The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, whe...The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.展开更多
In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous.By taking Neumann eigenvalues of measure differ...In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous.By taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals.These results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.展开更多
设∑′表示|Z|>1中单叶解析,在∞处有一个一阶极点的函数F(z)=z+sum from n=1 to ∞ b_n/z^n的全体。∑′中奇函数的子族记为∑′_(odd)而以∑′^(+1),∑′_(odd)^(-1)分别表示它们的逆函数子族。本文用变分法重新获得∑′_(odd)^(-1...设∑′表示|Z|>1中单叶解析,在∞处有一个一阶极点的函数F(z)=z+sum from n=1 to ∞ b_n/z^n的全体。∑′中奇函数的子族记为∑′_(odd)而以∑′^(+1),∑′_(odd)^(-1)分别表示它们的逆函数子族。本文用变分法重新获得∑′_(odd)^(-1)中一个准确估计,讨论了∑′_(odd)^(-1)中这个估计与Spriger猜想的关系。在∑′^(-1)中还给出了一个新的准确的估计。展开更多
文摘The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.
基金supported by National Basic Research Program of China (Grant No.2006CB805903)National Natural Science Foundation of China (Grant No.10531010)Doctoral Fund of Ministry of Education of China (Grant No.20090002110079)
文摘In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous.By taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals.These results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.
文摘设∑′表示|Z|>1中单叶解析,在∞处有一个一阶极点的函数F(z)=z+sum from n=1 to ∞ b_n/z^n的全体。∑′中奇函数的子族记为∑′_(odd)而以∑′^(+1),∑′_(odd)^(-1)分别表示它们的逆函数子族。本文用变分法重新获得∑′_(odd)^(-1)中一个准确估计,讨论了∑′_(odd)^(-1)中这个估计与Spriger猜想的关系。在∑′^(-1)中还给出了一个新的准确的估计。
