https://youtu.be/Let60cbAcyI

1. ήʔϜཧ࿦#4*$ԋश
ެཧ͔Β‫ٻ‬ΊΔަবղ

2. ަবղ͕ຬͨ͢΂͖ͭͷެཧ ෮श
φογϡަবղΛ‫ٻ‬ΊΔ

3. ަবղ͕ຬͨ͢΂͖ͭͷެཧ
ύϨʔτ࠷దੑ
͢΂ͯͷ ʹରͯ͠ Ͱ
গͳ͘ͱ΋ͭͷ ʹରͯ͠
Ͱ͋Δ ͷ఺ ͸ଘࡏ͠ͳ͍
ରশੑ
ަব໰୊ ͕ରশͳΒ͹
ˎަব໰୊͕ରশͰ͋Δͱ͸
ͳΒ͹
ਖ਼࣍ม‫͔׵‬Βͷಠཱੑ
ަব໰୊ ͕ަব໰୊ ͔Βޮ༻ͷਖ਼࣍ม‫׵‬ ʹΑͬͯಘΒΕΔͱ͖
ແؔ܎ͳ݁Ռ͔Βͷಠཱੑ
̎ͭͷަব໰୊ ͱ ʹ͓͍ͯ
ͱ͢Δ
΋͠
ͳΒ͹
Ͱ͋Δ
i = 1, 2 ti
≥ fi
(U, d) i
ti
fi
(U, d) U t = (t1
, t2
)
(U, d) f1
(U, d) = f2
(U, d)
d1
= d2
(u1
, u2
) ∈ U (u2
, u1
) ∈ U
(U′

, d′

) (U, d) ui′

= αi
ui
+ βi
, αi
0 (i = 1,2)
fi
(U′

, d′

) = αi
fi
(U, d) + βi
, αi
0 (i = 1,2)
(U, d) (T, d) T ⊂ U
f(U, d) ∈ T f(T, d) = f(U, d)

4. ަবͷෆҰக఺
φογϡੵΛߟ͑
φογϡަবղΛ‫ٻ‬ΊΔ
ύϨʔτ࠷దੑΑΓ
ͷؔ܎Λຬͨ͢͜ͱΛߟྀ͢
Δͱ
(9/5, 11/5)
max
(u1,u2)≥(9/5,11/5)
(u1 − 9/5)(u2 − 11/5)
u2 = −
1
3
(u1 − 5) + 3 ⇔ u1 = − 3u2 + 14
φογϡަবղΛ‫ٻ‬ΊΔ
ʗ D E
B
C
q(a, c)
q(b, c)
q(a, d)
q(b, d)
F1(q)
F2(q)
(1,1)
(2,4)
(5,3)
U
(9/5, 11/5)

5.
͜ΕΛ࠷େͱ͢Δͷ͸
φογϡަবղ͸
(u1 − 9/5)(u2 − 11/5) = (−3u2 + 14 − 9/5)(u2 − 11/5) = (−3u2 + 61/5)(u2 − 11/5)
u2 = 47/15
u1 = − 3u2 + 14 = − 3(47/15) + 14 = 23/5
(23/5, 47/15)
φογϡަবղΛ‫ٻ‬ΊΔ
ʗ D E
B
C
q(a, c)
q(b, c)
q(a, d)
q(b, d)
F1(q)
F2(q)
(1,1)
(2,4)
(5,3)
U
(9/5, 11/5)
11/5 61/15
47/15

6. ަবͷෆҰக఺
φογϡަবղ͸
(9/5, 11/5)
(23/5, 47/15)
φογϡަবղΛ‫ٻ‬ΊΔ
u1
u2
(1,1)
(2,4)
(5,3)
U
(9/5, 11/5)
(−4, − 6)
(1,9)
(16,4)
U′

