컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0481 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Numerical Analysis / Scientific Computations / Mathematics in Science and Technology (SS-14) |
| 영문제목 (Title(Eng.)) |
[CANCELLED] On sufficient condition for the existence of imaginary roots of a cubic polynomial equation |
| 저자(Author(s)) |
Enrico M. Yambao1, Ma. Carlota B. Decena1 Department of Mathematics and Physics, College of Science, University of Santo Tomas, España, Manila, Phillipines1 |
| 초록본문(Abstract) | Finding solution of polynomial equations, either by analytic or iterative approach, has been the subject of many investigations. Particularly of much attention is the solution of cubic equations with real coefficients, which serves as basis of important applications in engineering and applied sciences. The Van der Waal’s cubic equation of state, for example, is the most popular method among chemical engineers for estimating vapor-liquid equilibrium ratios of hydrocarbon mixtures at high pressure. In this method, the roots of the cubic equation of state are determinant in the actual vapor-liquid composition of the mixture. Moreover, for economists, the solution of cubic equations plays a vital role in their study of the economic growth rate which is presented as a cubic function known as the Von Neumann’s model. In most of these applications, the analysis is facilitated by characterizing the roots of these cubic equations. For most of the real world applications, resulting cubic functions do not usually appear to have integer coefficients in which root-finding is performed analytically. In such cases, iterative approach in finding the roots is highly relevant. Such methods are carried out with an assumption that either real or imaginary roots of the cubic polynomial equation exist. In this work, we particularly present a sufficient condition for the existence of imaginary roots of a cubic polynomial equation with real coefficients. The derivation is facilitated by considering the possible graphs of the corresponding cubic function. |
| 분류기호 (MSC number(s)) |
65Sxx |
| 키워드(Keyword(s)) | cubic polynomial equations, imaginary roots, graphical approach |
| 강연 형태 (Language of Session (Talk)) |
English |