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pr s s t s r s r s

Prs s t sr s - PowerPoint PPT Presentation

Dec 05, 2023 •228 likes •1.57k views

t str ss r ts qsts rt rst Prs s

  1. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❞✐s❝♊✈❡r② ♊❢ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ❚❀❡ s✐♠♣❧❡st r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛✈❡ ❜❡❡♥ ❊♥♊✇♥ ❢♊r❡✈❡r ✭ ❄✮ ✿ t❀❡ t❡tr❛❀❡❞r♊♥✱ ❝✉❜❡✱ ♩❝t❛❀❡❞r♊♥✳ ❆❝❝♩r❞✐♥❣ t♩ ❧❛t❡r s♩✉r❝❡s✱ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✇❛s ❞✐s❝♊✈❡r❡❞ ❜② ❛ P②t❀❛❣♊r❡❛♥ ♣❀✐❧♊s♊♣❀❡r✱ ❍✐♣♣❛s✉s ♊❢ ▌❡t❛♣♊♥t✉♠✱ ❜♩r♥ ❛♣♣r♊①✳ ✺✵✵❜❝✳ ❍❡ ✐s ❛❧s♩ ❝r❡❞✐t❡❞ ✇✐t❀ t❀❡ ❞✐s❝♊✈❡r② ♊❢ ✐rr❛t✐♊♥❛❧ ♥✉♠❜❡rs✳ ❆❝❝♩r❞✐♥❣ t♩ ■❛♠❜❧✐❝❀✉s✱ ❍✐♣♣❛s✉s ✇❛s ❛❧s♩ t❀❡ ✜rst t♩ ❞r❛✇ ♩r ❝♊♥str✉❝t t❀❡ ✬s♣❀❡r❡ ❝♊♥s✐st✐♥❣ ♊❢ ✶✷ r❡❣✉❧❛r ♣❡♥t❛❣♊♥s✬ ❬✳✳✳❪ ❛♥❞ t♩ ♠❛❊❡ t❀✐s ❝♊♥str✉❝t✐♊♥ ♣✉❜❧✐❝✱ ✇❀✐❝❀ ✇❛s ❝♊♥s✐❞❡r❡❞ ❛ ❝r✐♠✐♥❛❧ ❞✐✈✉❧❣❛t✐♊♥ ♊❢ P②t❀❛❣♊r❡❛♥ s❡❝r❡t ❊♥♊✇❧❡❞❣❡✳ ❚❀❡ ❞✐s❝♊✈❡r② ♊❢ ✐♥❝♊♠♠❡♥s✉r❛❜✐❧✐t② ❜② ❍✐♣♣❛s✉s ♊❢ ▌❡t❛♣♊♥t✉♠✱ ❑✉rt ✈♊♥ ❋r✐t③✱ ❆♥♥❛❧s ♊❢ ▌❛t❀✳ ✹✻ ✿✷ ✭✶✟✹✺✮ ♣♣✳ ✷✹✷✲✷✻✹✳ ❍✐♣♣❛s✉s ✐s s❛✐❞ t♩ ❀❛✈❡ ❜❡❡♥ ❞r♊✇♥❡❞ ❢♊r t❀✐s ✏♣✉❜❧✐❝❛t✐♊♥✑✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  2. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  3. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  4. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  5. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  6. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  7. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  8. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  9. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  10. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ✜rst ❝❧❛ss✐✜❝❛t✐♊♥ ❖♥❝❡ t❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ ✐s ❊♥♊✇♥✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥ ✐s ♩❜t❛✐♥❡❞ ❜② ❞✉❛❧✐t②✳ ❚❀❡ ✜♥❛❧ r❡s✉❧t ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✐s t❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ r❡❣✉❧❛r ♣♊❧②❀❡❞r❛✳ ❘❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❀❛❞ ❛ ❀✉❣❡ ✐♥✢✉❡♥❝❡ ♊♥ ❣r❡❡❊ ♣❀✐❧♊s♊♣❀②✳ ❆❝❝♩r❞✐♥❣ t♩ P❧❛t♩ ✭✹✷✌✲✞✹✌ ❇❈✮✱ t❀❡② ✇❡r❡ ✐♥ r❡❧❛t✐♊♥ t♩ t❀❡ ❢♊✉r ❡❧❡♠❡♥ts ✿ t❀❡ ❝✉❜❡✱ ✇✐t❀ t❀❡ ❡❛rt❀✱ t❀❡ t❡tr❛❀❡❞r♊♥✱ ✇✐t❀ ✜r❡✱ t❀❡ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ❛✐r✱ t❀❡ ✐❝♩s❛❀❡❞r♊♥✱ ✇✐t❀ ✇❛t❡r✳ ❚❀❡ ❞♊❞❡❝❛❀❡❞r♊♥ s❡r✈❡s ❢♊r t❀❡ ✏✜♥❛❧ ❛rr❛♥❣✲ ♠❡♥t ♊❢ t❀❡ ✉♥✐✈❡rs❡✑ ✭ ❄ ❄✮ ✭❚✐♠❡✉s✮ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  11. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❚❀❡ ❝❧❛ss✐✜❝❛✲ t✐♊♥ ✇❛s ❡①t❡♥❞❡❞ ❜② ❆r❝❀✐♠❡❞❡s ✭✷✜✌✲✷✶✷ ❇❈✮ t♩ s❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ✿ ✷ ✐♥✜♥✐t❡ ❢❛♠✐❧✐❡s✱ t❀❡ ♣r✐s♠s ❛♥❞ ❛♥t✐✲♣r✐s♠s✱ ❛♥❞ ✶✞ ✏s♣♊r❛❞✐❝✑ ♣♊❧②❀❡❞r❛✳ ❍♊✇❡✈❡r ❀✐s ✇♩r❊ ✇❛s ❧♩st✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  12. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❚❀❡ ❝❧❛ss✐✜❝❛✲ t✐♊♥ ✇❛s ❡①t❡♥❞❡❞ ❜② ❆r❝❀✐♠❡❞❡s ✭✷✜✌✲✷✶✷ ❇❈✮ t♩ s❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ✿ ✷ ✐♥✜♥✐t❡ ❢❛♠✐❧✐❡s✱ t❀❡ ♣r✐s♠s ❛♥❞ ❛♥t✐✲♣r✐s♠s✱ ❛♥❞ ✶✞ ✏s♣♊r❛❞✐❝✑ ♣♊❧②❀❡❞r❛✳ ❍♊✇❡✈❡r ❀✐s ✇♩r❊ ✇❛s ❧♩st✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  13. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❚❀❡ ❝❧❛ss✐✜❝❛✲ t✐♊♥ ✇❛s ❡①t❡♥❞❡❞ ❜② ❆r❝❀✐♠❡❞❡s ✭✷✜✌✲✷✶✷ ❇❈✮ t♩ s❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ✿ ✷ ✐♥✜♥✐t❡ ❢❛♠✐❧✐❡s✱ t❀❡ ♣r✐s♠s ❛♥❞ ❛♥t✐✲♣r✐s♠s✱ ❛♥❞ ✶✞ ✏s♣♊r❛❞✐❝✑ ♣♊❧②❀❡❞r❛✳ ❍♊✇❡✈❡r ❀✐s ✇♩r❊ ✇❛s ❧♩st✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  14. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ❚❀❡ ❝❧❛ss✐✜❝❛✲ t✐♊♥ ✇❛s ❡①t❡♥❞❡❞ ❜② ❆r❝❀✐♠❡❞❡s ✭✷✜✌✲✷✶✷ ❇❈✮ t♩ s❡♠✐✲r❡❣✉❧❛r ♣♊❧②❀❡❞r❛ ✿ ✷ ✐♥✜♥✐t❡ ❢❛♠✐❧✐❡s✱ t❀❡ ♣r✐s♠s ❛♥❞ ❛♥t✐✲♣r✐s♠s✱ ❛♥❞ ✶✞ ✏s♣♊r❛❞✐❝✑ ♣♊❧②❀❡❞r❛✳ ❍♊✇❡✈❡r ❀✐s ✇♩r❊ ✇❛s ❧♩st✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  15. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  16. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  17. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  18. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  19. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  20. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  21. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  22. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t P❛✐♥t❡rs ❛♥❞ ♣♊❧②❀❡❞r❛ ❆ str♊♥❣ ✐♥t❡r❡st ❢♊r ♣♊❧②❀❡❞r❛ ❛♣♣❡❛rs ❞✉r✐♥❣ t❀❡ ❘❡♥❛✐ss❛♥❝❡✱ ✇✐t❀ ♣❛✐♥t❡rs ❧✐❊❡ ❆❧❜r❡❝❀t ❉Ìr❡r ✭✶✹✌✶✲✶✺✷✜✮✳ ❚❀❡② ♊❢t❡♥ ❛♣♣❡❛r ✐♥ ❞r❛✇✐♥❣s ❛♥❞ ❛r❝❀✐✲ t❡❝t✉r❛❧ ♠♩t✐✈❡s✱ ❢♊r ✐♥st❛♥❝❡ ✐♥ t❀❡ ✇♩r❊ ♊❢ ▲✉❝❛ P❛❝✐♩❧✐ ✭✶✹✹✺✲✶✺✶✌✮✱ ✐❧❧✉str❛t❡❞ ❜② ▲❡♊♥❛r❞♩ ❞❛ ❱✐♥❝✐✳ ❉Ìr❡r ❛❧s♩ ✐♥tr♊❞✉❝❡s ❛ ♥❡✇ ❞❡s❝r✐♣t✐♊♥ ♊❢ ♣♊❧②❀❡❞r❛✱ ✐♥ ❛ ✢❛t ❢♊r♠✳ ❚❀❡ ❆r❝❀✐✲ ♠❡❞❡❛♥ ♣♊❧②❀❡❞r❛ ❛r❡ r❡✲❞✐s❝♊✈❡r❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  23. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  24. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  25. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  26. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  27. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  28. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  29. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  30. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❑❡♣❧❡r ❛♥❞ t❀❡ ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❏♊❀❛♥♥❡s ❑❡♣❧❡r ✭✶✺✌✶✲✶✻✞✵✮ ✇❛s ❢❛s❝✐✲ ♥❛t❡❞ ❜② ❣r❡❡❊ ♠❛t❀❡♠❛t✐❝s ✭♣♊❧②❀❡❞r❛ ❛♥❞ ❝♊♥✐❝s✮✳ ❑❡♣❧❡r ✜rst r❡❝♊✈❡rs ❆r❝❀✐✲ ♠❡❞❡s✬ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ s❡♠✐✲r❡❣✉❧❛r ♣♊✲ ❧②❀❡❞r❛✳ ❍❡ t❀❡♥ r❡❛❧✐③❡s t❀❛t ❊✉❝❧✐❞ ♊♥❧② ❝♊♥s✐❞❡rs✱ ✐♠♣❧✐❝✐t❧②✱ ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✱ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♥❡✇✱ ♥♊♥✲❝♊♥✈❡① r❡❣✉✲ ❧❛r ♣♊❧②❀❡❞r❛✳ ❚❀❡ ❧✐st ✇✐❧❧ ❜❡ ❝♊♠♣❧❡t❡❞ ❜② P♊✐♥s♩t ✭✶✌✌✌✲✶✜✺✟✮✱ ✇❀♊ r❡❝♊✈❡rs ❑❡♣❧❡r✬s t✇♩ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐s❝♊✈❡rs t✇♩ ♩t❀❡r ♊♥❡s✳ ❚❀❡ ❝❧❛ss✐✜❝❛t✐♊♥ ♊❢ ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✐s ✜♥✐s❀❡❞✱ t♩ ♠✐❧❧❡♥✐❛ ❛❢t❡r ❊✉❝❧✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  31. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ ❆♥♊t❀❡r ❜r❛♥❝❀ ♊❢ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊✲ ❧②❀❡❞r❛ ❛♣♣❡❛rs ✇❀❡♥ ▲❡❣❡♥❞r❡ r❡❛❞s ❛ ✭❜❛❞✮ tr❛♥s❧❛t✐♊♥ ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✳ ▲❡❣❡♥❞r❡ ❞✐s❝♊✈❡rs t❀❛t t✇♩ ♣♊❧②❀❡❞r❛ ✇✐t❀ ✐s♊♠❡tr✐❝ ❝♩rr❡s♣♊♥❞✐♥❣ ❢❛❝❡s ❛r❡ ❝♊♥❣r✉❡♥t✳ ❚❀❡ ♣r♊♊❢ ✐s ✇r✐tt❡♥ ♊♥❧② ✐♥ ✶✜✶✞ ❜② ❈❛✉❝❀② ✭✶✌✜✟✲✶✜✺✌✮✱ ✇✐t❀ t✇♩ ❣❛♣s✳ ❆♣♣❧✐❝❛t✐♊♥s ✿ r✐❣✐❞✐t② ♊❢ ❝♊♥✈❡① s✉r❢❛❝❡s✱ ❆❧❡①❛♥❞r♩✈ r✐❣✐❞✐t②✱ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ ❢♊r s♠♩♩t❀ ❛♥❞ ♣♊❧②❀❡❞r❛❧ ♠❡tr✐❝s✳✳✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  32. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ ❆♥♊t❀❡r ❜r❛♥❝❀ ♊❢ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊✲ ❧②❀❡❞r❛ ❛♣♣❡❛rs ✇❀❡♥ ▲❡❣❡♥❞r❡ r❡❛❞s ❛ ✭❜❛❞✮ tr❛♥s❧❛t✐♊♥ ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✳ ▲❡❣❡♥❞r❡ ❞✐s❝♊✈❡rs t❀❛t t✇♩ ♣♊❧②❀❡❞r❛ ✇✐t❀ ✐s♊♠❡tr✐❝ ❝♩rr❡s♣♊♥❞✐♥❣ ❢❛❝❡s ❛r❡ ❝♊♥❣r✉❡♥t✳ ❚❀❡ ♣r♊♊❢ ✐s ✇r✐tt❡♥ ♊♥❧② ✐♥ ✶✜✶✞ ❜② ❈❛✉❝❀② ✭✶✌✜✟✲✶✜✺✌✮✱ ✇✐t❀ t✇♩ ❣❛♣s✳ ❆♣♣❧✐❝❛t✐♊♥s ✿ r✐❣✐❞✐t② ♊❢ ❝♊♥✈❡① s✉r❢❛❝❡s✱ ❆❧❡①❛♥❞r♩✈ r✐❣✐❞✐t②✱ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ ❢♊r s♠♩♩t❀ ❛♥❞ ♣♊❧②❀❡❞r❛❧ ♠❡tr✐❝s✳✳✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  33. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ ❆♥♊t❀❡r ❜r❛♥❝❀ ♊❢ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊✲ ❧②❀❡❞r❛ ❛♣♣❡❛rs ✇❀❡♥ ▲❡❣❡♥❞r❡ r❡❛❞s ❛ ✭❜❛❞✮ tr❛♥s❧❛t✐♊♥ ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✳ ▲❡❣❡♥❞r❡ ❞✐s❝♊✈❡rs t❀❛t t✇♩ ♣♊❧②❀❡❞r❛ ✇✐t❀ ✐s♊♠❡tr✐❝ ❝♩rr❡s♣♊♥❞✐♥❣ ❢❛❝❡s ❛r❡ ❝♊♥❣r✉❡♥t✳ ❚❀❡ ♣r♊♊❢ ✐s ✇r✐tt❡♥ ♊♥❧② ✐♥ ✶✜✶✞ ❜② ❈❛✉❝❀② ✭✶✌✜✟✲✶✜✺✌✮✱ ✇✐t❀ t✇♩ ❣❛♣s✳ ❆♣♣❧✐❝❛t✐♊♥s ✿ r✐❣✐❞✐t② ♊❢ ❝♊♥✈❡① s✉r❢❛❝❡s✱ ❆❧❡①❛♥❞r♩✈ r✐❣✐❞✐t②✱ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ ❢♊r s♠♩♩t❀ ❛♥❞ ♣♊❧②❀❡❞r❛❧ ♠❡tr✐❝s✳✳✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  34. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ ❆♥♊t❀❡r ❜r❛♥❝❀ ♊❢ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊✲ ❧②❀❡❞r❛ ❛♣♣❡❛rs ✇❀❡♥ ▲❡❣❡♥❞r❡ r❡❛❞s ❛ ✭❜❛❞✮ tr❛♥s❧❛t✐♊♥ ♊❢ ❊✉❝❧✐❞✬s ❊❧❡♠❡♥ts ✳ ▲❡❣❡♥❞r❡ ❞✐s❝♊✈❡rs t❀❛t t✇♩ ♣♊❧②❀❡❞r❛ ✇✐t❀ ✐s♊♠❡tr✐❝ ❝♩rr❡s♣♊♥❞✐♥❣ ❢❛❝❡s ❛r❡ ❝♊♥❣r✉❡♥t✳ ❚❀❡ ♣r♊♊❢ ✐s ✇r✐tt❡♥ ♊♥❧② ✐♥ ✶✜✶✞ ❜② ❈❛✉❝❀② ✭✶✌✜✟✲✶✜✺✌✮✱ ✇✐t❀ t✇♩ ❣❛♣s✳ ❆♣♣❧✐❝❛t✐♊♥s ✿ r✐❣✐❞✐t② ♊❢ ❝♊♥✈❡① s✉r❢❛❝❡s✱ ❆❧❡①❛♥❞r♩✈ r✐❣✐❞✐t②✱ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ ❢♊r s♠♩♩t❀ ❛♥❞ ♣♊❧②❀❡❞r❛❧ ♠❡tr✐❝s✳✳✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  35. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ■♥✜♥✐t❡s✐♠❛❧ r✐❣✐❞✐t② ❆ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞ ✐❢ ✐♥❢✳ ❞❡❢♊r♠❛✲ t✐♊♥s ❧❡❛❞ t♩ ✐♥❢✳ ✈❛r✐❛t✐♊♥ ♊❢ t❀❡ ✏s❀❛✲ ♣❡s✑ ♊❢ t❀❡ ❢❛❝❡s✳ ■♠♣♊rt❛♥t ❢♊r ❡♥❣✐✲ ♥❡❡rs✮❛r❝❀✐t❡❝ts✳ ❉❡❀♥ ✭✶✟✶✻✮ ♣r♊✈❡s t❀❛t ❝♊♥✈❡① ♣♊❧②❀❡✲ ❞r❛ ❛r❡ ✐♥❢✳ r✐❣✐❞✳ ❆ ♥❡✇ q✉❡st✐♊♥ ❝❛♠❡ ✉♣ ✿ ✇❀❛t ❛❜♩✉t ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❄ ❚❀❡② ❝❛♥ ❜❡ ✐♥❢✳ ✢❡①✐❜❧❡ ❛♥❞ ❡✈❡♥ ✢❡①✐❜❧❡ ✭❈♊♥♥❡❧❧② ✶✟✌✜✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  36. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ■♥✜♥✐t❡s✐♠❛❧ r✐❣✐❞✐t② ❆ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞ ✐❢ ✐♥❢✳ ❞❡❢♊r♠❛✲ t✐♊♥s ❧❡❛❞ t♩ ✐♥❢✳ ✈❛r✐❛t✐♊♥ ♊❢ t❀❡ ✏s❀❛✲ ♣❡s✑ ♊❢ t❀❡ ❢❛❝❡s✳ ■♠♣♊rt❛♥t ❢♊r ❡♥❣✐✲ ♥❡❡rs✮❛r❝❀✐t❡❝ts✳ ❉❡❀♥ ✭✶✟✶✻✮ ♣r♊✈❡s t❀❛t ❝♊♥✈❡① ♣♊❧②❀❡✲ ❞r❛ ❛r❡ ✐♥❢✳ r✐❣✐❞✳ ❆ ♥❡✇ q✉❡st✐♊♥ ❝❛♠❡ ✉♣ ✿ ✇❀❛t ❛❜♩✉t ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❄ ❚❀❡② ❝❛♥ ❜❡ ✐♥❢✳ ✢❡①✐❜❧❡ ❛♥❞ ❡✈❡♥ ✢❡①✐❜❧❡ ✭❈♊♥♥❡❧❧② ✶✟✌✜✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  37. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ■♥✜♥✐t❡s✐♠❛❧ r✐❣✐❞✐t② ❆ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞ ✐❢ ✐♥❢✳ ❞❡❢♊r♠❛✲ t✐♊♥s ❧❡❛❞ t♩ ✐♥❢✳ ✈❛r✐❛t✐♊♥ ♊❢ t❀❡ ✏s❀❛✲ ♣❡s✑ ♊❢ t❀❡ ❢❛❝❡s✳ ■♠♣♊rt❛♥t ❢♊r ❡♥❣✐✲ ♥❡❡rs✮❛r❝❀✐t❡❝ts✳ ❉❡❀♥ ✭✶✟✶✻✮ ♣r♊✈❡s t❀❛t ❝♊♥✈❡① ♣♊❧②❀❡✲ ❞r❛ ❛r❡ ✐♥❢✳ r✐❣✐❞✳ ❆ ♥❡✇ q✉❡st✐♊♥ ❝❛♠❡ ✉♣ ✿ ✇❀❛t ❛❜♩✉t ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❄ ❚❀❡② ❝❛♥ ❜❡ ✐♥❢✳ ✢❡①✐❜❧❡ ❛♥❞ ❡✈❡♥ ✢❡①✐❜❧❡ ✭❈♊♥♥❡❧❧② ✶✟✌✜✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  38. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ■♥✜♥✐t❡s✐♠❛❧ r✐❣✐❞✐t② ❆ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞ ✐❢ ✐♥❢✳ ❞❡❢♊r♠❛✲ t✐♊♥s ❧❡❛❞ t♩ ✐♥❢✳ ✈❛r✐❛t✐♊♥ ♊❢ t❀❡ ✏s❀❛✲ ♣❡s✑ ♊❢ t❀❡ ❢❛❝❡s✳ ■♠♣♊rt❛♥t ❢♊r ❡♥❣✐✲ ♥❡❡rs✮❛r❝❀✐t❡❝ts✳ ❉❡❀♥ ✭✶✟✶✻✮ ♣r♊✈❡s t❀❛t ❝♊♥✈❡① ♣♊❧②❀❡✲ ❞r❛ ❛r❡ ✐♥❢✳ r✐❣✐❞✳ ❆ ♥❡✇ q✉❡st✐♊♥ ❝❛♠❡ ✉♣ ✿ ✇❀❛t ❛❜♩✉t ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❄ ❚❀❡② ❝❛♥ ❜❡ ✐♥❢✳ ✢❡①✐❜❧❡ ❛♥❞ ❡✈❡♥ ✢❡①✐❜❧❡ ✭❈♊♥♥❡❧❧② ✶✟✌✜✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  39. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ■♥✜♥✐t❡s✐♠❛❧ r✐❣✐❞✐t② ❆ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞ ✐❢ ✐♥❢✳ ❞❡❢♊r♠❛✲ t✐♊♥s ❧❡❛❞ t♩ ✐♥❢✳ ✈❛r✐❛t✐♊♥ ♊❢ t❀❡ ✏s❀❛✲ ♣❡s✑ ♊❢ t❀❡ ❢❛❝❡s✳ ■♠♣♊rt❛♥t ❢♊r ❡♥❣✐✲ ♥❡❡rs✮❛r❝❀✐t❡❝ts✳ ❉❡❀♥ ✭✶✟✶✻✮ ♣r♊✈❡s t❀❛t ❝♊♥✈❡① ♣♊❧②❀❡✲ ❞r❛ ❛r❡ ✐♥❢✳ r✐❣✐❞✳ ❆ ♥❡✇ q✉❡st✐♊♥ ❝❛♠❡ ✉♣ ✿ ✇❀❛t ❛❜♩✉t ♥♊♥✲❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❄ ❚❀❡② ❝❛♥ ❜❡ ✐♥❢✳ ✢❡①✐❜❧❡ ❛♥❞ ❡✈❡♥ ✢❡①✐❜❧❡ ✭❈♊♥♥❡❧❧② ✶✟✌✜✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  40. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❍②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ◗✉❡st✐♊♥s ♊♥ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊❧②❀❡❞r❛ ❝❛♥ ❜❡ ❝♊♥s✐❞❡r❡❞ ✐♥ t❀❡ ❀②♣❡r❜♩❧✐❝✮s♣❀❡r✐❝❛❧ ❝♊♥t❡①t✳ ❚❀❡ ✐♥❢✳ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ t✉r♥s ♩✉t t♩ ❜❡ ❛ ♣r♊❥❡❝t✐✈❡ ♣r♊♣❡rt② ✭❉❛r❜♊✉①✱ ❙❛✉❡r✮✱ ✐♥❞❡♣❡♥❞❡♥t ♊❢ t❀❡ ❣❡♊♠❡tr② ✭P♊❣♊r❡❧♊✈✮✳ ❋♩r ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ ♠♩r❡ ✐♠♣♊rt❛♥t t❀❛♥ ❡❞❣❡ ❧❡♥❣t❀s✱ ❞✉❡ t♩ P♊✐♥❝❛ré✬s t❀❡♊r❡♠ ✿ t❀❡ ❣r♊✉♣ ❣❡♥❡r❛t❡❞ ❜② r❡✢❡❝t✐♊♥s ✐♥ t❀❡ ❢❛❝❡s ✐s ❞✐s❝r❡t❡ ✐✛ t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ π/ ❊ ✳ ❆♥❞r❡❡✈ ✭✶✟✌✵✮ ❝❀❛r❛❝t❡r✐③❡❞ t❀❡ ♣♊ss✐❜❧❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ✭ < π/ ✷ ) ♊❢ ✜♥✐t❡ ✈♊❧✉♠❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛✳ ❘✐✈✐♥ ❛♥❞ ❍♊❞❣s♊♥ ✭✶✟✟✹✮ s❀♊✇❡❞ t❀❛t t❀✐s ✐s ❛ ❝♊♥s❡q✉❡♥❝❡ ♊❢ ❛♥ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ t❀❡♊r❡♠ ✐♥ ❛ s♣❛❝❡ ✏❞✉❛❧✑ t♩ t❀❡ ❀②♣❡r❜♩❧✐❝ s♣❛❝❡ ✭❈❛✉❝❀②✬s t❀♠ ✐s ✐♠♣♊rt❛♥t✮✳ ❙♣❛❝❡s ♩❜t❛✐♥❡❞ ❢r♩♠ ♣♊❧②❀❡❞r❛ ❝❛♥ ❡✈❡♥ ❜❡ ❢♊✉♥❞ ✐♥ t❀❡ r❡❛❧ ✇♩r❧❞✳ ❋♩r ✐♥st❛♥❝❡ t❀❡ ✉♥✐✈❡rs❡ ♠✐❣❀t ❜❡ ❛ ❞♊❞❡❝❛❀❡❞r❛❧ s♣❛❝❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  41. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❍②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ◗✉❡st✐♊♥s ♊♥ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊❧②❀❡❞r❛ ❝❛♥ ❜❡ ❝♊♥s✐❞❡r❡❞ ✐♥ t❀❡ ❀②♣❡r❜♩❧✐❝✮s♣❀❡r✐❝❛❧ ❝♊♥t❡①t✳ ❚❀❡ ✐♥❢✳ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ t✉r♥s ♩✉t t♩ ❜❡ ❛ ♣r♊❥❡❝t✐✈❡ ♣r♊♣❡rt② ✭❉❛r❜♊✉①✱ ❙❛✉❡r✮✱ ✐♥❞❡♣❡♥❞❡♥t ♊❢ t❀❡ ❣❡♊♠❡tr② ✭P♊❣♊r❡❧♊✈✮✳ ❋♩r ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ ♠♩r❡ ✐♠♣♊rt❛♥t t❀❛♥ ❡❞❣❡ ❧❡♥❣t❀s✱ ❞✉❡ t♩ P♊✐♥❝❛ré✬s t❀❡♊r❡♠ ✿ t❀❡ ❣r♊✉♣ ❣❡♥❡r❛t❡❞ ❜② r❡✢❡❝t✐♊♥s ✐♥ t❀❡ ❢❛❝❡s ✐s ❞✐s❝r❡t❡ ✐✛ t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ π/ ❊ ✳ ❆♥❞r❡❡✈ ✭✶✟✌✵✮ ❝❀❛r❛❝t❡r✐③❡❞ t❀❡ ♣♊ss✐❜❧❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ✭ < π/ ✷ ) ♊❢ ✜♥✐t❡ ✈♊❧✉♠❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛✳ ❘✐✈✐♥ ❛♥❞ ❍♊❞❣s♊♥ ✭✶✟✟✹✮ s❀♊✇❡❞ t❀❛t t❀✐s ✐s ❛ ❝♊♥s❡q✉❡♥❝❡ ♊❢ ❛♥ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ t❀❡♊r❡♠ ✐♥ ❛ s♣❛❝❡ ✏❞✉❛❧✑ t♩ t❀❡ ❀②♣❡r❜♩❧✐❝ s♣❛❝❡ ✭❈❛✉❝❀②✬s t❀♠ ✐s ✐♠♣♊rt❛♥t✮✳ ❙♣❛❝❡s ♩❜t❛✐♥❡❞ ❢r♩♠ ♣♊❧②❀❡❞r❛ ❝❛♥ ❡✈❡♥ ❜❡ ❢♊✉♥❞ ✐♥ t❀❡ r❡❛❧ ✇♩r❧❞✳ ❋♩r ✐♥st❛♥❝❡ t❀❡ ✉♥✐✈❡rs❡ ♠✐❣❀t ❜❡ ❛ ❞♊❞❡❝❛❀❡❞r❛❧ s♣❛❝❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  42. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❍②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ◗✉❡st✐♊♥s ♊♥ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊❧②❀❡❞r❛ ❝❛♥ ❜❡ ❝♊♥s✐❞❡r❡❞ ✐♥ t❀❡ ❀②♣❡r❜♩❧✐❝✮s♣❀❡r✐❝❛❧ ❝♊♥t❡①t✳ ❚❀❡ ✐♥❢✳ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ t✉r♥s ♩✉t t♩ ❜❡ ❛ ♣r♊❥❡❝t✐✈❡ ♣r♊♣❡rt② ✭❉❛r❜♊✉①✱ ❙❛✉❡r✮✱ ✐♥❞❡♣❡♥❞❡♥t ♊❢ t❀❡ ❣❡♊♠❡tr② ✭P♊❣♊r❡❧♊✈✮✳ ❋♩r ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ ♠♩r❡ ✐♠♣♊rt❛♥t t❀❛♥ ❡❞❣❡ ❧❡♥❣t❀s✱ ❞✉❡ t♩ P♊✐♥❝❛ré✬s t❀❡♊r❡♠ ✿ t❀❡ ❣r♊✉♣ ❣❡♥❡r❛t❡❞ ❜② r❡✢❡❝t✐♊♥s ✐♥ t❀❡ ❢❛❝❡s ✐s ❞✐s❝r❡t❡ ✐✛ t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ π/ ❊ ✳ ❆♥❞r❡❡✈ ✭✶✟✌✵✮ ❝❀❛r❛❝t❡r✐③❡❞ t❀❡ ♣♊ss✐❜❧❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ✭ < π/ ✷ ) ♊❢ ✜♥✐t❡ ✈♊❧✉♠❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛✳ ❘✐✈✐♥ ❛♥❞ ❍♊❞❣s♊♥ ✭✶✟✟✹✮ s❀♊✇❡❞ t❀❛t t❀✐s ✐s ❛ ❝♊♥s❡q✉❡♥❝❡ ♊❢ ❛♥ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ t❀❡♊r❡♠ ✐♥ ❛ s♣❛❝❡ ✏❞✉❛❧✑ t♩ t❀❡ ❀②♣❡r❜♩❧✐❝ s♣❛❝❡ ✭❈❛✉❝❀②✬s t❀♠ ✐s ✐♠♣♊rt❛♥t✮✳ ❙♣❛❝❡s ♩❜t❛✐♥❡❞ ❢r♩♠ ♣♊❧②❀❡❞r❛ ❝❛♥ ❡✈❡♥ ❜❡ ❢♊✉♥❞ ✐♥ t❀❡ r❡❛❧ ✇♩r❧❞✳ ❋♩r ✐♥st❛♥❝❡ t❀❡ ✉♥✐✈❡rs❡ ♠✐❣❀t ❜❡ ❛ ❞♊❞❡❝❛❀❡❞r❛❧ s♣❛❝❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  43. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❍②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ◗✉❡st✐♊♥s ♊♥ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊❧②❀❡❞r❛ ❝❛♥ ❜❡ ❝♊♥s✐❞❡r❡❞ ✐♥ t❀❡ ❀②♣❡r❜♩❧✐❝✮s♣❀❡r✐❝❛❧ ❝♊♥t❡①t✳ ❚❀❡ ✐♥❢✳ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ t✉r♥s ♩✉t t♩ ❜❡ ❛ ♣r♊❥❡❝t✐✈❡ ♣r♊♣❡rt② ✭❉❛r❜♊✉①✱ ❙❛✉❡r✮✱ ✐♥❞❡♣❡♥❞❡♥t ♊❢ t❀❡ ❣❡♊♠❡tr② ✭P♊❣♊r❡❧♊✈✮✳ ❋♩r ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ ♠♩r❡ ✐♠♣♊rt❛♥t t❀❛♥ ❡❞❣❡ ❧❡♥❣t❀s✱ ❞✉❡ t♩ P♊✐♥❝❛ré✬s t❀❡♊r❡♠ ✿ t❀❡ ❣r♊✉♣ ❣❡♥❡r❛t❡❞ ❜② r❡✢❡❝t✐♊♥s ✐♥ t❀❡ ❢❛❝❡s ✐s ❞✐s❝r❡t❡ ✐✛ t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ π/ ❊ ✳ ❆♥❞r❡❡✈ ✭✶✟✌✵✮ ❝❀❛r❛❝t❡r✐③❡❞ t❀❡ ♣♊ss✐❜❧❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ✭ < π/ ✷ ) ♊❢ ✜♥✐t❡ ✈♊❧✉♠❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛✳ ❘✐✈✐♥ ❛♥❞ ❍♊❞❣s♊♥ ✭✶✟✟✹✮ s❀♊✇❡❞ t❀❛t t❀✐s ✐s ❛ ❝♊♥s❡q✉❡♥❝❡ ♊❢ ❛♥ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ t❀❡♊r❡♠ ✐♥ ❛ s♣❛❝❡ ✏❞✉❛❧✑ t♩ t❀❡ ❀②♣❡r❜♩❧✐❝ s♣❛❝❡ ✭❈❛✉❝❀②✬s t❀♠ ✐s ✐♠♣♊rt❛♥t✮✳ ❙♣❛❝❡s ♩❜t❛✐♥❡❞ ❢r♩♠ ♣♊❧②❀❡❞r❛ ❝❛♥ ❡✈❡♥ ❜❡ ❢♊✉♥❞ ✐♥ t❀❡ r❡❛❧ ✇♩r❧❞✳ ❋♩r ✐♥st❛♥❝❡ t❀❡ ✉♥✐✈❡rs❡ ♠✐❣❀t ❜❡ ❛ ❞♊❞❡❝❛❀❡❞r❛❧ s♣❛❝❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  44. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❍②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ◗✉❡st✐♊♥s ♊♥ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊❧②❀❡❞r❛ ❝❛♥ ❜❡ ❝♊♥s✐❞❡r❡❞ ✐♥ t❀❡ ❀②♣❡r❜♩❧✐❝✮s♣❀❡r✐❝❛❧ ❝♊♥t❡①t✳ ❚❀❡ ✐♥❢✳ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ t✉r♥s ♩✉t t♩ ❜❡ ❛ ♣r♊❥❡❝t✐✈❡ ♣r♊♣❡rt② ✭❉❛r❜♊✉①✱ ❙❛✉❡r✮✱ ✐♥❞❡♣❡♥❞❡♥t ♊❢ t❀❡ ❣❡♊♠❡tr② ✭P♊❣♊r❡❧♊✈✮✳ ❋♩r ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ ♠♩r❡ ✐♠♣♊rt❛♥t t❀❛♥ ❡❞❣❡ ❧❡♥❣t❀s✱ ❞✉❡ t♩ P♊✐♥❝❛ré✬s t❀❡♊r❡♠ ✿ t❀❡ ❣r♊✉♣ ❣❡♥❡r❛t❡❞ ❜② r❡✢❡❝t✐♊♥s ✐♥ t❀❡ ❢❛❝❡s ✐s ❞✐s❝r❡t❡ ✐✛ t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ π/ ❊ ✳ ❆♥❞r❡❡✈ ✭✶✟✌✵✮ ❝❀❛r❛❝t❡r✐③❡❞ t❀❡ ♣♊ss✐❜❧❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ✭ < π/ ✷ ) ♊❢ ✜♥✐t❡ ✈♊❧✉♠❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛✳ ❘✐✈✐♥ ❛♥❞ ❍♊❞❣s♊♥ ✭✶✟✟✹✮ s❀♊✇❡❞ t❀❛t t❀✐s ✐s ❛ ❝♊♥s❡q✉❡♥❝❡ ♊❢ ❛♥ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ t❀❡♊r❡♠ ✐♥ ❛ s♣❛❝❡ ✏❞✉❛❧✑ t♩ t❀❡ ❀②♣❡r❜♩❧✐❝ s♣❛❝❡ ✭❈❛✉❝❀②✬s t❀♠ ✐s ✐♠♣♊rt❛♥t✮✳ ❙♣❛❝❡s ♩❜t❛✐♥❡❞ ❢r♩♠ ♣♊❧②❀❡❞r❛ ❝❛♥ ❡✈❡♥ ❜❡ ❢♊✉♥❞ ✐♥ t❀❡ r❡❛❧ ✇♩r❧❞✳ ❋♩r ✐♥st❛♥❝❡ t❀❡ ✉♥✐✈❡rs❡ ♠✐❣❀t ❜❡ ❛ ❞♊❞❡❝❛❀❡❞r❛❧ s♣❛❝❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  45. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❍②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❛♥❞ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ◗✉❡st✐♊♥s ♊♥ t❀❡ ❣❡♊♠❡tr② ♊❢ ♣♊❧②❀❡❞r❛ ❝❛♥ ❜❡ ❝♊♥s✐❞❡r❡❞ ✐♥ t❀❡ ❀②♣❡r❜♩❧✐❝✮s♣❀❡r✐❝❛❧ ❝♊♥t❡①t✳ ❚❀❡ ✐♥❢✳ r✐❣✐❞✐t② ♊❢ ♣♊❧②❀❡❞r❛ t✉r♥s ♩✉t t♩ ❜❡ ❛ ♣r♊❥❡❝t✐✈❡ ♣r♊♣❡rt② ✭❉❛r❜♊✉①✱ ❙❛✉❡r✮✱ ✐♥❞❡♣❡♥❞❡♥t ♊❢ t❀❡ ❣❡♊♠❡tr② ✭P♊❣♊r❡❧♊✈✮✳ ❋♩r ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ ♠♩r❡ ✐♠♣♊rt❛♥t t❀❛♥ ❡❞❣❡ ❧❡♥❣t❀s✱ ❞✉❡ t♩ P♊✐♥❝❛ré✬s t❀❡♊r❡♠ ✿ t❀❡ ❣r♊✉♣ ❣❡♥❡r❛t❡❞ ❜② r❡✢❡❝t✐♊♥s ✐♥ t❀❡ ❢❛❝❡s ✐s ❞✐s❝r❡t❡ ✐✛ t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❛r❡ π/ ❊ ✳ ❆♥❞r❡❡✈ ✭✶✟✌✵✮ ❝❀❛r❛❝t❡r✐③❡❞ t❀❡ ♣♊ss✐❜❧❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ✭ < π/ ✷ ) ♊❢ ✜♥✐t❡ ✈♊❧✉♠❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛✳ ❘✐✈✐♥ ❛♥❞ ❍♊❞❣s♊♥ ✭✶✟✟✹✮ s❀♊✇❡❞ t❀❛t t❀✐s ✐s ❛ ❝♊♥s❡q✉❡♥❝❡ ♊❢ ❛♥ ✐s♊♠❡tr✐❝ r❡❛❧✐③❛t✐♊♥ t❀❡♊r❡♠ ✐♥ ❛ s♣❛❝❡ ✏❞✉❛❧✑ t♩ t❀❡ ❀②♣❡r❜♩❧✐❝ s♣❛❝❡ ✭❈❛✉❝❀②✬s t❀♠ ✐s ✐♠♣♊rt❛♥t✮✳ ❙♣❛❝❡s ♩❜t❛✐♥❡❞ ❢r♩♠ ♣♊❧②❀❡❞r❛ ❝❛♥ ❡✈❡♥ ❜❡ ❢♊✉♥❞ ✐♥ t❀❡ r❡❛❧ ✇♩r❧❞✳ ❋♩r ✐♥st❛♥❝❡ t❀❡ ✉♥✐✈❡rs❡ ♠✐❣❀t ❜❡ ❛ ❞♊❞❡❝❛❀❡❞r❛❧ s♣❛❝❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  46. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❆♣♣❧✐❝❛t✐♊♥ ✐♥ ♣❀②s✐❝s ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  47. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ✇rt ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❚❀❡ ❆♥❞r❡❡✈ t❀♠ s✉❣❣❡sts t❀❡ ❢♊❧❧♊✇✐♥❣ ✿ ❛r❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ✐♥❢ r✐❣✐❞ ✇✐t❀ r❡s♣❡❝t t♩ t❀❡✐r ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❄ ❚❡s ✭❆♥❞r❡❡✈✮ ❢♊r ❛❝✉t❡ ❛♥❣❧❡s✳ ❆♥❛❧♊❣ ❢♊r ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✿ ❞♊❡s t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❞❡t❡r♠✐♥❡ t❀❡ ❢❛❝❡ ❛♥❣❧❡s ✭❙t♊❊❡r✮ ❄ ❆♥s✇❡r ✿ ❚❡s✱ r❡❝❡♥t❧② ❛♥♥♊✉♥❝❡❞ ❜② ▌❛③③❡♊ ✫ ▌♊♥t❝♩✉q✉✐♊❧✳ Pr♊♊❢ ✉s❡s ❞✐✣❝✉❧t ❛♥❛❧②t✐❝ ❛r❣✉♠❡♥ts ✭❡❧❧✐♣t✐❝ ♊♣❡r❛t♩rs ♊♥ ❝♊♥❡✲♠✢❞s✮✱ ♥♊ ✏❡❧❡♠❡♥t❛r②✑ ♣r♊♊❢ ❊♥♊✇♥✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  48. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ✇rt ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❚❀❡ ❆♥❞r❡❡✈ t❀♠ s✉❣❣❡sts t❀❡ ❢♊❧❧♊✇✐♥❣ ✿ ❛r❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ✐♥❢ r✐❣✐❞ ✇✐t❀ r❡s♣❡❝t t♩ t❀❡✐r ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❄ ❚❡s ✭❆♥❞r❡❡✈✮ ❢♊r ❛❝✉t❡ ❛♥❣❧❡s✳ ❆♥❛❧♊❣ ❢♊r ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✿ ❞♊❡s t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❞❡t❡r♠✐♥❡ t❀❡ ❢❛❝❡ ❛♥❣❧❡s ✭❙t♊❊❡r✮ ❄ ❆♥s✇❡r ✿ ❚❡s✱ r❡❝❡♥t❧② ❛♥♥♊✉♥❝❡❞ ❜② ▌❛③③❡♊ ✫ ▌♊♥t❝♩✉q✉✐♊❧✳ Pr♊♊❢ ✉s❡s ❞✐✣❝✉❧t ❛♥❛❧②t✐❝ ❛r❣✉♠❡♥ts ✭❡❧❧✐♣t✐❝ ♊♣❡r❛t♩rs ♊♥ ❝♊♥❡✲♠✢❞s✮✱ ♥♊ ✏❡❧❡♠❡♥t❛r②✑ ♣r♊♊❢ ❊♥♊✇♥✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  49. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ✇rt ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❚❀❡ ❆♥❞r❡❡✈ t❀♠ s✉❣❣❡sts t❀❡ ❢♊❧❧♊✇✐♥❣ ✿ ❛r❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ✐♥❢ r✐❣✐❞ ✇✐t❀ r❡s♣❡❝t t♩ t❀❡✐r ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❄ ❚❡s ✭❆♥❞r❡❡✈✮ ❢♊r ❛❝✉t❡ ❛♥❣❧❡s✳ ❆♥❛❧♊❣ ❢♊r ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✿ ❞♊❡s t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❞❡t❡r♠✐♥❡ t❀❡ ❢❛❝❡ ❛♥❣❧❡s ✭❙t♊❊❡r✮ ❄ ❆♥s✇❡r ✿ ❚❡s✱ r❡❝❡♥t❧② ❛♥♥♊✉♥❝❡❞ ❜② ▌❛③③❡♊ ✫ ▌♊♥t❝♩✉q✉✐♊❧✳ Pr♊♊❢ ✉s❡s ❞✐✣❝✉❧t ❛♥❛❧②t✐❝ ❛r❣✉♠❡♥ts ✭❡❧❧✐♣t✐❝ ♊♣❡r❛t♩rs ♊♥ ❝♊♥❡✲♠✢❞s✮✱ ♥♊ ✏❡❧❡♠❡♥t❛r②✑ ♣r♊♊❢ ❊♥♊✇♥✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  50. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ✇rt ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❚❀❡ ❆♥❞r❡❡✈ t❀♠ s✉❣❣❡sts t❀❡ ❢♊❧❧♊✇✐♥❣ ✿ ❛r❡ ❀②♣❡r❜♩❧✐❝ ♣♊❧②❀❡❞r❛ ✐♥❢ r✐❣✐❞ ✇✐t❀ r❡s♣❡❝t t♩ t❀❡✐r ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❄ ❚❡s ✭❆♥❞r❡❡✈✮ ❢♊r ❛❝✉t❡ ❛♥❣❧❡s✳ ❆♥❛❧♊❣ ❢♊r ❊✉❝❧✐❞❡❛♥ ♣♊❧②❀❡❞r❛ ✿ ❞♊❡s t❀❡ ❞✐❀❡❞r❛❧ ❛♥❣❧❡s ❞❡t❡r♠✐♥❡ t❀❡ ❢❛❝❡ ❛♥❣❧❡s ✭❙t♊❊❡r✮ ❄ ❆♥s✇❡r ✿ ❚❡s✱ r❡❝❡♥t❧② ❛♥♥♊✉♥❝❡❞ ❜② ▌❛③③❡♊ ✫ ▌♊♥t❝♩✉q✉✐♊❧✳ Pr♊♊❢ ✉s❡s ❞✐✣❝✉❧t ❛♥❛❧②t✐❝ ❛r❣✉♠❡♥ts ✭❡❧❧✐♣t✐❝ ♊♣❡r❛t♩rs ♊♥ ❝♊♥❡✲♠✢❞s✮✱ ♥♊ ✏❡❧❡♠❡♥t❛r②✑ ♣r♊♊❢ ❊♥♊✇♥✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  51. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❯♥❢♊❧❞✐♥❣ ❘❡❝❛❧❧ ❉Ìr❡r✬s ✢❛t r❡♣r❡s❡♥t❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✳ ◗ ✿ ✐s ✐t ❛❧✇❛②s ♣♊ss✐❜❧❡ t♩ ✏✉♥❢♊❧❞✑ ❛ ♣♊❧②❀❡❞r♊♥ ✐♥ t❀✐s ✇❛② ❄ ❈✉t ♊♥❧② ❛❧♊♥❣ ❡❞❣❡s ✭♩t❀❡r✇✐s❡✱ ❡❛s②✮✳ ◗ ✿ ❧❡t ❣ ❜❡ ❛ ✢❛t ♠❡tr✐❝ ✇✐t❀ ❝♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ♊♥ ❙ ✷ ✱ ❛♥❣❧❡s < ✷ π ✱ ✇✐t❀ ❛ ❞❡❝♊♠♣♊s✐t✐♊♥ ✐♥ ❝♊♥✈❡① ♣♊❧②❣♊♥s✳ ❈❛♥ ♊♥❡ ✉♥❢♊❧❞ ❜② ❝✉tt✐♥❣ ❛❧♊♥❣ s♊♠❡ ♊❢ t❀❡ ❡❞❣❡s ❄ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  52. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❯♥❢♊❧❞✐♥❣ ❘❡❝❛❧❧ ❉Ìr❡r✬s ✢❛t r❡♣r❡s❡♥t❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✳ ◗ ✿ ✐s ✐t ❛❧✇❛②s ♣♊ss✐❜❧❡ t♩ ✏✉♥❢♊❧❞✑ ❛ ♣♊❧②❀❡❞r♊♥ ✐♥ t❀✐s ✇❛② ❄ ❈✉t ♊♥❧② ❛❧♊♥❣ ❡❞❣❡s ✭♩t❀❡r✇✐s❡✱ ❡❛s②✮✳ ◗ ✿ ❧❡t ❣ ❜❡ ❛ ✢❛t ♠❡tr✐❝ ✇✐t❀ ❝♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ♊♥ ❙ ✷ ✱ ❛♥❣❧❡s < ✷ π ✱ ✇✐t❀ ❛ ❞❡❝♊♠♣♊s✐t✐♊♥ ✐♥ ❝♊♥✈❡① ♣♊❧②❣♊♥s✳ ❈❛♥ ♊♥❡ ✉♥❢♊❧❞ ❜② ❝✉tt✐♥❣ ❛❧♊♥❣ s♊♠❡ ♊❢ t❀❡ ❡❞❣❡s ❄ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  53. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❯♥❢♊❧❞✐♥❣ ❘❡❝❛❧❧ ❉Ìr❡r✬s ✢❛t r❡♣r❡s❡♥t❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✳ ◗ ✿ ✐s ✐t ❛❧✇❛②s ♣♊ss✐❜❧❡ t♩ ✏✉♥❢♊❧❞✑ ❛ ♣♊❧②❀❡❞r♊♥ ✐♥ t❀✐s ✇❛② ❄ ❈✉t ♊♥❧② ❛❧♊♥❣ ❡❞❣❡s ✭♩t❀❡r✇✐s❡✱ ❡❛s②✮✳ ◗ ✿ ❧❡t ❣ ❜❡ ❛ ✢❛t ♠❡tr✐❝ ✇✐t❀ ❝♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ♊♥ ❙ ✷ ✱ ❛♥❣❧❡s < ✷ π ✱ ✇✐t❀ ❛ ❞❡❝♊♠♣♊s✐t✐♊♥ ✐♥ ❝♊♥✈❡① ♣♊❧②❣♊♥s✳ ❈❛♥ ♊♥❡ ✉♥❢♊❧❞ ❜② ❝✉tt✐♥❣ ❛❧♊♥❣ s♊♠❡ ♊❢ t❀❡ ❡❞❣❡s ❄ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  54. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❯♥❢♊❧❞✐♥❣ ❘❡❝❛❧❧ ❉Ìr❡r✬s ✢❛t r❡♣r❡s❡♥t❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✳ ◗ ✿ ✐s ✐t ❛❧✇❛②s ♣♊ss✐❜❧❡ t♩ ✏✉♥❢♊❧❞✑ ❛ ♣♊❧②❀❡❞r♊♥ ✐♥ t❀✐s ✇❛② ❄ ❈✉t ♊♥❧② ❛❧♊♥❣ ❡❞❣❡s ✭♩t❀❡r✇✐s❡✱ ❡❛s②✮✳ ◗ ✿ ❧❡t ❣ ❜❡ ❛ ✢❛t ♠❡tr✐❝ ✇✐t❀ ❝♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ♊♥ ❙ ✷ ✱ ❛♥❣❧❡s < ✷ π ✱ ✇✐t❀ ❛ ❞❡❝♊♠♣♊s✐t✐♊♥ ✐♥ ❝♊♥✈❡① ♣♊❧②❣♊♥s✳ ❈❛♥ ♊♥❡ ✉♥❢♊❧❞ ❜② ❝✉tt✐♥❣ ❛❧♊♥❣ s♊♠❡ ♊❢ t❀❡ ❡❞❣❡s ❄ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  55. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ♊❢ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❉❡❢ ✿ P ⊂ R ✾ ✐s ✇❡❛❊❧② ❝♊♥✈❡① ✐❢ ✐ts ✈❡rt✐❝❡s ❛r❡ t❀❡ ✈❡rt✐❝❡s ♊❢ ❛ ✭str✐❝t❧②✮ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✳ ❉❡❢✳ P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ✐t ❝❛♥ ❜❡ ❝✉t ✐♥t♩ ❝♊♥✈❡① ♣✐❡❝❡s ✇✐t❀♊✉t ❛❞❞✐♥❣ ❛♥ ✐♥t❡r✐♩r ✈❡rt❡①✳ ❈♊♥❥✳ ❆ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞✳ ❊①t❡♥s✐♊♥ ♊❢ t❀❡ ❈❛✉❝❀②✲❉❡❀♥ r❡s✉❧t✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐s ♥❡❝❡ss❛r② ✿ ∃ ❛ ✭♥♊♥✲❞❡❝♊♠♣♊s❛❜❧❡✮ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ✈❡rt✐❝❡s ♊♥ ❙ ✷ ✱ ♥♊t ✐♥❢✳ r✐❣✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  56. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ♊❢ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❉❡❢ ✿ P ⊂ R ✾ ✐s ✇❡❛❊❧② ❝♊♥✈❡① ✐❢ ✐ts ✈❡rt✐❝❡s ❛r❡ t❀❡ ✈❡rt✐❝❡s ♊❢ ❛ ✭str✐❝t❧②✮ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✳ ❉❡❢✳ P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ✐t ❝❛♥ ❜❡ ❝✉t ✐♥t♩ ❝♊♥✈❡① ♣✐❡❝❡s ✇✐t❀♊✉t ❛❞❞✐♥❣ ❛♥ ✐♥t❡r✐♩r ✈❡rt❡①✳ ❈♊♥❥✳ ❆ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞✳ ❊①t❡♥s✐♊♥ ♊❢ t❀❡ ❈❛✉❝❀②✲❉❡❀♥ r❡s✉❧t✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐s ♥❡❝❡ss❛r② ✿ ∃ ❛ ✭♥♊♥✲❞❡❝♊♠♣♊s❛❜❧❡✮ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ✈❡rt✐❝❡s ♊♥ ❙ ✷ ✱ ♥♊t ✐♥❢✳ r✐❣✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  57. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ♊❢ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❉❡❢ ✿ P ⊂ R ✾ ✐s ✇❡❛❊❧② ❝♊♥✈❡① ✐❢ ✐ts ✈❡rt✐❝❡s ❛r❡ t❀❡ ✈❡rt✐❝❡s ♊❢ ❛ ✭str✐❝t❧②✮ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✳ ❉❡❢✳ P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ✐t ❝❛♥ ❜❡ ❝✉t ✐♥t♩ ❝♊♥✈❡① ♣✐❡❝❡s ✇✐t❀♊✉t ❛❞❞✐♥❣ ❛♥ ✐♥t❡r✐♩r ✈❡rt❡①✳ ❈♊♥❥✳ ❆ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞✳ ❊①t❡♥s✐♊♥ ♊❢ t❀❡ ❈❛✉❝❀②✲❉❡❀♥ r❡s✉❧t✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐s ♥❡❝❡ss❛r② ✿ ∃ ❛ ✭♥♊♥✲❞❡❝♊♠♣♊s❛❜❧❡✮ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ✈❡rt✐❝❡s ♊♥ ❙ ✷ ✱ ♥♊t ✐♥❢✳ r✐❣✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  58. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ♊❢ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❉❡❢ ✿ P ⊂ R ✾ ✐s ✇❡❛❊❧② ❝♊♥✈❡① ✐❢ ✐ts ✈❡rt✐❝❡s ❛r❡ t❀❡ ✈❡rt✐❝❡s ♊❢ ❛ ✭str✐❝t❧②✮ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✳ ❉❡❢✳ P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ✐t ❝❛♥ ❜❡ ❝✉t ✐♥t♩ ❝♊♥✈❡① ♣✐❡❝❡s ✇✐t❀♊✉t ❛❞❞✐♥❣ ❛♥ ✐♥t❡r✐♩r ✈❡rt❡①✳ ❈♊♥❥✳ ❆ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞✳ ❊①t❡♥s✐♊♥ ♊❢ t❀❡ ❈❛✉❝❀②✲❉❡❀♥ r❡s✉❧t✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐s ♥❡❝❡ss❛r② ✿ ∃ ❛ ✭♥♊♥✲❞❡❝♊♠♣♊s❛❜❧❡✮ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ✈❡rt✐❝❡s ♊♥ ❙ ✷ ✱ ♥♊t ✐♥❢✳ r✐❣✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  59. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❘✐❣✐❞✐t② ♊❢ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛ ❉❡❢ ✿ P ⊂ R ✾ ✐s ✇❡❛❊❧② ❝♊♥✈❡① ✐❢ ✐ts ✈❡rt✐❝❡s ❛r❡ t❀❡ ✈❡rt✐❝❡s ♊❢ ❛ ✭str✐❝t❧②✮ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✳ ❉❡❢✳ P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ✐t ❝❛♥ ❜❡ ❝✉t ✐♥t♩ ❝♊♥✈❡① ♣✐❡❝❡s ✇✐t❀♊✉t ❛❞❞✐♥❣ ❛♥ ✐♥t❡r✐♩r ✈❡rt❡①✳ ❈♊♥❥✳ ❆ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✐s ✐♥❢✳ r✐❣✐❞✳ ❊①t❡♥s✐♊♥ ♊❢ t❀❡ ❈❛✉❝❀②✲❉❡❀♥ r❡s✉❧t✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❞❡❝♊♠♣♊s❛❜❧❡ ✐s ♥❡❝❡ss❛r② ✿ ∃ ❛ ✭♥♊♥✲❞❡❝♊♠♣♊s❛❜❧❡✮ ♩❝t❛❀❡❞r♊♥✱ ✇✐t❀ ✈❡rt✐❝❡s ♊♥ ❙ ✷ ✱ ♥♊t ✐♥❢✳ r✐❣✐❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  60. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❆ ♣❛rt✐❛❧ r❡s✉❧t ❉❡❢ ✿ P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ♊♥❡ ❝❛♥ ❛❞❞ s✐♠♣❧✐❝❡s s♩ ❛s t♩ ❣♊ ❢r♩♠ P t♩ ✐ts ❝♊♥✈❡① ❀✉❧❧ t❀r♊✉❣❀ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✳ ❚❀♠ ❆ ✭■③♠❡st✐❡✈✱ ❙✳✮ ✿ ❛♥② ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥✱ ✐s ✐♥✜♥✐t❡s✐♠❛❧❧② r✐❣✐❞✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♠✐❣❀t ♥♊t ❜❡ ♥❡❝❡ss❛r② ✭ ❄ ❄✮ ■t ✐s ✈❡r② ✇❡❛❊ ❢♊r ♣♊❧②❀❡❞r❛ ❀♊♠❡♊♠♊r♣❀✐❝ t♩ ❛ s♣❀❡r❡✱ ❀♊✇❡✈❡r ❛♥ ❡①❛♠♣❧❡ ♊❢ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ♥♊♥ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✇❛s ❢♊✉♥❞ ✐♥ ✷✵✵✷ ✭❆✐❝❀❀♊❧③❡r✱ ❆❧❜♊✉❧✱ ❍✉rt❛❞♊✮✳ ❙♊♠❡ ♣r❡✈✐♊✉s r❡s✉❧ts✱ s♊♠❡ ✐♥ ❝♩❧❧❛❜♩r❛t✐♊♥ ✇✮ ❇♩❜ ❈♊♥♥❡❧❧②✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  61. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❆ ♣❛rt✐❛❧ r❡s✉❧t ❉❡❢ ✿ P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ♊♥❡ ❝❛♥ ❛❞❞ s✐♠♣❧✐❝❡s s♩ ❛s t♩ ❣♊ ❢r♩♠ P t♩ ✐ts ❝♊♥✈❡① ❀✉❧❧ t❀r♊✉❣❀ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✳ ❚❀♠ ❆ ✭■③♠❡st✐❡✈✱ ❙✳✮ ✿ ❛♥② ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥✱ ✐s ✐♥✜♥✐t❡s✐♠❛❧❧② r✐❣✐❞✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♠✐❣❀t ♥♊t ❜❡ ♥❡❝❡ss❛r② ✭ ❄ ❄✮ ■t ✐s ✈❡r② ✇❡❛❊ ❢♊r ♣♊❧②❀❡❞r❛ ❀♊♠❡♊♠♊r♣❀✐❝ t♩ ❛ s♣❀❡r❡✱ ❀♊✇❡✈❡r ❛♥ ❡①❛♠♣❧❡ ♊❢ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ♥♊♥ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✇❛s ❢♊✉♥❞ ✐♥ ✷✵✵✷ ✭❆✐❝❀❀♊❧③❡r✱ ❆❧❜♊✉❧✱ ❍✉rt❛❞♊✮✳ ❙♊♠❡ ♣r❡✈✐♊✉s r❡s✉❧ts✱ s♊♠❡ ✐♥ ❝♩❧❧❛❜♩r❛t✐♊♥ ✇✮ ❇♩❜ ❈♊♥♥❡❧❧②✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  62. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❆ ♣❛rt✐❛❧ r❡s✉❧t ❉❡❢ ✿ P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ♊♥❡ ❝❛♥ ❛❞❞ s✐♠♣❧✐❝❡s s♩ ❛s t♩ ❣♊ ❢r♩♠ P t♩ ✐ts ❝♊♥✈❡① ❀✉❧❧ t❀r♊✉❣❀ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✳ ❚❀♠ ❆ ✭■③♠❡st✐❡✈✱ ❙✳✮ ✿ ❛♥② ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥✱ ✐s ✐♥✜♥✐t❡s✐♠❛❧❧② r✐❣✐❞✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♠✐❣❀t ♥♊t ❜❡ ♥❡❝❡ss❛r② ✭ ❄ ❄✮ ■t ✐s ✈❡r② ✇❡❛❊ ❢♊r ♣♊❧②❀❡❞r❛ ❀♊♠❡♊♠♊r♣❀✐❝ t♩ ❛ s♣❀❡r❡✱ ❀♊✇❡✈❡r ❛♥ ❡①❛♠♣❧❡ ♊❢ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ♥♊♥ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✇❛s ❢♊✉♥❞ ✐♥ ✷✵✵✷ ✭❆✐❝❀❀♊❧③❡r✱ ❆❧❜♊✉❧✱ ❍✉rt❛❞♊✮✳ ❙♊♠❡ ♣r❡✈✐♊✉s r❡s✉❧ts✱ s♊♠❡ ✐♥ ❝♩❧❧❛❜♩r❛t✐♊♥ ✇✮ ❇♩❜ ❈♊♥♥❡❧❧②✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  63. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❆ ♣❛rt✐❛❧ r❡s✉❧t ❉❡❢ ✿ P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ♊♥❡ ❝❛♥ ❛❞❞ s✐♠♣❧✐❝❡s s♩ ❛s t♩ ❣♊ ❢r♩♠ P t♩ ✐ts ❝♊♥✈❡① ❀✉❧❧ t❀r♊✉❣❀ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✳ ❚❀♠ ❆ ✭■③♠❡st✐❡✈✱ ❙✳✮ ✿ ❛♥② ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥✱ ✐s ✐♥✜♥✐t❡s✐♠❛❧❧② r✐❣✐❞✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♠✐❣❀t ♥♊t ❜❡ ♥❡❝❡ss❛r② ✭ ❄ ❄✮ ■t ✐s ✈❡r② ✇❡❛❊ ❢♊r ♣♊❧②❀❡❞r❛ ❀♊♠❡♊♠♊r♣❀✐❝ t♩ ❛ s♣❀❡r❡✱ ❀♊✇❡✈❡r ❛♥ ❡①❛♠♣❧❡ ♊❢ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ♥♊♥ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✇❛s ❢♊✉♥❞ ✐♥ ✷✵✵✷ ✭❆✐❝❀❀♊❧③❡r✱ ❆❧❜♊✉❧✱ ❍✉rt❛❞♊✮✳ ❙♊♠❡ ♣r❡✈✐♊✉s r❡s✉❧ts✱ s♊♠❡ ✐♥ ❝♩❧❧❛❜♩r❛t✐♊♥ ✇✮ ❇♩❜ ❈♊♥♥❡❧❧②✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  64. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❆ ♣❛rt✐❛❧ r❡s✉❧t ❉❡❢ ✿ P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ✐❢ ♊♥❡ ❝❛♥ ❛❞❞ s✐♠♣❧✐❝❡s s♩ ❛s t♩ ❣♊ ❢r♩♠ P t♩ ✐ts ❝♊♥✈❡① ❀✉❧❧ t❀r♊✉❣❀ ✇❡❛❊❧② ❝♊♥✈❡① ♣♊❧②❀❡❞r❛✳ ❚❀♠ ❆ ✭■③♠❡st✐❡✈✱ ❙✳✮ ✿ ❛♥② ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥✱ ✐s ✐♥✜♥✐t❡s✐♠❛❧❧② r✐❣✐❞✳ ❚❀❡ ❀②♣♊t❀❡s✐s t❀❛t P ✐s ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♠✐❣❀t ♥♊t ❜❡ ♥❡❝❡ss❛r② ✭ ❄ ❄✮ ■t ✐s ✈❡r② ✇❡❛❊ ❢♊r ♣♊❧②❀❡❞r❛ ❀♊♠❡♊♠♊r♣❀✐❝ t♩ ❛ s♣❀❡r❡✱ ❀♊✇❡✈❡r ❛♥ ❡①❛♠♣❧❡ ♊❢ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ♥♊♥ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ ✇❛s ❢♊✉♥❞ ✐♥ ✷✵✵✷ ✭❆✐❝❀❀♊❧③❡r✱ ❆❧❜♊✉❧✱ ❍✉rt❛❞♊✮✳ ❙♊♠❡ ♣r❡✈✐♊✉s r❡s✉❧ts✱ s♊♠❡ ✐♥ ❝♩❧❧❛❜♩r❛t✐♊♥ ✇✮ ❇♩❜ ❈♊♥♥❡❧❧②✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  65. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚♩♩❧s ❢♊r t❀❡ ♣r♊♊❢ ❚❀❡ ♣r♊♊❢ ✉s❡s t❀r❡❡ t②♣❡s ♊❢ ♥♊t✐♊♥s✮r❡s✉❧ts✱ s♊♠❡ ♊❧❞✱ s♊♠❡ r❡❝❡♥t✳ t❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ♣♊❧②❀❡❞r❛❧ ❣❡♊♠❡tr② ✿ t❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❣❡♊♠❡tr✐❝ ❝♊♠❜✐♥❛t♩r✐❝s✎❛❧❣❡❜r❛✐❝ ❣❡♊♠❡tr② ✿ ❛ ✭❞✐✣❝✉❧t✮ r❡s✉❧t ♊❢ ▌♊r❡❧❧✐ ❛♥❞ ✭✐♥❞❡♣❡♥❞❡♥t❧②✮ ❲❧♊❞❛r❝③②❊ ✭✶✟✟✻✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  66. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚♩♩❧s ❢♊r t❀❡ ♣r♊♊❢ ❚❀❡ ♣r♊♊❢ ✉s❡s t❀r❡❡ t②♣❡s ♊❢ ♥♊t✐♊♥s✮r❡s✉❧ts✱ s♊♠❡ ♊❧❞✱ s♊♠❡ r❡❝❡♥t✳ t❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ♣♊❧②❀❡❞r❛❧ ❣❡♊♠❡tr② ✿ t❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❣❡♊♠❡tr✐❝ ❝♊♠❜✐♥❛t♩r✐❝s✎❛❧❣❡❜r❛✐❝ ❣❡♊♠❡tr② ✿ ❛ ✭❞✐✣❝✉❧t✮ r❡s✉❧t ♊❢ ▌♊r❡❧❧✐ ❛♥❞ ✭✐♥❞❡♣❡♥❞❡♥t❧②✮ ❲❧♊❞❛r❝③②❊ ✭✶✟✟✻✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  67. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚♩♩❧s ❢♊r t❀❡ ♣r♊♊❢ ❚❀❡ ♣r♊♊❢ ✉s❡s t❀r❡❡ t②♣❡s ♊❢ ♥♊t✐♊♥s✮r❡s✉❧ts✱ s♊♠❡ ♊❧❞✱ s♊♠❡ r❡❝❡♥t✳ t❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ♣♊❧②❀❡❞r❛❧ ❣❡♊♠❡tr② ✿ t❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❣❡♊♠❡tr✐❝ ❝♊♠❜✐♥❛t♩r✐❝s✎❛❧❣❡❜r❛✐❝ ❣❡♊♠❡tr② ✿ ❛ ✭❞✐✣❝✉❧t✮ r❡s✉❧t ♊❢ ▌♊r❡❧❧✐ ❛♥❞ ✭✐♥❞❡♣❡♥❞❡♥t❧②✮ ❲❧♊❞❛r❝③②❊ ✭✶✟✟✻✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  68. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚♩♩❧s ❢♊r t❀❡ ♣r♊♊❢ ❚❀❡ ♣r♊♊❢ ✉s❡s t❀r❡❡ t②♣❡s ♊❢ ♥♊t✐♊♥s✮r❡s✉❧ts✱ s♊♠❡ ♊❧❞✱ s♊♠❡ r❡❝❡♥t✳ t❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ♣♊❧②❀❡❞r❛❧ ❣❡♊♠❡tr② ✿ t❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❣❡♊♠❡tr✐❝ ❝♊♠❜✐♥❛t♩r✐❝s✎❛❧❣❡❜r❛✐❝ ❣❡♊♠❡tr② ✿ ❛ ✭❞✐✣❝✉❧t✮ r❡s✉❧t ♊❢ ▌♊r❡❧❧✐ ❛♥❞ ✭✐♥❞❡♣❡♥❞❡♥t❧②✮ ❲❧♊❞❛r❝③②❊ ✭✶✟✟✻✮✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  69. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ▲❡t ( â–Œ , ❣ ) ❜❡ ❛ ❘✐❡♠❛♥♥✐❛♥ ♠✢❞✱ ✇✐t❀ s❝❛❧❛r ❝✉r✈❛t✉r❡ ❙❝ ❣ ✳ ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ✿ ï¿œ ❙ ( ❣ ) = ❙❝ ❣ ❞✈ ❣ . â–Œ ❚❀♠ ✭❍✐❧❜❡rt ❄✮ ✿ ❙ ( â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ♊❢ ✜①❡❞ ✈♊❧✉♠❡✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ ❲✐t❀ ❜♊✉♥❞❛r② ✿ t❡r♠ ✐♥ ✐♥t❡❣r❛❧ ♠❡❛♥ ❝✉r✈❛t✉r❡✳ ❚❀♠ ✭❇❧❛s❝❀❊❡✱ ❍❡r❣❧♊t③✮ ✿ ❙ ( â–Œ , ∂ â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ✇✐t❀ ✜①❡❞ ✐♥❞✉❝❡❞ ♠❡tr✐❝ ♊♥ ∂ â–Œ ✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ Pr♊❜❧❡♠ ✿ ❙ ✐s ♥❡✐t❀❡r ❝♊♥✈❡① ♥♊r ❝♊♥❝❛✈❡ ✕ ❀❛r❞ t♩ ✜♥❞ ❝r✐t✐❝❛❧ ♣♊✐♥ts✳ ◆♩t ✉s❡❞ ♠✉❝❀ ✐♥ ♣r❛❝t✐❝❡✱ ❡❣ t♩ ✜♥❞ ❊✐♥st❡✐♥ ♠❡tr✐❝s✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  70. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ▲❡t ( â–Œ , ❣ ) ❜❡ ❛ ❘✐❡♠❛♥♥✐❛♥ ♠✢❞✱ ✇✐t❀ s❝❛❧❛r ❝✉r✈❛t✉r❡ ❙❝ ❣ ✳ ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ✿ ï¿œ ❙ ( ❣ ) = ❙❝ ❣ ❞✈ ❣ . â–Œ ❚❀♠ ✭❍✐❧❜❡rt ❄✮ ✿ ❙ ( â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ♊❢ ✜①❡❞ ✈♊❧✉♠❡✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ ❲✐t❀ ❜♊✉♥❞❛r② ✿ t❡r♠ ✐♥ ✐♥t❡❣r❛❧ ♠❡❛♥ ❝✉r✈❛t✉r❡✳ ❚❀♠ ✭❇❧❛s❝❀❊❡✱ ❍❡r❣❧♊t③✮ ✿ ❙ ( â–Œ , ∂ â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ✇✐t❀ ✜①❡❞ ✐♥❞✉❝❡❞ ♠❡tr✐❝ ♊♥ ∂ â–Œ ✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ Pr♊❜❧❡♠ ✿ ❙ ✐s ♥❡✐t❀❡r ❝♊♥✈❡① ♥♊r ❝♊♥❝❛✈❡ ✕ ❀❛r❞ t♩ ✜♥❞ ❝r✐t✐❝❛❧ ♣♊✐♥ts✳ ◆♩t ✉s❡❞ ♠✉❝❀ ✐♥ ♣r❛❝t✐❝❡✱ ❡❣ t♩ ✜♥❞ ❊✐♥st❡✐♥ ♠❡tr✐❝s✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  71. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ▲❡t ( â–Œ , ❣ ) ❜❡ ❛ ❘✐❡♠❛♥♥✐❛♥ ♠✢❞✱ ✇✐t❀ s❝❛❧❛r ❝✉r✈❛t✉r❡ ❙❝ ❣ ✳ ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ✿ ï¿œ ❙ ( ❣ ) = ❙❝ ❣ ❞✈ ❣ . â–Œ ❚❀♠ ✭❍✐❧❜❡rt ❄✮ ✿ ❙ ( â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ♊❢ ✜①❡❞ ✈♊❧✉♠❡✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ ❲✐t❀ ❜♊✉♥❞❛r② ✿ t❡r♠ ✐♥ ✐♥t❡❣r❛❧ ♠❡❛♥ ❝✉r✈❛t✉r❡✳ ❚❀♠ ✭❇❧❛s❝❀❊❡✱ ❍❡r❣❧♊t③✮ ✿ ❙ ( â–Œ , ∂ â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ✇✐t❀ ✜①❡❞ ✐♥❞✉❝❡❞ ♠❡tr✐❝ ♊♥ ∂ â–Œ ✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ Pr♊❜❧❡♠ ✿ ❙ ✐s ♥❡✐t❀❡r ❝♊♥✈❡① ♥♊r ❝♊♥❝❛✈❡ ✕ ❀❛r❞ t♩ ✜♥❞ ❝r✐t✐❝❛❧ ♣♊✐♥ts✳ ◆♩t ✉s❡❞ ♠✉❝❀ ✐♥ ♣r❛❝t✐❝❡✱ ❡❣ t♩ ✜♥❞ ❊✐♥st❡✐♥ ♠❡tr✐❝s✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  72. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ▲❡t ( â–Œ , ❣ ) ❜❡ ❛ ❘✐❡♠❛♥♥✐❛♥ ♠✢❞✱ ✇✐t❀ s❝❛❧❛r ❝✉r✈❛t✉r❡ ❙❝ ❣ ✳ ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ✿ ï¿œ ❙ ( ❣ ) = ❙❝ ❣ ❞✈ ❣ . â–Œ ❚❀♠ ✭❍✐❧❜❡rt ❄✮ ✿ ❙ ( â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ♊❢ ✜①❡❞ ✈♊❧✉♠❡✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ ❲✐t❀ ❜♊✉♥❞❛r② ✿ t❡r♠ ✐♥ ✐♥t❡❣r❛❧ ♠❡❛♥ ❝✉r✈❛t✉r❡✳ ❚❀♠ ✭❇❧❛s❝❀❊❡✱ ❍❡r❣❧♊t③✮ ✿ ❙ ( â–Œ , ∂ â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ✇✐t❀ ✜①❡❞ ✐♥❞✉❝❡❞ ♠❡tr✐❝ ♊♥ ∂ â–Œ ✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ Pr♊❜❧❡♠ ✿ ❙ ✐s ♥❡✐t❀❡r ❝♊♥✈❡① ♥♊r ❝♊♥❝❛✈❡ ✕ ❀❛r❞ t♩ ✜♥❞ ❝r✐t✐❝❛❧ ♣♊✐♥ts✳ ◆♩t ✉s❡❞ ♠✉❝❀ ✐♥ ♣r❛❝t✐❝❡✱ ❡❣ t♩ ✜♥❞ ❊✐♥st❡✐♥ ♠❡tr✐❝s✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  73. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ▲❡t ( â–Œ , ❣ ) ❜❡ ❛ ❘✐❡♠❛♥♥✐❛♥ ♠✢❞✱ ✇✐t❀ s❝❛❧❛r ❝✉r✈❛t✉r❡ ❙❝ ❣ ✳ ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ✿ ï¿œ ❙ ( ❣ ) = ❙❝ ❣ ❞✈ ❣ . â–Œ ❚❀♠ ✭❍✐❧❜❡rt ❄✮ ✿ ❙ ( â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ♊❢ ✜①❡❞ ✈♊❧✉♠❡✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ ❲✐t❀ ❜♊✉♥❞❛r② ✿ t❡r♠ ✐♥ ✐♥t❡❣r❛❧ ♠❡❛♥ ❝✉r✈❛t✉r❡✳ ❚❀♠ ✭❇❧❛s❝❀❊❡✱ ❍❡r❣❧♊t③✮ ✿ ❙ ( â–Œ , ∂ â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ✇✐t❀ ✜①❡❞ ✐♥❞✉❝❡❞ ♠❡tr✐❝ ♊♥ ∂ â–Œ ✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ Pr♊❜❧❡♠ ✿ ❙ ✐s ♥❡✐t❀❡r ❝♊♥✈❡① ♥♊r ❝♊♥❝❛✈❡ ✕ ❀❛r❞ t♩ ✜♥❞ ❝r✐t✐❝❛❧ ♣♊✐♥ts✳ ◆♩t ✉s❡❞ ♠✉❝❀ ✐♥ ♣r❛❝t✐❝❡✱ ❡❣ t♩ ✜♥❞ ❊✐♥st❡✐♥ ♠❡tr✐❝s✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  74. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ▲❡t ( â–Œ , ❣ ) ❜❡ ❛ ❘✐❡♠❛♥♥✐❛♥ ♠✢❞✱ ✇✐t❀ s❝❛❧❛r ❝✉r✈❛t✉r❡ ❙❝ ❣ ✳ ❚❀❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥❛❧ ✿ ï¿œ ❙ ( ❣ ) = ❙❝ ❣ ❞✈ ❣ . â–Œ ❚❀♠ ✭❍✐❧❜❡rt ❄✮ ✿ ❙ ( â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ♊❢ ✜①❡❞ ✈♊❧✉♠❡✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ ❲✐t❀ ❜♊✉♥❞❛r② ✿ t❡r♠ ✐♥ ✐♥t❡❣r❛❧ ♠❡❛♥ ❝✉r✈❛t✉r❡✳ ❚❀♠ ✭❇❧❛s❝❀❊❡✱ ❍❡r❣❧♊t③✮ ✿ ❙ ( â–Œ , ∂ â–Œ , ❣ ) ✐s ❝r✐t✐❝❛❧✱ ❛♠♊♥❣ ♠❡tr✐❝s ✇✐t❀ ✜①❡❞ ✐♥❞✉❝❡❞ ♠❡tr✐❝ ♊♥ ∂ â–Œ ✱ ✐✛ ❣ ✐s ❊✐♥st❡✐♥✳ Pr♊❜❧❡♠ ✿ ❙ ✐s ♥❡✐t❀❡r ❝♊♥✈❡① ♥♊r ❝♊♥❝❛✈❡ ✕ ❀❛r❞ t♩ ✜♥❞ ❝r✐t✐❝❛❧ ♣♊✐♥ts✳ ◆♩t ✉s❡❞ ♠✉❝❀ ✐♥ ♣r❛❝t✐❝❡✱ ❡❣ t♩ ✜♥❞ ❊✐♥st❡✐♥ ♠❡tr✐❝s✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  75. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  76. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  77. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  78. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  79. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  80. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  81. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  82. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  83. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ❚❀❡ ❙❝❀❧À✢✐ ❢♊r♠✉❧❛ ✿ ∀ ❞❡❢♊r♠❛t✐♊♥ ♊❢ ❛ ♣♊❧②❀❡❞r♊♥✱ ï¿œ ❧ ❡ ❞ Ξ ❡ = ✵ . ❡ ❈♊♥s✐❞❡r ❛ ♣♊❧②❀❡❞r♊♥ P ✇✐t❀ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ❚ ✱ ❛♥❞ ❞❡❢♊r♠❛t✐♊♥s ✇❀✐❝❀ ✈❛r② t❀❡ ❧❡♥❣t❀ ♊❢ t❀❡ ✐♥t❡r✐♩r ❛♥❣❧❡s✱ ✜①✐♥❣ t❀❡ ❜♊✉♥❞❛r② ♠❡tr✐❝✳ ❈♊♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♊♥ t❀❡ ✐♥t❡r✐♩r ❡❞❣❡s ✿ t♩t❛❧ ❛♥❣❧❡ ✐s ♥♊t ✷ π ✳ ❉❡❢ ✿ ï¿œ ï¿œ ❙ = ❧ ❡ ( ✷ π − Ξ ❡ ) + ❧ ❡ ( π − α ❡ ) , ❡ ∈ ❊ ✐ ❡ ∈ ❊ ❜ s✉♠ ♊✈❡r ✐♥t❡r✐♩r✱ r❡s♣✳ ❜♊✉♥❞❛r②✱ ❡❞❣❡s✳ ❉✐s❝r❡t❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♊♥✱ ❛❩❛ ❘❡❣❣❡ ❢✉♥❝t✐♊♥✱ ❡t❝✳ ❙♩ ❞❙ = ï¿œ ❡ ∈ ❊ ✐ ( ✷ π − Ξ ❡ ) ❞❧ ❡ ✱ ❛♥❞ t❀❡ ❍❡ss✐❛♥ ♊❢ ❙ ✐s − â–Œ ❚ = − ( ∂ξ ✐ /∂ ❧ ❥ ) ✳ ❘❡♠❛r❊ ✿ ✐❢ ❚ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ â–Œ ❚ ✐s ♥♊♥✲❞❡❣❡♥❡r❛t❡✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  84. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❈♊♥❝❛✈✐t② ♊❢ ❙ ❚❀♠ ❇✳ ▲❡t ◗ ❜❡ ❛ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✱ ❛♥❞ ❧❡t ❚ ❜❡ ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀♊✉t ✐♥t❡r✐♩r ✈❡rt❡①✳ ❚❀❡♥ â–Œ ❚ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✳ ❚❀♠ ❇ = ⇒ ❚❀♠ ❆ ✿ st❛rt ✇✐t❀ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ P ✵ ✳ ❈❀♊♊s❡ ❛ ❝♊♥❝❛✈❡ ❡❞❣❡ ❡ ✶ ❛♥❞ ✏✜❧❧ ✐t✑ ✇✐t❀ ❛ s✐♠♣❧❡①✱ t♩ ❣❡t P ✶ ✖ ❡ ✶ ✐s ❛♥ ✐♥t❡r✐♩r ❡❞❣❡ ♊❢ P ✶ ✳ ❘❡♣❡❛t ✇✐t❀ ❡ ✷ ✱ ❡t❝✳ ❆❢t❡r ❛ ✜♥✐t❡ ♥✉♠❜❡r ♊❢ st❡♣s✱ P ♥ ✐s t❀❡ ❝♊♥✈❡① ❀✉❧❧ ♊❢ P ✵ ✳ ❚♩ ❣♊ ❢r♩♠ â–Œ ❊ + ✶ t♩ â–Œ ❊ ✱ s✐♠♣❧② r❡♠♊✈❡ ❛ ❧✐♥❡ ❛♥❞ ❛ ❝♊❧✉♠♥ ✭❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❡ ❊ + ✶ ✮✳ ❙✐♥❝❡ â–Œ ♥ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✱ s♩ ✐s â–Œ ✵ ✳ ❚❀❡r❡❢♊r❡ P ✵ ✐s ✐♥❢ r✐❣✐❞✱ q❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  85. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❈♊♥❝❛✈✐t② ♊❢ ❙ ❚❀♠ ❇✳ ▲❡t ◗ ❜❡ ❛ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✱ ❛♥❞ ❧❡t ❚ ❜❡ ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀♊✉t ✐♥t❡r✐♩r ✈❡rt❡①✳ ❚❀❡♥ â–Œ ❚ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✳ ❚❀♠ ❇ = ⇒ ❚❀♠ ❆ ✿ st❛rt ✇✐t❀ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ P ✵ ✳ ❈❀♊♊s❡ ❛ ❝♊♥❝❛✈❡ ❡❞❣❡ ❡ ✶ ❛♥❞ ✏✜❧❧ ✐t✑ ✇✐t❀ ❛ s✐♠♣❧❡①✱ t♩ ❣❡t P ✶ ✖ ❡ ✶ ✐s ❛♥ ✐♥t❡r✐♩r ❡❞❣❡ ♊❢ P ✶ ✳ ❘❡♣❡❛t ✇✐t❀ ❡ ✷ ✱ ❡t❝✳ ❆❢t❡r ❛ ✜♥✐t❡ ♥✉♠❜❡r ♊❢ st❡♣s✱ P ♥ ✐s t❀❡ ❝♊♥✈❡① ❀✉❧❧ ♊❢ P ✵ ✳ ❚♩ ❣♊ ❢r♩♠ â–Œ ❊ + ✶ t♩ â–Œ ❊ ✱ s✐♠♣❧② r❡♠♊✈❡ ❛ ❧✐♥❡ ❛♥❞ ❛ ❝♊❧✉♠♥ ✭❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❡ ❊ + ✶ ✮✳ ❙✐♥❝❡ â–Œ ♥ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✱ s♩ ✐s â–Œ ✵ ✳ ❚❀❡r❡❢♊r❡ P ✵ ✐s ✐♥❢ r✐❣✐❞✱ q❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  86. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❈♊♥❝❛✈✐t② ♊❢ ❙ ❚❀♠ ❇✳ ▲❡t ◗ ❜❡ ❛ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✱ ❛♥❞ ❧❡t ❚ ❜❡ ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀♊✉t ✐♥t❡r✐♩r ✈❡rt❡①✳ ❚❀❡♥ â–Œ ❚ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✳ ❚❀♠ ❇ = ⇒ ❚❀♠ ❆ ✿ st❛rt ✇✐t❀ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ P ✵ ✳ ❈❀♊♊s❡ ❛ ❝♊♥❝❛✈❡ ❡❞❣❡ ❡ ✶ ❛♥❞ ✏✜❧❧ ✐t✑ ✇✐t❀ ❛ s✐♠♣❧❡①✱ t♩ ❣❡t P ✶ ✖ ❡ ✶ ✐s ❛♥ ✐♥t❡r✐♩r ❡❞❣❡ ♊❢ P ✶ ✳ ❘❡♣❡❛t ✇✐t❀ ❡ ✷ ✱ ❡t❝✳ ❆❢t❡r ❛ ✜♥✐t❡ ♥✉♠❜❡r ♊❢ st❡♣s✱ P ♥ ✐s t❀❡ ❝♊♥✈❡① ❀✉❧❧ ♊❢ P ✵ ✳ ❚♩ ❣♊ ❢r♩♠ â–Œ ❊ + ✶ t♩ â–Œ ❊ ✱ s✐♠♣❧② r❡♠♊✈❡ ❛ ❧✐♥❡ ❛♥❞ ❛ ❝♊❧✉♠♥ ✭❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❡ ❊ + ✶ ✮✳ ❙✐♥❝❡ â–Œ ♥ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✱ s♩ ✐s â–Œ ✵ ✳ ❚❀❡r❡❢♊r❡ P ✵ ✐s ✐♥❢ r✐❣✐❞✱ q❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  87. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❈♊♥❝❛✈✐t② ♊❢ ❙ ❚❀♠ ❇✳ ▲❡t ◗ ❜❡ ❛ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✱ ❛♥❞ ❧❡t ❚ ❜❡ ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀♊✉t ✐♥t❡r✐♩r ✈❡rt❡①✳ ❚❀❡♥ â–Œ ❚ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✳ ❚❀♠ ❇ = ⇒ ❚❀♠ ❆ ✿ st❛rt ✇✐t❀ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ P ✵ ✳ ❈❀♊♊s❡ ❛ ❝♊♥❝❛✈❡ ❡❞❣❡ ❡ ✶ ❛♥❞ ✏✜❧❧ ✐t✑ ✇✐t❀ ❛ s✐♠♣❧❡①✱ t♩ ❣❡t P ✶ ✖ ❡ ✶ ✐s ❛♥ ✐♥t❡r✐♩r ❡❞❣❡ ♊❢ P ✶ ✳ ❘❡♣❡❛t ✇✐t❀ ❡ ✷ ✱ ❡t❝✳ ❆❢t❡r ❛ ✜♥✐t❡ ♥✉♠❜❡r ♊❢ st❡♣s✱ P ♥ ✐s t❀❡ ❝♊♥✈❡① ❀✉❧❧ ♊❢ P ✵ ✳ ❚♩ ❣♊ ❢r♩♠ â–Œ ❊ + ✶ t♩ â–Œ ❊ ✱ s✐♠♣❧② r❡♠♊✈❡ ❛ ❧✐♥❡ ❛♥❞ ❛ ❝♊❧✉♠♥ ✭❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❡ ❊ + ✶ ✮✳ ❙✐♥❝❡ â–Œ ♥ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✱ s♩ ✐s â–Œ ✵ ✳ ❚❀❡r❡❢♊r❡ P ✵ ✐s ✐♥❢ r✐❣✐❞✱ q❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  88. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❈♊♥❝❛✈✐t② ♊❢ ❙ ❚❀♠ ❇✳ ▲❡t ◗ ❜❡ ❛ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✱ ❛♥❞ ❧❡t ❚ ❜❡ ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀♊✉t ✐♥t❡r✐♩r ✈❡rt❡①✳ ❚❀❡♥ â–Œ ❚ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✳ ❚❀♠ ❇ = ⇒ ❚❀♠ ❆ ✿ st❛rt ✇✐t❀ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ P ✵ ✳ ❈❀♊♊s❡ ❛ ❝♊♥❝❛✈❡ ❡❞❣❡ ❡ ✶ ❛♥❞ ✏✜❧❧ ✐t✑ ✇✐t❀ ❛ s✐♠♣❧❡①✱ t♩ ❣❡t P ✶ ✖ ❡ ✶ ✐s ❛♥ ✐♥t❡r✐♩r ❡❞❣❡ ♊❢ P ✶ ✳ ❘❡♣❡❛t ✇✐t❀ ❡ ✷ ✱ ❡t❝✳ ❆❢t❡r ❛ ✜♥✐t❡ ♥✉♠❜❡r ♊❢ st❡♣s✱ P ♥ ✐s t❀❡ ❝♊♥✈❡① ❀✉❧❧ ♊❢ P ✵ ✳ ❚♩ ❣♊ ❢r♩♠ â–Œ ❊ + ✶ t♩ â–Œ ❊ ✱ s✐♠♣❧② r❡♠♊✈❡ ❛ ❧✐♥❡ ❛♥❞ ❛ ❝♊❧✉♠♥ ✭❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❡ ❊ + ✶ ✮✳ ❙✐♥❝❡ â–Œ ♥ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✱ s♩ ✐s â–Œ ✵ ✳ ❚❀❡r❡❢♊r❡ P ✵ ✐s ✐♥❢ r✐❣✐❞✱ q❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  89. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❈♊♥❝❛✈✐t② ♊❢ ❙ ❚❀♠ ❇✳ ▲❡t ◗ ❜❡ ❛ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✱ ❛♥❞ ❧❡t ❚ ❜❡ ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀♊✉t ✐♥t❡r✐♩r ✈❡rt❡①✳ ❚❀❡♥ â–Œ ❚ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✳ ❚❀♠ ❇ = ⇒ ❚❀♠ ❆ ✿ st❛rt ✇✐t❀ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ P ✵ ✳ ❈❀♊♊s❡ ❛ ❝♊♥❝❛✈❡ ❡❞❣❡ ❡ ✶ ❛♥❞ ✏✜❧❧ ✐t✑ ✇✐t❀ ❛ s✐♠♣❧❡①✱ t♩ ❣❡t P ✶ ✖ ❡ ✶ ✐s ❛♥ ✐♥t❡r✐♩r ❡❞❣❡ ♊❢ P ✶ ✳ ❘❡♣❡❛t ✇✐t❀ ❡ ✷ ✱ ❡t❝✳ ❆❢t❡r ❛ ✜♥✐t❡ ♥✉♠❜❡r ♊❢ st❡♣s✱ P ♥ ✐s t❀❡ ❝♊♥✈❡① ❀✉❧❧ ♊❢ P ✵ ✳ ❚♩ ❣♊ ❢r♩♠ â–Œ ❊ + ✶ t♩ â–Œ ❊ ✱ s✐♠♣❧② r❡♠♊✈❡ ❛ ❧✐♥❡ ❛♥❞ ❛ ❝♊❧✉♠♥ ✭❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❡ ❊ + ✶ ✮✳ ❙✐♥❝❡ â–Œ ♥ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✱ s♩ ✐s â–Œ ✵ ✳ ❚❀❡r❡❢♊r❡ P ✵ ✐s ✐♥❢ r✐❣✐❞✱ q❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  90. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❈♊♥❝❛✈✐t② ♊❢ ❙ ❚❀♠ ❇✳ ▲❡t ◗ ❜❡ ❛ ❝♊♥✈❡① ♣♊❧②❀❡❞r♊♥✱ ❛♥❞ ❧❡t ❚ ❜❡ ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀♊✉t ✐♥t❡r✐♩r ✈❡rt❡①✳ ❚❀❡♥ â–Œ ❚ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✳ ❚❀♠ ❇ = ⇒ ❚❀♠ ❆ ✿ st❛rt ✇✐t❀ ❛ ✇❡❛❊❧② ❝♊♥✈❡①✱ ❞❡❝♊♠♣♊s❛❜❧❡ ❛♥❞ ❝♊❞❡❝♊♠♣♊s❛❜❧❡ ♣♊❧②❀❡❞r♊♥ P ✵ ✳ ❈❀♊♊s❡ ❛ ❝♊♥❝❛✈❡ ❡❞❣❡ ❡ ✶ ❛♥❞ ✏✜❧❧ ✐t✑ ✇✐t❀ ❛ s✐♠♣❧❡①✱ t♩ ❣❡t P ✶ ✖ ❡ ✶ ✐s ❛♥ ✐♥t❡r✐♩r ❡❞❣❡ ♊❢ P ✶ ✳ ❘❡♣❡❛t ✇✐t❀ ❡ ✷ ✱ ❡t❝✳ ❆❢t❡r ❛ ✜♥✐t❡ ♥✉♠❜❡r ♊❢ st❡♣s✱ P ♥ ✐s t❀❡ ❝♊♥✈❡① ❀✉❧❧ ♊❢ P ✵ ✳ ❚♩ ❣♊ ❢r♩♠ â–Œ ❊ + ✶ t♩ â–Œ ❊ ✱ s✐♠♣❧② r❡♠♊✈❡ ❛ ❧✐♥❡ ❛♥❞ ❛ ❝♊❧✉♠♥ ✭❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❡ ❊ + ✶ ✮✳ ❙✐♥❝❡ â–Œ ♥ ✐s ♣♊s✐t✐✈❡ ❞❡✜♥✐t❡✱ s♩ ✐s â–Œ ✵ ✳ ❚❀❡r❡❢♊r❡ P ✵ ✐s ✐♥❢ r✐❣✐❞✱ q❡❞✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  91. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙ ✇✐t❀ ✐♥t❡r✐♩r ✈❡rt✐❝❡s ❚❀♠ ❈ ✿ ❧❡t P ❜❡ ❝♊♥✈❡①✱ ❧❡t ❚ ❜❡ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀ ♥ ✐♥t❡r✐♩r ✈❡rt✐❝❡s✳ ❚❀❡♥ â–Œ ❚ ❀❛s ♥ ♥❡❣❛t✐✈❡ ❛♥❞ ✾ ♥ ③❡r♩ ❡✐❣❡♥✈❛❧✉❡s✳ ❈❧❡❛r❧② ❚❀♠ ❈ = ⇒ ❚❀♠ ❇✱ s♩ ✇❡ ❝♊♥❝❡♥tr❛t❡ ♊♥ ❚❀♠ ❈✳ ❚❀♠ ❈ ✐s tr✉❡ ✐♥ s♣❡❝✐❛❧ ❝❛s❡s ✿ ✐❢ ❚ ✵ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ ❛♥❞ ❛❧❧ s✐♠♣❧✐❝❡s s❀❛r❡ ❛ ✈❡rt❡① ✭■③♠❡st✐❡✈✮✳ ✐❢ ❚ ✵ ❀❛s ❡①❛❝t❧② ♊♥❡ ✐♥t❡r✐♩r ✈❡rt❡①✱ s❀❛r❡❞ ❜② ❛❧❧ s✐♠♣❧✐❝❡s ✭❇♊❜❡♥❊♊✲■③♠❡st✐❡✈✮✳ ❚♩ ♣r♊✈❡ ❚❀♠ ❈✱ s❀♊✇ t❀❛t ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ❚ ❝❛♥ ❜❡ ❝♊♥♥❡❝t❡❞ t♩ s✉❝❀ ❛ ❚ ✵ ❜② s✐♠♣❧❡ ♠♊✈❡s ✇❀✐❝❀ r❡s♣❡❝t ❚❀♠ ❈✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  92. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙ ✇✐t❀ ✐♥t❡r✐♩r ✈❡rt✐❝❡s ❚❀♠ ❈ ✿ ❧❡t P ❜❡ ❝♊♥✈❡①✱ ❧❡t ❚ ❜❡ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀ ♥ ✐♥t❡r✐♩r ✈❡rt✐❝❡s✳ ❚❀❡♥ â–Œ ❚ ❀❛s ♥ ♥❡❣❛t✐✈❡ ❛♥❞ ✾ ♥ ③❡r♩ ❡✐❣❡♥✈❛❧✉❡s✳ ❈❧❡❛r❧② ❚❀♠ ❈ = ⇒ ❚❀♠ ❇✱ s♩ ✇❡ ❝♊♥❝❡♥tr❛t❡ ♊♥ ❚❀♠ ❈✳ ❚❀♠ ❈ ✐s tr✉❡ ✐♥ s♣❡❝✐❛❧ ❝❛s❡s ✿ ✐❢ ❚ ✵ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ ❛♥❞ ❛❧❧ s✐♠♣❧✐❝❡s s❀❛r❡ ❛ ✈❡rt❡① ✭■③♠❡st✐❡✈✮✳ ✐❢ ❚ ✵ ❀❛s ❡①❛❝t❧② ♊♥❡ ✐♥t❡r✐♩r ✈❡rt❡①✱ s❀❛r❡❞ ❜② ❛❧❧ s✐♠♣❧✐❝❡s ✭❇♊❜❡♥❊♊✲■③♠❡st✐❡✈✮✳ ❚♩ ♣r♊✈❡ ❚❀♠ ❈✱ s❀♊✇ t❀❛t ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ❚ ❝❛♥ ❜❡ ❝♊♥♥❡❝t❡❞ t♩ s✉❝❀ ❛ ❚ ✵ ❜② s✐♠♣❧❡ ♠♊✈❡s ✇❀✐❝❀ r❡s♣❡❝t ❚❀♠ ❈✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  93. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙ ✇✐t❀ ✐♥t❡r✐♩r ✈❡rt✐❝❡s ❚❀♠ ❈ ✿ ❧❡t P ❜❡ ❝♊♥✈❡①✱ ❧❡t ❚ ❜❡ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀ ♥ ✐♥t❡r✐♩r ✈❡rt✐❝❡s✳ ❚❀❡♥ â–Œ ❚ ❀❛s ♥ ♥❡❣❛t✐✈❡ ❛♥❞ ✾ ♥ ③❡r♩ ❡✐❣❡♥✈❛❧✉❡s✳ ❈❧❡❛r❧② ❚❀♠ ❈ = ⇒ ❚❀♠ ❇✱ s♩ ✇❡ ❝♊♥❝❡♥tr❛t❡ ♊♥ ❚❀♠ ❈✳ ❚❀♠ ❈ ✐s tr✉❡ ✐♥ s♣❡❝✐❛❧ ❝❛s❡s ✿ ✐❢ ❚ ✵ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ ❛♥❞ ❛❧❧ s✐♠♣❧✐❝❡s s❀❛r❡ ❛ ✈❡rt❡① ✭■③♠❡st✐❡✈✮✳ ✐❢ ❚ ✵ ❀❛s ❡①❛❝t❧② ♊♥❡ ✐♥t❡r✐♩r ✈❡rt❡①✱ s❀❛r❡❞ ❜② ❛❧❧ s✐♠♣❧✐❝❡s ✭❇♊❜❡♥❊♊✲■③♠❡st✐❡✈✮✳ ❚♩ ♣r♊✈❡ ❚❀♠ ❈✱ s❀♊✇ t❀❛t ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ❚ ❝❛♥ ❜❡ ❝♊♥♥❡❝t❡❞ t♩ s✉❝❀ ❛ ❚ ✵ ❜② s✐♠♣❧❡ ♠♊✈❡s ✇❀✐❝❀ r❡s♣❡❝t ❚❀♠ ❈✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  94. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙ ✇✐t❀ ✐♥t❡r✐♩r ✈❡rt✐❝❡s ❚❀♠ ❈ ✿ ❧❡t P ❜❡ ❝♊♥✈❡①✱ ❧❡t ❚ ❜❡ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀ ♥ ✐♥t❡r✐♩r ✈❡rt✐❝❡s✳ ❚❀❡♥ â–Œ ❚ ❀❛s ♥ ♥❡❣❛t✐✈❡ ❛♥❞ ✾ ♥ ③❡r♩ ❡✐❣❡♥✈❛❧✉❡s✳ ❈❧❡❛r❧② ❚❀♠ ❈ = ⇒ ❚❀♠ ❇✱ s♩ ✇❡ ❝♊♥❝❡♥tr❛t❡ ♊♥ ❚❀♠ ❈✳ ❚❀♠ ❈ ✐s tr✉❡ ✐♥ s♣❡❝✐❛❧ ❝❛s❡s ✿ ✐❢ ❚ ✵ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ ❛♥❞ ❛❧❧ s✐♠♣❧✐❝❡s s❀❛r❡ ❛ ✈❡rt❡① ✭■③♠❡st✐❡✈✮✳ ✐❢ ❚ ✵ ❀❛s ❡①❛❝t❧② ♊♥❡ ✐♥t❡r✐♩r ✈❡rt❡①✱ s❀❛r❡❞ ❜② ❛❧❧ s✐♠♣❧✐❝❡s ✭❇♊❜❡♥❊♊✲■③♠❡st✐❡✈✮✳ ❚♩ ♣r♊✈❡ ❚❀♠ ❈✱ s❀♊✇ t❀❛t ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ❚ ❝❛♥ ❜❡ ❝♊♥♥❡❝t❡❞ t♩ s✉❝❀ ❛ ❚ ✵ ❜② s✐♠♣❧❡ ♠♊✈❡s ✇❀✐❝❀ r❡s♣❡❝t ❚❀♠ ❈✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

  95. ❚❀❡ ❜❡❣✐♥♥✐♥❣ ♊❢ t❀❡ st♩r② ❚❀❡ ❘❡♥❛✐ss❛♥❝❡ ▌♊❞❡r♥ t✐♠❡s ❖♣❡♥ q✉❡st✐♊♥s ❆ r✐❣✐❞✐t② r❡s✉❧t ❙ ✇✐t❀ ✐♥t❡r✐♩r ✈❡rt✐❝❡s ❚❀♠ ❈ ✿ ❧❡t P ❜❡ ❝♊♥✈❡①✱ ❧❡t ❚ ❜❡ ❛ tr✐❛♥❣✉❧❛t✐♊♥ ✇✐t❀ ♥ ✐♥t❡r✐♩r ✈❡rt✐❝❡s✳ ❚❀❡♥ â–Œ ❚ ❀❛s ♥ ♥❡❣❛t✐✈❡ ❛♥❞ ✾ ♥ ③❡r♩ ❡✐❣❡♥✈❛❧✉❡s✳ ❈❧❡❛r❧② ❚❀♠ ❈ = ⇒ ❚❀♠ ❇✱ s♩ ✇❡ ❝♊♥❝❡♥tr❛t❡ ♊♥ ❚❀♠ ❈✳ ❚❀♠ ❈ ✐s tr✉❡ ✐♥ s♣❡❝✐❛❧ ❝❛s❡s ✿ ✐❢ ❚ ✵ ❀❛s ♥♊ ✐♥t❡r✐♩r ✈❡rt❡①✱ ❛♥❞ ❛❧❧ s✐♠♣❧✐❝❡s s❀❛r❡ ❛ ✈❡rt❡① ✭■③♠❡st✐❡✈✮✳ ✐❢ ❚ ✵ ❀❛s ❡①❛❝t❧② ♊♥❡ ✐♥t❡r✐♩r ✈❡rt❡①✱ s❀❛r❡❞ ❜② ❛❧❧ s✐♠♣❧✐❝❡s ✭❇♊❜❡♥❊♊✲■③♠❡st✐❡✈✮✳ ❚♩ ♣r♊✈❡ ❚❀♠ ❈✱ s❀♊✇ t❀❛t ❛♥② tr✐❛♥❣✉❧❛t✐♊♥ ❚ ❝❛♥ ❜❡ ❝♊♥♥❡❝t❡❞ t♩ s✉❝❀ ❛ ❚ ✵ ❜② s✐♠♣❧❡ ♠♊✈❡s ✇❀✐❝❀ r❡s♣❡❝t ❚❀♠ ❈✳ ❏❡❛♥✲▌❛r❝ ❙❝❀❧❡♥❊❡r Pr♊❜❧Ú♠❡s ❛♥❝✐❡♥s ❡t ♥♊✉✈❡❛✉① s✉r ❧❡s ♣♊❧②Ú❞r❡s ❡✉❝❧✐❞✐❡♥s

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