Functional zoning is a key step for the integrated planning and scientific management of a national park.Selecting the Three-River-Source National Park(TNP)as the study area,this paper establishes an evaluation system...Functional zoning is a key step for the integrated planning and scientific management of a national park.Selecting the Three-River-Source National Park(TNP)as the study area,this paper establishes an evaluation system including 13 evaluation indexes which are classified into four categories,namely:ecosystem services;potential distribution of key species habitats;ecological sensitivity;and ecological resilience through the comprehensive analysis on the regional eco-environmental features in the study area.The results of the comprehensive analysis,combined with the functions and requirements of management of national parks,indicate that TNP is divided into the first-level zone(the core conservation area,the ecological restoration area and the traditional utilization area)with definite targets of space management and the second-level zone with implementation of control measures.This method of functional zoning lays a solid foundation for the scientific planning of TNP;moreover,our study provides new insights into other national parks’functional zoning.展开更多
Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk...Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.展开更多
Developed here is an integrated framework for identifying production–living–ecological space(PLES)quantitatively at grid scale from the perspective of multifunction land use,and 25 compound space types are classifie...Developed here is an integrated framework for identifying production–living–ecological space(PLES)quantitatively at grid scale from the perspective of multifunction land use,and 25 compound space types are classified to highlight the multiple functions of PLES.As a typical mountainous city in northern Hebei province,Zhangjiakou is used as a case study,and the results show that more than 80%of the land space in Zhangjiakou has remarkable triple functionality.The living-dominated space and the production-dominated space are distributed mainly in the valleys of the Yanghe,Sanggan,and Huliu rivers and have obvious spatial consistency,while the ecological-dominated space is concentrated mostly at the eastern Yanshan Mountains and southern Taihang Mountains and complements the other two types of space.The former two are spatially fragmented,while the latter has been expanding to the periphery over time.From 1990 to 2015,the ecological-dominated space has increased the most by 1555.02 km^(2),while the living-dominated space has increased the least by 816.79 km^(2).The types of PLES are more diverse in the medium and low mountains and the areas with gentle slope,and the influencing factors include natural ecological environment,socioeconomic development,human consumption demand,and institutional policies.Therefore,these findings can mitigate conflicts among PLES in mountainous and similar areas,and promote the balanced development of land space.展开更多
The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed par...The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance.展开更多
In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of t...In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.展开更多
A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.Th...A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.展开更多
In this paper we introduce the matrixβ-normed space and study the stability of the additive-quadratic type functional equation and the Pexider type functional equation in this type of spaces.
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s...The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.展开更多
This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firs...This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
In this article, we prove hyperstability results of the generalized Cauchy-Jensen functional equation αf(x+y/α+z)=f(x)+y(y)+αf(z)for any fixed positive integer α> 2 in ultrametric Banach spaces by using fixed p...In this article, we prove hyperstability results of the generalized Cauchy-Jensen functional equation αf(x+y/α+z)=f(x)+y(y)+αf(z)for any fixed positive integer α> 2 in ultrametric Banach spaces by using fixed point method.展开更多
In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dime...In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dimensional closed subspace of X＊ if and only if X＊ contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.展开更多
The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation i...The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.展开更多
Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s res...Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.展开更多
Chemical functionalization of graphene is a topic of paramount importance to broaden its applications in chemistry,physics,and biological science but remains a great challenge due to its low chemical activity and poor...Chemical functionalization of graphene is a topic of paramount importance to broaden its applications in chemistry,physics,and biological science but remains a great challenge due to its low chemical activity and poor dispersion.Here,we report a strategy for the photosynergetic electrochemical functionalization of graphene(EFG).By using chloride ion(Cl^(-))as the intercalation anions and co-reactants,the electrogenerated radicals confined in the expanded graphite layers enable efficient radical addition reaction,thus grasping crystallineperfect EFG.We found that the ultraviolet irradiation and applied voltage have increased the surface/interface concentration of Cl,thus boosting the functionalization of graphene.Theoretical calculation and experimental results verified the oxygen evolution reaction(OER)on EFG has been improved by regulating the doping of chlorine atoms.In addition,the reduced interlayer distance and enhanced electrostatic repulsion near the basal plane endow the fabricated EFG-based membrane with high salt retention.This work highlights a method for the in situ functionalization of graphene and the subsequent applications in OER and water desalination.展开更多
In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …...In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.展开更多
The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of no...The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.展开更多
Let G be an Abelian group and letρ：G×G→[0,∞） be a metric on G. Let E be a normed space. We prove that under some conditions if f：G→E is an odd function and Cx：G→E defined by Cx（y）：=2 f （x＋y）＋2 f ...Let G be an Abelian group and letρ：G×G→[0,∞） be a metric on G. Let E be a normed space. We prove that under some conditions if f：G→E is an odd function and Cx：G→E defined by Cx（y）：=2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y） is a cubic function for all x∈G, then there exists a cubic function C：G→E such that f？C is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y）=0 on Lipschitz spaces.展开更多
基金National Key Research and Development Program of China,No.2017YFC0503806
文摘Functional zoning is a key step for the integrated planning and scientific management of a national park.Selecting the Three-River-Source National Park(TNP)as the study area,this paper establishes an evaluation system including 13 evaluation indexes which are classified into four categories,namely:ecosystem services;potential distribution of key species habitats;ecological sensitivity;and ecological resilience through the comprehensive analysis on the regional eco-environmental features in the study area.The results of the comprehensive analysis,combined with the functions and requirements of management of national parks,indicate that TNP is divided into the first-level zone(the core conservation area,the ecological restoration area and the traditional utilization area)with definite targets of space management and the second-level zone with implementation of control measures.This method of functional zoning lays a solid foundation for the scientific planning of TNP;moreover,our study provides new insights into other national parks’functional zoning.
