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Ā
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Ȁ Ȁ
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Ȁ Ă
Ȁ ଏ
Ȁ Ā
Ȁ Ȁ Ȁ
Ā
ଏ Ă Ȁ
𝜑 𝜑 ଏ 𝑥𝜇 𝜑 𝑥𝜇 Ȃ𝜑
Ȁ Ā Ȁ 𝑥𝜇 𝜇 Ȁ
Ȁ
Ȁ 𝜑 𝜑 𝜋 𝐺𝑀 𝑁 𝑀 𝜇 𝜑
Ȁ
𝑔𝜇𝜈𝑣𝑖𝑠 𝐺𝜇𝜈 𝑥𝜇 𝜑 𝜋
𝑔𝑐𝑜𝑚𝜇𝜈 𝐺𝜇𝜈 𝑥𝜇 𝜑
Ā Ā
Ā
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȃ
Ȃ𝐺 𝑅𝑀 𝑁 Ȃ 𝐺𝑀 𝑁𝑅 Ȃ
𝑀 ̀
Ȃ
Ȃ𝐺𝐺𝑀 𝑁 𝑉𝑣𝑖𝑠ȂȂ𝑔𝑣𝑖𝑠𝑔𝜇𝜈𝑣𝑖𝑠𝛿 𝜇 𝑀𝛿
𝜈
𝑁𝛿 𝜑Ȃ𝜋
𝑉𝑐𝑜𝑚ȂȂ𝑔𝑐𝑜𝑚 𝑔𝜇𝜈𝑐𝑜𝑚𝛿 𝜇
𝑀𝛿𝑁𝜈 𝛿 𝜑
Ȁ
𝑅𝑀 𝑁 Ȃ𝐴̀𝐴𝑀 𝑁 ȂȂ𝑁̀𝐴𝐴𝑀 ̀𝐴𝑀 𝑁̀𝐶𝐴𝐶Ȃ̀𝐶𝑀 𝐴̀𝐴𝑁 𝐶
ଏ ଏ Ȁ Ȁ Ă Ă
𝐸 𝐸
̀𝐶𝑀 𝑁 𝐺𝐶𝐴 Ȃ𝑁𝐺𝑀 𝐴 Ȃ𝑀𝐺𝐴𝑁 ȂȂ𝐴𝐺𝑀 𝑁
Ȁ
Ȁ Ȁ
Ā Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ 𝑥𝜇
𝑑𝑠 𝑒Ȃ 𝜎 𝜑 𝜂𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈 𝑟𝑐𝑑𝜑
Ȁ
Ȁ ଏ Ȁ
Ā
Ȁ
ଏ Ȁ 𝑟𝑐 Ȁ
Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ Ā
𝑀 Ȃ Ă 𝑀
Ā
Ȁ
Ȁ Ȁ
̀ Ȃ𝜎
𝑟𝑐 𝑒
Ȃ 𝜎
̀ ̀ ̀ 𝜎 𝑟𝑐 𝑒
Ȃ 𝜎
̀ ̀ ̀ ̀ Ȃ𝜎
𝜎 ȂȂ𝜎 Ȃ𝜑 Ȁ
𝜎 Ȃ̀𝑟𝑐 𝑀 𝜎
𝑟𝑐
𝑉𝑐𝑜𝑚
𝑀 𝑟𝑐
𝛿 𝜑 𝑉𝑣𝑖𝑠 𝑀 𝑟𝑐
𝛿 𝜑Ȃ𝜋
Ȁ Ȁ Ă
Ȁ 𝜎
𝜑
𝜎 𝑟𝑐Ȃ𝜑Ȃ
√
Ȃ̀ 𝑀 Ȁ
̀
Ȁ 𝐴𝑑𝑆
𝜎 𝑟𝑐
√
Ȃ̀ 𝑀 𝛿 𝜑 Ȃ𝛿 𝜑Ȃ𝜋
𝑉𝑐𝑜𝑚 Ȃ𝑉𝑣𝑖𝑠 𝑀 𝑘
̀ Ȃ 𝑀 𝑘 𝑘
Ȁ Ȁ ଏ Ȁ Ȁ
𝑘𝑟𝑐 Ȁ Ā
Ȁ Ȁ
Ȁ Ȁ
Ȁ
ଏ
𝑑𝑠 𝑒Ȃ 𝑘𝑟𝑐Ȃ𝜑Ȃ𝜂
𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈 𝑟𝑐𝑑𝜑
Ȁ
Ȁ ଏ Ȁ Ȁ
ଏ Ȁ Ȁ
Ȁ Ȁ Ă
Ȁ
Ȁ
Ȁ Ā
𝑆𝑣𝑖𝑠 Ȃ
∫ √
Ȃ𝑔𝑣𝑖𝑠 𝑔𝜇𝜈
𝑣𝑖𝑠𝐷𝜇𝜙𝐷𝜈𝜙Ȃ𝜆 Ȃ𝜙Ȃ Ȃ𝑣
𝜆 Ȁ 𝑣 Ȁ
Ȁ Ȁ Ȁ
𝑑𝑒𝑡 𝑎𝑀𝑛 𝑛 𝑎𝑛𝑑𝑒𝑡 𝑀𝑛 𝑛 𝑎ȂĂ
𝑆𝑣𝑖𝑠 Ȃ
∫
𝑒Ȃ 𝑘𝑟𝑐𝜋 𝜂𝜇𝜈𝑒 𝑘𝑟𝑐𝜋𝐷
𝜇𝜙𝐷𝜈𝜙Ȃ𝜆 Ȃ𝜙Ȃ Ȃ𝑣
Ȁ Ȁ 𝜙Ă𝑒𝑘𝑟𝑐𝜋𝜙 ଏ
𝑆𝑣𝑖𝑠 Ȃ
∫
𝜂𝜇𝜈𝐷𝜇𝜙𝐷𝜈𝜙Ȃ𝜆 Ȃ𝜙Ȃ Ȃ𝑒Ȃ 𝑘𝑟𝑐𝜋𝑣
Ā Ȁ 𝑣 7Ă𝑒Ȃ𝑘𝑟𝑐𝜋𝑣
Ȁ Ā
𝑚 𝑒Ȃ𝑘𝑟𝑐𝜋𝑚
Ȁ
𝑘𝑟𝑐Ȃ
Ȁ
ଏ Ȁ
Ȁ 𝑟𝑐 Ă Ȃ Ȁ
Ȁ
Ȁ Ȁ
Ā
Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ
Ȁ Ā
Ȁ
Ȁ
Ȁ
Ȁ
Ȁ Ā
Ȁ Ȁ
Ȁ Ȁ
Ā Ȁ
Ȁ Ā Ȁ
Ȁ
Ȁ Ȁ
𝑔𝜇𝜈
𝐴𝜇
Ȁ ଏ Ȁ
܂𝜙܂ Ă
𝐺
Ȁ
Ԃ 𝜙 𝜋𝜆𝑇
Ȁ
Ā Ȁ
Ȁ
ଏ Ā Ȁ
𝜆 Ԃ 𝜙 Ȃ 𝜙 𝜇 𝜇 𝑇
Ȁ Ā Ā
Ā
Ȁ 𝜙 Ȁ
Ȁ Ȁ
𝑅𝜇𝜈 Ȃ 𝑔𝜇𝜈𝑅 Ȃ 𝜋
𝜙 𝑇
𝜇𝜈 𝑇𝜇𝜈 𝜙
Ȁ Ȁ
Ȁ Ā Ȁ
Ā Ȁ 𝜙 Ȁ
Ȁ Ā Ȁ
𝑇𝜇𝜈
𝑇𝜇𝜈 𝜇 Ȃ𝜇𝑇𝜇𝜈 ̀𝜇𝜌𝜇 𝑇𝜌𝜈 Ȃ̀𝜌𝜇𝜈𝑇𝜇𝜌
Ȁ 𝜙 ଏ
(
𝑅𝜇𝜈 Ȃ 𝛿𝜇𝜈𝑅)𝜙 𝜇 Ȃ 𝜋𝑇𝜙 𝜈 𝜇𝜇
Ā 𝑇𝜙 𝜈𝜇 𝜙
ଏ Ȁ
𝑇𝜙 𝜈𝜇 Ȁ ଏ
Ȁ Ā Ȁ 𝜙
Ԃ 𝜙
𝑇𝜙 𝜈𝜇 𝐴 𝜙 𝜙 𝜇𝜙 𝜈 𝐵 𝜙 𝛿𝜇𝜈𝜙 𝛼𝜙 𝛼 𝐶 𝜙 𝜙𝜇 𝜈 𝐷 𝜙 𝛿𝜇𝜈Ԃ 𝜙
ଏ
𝑇𝜙 𝜈 𝜇𝜇 𝐴 𝜙 𝐵 𝜙 𝜙𝜇𝜙
𝜈𝜙 𝜇 𝐴 𝜙 𝐷 𝜙 𝜙 𝜈Ԃ 𝜙 𝐷 𝜙 Ԃ 𝜙 𝜈
𝐴 𝜙 𝐵 𝜙 𝐶 𝜙 𝜙𝜇 𝜈 𝐶 𝜙 Ԃ 𝜙 𝜈
𝑋 ȂȂ𝑋 Ȃ𝜙 ଏ Ȁ
𝜙 𝜎𝑅𝜎𝜈 𝜙𝜇 𝜇 𝜈 Ȃ𝜙 𝜈 𝜇 𝜇 Ԃ 𝜙 𝜈ȂԂ 𝜙 𝜈
Ȁ Ā Ȁ
𝑅 𝜋
𝜙
[
𝜋𝜆Ԃ 𝜙 𝐴 𝜙 𝐵 𝜙 𝜙
𝜇𝜙
𝜇 𝐶 𝜙 𝐷 𝜙 Ԃ 𝜙
]
Ȁ ଏ
Ԃ 𝜙 𝜈 ȂԂ 𝜙 𝜈 Ȃ
𝜋 𝜙 𝜙 𝜈
[(
𝜋𝜆 𝐶 𝜙 𝐷 𝜙
)
Ԃ 𝜙 𝐴 𝜙 𝐵 𝜙 𝜙𝜇𝜙 𝜇
]
Ȁ
𝐷 𝜙 Ȃ𝐶 𝜙 Ȃ
𝜋 𝜙
(
𝜋𝜆 𝐶 𝜙 𝐷 𝜙
)
𝐴 𝜙 𝐷 𝜙
𝜙 𝐴 𝜙 𝐵 𝜙 𝐴
𝜙 𝐵 𝜙
𝐴 𝜙 𝐵 𝜙 𝐶 𝜙
ଏ Ȁ Ȁ
𝐴 𝜙 𝑤
𝜋𝜙 𝐵 𝜙 Ȃ 𝑤
𝜋𝜙
𝐶 𝜙 𝐷 𝜙 𝑤 Ȁ
𝑤 𝜆Ȃ 𝜆 𝑤
Ȁ Ȁ
Ԃ 𝜙 𝜋 𝑤𝑇 Ȁ
𝑅𝜇𝜈 Ȃ 𝑔𝜇𝜈𝑅 Ȃ
𝜋 𝜙 𝑇𝜇𝜈 Ȃ
𝑤
𝜙 𝜙 𝜇𝜙 𝜈 Ȃ 𝑔𝜇𝜈𝜙 𝛼𝜙
𝛼 Ȃ
𝜙 𝜙 𝜇 𝜈Ȃ𝑔𝜇𝜈Ԃ 𝜙
Ȁ Ā
𝜙 Ȁ ଏ Ȁ
Ȁ
𝑤 Ă Ȃ Ȁ
Ԃ 𝜙
(
𝑤
)
ଏ
𝜙 ܂𝜙܂
(
𝑤
)
𝐺
(
𝑤
)
Ȁ Ȁ Ȁ Ȁ
𝑤Ȃ ଏ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ԃ 𝜙 𝑇 𝑤
𝑤 Ȁ
Ȁ
ଏ Ȁ Ȁ Ȁ
𝑤
Ā
ଏ
Ȁ
ଏ Ȁ Ȁ
Ȁ
ଏ Ȁ Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ ଏ
