By means of dual variation method and deviation method this paper gives one kind of four order nonlinear differential equation and sufficient conditions for some kind of solutions .

借助双 变换 法及求导法则，给出一类四阶非线性微分方程，具有某种形式的解的充要条件，所得结论是对有关文献结果的深化与推广。

An universal dynamic equation for unrestrained body has been derived in the form of tensor by using variation method .

用张量形式通过 变 分 原理导出了无约束物体的动力学普适方程。

By using Rayleigh-Ritz variation method under additional restrain conditions the formula of critical loads of elastic buckling is obtained .

方法应用附加约束条件下 变 分 法的瑞利-里兹法，推导了弹性屈曲临界荷载的计算式并利用该方法进行了验证。

By using e of the theory of elasticity and variation method the problem of ground stress field in V-shaped river valleys is studied .

介绍了河谷地应力研究现状，利用弹性理论和 变 分 原理，研究了V型河谷岩体地应力问题，得到了河谷岩体中由于自重应力和构造应力引起的复杂应力场。

In this paper by using iteration and variation method the perturbation problem in quantum mechanics will be sloved .

本文把 变 分 法和迭代法结合起来考虑量子力学中的微扰问题，解决了微扰 方法不能解决的问题。

The nonlinear equation for remote sensing of water vapor was linearized by means of variation method .

运用 变 分 的 方法将遥感水汽的非线性方程线性化，讨论了线性化遥感方程的适用范围。

By the means of variation method the 1 + 2-dimensional symmetric paraxial sech optical beam properties is investigated in strongly nonlocal media the parameters evolution law and the critical power is obtained .

利用 变 分 法研究了1+2维轴对称傍轴Sech光束在强非局域介质中的传输特性，得到了Sech光束各参量的演化规律和一个临界功率。

The composition ratios of inclusion compounds were obtained by the continuous variation method .

用连续 递变 法测定了包合物的组成摩尔比。

Diffusion interface models particularly the phase-field model among them has been widely used in recent years . This paper gives a detailed mathematical derivation of the phase-field model for pure substance and the anisotropy is introduced by variation method .

扩散界面模型中的相区场方法近来得到了广泛应用，文章给出了纯物质凝固过程相区场模型的数学推导过程，并结合 变 分 方法将各向异性引入到模型中来。

In virtue of electromagnetic theory and variation method element analysis dispersion format and collective composite equation are given .

利用电磁场理论和 变 分 法建立了直线感应电动机起动时二维电磁场的数学模型，给出了正弦时变场单元分析过程和离散格式以及最终的总体合成方程。

Based on the generalized variation method and the energy equilibrium equation of the railway welded turnout structural system the railway welded turnout structur - al system is analyzed systematically by finite element method .

基于铁路无缝道岔结构体系分析的广义 变 分 法和能量平衡控制方程，利用有限元法对无缝道岔蛄构体系进行了全面分析。

It applies Minimax deviation method and coefficient of variation method to define weighting to avoid influences caused by human factors from subjective assignment .

该体系运用极小极大离差法进行指标的筛选，并应用 变异系数 法进行指标权重的确定。

This paper presents an analysis of curved box beam element considering shear lag and warping torsion effects . In this study the variation method is used to formulate the stiffness matrix and nodal loading vectors .

考虑剪力滞后效应和翘曲扭转的影响分析了一种曲梁单元，在研究中运用了 变 分 法形成刚度矩阵和节点荷载列阵。

We have studied the cyclotron-resonance frequency of a strong-coupling magnetopolaron in the quantum well wire with the use of variation method of Pekar type .

采用 变 分 法研究了量子阱线中强耦合磁极化子的回旋共振频率。

Combining fractional order differential theory with total variation method a new image denoising model was proposed which was based on fractional Partial Differential Equation ( PDE ) .

将分数阶微分理论和全 变 分 方法相结合应用于图像去噪，提出了一种基于分数阶偏微分方程的图像去噪新模型。

An Adaptive Total Variation Method Applied in Image Denoising

一种基于整体 变 分自适应图像平滑去噪的 方法

An electrostatic concentric spherical system model is used to test and verify the expressions of temporal aberrations given by DIM and the τ - variation method the analytical solutions prove that both of the two methods are correct and equivalent .

利用静电聚焦同心球系统理想模型的解析解检验了直接积分法（DIM）与τ 变 分 法求解成像系统时间像差系数的表达式，并证明了两者的正确性与等价性。

Based on two solving methods of mechanics problems : differential equation method and energy variation method recurrence formulae of Bernoulli series and Euler series are derived by solving a simply supported beam .

基于力学问题的二种求解方法：微分方程法和能量 变 分 法，对简支梁进行求解，导出了Bernouli级数和Euler级数的递推公式。

Dynamic pricing for perishable products by fuzzy decision and variation method

基于模糊决策与 变 分 法的易逝品动态定价

Lyapunov exponent for discrete and continuous dynamic systems are investigated and an effective criteria for determining chaos based on computing the largest Lyapunov exponent using variation method is proposed .

研究了离散动力系统和连续动力系统的Lyapunov指数，提出了定量识别混沌的新方法：计算最大Lvapunov指数的 变 分 法，为判定混沌是否存在提供了有效方法。

Multiscale Total Variation Method and Its Application in Time-Lapse Seismic

多尺度全 变 分 方法及其在时间推移地震中的应用

First we use variation method and Bessel function orthogonality to deduce the dispersion function of the slow-wave structure under the condition of neglecting the thickness of disk .

首先完善了忽略膜片厚度时同轴交错膜片加载慢波线的理论分析，采用 变 分 法和贝塞尔函数的正交性导出其色散方程，并对理论结果进行了 数值 计算。

Based on the equivalent resistance variation method a mathematical model for fatigue response under random cyclic loading is developed and the function of the full-range statistical distribution of resistance response error is also given under random loading .

在此基础上，根据电阻 变化等效 方法，建立了任意循环加载下疲劳响应的数学计算模型，并给出了任意加载下电阻响应误差的全域统计分布函数。

There arise many techniques in the study of existence of solution for operator equations such as topological transversality method upper and lower solutions method monotone iterative method and variation method and bountiful results are obtained .

在算子方程解的存在性研究中产生了许多方法，如拓扑度方法、上下解方法、单调迭代法、 变 分 方法等，获得了丰富的结果。

We must seek two main approximation methods of solution the variation method and perturbation theory .

我们必须寻求两个主要的近似解法、 变 分 法和微扰法。

The non-relativistic energies and wave functions are calculated by using Rayleigh-Ritz ′ s variation method .

非相对论能量及波函数用Rayleigh-Ritz 变 分 法确定；

Investigation of the Improved Lattice Gauge Actions by Means of the Variation Method

改进的格点规范作用 量 的 变 分 法研究

In this article we discribed the basic idea and reviewed the development of cluster variation method ( CVM ) .

本文提出了用于集团 变 分 法中计算相平衡的两相法和计算失稳点的单相法。