查询词典 dependent equations

At the same time, this thesis focuses on the theoretical research on the LBGK method and discusses the inner relation between the LBGK and the N-S equations.The relationship among the selection of velocity group , the forms of equilibrium distribution functions,and the macroscopic N-S equations is clearly revealed.LBGK method has many advantages, such as easy dealing with the complex boundary conditions and high amenability to parallel computing.

本文系统地总结了各种LBGK模型，特别是对LBGK模拟二相流和多相流模型进行了认真地研究；同时从新的角度对LBGK进行了理论研究，用全新的方法探讨了LBGK和N-S方程的本质联系，清晰地揭示了速度族的选择、平衡态分布函数的形式和宏观NS方程三者之间的关系。

In order to test and verify validity of analytical methods and codes, we solve the Poisson equations and the Helmholtz equations that have analytical solutions with complex geometry using spectral element methods.

作为验证分析方法的正确性和代码的有效性，本文使用谱元方法求解了有精确解的简单区域和复杂区域的 Poisson方程和 HellnholtZ方程。

An adaptive grid scheme controlling cell area is used to generated grids in the divergent section of symmetric annular nozzle, and the generated grids are used in the flowfield calculation through the uncoupled way. The elliptic equations are used to generate grids in three dimensional regions of FDN divergent section, the source terms used in the equations employ a mathematical form which is independent of the boundary shape and of the boundary grid point distribution, the free parameters contained in the source terms are determined by the two restraint conditions, the intersection angle of transverse grid lines with boundaries and the local curvature of the transverse grid lines at the boundaries, and the interior grid distribution controlled directly by the grid point distribution assigned on the boundaries is realized, it makes the grid more clustering near the nozzle wall. For the generated grids in the whole computational regions have a good smoothness and orthogonality, the accuracy of calculation in the flowfield is ensured.

对轴对称的环形喷管采用控制网格面积的自适应网格方法对扩散段部分进行了网格生成，并通过非耦合方式应用于喷管的流场计算中；对强制偏流喷管扩散段内的三维区域采用椭圆型方程进行网格生成，方程中的源项采用了与边界形状和边界网格点分布无关的数学形式，源项内的自由参数由横向网格线与边界的交角及横向网格线在边界处的局部曲率两个约束条件来确定，实现了由边界上的网格分布直接控制内部的网格点，使壁面附近具有较密集的网格，并且在整个计算区域内的网格都具有良好的光滑性和正交性，从而保证了流场计算的准确性。

The least norm solutions of symmetric and skew antisymmetric matrix equations (A~TXA, XA — YAD)=(D, 0)are also considered. 3. The least-squares solutions and the least norm solutions of the quaternion matrix equations AX = B and XD = E are studied by using

借助四元数的复表示方法，研究四元数矩阵方程组AX=B，XD=E的最小二乘问题和极小范数解的问题，并对主子阵约束下的方程组的解进行了讨论，得到了它们的显式表示。

The great advantage of using these difference equations is that they can be solved on a digital computer to provide approximate solutions to the differential equations.

将这个近似的差分式子代入微分方程中就得到了微分方程的差分近似，这个差分方程可直接用计算机进行求解，使计算方便快捷。

In order to obtain the variation law of temperature during casting solidification to improve casting quality,a finite element method combining with a finite difference method was used to discretize time and space variables in the governing equations of astable heat-conduction in the process of casting solidification so as to obtain the algebraic equations for casting and mold temperature.

为了掌握铸件凝固过程中温度场的变化规律以提高铸件质量，采用有限元和有限差分相结合的方法离散铸件凝固过程非稳态热传导方程的空间和时间变量，得到了关于金属铸件和铸型温度的代数方程。

The basic equations are expanded in asymptotic linear equations of each order according to small parameter of incident wave's field by perturbation method.

近年来随着计算技术的发展，有限元等数值法已广泛应用于波与结构相互作用'的计算分析。

Under some regular conditions, we propose estimating equations for H,β and θ, and computational algorithm for solving the equations. We prove that the estimators are asymptotically normally distributed.

进而我们提出了估计H、β和θ的一套估计方程，给出了求解这些方程的计算机算法，讨论了估计量的极限性质，证明了估计量是渐近正态的，并且其极限协方差阵可以被相合地估计。

Using SUSAN formed SIFT and ladder-image pyramid structure to achieve the same scale,new algorithm establish a unified set of over-determined equations of all match points.The over-determined linear equations coefficient matrix can be simplified to drop dimension,so simplify the structure of the augmented matrix and whose dimension is reduced to half.

研究了一种多目标识别算法，该算法用SUSAN角点形成SIFT特征点，采用阶梯图像金字塔结构实现尺度不变，为所有匹配点建立统一的超定线性方程组并对该方程组系数矩阵进行简化使其维数降低一半，得到增广矩阵。

By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.

利用一个新的辅助椭圆方程将求解非线性发展方程精确解的问题转化为一个代数方程组进行求解，与已有的辅助椭圆方程法的主要不同是，应用这一新的辅助椭圆方程后降低了平衡次数，减少了所得的代数方程组的个数和方程的项数，从而大大地简化了代数方程组的求解。

Aquatic or marsh-growing fern allies; known to have existed since the Cenozoic; sometimes included in Lycopodiales.

生活于水中或湿地的蕨类；从新生代生存至今；有时归于石松目之中。

The engine was uprated from a 90hp Franklin to a 125hp Lycoming.

改良过的引擎是从90hp到125hp莱康明富兰克林。