In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings a...In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.展开更多
Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, e...Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.展开更多
In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued ...In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.展开更多
Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-value...Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.展开更多
Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
Consider the continuous map f:x→X and the continuous map f of K,(X)into itself induced by f,where X is a metric space and K(X)the space of all non-empty compact subsets of x endowed with the Hausdorff metric.Accordin...Consider the continuous map f:x→X and the continuous map f of K,(X)into itself induced by f,where X is a metric space and K(X)the space of all non-empty compact subsets of x endowed with the Hausdorff metric.According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli,we investigate the relations between f and f in the related dynamical properties such as transitivity,weakly mixing and mixing,etc.And by using the obtained results,we give the satisfied answers to Roman-Flores's question and Fedeli's question.展开更多
In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in ...In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].展开更多
A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point th...A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.展开更多
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx...We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.展开更多
A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-...A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-cooperative generalized games is proved.展开更多
SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is...SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This展开更多
Network-on-Chip(NoC)systems are progressively deployed in connecting massively parallel megacore systems in the new computing architecture.As a result,application mapping has become an important aspect of performance ...Network-on-Chip(NoC)systems are progressively deployed in connecting massively parallel megacore systems in the new computing architecture.As a result,application mapping has become an important aspect of performance and scalability,as current trends require the distribution of computation across network nodes/points.In this paper,we survey a large number of mapping and scheduling techniques designed for NoC architectures.This time,we concentrated on 3D systems.We take a systematic literature review approach to analyze existing methods across static,dynamic,hybrid,and machine-learning-based approaches,alongside preliminary AI-based dynamic models in recent works.We classify them into several main aspects covering power-aware mapping,fault tolerance,load-balancing,and adaptive for dynamic workloads.Also,we assess the efficacy of each method against performance parameters,such as latency,throughput,response time,and error rate.Key challenges,including energy efficiency,real-time adaptability,and reinforcement learning integration,are highlighted as well.To the best of our knowledge,this is one of the recent reviews that identifies both traditional and AI-based algorithms for mapping over a modern NoC,and opens research challenges.Finally,we provide directions for future work toward improved adaptability and scalability via lightweight learned models and hierarchical mapping frameworks.展开更多
Spectrum map construction,which is crucial in cognitive radio(CR)system,visualizes the invisible space of the electromagnetic spectrum for spectrum-resource management and allocation.Traditional reconstruction methods...Spectrum map construction,which is crucial in cognitive radio(CR)system,visualizes the invisible space of the electromagnetic spectrum for spectrum-resource management and allocation.Traditional reconstruction methods are generally for twodimensional(2D)spectrum map and driven by abundant sampling data.In this paper,we propose a data-model-knowledge-driven reconstruction scheme to construct the three-dimensional(3D)spectrum map under multi-radiation source scenarios.We firstly design a maximum and minimum path loss difference(MMPLD)clustering algorithm to detect the number of radiation sources in a 3D space.Then,we develop a joint location-power estimation method based on the heuristic population evolutionary optimization algorithm.Considering the variation of electromagnetic environment,we self-learn the path loss(PL)model based on the sampling data.Finally,the 3D spectrum is reconstructed according to the self-learned PL model and the extracted knowledge of radiation sources.Simulations show that the proposed 3D spectrum map reconstruction scheme not only has splendid adaptability to the environment,but also achieves high spectrum construction accuracy even when the sampling rate is very low.展开更多
基金Foundation item： Supported by the Science Foundation from the Ministry of Education of Jiangsu Province（04KJD110168, 06KJBll0107）
文摘In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.
基金the Young Foundation of Sichuan Province(06ZQ026-037) the Education Department Foundation of Sichuan Province(2005A1212006A084)
文摘Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.
基金Supported by the Science Foundation of Hangzhou Normal University（02010180）
文摘In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.
文摘Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.
文摘Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
文摘In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
基金supported by the National Natural Science Foundation of China(Grant No.19971035)the Innovation Foundation of Jilin University(Grant No.2004CZ051).
文摘Consider the continuous map f:x→X and the continuous map f of K,(X)into itself induced by f,where X is a metric space and K(X)the space of all non-empty compact subsets of x endowed with the Hausdorff metric.According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli,we investigate the relations between f and f in the related dynamical properties such as transitivity,weakly mixing and mixing,etc.And by using the obtained results,we give the satisfied answers to Roman-Flores's question and Fedeli's question.
基金Supported by the National Natural Science Foundation of China(No.60574073,No.10471142)
文摘In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].
基金Supported by the National Natural Science Foundation of China (No. 10771173)the Natural Science Foundation of Henan Education Department (No. 2008B110012)+1 种基金the Science and Technology Program Project of Henan Province (No. 092300410187)the Youth Foundation of Luoyang Normal University
文摘A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.
基金the Natural Science Foundation of China (No. 10471151)the Educational Science Foundation of Chongqing (KJ051307).
文摘We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.
基金the National Natural Science Foundation of China(No.10561003)
文摘A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-cooperative generalized games is proved.
文摘SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This
文摘Network-on-Chip(NoC)systems are progressively deployed in connecting massively parallel megacore systems in the new computing architecture.As a result,application mapping has become an important aspect of performance and scalability,as current trends require the distribution of computation across network nodes/points.In this paper,we survey a large number of mapping and scheduling techniques designed for NoC architectures.This time,we concentrated on 3D systems.We take a systematic literature review approach to analyze existing methods across static,dynamic,hybrid,and machine-learning-based approaches,alongside preliminary AI-based dynamic models in recent works.We classify them into several main aspects covering power-aware mapping,fault tolerance,load-balancing,and adaptive for dynamic workloads.Also,we assess the efficacy of each method against performance parameters,such as latency,throughput,response time,and error rate.Key challenges,including energy efficiency,real-time adaptability,and reinforcement learning integration,are highlighted as well.To the best of our knowledge,this is one of the recent reviews that identifies both traditional and AI-based algorithms for mapping over a modern NoC,and opens research challenges.Finally,we provide directions for future work toward improved adaptability and scalability via lightweight learned models and hierarchical mapping frameworks.
基金National Key Scientific Instrument and Equipment Development Project under Grant No.61827801the open research fund of State Key Laboratory of Integrated Services Networks,No.ISN22-11+1 种基金Natural Science Foundation of Jiangsu Province,No.BK20211182open research fund of National Mobile Communications Research Laboratory,Southeast University,No.2022D04。
文摘Spectrum map construction,which is crucial in cognitive radio(CR)system,visualizes the invisible space of the electromagnetic spectrum for spectrum-resource management and allocation.Traditional reconstruction methods are generally for twodimensional(2D)spectrum map and driven by abundant sampling data.In this paper,we propose a data-model-knowledge-driven reconstruction scheme to construct the three-dimensional(3D)spectrum map under multi-radiation source scenarios.We firstly design a maximum and minimum path loss difference(MMPLD)clustering algorithm to detect the number of radiation sources in a 3D space.Then,we develop a joint location-power estimation method based on the heuristic population evolutionary optimization algorithm.Considering the variation of electromagnetic environment,we self-learn the path loss(PL)model based on the sampling data.Finally,the 3D spectrum is reconstructed according to the self-learned PL model and the extracted knowledge of radiation sources.Simulations show that the proposed 3D spectrum map reconstruction scheme not only has splendid adaptability to the environment,but also achieves high spectrum construction accuracy even when the sampling rate is very low.
