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Дата изменения: Thu Mar 20 15:33:08 2008
Дата индексирования: Mon Oct 1 21:40:26 2012
Кодировка:
Поисковые слова: m 13

. .
(, )
. , ,

t
j

(

x, y , z ) = t j = c o n s t

(

j =1 - 4

)

(1)

[1]. , x, y, z (1) ;
t 4 = f t1 , t 2 , t

(

3

)

.

(2)

, (1) , . ( ) [1]. , .

91

3. Part 3. Mathematical theory

, , . , t1 , t 2 z = 0 , , , . , , (2)
f f
i1 k1

y = 0 , t 3 , t 4

( ti ) , ( tk )

0, ,f
k2

f

i2

( ti )
0,

,1 1

( tk )

,

= 0 (i = 1, 2 ; k = 3, 4).

(3)

:

f i1 , f i 2 , 1

01

=0 ,

f k1 , f

k2

,1 1

0

=0 ,

(3ґ)

, . , , f
jr

(t )
j

f

jr

.

[2] 15 ( ), , [1]. . (2) , ( ) , -

92

. . -- -- 2007, . 2, . 91101 Rudakov B. P. -- MCE -- 2007, v. 2, p. 91101

( ) (3). , f (t1 , t 2 , t 3 ) ,

M =- t

( ) (t )
/ 42

/

41

, M =- t

( ) (t )
/ 43

/

41

,

(4)

G. f jr (3) , . , [2], (3),

f11 1, f 21 0, f31 -1, f 41 m , (m 0, ±1)

(5)

( ) T0 .

t j ( j =1 - 4 ) T0 :

= ( 1, 0, -1, m ) = ( 2 m

)(

m -1) ,

(6)

0; 1 ( (6)). . (2) T0 , M , M (4) :
f
j

(

j =1-3)

M=

f1 ( f

( f1 )1

/ 22 /

)

, M =-

(

2 f 2 - f1 ) ( f1 - 2 f 2 ( - 1) ( f1

2

) ( f3 )
3

/ 3

)1
/

f2 f

,

(7)

93

3. Part 3. Mathematical theory

( f j )/j

df dt

j j

. [2].

:
/ / M A ln , B ( ln MA )1 , D B ( ln MMAB )1 . M 1
/

(8)

1. (2) T0 , M , M (4) :
M 3 =0 , (ln M
/

)

// 12

=0 , ln M

()

// 13

=0

(9) (10)

(

ln MD = 0 .
1

)

/

M 3 =0 (7). T
0

/

,

, ( t j ( j =1-4) ) t 1 , t 2 t 3 , t 4 . t j

T

0

, -

, , t 2 , t3 [3]:

k2 = (ln M

)

// 13

/ f1 M , k 3 =- (lnM

2

)

// 12

f / M . 1

2

(11)

94

. . -- -- 2007, . 2, . 91101 Rudakov B. P. -- MCE -- 2007, v. 2, p. 91101

[1], T0 , k j = 0

(

j =1- 4 ) , (11)

(9). (10). (7) f [4], :

()
/ 1

//

2 21

=0 -

(f )

/

ij

= i y i (i, j =1, 2, 3) ,

j

(y )

/

11

=

y

2 1 1

f

- y1 (ln M

)

(12)

, (7),
y2 =
j

2 ( - 1) y 1 f 2 f 3M y1 f M , y 3 =- f1 2 ( 2 f 2 - f 1 )( f 1 - 2 f

2

)

,

(13)

i . [4] (12):
y1 f 1 - 4 f f1(2 f 2 - f
1

(

2

2 2

)(

)
2

f1 - 2 f

)

= A,

(14)

2 2 y 1 f 2 2 ( + 1) f 1 - 16 f 1 f 2 + 8( + 1) f 2 =B 2 2 ( 2 f 2 - f 1 )( f 1 - 2 f 2 ) f 1 - 4 f 2

(

)

(15)

(

2 ( - 1) y 1 f 2 2 f 2 - f 1 )( f 1 - 2 f

2

)

= ±D ,

(16)

A, B , D (8).

95

3. Part 3. Mathematical theory

t1 (12), (14)-(16) (9), , (16), (10). , ,

f t1 ,t2 ,t3 ,
A, B , D G. 2. (2) (3) (5) (.. T0 ), (12) ,
f 1 = a 33 f 1 , f 2 = a
33 f 2

(

)

, f3 = a

22 f 3

.

(17)

, x = 1, x = 0, x = -1, x = m, y = 0, z = 0 : , , , y = 0 y = 0 z = 0 z = 0 t j T 0 . (17) (12) ; : t i = t i1: f i = 1

( i =1, 3)

(18)

, , .. , , a 22 , a 33 .

