Lagrangian properties of turbulent channel flow : a numerical study
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(2) ौ Ƈ࢈ȩɟƇɟƚ ÷ ࡇ ߞߜߝߥĮëCߝߜߠߟ. ÷mRëC 4C 4°+÷°á÷ 4C ࢈ĆvģCáëv÷D 4C Į° ȩɔƛɟƛƚ ŏʕ ɯƚǞȘ Ƈƚ. Ȁ࢈ĆȘǞʲƚɟɯǞɾƛ +ȀŏʕƇƚ $ƚɟȘŏɟƇ ʿȩȘ ߝ DżȩȀƚ 4ȩżɾȩɟŏȀƚ ौ ߝߢߞ ƛżŏȘǞɛʕƚࡈ DȘƚɟǃƛɾǞɛʕƚࡈ bƛȘǞƚ żǞʲǞȀࡈ żȩʕɯɾǞɛʕƚ Cb ëɔƛżǞŏȀǞɾƛ Ƈƚ Ƈȩżɾȩɟŏɾ ࡇ ƛżŏȘǞɛʕƚ Ƈƚɯ _ȀʕǞƇƚɯ. ëȩʕɾƚȘʕƚ ɔʕųȀǞɛʕƚȒƚȘɾ Ȁƚ ߞߞࡕߜߟࡕߞߜߝߥࡈ ɔŏɟ ࡇ. ʕŏȘ vǃȘŏżǞȩ ÚΎͱ˨;̐Ύ. ŏǃɟŏȘǃǞŏȘ ɔɟȩɔƚɟɾǞƚɯ ȩǀ ɾʕɟųʕȀƚȘɾ żǕŏȘȘƚȀ ˚ȩʶࡇ ŏ ȘʕȒƚɟǞżŏȀ ɯɾʕƇʿ. 4ƚʲŏȘɾ Ȁƚ Dzʕɟʿ żȩȒɔȩɯƛ Ƈƚ ࡇ ˨ϑ˨χ ƚŏȘࡷÚǕǞȀǞɔɔƚ. Úɟȩǀƚɯɯƚʕɟ Ƈƚɯ ĆȘǞʲƚɟɯǞɾƛɯࡈ ĆȘǞʲƚɟɯǞɾƛ ʿȩȘ ߝ. ÚɟƛɯǞƇƚȘɾ. $̥̐ ƛɟƛȒǞƚ ë̐͑ͻ͖ϑϑ _ɟŏȘƀȩǞɯ ̊̊˨χ ǞżǕƚȀǞȘƚ Ύξ̙˨;ϑ ǞżȩȀŏɯ. 4Ǟɟƚżɾƚʕɟ Ƈƚ ɟƚżǕƚɟżǕƚࡈ +áë 4Ǟɟƚżɾƚʕɟ Ƈƚ ɟƚżǕƚɟżǕƚࡈ +áë ŏǣɾɟƚ Ƈƚ +ȩȘǀƛɟƚȘżƚɯࡈ vÚ ÷ȩʕȀȩʕɯƚ Úɟȩǀƚɯɯƚʕɟ Ƈƚɯ ĆȘǞʲƚɟɯǞɾƛɯࡈ ĆȘǞʲƚɟɯǞɾƛ bɟƚȘȩųȀƚ Ȁɔƚɯ. áŏɔɔȩɟɾƚʕɟ áŏɔɔȩɟɾƚʕɟ CʾŏȒǞȘŏɾɟǞżƚ CʾŏȒǞȘŏɾƚʕɟ. ģ͖;ͬΎϻ͖̐ vʲŏȘŏ $Ύϟξ͇Ύ͖; ǞżǺŏƦȀ. Úɟȩǀƚɯɯƚʕɟƚ Ƈƚɯ ĆȘǞʲƚɟɯǞɾƛɯࡈ ĆȘǞʲƚɟɯǞɾƛ ʿȩȘ ߝ 4Ǟɟƚżɾƚʕɟ Ƈƚ ɟƚżǕƚɟżǕƚࡈ +áë. 4ǞɟƚżɾɟǞżƚ Ƈƚ ɾǕƩɯƚ vȘʲǞɾƛ.
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(4) ĆvģCáëv÷D +Ć4C $Cáá4 ࡵ Į° ߝ ÚɟƛɯǞƇƚȘɾ Ƈƚ Ȁ࢈ĆȘǞʲƚɟɯǞɾƛ. ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ _ɟƛƇƛɟǞż _CĆáĮ. ÚɟƛɯǞƇƚȘɾ Ƈʕ +ȩȘɯƚǞȀ żŏƇƛȒǞɛʕƚ. ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ mŏȒƇŏ $C m4v4. ÚɟƛɯǞƇƚȘɾ Ƈʕ +ȩȘɯƚǞȀ Ƈ࢈ƇȒǞȘǞɯɾɟŏɾǞȩȘ. ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ 4ǞƇǞƚɟ áCģC. ģǞżƚࡷɔɟƛɯǞƇƚȘɾ Ƈʕ +ȩȘɯƚǞȀ _ȩɟȒŏɾǞȩȘ ƚɾ ģǞƚ ĆȘǞʲƚɟɯǞɾŏǞɟƚ. ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ ÚǕǞȀǞɔɔƚ +mCģvCá. ģǞżƚࡷɔɟƛɯǞƇƚȘɾ Ƈƚ Ȁŏ +ȩȒȒǞɯɯǞȩȘ áƚżǕƚɟżǕƚ. ࡏ _ŏųɟǞżƚ ģDC. 4Ǟɟƚżɾƚʕɟ bƛȘƛɟŏȀ Ƈƚɯ ëƚɟʲǞżƚɯ. ࡏ ȀŏǞȘ mCCĆ. +°Ú°ë÷Cë ë÷D _ŏżʕȀɾƛ Ƈƚ ƛƇƚżǞȘƚ ʿȩȘ Cɯɾ ࡵ +ȀŏʕƇƚ $ƚɟȘŏɟƇ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ ࡏ C÷vCC. _ŏżʕȀɾƛ Ƈƚ ƛƇƚżǞȘƚ ƚɾ Ƈƚ ŏǥƚʕɾǞɛʕƚ ʿȩȘ ëʕƇ ࡵ +ǕŏɟȀƚɯ ƛɟǞƚʕʾ. 4Ǟɟƚżɾƚʕɟ ࡇ Ȓƚ Ȁŏ Úɟȩǀƚɯɯƚʕɟƚ +ࡏ $Ćáv°. _ŏżʕȀɾƛ Ƈ࢈°ƇȩȘɾȩȀȩǃǞƚ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ 4ࡏ $°ĆábC°vë. vȘɯɾǞɾʕɾ Ƈƚɯ ëżǞƚȘżƚɯ ÚǕŏɟȒŏżƚʕɾǞɛʕƚɯ ƚɾ $ǞȩȀȩǃǞɛʕƚɯ. 4Ǟɟƚżɾƚʕɟ ࡇ Ȓƚ Ȁŏ Úɟȩǀƚɯɯƚʕɟƚ +ࡏ ģv+vbĆCáá. vȘɯɾǞɾʕɾ Ƈƚɯ ëżǞƚȘżƚɯ ƚɾ ÷ƚżǕȘǞɛʕƚɯ Ƈƚ Ȁŏ áƛŏƇŏɔɾŏɾǞȩȘ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ Įࡏ ÷v°. 4ƛɔŏɟɾƚȒƚȘɾ Ƈƚ ǀȩɟȒŏɾǞȩȘ ƚɾ +ƚȘɾɟƚ Ƈƚ áƚżǕƚɟżǕƚ ƚȘ $ǞȩȀȩǃǞƚ mʕȒŏǞȘƚ. 4Ǟɟƚżɾƚʕɟ ࡇ Ȓƚ Ȁŏ Úɟȩǀƚɯɯƚʕɟƚ ࡷࡏ ë+m°÷÷. +°Ú°ë÷Cë C÷ 4DÚá÷CC÷ë 4C ë+vC+Cë C÷ ÷C+m°°bvC _ŏżʕȀɾƛ Ƈƚɯ ëżǞƚȘżƚɯ ƚɾ ÷ƚżǕȘȩȀȩǃǞƚɯ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ _ࡏ 4C á+mv. 4ƛɔŏɟɾƚȒƚȘɾ $ǞȩȀȩǃǞƚ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ _ࡏ ÷mCģCá4. 4ƛɔŏɟɾƚȒƚȘɾ +ǕǞȒǞƚ $ǞȩżǕǞȒǞƚ. 4Ǟɟƚżɾƚʕɟ ࡇ Ȓƚ +ࡏ _Cvĭ. 4ƛɔŏɟɾƚȒƚȘɾ bCÚ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ mŏɯɯŏȘ m°Ćáv. 4ƛɔŏɟɾƚȒƚȘɾ vȘǀȩɟȒŏɾǞɛʕƚ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ ëࡏ °Ć+mC. 4ƛɔŏɟɾƚȒƚȘɾ ŏɾǕƛȒŏɾǞɛʕƚɯ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ bࡏ ÷°°ģ. 4ƛɔŏɟɾƚȒƚȘɾ ƛżŏȘǞɛʕƚ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ ࡏ $Ć__÷. 4ƛɔŏɟɾƚȒƚȘɾ ÚǕʿɯǞɛʕƚ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ ࡷ+ ÚCC÷. Ć_á ëżǞƚȘżƚɯ ƚɾ ÷ƚżǕȘǞɛʕƚɯ Ƈƚɯ żɾǞʲǞɾƛɯ ÚǕʿɯǞɛʕƚɯ ƚɾ ëɔȩɟɾǞʲƚɯ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Įࡏ ģÚ°ĆC. °ųɯƚɟʲŏɾȩǞɟƚ Ƈƚɯ ëżǞƚȘżƚɯ Ƈƚ Ȁ࢈ĆȘǞʲƚɟɯ Ƈƚ ʿȩȘ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ $ࡏ bĆv4Cá4°v. ÚȩȀʿɾƚżǕ ʿȩȘ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ Cࡏ ÚCááv. CżȩȀƚ ëʕɔƛɟǞƚʕɟƚ Ƈƚ +ǕǞȒǞƚ ÚǕʿɯǞɛʕƚ CȀƚżɾɟȩȘǞɛʕƚ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ bࡏ ÚvbĆ÷. vȘɯɾǞɾʕɾ ĆȘǞʲƚɟɯǞɾŏǞɟƚ Ƈƚ ÷ƚżǕȘȩȀȩǃǞƚ Ƈƚ ʿȩȘ ߝ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ +ࡏ ģv÷°. CżȩȀƚ ëʕɔƛɟǞƚʕɟƚ Ƈʕ Úɟȩǀƚɯɯȩɟŏɾ ƚɾ Ƈƚ Ȁ࢈CƇʕżŏɾǞȩȘ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ Ȁƚ Úɟȩǀƚɯɯƚʕɟ ࡏ °Ćbv°÷÷C. vȘɯɾǞɾʕɾ Ƈƚ ëżǞƚȘżƚ _ǞȘŏȘżǞƩɟƚ ƚɾ Ƈ࢈ɯɯʕɟŏȘżƚɯ. 4Ǟɟƚżɾƚʕɟ ࡇ ࡏ ࡏ C$°vëC.
