Supersaturated designs are factorial designs in which the number of main effects is greater than the number of experimental runs. In this paper, a discrete discrepancy is proposed as a measure of uniformity for supers...Supersaturated designs are factorial designs in which the number of main effects is greater than the number of experimental runs. In this paper, a discrete discrepancy is proposed as a measure of uniformity for supersaturated designs, and a lower bound of this discrepancy is obtained asa benchmark of design uniformity. A construction method for uniform supersaturated designs via resolvable balanced incomplete block designs is also presented along with the investigation of properties of the resulting designs. The construction method shows a strong link between these two different kinds of designs.展开更多
In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a trip...In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.展开更多
In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a...In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.展开更多
Ⅰ. INTRODUCTIONA triple system S<sub>λ</sub>（2, 3, v）is an ordered pair （V,）, where Vis a v-set, is a collection of 3-subsets （called triples ） of V such that each pair of distinct dements of V is ...Ⅰ. INTRODUCTIONA triple system S<sub>λ</sub>（2, 3, v）is an ordered pair （V,）, where Vis a v-set, is a collection of 3-subsets （called triples ） of V such that each pair of distinct dements of V is contained in exactly λ triples. An S<sub>2</sub>（2, 3, v）is called a twofold triple system.展开更多
The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference set D(2p.2p,p,2), where p is a prime or a prime power, ar...The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference set D(2p.2p,p,2), where p is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference set D(λ1p, k1, p, 2) and an orthogonal array(λ2p2, k2, p, 2) leads to another orthogonal array (λ1λ2p3 .k1k2+1 ,p, 2). This enables us to construct orthogonal arrays[2p(n+1)、1+2(p+p2 +…+pn),p,2],[4p(n+2),1+2p+4(p2+p3+…+p(n+1)),p, 2],and [8p(n+3),1+2P+4p2+8(p3+p4+…+p(n+2)),p,2]where p is a prime or a prime power.展开更多
The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical ind...The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).展开更多
Let X be the vertex set of Kn. A k-cycle packing of Kn is a triple （X, C, L）, where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C....Let X be the vertex set of Kn. A k-cycle packing of Kn is a triple （X, C, L）, where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C. A k-cycle packing （X, C, L） is called resolvable if C can be partitioned into almost parallel classes. A resolvable maximum k-cycle packing of Kn, denoted by k-RMCP（n）, is a resolvable k-cycle packing of Kn, （X, C, L）, in which the number of almost parallel classes is as large as possible. Let D（n, k） denote the number of almost parallel classes in a k-RMCP（n）. D（n, k） for k = 3, 4 has been decided. When n ≡ k （mod 2k） and k ≡1 （mod 2） or n ≡1 （mod 2k） and k e {6, 8, 10, 14} U{m： 5 ≤ m ≤ 49, m ≡1 （mod 2）}, D（n,k） also has been decided with few possible exceptions. In this paper, we shall decide D（n, 5） for all values of n ≥ 5.展开更多
A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in ...A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.展开更多
It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman s...It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman system NKS (2,4; v ) if and only if v ≡0 (mod 12) and v ≥24, except possibly when v =264 or 372.展开更多
This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.
Since we find out that the global spectral model with trapezoidal truncation has higher resolution in high latitudes(polar cap)than in low latitudes,this paper presents a global spectral model with variable poles whic...Since we find out that the global spectral model with trapezoidal truncation has higher resolution in high latitudes(polar cap)than in low latitudes,this paper presents a global spectral model with variable poles which can be located at the center of interested area.The transform methods from traditional global spectral model to the new model are given and applied to a shallow-water equation model.The control ex- periments for 72h predictions were carried out.The“northern pole”in the transformed model was located at 15°N,135°E.And the results showed that the predictions of weather systems in the area around the“new pole”(the polar cap,latitudes >60°)were better than those by the traditional model and the root mean square errors were improved.展开更多
Reasoning with inconsistent ontologies involves using an inconsistency reasoner to get meaningful answers from inconsistent ontologies. This paper introduces an improved inconsistency reasoner, which selects consisten...Reasoning with inconsistent ontologies involves using an inconsistency reasoner to get meaningful answers from inconsistent ontologies. This paper introduces an improved inconsistency reasoner, which selects consistent subsets using minimal inconsistent sets and a resolution method, to improve the run-time performance of the reasoning processing. A minimal inconsistent set contains a minimal explanation for the inconsistency of a given ontology. Thus, it can replace the consistency checking operation, which is executed frequently in existing approaches. When selecting subsets of the inconsistent ontology, formulas which can be directly or indirectly resolved with the negation of the query formula are selected because only those formulas affect the consequences of the reasoner. Therefore, the complexity of the reasoning processing is significantly reduced. Tests show that the run-time performance of the inconsistency reasoner is significantly improved.展开更多
Let k be any integer and k≥3. In this article it is proved that the necessary condition υ=k (mod k(k-1)) for the existence of an RB(v,k,1) is sufficient whenever u>exp{exp{k12k2}}.
