• 数学物理中可积系统相关的分析与计算：正反谱问题、正交多项式理论、数值数学、随机矩阵，代数组合等

   

070102-计算数学
070104-应用数学

可积系统与随机矩阵的理论与算法
可积系统、随机矩阵、代数组合及其应用

2009-09--2014-06   中国科学院数学与系统科学研究院   理学博士
2005-09--2009-06   北京理工大学   理学学士

   

2019-04~现在, 中国科学院数学与系统科学研究院, 副研究员
2017-11~2019-03,中国科学院数学与系统科学研究院计算数学所, 副研究员
2016-07~2017-10,中国科学院数学与系统科学研究院, 助理研究员
2014-11~2017-06,University of Saskatchewan, PIMS 博士后、访问学者

   

（1） 中国科学院青年创新促进会优秀会员, 特等奖, 院级, 2023
（2） 中国科学院数学与系统科学研究院陈景润未来之星, , 研究所（学校）, 2019
（3） 中国科学院数学与系统科学研究院年度重要科研进展奖, , 研究所（学校）, 2018
（4） 中国科学院数学与系统科学研究院突出成果奖, 研究所（学校）, 2016
（5） 中国科学院百篇优秀博士论文奖, 部委级, 2015
（6） 中国科学院院长奖学金, 部委级, 2014

   

