This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution ...This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.展开更多
The blockchain trilemma—balancing decentralization,security,and scalability—remains a critical challenge in distributed ledger technology.Despite significant advancements,achieving all three attributes simultaneousl...The blockchain trilemma—balancing decentralization,security,and scalability—remains a critical challenge in distributed ledger technology.Despite significant advancements,achieving all three attributes simultaneously continues to elude most blockchain systems,often forcing trade-offs that limit their real-world applicability.This review paper synthesizes current research efforts aimed at resolving the trilemma,focusing on innovative consensus mechanisms,sharding techniques,layer-2 protocols,and hybrid architectural models.We critically analyze recent breakthroughs,including Directed Acyclic Graph(DAG)-based structures,cross-chain interoperability frameworks,and zero-knowledge proof(ZKP)enhancements,which aimto reconcile scalability with robust security and decentralization.Furthermore,we evaluate the trade-offs inherent in these approaches,highlighting their practical implications for enterprise adoption,decentralized finance(DeFi),and Web3 ecosystems.By mapping the evolving landscape of solutions,this review identifies gaps in currentmethodologies and proposes future research directions,such as adaptive consensus algorithms and artificial intelligence-driven(AI-driven)governance models.Our analysis underscores that while no universal solution exists,interdisciplinary innovations are progressively narrowing the trilemma’s constraints,paving the way for next-generation blockchain infrastructures.展开更多
Primary healthcare service is the first line of defense to guard the health of the nation,and traditional Chinese medicine(TCM),with its characteristics of“simplicity,testing and inexpensiveness,”holistic outlook,an...Primary healthcare service is the first line of defense to guard the health of the nation,and traditional Chinese medicine(TCM),with its characteristics of“simplicity,testing and inexpensiveness,”holistic outlook,and the concept of treating the disease before it occurs,has a unique advantage in primary healthcare and a great demand for it.This paper analyzes the core challenges facing the cultivation of general medicine talents in TCM colleges and universities,such as the disconnection between cultivation goals and grassroots,the misalignment between practical ability and grassroots demand,and the lack of career attraction.On this basis,it puts forward a systematic reform path with the core concept of“rooting at the grassroots,highlighting characteristics,and strengthening competence”to cultivate talents that meet grassroots needs,aiming to provide theoretical references for TCM colleges and universities to cultivate excellent TCM talents who are“able to go down to the grassroots,be useful,stay in the field,and have development”,and to provide theoretical reference for the training of excellent TCM talents.The aim is to provide a theoretical reference for Chinese medicine colleges to cultivate excellent Chinese medicine talents who can“get down,use,stay and develop,”and to help the construction of a healthy China.展开更多
This paper analyzes the generalization of minimax regret optimization(MRO)under distribution shift.A new learning framework is proposed by injecting the measure of con-ditional value at risk(CVaR)into MRO,and its gene...This paper analyzes the generalization of minimax regret optimization(MRO)under distribution shift.A new learning framework is proposed by injecting the measure of con-ditional value at risk(CVaR)into MRO,and its generalization error bound is established through the lens of uniform convergence analysis.The CVaR-based MRO can achieve the polynomial decay rate on the excess risk,which extends the generalization analysis associated with the expected risk to the risk-averse case.展开更多
In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constrain...In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.展开更多
This article presents a novel optimization approach called RSWTLBO for accurately identifying unknown parameters in photovoltaic(PV)models.The objective is to address challenges related to the detection and maintenanc...This article presents a novel optimization approach called RSWTLBO for accurately identifying unknown parameters in photovoltaic(PV)models.The objective is to address challenges related to the detection and maintenance of PV systems and the improvement of conversion efficiency.RSWTLBO combines adaptive parameter w,Single Solution Optimization Mechanism(SSOM),and Weight Probability Exploration Strategy(WPES)to enhance the optimization ability of TLBO.The algorithm achieves a balance between exploitation and exploration throughout the iteration process.The SSOM allows for local exploration around a single solution,improving solution quality and eliminating inferior solutions.The WPES enables comprehensive exploration of the solution space,avoiding the problem of getting trapped in local optima.The algo-rithm is evaluated by comparing it with 10 other competitive algorithms on various PV models.The results demonstrate that RSWTLBO consistently achieves the lowest Root Mean Square Errors on single diode models,double diode models,and PV module models.It also exhibits robust performance under varying irradiation and temperature conditions.The study concludes that RSWTLBO is a practical and effective algorithm for identifying unknown parameters in PV models.展开更多
In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain a...In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.展开更多
The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con...The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
