简介:Inanabstractsetup,wegetstrongtypeinequalitiesinL~(p+1)byassumingweakorextra-weakinequalitiesinOrliczspaces.Forsomeclassesoffunctions,thenumberpisrelatedtoSimonenkoindices.WeapplytheresultstogetstronginequalitiesformaximalfunctionsassociatedtobestΦ-approximationoperatorsinanOrliczspaceL~Φ.
简介:Thebesthydraulicchannelsectionmakesthemaximumflowcapacityforthesameflowcross-area,andtheminimumcross-areaandwettedperimeterforthesamedischarge.Theconstructioncostcanbereducednearlytotheminimumatthesametime.Thehorizontalbottomparabolicsection(HBPsection)isacompositesection.Itisimportantfordesigntofindthebestcombinationformofthehorizontalbottomandtheparabolicsides.Thispaperstudiesthebesthydraulicsectionanditshydrauliccharacteristics.Theexplicitformulaeareproposedtodeterminethedimensionsandthebestcombinationformofthehorizontalbottomandtheparabolicsides.Theseexplicitformulaeandtheparametersmakeiteasytodesignthechannel.Itisshownthattheratiosofthesurfacewidthtothedepthandthebottomwidthtothedepthareconstantforthebesthydraulicsection.Thecomparisonswiththeclassicparabolic,rectangular,trapezoid,triangular,semi-cubicandhorizontal-bottomedsemi-cubicsectionsshowthattheHBPsectionhasthelargestflowcapacityandtheshortestwettedperimeterforthesameflowarea,andhasthesmallestflowareaforthesamedischarge.ItisindicatedthattheparabolicsidepartsofthebesthydraulicHBPsectionaredifferentfromthoseoftheclassicsection.TheresultsofthebesthydraulicsectionoftheclassicparabolicchannelcannotbeapplieddirectlytotheHBCsection.