廣西民族大學(xué)學(xué)報(bào)(自然科學(xué)版第15卷第4期JOURNAL OF GUANGXI UNIVERSITY FOR NATIONALITIESVol. 15 No 42009年12月( Natural Science EditionDec.2009有限型條件的應(yīng)用王飛1,鄧起榮2(1.長(zhǎng)治學(xué)院數(shù)學(xué)系,山西長(zhǎng)治046011;2.福建師范大學(xué)數(shù)學(xué)與計(jì)算機(jī)科學(xué)學(xué)院,福建福州350007)摘要:若自相似迭代函數(shù)系匣,}1(滿足:啊(x)=cx+b,b∈R其中00中國(guó)煤化工·收稿日期:20090925CNMHG基金項(xiàng)目:長(zhǎng)治學(xué)院科研項(xiàng)目(200909)作者簡(jiǎn)介:王飛(1981),男,山西運(yùn)城人,碩士研究生,長(zhǎng)治學(xué)院數(shù)學(xué)系助教,主要從事分形幾何研究.鄧起萊(1962-),男廣西桂林人,博士,教授,主要從事分形幾何及數(shù)理統(tǒng)計(jì)方面的研究8方數(shù)據(jù)2009年第4期●王飛鄧起榮/有限型條件的應(yīng)用對(duì)任意的k≥0及v∈A4,定義C;")-1記v1=j1jΩ(u)={;∈山,(Ω)∩(9)≠O}.j1j2…j如果詞v∈A4,v∈A,且存在相似變換r(x)Cu= Ci,jcx+d,d∈R,滿足{mo:∈9(v)}={:∈9(v)},rOs=s.又因?yàn)閏n2≤[max()]”則稱Ω(v)與Ω(u)是等價(jià)的,記為g(v)o∴cs[max(c)”,n-r≤logp/max(c),92(v),我們用[9(v)]記為9(v)的等價(jià)類1S≤m定義3如果存在有界不變開(kāi)集ΩcR,使得故對(duì)任意的v=j…∈∑我們有結(jié)論v=Q()]:∈UA,}是有限集,則稱選代函數(shù)系2,n∈A,n1≤1x(){}-1關(guān)于不變開(kāi)集Ω滿足有限型條件,稱為有于是對(duì)任意的j∈∑n=(1,2,…,m},我們可限型條件集選取整數(shù)n以及叫=j…j∈∑,使得∈A定義49如果存在c∈O,1)及一列正整數(shù)由于迭代函數(shù)系》1關(guān)于不變開(kāi)集Ω滿足有限型52-1,使得c=(c),則稱{ogc)1是可公度條件,故存在k>>0,使得[Q(u)]=[(u)]由引理1的結(jié)論知c,=c2,由v的選法得到主要結(jié)果(c)=,令可=k二,則c=,顯然存在引理1設(shè)豆是選代函數(shù)系(=的不變開(kāi)正整數(shù)易,,,…,,使得8=5設(shè)c·=,則集,則對(duì)任意的v∈A4,v∈Ax,[9(v)]=[9(v)]So當(dāng)且僅當(dāng)=(cC),因而{log}1是可共度的:單∈9(v)}={o:卓∈9(v)};且另一方面,因?yàn)閏,=(c),=1,2,…,m,由于(c)是單調(diào)遞減函數(shù),故c=(c·)m,對(duì)任意的k證明:由[(v)]=[9(v)]的定義可知以及v∈A4,設(shè)c=(c)*(c)',根據(jù)引理1的結(jié)論知dt,=c,即c=c;cr∈(1,2,…,maxs}是由[9(v)]唯一確定的,并記假設(shè)c=cc,即ccn=c→,故滿足定義2為r(v)]考慮映射:的相似變換r為∮.因而[()]=[9(v)]等[9(v)]→({向o:φ∈[9(v)]},r[9(v)])價(jià){:∈g2()}=事:∮∈(m)},此式與令如是的子集構(gòu)成的集族則{φ:φ∈g(v)}=φ:φ∈Ω(v)}等價(jià)上述映射是從{Lg()J:v∈4A}到中a×10,定理1迭代函數(shù)系{}-關(guān)于不變開(kāi)集Ω滿1,2,…,maxs}的一一映射由于φ是有限集則足有限型條件當(dāng)且僅當(dāng)=U1{:v,v∈A4,(2)中2是有限集,從而{[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數(shù)系{}1關(guān)于不變開(kāi)集滿足有限型條證明:一方面迭代函數(shù)系}1關(guān)于不變開(kāi)集g滿足有限型條件,不妨設(shè)定理2設(shè)迭代函數(shù)系{}1關(guān)于不變開(kāi)集S滿足有限型條件,若UC9是另一不變開(kāi)集,則迭代()]:v∈U4,}=()],[9(v)],,函數(shù)系1)1關(guān)于不變開(kāi)集U滿足有限型條件9(v)],v∈41≤k≤N證明:若U)∩U)≠D,則(9)∩由引理1知φ=UN1{o:卓∈(v)}是有限集TH中國(guó)煤化工1可知也是有限CNMH或立任取v=j…,∈∑,由于()+。是單調(diào)遞(下轉(zhuǎn)第93頁(yè))減的,故存在k≥0及n≥r>0,使得:*≤c<;2009年第4期●劉洋,王勇/一種求極大頻繁項(xiàng)集的挖掘方法[參考文獻(xiàn)][4]李超,余昭平,基于矩陣的 Apriori算法改進(jìn)[冂]、計(jì)算機(jī)工程,[l] Jiawei Han, Micheline Kamber.數(shù)據(jù)挖掘概念與技術(shù)[M].北京2006,(12)[2]丁艷輝,王洪國(guó)一種基于矩陣的關(guān)聯(lián)規(guī)則挖拯新算法[].計(jì)算機(jī)[責(zé)任編輯蘇琴]科學(xué),2006,(4)[責(zé)任校對(duì)黃祖賓][3]胡慧蓉王周敬,一種基于關(guān)系炬陣的關(guān)聯(lián)規(guī)則快速挖梹算法[]計(jì)算機(jī)應(yīng)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頁(yè))[參考文獻(xiàn)][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]鄧起蒙.[2]Edgar G. A. A fractal puzzle[J]. Math Intelligence, 1991,(13):44fine Measures[D].香港中文大學(xué)博士論文,2005,1-98[3]Strichartz R.S. Geometry of self-affine tiles I [J]. Indian Univ[責(zé)任編輯蘇琴]Math,,1999,(48):1-23.[責(zé)任校對(duì)方麗菁][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:中國(guó)煤化工re0