In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boun...In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.展开更多
In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） =...In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） = αuˊ（η）, uˊˊ（0） = 0, where φp（s） = ｜s｜p？2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.展开更多
Bistable beams,with their characteristic recoverable elastic large deformations,are widely utilized in reversible deformation designs.However,analytical modeling of bistable beams under third-order mode deformation re...Bistable beams,with their characteristic recoverable elastic large deformations,are widely utilized in reversible deformation designs.However,analytical modeling of bistable beams under third-order mode deformation remains a challenge.For example,theoretical research on bistable beams in existing energy-consuming materials has focused mainly on the deformation process of the second-order mode.To address this challenge,the present work establishes an analytical model for the deformation process of a bistable beam from the first-order mode to the third-order mode via the elliptic integral method.Additionally,judgment conditions for identifying the critical points of modal transitions are provided.Second,the analytical model allows for the calculation of the maximum instability force and the unstable equilibrium position when third-order mode deformation occurs in the bistable beam during the snap-through process.The unstable equilibrium position of the bistable beam during third-order mode deformation is significantly lower than the positions of the two fixed ends.The validity of the analytical model was confirmed through experiments and finite element modeling.In the compression experiments of bistable beams with identical dimensional parameters presented in the present work,the work done by the external force during the third-order mode deformation process is 2 times that of the second-order mode deformation process.This will provide a completely new approach for the design of energy-consuming materials based on bistable beams.展开更多
The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to...The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance Re, the dissociation energy De and the harmonic frequency We for the XIEg＋ state of sodium dimer in a number of basis sets. The conclusion is gained that the best Re, De and We results can be attained at the QCISD/6-311G（3df,3pd） level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0 nm and is fitted to the analytic Murrell-Sorbie function. The spectroscopic parameters De, DO, Re, ωe, ωe Xe, αe and Be are calculated to be 0.7219 eV, 0.7135 eV, 0.31813 nm, 151.63 cm^-1, 0.7288 cm^-1, 0.000729 cm^-1 and 0.1449 cm^-1, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G（3df,3pd） level of theory, a total of 63 vibrational states is found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants （Dr Hv, Lv, Mv, Nv and Ov） are reported for the first time for the first 31 vibrational states when J = 0.展开更多
Based on the covariant density functional theory,by employing the core–quasiparticle coupling(CQC)model,the nuclear level density of odd-A nuclei at the saddle point is achieved.The total level density is calculated ...Based on the covariant density functional theory,by employing the core–quasiparticle coupling(CQC)model,the nuclear level density of odd-A nuclei at the saddle point is achieved.The total level density is calculated via the convolution of the intrinsic level density and the collective level density.The intrinsic level densities are obtained in the finite-temperature covariant density functional theory,which takes into account the nuclear deformation and pairing self-consistently.For saddle points on the free energy surface in the(β_(2),γ)plane,the entropy and the associated intrinsic level density are compared with those of the global minima.By introducing a quasiparticle to the two neighboring even–even core nuclei,whose properties are determined by the five-dimensional collective Hamiltonian model,the collective levels of the odd-A nuclei are obtained via the CQC model.The total level densities of the^(234-240)U agree well with the available experimental data and Hilaire’s result.Furthermore,the ratio of the total level densities at the saddle points to those at the global minima and the ratio of the total level densities to the intrinsic level densities are discussed separately.展开更多
The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active spac...The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.展开更多
