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
For a long time,it has been argued that the theories and practices devoted to urban planning and management should conform to the fundamental role of planning policies in the production of urban space,but not merely t...For a long time,it has been argued that the theories and practices devoted to urban planning and management should conform to the fundamental role of planning policies in the production of urban space,but not merely the spatial distribution of the produced services.Towards this wider connotation,this study introduces the notion of Railwayscape,grounded on the theory of‘The Production of Space’,to examine the role of railway station districts as catalysts of urban development through the social production of urban space.The present research sets out to establish the notion of Railwayscape and apply it in a railway heritage,i.e.,the Darjeeling Himalayan Railway(DHR)and its point of inception,Siliguri City,India.Accordingly,a criteria-based evaluation of four railway station districts(New Jalpaiguri,Siliguri Town,Siliguri Junction,and Sukna)in Siliguri and its surroundings was performed.The information regarding the selected four railway station districts is obtained through field observation and key informant consultation,supplemented by published literature and remote sensing data.This evaluation is succeeded by the strengths,weaknesses,opportunities and threats(SWOT)analysis accentuating the potential strengths,weaknesses,opportunities and threats associated with the selected four railway station districts and their prospects to become the potential Railwayscape.The results of this research show that there is no railway station district in Siliguri that can fully meet the demands of the locals and tourists,therefore,relfecting a lack of awareness of the historical values of these districts.The results also indicate that there are significant differences in the relative potentials of railway station districts to become the Railwayscape in urban environment.The outcomes of this research,therefore,are expected to encourage policy-making insitutions and practitioners to realise the‘place value’of some railway station districts and their potentials to yield better economic,social and structural virtue for a wide range of actors.展开更多
In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the ...In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.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
Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model ...Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.展开更多
Traditional village production space is the basis of villagers’ survival and village development.Nowadays,its production function has been lost,but it still has ecological and cultural value.The formation of traditio...Traditional village production space is the basis of villagers’ survival and village development.Nowadays,its production function has been lost,but it still has ecological and cultural value.The formation of traditional village production space in the Pearl River Delta is closely related to the water system,soil,geology and landform,and three types of production space,including water transportation,agricultural production and manual workshop,have been formed.It has strong ecological adaptability,forms pastoral scenery with unique water village characteristics,and is closely related to the development of the village and the livelihood of the villagers.Under the influence of urbanization,they have undergone great changes,which are manifested in erosion and fragmentation.Therefore,they should be protected,inherited and developed.展开更多
This paper aims to discuss how the shaping of a city, Juiz de Fora, in Brazil, has resulted from the power of location of some social agents and from their disputes on the production of space. First, it introduces the...This paper aims to discuss how the shaping of a city, Juiz de Fora, in Brazil, has resulted from the power of location of some social agents and from their disputes on the production of space. First, it introduces the concept of social production of space, emphasizing the role of social agents in urban processes. Then, it presents specific aspects of the history of Juiz de Fora" its origins and how social agents and forces have played a significant role in shaping the built environment of the city--specially represented by main streets of the city. The paper studies how the social agents, with their different visions and goals, have influenced the process of formation and development of the city. This demonstrates the complexity of the existing relationships between the built environment and the social context that is specific to the city. Different urban forces fight for city spaces, construct and modify its territory so that their needs are fulfilled. Their strength, their experiences and efforts, and their ideas of a city are inscribed in urban landscapes; in similar ways, these are revealed by the city paths we follow here.展开更多
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 exploitat...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.展开更多
This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a...This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a first countable T_(0) space is sober if and only if it does not contain a∏_(2)^(0)-subspace homeomorphic either to S_(D),the natural number set equipped with the Scott topology,or to S_(1),the natural number set equipped with the cofinite topology,and it does not contain any directed closed subset without maximal elements either.Second,we show that if Y is sober,the function space TOP(X,Y)equipped with the Isbell topology(respectively,Scott topology)may be a non-sober space.Furthermore,we provide a uniform construction to d-spaces and well-filtered spaces via irreducible subset systems introduced in[9];we called this an H-well-filtered space.We obtain that,for a T_(0) space X and an H-well-filtered space Y,the function space TOP(X,Y)equipped with the Isbell topology is H-well-filtered.Going beyond the aforementioned work,we solve several open problems concerning strong d-spaces posed by Xu and Zhao in[11].展开更多
In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size condi...In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.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
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
In this paper the boundedness for the multilinear fractional integral operator Iα^(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for cl...In this paper the boundedness for the multilinear fractional integral operator Iα^(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.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
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
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 pr...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.展开更多
We present results on approximate solutions to the biadditive equationf(x+y,z-w)+f(x-y,z+w)=2f(x,z)-2f(y,w)on a restricted domain. The proof is based on a quite recent fixed point theorem in some function s...We present results on approximate solutions to the biadditive equationf(x+y,z-w)+f(x-y,z+w)=2f(x,z)-2f(y,w)on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.展开更多
A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.
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
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.