[1] Pan, Yan, Chang, XiangKe, Hu, XingBiao. An application of a qd-type discrete hungry Lotka-Volterra equation over finite fields to a decoding problem. STUDIES IN APPLIED MATHEMATICS[J]. 2023, 151(2): 450-474, http://dx.doi.org/10.1111/sapm.12584.
[2] Chang, XiangKe, Hu, XingBiao, Szmigielski, Jacek. Preface to the special issue: Orthogonal polynomials and integrable systems, Peakons, Toda lattices and Painlevé transcendents. PHYSICA D-NONLINEAR PHENOMENA[J]. 2023, 453: http://dx.doi.org/10.1016/j.physd.2023.133830.
[3] Chen, XiaoMin, Chang, XiangKe, He, Yi, Hu, XingBiao. Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm. NUMERICAL ALGORITHMS[J]. 2023, 92(1): 335-375, http://dx.doi.org/10.1007/s11075-022-01365-0.
[4] Chang, Xiang-Ke. Hermite--Pad\'{e} approximations with Pfaffian structures: Novikov peakon equation and integrable lattices. ADVANCES IN MATHEMATICS[J]. 2022, 402: 108338-108338, [5] Wang, Bao, Chang, XiangKe, Yue, XiaoLu. A generalization of Laurent biorthogonal polynomials and related integrable lattices. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL[J]. 2022, 55(21): 15-, http://dx.doi.org/10.1088/1751-8121/ac6405.
[6] Xiao-Lu Yue, Xiang-Ke Chang, Xing-Biao Hu, Ya-Jie Liu. Laurent biorthogonal polynomials and Painlevé-type equations. Proc. Amer. Math. Soc.[J]. 2022, 150(10): 4369-4381, [7] Wang Bao, Chang, Xiang-Ke, Hu, Xing-Biao, Li, ShiHao. Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame. International Mathematics Research Notices[J]. 2021, 2021(14): 11050-11092, [8] Liu, YaJie, Chang, XiangKe, He, Yi, Hu, XingBiao. Generalizations of Shanks transformation and corresponding convergence acceleration algorithms via pfaffians. NUMERICAL ALGORITHMS[J]. 2021, 88(4): 1733-1756, http://dx.doi.org/10.1007/s11075-021-01092-y.
[9] Chang, XiangKe, Li, ShiHao, Tsujimoto, Satoshi, Yu, GuoFu. Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices. JOURNAL OF NONLINEAR SCIENCE[J]. 2021, 31(2): [10] Pan, Yan, Chang, XiangKe, Hu, XingBiao. Decoding algorithm as a moment problem related to the extended Lotka-Volterra system. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL[J]. 2020, 53(5): https://www.webofscience.com/wos/woscc/full-record/WOS:000519001700001.
[11] Chang, XiangKe, He, Yi, Hu, XingBiao, Sun, JianQing, Weniger, Ernst Joachim. Construction of new generalizations of Wynn's epsilon and rho algorithm by solving finite difference equations in the transformation order. NUMERICAL ALGORITHMS[J]. 2020, 83(2): 593-627, http://dx.doi.org/10.1007/s11075-019-00695-w.
[12] Chang, XiangKe, Hu, XingBiao, Szmigielski, Jacek, Zhedanov, Alexei. Isospectral Flows Related to Frobenius-Stickelberger-Thiele Polynomials. COMMUNICATIONS IN MATHEMATICAL PHYSICS[J]. 2020, 377(1): 387-419, [13] Chang, XiangKe, Hu, XingBiao, Li, ShiHao. Moment modification, multipeakons, and nonisospectral generalizations. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2018, 265(9): 3858-3887, [14] Chang, Xiangke, Szmigielski, Jacek. Lax Integrability and the Peakon Problem for the Modified Camassa-Holm Equation. COMMUNICATIONS IN MATHEMATICAL PHYSICS[J]. 2018, 358(1): 295-341, [15] Wang, Bao, Chang, XiangKe, Hu, XingBiao, Li, ShiHao. On moving frames and Toda lattices of BKP and CKP types. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL[J]. 2018, 51(32): https://www.webofscience.com/wos/woscc/full-record/WOS:000437306500002.
[16] Chang, XiangKe, Hu, XingBiao, Li, ShiHao, Zhao, JunXiao. An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type. ADVANCES IN MATHEMATICS[J]. 2018, 338: 1077-1118, [17] Chang, XiangKe, He, Yi, Hu, XingBiao, Li, ShiHao. Partial-Skew-Orthogonal Polynomials and Related Integrable Lattices with Pfaffian Tau-Functions. COMMUNICATIONS IN MATHEMATICAL PHYSICS[J]. 2018, 364(3): 1069-1119, [18] Anco, Stephen C, Chang, Xiangke, Szmigielski, Jacek. The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type. STUDIES IN APPLIED MATHEMATICS[J]. 2018, 141(4): 680-713, [19] Chang, XiangKe, Hu, XingBiao, Li, ShiHao. Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type. NONLINEARITY[J]. 