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Math-Net.Ru
Общероссийский математический портал
А. М. Вершик, В. А. Залгаллер, С. С. Кутателадзе, В. Л. Макаров, Ю. Г. Решетняк, И. В. Романовский, Геннадий Шлемович Рубинштейн (некролог), УМН,
2005, том 60, выпуск 2(362), 145–146
DOI: https://doi.org/10.4213/rm1409
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11 марта 2020 г., 09:46:17
✁✁✂ ✄☎ ✆✝✞✟ ✠ ✝✡✞☛☞✌
✟ ☎ ✍✁✎ ✏✑✡ ☎ ✒✓✍ ✔
✕✖✗✘✙✚ ✛✜✢✘✛✜✢✚ ✣✘✖✤✚✙ ✥✜✕✤
✦✧★★✩✪✫✬ ✭✮✧✯✰✱✫✲ ✳✴✵✫★✭✶✧✬★
✷ ✸✹✺ ✷✻✻✼ ✽✾ ✿✹ ❀✷❁✸ ✽❂❃❄ ❅❆❇✿❆ ❈❉❂✿❊✹❋❈✺ ❃❂❉●
❍❂■ ❏❆❇❆❉❂❁✸✹❍❑✸✹❍❆❊❑❈❉❆▲ ✿✹❄❉▼ ◆■❂❏❑❈❈❂■ ❖❑✿✿✹❃❆P
◗❋❑✸❂❘❆❊ ❙❄❚❆✿❯❍❑P✿ ▼ ❄❊❑✿❆❉ ❆ ❈❂■✹❍✿❆❉ ❱✾❲✾ ❳✹✿●
❍❂■❂❘❆❊✹ ❘ ❃❑❋❑ ■✹❇❘❆❍❆✺ ✸✹❍❑✸✹❍❆❉❂ ❉❂✿❂✸❆❊❑❈❉❆▲
✸❑❍❂❃❂❘ ❆ ❚❋❆❇❉❆▲ ❘❂◆■❂❈❂❘ ❏❄✿❉❩❆❂✿✹❋❁❨❬✿❂✽❂ ✹✿✹❋❆❇✹✾
❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ■❂❃❆❋❈✺ ✷❭✹◆■❑❋✺ ❪❫✷❴✽✾ ❘ ❵❃❑❈❈❑ ✾
❛❂❈❋❑ ❂❉❂✿❊✹✿❆✺ ❈■❑❃✿❑P ❯❉❂❋❜ ❘ ❪❫✼✻ ✽✾ ❂✿ ◆❂❈❍❄◆❆❋
✿✹ ❏❆❇❆❉❂❁✸✹❍❑✸✹❍❆❊❑❈❉❆P ❏✹❉❄❋❬❍❑❍ ❵❃❑❈❈❉❂✽❂ ✽❂❈●
❄✿❆❘❑■❈❆❍❑❍✹ ▼ ✿❂ ❄❊❑❚❄ ◆■❑■❘✹❋✹ ❘❂P✿✹✾ ❙❄❚❆✿❯❍❑P✿
