查询词典 equation of variation

Two types of new Abel differential equation are structured by method of variation replacement, variation position transformation and compound function derivation law.

借助变量替换法、交换变量位置法及复合函数求导法则，构造出两类新的 Abel型微分方程，论证它们的可积性，提供可积的判据，从而推广有关文献的结论，扩大微分方程的可积范围。

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

At the latter consolidation stage, it was assumed that the water flow only depended on water pressure and was not influenced by the air. Then the independent continuity equation of water was set up to solve variation of water pressure with time. Besides, the water and air were regarded as mixed fluid, and the continuity equation of mixed fluid was set up.

在其后的固结过程中，假定水的流出仅仅取决于水压力，不受气的影响，单独建立水的连续性方程，解水压力随时间的变化；又将水和气看成混合的可压缩流体，建立混合流体的连续性，解混合流体压力随时间的变化。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

In chapter 4, some vector mathematical definitions are first given to position tolerance zones; second, the principle of variation geometry is introduced, and the mathematical foundation of automatic generation of a approximate linear equation of tolerance design function by variation geometry is first proven; tangent method and two-point slope method based variation geometry are main studied.

第四章首先对一些位置公差带给出了矢量化的数学定义；然后介绍了变动几何的原理，首次论证了变动几何能产生近似线性公差设计函数的数学依据，并着重研究了基于变动几何的切线法和二点斜率法。

Divide the whole region D into finite units and corresponding link points may be obtained. Constructing the equation of variation calculation about every element leads to the finite number of equations. Further more, algebra equation group for general synthesis are gained by adding these finite number of equations, that is,{T}={P} where is the coefficient matrix of the equation group, or say the temperature rigidity matrix,{T} is the row vector of unknown temperature and {P} is the row vector of the terms on the right side of the equation.

然后将整体区域D划分成有限个单元并得到相应的有限个节点，从而可以得到关于每个单元的变分计算方程，将这有限个方程相加就得到了总体合成的代数方程组，即{T}={P}，其中为方程组的系数矩阵，也称温度刚度矩阵，{T}为未知温度值的列向量，{P}为等式右端项组成的列向量。

By utilizing the expansion expression of equilibrium point of the system, the homogeneous equation s solution was obtained, and then the nonlinear differential equation was equivalent to its nonlinear Volterra's integral equation of the second kind by the constant variation method.

首先将系统在平衡点附近进行展开，求得其齐次方程的解，然后利用常数变易法将非线性微分方程变为等价的第二类非线性Volterra积分方程。

Based on variation principle, a free vibration variation-integration equation of cantilever curved pipe for conveying fluid is derived. This is a bending-torsion-fluid tree phase coupled dynamics problem. It is difficult to uncouple and to obtain bending and torsion analytic solution separately. We can only look for approximate solution or numeral results.

根据变分原理导出了悬臂输液曲管的变分－积分方程，这是弯曲－扭转－流体三相藕合的动力学问题，无法解藕而单独求出弯曲和扭转的解析解，只能作近似计算。

Mathematical analysis and experimental results show that this adaptive total variation denoising algorithm can solve the problem that Euler-Lagrange equation of the traditional total variation is not well posed, improve the deficiencies of the slow denosing speed, and reduce the step effect and noise leaving out resulting from using the traditional total variation.

数学分析和实验证明，论文提出的变分去噪模型克服了传统的总体变分模型的欧拉-拉格朗日方程非适定问题，改善了传统总体变分模型去噪速度慢、有阶梯效应、噪声遗漏等缺陷。

Then we obtain equation of variation by aciculate variation.Finally we obtain the inequality of variation of optional control.

然后利用针状变分求出系统的变分方程，从而得到了最优控制满足的变分不等式。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。