乘法的

Based on the early works, the C program language and the least square method were used to obtain the thermal viscoplastic constitutive equation.A mechanical thermal coupled model was created and DEFORM-2D was used to analyze the thermal and mechanical parameters' changing during the process of adiabatic shearing.

我们在所作的前期工作及国内外的研究成果的基础上，应用C语言程序实现了最小二乘法拟合热一粘塑性本构方程中待定参数的求解过程；在此基础上应用DEFORM 2D 有限元分析系统对，Ti-6A1-4V绝热剪切过程中的热一力变化历史进行了分析；在数值模拟结果的基础上，进行了再结晶动力学的分析与计算。

The mean velocity distributions in turbulent boundary layers of smooth surface and two different riblet surfaces are measured with IFA300 constant-temperature anemometer in low-speed wind tunnel to validate the full development of turbulent boundary laye. Friction velocity and wall friction stress of turbulent boundary layer are obtained with the least-squares fitted curve of the sublayer velocity distribution based on Spalding formula, and virtual origin position of riblet surface can be acquired accurately.

在低速风洞中来流速度一定的情况下使用IFA300恒温热线风速仪测量了光滑表面和两种不同尺寸的脊状表面湍流边界层平均速度分布剖面，并验证了试验段湍流发展的充分性；通过应用Spalding壁面公式使用最小二乘法精准拟合了实验测量的边界层内层速度分布曲线，得到了湍流边界层壁面摩擦速度并进一步求得湍流壁面摩擦应力，较准确地计算出脊状表面的虚拟原点位置，并通过与对数律公式拟合结果比较分析，证实了该方法更加准确有效。

From the results, it is found that the second graders, after appropriate teaching and guided activities, are able to comprehend and analyze the multiplication questions in unit transformation model.

研究结果显示，偏远地区二年级的学生，在透过适当的教学及引导活动的练习后，能够在使用「一组有几个，一共有几组」的语言模式下以单位量转换的模型来分析乘法问题。

The "compressed sparse row data format" is adopted to save storage and the "mode multiplication" is used to improve the computation efficiency, so that the finite integration equation is obtained with low storage and high efficiency. To solve the finite integration equation, which is a large-scale sparse algebraic eigenvalue problem under the condition specified, the Krylov subspace iteration method is introduced and the shift-invert Arnoldi method is proposed to exclude the unphysical static electro-magnetic solution and get the needed eigensolution around the specified eigenvalue.

采用"行索引稀疏格式"压缩存贮技术节约内存，采用大型稀疏矩阵的模式乘法，提高矩阵计算效率，高效获得了离散电场分量满足的有限积分方程；针对有限积分特征方程的求解，论文介绍了大型稀疏矩阵Krylov子空间迭代方法，并提出了位移求逆Arnoldi算法，以排除非物理的静态电磁场解，获得指定频率附近的特征值。

Several models of cylindricity error evaluation,such as MZC,LSC,MCC and MIC,were given,a constriction factor model of the Particle Swarm Optimization was introduced.

建立了圆柱度误差评价的最小区域法、最小二乘法、最小外接圆柱法和最大内接圆柱法的数学模型，将一种含收敛因子的粒子群优化算法应用于圆柱度误差的目标函数的优化问题。

Monte Carlo simulations were conducted to study the new approaches of QTL mapping, the results indicated that general least squares method, which was widely applied in mixed linear model, could unbiasedly estimate all genetic main effects, including additive effects, dominance effects and epistatic effects of additive by additive, additive by dominance, dominance by additive, dominance by dominance.

对新提出的QTL分析力法进行了Monte Carlo模拟研究，结果表明，广泛应用于混合线性模型的广义最小二乘法能够无偏估计加性效应，显性效应以及加加、加显、显加、显显上位性效应等各项遗传主效应；运用线性无偏预测法能够无偏预测上述各项遗传主效应与环境的互作效应；基于QTL效应的杂种优势预测也是无偏的。

Modeling and derivation mathematics result of the use of Matlab software Simulation tests of its accuracy and error analysis, to verify the measurement of two boring bar/boring displacement signal the feasibility of the entire system, so as to the smooth development has laid a theoretical foundation.

介绍了两点法测量镗刀位置信号的方案构思，采用最小二乘法对镗杆的圆度误差和被测圆面的偏心量进行了建模计算，并对数学推导的结果利用Matlab软件进行仿真检验，对其精度和误差作了分析，验证了两点法测量镗杆／镗刀位移信号的可行性，从而为整个系统的顺利开发奠定了理论基础。

The experiments for determining the reaction kinetics of Daqing atmospheric residue were performed in a continuous flow, expanded bed rector. Four-lumped reaction kinetic model was developed to account for various feed and product fractions of Daqing atmospheric residue (gases, gas oil, residue and coke). The amounts of olefins and alkyls in the gas products were further analyzed to determine reaction kinetics of gas product distributions. Hence, a combined five-lumped reaction kinetic model was obtained for catalytic pyrolysis of Daqing atmospheric residue. The kinetic constants both in four-lump model and five-lump model were evaluated. A simulator for catalytic pyrolysis process was developed by incorporating the five-lumped kinetic model into the hydrodynamic flow model.

其次利用改进的固定流化床装置考察大庆常压渣油催化裂解反应规律，筛选反应工艺参数；分析了催化裂解工艺存在的主要化学反应类型，提出了渣油一次反应和二次反应网络图；将反应原料油作为单独集总组分，而将产品中的轻质油、气体、焦炭分别作为集总，从而建立了四集总动力学模型；在此基础上，把气体产物中的目的产物低碳烯烃独立划分，得到五集总动力学模型；采用最小二乘法分析实验数据，分别得到四集总动力学模型和五集总动力学模型中各集总间相互反应转化的反应速率常数。

To solve this problem, it is necessary not only to consider the relationship caused by the difference of the method of projection, by that of the elements of ellipsoids and by that of the original data between the new and the old coordinates, but also to consider the observation errors caused by the two measurements.

解决这一问题必须考虑两种坐标间投影方法、椭圆体元素、起算数据等不同所引起的数学关系，而且还必须考虑到两次测量所引起的测量误差。本文所提出的数学模型确保以上所述数学关系准确，在此条件下，采用最小二乘法，使得由于地图投影等因素和测量误差所引起的新、旧坐标间的差异，一次加以处理。

On the base of the data measured on automotive mechanics parameters tester, through setting up a relationship between lateral angle of tire, body roll angle, aligning torque and lateral acceleration and using method of least square, for curve fitting on non-linear data, a relationship has been found between these data and stable steering characteristics.

本文以汽车力学参数试验台测出的数据为基础，通过建立轮胎侧偏角、车厢侧倾角、回正力矩与侧向加速度之间的关系，运用最小二乘法对测试数据进行非线性曲线拟合，找出了这些数据与汽车稳态转向特性之间的关系，并按国家标准GB/T13047-91中的有关规定对被测试车辆的稳态转向特性进行了评价

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。