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  equation
    Basic Study of Electromagnetic Scattering from Dielectric and Coated Structures--Integral Equation Method and Its Fast Solver
    介质以及涂敷介质结构电磁散射特性的基础研究——积分方程法及其快速求解
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    Studies on Equation of State and Opacity of Liquid Argon
    液氩物态方程和辐射不透明度研究
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    Generation of Shockwave for Equation of State Measurements Using Long-pulsed KrF Laser
    利用长脉冲KrF激光产生用于状态方程测量的冲击波
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    Researches on Electromagnetic Scattering Algorithms Based on Integral Equation
    基于积分方程的电磁散射算法研究
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    A Study on Exact Solutions and Lie Symmetries of Differential Equation with Symbolic Computation
    微分方程精确解及李对称符号计算研究
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  equations governing
    In this thesis, at first the dynamic scaling properties of kinetic roughening surfaces, the background knowledge of dynamic scaling theory, the widely-used dynamic equations governing surface growth and the analytical approximate approaches to these equationsare introduced in detail, and then our three main research works in this field are presented.
    本文较为详细地介绍了表面界面粗化生长的动力学标度性质、动力学标度理论的基本知识、用来描述表面界面生长过程的常见动力学方程、对动力学方程进行解析近似分析以确定其动力学标度性质的常用方法以及本文在这一领域所进行的研究工作。 本文的研究工作可以分为三个方面:
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    2) Based on the Maxwell equations of nonlinear media, high-order coupled equations governing the evolution of two orthogonal polarization components of the same wave are derived by using multi-dimension derivation expansion method of singular perturbation theory, and the suitable application range is presented.
    2)利用奇异摄动多重尺度导数展开法,从非线性介质中的Maxwell方程组出发,导出了包含高阶摄动项的同一光波不同偏振分量的耦合高阶非线性薛定谔方程,并给出了其适用范围。
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    Finally, various methods, which are used to obtain the analytical solutions of the nonlinear equations governing the nonlinear waves, are introduced in great detail. We mainly introduce three methods, that is, extended hyperbolic function method, generalized projected Ricatti equation expansion method and the Tanh-function method which based on the extended projective method. We will illustrate these methods by specific examples.
    最后详细介绍各种非线性波的主导方程精确解的构造方法,主要介绍了扩展的双曲函数法、扩展的Ricatti映射法以及扩展的基于映射法的Tanh函数法这三种方法,并结合实例展示这些方法的运用。
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    The equations governing the evolution of the amplitude and phase of the Langmuir-wave are derived fully relativistically. The bistable responses of both the saturated amplitude and steady amplitude of the Langmuirwave with respect to plasma frequency and pump intensity are studied, and the applications of hysteresis to laser-plasma Beat-Wave Accelerator are discussed.
    完全相对论性地导出了郎缪尔波振幅和位相的演变方程,分别研究了朗缪尔波饱和振幅和稳态振幅对等离子体频率和泵浦光强的双稳态响应,并讨论了滞后效应在激光等离子体拍频加速器中的应用。
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    Small amplitude soliton solutions are obtained which satisfy the coupled nonlinear Schrdinger equations governing optical pulses propagation in the birefringence optical fiber.
    采用小振幅孤波近似法,得到非线性耦合Schrdinger方程决定的双折射光纤中的小振幅孤波解,它们可以同时存在于正常色散区或者分别处于正常和反常色散区.
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  equation in a
    RADIAL SOLUTIONS OF THE DIRAC EQUATION IN A LEMAITRE METRIC
    Lemaitre度规中Dirac方程的径向解
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    Relativistic BBGKY Theory and Collision Integral of Boltzmann Equation in a Magnetized Relativistic Plasma
    相对论BBGKY理论和磁化相对论等离子体中波耳兹曼方程的碰撞积分(英文)
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    A STUDY OF THE LIQUID ISOTHERAL STATE EQUATION IN A BROAD PRESSURE RANGE
    宽压力范围内液体等温状态方程的研究
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    Reaction diffusion equation in a non isothermal system affected by electrical field and stability of CNO cycle
    存在电场的非等温系统反应扩散方程和CNO循环的稳定性分析
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    Exact Solutions of Nonlinear Dynamics Equation in a New Double-chain Model of DNA
    关于一个新的DNA双链模型的动力学方程的精确解
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  “方程”译为未确定词的双语例句
    Experimental Studies of Equation-of-State Driven by High Power Lasers——The Research of Absolute Measurement of High Pressure Equation-of-State of Aluminum
    高功率激光驱动高压状态方程的实验研究——A1高压状态方程绝对测量的探索
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    Structure and Potential Energy Function for Small Carbon Cluster and Its Ions and the New Vapor-Liquid Equilibrium for Hydrogen and Its Isotopes
    碳微团簇离子结构和势能函数与氢同位素的汽液平衡新方程
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    COHERENT POTENTIAL APPROXIMATIONS FOR n-COMPONENT LIQUID ALLOYS
    n元液态合金的相干势近似方程
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    TEST OF BERNOULLI EQUAFION USING GAS METHOD
    用气体法验证Bernoulli方程
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    ON SOLVING NEUTRON DIFFUSIONS WIT H FINITE ELEMENT METHOD—"3DFEMJS":A THREE—DIMENSION FEW GROUP NEUTRON DIFFUSION FINITE ELEMENT CODE
    用有限元法求解三维中子扩散方程的研究“三维中子扩散有限元程序3DFEMJS”
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  equation
For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rationalq-difference equation.
      
