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THE EXISTENCE OF PSEUDOHARMONIC MAPS FOR SMALL HORIZONTAL ENERGY

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Acta Mathematica Scientia 2024年第5期44卷 1955-1964页

作者： Biqiang ZHAO Shanghai center for mathematical sciences Fudan UniversityShanghai200433China

In this paper,we consider pseudoharmonic heat flow with small initial horizontal energy and give the existence of pseudoharmonic maps from closed pseudo-Hermitian manifolds into closed Riemannian manifolds.

关键词： pseudoharmonic map pseudoharmonic heat flow small horizontal energy

A general mirror equivalence theorem for coset vertex operator algebras

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Science China Mathematics 2024年第10期67卷 2237-2282页

作者： Robert McRae Yau mathematical sciences center Tsinghua UniversityBeijing 100084China

We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules Uiare simple and distinct and are objects of a semisimple braided ribbon category of Umodules,and the V-modules Viare semisimple and contained in a(not necessarily rigid) braided tensor category of *** also assume U=ComA(V).Under these conditions,we construct a braid-reversed tensor equivalence τ:u_(A)→v_(A),where u_(A)is the semisimple category of U-modules with simple objects Ui,i∈I,and v_(A)is the category of V-modules whose objects are finite direct sums of *** particular,the V-modules Viare simple and distinct,and v_(A)is a rigid tensor *** an application,we find a rigid semisimple tensor subcategory of modules for the Virasoro algebra at central charge 13+6p+6p^(-1),p∈Z_(≥2), which is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional ***,the Virasoro vertex operator algebra at central charge 13+6p+6p^(-1)is the PSL_(2)(C)-fixed-point subalgebra of a simple conformal vertex algebra w(-p),analogous to the realization of the Virasoro vertex operator algebra at central charge 13-6p-6p^(-1)as the PSL_(2)(C)-fixed-point subalgebra of the triplet algebra W(p).

关键词： vertex operator algebras coset conformal eld theory braid-reversed tensor equivalence Virasoro algebra

Point defects in 2-D liquid crystals with a singular potential:Profiles and stability

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Science China Mathematics 2024年第11期67卷 2515-2540页

作者： Zhiyuan Geng Wei Wang Basque center for Applied Mathematics School of mathematical sciences Zhejiang University

We study radial symmetric point defects with degree k/2 in the 2-D disk or R2in the Q-tensor framework with a singular bulk energy,which is defined by Bingham ***,we obtain the existence of solutions for the profiles of radial symmetric point defects with degree k/2 in the 2-D disk or ***,we prove that the solution is stable for |k| = 1 and unstable for |k| > *** identities are derived and utilized throughout the proof of existence and stability/instability.

关键词： radial symmetric point defects singular bulk potential Bingham closure stability

Markovian Quadratic BSDEs with an Unbounded Sub-quadratic Growth

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 441-462页

作者： Jingnan JU Shanjian TANG Shanghai center for mathematical sciences Fudan UniversityShanghai 200433China Department of Finance and Control sciences School of Mathematical SciencesFudan UniversityShanghai 200433China

This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal *** generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable *** existence and uniqueness results are given to these *** an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.

关键词： Markovian BSDE Quadratic growth Unbounded sub-quadratic term coeficients Coupled FBSDE

Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations

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Science China Mathematics 2024年第3期67卷 557-576页

作者： Jiaxiang Wang Bin Zhou Beijing International center for mathematical Research Peking UniversityBeijing 100871China School of mathematical sciences Peking UniversityBeijing 100871China

In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger types), isocapacitary inequalities, and the regularity of the complex Hessian and Monge-Amp`ere equations with respect to a general nonnegative Borel measure. We obtain a quantitative characterization for these relations through the properties of the capacity-minimizing functions.

关键词： complex Monge-Ampère equations plurisubharmonic functions Sobolev inequality Moser-Trudinger inequality

Aubry-Mather theory for contact Hamiltonian systems Ⅲ

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Science China Mathematics 2024年第11期67卷 2541-2570页

作者： Panrui Ni Lin Wang Shanghai center for mathematical sciences Fudan University School of Mathematics and Statistics Beijing Institute of Technology

By exploiting the contact Hamiltonian dynamics（T*M × R,Φ_t） around the Aubry set of contact Hamiltonian systems,we provide a relation among the Mather set,the Φ_t-recurrent set,the strongly static set,the Aubry set,the Ma?é set,and the Φ_t-non-wandering ***,we consider the strongly static set,as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing *** show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser（KAM） solutions and the existence of transitive orbits around the Aubry set.

关键词： Aubry-Mather theory weak KAM theory contact Hamiltonian systems Hamilton-Jacobi equations

Remarks on the Global Existence for Incompressible Navier-Stokes Equations

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Chinese Annals of Mathematics,Series B 2024年第4期45卷 529-536页

作者： Sheng WANG Zexian ZHANG Yi ZHOU Shanghai center for mathematical sciences Fudan University School of Mathematics Science Fudan University

In this article, the authors use the special structure of helicity for the threedimensional incompressible Navier-Stokes equations to construct a family of finite energy smooth solutions to the Navier-Stokes equations... 详细信息

关键词： 17B40 17B50 Critical norm Global existence Helicity Navier-Stokes euqations

Oscillatory Dynamics of Heterogeneous Stem Cell Regeneration

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Communications on Applied Mathematics and Computation 2024年第1期6卷 431-453页

作者： Xiyin Liang Jinzhi Lei School of mathematical sciences Center for Applied MathematicsTiangong UniversityTianjin300387China

Stem cell regeneration is an essential biological process in the maintenance of tissue homeostasis;dysregulation of stem cell regeneration may result in dynamic diseases that show oscillations in cell *** heterogeneity and plasticity are necessary for the dynamic equilibrium of tissue homeostasis;however,how these features may affect the oscillatory dynamics of the stem cell regeneration process remains poorly ***,based on a mathematical model of heterogeneous stem cell regeneration that includes cell heterogeneity and random transition of epigenetic states,we study the conditions to have oscillation solutions through bifurcation analysis and numerical *** results show various model system dynamics with changes in different parameters associated with kinetic rates,cellular heterogeneity,and *** show that introducing heterogeneity and plasticity to cells can result in oscillation dynamics,as we have seen in the homogeneous stem cell regeneration ***,increasing the cell heterogeneity and plasticity intends to maintain tissue homeostasis under certain *** current study is an initiatory investigation of how cell heterogeneity and plasticity may affect stem cell regeneration dynamics,and many questions remain to be further studied both biologically and mathematically.

关键词： Stem cell regeneration Heterogenous Hopf bifurcation Hematopoietic dynamical disease

NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS

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Acta Mathematica Scientia 2024年第5期44卷 1886-1902页

作者： Wenmin LIU Xuexiu ZHONG Jinfang ZHOU School of mathematical sciences South China Normal UniversityGuangzhou510631China South China Research center for Applied Mathematics and Interdisciplinary Studies&School of mathematical sciences South China Normal UniversityGuangzhou510631China

In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈ℝ×H^(1)(ℝ^(N))to the general Kirchhoff problem-M\left(\int_{\mathbb{R}^N}\vert\nabla u\vert^2{\rm d}x\right)\Delta u+\lambda u=g(u)~\hbox{in}~\mathbb{R}^N,u\in H^1(\mathbb{R}^N),N\geq 1,satisfying the normalization constraint\int_{\mathbb{R}^N}u^2{\rm d}x=c,where M∈C([0,∞))is a given function satisfying some suitable *** argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.

关键词： normalized solution Kirchhoff type equations general nonlinearities asymptotic behavior