等价方程

Rational fraction, rational base function and homogeneous coordinate.

NURBS曲线方程具有三种等价形式：有理分式表示、有理基函数表示和齐次坐标表示。

And designs a new algorithm which can judge whether or not a given nonnegative integral vector corresponds to a friable trasition sequence. Then the algorithm is used to analyze the reachability of net system which has unique reachable vector or has no T-invariants.

4对可达性与可达方程可满足性相互等价的证明进行补充，给出一个判定非负整数向量是否为可执行向量的判定算法，最后利用该算法对唯一可达向量网和不含T-不变量的Petri网的可达性进行判定。

First of all, the structural analysis under the action of random loads is carried out and the mean value and variance of all joint's displacement and bar's stress in the structure are obtained by means of three fundamental equations (equilibrium, physical and geometric) in structural mechanics, as well as the property of moment of random variable.

通过引入可靠性安全系数，并利用结构力学的三个基本方程，将结构的位移和杆件应力可靠性约束等价显示化为设计变量的线性函数，使原基于可靠性的优化模型转化为常规的序列线性规划问题，利用修正的单纯形法求解。

Byusing several technologies including linearization method, penalty function, virtual observation equation and equivalent weights method, the robust data reconciliation problem can be transformed into a least squares estimator problem.

通过使用线性化方法、罚函数法、虚拟测量方程和等价权法，鲁棒数据校正问题被转化为最小二乘估计问题。

Such as seeking the solution of inverse matrix and maximum unconcerned system of linear equations,and solution of matrix equation,proving equation of system of vectors,and judging the linear independence of system of vectors,etc.

可以用来求逆矩阵，求向量组的极大无关组，证明向量组等价，解线性方程组，解矩阵方程和判断向量组的线性相关性，等等。

Can be used to inverse matrix, and Vector Group's nothing to do great group that Vector Group equivalent, of linear equations, and the judgement of the matrix equation Vector Group's linear, and so on.

可以用来求逆矩阵，求向量组的极大无关组，证明向量组等价，解线性方程组，解矩阵方程和判断向量组的线性相关性，等等。

Moreover, Problem I can be transformed equivalently into a problem that finding the minimum norm least-squares solution of a new inconsistent matrix equation.

而问题Ⅰ可等价转化为求一个新的不相容矩阵方程的最小范数最小二乘解的问题。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

On the other hand, it is exemplified in the present paper that the principle of material frame – indifference with the admissible equivalent dynamic processes of a body by Truesdell and Noll (1965) [14] is more convenient than the form-invariance of constitutive functionals by Svendsen and Bertram (1999) [13] and Liu (2004)[4], especially for the rate-form constitutive equations.

通过例子说明了Truesdell和Noll 用等价动力过程，关于物质标架无关性原理的陈述，比Svendsen 和Bertram及Liu的本构关系在参考标架变换下的形式不变性更合理且方便，尤其是对微分方程形式的本构关系更是如此。

In this paper, we will study the definination of lines of curvature and the correlative conception, for example, normal curvature, principal direction and principal curvature and so on, the connection of lines of curvature and correlative conception, especially probe into the solution with the equation of lines of curvature and the equivalence with its determinant theorem.

本课题主要研究曲率线的定义及其相关概念如法曲率、主方向、主曲率等，曲率线与相关概念的关系，重点探讨了曲率线方程的求解及曲率线判定的等价定理。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失