Doris Lessing’s Farm Writing and Capitalist Colonial Space Production

Farm is a vital image in Doris Lessing’s fiction,which is also a result of colonial space production.Through a series of discriminative land policies in a colonial society,the white farmers implement labour exploitation towards natives.Meanwhile,this space also presents various contradictions among whites.Moreover,colonial space production also leads to the deconstruction of natural space.Lessing’s farm writing reveals her nostalgia of the natural landscape when the farm hasn’t been involved with the capitalist space production and her concern for human beings’unity.

A convergent flow in warped product spaces

In this paper,we study a kind of curvature flow in warped product spaces.We obtain convergence results under barrier conditions and restrictions on prescribed function.We also obtain the asymptotic behavior of a kind of inverse curvature flow in Schwarzschild manifold.

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.

SPECIAL ISSUE： SPACE PRODUCTION AND URBAN ORDER IN CONTEMPORARY CHINA--From Object to Perspective： A Shift of Significance in Space Production and Space Criticism--The Issue of Space in Conceptualizing Contemporary Chinese Urban Construction

Physical space refers to both natural space and social space, that is, social relations. Space production includes production in space and of space. Relations between these two dimensions and between physical space production and social space production constitute two basic relations in space production. The dialectical connotation of these two basic relations manifests the truth that space production can basically be summed up as reproduction of social relations. Therefore, arguments about space production can be seen as involving a fundamental shift of importance from object to perspective. Seen in this way, there remain some errors in ideas about today＇s Chinese urban construction, that is, the rupture and separation of object and perspective, resulting in unnecessary risks and costs in the progress of modem Chinese ttrbanization.

SPECIAL ISSUE： SPACE PRODUCTION AND URBAN ORDER IN CONTEMPORARY CHINA--The Capitalization of Space and Cultural Resistance

Urbanization is proceeding at full speed in China. Economic progress has been accompanied by enormous problems in our big cities, such as traffic congestion, air pollution, the coexistence of resource abuse and scarcity, etc.--and these are merely the problems visible on the surface. The capitalization of space in the course of urbanization has meant loss of diversity in urban culture and configuration and in the natural environment. In the long run, this will make human existence more objectified, functional and utilitarian. This paper argues that the fundamental reason for these problems lies in the value concepts guiding the production of space. Only when we abandon the existing values of consumer society, which revolve around ＂capital and technology appreciation,＂ and establish new values ＂putting people first＂ will we be able to withstand the mighty torrent of capitalized space production.

SPECIAL ISSUE： SPACE PRODUCTION AND URBAN ORDER IN CONTEMPORARY CHINA--The Loss of Urban Order and the Ethical Construction of Urban Order in Contemporary China

Rapidly urbanizing China is at a critical period in the construction of urban meaning and order. The city as an organic compound of space represents the organic integration in space of the elements of civilization, while its meaning provides the ethical ties that link these elements to form an organic whole. A city without a locus of meaning will be buffeted by risks and confrontations. The realization of sustainable urban prosperity requires the integration of the city as an ordered community of meaning at the same time as its physical forms take shape. An important practical path to achieving this aim is restructuring city space in a rational ＂spatial-ethical ecology＂ based on integrity and interaction of physical, social and psychological urban space, by means of collective action knitted together by meaning and carried out by communities and organizations.

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.

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.

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）.

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.

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.

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.

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.

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.

RELAXED INERTIAL METHODS FOR SOLVING SPLIT VARIATIONAL INEQUALITY PROBLEMS WITHOUT PRODUCT SPACE FORMULATION

Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are co-coercive.However,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive assumption.The methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.

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.

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.

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.

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.