An analytical evaluation method for output waveform quality of space vector pulse width modulation(PWM)strategies applied in neutral⁃point⁃clamped three⁃level converter(3L⁃NPC)is proposed in this paper.Low frequency e...An analytical evaluation method for output waveform quality of space vector pulse width modulation(PWM)strategies applied in neutral⁃point⁃clamped three⁃level converter(3L⁃NPC)is proposed in this paper.Low frequency error caused by neutral point voltage ripple and high frequency error introduced by space vector synthesis were both taken into account,and the unified error model of output current ripple was established.By taking continuous and discontinuous modulation strategies as examples,the unified error model was validated through Fourier analysis of the experimental results.The proposed evaluation method will be helpful for the switching sequence optimization and the modulation strategy selection.展开更多
This paper investigates the breaking point between fast- and slow-light in a degenerate two-level atomic system, where fast-light can be converted to slow-light arbitrarily on a single transition line by adjusting the...This paper investigates the breaking point between fast- and slow-light in a degenerate two-level atomic system, where fast-light can be converted to slow-light arbitrarily on a single transition line by adjusting the strength of the pumping field. An equivalent incoherent pumping rate is introduced in this simplified theoretical model which exploits the dependence of this feature. The experimental observation is presented as evidence of the breaking point where the injected power is about 0.08 mW.展开更多
功率变换器采用脉宽调制时产生的高共模电压CMV(common-mode voltage)会使电机轴电压过高,进而导致高频高幅值轴电流破坏电机绝缘、增加电磁干扰等。为减小中点钳位型NPC(neutral point clamped)三电平变换器的共模电压,提出了基于代数...功率变换器采用脉宽调制时产生的高共模电压CMV(common-mode voltage)会使电机轴电压过高,进而导致高频高幅值轴电流破坏电机绝缘、增加电磁干扰等。为减小中点钳位型NPC(neutral point clamped)三电平变换器的共模电压,提出了基于代数调制框架的共模电压抑制策略:首先,将占空比的确定问题转化为非齐次线性方程组的求解问题;然后,合理地选择调制自由度以实现中点电压NPV(neutral point voltage)平衡控制的目标;其次,根据占空比约束,选择偏置量获取最终占空比;最后,使中间相开关采用反相载波得到新的开关状态组合,实现降低共模电压的目的。所提调制策略无需额外的控制器,实现简单,在保证中点钳位型三电平变换器的中点电压具有良好平衡特性的前提下,可将共模电压降低至直流侧电压的1/6范围内。实验结果验证了所提调制策略的有效性和可行性。展开更多
文摘In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.
基金Supported by the HEBNSF of China(A2012506010)Supported by the YSF of Heibei Province(A2014506016)
文摘In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） = αuˊ（η）, uˊˊ（0） = 0, where φp（s） = ｜s｜p？2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.
基金supported by the Guangdong Province Basic and Applied Basic Research Fund(Grant No.2025A1515011975)the research project of Guangdong University of Technology(Grant No.2023SDKYA010)for their funding.
文摘Bistable beams,with their characteristic recoverable elastic large deformations,are widely utilized in reversible deformation designs.However,analytical modeling of bistable beams under third-order mode deformation remains a challenge.For example,theoretical research on bistable beams in existing energy-consuming materials has focused mainly on the deformation process of the second-order mode.To address this challenge,the present work establishes an analytical model for the deformation process of a bistable beam from the first-order mode to the third-order mode via the elliptic integral method.Additionally,judgment conditions for identifying the critical points of modal transitions are provided.Second,the analytical model allows for the calculation of the maximum instability force and the unstable equilibrium position when third-order mode deformation occurs in the bistable beam during the snap-through process.The unstable equilibrium position of the bistable beam during third-order mode deformation is significantly lower than the positions of the two fixed ends.The validity of the analytical model was confirmed through experiments and finite element modeling.In the compression experiments of bistable beams with identical dimensional parameters presented in the present work,the work done by the external force during the third-order mode deformation process is 2 times that of the second-order mode deformation process.This will provide a completely new approach for the design of energy-consuming materials based on bistable beams.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574039）, the Henan Innovation for University Prominent Research Talents （Grant No 2006KYCX002） and the Natural Science Foundation of Henan Province （Grant Nos 2006140008 and 2007140015）.
文摘The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance Re, the dissociation energy De and the harmonic frequency We for the XIEg＋ state of sodium dimer in a number of basis sets. The conclusion is gained that the best Re, De and We results can be attained at the QCISD/6-311G（3df,3pd） level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0 nm and is fitted to the analytic Murrell-Sorbie function. The spectroscopic parameters De, DO, Re, ωe, ωe Xe, αe and Be are calculated to be 0.7219 eV, 0.7135 eV, 0.31813 nm, 151.63 cm^-1, 0.7288 cm^-1, 0.000729 cm^-1 and 0.1449 cm^-1, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G（3df,3pd） level of theory, a total of 63 vibrational states is found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants （Dr Hv, Lv, Mv, Nv and Ov） are reported for the first time for the first 31 vibrational states when J = 0.
