查询词典 simultaneous equations

The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations.

用Prandtl 座标转换的观，将波形表面变成一规则的平面，其次用级分析，进一步推导出系统的边界层方程式。

The second part deals with renormalization group equations in general gauge field theories. In this part, the complete set of two-loop renormalization group equations in general gauge field theories is presented.

第二个部分主要讲述了规范场理论中的两圈重整化群方程，我们给出了一组完整的一般规范场的两圈重整化群方程。

If you later add more equations to the paper before the referenced equation, all the equations will automatically renumber and the cross-references will update.

就算以后您在前面加入新的公式，它们都会自动编号，交叉引用编号也会自动修改。

By solving the optimum -- diameter equations for the case of critical Reynold number, it has been found possible to decide whether any given flow will be turbulent or viscous in a pipe of optimum diameter. At these equations and ...

本 文所推导的公式及算图都是以我国目前的价格指标为依据，因此应用它来选取经济管径应当是适合于我国情况的。

Thirdly,we study certain Riemann boundary value problems and Singularintegral equations with values in a universal Clifford algebra 〓,by com-bining the classical methods of solving Riemann boundary value problems andsingular integral equations with the Taylor's expansion of regular function in Clif-ford analysis,proving a lemma which is similar to the Painleve theorem in theclassical complex analysis,and the Plemelj formula in Clifford analysis,we obtainthe better results under weaker condition than before.

第三，本文第一次借助于用来解决经典的Riemann边值问题与奇异积分方程的方法来研究Clifford分析中的某些Riemann边值问题与奇异积分方程，获得了在比以前文献中条件更弱的情况下，结论更广的结果，并且，它为更进一步地解决在Clifford分析中一般的Riemann边值问题与奇异积分方程提供了基本的解决思想，为这一新的研究领域奠定了基础。

It introduces partial fractions of meromorphic functions, product developments of entire functions, Hadamard's theorem, Riemann Zeta functions, Poisson-Jensen's formula; elliptic functions, including simply periodic functions and doubly periodic functions; algebraic functions and algebroid functions, Riemann surface, Nevanlinna theory, including characteristic functions, the first and second fundamental theorems, growth orders, etc; complex differential equations and complex functional equations, etc.

具体为：亚纯函数的部分分式、整函数的无穷乘积展开、Hadamard定理、Riemann Zeta函数、Poisson-Jensen公式；椭圆函数，包括单周期函数、双周期函数；代数函数和代数体函数、Riemann曲面简介；Nevanlinna理论简介，包括特征函数、第一和第二基本定理、增长级等；复微分方程和复函数方程，等等。在教学内容上充分体现基础性、新颖性。

In this method, the decision-making variables of GA are the unknown quantities of the non-linear equations, the target function for optimization is the minimum of the root-mean-square error between the computational value on the left and the real value on the right in equations, and the initial value is generated randomly in the feasible fields of the decision-making variables.

该算法以非线性方程组的待求量为决策变量，方程组两端向量的均方差最小值为目标函数，初值在决策变量可行域内随机产生。

Divide the whole region D into finite units and corresponding link points may be obtained. Constructing the equation of variation calculation about every element leads to the finite number of equations. Further more, algebra equation group for general synthesis are gained by adding these finite number of equations, that is,{T}={P} where is the coefficient matrix of the equation group, or say the temperature rigidity matrix,{T} is the row vector of unknown temperature and {P} is the row vector of the terms on the right side of the equation.

然后将整体区域D划分成有限个单元并得到相应的有限个节点，从而可以得到关于每个单元的变分计算方程，将这有限个方程相加就得到了总体合成的代数方程组，即{T}={P}，其中为方程组的系数矩阵，也称温度刚度矩阵，{T}为未知温度值的列向量，{P}为等式右端项组成的列向量。

In the analysis, a nonlinear wave vibration equation of the thin cylindrical shell including damping and items due to geometric nonlinearities was established and then transformed by Galerkin's method. With different combinations of modes different nonlinear differential equations in modal coordinates were obtained. The Runge Kutta method was used to solve the equations numerically and some features of nonlinear wave vibration were discussed.

在研究过程中，首先，考虑阻尼并引入几何非线性项，建立薄壁圆柱壳的非线性波动方程，然后，采用Galerkin方法对波动方程进行转换，选取不同的模态组合，得到相应模态坐标下的非线性微分方程，最后用Runge-Kutta法进行数值计算并对圆柱壳的非线性波动振动特性进行了分析。

Firstly,using the method of concentrate mass this paper establish a non-linear dynamics model of a two-stage gear train with backlashe between the gear pair,and through analysed the dynamics model,the torsional motion differential equations are got , on this basis,then calculate the torsional motion differential equations using Runge—Kutta method ,and discuss how to influence the dynamics characteristic of system when these parameters chage such as mesh frequentcies、 stiffness of the intermediate shaft、the ration of mesh frequentcies.and discuss when the chaos will happen under the change of these parameters.

首先用集中质量法建立系统的含间隙的非线性动力学模型，并根据牛顿力学定理，得到系统的运动微分方程。然后对所建立的运动微分方程运用四阶变步长Runge—Kutta方法进行了求解，并对计算结果进行分析，研究了齿轮啮合频率、中间联接轴的刚度，一、二级齿轮的啮合频率比等参数变化时，对系统非线性动力学特性的影响规律，并讨论了当参数如何变化时会导致系统的混沌响应的出现。

That's what makes this mod unique.

这也正是这个MOD独特。

I now feel furious and want to do something.

现在我觉得非常气愤，想做点什么。