When designing and building an optimal reverse osmosis (RO) desalination plant, it is important that engineers select effective membrane parameters for optimal application performance. The membrane selection can deter...When designing and building an optimal reverse osmosis (RO) desalination plant, it is important that engineers select effective membrane parameters for optimal application performance. The membrane selection can determine the success or failure of the entire desalination operation. The objective of this work is to review available membrane types and design parameters that can be selected for optimal application to yield the highest potential for plant operations. Factors such as osmotic pressure, water flux values, and membrane resistance will all be evaluated as functions of membrane parameters. The optimization of these parameters will be determined through the deployment of the solution-diffusion model devolved from the Maxwell Stephan Equation. When applying the solution-diffusion model to evaluate RO membranes, the Maxwell Stephan Equation provides mathematical analysis through which the steps for mass transfer through a RO membrane may be observed and calculated. A practical study of the use of the solution-diffusion model will be discussed. This study uses the diffusion-solution model to evaluate the effectiveness of a variety of Toray RO membranes. This practical application confirms two principal hypotheses when using the diffusion-solution model for membrane evaluation. First, there is an inverse relationship between membrane and water flux rate. Second, there is a proportional linear relationship between overall water flux rate and the applied pressure across a membrane.展开更多
In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model w...In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.展开更多
The feasibility of copper smelter slag processing by ammonia solution treatment was investigated. The central composite rotatable design(CCRD) and approximation method were used to determine the optimum conditions of ...The feasibility of copper smelter slag processing by ammonia solution treatment was investigated. The central composite rotatable design(CCRD) and approximation method were used to determine the optimum conditions of zinc and copper recovery to a solution. The experimental design was done at five levels of the four operating parameters which were the initial concentration of NH–3, the initial Cl ions concentration, leaching time and solid/liquid ratio. Two mathematical models describing dependence of metal recovery on the operating parameters were obtained. The models are successful in predicting the responses. It was found that optimal parameters for zinc and copper recovery are as follows(values for copper are given in brackets): initial CNH3 17.1%(19.9%), initial CCl– 160 g/L(160 g/L), leaching process duration 4.56 h(4.13 h), solid/liquid ratio 0.39(0.53). The maximum Zn and Cu recoveries to solution, obtained experimentally under the conditions, are 81.16% and 56.48%, respectively.展开更多
The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the pro...The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.展开更多
The boundary knot method(BKM) is a boundary-type meshfree method. Only non-singular general solutions are used during the whole solution procedures. The effective condition number(ECN), which depends on the right-hand...The boundary knot method(BKM) is a boundary-type meshfree method. Only non-singular general solutions are used during the whole solution procedures. The effective condition number(ECN), which depends on the right-hand side vector of a linear system, is considered as an alternative criterion to the traditional condition number. In this paper, the effective condition number is used to help determine the position and distribution of the collocation points as well as the quasi-optimal collocation point numbers. During the solution process, we propose an NMN-search algorithm. Numerical examples show that the ECN is reliable to measure the feasibility of the BKM.展开更多
By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and non...By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable coefficient KdV equation is given.展开更多
In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under ...In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.展开更多
Objective： To investigate the dynamics of vascular volume and the plasma dilution of lactated Ringer＇s solution in patients during the induction of general and epidural anesthesia. Methods： The hemodilution of i.v....Objective： To investigate the dynamics of vascular volume and the plasma dilution of lactated Ringer＇s solution in patients during the induction of general and epidural anesthesia. Methods： The hemodilution of i.v. infusion of 1000 ml of lactated Ringer＇s solution over 60 min was studied in patients undergoing general （n=31） and epidural （n= 22） anesthesia. Heart rate, arterial blood pressure and hemoglobin （Hb） concentration were measured every 5 rain during the study. Surgery was not started until the study period had been completed. Results： General anesthesia caused the greater decrease of mean arterial blood pressure （MAP） （mean 15% versus 9%; P〈0.01） and thereby followed by a more pronounced plasma dilution, blood volume expansion （VE） and blood volume expansion efficiency （VEE）. A strong linear correlation between hemodilution and the reduction in MAP （r=-0.50;P〈0.01） was found. At the end of infusion, patients undergoing general anesthesia retained 47% （SD 19%） of the infused fluid in the circulation, while epidural anesthesia retained 29% （SD 13%） （P〈0.001）. Correspondingly, a fewer urine output （mean 89 ml versus 156 ml; P〈0.05） and extravascular expansion （454 ml versus 551 ml; P〈0.05） were found during general anesthesia. Conclusion： We concluded that the induction of general anesthesia caused more hemodilution, volume expansion and volume expansion efficiency than epidural anesthesia, which was triggered only by the lower MAP.展开更多
In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, t...In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.展开更多
First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the gener...First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three 'harmonic functions'. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.展开更多
A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic w...A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.展开更多
In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical...In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.展开更多
基金supported by the Anhui Provincial Natural Science Foundation(2408085QA031)the third author's work was supported by the National Natural Science Foundation of China(12001033).
