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高兴

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,基础数学副教授。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
[1]  X. Gao and M. Wang, Infinitesimal unitary Hopf algebras and planar rooted                
    forests, Journal of Algebraic Combinatorics, accepted. 
[2]  X. Gao,  L. Guo, W.Y. Sit, S. Zheng, Rota-Baxter type operators, rewriting systems and   
    Gröbner-Shirshov bases,  arXiv:1412.8055. 
[3]  X. Gao, P. Lei and T. Zhang, Left counital Hopf algebras on free Nijenhuis
    algebras, Communications in Algebra,              
    https://doi.org/10.1080/00927872.2018.1459641
[4]  J. Zhang and X. Gao, Free operated monoids and rewriting systems, Semigroup       
    Forum, https://doi.org/10.1007/s00233-018-9939-0
[5]  X. Gao and T. Zhang, Averaging algebras, rewriting systems and Gröbner–Shirshov     
    bases, Journal of Algebra and Its Applications, 16(2)  2018, 1850130.
[6]  X. Gao, L. Guo and M. Rosenkranz, On rings of differential Rota–Baxter operators,     
    International Journal of Algebra and Computation, 28, 1 (2018).
[7]  X. Gao and William F. Keigher,Interlacing of Hurwitz  series,Communications in 
   Algebra,45(5)  (2017):2163~2185.  (SCI)
[8]  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. (SCI)
[9]  X. Gao and L. Guo, Rota's Classification Problem, rewriting systems and    
   Gr\"obner-Shirshov bases, Journal of Algebra,470(2017), 219-253.  (SCI)
[10] T.J Zhang,X. Gao and Li Guo,Hopf algebras of rooted forests, cocyles and free 
    Rota-Baxter algebras,Journal of Mathematical Physics,2016.10.01, 57.   (SCI)
[11] 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.  
[12]  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.   (SCI)
[13]  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. 
[14]  X. Gao,L. Guo and and Markus Rosenkranz, Free integro-differential algebras and    
     Gröbner–Shirshov bases, Journal of Algebra, 442 (2015), 354-396.  (SCI)
[15]  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,  L. Guo, Constructions of free commutative integro-differential algebras,   
     Lecture Notes in Comput. Sci., 8372 ( 2014), 1–22. 
[17]  W.Z Wang, Y.F. Luo, X. Gao, On incidence energy of some graphs, Ars Combinatorics      
114 (2014), 427-436.(SCI)
[18]  X. Gao,L. Guo* and S.H. Zheng, Free commutative integro-differential algebras and           
Gr¨obner-Shirshov bases, J. Algebra and Its Application, 13 (2014),1350160.  (SCI)
[19] X.X. Fan, Y.F. Luo, X. Gao, Tricyclic graphs with exactly two main eigenvalues, Cent.                   
    Eur. J. Math. 11(10), 2013, 1800-1816. (SCI)
[20] 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.
[21] X.X Fan, X. Gao and Y.F. Luo, Spectral characterations of a specific class of trees,   
Ars Combinatorics, 102 (2011), 147-159. (SCI)
[22] Y.F. Hao, X. Gao and Y.F. Luo, On Cayley graphs of symmetric inverse semigroups, Ars 
        Combinatorics, 100 (2011), 307-319. (SCI)
[23] Y.F. Hao, X. Gao and Y.F. Luo, On the Cayley graphs of Brandt semigroups, 
       Communications in Algebra, 39 (2011), 2874-2883.  (SCI)
[24] 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.
[25] Y. Dong and X. Gao *, D-Saturated Property of the Cayley graphs of Semigroups,       
Semigroup  Forum 80 (2010), 174–180. (SCI)
[26]  Y.F. Luo and X. Gao *, On the extendability of Bi-Cayley graphs, Discrete 
    Mathematics, 309 (2009), 5943–5949.   (SCI)
[27] X. Gao *, W.W Liu and Y.F. Luo, On Cayley graphs of normal bands, Ars Combinatorics, 100 (2011), 409-419.   (SCI) 
[28]  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.  (SCI)
[29] 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. (SCI)
[30] 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. (SCI)
[31] X. Gao* and Y.F. Luo, The spectrum of semi-Cayley graphs over abelian groups, Linear 
       Algebra and its Applications 432 (2010), 2974–2983.  (SCI)
项目成果
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(11371177),2014-2017,参与
荣誉、获奖
社会工作
其它信息

作者:高兴