(1+λu)-Constacyclic codes over Fp[u]/〈u〉

Motivated by the work in [1] of Abualrub and Siap (2009), we investigate (1+λu)-constacyclic codes over F_p[u]/〈u^m〉 of an arbitrary length, where λ is a nonzero element of F_p. We find the generator polynomials of (1+λu)-constacyclic codes over F_p[u]/〈u^m〉, and determine the number of (1+λu)-constacyclic codes over F_p[u]/〈u^m〉 for a given length, as well as the number of codewords in each such code. Some optimal linear codes over F₃ and F₅ are constructed from (1+λu)-constacyclic codes over F_p+uF_p under a Gray map.     

一类正整数n的广义k-有序分拆问题研究

文章主要研究以正整数n的广义k-有序分拆为求和下标,表达式为各分部ci作初等对称多项式变换后的求和计数公式。研究过程主要依据从特殊到一般的思想,运用组合分析和数学归纳法,最终得到这类问题一般情况下的计数公式。     

整系数多项式在有理数域内不可约的一种新判别方法

借鉴Eisenstein判别法的研究思路,给出了一种判别整系数多项式在有理数域内不可约的新方法。     

带约束多项式权重LPV模型辨识算法

针对复杂工业非线性系统建模难度大、精度低等问题,基于多模型插值的变参数线性（ LPV）模型辨识算法,提出双工作点变量条件下的带约束多项式权重函数结构及其参数寻优策略,以有效降低非线性系统辨识的难度并充分保证所建模型的全局稳定性。以高纯度分馏塔这一典型非线性工业过程为研究对象进行LPV模型建模与仿真,获得了较好的输出和阶跃响应曲线拟合结果,验证了LPV模型能够充分反映非线性系统的运行特性以及所提算法的有效性和实用性。     

机构学中的实数同伦法

在文献［１］的基础上,本文提出实数同伦法。该法用于在实数域内求解多项式方程组的全部孤立实零点。文中还提出偏离度等新概念。实数同伦法具有计算工作量小、求解迅速等特点。这为解决机构学中的多解问题提供了一个切实可行的方法。     

基于矩阵形表示的结式计算方法

引入了结式的矩阵形表示,提出了矩阵形结式的移位变换概念,并利用其得到了结式计算的一个简便方法。     

一类关于半正定规划的多项式原对偶内点算法

1 Introduction Interior-point methods (IPMs) for semidefinite opti-mization (SDO) have been studied intensively,due totheir polynomial complexity and practical efficiency.In the past decade , SDO has become a popular re-search area in mathematical programming when it be-came clear that the algorithm for linear opti mization(LO) can often be extended to the more general SDOcase. Other two factors are also responsible for thisincreasing interest in SDO. Firstly, SDO has a wideapplication…     

对根式q_1(a_1)~(n_1)+q_2(a_2)~(n_2)…+q_s(a_s)~(n_s)无理性的研究

利用对称多项式以及整系数方程根的有关性质,得到了形如q1+(a1)~(n1)+q2(a2)~(n2)+…+qs(as)~(ns)(a1、a2、…、as、n1、 n2、…、ns是大于1的正整数,a1、a2、…、as互不相等,q1、q2、…、qs为任意非零有理数)为无理数非常简单的一种判别方法．     

Explorations of the Gauss-Lucas Theorem

Abstract

The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows the plotting of zeros and critical points makes the result discoverable by students. We propose a visual investigation, followed by a series of exercises leading to different complete proofs of the theorem.     

在单链表上实现一元多项式的表示和相加

以单使表这种数据结构为工具，详细描述了一元多项式在计算机中的表示以及两个一元多项式相加运算在计算机中的实现。