(0, 0)
u′

1
u′

2
ਖ਼ΞϑΟϯ
ม‫׵‬
u′

1 = 5u1 − 9
u′

2 = 5u2 − 11
ަবͷෆҰக఺͕‫ͳʹ఺ݪ‬ΔΑ͏ʹม‫׵‬

7. ަবͷෆҰக఺
φογϡަবղ͸
(9/5, 11/5) (23/5, 47/15)
φογϡަবղΛ‫ٻ‬ΊΔ
ਖ਼ΞϑΟϯม‫׵‬
u′

′

1 =
1
28
u′

1
u′

′

2 =
3
28
u′

2
u′

′

1
u′

′

2
(−4, − 6)
(1,9)
(16,4)
U′

(0, 0)
u′

1
u′

2
(28,0)
(0,28/3)
(−4/28, − 18/28)
(1/28, 27/28)
(16/28, 12/28)
U′

′

(0, 0)
(0,1)
ύϨʔτ࠷దͳ௚ઢ͕܏͖ʹͳΔΑ͏ʹ
͸޷Έͷ໰୊
(1,0)

8. ަবͷෆҰக఺
φογϡަবղ͸
ӈਤͷΑ͏ͳ௚ઢ ʹରͯ͠ରশͳ
ͳΔू߹Λߟ͑Δ
ʹ͓͚Δަবղ͸
ύϨʔτ࠷దੑͱରশੑ͔Β
ΑΓແؔ܎ͳ݁Ռ͔ΒͷಠཱੑΑΓ
(9/5, 11/5) (23/5, 47/15)
u′

′

2 = u′

′

1
K, U′

′

⊂ K
(K, d′

′

) = (K, (0,0))
f(K, d) = (1/2, 1/2)
(1/2, 1/2) ∈ U′

′

f(U′

′

, d) = (1/2, 1/2)
φογϡަবղΛ‫ٻ‬ΊΔ
u′

′

1
u′

′

2
(−4/28, − 18/28)
(1/28, 27/28)
(16/28, 12/28)
U′

′

(0, 0)
(0,1)
(1,0)
ແؔ܎ͳ݁Ռ͔Βͷಠཱੑ
̎ͭͷަব໰୊ ͱ ʹ͓͍ͯ
ͱ͢Δ
΋͠
ͳΒ͹
Ͱ͋Δ
(U, d) (T, d) T ⊂ U
f(U, d) ∈ T f(T, d) = f(U, d)
ύϨʔτ࠷దੑ
ରশੑ
K
(1/2, 1/2)

9. ަবͷෆҰக఺
φογϡަবղ͸
ਖ਼ΞϑΟϯม‫͔׵‬ΒͷಠཱੑΑΓ
ਖ਼ΞϑΟϯม‫͔׵‬ΒͷಠཱੑΑΓ
(9/5, 11/5) (23/5, 47/15)
f(U′

′

, d) = (1/2, 1/2)
u′

′

1 =
1
28
u′

1, u′

′

2 =
3
28
u′

2 ⇔ u′

1 = 28u′

′

1, u′

2 =
28
3
u′

′

2
f(U′

, d) = (1/2 ⋅ 28, 1/2 ⋅ 28/3) = (14, 14/3)
u′

1 = 5u1 − 9, u′

2 = 5u2 − 11 ⇔ u1 =
u′

1 + 9
5
, u2 =
u′

2 + 11
5
f(U, d) = ((14 + 9)/5 ⋅ , (14/3 + 11)/5⋅) = (23/5, 47/15)
φογϡަবղΛ‫ٻ‬ΊΔ
u′

′

1
u′

′

2
(−4/28, − 18/28)
(1/28, 27/28)
(16/28, 12/28)
U′

′

(0, 0)
(0,1)
(1,0)
ύϨʔτ࠷దੑ
ରশੑ
K
(1/2, 1/2)

10. ήʔϜཧ࿦#4*$ԋश
ެཧ͔Β‫ٻ‬ΊΔަবղ
࣍ճɿԋश