This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are es...This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.展开更多
For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )...For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.展开更多
In this paper, the authors study the existence of positive solution of the following BVP {1/p(t)(P(t)x′)′+f(t,x(t),p(t)x′(t))=0,o〈t〈+∞ αx(0)-βlimt→0p(t)x′(t)=0,γ limt→+∞x(t)+δl...In this paper, the authors study the existence of positive solution of the following BVP {1/p(t)(P(t)x′)′+f(t,x(t),p(t)x′(t))=0,o〈t〈+∞ αx(0)-βlimt→0p(t)x′(t)=0,γ limt→+∞x(t)+δlimt→+∞p(t)x′(t)=0 on the semi-infinite interval. By considering characterization of the nonlinearity, they obtain some new existence results.展开更多
Load balancing plays a critical role in a cellular network. As one kind of cellular network, Radio-over-Fibre (RoF) system can provide ubiquitous high data-rate transmissions, which has attracted many attentions, bu...Load balancing plays a critical role in a cellular network. As one kind of cellular network, Radio-over-Fibre (RoF) system can provide ubiquitous high data-rate transmissions, which has attracted many attentions, but it also suffer load unbalancing problem. In order to improve the system performance, in this paper, we propose a novel loading balance scheme in RoF system based on differential game theory. The scheme formulates the load allocated to each RAP (Radio Access Point) as a Nasb Equilibrium, using non-cooperative differential game to obtain the optical load allocation of each RAP. The simulations performed show that the non-cooperative differential game algorithm is applicable and the optimal load solution can be achieved.展开更多
H stability is a new and important concept. In this paper,we discuss the equationx(t)=-a(t)x(t)+∫ t -∞ k(t,s-t,x(s)) d sand we gain a new decision theorem. Using this decision theorem,we obtained a very extensive re...H stability is a new and important concept. In this paper,we discuss the equationx(t)=-a(t)x(t)+∫ t -∞ k(t,s-t,x(s)) d sand we gain a new decision theorem. Using this decision theorem,we obtained a very extensive result of the H uniformly asymptotical stability of this equation. That is,eliminating the restriction that a(t) is bounded.展开更多
In this series of 65 cases of aplastic anemia, 26 cases were treated by the kidney-tonifying and mediating method, 19 cases by western drugs, and the remaining 20 cases only by tonifying the kidney as controls. The re...In this series of 65 cases of aplastic anemia, 26 cases were treated by the kidney-tonifying and mediating method, 19 cases by western drugs, and the remaining 20 cases only by tonifying the kidney as controls. The results showed that the kidney-tonifying and mediating method was significantly superior in the total effective rate to the method of western drugs and that of tonifying the kidney alone (P展开更多
Based on the Complex Orthogonal Linear Dispersion (COLD) code,a novel linear Differ- ential Space-Time Modulation (DSTM) design is proposed in this paper.Compared with the existing nonlinear DSTM schemes based on grou...Based on the Complex Orthogonal Linear Dispersion (COLD) code,a novel linear Differ- ential Space-Time Modulation (DSTM) design is proposed in this paper.Compared with the existing nonlinear DSTM schemes based on group codes,the proposed linear DSTM scheme is easier to design, enjoys full diversity and allows for a simplified differential receiver,which can detect the transmitted symbols separately.Furthermore,compared with the existing linear DSTM based on orthogonal design, our new construction can be applied to any number of transmit antennas.Similar to other algorithms, the proposed scheme also can be demodulated with or without channel estimates at the receiver,but the performance degrades approximately by 3dB when estimates are not available.展开更多
Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differen...Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.展开更多
In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservat...In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given formularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.展开更多
In this paper,we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay.By using matrix measure and Krasnoselskii's fixed point theorem,we obtained the suffcient con...In this paper,we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay.By using matrix measure and Krasnoselskii's fixed point theorem,we obtained the suffcient conditions of the existence of periodic solutions.展开更多
This paper aims to provide a design about a kind of low-cost "sub-mother" UAV small formation by using the low-cost micro-UAV as the platform. Combined with the current international situation in the UAV formation r...This paper aims to provide a design about a kind of low-cost "sub-mother" UAV small formation by using the low-cost micro-UAV as the platform. Combined with the current international situation in the UAV formation research, the modeling is based on the distributed control method and the behavior-based strategy. In this paper, some research to a few key issues has been carried out.展开更多
The brushless DC motor can be used in the marine electric propulsion system for its excellent control characteristics and large thrust. In order to estimate the operating performances of the brushless DC motor for the...The brushless DC motor can be used in the marine electric propulsion system for its excellent control characteristics and large thrust. In order to estimate the operating performances of the brushless DC motor for the high-power shipping during the design stage, the steady-state analysis is as important as the dynamic analysis generally. A mathematical model of the brushless DC propulsion motor is established according to the state-space method for the dynamic and steady-state performance analysis. The state-space mathematical model is a set of linear differential equations, so the steady-state currents of the armature windings can be gained directly by the symmetrical boundary conditions and the eigenvalues of the system matrix. The steady-state simulation results are compared with the dynamic ones to validate the correctness of this eigenvector method.展开更多
