Metric inequalities for routings on direct connections with application to line planning

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.     

高中化学与大学无机化学教材知识点的衔接研究*

作为化学教育专业的必修课程,无机化学起到了奠定师范生化学理论基础的重要作用。在衔接高中化学知识的前提下,开展大学无机化学教学有助于构建完整的化学知识教学体系、调动师范生学习的积极性,实现高中到大学无机化学课程学习的顺利过渡。笔者在教学实践、教育实习指导及调研的基础上,以人教版高中化学、北师大版《无机化学》教材内容为例,从教与学的角度探讨了高中化学和大学无机化学教材知识点的衔接情况,形成了部分经验积累和教学建议,为师范类专业认证背景下的无机化学课程教学提供借鉴和参考。     

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.     

极性晶体膜中强耦合激子的性质

在强耦合极化子模型基础上,采用Lee-Low-Pines(LLP)变分法研究了极性晶体膜中激子与表面光学(SO)声子强耦合、与体纵光学(LO)声子弱耦合体系的性质.讨论了极性晶体膜中激子的诱生势与膜厚度和温度的变化关系.结果表明:激子的诱生势不仅与电子-空穴间距离有关,而且与极性晶体膜厚度有关,同时温度对激子诱生势的影响十分显著.     

Fast multipole method for three-dimensional systems with periodic boundary condition in two directions

We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.     

Soliton squeezing generated in an all-fiber contiguration

We experimentally demonstrate amplitude squeezed soliton utilizing intensity-dependent self-phase modulation in an asymmetric Sagnac interferometer.The system.whose components are connected via ferrule connector/physical connection(FC/PC)fiber connectors,constitutes all-fiber configuration to generate squeezed soliton.Soliton amplitude reduction measured by homodyne detection is near 4.0 dB below the shot-noise level.Optimal squeezing fields in both simple and compact all-fiber configuration are obtained.     

Differential operators on a polarized abelian variety

Let be an ample line bundle over a complex abelian variety . We show that the space of all global sections over of and are both of dimension one. Using this it is shown that the moduli space of rank one holomorphic connections on a compact Riemann surface does not admit any nonconstant algebraic function. On the other hand, is biholomorphic to the moduli space of characters of , which is an affine variety. So is algebraically distinct from the character variety if is of genus at least one.

     

Projective Structure,Symplectic Connection and Quantization

Let X be a connected Riemann surface equipped with a projective structure . Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using , this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using , a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed.     

Lagrangian Theory of Tensor Fields over Spaces with Contravariant and Covariant Affine Connections and Metrics and Its Application to Einstein's Theory of Gravitation in V 4 Spaces

The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and a metric is considered. The functional, the Lie, the covariant, and the total variations of a Lagrangian density, depending on components of tensor fields (with finite rank) and their first and second covariant derivatives, are established. A variation operator is determined and the corollaries of its commutation relations with the covariant and the Lie differential operators are found. The canonical (common) method of Lagrangians with partial derivatives (MLPD) and the method of Lagrangians with covariant derivatives (MLCD) are outlined. They differ each other by the commutation relations the variation operator has to obey with the covariant and the Lie differential operator. The covariant Euler–Lagrange equations are found on the basis of the MLCD. The energy-momentum tensors are considered on the basis of the Lie variation and the covariant Noether identities.As an application of the investigated general scheme, (pseudo) Riemannian spaces with contravariant and covariant affine connections (whose components differ not only by sign) are considered as a special case of -spaces with Riemannian metric, symmetric covariant connection and a weaker definition of dual vector basis with conformal noncanonical contraction operator . The geodesic and autoparallel equations in -spaces are found as different equations in contrast to the case of V ₄-spaces. The Euler–Lagrange equations as Einstein's field equations in -spaces and the corresponding energy-momentum tensors (EMTs) are obtained and compared with the Einstein equations and the EMTs in V ₄-spaces. The geodesic and the auto-parallel equations are discussed.     

一种多波长窄线宽环形掺铒光纤激光器

本文提出了一种利用多个光纤光栅串接来实现环形掺铒光纤多波长,窄线宽激光器的新颖方法,并在实验中验证了这一设计的合理性,得到了稳定的双波长输出。