查询词典 derived equation

The particle motion differential equation is analysed detailedly and the three-dimensional direct numerical method of particle motion differential equation is established.

论文对颗粒运动微分方程进行详细的分析讨论，建立了三维颗粒运动微分方程的直接模拟数值方法。

The quaternion calculation for spacecraft attitude determination is investigated in this paper,including the transformation between quaternion and the direction cosine matrix,the quaternion differential equation,the selection of time steps for integrating the quaternion equation,and the compensation methods for the noncommutativity error in high dynamic motion.

介绍了四元数计算中的相关问题，包括四元数与方向余弦阵之间的转换、四元数运动方程、求解四元数运动方程时积分步长的选取和高动态应用中非互易误差的补偿，此外还介绍了对偶四元数的发展。

Using the directional derivative formula, the governing equation is discreted in the physical domain in which a nonorthogonal grid system is used. Two kinds of AF2 schemes, i. e. AF2-plane relaxation and full implicit AF2, for the TSD equation are proposed. Numerical results show that the full implicit AF2 scheme converges faster than AF2plane relaxation scheme. For the rectangular wing and swept wing, the results of the present method are compared with FP results, and the agreement is good.

采用适合于梯形机翼和后掠机翼的斜网格，利用方向导数公式直接在物理空间对主管方程进行离散；将近似因式分解方法应用于绕机翼的跨音速小扰动势流问题，提出AF2—面松弛和AF2全隐式两种迭代格式，并对它们的收敛速度进行比较，结果表明后者明显快于前者；直机翼和后掠机翼的算例表明，本文方法的结果与精确势流方法的结果吻合良好。

Apparently, the approximate controllability doesn"t hold for generally linear parabolic equations with bounded control. It doesn"t hold for the semilinear heat equations presented there,either. Then, it is proved by analyzing its" solutions that no matter how long the time T is , there are targets that can"t be approximated by the solution of heat equation with Dirichlet boundary conditions;If a given target satisying certain conditions can be reached by the solution of heat equation .

本文先针对两个具体的半线性热方程系统证明了控制加约束后系统是不能控的；然后通过分析方程的解，对带位势及Dirichlet边界条件的热方程系统，无论时间多大，都存在不能控的目标；文中还证明了满足一定条件的目标可达。

In this thesis, the virtual boundary integral equation is based on double layer potential with the virtual density to be determined on virtual boundary. Since this integral equation related to double layer potential only involves the computation of the normal derivative and second normal derivative of fundamental solution, the exponential integral function is not involved in it, so numerical computation for the exponential integral function is avoid.

本文则基于双层位势，引入虚拟矩密度函数来建立虚边界积分方程，并首先对时间变量进行解析积分，在虚、实边界上采用常单元和等额配点离散，该方程只涉及含基本解的法向导数及其二阶法向导数项的计算，对时间变量进行解析积分后，不会出现对指数积分函数的空间变量的积分计算。

Through the decompositions to common-shot gathers and common-offset gathers, one can obtain common p, plane wave gathers and common P plane wave gathers which are suitable to the single square root extrapolation equation and the double square root extrapolation equation, respectively.

通过对共炮点道集和共偏移距道集地震数据的平面波分解，分别得到适用於单平方根波场外推方程和双平方根波场外推方程的共P平面波道集和共P平面波道集。

The dynamical processes of nutrient release were described correctly by Elovich equation S(subscript t=a+blnt, double constant equation InS(subscript t=a+hlnt and parabola diffuse equationS(subscript t=a+bt^0.5 and nutrient release rate could be described by parameter b of all equations.

结果表明，20℃恒温模擬条件下缓释复合肥氮、磷、钾养分缓释性能较佳，3种养分释放的动力学过程可用Elovich方程S=a+blnt、双常数方程InS1=a+blnt和抛物线扩散方程S=a+bt^0.5表征，各方程参数b值均可用於描述缓释复合肥氮、磷、钾养分释放速率。

Comparing with the equation of common machine tools, this equation has three characteristics: It includes the variable frequency driver's energy loss;The variable frequency driver's no-sine voltage wave causes mechanical pulse losses in mechanical driving system;Equivalent palstance of main driving system is of uniform continuity.

该方程相对于普通机床功率平衡方程，具有变频器自身存在较大的能量损耗、变频器输出的非正弦波形电压带来的电气谐波损耗和机械传动系统的机械脉动损耗、主传动系统当量角速度具有一致连续性等三个重要特点。

The linear function applicable scope is broad, when the reservoir turnover water volume and the time, the student leaves the staircase mouth population and the time and the time and the motion communication speech spends the comparison and so on the relational question has the important application;The study linear function, may deepen in the life the linear question understanding and the understanding, is helpful in solves some simple function problem; The linear function some problem solving method has the universality in mathematics, the linear function related theory may use for to solve some other mathematics problem, For instance the dual linear equation group, a Yuan inequality, a Yuan quadratic equation most value question and some complex mathematics question, the light is studies the linear function the theory is insufficient, the key is can utilize actual the linear function goes is our final goal.

一次函数的适用范围广，在蓄水池的进出水量与时间、学生出楼梯口人数与时间与时间和移动通讯的话费比较等的关系问题时均有重要的应用；学习一次函数，可以加深生活中线性问题的认识与理解，有助于解决一些简单的函数问题；一次函数的一些解题方法在数学中具有普遍性，一次函数的有关理论可以用来解决一些其它的数学问题，比如二元一次方程组、一元一次不等式、一元二次方程的最值问题及一些复杂的数学问题，光是学习一次函数的理论是不够的，关键是能把一次函数运用到实际中去才是我们最终的目的。

The main works in this paper are as follows:(1). In this thesis, a new method, continuous linearization model, is constructed for the non-linear dynamic systems. The precision Duhamel integration solution for the linearization equation is also given from the theory of linear differential equation. The calculating results show that the new method can improve the calculation precision greatly. In fact, the truncation error is not limited by this method, it can arrive the precision according to the requirement.

本文的主要工作有以下几个方面：(1)由于非线性项的存在，使得多数情况下难以得到非线性动力方程的解析解表达式，目前常使用数值积分方法来求解非线性动力学方程的解，但常规计算方法的计算精度不很理想，本文提出了含Taylor展开项中高阶余项的非线性动力方程的线性化数值计算方法，构造了瞬态线性化方程，给出了Duhamel积分的表达式。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。