Based on the conception of P(ρ,σ)-set(XP ˉFρ, XPFσ), this paper studied the relation between outer P(ρ,σ)-set and outer P-set: give outer P(ρ,σ)-set and outer P-set relation theorem, outer P(ρ,σ)-set and nu...Based on the conception of P(ρ,σ)-set(XP ˉFρ, XPFσ), this paper studied the relation between outer P(ρ,σ)-set and outer P-set: give outer P(ρ,σ)-set and outer P-set relation theorem, outer P(ρ,σ)-set and numerical value σ relation theorem, outer P(ρ,σ)-set's range;studied other characteristics of outer P(ρ,σ)-set: give the finiteness theorem of outer P(ρ,σ)-set, the set chain theorem of outer P(ρ,σ)-set, the outer P(ρ,σ)-set probability interval finite partition theorem, and its corollary; also give generation, reduction, identification theorem of outer P(ρ,σ)-set, filter generation theorem of outer P(ρ,σ)-set; finally give its application.展开更多
Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=N_(G)(H)B and for every Hall σ_(i)-subgroup B_(i) of B,there exists an element x∈B such that HB_(i)^(...Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=N_(G)(H)B and for every Hall σ_(i)-subgroup B_(i) of B,there exists an element x∈B such that HB_(i)^(x)=B_(i)^(x) H.In this paper,the influence of σ-c-propermutable subgroups on the structure of finite groups is investigated,and some criteria for a normal subgroup of G to be hypercyclically embedded in G are derived.展开更多
In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe th...In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe those spaces which have property (MB) . Also, we show that if a Banach space X has property (MB) and Banach space Y does not contain , then every operator is completely continuous.展开更多
An induced matching M in a graph G is a matching such that V(M) induces a 1-regular subgraph of G. The induced matching number of a graph G, denoted by I M(G), is the maximum number r such that G has an induced matchi...An induced matching M in a graph G is a matching such that V(M) induces a 1-regular subgraph of G. The induced matching number of a graph G, denoted by I M(G), is the maximum number r such that G has an induced matching of r edges. Induced matching number of Pm×Pn is investigated in this paper. The main results are as follows:(1) If at least one of m and n is even, then IM(Pm×Pn=[(mn)/4].(2) If m is odd, then展开更多
Let , and for any , . If is positive, then B is considered as a large set with . Its difference set has both high density and rich structure. The set with is also relatively large and it is a long standing conjecture ...Let , and for any , . If is positive, then B is considered as a large set with . Its difference set has both high density and rich structure. The set with is also relatively large and it is a long standing conjecture that like sets with positive upper density they have arithmetic progression of arbitrary length. Here we show their difference set may not be substantial;for any there exists such that and .展开更多
In this paper,we define the weighted embedded homology of super-hypergraphs,give a quasi-partial order and a pseudo-metric on the set made up of all non-vanishing weights on a finite set,and clarify the relationship b...In this paper,we define the weighted embedded homology of super-hypergraphs,give a quasi-partial order and a pseudo-metric on the set made up of all non-vanishing weights on a finite set,and clarify the relationship between the torsion parts of weighted embedded homology with integer coefficients of super-hypergraphs under certain weights.展开更多
In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study ...In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.展开更多
Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous m...Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.展开更多
Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and ...Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and H containsexactly one Hallσi-subgroup of G for every i such thatσi∩π(G)≠Ø.A subgroupA of G is said to be H-permutable if A permutes with all members of the completeHallσ-set H of G.In this paper,we study the structure of G under the assuming thatsome subgroups of G areσ-permutable.展开更多
A subset S V in a graph G =（V, E） is a total [1, 2]-set if, for every vertex v ∈ V, 1 ≤ ｜N（v）∩S｜ ≤2. The minimum cardinality of a total [1, 2]-set of G is called the total [1, 2]-domination number, denoted...A subset S V in a graph G =（V, E） is a total [1, 2]-set if, for every vertex v ∈ V, 1 ≤ ｜N（v）∩S｜ ≤2. The minimum cardinality of a total [1, 2]-set of G is called the total [1, 2]-domination number, denoted byγt[1,2]（G）.We establish two sharp upper bounds on the total [1,2]-domination number of a graph G in terms of its order and minimum degree, and characterize the corresponding extremal graphs achieving these bounds. Moreover,we give some sufficient conditions for a graph without total [1, 2]-set and for a graph with the same total[1, 2]-domination number, [1, 2]-domination number and domination number.展开更多
Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show ...Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.展开更多
It is well known that impredicative type systems do not have set theoretical semantics. This paper takes a look at semantics of inductive types in impredicative type systems. A generalized inductive type is interprete...It is well known that impredicative type systems do not have set theoretical semantics. This paper takes a look at semantics of inductive types in impredicative type systems. A generalized inductive type is interpreted as an omega set generated by effectivizing a certain rule set. The result provides a semantic justification of inductive types in the calculus of constructions.展开更多
基金Foundation item： Supported by the Basic and Frontier Technology Research Projects of Henan Province （132300410289） Supported by the Natural Science Foundation of Fujian Province（2012D112）
文摘Based on the conception of P(ρ,σ)-set(XP ˉFρ, XPFσ), this paper studied the relation between outer P(ρ,σ)-set and outer P-set: give outer P(ρ,σ)-set and outer P-set relation theorem, outer P(ρ,σ)-set and numerical value σ relation theorem, outer P(ρ,σ)-set's range;studied other characteristics of outer P(ρ,σ)-set: give the finiteness theorem of outer P(ρ,σ)-set, the set chain theorem of outer P(ρ,σ)-set, the outer P(ρ,σ)-set probability interval finite partition theorem, and its corollary; also give generation, reduction, identification theorem of outer P(ρ,σ)-set, filter generation theorem of outer P(ρ,σ)-set; finally give its application.
