An LPDTS(υ) is a collection of 3(υ - 2) disjoint pure directed triple systems on the same set of υ elements. It is showed in Tian's doctoral thesis that there exists an LPDTS(υ) for υ≡ 0,4 (mod 6), υ≥ 4. I...An LPDTS(υ) is a collection of 3(υ - 2) disjoint pure directed triple systems on the same set of υ elements. It is showed in Tian's doctoral thesis that there exists an LPDTS(υ) for υ≡ 0,4 (mod 6), υ≥ 4. In this paper, we establish the existence of an LPDTS(υ) for υ≡ 1, 3 (mod 6), υ＞ 3. Thus the spectrum for LPDTS(υ) is completely determined to be the set {υ:υ≡0, 1 (mod 3),υ≥4}.展开更多
A directed triple system of order v, denoted by DTS(v, λ), is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to λ triples of B. An overlarg...A directed triple system of order v, denoted by DTS(v, λ), is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to λ triples of B. An overlarge set of disjoint DTS(v, λ), denoted by OLDTS(v, λ), is a collection {(Y\{y}, Ai)}i,such that Y is a (v + 1)-set, each (Y\{y}, Ai) is a DTS(v, λ) and all Ai's form a partition of all transitive triples of Y. In this paper, we shall discuss the existence problem of OLDTS(v, λ) and give the following conclusion: there exists an OLDTS(v, λ) if and only if either λ = 1 and v = 0, 1 (mod 3), or λ = 3 and v≠2.展开更多
A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belon...A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to A triples of B. An overlarge set of disjoint HTS（v, λ）, denoted by OLHTS（v, λ）, is a collection {（Y／{y}, .Ai）}i, such that Y is a （v ＋ 1）-set, each （Y／{y}, Ai） is an HTS（v, λ,） and all Ais form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS（v, A） and give the following conclusion： there exists an OLHTS（v, λ） if and only if λ= 1, 2, 4, v = 0, 1 （rood 3） and v ≥ 4.展开更多
A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） ...A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） （X,B） is called pure and denoted by PMTS（v） if （x, y, z） ∈ B implies （z, y, x） ∈B. A large set of MTS（v）s （LMTS（v）） is a collection of v - 2 pairwise disjoint MTS（v）s on a v-set. A self-converse large set of PMTS（v）s, denoted by LPMTS＊ （v）, is an LMTS（v） containing [ v-2/2] converse pairs of PMTS（v）s. In this paper, some results about the existence and non-existence for LPMTS＊ （v） are obtained.展开更多
Abstract A t-hyperwhesl （t 〉 3） of length l （or Wz（t） for brevity） is a t-uniform hypergraph （V, E）, where t E= {e1,e2,...,el} and vl,v2,...,vt are distinct vertices of V = Ui=1 ei such that for i= 1,...,1, ...Abstract A t-hyperwhesl （t 〉 3） of length l （or Wz（t） for brevity） is a t-uniform hypergraph （V, E）, where t E= {e1,e2,...,el} and vl,v2,...,vt are distinct vertices of V = Ui=1 ei such that for i= 1,...,1, vi,vi＋1 ∈ei and ei ∩ ej = P, j ∈ {i - 1, i,i ＋ 1}, where the operation on the subscripts is modulo 1 and P is a vertex of V which is different from vi, 1 〈 i 〈 l. In this paper, the minimum covering problem of MCλ（3, W（3）,v） is investigated. Direct and recursive constructions on MCλ（3, W（3）,v） are presented. The covering number cλ（3, W4（3）, v） is finally determined for any positive integers v 〉 5 and A.展开更多
A directed triple system of order v,denoted by DTS(v),is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of B.A DTS(v) (...A directed triple system of order v,denoted by DTS(v),is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of B.A DTS(v) (X,A) is called pure and denoted by PDTS(v) if (a,b,c) ∈ A implies (c,b,a) ∈/ A.An overlarge set of PDTS(v),denoted by OLPDTS(v),is a collection {(Y \{yi},Aij) : yi ∈ Y,j ∈ Z3},where Y is a (v+1)-set,each (Y \{yi},Aij) is a PDTS(v) and these Ais form a partition of all transitive triples on Y .In this paper,we shall discuss the existence problem of OLPDTS(v) and give the following conclusion: there exists an OLPDTS(v) if and only if v ≡ 0,1 (mod 3) and v 】 3.展开更多
Let H and J1 be both t-uniform hypergraphs. Let J2 be a sub-hypergraph of J1. In this paper, the metamorphosis of a hypergraph decomposition is introduced, denoted by (H, J1 】 J2)-design, which is a generalization of...Let H and J1 be both t-uniform hypergraphs. Let J2 be a sub-hypergraph of J1. In this paper, the metamorphosis of a hypergraph decomposition is introduced, denoted by (H, J1 】 J2)-design, which is a generalization of the concept of metamorphosis of a graph decomposition. Let Meta(J1】J2) denote the set of all integers v such that there exists a (Kv((3)), J1】J2)-design. We completely determine the set Meta(K4((3))】K4((3))-e).展开更多
A family (X, B1), (X, B2), . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and d...A family (X, B1), (X, B2), . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ (v) contained in the collection for any λ 【 λ. In 1995, Griggs and Rosa posed a problem: For which values of λ 】 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2, 3, 4 and v ≡ 1, 3 (mod 6).展开更多
