设 e=uv 是 G 中住一条边,e 的次数 d(e)=d(u)+d(v),其中 d(u)和d(u)分别为顶点 u 和 v 在 G 中的度数。本文的主要结果是:设 G 是几乎无桥的,n≥11阶简单连通图,若对任意相距为1的两边 e_0和 e_1,d(e_0)+d(e_1)≥2n-5,则 G 的线图 L(G...设 e=uv 是 G 中住一条边,e 的次数 d(e)=d(u)+d(v),其中 d(u)和d(u)分别为顶点 u 和 v 在 G 中的度数。本文的主要结果是:设 G 是几乎无桥的,n≥11阶简单连通图,若对任意相距为1的两边 e_0和 e_1,d(e_0)+d(e_1)≥2n-5,则 G 的线图 L(G)是泛圈的。展开更多
G 是一个有限群,M 是 G 的一个极小生成集。用 Cay(M:G)表示生成集为 M 的 G 上的一个 Cayley 图。Z_n 表示模 n 的剩余类加群。本文借助 Rankin 的一个引理,研究有向 Cayley 图的 Hamilton 回的存在性。作为 Rankin 引理的推论,给出了 ...G 是一个有限群,M 是 G 的一个极小生成集。用 Cay(M:G)表示生成集为 M 的 G 上的一个 Cayley 图。Z_n 表示模 n 的剩余类加群。本文借助 Rankin 的一个引理,研究有向 Cayley 图的 Hamilton 回的存在性。作为 Rankin 引理的推论,给出了 Cay(M:Z_n)存在 Hamilton 回的若干充分条件。展开更多
A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transf...A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transformation method in which the algebraic structure of systems has been used. The nonunitary evolution operator is also found by choosing a special gauge function. All auxiliary parameters introduced in the present approach are only determined by some algebraic equations. The dynamics of two quantum-nonautonomous systems ruled by non-Hermitian Hamiltonians, including a two-photon ionization process involving two-state only and a mesoscopic RLC circuit with a source, are treated as the demonstration of our general approach.展开更多
In this paper, we propose a fermionic generalization of KdV6 equation and study its integrability.Moreover,we show that this equation is a constraint Hamiltonian flow on the coadjoint orbit of Neveu-Schwarz superalgebra.
文摘设 e=uv 是 G 中住一条边,e 的次数 d(e)=d(u)+d(v),其中 d(u)和d(u)分别为顶点 u 和 v 在 G 中的度数。本文的主要结果是:设 G 是几乎无桥的,n≥11阶简单连通图,若对任意相距为1的两边 e_0和 e_1,d(e_0)+d(e_1)≥2n-5,则 G 的线图 L(G)是泛圈的。
文摘G 是一个有限群,M 是 G 的一个极小生成集。用 Cay(M:G)表示生成集为 M 的 G 上的一个 Cayley 图。Z_n 表示模 n 的剩余类加群。本文借助 Rankin 的一个引理,研究有向 Cayley 图的 Hamilton 回的存在性。作为 Rankin 引理的推论,给出了 Cay(M:Z_n)存在 Hamilton 回的若干充分条件。
文摘A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transformation method in which the algebraic structure of systems has been used. The nonunitary evolution operator is also found by choosing a special gauge function. All auxiliary parameters introduced in the present approach are only determined by some algebraic equations. The dynamics of two quantum-nonautonomous systems ruled by non-Hermitian Hamiltonians, including a two-photon ionization process involving two-state only and a mesoscopic RLC circuit with a source, are treated as the demonstration of our general approach.
基金Supported by the Fundamental Research Funds for the Central Universities and the Natural Science Foundation of China under Grant Nos.10971209 and 10871184
文摘In this paper, we propose a fermionic generalization of KdV6 equation and study its integrability.Moreover,we show that this equation is a constraint Hamiltonian flow on the coadjoint orbit of Neveu-Schwarz superalgebra.
