In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic top...In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset.展开更多
In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets a...In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are:(1) A uniform complete poset L is meet uniform continuous iff ↑(U∩↓x) is a uniform Scott set for each x∈L and each uniform Scott set U;(2) A uniform complete poset L is meet uniform continuous iff for each x∈L and each uniform subset S, one has x∧∨ S =∨{x∧s|s∈S}. In particular, a complete lattice L is meet uniform continuous iff L is a complete Heyting algebra;(3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous;(4) A uniform complete poset L is meet uniform continuous if L1 obtained by adjoining a top element 1 to L is a complete Heyting algebra;(5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous.展开更多
A new concept Graded Finite Poset is proposed in this paper. Through discussing some basic properties of it, we come to that the direct product of graded finite posets is connected if and only if every graded finite p...A new concept Graded Finite Poset is proposed in this paper. Through discussing some basic properties of it, we come to that the direct product of graded finite posets is connected if and only if every graded finite poset is connected. The graded function of a graded finite poset is unique if and only if the graded finite poset is connected.展开更多
Let X,Y be any posets,the semimodularity of cardinal power Yx with base Y and exponent X is studied. Some necessary or sufficient conditions for Yx to be semimodular are gaven,
The free object generated by a set in the category of complete L-fuzzy posets is discussed in this paper. The construction of a free complete L-fuzzy poset generated by a set is obtained, which is a generalization of ...The free object generated by a set in the category of complete L-fuzzy posets is discussed in this paper. The construction of a free complete L-fuzzy poset generated by a set is obtained, which is a generalization of the free complete lattice generated by a set.展开更多
A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. ...A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. Firstly, by associativity and the unitary property, we prove that the vector space with the conjunction product is a graded algebra. Then by the definition of free algebra, we prove that the algebra is free. Finally, by the coassociativity and the counitary property, we prove that the vector space with the unshuffle coproduct is a graded coalgebra.展开更多
Many research issues have been raised in Application Layer Multicasting(ALM),such as group management,security,integrity of data,link stress,link stretch,load balancing,fault tolerance and scalability,because of the s...Many research issues have been raised in Application Layer Multicasting(ALM),such as group management,security,integrity of data,link stress,link stretch,load balancing,fault tolerance and scalability,because of the shifting of the multicast protocol from the IP layer to the application layer.To address these issues many protocols have evolved by changing their topology structure.In this paper,the POSET protocol stack is proposed,which consists of three layers,such as communication control,POSET cube,and content distribution.The novelty of this paper is the lattice-based data distribution with POSET cube architecture.The results have been compared with the existing NICE and Narada protocols.The experimental results show that the proposed POSET protocol improves throughput between 7.14%and 40%and decreases the delay between 7.69%and 25%,compared to the existing NICE protocol.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1167100811101212)the University Science Research Project of Jiangsu Province(Grant No.15KJD110006)
文摘In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671008 11101212)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20170483)the Fund of University Speciality Construction of Jiangsu Province(Grant No.PPZY2015B109)
文摘In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are:(1) A uniform complete poset L is meet uniform continuous iff ↑(U∩↓x) is a uniform Scott set for each x∈L and each uniform Scott set U;(2) A uniform complete poset L is meet uniform continuous iff for each x∈L and each uniform subset S, one has x∧∨ S =∨{x∧s|s∈S}. In particular, a complete lattice L is meet uniform continuous iff L is a complete Heyting algebra;(3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous;(4) A uniform complete poset L is meet uniform continuous if L1 obtained by adjoining a top element 1 to L is a complete Heyting algebra;(5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous.
基金Supported by the National Natural Science Foundation of China（60474022） Supported by the Henan Innovation Project for University Prominent Research Talents（2007KYCX018）
文摘A new concept Graded Finite Poset is proposed in this paper. Through discussing some basic properties of it, we come to that the direct product of graded finite posets is connected if and only if every graded finite poset is connected. The graded function of a graded finite poset is unique if and only if the graded finite poset is connected.
文摘Let X,Y be any posets,the semimodularity of cardinal power Yx with base Y and exponent X is studied. Some necessary or sufficient conditions for Yx to be semimodular are gaven,
文摘The free object generated by a set in the category of complete L-fuzzy posets is discussed in this paper. The construction of a free complete L-fuzzy poset generated by a set is obtained, which is a generalization of the free complete lattice generated by a set.
文摘A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. Firstly, by associativity and the unitary property, we prove that the vector space with the conjunction product is a graded algebra. Then by the definition of free algebra, we prove that the algebra is free. Finally, by the coassociativity and the counitary property, we prove that the vector space with the unshuffle coproduct is a graded coalgebra.
基金supported by the university Grants Commission,New Delhi,India
文摘Many research issues have been raised in Application Layer Multicasting(ALM),such as group management,security,integrity of data,link stress,link stretch,load balancing,fault tolerance and scalability,because of the shifting of the multicast protocol from the IP layer to the application layer.To address these issues many protocols have evolved by changing their topology structure.In this paper,the POSET protocol stack is proposed,which consists of three layers,such as communication control,POSET cube,and content distribution.The novelty of this paper is the lattice-based data distribution with POSET cube architecture.The results have been compared with the existing NICE and Narada protocols.The experimental results show that the proposed POSET protocol improves throughput between 7.14%and 40%and decreases the delay between 7.69%and 25%,compared to the existing NICE protocol.