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(6) ŏǃɟŏȘǃǞŏȘ ɔɟȩɔƚɟɾǞƚɯ ȩǀ ɾʕɟųʕȀƚȘɾ żǕŏȘȘƚȀ ˚ȩʶࡇ ŏ ȘʕȒƚɟǞżŏȀ ɯɾʕƇʿ ̊χϑξ˨̐ϑ 5IF -BHSBOHJBO QFSTQFDUJWF EFTDSJCJOH B bPX GSPN UIF USBKFDUPSJFT PG bVJE USBDFST JT. B OBUVSBM GSBNFXPSL GPS TUVEZJOH EJTQFSTJPO QIFOPNFOB JO UVSCVMFOU bPXT *O XBMMCPVOEFE UVSCVMFODF UIF NPUJPO PG bVJE USBDFST JT BêFDUFE CZ NFBO TIFBS BOE CZ TUSPOH JOIPNPHFOFJUZ BOE BOJTPUSPQZ OFBS XBMMT 8F JOWFTUJHBUF UIF -BHSBOHJBO QSPQFSUJFT PG B UVSCVMFOU DIBOOFM bPX VTJOH EJSFDU OVNFSJDBM TJNVMBUJPOT BU B NPEFSBUF 3FZOPMET OVNCFS -BHSBOHJBO BDDFMFSBUJPO TUBUJTUJDT BSF DPNQBSFE UP QBSUJDMF USBDLJOH FYQFSJNFOUT QFSGPSNFE JO QBSBMMFM UP UIJT XPSL "T JO IPNPHFOFPVT JTPUSPQJD UVSCVMFODF )*5 UIF BDDFMFSBUJPO DPNQPOFOUT BMPOH -BHSBOHJBO QBUIT EFDPSSFMBUF PWFS UJNF TDBMFT SFQSFTFOUBUJWF PG UIF TNBMMFTU TDBMFT PG UIF bPX XIJMF UIF BDDFMFSBUJPO OPSN TUBZT DPSSFMBUFE GPS NVDI MPOHFS 5IF QFSTJTUFODF PG TNBMMTDBMF BOJTPUSPQZ GBS GSPN UIF XBMM JT EFNPOTUSBUFE JO UIF GPSN PG B OPO[FSP DSPTTDPSSFMBUJPO CFUXFFO BDDFMFSBUJPO DPNQPOFOUT "T B SFTVMU PG UIF BWFSBHF bVYFT PG LJOFUJD FOFSHZ JO XBMM UVSCVMFODF USBDFST JOJUJBMMZ MPDBUFE DMPTF UP UIF XBMM USBWFM BOE TQSFBE PWFS MPOHFS EJTUBODFT XIFO USBDLFE CBDLXBSET JO UJNF UIBO GPSXBSET 5IF SFMBUJWF EJTQFSTJPO PG USBDFS QBJST JT aOBMMZ JOWFTUJHBUFE "U TIPSU UJNFT QBJS TFQBSBUJPO JT CBMMJTUJD GPS BMM XBMM EJTUBODFT "T JO )*5 SFMBUJWF EJTQFSTJPO JT UJNF BTZNNFUSJD XJUI USBDFST TFQBSBUJOH GBTUFS XIFO USBDLFE CBDLXBSET JO UJNF "U MPOHFS UJNFT NFBO TIFBS EPNJOBUFT MFBEJOH UP SBQJE TFQBSBUJPO JO UIF NFBO bPX EJSFDUJPO " CBMMJTUJD DBTDBEF NPEFM QSFWJPVTMZ QSPQPTFE GPS )*5 JT BEBQUFE UP JOIPNPHFOFPVT bPXT ̥ІϾΎξ̙χ UVSCVMFODF -BHSBOHJBO EFTDSJQUJPO XBMM UVSCVMFODF DIBOOFM bPX EJSFDU OVNFSJDBM. TJNVMBUJPO EJTQFSTJPO BDDFMFSBUJPO. ÚɟȩɔɟǞƛɾƛɯ ȀŏǃɟŏȘǃǞƚȘȘƚɯ Ƈ࢈ʕȘ ƛżȩʕȀƚȒƚȘɾ Ƈƚ żŏȘŏȀ ɾʕɟųʕȀƚȘɾ ࡇ ʕȘƚ ƛɾʕƇƚ ȘʕȒƛɟǞɛʕƚ á̦χϟͻ̦ -B QFSTQFDUJWF MBHSBOHJFOOF EÆDSJWBOU VO ÆDPVMFNFOU TFMPO MFT USBKFDUPJSFT EF USBDFVST. bVJEFT FTU VOF BQQSPDIF OBUVSFMMF QPVS ÆUVEJFS MFT QIÆOPNÅOFT EF EJTQFSTJPO EBOT MFT ÆDPV MFNFOUT UVSCVMFOUT &O UVSCVMFODF EF QBSPJ MF NPVWFNFOU EFT USBDFVST FTU JObVFODÆ QBS MF DJTBJMMFNFOU NPZFO FU QBS VOF GPSUF JOIPNPHÆOÆJUÆ FU BOJTPUSPQJF FO QSPDIF QBSPJ 0O ÆUVEJF MFT QSPQSJÆUÆT MBHSBOHJFOOFT ErVO ÆDPVMFNFOU EF DBOBM UVSCVMFOU QBS TJNVMBUJPO OVNÆSJRVF EJSFDUF ½ VO OPNCSF EF 3FZOPMET NPEÆSÆ -FT TUBUJTUJRVFT ErBDDÆMÆSBUJPO MBHSBOHJFOOF TPOU DPNQBSÆFT BVY FYQÆSJFODFT EF TVJWJ EF QBSUJDVMFT SÆBMJTÆFT FO QBSBMMÅMF ½ DF USBWBJM $PNNF FO UVSCVMFODF IPNPHÅOF JTPUSPQF 5)* MFT DPNQPTBOUFT ErBDDÆMÆSBUJPO MF MPOH EFT USBKFDUPJSFT MBHSBOHJFOOFT TF EÆDPSSÅMFOU TVS EFT UFNQT DPNQBSBCMFT BVY QMVT QFUJUFT ÆDIFMMFT EF MrÆDPVMFNFOU UBOEJT RVF MB OPSNF EF MrBDDÆMÆSBUJPO SFTUF DPSSÆMÆF QMVT MPOHUFNQT -B QFSTJTUBODF ErBOJTPUSPQJF ½ QFUJUF ÆDIFMMF MPJO EF MB QBSPJ FTU DPOTUBUÆF QBS MrFYJTUFODF ErVOF DPSSÆMBUJPO DSPJTÆF OPO OVMMF FOUSF EFVY DPNQPTBOUFT EF MrBDDÆMÆSBUJPO 0O NPOUSF RVF FO DPOTÆRVFODF EFT bVY NPZFOT ErÆOFSHJF DJOÆUJRVF FO UVSCVMFODF EF QBSPJ QSÅT EFT QBSPJT MFT USBDFVST TF EÆQMBDFOU FU TrÆUBMFOU TVS EFT QMVT HSBOEFT EJTUBODFT RVBOE JMT TPOU TVJWJT FO BSSJÅSF EBOT MF UFNQT RVrFO BWBOU -B EJTQFSTJPO SFMBUJWF EF QBJSFT EF USBDFVST FTU BVTTJ ÆUVEJÆF "VY UFNQT DPVSUT MB TÆQBSBUJPO EFT QBJSFT FTU CBMJTUJRVF QPVS UPVUFT MFT EJTUBODFT ½ MB QBSPJ $PNNF FO 5)* MFT USBDFVST TF TÆQBSFOU QMVT SBQJEFNFOU MPSTRVrJMT TPOU TVJWJT FO BSSJÅSF EBOT MF UFNQT "VY UFNQT QMVT MPOHT MF DJTBJMMFNFOU NPZFO BDDÆMÅSF MB TÆQBSBUJPO EBOT MB EJSFDUJPO EF MrÆDPVMFNFOU NPZFO 6O NPEÅMF EF DBTDBEF CBMJTUJRVF JOJUJBMFNFOU QSPQPTÆ QPVS MB 5)* FTU BEBQUÆ BVY ÆDPVMFNFOUT JOIPNPHÅOFT Ύϑχࡷ̐ͱ̦χ UVSCVMFODF EFTDSJQUJPO MBHSBOHJFOOF UVSCVMFODF EF QBSPJ ÆDPVMFNFOU EF DBOBM. TJNVMBUJPO OVNÆSJRVF EJSFDUF EJTQFSTJPO BDDÆMÆSBUJPO. W.
