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4232 y(F)784 4236 y(\177)781 4232 y(ur)e(die)f(Hyp)s(ereb)s(enenprozesse)g(ist)h(die)g(L)2235 4236 y(\177)2235 4232 y(osung)f(sc)m(hon)i(l)2763 4236 y(\177)2763 4232 y(angst)f(b)s(ek)-5 b(ann)m(t:)27 b(es)g(ist)581 4344 y(das)33 b(einzige)f(rotationsin)m(v)-5 b(arian)m(te)32 b(W)-8 b(ahrsc)m(heinlic)m(hk)m(eitsma\031)33 b(auf)f Fm(G)p Fo(\()p Fm(d)22 b Fi(\000)f Fo(1)p Fm(;)15 b(d)p Fo(\),)35 b(die)581 4457 y Fk(isotr)-5 b(op)g(e)28 b(V)-7 b(erteilung)22 b Fo(\(Da)m(vidson,)h(Janson)e(&)h(Kallen)m(b)s(erg,)f (Thomas\).)i(F)3121 4461 y(\177)3118 4457 y(ur)f Fm(k)28 b(<)d(d)t Fi(\000)t Fo(1)581 4570 y(ist)30 b(das)h(Problem)e(teilw)m (eise)h(no)s(c)m(h)h(o\013en,)g(und)e(in)h(den)g(gel)2633 4574 y(\177)2633 4570 y(osten)h(F)2930 4574 y(\177)2930 4570 y(allen)f(k)m(enn)m(t)h(man)581 4683 y(die)f(gesam)m(ten)i (Klassen)d(der)h(maximalen)f(Ric)m(h)m(tungsma\031e)i Fm(\022)h Fo(\(Mec)m(k)m(e,)i(Thomas\).)722 4839 y(Hier)28 b(w)m(erden)g(not)m(w)m(endige)g(Bedingungen)f(f)2274 4843 y(\177)2271 4839 y(ur)h(ein)f(Maxim)m(um)h(angegeb)s(en.)h(Da-)581 4951 y(b)s(ei)24 b(stellt)h(es)h(sic)m(h)f(heraus,)g(dass)g(die)f(Sc)m (hnittzahlrose)h(des)g("maximalen")g(Prozesses)581 5064 y(\010)647 5031 y Fn(d)647 5092 y(k)716 5064 y Fo(fast)i(sic)m(her)g(k) m(onstan)m(t)h(sein)d(m)m(uss.)i(Hierb)s(ei)e(w)m(erden)h(Metho)s(den)h (der)f(V)-8 b(ariations-)581 5177 y(rec)m(hn)m(ung)36 b(auf)g(dem)g(Raum)g(der)g(signierten)f(Ma\031e)j(b)s(en)m(utzt)f (\(Molc)m(hano)m(v,)h(Zuev\).)581 5290 y(Der)j(Zusammenhang)f(mit)g (den)g(klassisc)m(hen)f(isop)s(erimetrisc)m(hen)g(Problemen)g(f)3487 5294 y(\177)3484 5290 y(ur)581 5403 y(zen)m(tralsymmetrisc)m(he)31 b(k)m(on)m(v)m(exe)h(K)1833 5407 y(\177)1833 5403 y(orp)s(er)d(wird)f (diskutiert.)2053 5652 y(2)p eop %%Page: 3 3 3 2 bop 183 548 a Fp(4)134 b(Nac)l(h)l(barsc)l(haftsrosen)183 751 y Fo(F)245 755 y(\177)242 751 y(ur)22 b Fm(k)s Fo(,)h Fm(r)i Fo(mit)c Fm(k)7 b Fo(+)e Fm(r)28 b(<)d(d)e Fo(sc)m(hneiden)f (sic)m(h)g(eine)g Fm(k)s Fo({Eb)s(ene)g(und)f(eine)h Fm(r)s