Grundlsee

Kniga posvyashchaetsya tsentral'noy probleme algebry - resheniyu algebraicheskogo uravneniya. Dlya algebraicheskogo uravneniya s deystvitel'nymi polozhitel'nymi kornyami reshenie polucheno s pomoshch'yu irratsional'noy iteratsionnoy funktsii. Predlozheno obobshchenie etogo sposoba resheniya na sluchay algebraicheskikh uravneniy s kompleksnymi kornyami. Razrabotan mnogomernyy iteratsionnyy metod resheniya vekovogo uravneniya, kharakteristicheskim uravneniem dlya kotorogo sluzhit algebraicheskoe uravnenie. K podobnoy matematicheskoy zadache privodit tselyy ryad naibolee znachimykh problem estestvennykh nauk i tekhniki. Postroeno transtsendentoe reshenie algebraicheskogo uravneniya obshchego vida: vse korni predstavleny stepennymi ryadami ego koeffitsientov. V prilozhenii knigi privoditsya reshenie geometricheskoy zadachi vychisleniya ob"ema oblasti peresecheniya trekh sfer. K ney svodyatsya vazhnye materialovedcheskie problemy, naprimer, kvaziklassicheskiy raschet matrichnykh elementov vekovogo uravneniya, opredelyayushchego elektronnyy energeticheskiy spektr veshchestva. Dlya proizvol'nykh znacheniy radiusov i mezhtsentrovykh rasstoyaniy trekh sfer ob"em ikh oblasti peresecheniya predstavlen kusochno-analiticheskoy kombinatsiey algebraicheskikh i obratnykh trigonometricheskikh funktsiy.