简介：TheauthorsproveaquantitativestabilityresultfortheBrunn-Minkowskzinequalityonsetsofequalvolume：If｜A｜=｜B｜〉0and｜A＋B｜^1/n=（2＋δ）｜A｜^1/nforsomesmallδthen,uptoatranslation,bothAandBareclose（intermsof5）toaconvexsetK.Althoughthisresultwasalreadyprovedbytheauthorsinapreviouspaper,thepresentpaperprovidesamoreelementaryproofthattheauthorsbelievehasitsowninterest.Also,theresulthereprovidesastrongerestimateforthestabilityexponentthanthepreviousresultoftheauthors.

简介：在这份报纸，我们考虑与一般抑制联系到线性有弹性的方程的一个半线性的概括夸张边界价值问题可变代表的术语和非线性打字。在合适的条件下面，本地、全球的存在定理被证明。答案的唯一被消除被另外的作者为不同特别问题强加了的一些假设得到了。我们证明有重要起始的资料的任何答案变得稳定。

简介：Apredator-preysystemwithaconstantproportionofpreyrefugeandstage-structureforpreyspeciesisproposedandstudiedinthispaper.Asetofconditionsforthepermanenceofthesystemisobtained.Thelocalstabilityofthesystemisdiscussedbythesignofeigenvalues.Furthermore,byusingtheiterativemethod,somesuitablesufficientconditionsfortheglobalattractivityoftheinteriorequilibriumisobtained.Ourstudyshowsthattheconstantproportionofpreyrefugecouldleadtomorecomplicatedynamicbehaviors.Numericalsimulationsarealsopresentedtoillustratethefeasibilityofthemainresults.