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(8) áƚȒƚɟżǞƚȒƚȘɾɯ %VSBOU DFUUF UIÅTF KrBJ FV MF QMBJTJS FU MB DIBODF ErJOUFSBHJS BWFD EF OPNCSFVTFT QFSTPOOFT RVJ POU JObVFODÆ ErVOF NBOJÅSF PV ErVOF BVUSF MFT USBWBVY QSÆTFOUÆT JDJ +F WPVESBJT UPVU ErBCPSE SFNFSDJFS *WBOB 7JOLPWJD EF NrBWPJS NPUJWÆ ½ GBJSF DFUUF UIÅTF FU ErBWPJS FV MB bFYJCJMJUÆ ErBEBQUFS MF TVKFU RVJ FO QSJODJQF EFWBJU QPSUFS TVS MB EJTQFSTJPO EF QBSUJDVMFT BV EFTTVT ErVOF DBOPQÆF WÆHÆUBMF ½ MB TJUVBUJPO FU ½ NFT JOUÆSxUT +rBJ CFBVDPVQ BQQSÆDJÆ OPT SÆVOJPOT JNQSPWJTÆFT FO USBWFSTBOU MF 1BSD EF MB 5xUF Er0S ½ WÆMP MF NBUJO +F MVJ TVJT BVTTJ USÅT SFDPOOBJTTBOU EF NrBWPJS FODPVSBHÆ ½ QSÆTFOUFS NFT USBWBVY EBOT EJêÆSFOUT DPOHSÅT BV OJWFBV MPDBM FU JOUFSOBUJPOBM +F SFNFSDJF .JDLBÈM #PVSHPJO ErBWPJS TVJWJ VOF QBSUJF EF NFT USBWBVY EF UIÅTF QPVS OPT EJTDVTTJPOT UPVKPVST USÅT ÆDMBJSBOUFT FU BHSÆBCMFT FU QMVT QBSUJDVMJÅSFNFOU QPVS TFT DPNNFOUBJSFT TVS VOF WFSTJPO QSÆMJNJOBJSF EF DF NBOVTDSJU +rBJ FV BVTTJ MF HSBOE QMBJTJS EF DPMMBCPSFS BWFD /JDL 4UFM[FONVMMFS FU /JDPMBT .PSEBOU RVF KF SFNFSDJF QPVS MFT OPNCSFVY ÆDIBOHFT FU EJTDVTTJPOT EPOU NFT USBWBVY POU CFBVDPVQ CÆOÆaDJÆ +F SFNFSDJF ÆHBMFNFOU MFT BVUSFT NFNCSFT EV QSPKFU "/3 -5*' 3PNBJO 7PML .JLIBFM (PSPLIPWTLJ 1FUFS )VDL FU "MFYJT #BSHF QPVS MFVST JEÆFT FU TVHHFTUJPOT MPST EFT SÆVOJPOT EF QSPKFU .FSDJ BVY NFNCSFT EV KVSZ FO QBSUJDVMJFS BVY SBQQPSUFVST +ÆSÆNJF #FD FU 'SBOÄPJT 4DINJUU QPVS MFVS EJTQPOJCJMJUÆ BJOTJ RVF QPVS MFVST DPNNFOUBJSFT QPTJUJGT FU USÅT DPOTUSVDUJGT FOWFST NFT USBWBVY EF UIÅTF $FUUF UIÅTF OrBVSBJU QBT FV MJFV TBOT MrJOUFSWFOUJPO Er&NNBOVFM .JHOPU MPSTRVF KrÆUBJT BV $IJMJ +F MF SFNFSDJF DIBMFVSFVTFNFOU QPVS TFT QSÆDJFVY DPOTFJMT QPVS MFT OPNCSFVTFT EJTDVTTJPOT JOGPSNFMMFT UPVU BV MPOH EF DFUUF UIÅTF FU QMVT HÆOÆSBMFNFOU QPVS TPO IPTQJUBMJUÆ FU BNJUJÆ .FSDJ ½ 4FSHF 4JNPÈOT ErBWPJS TPVUFOV FO UBOU RVF SFTQPOTBCMF EV HSPVQF 'MVJEFT $PNQMFYFT FU 5SBOTGFSUT BV -.'" NFT EÆQMBDFNFOUT ½ QMVTJFVST DPOHSÅT +F MF SFNFSDJF BVTTJ QPVS OPT EJTDVTTJPOT JOUÆSFTTBOUFT QPVS NrBWPJS BJEÆ ½ PCUFOJS VO CVSFBV ½ ¦DVMMZ FU FO HÆOÆSBM QPVS TPO TPVUJFO FU TB CPOOF IVNFVS +F SFNFSDJF .BSD #VêBU ErBWPJS NJT ½ EJTQPTJUJPO VOF WFSTJPO EV DPEF /BEJB4QFDUSBM QPVS VUJMJTBUJPO FU NPEJaDBUJPO EBOT MF DBESF EF DFUUF UIÅTF .FSDJ ½ $ISJTUPQIF 1FSB QPVS MrBENJOJTUSBUJPO EV DFOUSF EF DBMDVM 1$)1% ½ Mr6OJWFSTJUÆ -ZPO FU QPVS TB EJTQPOJCJMJUÆ ½ SÆQPOESF ½ NFT RVFTUJPOT .FSDJ ½ UPVT NFT DPMMÅHVFT EPDUPSBOUT FU QPTUEPDUPSBOUT RVF KrBJ SFODPOUSÆT TVS MFT USPJT TJUFT EV -.'" &O PSESF QMVT PV NPJOT DISPOPMPHJRVF KF SFNFSDJF 8FODIBP EF NrBWPJS BJEÆ ½ EÆNBSSFS BWFD MF DPEF %/4 .FSDJ %JNJUSJ 4ZMWJF FU 7JODFOU QPVS MB CPOOF BNCJBODF +F SFNFSDJF BVTTJ %POBUP 3PCFSU "MFLTBOES QPVS MFT DIPDPMBUT . "OESFB $FOL )FOSJ FU $PSFOUJO .FSDJ 3BaL QPVS MF TPVUJFO FU MFT DPOTFJMT EBOT MB EFSOJÅSF QBSUJF EF NB UIÅTF .FSDJ 5PN QPVS MFT DPNNFOUBJSFT USÅT PQQPSUVOT ½. WJJ.
(9) 3FNFSDJFNFOUT RVFMRVFT KPVST EF NB TPVUFOBODF (SBDJBT BM HSVQP EF DIJMFOPT Z QS¾DUJDBNFOUF DIJMFOPT FO -ZPO QPS MPT CVFOPT NPNFOUPT 'SBO $BSPM .BOV &WF $BSMPT $MBV Z "OUPJOF (SBDJBT .BSJFMMF QPS TFS VOB BNJHB JODSFÊCMF Z VOB HSBO JObVFODJB FO MPT ÖMUJNPT DBTJ EPT BPT "HSBEF[DP UBNCJÆO B NJ GBNJMJB QPS TV BQPZP DPOTUBOUF Z QPS BDFQUBS UFOFSNF UBO MFKPT +F SFNFSDJF aOBMFNFOU MF HPVWFSOFNFOU DIJMJFO ErBWPJS aOBODÆ DFUUF UIÅTF EBOT MF DBESF EV QSPHSBNNF $0/*$:5 #FDBT $IJMF .FT USBWBVY POU ÆHBMFNFOU CÆOÆaDJÆ EV TPVUJFO EF Mr"HFODF /BUJPOBMF EF MB 3FDIFSDIF EBOT MF DBESF EV QSPKFU "/3 -5*' BJOTJ RVF EF QMVTJFVST BMMPDBUJPOT EF SFTTPVSDFT JOGPSNBUJRVFT BV $*/&4. WJJJ.
(10) +ȩȘɾƚȘɾɯ ųɯɾɟŏżɾ ࡕ áƛɯʕȒƛ. ʲ. áƚȒƚɟżǞƚȒƚȘɾɯ. ʲǞǞ. +ȩȘɾƚȘɾɯ. Ǟʾ. Ǟɯɾ ȩǀ _Ǟǃʕɟƚɯ. ʾǞǞǞ. Ǟɯɾ ȩǀ ÷ŏųȀƚɯ. ʾʲǞǞ. ȩȒƚȘżȀŏɾʕɟƚ. ʾǞʾ. ųųɟƚʲǞŏɾǞȩȘɯ. ʾʾǞǞǞ. °ɔƚɟŏɾȩɟɯ ߝ. vȘɾɟȩƇʕżɾǞȩȘ. . . . ߞ. ʾʾʲ ߝ. -BHSBOHJBO EFTDSJQUJPO PG UVSCVMFOU bPXT &VMFSJBO BOE -BHSBOHJBO GPSNVMBUJPOT -BHSBOHJBO QSPQFSUJFT PG JTPUSPQJD UVSCVMFOU bPXT -BHSBOHJBO TUPDIBTUJD NPEFMT -BHSBOHJBO JOUFSNJUUFODZ -BHSBOHJBO BDDFMFSBUJPO "OJTPUSPQJD BOE JOIPNPHFOFPVT bPXT 8BMMCPVOEFE UVSCVMFODF 5VSCVMFOU DIBOOFM bPX 4DBMFT PG XBMMCPVOEFE UVSCVMFODF .FBO WFMPDJUZ QSPaMF $PIFSFOU TUSVDUVSFT -BHSBOHJBO JOWFTUJHBUJPOT PG XBMM UVSCVMFODF $IBOOFM bPX 1JQF BOE CPVOEBSZ MBZFS bPXT 0CKFDUJWFT BOE PVUMJOF . . . . . . . . . ʕȒƚɟǞżŏȀ ȒƚɾǕȩƇɯ. . %JSFDU OVNFSJDBM TJNVMBUJPOT (FOFSBM BTQFDUT PG TQFDUSBM NFUIPET "QQMJDBUJPO UP DIBOOFM bPX TJNVMBUJPOT 7BSJBUJPOBM GPSNVMBUJPO . ߟߡ. . . . . . . . . . . . . . . . JY.
(11) $POUFOUT . . . . . . . . . . ëǞȘǃȀƚࡷɔŏɟɾǞżȀƚ ƇǞɯɔƚɟɯǞȩȘ. ߥߡ. . .FBO XBMMOPSNBM QBSUJDMF EJTQMBDFNFOU .FBO TUSFBNXJTF QBSUJDMF EJTQMBDFNFOU . . . ߟ. ŏǃɟŏȘǃǞŏȘ ɯɾŏɾǞɯɾǞżɯ ȩǀ ŏżżƚȀƚɟŏɾǞȩȘ. . . . ߠ. Y. $IPJDF PG USJBM BOE UFTU GVODUJPOT 5FNQPSBM EJTDSFUJTBUJPO 4FRVFODF PG BO JUFSBUJPO $PNQVUBUJPO PG UIF BDDFMFSBUJPO aFME 1BSBMMFMJTBUJPO TUSBUFHZ %PNBJO EFDPNQPTJUJPO 1BSBMMFM aMF *0 1BSBNFUFST BOE WBMJEBUJPO PG UIF &VMFSJBO TPMWFS 4JNVMBUJPO QBSBNFUFST &VMFSJBO UXPQPJOU BVUPDPSSFMBUJPOT 7FMPDJUZ TUBUJTUJDT "DDFMFSBUJPO TUBUJTUJDT $PODMVTJPO -BHSBOHJBO USBDLJOH PG bVJE QBSUJDMFT (PWFSOJOH FRVBUJPOT BOE UJNF EJTDSFUJTBUJPO *OUFSQPMBUJPO PG &VMFSJBO aFMET *OUFSQPMBUJPO NFUIPET &WBMVBUJPO BOE DIPJDF PG JOUFSQPMBUJPO TDIFNF /PUF PO bVJE QBSUJDMF BDDFMFSBUJPOT *NQMFNFOUBUJPO EFUBJMT BOE QBSBMMFM TUSBUFHZ 7BMJEBUJPO BHBJOTU &VMFSJBO TUBUJTUJDT $PODMVTJPO (FOFSBM DPODMVTJPO . &YQFSJNFOUBM TFUVQ $IBOOFM bPX 1BSUJDMFT BOE 157 TZTUFN 7FMPDJUZ BOE BDDFMFSBUJPO QSPaMFT 7FMPDJUZ QSPaMFT "DDFMFSBUJPO QSPaMFT -BHSBOHJBO EFTDSJQUJPO PG XBMMCPVOEFE bPXT -BHSBOHJBO BDDFMFSBUJPO DPSSFMBUJPOT "DDFMFSBUJPO BVUPDPSSFMBUJPOT "DDFMFSBUJPO DSPTTDPSSFMBUJPOT "DDFMFSBUJPO NBHOJUVEF -BHSBOHJBO UJNF TDBMFT "DDFMFSBUJPO 1%'T $PODMVTJPO . ߣߝ. . . . . . . . . . .
