By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems...By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.展开更多
The agricultural production space,as where and how much each agricultural product grows,plays a vital role in meeting the increasing and diverse food demands.Previous studies on agricultural production patterns have p...The agricultural production space,as where and how much each agricultural product grows,plays a vital role in meeting the increasing and diverse food demands.Previous studies on agricultural production patterns have predominantly centered on individual or specific crop types,using methods such as remote sensing or statistical metrological analysis.In this study,we characterize the agricultural production space(APS)by bipartite network connecting agricultural products and provinces,to reveal the relatedness between diverse agricultural products and the spatiotemporal characteristic of provincial production capabilities in China.The results show that core products are cereal,pork,melon,and pome fruit;meanwhile the milk,grape,and fiber crop show an upward trend in centrality,which is in line with diet structure changes in China over the past decades.The little changes in community components and structures of agricultural products and provinces reveal that agricultural production patterns in China are relatively stable.Additionally,identified provincial communities closely resemble China's agricultural natural zones.Furthermore,the observed growth in production capabilities in North and Northeast China implies their potential focus areas for future agricultural production.Despite the superior production capa-bilities of southern provinces,recent years have witnessed a notable decline,warranting special attentions.The findings provide a comprehensive perspective for understanding the complex relationship of agricultural prod-ucts'relatedness,production capabilities and production patterns,which serve as a reference for the agricultural spatial optimization and agricultural sustainable development.展开更多
A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several exist...A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.展开更多
Taking Zhaoyu Historical City in Qixian County as an example,this paper explores the production process of tourism space in Zhaoyu Historical City in the context of consumption,based on Lefebvre's triadic dialecti...Taking Zhaoyu Historical City in Qixian County as an example,this paper explores the production process of tourism space in Zhaoyu Historical City in the context of consumption,based on Lefebvre's triadic dialectic theory.The study reveals that,driven by the development of tourism,subjects such as the government and planners possess absolute dominance over spatial representations,while residents demonstrate receptive and adaptive action strategies and social relations are reproduced,presenting a harmonious state.Further exploring the tourism community in the environmental performance of the subject of action,social relations,consumption demand,daily life practice,cultural capital,etc.,the daily life practice of the tourism community has transcended the original logic of tourism spatial production and has a certain extension.The mechanism analysis in this paper can help guide the healthy development of tourism space in the neighboring historical cities or communities and achieve the dual purpose of promoting the economic development of the community and heritage protection.展开更多
We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function ...We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function spaces.展开更多
The contradiction between the shortage of land for agriculture due to rapid expansion of industrialization and urbanization and increasing population pressure is projected to impose great threats to future food securi...The contradiction between the shortage of land for agriculture due to rapid expansion of industrialization and urbanization and increasing population pressure is projected to impose great threats to future food security.Agricultural land suitability evaluation is an effective approach to improve the utilization of land resources for crop production and thus enhance the capacity of food provision.In this study, we evaluated the land suitability for agriculture of the production space in the Taihang Mountains by three steps: establishing indicator system, determining weights for indicators, and constructing a fuzzy matter-element model to assess the grades of suitability.Results showed that the land suitability had a significant linear correlation with potential crop yields, indicating our evaluation was effective to predict crop production.The spatial pattern of land suitability for crop production demonstrated that land with higher suitability was generally located in piedmont plains and basins, while land with lower suitability was mostly situated in mountainous areas.The area of highly, moderately, marginally suitable and unsuitable land for agriculture was 32.13%, 28.58%, 37.49% and 1.80% of the production space, respectively.However, the correlation degree analysis indicated that the requirements of these four suitability grades were currently not satisfied but could be potentially fulfilled.In terms of indicator weights, soil properties were much more important than topography and location conditions to influence the grades of suitability.Among all indicators, slope, soil organic matter, soil texture and soil depth were the most influential factors, so slope farming prevention and organic fertilization were most likely to improve land suitability for agriculture.Compared the outputs of our land suitability evaluation model with the distribution of the existing croplands, we found that about 66.52% of marginally suitable and 54.55% of unsuitable land for agriculture were currently used for croplands.Therefore, de-farming policy should be implemented in areas of these two suitability grades.In contrast, cropland expansion was encouraged in the land that was highly or moderately suitable for agriculture.Our evaluation of agricultural land suitability is beneficial for future land use planning and decision-making in the Taihang Mountains.展开更多
In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space...In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.展开更多
By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé i...By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.展开更多
