"\u041D\u0435\u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u043E \u041C\u044E\u0440\u0445\u0435\u0434\u0430"@ru . . . . . . . "In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the \"bunching\" method, generalizes the inequality of arithmetic and geometric means."@en . . "muirheadstheorem"@en . "Muirhead's theorem"@en . . . . . . "\u041D\u0435\u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u043E \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u0435\u0442 \u0441\u0440\u0430\u0432\u043D\u0438\u0432\u0430\u0442\u044C \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u043E\u0432 \u043D\u0430 \u043E\u0434\u043D\u043E\u043C \u0438 \u0442\u043E\u043C \u0436\u0435 \u043D\u0430\u0431\u043E\u0440\u0435 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u0439 \u0430\u0440\u0433\u0443\u043C\u0435\u043D\u0442\u043E\u0432."@ru . "1047942"^^ . . . "En math\u00E9matiques, l'in\u00E9galit\u00E9 de Muirhead, appel\u00E9e ainsi d'apr\u00E8s Robert Franklin Muirhead, est une g\u00E9n\u00E9ralisation de l'in\u00E9galit\u00E9 arithm\u00E9tico-g\u00E9om\u00E9trique."@fr . . "Muirhead's inequality"@en . "\uBBA4\uC5B4\uD5E4\uB4DC\uC758 \uBD80\uB4F1\uC2DD(Muirhead's inequality, -\u4E0D\u7B49\u5F0F)\uC740 (Robert Franklin Muirhead)\uC758 \uC774\uB984\uC744 \uBD99\uC778 \uBD80\uB4F1\uC2DD\uC774\uB2E4. \uB274\uD134\uC758 \uBD80\uB4F1\uC2DD \uBC0F \uB9E4\uD074\uB85C\uB9B0\uC758 \uBD80\uB4F1\uC2DD\uACFC \uC720\uC0AC\uD558\uAC8C \uB300\uCE6D\uC801\uC778 \uD615\uD0DC\uC758 \uC2DD\uC5D0 \uAD00\uD55C \uBD80\uB4F1\uC2DD \uC911 \uD558\uB098\uB85C, \uC0C1\uB2F9\uD788 \uAC15\uB825\uD55C \uBD80\uB4F1\uC2DD\uC758 \uC77C\uC885\uC774\uB2E4. \uC774 \uBD80\uB4F1\uC2DD\uC744 \uC774\uC6A9\uD558\uC5EC \uC0B0\uC220-\uAE30\uD558 \uD3C9\uADE0 \uBD80\uB4F1\uC2DD\uC744 \uC720\uB3C4\uD560 \uC218\uB3C4 \uC788\uB2E4."@ko . "Nier\u00F3wno\u015B\u0107 Muirheada \u2013 uog\u00F3lnienie nier\u00F3wno\u015Bci mi\u0119dzy \u015Brednimi pot\u0119gowymi. Nier\u00F3wno\u015B\u0107 Muirheada zosta\u0142a udowodniona w 1903 roku, a jej uog\u00F3lnienie w 2009. Je\u017Celi s\u0105 liczbami nieujemnymi, takimi \u017Ce: dla to m\u00F3wimy, \u017Ce ci\u0105g majoryzuje ci\u0105g i piszemy Sformu\u0142owanie nier\u00F3wno\u015Bci: je\u017Celi ci\u0105g majoryzuje ci\u0105g to dla nieujemnych liczb gdzie oznacza sum\u0119 dla wszystkich permutacji zbioru"@pl . "\u041D\u0435\u0440\u0456\u0432\u043D\u0456\u0441\u0442\u044C \u041C\u044E\u0440\u0445\u0435\u0434\u0430 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u043F\u043E\u0440\u0456\u0432\u043D\u044E\u0432\u0430\u0442\u0438 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0434\u0435\u044F\u043A\u0438\u0445 \u0441\u0438\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u0456\u0432 \u043D\u0430 \u043E\u0434\u043D\u043E\u043C\u0443 \u0456 \u0442\u043E\u043C\u0443 \u0436 \u043D\u0430\u0431\u043E\u0440\u0456 \u043D\u0435\u0432\u0456\u0434'\u0454\u043C\u043D\u0438\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u044C \u0430\u0440\u0433\u0443\u043C\u0435\u043D\u0442\u0456\u0432."@uk . . . . "In algebra, la disuguaglianza di raggruppamento (detta anche bunching) dice che, date due somme simmetriche di monomi dello stesso grado, la minore \u00E8 quella in cui gli esponenti sono pi\u00F9 \"distribuiti\"."