(12) $POUFOUT . . ߡ. .FBOTRVBSF EJTQFSTJPO UIFPSZ BOE EFaOJUJPOT 4JOHMFQBSUJDMF EJTQFSTJPO JO JTPUSPQJD bPXT .FBOTRVBSF EJTQFSTJPO BU TIPSU UJNFT -BHSBOHJBO QPXFS BOE WFMPDJUZBDDFMFSBUJPO DPWBSJBODF .FBOTRVBSF EJTQFSTJPO JO UIF DIBOOFM .FBOTRVBSF TUSFBNXJTF EJTQMBDFNFOU .FBOTRVBSF TUSFBNXJTF EJTQFSTJPO .FBOTRVBSF XBMMOPSNBM EJTQMBDFNFOU .FBOTRVBSF TQBOXJTF EJTQFSTJPO $PODMVTJPO . . . . . . . . . . áƚȀŏɾǞʲƚ ƇǞɯɔƚɟɯǞȩȘ ȩǀ ɔŏɟɾǞżȀƚ ɔŏǞɟɯ. . . . . . . *OUSPEVDUJPO 3FMBUJWF EJTQFSTJPO JO JTPUSPQJD UVSCVMFOU bPXT 3FMBUJWF EJTQFSTJPO JO TIFBS BOE XBMMCPVOEFE bPXT 1BSUJDMF QBJS EBUBTFUT .FBOTRVBSF TFQBSBUJPO 4IPSUUJNF EJTQFSTJPO 4USVDUVSF GVODUJPOT Ǎӝ BOE Ǎեֵ #BMMJTUJD UJNF TDBMF /PSNBMJTFE NFBOTRVBSF TFQBSBUJPO 5FNQPSBM BTZNNFUSZ *ObVFODF PG UIF JOJUJBM TFQBSBUJPO .FBO TIFBS JObVFODF %FDPNQPTJUJPO PG UIF NFBOTRVBSF TFQBSBUJPO 4IPSUUJNF EJTQFSTJPO 5FNQPSBM BTZNNFUSZ 3FMBUJWF EJTQFSTJPO UFOTPS 4IPSUUJNF EJTQFSTJPO *OUFSNFEJBUF BOE MPOHUJNF EJTQFSTJPO 5JNF FWPMVUJPO PG DSPTTUFSN ׁׅ #BMMJTUJD EJTQFSTJPO NPEFM #BMMJTUJD DBTDBEF NPEFM JO JTPUSPQJD UVSCVMFODF #BMMJTUJD DBTDBEF NPEFM JO JOIPNPHFOFPVT UVSCVMFODF "QQMJDBUJPO UP UVSCVMFOU DIBOOFM bPX %JTDVTTJPO BOE QFSTQFDUJWFT $PODMVTJPO . ߝߝߡ. . . . . . . . ߢ. +ȩȘżȀʕɯǞȩȘ ŏȘƇ ɔƚɟɯɔƚżɾǞʲƚɯ. ߝߡߥ. . ëǞȘǃȀƚࡷɔȩǞȘɾ ɯɾŏɾǞɯɾǞżɯ ŏɾ 3F࠰ . ߝߢߟ. " 7FMPDJUZ BOE BDDFMFSBUJPO TUBUJTUJDT " %JTTJQBUJPO BOE UVSCVMFOU TDBMFT . YJ.
(13) $POUFOUT $. ƚŏȘ ŏǃɟŏȘǃǞŏȘ ƇʿȘŏȒǞżɯ ȩǀ ǺǞȘƚɾǞż ƚȘƚɟǃʿ. # 5PUBM LJOFUJD FOFSHZ CVEHFU # -BHSBOHJBO EZOBNJDT PG UIF UVSCVMFOU LJOFUJD FOFSHZ # %FDPNQPTJUJPO PG %ǝພ%Ǧ # 5VSCVMFOU LJOFUJD FOFSHZ CVEHFU # 1SPaMFT BU 3F࠰ $ǞųȀǞȩǃɟŏɔǕʿ. YJJ. ߝߢߣ. . . . . . . . . . . ߝߣߡ.
(14) Ǟɯɾ ȩǀ _Ǟǃʕɟƚɯ . 4DIFNBUJD PG B -BHSBOHJBO USBKFDUPSZ 7JTVBMJTBUJPO PG HSJEHFOFSBUFE UVSCVMFODF -BHSBOHJBO BOE &VMFSJBO WFMPDJUZ UJNF TFSJFT -BHSBOHJBO WFMPDJUZ BVUPDPSSFMBUJPO GVODUJPO -BHSBOHJBO JOUFSNJUUFODZ JO JTPUSPQJD UVSCVMFODF -BHSBOHJBO BDDFMFSBUJPO JO MBCPSBUPSZ FYQFSJNFOUT 4USVDUVSF PG UIF BDDFMFSBUJPO WFDUPS JO UVSCVMFOU bPXT $IBOOFM bPX HFPNFUSZ BOE DPPSEJOBUF TZTUFN .FBO WFMPDJUZ QSPaMF JO UVSCVMFOU CPVOEBSZ MBZFS $PIFSFOU NPUJPOT JO XBMM UVSCVMFODF /FBSXBMM TUSFBLT JO DIBOOFM bPX %/4 7JTVBMJTBUJPO PG OFBSXBMM WPSUJDFT JO DIBOOFM bPX %/4 $PODFQUVBM NPEFM PG IBJSQJO WPSUFY QBDLFUT 7JTVBMJTBUJPO PG 7-4.T JO UVSCVMFOU DIBOOFM bPX . . . . . . %PNBJO EFDPNQPTJUJPO DPOaHVSBUJPOT 5XPQPJOU WFMPDJUZ BOE BDDFMFSBUJPO BVUPDPSSFMBUJPOT .FBO BOE WBSJBODF WFMPDJUZ QSPaMFT .FBO BOE WBSJBODF BDDFMFSBUJPO QSPaMFT 4LFXOFTT BOE bBUOFTT BDDFMFSBUJPO QSPaMFT 4DIFNBUJD PG BO JOUFSQPMBUJPO DFMM "TTFTTNFOU PG EJêFSFOU JOUFSQPMBUJPO TDIFNFT GPS B TJOHMF QBSUJDMF -BHSBOHJBO BDDFMFSBUJPO BVUPDPSSFMBUJPOT JOUFSQPMBUJPO TDIFNFT "DDFMFSBUJPO PG B TJOHMF bVJE QBSUJDMF PWFS UJNF 8BMMOPSNBM CJOT GPS DPNQVUBUJPO PG -BHSBOHJBO TUBUJTUJDT "DDFMFSBUJPO WBSJBODF BOE TLFXOFTT &VMFSJBO-BHSBOHJBO DPNQBSJTPO. . . 4LFUDI PG UIF UVSCVMFOU DIBOOFM bPX FYQFSJNFOU BU -&(* .FBO BOE WBSJBODF WFMPDJUZ QSPaMFT .FBO BOE WBSJBODF BDDFMFSBUJPO QSPaMFT 4BNQMF IJHIBDDFMFSBUJPO QBSUJDMF USBKFDUPSJFT *MMVTUSBUJPO PG UIF -BHSBOHJBO BWFSBHJOH QSPDFEVSF -BHSBOHJBO BVUPDPSSFMBUJPOT PG BDDFMFSBUJPO 4BNQMF QBSUJDMF USBKFDUPSJFT QSPKFDUFE PO B ǫǬ QMBOF -BHSBOHJBO DSPTTDPSSFMBUJPOT PG BDDFMFSBUJPO ե -BHSBOHJBO BDDFMFSBUJPO DSPTTDPSSFMBUJPO ׁׅ 4DIFNBUJD PG B QBSUJDMF BQQSPBDIJOH UIF XBMM . . . . . . . . . . . . . . . . YJJJ.
(15) -JTU PG 'JHVSFT . &TUJNBUJPO PG -BHSBOHJBO WFMPDJUZ UJNF TDBMFT JO UIF FYQFSJNFOU -BHSBOHJBO WFMPDJUZ BOE BDDFMFSBUJPO UJNF TDBMFT -BHSBOHJBO BDDFMFSBUJPO UJNF TDBMFT OPSNBMJTFE CZ ࠬ -BHSBOHJBO UJNF TDBMF SBUJPT 5BZMPSTDBMF 3FZOPMET OVNCFS JO UIF DIBOOFM BU 3F࠰ "DDFMFSBUJPO QSPCBCJMJUZ EJTUSJCVUJPO GVODUJPOT 4LFXOFTT PG BDDFMFSBUJPO DPNQPOFOUT +PJOU 1%' PG TUSFBNXJTF BOE XBMMOPSNBM BDDFMFSBUJPO . . . . . . . .FBO XBMMOPSNBM USBDFS EJTQMBDFNFOU .FBO TUSFBNXJTF USBDFS EJTQMBDFNFOU .FBO TUSFBNXJTF WFMPDJUZ ็Ǩׁ ่ ǫա ࠬ .FBO WFMPDJUZBDDFMFSBUJPO QSPEVDU BDSPTT UIF DIBOOFM 4USFBNXJTF NFBOTRVBSF EJTQMBDFNFOU 4USFBNXJTF NFBOTRVBSF EJTQFSTJPO 8BMMOPSNBM NFBOTRVBSF EJTQFSTJPO 4QBOXJTF NFBOTRVBSF EJTQFSTJPO . . . . . . . 4DIFNBUJD PG QBSUJDMF QBJS EBUBTFUT 4BNQMF USBKFDUPSJFT PG UXP QBSUJDMF QBJST #BDLXBSE BOE GPSXBSE NFBOTRVBSF DIBOHF PG TFQBSBUJPO 4USVDUVSF GVODUJPOT Ǎӝ ǫ ɖ BOE Ǎեֵ ǫ ɖ $IBSBDUFSJTUJD CBMMJTUJD UJNF TDBMFT GPS TQBOXJTF TFQBSBUJPOT /PSNBMJTFE CBDLXBSE BOE GPSXBSE NFBOTRVBSF DIBOHF PG TFQBSBUJPO -PDBM TDBMJOH FYQPOFOUT PG UIF NFBOTRVBSF DIBOHF PG TFQBSBUJPO %JêFSFODF CFUXFFO CBDLXBSE BOE GPSXBSE NFBOTRVBSF TFQBSBUJPO 'PSXBSE NFBOTRVBSF DIBOHF PG TFQBSBUJPO GPS EJêFSFOU JOJUJBM DPOaH VSBUJPOT .FBOTRVBSF DIBOHF PG TFQBSBUJPO EVF UP UIF bVDUVBUJOH bPX -PDBM TDBMJOH FYQPOFOUT PG UIF NFBOTRVBSF TFQBSBUJPO CZ UIF bVDUVBUJOH bPX %JêFSFODF CFUXFFO CBDLXBSE BOE GPSXBSE NFBOTRVBSF TFQBSBUJPO CZ UIF bVDUVBUJOH bPX %JêFSFODF CFUXFFO CBDLXBSE BOE GPSXBSE NFBOTRVBSF TFQBSBUJPO CZ UIF bVDUVBUJOH bPX CZ TFQBSBUJPO DPNQPOFOU 3FMBUJWF EJTQFSTJPO UFOTPS .PEFMMFE BOE DPNQVUFE WFMPDJUZ TUSVDUVSF GVODUJPOT *OIPNPHFOFPVT CBMMJTUJD DBTDBEF NPEFM DPNQBSFE UP %/4 SFTVMUT 5SBKFDUPSJFT PG NPEFMMFE QBSUJDMF QBJST .PEFMMFE NFBOTRVBSF TFQBSBUJPO JO FBDI EJSFDUJPO . . . . . . . . . " 7FMPDJUZ TUBUJTUJDT &VMFSJBO-BHSBOHJBO DPNQBSJTPO " "DDFMFSBUJPO TUBUJTUJDT &VMFSJBO-BHSBOHJBO DPNQBSJTPO " %JTTJQBUJPO BOE ,PMNPHPSPW TDBMFT JO UIF DIBOOFM . YJW.
