高兴
职称:教授
研究所:基础数学研究所
所在部门:
办公室:
传真号码:
联系电话:
电子邮件:gaoxing@lzu.edu.cn
研究方向
学习经历
工作经历
教学及指导研究生情况
发表论文及专著
项目成果
荣誉、获奖
社会工作
其它信息
首页>师资队伍>全职教师>教授
兰州大学数学与统计学院 教授 高兴研究方向代数图论, 罗巴(Rota-Baxter)代数、算子代数
个人简历 高兴，男，博士，基础数学教授，博士生导师。在兰州大学数学与统计学院获得学士和博士学位。2015年8月至2016年8月间，在美国罗格斯大学交流访问。主要从事Rota-Baxter代数和代数图论等领域的研究，在Journal of Algebra、 Journal of Pure and Applied Algebra、Discrete Applied Math.等国际期刊上发表学术论文近三十篇。主持数学天元基金、青年科学基金、甘肃省自然科学基金项目, 曾参与国家自然科学基金项目2项和甘肃省自然科学基金项目1项。已经指导毕业硕士研究生3名。 罗巴(Rota-Baxter)代数简介： 罗巴代数在1960 年由美国概率论学家G.巴克斯特首先定义。很快得到Atkinson 等著名分析学家和Cartier,罗塔(Rota)等著名组合学家的重视。而在20世纪八十年代，李代数上的罗巴算子又以经典杨-巴克斯特方程的算子形式由前苏联理论物理学家独立发现。新世纪的开始标志着罗巴代数引人注目的复兴。2000年，罗巴代数作为一个基本结构出现在Connes (菲尔兹奖得主)和Kreimer 有关量子场论重整化的开创性工作中。同年Augiar 的工作将罗巴代数与结合杨-巴克斯特方程和Loday 的dendriform 代数联系起来。同年郭锂教授和Keigher把自由交换罗巴代数以混合洗牌(mixable shuffle)乘法构造出来，开始了交换罗巴代数的系统研究。而同年M.Hoffman定义拟洗牌(quasi-shuffle)乘法来研究数论中的多元zeta 值（MZV），成为罗巴代数在MZV 中应用的联接点。在此之后，出现了许多罗巴代数方面的文章，联系到量子场论（QFT），杨-巴克斯特方程，数论，operad，Hopf 代数，交换代数，组合和微分方程边值问题等。郭锂教授应邀为美国数学会会刊(Notice AMS)的WHAT IS …专栏撰文，把罗巴代数介绍给数学界,此文的发表，不仅说明罗巴代数和曾在此专栏介绍的其它领域一样，已成为公认的新兴学科，也认同郭锂教授在罗巴代数领域的领军地位。完成罗巴代数的首部专著《An Introduction to Rota-Baxter Algebra》，由美国International Press和中国高等教育出版社出版。
教学及指导学生情况已经指导毕业硕士研究生3名
发表论文及专著---------------------------------------------------accepted---------------------------------------------------[39 ] Y. Zhang and X. Gao*, Hopf algebras of planar binary trees: an operated algebra approach, Journal of Algebraic Combinatorics, https://doi.org/10.1007/s10801-019-00885-8[38 ] Y. Zhang*, D. Chen, X. Gao and Y.F. Luo, Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles, Pacific Journal of Mathematics, accepted. [37] X.S. Peng, Y. Zhang*, X. Gao and Y.F. Luo, Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems, Bulletin of the Belgian Mathematical Society Simon Stevin, accepted.[36] X. Gao, ?L. Guo*,?W.Y. Sit,?S. Zheng, Rota-Baxter type operators, rewriting systems and Gr?bner-Shirshov bases, ?arXiv:1412.8055. [35] X.M. Wang*, S.J. Xu and X. Gao, A Hopf algebra on subgraphs of a graph, Journal of Algebra and Its Applications, (2020) **. ---------------------------------------------------2019----------------------------------------------------- [34] M. Rosenkranz*, X. Gao and L. Guo, An algebraic study of multivariable integration and linear substitution, Journal of Algebra and Its Applications, 18(11) (2019), **.[33] Y.Y. Zhang and X. Gao*, Free Rota–Baxter family algebras and (tri)dendriform family algebras, Pacific Journal of Mathematics, 301 (2019), 741. [32] L. Qiao, X. Gao and L. Guo*, Rota-Baxter Modules Toward Derived Functors, Algebr Represent Theor 22 (2019), 321–343.?[31] X. Zhang, X. Gao and L. Guo*, Modified Rota–Baxter Algebras, Shuffle Products and Hopf Algebras, Bull. Malays. Math. Sci. Soc. 42 (2019), 3047–3072. [30] X. Gao* and X. Wang, Infinitesimal unitary Hopf algebras and planar rooted forests, Journal of Algebraic Combinatorics, 49 (2019), 437-460.-----------------------------------------------------2018-----------------------------------------------------[29] X. Gao, P. Lei and T. Zhang*, Left counital Hopf algebras on free Nijenhuis algebras, Communications in Algebra, 46(11) (2018), 4868–4883. [28] J. Zhang and X. Gao*, Free operated monoids and rewriting systems, Semigroup Forum, 97 (2018), 435–456. [27] X. Gao* and T. Zhang, Averaging algebras, rewriting systems and Gr?bner–Shirshov bases, Journal of Algebra and Its Applications, 16(2) 2018, **.[26] X. Gao, L. Guo and M. Rosenkranz*, On rings of differential Rota–Baxter operators, International Journal of Algebra and Computation, 28(1) (2018), 1-36. -----------------------------------------------------2017---------------------------------------------------[25] X. Gao and W. F. Keigher*，Interlacing of Hurwitz series，Communications in Algebra，45(5) (2017), 2163-2185. [24] X. Gao *，W. F. Keigher and M. Rosenkranz，Divided powers and compositions in integro-differential algebras，Journal of Pure and Applied Algebra，221 (2017), 2525-2556. [23] X. Gao and L. Guo*, Rota's Classification Problem, rewriting systems