AT1 SS 1995 Aufgabe 1:
a) :
1; 1 1
1 1 : (1) mit
: (3) und (2) Aus
y (3)
(2)
(1)
) ( 2 ) ( 1 ) ( 3 ) ( 2
) ( 3 ) ( 2 ) ( 1
) ( 3 ) ( 2
) ( 2 ) ( 1 ) ( 3 ) ( 2
) ( 1 )
( ) ( ) (
) ( ) ( 1 )
( 3 ) ( 2
) ( 2 ) ( 1 ) ( 3 ) ( 2 ) (
) ( 1 ) ( ) ( )
( 3 ) ( 2
) ( 2 ) ( 1 ) ( ) ( 3 ) ( 2
) (
) ( 1 )
( ) ( 3 ) ( 2
) (
) ( 3 ) ( 2
) ( )
( 3 ) ( 2 (t)
) ( ) ( 1
) ( 2 )
(
+
⋅ +
⋅
⋅
= ⋅
⋅ + + ⋅
⋅
=
=
⋅
=
+
⋅ + ⋅
⋅ ⋅
⋅
=
⋅ +
⋅ + ⋅
⋅
⋅
=
⋅ +
= ⋅
⋅ ⇒
⋅
=
−
⋅
=
⋅
−
=
s s s s
s s s
s s
s s s
s
s s
s s
s s s
s s s s
s s
s t t s
s
s s t s s
t
s t
s s
t
s s
t s
s t s
s t
F F F F
F F F
F F
F F F
F
F X
F Y
X F F
F F F F
Y F
F x F y
F
F F y F F
y
F A F y
F y
F F B y F
F B
y F A B
F B x A
b) :
); 1
(
1 1 1
1
1 1
1;
1 ;
;
2 2
1 2
2 1
2 2 1
2 2
2 2 1
3 2
2 2
1 1
T s s s K K K K
K K K
T s K K K s
T s K
K s T s K K
F
K s T F
s F K
K F
I
I I
I s
I
⋅ +
⋅ +
⋅
⋅ +
⋅
⋅
= ⋅
⋅ +
⋅ + +
⋅
⋅ ⋅ +
⋅
⋅ ⋅
⋅ +
=
⋅
⋅ =
= +
=
AT1 SS 1995 Aufgabe 2:
a) :
; 33 , 8
96 96 64 14
0 ] 1 [ ] 14 [ ] 64 [ ] 96 [
0 96
48 6
16 8
1
) 0 6 1 (
1 )
4 1 1 (
0 1
: Hurwitz
1 1 1
3 0 2 1
2 3
3 2
2 2 3 2 1
3 2 1
2 1
3 2 1 ) (
) (
) ( 3 ) ( 2 1
) (
2 1
) ( 2
1 )
(
3 ) ( ) (
=
⋅ +
=
⋅
⋅
=
⋅
= + +
⋅ +
⋅ +
⋅
= +
⋅ +
⋅ +
⋅ +
⋅ +
⋅ +
⋅ =
⋅ +
⋅ + +
=
⋅
⋅ +
⋅
⋅ +
= ⋅
⋅ +
=
=
=
⋅
⋅ +
= ⋅
⋅ ⇒
⋅
=
⋅
−
=
Krit
Krit s
s s
s s
s
s s
s s
K
K a a a a
K s
s s
K s s
s s
s
s s
K F F F
F F F
F F F F
F Y
F X
Y F F X
F X
F F A X F F A X
F X Y A
AT1 SS 1995 Aufgabe 3:
a) :
; 1 3
s -2 s
1 3 3
] [
] [ : F
: F
2 2 2 2 ) (
) ( 2
) ( 2 2 2 ) ( 2
1 2 2
2 2 2
1 ) (
) ( 1 ) ( 1 ) ( 1
1 2
+
=
⋅
⋅
⋅
= +
⇒ =
⋅ +
= +
⋅
⋅
⋅ +
=
⋅
⋅
⋅ −
⋅
⋅
= +
=
⇒ =
⋅
=
⋅
−
=
s
s T
s T K K Y
F X s
Y s T K K X
s s T
K s
T
s T K K
s K Y
F X Y
K X
s F
F F
s s
s s
s s s
s s
b) :
; 10 1
, 1 0
3
1 3 1 3
1 1 3 1
1
) 0 (
) ( ) (
⇒ =
=
=
+
⋅
⋅ +
+
= ⋅
⋅
+ +
= +
⋅
= +
=
→ R
R s
Z
R R R
s R z s
t t
K K F
K s K s
s s K
s F
F F F
z