◆■❂❯❑❋ ❘❈❝ ❘❂P✿❄ ❂❍ ❂❚❂■❂✿❜ ❞✿❑◆■❂◆❑❍■❂❘❈❉✹ ❃❂
❘❇✺❍❆✺ ❡❑■❋❆✿✹ ❘✿✹❊✹❋❑ ■✺❃❂❘❜✸ ▼ ✹ ❇✹❍❑✸ ▼ ◆❂❈❋❑ ❂❉❂✿●
❊✹✿❆✺ ❳❄P❚❜❯❑❘❈❉❂✽❂ ❘❂❑✿✿❂✽❂ ❄❊❆❋❆❢✹ ▼ ❉❂✸✹✿❃❆■❂✸
◆❂❃■✹❇❃❑❋❑✿❆P ❈❘✺❇❆ ❃❑P❈❍❘❄❝❢❑P ✹■✸❆❆ ✾ ❣✽❂ ❚❂❑❘❜❑
❇✹❈❋❄✽❆ ❚❜❋❆ ❂❍✸❑❊❑✿❜ ❃❘❄✸✺ ❂■❃❑✿✹✸❆ ❳■✹❈✿❂P ❤❘❑❇❃❜
❆ ✸❑❃✹❋✺✸❆ ✾
❛❂❈❋❑ ❃❑✸❂❚❆❋❆❇✹❩❆❆ ❘ ❪❫✼❭ ✽✾ ❖❑✿✿✹❃❆P ◗❋❑✸❂❘❆❊
❂
❘ ❇❂❚✿❂❘❆❋ ❄❊❑❚❄ ❘ ❵❃❑❈❈❉❂✸ ✽❂❈❄✿❆❘❑■❈❆❍❑❍❑ ✾ ✐ ❊❑❍●
❘❑■❍❂✽❂ ❉❄■❈✹ ❂✿ ◆❑■❑❘❑❋❈✺ ❘ ❱❑✿❆✿✽■✹❃❈❉❆P ✽❂❈❄✿❆❘❑■●
❈❆❍❑❍▼ ❉❂❍❂■❜P ❆ ❇✹❉❂✿❊❆❋ ❘ ❪❫✼❫ ✽✾ ❥❅❑ ❘ ❈❍❄❃❑✿❊❑❈❉❆❑ ✽❂❃❜ ❙❄❚❆✿❯❍❑P✿ ✹❉❍❆❘✿❂ ❘❉❋❝❊❆❋❈✺
❘ ✿✹❄❊✿❄❝ ■✹❚❂❍❄✾ ❲❈❍■❑❊✹ ❈ ❳✹✿❍❂■❂❘❆❊❑✸ ❘❂ ✸✿❂✽❂✸ ❂◆■❑❃❑❋❆❋✹ ❃✹❋❬✿❑P❯❆P ◆❄❍❬ ✸❂❋❂❃❂✽❂
❄❊❑✿❂✽❂ ❆ ❈❍✹❋✹ ✿✹❊✹❋❂✸ ❆▲ ✸✿❂✽❂❋❑❍✿❑✽❂ ❈❂❍■❄❃✿❆❊❑❈❍❘✹✾ ❣✽❂ ❃❆◆❋❂✸✿✹✺ ■✹❚❂❍✹ ❦❵ ■✹❇❃❑❋❑✿❆❆
❘❜◆❄❉❋❜▲ ✸✿❂❅❑❈❍❘❧ ◆■❑❃❈❍✹❘❋✺❑❍ ❂❚❈❍❂✺❍❑❋❬✿❂❑ ❆❈❈❋❑❃❂❘✹✿❆❑ ◆❂ ❍❑❂■❆❆ ❘❜◆❄❉❋❜▲ ✸✿❂❅❑❈❍❘▼
❘ ❉❂❍❂■❂✸ ❚❜❋ ■✹❇■✹❚❂❍✹✿ ✽❑❂✸❑❍■❆❊❑❈❉❆P ◆❂❃▲❂❃ ❉ ❄❈❍✹✿❂❘❋❑✿❆❝ ❍❑❂■❑✸ ❂❍❃❑❋❆✸❂❈❍❆ ❃❋✺ ❘❜●
◆❄❉❋❜▲ ✸✿❂❅❑❈❍❘❘ ❋❆✿❑P✿❜▲◆■❂❈❍■✹✿❈❍❘✹▲ ❂❚❢❑✽❂ ❘❆❃✹ ❆ ◆■❆❘❑❃❑✿ ■✺❃❆✿❍❑■❑❈✿❜▲◆■❆❋❂❅❑✿❆P
❂■❑✸✾
❨❍❆▲❲ ❍❑❫✼❫
