![]() ![]() Guo, An algebraic study of multivariable integration and linear substitution, Journal of Algebra and Its Applications, 18(11) (2019), 1950207. Luo, Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles, Pacific Journal of Mathematics, 302(2) 2019, 741-766. Manchon*, Free (tri)dendriform family algebras, Journal of Algebra, 547 (2020), 456-493. Gao, A Hopf algebra on subgraphs of a graph, Journal of Algebra and Its Applications, 19(09) (2020), 2050164. Gao*, Hopf algebras of planar binary trees: an operated algebra approach, Journal of Algebraic Combinatorics, 51 (2020), 567-588. Guo*, Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras, Journal of Algebra, 552 (2020), 134-170. Luo, Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems, Bulletin of the Belgian Mathematical Society Simon Stevin, 27 (2020), 219-243. ![]() Luo, Dendriform-Nijenhuis bialgebras and DN-associative Yang-Baxter equations, Journal of Algebra 575 (2021), 78-126. Guo*, Reynolds algebras and their free objects from bracketed words and rooted trees, J. Zhang, Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras,Journal of Algebra 586 (2021), 402-432. ![]() Luo*, Weighted infinitesimal unitary bialgebras of rooted forests, symmetric cocycles and pre-Lie algebras, Journal of Algebraic Combinatorics, 53 (2021), 771–803. Luo*, Universal enveloping of (modified) λ-differential Lie algebras, Linear and Multilinear Algebra, 70(6) (2022), 1102-1127. Guo*, Rota’s Program on Algebraic Operators, Rewriting Systems and Gröbner–Shirshov Bases, Advances in Mathematics (China), 51(1) (2022). Gao*, New Operated Polynomial Identities and Gröbner-Shirshov Bases, Mathematics, 10(6) (2022), 961-975. Gao*, Weighted infinitesimal unitary Bialgebras and weighted associative Yang–Baxter equations, Advances in Mathematics (China), 51(6) (2022), 1011-1028. Guo*, Hopf algebra of multidecorated rooted forests, free matching Rota–Baxter algebras and Gröbner–Shirshov bases, Pacific Journal of Mathematics, 317(2) (2022), 441-475. Gao, The dual of infinitesimal unitary Hopf algebras and planar rooted forests, International Electronic Journal of Algebra, 33 (2023), 178-204. Guo*, Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases, Journal of Algebra, 620 (2023), 585-629. Zhang, Operator forms of the nonhomogeneous associative classical Yang-Baxter equation, accepted by Advances in Theoretical and Mathematical Physics. Guo*, Compatible structures of nonsymmetric operads, Manin products and Koszul duality, accepted by Applied Categorical Structures. Zheng, Rota-Baxter type operators, rewriting systems and Gröbner-Shirshov bases, arXiv:1412.8055. Manchon*, Free Rota-Baxter family algebras and Free (tri)dendriform family algebras, accepted by Algebras and Representation Theory. Rota-Baxter algebra, algebraic graphy,operated algebra Publications Teaching and guiding the situation of graduate students Ph.D.LanZhou University, 2010, Pure Mathematics Biography Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Xing Gao Professor of Institute of Basic Mathematics.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.This Time in History In these videos, find out what happened this month (or any month!) in history.#WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.Demystified Videos In Demystified, Britannica has all the answers to your burning questions.Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives. ![]()
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