,
.
(3.8)
, (3.8) ; t , (3.8) .
.
(3.8):
= = . (3.9)
(3.9), . ,
= .
, ,
(3.10)
.. .
(3.10) , ξ , , , P (x)= P (x 1, , xn). ,
=
= .
∆i→0,
P{xi<ξi<xi + ∆1, , xm<ξm<xm + ∆m │ xi<ξi<xi +∆i, i = } → , (3.11)
(3.11) ξ1,, ξm ξm+1,, ξn:
(3.10),
:
(3.12)
(3.12) . t1=t1(x), t2=t2(x),, tm=tm(x). , yj=yj(x), j=1,,n-m, , ,
ti=ti(x), i=1,,m,
yj=yj(x), j=1,,n-m, (3.13)
. ξ() τ,η(t,y), τi = ti(ξ), ηj = yj(ξ), τ=(τ1,,τm), η=(η1,, ηn-m), t=(t1,,tm), y=(y1,,yn-m),
ξ()=τ,η(t,y)│J│, (3.14)
J . g(ξ1,, ξn). g(ξ1,, ξn) τ=t. xk(t,y)=xk, k= , x(t,y)= (x1(t,y),, xn(t,y)) , -1.
(3.15)
( (3.14)).
1. ξ=(ξ1,, ξn) - , (x; ) t(x)=(t1(x),,tm(x)) - ( m ) =(1, , n). t() , ξ=(ξ1,, ξn) t(ξ)=t .
|
|
: ξ(x; ) - , ξ(x; ) n - : =(1, , n) (t;y), (3.13).
, , . -, , (3.1), , . -, , , D < D .
, , .
2. (x; )
(x; ) =g(t(x); )h(x) (3.16)
t() .
. (3.8) ξ= t(ξ)=t
(3.17)
(3.16), (3.17)
.. t() .
, , = ,
(x; ) =
- t, .. (3.16).
(x; ) - , , (3.13) ξ(x; ) Pτ,η(t;y; ) (3.14).
η τ=t,
, , .
, , g(x)= 1 g()=0 , n Rn, , {ξ B | τ=t} n, t - . .
(3.14)
.. (3.16).
3. (-)
t - (x; ), (x) - , (3.1). t
D D .
. (3.15)
M
.. ( ,
, - ).
D :
D = M ( - )2 = M ( - + - )2 =
= M ( - )2 + M ( - )2 + 2M ( - ) ( - ). (3.18)
M ( - ) ( - )= M [ M ( - ) ( - )| t ]= M [( - ) M {( - )| t }],
M {( - )| t }=0, (3.18) D D . .
1. (3.1) (i= 1, i- , i =0 ). p. (3.1)
, 1++n .
2. (3.1) (,ξ).
.. - .
.3.3, . . -. p(x; )=p(x1,,xn; ) - , , =φ(x)=φ(x1,,xn) - x1,,xn . g()=M = . , ,
|
|
.
(3.19)
(3.20)
, ( ξ P(ξ; ))
(3.21)
p(; ).
4. ( -). p(; ) = φ() , (3.19) (3.20), :
(3.22)
. (3.19) (3.20) :
. (3.23)
(3.23) g () :
(3.24)
(3.24) φ1()=φ()- g (), φ2()= , -
:
(3.22).
1. 4 ,
p(; ) , .
2. (3.19) :
(3.21) :
(3.25)
,
.
3. (3.23) M , (3.21) :
4. 1,,n , pn(1,,n; ) :
pn(1,,n; ) = .
n :
(3.26)
- k, (3.22) :
(3.27)
(3.26)
.
5. , , (3.22) (3.27) . 4 (3.22) (3.27) . , , , , n→∞.
3. 1,,n - (, σ), σ - .
, ,
.. (3.27) .
, 4 .
2.
()= 1 .
1 . (3.22) (3.27) , - :
0≤()≤1. , 4 (3.22) (3.27) D , n→∞ , .
4. 1,.,n
(3.19)
=min xk ,
1≤ k<n
.
. 4 .
3. 0( n) n= n(1,.,n), 1,,n,
. n , 0( n)=1. , - 0(), n [ 0()nJ1 ] -1.
|
|
n→∞ n .
4. n n →∞ , :
,
.. . , 0()= 1, .
1,,n - (; ), r . ,
,
,
,
,
.
5. , :
, (3.28)
- , .
. , (3.28) :
- . .. mk , , k n→∞ .. ( , .. , 1) .
, 1.