Article(id=1242117754912838310, tenantId=1146029695717560320, journalId=1146031591421210625, issueId=1242117726773248217, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1238428800000, receivedDateStr=2009-03-31, revisedDate=1253721600000, revisedDateStr=2009-09-24, acceptedDate=null, acceptedDateStr=null, onlineDate=1259337600000, onlineDateStr=2009-11-28, pubDate=1259337600000, pubDateStr=2009-11-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1259337600000, onlineIssueDateStr=2009-11-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774073550197, creator=sys-migrate, updateTime=1774073550197, updator=sys-migrate, issue=Issue{id=1242117726773248217, tenantId=1146029695717560320, journalId=1146031591421210625, year='2009', volume='27', issue='0922', pageStart='1', pageEnd='140', issueExtLink='null', onlineDate='null', pubDate='1259337600000', pubDateStr='2009-11-28', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=3, issueType=-1, specialIssue=null, createTime=1774073543492, creator='sys-migrate', updateTime=1774073543492, updator='sys-migrate', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=102, endPage=104, ext={EN=ArticleExt(id=1242117757429420743, articleId=1242117754912838310, tenantId=1146029695717560320, journalId=1146031591421210625, language=EN, title=A Proof of Hausdorff Dimension of Cantor Set, columnId=1242116080374710456, journalTitle=Science & Technology Review, columnName=Articles, runingTitle=null, highlight=null, articleAbstract=This paper proposes a different method of proving Hausdorff dimension of Cantor set by considering character string or metric space. Using the principle of set finite covering and Lipschitz mapping, a mapping is constructed from the metric space that is defined by character string to Cantor set. The recurrence relationships are analyzed for the above mapping, which is shown to satisfy the biaxial Lipschitz inequality. It is proved that Hausdorff dimension of the metric space and that of Cantor set are equivalent. A method is found to prove Hausdorff dimension of Cantor set, which is different from the mass distribution principle, provides a way to avoid considering a suitable mass distribution, which is difficult, especially for the lower bound of the Hausdorff dimension, on its fractal set when applying the mass distribution principle for other complicated fractal sets, also has laid a theoretical foundation for studying the theories and methods for proving Hausdorff dimension, and the relations between character string and dimension., authors=null, authorsList=null, authorCompany=null, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=VnYxETNwiH15O4/PilCvbA==, pdfFileSize=832724, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1242117756515062456, articleId=1242117754912838310, tenantId=1146029695717560320, journalId=1146031591421210625, language=CN, title=Cantor集的Hausdorff维数证明, columnId=1146540929516700224, journalTitle=科技导报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=利用符号系统中的字符串和字符串定义的度量空间，结合集合有限覆盖原理和Lipschitz映射，建立一个由字符串定义的度量空间到Cantor集的映射，分析在此映射下的函数递推关系，推导出该函数满足双向Lipschitz不等式，由此得出了文中定义的度量空间的维数与Cantor集的Hausdorff维数相等，从而给出了Cantor集的Hausdorff维数的另一种不同于运用质量分布原理证明的方法，巧妙解决了Cantor集Hausdorff维数的证明问题，在研究方法上为研究其他复杂的分形集提供了避免利用质量分布原理时需要分配一个适当的质量分布（一般比较难找，尤其对维数的下界估计）在其分形集上的困难的尝试，也为今后研究Hausdorff维数的理论和证明方法，以及字符串和维数的关系提供了理论基础和依据。, authors=铁勇, authorsList=铁勇, authorCompany=曲靖师范学院数学与信息科学学院，云南曲靖 655011, correspAuthors=null, authorNote=null, correspAuthorsNote=铁勇, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=y2L38ItM3sZIueMeFZpAcQ==, pdfFileSize=832724, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null)}, authors=[Author(id=1299185515731907459, tenantId=1146029695717560320, journalId=null, articleId=1242117754912838310, orderNo=null, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=null, email=null, emailSecond=null, emailThird=null, correspondingAuthor=null, authorType=null, ext={CN=AuthorExt(id=null, tenantId=null, journalId=1146031591421210625, articleId=1242117754912838310, authorId=1299185515731907459, language=CN, stringName=铁勇, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=null, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null)}, companyList=null)], keywords=[Keyword(id=1242117756129182018, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=CN, orderNo=1, keyword=Cantor集), Keyword(id=1242117756213068100, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=CN, orderNo=1, keyword=字符串), Keyword(id=1242117756301148485, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=CN, orderNo=1, keyword=有限覆盖), Keyword(id=1242117756380844725, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=CN, orderNo=1, keyword=Hausdorff维数), Keyword(id=1242117757018378941, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=EN, orderNo=1, keyword=Cantor