给出一些特殊的整环与它的一元多项式环之间的关系。
In this paper we analyze the relation of some special domains and its monadic polynomial rings.
利用数域上一元多项式环与整数环相似的性质，建立数域上一元多项式环中的孙子定理，并给出它的简单应用。
Using the similarity between polynomial ring and integer ring the paper establishes Sunse's Theorem in the polynomial ring in number field, and offers its brief learning and practice.
当有限域的特征不整除群的阶时，给出了直接写出相应的多项式环的本原幂等元的方法，从而可以直接写出所有的极小循环码。
In the case of(Char(F_q), |G|)=1, we provide a method that writing down directly all the primitive idempotents of related polynomial ring, and hence that of all the minimum cyclic codes.
考察了除环上的l多项式的左因式、左根与左倍式的性质，给出了导数与左结矩阵的应用。
Left factors, left multiples and left roots of the polynomials over sfield are studed. Applications of derivative and left relative matrices are given.
有限交换环上的多项式函数的个数问题。
The number of polynomial function over a finite commutative ring.
本文解决了整环上两条序列的最短线性递归问题，并给出了递归极小多项式的方法。
This paper presents a solution to the problem of the shortest linear recurrence of two sequences over an integral domain and describes the recurrence of the minimal polynomial.
提出了一种多项式泛函网络运算新模型，来求解任意数域或环上多项式运算问题。
The new computing model of polynomial functional network is firstly proposed and the solving polynomials computing problem in arbitrary coefficients fields or ring is discussed.
应用化学图论计算了杂环芳烃HMO的选择本征值和本征多项式。
HMO characteristic polynomial and select eigenvalues for many heterocyclic benzenoids are calculated by using chemical graph theory methods.
本文研究了平面多项式向量场的全局与局部分叉，旨在研究高次平面非线性动力系统多极限环的存在性以及极限环的个数及其相对位置关系；
The main aim of this dissertation is to study the exist of limit cycles of plane nonlinear dynamic system of high degree and the number and the configurations of limit cycles.
多重线性中心多项式在PI—环论研究中扮演了一个非常重要的角色。引入矩阵序列及m次换位子的概念研究了矩阵环的多重线性中心多项式。
Multilinear central polynomials play a very important role in PI-theory. Introduce the concept of matrix sequence and k-commutator and study the multilinear central polynomials of matrix rings.
本文研究一类五次平面多项式系统赤道极限环分支问题。
In this paper, the problem of limit cycles bifurcated from the equator for a quintic polynomial system is investigated.
首次证明了拟五次多项式系统在无穷远点能分支出7个极限环。
It is the first time that 7 limit cycles can bifurcated from the infinity for a class of quasi quintic system.
第五章讨论了一类可化为abel方程的五次多项式系统的极限环的个数，得到此类平面五次多项式系统至多存在两个极限环的充分条件。
In the fifth section, we obtain some sufficient conditions under which a class of a planar quintic system has at most two limit cycles by transforming it into Abel equation.
第五章讨论了一类可化为abel方程的五次多项式系统的极限环的个数，得到此类平面五次多项式系统至多存在两个极限环的充分条件。
In the fifth section, we obtain some sufficient conditions under which a class of a planar quintic system has at most two limit cycles by transforming it into Abel equation.
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