Planar Digraphs of Digirth Five Are 2‐Colorable

Neumann‐Lara (1985) and ?krekovski conjectured that every planar digraph with digirth at least three is 2‐colorable, meaning that the vertices can be 2‐colored without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2‐colorable. The result also holds in the setting of list colorings.     

双色光晶格势阱中玻色-爱因斯坦凝聚体的Landau-Zener隧穿行为

考虑玻色-爱因斯坦凝聚体局限于周期性的双色光晶格势阱中,研究其中的Bloch能带结构、第一能隙和第二能隙的Landau-Zener隧穿行为.结果表明,随着双色光晶格势阱的主、次晶格相位差从0增加到π,Bloch能带中第一能隙宽度逐渐增加,而第二能隙宽度逐渐减小.同时发现,双色光晶格势阱的主、次晶格深度及其相位差对第一能隙和第二能隙的Landau-Zener隧穿性质有重要的影响.     

Reflexible maps and hypermaps with face–stabilisers pointwise stabilising half the faces

This paper deals mainly with reflexible hypermaps in which the stabiliser of a hyperface fixes exactly half the hyperfaces - these reflexible hypermaps are called here 2-dichromatic. The number of hyperfaces of any 2-dichromatic hypermap must be necessarily even and greater than or equal to 4. We prove that if then is necessarily orientable and of type , for some positive integers , and , and show that the automorphism group of a 2-dichromatic hypermap is a wreath product. We also construct an infinite family of orientable 2-dichromatic hypermaps of type with 2n hyperfaces (n even). If is a 2-dichromatic map then . In 1959 Sherk [19] described an infinite family of orientable maps, he denoted by , where , and are positive integers satisfying certain conditions. We find in the dual family a subfamily of infinitely many 2-dichromatic maps. Received 23 August 1999; revised 27 March 2000.     

List coloring digraphs

The dichromatic number of a digraph D is the least number k such that the vertex set of D can be partitioned into k parts each of which induces an acyclic subdigraph. Introduced by Neumann‐Lara in 1982, this digraph invariant shares many properties with the usual chromatic number of graphs and can be seen as the natural analog of the graph chromatic number. In this article, we study the list dichromatic number of digraphs, giving evidence that this notion generalizes the list chromatic number of graphs. We first prove that the list dichromatic number and the dichromatic number behave the same in many contexts, such as in small digraphs (by proving a directed version of Ohba's conjecture), tournaments, and random digraphs. We then consider bipartite digraphs, and show that their list dichromatic number can be as large as . We finally give a Brooks‐type upper bound on the list dichromatic number of digon‐free digraphs.     

Ionization Dynamics of 1D Model Atom in Ultra-Strong lω-2ω Laser Fields

We investigate the ionization dynamics of 1D model atom in ultra-strong dichromatic lω-2ω laser fields with a constant phase difference. We find numerically that both the total ionization and the distribution between forward and backward rates show clear phasedependent character. This phenomenon can be explained by the first-order high frequency Floquet theory. Finally, this phase-dependent character is testified u;ith pulsed laser fields provided the pulse is smoothly (adiabatically) turned on.     

High-fidelity image reproduction using angular distribution of reflected spectral intensity

A method to reproduce images of an object under various observation conditions is presented. In this method, a series of multispectral images is captured by rotating the object under a point light source of which spectral power distribution and the position are known. The captured images are decomposed into diffuse and specular reflection component images based on the dichromatic reflection and the Lambertian models. Next, the incident angle of the illumination light and the angle between viewing direction and regular reflection are calculated based on observation geometry. Finally, the image under observation geometry is synthesized using the light-ray rearrangement technique. The experiments are carried out using two-dimensional objects, leather and fabric. Most of the synthesized images are shown to be the same as the images actually captured under the assumed illumination geometry, even if the object has complex reflection like fabric for which it is difficult to apply the reflection model used in computer graphics.     

润滑油膜双色光干涉测量系统的特性研究

基于多光束干涉理论和摄像系统的光谱响应特性,建立了润滑油膜彩色光干涉测量的色度学模型,以红绿双色光干涉测量为例设计了计算机程序复现了油膜厚度测量的干涉图像。双色光干涉的理论计算和实验测量取得了很好的一致性。进一步的计算表明,润滑油膜双色光干涉图像的色彩主要受光源双色光的半峰全宽、析光膜厚度、垫层厚度及润滑介质特性的影响。在所设定的计算参数条件下,双色光的半峰全宽较窄,析光膜厚度为4～10nm和垫层厚度较薄时图像的对比度较高。     

Perfect Digraphs

The clique number of a digraph D is the size of the largest bidirectionally complete subdigraph of D. D is perfect if, for any induced subdigraph H of D, the dichromatic number defined by Neumann‐Lara (The dichromatic number of a digraph, J. Combin. Theory Ser. B 33 (1982), 265–270) equals the clique number . Using the Strong Perfect Graph Theorem (M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas, The strong perfect graph theorem, Ann. Math. 164 (2006), 51–229) we give a characterization of perfect digraphs by a set of forbidden induced subdigraphs. Modifying a recent proof of Bang‐Jensen et al. (Finding an induced subdivision of a digraph, Theoret. Comput. Sci. 443 (2012), 10–24) we show that the recognition of perfect digraphs is co‐‐complete. It turns out that perfect digraphs are exactly the complements of clique‐acyclic superorientations of perfect graphs. Thus, we obtain as a corollary that complements of perfect digraphs have a kernel, using a result of Boros and Gurvich (Perfect graphs are kernel solvable, Discrete Math. 159 (1996), 35–55). Finally, we prove that it is ‐complete to decide whether a perfect digraph has a kernel.     

NaF及其掺杂晶体F2心的二向色性研究

给出了ＮａＦ及其掺杂质Ｌｉ＾＋、Ｍｇ＾２＋、Ｃｕ＾２＋和ＯＨ＾－五种样品的Ｆ２心在偏振的氮分子激光照射下的二向色性吸收特性，对各种样品中Ｆ２心的转向效率进行了比较，并对结果进行了机理性的分析。     

Orientations of graphs with uncountable chromatic number

Motivated by an old conjecture of P. Erdős and V. Neumann‐Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number if its vertices cannot be covered by countably many independent sets, and a digraph has uncountable dichromatic number if its vertices cannot be covered by countably many acyclic sets. We prove that, consistently, there are digraphs with uncountable dichromatic number and arbitrarily large digirth; this is in surprising contrast with the undirected case: any graph with uncountable chromatic number contains a 4‐cycle. Next, we prove that several well‐known graphs (uncountable complete graphs, certain comparability graphs, and shift graphs) admit orientations with uncountable dichromatic number in ZFC. However, we show that the statement “every graph G of size and chromatic number ω₁ has an orientation D with uncountable dichromatic number” is independent of ZFC. We end the article with several open problems.