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(xué)位論文凸包及凸體的包含測度蔣慧峰指導(dǎo)教師姓名：申請學(xué)位級別：論文定稿日期：學(xué)位授予單位：學(xué)位授予日期：李德宜副教授武漢科技大學(xué)理學(xué)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(xué)碩士學(xué)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