Vertical cycle karst zone has been studied for more than 100 years, however karst subzones in the zone have never been divided and affected depth of CO2 from rainwater in the zone has never been studied. On the basis ...Vertical cycle karst zone has been studied for more than 100 years, however karst subzones in the zone have never been divided and affected depth of CO2 from rainwater in the zone has never been studied. On the basis of field observation, survey and chemical analysis, the difference of karst processes indicated by CaCO3 and pH values in fine and loose sedimentary strata as well as limestone strata, and the vertical cycle zone ascertained by predecessors can be divided into three subzones, that is, the upper first subzone, characterized by unsaturated water solution and strong dissolution processes, the middle second subzone, characterized by supersaturated water solution and precipitation, and the lower third subzone, characterized by unstable water solution and weak dissolution or weak precipitation. The three subzones can indicate the vertical CO2 cycle. In fine and loose sediment strata, the bottom of the first subzone is the lower boundary strongly influenced by CO2 from rainwater, soil and air; all CO2 from rainwater, soil and air is almost exhausted in the second subzone. In the early developmental period of karst process in limestone strata, karst funnels and vertical caves do not form, vertical seeping of rainwater and soil water is very slow, and CO2 from soil, rainwater and air almost can reach the third subzone, but in the middle and late developmental periods, karst funnels and vertical caves occur, CO2 from soil, rainwater and air can reach deep seasonal change zone and horizontal cycle zone and quicken development of karst morphology. Deep karst morphology near groundwater level under vertical cycle zone develops better in the middle and late periods of karst process.展开更多
Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function ?is called a signed dominating function (SDF) if ?for each vertex . The weight ?of f is defined by . The signed domination numb...Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function ?is called a signed dominating function (SDF) if ?for each vertex . The weight ?of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, ?(mod 3) and bounds for otherwise.展开更多
A sign pattern(matrix)is a matrix whose entries are the symbols+,-and 0.Foran n×n sign pattern matrix A,the sign pattern class of A,denoted by Q(A),is the set ofall n×n real matrices whose entries have signs...A sign pattern(matrix)is a matrix whose entries are the symbols+,-and 0.Foran n×n sign pattern matrix A,the sign pattern class of A,denoted by Q(A),is the set ofall n×n real matrices whose entries have signs indicated by the corresponding entries of A.We say that a sign pattern matrix A requires a matrix property P if every real matrix in Q(A)has the property P.A matrix with all distinct eigenvalues has many nice展开更多
In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign...In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign pattern matrix (or sign pattern).For a re-al matrix B,by sgn (B) we mean the sign pattern matrix in which each positive (respec-tively,negative,zero) entry of B is replaced by+(respectively,-,0).If A is an展开更多
Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination numbe...Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ′sc（G） = min{∑e∈E f（e）｜ f is an SCDF of G}. This paper will characterize all maxima] planar graphs G with order n ≥ 6 and γ′sc（G） =n.展开更多
基金National Natural Science Foundation of China, No.40571004 Project of Key Karst Dynamics Laboratory, MLR, No.2004-05 Project of State Key Laboratory of Loess and Quaternary Geology, CAS, No.SKLLQG0504
文摘Vertical cycle karst zone has been studied for more than 100 years, however karst subzones in the zone have never been divided and affected depth of CO2 from rainwater in the zone has never been studied. On the basis of field observation, survey and chemical analysis, the difference of karst processes indicated by CaCO3 and pH values in fine and loose sedimentary strata as well as limestone strata, and the vertical cycle zone ascertained by predecessors can be divided into three subzones, that is, the upper first subzone, characterized by unsaturated water solution and strong dissolution processes, the middle second subzone, characterized by supersaturated water solution and precipitation, and the lower third subzone, characterized by unstable water solution and weak dissolution or weak precipitation. The three subzones can indicate the vertical CO2 cycle. In fine and loose sediment strata, the bottom of the first subzone is the lower boundary strongly influenced by CO2 from rainwater, soil and air; all CO2 from rainwater, soil and air is almost exhausted in the second subzone. In the early developmental period of karst process in limestone strata, karst funnels and vertical caves do not form, vertical seeping of rainwater and soil water is very slow, and CO2 from soil, rainwater and air almost can reach the third subzone, but in the middle and late developmental periods, karst funnels and vertical caves occur, CO2 from soil, rainwater and air can reach deep seasonal change zone and horizontal cycle zone and quicken development of karst morphology. Deep karst morphology near groundwater level under vertical cycle zone develops better in the middle and late periods of karst process.
文摘Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function ?is called a signed dominating function (SDF) if ?for each vertex . The weight ?of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, ?(mod 3) and bounds for otherwise.
文摘A sign pattern(matrix)is a matrix whose entries are the symbols+,-and 0.Foran n×n sign pattern matrix A,the sign pattern class of A,denoted by Q(A),is the set ofall n×n real matrices whose entries have signs indicated by the corresponding entries of A.We say that a sign pattern matrix A requires a matrix property P if every real matrix in Q(A)has the property P.A matrix with all distinct eigenvalues has many nice
文摘In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign pattern matrix (or sign pattern).For a re-al matrix B,by sgn (B) we mean the sign pattern matrix in which each positive (respec-tively,negative,zero) entry of B is replaced by+(respectively,-,0).If A is an
基金Supported by Doctoral Scientific Research Fund of Harbin Normal University(Grant No.KGB201008)
文摘Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ′sc（G） = min{∑e∈E f（e）｜ f is an SCDF of G}. This paper will characterize all maxima] planar graphs G with order n ≥ 6 and γ′sc（G） =n.
