In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformatio...In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.展开更多
In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.展开更多
System of systems architecture(SoSA) has received increasing emphasis by scholars since Zachman ignited its flame in 1987. Given its complexity and abstractness, it is critical to validate and evaluate SoSA to ensur...System of systems architecture(SoSA) has received increasing emphasis by scholars since Zachman ignited its flame in 1987. Given its complexity and abstractness, it is critical to validate and evaluate SoSA to ensure requirements have been met.Multiple qualities are discussed in the literature of SoSA evaluation, while research on functionality is scarce. In order to assess SoSA functionality, an extended influence diagram(EID) is developed in this paper. Meanwhile, a simulation method is proposed to elicit the conditional probabilities in EID through designing and executing SoSA. An illustrative anti-missile architecture case is introduced for EID development, architecture design, and simulation.展开更多
The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplifiedmodified extended tanh-function method.Then, further analysis to some tanh-coth type solutions of nonlinear ev...First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplifiedmodified extended tanh-function method.Then, further analysis to some tanh-coth type solutions of nonlinear evolutionequations are given.The results show that when balance number m is one or two, the tanh-coth type solutions obtainedby the modified extended tanh-function method can be obtained by using the hyperbolic-function method.展开更多
A micro-extended-analog-computer (uEAC) is developed on the basis of Rubel' s extended analog computer(EAC) model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several f...A micro-extended-analog-computer (uEAC) is developed on the basis of Rubel' s extended analog computer(EAC) model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several feedback uEAC models, and a more flexible uEAC cell structure with a multi-level hierarchy are discussed. Futhermore, for the dynamic uEAC array with a linear Lukasiewicz function, a nonlinear differential equation description is presented, and then a sufficient global asymptotic stability condition is derived by utilizing a Lyapunov function and a Lipchitz function. Finally, comparative simulations for a cam servo mechanism system are conducted to verify the capability of the uEAC array as an adaptive controller.展开更多
The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct m...The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.展开更多
In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.展开更多
摩擦力是影响直线伺服系统低速运行与点对点定位精度的主要非线性扰动。广义麦克斯韦(generalized Maxwellslip,GMS)摩擦模型虽然可以准确描述摩擦特性用于前馈补偿,但其存在切换点过渡时振荡的问题,同时易受测量噪声和摩擦参数变化等...摩擦力是影响直线伺服系统低速运行与点对点定位精度的主要非线性扰动。广义麦克斯韦(generalized Maxwellslip,GMS)摩擦模型虽然可以准确描述摩擦特性用于前馈补偿,但其存在切换点过渡时振荡的问题,同时易受测量噪声和摩擦参数变化等影响。为此,该文提出基于平滑GMS模型和改进扩张状态观测器(extended state observer,ESO)的复合摩擦补偿策略。首先,引入过渡用双曲正切函数以解决GMS模型中在切换点的反复穿越问题,并给出该模型的离线辨识方法。其次,设计基于模型信息的四阶ESO补偿剩余摩擦力与未知扰动,并引入切比雪夫滤波器整定观测器增益,以降低扰动观测与噪声敏感之间的冲突。为验证所提摩擦补偿策略的有效性,在小型高精度永磁同步直线电机定位平台上进行定位实验。实验结果验证了所提摩擦补偿策略的可行性和有效性。展开更多
文摘In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.
基金supported by the National Natural Science Foundation of China(71571189)
文摘System of systems architecture(SoSA) has received increasing emphasis by scholars since Zachman ignited its flame in 1987. Given its complexity and abstractness, it is critical to validate and evaluate SoSA to ensure requirements have been met.Multiple qualities are discussed in the literature of SoSA evaluation, while research on functionality is scarce. In order to assess SoSA functionality, an extended influence diagram(EID) is developed in this paper. Meanwhile, a simulation method is proposed to elicit the conditional probabilities in EID through designing and executing SoSA. An illustrative anti-missile architecture case is introduced for EID development, architecture design, and simulation.
文摘The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
基金Supported by the Natural Science Foundation of China under Grant No.11071209
文摘First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplifiedmodified extended tanh-function method.Then, further analysis to some tanh-coth type solutions of nonlinear evolutionequations are given.The results show that when balance number m is one or two, the tanh-coth type solutions obtainedby the modified extended tanh-function method can be obtained by using the hyperbolic-function method.
基金The project supported by National Natural Science Foundation of China, the Natural Science Foundation of Shandong Province of China, and the Natural Scienoe Foundation of Liaocheng University
基金Supported by the National Natural Science Foundation of China(61433003,61273150)Beijing Higher Education Young Elite Teacher Project
文摘A micro-extended-analog-computer (uEAC) is developed on the basis of Rubel' s extended analog computer(EAC) model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several feedback uEAC models, and a more flexible uEAC cell structure with a multi-level hierarchy are discussed. Futhermore, for the dynamic uEAC array with a linear Lukasiewicz function, a nonlinear differential equation description is presented, and then a sufficient global asymptotic stability condition is derived by utilizing a Lyapunov function and a Lipchitz function. Finally, comparative simulations for a cam servo mechanism system are conducted to verify the capability of the uEAC array as an adaptive controller.
文摘The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.
文摘摩擦力是影响直线伺服系统低速运行与点对点定位精度的主要非线性扰动。广义麦克斯韦(generalized Maxwellslip,GMS)摩擦模型虽然可以准确描述摩擦特性用于前馈补偿,但其存在切换点过渡时振荡的问题,同时易受测量噪声和摩擦参数变化等影响。为此,该文提出基于平滑GMS模型和改进扩张状态观测器(extended state observer,ESO)的复合摩擦补偿策略。首先,引入过渡用双曲正切函数以解决GMS模型中在切换点的反复穿越问题,并给出该模型的离线辨识方法。其次,设计基于模型信息的四阶ESO补偿剩余摩擦力与未知扰动,并引入切比雪夫滤波器整定观测器增益,以降低扰动观测与噪声敏感之间的冲突。为验证所提摩擦补偿策略的有效性,在小型高精度永磁同步直线电机定位平台上进行定位实验。实验结果验证了所提摩擦补偿策略的可行性和有效性。