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The numerical results show that our method is effective. For the noncharacteristic Cauchy problem for 2-D and 3-D heat equation, we give the explicit H\"{o}lder type stability estimates by using weighted energy method. Especially,H\"{o}lder type stability estimate for discrete solutions of the heat equation is obtained through a fully discrete method. The numerical results are presented.

对于二维和三维的热传导方程的非特征Cauchy 问题，我们利用权函数方法，给出了一个显式的H\&{o}lder 型的稳定性估计，特别的，对于二维的非特征Cauchy问题，我们利用充分离散的方法，对二维问题的离散形式同样给出了H\&{o}lder 型的稳定性估计，同时，我们也给出了数值例子来说明我们的估计。

Numerical simulation for nonuniformly injected SOAs is an important basis for the device characterization, fabrication, and applications. We can conveniently and fleetly obtain the device characters and the effects of each design parameter through numerical simulation.

对非均匀注入SOA的数值仿真是研究其器件特性、器件制作、拓展其应用的重要基础，通过数值仿真我们可以方便快捷地获得器件的特性及各参数对其特性的影响，运用分析的结果来指导器件设计。

By using this method, the memory space is reduced observably while guaranteeing the numerical simulation accuracy through numerical simulation.

仿真结果表明，该方法在保证数值模拟精度的条件下，大幅削减了空间需求。

Some unique techniques including topographics smoothing, overbank flowing, numerical filtering, auto-adjusting of roughness were adopted in this numerical simulation, and ADI method was improved in sweep by two-direction and two-step scanning.

数值模拟中还采用了地形平滑、水流漫滩、数值滤波及自动调糙率等几种处理技术，并对ADI法进行了双向双步扫描改进。

However, such tidal overheight is often ignored in the current regional numerical simulation due to intensive computational requirement. Only the mean sea level is used as the fixed seaward boundary, which may wrongly predict the groundwater table position. Therefore, we aim to determine an equivalent seaward boundary through numerical modeling. The equivalent seaward boundary takes into account the tide-induced overheight effects.

然而，由于潮汐动边界处理的复杂性而导致巨大的计算量，在现有的区域地下水数学模型中，潮汐引起的海平面波动通常被忽略，仅仅以平均海平面高度作为模型的海岸边界条件，其预测出的地下水水位位置与实际情况可能会有一定的误差。

The key elements and techniques of the numerical wind tunnel are studied and analyzed.The basic idea of CFD is expatiated and the whole working process is presented.Discrete methods of the control equations based on the finite volume method and the PISO algorithm about the fluid numerical computation are researched also.

对基于CFD的数值风洞关键基础和技术进行研究分析，阐述了CFD的基本思想，研究了基于有限体积法的控制方程的离散方法以及流场的数值求解的PISO算法。

Organization: Manufacturing Engineering Institute, Chongqing UniversityAbstract: Based on the influences of opposite clearance on computer numerical control machining, the CNC code precompensation method of the CNC machining opposite clearance is introduced, and the precompensation process of opposite clearance is also introduced. The vector operation rules are used to research the algorithm of precompensation, and the proposed algorithm has been applied in a special numerical control equipment.

摘 要：在分析反向间隙对计算机数控（computer numerical control，CNC）加工影响的基础上，提出一种数控加工反向间隙的数控代码预补偿法，给出了反向间隙预补偿流程，并采用向量运算规则进行了预补偿实现算法研究，所提算法已在某专用数控设备上得到应用。

The velocity-stress pseudospectral method, an efficiently numerical modeling method, is easy to implement, with a high computation efficiency and can overcome numerical diffusion of the frequency efficiently.

模拟结果表明，伪谱法是一种有效的地震波数值模拟方法：易于实现，计算速度快、计算效率高，其计算速度是有限差分方法的数倍，能有效克服数值频散。

This paper uses a physical model to check the reliability of the numerical modeling proposed by Chen. As an example, this paper deals with a horizontal well pumpage underneath a river bed, or a vertical well adjacent to the bank of the river. We use the numerical method of Chen to simulate the groundwater flow pattern of the physical model.

论文针对具有典型意义的河床下水平井或傍河垂直井地下水流问题做了砂槽物理模拟，并用基于&渗流－管流耦合模型&和&等效渗透系数&的数值方法仿真模拟了此条件下地下水流的规律。

The numerical calculations of quaternion matrices The quaternionic quantum mechanics is a new coming disciplines of physics, because of noncommutation of quaternions, some numerical calculation methods of quaternion and quaterinon matrices are complicated and tedious.

四元数矩阵的数值计算问题四元数量子力学是近十几年来才发展起来的一门新兴的物理学科，由于四元数乘法的不可交换性，使得四元数量子力学中的四元数数学理论基础，特别是有关四元数问题的数值计算方法很不完备。

Putt your way through 36 fun-filled holes of minigolf on 3D designed courses with elevated greens, bunkers, bridges and water hazards, among other crazy obstacles.

您的推杆方式，通过36个有趣的填孔迷你的三维设计的课程，以提升绿党，掩体，桥梁和水的危害，除其他疯狂的障碍。

Some participles can be used either as attributes or as predicatives.

有些分词既可当定语用，也可当表语用。