Yi Zhang

ORCID: 0000-0002-2367-2497
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About
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Research Areas
  • Advanced Topics in Algebra
  • Algebraic structures and combinatorial models
  • Matrix Theory and Algorithms
  • Algebraic Geometry and Number Theory
  • Nonlinear Waves and Solitons
  • Advanced Algebra and Geometry
  • Rings, Modules, and Algebras
  • Advanced Topology and Set Theory
  • Geometry and complex manifolds
  • Homotopy and Cohomology in Algebraic Topology
  • Computability, Logic, AI Algorithms
  • Commutative Algebra and Its Applications
  • Advanced Combinatorial Mathematics
  • Finite Group Theory Research
  • Mathematical and Theoretical Analysis
  • Polynomial and algebraic computation
  • Advanced Operator Algebra Research
  • Graph theory and applications
  • Advanced Algebra and Logic
  • Graph Labeling and Dimension Problems
  • Mathematical functions and polynomials
  • semigroups and automata theory
  • Algebraic and Geometric Analysis
  • Advanced Graph Theory Research
  • advanced mathematical theories

Nanjing University of Information Science and Technology
2020-2024

Chinese Academy of Meteorological Sciences
2024

Xi’an Jiaotong-Liverpool University
2019-2023

Hainan University
2022

Lanzhou University
2017-2021

Lanzhou University of Finance and Economics
2019-2020

Google (United States)
2014-2018

Tsinghua University
2017-2018

Johann Radon Institute for Computational and Applied Mathematics
2018

Austrian Academy of Sciences
2018

10.1016/j.jalgebra.2020.02.011 article EN publisher-specific-oa Journal of Algebra 2020-02-15

10.1016/j.jpaa.2025.107924 article EN Journal of Pure and Applied Algebra 2025-02-28

10.1006/jabr.2000.8396 article EN publisher-specific-oa Journal of Algebra 2000-10-01

Abstract If is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable , no member which covered by finitely many from there such that for all are infinitely integers k f(k) = h(k) . However if V L exists a coanalytic satisfying this condition.

10.2178/jsl/1230396911 article EN Journal of Symbolic Logic 2008-12-01

In this paper, we define a new coproduct on the space of decorated planar rooted forests to equip it with weighted infinitesimal unitary bialgebraic structure. We introduce concept $\Omega$-cocycle bialgebras weight $\lambda$ and then prove that $H_{\mathrm{RT}}(X,\Omega)$, together set grafting operations $\{ B^+_\omega \mid \omega\in \Omega\}$, is free bialgebra $X$, involving version Hochschild 1-cocycle condition. As an application, cocycle structure undecorated forests, which object...

10.2140/pjm.2019.302.741 article EN Pacific Journal of Mathematics 2019-11-27

We study smooth toroidal compactifications of Siegel varieties thoroughly from the viewpoints Hodge theory and K\"ahler-Einstein metric. observe that any cusp a space can be identified as set certain weight one polarized mixed structures. then infinity boundary divisors compactifications, obtain global volume form formula an arbitrary variety $\scr{A}_{g,\Gamma} (g>1)$ with compactification $\overline{\scr{A}}_{g,\Gamma}$ such...

10.1353/ajm.2014.0024 article EN American Journal of Mathematics 2014-08-01

Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study algebraic structures with replicating operations. To understand their combinatorial nature, we first use rooted forests multiple decoration sets to construct free Hochschild 1-cocycle conditions. Applying universal property underlying operated method Gr\"obner-Shirshov bases, then objects category matching Rota-Baxter which is a generalization allow operators. Finally are equipped...

10.2140/pjm.2022.317.441 article EN Pacific Journal of Mathematics 2022-07-14

10.1007/s001530050002 article EN Archive for Mathematical Logic 2000-01-01

We equip a matrix algebra with weighted infinitesimal unitary bialgebraic structure, via construction of suitable coproduct. Furthermore, an Hopf algebra, under the view Aguiar, is constructed on algebra. By exploring relationship between bialgebras and pre-Lie algebras, we construct algebraic structure then new Lie also introduce associative Yang-Baxter equations (AYBEs) obtain solutions AYBEs bialgebras. give bijection equation weight $\lambda$ Rota-Baxter operators $-\lambda$ algebras. As...