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type.
      
The inverse conductivity problem to the the elliptic equation ${\rm div}((1+(k-1)\chi_D)\nabla u)=0\ {\rm in }\ \Omega$ is considered.
      
As applications, the wave equation on?+ × ?+ and the heat equation in a semi-infinite rod are considered in detail.
      
Pointwise fourier inversion: A wave equation approach
      
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  - equation
The integral-equation methods first proposed for solving filtration problems by Barenblatt [1] were subsequently used to good effect when studying cracked and porous media [2, 3].
      
However, the realization of the integral-equation method in the latter two cases [2, 3] contradicted the idea of interpenetrating continua which was used as a basis for the model of filtration in cracked and porous media [4].
      
A universal one-equation model for turbulent viscosity
      
The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model.
      
The flow past a circular cylinder with an isothermal surface at Mach numbers M∞=2 and 5 and Reynolds numbers ranging from 104 to 108 is investigated on the basis of the Reynolds equations using a differential two-equation turbulence model.
      
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  equations governing
Finite dimension of global attractors for dissipative equations governing modulated wave
      
The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.
      
The model consists of a system of partial differential equations governing intra-tumoral drug concentration and cancer cell density.
      
Difficulties associated with the fact that the transform is in general not single-sheeted arise when a linearizing hodograph transformation is applied to the equations governing the nonlinear filtration of an incompressible liquid.
      
Self-similar solution of the Navier-Stokes equations governing gas flows in rotary logarithmically spiral two-dimensional channe
      
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  equation in a
As applications, the wave equation on?+ × ?+ and the heat equation in a semi-infinite rod are considered in detail.
      
Some exact travelling wave solutions and rational travelling wave solutions of a surface wave equation in a convecting fluid are given in this paper.
      
Construction of solutions of the Boltzmann kinetic equation in a Knudsen layer
      
We consider the moment equation method for solving the Boltzmann equation in a Knudsen layer; the calculation of one of the moments of the collision integral is presented.
      
The problem arising for the Laplace equation in a region with an unknown boundary has been discussed previously in a somewhat different physical interpretation in [2].
      
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This paper investigates the general and complete form of slope-deflection equations used in structural analysis. The word "complete" indicates that all the possible deformations (deflections and rotations) and all the strain energies (due to shear, direct stress and flexure) are included in the equations. The definitions, numbers, and relations of member constants are then discussed and the general equations for computing these constants are given. By neglecting the factors of minor importance, the general form...

