非线性实验的哲学意义

以Chua电路、扭摆非线性振动和光学混沌3个非线性实验的实验现象,来阐明客观世界乃是确定性和随机性、有序与无序、稳定性与非稳定性的对立统一体,遵循着唯物辩证法的发展规律。长期的教学实践表明,非线性实验不仅对于学生研究自然现象客观规律的自然观及科学观的培养,而且对于学生认识客观事物的世界观及方法论的培养,都发挥了积极的促进作用。     

太阳能驱动全天候监控系统的实验设计

研发了一套太阳能全天候监控系统设计性实验。该实验通过对太阳能电池板基本物理性能的测定,了解其工作原理,然后选择合适的控制器件与负载,设计电路,最后形成一套由太阳能电池板提供能量,实现全天候监控的应用系统。该实验不仅能够作为设计性实验用于大学物理实验,而且可以应用于许多工程领域。     

Use of laser drilling in the manufacture of organic inverter circuits

Inverter circuits have been made by connecting two high-quality pentacene field-effect transistors. A uniform and pinhole-free 900 nm thick polyimide gate-insulating layer was formed on a flexible polyimide film with gold gate electrodes and partially removed by using a CO₂ laser drilling machine to make via holes and contact holes. Subsequent evaporation of the gold layer results in good electrical connection with a gold gate layer underneath the gate-insulating layer. By optimization of the settings of the CO₂ laser drilling machine, contact resistance can be reduced to as low as 3 Ω for 180 μm square electrodes. No degradation of the transport properties of the organic transistors was observed after the laser-drilling process. This study demonstrates the feasibility of using the laser drilling process for implementation of organic transistors in integrated circuits on flexible polymer films.     

Hard coloring problems in low degree planar bipartite graphs

In this paper we prove that the PRECOLORING EXTENSION problem on graphs of maximum degree 3 is polynomially solvable, but even its restricted version with 3 colors is NP-complete on planar bipartite graphs of maximum degree 4.The restricted version of LIST COLORING, in which the union of all lists consists of 3 colors, is shown to be NP-complete on planar 3-regular bipartite graphs.     

Compatible Eulerian circuits in Eulerian (di)graphs with generalized transition systems

A transition in a graph is defined as a pair of adjacent edges. A transition system of an Eulerian graph refers to a set of partitions such that for each vertex of the graph, there corresponds to a partition of the set of edges incident to the vertex into transitions. A generalized transition system $F\left(G\right)$ over a graph $G$ defines a set of transitions over $G$. A compatible Eulerian circuit of an Eulerian graph $G$ with a generalized transition system $F\left(G\right)$ is defined as an Eulerian circuit in which no two consecutive edges form a transition defined by $F\left(G\right)$. In this paper, we further introduce the concept of weakly generalized transition system which is an extension of the generalized transition system and prove some Ore-type sufficient conditions for the existence of compatible Eulerian circuits in Eulerian graphs with (weakly) generalized transition systems and obtain corresponding results for Eulerian digraphs. Our conditions improve some previous results due to Jackson and Isaak, respectively.     

Rainbow number of matchings in planar graphs

The rainbow number$rb(G,H)$ for the graph $H$ in $G$ is defined to be the minimum integer $c$ such that any $c$-edge-coloring of $G$ contains a rainbow $H$. As one of the most important structures in graphs, the rainbow number of matchings has drawn much attention and has been extensively studied. Jendrol et al. initiated the rainbow number of matchings in planar graphs and they obtained bounds for the rainbow number of the matching $k{K}_2$ in the plane triangulations, where the gap between the lower and upper bounds is $O\left(k^3\right)$. In this paper, we show that the rainbow number of the matching $k{K}_2$ in maximal outerplanar graphs of order $n$ is $n+O\left(k\right)$. Using this technique, we show that the rainbow number of the matching $k{K}_2$ in some subfamilies of plane triangulations of order $n$ is $2n+O\left(k\right)$. The gaps between our lower and upper bounds are only $O\left(k\right)$.     

Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable

It is known that planar graphs without cycles of length from 4 to 7 are 3-colorable (Borodin et al., 2005) [13] and that planar graphs in which no triangles have common edges with cycles of length from 4 to 9 are 3-colorable (Borodin et al., 2006) [11]. We give a common extension of these results by proving that every planar graph in which no triangles have common edges with k-cycles, where k∈{4,5,7} (or, which is equivalent, with cycles of length 3, 5 and 7), is 3-colorable.     

Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem

We illustrate a new way to study the stability problem in celestial mechanics. In this paper, using the variational nature of elliptic Lagrangian solutions in the planar three-body problem, we study the relation between Morse index and its stability via Maslov-type index theory of periodic solutions of Hamiltonian system. For elliptic Lagrangian solutions we get an estimate of the algebraic multiplicity of unit eigenvalues of its monodromy matrix in terms of the Morse index, which is the key to understand the stability problem. As a special case, we provide a criterion to spectral stability of relative equilibrium.     

The rectilinear distance Weber problem in the presence of a probabilistic line barrier

This paper considers the problem of locating a single facility in the presence of a line barrier that occurs randomly on a given horizontal route on the plane. The objective is to locate this new facility such that the sum of the expected rectilinear distances from the facility to the demand points in the presence of the probabilistic barrier is minimized. Some properties of the problem are reported, a solution algorithm is provided with an example problem, and some future extensions to the problem are discussed.     

任意基数集上的拟阵的圈及连通性

通过研究任意基数集上的拟阵圈的性质,继而得出当此拟阵连通时,它可由含任一给定元素的圈集唯一确定的结论.