Диссертация (1136178), страница 45

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ÈìååìZ0t√√√√dτln |τ − a| √ = 2( t − a) ln | t − a|+τ√√√√√+2( t + a) ln | t + a| − 4 tïðèa ≥ 0,Z0tp√√dτln |τ − a| √ = 2 t ln |t + |a|| − 4 t + 4 |a| arctgτst|a|392ïðèa < 0.Ñëåäîâàòåëüíî, ïðè∞Z0x − x− ≥ 0dt{ln |(x − z− ) − t| − ln |(x − x− ) − t|} √ = 0,tx − x− < 0à ïðèZ0∞√dt{ln |(x − z− ) − t| − ln |(x − x− ) − t|} √ = −2π x− − x.tÈòàê, äîêàçàíî, ÷òî√Π− (x, h) = −2π x− − xθ(x− −x)+O h3/8 (1+| ln |x−z− ||) .(4.354)Àíàëîãè÷íî ïðîâåðÿåòñÿ, ÷òî√Π+ (x, h) = −2π x − x+ θ(x−x+ )+O h3/8 (1+| ln |x−z+ ||) .(4.355)Ðàâåíñòâî (4.352) âûòåêàåò èç (4.353) (4.355).

Ëåììà äîêàçàíà.Íàêîíåö, íàì ïîòðåáóåòñÿ ôóíêöèÿdefW1 (x, h) = U (x) − h1/3 k1Zz+z−ln |x − x0 |pdx0 −0W (x , h)−2h2/3 b− ln |x − z− | − 2h2/3 b+ ln |x − z+ |.(4.356)Èç ôîðìóë (4.356), (4.321), (4.343), (4.352) âûòåêàåò, ÷òî ïðè(z− + ε, z+ − ε),1/3W1 − W = hãäånx ∈ε = h26/57Zz+k0 E(x) − k1z−h √x − xln |x − x0 |−0pdx − 2πk0 p×W (x0 , h)U 0 (x− )√iox − x+θ(x − x+ ) − 2h2/3 [b− ln |x − z− |+×θ(x− − x) + p0−U (x+ )h2/3 k02h2/3 k03+b+ ln |x − z+ |] + O(h ) = −Ω(x) +P1 E(x)+24+h2/3 Ω1 (x, h) + O h17/24 (1 + | ln |x − z− || + | ln |x − z+ ||) , h → 0.5/6(4.357)393ÇäåñüdefΩ1 (x, h) = k0 (b− + b+ )E(x) − 2(b− ln |x − z− | + b+ ln |x − z+ |).Ïåðåéäåì òåïåðü ê ðåøåíèþ çàäà÷è äëÿ ãëàâíîãî ïðèáëèæåíèÿê ôàçå.

ÑïðàâåäëèâàÔóíêöèÿÒåîðåìà 4.10.pS (x, h) = W1 (x, h)+ p0n 1O h2/3+2/19 ln (1+| ln |x−z− ||+hW1 (x, h)+| ln |x − z+ ||) + O1oh8/9h8/9+O,(x − z− )1/3(z+ − x)1/3(4.358)à òàêæå êîíñòàíòû1/3+2/19k = k1 + O h1ln ,hxe± = z± + O hÿâëÿþòñÿ àñèìïòîòè÷åñêèì ðåøåíèåì çàäà÷è(4.315), (4.319).2/3À èìåííî, çàäàííûå ôîðìóëàìè1lnh(4.359)(4.312), (4.313),(4.358), (4.359)ôóíêöèÿ S 0 (x, h) è êîíñòàíòû k , xe± óäîâëåòâîðÿþò óðàâíåíèþ(4.319)ñ òî÷íîñòüþ R∗ , ãäå R∗ èìååò âèäìèðîâêè(4.315)øåíèÿì(4.312), (4.313)(4.320),óñëîâèþ íîð-ñ òî÷íîñòüþ O(h1/3+2/19 ln 1/h), à òàêæå ñîîòíîñ òî÷íîñòüþ O(h2/3 ln 1/h).Äîêàçàòåëüñòâî.

