報告題目：Monotone rules for the ratio of two functions

　　報告人：楊鎮杭

　　時間：2024年6 月18日 15：00-16：00

　　地點：理學院1號樓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.

　　報告人簡介：

　　楊鎮杭，男，1963年4月出生，浙江浦江人氏，研究生學歷，高級講師。先后任杭州電力經濟管理學校副校長、浙江省電力公司科學研究院工會主席、浙江省供電服務中心副書記、浙江省電力學會副秘書長。受邀擔任《美國數學評論》評論員，30多家國內外數學刊物審稿人，現任全國不等式研究會副理事長。業余從事特殊函數和數論方向的研究，涵蓋（不完全）珈瑪、多重珈瑪函數、(廣義)橢圓積分、超幾何級數、貝塞爾函數、zeta函數、誤差函數等特殊函數，在Proc. Am. Math. Soc., J. Math. Anal. Appl., Result Math., J.Comput. Appl. Math., Appl. Math. Comput. 等國內外知名期刊發表SCI論文120余篇, 同時，首次引入了“雙參數齊次函數”、“Schur冪凸函數”、“混合完全單調性”等數學概念。先后與合作者探索建立了一系列單調法則和符號規則，如基于H-function 的L'Hospital單調法則，單峰型冪級數比的單調法則、單峰型Laplace積分比的單調法則，NP型冪級數（多項式）符號規則，Laplace積分符號規則等。2022年進入“全球前2%頂尖科學家終身成就榜”，2023年進入“愛思維爾中國高被引學者”榜單。