❪ ♠ ❪❫♥✷ ✽✽✾ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ■✹❚❂❍✹❋ ❈❍✹■❯❆✸ ❆✿❅❑✿❑■❂✸❁❍❑▲✿❂❋❂✽❂✸ ❳❆■❂❘❈❉❂✽❂ ❇✹●
❘❂❃✹ ▼ ❈ ❪❫♥✷ ◆❂ ❪❫♥❭ ✽✽✾ ♠ ❄❊❆❍❑❋❑✸ ✸✹❍❑✸✹❍❆❉❆ ❘ ❂❃✿❂P ❆❇ ❋❑✿❆✿✽■✹❃❈❉❆▲ ❯❉❂❋✾ ❵❃✿❂❘■❑✸❑✿●
✿❂ ❂✿ ❘❑❋ ◆■❑◆❂❃✹❘✹❍❑❋❬❈❉❄❝ ■✹❚❂❍❄ ❘ ♦❑❉❈❍❆❋❬✿❂✸ ❆✿❈❍❆❍❄❍❑ ❆ ❲❂❑✿✿❂❁✸❂■❈❉❂P ✹❉✹❃❑✸❆❆ ❆✸✾
♣✾q✾ ❳■❜❋❂❘✹✾ ❲ ❪❫♥❭ ✽✾ ◆❂❈❋❑ ❇✹❢❆❍❜ ❉✹✿❃❆❃✹❍❈❉❂P ❃❆❈❈❑■❍✹❩❆❆ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ◆❑■❑❯❑❋
✿✹ ❂❈✿❂❘✿❄❝ ■✹❚❂❍❄ ❘ ❲❂❑✿✿❂❁✸❂■❈❉❄❝ ✹❉✹❃❑✸❆❝▼ ❈❂❘✸❑❢✹✺ ❑❑ ❈ ◆■❑◆❂❃✹❘✹✿❆❑✸ ❘ ❱❑✿❆✿✽■✹❃●
❈❉❂✸ ✽❂❈❄✿❆❘❑■❈❆❍❑❍❑▼ ✽❃❑ ❂✿ ◆■❂❊❑❋ ◆❑■❘❜P ❉❄■❈ ✸✹❍❑✸✹❍❆❊❑❈❉❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺ ✿✹ ✸✹❍●
✸❑▲❑ ❱❖❥ ❆ ✿✹ ❇✿✹✸❑✿❆❍❂✸ ❦❯❑❈❍❂✸ ❉❄■❈❑❧ ❨❉❂✿❂✸❆❊❑❈❉❂✽❂ ❏✹❉❄❋❬❍❑❍✹✾ ✐ ❪❫♥❀ ✽✾ ❂✿ ❈❍✹❋ r◆❂
❈❂❘✸❑❈❍❆❍❑❋❬❈❍❘❄s ✿✹❄❊✿❜✸ ❈❂❍■❄❃✿❆❉❂✸ ❱✹❚❂■✹❍❂■❆❆ ◆❂ ◆■❆✸❑✿❑✿❆❝ ✸✹❍❑✸✹❍❆❊❑❈❉❆▲ ✸❑❍❂❃❂❘
❘ ❨❉❂✿❂✸❆❉❑ ✐❆❚❆■❈❉❂✽❂ ❂❍❃❑❋❑✿❆✺ ♣❉✹❃❑✸❆❆ ✿✹❄❉ ✾ ❲ ❪❫❭✷✽✾ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ◆❑■❑❑▲✹❋ ❘ q❂❘❂●
❈❆❚❆■❈❉❆P ✹❉✹❃❑✸✽❂■❂❃❂❉▼ ✽❃❑ ❘◆❋❂❍❬ ❃❂ ❈❘❂❑P ❉❂✿❊❆✿❜ ❈❂❈❍❂✺❋ ❘ ❯❍✹❍❑ t✿❈❍❆❍❄❍✹ ✸✹❍❑✸✹❍❆❉❆