This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and u...This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and uniqueness of solutions are proved via a purely probabilistic approach, while a priori estimate is given. Here, we allow the forward equation to be degenerate.展开更多
This paper proposes a control strategy that can realize seamless microgrid operation mode transition between grid-connected operation and stand-alone operation.The scenario of a microgrid based on master-slave control...This paper proposes a control strategy that can realize seamless microgrid operation mode transition between grid-connected operation and stand-alone operation.The scenario of a microgrid based on master-slave control is considered,where the master distributed generation(DG) unit operates in different control schemes in different microgrid operation modes,while other slave DG units operate with power/current control all the time.The proposed control strategy focuses on the master DG unit,and contains the control state/reference compensation algorithm and separation switch control logic.The proposed method can effectively reduce the impact on the critical loads and DG units caused by microgrid operation mode transitions.展开更多
We present a neuro-heuristic computing platform for finding the solution for initial value problems (IVPs) of non- linear pantograph systems based on functional differential equations (P-FDEs) of different orders....We present a neuro-heuristic computing platform for finding the solution for initial value problems (IVPs) of non- linear pantograph systems based on functional differential equations (P-FDEs) of different orders. In this scheme, the strengths of feed-forward artificial neural networks (ANNs), the evolutionary computing technique mainly based on genetic algorithms (GAs), and the interior-point technique (IPT) are exploited. Two types of mathematical models of the systems are constructed with the help of ANNs by defining an unsupervised error with and without exactly satisfying the initial conditions. The design parameters of ANN models are optimized with a hybrid approach GA-IPT, where GA is used as a tool for effective global search, and IPT is incorporated for rapid local convergence. The proposed scheme is tested on three different types oflVPs of P-FDE with orders 1-3 The correctness of the scheme is established by comparison with the existing exact solutions. The accuracy and convergence ofthc proposed scheme are further validated through a large number of numerical experiments by taking different numbers of neurons in ANN models.展开更多
Most systems arising in engineering fields are spatiotemporal processes in nature so that their behavior must depend on time as well as spatial position.These spatiotemporal processes are in general modeled by partial...Most systems arising in engineering fields are spatiotemporal processes in nature so that their behavior must depend on time as well as spatial position.These spatiotemporal processes are in general modeled by partial differential equations.Substantial literature on the research of distributed parameter systems(DPSs)has been reported over the past decades.Amount of results on analysis and control of DPSs have been developed in these research articles,which include not only extensions of finite-dimensional techniques to infinite-dimensional systems but also innovative infinite-dimensional analysis and control design approaches.Hence,a comprehensive survey of all the developments of DPSs is perhaps a very difficult task.This paper,however,attempts to present a brief yet reasonable overview of research on the analysis and control of distributed parameter systems for applications.To help readers,some simple mathematical descriptions and necessary figures are involved in this article.Finally,some open areas of research and possible directions have also been outlined.展开更多
Natural convection in air-filled rectangular cavities inclined with respect to gravity, so that the heated wall is facing upwards, is studied numerically under the assumption of two-dimensional laminar flow. A computa...Natural convection in air-filled rectangular cavities inclined with respect to gravity, so that the heated wall is facing upwards, is studied numerically under the assumption of two-dimensional laminar flow. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum and energy transfer governing equations. Simulations are performed for height-to-width aspect ratios of the enclosure from 0.25 to 8, Rayleigh numbers based on the length of the heated and cooled walls from 10~2 to 10~7, and tilting angles of the enclosure from 0° to 75°. The existence of an optimal tilting angle is confirmed for any investigated configuration, at a location that increases as the Rayleigh number is decreased, and the height-to-width aspect ratio of the cavity are increased, unless the value of the Rayleigh number is that corresponding to the onset of convection or just higher. Dimensionless correlating equations are developed to predict the optimal tilting angle and the heat transfer performance of the enclosure.展开更多
By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value prob...By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value problem(BVP,for short) on unbounded domains.Moreover,an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results.展开更多
文摘This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.