Ā Ȁ
Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ȁ
ଏ Ȁ
Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ā Ȁ ଏ
Ā Ā
Ȁ
Ȁ Ȁ
Ȁ Ȁ Āଏ
Ā Ȁ
Ā Ȁ Ȁ
Ȁ Ā
Ā Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ā
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Āଏ
Ȁ
Ā ଏ
Ȁ
Ā Ā
ଏ Ȁ Ȁ
Ā
Ȁ
Ȁ Ȁ
Ȁ
Ȁ ଏ Ȁ
Ȁ 𝑝 Ȁ
𝑅𝜇𝜈 Ȃ𝜇𝜎Ȃ𝜈𝜎 𝜀
(
𝑇𝜈𝜇Ȃ 𝛿
𝜇 𝜈
𝑝 𝑇
) Ȃ 𝛿
𝜇 𝜈̀
𝑝
̀ 𝜎 𝑇𝜇
𝜈
𝑇 𝜀 Ȃ
𝑀𝑝𝑝 𝑀
𝑝 𝑝
𝑝 Ȁ Ȁ
𝑝 Ȁ 𝑝 Ȁ
Ȁ Ā Ȁ 𝑤 𝛽 Ȃ
Ȁ Ȁ Ā
Ȁ 𝜙
𝜀𝑒
Ȃ 𝛽𝜎
Ȁ
𝑔𝜇𝜈 𝑒 𝛽𝜎𝑔𝜇𝜈
ଏ
𝑧
Ā
𝑑𝑠 𝑒𝐴 𝑟 Ȃ𝑑𝑡 𝑑𝑧𝑖 𝑑𝑟 𝑒𝐶 𝑟 𝑑𝜃
𝑖 𝑝 Ā
Ȁ 𝑧 Ȁ Ā Ȁ
𝑝
Ă 𝜋𝐹𝜇𝜈𝐹𝜇𝜈 𝐷𝜇̀ 𝐷𝜇̀ Ȃ 𝜆 ̀Ȃ̀Ȃ𝜂
𝐷𝜇 Ȃ𝜇 𝑖𝑒𝐴𝜇 𝐹𝜇𝜈 Ȃ𝜇𝐴𝜈 ̀ Ȁ
𝐴𝜇 ̀ Ȁ Ȁ
𝐴𝜇
𝑒 𝑃 Ȃ Ȃ𝜇𝜃 ̀ 𝜂𝑋𝑒𝑖𝜃
𝑃 𝑋 Ȁ Ȁ 𝑟
Ā
Ȁ
𝑒𝐶 Ă𝑟 Ȃ 𝐺𝜂 𝑃 Ă Ȃ Ȃ 𝐺𝜂 𝛾𝑟 𝑒Ȃ Ȃ 𝑟
𝑋 Ă𝛾𝑟Ȃ 𝑒Ȃ Ȃ 𝑟
𝛾 Ȁ
𝑒𝐶 Ȁ
ଏ Ā
Ā Ȁ
𝑇𝑡𝑡 𝑇𝑧𝑧 Ȃ
𝜂 (
𝑋 𝑒 𝛽𝜎 𝑒Ȃ𝐶𝑋 𝑃 𝑒 𝛽𝜎 𝑋 Ȃ 𝑒 𝛽𝜎 𝑒Ȃ𝐶𝑃 )
𝑧
𝑧 Ȁ Ā
𝑇𝑟𝑟 𝜂 (𝑋 𝑒 𝛽𝜎Ȃ𝑒Ȃ𝐶𝑋 𝑃 𝑒 𝛽𝜎 Ȃ 𝑋 Ȃ 𝑒 𝛽𝜎 𝑒Ȃ𝐶𝑃 ) 𝑇𝜃𝜃
𝜂 (
Ȃ𝑋 𝑒 𝛽𝜎 𝑒Ȃ𝐶𝑋 𝑃 𝑒 𝛽𝜎 Ȃ 𝑋 Ȃ 𝑒 𝛽𝜎 𝑒Ȃ𝐶𝑃 ) 𝑄 𝑄 ȂȂ𝑄 Ȃ𝑟
Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ā 𝑟𝑐 Ȁ
Ȁ
Ȁ ଏ
𝑒𝛽𝜎 Ȃ Ȁ Ā
Ȁ Ȁ
𝑟 Ȃ Ȁ
𝑒𝛽𝜎 Ȃ Ȁ
Ȁ
𝑇𝑡𝑡Ȃ 𝑇
𝑝 Ȃ
( Ȃ𝑝
𝑝
)
𝜂 𝛾 𝑒Ȃ
Ȃ 𝑟
𝑟
𝑇𝑟𝑟Ȃ 𝑇
𝑝 𝑇
𝜃 𝜃 Ȃ
𝑇
𝑝 Ȃ
𝜂 𝛾 𝑝
𝑒Ȃ Ȃ 𝑟
𝑟 𝑟
Ȁ Ȁ Ȁ
Ȁ
Ā
𝑟 Ȁ
Ā Ā
Ȁ Ȁ
Ȁ Ȁ ଏ Ȁ
Ȁ Ȁ
Ȁ
𝐶 𝐶 𝑝 𝐴𝐶 Ȃ Ȃ 𝑓 𝑟 ̀ 𝑝 𝐴 𝑝 𝐴 𝐴𝐶 Ȃ 𝑝Ȃ 𝑓 𝑟 ̀
𝑝 Ȁ 𝑓 𝑟
𝑓 𝑟 Ȃ 𝜀𝜂 𝛾 𝑝
𝑒Ȃ Ȃ 𝑟
𝑟
Ȁ Ȁ
Ȁ ଏ
Ȁ Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ ଏ Ȁ
ଏ 𝑥 𝑦
𝑥 𝑝𝐴 𝐶
𝑦 𝐶 Ȁ
Ȃ 𝜎 𝑝 (𝐴 𝐴 Ȃ𝐴𝐶)
𝜎 Ā Ȁ
Ā Ȁ
𝐴
Ȃ 𝜎 𝑝 ( 𝑝Ȃ 𝑓 ̀
𝑝 Ȃ
𝑝𝐴
Ȃ𝐴𝐶)
ଏ Ȁ
𝑥 Ȃ𝑦 𝑝
𝑝𝐴
𝐴𝐶 Ȁ
𝜎 Ȃ 𝑝 Ȃ 𝑓Ȃ ̀ 𝑝
𝑝 𝑥 Ȃ𝑦
Ȁ Ȁ
𝜎 ଏ
𝑥 𝑦 Ȃ 𝑥 𝑦
Ȁ Ȁ Ȁ
Ȁ Ȁ
𝑦 Ȃ 𝑓 ̀
𝑝 Ȃ 𝑝 𝑥𝑦 𝑝 Ȃ𝑦 ଏ
𝑥 𝑝 𝑝Ȃ 𝑓 ̀Ȃ
𝑝 𝑝 𝑥 Ȃ𝑥𝑦
Ȁ Ȁ Ȁ Ȁ
Ȁ Ā Ȁ 𝑟
Ȁ Ȁ Ȁ
Ā
𝑥 𝑦 ̀( ̀ 𝑓 𝑝 𝑝Ȃ ̀
𝑝 Ȃ 𝑓
)
̀Ȃ (
𝑝
̀𝑝 𝑓 𝑝 Ȃ 𝑝
)
Ȁ
Ȁ 𝑥 𝑦
𝑥 𝑦 Ȃ Ȁ ଏ Ȁ Ȁ
ଏ Ȁ ଏ
𝑥 𝑦
Ā ଏ Ȁ
Ȁ
Ā
Ȁ Ȁ ଏ 𝑝
𝑟 𝜃 𝑝
Ȁ 𝑥 𝑦
𝐴 (
̀ 𝑓
)
̀ 𝑓
𝐶 (
̀ 𝑓
)
̀Ȃ 𝑓 Ȁ
Ȁ 𝑟 Ȃ Ȁ Ā
Ȁ
Ȁ ̀ 𝑓 𝑟
̀ Ȃ𝜀Ȃ𝜂 𝛾 𝑒Ȃ
Ȃ 𝑟
𝑟 Ȁ
Ā
Ȁ 𝑟 Ȃ
Ȁ
Ȁ Ȁ Ā
𝑑𝑠 𝑊 𝑟 𝜂𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈 𝑒 𝛽𝜎𝑑𝑟 𝐻 𝑟 𝑑𝜃
𝑊 𝑟 Ȃ 𝑒 𝛽𝜎 𝐴 𝐻 𝑟 Ȃ 𝑒 𝛽𝜎 𝐶 𝐴 𝐶 𝜎 Ȁ
Ȁ Ȁ 𝑊 𝑟
Ā Ȁ
Ȁ ଏ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
𝑓 𝑟 Ă 𝐴 𝐶 𝑐𝑡𝑒
𝑑𝑠 𝑒̀ 𝑟 𝜂𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈 𝑑𝜃 𝑑𝑟
𝑥𝜇 𝜃 𝑟
Ȁ
Ȁ
Ȁ Ȁ Ȁ ଏ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ā Ȁ
Ā
ଏ Ȁ
Ȁ
Ȁ
Ȁ Ȁ
ଏ Ȁ
Ȁ Ȁ
Ȁ Ȁ
𝑝 Ȁ Ȁ
𝑔𝜇𝜈
𝜙 ଏ Ȁ Ȁ
Ȁ Ā
Ā Ȁ Ā 𝜙Ȁ 𝒢𝑒Ȃ 𝛼𝜙
𝛼 𝑤 𝑤 Ȁ 𝒢
𝑝 Ȁ Ā
Ȁ
𝑔𝜇𝜈 𝑒 𝛼𝜙𝑔𝜇𝜈
Ȁ ଏ
𝑧 𝑈
Ā
𝑑𝑠 Ȃ𝑔 𝑟 𝑑𝑡 𝑑𝑟 𝑔 𝑟 𝑑𝜃 𝑔 𝑟 𝑑𝑧𝑖
𝑖 𝑝
Ā
𝑇𝑟𝑟 𝑇𝑧𝑧 𝑇𝑡𝑡 Ȃ𝑇𝜃𝜃 Ȃ𝜎 𝑟
𝜎 𝑟 Ȁ
Ȁ 𝑟 𝑟𝑏 𝑟𝑏
𝑔𝜇𝜈 Ȁ
𝑅𝜇𝜈 Ȃ𝜇𝜙Ȃ𝜈𝜙 𝜋𝒢
(
𝑇𝜈𝜇Ȃ 𝛿
𝜇 𝜈𝑇
𝑝
)
Ԃ 𝜙 Ȃ 𝜋𝒢𝛼𝑇
Ȁ
Ȃ𝜇𝑇𝜈𝜇 𝛼𝑇 Ȃ𝜈𝜙 Ȃ𝜇 𝑝 Ȁ
Ȁ
𝜎
𝜎 𝑔
𝑔
𝑝Ȃ 𝑔
𝑔 𝛼𝜙 Ȁ 𝜎 𝜎 𝜋𝒢 𝑒 𝛼𝜙
𝑔 𝑔 𝑝Ȃ
𝜎 Ȁ Ā
𝜙
[
𝑔 𝑝
𝑔
𝑔
𝑔
]
𝜙 𝛼𝜎 𝑒
𝛼𝜙
𝑔 𝑔𝑝Ȃ
Ȁ Ȁ
Ȁ
Ȃ𝑔
𝑔
Ȃ𝑝 𝑔
𝑔 Ȃ
𝑔𝑔
𝑔𝑔 𝜋𝒢𝜎
( Ȃ𝑝 𝑝 ) Ȃ𝑔 𝑔 𝑔 𝑔 Ȃ
𝑝 𝑔𝑔
𝑔 𝑔 𝜋𝒢𝜎
(
𝑝 𝑝
)
Ȃ 𝑝 𝑔
𝑔 𝑝 𝑔 𝑔 Ȃ 𝑔 𝑔 𝑔
