By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturb...By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.展开更多
To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence ra...To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.展开更多
On the basis of an introduction of the Wigner Higher-Order spectra (WHOS) and a general class of time-frequency higher-order moment spectra, the geophysical signal was analyzed using the higher order time-frequency di...On the basis of an introduction of the Wigner Higher-Order spectra (WHOS) and a general class of time-frequency higher-order moment spectra, the geophysical signal was analyzed using the higher order time-frequency distributions (TFD). Simulation results obtained in this paper show that the higher-order TFD (Wigner Bispectrum, Wigner Trispectrum and Choi-Williams Trispectrum) have much better Time-Frequency Concentration than the second-order TFD, and the reduced interference higher-order TFD such as CWT can effectively reduce the cross-term in multicomponent signals and simultaneously obtain high time-frequency concentration.展开更多
We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field ...We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field may have an obvious influence on the cutoff, intensity or plateau structure of the high-order harmonic spectrum. Generally speaking, the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.展开更多
In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obt...In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L<sub>∞</sub>-norm. The convergence order is O(τ<sup>2-α</sup> + h<sup>4</sup>). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.展开更多
随着风电等间歇性新能源的大规模并网,电网运行状态变化频繁,传统基于典型运行方式计算的输电断面极限传输功率(Total Transfer Capability,TTC)适用性降低。文中提出一种基于数据挖掘的输电断面动态TTC在线构建方法。首先,基于风电和...随着风电等间歇性新能源的大规模并网,电网运行状态变化频繁,传统基于典型运行方式计算的输电断面极限传输功率(Total Transfer Capability,TTC)适用性降低。文中提出一种基于数据挖掘的输电断面动态TTC在线构建方法。首先,基于风电和负荷的超短期预测及预测误差的高阶不确定性,采样生成“风电-负荷”二维数组及相应运行状态集,对部分运行状态计算其TTC,获得用于构建输电断面动态TTC的有标记/无标记知识库;然后,通过混合互信息法选择出与TTC存在强关联的特征属性;最后,利用半监督协同训练,建立TTC偏差与特征属性之间的定量关系,进而得到输电断面动态TTC。算例验证表明,该方法不仅能够基于超短期预测及预测误差的不确定性准确估计输电断面TTC,而且能够量化提供提高TTC的调度信息,同时,采用半监督数据挖掘技术,减少了计算TTC的次数,构建动态TTC速度快,能够较好的适应在线运行方式。展开更多
基金Supported by the Innovation Talents of Science and Technology of Henan University(2009-HASTIT-007)Supported by the Natural Science Program of Department of Education(2011A110006)
文摘By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.
基金supported by the National Natural Science Foundation of China(No.11601517)the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)
文摘To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.
基金Supported by the National Natural Science Foundation of China( 4 990 40 10 )
文摘On the basis of an introduction of the Wigner Higher-Order spectra (WHOS) and a general class of time-frequency higher-order moment spectra, the geophysical signal was analyzed using the higher order time-frequency distributions (TFD). Simulation results obtained in this paper show that the higher-order TFD (Wigner Bispectrum, Wigner Trispectrum and Choi-Williams Trispectrum) have much better Time-Frequency Concentration than the second-order TFD, and the reduced interference higher-order TFD such as CWT can effectively reduce the cross-term in multicomponent signals and simultaneously obtain high time-frequency concentration.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10734080,11074263,60978013,60921004,and 10874194)the Doctor Fund of Henan Polytechnic University (Grant No. B2011-076)
文摘We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field may have an obvious influence on the cutoff, intensity or plateau structure of the high-order harmonic spectrum. Generally speaking, the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.
文摘In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L<sub>∞</sub>-norm. The convergence order is O(τ<sup>2-α</sup> + h<sup>4</sup>). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.
文摘随着风电等间歇性新能源的大规模并网,电网运行状态变化频繁,传统基于典型运行方式计算的输电断面极限传输功率(Total Transfer Capability,TTC)适用性降低。文中提出一种基于数据挖掘的输电断面动态TTC在线构建方法。首先,基于风电和负荷的超短期预测及预测误差的高阶不确定性,采样生成“风电-负荷”二维数组及相应运行状态集,对部分运行状态计算其TTC,获得用于构建输电断面动态TTC的有标记/无标记知识库;然后,通过混合互信息法选择出与TTC存在强关联的特征属性;最后,利用半监督协同训练,建立TTC偏差与特征属性之间的定量关系,进而得到输电断面动态TTC。算例验证表明,该方法不仅能够基于超短期预测及预测误差的不确定性准确估计输电断面TTC,而且能够量化提供提高TTC的调度信息,同时,采用半监督数据挖掘技术,减少了计算TTC的次数,构建动态TTC速度快,能够较好的适应在线运行方式。