❆✸✾ ✐✾ ❱✾ ✐❂❚❂❋❑❘✹✾ ❲ ❪❫❭♥ ✽✾ ❂✿ ❇✹❢❆❍❆❋ ❃❂❉❍❂■❈❉❄❝ ❃❆❈❈❑■❍✹❩❆❝ ✾ ❞❂❋✽❆❑ ✽❂❃❜ ❖✾◗✾ ❙❄❚❆✿●
❯❍❑P✿ ❇✹❘❑❃❂❘✹❋ ❂❍❃❑❋❂✸ ❘❜◆❄❉❋❂✽❂ ✹✿✹❋❆❇✹ ❆ ❍❑❂■❆❆ ❨❉❈❍■❑✸✹❋❬✿❜▲ ❇✹❃✹❊ ❆ ■✹❚❂❍✹❋ ◆■❂❏❑❈●
❈❂■❂✸ q❂❘❂❈❆❚❆■❈❉❂✽❂ ✽❂❈❄✿❆❘❑■❈❆❍❑❍✹✾
❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ✹❘❍❂■ ❂❉❂❋❂ ❪✻✻ ✿✹❄❊✿❜▲ ■✹❚❂❍▼ ◆❂❈❘✺❢❑✿✿❜▲ ■✹❇✿❂❂❚■✹❇✿❜✸ ❇✹❃✹❊✹✸
✹✿✹❋❆❇✹ ❆ ❑✽❂ ◆■❆❋❂❅❑✿♠❆P ✾ ❵❈✿❂❘✿❜❑ ❑✽❂ ❆❈❈❋❑❃❂❘✹✿❆✺ ❈❂❈■❑❃❂❍❂❊❑✿❜ ❘ ❈❋❑❃❄❝❢❆▲ ❍■❑▲ ✿✹◆■✹❘●
❋❑✿❆✺▲✉ ❍❑❂■❆✺ ❘❜◆❄❉❋❜▲ ✸✿❂❅❑❈❍❘ ❆ ❘❜◆❄❉❋❜▲ ❏❄✿❉❩❆P▼ ❍❑❂■❆✺ ❃❘❂P❈❍❘❑✿✿❂❈❍❆ ❃❋✺ ❨❉❈❍■❑●
❪✼❭
✁✂✂✄☎✆✝ ✞✟✁✠✡☛✆☞ ✌✍✎✆✂✞✏✁✝✂
✸✹❋❬✿❜▲ ❇✹❃✹❊▼ ❊❆❈❋❑✿✿❜❑ ✸❑❍❂❃❜ ✸✹❍❑✸✹❍❆❊❑❈❉❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺ ❆ ❆▲ ◆■❆✸❑✿❑✿❆✺ ❘ ◆❋✹●
✿❂❘❂❁❨❉❂✿❂✸❆❊❑❈❉❆▲ ❇✹❃✹❊✹▲ ✾ ❲❈❑ ❍■❆ ❩❆❉ ❋✹ ❍❑❈✿❂ ❈❘✺❇✹✿❜ ❍❑✸✹❍❆❊❑❈❉❆ ❆ ✿❑■✹❇❃❑❋❆✸❜ ❘❂ ❘■❑✸❑●
✿❆ ✾ ✑✹■✹❉❍❑■✿❂P ❂❈❂❚❑✿✿❂❈❍❬❝ ❍❘❂■❊❑❈❍❘✹ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿✹ ✺❘ ❋✺❑❍❈✺ ❘❇✹❆✸❂◆■❂✿❆❉✿❂❘❑✿❆❑
❆❃❑P ❆ ✸❑❍❂❃❂❘ ■✹❇❋❆❊✿❜▲ ❂❚❋✹❈❍❑P ✸✹❍❑✸✹❍❆❉❆ ✾
❙✹❇■✹❚❂❍✹✿✿❜P ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿❂✸ ❨❋❑✸❑✿❍✹■✿❂❁✽❑❂✸❑❍■❆❊❑❈❉❆P ◆❂❃▲❂❃ ❉ ◆❂❈❍■❂❑✿❆❝ ❍❑❂●