𝑔 𝜋𝒢𝜎
( Ȃ𝑝
𝑝
)
𝜙
ଏ Ȁ 𝑢
𝑢 𝑔 𝑔𝑝
Ȁ Ȁ Ȁ 𝜎
Ȁ Ȁ 𝑑 𝑑𝑟 ( 𝑢𝑑𝜙 𝑑𝑟 )
𝛼𝜎 𝑢 𝑒
𝛼𝜙
𝑔 𝑔 𝑝Ȃ
𝑑 𝑑𝑟 (𝑢 𝑔 𝑑𝑔 𝑑𝑟 ) Ȃ 𝜋𝑢𝜎 ( Ȃ𝑝 𝑝 ) 𝑑 𝑑𝑟 (𝑢 𝑔 𝑑𝑔 𝑑𝑟 ) Ȃ 𝜋𝑢𝜎 ( 𝑝 𝑝 ) ଏ ଏ
𝑝 𝑝 𝑔
𝑔
𝑝 𝑔𝑔
𝑔 𝑔 𝜋𝒢𝜎 𝑝Ȃ 𝜙
Ȁ Ȁ
Ȁ 𝑟 ଏ
𝑢𝑑𝑟
𝑑𝑟 ଏ
𝑑𝑠 Ȃ𝑔 𝑟 𝑑𝑡 𝑔 𝑝 𝑔 𝑑𝑟 𝑔 𝑟 𝑑𝜃 𝑔 𝑟 𝑑𝑧𝑖
ଏ Ā ȂȂ 𝑟
Ȃ 𝑟Ă ȂȂ Ȁ
Ȁ 𝑟 Ȃ𝑟𝑏 Ȁ
𝑑 𝜙
𝑑𝑟 𝛼𝜎 𝑔
𝑝 𝑒 𝛼𝜙 𝑑 𝑑𝑟 ( 𝑔 𝑑𝑔 𝑑𝑟
) Ȃ Ȃ𝑝 𝜎 𝑔
𝑝 𝑒 𝛼𝜙 𝑝 𝑑 𝑑𝑟 ( 𝑔 𝑑𝑔 𝑑𝑟
) Ȃ 𝑝 𝜎 𝑔
𝑝 𝑒 𝛼𝜙 𝑝 Ȁ 𝑢 Ȁ 𝑔 𝑔 Ȁ
𝑔 𝑔 𝑒𝜅 𝑟𝑒Ȃ
𝛼 𝑝 𝑝 𝜙
Ȁ
𝑔 𝑔 𝑒𝜅𝑟𝑒Ȃ
𝜅 𝜅 𝑔 𝑔 Ȁ
𝑝
𝑝
Ȁ Ȁ
Ȁ 𝑔 𝑔
(
𝛼
)
𝜙 Ȃ 𝜅
𝛼 𝜙
Ȃ𝜅
(
𝜅 𝜅
)
Ȁ Ȁ
𝜙 𝜙 𝑟 𝜙 𝜙
𝜙
𝜙 𝜅
𝛼 𝛼 𝛼
[
𝜅
𝛼 𝜅 𝜅 𝜅 𝛼
]
Ȁ
Ȁ Ȁ
Ā
Ȁ
𝑑𝑠 𝑔 𝑒𝜅 𝛼𝛼 𝜙 𝑟𝜂𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈 𝑔 𝑒𝜅 Ȃ 𝛼
𝛼 𝜙 𝑟𝑑𝜃
𝑔 𝑔 𝑒 𝜅 𝜅 𝛼𝛼 𝜙 𝑟𝑑𝑟
Ā Ȁ 𝜙
𝒢𝑒Ȃ
𝛼𝜙 𝑟
Ȁ
Ā Ȁ Ā
Ȁ Ȁ
𝑝Ȃ Ȁ Ȁ
Ȁ Ȁ 𝑝
Ȁ ଏ
Ȁ
Ȁ Ā
Ȁ
𝑅
[
𝜙 𝛼 Ȃ Ȃ𝛼 𝜅 𝜅 𝜅 Ȃ 𝛼𝜅 𝜙 𝜙 ]
𝑔 𝑔 𝛼 𝑒
Ȃ𝜎𝑟Ȁ
Ȁ
𝜎Ȃ 𝜅 𝜅 ( 𝛼𝛼 )𝜙 𝜎Ȁ 𝑟Ă ȂȂ
𝑟Ă Ȃ Ȁ
ଏ Ȁ Ȁ
Ā Ȁ
Ȁ
Ȁ
ଏ
Ȁ
Ȁ Āଏ
Ȁ Ȁ
Ȁ
Ā Ȁ
Ȁ Ȁ Ā
Ȁ 𝜎
ଏ
Ȁ
Ā 𝜎Ȁ Ȁ
Ā Ȁ 𝜅 𝜅
𝛼 Ȃ 𝛼 𝜅 𝛼 Ȃ 𝛼 𝜅 𝜅 𝛼 𝜅
Ȁ 𝛼 Ȁ Ȁ 𝜅 𝜅
Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ā
Ȁ
Ȁ Ȁ Ȁ
Ȁ
𝑤Ȃ Ā
Ȁ Ā 𝜅 𝜅
Ȁ
𝜅 𝜅
Ā
Ā Ȁ
Ȁ Ȁ Ā 𝜙
𝜙 Ȃ 𝜅
𝛼 𝛼
ଏ
𝐴Ȃ𝜅 ( 𝛼 𝛼
)
𝜙
𝐵 Ȃ𝜅 (Ȃ 𝛼 𝛼
)
𝜙
𝐶 Ȃ 𝜅 𝜅 ( 𝛼
𝛼
)
𝜙
Ȁ 𝑥𝜇 𝜃 𝑟
Ā Ā
𝐴 𝜅
[ Ȃ
(
𝛼 𝛼
)]
𝐵 Ȃ 𝜅
[ (
Ȃ 𝛼
𝛼
)]
𝐶 𝜅
[ Ȃ
(
𝛼 𝛼
)]
Ȁ
𝑅 𝜅 𝑒Ȃ
𝐶𝑟
𝑔 𝑔 𝛼
[
𝛼 Ȃ Ȃ
]
ଏ Ā
Ā Ȁ 𝜙Ȃ
Ȁ
𝐴 𝜅 𝐵 Ȃ 𝜅
𝐶 𝜅
𝑅 𝜙
𝜙
Ȁ
𝑑𝑠 𝑒𝜅𝑟𝑔 𝜂𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈 𝑔 𝑒
Ȃ𝜅𝑟
𝑑𝜃 𝑔 𝑔 𝑒 𝜅𝑑𝑟
Ȁ
𝑑𝜌 𝐶 𝑒𝐶𝑟𝑑𝑟
𝐶 𝑔 𝑔
𝑒𝜉𝑟
(
𝐶𝜌 𝐶
𝜉 ଏ Ā 𝜌𝑏 𝜌
Ȃ 𝜌𝑏 Ā
Ȁ 𝑔 𝑔
Ȁ
𝑑𝑠 ( 𝜅𝜌) 𝜂𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈
( 𝜅𝜌)Ȃ
𝑑𝜃 𝑑𝜌
ଏ 𝜌𝑏 Ă
Ȁ Ȁ Ȁ
𝜌 Ă Ȃ 𝑅 𝑅𝜇𝜈𝑅
𝜇𝜈 𝜇 𝜈
Ȁ Ȁ
𝜌Ă 𝑅𝜇𝜈𝛾𝛿𝑅𝜇𝜈𝛾𝛿Ȃ 𝜌 𝐶𝜇𝜈𝛾𝛿𝐶𝜇𝜈𝛾𝛿Ȃ
𝜌 𝐶𝜇𝜈𝛾𝛿
Ā 𝜌 𝜌𝑏 Ā
ଏ 𝑑𝜃 Ȁ 𝜌 ଏ Ā
Ȁ
Ȁ ଏ
ଏ Ȁ Ā ଏ 𝑑𝜃
ଏ Ā ଏ
ଏ
𝑑𝜃 𝜌
ଏ Ȁ
Ă 𝑆
Ȁ
Ȁ 𝜌
Ā Ā Ȁ
ଏ Ȁ
ଏ Ȁ
𝑀
( 𝜅𝜌𝑏)Ȃ 𝑀
𝜋
Ȁ Ȁ Ȁ
ଏ
𝜌𝑏
𝜅
( 𝜋
𝑀
)
Ȁ Ȁ
Ȁ 𝑀
𝑀 𝑀𝑃 𝑙 𝜋
(
𝜅
)
𝜌𝑏
𝑀𝑃 𝑙 Ȁ
Ȁ 𝑀 Ȃ 𝑀𝑤𝑒𝑎𝑘
Ȁ Ȁ 𝜅
Ȁ
Ȁ Ā Ȁ Ā Ȁ
Ȁ
𝜅
Ȁ Ȁ
Ȁ Ā
Ȁ Ā
Ȁ ଏ Ȁ
Ā 𝜅 𝜅
Ȁ Ȁ Ȁ
Ȁ 𝜌 𝜌𝑏
𝜙 Ȁ
𝜙
𝐴 𝜅
[
Ȃ ( 𝛼
𝛼
)]
𝐵 Ȃ 𝜅
[
(Ȃ 𝛼
𝛼
)]
𝐶 𝜅
[
Ȃ ( 𝛼𝛼 ) ]
𝑅 𝜅 𝛼
𝑔 𝑔 𝛼 𝑒
Ȃ𝜅 Ȃ𝛼 𝑟
𝛼
Ā Ȁ
𝜅 𝑔 𝑔 Ȁ
Ȁ
𝑑𝑠 𝜌 ȂȂ 𝛼𝛼 𝜂𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈 𝜌
Ȃ𝛼
Ȃ 𝛼 𝑑𝜃 𝑑𝜌
ଏ 𝑑𝜃
𝜌
𝜌 𝑅 Ȃ 𝜌
𝜌𝑏 Ă Ȁ
Ă 𝑆 Ȁ
Ȁ
𝜌𝑏
(𝑀
𝜋
) Ȃ 𝛼 Ȃ 𝛼
𝜌𝑏
Ȁ 𝛼
Ȁ ଏ
Ā 𝜙Ȁ Ȃ 𝜌 𝛼 Ȃ 𝛼
Ȁ
ଏ Ȁ
Ȁ
Ȁ Ȁ
ଏ Ȁ
ଏ Ȁ
Ȁ Ȁ
Ȁ
Ā
Ȁ Ȁ
ଏ Ȁ
Ȁ
Ȁ Ȁ
Ȁ
Ȁ Ā Ȁ Ȁ
Ȁ Ā
𝜌𝑏 Ă
Ȁ Ă Ā
Ā
ଏ Ȁ
Ȁ Ā
Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ā
Ȁ Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ Ā
Ā
Ȁ
Ā Ā
Ā
Ȁ ଏ
Ȁ Ȁ
Ȁ Ȁ
Ȁ
Ā Ȁ Ȁ
Ȁ ଏ
Ă
ଏ Ȁ
Ȁ
Ă Ȁ
Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ Ā
Ȁ ଏ
Ȁ
Ā Ȁ Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ Ā
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
ଏ Ȁ
𝑀 𝑔𝑎𝑏
𝑀 𝑔𝑎𝑏 𝑝 𝑀
𝑉𝑝
𝑉𝑝