Ïîäñòàâèì (4.358), (4.359) â (4.319) è âîñïîëüçóåìñÿ ðàâåíñòâàìè (4.343), (4.357), (4.325), (4.326). Òîãäà ïðè(ex− + ε, xe+ − ε)1/3hk1hZx∈óðàâíåíèå (4.319) ïðèìåò âèäz+z−ln |x − x0 |pdx0 −0W (x , h)Zz+ −εz− +εiln |x − x0 |0pdx −W1 (x0 , h)Z z− +ε h1/3 k1 h √x0 − z− dx0 i−−p2 ε ln |x − z− | +ln 1 −√ 0x−zx−zU 0 (x− )−−z−Z z+h1/3 k1 h √z+ − x0 dx0 i−p2 ε ln |x − z+ | +ln 1 −=√0z−xz+ − x0−U (x+ )+z+ −ε12/3+2/19=O hln (1 + | ln |x − xe− || + | ln |x − xe+ ||) +h+O(h8/9 /(x − xe− )1/3 ) + O(h8/9 /(ex+ − x)1/3 ).(4.360)394Ïîñêîëüêó ïðè1/3Zh→0z+ −εhz− +ε11ln |x − x | p−pdx0 =00W (x , h)W1 (x , h)01=O hln (1 + | ln |x − xe− || + | ln |x − xe+ ||) ,hZ z− +εh1/3 h √ln |x − x0 |01/3pdx = p2 ε ln |x − z− |+hW (x0 , h)U 0 (x− )z−Z z− +ε x0 − z− dx0 i+ O h2/3+13/57 (1 + | ln |x − xe− ||) ,+ln 1 −√ 0x − z− x − z−z−Z z+h √h1/3ln |x − x0 |1/30phdx = p2 ε ln |x − z+ |+W (x0 , h)−U 0 (x+ )z+ −εZ z+z+ − x0 dx0 i2/3+13/57++Oh(1+|ln|x−xe||),ln 1 −√+z+ − x z+ − x0z+ −ε2/3+2/19ñîîòíîøåíèå (4.360) èìååò ìåñòî.Äàëåå ïîäñòàâèì (4.358), (4.359) â óñëîâèå íîðìèðîâêè (4.315).Ïîëó÷àåì ðàâåíñòâîh1/3√√Z z+ −εk1 dx0kk1 ε 1 ε1/3p++hb+ + p=b− + p0 , h)0 (x )U 0 (x− )2W(x−Uz− +ε1+11/3+2/19=1+O hln , h → 0,hêîòîðîå ñïðàâåäëèâî, òàê êàê k1 çàäàåòñÿ ôîðìóëîé (4.342) è èìåþòìåñòî îöåíêèZz+ −ε z− +εZ1101/3+2/19p−pdx = O hW1 (x0 , h)W (x0 , h)z− +εdx01ln ,hεp−p= O(h1/3+13/57 ),002 W (x , h)U (x− )z−√Z z+dx0εp−p= O(h1/3+13/57 ).00−U (x+ )z+ −ε 2 W (x , h)(4.361)(4.362)(4.363)395Ïðè äîêàçàòåëüñòâå (4.361) (4.363) èñïîëüçîâàëèñü ñîîòíîøåíèÿ(4.357), (4.325), (4.326).Íàêîíåö, ïîäñòàâëÿÿ (4.358), (4.359) â (4.312), ïîëó÷àåì ðàâåíñòâî1/3 Z z− +εkhln |x0 − z− | 0101/3√ 0dx −U (x− )h x−,1 − px − z−U 0 (x− ) z−Z z+ −εZ z+01/3ln|x−z|hkln |x0 − z− | 0−1p√−h1/3 k1dx =dx0 − pW1 (x0 , h)−U 0 (x+ ) z+ −ε z+ − x0z− +ε12/3= O h ln , h → 0.hÎíî âûïîëíåíî â ñèëó (4.344), (4.329) è îöåíîêh1/3pU 0 (x− )Zz− +εz−ln |x0 − z− | 0√ 0dx − h1/3x − z−12/3+13/57=O hln ,hZz+ −εz− +εZz−ln |x0 − z− | 0pdx =W (x0 , h)1h−ln |x − z− | pW1 (x0 , h)z− +ε 1 2 1h1/302/3+2/19−p, pdx = O h×lnhW (x0 , h)−U 0 (x+ )Z z+Z z+ln |x0 − z− | 0ln |x0 − z− | 01/3√p×dx − hdx = O(h2/3+13/57 ).0z+ − xW (x0 , h)z+ −εz+ −ε1/30Ñîîòíîøåíèå (4.313) ïðîâåðÿåòñÿ àíàëîãè÷íî.

