构造方程组解特殊一元方程

在初中数学竞赛试卷中,解方程是一个常考常新的热点,而解答这些竞赛题,如果我们使用常规方法,如直接去分母、去括号、对方程两边同次方去根号,往往很难奏效.这就需要解题者具有敏锐的洞察力,通过引入辅助元,进行局部换元,将隐含在原方程中的等量关系揭示出来,建立方程组来求解.本文针对这类特殊方程介绍构造方程组求解的方法.

卷积码盲识别树图遍历算法研究与仿真实验

针对现有卷积码盲识别算法在校验矩阵相同的情况下识别性能不佳的问题,提出一种基于树图遍历的卷积码盲识别算法,并对算法识别准确率进行仿真实验。算法基本思想是:遍历所有可能的输入序列,并依据输入序列构造下一状态,根据输入序列和状态这两个参数在卷积码树图中寻找符合要求的路径,识别出卷积码的输入⁃状态⁃输出转移表,然后构造方程组,估计出生成矩阵。实验结果表明,该算法能够有效地对卷积码进行盲识别,规避了从校验矩阵反推生成矩阵的过程中存在多个可能的生成矩阵的问题。

Purely Hom-Lie bialgebras

In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra. Using the coadjoint representation, we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras. Finally, we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.

Construction of Dulac functions for mathematical models in population biology

In this paper, we present a method for constructing a Dulac function for mathematical models in population biology, in the form of systems of ordinary differential equations in the plane.