𝑝 𝑝 𝑉𝑝 Ȁ 𝑀
𝑝 Ȃ 𝑀
Ā 𝑀 𝑔𝑎𝑏
Ȁ 𝑀 𝑔𝑎𝑏
𝜆 𝑡
𝑝Ȃ𝜆 𝑡𝑎
𝑝 Ȃ 𝑀 𝐼 𝑝 ଏ
𝑝 𝐼 𝑝 𝑞Ȃ𝑀 Ȃ𝜆 𝑡 𝑐𝑜𝑚 𝜆 𝑝 𝑒 𝜆 𝑞
𝑆 Ȃ𝑀 ଏ 𝐼 𝑆
𝐼 𝑆 ∪
𝑝Ȃ𝑆
𝐼 𝑝
ଏ Ȁ 𝑆 Ȃ 𝑀
Ȁ 𝑝 𝑞 Ȃ 𝑆 𝑞 Ȃ𝐼 𝑝 𝐼 𝑝 ∩
𝑆 Ȃ
𝑆 ଏ Ā Ȁ
𝑆 𝐷 𝑆
𝐷 𝑆 𝑝Ȃ𝑀 𝑡𝑜𝑑𝑎 𝑐𝑢𝑟𝑣𝑎 𝑐𝑎𝑢𝑠𝑎𝑙 𝑞𝑢𝑒 𝑝𝑎𝑠𝑠𝑎 𝑝𝑜𝑟 𝑝 𝑒 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑎 𝑆
Ȁ Ȁ Ā
Ȁ Ā 𝑝 𝑀
ଏ Ȁ ଏ
Ȁ Ȁ 𝐼 𝑆 ଏ
𝑆 𝐷 𝑆 ଏ
𝑆 𝐷 𝑆
Ā Ȁ 𝑆 𝐷 𝑆 𝐷 𝑆 ∪
𝐷Ȃ 𝑆
Ā
Ȁ 𝑆
ଏ Ȁ ̀
𝐷 ̀ 𝑀 Ā ଏ 𝑀 𝑔𝑎𝑏
Ā ̀
ଏ Ȁ Ȁ
𝑀 𝑔𝑎𝑏 Ȁ
𝑓 Ā 𝑓
Ā Ȁ Ā
Ă ̀ ̀ Ā
Ȁ 𝑀 𝑔𝑎𝑏
𝑀 𝑔𝑎𝑏 Ā
̀𝑡 Ȁ 𝑡 𝑛𝑎
Ā ̀𝑡
𝑔𝑎𝑏 Ȃ𝐷 Ă𝑎𝑏 ̀𝑡
Ă𝑎𝑏 𝑔𝑎𝑏 𝑛𝑎𝑛𝑏
𝑡𝑎 𝑀 𝑡𝑎Ȃ
𝑎𝑡 Ȃ𝑎
𝑡𝑎 ̀
𝑡
ଏ Ȁ 𝑁 𝑁𝑎 𝑡𝑎
𝑁 Ȃ𝑡𝑎𝑛𝑎
𝑁𝑎 Ă𝑎𝑏𝑡𝑏
𝑁𝑎 Ā Ȁ ̀
𝑡
Ă𝑎𝑏 Ȁ Ă𝑎𝑏
Ȁ Ȁ
Ȁ Ȁ Ȁ
Ă𝑎𝑏 Ȁ Ā
Ȁ Ȁ
Ȁ ଏ Ȁ
ଏ Ā
Ā
̀ Ȁ
𝑛𝑎 Ȁ
̀ Ā ଏ
𝐾𝑎𝑏 Ȃ𝑎𝑛𝑏
̀ 𝐾𝑎𝑏 Ȃ̀ 𝐾𝑎𝑏𝑛𝑏
ଏ Ā
Ā Ȁ
Ȁ Ȁ
Ā
ଏ 𝜙𝑡 ଏ Ȁ
𝑀 𝑣𝑎
𝑇𝑎 𝑎𝑘
𝑏 𝑏𝑙 Ă𝑣
Ă𝑣𝑇𝑎 𝑎𝑘𝑏 𝑏𝑙 𝑣
𝑐Ȃ
𝑐𝑇𝑎 𝑎𝑘𝑏 𝑏𝑘 Ȃ
𝑘
∑
𝑖
𝑇𝑎 𝑐 𝑎𝑘
𝑏 𝑏𝑘Ȃ𝑐𝑣
𝑎𝑖
𝑙
∑
𝑗
𝑇𝑎 𝑎𝑘
𝑏 𝑐 𝑏𝑘Ȃ𝑏𝑖𝑣
𝑐
Ă𝑣𝑔𝑎𝑏 𝑣𝑐Ȃ𝑐𝑔𝑎𝑏 𝑔𝑐𝑏Ȃ𝑎𝑣𝑐 𝑔𝑎𝑐Ȃ𝑏𝑣𝑐 Ȃ𝑎𝑣𝑏 Ȃ𝑏𝑣𝑎
Ȁ Ā Ȁ
ଏ Ȁ
Ā ଏ Ȁ
𝐾𝑎𝑏 Ă𝑛𝑔𝑎𝑏 Ă𝑛 Ă𝑎𝑏Ȃ𝑛𝑎𝑛𝑏 Ă𝑛Ă𝑎𝑏
Ȁ Ă𝑛 𝑛𝑎𝑛𝑏
Ȁ
Ā 𝑀
Ȁ Ā ଏ
𝑔𝑎𝑏 Ȁ
Ȃ𝑎 Ȃ𝑎𝑔𝑏𝑐
𝑔𝑎𝑏 Ă𝑎𝑏
Ȁ 𝐷𝑎 ̀ 𝐷𝑎Ă𝑏𝑐
ଏ Ȁ
̀
𝑀 ଏ
ଏ Ă𝑏
𝑎
𝑣𝑎 𝑝Ȃ̀
Ȁ ̀ 𝑣𝑎
𝑣Ȃ𝑛𝑎 𝑣𝑎
Ȃ 𝑣Ȃ𝑎𝑛𝑎 𝑣Ȃ 𝑣𝑎 𝑣𝑎Ȃ 𝑣𝑎
̀ 𝑝 Ȁ 𝑣Ȃ 𝑣𝑎 Ă𝑎
𝑏𝑣𝑏
Ă𝑎𝑏 𝑔𝑎𝑏 𝑛𝑎𝑛𝑏 Ā 𝑔𝑎𝑏
𝑇𝑎 𝑎𝑘
𝑏 𝑏𝑙 𝑝 Ȃ ̀
̀ 𝑝 𝑇𝑎 𝑎𝑘
𝑏 𝑏𝑙 Ă
𝑎
𝑐 Ă𝑎𝑘𝑐𝑘Ă
𝑑
𝑏 Ă
𝑑𝑙
𝑏𝑙 𝑇
𝑐 𝑐𝑘
𝑑 𝑑𝑙
ଏ 𝑝Ȃ̀
𝑝 𝑀 𝑝
Ā ଏ Ă𝑎
𝑏 Ȁ
𝑀 𝑝 ̀ 𝑝 𝑇𝑎 𝑎𝑘
𝑏 𝑏𝑙
̀ Ȁ ଏ Ȃ𝑐𝑇𝑎 𝑎𝑘𝑏 𝑏𝑙
𝑇𝑎 𝑎𝑘
𝑏 𝑏𝑙 ̀
Ă𝑐
𝑑Ȃ𝑐𝑇𝑎 𝑎𝑘𝑏 𝑏𝑙 ଏ
𝑀 𝑔𝑎𝑏 ̀ Ā
𝐷𝑐𝑇𝑎 𝑎𝑘𝑏 𝑏𝑙 Ă
𝑎
𝑑 Ă
𝑒𝑙
𝑏𝑙 Ă
𝑓
𝑐 Ȃ𝑓𝑇𝑑 𝑑𝑘𝑒 𝑒𝑙
Ȃ𝑎 𝑔𝑎𝑏
ଏ Ȁ 𝑅 𝑑
𝑎𝑏𝑐 ̀
𝑅 𝑑
𝑎𝑏𝑐 𝑣𝑐 ̀ Ȁ
𝑅𝑎𝑏𝑐𝑑𝑣𝑑 𝐷𝑎𝐷𝑏𝑣𝑐Ȃ𝐷𝑏𝐷𝑎𝑣𝑐
Ȁ Ȁ
𝐷𝑎𝐷𝑏𝑣𝑐 𝐷𝑎 Ă𝑏𝑑Ă𝑐𝑒Ȃ𝑑𝑣𝑒 Ă𝑎𝑓Ă 𝑔 𝑏 Ă
𝑘
𝑐 Ȃ𝑓 Ă𝑔𝑑Ă𝑘𝑒Ȃ𝑑𝑣𝑒
Ȁ Ȁ Ȁ
Ȁ Ȁ Ă𝑎𝑓Ă
𝑔
𝑏 Ă𝑐𝑒Ȃ𝑓Ă𝑔𝑑
Ā Ă 𝑓
𝑎 Ă 𝑔
𝑏 Ă𝑐𝑒Ȃ𝑓Ă𝑔𝑑 Ă𝑐𝑒𝐾𝑎𝑏𝑛𝑑
Ȁ ଏ
𝐷𝑎𝐷𝑏𝑣𝑐 Ă𝑎𝑓Ă𝑏𝑑Ă𝑐𝑒Ȃ𝑓Ȃ𝑑𝑣𝑒 Ă𝑐𝑒𝐾𝑎𝑏𝑛𝑑Ȃ𝑑𝑣𝑒 Ă𝑏𝑑𝐾𝑎𝑐𝑛𝑒Ȃ𝑑𝑣𝑒
𝐷𝑏𝐷𝑎𝑣𝑐 𝑅𝑎𝑏𝑐𝑑
Ā Ȁ Ȁ
Ȁ
𝑅𝑎𝑏𝑐𝑑 Ă𝑎𝑓Ă 𝑔
𝑏 Ă𝑐𝑘Ă𝑗𝑑𝑅 𝑗
𝑓 𝑔𝑘Ȃ𝐾𝑎𝑐𝐾𝑏𝑑 𝐾𝑏𝑐𝐾𝑎𝑑
Ȁ
𝐷𝑎𝐾𝑎𝑏 Ȃ𝐷𝑏𝐾𝑎𝑎 𝑅𝑐𝑑𝑛𝑑Ă𝑐𝑏
Ȁ Ȁ
Ȁ Ā ଏ Ȁ
Ā Ȁ Ȁ
Ȁ Ȁ
Ā Ȁ
Ȁ Ā
Ā
ଏ
Ȁ Ā
Ă
Ȁ
Ȁ Ȁ
ଏ
Ȁ Ā
Ȁ
Ȁ Ā
Ȁ Ȁ
Ȁ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ā
Ȁ
Ā ଏ
Ā
Ȁ Ȁ
Ȁ
Ȁ ଏ Ȁ
Ā
Ȁ Ā
Ȁ Ă 𝑆
𝐷 Ȁ
Ă Ȁ Ȃ𝜇
Ȁ 𝐷𝜇
Ā
𝑞𝜇𝜈 𝑔𝜇𝜈
𝑞𝜇𝜈 𝑔𝜇𝜈 Ȃ𝑛𝜇𝑛𝜈
𝑛𝜇 Ȁ
Ȁ
𝑅𝛽𝛾𝛿𝛼 𝑅𝜇𝜈𝜌𝜎𝑞𝜇𝛼𝑞𝛽𝜈𝑞𝛾𝜌𝑞𝛿𝜎 𝐾𝛼𝛾𝐾𝛽𝛿 Ȃ𝐾𝛼𝛿𝐾𝛽𝛾
Ȁ ଏ
𝐷𝜈𝐾𝜇𝜈Ȃ𝐷𝜇𝐾 𝑅𝜌𝜎𝑛𝜎𝑞𝜇𝜌
𝐾𝜇𝜈 𝑞𝛼𝜇𝑞𝜈𝛽Ȃ𝛼𝑛𝛽 Ȁ
Ā 𝛼
𝛾
𝑅𝛽𝛿 𝑅𝜈𝜎𝑞𝛽𝜈𝑞𝛿𝜎Ȃ 𝑅𝜈𝜌𝜎𝜇 𝑛𝜇𝑛𝜌𝑞𝛽𝜈𝑞𝛿𝜎 𝐾𝐾𝛽𝛿Ȃ𝐾𝛾𝛿𝐾𝛽𝛾
𝑞𝜇𝜈 𝑅 𝜇𝜈
𝑅 𝑅𝜈𝜎𝑞𝜈𝜎 Ȃ 𝑅𝜇𝜈𝜌𝜎𝑛𝜇𝑛𝜌𝑞𝜈𝜎 𝐾 Ȃ𝐾𝛼𝛽𝐾𝛼𝛽
𝐺𝛽𝛿 𝐺𝜈𝜎𝑞𝛽𝜎𝑞𝛿𝜎 𝑅𝜈𝜎𝑛𝜈𝑛𝜎𝑞𝛽𝛿 𝐾𝐾𝛽𝛿 Ȃ𝐾𝛿𝛾𝐾𝛽𝛾
Ȃ 𝑞𝛽𝛿 𝐾 Ȃ𝐾𝛼𝛾𝐾𝛼𝛾 Ȃ𝐸Ȁ𝛽𝛿
ଏ 𝐸Ȁ𝛽𝛿 𝑅𝜇𝜈𝜌𝜎𝑛𝜇𝑛𝜌𝑞𝛽𝜈𝑞𝛿𝜎
Ȁ Ȁ
Ȁ
Ȁ
Ȁ Ȁ
Ā Ȁ
Ȁ Ȁ
Ȁ Ȁ 𝑛
𝑛𝑅
𝛼𝛽𝜇𝜈 𝑛𝐶𝛼𝛽𝜇𝜈
𝑛Ȃ
(
𝑛𝑅
𝛼 𝜇𝑔𝜈 𝛽Ȃ𝑛𝑅𝛽 𝜇𝑔𝜈 𝛼
)
Ȃ
𝑛Ȃ 𝑛Ȃ
Ā Ȁ 𝑛 𝐸Ȁ𝜇𝜈
Ȁ
𝐸𝛽𝛿 𝐸𝛽𝛿
(
𝑅𝜇𝜌𝑛𝜇𝑛𝜌𝑞𝛽𝛿 𝑅𝜈𝜎𝑞𝛽𝜈𝑞𝛿𝜎
)
Ȃ 𝑅𝑞𝛽𝛿
ଏ 𝐸𝛽𝛿 𝐶𝜇𝜈𝜌𝜎𝑛𝜇𝑛𝜌𝑞𝛽𝜈𝑞𝜌𝜎 ଏ
Ȁ
𝐺𝛽𝛿 𝐺𝜈𝜎𝑞𝛽𝜈𝑞𝛿𝜎 Ȃ 𝑅𝑞𝛽𝛿 Ȃ 𝑅𝜈𝜎𝑞𝜈𝜎𝑞𝛽𝛿 𝐾𝐾𝛽𝛿Ȃ𝐾𝛾𝛿𝐾𝛽𝛾
Ȃ 𝑞𝛽𝛿 𝐾 Ȃ𝐾𝛼𝛾𝐾𝛼𝛾 Ȃ𝐸𝛽𝛿
Ȁ Ȁ
ଏ Ā Ȁ
Ȁ Ȁ Ȁ
Ȁ
𝐺𝜇𝜈
𝜋 𝜙 𝑇𝑀 𝜇𝜈
𝑤 𝜙
(
Ȃ𝜇𝜙Ȃ𝜈𝜙Ȃ 𝑔𝜇𝜈Ȃ𝛼𝜙Ȃ𝛼𝜙
)
𝜙
(
Ȃ𝜇Ȃ𝜈𝜙Ȃ𝑔𝜇𝜈Ԃ 𝜙
)
Ȁ
Ԃ 𝜙 𝜋 𝑤𝑇𝑀
𝑇𝑀 𝜇𝜈 ଏ Ā
Ȁ
𝑅 Ȃ 𝜋 𝜙 ( 𝑤Ȃ 𝑤 ) 𝑇𝑀 𝑤
𝜙 Ȃ𝛼𝜙Ȃ
𝛼𝜙
𝑅𝜇𝜈
𝜋 𝜙
[
𝑇𝑀 𝜇𝜈 Ȃ 𝑔𝜇𝜈
( 𝑤 𝑤 ) 𝑇𝑀 ]