Fo({Eb)s(ene)g(in)f Fl(R)3027 718 y Fn(d)3096 751 y Fo(in)183 864 y(allgemeiner)h(Lage)i(nic)m(h)m(t.)g(Deshalb)e (wird)g(b)s(ei)g(der)h(Einf)2116 868 y(\177)2113 864 y(uhrung)c(der)k(Sc)m(hnittzahlrose)183 977 y(die)36 b(F)-8 b(orderung)36 b Fm(k)28 b Fo(+)c Fm(r)38 b Fj(>)e Fm(d)h Fo(gestellt.)g(Wir)f(sind)f(in)h(der)g(Lage,)i(ein)e(Analogon)h (der)183 1090 y(Sc)m(hnittzahlrose)29 b(f)848 1094 y(\177)845 1090 y(ur)g(den)h(F)-8 b(all)30 b Fm(k)24 b Fo(+)19 b Fm(r)28 b(<)d(d)31 b Fo(zu)f(de\014nieren.)324 1203 y(Es)23 b(sei)h Fm(\021)j Fo(eine)d Fm(r)s Fo({dimensionale)d(T)-8 b(esteb)s(ene)25 b(in)e Fl(R)2025 1170 y Fn(d)2072 1203 y Fo(.)h(F)2183 1207 y(\177)2180 1203 y(ur)f(jede)i Fm(k)s Fo({Eb)s(ene)e Fm(\030)28 b Fo(aus)c(\010)3129 1170 y Fn(d)3129 1230 y(k)183 1315 y Fo(mit)29 b(dem)h(Abstand)f(v)m(on)h Fm(\021)k Fo(nic)m(h)m(t)c(gr)1470 1319 y(\177)1470 1315 y(o\031er)h(als)e(eins)g(wird)f(in)h Fm(\030)34 b Fo(der)c(Punkt)f (markiert,)183 1428 y(der)23 b(den)g(Abstand)g(zwisc)m(hen)g Fm(\030)28 b Fo(und)22 b Fm(\021)27 b Fo(realisiert.)c(Die)h(Menge)h (aller)d(solc)m(hen)i(Punkte)183 1541 y(in)35 b Fl(R)354 1508 y Fn(d)437 1541 y Fo(ist)h(ein)f(Punktprozess,)h(dessen)g(In)m (tensit)1908 1545 y(\177)1908 1541 y(at)h(W)-8 b(ert)37 b(der)f Fk(Nachb)-5 b(arschaftsr)g(ose)183 1654 y(von)37 b Fo(\010)425 1621 y Fn(d)425 1682 y(k)505 1654 y Fk(f)533 1658 y(\177)533 1654 y(ur)g Fm(\021)i Fo(genann)m(t)d(und)d(mit)i Fm(N)1523 1669 y Fn(k)r(r)1600 1654 y Fo(\()p Fm(\021)s Fo(\))h(b)s(ezeic)m(hnet)g(wird.)d(W)-8 b(eiter)36 b(w)m(erden)f(die) 183 1767 y(Eigensc)m(haften)e(der)f(Nac)m(h)m(barsc)m(haftsrosen)j Fm(N)1836 1782 y Fn(k)r(r)1945 1767 y Fo(und)d(deren)g(Zusammenhang)g (mit)183 1880 y(den)d(Sc)m(hnittzahlrosen)g(der)h Fk(dualen)k(Pr)-5 b(ozesse)31 b Fo(un)m(tersuc)m(h)m(t.)183 2166 y Fp(5)134 b(Charakteristisc)l(he)33 b(Eigensc)l(haften)e(der)f(Sc)l(hnittzahl-) 384 2316 y(rosen)183 2519 y Fo(Es)42 b(sei)f Fm(f)52 b Fo(eine)42 b(F)-8 b(unktion)41 b(auf)h Fm(G)p Fo(\(1)p Fm(;)15 b(d)p Fo(\).)44 b(Am)m(bartzumian)e(und)f(Matheron)i(hab)s(en) 