文摘This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.
文摘The blockchain trilemma—balancing decentralization,security,and scalability—remains a critical challenge in distributed ledger technology.Despite significant advancements,achieving all three attributes simultaneously continues to elude most blockchain systems,often forcing trade-offs that limit their real-world applicability.This review paper synthesizes current research efforts aimed at resolving the trilemma,focusing on innovative consensus mechanisms,sharding techniques,layer-2 protocols,and hybrid architectural models.We critically analyze recent breakthroughs,including Directed Acyclic Graph(DAG)-based structures,cross-chain interoperability frameworks,and zero-knowledge proof(ZKP)enhancements,which aimto reconcile scalability with robust security and decentralization.Furthermore,we evaluate the trade-offs inherent in these approaches,highlighting their practical implications for enterprise adoption,decentralized finance(DeFi),and Web3 ecosystems.By mapping the evolving landscape of solutions,this review identifies gaps in currentmethodologies and proposes future research directions,such as adaptive consensus algorithms and artificial intelligence-driven(AI-driven)governance models.Our analysis underscores that while no universal solution exists,interdisciplinary innovations are progressively narrowing the trilemma’s constraints,paving the way for next-generation blockchain infrastructures.
文摘Primary healthcare service is the first line of defense to guard the health of the nation,and traditional Chinese medicine(TCM),with its characteristics of“simplicity,testing and inexpensiveness,”holistic outlook,and the concept of treating the disease before it occurs,has a unique advantage in primary healthcare and a great demand for it.This paper analyzes the core challenges facing the cultivation of general medicine talents in TCM colleges and universities,such as the disconnection between cultivation goals and grassroots,the misalignment between practical ability and grassroots demand,and the lack of career attraction.On this basis,it puts forward a systematic reform path with the core concept of“rooting at the grassroots,highlighting characteristics,and strengthening competence”to cultivate talents that meet grassroots needs,aiming to provide theoretical references for TCM colleges and universities to cultivate excellent TCM talents who are“able to go down to the grassroots,be useful,stay in the field,and have development”,and to provide theoretical reference for the training of excellent TCM talents.The aim is to provide a theoretical reference for Chinese medicine colleges to cultivate excellent Chinese medicine talents who can“get down,use,stay and develop,”and to help the construction of a healthy China.
基金Supported by Education Science Planning Project of Hubei Province(2020GB198)Natural Science Foundation of Hubei Province(2023AFB523).
文摘This paper analyzes the generalization of minimax regret optimization(MRO)under distribution shift.A new learning framework is proposed by injecting the measure of con-ditional value at risk(CVaR)into MRO,and its generalization error bound is established through the lens of uniform convergence analysis.The CVaR-based MRO can achieve the polynomial decay rate on the excess risk,which extends the generalization analysis associated with the expected risk to the risk-averse case.
基金supported by the NSFC(12271184)the Guangzhou Basic and Applied Basic Research Foundation(2024A04J10001).
文摘In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.
基金supported in part by the Natural Science Foundation of Zhejiang Province(LTGS23E070001)National Natural Science Foundation of China(62076185,62301367).
文摘This article presents a novel optimization approach called RSWTLBO for accurately identifying unknown parameters in photovoltaic(PV)models.The objective is to address challenges related to the detection and maintenance of PV systems and the improvement of conversion efficiency.RSWTLBO combines adaptive parameter w,Single Solution Optimization Mechanism(SSOM),and Weight Probability Exploration Strategy(WPES)to enhance the optimization ability of TLBO.The algorithm achieves a balance between exploitation and exploration throughout the iteration process.The SSOM allows for local exploration around a single solution,improving solution quality and eliminating inferior solutions.The WPES enables comprehensive exploration of the solution space,avoiding the problem of getting trapped in local optima.The algo-rithm is evaluated by comparing it with 10 other competitive algorithms on various PV models.The results demonstrate that RSWTLBO consistently achieves the lowest Root Mean Square Errors on single diode models,double diode models,and PV module models.It also exhibits robust performance under varying irradiation and temperature conditions.The study concludes that RSWTLBO is a practical and effective algorithm for identifying unknown parameters in PV models.
文摘In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.
