Application of Connection in Molecular Dynamics

The evolution of electronic states in molecule has two origins: dynamical one produced by Schr¨odinger equation and kinematical one caused by base transformation due to nuclear motion.In current theories,the former gets analytic expression; the latter depends on heavy numerical calculation,which contains uncertainty.By using connection of fiber bundles,this paper establishes an analytic formula for the latter,and the numerical work is simplified.It shows the mathematical structure of molecule is fiber bundle.     

Independence of Yang-Mills Equations with Respect to the Invariant Pairing in the Lie Algebra

It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent with respect to the pairing. PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13     

On the asymptotic number of inequivalent binary self-dual codes

Let Ψn be the number of inequivalent self-dual codes in . We prove that , where . Let Δn be the number of inequivalent doubly even self-dual codes in . We also prove that .     

Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials p_k(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑ_m(x) p_n(x;q), where ϑ_m(x) is x^mor (x;q)_m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.     

The unitary connections on the complex Grassmann manifold

In the complex Grassmann manifold ℱ(m,n), the space of complexn-planes passes through the origin of C^m+n; the local coordinate of the space can be arranged into anm ×n matrixZ. It is proved that

Blow-Up Solutions of Modified Schrödinger Maps

We study blow-up solutions of modified Schrödinger maps. We observe the pseudo-conformal invariance by which explicit blow-up solutions can be constructed.     

柔性电子学中的表界面化学

柔性电子作为新兴的研究热点, 涉及材料、 化学、 物理等多个基础学科的交叉, 以及在生物医用、 可穿戴设备及人工智能等多个领域的应用. 柔性电子设备的制造加工过程中会用到弹性基底、 导电层、 功能层等多种性质各异的材料, 其互相之间的整合受到它们表面性质和界面结合力的限制; 器件的功能、 可靠性、 对环境的敏感性等也受到了器件表界面性质的影响; 因此, 对材料和器件表界面的处理在柔性电子学中具有重要作用. 本文对柔性电子学中常用的表界面化学过程分为3大类进行介绍: 表面电化学过程, 基于特定化合物反应产生的电流制备电化学传感器, 利用电流/电压控制表面负载化合物; 表面修饰, 通过表面改性提高材料的加工性能, 共价修饰分子层或其它材料赋予器件特殊功能性质或保护层; 不同材料之间的界面连接, 通过共价连接或化学反应辅助的物理交联实现不同材料的结合, 提高柔性器件的稳定性, 实现柔性设备的整合. 对各应用进行总结和举例后, 讨论了存在的问题, 并对未来的发展方向及前景进行了展望.