简介:1.IntroductionLetRbethecollectionofallrealnumbers,andZthecollectionofallintegers.Iff1(x)andf2(x)aretwofunctionsinL2(R),theinnerproduct
简介:Thispapercontainsadetailed,selfcontainedandmorestreamlinedproofofthel~2decouplingtheoremforhypersurfacesfromthepaperofBourgainandDemeterin2015.TheauthorshopethiswillserveasagoodwarmupforthereadersinterestedinunderstandingtheproofofVinogradov'smeanvaluetheoremfromthepaperofBourgain,DemeterandGuthin2015.
简介:MakinguseoftheZ2×Z2symmetry,wecouldstudythestructurenearmultipleS-treakingturningpoints.Inparticular,weshowthatthereexisttwokindsofsingularpointpaththroughdoubleSbreakingturningpointsandtripleSbieakingturningpoints,onetsquadraticturningporntpathandoneisquadraticpitchforkbifurcationpointpath.SomesimpleregularextendedsystemstocornputedoubleandtripleS-breakingturningpointsareproposed.Numericalexamplesarealsogreen
简介:AgraphGiscalledchromatic-choosableifitschoicenumberisequaltoitschromaticnumber,namelych(G)=χ(G).Ohba’sconjecturestatesthateverygraphGwith2χ(G)+1orfewerverticesischromaticchoosable.ItisclearthatOhba’sconjectureistrueifandonlyifitistrueforcompletemultipartitegraphs.Recently,Kostochka,StiebitzandWoodallshowedthatOhba’sconjectureholdsforcompletemultipartitegraphswithpartitesizeatmostfive.Butthecompletemultipartitegraphswithnorestrictionontheirpartitesize,forwhichOhba’sconjecturehasbeenverifiedarenothingmorethanthegraphsKt+3,2*(k-t-1),1*tbyEnotomoetal.,andKt+2,3,2*(k-t-2),1*tfort≤4byShenetal..Inthispaper,usingtheconceptoff-choosable(orL0-size-choosable)ofgraphs,weshowthatOhba’sconjectureisalsotrueforthegraphsKt+2,3,2*(k-t-2),1*twhent≥5.Thus,Ohba’sconjectureistrueforgraphsKt+2,3,2*(k-t-2),1*tforallintegerst≥1.
简介:针对嫦娥三号软着陆轨道设计与控制策略问题,在合理假设的前提下,建立动力学模型,求解得到了嫦娥三号着陆准备轨道近月点和远月点的速度。针对软着陆过程的6个阶段,通过受力分析,建立了嫦娥三号运动的微分方程模型,以燃料消耗最小为优化目标,以每个阶段的起止状态为约束条件,将软着陆轨道的优化设计问题转化为主发动机推力的泛函极值问题,并将其控制函数转化为近似的多项式函数优化问题。运用四阶Runge-Kutta差分迭代方法进行求解计算,从而得到各个阶段的最优控制函数和控制策略。结果表明,嫦娥三号软着陆过程耗时695s,消耗燃料1269.1kg。