Coxeter Transformation and Quasiquivers

Mathematical Notes -     

Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.     

障碍拟阵图

Let G be a simple graph and T={S :S is extreme in G}. If M(V(G), T) is a matroid, then G is called an extreme matroid graph. In this paper, we study the properties of extreme matroid graph.     

Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Optical Diffractive Memories: Angular Selectivity and Diffraction Efficiency in Dichromated Gelatin

Two thousand images of resolution 512×512 pixels as a regular matrix pattern of 10×10 elements are stored, where each element is angularly multiplexed 20 times in a 25 μm thickness of dichromated gelatin emulsion without cross-talk effect. The surface area of the matrix is 1 cm². We show good concordance of the angular selectivity between the experimental result and theory. The diffraction efficiency of each 20 multiplexed images is measured and has nearly the same value. Examples of reconstructed images for multiple applications are given, for example, storage of 160,000 images on a 3′1/2 floppy disc format, which is about 100 min of black and white film. Application can be made to automobile cartography and storage of X-ray images as well as weather forecast images. Colored diffractive images are also possible and are illustrated.     

拟阵与概念格的关系

本文以构造的方式建立起拟阵与概念格的联系,得到在同构意义下每个拟阵是一个概念格,但反之不然的结论;该结论使得利用概念格的性质研究拟阵成为现实,特别为将建造概念格的算法尤其是已计算机化的算法应用于求取拟阵奠定了基础,也为拟阵论成为研究概念格性质的辅助工具打下基础．     

Layer arrangement in the structure of octakis-(trimethylsiloxy)octasilsesquioxane and dodecakis-(trimethylsiloxy)cyclohexasiloxane

Layers of [(CH₃)₃SiO]₈(SiO_1.5)₈ and [(CH₃)₃SiO]₁₂(SiO)₆ organosilicon compounds obtained by chemical vapor deposition were investigated by X-ray diffraction (DRON-RM4, R = 192 mm, CuK radiation) and Raman spectroscopy (Triplemate, SPEX). The layers were found to be ideally oriented polycrystalline films. The octakis-(trimethylsiloxy)octasilsesquioxane polycrystals are oriented in one crystallographic direction — [001], while the dodecakis-(trimethylsiloxy)cyclohexa-siloxane polycrystals are oriented in the and directions. Crystal structure analysis in these directions yielded the type of the planar lattice followed by the molecules and their orientation relative to the support.Original Russian Text Copyright © 2004 by S. A. Gromilov, T. V. Basova, D. Yu. Emelyanov, A. V. Kuzmin, and S. A. ProkhorovaTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 497–501, May–June 2004.     

溶胶-凝胶法制备高取向Bi4Ti3O12/SrTiO3(100)薄膜

Bi4Ti3O12具有良好的铁电、电光等性能山、特别是Bi4Ti3O12薄膜很适合作永久性存储材料，也可用于电光器件问．在微电子学、光电子学、集成光学、集成铁电学等领域均有广泛开发和应用前景，国外已用溅射法、激光沉积法制备出c轴取向Bi。Ti3Ol。薄膜【’，＼山东大学用MOCVD法制     

LB膜诱导Ba(NO3)2晶体取向生长

In this work, Ba(NO₃)₂ crystals with single crystal face were induced by using the the method of bio-mimetic mineralization and double LB films of behenic acid (BA) as the template. The crystals were characterized by Scanning Electron Microscope (SEM) and X-Ray Diffraction (XRD). The crystals were observed in regular square shape with uniform size about 5～8 μm by SEM, and they were found by XRD to grow along the (111) plane. From these experiments, we can conclude that the good selection of the (111) crystal face of Ba(NO₃)₂ is due to the electrostatic interactions , the match between this crystal face and the definite lattice structure of the LB films.