基金University Grants Commission for the Junior Research Fellowship(Ref No.190510006296).
文摘For a long time,it has been argued that the theories and practices devoted to urban planning and management should conform to the fundamental role of planning policies in the production of urban space,but not merely the spatial distribution of the produced services.Towards this wider connotation,this study introduces the notion of Railwayscape,grounded on the theory of‘The Production of Space’,to examine the role of railway station districts as catalysts of urban development through the social production of urban space.The present research sets out to establish the notion of Railwayscape and apply it in a railway heritage,i.e.,the Darjeeling Himalayan Railway(DHR)and its point of inception,Siliguri City,India.Accordingly,a criteria-based evaluation of four railway station districts(New Jalpaiguri,Siliguri Town,Siliguri Junction,and Sukna)in Siliguri and its surroundings was performed.The information regarding the selected four railway station districts is obtained through field observation and key informant consultation,supplemented by published literature and remote sensing data.This evaluation is succeeded by the strengths,weaknesses,opportunities and threats(SWOT)analysis accentuating the potential strengths,weaknesses,opportunities and threats associated with the selected four railway station districts and their prospects to become the potential Railwayscape.The results of this research show that there is no railway station district in Siliguri that can fully meet the demands of the locals and tourists,therefore,relfecting a lack of awareness of the historical values of these districts.The results also indicate that there are significant differences in the relative potentials of railway station districts to become the Railwayscape in urban environment.The outcomes of this research,therefore,are expected to encourage policy-making insitutions and practitioners to realise the‘place value’of some railway station districts and their potentials to yield better economic,social and structural virtue for a wide range of actors.
文摘In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.
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.
文摘Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.
基金Sponsored by The 2017 Discipline Co-construction Project of the 13^(th) Five-Year Plan of Philosophy and Social Sciences in Guangdong Province (GD17XGL62)。
文摘Traditional village production space is the basis of villagers’ survival and village development.Nowadays,its production function has been lost,but it still has ecological and cultural value.The formation of traditional village production space in the Pearl River Delta is closely related to the water system,soil,geology and landform,and three types of production space,including water transportation,agricultural production and manual workshop,have been formed.It has strong ecological adaptability,forms pastoral scenery with unique water village characteristics,and is closely related to the development of the village and the livelihood of the villagers.Under the influence of urbanization,they have undergone great changes,which are manifested in erosion and fragmentation.Therefore,they should be protected,inherited and developed.
文摘This paper aims to discuss how the shaping of a city, Juiz de Fora, in Brazil, has resulted from the power of location of some social agents and from their disputes on the production of space. First, it introduces the concept of social production of space, emphasizing the role of social agents in urban processes. Then, it presents specific aspects of the history of Juiz de Fora" its origins and how social agents and forces have played a significant role in shaping the built environment of the city--specially represented by main streets of the city. The paper studies how the social agents, with their different visions and goals, have influenced the process of formation and development of the city. This demonstrates the complexity of the existing relationships between the built environment and the social context that is specific to the city. Different urban forces fight for city spaces, construct and modify its territory so that their needs are fulfilled. Their strength, their experiences and efforts, and their ideas of a city are inscribed in urban landscapes; in similar ways, these are revealed by the city paths we follow here.
文摘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.
文摘This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a first countable T_(0) space is sober if and only if it does not contain a∏_(2)^(0)-subspace homeomorphic either to S_(D),the natural number set equipped with the Scott topology,or to S_(1),the natural number set equipped with the cofinite topology,and it does not contain any directed closed subset without maximal elements either.Second,we show that if Y is sober,the function space TOP(X,Y)equipped with the Isbell topology(respectively,Scott topology)may be a non-sober space.Furthermore,we provide a uniform construction to d-spaces and well-filtered spaces via irreducible subset systems introduced in[9];we called this an H-well-filtered space.We obtain that,for a T_(0) space X and an H-well-filtered space Y,the function space TOP(X,Y)equipped with the Isbell topology is H-well-filtered.Going beyond the aforementioned work,we solve several open problems concerning strong d-spaces posed by Xu and Zhao in[11].
基金Supported by the National Natural Science Foundation of China(12071437)the Natural Science Foundation of Zhejiang Province,China(LQ22A010018)。
文摘In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.
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 Sciences Foundation of China (10771110)the Natural Science Founda- tion of Ningbo City (2006A610090)
文摘In this paper the boundedness for the multilinear fractional integral operator Iα^(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.
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supported by the University of KwaZulu-Natal(UKZN)Doctoral Scholarshipsupported by the National Research Foundation(NRF)South Africa(S&F-DSI/NRF Free Standing Postdoctoral Fellowship(120784)supported by the National Research Foundation(NRF)South Africa Incentive Funding for Rated Researchers(119903).
文摘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.
文摘We present results on approximate solutions to the biadditive equationf(x+y,z-w)+f(x-y,z+w)=2f(x,z)-2f(y,w)on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.
文摘A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.
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.