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
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
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.
