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Search Results: 1 - 10 of 89585 matches for " Gang Liu "
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Existence and Uniqueness of Solutions to Impulsive Fractional Integro-Differential Equations with Nonlocal Conditions  [PDF]
Zhenghui Gao, Liu Yang, Gang Liu
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.46118
Abstract: In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.
Weinstein Conjecture and GW Invariants
Gang Liu,Gang Tian
Mathematics , 1997,
Abstract: In this paper, we establish a general relationship between the nonvanishing of GW invariants with the existence of the closed orbits of a Hamiltonian system. As an application, we completely solved the stabilized Weinstein conjecture.
Periodic molecular dynamics with many-body potential under external stress
Gang Liu
Physics , 2005,
Abstract: The dynamical equations for periodic systems under constant external stress (cond-mat/0209372) have been extended to many-body potential case. Rather than introducing Lagrangian dynamics, Newtonian dynamics was employed directly. The kinetic energy term of stress and the imagined force only due to particles' passing through geometric planes or boundaries were also discussed.
Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress
Gang Liu
Physics , 2002, DOI: 10.1139/cjp-2014-0518
Abstract: The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton's second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.
Compactification of the moduli space in symplectization and hidden symmetries of its boundary
Gang Liu
Physics , 2000,
Abstract: In this paper, we establish the compactification of the moduli space in symplectization and and studied the hidden symmetries of its boundary.
Various Newtonian stresses from macroscopic fluid to microscopic celled fluid
Gang Liu
Physics , 2004,
Abstract: We showed that various expressions of stress in different models of fluids and in different forms of applying Newton's Second Law can be chosen, however there is always one Newton's Second Law which restricts and provides flexibility in these expressions. When fluids are regarded as being made of cells from a microscopic point of view, temperature force (gradient of internal kinetic energy) can also drive them flow.
Comment on "Crystal Structure and Pair Potentials: A Molecular-Dynamics Study"
Gang Liu
Physics , 2003,
Abstract: The dynamical equations for particles in the Parrinello-Rahman Molecular Dynamics were compared with the Newton's Second Law. The discrepancy is due to using the in-complete particles' kinetic energy in the Lagrangian.
Local volume comparison for Kahler manifolds
Gang Liu
Mathematics , 2011,
Abstract: On Kahler manifolds with Ricci curvature lower bound, assuming the real analyticity of the metric, we establish a sharp relative volume comparison theorem for small balls. The model spaces being compared to are complex space forms, i.e, Kahler manifolds with constant holomorphic sectional curvature. Moreover, we give an example showing that on Kahler manifolds, the pointwise Laplacian comparison theorem does not hold when the Ricci curvature is bounded from below.
Kahler manifolds with Ricci curvature lower bound
Gang Liu
Mathematics , 2011,
Abstract: On Kahler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov's relative volume comparison, Bonnet-Meyers theorem, and Yau's gradient estimate for positive harmonic functions. The tool is a Bochner type formula reflecting the Kahler structure.
3-manifolds with nonnegative Ricci curvature
Gang Liu
Mathematics , 2011,
Abstract: For a noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to $\mathbb{R}^3$ or the universal cover splits. As a corollary, it confirms a conjecture of Milnor in dimension 3.
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