A proper vertex coloring of a graph G is acyclic if there is no bicolored cycles in G.A graph G is acyclically k-choosable if for any list assignment L={L(v):v∈V(G)}with|L(v)|≥k for each vertex v∈V(G),there exists ...A proper vertex coloring of a graph G is acyclic if there is no bicolored cycles in G.A graph G is acyclically k-choosable if for any list assignment L={L(v):v∈V(G)}with|L(v)|≥k for each vertex v∈V(G),there exists an acyclic proper vertex coloringφof G such thatφ(v)∈L(v)for each vertex v∈V(G).In this paper,we prove that every graph G embedded on the surface with Euler characteristic numberε=-1 is acyclically 11-choosable.展开更多
According to the distribution of high fluoride\|bearing groundwater in Liaoning Province, China, the cause of formation and hydrogeochemical characteristics as well as its relationship with human health and illness r...According to the distribution of high fluoride\|bearing groundwater in Liaoning Province, China, the cause of formation and hydrogeochemical characteristics as well as its relationship with human health and illness rate were discussed. Strategies to prevent and control fluoride pollution have also been outlined.展开更多
In this paper, based on Cobb-Douglas production function, the structural stability of the supply chain system are analyzed by employing Lyapunov criteria. That the supply chain system structure, with the variance of t...In this paper, based on Cobb-Douglas production function, the structural stability of the supply chain system are analyzed by employing Lyapunov criteria. That the supply chain system structure, with the variance of the rate of re-production input funding, becomes unstable is proved. Noticeably, the solutions shows that when the optimal combination of input parameter element, the qualitative properties of supply chain system change and the supply chain system becomes unstable.展开更多
The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds: reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, ...The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds: reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.展开更多
Let RP(k) denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP(3)× RP(1), RP(2) ...Let RP(k) denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP(3)× RP(1), RP(2) × RP(1), RP(2)× RP(1)× RP(1) or RP(3)× RP(2).展开更多
Multivariate spline function is an important research object and tool in Computational Geometry. The singularity of multivariate spline spaces is a difficult problem that is ineritable in the research of the structure...Multivariate spline function is an important research object and tool in Computational Geometry. The singularity of multivariate spline spaces is a difficult problem that is ineritable in the research of the structure of multivariate spline spaces. The aim of this paper is to reveal the geometric significance of the singularity of bivariate spline space over Morgan-Scott type triangulation by using some new concepts proposed by the first author such as characteristic ratio, characteristic mapping of lines (or ponits), and characteristic number of algebraic curve. With these concepts and the relevant results, a polished necessary and sufficient conditions for the singularity of spline space S u+1^u (△MS^u) are geometrically given for any smoothness u by recursion. Moreover, the famous Pascal's theorem is generalized to algebraic plane curves of degree n≥3.展开更多
Let Z2 denote a cyclic group of 2 order and Z_(2)^(2)=Z_(2)×Z_(2)the direct product of groups.Suppose that(M,Φ)is a closed and smooth manifold M with a smooth Z_(2)^(2)-action whose fixed point set is the disjoi...Let Z2 denote a cyclic group of 2 order and Z_(2)^(2)=Z_(2)×Z_(2)the direct product of groups.Suppose that(M,Φ)is a closed and smooth manifold M with a smooth Z_(2)^(2)-action whose fixed point set is the disjoint union of two real projective spaces with the same dimension.In this paper,the authors give a sufficient condition on the fixed data of the action for(M,Φ)bounding equivariantly.展开更多
Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP(ξ^κ)] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of thi...Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP(ξ^κ)] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.展开更多
基金NSFC(Grant Nos.12101285,12171222)Basic and Applied Basic Research Foundation and Jointof Guangdong Province,China(Grant No.2019A1515110324)+1 种基金Guangdong Basic and Applied Basic Research Foundation(Natural Science Foundation of Guangdong Province,China,Grant No.2021A1515010254)Foundation of Lingnan Normal University(Grant Nos.ZL2021017,ZL1923)。
文摘A proper vertex coloring of a graph G is acyclic if there is no bicolored cycles in G.A graph G is acyclically k-choosable if for any list assignment L={L(v):v∈V(G)}with|L(v)|≥k for each vertex v∈V(G),there exists an acyclic proper vertex coloringφof G such thatφ(v)∈L(v)for each vertex v∈V(G).In this paper,we prove that every graph G embedded on the surface with Euler characteristic numberε=-1 is acyclically 11-choosable.
文摘According to the distribution of high fluoride\|bearing groundwater in Liaoning Province, China, the cause of formation and hydrogeochemical characteristics as well as its relationship with human health and illness rate were discussed. Strategies to prevent and control fluoride pollution have also been outlined.
基金Supported by the National Excellent Youth Science Foundation of China (No.79725002)
文摘In this paper, based on Cobb-Douglas production function, the structural stability of the supply chain system are analyzed by employing Lyapunov criteria. That the supply chain system structure, with the variance of the rate of re-production input funding, becomes unstable is proved. Noticeably, the solutions shows that when the optimal combination of input parameter element, the qualitative properties of supply chain system change and the supply chain system becomes unstable.
基金Supported by the National Natural Science Foundation of China (Grant No. 10571051 and 10871064 )the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20040542006)the Key Labor. of Coput.Stoch.Math.Univ. of Hunan (No. 09K026)
文摘The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds: reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.
基金Project Supported by NSFC (10371029),HNSF (103144)and SRF for ROCS, SEM
文摘Let RP(k) denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP(3)× RP(1), RP(2) × RP(1), RP(2)× RP(1)× RP(1) or RP(3)× RP(2).
基金Supported by the National Natural Science Foundation of China (Grant Nos.10771028 60533060)+1 种基金the programof New Century Excellent Fellowship of NECCfunded by a DoD fund (Grant No.DAAD19-03-1-0375)
文摘Multivariate spline function is an important research object and tool in Computational Geometry. The singularity of multivariate spline spaces is a difficult problem that is ineritable in the research of the structure of multivariate spline spaces. The aim of this paper is to reveal the geometric significance of the singularity of bivariate spline space over Morgan-Scott type triangulation by using some new concepts proposed by the first author such as characteristic ratio, characteristic mapping of lines (or ponits), and characteristic number of algebraic curve. With these concepts and the relevant results, a polished necessary and sufficient conditions for the singularity of spline space S u+1^u (△MS^u) are geometrically given for any smoothness u by recursion. Moreover, the famous Pascal's theorem is generalized to algebraic plane curves of degree n≥3.
基金supported by the National Natural Science Foundation of China(No.11771116)。
文摘Let Z2 denote a cyclic group of 2 order and Z_(2)^(2)=Z_(2)×Z_(2)the direct product of groups.Suppose that(M,Φ)is a closed and smooth manifold M with a smooth Z_(2)^(2)-action whose fixed point set is the disjoint union of two real projective spaces with the same dimension.In this paper,the authors give a sufficient condition on the fixed data of the action for(M,Φ)bounding equivariantly.
基金This work is supported by HNSF(Grant No:103144) NNSF of China(10371029)
文摘Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP(ξ^κ)] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.