■❆❆ ❘❜◆❄❉ ❋❜▲ ✸✿❂❅❑❈❍❘▼ ❂◆❆■✹❝❢❆P❈✺ ✿✹ ◆■❂❘❑❃❑✿✿❂❑ ❆✸ ❆❈❈❋❑❃❂❘✹✿❆❑ ✽■✹✿❑❘❜▲ ❈❍■❂❑✿❆P▼ ◆❂❇●
❘❂❋❆ ❋ ◆❂❋❄❊❆❍❬ ◆■✹❉❍❆❊❑❈❉❆ ❂❉❂✿❊✹❍❑❋❬✿❜❑ ❏❂■✸❜ ❍❑❂■❑✸ ❂❚ ❂❍❃❑❋❆✸❂❈❍❆ ❘❜◆❄❉ ❋❜▲ ✸✿❂❅❑❈❍❘
❘ ❂❚❢❆▲ ❋❆✿❑P✿❜▲ ◆■❂❈❍■✹✿❈❍❘✹▲ ✾ ❡❂❋❑❑ ❍❂✽❂ ▼ ❨❍❆ ❍❑❂■❑✸❜ ❄❈❍✹✿✹❘ ❋❆❘✹❝❍❈✺ ❘ ❍✹❉ ✿✹❇❜❘✹❑✸❜▲
❂❈❑❘❜▲ ◆■❂❈❍■✹✿❈❍❘✹▲▼ ❘❉ ❋❝❊✹❝❢❆▲ ◆❂✸❆✸❂ ❋❆✿❑P✿❜▲ ◆■❂❈❍■✹✿❈❍❘✹ ❱❂❚✹❊❑❘❈❉❂✽❂ ❆ ✿❑❉❂❍❂■❜❑
❃■❄✽❆❑ ✾ ❙✹❇❘❆❍❜P ◆■❆ ❨❍❂✸ ✹◆◆✹■✹❍ ◆❂❇❘❂❋❆ ❋ ❂❃✿❂❘■❑✸❑✿✿❂ ■❑❯❆❍❬ ✿❑❉❂❍❂■❜❑ ❇✹❃✹❊❆▼ ❂❍✿❂❈✺●
❢❆❑❈✺ ❉ ❂❈✿❂❘✹✿❆✺✸ ✽❑❂✸❑❍■❆❆ ✾
❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ◆■❑❃❋❂❅❆ ❋ ❆ ❃❑❍✹❋❬✿❂ ■✹❇■✹❚❂❍✹❋ ❂❃❆✿ ❆❇ ✿✹❆❚❂❋❑❑ ❂❚❢❆▲ ◆❂❃▲❂❃❂❘ ❉ ◆❂●
❈❍■❂❑✿❆❝ ❃❘❂P❈❍❘❑✿✿❜▲ ❨❉❈❍■❑✸✹❋❬✿❜▲ ❇✹❃✹❊▼ ❘ ❉❂❍❂■❂✸ ❈❄❢❑❈❍❘❑✿✿❄❝ ■❂❋❬ ❆✽■✹❝❍ ❍❑❂■❑✸❜
❂❍❃❑❋❆✸❂❈❍❆ ❘❜◆❄❉ ❋❜▲ ✸✿❂❅❑❈❍❘ ✾ ❛■❆ ❨❍❂✸ ✿✹■✺❃❄ ❈ ❉ ❋✹❈❈❆❊❑❈❉❆✸❆ ❍❑❂■❑✸✹✸❆ ❈❆❈❍❑✸✹❍❆❊❑❈❉❆
❚❜ ❋ ❆❈◆❂❋❬❇❂❘✹✿ ■✺❃ ❚❂❋❑❑ ❍❂✿❉❆▲ ❍❑❂■❑✸ ❂❍❃❑❋❆✸❂❈❍❆ ✾ ❛❑■❘❜✸ ❘✹■❆✹✿❍❂✸ ❘ ◆❂❈❍■❂❑✿❆❆ ❄❉✹❇✹✿●
✿❂✽❂ ◆❂❃▲❂❃✹ ❈❍✹❋❂ ❆❈❈❋❑❃❂❘✹✿❆❑ ✽❑❂✸❑❍■❆❊❑❈❉❂P ❇✹❃✹❊❆ ❂ ❉■✹P✿❑P ❍❂❊❉❑ ◆❑■❑❈❑❊❑✿❆✺ ❂❈❆ ❈ ❘❜●
