IIO C]'ttlgglst ljptiXOIHTC.fl HCrro"Tb3OBaTb OIHy pe3"1H3ar{Hto C,,ryqar?HO_
fo Ilpoqecca-pfiA Ha6JrioAeFrHft. oliraxo BBr{Ay rofo, r{To cTa-I(HoHapHblll cryqaliHblll ilpouecc ripoTeKaeT Bo BpeMeHH .q,ocTaToqHoOAHOPOAHO, 3TA CAHHCTBCHHAfl PCA,'I}I3AqHfi MO}hCT C.[YXiHTb HCXOA-
HbI.M Y.aTepHa"rIolu 4",1fl noxyrteHHfl neo6xoAllMbix xapaKTepHCrr{i{ c"rrv:
f rc, - e-i) (Q;*. - Qi *,)
i:l
tt -
oioi +=(z -r- l)
t[e n - qHcJIo rireHoB pfrAa; T - fiopflAoK cABHf a, H3Mellflr0nlUlrCA Or
a lo m (r:0, 1, 2,...,m); Qr- pacxoA BoAbtr, BKJlrioqaloulHir 3Haqe-
r{Hfl or Q,:Qr Ao Q,:Qn-ri Qr lr 6t-cpeAHee 3HaqeHHe pacxoAog
qqAbr H-craHAapr Anfl sroli qacrH pflaa ua6.nioAenuft (or I no n--c);
Q+t- pacxoA BoAbt, BKnloqarolqHrt 3HaqellHr oT Q;+r Ao Qn', Qi*, u
6;+t--lCpeAIIee 3HaqeHHe paCXoAoB BOAbI H cTaHLapT AJtfr,3TOfi qaCTli
pfrEa Ha6nrcAeuurl (or t{t po n).
B saeHcHM.ocrH or BbrqHcJrerrribIX no pflAy Ha6JrroAeHHfi 3a croKoM
peKH I{o3cF+HuHeHToB Koppe,IIrqHr{ B aBroxoppe"rlfirrr-roH}rbrx QyHxull-
RX C yqeTOM TOqHOCTH Or{eHKH STHX KO3QolirIEeHrOB rr0 KOpOTKHM
BbISopKaI{ B rHApoJIorr.{H npr.tMellfiror pagJrHqHbre MaTeMarHrrecKxe Mo-
AenH peqHofo cToKa.
54
Cnelyer 3aMert.irb, r{To docrarott
CJIe)KHBaercfl TeHAeHI{Hfl K O6pa3oBaHHI.O
rpyrlrrHpoBoK fleT c ttoBbIlrlesHoit HIIH
noHHx(eHHor:r BoAHocrbio. OAHaxo B qe-
peAoBaHHH 3rHX f pynnl{poBoK rpyAHo 0
ynoBHTb orI{eT,rIHBO BbIpaX{eHHyIO IIe-
pHoAHqecKyro 3aKoHoMepHocrb, a feHe-
THqecKHe fIpHtIHHbI OOpa3OBaHllfl HX He
ilP€ACTANIflIOTCfi AOCTATOqHO,flCHL{}I,Ii.
floarouy B npaKrHKe BoAoxo3qficreeH-
Hbrx H BOAHO3HepfeTHr{ecKHX pacqeToB
B CCCP noryr{ru'Io irl6poKoe pacnpo-
crpaHeHHe rrpeAcraBJreHHe MHoToJIeTHHX
xone6annfi croKa peK KaK cnyqafiHoro
npoqeCca, OIIHCL{BaeMOfO MaTelt{aTHqecKH U e
l/( ^ - --
n fi IvI Fi ivi a D'K O Ba.
B npocrerirueii Qopve MapKoBcxnx qeneir, Hau6oree qacro Hcno;tbsyeMblx B Ha-
-cTogtqee Bpet'(fl B Bon,o-\oggftcreerrrrbrx pacqeTax, yt{HTblBaeTCff KOppe.rlfiqHoHHaff
cBf3b ToJrbKo Me:+(.Iy HenocpeacTBeHHo cliexHbll{lr t{.rIeFIa}{H THLpOXOFIIqeCKOTO pf,l.a.
3ra cessu HMeer ,nocraroqHo qcnhrli $u:n,lecrlrii ct'tuc.r. Otia xapaxrepH3)'er <HHep-
rlr{rc> u roae6asHfl.\ croKa peK, ffsxrtouytocq cneAcrBHelvt 3aBHcItMocrt{ roAoBofo
,croKa or HaJrHrrHfl sa BoAoc6ope peKi{ 3anacoB BoAbr, o6pasyroursx 6oaee HnH MeHee
3r{asHrerbHHe ocrarKs, nepexoAqulr{e H3 foAa B roA. Apyroir eaxgoil npntttttoti'
{oppennpoBaHHocrrr croKa Bo BpeMeHH Mo}Ker 6urr B;IHflHl{e Ha Hero HcrtapeHns
c noBepxuocrx BoAoc6opuoro 6accefisa.
KoppernunoHHafl Qyrxurrn npocroro MapKoBcKoro npol{ecca npeAcrasneua Ha
.plrc. 3.14. Anq Bb{qr.rciensn xosQQHqreurots aBroKopperlfiqrrll n npocrofi uaprcoecxofi
:qellfi Hc[Onb3yercfi BHpax(eHne
, < 
- t l, (3.3t)
TAe r1 - xoa$Snqtrenr KoppensUHir r{ei+..q,)' HenocpeAcrBeI{Ho c}te)KI{tdMt tIJIeHaMii
frlApoJrorHqecKoro pflAa.
Car'rofi npocrofi MoAenblo KoJ'redaHriir roAoaoro croxa B pacqerax ero MHoroiler-
rnero perynlrpoeaHHff B BoAoxpaHHnHulex rBJlflercs N{oAenb, n xoropoft orcyrcrtsyer
cBfl3b Mex(Ay croKaMrr cMelKubrx .'ier. 3ra npocrefiurafl MoAenb B TeqeHHe pnAa ner
.rrrHpoKo r{cnorb3oBaJracb B soAoxosgficreeHHoR ilpaKTttKe- 3areu ona ycrynHr't& Mecro
:MoAeJrrr npocrort uenn llapKoBa co cpeAHElrr xoeQQuutteHToM Koppe-
JrRq,HH MelKAy croKaMH cMex(Hbrx ner peK CCCP, paBHHrr{ 11:0,3. flpn noslrtox-
IrocTH nonyqlrTb no pflAy ua6rrioAeuari AocraroqHo ToqHyro ouenii5r HHA:{BHAyairbHo-
ro xoaQQl{UHeHTa KoppenffUrnr Mex(A}' croKa}{H cMex(Hbix Jter ero HcnoJlb3ylor B Mo-
J,enH npocrofr uenn Maproaa npH npoBeaernrr{ eoAoxossficrBeHlntx pacqeroB. B ue-
+(oropbrx oco6o cJroxrrbrx cnyr{aflx Anrr lutoAen}IpoBaHIifl HcrIoilb3ytor Mttoro3BerFrbre
ilapKoBcKlre uent{, B ociloBe KoTopt{x r'le)KaT aBToKoppeJlfll{]tollHHe rpyttxllHlt I'H.|{po-
JIOTHqecKUX prrAOB.
'55
0r2
-n 2U,L
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Puc. 3.14. AeroKoppenffur/.or{Haq
Qynxuun rn.IponofnqecKoco pfl-
Aa p. Hapuna (r. Vu-Kyprau):
1-eunlrpnvecKue AaHHble; 2-npo-
crac qeub Mapxoea
(3.30)
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