183 2632 y(die)g(not)m(w)m(endigen)g(und)g(hinreic)m(henden)e (Bedingungen)i(daf)2354 2636 y(\177)2351 2632 y(ur)f(gefunden,)i(dass)f Fm(f)183 2744 y Fo(die)28 b(Sc)m(hnittzahlrose)h(eines)g(Hyp)s(ereb)s (enenprozesses)g(\010)2161 2711 y Fn(d)2161 2772 y(d)p Ff(\000)p Fg(1)2321 2744 y Fo(mit)g(Geraden)h(ist.)f(Hier)183 2857 y(w)m(erden)24 b(w)m(eitere)793 2861 y(\177)793 2857 y(ahnlic)m(hen)f(Kriterien)g(b)s(ewiesen.)h(Die)h(Bew)m(eise)g (lassen)f(sic)m(h)h(auf)f(die)183 2970 y(Charakterisierungss)968 2974 y(\177)968 2970 y(atze)29 b(f)1188 2974 y(\177)1185 2970 y(ur)g(Zonoide)h(zur)1775 2974 y(\177)1772 2970 y(uc)m(kf)1939 2974 y(\177)1936 2970 y(uhren)e(\(Go)s(o)s(dey)-8 b(,)32 b(W)-8 b(eil\).)183 3256 y Fp(6)134 b(Hauptergebnisse)183 3459 y Fo(Im)27 b(folgenden)g(w)m(erden)g(n)m(ur)g(ausgew)1476 3463 y(\177)1476 3459 y(ahlte)h(Hauptresultate)g(erw)2465 3463 y(\177)2465 3459 y(ahn)m(t.)g(Mit)g Fm(\033)s Fo(\()p Fi(\001)p Fo(\))h(b)s(e-)183 3572 y(zeic)m(hnen)g(wir)f(jew)m(eils)h (das)g(einzige)g(rotationsin)m(v)-5 b(arian)m(te)30 b(W)-8 b(ahrsc)m(heinlic)m(hk)m(eitsma\031)183 3685 y(auf)30 b(dem)g(en)m(tsprec)m(henden)g(In)m(tegrationsraum.)183 3872 y Fe(Satz)35 b(1)g(\(Umk)m(ehrformel)e(f)1271 3877 y(\177)1268 3872 y(ur)i(die)g(Sc)m(hnittzahlrose\).)183 3985 y Fk(Es)d(sei)f Fo(\010)518 3952 y Fn(d)518 4012 y(d)p Ff(\000)p Fg(1)681 3985 y Fk(ein)h(station)1101 3989 y(\177)1102 3985 y(ar)-5 b(er)35 b(Hyp)-5 b(er)g(eb)g(enenpr)g (ozess)34 b(mit)f(Intensit)2569 3989 y(\177)2570 3985 y(at)g Fm(\025)25 b Fo(=)g(1)p Fk(,)33 b(R)n(ich-)183 4098 y(tungsverteilung)f Fm(\022)j Fk(und)e(Schnittzahlr)-5 b(ose)36 b(mit)d Fm(r)s Fk({Eb)-5 b(enen)32 b Fm(T)2317 4113 y Fn(d)p Ff(\000)p Fg(1)p Fn(;r)2502 4098 y Fm(\022)s Fk(,)f Fo(1)26 b Fm(<)f(r)j Fj(6)e Fm(d)20 b Fi(\000)g Fo(1)p Fk(,)183 4211 y Fm(d)25 b Fj(>)g Fo(3)p Fk(.)33 b(Es)f(wer)-5 b(de)34 b(die)f(F)-7 b(unktion)33 b Fm(l)r Fo(\()p Fm(v)s Fo(\))p Fk(,)g Fm(v)c Fi(2)c Fe(S)1800 4178 y Fn(d)p Ff(\000)p Fg(1)1963 4211 y Fk(dur)-5 b(ch)34 b(die)f(F)-7 b(ormel)205 4469 y Fm(l)r Fo(\()p Fm(v)s