◆❄❉ ❋❜✸ ✸✿❂❅❑❈❍❘❂✸✾ ✐ ◆❂✸❂❢❬❝ ❍✹❉❂P ❊✹❈❍✿❂P ❈▲❑✸❜ ❃❘❂P❈❍❘❑✿✿❂❈❍❆ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ❆❇❄❊❆ ❋
■✹❇❋❆❊✿❜❑ ❉ ❋✹❈❈❜ ❇✹❃✹❊ ❋❆✿❑P✿❂✽❂ ❆ ❘❜◆❄❉ ❋❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺▼ ❍❑❂■❆❆ ❆✽■ ❆ ✿✹❆ ❋❄❊❯❑✽❂
◆■❆❚❋❆❅❑✿❆✺ ✾
❵❈❂❚❂ ❈❋❑❃❄❑❍ ❂❍✸❑❍❆❍❬ ❈❑■❆❝ ❈❂❘✸❑❈❍✿❜▲ ■✹❚❂❍ ❱✾❲✾ ❳✹✿❍❂■❂❘❆❊✹ ❆ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿✹ ▼
❈❘✺❇✹✿✿❜▲ ❈ ◆■❂❚❋❑✸❂P ✒❂✿❅✹✾ ❙✹❇❘❆❍❜P ◆■❆ ■❑❯❑✿❆❆ ❨❍❆▲ ❇✹❃✹❊ ✹◆◆✹■✹❍ ◆■❂❊✿❂ ❘❂❯❑❋ ❘ ✸✹❍❑●
✸✹❍❆❊❑❈❉❆P ❍❑❇✹❄■❄❈ ✾ t❈❈❋❑❃❂❘✹✿❆❝ ❏❄✿❉❩❆❂✿✹❋❬✿❂✽❂ ◆■❂❈❍■✹✿❈❍❘✹ ❳✹✿❍❂■❂❘❆❊✹♠ ❙❄❚❆✿❯❍❑P●
✿✹ ◆❂❈❘✺❢❑✿❂ ❇✿✹❊❆❍❑❋❬✿❂❑ ❊❆❈❋❂ ❍❑❂■❑❍❆❊❑❈❉❆▲ ❆ ◆■❆❉ ❋✹❃✿❜▲ ■✹❚❂❍✾ ❲ ❃✹❋❬✿❑P❯❑✸ ❖✾◗✾ ❙❄●
❚❆✿❯❍❑P✿ ✿✹ ❂❈✿❂❘❑ ■✹❇■✹❚❂❍✹✿✿❂P ❆✸ ❂❚❢❑P ❍❑❂■❆❆ ◆❂❋❄❊❆ ❋ ■✺❃ ✿❂❘❜▲ ❘✹❅✿❜▲ ■❑❇❄❋❬❍✹❍❂❘ ◆❂
❉❂✿❉■❑❍✿❜✸ ❉❂✿❑❊✿❂✸❑■✿❜✸ ❆ ❚❑❈❉❂✿❑❊✿❂✸❑■✿❜✸ ❨❉❈❍■❑✸✹❋❬✿❜✸ ❇✹❃✹❊✹✸✾ t✸ ❚❜ ❋❆ ◆❂❋❄❊❑✿❜
❆❇✺❢✿❜❑ ■❑❇❄❋❬❍✹❍❜ ❂ ◆■❑❂❚■✹❇❂❘✹✿❆❆ ❉❘✹❇❆❘❜◆❄❉ ❋❜▲ ❏❄✿❉❩❆P ❘ ❘❜◆❄❉ ❋❜❑▼ ◆■❑❃❈❍✹❘ ❋✺❝❢❆❑
❈❂❚❂P ◆■❆✿❩❆◆❆✹❋❬✿❂❑ ■❑❯❑✿❆❑ ◆■❂❚❋❑✸❜▼ ◆❂❈❍✹❘ ❋❑✿✿❂P ✓❑✿▲❑❋❑✸ ❑❢❑ ❘ ❪❫♥❴ ✽✾ ❲ ❂❚❋✹❈❍❆ ❊❆❈●
