不可约方程

It s still imperfect about algebroid function, such as the relationship between the growth of algebroid function and the growth of irreducible equation coefficient, which defined the algebroid function.

中文摘要：关于代数体函数，有些结论仍不够完善，例如代数体函数的增长级与决定它的不可约方程的系数的关系。

Firstly, it's proved that the base of free monoid is unique, and that the equation of a base, a generating set and a irreducible generating set in the semigroup with length; Secondly, it's given the relation of a primitive word and a word of indecomposable--Let and is indecomposable, then is primitive ;And by using the length's method and chart,some properties of primitive word have been proved and the solutions of the equation , are discussed; Lastly, on the base of some proposition in Free monoids and Languages ,the proofs of some properties are improved by instruction. For example: Let be a primitive word over X, where .Then is a code. And let then if and only if {} is a code.

首先，讨论了含幺半群中基的基本性质及基与最小生成元集的联系，并给出了含幺半群中基、生成元集、不可约生成元集三者之间的关系；证明了在有唯一长度的半群S中，不可约生成元集、基、最小生成元集三者之间的等价关系；其次，讨论了字的组合与分解性，得出了字的本原性与不可分解性之间的关系---若为不可分解的，则一定是本原的，反之，不一定真；并运用图示法证明了字的可补性理论，讨论了方程，的可解性；在此基础上，用归纳法进一步证明了本原字与码的有关命题--若是X上的一个本原字，其中，则是一个码；若则当且仅当{}是一个码。

For the group representation, this paper improves the known method of determining the irreducibility. Instead of solving equations and checking every combination of the roots, we calculate the value of a polynomial.

对于自由群的表示，本文首先将不可约性的判别方法，由已有文献中解方程，并对方程的根作组合的方法，改进为直接计算某个多项式的值的方法，并进一步给出区分绝对不可约性和非绝对不可约性的判别准则。

At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods , and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search.At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings.

本文首先介绍了Newton型迭代法的基础知识，然后着重介绍了B-可微方程的Newton法，给出B-可微法的局部收敛结论，推广了古典的Newton法，但由于收敛的局部性，该算法仍有一定的不足之处；文章在证明大范围收敛定理时，假设M是不可约对角优势矩阵，采用一维Newton寻查的方法，保证算法的收敛性。

For different polynomials g, if the characteristic polynomial of a n matrix A is irreducible, then we get some theorems to determine matrix equations g =A solvable; if it is reducible, then, to see n-dimension space vectors M over a field F as F-module, we use module theory to determine these equations solvable such that it is simpler and clearer to investigate these questions.

对于不同多项式g，当n阶矩阵A的特征多项式为不可约的，我们给出了矩阵方程g=A有解的判定定理；当A的特征多项式为可约的，把域F上的n维线性空间M作为由A导出的F -模，我们利用模论知识来决定矩阵方程g=A有解性，从而使这一问题变了简单，研究思路更加清晰。

Application of HHGL to lithium atom As a starting point for exactly solving schrodingerequation for lithium,the part has twofold purpose,one isto derive the coupled hyperradial differential equation,and discuss whether HHGL can be used or not,the other isto build the symmetric basis functionfor twodimensional irreducible representation of 〓 permutationgroup and estimate the ground-state eigenenergy.

首先根据Pauli原理的要求，将N电子原子的波函数向〓群不可约表示之基展开，积分掉角度部分，推导出N电子原子的超球径耦合微分方程，其形式与氦原子耦合微分方程相似，差别表现在矩阵元〓的计算上。

Using Pell equations on A,we give a new proof of the well-known fact that ifthe ideal class number of a real quadratic function field K = k equals to 1,thenD must be P or QR, where P,Q,R∈A are monic and irreducible ,and Q,R have odddegrees.

二我们应用A上的Pell方程这一初等方法重新证明一个已知的结果：实二次函数域K = k理想类数为1时， D只能为P或QR，其中P，Q，R∈A首一不可约且Q，R次数为奇数。

Chapter 2 is devoted to the discussion of the asymptotic synchronization of par-tially coupled Lorenz systems with the external coupling matrices being n×n irreduciblesymmetric real matrices having zero row sums and nonpositive off-diagonal elements.

在第二章我们讨论了当外部耦合矩阵是n×n阶实对称不可约，行和为零且对角线以外的元素非正的矩阵时部分耦合非恒同Lorenz方程格点系统的渐近同步问题。

In order to determine the solution set of the equation , by the means of meet-irreducible element and irredundant finite meet-decomposition, we first obtain the maximal solutions to the simple equation in the case that b has an irredundant finite meet-decomposition, and then consider the relation between the equation and the equation , based on this, we obtain the maximal solutions to the equation in the case that each element of the matrix B has an irredundant finite meet-decomposition and so determine its solution set completely.

为了确定方程的解集，本文利用交既约元与不可缩短的有限交分解等工具，同样地先求出简单形式的型矩阵方程的所有极大解，然后讨论方程与方程之间的关系，在此基础上，在B的每个元素均有不可缩短的有限交分解的情况下，求出了方程的所有极大解，从而完全确定了方程的解集。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

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镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。