(16) -JTU PG 'JHVSFT # .FBO LJOFUJD FOFSHZ CVEHFU # .FBO -BHSBOHJBO EFSJWBUJWF PG UIF UVSCVMFOU LJOFUJD FOFSHZ . YW.
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(18) Ǟɯɾ ȩǀ ÷ŏųȀƚɯ . /VNFSJDBM QBSBNFUFST GPS DIBOOFM bPX %/4 1FSGPSNBODF PG JOUFSQPMBUJPO TDIFNFT . . . 1BSUJDMF QBJS EBUBTFUT . YWJJ.
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(20) ȩȒƚȘżȀŏɾʕɟƚ /PUBUJPO. %FTDSJQUJPO. ɇ Ǖա Ǖ֙. bVJE PS QBSUJDMF BDDFMFSBUJPO DPOTUBOU GPS EJTTJQBUJPOSBOHF -BHSBOHJBO WFMPDJUZ TUSVDUVSF GVODUJPO ƾӝ TQFDUSBM DPFëDJFOU. Ƽ. BEEJUJWF DPOTUBOU GPS MPHBSJUINJD MBX PG UIF XBMM. ƽա ƽӝ. DPOTUBOU GPS JOFSUJBMSBOHF -BHSBOHJBO WFMPDJUZ TUSVDUVSF GVODUJPO ƾӝ ,PMNPHPSPW DPOTUBOU GPS JOFSUJBMSBOHF &VMFSJBO WFMPDJUZ TUSVDUVSF GVOD UJPO Ǎӝ. ƾ Ȱ ƾ֡ ǘ֡. TFQBSBUJPO EJTUBODF CFUXFFO UXP QBSUJDMFT ]Ȱ]. TFQBSBUJPO WFDUPS CFUXFFO UXP QBSUJDMFT -BHSBOHJBO ǢUI PSEFS WFMPDJUZ TUSVDUVSF ็]ɚ Ǧ
(21) ࠬ ɚ Ǧ ]֡ ่. TQIFSJDBM QBSUJDMF EJBNFUFS. ƿ ɋա ɋօ. UPUBM LJOFUJD FOFSHZ əӝ . JOJUJBM PSJFOUBUJPO PG B QBSUJDMF QBJS $BSUFTJBO VOJU WFDUPS. Ȳ Ɍ ǀե. /POMJOFBS BOE GPSDJOH UFSNT PG UIF /BWJFS4UPLFT FRVBUJPOT ۳ ə ə Ɍ. 'PSDJOH UFSN JO /BWJFS4UPLFT FRVBUJPOT BDDFMFSBUJPO bBUOFTT. Ǜ ǁ֡. 3JDIBSETPOrT DPOTUBOU NFBO TUSFBNXJTF QSFTTVSF HSBEJFOU ࡴǢພࡴǪ. ǜ. DIBOOFM IBMGXJEUI. ਥ. JNBHJOBSZ VOJU ဨ. ǝ. UVSCVMFOU LJOFUJD FOFSHZ ə࿊ӝ . GVODUJPO. . YJY.
(22) /PNFODMBUVSF /PUBUJPO. %FTDSJQUJPO. Ǣ ۳Ǣա. UVSCVMFOU LJOFUJD FOFSHZ QSPEVDUJPO UFSN ǧ࿊ׁ ǧ࿊ ׅEֳ. Eׅ bVJE QSFTTVSF NFBO QSFTTVSF HSBEJFOU. Ⱦ 3F 3Fթ 3Fވ 3F࠰. DIBOHF PG TFQBSBUJPO CFUXFFO UXP QBSUJDMFT Ȱ Ȱա. DFOUSFMJOF 3FZOPMET OVNCFS Ǐա ǜ ޜ CVML 3FZOPMET OVNCFS Ǐթ ǜ ޜ 5BZMPSTDBMF 3FZOPMET OVNCFS ǝဨ . ܰޜ GSJDUJPO 3FZOPMET OVNCFS ǧ࠰ ǜ ޜ. Ǎӝ. UPUBM. &VMFSJBO. TFDPOEPSEFS. WFMPDJUZ. TUSVDUVSF. ӝ. GVODUJPO. 4U 4Uޠ. උə ɜ
(23) ɖ ə ɜ ඌ. BDDFMFSBUJPO TLFXOFTT UPUBM &VMFSJBO NJYFE WFMPDJUZBDDFMFSBUJPO TUSVDUVSF GVODUJPO උə ɜ
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(25) ɖ ɇ ɜ ඌ. &VMFSJBO TFDPOEPSEFS WFMPDJUZ TUSVDUVSF GVODUJPO UFOTPS උǧօ ɜ
(26) ɖ ǧօ ɜ ඌඋǧ։ ɜ
(27) ɖ ǧ։ ɜ ඌ. 4UPLFT OVNCFS ࠬ֡ ࠬ 4UPLFT OVNCFS CBTFE PO WJTDPVT UJNF ࠬ֡
(28) ࠬ֡ ࠬ ޠ. Ǧա ǎե ǎ֏ ǎ֙. CBMMJTUJD UJNF TDBMF JO QBJS EJTQFSTJPO Ǎӝ ]Ǎեֵ ]. -BHSBOHJBO BDDFMFSBUJPO UJNF TDBMF -BHSBOHJBO JOUFHSBM UJNF TDBMF $IFCZTIFW QPMZOPNJBM. Ǐ ə Ǐա Ǐթ ǧ֙ ǧ࠰. NFBO TUSFBNXJTF WFMPDJUZ bVJE WFMPDJUZ NFBO DFOUSFMJOF WFMPDJUZ CVML WFMPDJUZ USJBM GVODUJPO JO TQFDUSBM NFUIPET GSJDUJPO WFMPDJUZ ဨֽࠬ . ǐ ɚ. TQBDF PG UFTU GVODUJPOT QBSUJDMF WFMPDJUZ. Ǒ ǩ. TQBDF PG USJBM GVODUJPOT XFJHIU GVODUJPO JO TQFDUSBM NFUIPET. ɜ. QBSUJDMF QPTJUJPO. օ։. SFMBUJWF EJTQFSTJPO UFOTPS ็njօ Ǧ nj։ Ǧ ่. Ǎե Ǎեֵ Ǎօ։. YY.
(29) /PNFODMBUVSF /PUBUJPO. %FTDSJQUJPO. ڈ ڈJO ٤ ܀ ܤ ܤǪ. ܤօ։ ޠܤ ܰ ܰ֯ ࡨ֡ ݈ ݬ ޜ ճ ǫ ɖ. օ։ ࠬ ǫա. ֡ ࠔֵӝ ࠬ֡ ֽࠬ. -BHSBOHJBO QPXFS ɚ ɇ. JOQVU QPXFS QFS VOJU NBTT TQBUJBM EPNBJO QFSTJTUFODF QBSBNFUFS CBMMJTUJD QBJS EJTQFSTJPO NPEFM. CPVOEBSZ MBZFS UIJDLOFTT %JSBD EFMUB GVODUJPO ,SPOFDLFS EFMUB GVODUJPO WJTDPVT MFOHUI ޜǧ࠰. NFBO UVSCVMFOU FOFSHZ EJTTJQBUJPO SBUF ࡴ ޜ։ ǧ࿊օ ࡴ։ ǧ࿊օ. UPUBM FOFSHZ EJTTJQBUJPO SBUF ࡴ ޜ։ ǧօ ࡴ։ ǧօ. TDBMJOH FYQPOFOU PG JOFSUJBMSBOHF -BHSBOHJBO WFMPDJUZ TUSVDUVSF GVOD UJPO ƾ֡ ,PMNPHPSPW MFOHUI TDBMF ޜӗ ܰ џͳ. WPO ,¾SN¾O DPOTUBOU GPS MPHBSJUINJD MBX PG UIF XBMM bVJE LJOFNBUJD WJTDPTJUZ bVJE EFOTJUZ &VMFSJBO UXPQPJOU DPSSFMBUJPO -BHSBOHJBO DPSSFMBUJPO QBSUJDMF EFOTJUZ WFMPDJUZ WBSJBODF ǧ࿊ӝ օ JTPUSPQJD bPXT POMZ. QBSUJDMF SFMBYBUJPO UJNF ֡ ǘ֡ӝ . ޜ XBMM TIFBS TUSFTT ޜEǏພEǫ ມ ׅա. ࠬ ࠬޠ ީ ߌօ. ,PMNPHPSPW UJNF TDBMF ဨ ܰޜ WJTDPVT UJNF ޜǧӝ࠰. bVJE WPSUJDJUZ ۳ ə. UFTU GVODUJPO JO TQFDUSBM NFUIPET. YYJ.
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(31) ųųɟƚʲǞŏɾǞȩȘɯ /PUBUJPO. %FTDSJQUJPO. $'-. $PVSBOU'SJFESJDIT-FXZ DPOEJUJPO. %/4. EJSFDU OVNFSJDBM TJNVMBUJPO. ''5. GBTU 'PVSJFS USBOTGPSN. )*5 )4'. IPNPHFOFPVT JTPUSPQJD UVSCVMFODF IPNPHFOFPVT TIFBS bPX. *0. JOQVUPVUQVU. -&4 -4.. MBSHF FEEZ TJNVMBUJPO MBSHF TDBMF NPUJPO. .1* .83. .FTTBHF 1BTTJOH *OUFSGBDF NFUIPE PG NFBO XFJHIUFE SFTJEVBMT. 1%' 157. QSPCBCJMJUZ EFOTJUZ GVODUJPO QBSUJDMFUSBDLJOH WFMPDJNFUSZ. 4%&. TUPDIBTUJD EJêFSFOUJBM FRVBUJPO. 5,&. UVSCVMFOU LJOFUJD FOFSHZ. 7-4.. WFSZ MBSHF TDBMF NPUJPO. YYJJJ.
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(33) °ɔƚɟŏɾȩɟɯ /PUBUJPO. %FTDSJQUJPO. ใǚ Ǜไ. JOOFS QSPEVDU CFUXFFO UXP GVODUJPOT. ǒ. DPNQMFY DPOKVHBUF. % %Ǧ. -BHSBOHJBO EFSJWBUJWF BMPOH bVJE QBSUJDMF QBUIT. ǒ. &VMFSJBO NFBO. ็ǒ่. -BHSBOHJBO NFBO. ǒ
(34). RVBOUJUZ TDBMFE JO XBMM VOJUT CZ ǧ࠰ BOE ޜ. YYW.