A family （X, B1）,（X, B2）,..., （X, Bq） of q STS（v）s is a λ-fold large set of STS（v） and denoted by LSTSλ（v） if every 3-subset of X is contained in exactly A STS（v）s of the collection. It is indecomposab...A family （X, B1）,（X, B2）,..., （X, Bq） of q STS（v）s is a λ-fold large set of STS（v） and denoted by LSTSλ（v） if every 3-subset of X is contained in exactly A STS（v）s of the collection. It is indecomposable and denoted by IDLSTSx（v） if there does not exist an LSTSx, （v） contained in the collection for any λ 〈 λ. In this paper, we show that for λ = 5, 6, there is an IDLSTSλ（v） for v ≡ 1 or 3 （rood 6） with the exception IDLSTS6（7）.展开更多
This research provides an exploration of a biomimetic approach in the process of designing a candelabra model using linear shaped leaves of a Bell flower.The design process described in this research contains two step...This research provides an exploration of a biomimetic approach in the process of designing a candelabra model using linear shaped leaves of a Bell flower.The design process described in this research contains two steps:biological and geometrical.In the first biological step,a proper model for the creation of an urban element was found from nature in a Bell flower(Campanula persicifolia L.).The upper leaves of the selected plant,which are small with a linear spear and sharpening at the top,were chosen for the modeling process.The second step included applying two geometrical methods,i.e.,Voronoi diagrams and Delaunay triangulation.A geometrical leaf form of the selected plant species and the modeling process were obtained using aparametric modeling software,Blender.Using different Blender plug-ins and modifiers,Delaunay triangulation and Voronoi diagram were implemented by marking the starting points on the leaf form in the image data source,adjusting the Delaunay triangulation parameters,and creating Voronoi diagrams in which the Voronoi points were located at the shortest distance from the edges of the Voronoi polygon.Consequently,a three dimensional model of a candelabra was developed through this study.展开更多
Collecting silver artefacts has traditionally been a very popular hobby.Silver is addictive,therefore the number of potential collectors and investors appears to grow each year.Unfortunately,increases in the interest ...Collecting silver artefacts has traditionally been a very popular hobby.Silver is addictive,therefore the number of potential collectors and investors appears to grow each year.Unfortunately,increases in the interest and buying potentials resulted in a number of forgeries manufactured and introduced to the open antique market.The items such as early silver candlesticks dictate a very high price,for many high quality fakes show very good appearances and matching similarities with originals.Such copies are traditionally manufactured by casting using the original items as patterns.Small details and variances in design features,position and shape of hallmarks,including the final surface quality are usual features to distinguish the fakes from the originals.This paper presents results of a study conducted on several silver candlesticks,including two artefacts bearing features of those produced in the mid 18th century,one original Italian candelabrum from Fascist era,and small candlesticks made in the early 20th century.Also,the paper presents some interesting contemporary coins-replicas of many those produced in different countries.The coins were offered for sale by unscrupulous dealers via auctions and e-bays.Finally the main results and findings from this study are discussed from a manufacturing point of view,such as fabrication technology,surface quality and hallmarks,which will help the collectors,dealers and investors to detect and avoid forgeries.展开更多
In this paper,we investigate a generalization of graph decomposition,called hypergraph decomposition.We show that a decomposition of a 3-uniform hypergraph K_v^(3)into a special kind of hypergraph K_4^(3)-e exists if ...In this paper,we investigate a generalization of graph decomposition,called hypergraph decomposition.We show that a decomposition of a 3-uniform hypergraph K_v^(3)into a special kind of hypergraph K_4^(3)-e exists if and only if v≡0,1,2(mod 9)and v≥9.展开更多
A t-hyperwheel(t≥3) of length l(or W l(t) for brevity) is a t-uniform hypergraph(V,E) ,where E = {e1,e2,. . .,el} and v1,v2,. . .,vl are distinct vertices of V = il=1 ei such that for i = 1,. . .,l,vi,vi+1 ∈ ei and ...A t-hyperwheel(t≥3) of length l(or W l(t) for brevity) is a t-uniform hypergraph(V,E) ,where E = {e1,e2,. . .,el} and v1,v2,. . .,vl are distinct vertices of V = il=1 ei such that for i = 1,. . .,l,vi,vi+1 ∈ ei and ei ∩ ej = P,j ∈/{i-1,i,i + 1},where the operation on the subscripts is modulo l and P is a vertex of V which is different from vi,1 i l. In this paper,we investigate the maximum packing problem of MPλ(3,W 4( 3) ,v) . Finally,the packing number Dλ(3,W 4( 3) ,v) is determined for any positive integers v 5 and λ.展开更多
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10371002)the Tianyuan Mathematics Foundation of the National Natural Science Foundation of China(Grant No.10526032)the Natural Science Foundation of Universities of Jiangsu Province(Grant No.05KJB110111).