文摘Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.
基金National Natural Science Foundation of China,No.41971238,No.42101282,No.42001234。
文摘Developed here is an integrated framework for identifying production–living–ecological space(PLES)quantitatively at grid scale from the perspective of multifunction land use,and 25 compound space types are classified to highlight the multiple functions of PLES.As a typical mountainous city in northern Hebei province,Zhangjiakou is used as a case study,and the results show that more than 80%of the land space in Zhangjiakou has remarkable triple functionality.The living-dominated space and the production-dominated space are distributed mainly in the valleys of the Yanghe,Sanggan,and Huliu rivers and have obvious spatial consistency,while the ecological-dominated space is concentrated mostly at the eastern Yanshan Mountains and southern Taihang Mountains and complements the other two types of space.The former two are spatially fragmented,while the latter has been expanding to the periphery over time.From 1990 to 2015,the ecological-dominated space has increased the most by 1555.02 km^(2),while the living-dominated space has increased the least by 816.79 km^(2).The types of PLES are more diverse in the medium and low mountains and the areas with gentle slope,and the influencing factors include natural ecological environment,socioeconomic development,human consumption demand,and institutional policies.Therefore,these findings can mitigate conflicts among PLES in mountainous and similar areas,and promote the balanced development of land space.
文摘The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance.
基金supported by the Natural Science Foundation of Yibin University (No. 2009Z003)
文摘In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.
基金supported by National Natural Science Funds for Young Scholar(No.50903027)the Natural Science Foundation of Hebei Province(No.E2010000058)Education Department Science Research Plan of Hebei Province(No.2007307).
文摘A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.
基金Supported by the National Natural Science Foundation of China(Grant No.11371119)the Key Foundation of Education Department of Hebei Province(Grant No.ZD2016023)the Foundation of Education Department of Hebei Province(Grant No.Z2014031)
文摘In this paper we introduce the matrixβ-normed space and study the stability of the additive-quadratic type functional equation and the Pexider type functional equation in this type of spaces.
文摘The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
基金co-supported by the National Natural Science Foundation of China(Nos.12372048,12102343)the Key Program of the National Natural Science Foundation of China(No.U2013206)+1 种基金the China Postdoctoral Science Foundation(No.2023M742835)the Guangdong Basic and Applied Basic Research Foundation,China(No.2023A1515011421).
文摘This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
基金Science Achievement Scholarship of Thailand, which provides funding for research
文摘In this article, we prove hyperstability results of the generalized Cauchy-Jensen functional equation αf(x+y/α+z)=f(x)+y(y)+αf(z)for any fixed positive integer α> 2 in ultrametric Banach spaces by using fixed point method.
基金partially supported by NSFC,grant 11371296PhD Programs Foundation of MEC,Grant 20130121110032
文摘In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dimensional closed subspace of X＊ if and only if X＊ contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.
文摘The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.
文摘Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.
基金supported by the Natural Science Foundation of Guangxi Province(2021GXNSFBA220077,GUIKE AD23026050)National Natural Science Foundation of China(22102035 and 22162006)Innovation Project of Guangxi Graduate Education(XYCBZ2024021).
文摘Chemical functionalization of graphene is a topic of paramount importance to broaden its applications in chemistry,physics,and biological science but remains a great challenge due to its low chemical activity and poor dispersion.Here,we report a strategy for the photosynergetic electrochemical functionalization of graphene(EFG).By using chloride ion(Cl^(-))as the intercalation anions and co-reactants,the electrogenerated radicals confined in the expanded graphite layers enable efficient radical addition reaction,thus grasping crystallineperfect EFG.We found that the ultraviolet irradiation and applied voltage have increased the surface/interface concentration of Cl,thus boosting the functionalization of graphene.Theoretical calculation and experimental results verified the oxygen evolution reaction(OER)on EFG has been improved by regulating the doping of chlorine atoms.In addition,the reduced interlayer distance and enhanced electrostatic repulsion near the basal plane endow the fabricated EFG-based membrane with high salt retention.This work highlights a method for the in situ functionalization of graphene and the subsequent applications in OER and water desalination.
文摘In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.
基金supported by the Natural Science Foundation of Yibin University(No.2009Z03)
文摘The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.
文摘Let G be an Abelian group and letρ：G×G→[0,∞） be a metric on G. Let E be a normed space. We prove that under some conditions if f：G→E is an odd function and Cx：G→E defined by Cx（y）：=2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y） is a cubic function for all x∈G, then there exists a cubic function C：G→E such that f？C is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y）=0 on Lipschitz spaces.