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(55) ဴ܀џ ܀ӝ ࠔֵӝ EǑ Ǧ. ա. . BOE UIF WFMPDJUZ BOE QPTJUJPO BSF PCUBJOFE CZ TVDDFTTJWF JOUFHSBUJPOT PG UIF BDDFMFSBUJPO Ǖ Ǧ 5IF QBSBNFUFST ܀џ BOE ܀ӝ BSF SFMBUFE UP UIF JOUFHSBM BOE ,PMNPHPSPW UJNF TDBMFT 5IFZ BSF EFaOFE TP UIBU UIF NPEFM NBUDIFT UIF -BHSBOHJBO TUSVDUVSF GVODUJPOT ƾӝ ࠬ. QSFEJDUFE CZ , UIFPSZ CPUI JO UIF EJTTJQBUJPO BOE JOFSUJBM SBOHFT *O UIF EJTTJQBUJPO SBOHF UIF , QSFEJDUJPO JT HJWFO CZ < Q > ƾӝ ࠬ Ǖա ܰӗӝ ޜџӝ ࠬ ӝ. GPS. ࠬ ཫ ࠬ . . 5IF OPOEJNFOTJPOBM QBSBNFUFS Ǖա JT FRVBM UP UIF BDDFMFSBUJPO WBSJBODF ็Ǖ Ǧ ӝ ่ OPSNBM JTFE CZ ܰ BOE " ޜT XJUI ƽա , UIFPSZ QSFEJDUT UIBU Ǖա JT B VOJWFSTBM DPOTUBOU GPS IJHI 3FZOPMET OVNCFST bPXT "T EJTDVTTFE JO TFDUJPO DVSSFOUMZ BWBJMBCMF EBUB TVHHFTUT UIBU Ǖա BDUVBMMZ TUSPOHMZ WBSJFT XJUI 3FZOPMET OVNCFS 5IF WFMPDJUZ BVUPDPSSFMBUJPO GVODUJPO ֹ ࠬ SFTVMUJOH GSPN 4BXGPSErT TFDPOEPSEFS NPEFM JT FYQSFTTFE BT UIF EJG GFSFODF CFUXFFO UXP FYQPOFOUJBMT BOE CZ DPOTUSVDUJPO TJODF EJTTJQBUJPO TDBMFT BSF QSPQFSMZ BDDPVOUFE GPS JUT EFSJWBUJWF DPSSFDUMZ WBOJTIFT BU ࠬ . 5IF FNQJSJDBM MBX PG aOJUF FOFSHZ EJTTJQBUJPO TUBUFT UIBU ܴ SFNBJOT aOJUF BU WBOJTIJOH WJTDPTJUZ <> 5IFSFGPSF JO UIF MJNJU PG JOaOJUF 3FZOPMET OVNCFS ޠஒ ա UIF ,PMNPHPSPW UJNF TDBMF ࠰ ܴޠ ݍѠӞ UFOET UP [FSP. .
(56) *OUSPEVDUJPO 3. Probability. 100 a 10–2. b. K41. 2. 10–4 1 10–6 10–8. –10. 0. 10. 0. 0. 2. 4. 6 p. 8. 10. 12. _Ǟǃʕɟƚ ߝࡏߡࡏ -BHSBOHJBO JOUFSNJUUFODZ JO JTPUSPQJD UVSCVMFODF B 1%' PG WFMPDJUZ JODSFNFOUT ࠱Ǩ. GSPN FYQFSJNFOUT BU 3F މGPS UJNF MBHT ࠬǎ BOE 5IF DVSWFT BSF EJTQMBZFE XJUI B WFSUJDBM TIJGU GPS DMBSJUZ $SPTTFT DPSSFTQPOE UP B NPEFM QSFEJDUJPO 3FQSPEVDFE GSPN .PSEBOU FU BM <> C &YUFOEFE TFMGTJNJMBSJUZ FTUJNBUFT PG UIF TDBMJOH FYQPOFOU SBUJP ࡨ֢ ࡨӞ JO UIF JOFSUJBM SBOHF .BSLFST DPSSFTQPOE UP EJêFSFOU TJNVMBUJPOT BOE FYQFSJNFOUT CMVF aMMFE DJSDMFT 4BXGPSE BOE :FVOH <> 3F މv NBHFOUB TRVBSFT #FO[J FU BM <> 3F މSFE DSPTTFT .PSEBOU FU BM <> 3F މv DZBO PQFO DJSDMFT 9V FU BM <> 3F މv 5IF CMBDL TPMJE MJOF SFQSFTFOUT UIF , QSFEJDUJPO ࡨ֢ Ǣ 0UIFS MJOFT DPSSFTQPOE UP EJêFSFOU NPEFM QSFEJDUJPOT 3FQSPEVDFE GSPN 4BXGPSE BOE :FVOH <>. ߝࡏߝࡏߠ ŏǃɟŏȘǃǞŏȘ ǞȘɾƚɟȒǞɾɾƚȘżʿ. &YQFSJNFOUBM BOE OVNFSJDBM -BHSBOHJBO TUVEJFT PG UVSCVMFOU bPXT IBWF TIPXO UIBU UIF -BHSBOHJBO WFMPDJUZ JODSFNFOUT ࠰Ǩ JOUSPEVDFE JO TFDUJPO BSF BDUVBMMZ IJHIMZ JOUFSNJUUFOU BU TNBMM UJNF MBHT ࠬ <> 5IBU JT bVJE QBSUJDMFT JO WFSZ SBSF PDDBTJPOT TFF BCSVQU DIBOHFT JO UIFJS WFMPDJUZ PWFS TIPSU UJNF TQBOT 5IJT JT NBOJGFTUFE CZ 1%'T PG WFMPDJUZ JODSFNFOUT ࠰Ǩ XIJDI BSF TUSPOHMZ OPO(BVTTJBO XIFO ࠬ JT TNBMM aH B. XJUI IFBWZ TUSFUDIFE FYQPOFOUJBM UBJMT DPSSFTQPOEJOH UP SBSF FWFOUT BTTPDJBUFE UP WFSZ JOUFOTF WFMPDJUZ JODSFNFOUT < > 5IJT JOUFSNJUUFODZ JT OPU DBQUVSFE CZ UIF TJNQMF -BHSBOHJBO TUPDIBTUJD NPEFMT JOUSPEVDFE JO TFDUJPO &RVJWBMFOUMZ JOUFSNJUUFODZ JT SFbFDUFE JO B EFQBSUVSF GSPN ,PMNPHPSPW , UIFPSZ XIJDI QSFEJDUT UIBU UIF -BHSBOHJBO WFMPDJUZ TUSVDUVSF GVODUJPO PG PSEFS Ǣ TIPVME TDBMF BT ֡ Ǣ x . ƾ֡ ࠬ ༮ ็ ມ ࠰Ǩ Ǧ ມ ่ ྡྷ ܰࠬ ֡ӝ GPS JOFSUJBMSBOHF UJNF JODSFNFOUT ࠬ "UUFNQUT IBWF CFFO NBEF UP EFUFSNJOF UIF BDUVBM TDBMJOH FYQPOFOUT ࡨ֡ TVDI UIBU ƾ֡ ࠬ ྡྷ ࠬ ֢ GSPN -BHSBOHJBO UVSCVMFODF EBUB BOE UP DPNQBSF UIFN XJUI UIF , QSFEJDUJPO ࡨ֡ Ǣ 'PS UIF QBSUJDVMBS DBTF Ǣ JU IBT CFFO BSHVFE <> UIBU BT B DPOTFRVFODF PG UIF MJOFBS EFQFOEFODF PG ƾӝ ࠬ PO ܰ JO FR UIF TDBMJOH FYQPOFOU ࡨӝ JT OPU BêFDUFE CZ JOUFSNJUUFODZ JF ࡨӝ BT. .
(57) -BHSBOHJBO EFTDSJQUJPO PG UVSCVMFOU bPXT QSFEJDUFE CZ , UIFPSZ "U UIF aOJUF 3FZOPMET OVNCFST PG MBCPSBUPSZ FYQFSJNFOUT BOE TJNVMBUJPOT DMFBS QPXFS MBXT ƾ֡ ࠬ ྡྷ ࠬ ֢ BSF HFOFSBMMZ OPU PCTFSWFE <> 5IFSFGPSF UP EFUFSNJOF UIF ࡨ֡ FYQPOFOUT GSPN BWBJMBCMF EBUB SFTFBSDIFST IBWF SFTPSUFE UP UIF FYUFOEFE TFMG TJNJMBSJUZ QSPDFEVSF aSTU JOUSPEVDFE JO UIF DPOUFYU PG &VMFSJBO TUSVDUVSF GVODUJPOT <> *O UIF QSFTFOU DPOUFYU UIJT DPSSFTQPOET UP FTUJNBUJOH UIF TDBMJOH FYQPOFOUT ࡨ֡ GSPN DVSWFT PG ƾ֡ ࠬ QMPUUFE BHBJOTU ƾӝ ࠬ JOTUFBE PG BHBJOTU ࠬ 5IJT JNNFEJBUFMZ MFBET UP FTUJNBUFT PG UIF TDBMJOH FYQPOFOU SBUJPT ࡨ֡ ࡨӝ *O BEEJUJPO UIF BTTVNQUJPO UIBU ƾӝ ࠬ ྡྷ ࠬ JO UIF JOFSUJBM SBOHF JF ࡨӝ NBZ CF VTFE UP EFUFSNJOF UIF PUIFS TDBMJOH FYQPOFOUT ࡨ֡ &YUFOEFE TFMGTJNJMBSJUZ IBT SFTVMUFE JO SFMBUJWFMZ SPCVTU TDBMJOH FYQPOFOUT SFQSPEVDFE JO WBSJPVT OVNFSJDBM BOE FYQFSJNFOUBM TFUUJOHT < > "T TIPXO JO aH C UIF DPOTFOTVT JT UIBU UIF , QSFEJDUJPOT EP OPU IPME GPS -BHSBOHJBO TUSVDUVSF GVODUJPOT PG PSEFS IJHIFS UIBO DPOaSNJOH UIF JOUFSNJUUFODZ PG -BHSBOHJBO WFMPDJUZ JODSFNFOUT JO UVSCVMFOU bPXT ߝࡏߝࡏߡ ŏǃɟŏȘǃǞŏȘ ŏżżƚȀƚɟŏɾǞȩȘ. 