報(bào)告題目：Monotone rules for the ratio of two functions

　　報(bào)告人：楊鎮(zhèn)杭

　　時(shí)間：2024年6 月18日 15：00-16：00

　　地點(diǎn)：理學(xué)院1號(hào)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(bào)告人簡介：

　　楊鎮(zhèn)杭,，男,，1963年4月出生，浙江浦江人氏,，研究生學(xué)歷,，高級(jí)講師。先后任杭州電力經(jīng)濟(jì)管理學(xué)校副校長,、浙江省電力公司科學(xué)研究院工會(huì)主席,、浙江省供電服務(wù)中心副書記、浙江省電力學(xué)會(huì)副秘書長,。受邀擔(dān)任《美國數(shù)學(xué)評(píng)論》評(píng)論員,，30多家國內(nèi)外數(shù)學(xué)刊物審稿人，現(xiàn)任全國不等式研究會(huì)副理事長,。業(yè)余從事特殊函數(shù)和數(shù)論方向的研究,，涵蓋（不完全）珈瑪、多重珈瑪函數(shù),、(廣義)橢圓積分,、超幾何級(jí)數(shù)、貝塞爾函數(shù),、zeta函數(shù),、誤差函數(shù)等特殊函數(shù)，在Proc. Am. Math. Soc., J. Math. Anal. Appl., Result Math., J.Comput. Appl. Math., Appl. Math. Comput. 等國內(nèi)外知名期刊發(fā)表SCI論文120余篇, 同時(shí),，首次引入了“雙參數(shù)齊次函數(shù)”,、“Schur冪凸函數(shù)”、“混合完全單調(diào)性”等數(shù)學(xué)概念,。先后與合作者探索建立了一系列單調(diào)法則和符號(hào)規(guī)則,，如基于H-function 的L'Hospital單調(diào)法則，單峰型冪級(jí)數(shù)比的單調(diào)法則,、單峰型Laplace積分比的單調(diào)法則,，NP型冪級(jí)數(shù)（多項(xiàng)式）符號(hào)規(guī)則，Laplace積分符號(hào)規(guī)則等,。2022年進(jìn)入“全球前2%頂尖科學(xué)家終身成就榜”,，2023年進(jìn)入“愛思維爾中國高被引學(xué)者”榜單,。