A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several exist...A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.展开更多
In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an a...In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.展开更多
In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product space...In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.展开更多
Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We...Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.展开更多
In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan (2006). ...In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan (2006). Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.展开更多
Grain production space reconstruction referred to the changes in the quantity,quality and pattern of grain produc-tion space caused by functional tradeoffs and conflicts between grain production space,urban-rural deve...Grain production space reconstruction referred to the changes in the quantity,quality and pattern of grain produc-tion space caused by functional tradeoffs and conflicts between grain production space,urban-rural development space,and ecological service space.Exploring tradeoffs between land system functions caused by grain produc-tion space reconstruction was particularly important for ensuring food security,promoting the construction of ecological civilization,and achieving sustainable development.Therefore,this study identified four relationships of land system functions during the process of grain production space reconstruction(1980-2018)in China by using Set Pair Analysis.Research results showed that the reconstruction of grain production space was achieved mainly through three pathways:Grain for Green,deforestation and reclamation,and urban expansion.Generally,ecological service had spatial negative correlation with grain production,economic development and population carrying capacity(P<0.01),but grain production,economic development and population carrying capacity were positively correlated with each other(P<0.01).In the process of grain production space reconstruction,eco-logical services and economic development,ecological services and population carrying capacity had all shown inverse synergies;there was a tradeoffbetween grain production and ecological services,a codirectional tradeoffbetween grain production and economic development,but a strong synergy between economic development and population carrying capacity.However,the functions of land systems only appeared as synergies or tradeoffs,and there were no inverse synergies and codirectional tradeoffs in the separate processes of Grain for Green,deforestation and reclamation,and urban expansion.It can be concluded that the relationships between land system functions were relatively simple in a single process,but it became complex and diverse when multiple processes were integrated for system analysis.展开更多
By using the Littlewood-Paley decomposition and the interpolation theory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金This project is supported by the NNSF of China (19871059) and the Natural Science Foundation of Sichuan Education Department (2003A081).
文摘By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.
基金supported by the Institute of Atmospheric Environment,China Meteorological Administration,Shenyang(Grant No.2021SYIAEKFMS27)Key Laboratory of Farm Building in Structure and Construction,Ministry of Agriculture and Rural Affairs,P.R.China(Grant No.202003)the National Foundation of China Scholarship Council(Grant No.202206040102).
文摘The agricultural production space,as where and how much each agricultural product grows,plays a vital role in meeting the increasing and diverse food demands.Previous studies on agricultural production patterns have predominantly centered on individual or specific crop types,using methods such as remote sensing or statistical metrological analysis.In this study,we characterize the agricultural production space(APS)by bipartite network connecting agricultural products and provinces,to reveal the relatedness between diverse agricultural products and the spatiotemporal characteristic of provincial production capabilities in China.The results show that core products are cereal,pork,melon,and pome fruit;meanwhile the milk,grape,and fiber crop show an upward trend in centrality,which is in line with diet structure changes in China over the past decades.The little changes in community components and structures of agricultural products and provinces reveal that agricultural production patterns in China are relatively stable.Additionally,identified provincial communities closely resemble China's agricultural natural zones.Furthermore,the observed growth in production capabilities in North and Northeast China implies their potential focus areas for future agricultural production.Despite the superior production capa-bilities of southern provinces,recent years have witnessed a notable decline,warranting special attentions.The findings provide a comprehensive perspective for understanding the complex relationship of agricultural prod-ucts'relatedness,production capabilities and production patterns,which serve as a reference for the agricultural spatial optimization and agricultural sustainable development.
文摘A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.
文摘Taking Zhaoyu Historical City in Qixian County as an example,this paper explores the production process of tourism space in Zhaoyu Historical City in the context of consumption,based on Lefebvre's triadic dialectic theory.The study reveals that,driven by the development of tourism,subjects such as the government and planners possess absolute dominance over spatial representations,while residents demonstrate receptive and adaptive action strategies and social relations are reproduced,presenting a harmonious state.Further exploring the tourism community in the environmental performance of the subject of action,social relations,consumption demand,daily life practice,cultural capital,etc.,the daily life practice of the tourism community has transcended the original logic of tourism spatial production and has a certain extension.The mechanism analysis in this paper can help guide the healthy development of tourism space in the neighboring historical cities or communities and achieve the dual purpose of promoting the economic development of the community and heritage protection.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173 and 11026104)
文摘We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function spaces.