文摘An LPDTS(υ) is a collection of 3(υ - 2) disjoint pure directed triple systems on the same set of υ elements. It is showed in Tian's doctoral thesis that there exists an LPDTS(υ) for υ≡ 0,4 (mod 6), υ≥ 4. In this paper, we establish the existence of an LPDTS(υ) for υ≡ 1, 3 (mod 6), υ＞ 3. Thus the spectrum for LPDTS(υ) is completely determined to be the set {υ:υ≡0, 1 (mod 3),υ≥4}.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10671055)Tianyuan Mathematics Foundation of NSFC(Grant No.10526032)the Natural Science Foundation of Universities of Jiangsu Province(Grant No.05KJB110111)
文摘A directed triple system of order v, denoted by DTS(v, λ), is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to λ triples of B. An overlarge set of disjoint DTS(v, λ), denoted by OLDTS(v, λ), is a collection {(Y\{y}, Ai)}i,such that Y is a (v + 1)-set, each (Y\{y}, Ai) is a DTS(v, λ) and all Ai's form a partition of all transitive triples of Y. In this paper, we shall discuss the existence problem of OLDTS(v, λ) and give the following conclusion: there exists an OLDTS(v, λ) if and only if either λ = 1 and v = 0, 1 (mod 3), or λ = 3 and v≠2.
基金Supported by the National Natural Science Foundation of China(No.10971051 and 11071056)
文摘A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to A triples of B. An overlarge set of disjoint HTS（v, λ）, denoted by OLHTS（v, λ）, is a collection {（Y／{y}, .Ai）}i, such that Y is a （v ＋ 1）-set, each （Y／{y}, Ai） is an HTS（v, λ,） and all Ais form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS（v, A） and give the following conclusion： there exists an OLHTS（v, λ） if and only if λ= 1, 2, 4, v = 0, 1 （rood 3） and v ≥ 4.
基金Supported by National Natural Science Foundation of China (Grant No.10771051)
文摘A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） （X,B） is called pure and denoted by PMTS（v） if （x, y, z） ∈ B implies （z, y, x） ∈B. A large set of MTS（v）s （LMTS（v）） is a collection of v - 2 pairwise disjoint MTS（v）s on a v-set. A self-converse large set of PMTS（v）s, denoted by LPMTS＊ （v）, is an LMTS（v） containing [ v-2/2] converse pairs of PMTS（v）s. In this paper, some results about the existence and non-existence for LPMTS＊ （v） are obtained.
基金Supported by the National Natural Science Foundation of China (No.10771013 and 10831002)
文摘Abstract A t-hyperwhesl （t 〉 3） of length l （or Wz（t） for brevity） is a t-uniform hypergraph （V, E）, where t E= {e1,e2,...,el} and vl,v2,...,vt are distinct vertices of V = Ui=1 ei such that for i= 1,...,1, vi,vi＋1 ∈ei and ei ∩ ej = P, j ∈ {i - 1, i,i ＋ 1}, where the operation on the subscripts is modulo 1 and P is a vertex of V which is different from vi, 1 〈 i 〈 l. In this paper, the minimum covering problem of MCλ（3, W（3）,v） is investigated. Direct and recursive constructions on MCλ（3, W（3）,v） are presented. The covering number cλ（3, W4（3）, v） is finally determined for any positive integers v 〉 5 and A.
基金supported by National Natural Science Foundation of China (Grant No.10971051)Natural Science Foundation of Hebei Province,China (Grant No.A2010000353)
文摘A directed triple system of order v,denoted by DTS(v),is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of B.A DTS(v) (X,A) is called pure and denoted by PDTS(v) if (a,b,c) ∈ A implies (c,b,a) ∈/ A.An overlarge set of PDTS(v),denoted by OLPDTS(v),is a collection {(Y \{yi},Aij) : yi ∈ Y,j ∈ Z3},where Y is a (v+1)-set,each (Y \{yi},Aij) is a PDTS(v) and these Ais form a partition of all transitive triples on Y .In this paper,we shall discuss the existence problem of OLPDTS(v) and give the following conclusion: there exists an OLPDTS(v) if and only if v ≡ 0,1 (mod 3) and v 】 3.
