有限型条件的应用

广西民族大学学报(自然科学版第15卷第4期JOURNAL OF GUANGXI UNIVERSITY FOR NATIONALITIESVol. 15 No 42009年12月( Natural Science EditionDec.2009有限型条件的应用王飞1,邓起荣2(1.长治学院数学系,山西长治046011;2.福建师范大学数学与计算机科学学院,福建福州350007)摘要:若自相似迭代函数系匣,}1(满足:啊(x)=cx+b,b∈R其中00中国煤化工·收稿日期:20090925CNMHG基金项目:长治学院科研项目(200909)作者简介:王飞(1981),男,山西运城人,硕士研究生,长治学院数学系助教,主要从事分形几何研究.邓起莱(1962-),男广西桂林人,博士,教授,主要从事分形几何及数理统计方面的研究8方数据2009年第4期●王飞邓起荣/有限型条件的应用对任意的k≥0及v∈A4,定义C;")-1记v1=j1jΩ(u)={;∈山,(Ω)∩(9)≠O}.j1j2…j如果词v∈A4,v∈A,且存在相似变换r(x)Cu= Ci,jcx+d,d∈R,满足{mo:∈9(v)}={:∈9(v)},rOs=s.又因为cn2≤[max()]”则称Ω(v)与Ω(u)是等价的,记为g(v)o∴cs[max(c)”,n-r≤logp/max(c),92(v),我们用[9(v)]记为9(v)的等价类1S≤m定义3如果存在有界不变开集ΩcR,使得故对任意的v=j…∈∑我们有结论v=Q()]:∈UA,}是有限集,则称选代函数系2,n∈A,n1≤1x(){}-1关于不变开集Ω满足有限型条件,称为有于是对任意的j∈∑n=(1,2,…,m},我们可限型条件集选取整数n以及叫=j…j∈∑,使得∈A定义49如果存在c∈O,1)及一列正整数由于迭代函数系》1关于不变开集Ω满足有限型52-1,使得c=(c),则称{ogc)1是可公度条件,故存在k>>0,使得[Q(u)]=[(u)]由引理1的结论知c,=c2,由v的选法得到主要结果(c)=,令可=k二,则c=,显然存在引理1设豆是选代函数系(=的不变开正整数易,,,…,,使得8=5设c·=,则集,则对任意的v∈A4,v∈Ax,[9(v)]=[9(v)]So当且仅当=(cC),因而{log}1是可共度的:单∈9(v)}={o:卓∈9(v)};且另一方面,因为c,=(c),=1,2,…,m,由于(c)是单调递减函数,故c=(c·)m,对任意的k证明:由[(v)]=[9(v)]的定义可知以及v∈A4,设c=(c)*(c)',根据引理1的结论知dt,=c,即c=c;cr∈(1,2,…,maxs}是由[9(v)]唯一确定的,并记假设c=cc,即ccn=c→,故满足定义2为r(v)]考虑映射:的相似变换r为∮.因而[()]=[9(v)]等[9(v)]→({向o:φ∈[9(v)]},r[9(v)])价{:∈g2()}=事:∮∈(m)},此式与令如是的子集构成的集族则{φ:φ∈g(v)}=φ:φ∈Ω(v)}等价上述映射是从{Lg()J:v∈4A}到中a×10,定理1迭代函数系{}-关于不变开集Ω满1,2,…,maxs}的一一映射由于φ是有限集则足有限型条件当且仅当=U1{:v,v∈A4,(2)中2是有限集,从而{[9(v)]:v∈U,}是有限集,(9)≠O}是有限集且{logc1}1是可公度的故迭代函数系{}1关于不变开集满足有限型条证明:一方面迭代函数系}1关于不变开集g满足有限型条件,不妨设定理2设迭代函数系{}1关于不变开集S满足有限型条件,若UC9是另一不变开集,则迭代()]:v∈U4,}=()],[9(v)],,函数系1)1关于不变开集U满足有限型条件9(v)],v∈41≤k≤N证明:若U)∩U)≠D,则(9)∩由引理1知φ=UN1{o:卓∈(v)}是有限集TH中国煤化工1可知也是有限CNMH或立任取v=j…,∈∑,由于()+。是单调递(下转第93页)减的,故存在k≥0及n≥r>0,使得:*≤c<;2009年第4期●刘洋,王勇/一种求极大频繁项集的挖掘方法[参考文献][4]李超,余昭平,基于矩阵的 Apriori算法改进[冂]、计算机工程,[l] Jiawei Han, Micheline Kamber.数据挖掘概念与技术[M].北京2006,(12)[2]丁艳辉,王洪国一种基于矩阵的关联规则挖拯新算法[].计算机[责任编辑苏琴]科学,2006,(4)[责任校对黄祖宾][3]胡慧蓉王周敬,一种基于关系炬阵的关联规则快速挖梹算法[]计算机应用,2005,(7)An Approach of Mining the Maximal Frequent ItemsetsLiU Yang, WANG YongCollege of Mathematics and Computer Science, guangriUniversity for Nationalities, Nanning 530006, China)Abstract: An improving Apriori algorithm is presented in this paper. The approach of this algorithmcan be described as following steps first step is to translate the original data into item -code, and next stepis to use the "or"operation to determine the frequent candidacy itemsets, third step is to make use of"andoperation to get the frequent itemsets. Finally we get the maximal frequent itemsets which is satisfied themin-support given by us. Here is the length of itemset and it is determined by the algorithm automaticallyKey words data mining; item coding; frequent itemsets上接第85页)[参考文献][5]Ngai S. M. Hausdorff dimension of self-similar sets with overlaps[1] Hutchinsion J E. Fractal and self similarity [J]. Indian Univ[J]. London math.Soe.2001,63(2):655-672[6]邓起蒙.[2]Edgar G. A. A fractal puzzle[J]. Math Intelligence, 1991,(13):44fine Measures[D].香港中文大学博士论文,2005,1-98[3]Strichartz R.S. Geometry of self-affine tiles I [J]. Indian Univ[责任编辑苏琴]Math,,1999,(48):1-23.[责任校对方丽菁][4]Rao H, Wen Z Y. A class of self-similar fractals with overlapstructure[J]. Adv in Appl Math, 1998, (20):50-72.Application to the Finite Type ConditionWANG Fei, dENG Qi-rong(1. Department of Mathematics, Changzhi University, Changzhi 046011, China; 2. School of Mathematicaland Computer Sciences, Fujian Normal University, Fuzhou 350007, China)Abstract:If self-similar IFS JP-1( which satisfies:中国煤化工re0