Strong edge-coloring for planar graphs with large girth

A strong edge-coloring of a graph $G=(V,E)$ is a partition of its edge set $E$ into induced matchings. Let $G$ be a connected planar graph with girth $k\ge 26$ and maximum degree $\Delta$. We show that either $G$ is isomorphic to a subgraph of a very special $\Delta$-regular graph with girth $k$, or $G$ has a strong edge-coloring using at most $2\Delta +\lceil \frac{12(\Delta -2)}{k}\rceil$ colors.     

Optimal Planar Interception with Fixed End Conditions: Approximate Solutions

In a previous paper (Ref. 1), an exact solution of the optimal planar interception with fixed end conditions was derived in closed form. The optimal control was expressed as an explicit function of the state variables and two fixed parameters, obtained by solving a set of nonlinear algebraic equations involving elliptic integrals. In order to facilitate the optimal control implementation, the present paper derives a highly accurate simplified solution assuming that the ratio of the pursuer turning radius to the initial range is small. An asymptotic expansion further reduces the computational workload. Construction of a near-optimal open-loop control, based on the approximations, completes the present paper.     

Colloidal ZnO nanostructures and functional coatings: A survey

The past research work devoted to ZnO nanocolloidal sol-gel route is reviewed. It highlights the cluster chemistry of alcoholic ZnAc₂ solutions and the results of ZnO colloid growth investigations performed worldwide. Moreover, the role of doping and co-doping in the processing of functional ZnO coatings is discussed. The possibilities of tuning the optical properties are also reported with a particular attention to luminescence. The last part of this paper deals with electrical and photoelectrochemical properties of ZnO nanocrystals and their aggregates. This contribution is dedicated to the 80th birthday of Prof. Arnim Henglein from the Hahn-Meitner-Institut in Berlin and to the memory of Prof. Jacques Mugnier from the Université Claude-Bernard Lyon 1 in France.     

Confinement in a planar waveguide with porous silicon omnidirectional mirrors as confining walls

We present the design and study of waveguide structures based on porous silicon where the light confinement is not due to the usual total reflection effect but to the use of photonic crystals (PCs) as confining walls. These PC are omnidirectional mirrors (OMs), consisting of the periodic repetition of two porous silicon layers with different refractive indices and thicknesses. They reflect the radiation for all angles of incidence within a frequency range called the omnidirectional band gap (OBG). We have followed the PC formalism to investigate the properties of the OM as a multimode waveguide: the number of modes within the band gap, their field spatial distribution and their confinement as a function of the frequency and the core thickness.     

Synthesis and chiroptical properties of two new planar-chiral macrocycles

Could simple intraannular-arm macrocyclic systems exist in enantiopure stable forms? The effective synthesis of two representative compounds of such a class, their resolution into enantiomers, and experiments justifying their stability toward racemization are presented.     

Drawing c-planar biconnected clustered graphs

In a graph, a cluster is a set of vertices, and two clusters are said to be non-intersecting if they are disjoint or one of them is contained in the other. A clustered graph C consists of a graph G and a set of non-intersecting clusters. In this paper, we assume that C has a compound planar drawing and each cluster induces a biconnected subgraph. Then we show that such a clustered graph admits a drawing in the plane such that (i) edges are drawn as straight-line segments with no edge crossing and (ii) the boundary of the biconnected subgraph induced by each cluster is a convex polygon.     

Loss in a rectangular optical waveguide induced by the crossover of a second waveguide

We calculate the loss induced in a single-mode rectangular optical waveguide by the presence of a second waveguide, perpendicular to the first, which crosses over the first waveguide at a variable distance d. Our calculation is applied to the analysis of several doped silica waveguides of practical importance for optical circuit design.     

平面交叉玻璃波导型微透镜阵列光学性能研究

介绍了平面交叉玻璃光波导型半球形微透镜阵列的制作方法.利用积分形式的光线方程式讨论了半球形微透镜的光学特性,得到了半球形微透镜的光线轨迹方程式和焦距表示式,理论结果与实验数据是一致的.     

Roughness reduction in submicron waveguides by low-molecular weight development

Roughness reduction of a submicron waveguide profile in chemically amplified negative resist is here performed by proper selection of an alkali-based developer, taking into account that its smaller molecules lead to smoother resist surface by altering the developing mechanism of aggregate extraction performed with standard quaternary ammonium hydroxide. Roughness is then analyzed by means of classical Atomic Force Microscope inspection; furthermore, a non-invasive line edge roughness analysis approach based on top-down scanning electron microscope acquisition gives comparable results, in terms of standard deviation and molecular aggregate periodicity.