An m-cycle system of order v and index λ, denoted by m-CS(v,λ), is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS(v,λ) is α-resolvable if its cycles can be partitioned into cla...An m-cycle system of order v and index λ, denoted by m-CS(v,λ), is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS(v,λ) is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m|λv(v-1)/2,2|λ(v -1),m|αv,α|λ(v-1)/2. It is shown in this paper that these conditions are also sufficient when m = 4.展开更多
基金This work was partially supported by the Hong Kong RGC (HKUB RC/98-99/Gen-370) the YNSFC (10001026) the National Natural Science Foundation of China (Grant No. 10171051). Theresearch was carried out while the last two authors were visiting Hong Kong Ba
文摘Supersaturated designs are factorial designs in which the number of main effects is greater than the number of experimental runs. In this paper, a discrete discrepancy is proposed as a measure of uniformity for supersaturated designs, and a lower bound of this discrepancy is obtained asa benchmark of design uniformity. A construction method for uniform supersaturated designs via resolvable balanced incomplete block designs is also presented along with the investigation of properties of the resulting designs. The construction method shows a strong link between these two different kinds of designs.
文摘In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.
基金the National Natural Science Foundation of China(No.10671055)Natural Science Foundation of Hebei(No.A2007000230)
文摘In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONA triple system S<sub>λ</sub>（2, 3, v）is an ordered pair （V,）, where Vis a v-set, is a collection of 3-subsets （called triples ） of V such that each pair of distinct dements of V is contained in exactly λ triples. An S<sub>2</sub>（2, 3, v）is called a twofold triple system.
文摘The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference set D(2p.2p,p,2), where p is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference set D(λ1p, k1, p, 2) and an orthogonal array(λ2p2, k2, p, 2) leads to another orthogonal array (λ1λ2p3 .k1k2+1 ,p, 2). This enables us to construct orthogonal arrays[2p(n+1)、1+2(p+p2 +…+pn),p,2],[4p(n+2),1+2p+4(p2+p3+…+p(n+1)),p, 2],and [8p(n+3),1+2P+4p2+8(p3+p4+…+p(n+2)),p,2]where p is a prime or a prime power.
文摘The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).
文摘Let X be the vertex set of Kn. A k-cycle packing of Kn is a triple （X, C, L）, where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C. A k-cycle packing （X, C, L） is called resolvable if C can be partitioned into almost parallel classes. A resolvable maximum k-cycle packing of Kn, denoted by k-RMCP（n）, is a resolvable k-cycle packing of Kn, （X, C, L）, in which the number of almost parallel classes is as large as possible. Let D（n, k） denote the number of almost parallel classes in a k-RMCP（n）. D（n, k） for k = 3, 4 has been decided. When n ≡ k （mod 2k） and k ≡1 （mod 2） or n ≡1 （mod 2k） and k e {6, 8, 10, 14} U{m： 5 ≤ m ≤ 49, m ≡1 （mod 2）}, D（n,k） also has been decided with few possible exceptions. In this paper, we shall decide D（n, 5） for all values of n ≥ 5.
基金supported by National Natural Science Foundation of China (Grant Nos.10771051,10831002)
文摘A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.
文摘It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman system NKS (2,4; v ) if and only if v ≡0 (mod 12) and v ≥24, except possibly when v =264 or 372.
文摘This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.
文摘Since we find out that the global spectral model with trapezoidal truncation has higher resolution in high latitudes(polar cap)than in low latitudes,this paper presents a global spectral model with variable poles which can be located at the center of interested area.The transform methods from traditional global spectral model to the new model are given and applied to a shallow-water equation model.The control ex- periments for 72h predictions were carried out.The“northern pole”in the transformed model was located at 15°N,135°E.And the results showed that the predictions of weather systems in the area around the“new pole”(the polar cap,latitudes >60°)were better than those by the traditional model and the root mean square errors were improved.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education of MOE, P.R.C (No.20096102120037)
文摘Reasoning with inconsistent ontologies involves using an inconsistency reasoner to get meaningful answers from inconsistent ontologies. This paper introduces an improved inconsistency reasoner, which selects consistent subsets using minimal inconsistent sets and a resolution method, to improve the run-time performance of the reasoning processing. A minimal inconsistent set contains a minimal explanation for the inconsistency of a given ontology. Thus, it can replace the consistency checking operation, which is executed frequently in existing approaches. When selecting subsets of the inconsistent ontology, formulas which can be directly or indirectly resolved with the negation of the query formula are selected because only those formulas affect the consequences of the reasoner. Therefore, the complexity of the reasoning processing is significantly reduced. Tests show that the run-time performance of the inconsistency reasoner is significantly improved.
基金the National Natural Science Foundation of China (No.19701002) HuoYingdong Foundation.
文摘Let k be any integer and k≥3. In this article it is proved that the necessary condition υ=k (mod k(k-1)) for the existence of an RB(v,k,1) is sufficient whenever u>exp{exp{k12k2}}.
基金the National Natural Science Foundation of China (No.10971051)
文摘An m-cycle system of order v and index λ, denoted by m-CS(v,λ), is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS(v,λ) is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m|λv(v-1)/2,2|λ(v -1),m|αv,α|λ(v-1)/2. It is shown in this paper that these conditions are also sufficient when m = 4.
