数学学科2024系列学术报告之十九

　　报告题目：Monotone rules for the ratio of two functions

　　报告人：杨镇杭

　　时间：2024年6 月18日 15：00-16：00

　　地点：理学院1号楼1-301

　　摘要：

　　As pointed out by Anderson et al in 1990s if one is attempting to establish the monotonicity of a quotient of two functions, one often finds that the derivative of the quotient is quite messy and the process tedious. This inspired mathematicians to find various monotone rules for the ratio of two functions so that the judgments of monotonicity become to be easier. Up to now, many such rules were found and have been widely applied. In this talk, we introduce and analyze monotone rules for the ratio of general functions monotone rules for the ratio of two power series, monotone rules for the ratio of two polynomials, monotone rules for the ratio of two integrals with variables. Furthermore, we introduce and analyze two signs rules which are closely related to monotone rules for the ratio of two power series and two Laplace integrals, respectively. Finally, we introduce and analyze several higher-order monotone rules for the ratio of two power series, and propose two conjectures on the completely monotone rules for the ratio of two Laplace integrals.

　　报告人简介：

　　杨镇杭，男，1963年4月出生，浙江浦江人氏，研究生学历，高级讲师。先后任杭州电力经济管理学校副校长、浙江省电力公司科学研究院工会主席、浙江省供电服务中心副书记、浙江省电力学会副秘书长。受邀担任《美国数学评论》评论员，30多家国内外数学刊物审稿人，现任全国不等式研究会副理事长。业余从事特殊函数和数论方向的研究，涵盖（不完全）珈玛、多重珈玛函数、(广义)椭圆积分、超几何级数、贝塞尔函数、zeta函数、误差函数等特殊函数，在Proc. Am. Math. Soc., J. Math. Anal. Appl., Result Math., J.Comput. Appl. Math., Appl. Math. Comput. 等国内外知名期刊发表SCI论文120余篇, 同时，首次引入了“双参数齐次函数”、“Schur幂凸函数”、“混合完全单调性”等数学概念。先后与合作者探索建立了一系列单调法则和符号规则，如基于H-function 的L'Hospital单调法则，单峰型幂级数比的单调法则、单峰型Laplace积分比的单调法则，NP型幂级数（多项式）符号规则，Laplace积分符号规则等。2022年进入“全球前2%顶尖科学家终身成就榜”，2023年进入“爱思维尔中国高被引学者”榜单。