文摘For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.
基金Supported by the Natural Scientific Fund of Zhejiang Province(Y604127)Supported by the Educational Scientific Fund of Zhejiang Province(20030594)
文摘In this paper, the authors study the existence of positive solution of the following BVP {1/p(t)(P(t)x′)′+f(t,x(t),p(t)x′(t))=0,o〈t〈+∞ αx(0)-βlimt→0p(t)x′(t)=0,γ limt→+∞x(t)+δlimt→+∞p(t)x′(t)=0 on the semi-infinite interval. By considering characterization of the nonlinearity, they obtain some new existence results.
基金This research was supported by the Fundamental Research Funds for the Central Universities,also supported by the National Natural Science Foundation of P.R.China
文摘Load balancing plays a critical role in a cellular network. As one kind of cellular network, Radio-over-Fibre (RoF) system can provide ubiquitous high data-rate transmissions, which has attracted many attentions, but it also suffer load unbalancing problem. In order to improve the system performance, in this paper, we propose a novel loading balance scheme in RoF system based on differential game theory. The scheme formulates the load allocated to each RAP (Radio Access Point) as a Nasb Equilibrium, using non-cooperative differential game to obtain the optical load allocation of each RAP. The simulations performed show that the non-cooperative differential game algorithm is applicable and the optimal load solution can be achieved.
文摘H stability is a new and important concept. In this paper,we discuss the equationx(t)=-a(t)x(t)+∫ t -∞ k(t,s-t,x(s)) d sand we gain a new decision theorem. Using this decision theorem,we obtained a very extensive result of the H uniformly asymptotical stability of this equation. That is,eliminating the restriction that a(t) is bounded.
文摘In this series of 65 cases of aplastic anemia, 26 cases were treated by the kidney-tonifying and mediating method, 19 cases by western drugs, and the remaining 20 cases only by tonifying the kidney as controls. The results showed that the kidney-tonifying and mediating method was significantly superior in the total effective rate to the method of western drugs and that of tonifying the kidney alone (P
基金Supported by the National Natural Science Foundation of China (No.60372055)National High Technology Research and Development Project of China (No.2003AA123320)the National Doctoral Foundation of China (No.20020698024,No.20030698027).
文摘Based on the Complex Orthogonal Linear Dispersion (COLD) code,a novel linear Differ- ential Space-Time Modulation (DSTM) design is proposed in this paper.Compared with the existing nonlinear DSTM schemes based on group codes,the proposed linear DSTM scheme is easier to design, enjoys full diversity and allows for a simplified differential receiver,which can detect the transmitted symbols separately.Furthermore,compared with the existing linear DSTM based on orthogonal design, our new construction can be applied to any number of transmit antennas.Similar to other algorithms, the proposed scheme also can be demodulated with or without channel estimates at the receiver,but the performance degrades approximately by 3dB when estimates are not available.
文摘Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.
基金Supported by the NSF of Henan Prevince(062110300)
文摘In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given formularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.
基金Supported by the National Nature Science Foundation of China(10771001) Supported by the Key Program of Ministry of Education of China(205068) Supported by the Foundation of Education Department of Anhui province(KJ2008B152) Supported by the Foundation of Innovation Team of Anhui University
文摘In this paper,we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay.By using matrix measure and Krasnoselskii's fixed point theorem,we obtained the suffcient conditions of the existence of periodic solutions.
文摘This paper aims to provide a design about a kind of low-cost "sub-mother" UAV small formation by using the low-cost micro-UAV as the platform. Combined with the current international situation in the UAV formation research, the modeling is based on the distributed control method and the behavior-based strategy. In this paper, some research to a few key issues has been carried out.
