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Weak KAM theory for two classes of almost periodic Hamiltonian systems

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Science China mathematics 2025年

作者： Xun Niu Kaizhi Wang Yong Li school of mathematics and statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal University school of Mathematical Sciences Shanghai Frontier Science Center of Modern Analysis (CMA-Shanghai)Shanghai Jiao Tong University Institute of mathematics Jilin University

The purpose of this paper is to investigate the dynamics of Bohr almost periodic and Levitan almost periodic Hamiltonian systems via the weak KAM theory. We obtain minimal measures and weak KAM solutions in both cases. The weak KAM solution is a weak solution to the Hamilton-Jacobi equation, which formally transforms the original Hamiltonian systems into an integrable one. Consequently, we get the existence of an invariant torus in the aforementioned weak sense.

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Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus

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Science China mathematics 2025年

作者： Xin Lü Shengli Tan Kang Zuo school of Mathematical Sciences Key Laboratory of Mathematics and Engineering Applications(Ministry of Education) Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal University school of mathematics and statistics Wuhan University Institut für Mathematik Universit?t Mainz

We show that there does not exist any Shimura curve with a strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus g≥4. In particular, Shimura curves of Mumford type are not...

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EQUIVARIANT HEAT INVARIANTS OF THE LAPLACIAN AND NONMININMAL OPERATORS ON DIFFERENTIAL FORMS

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Acta Mathematica Scientia 2011年第3期31卷 805-814页

作者：王勇 school of mathematics and statistics northeast normal university

In this paper,we compute the first two equivariant heat kernel coeffcients of the Bochner Laplacian on differential *** first two equivariant heat kernel coeffcients of the Bochner Laplacian with torsion are also *** also study the equivariant heat kernel coeffcients of nonminimal operators on differential forms and get the equivariant Gilkey-Branson-Fulling formula.

关键词： equivariant heat kernel asymptotics Bochner Laplacian nonmininmal operators Gilkey-Branson-Fulling formula

Weakly k-hyponormal and polynomially hyponormal commuting operator pairs

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Science China mathematics 2015年第2期58卷 405-422页

作者： DUAN Yong Jiang QI Ting Ting school of mathematics and statistics Northeast Normal University

We introduce the notion of weak k-hyponormality and polynomial hyponormality for commuting operator pairs on a Hilbert space and investigate their relationship with k-hyponormality and *** provide examples of 2-variable weighted shifts which are weakly 1-hyponormal but not *** relating the weak k-hyponormality and k-hyponormality of a commuting operator pair to positivity of restriction of some linear functionals to corresponding cones of functions,we prove that there is an operator pair that is polynomially hyponormal but not 2-hyponormal,generalizing Curto and Putinar’s result(1991,1993)to the two-variable case.

关键词： weakly k-hyponormal k-hyponormal polynomially hyponormal subnormal commuting operator pair

DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA

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Acta Mathematica Scientia 2008年第4期28卷 933-948页

作者：张庆成张永正 school of mathematics and statistics Northeast Normal University

In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color ***,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.

关键词： Derivation central extension double extension quadratic Lie color algebra

On the Number of Integral Ideals in Two Different Quadratic Number Fields

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Chinese Annals of mathematics,Series B 2016年第4期37卷 595-606页

作者： Zhishan YANG school of mathematics and statistics Northeast Normal University

Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of aK（n）,This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sumwhere K1 and K2 are two different quadratic fields.

关键词： Asymptotic formula Integral ideal Number field 17B40 17B50

On Lawson's Area-minimizing Hypercones

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Acta Mathematica Sinica,English Series 2016年第12期32卷 1465-1476页

作者： Yong Sheng ZHANG school of mathematics and statistics Northeast Normal University

We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces （classified by Lawlor） following Lawson＇s original idea in his 72＇ Trans. A.M.S. paper ＂The equivariant Plateau problem and interior regularity＂. Moreover, each of them enjoys （coflat） calibrations singular only at the origin.

关键词： Area-minimizing hypercone coflat calibration comass

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

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Science China mathematics 2016年第4期59卷 809-822页

作者： WEI QingMeng school of mathematics and statistics Northeast Normal University

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field *** full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all *** addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal *** also study a stochastic linear quadratic control problem with state constraints.

关键词： mean-field forward-backward stochastic differential equations maximum principle state constraints

A likelihood-based method for haplotype association studies of case-control data with genotyping uncertainty

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Science China mathematics 2006年第1期49卷 130-144页

作者： ZHU Wensheng GUO Jianhua school of mathematics and statistics Northeast Normal University Changchun 130024 China School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

This paper discusses the associations between traits and haplotypes based on Fl (fluorescent intensity) data sets, We consider a clustering algorithm based on mixtures of t distributions to obtain all possible genotypes of each individual (i.e. "GenoSpectrum"). We then propose a likelihood-based approach that incorporates the genotyping uncertainty to assessing the associations between traits and haplotypes through a haplotypebased logistic regression model, Simulation studies show that our likelihood-based method can reduce the impact induced by genotyping errors.

关键词： haplotype-based association GenoSpectrum case-control study genotyping error logistic regres-