完备度量空间中的Moran集

给出了(C,s)-齐性空间中Moran集的Hausdorff维数和packing维数,从而推广了华苏和饶辉的结果.     

Moran sets in complete metric space

The Hausdorff dimensions and packing dimensions of Moran sets in the (C ,s)- homogeneous space are presented, which generalizes the results of Hua and Rao.     

Dimensional results for the Moran-Sierpinski gasket

In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the technique of Moran set, the Hausdorff, packing, and upper box dimensions of the Moran-Sierpinski gasket are given. The dimensional results of the Sierpinski gasket can be seen as a special case of this paper.     

一类一维齐次Moran集的维数结果

为了研究一维齐次Moran集的维数,利用由基本区间形成的连通分支构造了一类■齐次Moran集,证明该类集合的packing维数和上盒维数在■时为所有一维齐次Moran集对应维数的最小值。此外,对于该类集合的上盒维数,得到在一些条件下的取值范围,并找到其达到准确值的一个充分条件。     

Dimensions of a class of high-dimensional homogeneous Moran sets and Moran class

A class of high-dimensional homogeneous Moran sets and Moran classes are introduced and some dimensional properties are studied. The Hausdorff dimension, modified lower box-counting dimension, lower and upper box-counting dimension, and packing dimension of high-dimensional homogeneous and partial homogeneous Cantor sets are determined. Moreover, a kind of fractal E is obtained, which is not regular but with the property Dimw(Ed)=dDimw(E), where w denotes any of the dimensions mentioned above.     

一类齐次完全集的拟对称极小性

研究齐次完全集的拟对称极小性.利用质量分布原理,证明了一类特殊的Hausdorff维数为1的齐次完全集是拟对称Hausdorff极小集.还证明了类似结论对packing维数也成立.     

广义{mk}-拟齐次Cantor集的Hausdorff维数介值性

为了进一步探索Hausdorff维数的取值介于两最值之间的齐次Moran集的结构，引进了广义{m_k}-拟齐次Cantor集。运用质量分布原理讨论该类集合的Hausdorff维数，证明了对任意介于齐次Moran集Hausdorff维数的最大值与最小值之间的值，都存在一类广义{m_k}-拟齐次Cantor集，使得其Hausdorff维数与该值相等。     

Rethinking atomic packing and cluster formation in metallic liquids and glasses

In traditional view,atomic packing is random in glasses made of metallic elements with non-directional interactions as the glass-forming liquid needs to be excited to remain in liquid state before being cooled sufficiently fast to a glass. Locally ordered packing however is possible if certain conditions are favorable,such as a strong bonding between elements,or low configuration energy of a cluster of atoms as suggested by Frank. In alloy systems made of different metallic elements,we show that Frank’s criterion alone does not necessarily lead to certain specific local ordered packing or cluster formation such as icosahedral packing. In this context,we revisit the issue of atomic packing and cluster formation,and show that an alloy system with fairly random liquid configuration could be sufficient to produce a variety of noticeable locally ordered packing with low energy,albeit largely statistical in nature. Therefore,we emphasize the importance of the system parameters such as the atomic size,alloy concentration,and interaction potential in their collective contribution to local atomic packing.     

2-Space Bounded Online Cube and Hypercube Packing

We consider the problem of packing d-dimensional cubes into the minimum number of 2-space bounded unit cubes. Given a sequence of items, each of which is a d-dimensional.d 3/ hypercube with side length not greater than 1 and an infinite number of d-dimensional.d 3/ hypercube bins with unit length on each side, we want to pack all of the items in the sequence into the minimum number of bins. The constraint is that only two bins are active at anytime during the packing process. Each item should be orthogonally packed without overlapping other items. Items are given in an online manner without the knowledge of or information about the subsequent items. We extend the technique of brick partitioning for square packing and obtain two results: a three-dimensional box and d-dimensional hyperbox partitioning schemes for cube and hypercube packing, respectively. We design5.43-competitive and 32/21 2d-competitive algorithms for cube and hypercube packing, respectively. To the best of our knowledge these are the first known results on 2-space bounded cube and hypercube packing.     

Moran’s I指数与DEM 网格大小关系的研究

数字高程模型(Digital Elevation Model,简称DEM)作为真实地形的一种数字化模拟,网格间存在着某种空间自相关性.Moran’s I是一种常见的空间自相关程度量化指标.为了研究Moran’s I与DEM网格大小之间的关系,文章在分辨率为30 m×30 m的DEM上随机选取了35个采样点.又以每个采样点为中心,选取n×n(n=3,5,7,…,25)大小的DEM网格,计算并记录对应于每个网格的Moran’s I指数值,绘出各采样点的Moran’s I指数值随n变化的曲线.研究发现:大多数采样点的Moran’s I曲线呈现出一致的变化趋势;同时发现少数采样点的Moran’s I曲线出现局部的变化异常.对这些异常进行分析后发现,Moran’s I值随n变化的趋势与DEM网格高程值的离散程度(地形)有关.     