set), Keyword(id=1242117757102265023, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=EN, orderNo=1, keyword=character string), Keyword(id=1242117757169373890, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=EN, orderNo=1, keyword=finite covering), Keyword(id=1242117757282615629, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117754912838310, language=EN, orderNo=1, keyword=Hausdorff dimension)], refs=null, funds=null, companyList=null, figs=null, attaches=null, journal=Journal(id=1125356956822126595, delFlag=0, nameCn=科技导报, nameEn=Science & Technology Review, nameHistory1=null, nameHistory2=null, issn=1000-7857, eissn=, cn=11-1421/N, coden=null, periodic=3, language=CN, oaType=0, ccby=null, superviseOffice=null, ownerOffice=null, pubOffice=null, editorOffice=null, officeType=null, aims=null, clcCode=null, officeProv=null, officeCity=null, officeAddr=null, officeZip=null, officeEmail=null, officePhone=null, editDirector=null, officeDirector=null, officeDirectorPhone=null, officeStaffNum=null, officeEmpNum=null, coverPicUrl=wfghvu3bhh/dKxuZ+ucVHA==, journalPrice=null, startedYear=null, abbrevIsoEn=Sci Technol Rev, journalRemark=null, publicationField=null, createdTime=null, updatedTime=1784015846012, createdBy=null, updatedBy=13041195026, firstLetterCn=K, firstLetterEn=K, subjectCode=Natural Sciences, subjectName=自然科学, subjectCodeEn=Natural Sciences, subjectNameEn=null, picCn=wfghvu3bhh/dKxuZ+ucVHA==, picEn=yjSfclmpNm7ihn9NbTZ69g==, jcr=null, cjcr=null, exts=[JournalExt(id=1283818766098219763, language=CN, name=科技导报, nameHistory1=null, nameHistory2=null, managedBy=中国科学技术协会, sponsoredBy=中国科学技术协会, publishedBy=科技导报社, editorOffice=, officeProv=null, officeCity=null, officeAddr=, officeZip=, editDirector=, officeDirector=null, officePhone=null, coverPicUrl=null, journalRemark=, submitArticleUrl=null, websiteUrl=http://www.kjdb.org/CN/home, createdTime=1784015846037, updatedTime=1784015846037, createdBy=13041195026, updatedBy=13041195026, submissionGuidelinesUrl=http://www.kjdb.org/CN/column/column7.shtml, submissionAuthorUrl=https://kjdbauthor.cast.org.cn/webm, submissionEditorUrl=https://kjdbeditor.cast.org.cn/webm/, submissionReviewUrl=https://kjdbauthor.cast.org.cn/webm, submissionCeEditorUrl=https://kjdbeditor.cast.org.cn/webm/, submissionAeEditorUrl=https://kjdbeditor.cast.org.cn/webm/, option={"copyright":""}), JournalExt(id=1283818766144357108, language=EN, name=Science & Technology Review, nameHistory1=null, nameHistory2=null, managedBy=, sponsoredBy=, publishedBy=, editorOffice=, officeProv=null, officeCity=null, officeAddr=, officeZip=, editDirector=, officeDirector=null, officePhone=null, coverPicUrl=null, journalRemark=, submitArticleUrl=null, websiteUrl=http://www.kjdb.org/EN/home, createdTime=1784015846048, updatedTime=1784015846048, createdBy=13041195026, updatedBy=13041195026, submissionGuidelinesUrl=http://www.kjdb.org/EN/column/column7.shtml, submissionAuthorUrl=https://kjdbauthor.manuscriptcloud.com/login, submissionEditorUrl=https://kjdbeditor.manuscriptcloud.com/login, submissionReviewUrl=https://kjdbauthor.manuscriptcloud.com/login, submissionCeEditorUrl=https://kjdbeditor.manuscriptcloud.com/login, submissionAeEditorUrl=https://kjdbeditor.manuscriptcloud.com/login, option={"copyright":""})], databaseList=null, tenantJournalId=1146031591421210625, websiteList=[Website(id=1146104741081231361, webName=null, webTitle=null, webDomain=null, webCopyrigh=null, webIpcNo=null, seoTitle=null, seoKeywords=null, seoDescription=null, tenantJournalId=null, journalId=1146031591421210625, journalNameCn=null, journalNameEn=null, grayFlag=null, tenantId=1146029695717560320, platformId=null, journalGroupId=null, journalGroupNameCn=null, journalGroupNameEn=null, type=1, domain=https://castjournals.cast.org.cn/joweb/kjdb/CN, language=CN, createTime=1751182263881, createBy=18614031015, updateTime=1751778001962, updateBy=18614031015, name=科技导报, tplId=1146099689490845704, title=科技导报, delFlag=0, indexPage=/home, props=[WebsiteProps(id=1148021146403992296, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146104741081231361, code=articleTextType, value=kx