The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Sch...The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.展开更多
The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper...The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.展开更多
In this paper, the periodic solutions of the smooth and discontinuous （SD） oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic...In this paper, the periodic solutions of the smooth and discontinuous （SD） oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth （e 〉 0） and discontin- uous （ce = 0） stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems.展开更多
To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function U to be expressed as linear independent functions. The new soliton and periodic solution...To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function U to be expressed as linear independent functions. The new soliton and periodic solutions of some fifth\|order nonlinear partial differential equations are obtained.展开更多
he present paper focuses on the modifying effects of ion beam mixing, ion im-planting and ion sputtering on hydrogen evolution electrodes. It was discovered thatthe four types of electrodes possessed excellent catalyt...he present paper focuses on the modifying effects of ion beam mixing, ion im-planting and ion sputtering on hydrogen evolution electrodes. It was discovered thatthe four types of electrodes possessed excellent catalytic activity in acid or alkalinemedia and potential stability in long term electrolysis of water under high currentdensity. Their stability and applying life-span greatly surpass those of other elec-trodes activated by electrodepositing and other method. The effects of temperatureand roughness on function of electrodes were also examined. XPS and AES wereapplied to analyse the surface composition and bond states of the electrodes, andthe distribution of concentration varying with depth, and to explain the law of theexperiments .展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61072147 and 11271008)
文摘The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.
基金Supported by the National Natural Science Foundation of China(10771171)Supported by the 555 Innovation Talent Project of Gansu Province(GS-555-CXRC)+1 种基金Supported by the Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212)Supported by the Youth Foundation of Dingxi Advanced Teachers College(1333)
文摘The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.
基金supported by the National Natural Science Foundation of China(11072065)
文摘In this paper, the periodic solutions of the smooth and discontinuous （SD） oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth （e 〉 0） and discontin- uous （ce = 0） stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems.
文摘To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function U to be expressed as linear independent functions. The new soliton and periodic solutions of some fifth\|order nonlinear partial differential equations are obtained.
文摘he present paper focuses on the modifying effects of ion beam mixing, ion im-planting and ion sputtering on hydrogen evolution electrodes. It was discovered thatthe four types of electrodes possessed excellent catalytic activity in acid or alkalinemedia and potential stability in long term electrolysis of water under high currentdensity. Their stability and applying life-span greatly surpass those of other elec-trodes activated by electrodepositing and other method. The effects of temperatureand roughness on function of electrodes were also examined. XPS and AES wereapplied to analyse the surface composition and bond states of the electrodes, andthe distribution of concentration varying with depth, and to explain the law of theexperiments .
文摘为了提升分类模型对非平衡数据的分类性能,提出一种EMWRS(expectation-maximization weighted resampling)抽样算法和WCELoss(weighted cross entropy loss function)损失函数,在数据预处理阶段采用高斯混合模型得知数据分布特点,根据其聚类结果分析每个聚类簇中样本权重,以及样本分布和对应权重对数据进行采样,降低数据集不平衡程度;再依据样本比例权重对少数类和多数类赋予不同的代价损失,构建卷积神经网络模型,提高非平衡数据集的分类准确性。构建的卷积神经网络以F1和G-mean为评价指标,在UCI(university of California irvine)公共数据集adult上与SMOTE(synthetic minority over-sampling technique)和ADASYN(adaptive synthetic sampling)等多种经典算法进行比较,结果显示在这两种评价指标中所提模型均为第一,这表明改进后的卷积神经网络模型能够很好地提高少数类分类正确率。