基金supported by National Natural Science Foundation of China (Grant Nos.10771013, 10901016) and by Prin, Pra and Indam (GNSAGA)
文摘Let H and J1 be both t-uniform hypergraphs. Let J2 be a sub-hypergraph of J1. In this paper, the metamorphosis of a hypergraph decomposition is introduced, denoted by (H, J1 】 J2)-design, which is a generalization of the concept of metamorphosis of a graph decomposition. Let Meta(J1】J2) denote the set of all integers v such that there exists a (Kv((3)), J1】J2)-design. We completely determine the set Meta(K4((3))】K4((3))-e).
基金supported by National Natural Science Foundation of China (Grant Nos.10971051, 10701060, 10831002)Qing Lan Project of Jiangsu Province, China
文摘A family (X, B1), (X, B2), . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ (v) contained in the collection for any λ 【 λ. In 1995, Griggs and Rosa posed a problem: For which values of λ 】 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2, 3, 4 and v ≡ 1, 3 (mod 6).
基金Supported by National Natural Science Foundation of China (Grant Nos. 10971051 and 11071056)
文摘A family （X, B1）,（X, B2）,..., （X, Bq） of q STS（v）s is a λ-fold large set of STS（v） and denoted by LSTSλ（v） if every 3-subset of X is contained in exactly A STS（v）s of the collection. It is indecomposable and denoted by IDLSTSx（v） if there does not exist an LSTSx, （v） contained in the collection for any λ 〈 λ. In this paper, we show that for λ = 5, 6, there is an IDLSTSλ（v） for v ≡ 1 or 3 （rood 6） with the exception IDLSTS6（7）.
基金The Ministry of Education,Science and Technological Development of the Republic of Serbia,No.TP 36008(451–02-68/2020/14/2000169).
文摘This research provides an exploration of a biomimetic approach in the process of designing a candelabra model using linear shaped leaves of a Bell flower.The design process described in this research contains two steps:biological and geometrical.In the first biological step,a proper model for the creation of an urban element was found from nature in a Bell flower(Campanula persicifolia L.).The upper leaves of the selected plant,which are small with a linear spear and sharpening at the top,were chosen for the modeling process.The second step included applying two geometrical methods,i.e.,Voronoi diagrams and Delaunay triangulation.A geometrical leaf form of the selected plant species and the modeling process were obtained using aparametric modeling software,Blender.Using different Blender plug-ins and modifiers,Delaunay triangulation and Voronoi diagram were implemented by marking the starting points on the leaf form in the image data source,adjusting the Delaunay triangulation parameters,and creating Voronoi diagrams in which the Voronoi points were located at the shortest distance from the edges of the Voronoi polygon.Consequently,a three dimensional model of a candelabra was developed through this study.
文摘Collecting silver artefacts has traditionally been a very popular hobby.Silver is addictive,therefore the number of potential collectors and investors appears to grow each year.Unfortunately,increases in the interest and buying potentials resulted in a number of forgeries manufactured and introduced to the open antique market.The items such as early silver candlesticks dictate a very high price,for many high quality fakes show very good appearances and matching similarities with originals.Such copies are traditionally manufactured by casting using the original items as patterns.Small details and variances in design features,position and shape of hallmarks,including the final surface quality are usual features to distinguish the fakes from the originals.This paper presents results of a study conducted on several silver candlesticks,including two artefacts bearing features of those produced in the mid 18th century,one original Italian candelabrum from Fascist era,and small candlesticks made in the early 20th century.Also,the paper presents some interesting contemporary coins-replicas of many those produced in different countries.The coins were offered for sale by unscrupulous dealers via auctions and e-bays.Finally the main results and findings from this study are discussed from a manufacturing point of view,such as fabrication technology,surface quality and hallmarks,which will help the collectors,dealers and investors to detect and avoid forgeries.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10371002)
文摘In this paper,we investigate a generalization of graph decomposition,called hypergraph decomposition.We show that a decomposition of a 3-uniform hypergraph K_v^(3)into a special kind of hypergraph K_4^(3)-e exists if and only if v≡0,1,2(mod 9)and v≥9.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771013, 10831002)
文摘A t-hyperwheel(t≥3) of length l(or W l(t) for brevity) is a t-uniform hypergraph(V,E) ,where E = {e1,e2,. . .,el} and v1,v2,. . .,vl are distinct vertices of V = il=1 ei such that for i = 1,. . .,l,vi,vi+1 ∈ ei and ei ∩ ej = P,j ∈/{i-1,i,i + 1},where the operation on the subscripts is modulo l and P is a vertex of V which is different from vi,1 i l. In this paper,we investigate the maximum packing problem of MPλ(3,W 4( 3) ,v) . Finally,the packing number Dλ(3,W 4( 3) ,v) is determined for any positive integers v 5 and λ.