Òåîðåìà äîêàçàíà.2.9.Àñèìïòîòè÷åñêèå ñîáñòâåííûå çíà÷åíèÿ. ÃëàâíîåïðèáëèæåíèåÏîëó÷èì, íàêîíåö, óðàâíåíèå (0.54), èç êîòîðîãî íàõîäÿòñÿàñèìïòîòè÷åñêèå ñîáñòâåííûå çíà÷åíèÿO(n−7/10 )ïðèn→∞λn (h) = O(1)ñ òî÷íîñòüþ(ãëàâíîå ïðèáëèæåíèå).Åñëè îãðàíè÷èòüñÿ òàêîé òî÷íîñòüþ, òî â ïðàâèëå êâàíòîâàíèÿ(4.301) ôóíêöèþS0,0 ìîæíî çàìåíèòü åå àñèìïòîòèêîé ïðè ξ → +∞pS0,0 (ξ, ek) = 2ξ 3/2 /3 + O( ξ ln ξ).(4.364)396Òîãäà ñ ó÷åòîì (4.310) ïðàâèëî (4.301) ïðèìåò âèäZ1 n 2 3/2 p 0U (ex− ) +εh 3xe+ −εxe− +εo2 3/2 p0S (x, h) dx + ε−U (ex+ ) =301ln ,ãäå n öåëûå.hS 0 (x, h), à òàêæå êîíñòàíòû k , xe− , xe+−1/3+13/57= πn + O h (4.365) ôóíêöèÿ(4.365)ÿâëÿþòñÿðåøåíèåì çàäà÷è (4.312), (4.313), (4.315), (4.319) äëÿ ãëàâíîãî ïðèáëèæåíèÿ ê ôàçå.Ïîäñòàâëÿÿ ôîðìóëû (4.358), (4.359) äëÿ àñèìïòîòè÷åñêîãî ðåøåíèÿ çàäà÷è (4.312), (4.313), (4.315), (4.319) â (4.365), ïîëó÷àåìóðàâíåíèå1 n 2 3/2 p 0εU (x− ) +h 3Zo2 3/2 p0W1 (x, h) dx + ε−U (x+ ) =3z− +ε−1/3+2/19= πn + O hz+ −ε p1ln ,hãäån öåëûå.(4.366)Íàéäåì àñèìïòîòèêó âõîäÿùåãî â (4.366) èíòåãðàëà.

ÏîñêîëüêóZz− +ε pZW (x, h) dx =z−z− +ε pU 0 (x− )(x − z− ) dx + O(h1/3 ε3/2 ) =z−pU 0 (x− )2ε3/2 /3 + O(h58/57 ), h → 0,ppW (x, h) dx = −U 0 (x+ )2ε3/2 /3 + O(h58/57 ),=Zz+h → 0,z+ −εòî (4.366) ìîæíî çàïèñàòü â âèäå1nhZz+z−ZpW (x, h) dx +z+ −εopp( W1 (x, h) − W (x, h)) dx =z− +ε−1/3+2/19= πn + O h1ln .h(4.367)397Äàëåå, èñïîëüçóÿ (4.357), (4.325), (4.326), èìååì1hZz+ −εz− +εZ z+ −εppk02Ω(x)p( W1 (x, h) − W (x, h)) dx = − 1/3dx+4hW(x,h)z− +εk 3 P1+ 0 1/38hz+ −εZz− +ε1pdx + 1/32hW (x, h)E(x)+O(h−1/3+1/24 ),Ëåììà 4.48.z+ −εz− +εΩ (x, h)p1dx+W (x, h)h → 0.Ïðè h → 0 ñïðàâåäëèâû ðàâåíñòâàZz+ −εz− +εZZz+ −εΩ(x)pdx = P2 + O(h1/6 ),W (x, h)ZE(x)x+E(x)pdx + O(h1/6 ),U (x)z− +εx−Z1 z+ −ε Ω1 (x, h)11/6pdx = P + O h ln ,2 z− +εhW (x, h)pdx =W (x, h)(4.368)(4.369)ãäå∞n θ(x − x )θ(x − x)θ(x − x− )E(x− )−+P2 =E(x)E(x) −−3/23/2−∞U (x)U 0 (x− )(x − x− )3/2Zoθ(x+ − x)E(x+ )−dx,3/203/2− U (x+ )(x+ − x)à P , θ(x), b− , b+ îïðåäåëåíû ôîðìóëàìèÄîêàçàòåëüñòâî.