5IF -BHSBOHJBO WFMPDJUZ JODSFNFOUT ࠰Ǩ BSF FWJEFOUMZ SFMBUFE UP UIF -BHSBOHJBO QBSUJDMF BDDFMFSBUJPO XIJDI JT PCUBJOFE GSPN ࠰Ǩ JO UIF MJNJU PG TNBMM ࠬ 8F IBWF PCTFSWFE BCPWF UIBU UIF -BHSBOHJBO WFMPDJUZ JODSFNFOUT CFDPNF NPSF BOE NPSF JOUFSNJUUFOU BT UIF UJNF MBH ࠬ JT SFEVDFE 'SPN UIJT JU DBO CF BOUJDJQBUFE UIBU UIF BDDFMFSBUJPO JT B IJHIMZ JOUFSNJUUFOU RVBOUJUZ JO UVSCVMFOU bPXT -BHSBOHJBO BDDFMFSBUJPOT XFSF aSTU NFBTVSFE JO UVSCVMFOU MBCPSBUPSZ bPXT CZ 7PUI FU BM <> 4PPO BGUFS JU XBT PCTFSWFE UIBU UIF BDDFMFSBUJPO PG bVJE QBSUJDMFT JT WFSZ JOUFSNJUUFOU BOE DIBSBDUFSJTFE CZ IJHIMZ OPO(BVTTJBO 1%'T XJUI MPOH TUSFUDIFE FYQPOFOUJBM UBJMT < > BT TFFO JO aH B "T FYQFDUFE UIF TIBQF PG UIF BDDFMFSBUJPO 1%'T SFTFNCMFT UIBU PG UIF WFMPDJUZ JODSFNFOUT ࠰Ǩ GPS TNBMM ࠬ aH B 5IF JOTFU ӝ PG aH B TIPXT UIF bBUOFTT GBDUPS ็Ǖͳ ่็Ǖӝ ่ SFQSFTFOUJOH UIF EFQBSUVSF PG UIF BDDFMFSBUJPO EJTUSJCVUJPO GSPN (BVTTJBOJUZ 5IF MBSHF bBUOFTT WBMVFT XIJDI DBO CF DPOUSBTUFE UP UIF WBMVF PG BTTPDJBUFE UP B (BVTTJBO EJTUSJCVUJPO RVBOUJGZ UIF IJHI JOUFSNJUUFODZ PG UIF BDDFMFSBUJPO BT UIFZ JOEJDBUF UIBU FYUSFNF BDDFMFSBUJPOT NVDI IJHIFS UIBO UIF TUBOEBSE EFWJBUJPO PDDVS SFMBUJWFMZ GSFRVFOUMZ JO UVSCVMFOU bPXT )JHIBDDFMFSBUJPO FWFOUT JO UVSCVMFOU bPXT IBWF CFFO MJOLFE UP bVJE QBSUJDMFT CFJOH USBQQFE JO IFMJDBM NPUJPOT TVDI BT UIF POF WJTVBMJTFE JO aH C *O UIF aHVSF UIF TJ[F PG UIF IFMJDBM MPPQT JT BCPVU ݈ XIFSF ݈ ޜӗ ܰ џͳ JT UIF ,PMNPHPSPW MFOHUI TDBMF BTTPDJBUFE UP UIF TNBMMFTU TDBMFT PG UVSCVMFOU NPUJPO XIJMF DIBOHFT PG PSJFOUBUJPO PDDVS PWFS QFSJPET PG UIF PSEFS PG UIF ,PMNPHPSPW UJNF TDBMF ࠬ >< 5IJT TVHHFTUT UIBU DIBOHFT PG BDDFMFSBUJPO PDDVS WFSZ SBQJEMZ BOE BSF BTTPDJBUFE UP TNBMMTDBMF UVSCVMFOU . "T OPUFE CZ 9V FU BM <> UIJT JT BOBMPHPVT UP UIF DBTF PG UIF UIJSEPSEFS &VMFSJBO WFMPDJUZ TUSVDUVSF GVODUJPO ֫Ә ֩ <ֵ໌ ɜ
(58) ɖ ֵ໌ ɜ >Ә XIFSF ֵ໌ ə ɖ ֩ BOE ֩ ]ɖ] XJUI UIF EJêFSFODF UIBU UIFSF JT BO FYBDU FYQSFTTJPO GPS ֫Ә ֩ JO UIF MJNJU PG JOaOJUF 3FZOPMET OVNCFS OBNFMZ ,PMNPHPSPWrT GPVSaGUIT MBX ֫Ә ֩ ʹͰ ܴ֩ < > $ISPOPMPHJDBMMZ UIF JOUFSNJUUFODZ PG UIF BDDFMFSBUJPO XBT TUVEJFE CFGPSF UIBU PG UIF -BHSBOHJBO WFMPDJUZ JODSFNFOUT. .
(59) *OUSPEVDUJPO 100. Probability. 10 10. –1. a. 100. b. z. 50. –2. 10. 0. 0. 500. 1000. –3. 10–4. 1 mm. –5. 10. x. y. 10–6 –20. 0. 20. 0. 16 000. Acceleration (m s–2). _Ǟǃʕɟƚ ߝࡏߢࡏ -BHSBOHJBO BDDFMFSBUJPO JO MBCPSBUPSZ FYQFSJNFOUT B 1%'T PG BDDFMFSBUJPO OPSNBM. JTFE CZ JUT TUBOEBSE EFWJBUJPO BU EJêFSFOU 3FZOPMET OVNCFST %BTIFE MJOF (BVTTJBO EJTUSJCVUJPO XJUI VOJU WBSJBODF TPMJE MJOF aU PG 3F މEBUB *OTFU bBUOFTT PG UIF BDDFMFSBUJPO EJTUSJCV Ӟ UJPO ็Ǖʹ ่็ǕӞ ่ BT B GVODUJPO PG 3F މ3FQSPEVDFE GSPN -B 1PSUB FU BM <> C 5SBKFDUPSZ PG B IJHIBDDFMFSBUJPO TQIFSJDBM USBDFS QBSUJDMF EJBNFUFS ŊN JO B UVSCVMFOU bPX BU 3F މ $PMPVST SFQSFTFOU UIF BDDFMFSBUJPO NBHOJUVEF 3FQSPEVDFE GSPN 7PUI FU BM <>. TUSVDUVSFT DMPTF UP UIF EJTTJQBUJPO SBOHF 5IFTF TUSVDUVSFT DBO CF JEFOUJaFE BT UIF JOUFOTF FMPOHBUFE WPSUFY aMBNFOUT PG EJBNFUFS PG PSEFS ݈ XIJDI BSF B TJHOBUVSF PG TNBMMTDBMF JOUFSNJUUFODZ JO UVSCVMFOU bPXT < > *OUVJUJWFMZ B bVJE QBSUJDMF SPUBUJOH JO IFMJDBM NPUJPO FYQFSJFODFT B DFOUSJQFUBM BDDFMFS BUJPO UPXBSET UIF DFOUSF PG SPUBUJPO $FOUSJQFUBM BDDFMFSBUJPOT BSF BTTPDJBUFE UP DIBOHFT PG PSJFOUBUJPO PG B QBSUJDMF USBKFDUPSZ )FODF JU NBZ CF TQFDVMBUFE UIBU WPSUFY aMBNFOUT DPOUSJCVUF UP UIF JOUFSNJUUFODZ PG BDDFMFSBUJPO CZ JOEVDJOH IJHINBHOJUVEF DFOUSJQFUBM BDDFMFSBUJPOT BTTPDJBUFE UP TIBSQ DIBOHFT PG PSJFOUBUJPO PG USBQQFE bVJE QBSUJDMFT 5IJT IZQPUIFTJT XBT FYBNJOFE CZ 5PTDIJ FU BM <> XIP DPNQBSFE UIF 1%' PG UIF DFOUSJ QFUBM BDDFMFSBUJPO Ǖխ ]ɇ ɚ]]ɚ] XJUI UIBU PG UIF MPOHJUVEJOBM BDDFMFSBUJPO BMJHOFE XJUI UIF WFMPDJUZ ɚ Ǖ֑ ɇ ɚ ]ɚ] 5IFZ GPVOE UIF DFOUSJQFUBM DPNQPOFOU UP CF NVDI NPSF JOUFSNJUUFOU UIBO UIF MPOHJUVEJOBM POF JO TVQQPSU PG UIF BCPWF IZQPUIFTJT *G XF BHBJO TVQQPTF UIBU UIF BDDFMFSBUJPO PG B USBDFS USBQQFE JO B WPSUJDBM TUSVDUVSF JT NBJOMZ EFUFSNJOFE CZ B DFOUSJQFUBM DPNQPOFOU UIF BCPWF QJDUVSF BMTP TVHHFTUT UIBU BT UIF USBDFS DJSDVMBUFT JO IFMJDBM NPUJPO JUT BDDFMFSBUJPO WFDUPS DPOUJOVPVTMZ DIBOHFT EJSFDUJPO BT JU JT NBJOMZ EJSFDUFE UPXBSET UIF WPSUFY BYJT XIJMF UIF BDDFMFSBUJPO NBHOJUVEF DIBOHFT NPSF TMPXMZ 5P JMMVTUSBUF UIJT JEFB XF DPNF CBDL UP UIF TJNQMF UXPEJNFOTJPOBM QPJOU WPSUFY NPEFM CSJFbZ NFOUJPOFE JO TFDUJPO " QPJOU WPSUFY JOEVDFT B WFMPDJUZ aFME JO QPMBS DPPSEJOBUFT ə ߘǤ ɋ࠼ XIFSF JT UIF WPSUFY DJSDVMBUJPO 5IF DJSDVMBS QBUI PG B bVJE QBSUJDMF JO UIJT WFMPDJUZ aFME JT EFQJDUFE JO aH B *O UIJT JEFBM FYBNQMF UIF bVJE QBSUJDMF BDDFMFSBUJPO POMZ IBT B DFOUSJQFUBM DPNQPOFOU XIJDI JT DPOTUBOU JO NBHOJUVEF JF JUT TQFFE ]ɚ] TUBZT DPOTUBOU XIJMF UIF PSJFOUBUJPO PG EJTQMBDFNFOU DIBOHFT TUFBEJMZ .PSFPWFS UIF PSJFOUBUJPO PG UIF. .