𝜙Ȃ𝜇Ȃ𝜈𝜙 𝑤
𝜙 Ȃ𝜇𝜙Ȃ𝜈𝜙
Ȁ
𝐺𝛽𝛿
[
𝜋
𝜙 𝑇𝑀 𝜈𝜎 𝜙Ȃ𝜈Ȃ𝜎𝜙 𝑤
𝜙 Ȃ𝜈𝜙Ȃ𝜎𝜙
]
𝑞𝛽𝜈𝑞𝛿𝜎Ȃ𝑞𝜈𝜎𝑞𝛽𝛿
𝜋 𝜙𝑞𝛽𝛿𝑇𝑀
(
𝑤 𝑤
)
Ȃ 𝑤
𝜙 𝑞𝛽𝛿Ȃ𝛼𝜙Ȃ
𝛼𝜙 𝐾𝐾
𝛽𝛿Ȃ𝐾𝛾𝛿𝐾𝛽𝛾
Ȁ ଏ
𝐷𝜈𝐾𝜇𝜈Ȃ𝐷𝜇𝐾
[
𝜋
𝜙 𝑇𝑀 𝜌𝜎 𝜙Ȃ𝜌Ȃ𝜎𝜙 𝑤
𝜙 Ȃ𝜌𝜙Ȃ𝜎𝜙
]
𝑛𝜎𝑞𝜇𝜌
Ȁ Ȁ
Ȁ Ȁ
Ȁ
Ā
Ȁ Ă
Ȁ Ā
Ȁ ଏ Ā
ଏ Ȁ
Ȁ
Ȁ
Ȁ Ā ଏ ଏ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
𝑦 Ā
Ȁ 𝑦
𝑦 𝑦
𝜒
𝜒 𝜒 Ȃ𝜒Ȃ
𝜒 𝜒 𝑦Ă
Ȁ ଏ
𝜒 Ā
Ȁ ̀
𝑔𝜇𝜈 ̀ 𝑦 𝑔𝜇𝜈 ̀ Ȃ𝑦 𝑔𝜇𝜈Ȃ
Ȁ 𝑔𝜇𝜈 𝑔Ȃ 𝜇𝜈
Ȁ
̀ 𝑦 𝑦 𝑦 𝑦
̀ 𝑦 ̀ 𝑦 ̀ 𝑦 ̀ Ȃ𝑦
𝑑̀ 𝑦
𝑑𝑦 𝛿 𝑦
𝛿 𝑦 Ȁ Ȁ Ȁ
̀
𝑔𝜇𝜈 𝛼 ̀ 𝑦 𝑔𝜇𝜈 𝛼 ̀ Ȃ𝑦 𝑔Ȃ𝜇𝜈 𝛼 𝛿 𝑦 𝑔𝜇𝜈 𝑛𝛼
Ā ଏ Ȁ Ā
̀ 𝑦 𝛿 𝑦 Ȁ Ȁ ଏ
𝑔𝜇𝜈 Ā
Ȁ
Ȁ
𝑔𝜇𝜈 𝛼 𝑘𝜇𝜈𝑛𝛼
𝑘𝜇𝜈
Ȁ ଏ
ଏ Ȁ Ȁ
Ȁ
Ȁ
̀𝛼𝜇𝜈 ̀ 𝑦 ̀𝜇𝜈𝛼 ̀ Ȃ𝑦 ̀Ȃ𝜇𝜈𝛼 ̀ 𝛼
𝜇𝜈 Ȁ Ā 𝑔𝜇𝜈
̀𝛼𝜇𝜈 𝛽 ̀ 𝑦 ̀𝜇𝜈 𝛽𝛼 ̀ Ȃ𝑦 ̀Ȃ𝜇𝜈 𝛽𝛼 𝛿 𝑦 ̀𝛼𝜇𝜈 𝑛𝛽
ଏ
𝑅𝛼𝜇𝜈𝛽 ̀ 𝑦 𝑅𝜇𝜈𝛽𝛼 ̀ Ȃ𝑦 𝑅Ȃ𝜇𝜈𝛽𝛼 𝛿 𝑦 (̀𝛼𝜇𝛽 𝑛𝜈Ȃ ̀𝛼𝜇𝜈 𝑛𝛽
)
Ȁ
Ȁ
Ȁ
(
̀𝛼𝜇𝛽 𝑛𝜈Ȃ ̀𝛼𝜇𝜈 𝑛𝛽
)
𝑘𝛽𝛼𝑛𝜇𝑛𝜈 Ȃ𝑘𝛼𝜈𝑛𝜇𝑛𝛽Ȃ𝑘𝜇𝛽𝑛𝛼𝑛𝜈 𝑘𝜇𝜈𝑛𝛼𝑛𝛽
ଏ ଏ
Ȁ 𝛿 𝑘𝜇𝜈 𝑆𝜇𝜈
𝑆𝜇𝜈 Ȃ 𝑘𝛾𝜇𝑛𝛾𝑛𝜈 𝑘𝛾𝜈𝑛𝛾𝑛𝜇Ȃ𝑘𝑛𝜇𝑛𝜈 Ȃ𝑘𝜇𝜈Ȃ 𝑘𝛾𝜎𝑛𝛾𝑛𝜎Ȃ𝑘 𝑔𝜇𝜈
Ȁ Ȁ Ȁ
Ȁ
𝜙 ̀ 𝑦 𝜙 ̀ Ȃ𝑦 𝜙Ȃ
𝜙 𝜇 ̀ 𝑦 𝜙 𝜇 ̀ Ȃ𝑦 𝜙Ȃ𝜇 𝛿 𝑦 𝜙 𝑛𝜇
ଏ 𝜙
̀ 𝑦 𝛿 𝑦 Ȁ Ȁ
Ȁ
𝜙 𝜇 𝜈 ̀ 𝑦 𝜙 𝜇 𝜈 ̀ Ȃ𝑦 𝜙Ȃ𝜇 𝜈 𝛿 𝑦 𝜙 𝜇𝑛𝜈
𝑇𝜇𝜈𝑡𝑜𝑡𝑎𝑙 ̀ 𝑦 𝑇𝜇𝜈 ̀ Ȃ𝑦 𝑇𝜇𝜈Ȃ 𝛿 𝑦 𝑇𝜇𝜈
𝑇𝜇𝜈 ଏ
Ȁ Ȁ
𝜙
̀ 𝑦 𝜙
̀ Ȃ𝑦 𝜙Ȃ
𝜙 Ȁ Ȁ
𝛿 Ȁ
𝐵𝐷 𝜇𝜈 Ȁ
𝜋 𝜙
(
𝑇𝜇𝜈Ȃ
𝑔𝜇𝜈
𝑤𝑇
)
𝜙 𝜙 𝜇𝑛𝜈 Ȃ 𝐵𝐷 𝜇𝜈
𝑆𝜇𝜈 𝐵𝐷 𝜇𝜈 𝑆𝜇𝜈𝑛𝜈 Ȁ
𝜙 𝜇
𝜋 𝑤𝑇 𝑛𝜇
𝑇𝜇𝜈𝑛𝜈 𝑇𝜇𝜈 Ā Ȁ
𝑔𝜇𝜈 𝛼 𝑘𝜇𝜈𝑛𝛼 Ȁ
𝐵𝐷 𝜇𝜈
𝜋 𝜙
(
𝑇𝜇𝜈 Ȃ𝑞𝜇𝜈
𝑇 𝑤
)
Ȁ 𝑣𝑎
Ā Ȁ 𝑥𝜇 𝑥𝜇 𝑣𝑎
𝑒𝜇𝑎 Ȃ𝑥
𝜇
Ȃ𝑣𝑎
Ȁ
𝑑𝑠 𝑔𝜇𝜈𝑑𝑥𝜇𝑑𝑥𝜈
𝑔𝜇𝜈
(
Ȃ𝑥𝜇
Ȃ𝑣𝑎𝑑𝑣 𝑎
)(
Ȃ𝑥𝜈
Ȃ𝑣𝑏𝑑𝑣 𝑏
)
𝑞𝑎𝑏𝑑𝑣𝑎𝑑𝑣𝑏
Ȁ 𝑞𝑎𝑏 𝑔𝜇𝜈𝑒𝜇𝑎𝑒𝜈𝑏 Ȁ
𝐵𝐷 𝑎𝑏 𝐵𝐷 𝛼𝛽𝑒𝛼𝑎𝑒 𝛽
𝑏 Ȃ𝑘𝛼𝛽𝑒 𝛼 𝑎𝑒
𝛽
𝑏 𝑘Ȃ𝑘𝜇𝜈𝑛 𝜇𝑛𝜈 𝑞
𝑎𝑏
Ȃ𝑘𝛼𝛽𝑒𝛼𝑎𝑒 𝛽
𝑏 𝑞𝑚𝑛𝑘𝜇𝜈𝑒𝜇𝑚𝑒𝜈𝑛𝑞𝑎𝑏
ଏ 𝑘𝜇𝜈 Ā
Ȃ𝛼𝑛𝛽 Ȃ̀𝛾𝛼𝛽 𝑛𝛾 𝑘𝛼𝛽Ȃ𝑘𝛾𝛼𝑛𝛽𝑛𝛾Ȃ𝑘𝛾𝛽𝑛𝛼𝑛𝛾
𝑛𝛾 Ȁ
𝑥𝜇 𝑦 𝑛𝛾 Ȁ
Ă Ȁ
𝐾𝑎𝑏 Ȃ𝛼𝑛𝛽 𝑒𝛼𝑎𝑒 𝛽
𝑏 𝑘𝛼𝛽𝑒𝛼𝑎𝑒 𝛽 𝑏 Ȁ 𝜋 𝜙 (
𝑇𝑎𝑏Ȃ𝑞𝑎𝑏
𝑇 𝑤
)
Ȁ Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
𝑤Ă Ȃ 𝜙 Ă 𝐺 Ȁ Ȁ
Ȁ
Ȁ Ȁ Ā
Ā Ȁ Ă
Ā Ă
𝑛𝜇 𝑛𝜇 Ă Ȃ𝑛Ȃ𝜇
𝐾𝜇𝜈 Ȃ𝜇𝑛𝜈 Ā
Ā 𝐾𝜇𝜈 Ă Ȃ𝐾Ȃ
𝜇𝜈 Ȁ
𝐾𝜇𝜈 Ȃ𝐾𝜇𝜈Ȃ 𝜋 𝜙
( Ȃ𝑇𝜇𝜈
𝑞𝜇𝜈 𝑤 𝑇
𝑤
)
𝐾 Ȃ𝐾Ȃ 𝜋 𝜙 ( 𝑤Ȃ 𝑤 ) 𝑇 Ȁ Ā Ȁ Ā
Ȁ Ă Ȁ
Ȁ
Ā Ȁ Ȁ
Ȁ Ȁ
Ȃ Ȁ
𝐺𝛽𝛿
[
𝜋
𝜙 𝑇𝑀 𝜈𝜎 𝜙Ȃ𝜈Ȃ𝜎𝜙 𝑤
𝜙 Ȃ𝜈𝜙Ȃ𝜎𝜙
]
𝑞𝛽𝜈𝑞𝛿𝜎Ȃ𝑞𝜈𝜎𝑞𝛽𝛿
𝜋 𝜙𝑞𝛽𝛿𝑇𝑀
(
𝑤 𝑤
)
Ȃ 𝑤
𝜙 𝑞𝛽𝛿Ȃ𝛼𝜙Ȃ
𝛼𝜙 (𝜋
𝜙
) [
𝑇 𝑇𝛽𝛿
(
𝑤 𝑤
)
Ȃ 𝑇 𝑞𝛽𝛿
𝑤 𝑤
𝑤 Ȃ 𝑇
𝛾
𝛿𝑇𝛽𝛾 𝑞𝛽𝛿𝑇 𝛼𝛾𝑇
𝛼𝛾
] Ȃ𝐸𝛽𝛿
𝐸𝜇𝜈 Ȁ Ȁ
𝑦Ă
Ȁ Ȁ 𝐾 𝐾Ȃ
𝐾 Ȃ𝐾Ȃ Ȁ
Ā
Ȁ Ȁ
𝑇𝑀 𝜇𝜈 Ȃ̀𝑔𝜇𝜈 𝛿 𝑦 𝑇𝜇𝜈
𝑇𝜇𝜈 Ȃ𝜆𝑞𝜇𝜈 𝜏𝜇𝜈
̀ 𝜆 Ȁ
Ȁ Ȁ Ȁ
Ȁ
Ȁ
Ā Ā
𝛿 𝑦 Ȁ Ȁ
Ȁ
Ȁ ଏ Ȁ
𝐺𝛽𝛿
[
𝜙Ȃ𝜈Ȃ𝜎𝜙 𝑤
𝜙 Ȃ𝜈𝜙Ȃ𝜎𝜙
]
𝑞𝛽𝜈𝑞𝛿𝜎 Ȃ𝑞𝜈𝜎𝑞𝛽𝛿 𝜋̀𝜏𝛽𝛿 Ȃ̀ 𝑞𝛽𝛿
(𝜋
𝜙
)
̀𝛽𝛿Ȃ𝐸𝛽𝛿
̀ 𝜋 𝑤Ȃ 𝜆
𝜙 𝑤
̀ Ȃ 𝜋̀ Ȃ 𝑤
𝜙 𝑤
(𝜋
𝜙
) [ 𝑤
𝜋 Ȃ𝛼𝜙Ȃ
𝛼𝜙 𝑤Ȃ 𝜆
𝑤 𝑤Ȃ 𝜆 𝜏
]
̀𝛽𝛿 𝑞𝛽𝛿𝜏𝛼𝛾𝜏𝛼𝛾Ȃ 𝜏𝛾𝛿𝜏𝛾𝛽
( 𝑤
𝑤
)
𝜏 𝜏𝛽𝛿Ȃ
𝑤 𝑤
𝑤 𝑞𝛽𝛿𝜏 Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ā
Ȁ
Ȁ Ȁ
Ȁ ଏ Ȁ
ଏ
Ȁ ଏ Ȁ Ȁ
Ȁ 𝐸𝜇𝜈 Ȁ
Ȁ Ȁ
ଏ 𝑦
Ȁ ̀ ̀ 𝜙 𝑦
Ȁ Ȁ ଏ
Ȁ Ȁ
Ȁ Ȁ
Ȁ
Ȁ Ā ଏ Ȁ
Ȁ Ȁ
̀ Ȁ
Ȁ
ଏ Ȁ ̀ 𝜏
𝜙 𝑦 𝐵𝐶 ̀ 𝐴 𝑦Ȃ𝐷 𝐴𝐵̀
𝐷 Ȁ 𝐴 𝜋 Ȃ𝑤𝑤 𝐵 𝑤 𝐶 𝜋 𝑤Ȃ 𝜆 𝑤Ȃ 𝜆 𝜏
𝑤
̀
Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ Ā
Ȁ Ȁ ଏ
Ȁ ଏ
ଏ Ā Ȁ
Ȁ Ȁ
𝜋 𝜙
[
Ȃ𝐷𝜈𝜏𝜇𝜈
𝑤𝐷𝜇𝜏
] [