and Gr?bner-Shirshov bases, Journal of Algebra，470(2017), 219-253. -----------------------------------------------------2016-----------------------------------------------------[22] T.J Zhang，X. Gao and Li Guo*，Hopf algebras of rooted forests, cocyles and free Rota-Baxter algebras，Journal of Mathematical Physics，57 (2016) .101701. [21] X. Gao*，Q. Li, J.W. Wang and W.Z. Wang, On 2-Extendable Quasi-abelian Cayley Graphs, Bull. Malays. Math. Sci. Soc. 39 (2016), S43–S57. ----------------------------------------------------2015-----------------------------------------------------[20] X. Gao Huazhong Lv and Yifei Hao, The Laplacian and signless Laplacian spectrum of semi-Cayley graphs over abelian groups, J. Appl. Math. Comput., 2015: 1-13. [19] 高兴*，吕华众，王维忠，The extendability of Bi-Cayley graphs of dihedral groups, 浙江大学学报, 42 (2015), 526-528. [18] X. Gao，L. Guo and and M. Rosenkranz, Free integro-differential algebras and Gr?bner–Shirshov bases, Journal of Algebra, 442 (2015), 354-396. -----------------------------------------------------2014-----------------------------------------------------[17] 樊馨蔓，杨东，高兴，单演半群的Г图，浙江大学学报, 41(3) ( 2014), 258-260.[16] X. Gao and L. Guo*, Constructions of free commutative integro-differential algebras, Lecture Notes in Comput. Sci., 8372 (2014), 1–22. [15] W.Z Wang*, Y.F. Luo and X. Gao, On incidence energy of some graphs, Ars Combinatorics, 114 (2014), 427-436. [14] X. Gao，L. Guo* and S.H. Zheng, Construction of free commutative integro-differential algebras by the method of Gr?bner-Shirshov bases, J. Algebra and Its Application, 13 (2014)，**. -----------------------------------------------------2013-----------------------------------------------------[13] X.X. Fan, Y.F. Luo and X. Gao, Tricyclic graphs with exactly two main eigenvalues, Cent. Eur. J. Math. 11(10) 2013, 1800-1816. -----------------------------------------------------2012-----------------------------------------------------[12] 樊馨蔓，高兴，杨东，完全单周期半群的Cayley图的可迁性，兰州大学学报，48(6) 2012, 102--104.[11] X. Gao *，Y.F. Luo and W.W. Liu, Kirchhoff index in line, subdivision and total graphs of a regular graph, Discrete Applied Mathematics, 160 (2012) , 560-565.-----------------------------------------------------2011-----------------------------------------------------[10] X.X Fan*, X. Gao and Y.F. Luo, Spectral characterations of a specific class of trees, Ars Combinatorics, 102 (2011), 147-159. [9] Y.F. Hao*, X. Gao and Y.F. Luo, On Cayley graphs of symmetric inverse semigroups, Ars Combinatorics, 100 (2011), 307-319. [8] Y.F. Hao*, X. Gao and Y.F. Luo, On the Cayley graphs of Brandt semigroups, Communications in Algebra, 39 (2011), 2874-2883. [7] X. Gao *, W.W Liu and Y.F. Luo, On Cayley graphs of normal bands, Ars Combinatorics, 100 (2011), 409-419.[6] X. Gao *, W.W. Liu and Y.F. Luo, On the extendability of certain semi-Cayley graphs of fifnite abelian groups, Discrete Mathematics, 311 (2011), 1978–1987. [5] X. Gao *，Y.F. Luo and W.W. Liu, Resistance distances and the Kirchhoff index in Cayley graphs, Discrete Applied Mathematics 159 (2011), 2050–2057. -----------------------------------------------------2010-----------------------------------------------------[4] X. Gao * and Y.F. Luo, The zero-divisor graph of a completely 0-simple semigroup, Southeast Asian Bulletin of Mathematics 34 (2010), 657–662.[3] Y. Dong and X. Gao *, D-Saturated Property of the Cayley graphs of Semigroups,Semigroup Forum 80 (2010), 174–180. [2] X. Gao* and Y.F. Luo, The spectrum of semi-Cayley graphs over abelian groups, Linear Algebra and its Applications 432 (2010), 2974–2983. -----------------------------------------------------2009-----------------------------------------------------[1] Y.F. Luo and X. Gao *, On the extendability of Bi-Cayley graphs, Discrete Mathematics, 309 (2009), 5943–5949.
项目成果国家自然科学基金（面上项目），2021--2024，主持;国家自然科学基金（青年基金），2013--2015，主持;甘肃省自然科学基金，2013--2015，主持;国家自然科学基金（天元基金），2011.1--2011.12，主持;中央高校基本科研业务费，2011--2012， 主持;中央高校基本科研业务费，2013.1--2014.6， 主持.国家自然科学基金面上项目(**)，2014-2017，参与
荣誉、获奖
社会工作
其它信息
作者:高兴