基金Under the auspices of the National Basic Research Program of China(No.2015CB452705)
文摘The contradiction between the shortage of land for agriculture due to rapid expansion of industrialization and urbanization and increasing population pressure is projected to impose great threats to future food security.Agricultural land suitability evaluation is an effective approach to improve the utilization of land resources for crop production and thus enhance the capacity of food provision.In this study, we evaluated the land suitability for agriculture of the production space in the Taihang Mountains by three steps: establishing indicator system, determining weights for indicators, and constructing a fuzzy matter-element model to assess the grades of suitability.Results showed that the land suitability had a significant linear correlation with potential crop yields, indicating our evaluation was effective to predict crop production.The spatial pattern of land suitability for crop production demonstrated that land with higher suitability was generally located in piedmont plains and basins, while land with lower suitability was mostly situated in mountainous areas.The area of highly, moderately, marginally suitable and unsuitable land for agriculture was 32.13%, 28.58%, 37.49% and 1.80% of the production space, respectively.However, the correlation degree analysis indicated that the requirements of these four suitability grades were currently not satisfied but could be potentially fulfilled.In terms of indicator weights, soil properties were much more important than topography and location conditions to influence the grades of suitability.Among all indicators, slope, soil organic matter, soil texture and soil depth were the most influential factors, so slope farming prevention and organic fertilization were most likely to improve land suitability for agriculture.Compared the outputs of our land suitability evaluation model with the distribution of the existing croplands, we found that about 66.52% of marginally suitable and 54.55% of unsuitable land for agriculture were currently used for croplands.Therefore, de-farming policy should be implemented in areas of these two suitability grades.In contrast, cropland expansion was encouraged in the land that was highly or moderately suitable for agriculture.Our evaluation of agricultural land suitability is beneficial for future land use planning and decision-making in the Taihang Mountains.
基金supported by NSFC(11471309,11271162,and11561062)Project of Henan Provincial Department of Education(18A110028)+1 种基金the Nanhu Scholar Program for Young Scholars of XYNUDoctoral Scientific Research Startup Fund of Xinyang Normal University(2016)
文摘In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.
基金supported by the National Natural Science Foundation of China(10871025)
文摘By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.
文摘A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.
文摘In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.
基金the Project of Development Plan of the State Key Fundamental Research Major Project of NNSFC,and NSFZJ.
文摘In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.
基金The Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province.
文摘Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.
基金Supported by the National Natural Science Foundation of China(11371284)the Natural Science Foundation of Henan Province(14B110037)
文摘In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan (2006). Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.
基金conducted under the auspice of National Natural Science Foundation of China(Grant No.41701094).
文摘Grain production space reconstruction referred to the changes in the quantity,quality and pattern of grain produc-tion space caused by functional tradeoffs and conflicts between grain production space,urban-rural development space,and ecological service space.Exploring tradeoffs between land system functions caused by grain produc-tion space reconstruction was particularly important for ensuring food security,promoting the construction of ecological civilization,and achieving sustainable development.Therefore,this study identified four relationships of land system functions during the process of grain production space reconstruction(1980-2018)in China by using Set Pair Analysis.Research results showed that the reconstruction of grain production space was achieved mainly through three pathways:Grain for Green,deforestation and reclamation,and urban expansion.Generally,ecological service had spatial negative correlation with grain production,economic development and population carrying capacity(P<0.01),but grain production,economic development and population carrying capacity were positively correlated with each other(P<0.01).In the process of grain production space reconstruction,eco-logical services and economic development,ecological services and population carrying capacity had all shown inverse synergies;there was a tradeoffbetween grain production and ecological services,a codirectional tradeoffbetween grain production and economic development,but a strong synergy between economic development and population carrying capacity.However,the functions of land systems only appeared as synergies or tradeoffs,and there were no inverse synergies and codirectional tradeoffs in the separate processes of Grain for Green,deforestation and reclamation,and urban expansion.It can be concluded that the relationships between land system functions were relatively simple in a single process,but it became complex and diverse when multiple processes were integrated for system analysis.
基金The NSF(11561057,11226104)of Chinathe NSF(20151BAB211002,20151BAB201007)of Jiangxi Province+1 种基金the Science Foundation(GJJ151054,GJJ151061)of Jiangxi Education Departmentthe Scientific Research Project of Shangrao Normal University
文摘By using the Littlewood-Paley decomposition and the interpolation theory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.