文摘The brushless DC motor can be used in the marine electric propulsion system for its excellent control characteristics and large thrust. In order to estimate the operating performances of the brushless DC motor for the high-power shipping during the design stage, the steady-state analysis is as important as the dynamic analysis generally. A mathematical model of the brushless DC propulsion motor is established according to the state-space method for the dynamic and steady-state performance analysis. The state-space mathematical model is a set of linear differential equations, so the steady-state currents of the armature windings can be gained directly by the symmetrical boundary conditions and the eigenvalues of the system matrix. The steady-state simulation results are compared with the dynamic ones to validate the correctness of this eigenvector method.
文摘This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and uniqueness of solutions are proved via a purely probabilistic approach, while a priori estimate is given. Here, we allow the forward equation to be degenerate.
基金supported by the National Basic Research Program of China ("973" Project) (Grant No. 2009CB219700)the National Natural Science Foundation of China (Grant No. 50837001)
文摘This paper proposes a control strategy that can realize seamless microgrid operation mode transition between grid-connected operation and stand-alone operation.The scenario of a microgrid based on master-slave control is considered,where the master distributed generation(DG) unit operates in different control schemes in different microgrid operation modes,while other slave DG units operate with power/current control all the time.The proposed control strategy focuses on the master DG unit,and contains the control state/reference compensation algorithm and separation switch control logic.The proposed method can effectively reduce the impact on the critical loads and DG units caused by microgrid operation mode transitions.
文摘We present a neuro-heuristic computing platform for finding the solution for initial value problems (IVPs) of non- linear pantograph systems based on functional differential equations (P-FDEs) of different orders. In this scheme, the strengths of feed-forward artificial neural networks (ANNs), the evolutionary computing technique mainly based on genetic algorithms (GAs), and the interior-point technique (IPT) are exploited. Two types of mathematical models of the systems are constructed with the help of ANNs by defining an unsupervised error with and without exactly satisfying the initial conditions. The design parameters of ANN models are optimized with a hybrid approach GA-IPT, where GA is used as a tool for effective global search, and IPT is incorporated for rapid local convergence. The proposed scheme is tested on three different types oflVPs of P-FDE with orders 1-3 The correctness of the scheme is established by comparison with the existing exact solutions. The accuracy and convergence ofthc proposed scheme are further validated through a large number of numerical experiments by taking different numbers of neurons in ANN models.
基金supported by the National Science Fund for Distinguished Young Scholars(61125306)the National Natural Science Foundation of China(6107405791016004)
文摘Most systems arising in engineering fields are spatiotemporal processes in nature so that their behavior must depend on time as well as spatial position.These spatiotemporal processes are in general modeled by partial differential equations.Substantial literature on the research of distributed parameter systems(DPSs)has been reported over the past decades.Amount of results on analysis and control of DPSs have been developed in these research articles,which include not only extensions of finite-dimensional techniques to infinite-dimensional systems but also innovative infinite-dimensional analysis and control design approaches.Hence,a comprehensive survey of all the developments of DPSs is perhaps a very difficult task.This paper,however,attempts to present a brief yet reasonable overview of research on the analysis and control of distributed parameter systems for applications.To help readers,some simple mathematical descriptions and necessary figures are involved in this article.Finally,some open areas of research and possible directions have also been outlined.
文摘Natural convection in air-filled rectangular cavities inclined with respect to gravity, so that the heated wall is facing upwards, is studied numerically under the assumption of two-dimensional laminar flow. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum and energy transfer governing equations. Simulations are performed for height-to-width aspect ratios of the enclosure from 0.25 to 8, Rayleigh numbers based on the length of the heated and cooled walls from 10~2 to 10~7, and tilting angles of the enclosure from 0° to 75°. The existence of an optimal tilting angle is confirmed for any investigated configuration, at a location that increases as the Rayleigh number is decreased, and the height-to-width aspect ratio of the cavity are increased, unless the value of the Rayleigh number is that corresponding to the onset of convection or just higher. Dimensionless correlating equations are developed to predict the optimal tilting angle and the heat transfer performance of the enclosure.
基金Foundation item: the National Natural Science Foundation of China (No. 10671167) the Natural Science Foundation of Liaocheng University (No. 31805).
文摘By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value problem(BVP,for short) on unbounded domains.Moreover,an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results.