文摘Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=N_(G)(H)B and for every Hall σ_(i)-subgroup B_(i) of B,there exists an element x∈B such that HB_(i)^(x)=B_(i)^(x) H.In this paper,the influence of σ-c-propermutable subgroups on the structure of finite groups is investigated,and some criteria for a normal subgroup of G to be hypercyclically embedded in G are derived.
文摘In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe those spaces which have property (MB) . Also, we show that if a Banach space X has property (MB) and Banach space Y does not contain , then every operator is completely continuous.
文摘An induced matching M in a graph G is a matching such that V(M) induces a 1-regular subgraph of G. The induced matching number of a graph G, denoted by I M(G), is the maximum number r such that G has an induced matching of r edges. Induced matching number of Pm×Pn is investigated in this paper. The main results are as follows:(1) If at least one of m and n is even, then IM(Pm×Pn=[(mn)/4].(2) If m is odd, then
文摘Let , and for any , . If is positive, then B is considered as a large set with . Its difference set has both high density and rich structure. The set with is also relatively large and it is a long standing conjecture that like sets with positive upper density they have arithmetic progression of arbitrary length. Here we show their difference set may not be substantial;for any there exists such that and .
基金Supported by the Science and Technology Project of Hebei Education Department (ZD2022168)the Research and Innovation Team of Cang‐zhou Normal University (cxtdl2304)。
文摘In this paper,we define the weighted embedded homology of super-hypergraphs,give a quasi-partial order and a pseudo-metric on the set made up of all non-vanishing weights on a finite set,and clarify the relationship between the torsion parts of weighted embedded homology with integer coefficients of super-hypergraphs under certain weights.
文摘In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10471084)by Guangdong Provincial Natural Science Fundation(Grant No.04010985).
文摘Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.
基金a NNSF grant of China(Grant#11371335)Wu Wen-TsunKey Laboratory of Mathematics of Chinese Academy of Sciences.Research of the third author is supported by Chinese Academy of Sciences Visiting Professorship for Senior International Scientists(Grant No.2010T2J12).
文摘Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and H containsexactly one Hallσi-subgroup of G for every i such thatσi∩π(G)≠Ø.A subgroupA of G is said to be H-permutable if A permutes with all members of the completeHallσ-set H of G.In this paper,we study the structure of G under the assuming thatsome subgroups of G areσ-permutable.
基金Supported by the National Natural Science Foundation of China(No.11001269,No.11571294)
文摘A subset S V in a graph G =（V, E） is a total [1, 2]-set if, for every vertex v ∈ V, 1 ≤ ｜N（v）∩S｜ ≤2. The minimum cardinality of a total [1, 2]-set of G is called the total [1, 2]-domination number, denoted byγt[1,2]（G）.We establish two sharp upper bounds on the total [1,2]-domination number of a graph G in terms of its order and minimum degree, and characterize the corresponding extremal graphs achieving these bounds. Moreover,we give some sufficient conditions for a graph without total [1, 2]-set and for a graph with the same total[1, 2]-domination number, [1, 2]-domination number and domination number.
文摘Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.
基金This work is funded by the National Natural Science Foundation of China (No.69973030). It is alsosupported by BASICS, Center o
文摘It is well known that impredicative type systems do not have set theoretical semantics. This paper takes a look at semantics of inductive types in impredicative type systems. A generalized inductive type is interpreted as an omega set generated by effectivizing a certain rule set. The result provides a semantic justification of inductive types in the calculus of constructions.
