29032.低維含參變量矩陣極端性的研究

1、聲明尸明本學(xué)位論文是我在導(dǎo)師的指導(dǎo)下取得的研究成果，盡我所知，在本學(xué)位論文中，除了加以標(biāo)注和致謝的部分外，不包含其他人已經(jīng)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(jī)構(gòu)的學(xué)位或?qū)W歷而使用過的材料與我一同工作的同事對本學(xué)位論文做出的貢獻(xiàn)均已在論文中作了明確的說明研究生簽名：年月日學(xué)位論文使用授權(quán)聲明南京理工大學(xué)有權(quán)保存本學(xué)位論文的電子和紙質(zhì)文檔，可以借閱或上網(wǎng)公布本學(xué)位論文的部分或全部內(nèi)容，可以向有關(guān)部門或機(jī)構(gòu)送交并授權(quán)其保存、借閱

2、或上網(wǎng)公布本學(xué)位論文的部分或全部內(nèi)容對于保密論文，按保密的有關(guān)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