The vertex-transitive TLF-planar graphs

We consider the class of the topologically locally finite (in short TLF) planar vertex-transitive graphs. We characterize these graphs by finite combinatorial objects called labeling schemes. As a result, we are able to enumerate and describe all TLF-planar vertex-transitive graphs of given degree, as well as most of their transitive groups of automorphisms. In addition,we are able to decide whether a given TLF-planar transitive graph is Cayley or not. This class contains all the one-ended planar Cayley graphs and the normal transitive tilings of the plane.     

Planar graphs without 5-cycles or without 6-cycles

Let G be a planar graph without 5-cycles or without 6-cycles. In this paper, we prove that if G is connected and δ(G)≥2, then there exists an edge xy∈E(G) such that d(x)+d(y)≤9, or there is a 2-alternating cycle. By using the above result, we obtain that (1) its linear 2-arboricity , (2) its list total chromatic number is Δ(G)+1 if Δ(G)≥8, and (3) its list edge chromatic number is Δ(G) if Δ(G)≥8.     

An oriented coloring of planar graphs with girth at least five

An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that every oriented graph with a maximum average degree less than and girth at least 5 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least 5 has an oriented chromatic number at most 16, that improves the previous known bound of 19 due to Borodin et al. [O.V. Borodin, A.V. Kostochka, J. Nešet?il, A. Raspaud, É. Sopena, On the maximum average degree and the oriented chromatic number of a graph, Discrete Math. 206 (1999) 77-89].     

Planar graphs without 3-, 7-, and 8-cycles are 3-choosable

A graph G is k-choosable if every vertex of G can be properly colored whenever every vertex has a list of at least k available colors. Grötzsch’s theorem [4] states that every planar triangle-free graph is 3-colorable. However, Voigt [M. Voigt, A not 3-choosable planar graph without 3-cycles, Discrete Math. 146 (1995) 325-328] gave an example of such a graph that is not 3-choosable, thus Grötzsch’s theorem does not generalize naturally to choosability. We prove that every planar triangle-free graph without 7- and 8-cycles is 3-choosable.     

Large-angle channeling radiation from relativistic electrons in optically transparent crystals

In the work within the frame of quantum electrodynamics are obtained new formulae describing the large-angle photon emission from channeled electrons with taking into account of the dispersion of refractive index. Calculations based on these formulae show that the spectral and angular distributions of large-angle optical and ultraviolet radiation from planar channeled sub-GeV electrons in optically transparent crystal reflect the band structure of transverse energy levels of channeled electrons. Comparison with ordinary Cherenkov radiation spectrum reveals that channeling (depending on the beam energy) leads to sufficient change of the large-angle emission spectrum.     

基于阵列倏逝波荧光传感器的雌二醇免疫检测方法

近年来,环境内分泌干扰物愈来愈受到人们的关注。对其用传统的检测技术分析,过程复杂、耗时长、价格昂贵,因此急需发展灵敏度高、反应迅速快、价格低廉的检测手段。介绍了一种平面波导型阵列倏逝波荧光生物传感器,在对系统光路参数进行模拟优化的基础上,可实现24个传感位点的同步、快速、灵敏检测。基于此阵列倏逝波荧光传感器,运用间接竞争免疫检测模式,优化并建立环境内分泌干扰物雌二醇的标准检测条件。实验结果表明,入射角在61.8°时,系统灵敏度最高。该方法对雌二醇检测线性检测区间为0.08~2.52 μg·L-1,检测限为0.05 μg·L-1,半抑制浓度为0.46 μg·L-1,完成单次样品的检测时间为20 min。利用该传感器对污水处理厂出水进行加标回收测试,回收率在84%~120%之间,相对标准偏差小于15%,表明该方法能够用于实际水体中雌二醇的快速检测。     

包含ptC的Au(I)配合物催化烯丙基醋酸盐重排反应的理论研究

理论上,采用密度泛函理论研究两类包含平面四配位碳的Au(I)配合物([Au(C3H2BR)]⁺, R = Me, t-Bu)催化烯丙基醋酸盐的重排反应。计算结果表明,配合物[Au(C₃H₂BR)]+催化烯丙基醋酸盐重排反应相比较文献中报道的催化剂[Au(NHC)]⁺而言,能垒降低了9.2-11.7 kJ.mol^-1。因此,除了配体CO和NHC之外,配合物[Au(C₃H₂BR)]⁺中的新型配体将会在配位化学以及有机化学中具有应用潜力。     

变折射率方形孔径平面微透镜阵列的聚焦和散焦特性

为提高变折射率平面微透镜阵列的填充率,利用光刻工艺和离子交换技术制备了填充率近达100%的方形孔径平面微透镜阵列,并对其透镜元及相邻透元间间隙构成的角落区域的成像进行了理论和实验研究.根据变折射率介质光线追迹法,利用MATLAB软件模拟,发现在透镜元区域和角落区域成像特性相反.成像系统测试表明:由于透镜元区域和角落区域的折射率分布变化规律不同,透镜元与角落区域对物体分别成倒立实像和正立虚像;透镜阵列可实现聚焦和散焦功能;角落区域得到充分的离子交换使得间隙足够小,形成了从该区域中心向外逐渐增大的新型梯度折射率模型.     

SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY

The relationship between a link diagram and its corresponding planar graph is briefly reviewed.A necessary and sufficient condition is given to detect when a planar graph corresponds to a knot.The rela...