10.48550/arxiv.1811.00842 preprint EN other-oa arXiv (Cornell University) 2018-01-01

10.1007/s10801-019-00885-8 article EN Journal of Algebraic Combinatorics 2019-05-20

Abstract This study presents an extension of a dry‐environment convection scheme (Tiedtke–Bechtold) to couple with boundary‐layer moist turbulence scheme. The deep and shallow convective updraught is modified develop in environment the large‐scale budget cloud condensate takes account influence compensation subsidence. An ambiguous layer introduced sub‐cloud transport mimic non‐local that ignored local Long‐term global simulation suggests improve low short‐wave radiative forcing. includes...

10.1002/qj.4763 article EN Quarterly Journal of the Royal Meteorological Society 2024-05-20

10.1007/s10114-018-7260-1 article EN Acta Mathematica Sinica English Series 2018-07-25

We introduce a new operator – modified λ-differential from usual differential operator. construct the free (modified) (k,∂)-algebra on (k,∂)-module, and apply it to erect universal enveloping algebra of Lie (k,∂)-algebra. The corresponding Poincaré-Birchoff-Witt theorems are obtained. Wronskian envelope (k,−λidk)-algebra is also constructed.

10.1080/03081087.2020.1753641 article EN Linear and Multilinear Algebra 2020-04-21

10.1016/j.apal.2005.08.002 article EN publisher-specific-oa Annals of Pure and Applied Logic 2006-06-12

Unifying various generalizations of Reynolds operators, the relative cocycle weighted operators are studied. We give a characterization in context pre-Lie algebras. construct an explicit graded Lie algebra whose Maurer-Cartan elements given by operator, which makes it possible to cohomology for operators. This can be seen as certain with coefficients suitable representation. Finally, we introduce notion NS-pre-Lie algebras and show induce L-dendriform

10.1080/00927872.2023.2232853 article EN Communications in Algebra 2023-07-13

The paper considers the possible cardinalities of maximal cofinitary groups and cofinalities permutation on set natural numbers. These two cardinals are compared with some other well-known cardinal invariants which related to covering properties in several forcing models. An application combinatorial group theory a construction partially ordered is presented.

10.1112/s0024610700001575 article EN Journal of the London Mathematical Society 2001-02-01

Motivated by comatrix coalgebras, we introduce the concept of a Newtonian coalgebra. We construct an infinitesimal unitary bialgebra on matrix algebras, via construction suitable coproduct. As consequence, coalgebra is established. Furthermore, Hopf algebra, under view Aguiar, constructed algebras. By close relationship between pre-Lie algebras and bialgebras, erect algebra new Lie Finally, weighted non-commutative polynomial also given.

10.1080/00927872.2019.1612422 article EN Communications in Algebra 2019-05-16

We introduce the notion of a matching Rota-Baxter algebra motivated by recent work on multiple pre-Lie algebras arising from study algebraic renormalization regularity structures~[10,18]. This is also related to iterated integrals with kernels and solutions associative polarized Yang-Baxter equation. Generalizing natural connection dendriform , we obtain algebras. As in classical case one operation, are which coincide aforementioned More general notions results tridendriform PostLie obtained.

10.48550/arxiv.1909.10577 preprint EN other-oa arXiv (Cornell University) 2019-01-01

As an algebraic meaning of the nonhomogenous associative Yang-Baxter equation, weighted infinitesimal bialgebras play important role in mathematics and mathematical physics. In this paper, we introduce concept Hopf modules show that any module carries a natural structure unitary over quasitriangular bialgebra. We decorate planar rooted forests new way, prove space forests, together with coproduct family grafting operations, is free $\Omega$-cocycle bialgebra weight zero on set. A...

10.48550/arxiv.1810.10790 preprint EN other-oa arXiv (Cornell University) 2018-01-01
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