消元式

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。

The variable geometry truss mechanisms have been studied extensively and systematically by this project. The research plan has been completed all sidedly, and expected results have been obtained. Three new kinds of combination decahedrons and a new class of variable geometry truss mechanism, which is composed of an octahedron and three tetrahedrons connected in parallel form, are proposed. The position analyses for decahedrons, dodecahedrons, triple-octahedrons, combinations decahedron and a new type of structure of variable geometry truss mechanisms are presented by introducing additional extra linear displacement sensors and using resultant elimination and homotopy continuation algorithms. The method of kinematical analysis of variable geometry truss mechanisms is established.

课题组对变几何桁架机构进行了深入的研究，全面地完成了研究计划，取得了预期的成果；提出了三种新的十面体组合机构以及由一个八面体和三个四面体组成的新型变几何桁架机构的结构形式；应用结式消元、附加传感器和同伦方法等提出了十面体、十二面体、三重八面体、组合十面体和新型变几何桁架机构的位置分析方法；建立了变几何桁架机构运动分析的一般方法；建立了简洁的凯恩和拉格伦日动力学的模型；应用有限元和子结构方法，提出了变几何柞架机构弹性动力学模型，导出了逆动力学方程的显式形式；设计和研制了一台可折叠的八面体变几何杵架机构装置等。

The paper emphatically summarizes the classification, thinking mode, present status, problems and devolopment of methods for solving nonlinear system of equations, and specially recommends some practical and new methods, such as the elimination by eliminant with aid of basic sets, homotopy method and decomposition method, etc.

综述了机构学中常见非线性问题的数学模型及其解法，着重述评非线性代数方程组解法的分类、求解思路、研究现状、存在问题和发展方向，特别推荐基组结式消元法、同伦法和分解法等实用新型的解

Extraneous roots are found during the process to obtain the other 3 variables by using Euclidean algorithm.

首先使用结式对四个多项式方程直接消元，得到一个一元52次的多项式方程，用辗转相除法求其他三个变量的过程中发现了6个增根。

Firstly, four geometric loop equations are set up by using vector method in complex number fields. Secondly, three constraint equations are used to construct the Dixon resultants, which is a 6×6 matrix and contain two variables to be eliminated. Extract the greatest common divisor of two rows and two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant.

首先使用矢量法和复数法建立4个几何约束方程式；再使用Dixon结式法对3个方程式构造一个含有2个变元的6×6 Dixon矩阵，提取其中2行列元素的公因式，将新矩阵的行列式展开后得到二元高次多项式方程，该方程与剩下一个方程使用Sylvester结式消去一变元，得到一元高次方程。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。