基金supported by the China Institute of Atomic Energy(No.401Y-FW-GKXJ-21-1496)the Natural Science Foundation of Henan Province(No.202300410480 and 202300410479)+1 种基金the Open Project of Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology(No.NLK2021-01)the National Natural Science Foundation of China(No.U2032141).
文摘Based on the covariant density functional theory,by employing the core–quasiparticle coupling(CQC)model,the nuclear level density of odd-A nuclei at the saddle point is achieved.The total level density is calculated via the convolution of the intrinsic level density and the collective level density.The intrinsic level densities are obtained in the finite-temperature covariant density functional theory,which takes into account the nuclear deformation and pairing self-consistently.For saddle points on the free energy surface in the(β_(2),γ)plane,the entropy and the associated intrinsic level density are compared with those of the global minima.By introducing a quasiparticle to the two neighboring even–even core nuclei,whose properties are determined by the five-dimensional collective Hamiltonian model,the collective levels of the odd-A nuclei are obtained via the CQC model.The total level densities of the^(234-240)U agree well with the available experimental data and Hilaire’s result.Furthermore,the ratio of the total level densities at the saddle points to those at the global minima and the ratio of the total level densities to the intrinsic level densities are discussed separately.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574039） and Henan Innovation for University Prominent Research Talents of China （Grant No 2006KYCX002）.Acknowledgment We heartily thank Professor Zhu Z H, of Sichuan University, for helpful discussion about the reasonable dissociation limit of ^7Li2（2^1Пu） during the planning stages of these calculations.
文摘The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.
基金National Natural Science Foundation of China(Grant Nos.51807140 and 51690183).
文摘An analytical evaluation method for output waveform quality of space vector pulse width modulation(PWM)strategies applied in neutral⁃point⁃clamped three⁃level converter(3L⁃NPC)is proposed in this paper.Low frequency error caused by neutral point voltage ripple and high frequency error introduced by space vector synthesis were both taken into account,and the unified error model of output current ripple was established.By taking continuous and discontinuous modulation strategies as examples,the unified error model was validated through Fourier analysis of the experimental results.The proposed evaluation method will be helpful for the switching sequence optimization and the modulation strategy selection.
基金Project supported by the Key Program of the National Natural Science Foundation of China (Grant No.60837004)the Key Project of Jiangxi Electric Power Company (Grant Nos.200950801 and 200950802)
文摘This paper investigates the breaking point between fast- and slow-light in a degenerate two-level atomic system, where fast-light can be converted to slow-light arbitrarily on a single transition line by adjusting the strength of the pumping field. An equivalent incoherent pumping rate is introduced in this simplified theoretical model which exploits the dependence of this feature. The experimental observation is presented as evidence of the breaking point where the injected power is about 0.08 mW.
文摘功率变换器采用脉宽调制时产生的高共模电压CMV(common-mode voltage)会使电机轴电压过高,进而导致高频高幅值轴电流破坏电机绝缘、增加电磁干扰等。为减小中点钳位型NPC(neutral point clamped)三电平变换器的共模电压,提出了基于代数调制框架的共模电压抑制策略:首先,将占空比的确定问题转化为非齐次线性方程组的求解问题;然后,合理地选择调制自由度以实现中点电压NPV(neutral point voltage)平衡控制的目标;其次,根据占空比约束,选择偏置量获取最终占空比;最后,使中间相开关采用反相载波得到新的开关状态组合,实现降低共模电压的目的。所提调制策略无需额外的控制器,实现简单,在保证中点钳位型三电平变换器的中点电压具有良好平衡特性的前提下,可将共模电压降低至直流侧电压的1/6范围内。实验结果验证了所提调制策略的有效性和可行性。