Fo(\))26 b(=)504 4408 y(2)549 4375 y Fn(r)r Fg(+1)678 4408 y Fm(k)725 4422 y Fn(r)r Ff(\000)p Fg(1)p 483 4448 391 4 v 483 4531 a Fm(!)540 4545 y Fn(r)578 4531 y Fo(\()p Fm(r)d Fi(\000)d Fo(2\)!)884 4469 y Fi(\002)295 4801 y(\002)381 4673 y Fh(\022)524 4740 y Fm(d)p 443 4780 210 4 v 443 4863 a(d)p Fo(\()p Fm(x)577 4837 y Fg(2)617 4863 y Fo(\))647 4673 y Fh(\023)702 4695 y Fn(r)r Ff(\000)p Fg(1)825 4591 y Fh(2)825 4751 y(6)825 4809 y(4)932 4659 y Fn(x)886 4677 y Fh(Z)893 4937 y Fg(0)992 4801 y Fm(y)1040 4763 y Fn(r)r Ff(\000)p Fg(1)1168 4801 y Fo(\()p Fm(x)1255 4763 y Fg(2)1315 4801 y Fi(\000)g Fm(y)1454 4763 y Fg(2)1493 4801 y Fo(\))1538 4735 y Fc(r)r Fb(\000)p Fd(3)p 1538 4748 109 3 v 1578 4790 a(2)1709 4677 y Fh(Z)1429 4956 y Fn(d)p Fg(\()p Fa(S)1537 4927 y Fc(r)r Fb(\000)p Fd(1)1537 4967 y Fc(\021)1651 4956 y Fn(;)11 b(v)r Fg(\)=arccos)j Fn(y)1847 4801 y Fo(\()q Fm(T)1936 4816 y Fn(d)p Ff(\000)p Fg(1)p Fn(;r)2120 4801 y Fm(\022)s Fo(\))g(\()p Fm(\021)s Fo(\))h Fm(\033)s Fo(\()p Fm(d\021)s Fo(\))g Fm(dy)2678 4591 y Fh(3)2678 4751 y(7)2678 4809 y(5)2742 4587 y(\014)2742 4642 y(\014)2742 4696 y(\014)2742 4751 y(\014)2742 4806 y(\014)2742 4860 y(\014)2742 4915 y(\014)2773 4990 y Fn(x)p Fg(=1)183 5167 y Fk(de\014niert,)36 b(wob)-5 b(ei)37 b Fm(d)p Fo(\()p Fi(\001)p Fm(;)15 b Fi(\001)p Fo(\))37 b Fk(den)f(ge)-5 b(o)g(d)1409 5171 y(\177)1410 5167 y(atischen)38 b(A)n(bstand)f(auf)f Fe(S)2342 5134 y Fn(d)p Ff(\000)p Fg(1)2472 5167 y Fk(,)g Fe(S)2594 5134 y Fn(r)r Ff(\000)p Fg(1)2594 5190 y Fn(\021)2758 5167 y Fk(die)g(Unter-)183 5290 y(sph)311 5294 y(\177)312 5290 y(ar)-5 b(e)28 b Fe(S)519 5257 y Fn(d)p Ff(\000)p Fg(1)655 5290 y Fi(\\)6 b Fm(\021)s Fk(,)25 b(und)i Fm(!)1053 5304 y Fn(i)1106 5290 y Fk(\()p Fm(k)1190 5304 y Fn(i)1219 5290 y Fk(\))f(die)g(Ob)-5 b(er\015)1663 5294 y(\177)1664 5290 y(ache)27 b(\(bzw.)f(das)h(V)-7 b(olumen\))26 b(der)h(Einheits-)183 5403 y(kugel)40 b(in)h Fl(R)601 5370 y Fn(i)676 5403 y Fk(b)-5 b(ezeichnen.)41 b(Ist)h Fm(g)i Fk(eine)d(b)-5 b(eliebige)40 b(ger)-5 b(ade)42 b Fm(m)p Fk({mal)h(di\013er)-5 b(enzierb)g(ar)g(e)1654 