凸包及凸體的包含測度.pdf

1、分類號UDC密級y777764武￡薹觸撥夫多碩士學位論文凸包及凸體的包含測度蔣慧峰指導教師姓名：申請學位級別：論文定稿日期：學位授予單位：學位授予日期：李德宜副教授武漢科技大學理學院答辯委員會主席：任德麟教授評閱人任德麟謝鵬教授副教授第Ⅱ頁武漢科技大學碩士學位論文AbstractConvexbodiesaretheresearchobjectsinthepaperThepaperisconcemedwithtwoaspects：Anec

2、essaryandsufficientconditionforconvexhullofasetinE2beingclosed；ConvexbodyanditscontainmeasureThisessayisorganizedasfollows：①ifAisallopenset，thenconvAisopent”ThuswhetherornottheconvexhullofaclosedsetisalsoclosedTheansweri

3、sclearlynegativeForexample，inE2，if一：杠，ylx“Y1，YoJ，thenAisaclosedset，butc伽vA=缸，YlY0Jisnotclosed![WhichsetsatisfiesitsconvexhulliSclosedWhatiSthecharacterofasetthatitsconvexhulliSclosedThatistosaywhatisthenecessaryandsuffic

4、ientconditionforconvexhullofasetinE2beingclosedThistopicjustlygivesoutanecessaryandsufficientconditionforconvexhullofasetinE2whichiSclosedthroughtheresearchofconvexhullofasetinE2andtwonewconcepts：criticalsupportinglinean

5、dleftcriticalinteriorpointandrightcriticalinteriorpoint②ConvexbodyandjtscontainmeasureTwonewconcepts，thegeneralizedsupportfunctionandrestrictedchordfunction，bothreferringtotheconvexsethavebeenintroducedinReference∽Genera

6、lformulatetoyieldthekinematicmeasureofasegmentoffixedlengthinaconvexsetwereestablishedbasedontheseconcentsandadiscussionwasgivenwithrespecttectangulardomainTheReference【14ldealswithsomeotherwiseshapedfigures：theparallelo

7、gram，triangleandregularhexagonAsforthesefigures，theauthorssucceedingivingtheirgeneralizedsupportfunctionsandrestrictedchordfunctions，andderivingtheindividualexpressionsforthekinematicmeasurementionedaboveAwaycalledpartin

8、tersectionwithstronglivesandthegeneralizedsupportfunctionandrestrictedchordfunctionhasbeenusedinthistopicWeusethesimplemathsandtheralatedtheoryofmeasuretoderivetheindividualexpressionsforthekinematicmeasureoftheotherconv