𝜙Ȃ𝜌Ȃ𝜎𝜙 𝑤
𝜙 Ȃ𝜌𝜙Ȃ𝜎𝜙
]
𝑛𝜎𝑞𝜇𝜌
Ā 𝐷𝛽 𝐺
𝛽𝛿 Ā
𝐸𝜇𝜈 𝜏𝜇𝜈
𝐷𝛽𝐸𝛽𝛿
𝜋 𝜙 𝐷
𝛽𝜏 𝛽𝛿 Ȃ
𝜋 𝑤Ȃ 𝜆 𝑤 𝐷𝛿𝜏
(𝜋
𝜙
)
𝐷𝛽̀𝛽𝛿
𝐷𝜇̀
𝜇𝜈 Ȁ
𝐷𝜇𝜏
𝜇𝜈 Ȁ 𝜏𝜇𝜈
𝐷𝛽𝐸 𝛽𝛿
Ā
Ā Ȁ Ȁ
Ȁ Ă
Ā Ā
Ȁ Ȁ
Ȁ Ȁ Ā
Ȁ Ȁ
Ă
Ȁ Ă Ȁ
Ȁ Ȁ
Ā Ȁ Ȁ
Ă Ȁ Ȁ
Ȁ Ȁ
Ȁ Ă
Ȁ
Ȁ
Ă
Ă Ȁ
ଏ Ȁ Ȁ Ȁ
Ȁ
Ȁ ଏ
Ȁ
Ȁ Ă
Ā Ȁ Ā
Ȁ
Ȁ Ȁ
Ȁ Ă Ȁ
Ā Ā
Ȁ
Ȁ Ā Ȁ
Ȁ
Ā ଏ Ȁ
𝜒
܂𝜒܂ 𝜒 𝜒Ȃ
Ȁ Ȁ
𝑛𝛼 Ā Ȁ
Ă Ā
Ă
Ȁ
Ȁ Ȁ Ă Ȁ Ȁ
ଏ Ȁ Ā Ā
Ă 𝑆 Ȁ ଏ
Ā
Ȁ
Ȁ
Ă
Ȁ Ȁ
Ȁ
Ȁ Ȁ
𝑞𝜇𝜈 𝑔𝜇𝜈 Ȃ𝑛𝜇𝑛𝜈
Ȁ ଏ
𝐴𝐵 ܂𝐴܂𝐵 𝐴܂𝐵܂
܂𝐴𝐵܂ ܂𝐴܂܂𝐵܂ 𝐴 𝐵
Ȁ
𝑅𝜇𝜈 𝑌𝜇𝜈 𝐾𝐾𝜇𝜈 Ȃ𝐾𝜇𝜆𝐾𝜆𝜈
𝑌𝜇𝜈
𝑌𝜇𝜈 𝑅𝛼𝛽𝑞𝜇𝛼𝑞𝛽𝜈 𝑅𝛼𝛽𝑞𝛼𝛽𝑞𝜇𝜈Ȃ 𝑅𝑞𝜇𝜈 𝐸𝜇𝜈
𝐸𝜇𝜈 Ȁ Ȁ
Ȁ Ȁ Ȁ
𝑌𝜇𝜈 𝑌𝜇𝜈𝑛𝜈
𝑌 Ȃ 𝐺𝜇𝜈𝑛𝜇𝑛𝜈 Ȁ
ଏ Ȁ
Ȁ ଏ Ȁ
𝑅𝜇𝜈 𝑌𝜇𝜈 ܂𝐾܂𝐾𝜇𝜈 𝐾 ܂𝐾𝜇𝜈܂ Ȃ ܂𝐾𝜇𝛼܂𝐾𝜈 𝛼
𝐾 𝐾𝜇𝜈 Ȁ Ȁ
Ȁ
𝑇𝜇𝜈 Ȃ̀𝑔𝜇𝜈 𝛿𝑆𝜇𝜈
𝑆𝜇𝜈 Ȃ𝜆𝑞𝜇𝜈 𝜏𝜇𝜈
𝐾𝜇𝜈 Ȃ
𝜋 𝜙
(
𝜏𝜇𝜈
𝑞𝜇𝜈
𝑤 𝑤Ȃ 𝜆Ȃ 𝑤 𝜏
)
𝐾 𝜋 𝑤Ȃ
𝜙 𝑤 𝜏Ȃ 𝜆
Ȁ ଏ
Ȃ( 𝜋
𝜙
)Ȃ
𝑌𝜇𝜈 ܂𝐾𝛼 𝜇܂𝜏𝜈𝛼Ȃ
(
𝜏𝜇𝜈
𝑞𝜇𝜈
𝑤 𝑤Ȃ 𝜆Ȃ 𝑤 𝜏
) ܂𝐾܂
Ȃ𝑤 𝜆Ȃ 𝑤 𝜏
𝑤 ܂𝐾𝜇𝜈܂ Ȁ
Ȁ Ā
Ȁ ଏ Ȁ
܂ 𝑅𝜇𝜈܂ 𝑅𝜇𝜈 ܂𝑌𝜇𝜈܂
(
𝐾 𝐾𝜇𝜈 Ȃ 𝐾𝜇𝛼 𝐾𝜈𝛼
)
܂𝐾܂܂𝐾𝜇𝜈܂ Ȃ ܂𝐾𝜇𝛼܂܂𝐾𝜈𝛼܂
Ȁ Ȁ 𝑞𝜇𝜈
𝑅 ܂𝑌܂ (𝐾 Ȃ 𝐾𝜇𝜈 𝐾𝜇𝜈
)
܂𝐾܂ Ȃ ܂𝐾𝜇𝜈܂܂𝐾𝜇𝜈܂
Ȁ Ȁ ଏ Ȁ Ȁ
Ȁ Ā
Ȁ Ȁ
Ā
Ȁ 𝑌𝜇𝜈
𝐾𝜇𝜈
𝑌𝜇𝜈
𝑌
𝑞𝜇𝜈 𝜛𝜇𝜈
𝐾𝜇𝜈
𝐾
𝑞𝜇𝜈 𝜁𝜇𝜈
𝜛𝜇𝜈
(
𝑅𝛼𝛽𝑞𝜇𝛼𝑞𝜈𝛽Ȃ 𝑅𝛼𝛽𝑞𝛼𝛽𝑞𝜇𝜈
)
𝐸𝜇𝜈 Ȁ
𝜁𝜇𝜈 𝑛𝛼 Ȁ
ଏ
𝐺𝜇𝜈 𝑅𝜇𝜈 Ȃ 𝑞𝜇𝜈 𝑅 Ȃ̀ 𝑞𝜇𝜈 𝐺𝑁 𝜏𝜇𝜈 𝜋𝜇𝜈 ܂𝜛𝜇𝜈܂
܂𝐾܂܂𝜁𝜇𝜈܂ Ȃ ܂𝜁𝜇𝛼܂܂𝜁𝜈𝛼܂
̀
̀ ܂𝑌܂ ܂𝐾܂ Ȃ ܂𝜁𝛼𝛽܂܂𝜁𝛼𝛽܂
( 𝜋
𝜙
) 𝜆 𝑤Ȃ
𝑤 𝜏 𝜆 𝑤Ȃ 𝐺𝑁
𝐺𝑁
( 𝜋
𝜙
) 𝜆 𝑤Ȃ
𝑤 𝜋𝜇𝜈
𝜋𝜇𝜈
( 𝜋
𝜙
) 𝜏 𝜏𝜇𝜈 𝑤
𝑤 Ȃ
( 𝜋
𝜙
)
𝜏𝜇𝛼𝜏𝜈𝛼
( 𝜋
𝜙
)
𝜏𝛼𝛽𝜏𝛼𝛽𝑞𝜇𝜈
Ȃ ( 𝜋
𝜙
) 𝜏 𝑞𝜇𝜈
𝑤 𝑤 𝑤
Ȁ
̀ ଏ
Ȁ
Ȁ ܂𝑌܂ Ȁ
Ȁ
܂𝑌܂ Ȃ (〈
𝜋 𝜙 𝑇𝜇𝜈𝑛
𝜇𝑛𝜈
〉 〈
𝑤 𝜙
(
𝜙𝜇𝜙𝜈𝑛𝜇𝑛𝜈 Ȃ 𝜙 𝛼𝜙 𝛼
)〉
〈
𝜙
(
𝜙𝜇 𝜈𝑛𝜇𝑛𝜈 Ȃ
𝜋 𝑤𝑇
Ȁ
܂𝑌܂ ܂𝜛܂ Ȁ Ă
Ȁ Ȁ
Ȁ
Ȁ Ȁ
ଏ Ȁ ̀ 𝐺𝑁
Ȁ
Ȁ Ȁ Ȁ
܂𝜛܂ Ȁ
Ȁ ܂𝜁𝜇𝜈܂
Ȁ Ȁ Ȁ
ଏ Ȁ Ā Ȁ ଏ
𝑛𝜇
܂𝜁𝜇𝜈܂ Ȁ Ă Ȁ
ଏ Ā
ଏ ଏ Ȁ Ā
Ă Ȁ
ଏ ܂𝐾𝜇𝜈܂
Ȁ
Ā Ȁ Ȁ
܂𝐾𝜇𝜈܂
ଏ
Ȁ
𝜏𝜇𝜈 Ȃ𝜏𝜇𝜈 𝐴𝜆 𝐵𝜏 𝑞𝜇𝜈
𝐴 𝐵 Ȁ 𝐾𝜇𝜈
Ȁ
𝜏𝜇𝜈 Ȁ
Ȁ 𝑤Ȃ
𝑌𝜇𝜈 ܂𝐾܂𝐾𝜇𝜈
𝜋 𝜙 ܂𝐾
𝛼 𝜇 ܂𝜏Ȁ𝜈 𝛼
Ȁ 𝐴 Ȃ𝑤𝑤 𝐵 Ȃ 𝑤 𝑤
Ȁ
𝐴 Ȃ 𝑛Ȃ
𝑛Ȃ 𝐵 Ȃ 𝑛Ȃ 𝑤Ă Ȃ
𝑛 ଏ
Ȁ
𝜏𝜇𝜈 𝜏𝜇𝜈 Ȃ
𝑤 𝜆Ȃ 𝑤 𝜏 𝑤 𝑞𝜇𝜈
𝐾𝜇𝜈 Ȃ
𝜋 𝜙
(
Ȁ 𝜏𝜇𝜈 Ȃ
Ȁ 𝜏 𝑞𝜇𝜈 ) ଏ 𝐾 𝜋 𝜙 Ȁ 𝜏 Ȁ 𝜏𝜇𝜈
𝑑𝑒𝑡 𝜏Ȁ𝜇𝜈 Ȃ ଏ Ȁ 𝜏ȀȂ 𝜇𝜎𝜏Ȁ𝜇𝜈 𝛿𝜈𝜎
Ȁ Ȁ𝜏Ȃ 𝜇𝜈
𝜋 𝜙 ܂𝐾܂
Ȁ
𝜏Ȃ 𝜇𝜈 𝑌 𝜇𝜈
Ȃ Ȁ𝜏Ȃ 𝜇𝜇𝜏Ȁ𝜈 𝜈
ଏ Ā
Ȃ 𝜏ȀȂ 𝜇
𝜇𝜏Ȁ𝜈𝜈 Ȁ Ȁ
𝑛 Ȃ Ȃ 𝜏ȀȂ 𝜇
𝜇𝜏Ȁ𝜈𝜈 Ȁ Āଏ
Ȁ Ȁ
Ȁ
Ā Ȁ
Ȃ 𝜏ȀȂ 𝜇𝜇𝜏Ȁ𝜈𝜈
Ȁ Ȁ ଏ
Ȃ 𝜙𝜋܂𝐾𝜇𝛼܂𝜏Ȁ𝜈 𝛼 𝑌𝜇𝜈
Ȁ
𝜏Ȃ 𝛼𝛽 𝑌 𝛼𝛽
Ȃ 𝜏ȀȂ 𝜎 𝜎Ȁ𝜏
𝛾 𝛾
( Ȃ𝜏Ȁ𝜇𝜈
Ȁ 𝜏
𝑞𝜇𝜈
)
𝜋 𝜙 ܂𝐾
𝛼
𝜇܂𝜏Ȁ𝜈 𝛼Ȃ Ȃ𝑌Ȁ𝜇𝜈
Ȁ
𝑌𝜇𝜈 𝑌𝜇𝜈
Ȁ
𝜏Ȃ 𝛼𝛽 𝑌 𝛼𝛽
Ȃ 𝜏ȀȂ 𝜎 𝜎𝜏Ȁ
𝛾 𝛾
( Ȃ𝜏Ȁ𝜇𝜈
Ȁ 𝜏
𝑞𝜇𝜈
)
܂𝐾𝜇𝜈܂ Ȁ Ȁ
Ȁ Ȁ Ȁ
Ȁ
Ă𝜇𝑖 𝑖 Ā Ȁ
Ȁ Ȁ
Ȁ
Ă𝜇𝑖 Ă𝜇 𝑗 𝜂𝑖 𝑗
∑
𝑖 𝑗
𝜂𝑖 𝑗 Ă𝜇𝑖 Ă𝜈 𝑗
∑
𝑗
Ă𝜇𝑗 Ă𝜈 𝑗 𝑞𝜇𝜈
𝜂𝑖 𝑗 Ȁ Ȁ
Ȁ Ā 𝑖 Ȁ
Ȁ
Ȁ 𝜏Ȁ
Ȁ 𝜏𝜇𝜈
∑
𝑖
Ȁ
𝜏𝑖 Ă𝜇𝑖 Ă𝜈 𝑖
ଏ ଏ 𝜏Ȁ𝑖 Ȁ
Ă𝜇𝑖 Ă𝜈
𝑗 Ȁ
𝜋
𝜙 ܂𝐾𝜇𝜈܂ Ȃ
∑
𝑖 𝑗
Ă𝜇𝑖 Ă𝜈 𝑗
Ȁ
𝜏𝑖 𝜏Ȁ𝑗
Ȁ 𝑌𝑖 𝑗
ଏ 𝑌Ȁ𝑖 𝑗 ȂĂ𝜇𝑖 Ă𝜈 𝑗 𝑌Ȁ𝜇𝜈 Ȁ
Ȁ ଏ
Ā
∑
𝑖 𝑗
Ă𝜇𝑖 Ă𝜈 𝑗
Ȁ
𝜏𝑖 𝜏Ȁ𝑗
Ȁ
𝑌𝑖 𝑗 𝜏ȀȂ 𝜇𝛼 𝑌Ȁ𝛼𝜈
ଏ Ȁ Ȁ
Ā 𝜋
𝜙 ܂𝐾𝜇𝜈܂ Ȃ 𝜏Ȁ
Ȃ 𝛼 𝜇 𝑌𝛼𝜈
Ȁ
𝜏Ȃ 𝛽𝛾 𝑌 𝛽𝛾
Ȃ 𝜏ȀȂ 𝜎 𝜎𝜏Ȁ
𝜌 𝜌
(
𝑞𝜇𝜈 Ȃ
Ȁ 𝜏𝜌
𝜌 𝜏ȀȂ 𝜇𝜈)
Ȃ ∑
𝑖Ȃ 𝑗
Ă𝜇𝑖 Ă𝜈 𝑗
Ȁ
𝜏𝑖 𝜏Ȁ𝑗
𝜛 𝑖 𝑗
Ȁ Ȁ 𝜛 𝑖 𝑗 ȂĂ𝜇𝑖 Ă𝜈 𝑗 𝜛𝜇𝜈 Ȁ
Ȁ ܂𝐾܂ ܂𝜁𝜇𝜈܂
Ȁ
ଏ Ȁ
Ă Ȁ
Ȁ 𝐺𝑖 𝑖 Ȃ̀ 𝐺𝑁 𝜏𝑖 𝜋𝑖 ܂𝜛𝑖 𝑖 ܂ ܂𝐾܂܂𝜁𝑖 𝑖܂
∑
𝑘
𝜋𝑖
(
𝜋 𝜙
) (
𝑤
𝑤 𝜏 𝜏𝑖 Ȃ𝜏𝑖