5652 y Fo(3)p eop %%Page: 4 4 4 3 bop 581 548 a Fk(F)-7 b(unktion)33 b(auf)g Fe(S)1177 515 y Fn(d)p Ff(\000)p Fg(1)1340 548 y Fk(f)1368 552 y(\177)1368 548 y(ur)g Fm(m)25 b Fj(>)g Fo(\()p Fm(d)c Fo(+)f(5\))p Fm(=)p Fo(2)p Fk(,)34 b(so)f(gilt)616 687 y Fh(Z)561 957 y Fa(S)606 938 y Fc(d)p Fb(\000)p Fd(1)711 810 y Fm(g)s Fo(\()p Fm(v)s Fo(\))15 b Fm(\022)935 773 y Ff(?)995 810 y Fo(\()p Fm(dv)s Fo(\))26 b(=)1296 749 y(\()p Fi(\000)p Fo(1\))1482 716 y Fn(d)p Ff(\000)p Fg(2)1613 749 y Fo(2)1658 716 y Fn(d)p Ff(\000)p Fg(4)p 1291 789 503 4 v 1291 874 a Fo(\()p Fm(d)21 b Fi(\000)f Fo(3\)!)15 b Fm(!)1665 843 y Fg(2)1662 904 y Fn(d)p Ff(\000)p Fg(1)1803 810 y Fi(\002)565 1213 y(\002)650 1089 y Fh(Z)595 1360 y Fa(S)640 1341 y Fc(d)p Fb(\000)p Fd(1)745 1213 y Fm(l)r Fo(\()p Fm(u)p Fo(\)\()p Fi(4)1012 1227 y Fg(0)1073 1213 y Fo(+)20 b Fm(d)g Fi(\000)g Fo(1\))1402 1085 y Fh(\022)1547 1152 y Fm(d)p 1465 1192 213 4 v 1465 1276 a(d)p Fo(\()p Fm(\026)1602 1249 y Fg(2)1641 1276 y Fo(\))1672 1085 y Fh(\023)1727 1108 y Fn(d)p Ff(\000)p Fg(2)1842 1003 y Fh(2)1842 1163 y(6)1842 1221 y(4)2032 1089 y(Z)1883 1358 y Fn(<)-12 b(u;v)j(>)2067 1339 y Fd(2)2101 1358 y Fn(>\026)2198 1339 y Fd(2)2248 1152 y Fm(g)s Fo(\()p Fm(v)s Fo(\))27 b Fi(j)p Fm(<)10 b(u;)15 b(v)e(>)p Fi(j)41 b Fm(!)2887 1167 y Fn(d)2927 1152 y Fo(\()p Fm(dv)s Fo(\))p 2248 1192 845 4 v 2296 1301 a(\()p Fm(<)10 b(u;)15 b(v)e(>)2632 1275 y Fg(2)2697 1301 y Fi(\000)p Fm(\026)2823 1275 y Fg(2)2862 1301 y Fo(\))2897 1265 y Fg(2)p Ff(\000)2997 1238 y Fc(d)p 2998 1250 33 3 v 2999 1291 a Fd(2)3102 1003 y Fh(3)3102 1163 y(7)3102 1221 y(5)3163 1000 y(\014)3163 1054 y(\014)3163 1109 y(\014)3163 1163 y(\014)3163 1218 y(\014)3163 1272 y(\014)3163 1327 y(\014)3193 1386 y Fn(\026)p Fg(=0)3300 1213 y Fm(!)3357 1228 y Fn(d)3397 1213 y Fo(\()p Fm(du)p Fo(\))p Fm(;)581 1577 y Fk(wob)-5 b(ei)25 b Fi(4)900 1591 y Fg(0)964 1577 y Fk(der)g(Beltr)-5 b(ami)27 b({)e(L)-5 b(aplac)g(e)26 b(Op)-5 b(er)g(ator)27 b(ist,)e(und)g(mit)g Fm(\022)2766 1544 y Ff(?)2848 1577 y Fk(das)h(Ma\031)e Fm(\022)3250 1544 y Ff(?)3309 1577 