In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applicati...In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applications.The main results improve and generalize the corresponding results in previous papers.展开更多
In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the syst...In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.展开更多
The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point ...The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point theorem is equivalent to the generalized Ekeland variational principle.展开更多
Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructi...Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructive to consider the issue of optimal city size and review the literature over the past decades on optimal city size theory.Based on the progress in recent years of comparative analysis and inductive research,from both theoretical and empirical perspectives,this paper outlines the original definitions proposed for optimal city size and discusses some of the advantages and disadvantages of the various theories.The two prevailing models in the classical analysis of optimal city size,the Henry George Theorem(HGT)and the neoclassical approach,are examined later.This paper then introduces the supply oriented dynamic model(SOUDY model)and offers a plausible model for optimal city size based on the general equilibrium analysis,which is related to sustainable development.The results show that:(1)Simple optimal city size theories come from the cost-benefit analysis developed by main stream economics,and therefore cannot overcome the defect that the optimal size of cities is the same since the same production function;(2)The Henry George Theorem,which is one of the classical analysis paradigms of optimal city size,has been used more frequently in recent years to research the issues of optimal tax and public goods and has gradually lost its connection to the topic of optimal city size;(3)The neoclassical approach to optimal city size consists of externalities influencing optimal city size,the equilibrium and optimal models for city size,the optimal town,product variety and city size distribution.This kind of research is still in the mainstream of the study of optimal city size.Compared to single optimal city size,more attention is paid to the optimal distribution of city size;and(4)The supply-oriented dynamic model allows for the integration of a spatial dimension into the economic research of optimal city size,and the constraint between city level and city size is relaxed and this has more power to explain real-world problems.At the same time,the general equilibrium analysis,as a significant economic research method,provides a new perspective for the study of optimal city size.The supply-oriented dynamic model and general equilibrium analysis are two new research paradigms that deserve more attention in the analysis of optimal city size.展开更多
文摘In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applications.The main results improve and generalize the corresponding results in previous papers.
文摘In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.
基金Tianyuan Young Mathematics of China under Grant (10526025)Science Foundation of Nanjing Normal University under Grant(2002SXXXGQ2B20)
文摘The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point theorem is equivalent to the generalized Ekeland variational principle.
基金The Scientific Research Project of Hunan Education Department(18C0964)The 2016 Scientific Research Fund Project for Young Teachers of Hunan University of Finance and Economics(Q201604)
文摘Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructive to consider the issue of optimal city size and review the literature over the past decades on optimal city size theory.Based on the progress in recent years of comparative analysis and inductive research,from both theoretical and empirical perspectives,this paper outlines the original definitions proposed for optimal city size and discusses some of the advantages and disadvantages of the various theories.The two prevailing models in the classical analysis of optimal city size,the Henry George Theorem(HGT)and the neoclassical approach,are examined later.This paper then introduces the supply oriented dynamic model(SOUDY model)and offers a plausible model for optimal city size based on the general equilibrium analysis,which is related to sustainable development.The results show that:(1)Simple optimal city size theories come from the cost-benefit analysis developed by main stream economics,and therefore cannot overcome the defect that the optimal size of cities is the same since the same production function;(2)The Henry George Theorem,which is one of the classical analysis paradigms of optimal city size,has been used more frequently in recent years to research the issues of optimal tax and public goods and has gradually lost its connection to the topic of optimal city size;(3)The neoclassical approach to optimal city size consists of externalities influencing optimal city size,the equilibrium and optimal models for city size,the optimal town,product variety and city size distribution.This kind of research is still in the mainstream of the study of optimal city size.Compared to single optimal city size,more attention is paid to the optimal distribution of city size;and(4)The supply-oriented dynamic model allows for the integration of a spatial dimension into the economic research of optimal city size,and the constraint between city level and city size is relaxed and this has more power to explain real-world problems.At the same time,the general equilibrium analysis,as a significant economic research method,provides a new perspective for the study of optimal city size.The supply-oriented dynamic model and general equilibrium analysis are two new research paradigms that deserve more attention in the analysis of optimal city size.
