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This paper deals with the near-invariant tori for Poisson systems. It is shown that the orbits with the initial points near the Diophantine torus approach some quasi-periodic orbits over an extremely long time. In particular, the results hold for the classical Hamiltonian system, and in this case the drift of the motions is smaller than one in the past works. 相似文献
904.
Ioannis K. Argyros 《Numerical Functional Analysis & Optimization》2019,40(3):303-318
The convergence set for Newton’s method is small in general using Lipschitz-type conditions. A center-Lipschitz-type condition is used to determine a subset of the convergence set containing the Newton iterates. The rest of the Lipschitz parameters and functions are then defined based on this subset instead of the usual convergence set. This way the resulting parameters and functions are more accurate than in earlier works leading to weaker sufficient semi-local convergence criteria. The novelty of the paper lies in the observation that the new Lipschitz-type functions are special cases of the ones given in earlier works. Therefore, no additional computational effort is required to obtain the new results. The results are applied to solve Hammerstein nonlinear integral equations of Chandrasekhar type in cases not covered by earlier works. 相似文献
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冷却法测量金属比热容误差探讨 总被引:1,自引:0,他引:1
本文对冷却法测量金属比热容实验的原理和仪器做了简要介绍,并着重对该实验误差的主要来源进行了探讨。 相似文献
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Pengcong Mu & Weiying Zheng 《计算数学(英文版)》2023,41(5):910-933
In this paper, we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model. The model consists of five nonlinear elliptic equations, and two of them describe quantum corrections for quasi-Fermi levels. We propose an interpolated-exponential finite element (IEFE) method for solving the two quantum-correction equations. The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations. Moreover, we solve the two continuity equations with the edge-averaged finite element (EAFE) method to reduce numerical oscillations of quasi-Fermi levels. The Poisson equation of electrical potential is solved with standard Lagrangian finite elements. We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional. A Newton method is proposed to solve the nonlinear discrete problem. Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V. 相似文献