简介:LetXbeanm-symmetricMarkovprocessandMamultiplicativefunctionalofXsuchthattheM-subprocessofXisalsom-symmetric.TheauthorcharacterizestheDirichletformassociatedwiththesubprocessintermsofthatassociatedwithXandthebivariateRevuzmeasureofM.
简介:研究Kac方程的初值问题.证明了该类方程存在唯一的全局分布解.并且使用一种新的线性化方法证明了该类方程的解具有相应的多项式衰减性.
简介:AFeynmandiagramtheoryforacousto-optic(AO)interactionsisestablished,whichprovidesageneralmethodtocalculatethescatteringamplitudesandintensitiesforbothsingle-frequencyandmultifrequcncyAOinteractions.ThemethodisbasedoncountingthenumberofallowableFeynmandiagrams.Thefollowingimportantassertionhasbeenprovedrigorouslyinthispaper.TheratiosofthenumbersofFeynmandiagramsallowableinvariousBraggdiffractions(isotropie,nondegeneratcbirefringent,anddegeneratebirefringent)tothatinRaman-Nathdiffractionareindependentofthenumberofdifferentacousticfrequencies,beingafunctiononlyoftheorderoftheFeynmandiagramandthediffractionorderofthefinalstate.Generalexpressionsfortheseratiosarcobtained.Basedonthis,completeperturbationsolutionsforthescatteringamplitudesandintensitiesareobtainedforanykindofAOinteractions,anynumberofacousticfrcquencies,andanyfinalstate.Thistheorygivesallresultsobtain