Ïóñòüh1/3 (|x+,1 | + 1).ZZ−ze−x−(0.57), (4.105), (0.58).defdefze− = z− + h1/3 (|x−,1 | + 1), ze+ = z+ −Òîãäà â ñèëó (4.325), (4.326), (4.321)z+ −εz− +ε(4.370)ZΩ(x)pdx − P2 =W (x, h)Ω(x)pdx +U (x)Zze+ze−ze−Ω(x)pdx−W (x, h)z− +ε11 Ω(x) p−pdx+W (x, h)U (x)398z+ −εZ+Ω(x)pze+W (x, h)Zx+dx −ze+Ω(x)pdx = O(h1/6 ),U (x)h → 0.Ðàâåíñòâî (4.368) äîêàçûâàåòñÿ àíàëîãè÷íî.Äàëåå, èìååìz+ −εZz− +εΩ (x, h)p1dx −W (x, h)ze−ZΩ1 (x, h)pdx +U (x)Zx+ZΩ1 (x, h)pdx =U (x)x−Zze−Ω (x, h)p1dx−W (x, h)z− +εze+1 1−Ω1 (x, h) p−pdx+W (x, h)U (x)x−ze−Z z+ −εZ x+Ω1 (x, h)Ω1 (x, h)11/6pp+dx −dx = O h ln , h → 0.hW (x, h)U (x)ze+ze+Òàê êàê â ñèëó (4.333), (4.151)Zx+x−(ln |x − z− | − ln |x − x− |)pdx =U (x)Zdxx+Zx+x−z− − x− ln 1 −×x − x−z− − x− √ln 1 −x−xdx=−x − x−+O×pU 0 (x− )(x − x− )x−p= O( |z− − x− |) = O(h1/6 ),Z x+(ln |x − z+ | − ln |x − x+ |)pdx = O(h1/6 ),U (x)x−òîZx+Ω1 (x, h)pdx =U (x)Zx+1 pk0 (b− + b+ )E(x)−U (x)x−x−−2[b− ln |x − x− | + b+ ln |x − x+ |] dx + O(h1/6 ), h → 0.(4.371)Äëÿ ïîëó÷åíèÿ (4.369) â ïðàâîé ÷àñòè (4.371) îñòàåòñÿ ïðîèíòåãðèðîâàòü ïî ÷àñòÿì.

Ëåììà äîêàçàíà.Òàêèì îáðàçîì, óðàâíåíèå (4.367) ïðèíèìàåò âèä1hZz+z−pZo1 n k03 P1 x+ E(x)k02pW (x, h) dx + 1/3dx − P2 + P =84hU (x)x−= πn + O(h−1/3+1/24 ),(4.372)399ãäån öåëûå, àP1 , P2 , Pîïðåäåëåíû ôîðìóëàìè (4.338), (4.370),(0.57).Äëÿ äàëüíåéøåãî ïðåîáðàçîâàíèÿ (4.372) âîñïîëüçóåìñÿ ñëåäóþùåé ëåììîé.Ïðè h → 0 ñïðàâåäëèâî ðàâåíñòâîËåììà 4.49.z+ZpZx+W (x, h) dx =x−z−Zph1/3 k0 x+ E(x)pU (x) dx −dx−2U(x)x−h2/3 k02 P3−+ O(h7/10 ),8ãäå êîíñòàíòà P3 çàäàíà ôîðìóëîé(4.373)∞n θ(x − x )θ(x − x)θ(x − x− )E 2 (x− )−+2P3 =E (x) −−3/23/2−∞U (x)U 0 (x− )(x − x− )3/2Zoθ(x+ − x)E 2 (x+ )−dx.3/203/2− U (x+ )(x+ − x)(4.374)Äîêàçàòåëüñòâî.

