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Iteratsionnye I Transtsendentnoe Resheniya Algebraicheskikh Uravneniy Chkhartishvili Levan

Iteratsionnye I Transtsendentnoe Resheniya Algebraicheskikh Uravneniy

Chkhartishvili Levan

Published July 28th 2012
ISBN : 9783847397106
Paperback
88 pages
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 About the Book 

Kniga posvyashchaetsya tsentralnoy probleme algebry - resheniyu algebraicheskogo uravneniya. Dlya algebraicheskogo uravneniya s deystvitelnymi polozhitelnymi kornyami reshenie polucheno s pomoshchyu irratsionalnoy iteratsionnoy funktsii.MoreKniga posvyashchaetsya tsentralnoy probleme algebry - resheniyu algebraicheskogo uravneniya. Dlya algebraicheskogo uravneniya s deystvitelnymi polozhitelnymi kornyami reshenie polucheno s pomoshchyu irratsionalnoy 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 obema oblasti peresecheniya trekh sfer. K ney svodyatsya vazhnye materialovedcheskie problemy, naprimer, kvaziklassicheskiy raschet matrichnykh elementov vekovogo uravneniya, opredelyayushchego elektronnyy energeticheskiy spektr veshchestva. Dlya proizvolnykh znacheniy radiusov i mezhtsentrovykh rasstoyaniy trekh sfer obem ikh oblasti peresecheniya predstavlen kusochno-analiticheskoy kombinatsiey algebraicheskikh i obratnykh trigonometricheskikh funktsiy.