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Zeros distribution of reverse strong Tur´an expressions
报告人:刘丽教授, 曲阜师范大学 时间:2021年11月25日9:00 字号:

方式:腾讯会议 555 201 503 (password: 6666)

邀请人:郭飞教授

摘要:The Tur´an expression introduced by Tur´an, who found the Tur´an inequalities of Legendre polynomials in 1950. The (Hurwitz) stability of Tur´an expression is stronger that the q-log-concavity or q-log-convexity of original polynomial sequence.
In this talk, we mainly discuss two recurrence sequences, whose reverse strong Tur´an expressions are weakly (Hurwitz) stable or have only real zeros. As applications, we obtain the reverse strong Tur´an expressions of Bell polynomials, Dowling polynomials, ordered Bell polynomials, ordered Dowling polynomials and associated Lah polynomials are weakly (Hurwitz) stable respectively. And the reverse reverse strong Tur´an expressions of Delannoy polynomials, Morgan-Voyce polynomials, some independence polynomials and sextet polynomials have only real zeros respectively. Finally, we give some open problems related to the Eulerian polynomials and Narayana polynomials. (Joint work with Xue Yan)

刘丽, 曲阜师范大学教授、博士生导师,山东省泰山学者青年专家,霍英东青年教师奖获得者,山东省组合数学及其应用创新团队带头人,山东省高校青年教师教学比赛二等奖获得者,济宁市自然科学学科带头人。主要从事多项式零点分布、矩阵全正性和组合不等式的研究。在Advances in Applied Mathematics等国际知名期刊上发表高水平论文20余篇。现主持国家自然科学基金面上项目1项,主持完成国家自然科学基金项目2项、省部级项目7项,首位荣获省高等学校科学技术奖一等奖1项。


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