Let Cnk denote the set of all t -subsets of an n -set. Assume A ∈ Cnk and B∈Cn.b (A,B) is called a cross-2-intersecting family if |A∩B|≥2 for any A∈A, B∈B.In this paper, the best upper bounds of the cardinalitie...Let Cnk denote the set of all t -subsets of an n -set. Assume A ∈ Cnk and B∈Cn.b (A,B) is called a cross-2-intersecting family if |A∩B|≥2 for any A∈A, B∈B.In this paper, the best upper bounds of the cardinalities for non-empty cross-2-intersecting families of a- and i- subsets are obtained for some n and b . A new proof for a Frankl-Tokushige theorem [6] is also given.展开更多
Let n, s1,s2, and sn be positive integers. Assume M(s1 s2,,sn)={(x1,x2,... ,xn)|0≤xi≤si, xi is an integer for each i}.For a=(a1,a2,....,an)∈M(s1,s2,...,sn.),M(s1,s2,....,sn.), and A{1,2,..,n}, denote sp(a)={j |1≤ ...Let n, s1,s2, and sn be positive integers. Assume M(s1 s2,,sn)={(x1,x2,... ,xn)|0≤xi≤si, xi is an integer for each i}.For a=(a1,a2,....,an)∈M(s1,s2,...,sn.),M(s1,s2,....,sn.), and A{1,2,..,n}, denote sp(a)={j |1≤ j≤n, aj≥p}, Sp(r)={sp(a) |aam}, and WP(A)=P(si-p).Fis called an I-intersecting family if, for any a,6eF, a.Abi=min(ai,6i)>p for at least t i'8. F iscalled a greedy Ir-illtersecting flaily if F is an Ir-intersecting family and WP(A)ZWr(B+A') forany ASp and any BOA with B=t-1.In this paper, we obtain a sharp upper bound of for greedy Ir-intersecting families inM(sl,s2Z,'',sn.) for the case 2p5B' (IBIds) and 81 >BZ >...>B..展开更多
In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski...In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski type inequalities of general Lp-intersection bodies for dual quermassintegrals, respectively. As applications, inequalities of volume are derived.展开更多
9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB int...9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB into point-set topology problem in terms of the intersections ofA’s boundary (?A), interior (A 0) and (A ?) withB’s boundary (?B), interior (B 0) and exterior (B ?). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object’s exterior as its complement, and it is difficult to distinguish different disjoint relations and relations between complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements (?A∩B ?,A 0∩?B ?,A ?∩?B,A ?∩B 0 andA ?∩B ?)since the complements are infinitive. The authors suggest to re-define the exterior of spatial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-intersection (VNI) is proposed and used for formalizing topological relations between spatial bojects. By improving the 9-intersection model, it is now possible to distinguish disjoint relations and to deal with objects with holes. Also it is possible to compute the exterior-based intersections and manipulate spatial relations with the VNI.展开更多
In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed inter...In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.展开更多
There is growing interest in globally modelling the entire planet.Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigate...There is growing interest in globally modelling the entire planet.Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigated,few studies have focused on the topological relations between spherical spatial regions with holes.The 16-intersection model(16IM)is proposed to describe the topological relations between spatial regions with holes.A total of 25 negative conditions are proposed to eliminate the impossible topological relations between spherical spatial regions with holes.The results show that(1)3 disjoint relations,3 meet relations,66 overlap relations,7 cover relations,3 contain relations,1 equal relation,7 coveredBy relations,3 inside relations,1 attach relation,52 entwined relations,and 28 embrace relations can be distinguished by the 16IM and that(2)the formalisms of attach,entwined,and embrace relations between the spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on the simplified 16IM are different,whereas the formalisms of other types of relations between spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on a simplified 16IM are the same.展开更多
基金Suppored by Postdoctral Fellowship Foundation of China
文摘Let Cnk denote the set of all t -subsets of an n -set. Assume A ∈ Cnk and B∈Cn.b (A,B) is called a cross-2-intersecting family if |A∩B|≥2 for any A∈A, B∈B.In this paper, the best upper bounds of the cardinalities for non-empty cross-2-intersecting families of a- and i- subsets are obtained for some n and b . A new proof for a Frankl-Tokushige theorem [6] is also given.
文摘Let n, s1,s2, and sn be positive integers. Assume M(s1 s2,,sn)={(x1,x2,... ,xn)|0≤xi≤si, xi is an integer for each i}.For a=(a1,a2,....,an)∈M(s1,s2,...,sn.),M(s1,s2,....,sn.), and A{1,2,..,n}, denote sp(a)={j |1≤ j≤n, aj≥p}, Sp(r)={sp(a) |aam}, and WP(A)=P(si-p).Fis called an I-intersecting family if, for any a,6eF, a.Abi=min(ai,6i)>p for at least t i'8. F iscalled a greedy Ir-illtersecting flaily if F is an Ir-intersecting family and WP(A)ZWr(B+A') forany ASp and any BOA with B=t-1.In this paper, we obtain a sharp upper bound of for greedy Ir-intersecting families inM(sl,s2Z,'',sn.) for the case 2p5B' (IBIds) and 81 >BZ >...>B..
基金the National Natural Science Foundation of China(11371224)the Innovation Foundation of Graduate Student of China Three Gorges University(2019SSPY146)。
文摘In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski type inequalities of general Lp-intersection bodies for dual quermassintegrals, respectively. As applications, inequalities of volume are derived.
基金Project supported by the National Natural Science Foundation of China(No.49471059)
文摘9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB into point-set topology problem in terms of the intersections ofA’s boundary (?A), interior (A 0) and (A ?) withB’s boundary (?B), interior (B 0) and exterior (B ?). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object’s exterior as its complement, and it is difficult to distinguish different disjoint relations and relations between complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements (?A∩B ?,A 0∩?B ?,A ?∩?B,A ?∩B 0 andA ?∩B ?)since the complements are infinitive. The authors suggest to re-define the exterior of spatial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-intersection (VNI) is proposed and used for formalizing topological relations between spatial bojects. By improving the 9-intersection model, it is now possible to distinguish disjoint relations and to deal with objects with holes. Also it is possible to compute the exterior-based intersections and manipulate spatial relations with the VNI.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065)the Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)
文摘In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.
基金This research was supported by the National Basic Research Program of China(973 Program)[No.2015CB954103]Priority Academic Program Development of Jiangsu Higher Education Institutions[No.164320H116].
文摘There is growing interest in globally modelling the entire planet.Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigated,few studies have focused on the topological relations between spherical spatial regions with holes.The 16-intersection model(16IM)is proposed to describe the topological relations between spatial regions with holes.A total of 25 negative conditions are proposed to eliminate the impossible topological relations between spherical spatial regions with holes.The results show that(1)3 disjoint relations,3 meet relations,66 overlap relations,7 cover relations,3 contain relations,1 equal relation,7 coveredBy relations,3 inside relations,1 attach relation,52 entwined relations,and 28 embrace relations can be distinguished by the 16IM and that(2)the formalisms of attach,entwined,and embrace relations between the spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on the simplified 16IM are different,whereas the formalisms of other types of relations between spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on a simplified 16IM are the same.