Densification of the packing structure under vibrations

Two packing structures with the maximum packing densities of 0.64 and 0.74 for the amorphous state and crystalline state, respectively, were numerically reproduced in the packing densification of equal spheres subjected to onedimensional and three-dimensional vibrations using the discrete element method (DEM), and the results were physically validated. These two packing structures were analyzed in terms of coordination number (CN), radial distribution function (RDF), angular distribution function (ADF), and pore size distribution (Voronoi/Delaunay tessellation). It is shown that CN distributions have the peak values of 7 and 12 for the amorphous state and crystalline state, respectively. RDF and ADF distributions show isolated peaks and orientation preferences for the crystalline state, indicating the long range and angle correlation among particles commonly observed in the crystalline state. Voronoi/Delaunay tessellation also shows smaller and narrower pore size distribution for the crystalline state.     

一类Moran测度的加细重分形分析

主要研究了在2种压缩方式和2种测度分配方式下的Moran集上的Moran测度的重分形分析。在假设2种方式的频率存在的前提下，得到了关于上、下局部维数所确定的水平集的Hausdorff维数和Packing维数，证明此类Moran测度满足重分形机制。     

昆嵛山腮扁叶蜂幼虫空间自相关研究

运用全局Moran’s Ⅰ和局部Moran’s Ⅰ方法对昆嵛山腮扁叶蜂幼虫空间分布的自相关性进行了研究。结果表明：昆嵛山腮扁叶蜂幼虫在样地的分布具有一定的空间自相关性,但未达到显著的程度,没有形成特定的空间分布格局;局部空间自相关分析结果显示也没有局部空间聚集现象。由于样地环境比较单一,因此只考虑昆嵛山腮扁叶蜂易感林木的空间自相关对昆嵛山腮扁叶蜂空间自相关的影响。用相关性分析昆嵛山腮扁叶蜂全局Moran’s Ⅰ值和易感林木全局Moran’s Ⅰ值的相关性可知,昆嵛山腮扁叶蜂全局空间自相关性受易感林木全局空间自相关性显著影响。     

A STUDY OF THE MORPHOLOGY OF POLY(1,4 PHENYLEN TEREPHATHALAMIDE) (PPTA) PULP

The morphology of PPTA pulp is investigated by means of optical microscope and scanningelectron microscope (SEM). It shows that PPTA pulp has feather-like branch, needle point-likeend, and irregular cross-section, which are very important for PPTA pulp as a reinforcer. Theseparation limitation of PPTA pulp is also investigated from both torn and brittle break cross-sec-tion. A packing mechanism is proposed to illustrate the microfibril packing in the gel system.     

GF（2）上向量的相对长度,Packing及Covering界

本文证明向量的相对长度与Hamming距离非常类似,即在一定条件下也存在packing与covering界。     

一种求解矩形packing问题的智能枚举算法

矩形packing问题有许多工业应用,如码头货物装载,木材下料,超大规模集成电路（VLSI）布局设计,新闻排版等。国内外已提出了许多求解此问题的算法,如：遗传算法,模拟退火算法以及启发式算法等。在目前已有研究的基础上,提出了一种智能枚举算法,该算法的关键在于设计一种快速有效的枚举策略。用Hopper和Turton提出的21个矩形packing实例对所提出的算法性能进行了实算测试,平均面积未利用率为0.04%,平均计算时间为277.69 s,并求得了其中18个实例的最优解。实算结果表明：该算法对求解矩形packing问题是行之有效的。     

一类总体有限的随机进化博弈的极限动态

针对有限总体的进化博弈,其内在的动态平衡可以描述为Moran过程或者Wright-Fisher过程.本文从有限总体的Moran过程和Wright-Fisher过程出发,讨论了当总体趋于无限时,对称博弈的进化动态,给出了不同博弈机制下相应的复制动态方程,并比较了Moran过程和Wright-Fisher过程所描述的进化动态.本文还对各种机制得到的动态方程进行了数值模拟,结果表明,我们得到的动态方程对于本文中不同机制下的随机进化过程具有良好的模拟效果.     

R~3中一类齐次Moran集的Hausdorff维数

本文重新构造了三维空间中单位正方体类似Cantor集,得到R~3中一类齐次Moran集,记此Moran集类为M{J,{l_k},{n_k,c_k}},并采用单调收敛定理和位势理论研究出它们的维数相同,并给出具体的Hausdorff维数.     

广义Mycielski图的补图的若干参数

为了寻找一类具有任意大色数但不含三角形的图类,Mycielski提出了一种有趣的图变换,称之为图G的Mycielskian图,记为μ(G).Lam等对μ(G)的定义做了一个自然的推广,提出了广义Mycielskian图(也被Tardif称为cones over图),记为μm(G),其中m代表正整数.本文中给出了广义Mycielskian图的补图的控制数、全控制数、packing数和open packing数的明确结果.     

平面上两个数字集生成的一类Moran测度的谱性

设Mn=(anbn)(n≥1)为任意扩张矩阵,D={(00),(10)}? Z2.该文通过构造一维2个数字集生成Moran测度的谱,得到了 Moran测度μMn,D为谱测度的充要条件是an(n≥2)均为偶数,进一步给出了μMn,D的一类谱的结构.