y Fo(\()p Fm(dv)s Fo(\))i(=)581 1689 y Fm(\022)s Fo(\()p Fm(dv)756 1656 y Ff(?)815 1689 y Fo(\))33 b Fk(auf)g Fe(S)1097 1656 y Fn(d)p Ff(\000)p Fg(1)1260 1689 y Fk(b)-5 b(ezeichnet)33 b(wir)-5 b(d.)722 1877 y Fo(Die)27 b Fk(R)-5 b(adon)32 b({)e(T)-7 b(r)i(ansformation)31 b Fm(R)1954 1891 y Fn(ij)2014 1877 y Fo(,)c(1)f Fj(6)f Fm(i)h(<)f(j)30 b Fj(6)25 b Fm(d)14 b Fi(\000)g Fo(1)27 b(auf)g Fm(L)2980 1844 y Fg(1)3034 1877 y Fo(\()p Fm(G)p Fo(\()p Fm(i;)15 b(d)p Fo(\)\))29 b(wird)581 1990 y(durc)m(h)g(die)h(Gleic)m(h)m(ung) 1394 2230 y(\()p Fm(R)1498 2244 y Fn(ij)1559 2230 y Fm(f)10 b Fo(\))15 b(\()p Fm(\030)t Fo(\))26 b(=)2070 2106 y Fh(Z)1880 2373 y Fn(\021)r Ff(2)p Fn(G)p Fg(\()p Fn(i;d)p Fg(\):)12 b Fn(\021)r Ff(\032)p Fn(\030)2347 2230 y Fm(f)e Fo(\()p Fm(\021)s Fo(\))15 b Fm(\033)s Fo(\()p Fm(d\021)s Fo(\))581 2561 y(b)s(estimm)m(t.)47 b(F)1090 2565 y(\177)1087 2561 y(ur)h Fm(\013)54 b(>)g Fo(0,)49 b Fm(i)32 b Fo(+)f Fm(j)60 b Fj(>)54 b Fm(d)48 b Fo(sei)f Fm(T)2275 2528 y Fn(\013)2262 2587 y(ij)2372 2561 y Fo(ein)g(Op)s(erator)h(auf)f(dem)g (Raum)608 2668 y(~)581 2692 y Fe(M)16 b Fo(\()p Fm(G)p Fo(\()p Fm(i;)f(d)p Fo(\)\))32 b(der)e(signierten)e(Ma\031e)k(auf)e Fm(G)p Fo(\()p Fm(i;)15 b(d)p Fo(\),)32 b(der)e(durc)m(h)f(die)h(Gleic) m(h)m(ung)1503 2864 y Fh(\000)1545 2937 y Fm(T)1611 2900 y Fn(\013)1598 2960 y(ij)1660 2937 y Fm(\022)1706 2864 y Fh(\001)1762 2937 y Fo(\()p Fm(\030)t Fo(\))c(=)2048 2813 y Fh(Z)1978 3080 y Fn(G)p Fg(\()p Fn(i;d)p Fg(\))2188 2937 y Fo([)p Fm(\030)t(;)15 b(\021)s Fo(])2370 2900 y Fn(\013)2436 2937 y Fm(\022)s Fo(\()p Fm(d\021)s Fo(\))581 3281 y(de\014niert)29 b(ist.)h(F)-8 b(alls)30 b Fm(\013)c Fo(=)f(1,)31 b(ist)e Fm(T)1779 3248 y Fg(1)1766 3306 y Fn(ij)1827 3281 y Fm(\022)k Fo(die)c(gew)2200 3285 y(\177)2200 3281 y(ohnlic)m(he)h(Sc)m(hnittzahlrose)f Fm(T)3244 3295 y Fn(ij)3305 3281 y Fm(\022)s Fo(.)581 3468 y Fe(Satz)35 b(2)g(\(Die)g(F)-9 b(ormel)34 b(v)m(om)h(Cauc)m(h)m (y)g({)g(Kub)s(ota)g({)g(T)m(yp\).)581 3581 y Fk(F)640 3585 y(\177)640 3581 y(ur)e(al)5 b(le)33 b Fm(\013)26 b(>)f Fo(0)33 b Fk(und)g(Dimensionen)f