简介:Weestablishseveralfundamentalidentities,includingrecurrencerelations,degreeelevationformulas,partitionofunityandMarsdenidentity,forquantumBernsteinbasesandquantumBeziercurves.WealsodeveloptwotermrecurrencerelationsforquantumBernsteinbasesandrecursiveevaluationalgorithmsforquantumBeziercurves.Ourproofsusestandardmathematicalinductionandotherelementarytechniques.
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.
简介:InthispaperweproposetheqanaloguesofmodifiedBaskakov-Sz′aszoperators.Weestimatethemomentsandestablisheddirectresultsintermofmodulusofcontinuity.Anestimatefortherateofconvergenceandweightedapproximationpropertiesoftheqoperatorsarealsoobtained.
简介:Thepolarizationevolutionofvectorbeams(VBs)generatedbyq-platesisinvestigatedtheoreticallyandexperimentally.AnanalyticalmodelisdevelopedfortheVBcreatedbyageneralquarter-waveq-platebasedonvectordiffractiontheory.ItisfoundthatthepolarizationdistributionofVBsvarieswithpositionandthevalueq.Inparticular,fortheincidenceofcircularpolarization,theexitvectorvortexbeamhaspolarizationstatesthatcoverthewholesurfaceofthePoincarésphere,therebyconstitutingafullPoincarébeam.Fortheincidenceoflinearpolarization,theVBisnotcylindricalbutspecularlysymmetric,andexhibitsanazimuthalspinsplitting.Theseresultsareinsharpcontrastwiththosederivedbythecommonlyusedmodel,i.e.,regardingtheincidentlightasaplanewave.Byimplementingq-plateswithdielectricmetasurfaces,furtherexperimentsvalidatethetheoreticalresults.
简介:ThispapereonsidersanARIMA(p,d,q)medel.Amethodforestimatingtheorderdandtestingthehypothesis:d=d0isgiven.Theasymptoticpropertiesoftheestimatorhavebeendiscussed.