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THE FULL DISCRETE DISCONTINUOUS FINITE ELEMENT ANALYSIS FOR FIRST-ORDER LINEAR HYPERBOLICEQUATION

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Journal of Computational mathematics 1999年第1期17卷 97-112页

作者： Che Sun Shu-jie Qin(Department of mathematics, nankai University, Tianjin 300071, China) Department of mathematics Nankai University Tianjin 300071 China

In this paper, the full discrete discontinuous Galerkin finite element method to solove 2-dimensional first-order linear hyperbolic problem is considered. Two practical schemes, Euler scheme and Crank-Nicolson scheme, are constructed. For each of them, the stability and error estimation with optimal order approximation is established in the norm stronger than L-2-norm.

关键词： hyperbolic equation discontinuous FEM Euler scheme

Non-hyperbolic Closed Characteristics on Non-degenerate Star-shaped Hypersurfaces in R2n

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Acta Mathematica Sinica,English Series 2018年第1期34卷 1-18页

作者： Hua Gui DUAN Hui LIU Yi Ming LONG Wei WANG School of Mathematical Sciences and LPMC Nankai University School of mathematics and Statistics Wuhan University Chern institute of mathematics and LPMC Nankai University School of Mathematical Sciences and LMAM Peking University

In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on E and at least （n - 1） of them are non-hyperbolic. Here we call a compact star-shaped hypersurfaee E ∈R2 index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic （T, y） on E possesses positive mean index and whose Maslov-type index i（y, m） of its m-th iterate satisfies i（y, m） ≠-1 when n is even, and i（y, rn） ≠2{-1,0} when n is odd for all rn E N.

关键词： Closed characteristic star-shaped hypersurface non-hyperbolic Maslov-type index

Geometric characterizations for variational minimization solutions of the 3-body problem

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Chinese Science Bulletin 1999年第18期44卷 1653-1655页

作者： LONG Yiming and ZHANG Shiqing1. nankai institute of mathematics , nankai University , Tianjin 300071 , China 2. Department of Applied mathematics, Chongqing University, Chongqing 400044, China Associate Member of the ICTP. nankai institute of mathematics Nankai University Tianjin China Department of Applied mathematics Chongqing University Chongqing China

For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in 3 or 2 are also planar equilateral triangle circular solutions.

关键词： 3-body problem variational minimization equilateral triangle circular solution.

Normal Forms of Symplectic Matrices

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Acta Mathematica Sinica,English Series 2000年第2期16卷 237-260页

作者： Yiming Long nankai institute of mathematics.nankai University,Tianjin 300071,P.R.China Di Dong Department of mathematics.SUNY at Stony Brook,Stony Brook,NY 111794-3651,USA Associate Member of the ICTP nankai institute of mathematics Nankai University Tianjin 300071 P. R. China Department of mathematics SUNY at Stony Brook Stony Brook NY 111794-3651 USA

In this paper,we prove that for every symplectic matrix M possessing eigenvalues on the unit circle,there exists a symplectic matrix P such that P-1 MP is a symplectic matrix of the normal forms defined in this paper.

关键词： Normal form Symplectic matrix Eigenvalue Symplectic transformation

Some Abstract Critical Point Theorems for Self-adjoint Operator Equations and Applications

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Chinese Annals of mathematics,Series B 2011年第1期32卷 1-14页

作者： Chungen LIU Qi WANG School of mathematics and LPMC Nankai University Tianjin 300071 China School of mathematics Nankai University Tianjin 300071 China

By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.

关键词： Self-adjoint operator equations Index theory Relative Morse index Dual variational method Morse theory Hamiltonian systems

Traversable braneworld wormholes supported by astrophysical observations

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Frontiers of physics 2018年第1期13卷 109-118页

作者： Deng Wang Xin-He Meng Theoretical Physics Division Chern Institute of Mathematics Nankai University Tianjin 300071 China Department of Physics Nankai University Tianjin 300071 China

In this study, we investigate the characteristics and properties of a traversable wormhole constrained by the current astrophysical observations in the framework of modified theories of gravity （MOG）. As a concrete case, we study traversable wormhole space-time configurations in the Dvali-Gabadadze- Porrati （DGP） braneworld scenario, which are supported by the effects of the gravity leakage of extra dimensions. We find that the wormhole space-time structure will open in terms of the 2o confidence level when we utilize the joint constraints supernovae （SNe） Ia ＋ observational Hubble parameter data （OHD）＋ Planck ＋ gravitational wave （GW） and z 〈 0.2874. Furthermore, we obtain several model-independent conclusions, such as （i） the exotic matter threading the wormholes can be divided into four classes during the evolutionary processes of the universe based on various energy conditions; （ii） we can offer a strict restriction to the local wormhole space-time structure by using the current astrophysical observations; and （iii） we can clearly identify a physical gravitational resource for the wormholes supported by astrophysical observations, namely the dark energy components of the universe or equivalent space-time curvature effects from MOG. Moreover, we find that the strong energy condition is always violated at low redshifts.

关键词： braneworld model traversable wormholes astrophysical observations

Discrete α-Yamabe flow in 3-dimension

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Frontiers of mathematics in China 2017年第4期12卷 843-858页

作者： Huabin GE Shiguang MA institute of mathematics Beijing Jiaotong University Beijing 100044 China Department of mathematics and LPMC Nankai University Tianjin 300071 China

We generalize the discrete Yamabe flow to α order. This Yamabe flow deforms the α-order curvature to a constant. Using this new flow, we manage to find discrete α-quasi-Einstein metrics on the triangulations of S3.

关键词： α-Yamabe flow α-quasi Einstein metric ball packing metric

Multi-channel surface acoustic wave device and its application on all-fiber acousto-optic modulation

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Chinese Optics Letters 2010年第1期8卷 107-110页

作者：赵路明赵启大 institute of Physics Nankai University institute of Modern Optics Nankai University

The interaction of multi-channel surface acoustic waves （SAWs） and a guided optical wave in fiber is studied, and the corresponding coupled wave equations are derived. A novel two-channel SAW all-fiber acousto-optic... 详细信息

关键词： Acoustic waves Acoustics Acoustoelectric effects Wave equations

A Cheeger-Müller Theorem for Delocalized L^(2)-analytic Torsion Form

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Acta Mathematica Sinica,English Series 2024年第11期40卷 2615-2670页

作者： Guo Lin AN Chern institute of mathematics and LPMC Nankai UniversityTianjin300071P.R.China

In this paper we define the delocalized L^(2)-analytic torsion form and the delocalized L^(2)-combinatorial torsion *** using the method of Bismut-Goette,under the conditions of positive Novikov-Shubin invariants,nontrivial finite conjugacy class and the existence of a family of fiberwise Morse functions whose gradient fields satisfy the Thom-Smale transversality condition in every fiber,we prove the Cheeger-Müller type relation between the delocalized L^(2)-analytic torsion form and the delocalized L^(2)-combinatorial torsion form.

关键词： Delocalized trace Novikov-Shubin invariant delocalized L^(2)-analytic torsion form delocalized L^(2)-combinatorial torsion form