Fm(i)p Fk(,)h Fm(j)5 b Fk(,)33 b Fm(k)j Fk(mit)d Fm(i)20 b Fo(+)g Fm(k)29 b Fj(>)c Fm(d)p Fk(,)32 b Fm(i)26 b(<)f(j)38 b Fk(gilt)1742 3785 y Fm(R)1811 3799 y Fn(ij)1871 3785 y Fm(T)1937 3747 y Fn(\013)1924 3808 y(k)r(i)2017 3785 y Fo(=)25 b Fm(c)p Fo(\()p Fm(\013)p Fo(\))p Fm(T)2346 3747 y Fn(\013)2333 3808 y(k)r(j)581 4004 y Fk(auf)796 3980 y Fo(~)769 4004 y Fe(M)16 b Fo(\()p Fm(G)p Fo(\()p Fm(i;)f(d)p Fo(\)\))r Fk(,)32 b(wob)-5 b(ei)1440 4324 y Fm(c)p Fo(\()p Fm(\013)p Fo(\))27 b(=)1730 4211 y Fn(d)p Ff(\000)p Fn(k)r Ff(\000)p Fg(1)1782 4238 y Fh(Y)1784 4436 y Fn(l)q Fg(=0)1975 4230 y Fo(\000)2047 4129 y Fh(\020)2111 4189 y Fn(j)t Ff(\000)p Fn(l)p 2111 4209 110 4 v 2148 4261 a Fg(2)2230 4129 y Fh(\021)2300 4230 y Fo(\000)2372 4156 y Fh(\000)2423 4194 y Fn(i)p Ff(\000)p Fn(l)q Fg(+)p Fn(\013)p 2423 4209 201 4 v 2506 4261 a Fg(2)2634 4156 y Fh(\001)p 1975 4304 701 4 v 1975 4419 a Fo(\000)2047 4345 y Fh(\000)2098 4383 y Fn(i)p Ff(\000)p Fn(l)p 2098 4398 101 4 v 2131 4450 a Fg(2)2209 4345 y Fh(\001)2266 4419 y Fo(\000)2338 4318 y Fh(\020)2402 4378 y Fn(j)t Ff(\000)p Fn(l)q Fg(+)p Fn(\013)p 2402 4398 210 4 v 2489 4450 a Fg(2)2621 4318 y Fh(\021)2686 4324 y Fm(:)581 4645 y Fe(Satz)35 b(3)g(\(Not)m(w)m (endige)f(Bedingungen)i(f)2176 4650 y(\177)2173 4645 y(ur)f(ein)g(Maxim)m(um\).)581 4758 y Fk(Es)47 b(sei)g Fm(\022)924 4772 y Fg(0)1010 4758 y Fk(die)g(R)n(ichtungsverteilung)g (von)g Fo(\010)2248 4725 y Fn(d)2248 4786 y(k)2337 4758 y Fk(mit)g(Intensit)2819 4762 y(\177)2820 4758 y(at)h Fm(\025)k Fo(=)f(1)p Fk(,)c(die)g(die)581 4871 y(Schnittintensit)1155 4875 y(\177)1156 4871 y(at)g(zweiter)f(Or)-5 b(dnung)45 b Fm(\025)2042 4897 y Fn(X)2100 4906 y Fd(2)2135 4897 y Fg(\(\010)2213 4874 y Fc(d)2213 4921 y(k)2251 4897 y Fg(\))2328 4871 y Fk(maximisiert.)h(Ist)g Fm(c)3056 4885 y Fn(max)3245 4871 y Fk(der)g(ma-)581 4992 y(ximale)34 b(Wert)e(von)h Fm(\025)1328 5019 y Fn(X)1386 5028 y Fd(2)1421 5019 y Fg(\(\010)1499 4996 y Fc(d)1499 5042 y(k)1537 5019 y Fg(\))1569 4992 y Fk(,)f(so)i(gilt)e(f)1929 4996 y(\177)1929 4992 y(ur)h(die)f(Schnittzahlr)-5 