and analyzing high order derivatives suggested by certain authors, discussions are made and preliminary conclusions are drawn, namely,τ~L/U, W≤ MUH/L and  nf/x n~F/L n,n>1 for a single scale motion.
     对在一些作者中 ,在决定时间特征尺度、垂直速度特征尺度和分析高阶微商量级上的分歧进行了讨论 ,得出了初步结论。 即对于单一尺度的运动 ,τ~ L/U、W≤ MUH/L 和 nf/ xn~ F/Ln。
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  “high order derivatives”译为未确定词的双语例句
     High order combined geometric chromatic aberrations were calculated with Differential Algebra,a method which is capable of directly evaluating arbitrarily high order derivatives with accuracy up to the upper limit of the computer to be used.
     微分代数是计算机数值计算领域中的一种强有力的新型数学方法 ,它为任意高阶微分的计算提供了一种可达到机器精度的极为简便的手段。
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     In this paper a novel nonlinear method is proposed to meet the precision demand based on the separation technique in frequency domain. After the features of high order derivatives of signal and noise in observed data are analyzed the problem of separating signal from noise is converted into an extremum problem, with the high order difference of stationary time series invariant to the variance.
     为此提出了一种可给出信号高精度估计的非线性方法 ,分析了信号k阶导数的特点和噪声特性 ,在平稳时间序列的高阶差分对方差不变性的基础上 ,将信噪分离的参数估计问题转化为一类极值问题。
短句来源
     In the process of system dynamic trajectory simulation and integration of sensitivity dynamic equations,Taylor series expansion technique is used to calculate the high order derivatives of rotor angles,speed and sensitivity variables with respect to time. Therefore,bigger simulation time step can be employed,which can improve computation speed while keeping normal calculating precision.
     在系统持续故障仿真和灵敏度动态方程计算过程中,引入高阶Taylor级数展开技术,可以在保持计算精度的前提下提高计算步长,显著提高计算速度。
短句来源
     In the process of state estimation, AC and DC equations are solved in turn, keeping all high order derivatives of Taylor series for the DC equation.
     在估计过程中交直流方程交替求解,并对直流方程采用保留泰勒级数展开式中所有高阶项的方法。
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  high order derivatives
The proof consists in studying high order derivatives of the pressure pγ(h), which is related to the free energy fγ(m) by a Legendre transform.
      
Given an algorithmUL that finds all the solutions of linear homogeneous differential and difference equations in some linear space L, we describe two algorithms that construct all solutions whose high order derivatives (or differences) are in L.
      
In this paper the uniform convergence of high order derivatives of ?n to the corresponding derivatives of ? is proved.
      
Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained.
      
Reconstruction of high order derivatives from input data
      
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In this paper we discussed mixed problems for the second order quasi-linear hyperbolic partial differential equations, which involve small parameter in the higher order derivatives. As ε=0, the original equations are degenerated into the lower order differential equation, and the part of boundary conditions is losed. The problems of this type are called a singular perturbation problems. We constructed an asymptotic solution of the presented problem and invstegated the asymptotic behaviour of...

In this paper we discussed mixed problems for the second order quasi-linear hyperbolic partial differential equations, which involve small parameter in the higher order derivatives. As ε=0, the original equations are degenerated into the lower order differential equation, and the part of boundary conditions is losed. The problems of this type are called a singular perturbation problems. We constructed an asymptotic solution of the presented problem and invstegated the asymptotic behaviour of the solution.

在本文中讨论了含有小参数ε在高阶导数项的二阶拟线性双曲型方程混合问题的渐近解,当ε=0时原方程退化为低价的偏微分方程,失去部份的边界条件。这类问题称为奇异摄动问题。我们构造了这一问题解的浙近表示并研究了解的渐近性质。

In this paper we discussed mixed problems for the second order quasi-linear hyperbolic partial differential equations, which involve small parameter in the higher order derivatives. As ε=0, the original equations are degenerated into the lower order differential equation, and the part of boundary conditions is losed. The problems of this type are called a singular perturbation problems. We constructed an asymptotic solution of the presented problem and invstegated the asymptotic behaviour of...

In this paper we discussed mixed problems for the second order quasi-linear hyperbolic partial differential equations, which involve small parameter in the higher order derivatives. As ε=0, the original equations are degenerated into the lower order differential equation, and the part of boundary conditions is losed. The problems of this type are called a singular perturbation problems. We constructed an asymptotic solution of the presented problem and invstegated the asymptotic behaviour of the solution.

在本文中讨论了含有小参数ε在高阶导数项的二阶拟线性双曲型方程混合问题的渐近解,当ε=0时原方程退化为低价的偏微分方程,失去部份的边界条件。这类问题称为奇异摄动问题。我们构造了这一问题解的浙近表示並研究了解的渐近性质。

This paper deals with the near-tip singular fields for Mode-Ⅲ crack growing quasi-statically and steadily in a power hardening medium. In Section 2 the basic equations are set up and in Section 3 the contiguity conditions for neighbouring domains (3.1), (3.7) and also the supplementary conditions (3.8) for the unloading boundary and (3.15) for the reloading boundary are derived. As shown in Fig. 1, the near-tip region (upper half-plane) is composed of the active plastic zone Ⅱ, the unloading wake zone Ⅲ, and...

This paper deals with the near-tip singular fields for Mode-Ⅲ crack growing quasi-statically and steadily in a power hardening medium. In Section 2 the basic equations are set up and in Section 3 the contiguity conditions for neighbouring domains (3.1), (3.7) and also the supplementary conditions (3.8) for the unloading boundary and (3.15) for the reloading boundary are derived. As shown in Fig. 1, the near-tip region (upper half-plane) is composed of the active plastic zone Ⅱ, the unloading wake zone Ⅲ, and the reloading plastic zone Ⅳ, subtending angles θP, (π - θp - θs) and θs respectively.In Sections 4 and 5 the stress fuction (?)is solved in the form of a series (4.1) in [In (A/r)]-1, and the near-tip stress and strain fields are obtained to within a parameter, say the parameter 8 ( = cFn-1G, n, c being material constants, G the shear modulus and F the intensity of stress singularity), which varies in a range Str≤S≤ Sb, corresponding to the segments MnNn on the S versus θP curves in Fig. 4. θs versus θp curve is given in Fig. 3. Mn state corresponds to a trivial solution (5.16), with the same values of angles θP,tr and θs,tr as for elastic perfectly-plastic medium. Nn state corresponds to the upper bound θb of the angle θP. θb is the natural boundary for the solution of the differential equation (5.11), i.e. θb is determined by the condition that the coefficients of the highest-order derivative f1*"(θ) in (5.11) should vanish at θ = θb (see (5.17)). For elastic perfectly-plastic material (n→∞), MnNn in Fig. 4 shrinks to a point (θP = θp,tr S = 0.5), which corresponds to the solution given by Chitaley and McClintock. For several values of n, the near-tip stress and strain distribution is shown in Fig. 5 and 6. It is seen from these Figures that the difference between the extreme states Mn and Nn is only slight. It is expected that a inner boundary-layer type of solution exists in the neighbourhood of the unloading boundary Γa (Fig. 1). The consideration of this boundary-layer solution will be necessary for the determination of the unique true solution (corresponding to some state on the segment MnNn in Fig. 4), with vanishing plastic strain rates on the unloading boundary, λ|ΓB = 0. The determination of this unique true solution will be given in a separate paper.

幂硬化材料稳恒扩展裂纹奇异场的分析是久未解决的困难问题。本文对Ⅲ型问题得到了含有对数奇异性的解,给出了尖端附近应力与应变的奇异场的可能变化范围。

 
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