Two definitions are given that Definitionl： an induced subgraph by a vertex vie G and its neighbors in G is defined as a vertex adjacent closed subgraph, and denoted by Qi （=G[V（Nvi）]）, with the vertex vi called ...Two definitions are given that Definitionl： an induced subgraph by a vertex vie G and its neighbors in G is defined as a vertex adjacent closed subgraph, and denoted by Qi （=G[V（Nvi）]）, with the vertex vi called the hub; and Definition2： A r（k,I）-I vertices graph is called the （k,l）-Ramsey graph, denoted by RG（k,1）, if RG（k,1） only contains cliques Kk.1 and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG（k,I） contains only Kk-2. Meanwhile, the RG（k,l）＇s complement RG（I,k） contains only cliques Kl.l, and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG（I,k） contains only Ki.2. On the basis of those definitions, two theorems are put forward and proved in this paper. They are Theoreml： the biggest clique in G is contained in some Qi of G, and Theorem 2： r（k,1） = [V（RG（k,I））I ＋ 1. With those definitions and theorems as well as analysis of chord property, a method for quick inspection and building RG（k,1） is proposed. Accordingly, RG（4,6） is built, it is a strongly 14-regular graph on order 35. We have tested RG（4,6） and its complement, as a result, they meet the defintion2, so we proclaim that r（4,6）=36.展开更多
A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean...A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution.A surface Σ is a graph in M_1×M_2 where M_1 and M_2 are Riemann surfaces. if<e_1∧e_2.ω>≥v_0>0 where w_1 is a Khler form on M_1.We prove that.if M is a Khler-Einstein surface with scalar curvature R.v_0≥ on the initial surface,then the mean curvature flow has a global solution and it sub-converges to a minimal surface,if.in addition.R≥0 it converges to a totally geodesic surface which is holomorphic.展开更多
Effects of meta-substituent of 3,4＇/4,3＇/3,3＇-substituted benzylideneanilines （XBAYs） on the electrochemical reduction potentials （E（Red）） were investigated, in which 49 samples of target compounds were synth...Effects of meta-substituent of 3,4＇/4,3＇/3,3＇-substituted benzylideneanilines （XBAYs） on the electrochemical reduction potentials （E（Red）） were investigated, in which 49 samples of target compounds were synthesized, and their reduction potentials were measured by cyclic voltammetry. The substituent effects on the E（Red） of target compounds were analyzed and an optimality equation with four parameters （Hammett constant a of X, Hammett constant a of Y, excited-state substituent constant σexCC of X, and the substituent specific cross-interaction effect △σexCC2 between X and Y） was obtained. The results show that the factors affecting the E（Red） of 3,4＇/4,31/3,3P-substituted XBAYs are different from those of 4,4＇-substituted XBAYs. For 3,4＇/4,3＇/3,3＇-substituted XBAYs, σ（X） and σ（Y） must be employed, and the contribution of △σexCC2 is important and not negligible. Compared with 4,4＇-substituted XBAYs, X group contributes less to 3,4＇/4,3＇/3,3＇-substituted XBAYs, while Y group contributes more to them. Additionally, it was observed that either para-substituted XBAYs or meta-substituted XBAYs, the substituent effects of X are larger than those of Y on the E（Red） of substituted XBAYs.展开更多
文摘Two definitions are given that Definitionl： an induced subgraph by a vertex vie G and its neighbors in G is defined as a vertex adjacent closed subgraph, and denoted by Qi （=G[V（Nvi）]）, with the vertex vi called the hub; and Definition2： A r（k,I）-I vertices graph is called the （k,l）-Ramsey graph, denoted by RG（k,1）, if RG（k,1） only contains cliques Kk.1 and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG（k,I） contains only Kk-2. Meanwhile, the RG（k,l）＇s complement RG（I,k） contains only cliques Kl.l, and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG（I,k） contains only Ki.2. On the basis of those definitions, two theorems are put forward and proved in this paper. They are Theoreml： the biggest clique in G is contained in some Qi of G, and Theorem 2： r（k,1） = [V（RG（k,I））I ＋ 1. With those definitions and theorems as well as analysis of chord property, a method for quick inspection and building RG（k,1） is proposed. Accordingly, RG（4,6） is built, it is a strongly 14-regular graph on order 35. We have tested RG（4,6） and its complement, as a result, they meet the defintion2, so we proclaim that r（4,6）=36.
基金supported in part by a Sloan fellowship and an NSERC grant for Chenby a grant from NSF of China for Li.by a grant from NSF of USA for Tian
文摘A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution.A surface Σ is a graph in M_1×M_2 where M_1 and M_2 are Riemann surfaces. if<e_1∧e_2.ω>≥v_0>0 where w_1 is a Khler form on M_1.We prove that.if M is a Khler-Einstein surface with scalar curvature R.v_0≥ on the initial surface,then the mean curvature flow has a global solution and it sub-converges to a minimal surface,if.in addition.R≥0 it converges to a totally geodesic surface which is holomorphic.
文摘Effects of meta-substituent of 3,4＇/4,3＇/3,3＇-substituted benzylideneanilines （XBAYs） on the electrochemical reduction potentials （E（Red）） were investigated, in which 49 samples of target compounds were synthesized, and their reduction potentials were measured by cyclic voltammetry. The substituent effects on the E（Red） of target compounds were analyzed and an optimality equation with four parameters （Hammett constant a of X, Hammett constant a of Y, excited-state substituent constant σexCC of X, and the substituent specific cross-interaction effect △σexCC2 between X and Y） was obtained. The results show that the factors affecting the E（Red） of 3,4＇/4,31/3,3P-substituted XBAYs are different from those of 4,4＇-substituted XBAYs. For 3,4＇/4,3＇/3,3＇-substituted XBAYs, σ（X） and σ（Y） must be employed, and the contribution of △σexCC2 is important and not negligible. Compared with 4,4＇-substituted XBAYs, X group contributes less to 3,4＇/4,3＇/3,3＇-substituted XBAYs, while Y group contributes more to them. Additionally, it was observed that either para-substituted XBAYs or meta-substituted XBAYs, the substituent effects of X are larger than those of Y on the E（Red） of substituted XBAYs.