Èñïîëüçóÿ (4.331), à òàêæå ôîðìóëó Òåéëîðà,ïîëó÷àåìz− +h1/5ZZpW (x, h) dx −z−Zz− +h1/5ppU (x) dx = W 0 (z− , h)×x−z− +h1/5×√z−Zp− U 0 (x− )W 00 (z− , h)x − z− dx + p4 W 0 (z− , h)z− +h1/5x−√Zz− +h1/5(x − z− )3/2 dx−z−U 00 (x− )x − x− dx − p4 U 0 (x− )Zz− +h1/5(x − x− )3/2 dx+z−1/22+O(h7/10 ) = h3/10 U 0 (x− )+h1/3 k0 Φ− +h1/3 x−,1 U 00 (x− )+O(h2/3 )−3 p2 1/5U 00 (x− )1/32/3 3/20− h + h x−,1 + O(h )U (x− ) + ph1/2 −0310 U (x− )5/2U 00 (x− )− ph1/2 1 + h2/15 x−,1 + O(h7/15 )+ O(h7/10 ) =10 U 0 (x− )400hh17/30 2 ip 0h19/30 k0 Φ−13/30=− hx−,1 +x−,1U (x− ) + p+43 U 0 (x− )h19/30 U 00 (x− )px−,1 + O(h7/10 ),+12U 0 (x− )h → 0.(4.375)Àíàëîãè÷íî, â ñèëó (4.332)Zz+ZpW (x, h) dx −x+hpU (x) dx = − h13/30 x+,1 +z+ −h1/5z+ −h1/5h17/30 2 iph19/30 k0 Φ+h19/30 U 00 (x+ )p+−U 0 (x+ ) + px+,1+x+,1 +4123 −U 0 (x+ )−U 0 (x+ )+O(h7/10 ),h → 0.(4.376)Íàêîíåö, èìååìZz+ −h1/5pp( W (x, h) − U (x)) dx =z− +h1/5z+ −h1/5h1/3 k0 E(x) h2/3 k02 E 2 (x) o=− p−dx + O(h7/10 ) =3/28(U (x))2 U (x)z− +h1/5ZZh1/3 k0 x+ E(x)h2/3 k02 x+ n E 2 (x)p−=−dx −28(U (x))3/2U (x)x−x−oE 2 (x− )E 2 (x+ )1− 0−dx+×2(U (x− ))3/2 (x − x− )3/2 (−U 0 (x+ ))3/2 (x+ − x)3/2√n Z z− +h1/5 hix − x− U 00 (x− )13/2p×−+O((x−x− ) ) ×0 (x ))3/20 (x )(x − x )4(UU−x−−−Zn×[h1/3 x−,1 U 0 (x− ) − h1/3 k0 Φ− (x − x− ) + O(h1/3 (x − x− )2 )] dx+√Z x+hi1x+ − xU 00 (x+ )3/2p+−+ O((x+ − x) ) ×4(−U 0 (x+ ))3/2U 0 (x+ )(x − x+ )z+ −h1/5o1/301/31/32×[h x+,1 (−U (x+ )) − h k0 Φ+ (x+ − x) + O(h (x+ − x) )] dx −hih2/3 p 0222−U (x− )x−,1 −+−8(z+ − x− − h1/5 )1/2 (z− − x− + h1/5 )1/2401ih2h2/3 p220−+−−U (x+ )x+,18(x+ − z+ + h1/5 )1/2 (x+ − z− − h1/5 )1/2Z x+1/3hkE(x)h2/3 k02 P3 1 n 13/3007/10p+O(h ) = −dx −+hx−,1 ×282U (x)x−i h17/30 php2/150× U (x− ) 2 + h x−,1 −U 0 (x− )x2−,1 + h13/30 x+,1 ×2phi h17/30 −U 0 (x+ )x2pk0 Φ− 2 19/30+,12/150−ph−× −U (x+ ) 2+h x+,1 −2U 0 (x− ) 32 19/30 x−,1 U 00 (x− )h19/30 x+,1 U 00 (x+ )h19/30 opp−ph−−+−U 0 (x+ ) 36 U 0 (x− )6 −U 0 (x+ )k0 Φ++O(h7/10 ),h → 0.(4.377)Ñêëàäûâàÿ (4.375) (4.377), ïðèõîäèì ê (4.373).

