查询词典 condition equation

Based on second-order Laplace equation and boundary condition, obtains the integral equation after Green transformation.

基于二维Laplace方程和边界条件，经过Green转换得到以势函数及势函数法向导数为未知量的积分方程。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

The standard cell potential of each condition and the activity coefficients of KI in the mixed solvent were obtained by associating the experimental values using power series expansion method, the extended Debye-Hückel equation and the Pitzer equation.

用电动势法测定了KI在甲醇含量为0%、20%、60%、100%的甲醉－水混合溶剂中的电动势，用幂级数展开方法、扩展的Debye-Hückel方程及Pitzer方程关联不同溶剂组成下电动势的实验值，得到电池的标准电动势Eo和KI在混合溶剂中的活度系数。

In this paper, we discuss when a quartic equation has no real roots, and obtain a necessary and sufficient condition on a quartic equation which has no real roots.

本文讨论了一元四次方程无实根的一些充分、要条件，并得到了一元四次方程无实根的一个充要条件。

First, an appropriate regularizer R is chosen to weaken the ill-condition of the normal equation based on TIKHONOV regularization method, according to the characteristics of the normal equation formed by DD phase observations of the single frequency GPS receivers.

在分析病态法矩阵结构特性的基础上，基于TIKHONOV正则化原理，提出一种选择正则化矩阵R的新方法，减弱法方程的病态性。

It including the pitch point electric current equation andthe return route voltage equation two parts, former pointed out that,regarding any pitch point (3 or 3 above legs points of intersection),flows in and flows out the pitch point various electric currents algebra and is zero, this is the constant condition request, latter pointed out, regarding any closed path, each part of loss of voltage algebra and is zero, this is the electrostatic field ring circuit theorem result, two constituted the complete system of equations.

它包括沥青点电流方程强大的回路电压方程由两部分组成，前者指出，对于任何节点（ 3层或3条以上的腿分的交汇点），流入和流出草地点不同电流代数和是为零，这是恒定的条件要求，后者指出，对于任何封闭道路，每部分的损失电压代数和为零，这是静电场的环形电路定理的结果，构成了两个完整的系统方程式。

The major implementations of the developed model include: Pseudo-spectral and finite-difference schemes are employed to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. A second-order Runge-Kutta method is adopted to integrate in time for the velocity field and the free-surface elevation. The solenoidal condition of the velocity field is satisfied by solving the transformed pressure Poisson equation. A modified secant method is used to accelerate the iterative solution of the non-separable Poisson equation.

模式的主要数值方法包括：分别以拟频谱法以及二阶有限差分法近似控制方程与边界条件中的水平与垂直导数；以二阶Runge-Kutta法进行非稳态的自由液面位移与流场速度的时间积分；利用改良式割线叠代法求解计算区间中不可分离的压力Poisson方程式，以满足不可压缩流条件。

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。