查询词典 structure equations

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。

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。

In the fourth chapter, all the calculating equations of fault vibration frequency of gear shafting components of gear unit are summarized and the calculating equations of fault vibration fiequency of commonly used barrel-shaped roller bearing are deducted.

另外，为了防止齿轮减速机在工作时发生突发性事故和更好地延长齿轮轴系部件的寿命，需对具体的齿轮减速机设备进行在线监测和智能故障诊断方面的研究。

Instead of Gronwall\'s inequality,the non-linear Bihari inequality is crutial in dealing with the non-Lipschitz equations.Moreover,we emphasize that the dominating functions in non-Lipschitz conditions always satisfy concavity and some non-integrability near zero.The concavity is for using Jensen\'s inequality.Because of the non-integrability near zero,we can apply the comparison theorem of ordinary differential equations together with Bihari\'s inequality to yield many results.

3作为Gronwall不等式的推广，Bihari不等式在处理具有非Lipschitz系数的方程时不可或缺；同时应当注意，非Lipschitz条件中所涉及的控制函数总是满足凹性和某种零点处的不可积性：凹性是为了利用Jensen不等式；零点处的不可积性使得Bihari不等式与常微分方程中的比较定理结合在一起从而完成很多结论的证明。

The system can be widely used in belt weighing and batching process control,etc.

介绍了基于智能模糊控制的嵌入式配料系统的设计方法，对模糊PID控制过程和系统调零作了重点的讨论，同时给出了PID控制的程序流程图和系统定长调零子程序。

"I dunno," she answered,"but if you show me aroun', I'll recognize it from the lighthouse just outside the porthole."

"我不知道，"她回答说，"如果你能带我转转，我能认出来的，因为灯塔就在舷窗外。"