29032.低維含參變量矩陣極端性的研究

1、聲明尸明本學位論文是我在導師的指導下取得的研究成果，盡我所知，在本學位論文中，除了加以標注和致謝的部分外，不包含其他人已經發(fā)表或公布過的研究成果，也不包含我為獲得任何教育機構的學位或學歷而使用過的材料與我一同工作的同事對本學位論文做出的貢獻均已在論文中作了明確的說明研究生簽名：年月日學位論文使用授權聲明南京理工大學有權保存本學位論文的電子和紙質文檔，可以借閱或上網公布本學位論文的部分或全部內容，可以向有關部門或機構送交并授權其保存、借閱

2、或上網公布本學位論文的部分或全部內容對于保密論文，按保密的有關規(guī)定和程序處理研究生簽名：年月曰Abstract碩士論文AbstractTheDiophantineapproximationisabranchofNumberTheoryRecentlythestudyofDiophantineapproximationonmanifoldshasbeendevelopedintoallactiveresearchdirection，t—O

3、studythemeasuretheoryofDiophantineapproximationorDiophantineapproximationwithdependentquantitiesAtpresent，themethodofdynamicsystemiswidelyusedandbecomesoneoftheveryeffectivetoolsonthemainfoldofDiophantineapproximationThe

4、rearelotsofresultshavebeenachievedonthestudyofDiophantineapproximationofvectorsandmatrices、訪thdependentquantitiesThisthesisfocusesonDiophantineapproximationpropertiesoflowlevelmatriceswithdependentquantitiesandtostudythe

5、extremalofmatricesM2。Whenthecorrespondingfu。nctionis(C，口)一good，wederivedtheextremalofthemarxunderpartlyplanarThemainconclusionsofthispaperare：(1)ForanyYofM23，whichisthespaceof2x3matrix，ifitsany2x3，2x2submatrixofYisnonpla

6、narYisextremal(2)ForanyYofM24，whichisthespaceof2x4matrix，ifitsany2x4，2x3，2x2sub—matrixofYisnonplanarYisextremal(3)ForanyYofM2。whichisthespaceof2xnmatrix，when刀isevennumberiftheany2門，2／Il，2insubmatrixofYisnonplanarYisextre

7、malWhennisoddnumb二“‘ler，iftheany2x玎，2玎一1，2半submatrixofYisnonplanarYisextremal二Theproofofthemaintheoremsofthispaperisbasedonthecorrespondencebetweenap。proximationpropertiesofnumbersandorbitpropertiesofcertainflowsonhomoge

8、neousspacesByuseofquantitativenondivergenceestimatesforunipotentflowsonthespaceoflatticesvectorshavebeenprojecttoaspecificlinearspaceWithnon—zeronatureofinfimum，weobtainedtheconditionofnonplanar，whichguaranteetheextremal