文摘The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
文摘When designing and building an optimal reverse osmosis (RO) desalination plant, it is important that engineers select effective membrane parameters for optimal application performance. The membrane selection can determine the success or failure of the entire desalination operation. The objective of this work is to review available membrane types and design parameters that can be selected for optimal application to yield the highest potential for plant operations. Factors such as osmotic pressure, water flux values, and membrane resistance will all be evaluated as functions of membrane parameters. The optimization of these parameters will be determined through the deployment of the solution-diffusion model devolved from the Maxwell Stephan Equation. When applying the solution-diffusion model to evaluate RO membranes, the Maxwell Stephan Equation provides mathematical analysis through which the steps for mass transfer through a RO membrane may be observed and calculated. A practical study of the use of the solution-diffusion model will be discussed. This study uses the diffusion-solution model to evaluate the effectiveness of a variety of Toray RO membranes. This practical application confirms two principal hypotheses when using the diffusion-solution model for membrane evaluation. First, there is an inverse relationship between membrane and water flux rate. Second, there is a proportional linear relationship between overall water flux rate and the applied pressure across a membrane.
文摘In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.
文摘The feasibility of copper smelter slag processing by ammonia solution treatment was investigated. The central composite rotatable design(CCRD) and approximation method were used to determine the optimum conditions of zinc and copper recovery to a solution. The experimental design was done at five levels of the four operating parameters which were the initial concentration of NH–3, the initial Cl ions concentration, leaching time and solid/liquid ratio. Two mathematical models describing dependence of metal recovery on the operating parameters were obtained. The models are successful in predicting the responses. It was found that optimal parameters for zinc and copper recovery are as follows(values for copper are given in brackets): initial CNH3 17.1%(19.9%), initial CCl– 160 g/L(160 g/L), leaching process duration 4.56 h(4.13 h), solid/liquid ratio 0.39(0.53). The maximum Zn and Cu recoveries to solution, obtained experimentally under the conditions, are 81.16% and 56.48%, respectively.
文摘The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.
基金Supported by the Natural Science Foundation of Anhui Province(1908085QA09)Higher Education Department of the Ministry of Education(201802358008)
文摘The boundary knot method(BKM) is a boundary-type meshfree method. Only non-singular general solutions are used during the whole solution procedures. The effective condition number(ECN), which depends on the right-hand side vector of a linear system, is considered as an alternative criterion to the traditional condition number. In this paper, the effective condition number is used to help determine the position and distribution of the collocation points as well as the quasi-optimal collocation point numbers. During the solution process, we propose an NMN-search algorithm. Numerical examples show that the ECN is reliable to measure the feasibility of the BKM.
基金Supported by the Develop Programme Foundation of the National Basic research(G1 9990 3 2 80 1 )
文摘By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable coefficient KdV equation is given.
基金Foundation item： Supported by the Natural Science Foundation of China（10871216） Supported by the Natural Science Foundation Project of CQ CSTC（2008BB0346, 2007BB0441） Supported by the Excellent Young Teachers Program of Chongqing Jiaotong University（EYT08-016） Acknowledgement The author would like to thank the anonymous referee for the valuable remarks that helped considerably to correct and to improve the presentation.
文摘In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.
基金Project (No. 20051899) supported by Office of Education of Zheji-ang Province, China
文摘Objective： To investigate the dynamics of vascular volume and the plasma dilution of lactated Ringer＇s solution in patients during the induction of general and epidural anesthesia. Methods： The hemodilution of i.v. infusion of 1000 ml of lactated Ringer＇s solution over 60 min was studied in patients undergoing general （n=31） and epidural （n= 22） anesthesia. Heart rate, arterial blood pressure and hemoglobin （Hb） concentration were measured every 5 rain during the study. Surgery was not started until the study period had been completed. Results： General anesthesia caused the greater decrease of mean arterial blood pressure （MAP） （mean 15% versus 9%; P〈0.01） and thereby followed by a more pronounced plasma dilution, blood volume expansion （VE） and blood volume expansion efficiency （VEE）. A strong linear correlation between hemodilution and the reduction in MAP （r=-0.50;P〈0.01） was found. At the end of infusion, patients undergoing general anesthesia retained 47% （SD 19%） of the infused fluid in the circulation, while epidural anesthesia retained 29% （SD 13%） （P〈0.001）. Correspondingly, a fewer urine output （mean 89 ml versus 156 ml; P〈0.05） and extravascular expansion （454 ml versus 551 ml; P〈0.05） were found during general anesthesia. Conclusion： We concluded that the induction of general anesthesia caused more hemodilution, volume expansion and volume expansion efficiency than epidural anesthesia, which was triggered only by the lower MAP.
基金Supported by the Research Foundation of Jinan University(04SKZD01).
文摘In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.
文摘First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three 'harmonic functions'. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.
文摘A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.
文摘In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.