, createTime=1751639170504, updateTime=1751639170504, creator=18614031015, updator=18614031015), WebsiteProps(id=1148021146378826469, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146104741081231361, code=banner, value=null, createTime=1751639170498, updateTime=1751639170498, creator=18614031015, updator=18614031015), WebsiteProps(id=1148021146366243556, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146104741081231361, code=logo, value=https://castjournals.cast.org.cn/joweb/kjdb/CN/file/pic?fileId=9GHSf7eGlIPH0Tv/OOdstA==, createTime=1751639170495, updateTime=1751639170495, creator=18614031015, updator=18614031015), WebsiteProps(id=1148021146395603687, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146104741081231361, code=picServerUrl, value=https://castjournals.cast.org.cn/joweb/kjdb/CN/file/pic, createTime=1751639170502, updateTime=1751639170502, creator=18614031015, updator=18614031015), WebsiteProps(id=1148021146387215078, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146104741081231361, code=staticResourcePath, value=https://castjournals.cast.org.cn/joweb/cast_kjdb_cn_619/, createTime=1751639170500, updateTime=1751639170500, creator=18614031015, updator=18614031015)]), Website(id=1146105254833139715, webName=null, webTitle=null, webDomain=null, webCopyrigh=null, webIpcNo=null, seoTitle=null, seoKeywords=null, seoDescription=null, tenantJournalId=null, journalId=1146031591421210625, journalNameCn=null, journalNameEn=null, grayFlag=null, tenantId=1146029695717560320, platformId=null, journalGroupId=null, journalGroupNameCn=null, journalGroupNameEn=null, type=1, domain=https://castjournals.cast.org.cn/joweb/kjdb/EN, language=EN, createTime=1751182386363, createBy=18614031015, updateTime=1753500121937, updateBy=18614031015, name=科技导报, tplId=1146101810881728533, title=Science & Technology Review, delFlag=0, indexPage=/home, props=[WebsiteProps(id=1155838567709528217, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146105254833139715, code=articleTextType, value=kx, createTime=1753502988984, updateTime=1753502988984, creator=18614031015, updator=18614031015), WebsiteProps(id=1155838567692750998, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146105254833139715, code=banner, value=null, createTime=1753502988980, updateTime=1753502988980, creator=18614031015, updator=18614031015), WebsiteProps(id=1155838567688556693, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146105254833139715, code=logo, value=https://castjournals.cast.org.cn/joweb/kjdb/EN/file/pic?fileId=9GHSf7eGlIPH0Tv/OOdstA==, createTime=1753502988979, updateTime=1753502988979, creator=18614031015, updator=18614031015), WebsiteProps(id=1155838567705333912, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146105254833139715, code=picServerUrl, value=https://castjournals.cast.org.cn/joweb/kjdb/EN/file/pic, createTime=1753502988983, updateTime=1753502988983, creator=18614031015, updator=18614031015), WebsiteProps(id=1155838567701139607, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1146105254833139715, code=staticResourcePath, value=https://castjournals.cast.org.cn/joweb/cast_kjdb_en_623/, createTime=1753502988982, updateTime=1753502988982, creator=18614031015, updator=18614031015)])], journalTitle=科技导报, weixinUrl=null, journalUrl=null, iacademicId=null, status=1, seqNo=null, journalTitleEn=Science & Technology Review, journalPhotoCn=wfghvu3bhh/dKxuZ+ucVHA==, journalPhotoEn=yjSfclmpNm7ihn9NbTZ69g==, journalFirstLetter=K, journalRecommend=null, journalNew=null, journalCollection=1, jcrJf=null, cjcrJf=0.91, jcrJfStr=null, cjcrJfStr=null, submissionFirstDecision=null, sciSubjectClassification=null, casSubjectClassification=null, citeScore=null, totalCitationFrequency=null, icpCode=null, psCode=null, advertisingLicenseCode=null, copyrightInformation=null, country=null, option=, provinceCode=null, provinceName=null, collectFlag=false, interPubPlatform=, interPubPlatformUrl=null), detailUrlCn=https://castjournals.cast.org.cn/joweb/kjdb/CN/Y2009/V27/I0922/102, detailUrlEn=https://castjournals.cast.org.cn/joweb/kjdb/EN/Y2009/V27/I0922/102, pdfUrlCn=https://castjournals.cast.org.cn/joweb/kjdb/CN/PDF/Y2009/V27/I0922/102, pdfUrlEn=https://castjournals.cast.org.cn/joweb/kjdb/EN/PDF/Y2009/V27/I0922/102, aliStartDate=null, aliEndDate=null, collectionFlag=false, citedCount=null, citedUrl=null, previewStatus=0, delFlag=0, hasFullText=0, orderTime=1259337600000, fullTextJson=null, articleText=null, reference=null)