查询词典 equations

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

Cardano's Ars Magna is a landmark in the history of mathematics. It started the theoretical research on algebraic equations, solved the polynomial equations of third-degree and forth-degree in a general and systematical way, and studied the imaginary number as well as its operations for the first time.

卡尔达诺的《大术》在数学史上具有重要的地位，它开创了代数方程的理论研究，首次系统地给出了三、四次多项式方程的一般解法，并且最早讨论了虚数及其运算。

Kirchhoff's Voltage Law tells us that the algebraic sum of all voltages in loop must be equal zero, so we can create more equations with current terms (I1, I2, and I3) for our simultaneous equations.

基尔霍夫的电压定律告诉我们，在环路中的所有电压的代数和必定等于零，因此我们可以为四个同时的方程式列出更多带有电流项（I1， I2，和 I3）的方程式。

In this paper, we present a method to solve system of algebraic equations or system of parametric algebraic equations by computing the normal zero decomposition of polynomial systems.

本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法。

In order that the state equations are standard or normal form, the instatevariables iR and uR in these equations should be expressed as the algebroidal function of exciting source and the state variables.

为使状态方程呈标准形式，方程中的非状态变量iR和uR必须表为激励源和状态量的函数。

Nonlinear elliptic partial different equations of second order is amain branch of nonlinear partial different equations.It has many ap-plications in mathematics,physics,science and technology,engineer-ing.

二阶非线性椭圆型偏微分方程是非线性偏微分方程的重要分支，它在数学、物理、科技和工程中有着广泛的应用。

At the same time, this thesis focuses on the theoretical research on the LBGK method and discusses the inner relation between the LBGK and the N-S equations.The relationship among the selection of velocity group , the forms of equilibrium distribution functions,and the macroscopic N-S equations is clearly revealed.LBGK method has many advantages, such as easy dealing with the complex boundary conditions and high amenability to parallel computing.

本文系统地总结了各种LBGK模型，特别是对LBGK模拟二相流和多相流模型进行了认真地研究；同时从新的角度对LBGK进行了理论研究，用全新的方法探讨了LBGK和N-S方程的本质联系，清晰地揭示了速度族的选择、平衡态分布函数的形式和宏观NS方程三者之间的关系。

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。

World War II: Battle of Saipan - Americans take Saipan.

1944年的今天，美国在塞班战役中拿下塞班岛。

When the scorner, the rejecter of truth, has become presumptuous; when the routine of work in the various money-making lines is carried on without regard to principle; when the student is eagerly seeking knowledge of everything but his Bible, Christ comes as a thief.{DA 635.3

当讥诮和拒绝真理的人，到了任意妄为时，当追求财利者罔顾按道义经营谋利时，当学人正在兢兢业业地研究各种知识，而单把圣经丢在一边时，基督要像贼一样来临。