(60) a. y. r. x. Auto-correlation coecient. -BHSBOHJBO EFTDSJQUJPO PG UVSCVMFOU bPXT 1. b. 1. 0.8 0.6. 0.8. 0.4 0.2. 0.6. 0 10. 1. 0.4 0.2 0 0. 5. 10. 15. _Ǟǃʕɟƚ ߝࡏߣࡏ 4USVDUVSF PG UIF BDDFMFSBUJPO WFDUPS JO UVSCVMFOU bPXT B -BHSBOHJBO QBUI JOEVDFE. CZ B QPJOU WPSUFY JO UXP EJNFOTJPOT 5IF WPSUJDJUZ aFME JT PG UIF GPSN ީ ɜ ܤɜ ɋ XIFSF JT UIF WPSUFY DJSDVMBUJPO BOE ܤJT UIF %JSBD EFMUB 'MVJE QBSUJDMFT USBWFM JO DJSDVMBS PSCJUT 5IF -BHSBOHJBO WFMPDJUZ BOE BDDFMFSBUJPO IBWF DPOTUBOU NBHOJUVEFT CVU WBSZJOH PSJFOUBUJPOT PWFS UJNF C "VUPDPSSFMBUJPO PG BDDFMFSBUJPO NBHOJUVEF ]ɇ] TPMJE MJOF BOE PG UIF BDDFMFSBUJPO DPNQPOFOUT Ǖׂ Ǖ ׆BOE Ǖ 5SJBOHMFT SFQSFTFOU DSPTTDPSSFMBUJPOT CFUXFFO BDDFMFSBUJPO DPNQPOFOUT 5IF bPX JT ESJWFO CZ UXP DPVOUFSSPUBUJOH EJTLT JO B DZMJOESJDBM UBOL BU 3F* މOTFU TBNF DVSWFT JO TFNJMPHBSJUINJD TDBMF 3FQSPEVDFE GSPN .PSEBOU FU BM <>. BDDFMFSBUJPO WFDUPS DMFBSMZ DIBOHFT PWFS UJNF BT UIF USBDFS SPUBUFT BCPVU UIF WPSUFY 1PJOU WPSUJDFT IBWF BMSFBEZ CFFO VTFE UP EFTDSJCF UIF -BHSBOHJBO EZOBNJDT PG UVSCVMFODF "O FYBNQMF JT UIF XPSL PG 3BTU BOE 1JOUPO <> XIP JOUSPEVDFE B NPEFM PG JOUFSBDUJOH QPJOU WPSUJDFT UP FYQMBJO UIF -BHSBOHJBO JOUFSNJUUFODZ PG UVSCVMFODF 5IF BCPWF TJNQMF NPEFM NBZ TFSWF BT BO FYQMBOBUJPO GPS UIF PCTFSWBUJPO UIBU JO UVSCVMFOU bPXT UIF -BHSBOHJBO BDDFMFSBUJPO NBHOJUVEF ]ɇ] TUBZT DPSSFMBUFE GPS NVDI MPOHFS UIBO UIF DPNQPOFOUT PG UIF BDDFMFSBUJPO WFDUPS < > "T TFFO JO aH C UIF BDDFMFSBUJPO DPNQPOFOUT DPNQMFUFMZ EFDPSSFMBUF PWFS B UJNF DPNQBSBCMF UP ࠬ TVHHFTUJOH UIBU UIFJS EZOBNJDT BSF HPWFSOFE CZ UIF TNBMMTDBMF UVSCVMFOU NPUJPOT BT BMTP IJOUFE CZ UIF USBKFDUPSZ JO aH C 5IF NVDI MPOHFS EFDPSSFMBUJPO UJNF PG ]ɇ] DPNQBSBCMF UP ǎ֏ <> JOEJDBUFT UIBU UIF SBQJE WBSJBUJPOT PG UIF BDDFMFSBUJPO DPNQPOFOUT DPSSFTQPOE UP DIBOHFT PG PSJFOUBUJPO PG UIF BDDFMFSBUJPO WFDUPS MJLFMZ EVF UP UIF BDUJPO PG WPSUFY aMBNFOUT BOE TJNJMBS TNBMMTDBMF TUSVDUVSFT 5IF USBQQJOH FWFOUT EFTDSJCFE BCPWF BSF BMTP FYQFDUFE UP IBWF BO JObVFODF PO UIF -BHSBOHJBO WFMPDJUZ JODSFNFOUT BU aOJUF UJNF MBH ࠬ BOE UIVT PO UIF TUSVDUVSF GVODUJPOT EJTDVTTFE JO TFDUJPO 5IF FêFDU PG TVDI FWFOUT IBT CFFO BOBMZTFE CZ aMUFSJOH PVU UIFJS DPOUSJCVUJPOT UP UIF -BHSBOHJBO TUSVDUVSF GVODUJPOT ƾ֡ ࠬ <> BOE CZ DPNQBSJOH UIF TUBUJTUJDT UP UIPTF PCUBJOFE GPS IFBWZ JOFSUJBM QBSUJDMFT <> XIJDI BSF VTVBMMZ FYQFMMFE GSPN TNBMMTDBMF IFMJDBM NPUJPOT EVF UP UIFJS JOFSUJB 5IFTF TUVEJFT . *O PUIFS XPSET UIF SFTQPOTF UJNF PG UIF IFBWZ JOFSUJBM QBSUJDMFT RVBOUJaFE CZ UIF 4UPLFT OVNCFS JT UPP MBSHF DPNQBSFE UP UIF DIBSBDUFSJTUJD QFSJPE PG UIF TNBMMTDBMF IFMJDBM NPUJPOT XIJDI JT DPNQBSBCMF. .
(61) *OUSPEVDUJPO GPVOE UIBU USBQQJOH FWFOUT FOIBODF JOUFSNJUUFODZ PG -BHSBOHJBO WFMPDJUZ JODSFNFOUT GPS UJNF MBHT VQ UP ࠬ XIJDI IFMQFE FYQMBJO EJTDSFQBODJFT CFUXFFO UIF TDBMJOH FYQPOFOUT FTUJNBUFE GSPN OVNFSJDBM TJNVMBUJPOT BOE FYQFSJNFOUT <> ߝࡏߝࡏߢ ȘǞɯȩɾɟȩɔǞż ŏȘƇ ǞȘǕȩȒȩǃƚȘƚȩʕɯ ˚ȩʶɯ. .PTU PG UIF -BHSBOHJBO JOWFTUJHBUJPOT DJUFE BCPWF IBWF CFFO QFSGPSNFE JO OPNJOBMMZ JTPUSPQJD UVSCVMFOU bPXT 8F aSTU NBLF TPNF QSFDJTJPOT SFHBSEJOH UIF TUBUJTUJDBM JTP USPQZ PG UIPTF bPXT /VNFSJDBM TUVEJFT PG )*5 BSF HFOFSBMMZ QFSGPSNFE VTJOH EJSFDU OVNFSJDBM TJNVMBUJPO %/4 JO XIJDI UIF /BWJFSv4UPLFT FRVBUJPOT BSF TPMWFE VQ UP UIF TNBMMFTU TDBMFT PG NPUJPO 5IF QIZTJDBM EPNBJO JT B USJQMZ QFSJPEJD CPY JF B DVCF XJUI QFSJPEJD CPVOEBSZ DPOEJUJPOT 5IJT FOBCMFT UIF VTF PG QTFVEPTQFDUSBM NFUIPET CZ EFDPNQPTJOH UIF WFMPDJUZ aFME JOUP 'PVSJFS NPEFT TFF TFDUJPO GPS EFUBJMT 5P FOTVSF UIF TUBUJTUJDBM TUBUJPOBSJUZ PG UIF bPX JF UP DPNQFOTBUF GPS UIF FOFSHZ EJTTJQBUFE BU UIF TNBMM TDBMFT B MBSHFTDBMF GPSDJOH DPSSFTQPOEJOH UP UIF Ɍ UFSN JO FR C NVTU CF BQQMJFE 'PS UIF bPX UP CF JTPUSPQJD UIF GPSDJOH UFSN XIJDI DBO CF TUPDIBTUJD JT DIPTFO BT TUBUJTUJDBMMZ JTPUSPQJD 4UJMM TPNF XFBL BOJTPUSPQZ VTVBMMZ QFSTJTUT EVF UP UIF JOIFSFOU BOJTPUSPQZ PG UIF DVCJDBM HSJE 'PS JOTUBODF TNBMM EJêFSFODFT NBZ CF PCTFSWFE GPS UXPQPJOU TUBUJTUJDT DPNQVUFE BMPOH B MJOF QBSBMMFM UP UIF HSJE TBZ QBSBMMFM UP UIF Ǫ BYJT BOE BMPOH B EJBHPOBM PG UIF DVCF <> 5IF DBTF PG MBCPSBUPSZ FYQFSJNFOUT JT NPSF DPNQMFY BT UIF VOBWPJEBCMF QSFTFODF PG TPMJE CPVOEBSJFT BOE UIF GPSDJOH NFDIBOJTN JOWBSJBOUMZ JOUSPEVDF TPNF BOJTPUSPQZ JOUP UIF bPX 5IF BJN JT GPS UIFTF BOJTPUSPQZHFOFSBUJOH GFBUVSFT UP CF GBS FOPVHI GSPN UIF NFBTVSFNFOU SFHJPO XIFSF UIF bPX JT BOBMZTFE TP UIBU UIF TNBMMTDBMF TUBUJTUJDT DBO CF DPOTJEFSFE BT JTPUSPQJD JO UIBU SFHJPO 5IF FYQFSJNFOUT DJUFE JO UIF QSFWJPVT TFDUJPOT XFSF BMM DPOEVDUFE JO WPO ,¾SN¾O TXJSMJOH bPXT CFUXFFO UXP DPBYJBM DPVOUFSSPUBUJOH EJTLT JO B DZMJOESJDBM UBOL < > 5IJT DIPJDF PG bPX JT QBSUJDVMBSMZ DPOWFOJFOU BT JU BMMPXT GPS WFSZ IJHI 3FZOPMET OVNCFST JO B DPOaOFE HFPNFUSZ *O aH C UIF BVUPDPSSFMBUJPO DVSWFT BTTPDJBUFE UP UIF UISFF BDDFMFSBUJPO DPNQPOFOUT Ǫ BOE ǫ BSF QBSBMMFM UP UIF EJTLT Ǭ JT UIF BYJBM EJSFDUJPO EJTQMBZ WFSZ TJNJMBS SFTVMUT JOEJDBUJOH UIBU UIF bPX JT OFBSMZ JTPUSPQJD 5IF JTPUSPQZ JT BMTP TVQQPSUFE CZ UIF WBOJTIJOH DSPTT DPSSFMBUJPOT CFUXFFO BDDFMFSBUJPO DPNQPOFOUT "T TIPXO MBUFS JO TFDUJPO UIJOHT BSF WFSZ EJêFSFOU JO IJHIMZ BOJTPUSPQJD bPXT /FWFSUIFMFTT TPNF BOJTPUSPQZ NBZ TUJMM QFSTJTU JO UIF NFBTVSFNFOUT 'PS JOTUBODF VTJOH UIF TBNF WPO ,¾SN¾O FYQFSJNFOUBM BQQBSBUVT BT JO <> 0VFMMFUUF FU BM <> TIPXFE UIBU UIF TFDPOEPSEFS -BHSBOHJBO TUSVDUVSF GVODUJPO ƾӝ XBT DMFBSMZ BOJTPUSPQJD /BNFMZ GPS BMM UJNF MBHT ࠬ DPNQVUJOH ƾӝ ࠬ GSPN UIF Ǫ BOE ǫ WFMPDJUZ DPNQPOFOUT QBSBMMFM UP UIF EJTLT SFTVMUFE JO MBSHFS WBMVFT UIBO UIF TUBUJTUJDT BTTPDJBUFE UP UIF Ǭ DPNQPOFOU *O DPODMVTJPO FWFO JO DPOUSPMMFE TFUUJOHT TVDI BT UIF FYQFSJNFOUBM JOTUBMMBUJPOT SFGFS FODFE BCPWF JU JT WFSZ EJëDVMU UP BWPJE BOJTPUSPQZ JO SFBM bPXT 1SBDUJDBM bPXT GPVOE JO OBUVSBM BOE JOEVTUSJBM BQQMJDBUJPOT BSF NVDI NPSF DPNQMFY UIBO JEFBM JTPUSPQJD bPXT EVF UP TFWFSBM GBDUPST XIJDI NBZ JODMVEF v UP POMZ OBNF B GFX v UFNQPSBM WBSJBCJMJUZ UP ࠰) ݍFODF UIF QBSUJDMFT BSF OPU qGBTUr FOPVHI UP SFTQPOE UP UIF TPMJDJUBUJPOT PG TNBMM WPSUFY aMBNFOUT. .
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