@it . "\u041D\u0435\u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u043E \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u0435\u0442 \u0441\u0440\u0430\u0432\u043D\u0438\u0432\u0430\u0442\u044C \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u043E\u0432 \u043D\u0430 \u043E\u0434\u043D\u043E\u043C \u0438 \u0442\u043E\u043C \u0436\u0435 \u043D\u0430\u0431\u043E\u0440\u0435 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u0439 \u0430\u0440\u0433\u0443\u043C\u0435\u043D\u0442\u043E\u0432."@ru . . "1105413295"^^ . . . . . "In algebra, la disuguaglianza di raggruppamento (detta anche bunching) dice che, date due somme simmetriche di monomi dello stesso grado, la minore \u00E8 quella in cui gli esponenti sono pi\u00F9 \"distribuiti\"."@it . . "\uBBA4\uC5B4\uD5E4\uB4DC\uC758 \uBD80\uB4F1\uC2DD"@ko . . . . "Disuguaglianza di raggruppamento"@it . . . . "\u041D\u0435\u0440\u0456\u0432\u043D\u0456\u0441\u0442\u044C \u041C\u044E\u0440\u0445\u0435\u0434\u0430 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u043F\u043E\u0440\u0456\u0432\u043D\u044E\u0432\u0430\u0442\u0438 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0434\u0435\u044F\u043A\u0438\u0445 \u0441\u0438\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u0456\u0432 \u043D\u0430 \u043E\u0434\u043D\u043E\u043C\u0443 \u0456 \u0442\u043E\u043C\u0443 \u0436 \u043D\u0430\u0431\u043E\u0440\u0456 \u043D\u0435\u0432\u0456\u0434'\u0454\u043C\u043D\u0438\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u044C \u0430\u0440\u0433\u0443\u043C\u0435\u043D\u0442\u0456\u0432."@uk . . "Die Muirhead-Ungleichung ist eine Verallgemeinerung der Ungleichung vom arithmetischen und geometrischen Mittel."@de . . . "Nier\u00F3wno\u015B\u0107 Muirheada"@pl . "6786"^^ . "Nier\u00F3wno\u015B\u0107 Muirheada \u2013 uog\u00F3lnienie nier\u00F3wno\u015Bci mi\u0119dzy \u015Brednimi pot\u0119gowymi. Nier\u00F3wno\u015B\u0107 Muirheada zosta\u0142a udowodniona w 1903 roku, a jej uog\u00F3lnienie w 2009. Je\u017Celi s\u0105 liczbami nieujemnymi, takimi \u017Ce: dla to m\u00F3wimy, \u017Ce ci\u0105g majoryzuje ci\u0105g i piszemy Sformu\u0142owanie nier\u00F3wno\u015Bci: je\u017Celi ci\u0105g majoryzuje ci\u0105g to dla nieujemnych liczb gdzie oznacza sum\u0119 dla wszystkich permutacji zbioru"@pl . "En math\u00E9matiques, l'in\u00E9galit\u00E9 de Muirhead, appel\u00E9e ainsi d'apr\u00E8s Robert Franklin Muirhead, est une g\u00E9n\u00E9ralisation de l'in\u00E9galit\u00E9 arithm\u00E9tico-g\u00E9om\u00E9trique."@fr . "Muirhead-Ungleichung"@de . . "\uBBA4\uC5B4\uD5E4\uB4DC\uC758 \uBD80\uB4F1\uC2DD(Muirhead's inequality, -\u4E0D\u7B49\u5F0F)\uC740 (Robert Franklin Muirhead)\uC758 \uC774\uB984\uC744 \uBD99\uC778 \uBD80\uB4F1\uC2DD\uC774\uB2E4. \uB274\uD134\uC758 \uBD80\uB4F1\uC2DD \uBC0F \uB9E4\uD074\uB85C\uB9B0\uC758 \uBD80\uB4F1\uC2DD\uACFC \uC720\uC0AC\uD558\uAC8C \uB300\uCE6D\uC801\uC778 \uD615\uD0DC\uC758 \uC2DD\uC5D0 \uAD00\uD55C \uBD80\uB4F1\uC2DD \uC911 \uD558\uB098\uB85C, \uC0C1\uB2F9\uD788 \uAC15\uB825\uD55C \uBD80\uB4F1\uC2DD\uC758 \uC77C\uC885\uC774\uB2E4. \uC774 \uBD80\uB4F1\uC2DD\uC744 \uC774\uC6A9\uD558\uC5EC \uC0B0\uC220-\uAE30\uD558 \uD3C9\uADE0 \uBD80\uB4F1\uC2DD\uC744 \uC720\uB3C4\uD560 \uC218\uB3C4 \uC788\uB2E4."@ko . . . "In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the \"bunching\" method, generalizes the inequality of arithmetic and geometric means."@en . . . "\u041D\u0435\u0440\u0456\u0432\u043D\u0456\u0441\u0442\u044C \u041C\u044E\u0440\u0445\u0435\u0434\u0430"@uk . . . "In\u00E9galit\u00E9 de Muirhead"@fr . . . . "Die Muirhead-Ungleichung ist eine Verallgemeinerung der Ungleichung vom arithmetischen und geometrischen Mittel."@de . . . . . . . . . .