b(ose)36 b Fm(T)2874 5007 y Fn(k)r(k)2955 4992 y Fm(\022)2998 5006 y Fg(0)3038 4992 y Fk(:)653 5193 y Fe(\(i\))44 b Fo(\()q Fm(T)897 5208 y Fn(k)r(k)978 5193 y Fm(\022)1021 5207 y Fg(0)1060 5193 y Fo(\))16 b(\()p Fm(\021)s Fo(\))26 b(=)f(2)p Fm(c)1435 5207 y Fn(max)1645 5193 y Fm(\022)1688 5207 y Fg(0)1727 5193 y Fk({f.s.;)624 5380 y Fe(\(ii\))44 b Fo(\()q Fm(T)897 5395 y Fn(k)r(k)978 5380 y Fm(\022)1021 5394 y Fg(0)1060 5380 y Fo(\))16 b(\()p Fm(\021)s Fo(\))26 b Fj(6)f Fo(2)p Fm(c)1435 5394 y Fn(max)1612 5380 y Fk(f)1640 5384 y(\177)1640 5380 y(ur)33 b(al)5 b(le)33 b Fm(\021)28 b Fi(2)d Fm(G)p Fo(\()p Fm(k)s(;)15 b(d)p Fo(\))p Fk(.)2053 5652 y Fo(4)p eop %%Page: 5 5 5 4 bop 183 548 a Fe(Satz)35 b(4)g(\(Eigensc)m(haften)f(der)h(Nac)m(h)m (barsc)m(haftsrosen\).)183 661 y Fk(Ist)e Fm(N)391 676 y Fn(k)r(r)500 661 y Fk(die)f(Nachb)-5 b(arschaftsr)g(ose)36 b(von)d Fo(\010)1669 628 y Fn(d)1669 689 y(k)1744 661 y Fk(f)1772 665 y(\177)1772 661 y(ur)g Fm(k)23 b Fo(+)d Fm(r)28 b(<)d(d)p Fk(,)33 b(so)g(gilt)678 893 y Fm(N)751 908 y Fn(k)r(r)827 893 y Fo(\()p Fm(\021)s Fo(\))26 b(=)f Fm(k)1114 908 y Fn(d)p Ff(\000)p Fn(k)r Ff(\000)p Fn(r)1352 792 y Fh(\020)1407 893 y Fm(T)1460 908 y Fn(d)p Ff(\000)p Fn(k)r(;d)p Ff(\000)p Fn(r)1738 893 y Fm(\022)1784 855 y Ff(?)1843 792 y Fh(\021)1912 893 y Fo(\()p Fm(\021)1995 855 y Ff(?)2055 893 y Fo(\))p Fm(;)108 b(\021)29 b Fi(2)c Fm(G)p Fo(\()p Fm(r)m(;)15 b(d)p Fo(\))p Fm(;)183 1131 y Fk(wob)-5 b(ei)49 b Fm(T)498 1146 y Fn(d)p Ff(\000)p Fn(k)r(;d)p Ff(\000)p Fn(r)777 1131 y Fm(\022)823 1098 y Ff(?)929 1131 y Fk(die)g(Schnittzahlr)-5 b(ose)52 b(der)d(dualen)h Fo(\()p Fm(d)32 b Fi(\000)g Fm(k)s Fo(\))p Fk({Eb)-5 b(enenpr)g(ozesse)183 1243 y Fo(\010)249 1210 y Fn(d)249 1271 y(d)p Ff(\000)p Fn(k)435 1243 y Fk(\(d.h.)27 b(mit)g(Intensit)1109 1247 y(\177)1110 1243 y(at)g Fm(\025)g Fk(und)g(R)n(ichtungsverteilung) f Fm(\022)2314 1210 y Ff(?)2372 1243 y Fk(\))h(mit)f Fo(\()p Fm(d)7 b Fi(\000)g Fm(r)s Fo(\))p Fk({Eb)-5 b(enen)183 1356 y(ist.)1654 5652 y Fo(5)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF