a a

t Tdt = 0 t t t Ldt = 0 L = p q& H = T H k k d L L k n dt q& q = 0= k & H H Pk = q & k = k = n q p k k k P& k H & H = Q K = k = n Q k Pk H = H ( Q P ) k k p dq P dq = S k k k k S S pk = P k = k = n q Q k k

u v u v ( u iv j ) qp ( ) q p p q k k k k S Pk = Wk = q k q p W J Η q p Η W & H W & H k = J k = J k Wk J k fk Η J S J H Wk = vkt + δ k v k = = J ds S = dq = p q Jdq q k k k k k S q J= p q Jdq 0 q k S pk S q J) Wk = J k k k k

π mz e 4 E = ( J + J + J ) ν θ ψ

GmM F = r R = m r v r R ( ) v GmM = 3 r R

cos cos / ( )cos θ θ θ = + + v c v c u c n n v = ± ( )

ϖ ( v / c) V 77 r V = 0 777 V = 4πρ 83 F = I I ds r ds + ds r ds ds ds r 3 [( ) ( ) ( ) ] r = I I ds r ds + ds ds r 3 [( ) ( ) ] r B = I ds r s 3 r

F = I ds B D curlh = j + j = ρv t B curle = t D t A B = curlae = gradϕ t ( mksa)

diva + µε ϕ t = 0 ρ A = µ j ϕ = = µε ε t ϕ v = µε µ ε = c c 0 0 c / ε d ( σv) = ρ( E + v B) dt Q = ( p&) 3 πε c 6 0 e = ( z&) 3 6πε 0c e 3 = ( z&) 3 3c ( ea) 4 < Q >= ω 3 3c

ϕ A B = curlae = gradϕ t ϕ ϕ χ A= A + gradχ ϕ = ϕ c t χ χ = = c t ϕ diva + = 0 c t

x= β ( x vt), y= y z = z ct = ( ct βx) β = v / c β i Αx ΑyΑ zϕ ( x, y, z, ict) c i Αx Αy Αzϕ c

i ΑΑ xα yα zϕ s pv xpv ypv zicρ c A A ν µ ε 0 F = = F G µ v νµ µν X X µ f µ ν D curlh = ρνdivd = ρ t B curle + = 0 t ρ + divρv = 0 t A = µ 0ρν ϕ = ε ρ 0 µν G µν = sµν x ν Fµν Fνλ + = 0 x λ x ν sµ = 0 x µ 0 t B = t A + t A ( ' )

( β = v ) c L = L β L 0 τ t = τ β 0 β ν = + β ν + β β ν 0 0 0 ν cos θ' + v / c cosθ = + ( v / c) cos θ' u' v u v x + ' y + ux = u y = + u ' x/ c + u ' x / c u' z + v uz = + u ' / c c ± v u = n c = ± ( ) ± v cn n n v ( / ) x

dt = dz dv = dv0 = 0 = v c ( / ) u v v x y v z ic ( ) du 0 = F = 3 4 d m du 0 = F F f dv d = m d ( ) ( m d F u = 0 u u) = 0 ( c ) = 0 d d ( k 4 4 v) + F u = d m0c ( ) = ( k v) d T = m0c ( ) = ( m m0) c m0 m = m d 0 u = F d 0

v = R ( R / c) R = R R ( R / c) = p ( ah / c ) 0 + ( ah / c )

ds = g x dx R g R = kt R g R = kt 3+ V g V = 4 R g R = kt km V = r

R g R g = kt ds M dr ( ) = ( r )( cdt) r 3 M r r 3 + r d+ ( r sin ϕ d ) ( dr) ds = ( r )( cdt) 3 M r r 3 + r d+ ( r sin ϕ d )

ϕ

x' a a a x y' a a a y z' = 3 3 a a a z 3 3 33 k a a = ik jk ij

x ' = ( x vt ) t ' ( = t c x)

t B = t A + t A ( ' )

3 4 ds = dx + dx + dx + dx = dx' + dx' + dx' 3 + dx' 4 ds = g dx dx ds = dx

ds = g dx dx

ϕ g ϕ= g = = ϕ 3 k lm 40 g ϕ = 0 = 0 G G 3 ϕ = 4 k G = kt T T ϕ g ρ + div( ρv ) = 0 T ; = 0 t T m d r 4 du k = ϕ + dt ds lm u ' um = 0

( = 0 6

0 + 964 Κ Τ x A' = A + grad ϕ' = ϕ c t ' = exp( ie ) hc x

ds = Q T S Q T

( n) ( n n n ) s i= n i = N 3

n ε = i i E i= s N N n n IIn!! i W ( n) N! IIn! ( ) = n + n + n 3 i sni sn i NK( n) ( ni + )ln ni ln i N i N S s/ W( n) = N ( ) exp( NK ( n) ) N sn i NK ( n) = ( + ln ) n i i N ln sn Ni + + µε + = 0 i n = Ae µε A i i ε = m(& x + y& + z&) W n = Ae (n ) i µε i 3 3 fd rd v =

ω sω ni sni 3 3 3 3 3 3 Ω d rd v d rd vfd rd v N N = sni K( n) = ni ln f ln( f ) d rd v N N Ω 3 3 i dh dh H 0 = 0 H dt dt H H pk = q & k = k = 3N q p k k é

t+ T f = lim f p k q k dt T T ( ) t P q f k k ρ p q t = 0 t ρ + ρ H = 0 t < f >= f q p ρ 0 q p dq dp k k k k N f =< f >

ρdω = Ω σ ln ρ= ρlnpd δ ρlnρdω > 0 Ω E 0 E E 0 + E 0 = 0 < f >= fρ p q 0 dω Ω < E >= EρdΩ Ω E Ae 0 < /PARA/ > E E = mv x + vy + v z

kt 845 kt ü

W II G G G N jj j j = j N! j N N j = = N ε = E = G j = γ+ βε j e βε j N j = G je = 0 G j = γ+ βε j e + j kt x hv kt ktx = x e kt j

ν ν ψ d 8d ν ν = kt 3 c 8ν dν aν ψ νdν = 3 c exp( bν / T) ν ν ν ψ d 8d x h ν ν = x = 3 x c e kt

hν h 97 p = = c λ h E = hνp = C R x e x h v = 3 x = ν x ( e ) kt

p dq = n hn = 3 i = r θ ϕ i i i i hν = E E M N

E h p h = = ν

Bds δ = 0 u = c / n n A u t Tdt = 0 ( T = mv ) t = u Tdt = pds ν B ds B pds = 0 A A p n x y z u = c n

ie p c iw exp ik r - wt k r,ict c h k = h = ν = p E h = h p h = 97 G P p ( S) n ( r) = 0 ( + k ) ψ = 0

0 ( S) ( E V) = h + ( E V) ψ = 0 m ψ * Qψdxdz =< Q > h E = hνp = λ x p h x

0 q mn exp( πiν mnt) q 0 0* mn = q mn

( xx) = x x mn mj jn j E = ( n n + ) h ν = pdq pq h qp = πi I H q& P& H = = P q h h h pz i x i y i z pq h qp = i E x x x = x h j

* mn m n F ψ F ψ dq ( F + G) = F + G ( FG) = F G mn mn mn mn mi in i

h E = hνp = pq h qp = πi I h x p x 4π

< a= q >< q a > k < a= < aq > q k < aq k >< q ka >= < aq k > = k k k k k k h pq qp = πi

Q a Q a < aq k > dq k k h x p x π h a t >= H a t > πi t,,

h ψ = Hψ πi t t ϕ ϕ ϕϕ

ϕ

E h p h = = ν λ

h q= p π i q h E = hνp = λ h pq qp = πi h p q = 97 97 4 π

( q, h πi q 96 3 h p πi q h p p πi q h h p k = π λ

h h Ψ ( + V) Ψ = m i t h e γ µ ( µ µ ) ( ) i x c A Ψ imcψ = 0 h ( imc) ( ) i x = µ Ψ0 0 0 ie = exp( ) ( 3) hc A dx ie hc A dx x x x ( ) ( ) ( ) x () A' = A + ' = t h e = ( ' ) = ' ( ) i x c A imc 3 ' = exp( ie ) hc x x x x () () ( ) ()

dx 4 = 0 A dx Adx A dx ( ) c Ads Ads ( Adx) = H d 0 c A i c A A ν F = ν x x

5 3 4 A A A 3 A 4 R g R = kt dx T = mu u u = d

p dq = n h k k k pq h qp = πi I h E = hνp = λ h Ψ λ = c c t mc

α = e hc

Z = 37 h i x im c 0 0 π + = Ψ

+ d d u d d d

A' = A+ x ie ' = exp( ) hc n p + + e + v Q = I 3 + Y I3 I z

+ 0 p u u d n u d d u d u u d d d u

Et te h = πi

7 7 846 930 7 9 9 9 9 85 83 9 H 884 9-88 887

84 9 90 960-9 90 896 9 900 90 9 90 905 94 9 90-85 90 90-903 903 79 87 905 96 905 93 905 907

9 93 885-94 93-9 H 90-947 946 0 0 93 J.J. 94 0 0 905 94 B-C-S 957

890 96 907 99 95-96 9 95-96 95-96 960 930 95-96 J. 0 60 95-96 0 60 967 954 960 97 0 9 93 95

95 0 0 95-97 94 G.P. 98 96 96 97 97 0 0-40 97 98 0 30-0 93 99 93 934 93 0 30 98 93 930 98 959 930 93 - - 0 30 0 30 40 946 935 947

00 0 40 50 0 40 0 30 937 938 939 94 944 939 40 40 947 40 50 g 947 50 50 50 50

K 50 - -e 956 956 956 PC T 957 964 96 50 R.G. Y. D. 960 959 3K 964 965 50 SU 3 60 964 SU 3 60 60 964 J/ 974-964 954 W Z 0 983 984 SU U 967 curle H c t ( ) 4 E curlh = v + c c t ( 3)

E c t E div( ρν) + ( 5) t ϕ A E = gradϕ c t ( 7) E + A c t = grad ϕ ( a ) ϕ A = 4π ρν ( a) c = + + x y z c t ϕ ϕ diva + = 0 c t f = ρe + ρ ν H ( f ) c x' = a x x, x, x, x x, y, z, ict = 3 4 ( 8) 0 0 i a 0 0 0 = 0 0 0 i0 0 v = = c = 0

ϕ A = 4 c I A λ = 0 = 3 4 (e ) x λ A A Fµν = = Fνµ ( 9) x x F µν = 0 H z H y iex Hz 0 H x ie y Hy Hx 0 iez iex iey ie z 0 Fλµ F Fµν + + λ µ ν ( a + b) x x x ν λ µ Fλµ π λ x = 4 c I ( b + c ) µ Fλµ = 3 4 x µ f = c F I = 3 4 F = F (f +0 ) 4 x

T = ( F F + F 4 4 Txx = ( E x E y Ez + Hx Hy H z) 8 Txy = ( E xey + H xh y) 4 i i T E H c S x4 = ( ) x = x 4 T44 = E + H u 8 T f = ( f + 0)' x c i f = 0 4 T4 u = divs + = 0 x t v dt = rd r = = c dx4 icdt = = ir ds ds

dx u = ds c f(f f f 3 = f 4 = i R c u u 0 T R + S S = f x R x R x = c u ( u + c u 0 ) 0 x u x 3 x j x 4 x4 ( 0 u ) = ( 0 ) + ( 0 ) x x s x s j= = div( v ) + c t T = 0 x j T x u 4 = 0 0 c u x f = 0 0 c du = f = 3 4 ds 3 3 d x 0 = d x 0V0 = m 0 V 0 = V m c du 3 0 = r f d x F ds 4

dt dτ = r V dx dx dx3 dx4 dt dt dt dt du d dx dt dv s = ( = ) ds c dτ dt dτ c dτ d m V F dτ ( ) 0 = d dt d r ( f v) + ( m icr) icr = dτ m0c = ( f v) 0 0 m0c f m 0 m0c T T = m0c ( m m0) c R g R = kt ( ) ds = g dr + g d+ g dψ + g dt ( ) 33 44

g = e g 44 = e g = r g 33 = r sin ( 3) g = 0 { } = + g g g ( ) gx x x d { } { } { 33 } = = re = r sin e dr d { 44 } = e { } = { 33 } = sin cos dr r d { 33 } = { 33 } = cot { 4 4} = ( 4) r dr R µν ν ρ = { µρρ } { µν ρ } { µρ α}{ αν ρ } { µν α}{ αρ ρ} χ χ + ( 5 ) T T µ ν ; = 0 ( 6) T = 0 ( 7) dt d T dr r dr r T T 3 d dr T 4 + ( + ) ( + 3 ) 4 = 0 dt 3 + cot ( T T3 ) = 0 ( 8) d 3 4 dt T 3 4 = = 0 dψ dt R = 0 ( 9) i Rii g ii R = ktii = kgiiti i = 3 4 ( 0)

d d d d R = e + ( ) dr 4 dr dr 4 dr + r e d ( ) + ( e ) ( ) ddr dr r d e + = + ke T ( a) r dr r d d dd e + ( + )( ) = kt b ( ) dr 4 dr r dr dr d d dd 3 e + ( + )( ) = kt 3 dr 4 dr r dr dr ( c) d e 4 e + = ke T 4 r dr r ( d) 3 T = T 3 d ( e ) = ke rt ( 4) dr r d 4 + ( e ) = ke rt4 ( 5) dr r d d d d + ( + )( ) = ke T dr dr r dr dr 3 6 T = T = T3 4 = T 4 3 4 T = T = T = T r 0 7 34 r r = q 8 M e = ( 9) r 4 lime = lime = r r

M g = e = g44 e M r = = ( 0) r M ds = dr r d r d dt M r sin ψ + ( ) ( ) r

+ = M dr ( )dt 0 M r r r rs t = r r0 + rs ln ( 3) r0 rs k Γ 4 e = T r r dr r 4 ( ) ( 4) 0 Γ 4 + = k ( T T ) re dr ( 5) 0 4 4 T T r 4 7 4 k Γ 4 T4 ( r) r dr = 0 r 0 B

ax at ( + ) = + ( ) c c ax ax at ( + ) = ( + ) + ( ) c c c at ax at ax at = ln( + + ) ln( + ) c c c c c ax ds = dx + c dt = dx + c ( + ) dt c T s' v ( ) T c s 0 T ' = 4c v s a tanh ( 0 c ) + τ

T s' T s T s' T s c v ( ) v c 0 0 T s' c v0 v 0 v0 = ( ) tanh ( ) ( ) T v c c c s 0 v0 ( ) << c

f + f r t = t t f c = ν ν ν ν t dw f r ' t f r ' t f r ν t f r ν t f( r v td ν = n r t f c f r v t f r v t t H t = f r ν t Inf r ν tdrdv dh < 0 dt n + div( nu) = 0 t Pxj ρ + u ux + = 0ρ = mn r t t r 3 n nk + u T + divj + PijD ij = 0 t j ij

D xy u u x y = + D ij = divu y x n r t= fdν u r t= νfdν p r t= mu U fdν xy x y m T r t= f r t dv 3nk ν ν J r t= mu Uxf r ν td ν U r t= ν u r t f c t m kt = σ ζ ( m ) 0 5k k = 4m

f c t f c t W ( t) = W ( t + t) = k k A k jk i = A = k ik i

W t t A W ( t) = a W ( t) t i W t t ( t ) ( t ) ( A ) A ( t ) i dwi ( t) dt k ik i ik k k k = ( a W a W ) k k ik k ki i ( a ikwk a kiwi ) = 0 k y/ x x ln z dz = y (ln y ln x ) + x y0 W t + t W t + t W t W t i ( )ln i( ) i( )ln i( ) i i ik Wk ( t) = A ki ( t + t ) ln Wi ( t + t ) i W ( t )ln W ( t ) W ( t + t )ln W ( t + t ) i i i i i W ( t )ln W ( t ) = W ( t + t ) ln W ( t + t ) i i i i i i A A = A A A ki 0A ki k k ik i A A ki i ki = δ ki ij kj 96 W ( t t) = A W (t) i ik k k

FN FN H N FN H N + t ( = r p p r ) 0 i i i x r r t t v u = ( kt ) m 0 0 0 u r t u r0 x = τ = v = t 0 = r t u u 0 0 0 ϕ i 3 r0 N N ( ) ( ) V FN dxdv = F ( r 3 0 N S N S s ) F ( dxdv) S,,, N V N = 3 r0 N F ( x V τ) = ( ) F ( x, x, V, V, ) dx dv V τ Θ i = W ( ) Θ = i j S i ij v v < i< j Vi v i 0 FN ϕ + ( Vi i 0 Θ N ) FN = 0 τ kt i FS ϕ N s ϕ + ( V F τ kt N kt nr L F i i 0 S ) S = 0 3 Θ ( 0 ) s s + i

n = N V S Ls = dx jdv j( Wij j = s + V i= N F N ϕ0 ( + V ) F ( x V t) = ( ) τ kt nr dx dv x W 3 0 V F ( x V x V τ) i t 0 r0 L = t = t = u u u 0 0 s L u = -4 0 cm L u s nr0 3 r0 t 0 nr0 = = 0 t 4 ϕ n kt 0

S B S A = B A dq A IR C T dq T

ux F x = - z ( + u ) ux = X + u x t x T J x = k k t T C v = k T t = D n D n t = D n n j = V = σ V V t

J = n J = -k T + n N = T N = -D n + T u t + divj = 0 T s t + divj = 0 s J t + div T = T J T J / T S = J T J = k T s k + divs = ( T) Θ t T

Θ = 0 = T J X X T ( ) T J = K T k T J i = k ij ij = x y z x Θ = T J = i k T x T i i j i, j ij j T x i T x 0 k x x ij i j j J = k T + n N T D n = T J( )X = L T X X, L X X, L L L 0 L L 0

S = S a a 0 ij i j ij S a a ij ij i j ( S ) Xi = = Sija j a i j da i J i = = a i dt = d S = S a& a = J X dt i, j ij i j i i i &a i a i ( t + τ) a i ( t) τ J i = L ik X k k t + t = L X ( t) i i ij j j

J j = a j( t + γ) a j( t) = L jmx m( t) τ m { j } a t J t = i j a i t a t + a j t τ L a tx t m = k L m jm i m jm im { } a t J t = j i a j t a j t + a i t τ

u t + div J + I = 0 J = k T ( + 0 ) e 0 E = I ε T ( ) σ e

E = 0 = / N N T = divj + E I 0 divi S t e D T T + divs = J + t T T T I E + T 0 et 0 SJ + I T e X = T T 0 0 X = E + T ( ) = Φ + T et et 0 0 L = kt + σ + T ε + e e L = σt ε + 0 e 0 L = σ + L = e 0 s + divs = k T Tε IT TI ( ) + ( )( ) + t T σ = LijX ix j T i = k( T) + TI T > 0 σ T = 0 T I T

J = a x i j ij j

ε ( ε ) d ( ε ε) = = / kt () dβ ( ε ) = ε ( ) ε ε = nε 0 ( ε) = ε 0 ( ε ) ( n ) = n ( 3) dn ε 0 = ( n + n) ε0 dβ n = α+ βε e 0 a T 0 ε = n ε = nhν 0

q t a cosn νt + b sinnvt = n n n= 0 * q = n a n ib n q n = q n nν q n q& qq& q ν ν 3ν πinνt * πiνmnt q ne q mn = q mnq mne q mn πiνmnt πiν knt πi( νmk + ν kn ) t ( qq ) = q e q e = q q e mn k mk = ( q q ) e k mk kn πiνmnt (&) q = πiν q e mn mn mn kn πiν mn t k mk kn q e n πinνt J = pdq v = pqdt & 0

v πinνt πimνt J = p e πimνq e dt 0 n m n m n n k 0 n, k τ= v πikνt = πiν p q ( k n) e dt = πi τp q J = = πi J τ ( J p q τ τ) F F J F F A( q q = q q τ τ ) τ τ J τh J τh ( p τq τ) (,, ) h h p q n n τ n τ n τ τ = (,,,, ) h p q q p n n τ n τ n n n+ τ n+ τ n τ J J πi = ( p n, n τq n τ, n q n, n+ τpn+ τ, n) h τ ( pq pq ) = h nn πi pq pq = h E πi E pq pq = h πi E Fq qf = h F Fp pf = h F πi p πi q τ τ

( Hq qh) mn ( H H )( q) = hν ( q) πiνmnt q& mn = i ν mn q mne = i ν mn ( q) mn H i q& = = Hq qh p h H i p = = Hq qh q h mn mn mn mn mn Bds B ds δ = δ A u = 0 A νλ B B δ Tdt = δ m( E V) ds = δ pds = 0 A A = h p B A H q p = S t = S q t S p i p i

H q p = S t = E q ψ ψ = u t E = hνp = h λ u = v = E p E u = m( E V) ϕ h ( + V) ϕ = Eϕ 8m h h Ψ ( + V) Ψ = 8 m i t h p i q ϕ ϕ h H J ( ) ( ) q i q n n Ψ Ψ = u t

C S * n j τ j = v v d C c v c C j j nj

dn N = dt t N N E E n E = E n N βε N = N e β = / kt AN b N n b N n AN + b N n = bn n βε βε N = N e n e N = nn = nn dn = AN + bnn bnn = An ( N N ) + N dt n 0 dn = AN dt

* n n n < A >= u Au dτ = a u = S v S = n nj j j j nj < C >= u Cu dτ = S S v Cv dτ = S c * * n n nj nk j k nj j j, k j p q pq qp = h i Ψ

é é é

A A + χ x ie ψψ exp( χ ) hc A A + χ x ie ψψ exp( χ ) hc exp( ie χ hc ) exp( ie χ hc ) U ie ( ) hc χ e

I 3 = u' a b u u ' = c d u a b a b c d = b * a * * * aa + bb = a b * * b a * * * * u ' u ' +u ' u ' = u u + u u SU R 3 u u Θ u' u u i n ' exp ( ) = σ Θ u o i σ x = 0 σy = σ i o z = 0 0 0 u' 0 u u i n ' 0 ( ) = σ Θ u i = + σ u xθ x u x SU I =

Q = I 3 + Y 8 ( J = ) 0 J

B=0 I 3 Y S K + 493 K * 89 K 0 498 K *0 89 + 40 + 769 0 0 0 35 0 769 0 0 0 548 769 0 0 0 40 769 0 0 K 0 498 K*0 89 K 49 K* 89 958 ϕ 09 0 0 0 D (8) D () D (8) D () J = B= I 3 Y S J = 3 I 3 Y S P (938) n (939) 0 (36) 3 0 (36) (89) 0 (36) 0 0 0 0 (9) 0 0 (36) 3 0 (5) 0 0 *+ (38) 0 (97) 0 *0 (38) 0 0 0 (34) * (38) 0 (3) * (530) * (530) (675) 3 3 D (8) D (0)

u d s u d s

u c t d s b e v e τ ν ν τ u( ) 3 c( ) 3 t( ) 3 d( ) 3