Ëåììà äîêàçàíà.Ñ ó÷åòîì (4.373) ïðàâèëî (4.372) ïðèíèìàåò âèä1hZx+×x−Zx+x−pk0U (x) dx − 2/32hZx+x−E(x)1 n k03 P1pdx + 1/3×8hU (x)oE(x)k02k02pdx − P2 − P3 + P = πn + O(h−1/3+1/30 ), h → 0,48U (x)(4.378)ãäån öåëûå, U (x), k0 , E(x), P1 , P2 , P3 , Pîïðåäåëÿþòñÿ ôîðìóëàìè(0.55), (4.322), (0.56), (4.338), (4.370), (4.374), (0.57). Ñîîòíîøåíèå(4.378) ïðåäñòàâëÿåò ñîáîé óðàâíåíèå äëÿ íàõîæäåíèÿ ÷èñåëλ =λn (h).Èòàê, äîêàçàíà ñëåäóþùàÿ çàêëþ÷èòåëüíàÿ òåîðåìà.Òåîðåìà 4.11.ïðàâèëîìÏóñòü âûïîëíåíî óñëîâèå(4.378)(4.172).Òîãäà çàäàííûå÷èñëà λ = λn (h) ÿâëÿþòñÿ àñèìïòîòè÷åñêèìèñîáñòâåííûìè çíà÷åíèÿìè çàäà÷èO(n−7/10 ) ïðè n → ∞.(0.51) (0.53)c òî÷íîñòüþ402Ÿ 3.Ëîêàëèçàöèÿ â ïëîñêèõ äèñêàõ3.1.Ââåäåíèå ê Ÿ3Ðàññìîòðèì çàäà÷ó íà ñîáñòâåííûå çíà÷åíèÿ (0.59), (0.60) âL2 (R3 ) [41], ãäå ∆ îïåðàòîð Ëàïëàñà, ε > 0 ìàëûé ïàðàìåòð, a,α ïîëîæèòåëüíûå êîíñòàíòû. Äëÿ ýòîé çàäà÷è ⠟3 áóäåò ïîñòðîåíà ñåðèÿ àñèìïòîòè÷åñêèõ ñîáñòâåííûõ çíà÷åíèé Λ = Λn,m (ε), n →∞, m → ∞ è ñîîòâåòñòâóþùèõ ñîáñòâåííûõ ôóíêöèé ψ = ψn,m ,∞íîñèòåëÿìè êîòîðûõ ïî mod O(ε ) ÿâëÿþòñÿ ïëîñêèå äèñêè (0.61).Ðåøåíèå (0.59) áóäåì èñêàòü â âèäå (0.62), ãäå ν îïðåäåëåíîôîðìóëîé (0.63), à M = M (ε) óäîâëåòâîðÿåò íåðàâåíñòâàì0 < c0 ≤ M ≤ c1 .Çäåñüc0 , c1(4.379) íåêîòîðûå êîíñòàíòû.Ïîñëå ïîäñòàíîâêè (0.62) â (0.59), (0.60) ïîëó÷àåòñÿ ñëåäóþùàÿçàäà÷à äëÿ ôóíêöèèε2p:∂ 2 p n ε2−2ν 2ε222 α/2++ − 2 M − a(ρ + z ) + 2 +∂ρ2 ∂z 2ρ4ρ ∂ 2pZ∞Z ∞+Λ +0oW (ρ, ρ , z, z )p (ρ , z ) dz dρ p = 0,0020000(4.380)−∞Z∞Z ∞p2 (ρ0 , z 0 ) dz 0 dρ0 = 1,(4.381)−∞0ãäå ÿäðî èíòåãðàëüíîãî îïåðàòîðà èìååò âèä1W =2πZ02πdϕp.(z − z 0 )2 + ρ2 + (ρ0 )2 − 2ρρ0 cos ϕW âûðàæàåòñÿ ÷åðåç ïîëíûé ýëëèïòè÷åñêèé èíòåãðàë ïåððîäà K(κ) ñëåäóþùèì îáðàçîì:Ôóíêöèÿâîãî2√2i ρρ0W = pK p.π (z − z 0 )2 + (ρ − ρ0 )2(z − z 0 )2 + (ρ − ρ0 )2403Èñïîëüçóÿ òîæäåñòâî [4]ãäå ìîäóëüiκ 1K −√,K(κ) = √1 − κ21 − κ2p√κ = 2i ρρ0 / (z − z 0 )2 + (ρ − ρ0 )2 , ïîëó÷àåìïðåäñòàâ-ëåíèå (0.67) äëÿ èíòåãðàëüíîãî ÿäðà.

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