简介:Weconsiderforafixedμ,theclassofpolynomialsPn,μ,s:=P(z)=zsanzn-s+n-s∑j=μan-jzn-j-s;1≤μ≤n-sofdegreen,havingallzerosin|z|≤k,k≤1,withs-foldzerosattheorigin.Inthispaper,wehaveobtainedinequalitiesinthereversedirectionfortheaboveclassofpolynomials.Besides,extensionsofsomeTuran-typeinequalitiesforthepolarderivativeofpolynomialshavebeenconsidered.
简介:AnefficientroutetoprepareL-glucoseandL-galactoseisdescribed.TheL-sugarsareachievedbyusingthestrategyofswitchingthefunctionalgroupsatC1andC5ofD-glucoseandD-mannose.TheoxidationandreductionofthesilylenoletheratC1andthelead(IV)tetraacetatemediatedoxidativedecarboxylationatC5arethekeysteps.L-GlucoseandL-galactosearepreparedinaconvenientandinexpensiveway.
简介:Lp-LqdecayestimateofsolutiontoCauchyproblemofalinearthermoviscoelasticsystemisstudied.Byusingadiagonalizationargumentoffrequencyanalysis,thecoupledsystemwillbedecoupledmicrologically.Thenwiththehelpoftheinformationofcharacteristicrootsforthecoefficientmatrixofthesystem,Lp-LqdecayestimateofparabolictypeofsolutiontotheCauchyproblemisobtained.