❋❑✿✿❜▲ ✸❑❍❂❃❂❘ ✸✹❍❑✸✹❍❆❊❑❈❉❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺ ❂❈✿❂❘✿❜❑ ■❑❇❄❋❬❍✹❍❜ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿✹
❈❘✺❇✹✿❜▼ ❘ ◆❑■❘❄❝ ❂❊❑■❑❃❬▼ ❈ ❈❂❇❃✹✿❆❑✸ ❈◆❑❩❆✹❋❬✿❜▲ ✹❋✽❂■❆❍✸❂❘ ❃❋✺ ■❑❯❑✿❆✺ ❇✹❃✹❊ ❚❂❋❬❯❂✽❂
❂❚✔❑✸✹✾ ❵✿ ◆■❑❃❋❂❅❆ ❋ ■✺❃ ❨❏❏❑❉❍❆❘✿❜▲ ❆❃❑P ❆❈◆❂❋❬❇❂❘✹✿❆✺ ❈◆❑❩❆✹❋❬✿❂P ❈❍■❄❉❍❄■❜ ✸✹❍■❆❩❜▼
◆❂❇❘❂❋❆❘❯❆▲ ❈❂❇❃✹❍❬ ❨❉❂✿❂✸✿❜❑ ❘❜❊❆❈❋❆❍❑❋❬✿❂❑ ❈▲❑✸❜ ❃❋✺ ❇✹❃✹❊ ❋❆✿❑P✿❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺
❚❋❂❊✿❂P ❈❍■❄❉❍❄■❜ ✾ ❵✽■❂✸✿✹✺ ❇✹❈❋❄✽✹ ◆■❆✿✹❃❋❑❅❆❍ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿❄ ❘ ◆■❂◆✹✽✹✿❃❆■❂❘✹✿❆❆
✸❑❍❂❃❂❘ ❋❆✿❑P✿❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺▼ ❂❈❂❚❑✿✿❂ ❘ ◆❑■❘❜❑ ✽❂❃❜ ❈❍✹✿❂❘ ❋❑✿❆✺ ❨❍❂✽❂ ✿✹◆■✹❘ ❋❑✿❆✺
❘ ✿✹❯❑P ❈❍■✹✿❑ ✾ ❛❂❃ ■❄❉❂❘❂❃❈❍❘❂✸ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿✹ ❘ ❍❂ ❘■❑✸✺ ❚❜ ❋ ❂❈❄❢❑❈❍❘ ❋❑✿ ■✺❃ ■✹❚❂❍
◆❂ ❘✿❑❃■❑✿❆❝ ✸❑❍❂❃❂❘ ❋❆✿❑P✿❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺ ❘ ▲❂❇✺P❈❍❘❑✿✿❄❝ ◆■✹❉❍❆❉❄▼ ❘ ❊✹❈❍✿❂❈❍❆▼ ❘
◆❋✹✿❆■❂❘✹✿❆❆ ❇✹❉✹❇✹ ❆ ■✹❈❉■❂✺ ◆■❂✸❜❯❋❑✿✿❜▲ ✸✹❍❑■❆✹❋❂❘ ✿✹ ❳❆■❂❘❈❉❂✸ ❇✹❘❂❃❑▼ ✒❂❈❉❂❘❈❉❂✸
