This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we stu...This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.展开更多
Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solut...Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.展开更多
The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then...The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.展开更多
The difference equation △xn＋ pnxn-k = f（n,xn-1,...,xn-1m）, n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient co...The difference equation △xn＋ pnxn-k = f（n,xn-1,...,xn-1m）, n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient conditions for the global asymptotic stability of zero solution of the equation are obtained.展开更多
In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When t...In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When these arbitrary functions are taken assome special functions, these solutions possess abundant structures. These solutions containsoliton-like solutions and rational solutions.展开更多
The study aimed to examine changes in trabecular bone microstructure （TBMS） during the period of 5 weeks after the injury in a rat model of spinal cord injury （SCI）. Eight-week-old male Wistar rats underwent surgi...The study aimed to examine changes in trabecular bone microstructure （TBMS） during the period of 5 weeks after the injury in a rat model of spinal cord injury （SCI）. Eight-week-old male Wistar rats underwent surgical transection of the lower thoracic spinal cord （SCI, n = 16） or sham operation （SHAM, n = 14）. TBMS （tissue volume, bone volume, bone volume fraction, trabecular thickness, width, number, separation, connectivity density, and trabecular bone pattern factor）, assessed using a micro-computed tomography, was deteriorated 1, 3 and 5 weeks after SCI. In addition, both bone mass and serum biochemical parameters were determined. Dry bone weight, ash weight, bone mineral content （BMC）, and BMC/tissue-volume were significantly lower in the SCI group than in the SHAM group throughout the experimental period. Serum inorganic phosphate and alkaline phosphatase levels were significantly lower in the SCI group than in the SHAM group 1 week after the surgery. SCI resulted in rapid deterioration of both bone mass and microstructure. These changes appeared as early as 1 week after SCI. Based on the authors＇ results, it should be noted that in SCI patients, interventions for preventing bone loss should start as soon as possible after the injury.展开更多
Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we...Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.展开更多
In this paper,the fixed_point theorem is used to estimated an asymptotic solution of initial value problems for a class of third nonlinear differential equations which has double initial_layer properties. We obtain th...In this paper,the fixed_point theorem is used to estimated an asymptotic solution of initial value problems for a class of third nonlinear differential equations which has double initial_layer properties. We obtain the uniformly valid asymptotic expansion of any orders including boundary layers.展开更多
Urbanization of China is substantial and growing, and water resources are crucial for both economic and social sustainable development. Unfortunately, the frequency and intensity of water contamination events are incr...Urbanization of China is substantial and growing, and water resources are crucial for both economic and social sustainable development. Unfortunately, the frequency and intensity of water contamination events are increasing at an unprecedented rate and often accompanied by increased pollutant loading due to human activities such as irreversible industrialization and urbanization. The impacts of human pollution are most evident and of greatest concern at the microbial level. The research of the Aquatic Ecohealth Group, Key Laboratory of Urban Environment and Health, Institute of Urban Environment, Chinese Academy of Sciences, has been focusing mainly on aquatic microorganisms in the urban environment, from drinking water and landscape water to waste water. Its projects fall into three categories: biomonitoring and bioassessment, microbial ecology and diversity, ecotoxicology and environmental microbiology. Its scientif ic topics include the aquatic ecological safety and microbial food web.展开更多
The extinction of a class of superprocesses associated with general branching characterstics and underlying Markov processes is investigated. The extinction is closely associated with the branching characteristics and...The extinction of a class of superprocesses associated with general branching characterstics and underlying Markov processes is investigated. The extinction is closely associated with the branching characteristics and the recurrence and transience of underlying processes.展开更多
In this paper, we establish a criterion of unformly asymptotic stability for finite delay difference systems in terms of two measures by employing Lyapunov functionals method.
