Variable pump driving variable motor(VPDVM) is the future development trend of the hydraulic transmission of an unmanned ground vehicle(UGV).VPDVM is a dual-input single-output nonlinear system with coupling,which is ...Variable pump driving variable motor(VPDVM) is the future development trend of the hydraulic transmission of an unmanned ground vehicle(UGV).VPDVM is a dual-input single-output nonlinear system with coupling,which is difficult to control.High pressure automatic variables bang-bang(HABB) was proposed to achieve the desired motor speed.First,the VPDVM nonlinear mathematic model was introduced,then linearized by feedback linearization theory,and the zero-dynamic stability was proved.The HABB control algorithm was proposed for VPDVM,in which the variable motor was controlled by high pressure automatic variables(HA) and the variable pump was controlled by bang-bang.Finally,simulation of VPDVM controlled by HABB was developed.Simulation results demonstrate the HABB can implement the desired motor speed rapidly and has strong robustness against the variations of desired motor speed,load and pump speed.展开更多
Nine Platanus acerifolia (Ait.) Willd. trees growing in the Nanjing Children Teacher’s School, Nanjing,China, were selected to determine the contents of 13 chemical elements both in the 1994’s growth rings,C(Z, t), ...Nine Platanus acerifolia (Ait.) Willd. trees growing in the Nanjing Children Teacher’s School, Nanjing,China, were selected to determine the contents of 13 chemical elements both in the 1994’s growth rings,C(Z, t), and in the soils near the roots, C’(Z, t), of the trees. The results showed that the relationship between C(Z, t) and C’(Z, t) followed the logarithmic linear correlation model, lgC’(Z, t)=a(Z)+b(Z) ig C (Z, t).Based on this model the chrono-sequences of chemical element contents in the soils were reproduced from those in the tree rings; i.e., the dynamic variations in the chemical element contents of the soils at the sites were traced. In this study the chrono-sequences of the chemical elements including Cd, Ph, Mn, Co and Zn in the soils near the roots of a Platanus acerifolia tree from 1957 to 1994 were established, and the background values of Cd, Pb, Mn, Co and Zn in the soil were calculated by taking the lowest values of the chrono-sequences of the element contents as upper limits of the background values.展开更多
In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Fie...In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.展开更多
Ship maneuverability, in the field of ship engineering, is often predicted by maneuvering motion group （MMG） mathematical model. Then it is necessary to determine hydrodynamic coefficients and interaction force coef...Ship maneuverability, in the field of ship engineering, is often predicted by maneuvering motion group （MMG） mathematical model. Then it is necessary to determine hydrodynamic coefficients and interaction force coefficients of the model. Based on the data of free running model test, the problem for obtaining these coefficients is called inverse one. For the inverse problem, ill-posedness is inherent, nonlinearity and great computation happen, and the computation is also insensitive, unstable and time-consuming. In the paper, a regularization method is introduced to solve ill-posed problem and genetic algorithm is used for nonlinear motion of ship maneuvering. In addition, the immunity is applied to solve the prematurity, to promote the global searching ability and to increase the converging speed. The combination of regularization method and immune genetic algorithm（RIGA） applied in MMG mathematical model, showed rapid converging speed and good stability.展开更多
In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this ...In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.展开更多
基金Project(51375029)supported by the National Natural Science Foundation of ChinaProject(20091102120038)supported by Specialized Research Fund for Doctoral Program of Higher Education of China
文摘Variable pump driving variable motor(VPDVM) is the future development trend of the hydraulic transmission of an unmanned ground vehicle(UGV).VPDVM is a dual-input single-output nonlinear system with coupling,which is difficult to control.High pressure automatic variables bang-bang(HABB) was proposed to achieve the desired motor speed.First,the VPDVM nonlinear mathematic model was introduced,then linearized by feedback linearization theory,and the zero-dynamic stability was proved.The HABB control algorithm was proposed for VPDVM,in which the variable motor was controlled by high pressure automatic variables(HA) and the variable pump was controlled by bang-bang.Finally,simulation of VPDVM controlled by HABB was developed.Simulation results demonstrate the HABB can implement the desired motor speed rapidly and has strong robustness against the variations of desired motor speed,load and pump speed.
文摘Nine Platanus acerifolia (Ait.) Willd. trees growing in the Nanjing Children Teacher’s School, Nanjing,China, were selected to determine the contents of 13 chemical elements both in the 1994’s growth rings,C(Z, t), and in the soils near the roots, C’(Z, t), of the trees. The results showed that the relationship between C(Z, t) and C’(Z, t) followed the logarithmic linear correlation model, lgC’(Z, t)=a(Z)+b(Z) ig C (Z, t).Based on this model the chrono-sequences of chemical element contents in the soils were reproduced from those in the tree rings; i.e., the dynamic variations in the chemical element contents of the soils at the sites were traced. In this study the chrono-sequences of the chemical elements including Cd, Ph, Mn, Co and Zn in the soils near the roots of a Platanus acerifolia tree from 1957 to 1994 were established, and the background values of Cd, Pb, Mn, Co and Zn in the soil were calculated by taking the lowest values of the chrono-sequences of the element contents as upper limits of the background values.
文摘In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.
文摘Ship maneuverability, in the field of ship engineering, is often predicted by maneuvering motion group （MMG） mathematical model. Then it is necessary to determine hydrodynamic coefficients and interaction force coefficients of the model. Based on the data of free running model test, the problem for obtaining these coefficients is called inverse one. For the inverse problem, ill-posedness is inherent, nonlinearity and great computation happen, and the computation is also insensitive, unstable and time-consuming. In the paper, a regularization method is introduced to solve ill-posed problem and genetic algorithm is used for nonlinear motion of ship maneuvering. In addition, the immunity is applied to solve the prematurity, to promote the global searching ability and to increase the converging speed. The combination of regularization method and immune genetic algorithm（RIGA） applied in MMG mathematical model, showed rapid converging speed and good stability.
文摘In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.