( ∑
𝑗𝜏𝑗
)
Ȃ 𝑤 𝑤𝑤 𝜏
)
Ȁ
𝐺𝑖 𝑗 ܂𝜛 𝑖 𝑗 ܂ ܂𝐾܂܂𝜁𝑖 𝑗 ܂
∑
𝑘
܂𝜁𝑖𝑘 ܂܂𝜁𝑗 𝑘 ܂
Ă Ā
Ă
Ȁ Ȁ
Ā Ā Ā
ଏ Ȁ Ā
Ȁ ଏ 𝑆
Ā Ȁ Ȁ
ଏ ଏ Ȁ Ā
Ȁ Ȁ Ă
Ȁ
Ȁ
Ā Ȁ
ଏ Ȁ Ā
Ȁ
ଏ Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ā Ȁ
Ā Ā
Ȁ Ȁ
Ȁ Ā
Ȁ
Ă
Ȁ Ȁ Ȁ 𝜆 𝜆
ଏ 𝑤Ȃ Ȁ
Ȁ Ȁ
Ȁ
𝑤Ȃ
Ȁ Ȁ
ଏ Ȁ 𝑤Ȃ
Ȁ Ȁ
ଏ Ȁ Ȁ
Ȁ Ȁ
Ā Ȁ
Ȁ Ȁ
Ȁ
Ā Ā
Ā
Ȁ
ଏ
Ā Ȁ
ଏ Ȁ
Ȁ Ȁ ଏ
Ȁ
Ā Ȁ Ȁ Ȁ Ā
Ā ଏ Ȁ
Ȁ Ȁ
Ȁ
Ā Ȁ
Ȁ Ā
Ȁ Ȁ
Ā ଏ Ā
Ȁ
Ȁ Ȁ
Ā Ȁ Ȁ
Ā Ȁ ଏ Ȁ
Ȁ Ā Ȁ
Ȁ
Ă 𝑆 Ȁ
Ȁ Ā
Ȁ
Ȁ
Ā
Ā ଏ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ă Ȁ
Ȁ Ā
Ȁ Ȁ Ȁ
ଏ Ȁ Ȁ
Ȁ Ā
Ā ଏ Ȁ Ā Ȁ
Ȁ Ȁ
Ă Ȁ Ȁ Ȁ
Ȁ ଏ
ଏ Ȁ
Ȁ ଏ Ā Ȁ
Ā ଏ Ȁ
Ā Ȁ Ā
Ā Ā
Ā
Ȁ Ȁ ଏ
Ā Ȁ
Ȁ ଏ Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
ଏ Ȁ Ȁ
Ȁ ଏ Ȁ
Ȁ Ā Ȁ
Ȁ
Ȁ Ȁ Ȁ ଏ
ଏ Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ
Ā Ȁ
Ȁ Ȁ
Ȁ
Ȁ
Ā Ȁ ଏ
Ȁ
Ȁ
Ā
Ȁ Ȁ Ȁ
Ȁ Ā
Ȁ
Ă
Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ
𝑣𝑡𝑔 𝑟 Ȁ
Ȁ Ā Ȁ 𝑀 𝑟
ଏ Ȁ 𝑀 𝑟 𝑟𝑣𝑡𝑔
𝐺 Ȁ Ā Ȁ
Ȁ
Ā Ȁ Ȁ
Ȁ
𝑣𝑡𝑔Ȃ Ȃ
𝑟 Ȁ
Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ
Ȁ Ȁ
Ȁ Ȁ Ā
Ȁ
Ȁ
Ȁ Ȁ
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Ȁ Ā Ā Ȁ
Ȁ Ȁ ଏ
Ȁ
Ȁ
Ā
Ȁ Ȁ
Ȁ Ȁ
Ȁ
Ā Ā
Ā
Ȁ Ȁ
Ā Ȁ
Ȁ
Ȁ
Ȁ
Ȁ
Ȁ Ā Ȁ
Ȁ Ȁ Ȁ ଏ Ȁ
Ȁ Ā Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ
𝐼 Ă
𝑥 𝐼 ĂĂ 𝑡7Ă𝑥 𝑡
Ȁ 𝑡 ȂĂ Ȁ
Ȁ
𝑥 𝑓 𝑥
𝑥 Ȁ 𝑡 𝑓 𝑥 Ȁ
Ȁ 𝑥 𝑓 Ȁ
𝑡 Ȁ 𝑥 Ȁ 𝐼 𝑥 𝑡Ȁ 𝑓 𝑥 𝑡
𝑡Ȃ𝐼
Ȁ Ā Ȁ
Ȁ Ȁ
Ȁ Ȁ ଏ Ȁ
Ā Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ā 𝑓 ĂĂĂ 𝐶 Ă Ă Ȁ
Ā 𝐶 Ă Ă Ā
𝜑 𝑡 𝑥 𝑥 𝑡
𝜑 𝑥 𝑥
Ȁ 𝜑 𝑡 𝑥 ଏ 𝑥Ȁ 𝑓 𝑥
𝑓 Ȁ 𝐶 Ȁ 𝑡 ଏ 𝜑 𝑡 𝑥
Ă Ā 𝑥 7Ă𝜑 𝑡 𝑥
𝜑 𝑥 𝑥 Ȁ
𝜑 𝑡 𝑠 𝑥 𝜑 𝑡 𝜑 𝑠 𝑥
𝜑 𝑡 𝑥 𝐶 𝑡 𝐶 𝜑 Ȃ𝑡 𝑥
Ă Ȁ
Ȁ 𝐶 Ă Ȁ Ȁ
ଏ Ȁ Ȁ
Ȁ Ă
ଏ Ȁ 𝑥 Ȃ Ă Ā Ā
Ȁ
𝑥 𝑓 𝑥 𝑓 𝑥
𝑓 𝑥 Ȁ 𝑥Ȁ 𝑥 𝑡
𝜑 𝑡 𝑥 𝑥 Ā ଏ 𝜑
𝑓 Ȁ 𝐶 𝑥 Ā
Ȁ
𝑥 𝑓 𝑥 𝑓 𝑥 𝑓 𝑥 Ȃ Ȁ
Ā 𝑥 𝑓 𝑥 𝑓 𝑥
Ȁ ଏ Ȁ Ā
ଏ Ȁ Ā 𝑥 𝑥Ȁ 𝑓 𝑥 Ā
𝑓 𝑥 Ȃ 𝑓 𝑥 Ȁ 𝑥 Ā
Ȁ
Ȁ
Ȁ ଏ Ȁ
𝐼 Ă
𝑥𝑖 Ă ĂĂ
𝑡7Ă𝑥𝑖 𝑡
𝑖 Ȁ 𝐶 𝑡
𝑓𝑖 Ă ĂĂ
𝑥 𝑥 7Ă𝑓𝑖 𝑥 𝑥
𝑖 Ȁ Ȁ
Ȁ
Ȁ
𝑥 𝑓 𝑥 𝑥 Ȁ
𝑥 𝑓 𝑥 𝑥
Ȁ Ȁ ଏ ȂĂ𝑥 𝑥 𝑥
Ȁ
Ȃ
Ă𝑥 𝑥Ȁ 𝑥Ȁ ȂĂ𝑓 𝑓 𝑓 Ȁ
Ȁ
Ȃ
Ă𝑥 ȂĂ𝑓 ȂĂ𝑥
Ȁ
Ȁ
Ȃ
Ă𝑥 ȂĂ𝑓 ȂĂ𝑥 Ȃ
Ă𝑥 𝑡 ȂĂ𝑥
ଏ Ȁ ȂĂ𝑥 Ȃ Ă Ā ȂĂ𝑥Ȁ
Ȃ
Ă𝑓 ȂĂ𝑥 ȂĂ𝑓 ȂĂ𝑥
ଏ Ȁ
ଏ Ȁ
ଏ Ȁ Ā ȂĂ𝑥 Ȁ ȂĂ𝑥Ȁ
Ȃ
Ă𝑓 ȂĂ𝑥 𝜖 𝛿
𝜖 ȂĂ𝑥 ȂȂĂ𝑥 Ȃ ȂĂ𝑥Ȃ Ȃ 𝛿 Ȁ 𝜑 𝑡 ȂĂ𝑥 Ȁ
Ȃ
Ă𝑥 Ȁ 𝜂
𝛿 ȂĂ𝑥 ȂȂĂ𝑥 Ȃ ȂĂ𝑥Ȃ 𝛿 𝑡𝑥 Ȃ𝜑 𝑡𝑥 ȂĂ𝑥 Ȃ ȂĂ𝑥Ȃ 𝜂
ଏ Ȁ Ā ȂĂ𝑥
Ȁ 𝑟 Ȃ𝜑 𝑡 ȂĂ𝑥 Ȃ ȂĂ𝑥Ȃ Ă 𝑡 Ă Ȃ
Ȃ
Ă𝑥 ȂȂĂ𝑥 Ȃ ȂĂ𝑥Ȃ 𝑟
ଏ Ȁ
Ā Ȁ
Ȁ
Ȃ
Ă𝑥 Ȁ ȂĂ𝑓
Ȁ ȂĂ𝑓 𝑓 𝑓 Ȁ 𝐶
𝐷ȂĂ𝑓 ȂĂ𝑥
à Ȃ𝑓 ȂĂ𝑥
Ȃ𝑥
Ȃ𝑓 ȂĂ𝑥 Ȃ𝑥 Ȃ𝑓 ȂĂ𝑥
Ȃ𝑥
Ȃ𝑓 ȂĂ𝑥 Ȃ𝑥
)
Ȃ
Ă𝑓 ȂĂ𝑥
ଏ Ȁ ȂĂ𝑥 Ā ĂȂ𝑥Ȁ ȂĂ𝑓 ȂĂ𝑥 Ȁ Ȁ
Ȁ
Ȃ
Ă𝑥 𝐷ȂĂ𝑓 ȂĂ𝑥 ȂĂ𝑥 Ȁ
Ȁ ȂĂ𝑓 Ā ȂĂ𝑥
Ȃ
Ă𝑓 Ȁ 𝐶
𝐷ȂĂ𝑓 ȂĂ𝑥 Ȁ Ȁ Ā ȂĂ𝑥 Ȁ
Ȁ
Ȃ
Ă𝑥 ȂĂ𝑓 ȂĂ𝑥 Ȃ
Ă𝑓 Ȁ 𝐶
𝐷ȂĂ𝑓 ȂĂ𝑥 Ȁ Ā ȂĂ𝑥 Ȁ
Ȁ
Ȃ
Ă𝑥 ȂĂ𝑓 ȂĂ𝑥
Ā Ȁ
Ā Ȁ
Ȁ Ȁ Ȁ
Ȁ
Ȁ Ā
Ȁ
Ȁ Ȁ
ଏ Ȁ
Ȁ Ȁ
ଏ Ȁ ଏ Ȁ Ȁ
ଏ Ȁ 𝛾 ȂĂ𝑥 𝛾 ȂĂ𝑥
𝛾Ȃ ȂĂ𝑥 ȂĂ𝑥 Ȁ ଏ
Ă 𝑥 𝑥
𝛾 ȂĂ𝑥 ∪
𝑡Ȃ 𝛼 𝛽
𝜑 𝑡 ȂĂ𝑥
𝛾 ȂĂ𝑥 ∪
𝑡Ȃ 𝛽
𝜑 𝑡 ȂĂ𝑥
𝛾Ȃ ȂĂ𝑥 ∪
𝑡Ȃ𝛼
𝜑 𝑡 ȂĂ𝑥
𝛾 ȂĂ𝑥 Ȁ ଏ
Ȃ
Ă𝑥 𝑥 𝑥
ଏ Ȁ Ȁ ȂĂ𝑥Ȁ ȂĂ𝑓 ĂȂ𝑥 ȂĂ𝑥Ȁ ȂĂ𝑔 ȂĂ𝑥
ଏ 𝑈 𝑉 Ă Ȁ
ଏ ȂĂĂ 𝑈 Ă𝑉 ȂĂĂ
Ȃ
Ă𝑓 ȂĂ𝑔 Ȁ
Ȁ
Ȃ
Ă𝑥 Ā
Ȁ
Ȃ
Ă𝑥 ȂĂ𝑓 ȂĂ𝑥 Ȁ ȂĂ𝑥 ȂĂ𝑓
Ȁ
Ȃ
Ă𝑥 𝐷ȂĂ𝑓 ȂĂ𝑥 ȂĂ𝑥
Ȁ
Ā
Ȁ Ȁ
Ȁ
Ȁ
Ȁ
Ȁ
Ā Ȁ
Ȁ Ȁ
Ȁ Ā
Ā
Ā Ȁ Ȁ Ā
Ȁ
Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ
Ȁ
Ȁ Ȁ
ଏ ଏ Ȁ
𝐷 Ȁ
𝑑𝑠 𝐺𝐴𝐵𝑑𝑋𝐴𝑑𝑋𝐵 𝑊 𝑟 𝑔𝛼𝛽𝑑𝑥𝛼𝑑𝑥𝛽 𝑔𝑎𝑏 𝑟 𝑑𝑟𝑎𝑑𝑟𝑏
Ȁ 𝑋𝐴 𝐷
𝑥𝛼 𝑝 Ȁ 𝑟𝑎
𝐷Ȃ𝑝Ȃ Ȁ
𝐷 𝑝 𝑊 𝑟 𝑒Ȃ 𝑘Ȃ𝑟Ȃ
Ȁ 𝑞 𝑝
𝑞Ȃ𝑝 Ȁ Ȁ ଏ
ଏ Ȁ Ā
𝐷
𝑅𝜇𝜈 𝑅𝜇𝜈Ȃ
𝑔𝜇𝜈
𝑝 𝑊𝑝Ȃ Ȃ 𝑊 𝑝
𝑅𝑎𝑏 𝑅Ȁ𝑎𝑏Ȃ
𝑝
𝑊 Ȃ𝑎Ȃ𝑏𝑊 Ȁ
𝑅𝑎𝑏 Ȃ𝑎 Ȃ Ȁ
Ā 𝑔𝑎𝑏
𝑅𝜇𝜈 𝑔𝜇𝜈 Ȁ
𝑅 𝐺𝐴𝐵𝑅
𝐴𝐵 𝑅 𝑔𝜇𝜈𝑅𝜇𝜈 𝑅Ȁ 𝑔𝑎𝑏𝑅Ȁ𝑎𝑏
Ȁ
𝑝
(
𝑊Ȃ 𝑅Ȃ𝑅𝜇𝜇) 𝑝𝑊Ȃ Ȃ𝑊 Ȃ Ȃ𝑊 𝑊Ȃ Ȃ 𝑊
𝑝
(
Ȁ
𝑅Ȃ𝑅𝑎𝑎) 𝑊Ȃ Ȃ 𝑊 𝑅𝜇
𝜇 Ȃ𝑊Ȃ 𝑔𝜇𝜈𝑅𝜇𝜈 𝑅𝑎𝑎 Ȃ𝑔𝑎𝑏𝑅𝑎𝑏 Ȁ 𝑅 𝑅𝜇𝜇 𝑅𝑎𝑎
𝜉 ଏ
Ȃ Ȃ 𝑊𝜉Ȃ𝑊 𝑊𝜉 𝜉𝑊Ȃ Ȃ𝑊 Ȃ Ȃ𝑊 𝑊Ȃ Ȃ 𝑊
Ȁ Ȁ
Ȃ Ȃ 𝑊𝜉Ȃ𝑊 𝑊
𝜉
𝑝 𝑝 𝜉 𝑊
Ȃ 𝑅Ȃ𝑅𝜇
𝜇 𝑝Ȃ𝜉 𝑅ȀȂ𝑅𝑎𝑎
Ȁ
Ȁ Ȁ
Ȁ
Ȁ Ȁ
𝑅𝑀 𝑁 Ȃ 𝐺𝑀 𝑁𝑅
𝜋 𝜙 𝑇𝑀 𝑁
𝑤 𝜙
(
Ȃ𝑀𝜙Ȃ𝑁𝜙Ȃ Ȃ𝐴𝜙Ȃ𝐴𝜙𝐺𝑀 𝑁
)
𝜙
(
Ȃ𝑀Ȃ𝑁𝜙Ȃ
𝜋
𝑤𝑇 𝐺𝑀 𝑁
)
Ȁ Ȁ
𝑅𝑀 𝑁
𝜋 𝜙
(
𝑇𝑀 𝑁
𝑤 𝑇
Ȃ𝐷 𝑤 𝐺𝑀 𝑁
) 𝑤
𝜙 Ȃ𝑀𝜙Ȃ𝑁𝜙 𝜙Ȃ𝑀Ȃ𝑁𝜙 𝑇𝜇
𝜇 Ȃ𝑊Ȃ 𝑔𝜇𝜈𝑇𝜇𝜈 𝑇 𝑇𝜇𝜇 𝑇𝑚𝑚 𝑅𝜇𝜇 𝑅𝑚𝑚
𝑅𝜇𝜇 𝜋
𝜙 𝐷Ȃ 𝑤
(
𝐷 𝑤 𝐷Ȃ𝑝Ȃ Ȃ 𝑝 𝑇𝜇𝜇Ȃ 𝑤 𝑝 𝑇𝑚𝑚) 𝑤𝑊Ȃ
𝜙 Ȃ
𝜈𝜙
Ȃ𝜈𝜙
𝑊Ȃ
𝜙 Ȃ
𝜈
Ȃ𝜈𝜙
𝑅𝑚𝑚 𝜋
𝜙 𝐷Ȃ 𝑤
(
𝐷 𝑤 𝑝Ȃ Ȃ 𝑝Ȃ 𝑇𝑚𝑚Ȃ 𝑤 𝐷Ȃ𝑝Ȃ 𝑇𝜇𝜇) 𝑤
𝜙 Ȃ
𝑚𝜙Ȃ 𝑚𝜙
𝜙Ȃ
𝑚Ȃ 𝑚𝜙
Ȁ
Ȃ Ȃ 𝑊𝜉Ȃ𝑊 𝑊
𝜉
𝑝 𝑝
(
𝜉𝑊Ȃ 𝑅 𝑝Ȃ𝜉 𝑅ȀȂ 𝜋
𝜙 𝐷Ȃ 𝑤
(
𝑇𝜇𝜇 𝜉 𝐷 𝑤 𝐷Ȃ𝑝Ȃ Ȃ 𝑝 Ȃ 𝑝 𝑤 𝐷Ȃ𝑝Ȃ
𝑇𝑚𝑚 𝜉 Ȃ 𝑤𝑝Ȃ𝐷 Ȃ 𝑝 𝑝 𝐷Ȃ 𝑝Ȃ 𝑤 𝑝Ȃ
)
Ȃ 𝜙𝑤 𝜉𝑊Ȃ Ȃ𝜇𝜙Ȃ𝜇𝜙 𝑝Ȃ𝜉 Ȃ𝑚𝜙Ȃ𝑚𝜙 Ȃ
𝜙 𝜉𝑊
Ȃ Ȃ𝜇
Ȃ𝜇𝜙
𝑝Ȃ𝜉 Ȃ𝑚Ȃ𝑚𝜙
)
Ȁ ଏ Ȁ
Ȁ Ȁ ଏ Ȁ
Ȃ𝜇𝜙
∮
ଏ
∮ 𝑊𝜉
𝜙
(
𝑇𝜇𝜇𝜉 𝐷 𝑤 𝐷Ȃ𝑝Ȃ Ȃ 𝑝 Ȃ 𝑝 𝑤 𝐷Ȃ𝑝Ȃ
𝑇𝑚𝑚 𝜉 Ȃ 𝑤𝑝Ȃ𝐷 Ȃ 𝑝 𝑝 𝐷Ȃ 𝑝Ȃ 𝑤 𝑝Ȃ Ȃ( 𝜋 𝜙
)Ȃ
𝐷Ȃ 𝑤
𝜉𝑊Ȃ 𝑅 𝑝Ȃ𝜉 𝑅Ȁ ( 𝜋 𝜙
)Ȃ
𝐷Ȃ 𝑤 (𝑤
𝜙 Ȃ
𝑚𝜙
Ȃ𝑚𝜙
𝜙Ȃ
𝑚
Ȃ𝑚𝜙
))
Ȁ Ā Ȁ Ȁ
Ȁ Ȁ Ȁ
𝑤 Ȃ
Ȁ 𝑤Ă Ȃ 𝜙Ă 𝐺𝑁 Ȁ
Ȁ Ȁ
Ȁ
ଏ ଏ
ଏ
𝑇𝑀 𝑁 Ȃ̀𝐺𝑀 𝑁 Ȃ
∑
𝑖
𝑇𝑞𝑖 𝑃 𝐺𝑀 𝑁 𝑞𝑖 ̀𝐷Ȃ𝑞Ȃ 𝑟Ȃ𝑟𝑖 𝜏𝑀 𝑁
̀ 𝑇𝑞𝑖 Ȁ ̀𝐷Ȃ𝑞Ȃ 𝑟Ȃ𝑟𝑖
Ȁ Ȁ
𝑃 𝐺𝑀 𝑁 𝑞𝑖 Ȁ
𝜏𝑀 𝑁 Ȁ
𝑇𝜇𝜇 Ȃ 𝑝 ̀ 𝜏𝜇𝜇Ȃ∑
𝑖
𝑇𝑞𝑖 ̀𝐷Ȃ𝑞Ȃ 𝑟Ȃ𝑟𝑖 𝑝
𝑇𝑚𝑚 Ȃ 𝐷Ȃ𝑝Ȃ ̀ 𝜏𝑚𝑚Ȃ∑
𝑖
𝑇𝑞𝑖 ̀𝐷Ȃ𝑞Ȃ 𝑟Ȃ𝑟𝑖 𝑞Ȃ𝑝
Ȁ
Ȁ Ȁ
∮ 𝑊𝜉
𝜙
(
Ȃ̀ 𝑐 𝑝 𝑏𝐷 Ȃ∑
𝑖
𝑐𝑝 𝑎 𝑏𝑞 𝑇𝑞𝑖 ̀𝐷Ȃ𝑞Ȃ 𝑟Ȃ𝑟𝑖 𝑎𝑇𝜇𝜇 𝑏𝑇𝑚𝑚
Ȃ ( 𝜋
𝜙
)Ȃ
𝐷Ȃ 𝑤 𝜉𝑊Ȃ 𝑅 𝑝Ȃ𝜉 𝑅Ȁ ( 𝜋 𝜙
)Ȃ
𝐷Ȃ 𝑤
(𝑤
𝜙 Ȃ
𝑚𝜙
Ȃ𝑚𝜙
𝜙Ȃ
𝑚
Ȃ𝑚𝜙
))
ଏ 𝑎 Ȃ 𝜉 𝐷 𝑤 𝐷 Ȃ𝑝Ȃ Ȃ 𝑝 Ȃ 𝑝 𝑤 𝐷Ȃ𝑝Ȃ
𝑏Ȃ𝜉Ȃ 𝑤𝑝Ȃ𝐷 Ȃ 𝑝 𝑝 𝐷Ȃ 𝑝Ȃ 𝑤 𝑝Ȃ 𝑐Ȃ𝑎Ȃ𝑏
Ȁ Ȁ Ȁ
ଏ Ȁ
𝜙 𝑤 𝐶 𝑟 𝐶 𝑤
𝐶 𝐶 Ȁ Ȁ
Ȁ Ȁ
Ȁ Ā
ଏ Ȁ Ȁ
Ȁ Ȁ Ā 𝜙
Ā ଏ Ȁ
Ȁ
Ȁ Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ
Ȁ Ȁ Ȁ Ā
Ȁ
𝐷 𝑝 𝑞
Ȁ 𝐷 𝑝
𝑞 𝑎 𝜉 𝑤 Ȃ 𝑤 𝑏 Ȃ 𝜉 𝑤 𝑤 𝑐
𝜉 𝑤 Ȃ 𝑤 Ȁ
∮ 𝑊𝜉
𝜙
(
Ȃ ̀ 𝜉Ȃ𝑤 𝜉 Ȃ Ȃ ∑
𝑖
𝜉 𝑤 𝜉Ȃ Ȃ 𝑇 𝑖 ̀ 𝑟Ȃ𝑟𝑖
𝜏𝜇𝜇𝜉 𝑤 Ȃ 𝑤 𝜏𝑚𝑚 Ȃ 𝜉 𝑤 𝑤 Ȃ 𝑤
( 𝜋
𝜙
)Ȃ
𝜉𝑊Ȃ 𝑅 Ȃ𝜉 𝑅Ȁ 𝑤 Ȃ𝜉 ( 𝜋 𝜙
)Ȃ (𝑤
𝜙 Ȃ
𝑚𝜙
Ȃ𝑚𝜙
𝜙Ȃ
𝑚
Ȃ𝑚𝜙
))
Ȁ Ȁ
Ȁ 𝜏𝜇𝜇 𝜏𝑚𝑚
Ȁ Ȁ Ā
̀ Ȁ
Ȁ ̀ 𝜉
Ȁ Ȁ Ā Ȁ
Ȁ Ȁ Ȁ 𝜉 Ȃ
Ȁ
∮ (
𝑤 𝜙 Ȃ
𝑚𝜙Ȃ 𝑚𝜙
𝜙Ȃ
𝑚Ȃ
𝑚𝜙Ȃ 𝑅Ȁ 𝑊Ȃ 𝑅
)
Ȃ 𝜋 𝑤
𝑤
∑
𝑖
𝑇 𝑖
∮ ̀ 𝑟 Ȃ𝑟𝑖
𝜙
𝜒 𝜋 ∮ Ȁ
𝑅 𝜒 Āଏ Ȁ Ȁ Ȁ ∮ ( 𝑤 𝜙 Ȃ 𝑚𝜙
Ȃ𝑚𝜙
𝜙Ȃ
𝑚
Ȃ𝑚𝜙
𝑊Ȃ
𝑅
)
𝜋𝜒
Ȃ 𝜋 𝑤
𝑤
∑
𝑖
𝑇 𝑖 𝐿𝑖𝜙Ȃ 𝑟𝑖
𝐿𝑖 Ȁ 𝑆 Ȁ ଏ
𝜙 𝑟𝑖 Ȁ 𝑟𝑖
Ȁ ଏ Ā
Ā Ȁ Ȁ
Ȁ 𝑤
Ȁ
Ȁ 𝜉
ଏ Ȁ 𝜉 ଏ
𝑤 𝜋
∮
𝑊 𝑅 𝑤Ȃ ∑
𝑖
𝑇 𝑖 𝑊 𝑟𝑖 𝜙Ȃ 𝑟𝑖 𝐿𝑖
Ȁ Ȁ Ȁ
Ȁ Ā
Ȁ 𝜒 Ȁ
Ȁ
Ȁ
Ā Ȁ
ଏ Ȁ Ȁ
Ȁ Ȁ Ȁ Ȁ
Ȁ
Ā Ȁ
Ȁ Ȁ
Ȁ
ଏ
ଏ
Ȁ
Ȁ ଏ
Ȁ ଏ
ଏ Ȁ
ଏ
Ȁ ଏ
Ȁ ଏ Ȁ
Ȁ
Ȁ
Ȁ Ȁ
