In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a dou...In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Kortcweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the com- plex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.展开更多
We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, ...We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or?θ(p,l,q) as the induced subgraph. In this paper, by using three graph transformations which do not change the singularity of the graph, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained.展开更多
This study proposes two speed controllers based on a robust adaptive non-singular terminal sliding mode control approach for the cooperative adaptive cruise control problem in a connected and automated vehicular plato...This study proposes two speed controllers based on a robust adaptive non-singular terminal sliding mode control approach for the cooperative adaptive cruise control problem in a connected and automated vehicular platoon.The delay-based spacing policy is adopted to guarantee that all vehicles in the platoon track the same target velocity profile at the same position while maintaining a predefined time gap.Factors such as nonlinear vehicle longitudinal dynamics,engine dynamics with time delay,undulating road profiles,parameter uncertainties,and external disturbances are considered in the system modeling and controller design.Different control objectives are assigned to the leading and following vehicles.Then,controllers consisting of a sliding mode controller with parameter adaptive laws based on the ego vehicle’s state deviation and linear coupled state errors,and a Smith predictor for time delay compensation are designed.Both inner stability and strong string stability are guaranteed in the case of nonlinear sliding manifolds.Finally,the effectiveness of the proposed controllers and the benefits of 44.73%shorter stabilization time,11.20%less speed overshoot,and virtually zero steady-state inner vehicle distance deviation are illustrated in a simulation study of a seven-vehicle platoon cooperative adaptive cruise control and comparison experiments with a coupled sliding mode control approach.展开更多
This paper presents a novel non-singular fast terminal sliding mode control(NFTSMC)based on the deep flux weakening switching point tracking method in order to improve the control performance of permanent interior mag...This paper presents a novel non-singular fast terminal sliding mode control(NFTSMC)based on the deep flux weakening switching point tracking method in order to improve the control performance of permanent interior magnet synchronous motor(IPMSM)drive systems.The mathematical model of flux weakening(FW)control is established,and the deep flux weakening switching point is calculated accurately by analyzing the relationship between the torque curve and voltage decline curve.Next,a second-order NFTSMC is designed for the speed loop controller to ensure that the system converges to the equilibrium state in finite time.Then,an extended sliding mode disturbance observer(ESMDO)is designed to estimate the uncertainty of the system.Finally,compared with both the PI control and sliding mode control(SMC)by simulations and experiments with different working conditions,the method proposed has the merits of accelerating convergence,improving steady-state accuracy,and minimizing the current and torque pulsation.展开更多
In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete form...In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5<sup>th</sup> order Butcher’s algorithm in predictor-corrector form.展开更多
In Moffat stochastic gravity arguments, the spacetime geometry is assumed to be a fluctuating background and the gravitational constant is a control parameter due to the presence of a timedependent Gaussian white noi...In Moffat stochastic gravity arguments, the spacetime geometry is assumed to be a fluctuating background and the gravitational constant is a control parameter due to the presence of a timedependent Gaussian white noise ξ(t). In such a surrounding, both the singularities of gravitational collapse and the Big Bang have a zero probability of occurring. In this communication, we generalize Moffat’s arguments by adding a random temporal tiny variable for a smoothing purpose and creating a white Gaussian noise process with a short correlation time. The Universe accordingly is found to be non-singular and is dominated by an oscillating gravity. A connection with a quantum oscillator was established and analyzed. Surprisingly, the Hubble mass which emerges in extended supergravity may be quantized.展开更多
A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theor...A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame＇ constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular （but sometimes singular or even hypersingular） stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.展开更多
Two spherically symmetric non-singular black hole solutions in Moiler tetrad theory of gravitation have been obtained. Although the two solutions have the same form of metric （spherically symmetric nonsingular black ...Two spherically symmetric non-singular black hole solutions in Moiler tetrad theory of gravitation have been obtained. Although the two solutions have the same form of metric （spherically symmetric nonsingular black hole）, their energy contents are different. We use another method given by Gibbons and Hawking to calculate the energy content of these solutions. We also obtained different value of energy. Study the requirements of a satisfactory energymomentum complex given by Moiler we find that the second solution, which behaves as 1/√r, is not transformed as a four-vector under Lorentz transformation.展开更多
A theory of gravitation in flat space-time is applied to homogeneous, isotropic cosmological models. There are non-singular cosmological models. A natural interpretation is a non-expanding universe. The redshift is an...A theory of gravitation in flat space-time is applied to homogeneous, isotropic cosmological models. There are non-singular cosmological models. A natural interpretation is a non-expanding universe. The redshift is an intrinsic effect and not a Doppler effect. The universe contains only energy in the beginning, i.e. no matter exists. In the course of time matter and radiation are created from energy where the whole energy is conserved. Matter increases with time but a certain time after the beginning of the universe the creation of matter is finished and the universe appears like a static one. A modified Hubble law is considered which may explain the high redshifts of objects in the universe without the assumption of dark energy.展开更多
基金Supported by the National Science Council of the Republic of China under Grant No.NSC101-2115-M-126-002the National Natural Science Foundation of China under Grant No.11371241Project of "The First-class Discipline of Universities in Shanghai"
文摘In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Kortcweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the com- plex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.