Pulse detonation engine (PDE) is expected for a next-generation propulsion system. PDE is a promising engine that can generates power and thrust by using intermittent detonation. Promotion of deflagration to detonatio...Pulse detonation engine (PDE) is expected for a next-generation propulsion system. PDE is a promising engine that can generates power and thrust by using intermittent detonation. Promotion of deflagration to detonation transition (below DDT) is a key issue to realize this system. PDE has experimentally been investigated, and it was confirmed that detonation tubes with U-shaped bends are useful for fast DDT. However, the mechanism of DDT promotion due to U-bends has not been well clarified. In the present study, the influence of a U-bend on detona-tion wave propagation is researched with computational fluid dynamics (CFD). The numerical results show that detonation wave disappears once near the U-bend inlet and restarts after passing through it. In addition, it was found that the use of the U-bend with small channel width and curvature radius can induce fast DDT.展开更多
A micro turbo-expander capable of high working speed was specially manufactured for use in an organic Rankine cycle (ORC).A series of tests were executed to examine the performance of the machine.In the experiment,the...A micro turbo-expander capable of high working speed was specially manufactured for use in an organic Rankine cycle (ORC).A series of tests were executed to examine the performance of the machine.In the experiment,the machine was tested under different inlet pressure conditions (0.2-0.5 MPa).Data such as the compressed air pressure,temperatures of the inlet and the outlet,rotational speed,and electric power generation were analyzed to discover underlying relationships.During the test,the rotational speed of the machine reached as high as 54 000 r/min,the peak value of the temperature drop between the inlet and the outlet reached 42 ℃,the maximum electric power generated by the motor-generator attached to the machine reached 630 W,and the efficiency of the machine reached 0.43.展开更多
In this paper,the problem of time optimal feedrate generation under confined feedrate,axis accelerations,and axis tracking errors is considered.The main contribution is to reduce the tracking error constraint to const...In this paper,the problem of time optimal feedrate generation under confined feedrate,axis accelerations,and axis tracking errors is considered.The main contribution is to reduce the tracking error constraint to constraints about the axis velocities and accelerations,when the tracking error satisfies a second order linear ordinary differential equation.Based on this simplification on the tracking error,the original feedrate generation problem is reduced to a new form which can be efficiently solved with linear programming algorithms.Simulation results are used to validate the methods.展开更多
Smart environment is being used in many areas to deliver more services to individuals in a physical space, such as a hospital. In the UK, the National Health Service(NHS) provides free and high quality healthcare serv...Smart environment is being used in many areas to deliver more services to individuals in a physical space, such as a hospital. In the UK, the National Health Service(NHS) provides free and high quality healthcare service for all residents. Smart hospital environment is able to support NHS and provide more convenience. Patient flow scheduling is a crucial section in a smart hospital environment. Smart hospital environment aims to provide a smart environment in the hospital to facilitate individual experience and improve the quality of healthcare service.First of all, this paper investigates a real world patient flow scenario of a hospital in the UK and models a general scheduling scheme based on the scenario using a compositional formal approach, i.e. performance evaluation process algebra(PEPA). This scheduling scheme uses an easy-implemented solution(the grouping scheme) to reduce the waiting queue in the hospital. Secondly, fluid flow analysis is used for the performance analysis by generating a set of ordinary differential equations(ODEs) in terms of the PEPA model.展开更多
文摘This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.
文摘Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.
文摘The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
基金Supported by Natural Science Foundaton of Henan Providence(0111051200)
文摘The difference equation △xn＋ pnxn-k = f（n,xn-1,...,xn-1m）, n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient conditions for the global asymptotic stability of zero solution of the equation are obtained.
文摘In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When these arbitrary functions are taken assome special functions, these solutions possess abundant structures. These solutions containsoliton-like solutions and rational solutions.
文摘The study aimed to examine changes in trabecular bone microstructure （TBMS） during the period of 5 weeks after the injury in a rat model of spinal cord injury （SCI）. Eight-week-old male Wistar rats underwent surgical transection of the lower thoracic spinal cord （SCI, n = 16） or sham operation （SHAM, n = 14）. TBMS （tissue volume, bone volume, bone volume fraction, trabecular thickness, width, number, separation, connectivity density, and trabecular bone pattern factor）, assessed using a micro-computed tomography, was deteriorated 1, 3 and 5 weeks after SCI. In addition, both bone mass and serum biochemical parameters were determined. Dry bone weight, ash weight, bone mineral content （BMC）, and BMC/tissue-volume were significantly lower in the SCI group than in the SHAM group throughout the experimental period. Serum inorganic phosphate and alkaline phosphatase levels were significantly lower in the SCI group than in the SHAM group 1 week after the surgery. SCI resulted in rapid deterioration of both bone mass and microstructure. These changes appeared as early as 1 week after SCI. Based on the authors＇ results, it should be noted that in SCI patients, interventions for preventing bone loss should start as soon as possible after the injury.
文摘Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.
文摘In this paper,the fixed_point theorem is used to estimated an asymptotic solution of initial value problems for a class of third nonlinear differential equations which has double initial_layer properties. We obtain the uniformly valid asymptotic expansion of any orders including boundary layers.
