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1 ( 23 )

2 ( 23 ) (1,2 ) 1 1 I, I II, II ( ), ( ) ( ) 2 (2 ) 2 1, (2,3,4 ) 2 1 A, A 4+2 C, C B, B 4+2 D, D [ ] 2 3 1,, A, ,, A A, [ C], A, B, B 2 A, B, [ F], A,, B, [ ], [ ] 4 1 B, ( ), C, C, D 2 E, B, B 4 2 ( ), G, [ C], [ F] 2 ( ), ( ) [ ], [ ] 4 16 : 2,3 (,2 ). : 4 (,2 ), (,2 ) (,2 ) (2 ). :. : C, F, 3 2, 4 2. : 2 2, 3 2, 4 2. :. 1

3 I ( ) ( ) :. ( ),.. ( )...,. 1. ( ), 2.,,, 3. 4., 5. 6., 7. R n (R 2, ),,,,, :.,. 2

4 I ( ) ( ) :.,,.,., 1,,., 1,,,,. 1.,, 2.,, 1 3.,, 4.,, 5.,,, 6.,,, 7., 8.,,,,,,,, :. ϵ δ, ( ). 3

5 ( ) ( ) :.... I ,,,, :.,,.. ( ) ( ) : 1 1 I 1., ),,, 2. :,,,,, 3. :,, (, ) 1 : ϵ δ,... 4

6 II ( ) ( ) : I,.,.,..,,.... (, ),. 1., 2., 3., 4., 5. 6.,,, 7., 8.,,,,,, 5

7 II ( ) ( ) :.,,.,.,,,. 1,,,,,, , 3. 4., 5., 6., 7. 8.,,,,,, :. ϵ δ, ( ). 6

8 ( )( ) ( ) :.. 1.,,, 2.,, ( ),,, 7

9 ( )( ) ( ) :, ϵ δ,... ϵ δ, , 3.,,, 4.,, 5.,,, 6. ( ) : ( ),,,, ϵ δ, : I, II. ( )( ) ( ) :. :. 8

10 ( ),, ( ) :,,,,,,,. 1.,,,,,,,, 2. 2,, n 3. : 9

11 ( ) ( ) : I, II (,,, ) (,,,, ),, ( ) ( ) : ( ).,,., , (, ),,,,, div, rot, grad : I, II. ϵ δ, ( ). 10

12 A,B,C,D.,. ( ) ( ) :..,. 1., 2., 3. 4., : II.. ( ) ( ) :. 11

13 ( ) ( ) :...,.. 1. :,,,,,,,,, (, )., 2., (, ),,,,,,,,,, (,,, ) 3. R n,,,,,,, 4. :,,,,,,,,,,,,, 5. ( ),,, -, :.. ( ) ( ) :. 12

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15 ( ) ( ) : ( ), , 3., 4., 5. 6., 7. 8.,,, 1., 2.,,, k 3., 4., 5., 6. :,,, 7. 8.,,,,,, :. ( ) ( ) :. 14

16 ( ) ( ) :,.,.,,.., , 15

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18 ( ) ( ) : : ( ) ( ) : : 17

19 ( ) ( ) :..,..,..,.,,,..,..,. 1., 2., 3., :. ( ) ( ) :. 18

20 ( ) ( ) :, ( ).,. ( ).....,,,,,,.. 1.,,,, 2.,, 3.,, :. ( ) ( ) : 19

21 ( ) ( ) :,..,..,..,

22 ( ) ( ) :,.,,..,,. 1.,,,, 2.,,,,, 3., 4., 5., ( ) ( ) :. 21

23 ( ) ( ) :.....,..,. 1.,,, 2. 3., 4. (, ) ( ) ( ) :..,. 1., 2., 3., 4. 22

24 ( )( ) ( ) : ( ), Hom

25 ( ) ( ) :,.,,,,,,,,, ,, 5.,, : 24

26 ( ) ( ) : ( ),..., : ( ) ( ) : ( ) ( ). 25

27 ( ) ( ) : :,. 26

28 ( )( ) ( ) :,,,.,,. A,B.,. A : (orientation),,,,, B :,,, :,,. 27

29 ( ) ( ) : (,.,..,.,,,..,,,. 1.,, 2.,,,, 3. (,,, ) 4.,,,, :. 28

30 ( ) ( ) :.,,,.,,.,,,., ,.,.. 1.,, 2. :, 3. (,,,, ) : ( ). 29

31 ( ) ( ) ( ) : ( ) R n.,,,..,,,,,,,, , 3., 4., 5.,,, 6.,, L p 7. ( ),,, :,.,. 30

32 ( ) ( ) :.,.,,,,,,,..,.,.,... 1.,, 2., ( ) 3., 4. (,, ), 5., : (. 31

33 ( ) ( ) :, ( )., ( ),... ( )..,,.,. ( ),. (,,, ) : ( ) ( ). 32

34 (, ) ( ) :,,,,,,,,,, IT.,,.,.,,,.,. 1.,,, 2. ( / ),,,,,,, 3.,,,,,,, 4.,,,, 5.,,,,,,,,, : ( ). 33

35 ( ) ( ) :,.,.... p (L p ),, W m,p,.... p,,.,. 1., 2. p (,,,, ) 3. 4., 5.,,, 6. ( ) : ( ). 34

36 ( )( )( ) ( ) :.. p.,,,,,. D , 3. 4., 5., ( ) 6A: 6B: 6C: 6D: :.. 35

37 ( ) ( ) :.,. 1. ( ). 2. ( ) ( ) 2. ( ) 3. ( ) 4. (, ) 5. (,, DE ) 6. (, ) :.. ( ) ( ) :.,. :. 36

38 ( ) ( ) : ( ) : ( ),, ( ). ( ) :. 37

39 ( )( ) ( ) :.. PDE.,

40 (,, ) ( ) : χ 2 t F (, ). 39

41 ( ), ( ) :, ( ) :, (, ) :. ( )(,, ).,. ( )( ).., (B5, ) 11 1 (A4, ) 12 9 ( 13 ) ( ) 18 2 ( 18 ) 23 3 ( 23 )

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