文摘We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or?θ(p,l,q) as the induced subgraph. In this paper, by using three graph transformations which do not change the singularity of the graph, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained.
基金the Research Project of CASCO Signal Ltd.(No.RE.Z0120032)。
文摘This study proposes two speed controllers based on a robust adaptive non-singular terminal sliding mode control approach for the cooperative adaptive cruise control problem in a connected and automated vehicular platoon.The delay-based spacing policy is adopted to guarantee that all vehicles in the platoon track the same target velocity profile at the same position while maintaining a predefined time gap.Factors such as nonlinear vehicle longitudinal dynamics,engine dynamics with time delay,undulating road profiles,parameter uncertainties,and external disturbances are considered in the system modeling and controller design.Different control objectives are assigned to the leading and following vehicles.Then,controllers consisting of a sliding mode controller with parameter adaptive laws based on the ego vehicle’s state deviation and linear coupled state errors,and a Smith predictor for time delay compensation are designed.Both inner stability and strong string stability are guaranteed in the case of nonlinear sliding manifolds.Finally,the effectiveness of the proposed controllers and the benefits of 44.73%shorter stabilization time,11.20%less speed overshoot,and virtually zero steady-state inner vehicle distance deviation are illustrated in a simulation study of a seven-vehicle platoon cooperative adaptive cruise control and comparison experiments with a coupled sliding mode control approach.
基金supported by the Natural Science Foundation of China under Grant No.61733004the Scientific Research Fund of the Hunan Provincial Education Department under Grand No.18A267.
文摘This paper presents a novel non-singular fast terminal sliding mode control(NFTSMC)based on the deep flux weakening switching point tracking method in order to improve the control performance of permanent interior magnet synchronous motor(IPMSM)drive systems.The mathematical model of flux weakening(FW)control is established,and the deep flux weakening switching point is calculated accurately by analyzing the relationship between the torque curve and voltage decline curve.Next,a second-order NFTSMC is designed for the speed loop controller to ensure that the system converges to the equilibrium state in finite time.Then,an extended sliding mode disturbance observer(ESMDO)is designed to estimate the uncertainty of the system.Finally,compared with both the PI control and sliding mode control(SMC)by simulations and experiments with different working conditions,the method proposed has the merits of accelerating convergence,improving steady-state accuracy,and minimizing the current and torque pulsation.
文摘In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5<sup>th</sup> order Butcher’s algorithm in predictor-corrector form.
文摘In Moffat stochastic gravity arguments, the spacetime geometry is assumed to be a fluctuating background and the gravitational constant is a control parameter due to the presence of a timedependent Gaussian white noise ξ(t). In such a surrounding, both the singularities of gravitational collapse and the Big Bang have a zero probability of occurring. In this communication, we generalize Moffat’s arguments by adding a random temporal tiny variable for a smoothing purpose and creating a white Gaussian noise process with a short correlation time. The Universe accordingly is found to be non-singular and is dominated by an oscillating gravity. A connection with a quantum oscillator was established and analyzed. Surprisingly, the Hubble mass which emerges in extended supergravity may be quantized.
基金supported by the General Secretariat of Research and Technology(GSRT)of Greece(Helenic/ERC-13(88257-IL-GradMech-ASM)ARISTEIA II(5152-SEDEMP)THALES/INTERMONU68/1117)
文摘A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame＇ constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular （but sometimes singular or even hypersingular） stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.
文摘Two spherically symmetric non-singular black hole solutions in Moiler tetrad theory of gravitation have been obtained. Although the two solutions have the same form of metric （spherically symmetric nonsingular black hole）, their energy contents are different. We use another method given by Gibbons and Hawking to calculate the energy content of these solutions. We also obtained different value of energy. Study the requirements of a satisfactory energymomentum complex given by Moiler we find that the second solution, which behaves as 1/√r, is not transformed as a four-vector under Lorentz transformation.
文摘A theory of gravitation in flat space-time is applied to homogeneous, isotropic cosmological models. There are non-singular cosmological models. A natural interpretation is a non-expanding universe. The redshift is an intrinsic effect and not a Doppler effect. The universe contains only energy in the beginning, i.e. no matter exists. In the course of time matter and radiation are created from energy where the whole energy is conserved. Matter increases with time but a certain time after the beginning of the universe the creation of matter is finished and the universe appears like a static one. A modified Hubble law is considered which may explain the high redshifts of objects in the universe without the assumption of dark energy.