, 0, ±1 , 3. (2) T0 , M , M (4), 1, :

96

. . -- -- 2007, . 2, . 91101 Rudakov B. P. -- MCE -- 2007, v. 2, p. 91101

2 D - AB = +1 2 2 2 -1 D A + D - 2 AB

2

()

2

.

(19)

(2) ( 1 2 =1 1 ); (3) T 0 , ( ) . (19) , A, B , D (14)-(16). . (19)

-1 = ±k , +1
,
k= D D - AB
2

(20)

A + D - 2 AB

2

2

(21)

(14-16) ,
2 2 y A + D - 2 AB = 1 f1 2

(22)

G. (16) (20) (12) :

97

3. Part 3. Mathematical theory

1).

f2 =

(

1 + 1)
j i

1

f1 ,

(23) (24) (25)

( fi)
y1 = f
2 1

/ j

=i y
2

(

i =1, 3; j =1- 3) ,

A + D - 2 AB , y 3 =- f 3 MD .
2

2 = 1 + k A - k D -2AB .

D

D

(26) (27) (28) (29) (30) (31) (32) (33)

2).

f2 =

(

1 + 1) f1 , 41
j i

( fi)

/ j

=i y
2

(

i =1, 3; j =1- 3) ,

y1 =- f
3).

1

A + D - 2 AB , y 3 =- f 3 MD . f2 =

2

(

1 + 1)
4
j i

f1 ;
i =1, 3; j =1- 3) ,

( fi)
y1 =- f 4).
2 1

/ j

=i y
2

(

A + D - 2 AB , y 3 = f 3 M D ; f2 =

(

1 + 1)
j i

1

f

1

( fi)

/ j

=i y
2

(

i =1, 3; j =1- 3) , y 3 = f 3 MD .

(34) (35)

y1 = f

1

A + D - 2 AB ,

2

(7) : (23-24),
98

. . -- -- 2007, . 2, . 91101 Rudakov B. P. -- MCE -- 2007, v. 2, p. 91101

(27-28), (30-31), (33-34). (7) (9), (10), (19). (24),(28), (32), (34) [4]. , , , . [5]. (23-24) (18), :
t1 f 1 = ex p t 11 1 2 2 f1 , A + D - 2 A B d t1 , f 2 = 1 +1

(

)

t3 f 3 = ex p - MD d t 3 . t 31

(40)

(27-28), (30-31), (33-34). (18) ( , , f

( 2)

j

,f

( 3)

j

,f

( 4)

j

) -

(40), :
f

( 2)
1

=1 f 1 , =1 f 1 ,

f

( 2)
2

=1 =

(4 f )
2
1

, ,

f 3(2 ) = f 3 ;
2

(41) (42) (43)

f

( 3)
1

f

( 3)
2

(4f )
1 ,

f

( 3)
3

=1 f 3 ;

f1(4 ) = f1 ,

f

(4)
2

=f

2

f

( 4)
3

=1 f 3 .

(17), , a 22 , a 33 , (41-43). = - 1 .

99

3. Part 3. Mathematical theory

4. (2) T0 = - 1 , M , M (4), 1, :

D -AB=0.
f
j

2

(

j = 1 - 3) ,

( ) . :
t1 f 1 = ex p t 11 A -D
2 2

2 , f = f A + A -D d t1 2D 21

2

,

t3 f 3 = exp - MD dt 3 . t 31

(44)

(44) (41)-(43), 1 = - 1

4 [1] : 1. (2) , , , , ( ). 2. (40) - (43) ( 0, ±1 ) =-1 , T 0 ( ). 3. 3 .
100

. . -- -- 2007, . 2, . 91101 Rudakov B. P. -- MCE -- 2007, v. 2, p. 91101

1. . . - .: . - , 1959. - 144 . 2. ..(). . // ... . . -. 1965. . 31. .2950. 4. ... , . - : , 2003. - 246 . 5. .. . .:. - , 1947. - 360 . 6. .. . .: , 1964. - 662 .

ABOUT THE CONDITIONS AND METHODS OF RECTIFIABILITY OF SOME SPACE HEXAGON WEBS Rudakov B. P.
(Russia, Tyumen)
In the article are esteemed compound scale nomograph of a zero genre of a special kind for equations with four variable. In the terms of geometry of webs the special classes of hexagon webs for the indicated equations are studied, the conditions and effective methods of their rectifiability are retrieved, the problem of uniqueness is reviewed

101