2018, 31(10): 4746-4775, [20] Chang, XiangKe, He, Yi, Hu, XingBiao, Li, ShiHao. A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians. NUMERICAL ALGORITHMS[J]. 2018, 78(1): 87-106, [21] Chang, Xiangke, He, Yi, Hu, Xingbiao, Li, Shihao, Tam, Honwah, Zhang, Yingnan. Coupled modified KdV equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property. SCIENCE CHINA MATHEMATICS[J]. 2018, 61(6): 1063-1078, [22] Chang, Xiangke, Szmigielski, Jacek. Liouville Integrability of Conservative Peakons for a Modified CH equation. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS[J]. 2017, 24(4): 584-595, https://www.webofscience.com/wos/woscc/full-record/WOS:000414999400010.
[23] Chang, XiangKe, Hu, XingBiao, Lei, Hongchuan, Yeh, YeongNan. Combinatorial proofs of addition formulas. ELECTRONIC JOURNAL OF COMBINATORICS[J]. 2016, 23(1): http://apps.webofknowledge.com/CitedFullRecord.do?product=UA&colName=WOS&SID=5CCFccWmJJRAuMzNPjj&search_mode=CitedFullRecord&isickref=WOS:000369985900008.
[24] Chang, Xiangke, Szmigielski, Jacek. Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS[J]. 2016, 23(4): 563-572, https://www.webofscience.com/wos/woscc/full-record/WOS:000386429700007.
[25] Sun, YePeng, Chang, XiangKe, He, Yi. On three-term recurrence and Christoffel-Darboux identity for orthogonal rational functions on the real line. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS[J]. 2016, 27(4): 268-280, http://ir.wipm.ac.cn/handle/112942/9222.
[26] Chang, XiangKe, Hu, XingBiao, Szmigielski, Jacek. Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice. ADVANCES IN MATHEMATICS[J]. 2016, 299: 1-35, [27] Chang, XiangKe, Chen, XiaoMin, Hu, XingBiao, Tam, HonWah. About several classes of bi-orthogonal polynomials and discrete integrable systems. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL[J]. 2015, 48(1): https://www.webofscience.com/wos/woscc/full-record/WOS:000346267600014.
[28] Chang, XiangKe, Hu, XingBiao, Xin, Guoce. HANKEL DETERMINANT SOLUTIONS TO SEVERAL DISCRETE INTEGRABLE SYSTEMS AND THE LAURENT PROPERTY. SIAM JOURNAL ON DISCRETE MATHEMATICS[J]. 2015, 29(1): 667-682, [29] Zhang YingNan, Chang XiangKe, Hu Juan, Hu XingBiao, Tam HonWah. Integrable discretization of soliton equations via bilinear method and Backlund transformation. SCIENCE CHINA-MATHEMATICS[J]. 2015, 58(2): 279-296, http://ir.amss.ac.cn/handle/2S8OKBNM/47038, http://www.irgrid.ac.cn/handle/1471x/6871151, http://ir.amss.ac.cn/handle/2S8OKBNM/47039.
[30] Chen, XiaoMin, Chang, XiangKe, Sun, JianQing, Hu, XingBiao, Yeh, YeongNan. Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions. NONLINEARITY[J]. 2015, 28(7): 2279-2306, [31] Chang, Xiangke, Chen, Xiaomin, Hu, Xingbiao. A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions. ADVANCES IN MATHEMATICS[J]. 2014, 263: 154-177, [32] Chang, XiangKe, Hu, XingBiao, Zhang, YingNan. A direct method for evaluating some nice Hankel determinants and proofs of several conjectures. LINEAR ALGEBRA AND ITS APPLICATIONS[J]. 2013, 438(5): 2523-2541, http://dx.doi.org/10.1016/j.laa.2012.10.050.
[33] Sun, JianQing, Chang, XiangKe, He, Yi, Hu, XingBiao. An Extended Multistep Shanks Transformation and Convergence Acceleration Algorithm with Their Convergence and Stability Analysis. NUMERISCHE MATHEMATIK[J]. 2013, 125(4): 785-809, [34] Chang, XiangKe, Hu, XingBiao, Yu, GuoFu. An integrable semi-discrete equation and combinatorial numbers with their combinatorial interpretations. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS[J]. 2013, 19(7): 1093-1107, https://www.webofscience.com/wos/woscc/full-record/WOS:000321612500004.
[35] Chang, XiangKe, Hu, XingBiao. A conjecture based on Somos-4 sequence and its extension. LINEAR ALGEBRA AND ITS APPLICATIONS[J]. 2012, 436(11): 4285-4295, http://dx.doi.org/10.1016/j.laa.2012.01.016.

（1） 可积系统与数值算法, 科学出版社, 2014-12, 第 4 作者

   

（ 1 ） 尖峰孤子相关的若干等谱及非等谱问题, 负责人, 国家任务, 2018-01--2020-12
（ 2 ） 基金委重点项目, 参与, 国家任务, 2018-01--2022-12
（ 3 ） 中国科学院青年创新促进会, 负责人, 中国科学院计划, 2019-01--2022-12
（ 4 ） 若干双正交有理函数的可积结构及其应用, 负责人, 国家任务, 2022-01--2025-12
（ 5 ） 国家自然科学基金委优秀青年科学基金, 负责人, 国家任务, 2023-01--2025-12