简介:<正>Foranyintegersa1,a2,a3,a4andcwitha1a2a3a40(modp),thispapershowsthatthereexistsasolutionX=(x1,x2,x3,x4)∈Z4ofthecongruencea1x12+a2x22+a3x32+a4x42≡c(modp)suchthat‖X‖=max{|x1|,|x2|,|x3|,|x4|}《p1/2logp.
简介:一、启发提问在统计初步中,如果要研究一组数据平均水平或集中趋势,则只需研究这组数据的.如果要研究一组数据的波动大小,则要研究这组数据的或;如果还要研究在哪一个范围内的数据较多,在哪一个范围内的数据较少,这就需要研究这组数据的.二、读书自学 教材P185-P189三、启读指导1.获得一组数据的频率分布的一般步骤是:(1),(2),(3),(4),(5),(6).2.在P185例中,这组数据的最大值是,最小值是,它们的差是cm.3.当数据在100个以内时.按照数据的多少,常分成组.这是分组的经验法则.4.组距是指每个小组的两个端点的.5.实际决定组数时,常有一个尝试的过程;先定,再算出相应的,再看
简介:Thispaperproposesandmakesastudyofanewmodel(calledthe3/2plusjumpsmodel)forVIXoptionpricing.Themodelallowsthemean-reversionspeedandvolatilityofvolatilitytobehighlysensitivetotheactuallevelofVIX.Inparticular,thepositivevolatilityskewisaddressedbythe3/2plusjumpsmodel.Dailycalibrationisusedtoprovethattheproposedmodelpreservesitsvalidityandreliabilityforbothin-sampleandout-of-sampletests.Theresultsshowthatthemodelsarecapableoffittingthemarketpricewhilegeneratingpositivevolatilityskew.
简介:X-rayimagingistheconventionalmethodfordiagnosingtheorthopedicconditionofapatient.ComputerizedTomography(CT)scanningisanotherdiagnosticmethodthatprovidespatient’s3Danatomicalinformation.However,bothmethodshavelimitationswhendiagnosingthewholeleg;X-rayimagingdoesnotprovide3Dinformation,andnormalCTscanningcannotbeperformedwithastandingposture.Obtaining3Ddataregardingthewholeleginastandingpostureisclinicallyimportantbecauseitenables3Danalysisintheweightbearingcondition.Basedontheseclinicalneeds,ahardware-basedbi-planeX-rayimagingsystemhasbeendeveloped;itusestwoorthogonalX-rayimages.However,suchmethodshavenotbeenmadeavailableingeneralclinicsbecauseofthehightcost.Therefore,weproposedawidelyadaptivemethodfor2DX-rayimageand3DCTscandata.Bythismethod,itispossibletothreedimensionallyanalyzethewholeleginstandingposture.TheoptimalpositionthatgeneratesthemostsimilarimageisthecapturedX-rayimage.Thealgorithmverifiesthesimilarityusingtheperformanceoftheproposedmethodbysimulation-basedexperiments.Then,weanalyzedtheinternal-externalrotationangleofthefemurusingrealpatientdata.Approximately10.55degreesofinternalrotationswerefoundrelativetothedefinedanterior-posteriordirection.Inthispaper,wepresentausefulregistrationmethodusingtheconventionalX-rayimageand3DCTscandatatoanalyzethewholelegintheweight-bearingcondition.
简介:AgraphGiscalledchromatic-choosableifitschoicenumberisequaltoitschromaticnumber,namelych(G)=χ(G).Ohba’sconjecturestatesthateverygraphGwith2χ(G)+1orfewerverticesischromaticchoosable.ItisclearthatOhba’sconjectureistrueifandonlyifitistrueforcompletemultipartitegraphs.Recently,Kostochka,StiebitzandWoodallshowedthatOhba’sconjectureholdsforcompletemultipartitegraphswithpartitesizeatmostfive.Butthecompletemultipartitegraphswithnorestrictionontheirpartitesize,forwhichOhba’sconjecturehasbeenverifiedarenothingmorethanthegraphsKt+3,2*(k-t-1),1*tbyEnotomoetal.,andKt+2,3,2*(k-t-2),1*tfort≤4byShenetal..Inthispaper,usingtheconceptoff-choosable(orL0-size-choosable)ofgraphs,weshowthatOhba’sconjectureisalsotrueforthegraphsKt+2,3,2*(k-t-2),1*twhent≥5.Thus,Ohba’sconjectureistrueforgraphsKt+2,3,2*(k-t-2),1*tforallintegerst≥1.