简介:Weestablishseveralfundamentalidentities,includingrecurrencerelations,degreeelevationformulas,partitionofunityandMarsdenidentity,forquantumBernsteinbasesandquantumBeziercurves.WealsodeveloptwotermrecurrencerelationsforquantumBernsteinbasesandrecursiveevaluationalgorithmsforquantumBeziercurves.Ourproofsusestandardmathematicalinductionandotherelementarytechniques.
简介:Supernova(SN)neutrinosdetectedontheEartharesubjecttotheshockwaveeffects,theMikheyev–Smirnov–Wolfenstein(MSW)effects,theneutrinocollectiveeffectsandtheEarthmattereffects.Consideringtherecentexperimentalresultaboutthelargemixingangleθ13(■8.8°)providedbytheDayaBayCollaborationandapplyingtheavailableknowledgefortheneutrinoconversionprobabilityinthehighresonanceregionofSN,PH,whichisintheformofhypergeometricfunctioninthecaseoflargeθ13,wededucetheexpressionofPHtakingintoaccounttheshockwaveeffects.ItisfoundthatPHisnotzeroinacertainrangeoftimeduetotheshockwaveeffects.Afterconsideringallthefourphysicaleffectsandscanningrelevantparameters,wecalculatetheeventnumbersofSNneutrinosforthe"Garching"distributionofneutrinoenergyspectrum.Fromthenumericalresults,itisfoundthatthebehaviorsofneutrinoeventnumbersdetectedontheEarthdependontheneutrinomasshierarchyandneutrinospectrumparametersincludingthedimensionlesspinchingparameterβα(whereαreferstoneutrinoflavor),theaverageenergy
简介:Inthispaper,wearedealingwithq-Bernstein-Durrmeyer-Stancuoperators.Firstly,wehaveestimatedmomentsoftheseoperators.Thenwehavediscussedsomeapproximationpropertiesandasymptoticformulas.WehaveobtainedbetterestimationsbyusingKingtypeapproachandgivenstatisticalconvergencefortheoperators.
简介:TheauthorsconsidertheextendedHeckegroupsH(λq)generatedbyT(z)=-1/z,S(z)=-1/(z+λq)andR(z)=1/-zwithλq=2cos(π/q)forq≥3aninteger.Inthispaper,theevensubgroupHe(λq),thesecondcommutatorsubgroupH"(λq)andtheprincipalcongruencesubgroupsHp(λq)oftheextendedHeckegroupsH(λq)arestudied.Also,relationsbetweenthemaregiven.