简介:Ageneralprocedureforconstructingmultivariatenon-tensor-productwaveletsthatgen-erateanorthogonaldecompositionofL~2(R~),s≥1,isdescribedandappliedtoyieldexplicitformulasforcompactlysupportedspline-waveletsbasedonthemultiresolutionanalysisofL~2(R~s),1≤s≤3,generatedbyanyboxsplinewhosedirectionsetconstitutesaunimodularmatrix.Inparticular,whenunivariatecardinalB-splinesareconsidered,theminimallysup-portedcardinalspline-waveletsofChuiandWangarerecovered.Arefinedcomputationalschemefortheorthogonalizationofspaceswithcompactlysupportedwaveletsisgiven.Arecursiveapproximationschemefor“truncated”decompositionsequencesisdevelopedandasharperrorboundisincluded.Aconditiononthesymmetryoranti-symmetryofthewaveletsisappliedtoyieldsymmetricbox-splinewavelets.
简介:CADprocessforstructuredesignofboxculvertisintroduced.Itfollowsthetraditionalwayofculvertdesign.Allworkingconditionsofculvertaretakenintoaccount.Itcangenerateloaddiagram,bendingmomentdiagramandbendingmomentenvelopediagramforasingle-hole,double-holeortriple-holeboxculvert.Thatistosay,thewholeCADprocessfortheboxculvertstructuredesignisrealizedwiththeself-developedsystem.IthasbeenusedtoaccomplishseveralprojectsinChinaandtheresultsaresatisfactory.
简介:AdegreeelevationformulaformultivariatesimplexsplineswasgivenbyMicchelli[6]andextendedtoholdformultivariateDirichletsplinesin[8].Wereportsimilarformulaeformultivariateconesplinesandboxsplines.Tothisend,weutilizearelationduetoDahmenandMicchelli[4]thatconnectsboxsplinesandconesplinesandadegreereductionformulagivenbyCohen,Lyche,andRiesenfeldin[2].
简介:ThepresentpaperinvestigatesthefractalstructureoffractionalintegralsofWeierstrassfunctions.Theexactboxdimensionforsuchfunctionsmanyimportantcasesisestablished.Weneedtopointoutthat,althoughtheresultitselfachievedinthepresentpaperisinteresting,thenewtechniqueandmethodshouldbeemphasized.ThesenovelideasmightbeusefultoestablishtheboxdimensionorHausdorffdimension(especiallyforthelowerbounds)formoregeneralgroupsoffunctions.