环状硅酸盐图的友好指数集

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).     

2-阶邻域连通无爪图的Hamilton性

设Ｇ是无爪图．对ｘ∈Ｖ（Ｇ），若Ｇ［Ｎ（ｘ）］不连通，则存在ｙｉ∈Ｖ（Ｇ）－｛ｘ｝（ｉ－１，２），使｜Ｎ（ｙｉ）∩Ｋｉ（ｘ）｜≥２，且｜Ｎ（ｙｉ）∩Ｎ（Ｋｉ＋１（ｘ））｛ｘ｝｜≥２（ｉ模２），那么称无爪图Ｇ是强２－阶邻域连通的，其中Ｋ１（ｘ），Ｋ２（ｘ）分别表示Ｇ［Ｎ（ｘ）］的两个分支．本文证明了：连通且强２－阶邻域连通的无爪图是Ｈａｍｉｌｔｏｎ图．     

具有势函数V（r）＝A_1r~（－10）－A_2r~（－6）的分子晶体的Hami

采用连续分数法得到了具有分子晶体中的分子之间的相互作用势为Ｖ（ｒ）＝Ａ１ｒ－１０－Ａ２ｒ－６（Ａ１，Ａ２＞０）的分子晶体的Ｈａｍｉｌｔｏｎｉａｎ算子的精确的能量本征值（即分子晶体的束缚能的精确值）。     

合肥光源逐圈束流位置监测系统中的定时系统

 定时系统是合肥光源逐圈束流位置监测和相空间测量系统中的重要组成部分,其主要目的是为数据采集卡提供与环内电子束团同步的时钟信号。该系统包含高速ECL时钟成形、分频电路、程控延时电路、控制模块等部分。可实现延时范围0～220ns,最小延时步距0.5ns,调整精度0.1ns,时钟抖动小于200ps。系统控制软件基于客户/服务器结构,操作灵活、方便。     

环圈量子引力简介

大家知道，弦理论（String theory）是企图和谐地统一量子力学和广义相对论这两个已知的然而却互不相容的关于“小”和“大”的理论体系．本文介绍的环圈量子引力（Loop Quantum Gravity）理论（以下简称“L理论”）也是为此目的兴起的另一种理论．     

半球上导线不同绕法在球心处磁场的差别

在《物理学教程》中有这样一道习题：半径为R的木球上均匀绕有密集的细导线，线圈平面彼此平行，且以单层线圈覆盖住半个球面，设线圈的总匝数为N．通过线圈的电流为I．求球心O处的磁感强度．     

Persistent Current in a Mesoscopic Ring Side-Attached with a Quantum Dot

We theoretically investigate properties of the ground state of a closed dot-ring system with a magnetic flux in the Kondo regime by means of a tight-banding Anderson Hamiltonian, using the Slave-Boson mean-field approach. The persistent current shows interesting dependences on the parity and on the size of the system. The signature of Kondo resonance at ζk/L = 0.15 is expected to be observed experimentally in the future. With the intensity of the coupling tD changes from weak to strong, the properties of the system changes largely, which are different from the in-line one because of the attached dot.     

完全r部图Kr（t）的{=C3，C2k}-强制分解（k≥4）的渐近存在性

研究基于顶点集V=Ui=1^rVi（其中｜Vi｜=t，i=1，2，……，r）的完全r部图Kr（t）的3圈和2k圈{C3，C2k}-强制分解（k≥4）的存在性问题．通过构造并运用Kr（t）的两种分解法，证明了Kr（t）的〈C3，C2k}-强制分解（k≥4）的渐近存在性，即对于任意给定的正整数k≥4，存在常数r0（k）=5k＋2，使得当r≥r0（k）时，Kr（t）的{C3，C2k}-强制分解存在的必要条件也是充分的．     

有向图n·■_m的优美性

给定有向图D(V,E),如果存在一个单射f:V(D)→{0,1,…,|E|}使得对于每条有向边(u,v),诱导函数f′:E(D)→{1,2,…,|E|}是一个双射函数,其中,f′(u,v)=[f(v)-f(u)](mod(|E|+1)),则f称为有向图D(V,E)的优美标号,f′称为有向图D(V,E)的诱导的边的优美标号.本文讨论了有向图n.■m的优美性,并且证明了当m=23且n为偶数时,n.■m是优美有向图.     

局部大边宽嵌入图的面圈和C-桥的结构

In this paper,we show that for a locally LEW-embedded 3-connected graph G in orientable surface,the following results hold:1) Each of such embeddings is minimum genus embedding;2) The facial cycles are precisely the induced nonseparating cycles which implies the uniqueness of such embeddings;3) Every overlap graph O(G,C) is a bipartite graph and G has only one C-bridge H such that CUH is nonplanar provided C is a contractible cycle shorter than every noncontractible cycle containing an edge of C.This ext...