❇✹❘❂❃❑ ✸✹❋❂❋❆❍■✹❅✿❜▲ ✹❘❍❂✸❂❚❆ ❋❑P ❆ ❃■ ✾
q✹■✺❃❄ ❈ ✿✹❄❊✿❂P ❆ ✿✹❄❊✿❂❁◆■❂❆❇❘❂❃❈❍❘❑✿✿❂P ❃❑✺❍❑❋❬✿❂❈❍❬❝ ❚❂❋❬❯❂❑ ❘✿❆✸✹✿❆❑ ❖❑✿✿✹❃❆P
◗❋❑✸❂❘❆❊ ❄❃❑❋✺ ❋ ◆❂❃✽❂❍❂❘❉❑ ❉✹❃■❂❘ ✾ ❣✸❄ ◆■❆✿✹❃❋❑❅❆❍ ❇✹❈❋❄✽✹ ◆❂❈❍✹✿❂❘❉❆ ❂❃✿❂✽❂ ❆❇ ◆❑■❘❜▲
❘ ❈❍■✹✿❑ ❄✿❆❘❑■❈❆❍❑❍❈❉❆▲ ❉❄■❈❂❘ ✸✹❍❑✸✹❍❆❊❑❈❉❂✽❂ ◆■❂✽■✹✸✸❆■❂❘✹✿❆✺ ✾ t❍❂✽❂✸ ✸✿❂✽❂❋❑❍✿❑P
❋❑❉❍❂■❈❉❂P ■✹❚❂❍❜ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿✹ ❈❍✹❋ ❑✽❂ ❄❊❑❚✿❆❉ ❦❳❂✿❑❊✿❂✸❑■✿❜❑ ✸❂❃❑❋❆ ❂◆❍❆✸❆❇✹❩❆❆❧▼
◆❂❈❋❄❅❆❘❯❆P ❂❈✿❂❘❂P ❉✿❆✽❆ ❦✒✹❍❑✸✹❍❆❊❑❈❉❂❑ ◆■❂✽■✹✸✸❆■❂❘✹✿❆❑❧▼ ✿✹◆❆❈✹✿✿❂P ❈❂❘✸❑❈❍✿❂ ❈
✕✾♣✾ ✒❄▲✹❊❑❘❂P ✾ ❱❑❉❩❆❂✿✿❜❑ ❉❄■❈❜▼ ❈❑✸❆✿✹■❜▼ ■❄❉❂❘❂❃❆✸❜❑ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿❂✸ ▼ ❘❈❑✽❃✹ ◆■❆●
❘ ❋❑❉✹❋❆ ✸❂❋❂❃❑❅❬ ✾ ❙✹❚❂❍❑ ❈ ✸❂❋❂❃❜✸❆ ❄❊❑✿❜✸❆ ❖✾◗✾ ❙❄❚❆✿❯❍❑P✿ ❄❃❑❋✺ ❋ ❂✽■❂✸✿❂❑ ❘✿❆✸✹✿❆❑▼
✿❑ ❅✹❋❑✺ ✿❆ ❘■❑✸❑✿❆▼ ✿❆ ❈❆ ❋✾
❲❈❑▼❉❍❂ ❇✿✹❋ ❇✹✸❑❊✹❍❑❋❬✿❂✽❂ ❄❊❑✿❂✽❂ ❆ ❊❑❋❂❘❑❉✹ ▼ ❖❑✿✿✹❃❆✺ ◗❋❑✸❂❘❆❊✹ ❙❄❚❆✿❯❍❑P✿✹ ▼ ❈❂▲■✹●
✿✺❍ ❂ ✿❑✸ ❃❂❚■❄❝ ◆✹✸✺❍❬ ✾
✖✗✘✗ ✙✚✛✜✢✣✤ ✙✗✖✗ ✥✦✧★✦✧✧ ✚✛✤ ✩✗ ✩✗ ✪✫✬✦✬✚✧ ✦✭✮✚✤
✙✗ ✯✗ ✘✦✣✦✛✰✱✤ ✲ ✗✳✗ ✴✚✜ ✚✬✵✶✣✤ ✷ ✗✙✗ ✴ ✰✸ ✦✵✰✱✹✣✢✺