文摘Urbanization of China is substantial and growing, and water resources are crucial for both economic and social sustainable development. Unfortunately, the frequency and intensity of water contamination events are increasing at an unprecedented rate and often accompanied by increased pollutant loading due to human activities such as irreversible industrialization and urbanization. The impacts of human pollution are most evident and of greatest concern at the microbial level. The research of the Aquatic Ecohealth Group, Key Laboratory of Urban Environment and Health, Institute of Urban Environment, Chinese Academy of Sciences, has been focusing mainly on aquatic microorganisms in the urban environment, from drinking water and landscape water to waste water. Its projects fall into three categories: biomonitoring and bioassessment, microbial ecology and diversity, ecotoxicology and environmental microbiology. Its scientif ic topics include the aquatic ecological safety and microbial food web.
文摘The extinction of a class of superprocesses associated with general branching characterstics and underlying Markov processes is investigated. The extinction is closely associated with the branching characteristics and the recurrence and transience of underlying processes.
基金This work is supported by Mathematics Tianyuan Fund (No.A0324624),NNSF of China (No.10371040),Shanghai Priority Academic Discipline.
文摘In this paper, we establish a criterion of unformly asymptotic stability for finite delay difference systems in terms of two measures by employing Lyapunov functionals method.
文摘Pulse detonation engine (PDE) is expected for a next-generation propulsion system. PDE is a promising engine that can generates power and thrust by using intermittent detonation. Promotion of deflagration to detonation transition (below DDT) is a key issue to realize this system. PDE has experimentally been investigated, and it was confirmed that detonation tubes with U-shaped bends are useful for fast DDT. However, the mechanism of DDT promotion due to U-bends has not been well clarified. In the present study, the influence of a U-bend on detona-tion wave propagation is researched with computational fluid dynamics (CFD). The numerical results show that detonation wave disappears once near the U-bend inlet and restarts after passing through it. In addition, it was found that the use of the U-bend with small channel width and curvature radius can induce fast DDT.
基金Project (Nos.50974150 and 50708105) supported by the National Natural Science Foundation of China
文摘A micro turbo-expander capable of high working speed was specially manufactured for use in an organic Rankine cycle (ORC).A series of tests were executed to examine the performance of the machine.In the experiment,the machine was tested under different inlet pressure conditions (0.2-0.5 MPa).Data such as the compressed air pressure,temperatures of the inlet and the outlet,rotational speed,and electric power generation were analyzed to discover underlying relationships.During the test,the rotational speed of the machine reached as high as 54 000 r/min,the peak value of the temperature drop between the inlet and the outlet reached 42 ℃,the maximum electric power generated by the motor-generator attached to the machine reached 630 W,and the efficiency of the machine reached 0.43.
基金partially supported by a National Key Basic Research Project of China under Grant No.2011CB302400the Natural Science Foundation of China under Grant No.60821002
文摘In this paper,the problem of time optimal feedrate generation under confined feedrate,axis accelerations,and axis tracking errors is considered.The main contribution is to reduce the tracking error constraint to constraints about the axis velocities and accelerations,when the tracking error satisfies a second order linear ordinary differential equation.Based on this simplification on the tracking error,the original feedrate generation problem is reduced to a new form which can be efficiently solved with linear programming algorithms.Simulation results are used to validate the methods.
基金the National Natural Science Foundation of China(Nos.61502206 and 61472343)the Natural Science Foundation of Jiangsu Province(Nos.BK20160543 and BK20150523)the Open Project of Key Laboratory of Jiangsu Province(No.BM20082061507)
文摘Smart environment is being used in many areas to deliver more services to individuals in a physical space, such as a hospital. In the UK, the National Health Service(NHS) provides free and high quality healthcare service for all residents. Smart hospital environment is able to support NHS and provide more convenience. Patient flow scheduling is a crucial section in a smart hospital environment. Smart hospital environment aims to provide a smart environment in the hospital to facilitate individual experience and improve the quality of healthcare service.First of all, this paper investigates a real world patient flow scenario of a hospital in the UK and models a general scheduling scheme based on the scenario using a compositional formal approach, i.e. performance evaluation process algebra(PEPA). This scheduling scheme uses an easy-implemented solution(the grouping scheme) to reduce the waiting queue in the hospital. Secondly, fluid flow analysis is used for the performance analysis by generating a set of ordinary differential equations(ODEs) in terms of the PEPA model.
