Let G be a graph and A=(aij)n×n be the adjacency matrix of G, the eigenvalues of A are said to be the eigenvalues of the graph G, and to form the spectrum of this graph. The numbers of positive, negative and zero...Let G be a graph and A=(aij)n×n be the adjacency matrix of G, the eigenvalues of A are said to be the eigenvalues of the graph G, and to form the spectrum of this graph. The numbers of positive, negative and zero eigenvalues in the spectrum of the graph G are called positive and negative inertia indexes and nullity of the graph G, are denoted by p(G), n(G), η(G), respectively, and are collectively called inertia indexes of the graph G. The inertia indexes have many important applications in chemistry and mathematics. The purpose of the research of this paper is to calculate the inertia indexes of one special kind of tricyclic graphs. A new calculation method of the inertia indexes of this tricyclic graphs with large vertices is given, and the inertia indexes of this tricyclic graphs with fewer vertices can be calculated by Matlab.展开更多
A mixed graph G^(-) is obtained by orienting some edges of G, where G is the underlying graph of G^(-) . The positive inertia index, denoted by p~+( G), and the negative inertia index, denoted by n~-(G^(-) ), of a mix...A mixed graph G^(-) is obtained by orienting some edges of G, where G is the underlying graph of G^(-) . The positive inertia index, denoted by p~+( G), and the negative inertia index, denoted by n~-(G^(-) ), of a mixed graph G^(-) are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of G^(-) , respectively. In this paper, the positive and negative inertia indices of the mixed unicyclic graphs are studied. Moreover, the upper and lower bounds of the positive and negative inertia indices of the mixed graphs are investigated, and the mixed graphs which attain the upper and lower bounds are characterized respectively.展开更多
以辽西北为研究区域,选取典型干旱年2009年作物(春玉米)主要生长季,采用表观热惯量(apparent thermal inertia,ATI)、距平植被指数(anomalies of vegetation index,AVI)和植被供水指数(vegetation supply water index,VSWI)3种基于不同...以辽西北为研究区域,选取典型干旱年2009年作物(春玉米)主要生长季,采用表观热惯量(apparent thermal inertia,ATI)、距平植被指数(anomalies of vegetation index,AVI)和植被供水指数(vegetation supply water index,VSWI)3种基于不同理论的遥感干旱指数方法对土壤水分进行反演,分析其监测效果。结果表明,3种指数分别在一定程度上反映出了辽西北地区2009年的旱情趋势,但得到的反演结果并不一致;ATI在中高植被覆盖率下的监测效果高于预期结果,比较符合历史气象资料;AVI可以有效反映当年作物主要生长季各时期相对的受旱状况;VSWI夸大了植被的影响作用,存在严重的滞后性。展开更多
文摘Let G be a graph and A=(aij)n×n be the adjacency matrix of G, the eigenvalues of A are said to be the eigenvalues of the graph G, and to form the spectrum of this graph. The numbers of positive, negative and zero eigenvalues in the spectrum of the graph G are called positive and negative inertia indexes and nullity of the graph G, are denoted by p(G), n(G), η(G), respectively, and are collectively called inertia indexes of the graph G. The inertia indexes have many important applications in chemistry and mathematics. The purpose of the research of this paper is to calculate the inertia indexes of one special kind of tricyclic graphs. A new calculation method of the inertia indexes of this tricyclic graphs with large vertices is given, and the inertia indexes of this tricyclic graphs with fewer vertices can be calculated by Matlab.
基金the National Natural Science Foundation of China (Nos. 11971054 and 12161141005)the Fundamental Research Funds for the Central Universities (No. 2016JBM071)。
文摘A mixed graph G^(-) is obtained by orienting some edges of G, where G is the underlying graph of G^(-) . The positive inertia index, denoted by p~+( G), and the negative inertia index, denoted by n~-(G^(-) ), of a mixed graph G^(-) are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of G^(-) , respectively. In this paper, the positive and negative inertia indices of the mixed unicyclic graphs are studied. Moreover, the upper and lower bounds of the positive and negative inertia indices of the mixed graphs are investigated, and the mixed graphs which attain the upper and lower bounds are characterized respectively.
文摘以辽西北为研究区域,选取典型干旱年2009年作物(春玉米)主要生长季,采用表观热惯量(apparent thermal inertia,ATI)、距平植被指数(anomalies of vegetation index,AVI)和植被供水指数(vegetation supply water index,VSWI)3种基于不同理论的遥感干旱指数方法对土壤水分进行反演,分析其监测效果。结果表明,3种指数分别在一定程度上反映出了辽西北地区2009年的旱情趋势,但得到的反演结果并不一致;ATI在中高植被覆盖率下的监测效果高于预期结果,比较符合历史气象资料;AVI可以有效反映当年作物主要生长季各时期相对的受旱状况;VSWI夸大了植被的影响作用,存在严重的滞后性。