This paper investigates the general and complete form of slope-deflection equations used in structural analysis. The word "complete" indicates that all the possible deformations (deflections and rotations) and all the strain energies (due to shear, direct stress and flexure) are included in the equations. The definitions, numbers, and relations of member constants are then discussed and the general equations for computing these constants are given. By neglecting the factors of minor importance, the general form is reduced to the usual slope-deflection equations. Some special forms of such equations which are useful in certain practical problems are also discussed briefly, such as the slope-deflection equations including the effect of direct stress on flexure and the slope-deflection equations of semi-rigid frames. Slope deflection equations for trussed bents are also presented.

本文旨在:(1)提出完全的角变位移方程,使可精确的解算任何形式的平面刚构,只要其能视为由若干桿件组成即可。这里的所谓“完全”,系指方程中已包括一切可能的形变值在内,而且包括轴向应力及剪应力之影响。(2)全面的讨论桿件常数的定义、数量和相互关系,并供给计算各常数的最一般性公式。(3)将上述全面的和精确的公式逐步简化,以便与目前常用的公式比较。(4)讨论某些特殊情况。

In this paper it is shown that our volume visco-elastic theory of fluids is applicable not merely to the case of structural relaxation as apparently regarded by some authors, but is equally

在这篇论文里我们证明,与某些作者所了解的不同,我们的流体的容变粘滞弹性理论不仅仅是在结构弛豫的情况中有效,而是对所有三种弛豫——热弛豫、结构弛豫与化学弛豫——都是同样有效的。从我们的容变不可逆性方程可以推到Herzfeld与Rice原为热弛豫所假定的热不可逆性方程。又可以证明的是在化学弛豫的情况中我们的容变不可逆性方程也包含着Liebermann由分子运动理论考究所得到的化学不可逆性方程。 关于这理论在声吸收及速变现象中的应用,我们证明利用适当的热力学考究便可以从我们的压缩性理论所给的结果直接推到在热弛豫情况下有效的Bourgin-Kneser方程及在化学弛豫情况下可以有效的Liebermann方程。这个推导并揭发出来Liebermann的声吸收方程仅对液体说可以是一个良好的近似。 我们附带地指出,在气体的情况中,某些已发表的声吸收及速变的实量结果的准确度已可以使我们从这些结果来算定气体的静态与立刻两压缩系数β_0及β_∞,从而确定热容量的两比值γ_0及γ_∞与外态内态两热容量C~(e)及C~(i)。这样我们又能从这些结果取得...

在这篇论文里我们证明,与某些作者所了解的不同,我们的流体的容变粘滞弹性理论不仅仅是在结构弛豫的情况中有效,而是对所有三种弛豫——热弛豫、结构弛豫与化学弛豫——都是同样有效的。从我们的容变不可逆性方程可以推到Herzfeld与Rice原为热弛豫所假定的热不可逆性方程。又可以证明的是在化学弛豫的情况中我们的容变不可逆性方程也包含着Liebermann由分子运动理论考究所得到的化学不可逆性方程。 关于这理论在声吸收及速变现象中的应用,我们证明利用适当的热力学考究便可以从我们的压缩性理论所给的结果直接推到在热弛豫情况下有效的Bourgin-Kneser方程及在化学弛豫情况下可以有效的Liebermann方程。这个推导并揭发出来Liebermann的声吸收方程仅对液体说可以是一个良好的近似。 我们附带地指出,在气体的情况中,某些已发表的声吸收及速变的实量结果的准确度已可以使我们从这些结果来算定气体的静态与立刻两压缩系数β_0及β_∞,从而确定热容量的两比值γ_0及γ_∞与外态内态两热容量C~(e)及C~(i)。这样我们又能从这些结果取得一些有关分子构造及分子碰撞过程中能量转移的结论。 最后,我们讨论了我们的容变粘滞系数的定义的适当性。

It is shown that the modified Schrodinger equation proposed by Janossy cannot describe the behavior of the electron correctly. However, it is further shown that the equation can be regarded as a model of a possible phenomenalogical theory of nuclei or as a model of a possible theory of elementary particles. The quantization of the equation is discussed.

本文指出杨诺赛波动方程作为电子的个体理论的困难;指出这一类型波动方程可以作为原子核系综理论的数学形式,也可以作为元粒子系综理论的数学形式。本文并讨论了这一类型波动方程的第二级量子化问题。

 
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