一个几何问题的解决与推广

建立了与△ＡＢＣ内角平分线ＡＡ’，ＢＢ’，ＣＣ’有关的一个不等式讨论了的上、下界．     

Control of beam halo-chaos by Gauss function in the triangle periodic-focusing channel

This paper studies the Kapchinsky-Vladimirsky （K-V） beam through a triangle periodic-focusing magnetic field by using the particle-core model. The beam halo-chaos is found, and an idea of Gauss function controller is proposed based on the strategy of controlling the halo-chaos. It performs multiparticle simulation to control the halo by using the Gauss function control method. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively, and that the radial particle density is uniform at the centre of the beam as long as the control method and appropriate parameter are chosen.     

Sierpiński triangles formed by molecules with linear backbones on Au(111)

Sierpiński triangle fractal crystals are formed by Co and molecules with linear backbones on Au(111).     

Further extensions of the Grötzsch Theorem

The Grötzsch Theorem states that every triangle-free planar graph admits a proper 3-coloring. Among many of its generalizations, the one of Grünbaum and Aksenov, giving 3-colorability of planar graphs with at most three triangles, is perhaps the most known. A lot of attention was also given to extending 3-colorings of subgraphs to the whole graph. In this paper, we consider 3-colorings of planar graphs with at most one triangle. Particularly, we show that precoloring of any two non-adjacent vertices and precoloring of a face of length at most 4 can be extended to a 3-coloring of the graph. Additionally, we show that for every vertex of degree at most 3, a precoloring of its neighborhood with the same color extends to a 3-coloring of the graph. The latter result implies an affirmative answer to a conjecture on adynamic coloring. All the presented results are tight.     

Synthesis,Structural Characterization and Reactivity of Two New Triangular Molybdenum Cluster Compounds：Mo3T37—[S2CN（CH2CH2OH）2]3I and Mo3Te4Y3[S2P（^iPrO）2]3I（Y3=1.43Te＋1.57S）

Two triangular molybdenum‐tellurium clusters, Mo₃Te₇‐[S₂CN (CH₂CH₂OH₂]₃I (1) and Mo₃Te₄Y₃[S₂P(ⁱPrO)₂]₃I (Y₃ = 1. 43Te+ 1.57S) (2), were obtained from the reaction of K · HOdtc [HOdtc = S₂CN(CH₂CH₂OH)₂] or K·ⁱPr₂dtp (ⁱPr₂dtp = S₂P[OCH(CH₃)₂]₂) with a mixed product of elements Mo, Te(S) and I₂ at high temperature. The structures of the two compounds were determined by X‐ray crystallography study. Crystal data are, (1): monoclinic, P2₁/n, a = 1.6256(3), b = 1.3264(2), c = 1.8808(4) nm, β=96.923°, V = 4.025.9 (14) nm³, D_cal = 3.050g·cm‐³, Z = 4, and (2): monoclinic, P2₁/n, a = 1.4564(2), b = 2.3917(4), c = 1.5094(3) nm, β = 114.35(2)°, V = 4.0259(14) nm³, D_cal = 2.449 g·cm^?3 and Z = 4. Single crystal analyses show that 1 consists of discrete Mo₃Te₇[S₂CN(CH₂CH₂OH)₂]₃I connected into three‐dimensional framework via hydrogen bonds, while 2 forms a linear chain via Te(S)—I interaction.     

Maximal Induced Matchings in Triangle‐Free Graphs

An induced matching in a graph is a set of edges whose endpoints induce a 1‐regular subgraph. It is known that every n‐vertex graph has at most  maximal induced matchings, and this bound is the best possible. We prove that every n‐vertex triangle‐free graph has at most  maximal induced matchings; this bound is attained by every disjoint union of copies of the complete bipartite graph K_{3, 3}. Our result implies that all maximal induced matchings in an n‐vertex triangle‐free graph can be listed in time , yielding the fastest known algorithm for finding a maximum induced matching in a triangle‐free graph.     

The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature

We study the class of closed -dimensional Riemannian manifolds with uniformly bounded diameter and total absolute curvature. Our first theorem states that this class of manifolds is precompact with respect to the Gromov-Hausdorff distance. Our goal in this paper is to completely characterize the topological structure of all the limit spaces of the class of manifolds, which are, in general, not topological manifolds and even may not be locally -connected. We also study the limit of -manifolds with -curvature bound for .

     

On the <Emphasis Type="Italic">C</Emphasis>*-valued triangle equality and inequality in Hilbert <Emphasis Type="Italic">C</Emphasis>*-modules

We prove that for two elements x, y in a Hilbert C*-module V over a C*-algebra the C*-valued triangle equality |x + y| = |x| + |y| holds if and only if 〈x, y〉 = |x| |y|. In addition, if has a unit e, then for every x, y ∊ V and every ɛ > 0 there are contractions u, υ ∊ such that |x + y| ≦ u|x|u* + υ|y|υ* + ɛe.      

高压超快三角波脉冲的产生

本文讨论了使用高压功率晶体管作为开关器件研制的高压超快速斜坡脉冲发生器.得到的脉冲幅值为±1kV,上升时间为10ns,大大提高了脉冲电路的耐大电流冲击性.利用开关器件可耐大电流冲击的特点合成了三角波脉冲,三角波脉冲半宽为10ns左右,通过改变电路参量可得到不同的半宽.     

用于三角方向鉴别测量的客观判别模型

为减小人为因素对三角方向鉴别测量的影响,有效提高测量效率,研究了以机器视觉系统替代观察者进行三角方向鉴别测量的途径,建立了一种专门针对三角方向鉴别测量的客观判别模型。该模型以人眼视觉系统对信号的处理过程以及人眼视觉系统的主要效应为基础,利用方向通道滤波器实现图像信号分解,通过计算视觉特征矢量相关度,实现三角形靶标方向的判别。结合凝视型成像系统虚拟样机提供的三角形靶标,进行了客观判别模型与观察者的判别性能对比实验,并给出三组不同靶标尺寸下的对比实验结果。实验结果表明,客观判别模型很好地预测了观察者的判别性能。