頁籤選單縮合
題 名 | Absence of Positive Roots of Sextic Polynomials |
---|---|
作 者 | 黃少遠; 鄭穗生; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 15:6 2011.12[民100.12] |
頁 次 | 頁2609-2646 |
分類號 | 314 |
關鍵詞 | Sextic polynomial; Envelope; Characteristic region; Positive root; |
語 文 | 英文(English) |
英文摘要 | Given a general monic sextic polynomial with six real coefficients, necessary and sufficient conditions are found such that the polynomial does not have any positive roots. This 'nonlinear eigenvalue problem' is a relatively difficult one since we have 6 real parameters. Fortunately, we succeed in applying the Cheng-Lin envelope method in [1] together with several new ideas and techniques to express our criteria in terms of roots of quartic polynomials and explicit parametric curves and therefore our problem is completely solved. Several specific examples are also included to illustrate various applications including the seeking of periodic solutions of the logistic equation studied in chaos theory. |
本系統中英文摘要資訊取自各篇刊載內容。