Liouville定理的推广及应用

Liouville定理是复变函数论中的一个重要定理,它在全纯函数理论中的重要地位是显而易见的.给出Liouville定理的推广形式,并归类总结了它在不同领域中的应用.     

决定周期为up~n序列的极小多项式的快速算法(英文)

给出了一个快速算法决定有限域Fq上周期为upn序列的极小多项式.设p,q,u为不同素数,q为模p2的本原根,m为最小正整数使得qm≡1modu和gcd(m,p(p-1))=1.利用一个算法把有限域Fq上周期为upn序列化为几个有限域Fq(ζ)上周期为pn序列,其中ζ为一个u次本原单位根,从而利用肖国正等的算法得到每个周期为pn序列的极小多项式.     

基于光子晶体的高效太阳能电池反射器的研究

设计了一种一维光子晶体的太阳能电池底部反射器,采用平面波展开法(PWM)计算禁带,得到当两个材料的介电常数差越大时,完全禁带越宽,对于Si/Air和Si/SiO2都在700～1 200 nm出现完全禁带,在此基础上利用勒让德多项式展开方法(LPEM)对该结构进行最优化,寻找到了高反射率时周期层数N,并考察了当入射角度不同时反射谱效率的问题,得出随着入射角度的增加,两种不同结构的一维光子晶体完全禁带均出现蓝移,证明了此种结构反射器具有高效的全方位反射性。把这种结构的背反射层用作太阳能电池的反射器可以大大提高电池的捕光能力,从而提高太阳能电池的的转化效率。     

整系数多项式有理根存在性的新判别法

给出了一种与艾森斯坦判别法截然不同的判断整系数多项式无有理根的方法,这种判别法不仅能够解决一类不能由艾森斯坦判别法直接判别的整系数多项式,而且对于复杂的整系数多项式能够做出迅速判断,对判断整系数多项式有理根的存在性有重要意义。     

Static Versus Dynamic Disposition: The Role of GeoGebra in Representing Polynomial-Rational Inequalities and Exponential-Logarithmic Functions

This study investigates prospective secondary mathematics teachers’ visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a framework of productive disposition and visual representations in pre-calculus. The main result was that the role of GeoGebra as a cognitive tool fostered the research participants’ productive disposition, despite recurrent mismatches between the algebraic and visualized formalisms. Moreover, participants exhibiting dynamic productive disposition seemed to understand and make better sense of the conceptual underpinnings of the mathematical content they explored in contrast to those embracing static productive disposition.     

Optimal controller for uncertain stochastic polynomial systems

This paper presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with linear control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, the paper gives closed-form solutions of the optimal regulator and controller problems for stochastic polynomial systems with linear control input and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.     

目标函数的埃尔米特插值技术

构建了2维埃尔米特插值多项式,对分片埃尔米特插值多项式进行了实例验证。     

Bernstein多项式逼近度的估计

给出Bernstein多项式逼近阶的新估计,推进了文[2]的结果。     

一类图的伴随多项式的因式分解及色性

通过研究一类S-型图的伴随多项式的因式分解,证明了这类图的补图的色等价图的结构性质和非色唯一性.     

n阶双圈图的邻接谱半径

何常香等人通过对双圈图进行收缩、夺邻、嫁接等运算，找出了．双圈图中邻接半径前三大的图，并给出了它们的邻接谱半径．亓静在本文中考虑了点数n≥12的双圈图，推广了上述结论，找出了双圈图中前五大邻接谱半径，并给出了相应的双圈图．