NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

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.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

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.

COINCIDENCE THEOREMS IN PRODUCT G-CONVEX SPACES

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.

Evolving patterns of agricultural production space in China:A network-based approach

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.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

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.

Heritage Communities in Consumer Contexts Spatial Production of Tourism Research-Take Qixian Zhao Yu Historical City as an Example

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.

基于Cite space的我国蔬菜制种产业研究热点与趋势分析

运用可视化工具Cite Space和文献计量方法,对刊载在中国知网数据库所有与蔬菜制种相关主题的1212篇相关文献进行分析,并总结了我国蔬菜制种产业的热点及发展趋势。研究发现,蔬菜制种产业的研究热点主要集中在制种技术、杂交制种、种子产量、杂交授粉、杂种纯度等方面。我们建议后续应加强核心技术攻关,加快生物技术在蔬菜制种上的应用、强化基地建设,提高蔬菜制种产业化水平、加强研究主体间的合作与交流,重视制种人才培养,打造智慧农业。本研究可为进一步完善我国蔬菜制种产业提供借鉴。

Boundedness of Hausdorff operators on some product Hardy type spaces

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.

Agricultural Land Suitability of Production Space in the Taihang Mountains, China

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.

SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES

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.

Boundedness of Caldero'n-Zygmund operators in product Hardy spaces

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.

Integrability of the general product Hardy operators on the product Hardy spaces

In this paper,we prove that the general product Hardy operators are bounded from the product Hardy space H1n（Rm1×···×Rmn） to L1（R（∑ni=1mi）.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G_CONVEX SPACES AND APPLICATIONS (Ⅱ)

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.

Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

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.

SOME ROUGH OPERATORS ON PRODUCT SPACES

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.

The Loeb Space of Denumerable Infinite Dimensional Probability Product Measure Spaces

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.

Risk measures with comonotonic subadditivity or convexity on product spaces

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.

Grain production space reconstruction and land system function tradeoffs in China

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.

基于Cite Space的生态产品价值实现研究的演化路径与趋势

生态产品价值实现是推进生态文明建设和落实“绿水青山就是金山银山”理论的实践载体,学界围绕生态产品价值实现作了大量研究。为明晰目前生态产品价值实现的研究进展、演化路径及发展趋势,基于文献计量工具Cite Space对CNKI数据库中567篇国内生态产品价值实现研究论文的关键词时区图、聚类图、突现词视图进行可视化分析。研究结果表明:生态产品价值实现机制的研究主要经历了价值实现理念提出、试点探索、全面推进等三大阶段,具体研究内容涵盖了生态产品价值实现的内涵研究、理论与实践研究等,不同时期生态产品价值实现的研究重点也不同。基于图谱的可视化分析,指出未来生态产品价值实现应以经济、社会和生态效益有机融合为目标,健全价值实现的制度体系,强化多主体协同供给,深入挖掘乡村生态产品,全面有效推进生态文明建设。

Boundedness of Fractional Integrals with a Rough Kernel on the Product Triebel-Lizorkin Spaces

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.