不定方程组

By using the Euclidean algorithm and invertible linear transformation over a polynomial ring, the solutions of polynomial indeterminate equations of first degree was investigated in theory, and its matrix solution based on the elementary matrix transformation was proposed.

利用欧几里德算法和多项式环上的可逆线性变换，从理论上对多项式环上的一次不定方程组的解进行深入的研究，给出了用矩阵的初等变换求解多项式环上的一次不定方程组的矩阵解法，并利用MATLAB数学软件开发了相应的计算机程序。

By using the Euclidean algorithm and invertible linear transformation over an integral ring, the solution of integral indeterminate equations of the first degree was investigated in theory, and its matrix solution based on the elementary matrix transformation was proposed.

用欧几里德算法和整数环上的可逆线性变换，从理论上对整数一次不定方程组的解进行了深入研究，提出了用矩阵的初等变换求解整数一次不定方程组的矩阵解法，并利用MATLAB数学软件开发了相应的计算机程序。

algebra ; general solution ; matrix solution ; program ; Euclidean algorithm ; MATLAB

1通解与算法数域F}多项式环厂刘上多元一次不定方程组的一般形式为

The resulting linear system, the coefficient matrix of which is, typically, a 2 x 2 block symmetric or non-symmetric and singular or non-singular indefinite matrix, is of high order and ill conditioned. In order to solve such system we have to use iterative methods with fast convergence speed.

所得的离散方程组（其系数矩阵典型地是 2 x 2 块对称或非对称，奇异或非奇异的不定矩阵）是高阶和病态的，为了求解这样的方程组我们必需使用快速收敛的迭代方法。

The so-called indeterminate equation is the solution in the range of integers, positive integers, rational numbers or integers of the equation or algebraic equations, whose unknowns are usually more than the number of equations ...

所谓不定方程是指解的范围为整数、正整数、有理数或代数整数的方程或方程组，其未知数的个数通常多于方程的。。。

"Find wallet"and"buy horses"are one-degree indeterminate linear equations, which can be solved by removed parameter, making no significant impact in the history of development of the indeterminate linear equation. 3、the problem of remainder arises with divining number. In sum, indeterminate problem borrowed from the eastern countries is to show Fibonacci's mathematical charm. He did not make in-depth study of the problem, but it is fascinating to the later European scholars, because these issues are interesting, and Fibonacci's solution is creative.

本论文通过对散布在《计算之书》各个章节中的三类不定问题进行系统梳理之后发现：《计算之书》"买鸟问题"的解法是"合金法"，此方法是用来解答三种以上钱币配置问题整数解的情况；"捡钱包问题"和"买马问题"是一次不定方程组问题，解答过程相当于现今的一次方程组问题，通常通过"消参"即可解决，在历史上没有对不定分析问题的研究产生明显影响；而"剩余问题"是以占卜猜数问题的形式呈现计算过程，虽然斐波那契没有对不定问题进行深入研究，但正是因为这些问题的趣味性，以及斐波那契某些解法的独创性而引起以后欧洲学者对此类问题的兴趣，并由此将不定分析问题研究引入欧洲。

In addition, the program for the matrix solution was given by using MAT-LAB mathematical software.

同时利用MATLAB数学软件给出相应的计算机求解风x 上一次不定方程组的通用程序，该问题的研究将对函数论和多项式逼近的研究起到一定的作用。

In the application of this new method, parallelism is outstamding, and the various domain for a mixed problem can also be treated respectively.

方法的实施与方程组的可解性无关，这对於求解变系数不定常问题是有意义的。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。