• 제목/요약/키워드: Cubic equation

검색결과 273건 처리시간 0.025초

CUBIC FORMULA AND CUBIC CURVES

  • Woo, Sung Sik
    • 대한수학회논문집
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    • 제28권2호
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    • pp.209-224
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    • 2013
  • The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for $y^2=x^3+b$.

삼차방정식에 관한 Omar Khayyām의 기하학적 해법의 재해석과 시각화 - 항이 4개인 삼차방정식의 6가지 - (Reinterpretation and visualization of Omar-Khayyam's geometric solution for the cubic equation - 6 cases of the cubic equation with 4 terms -)

  • 김향숙;김미연;심효정;박명은
    • East Asian mathematical journal
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    • 제37권4호
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    • pp.499-521
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    • 2021
  • This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.

ORTHOGONAL STABILITY OF AN EULER-LAGRANGE-JENSEN (a, b)-CUBIC FUNCTIONAL EQUATION

  • Pasupathi, Narasimman;Rassias, John Michael;Lee, Jung Rye;Shim, Eun Hwa
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제29권2호
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    • pp.189-199
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    • 2022
  • In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

ON CHARACTERIZATIONS OF SET-VALUED DYNAMICS

  • Chu, Hahng-Yun;Yoo, Seung Ki
    • 대한수학회보
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    • 제53권4호
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    • pp.959-970
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    • 2016
  • In this paper, we generalize the stability for an n-dimensional cubic functional equation in Banach space to set-valued dynamics. Let $n{\geq}2$ be an integer. We define the n-dimensional cubic set-valued functional equation given by $$f(2{{\sum}_{i=1}^{n-1}}x_i+x_n){\oplus}f(2{{\sum}_{i=1}^{n-1}}x_i-x_n){\oplus}4{{\sum}_{i=1}^{n-1}}f(x_i)\\=16f({{\sum}_{i=1}^{n-1}}x_i){\oplus}2{{\sum}_{i=1}^{n-1}}(f(x_i+x_n){\oplus}f(x_i-x_n)).$$ We first prove that the solution of the n-dimensional cubic set-valued functional equation is actually the cubic set-valued mapping in [6]. We prove the Hyers-Ulam stability for the set-valued functional equation.

ON THE FUZZY STABILITY OF CUBIC MAPPINGS USING FIXED POINT METHOD

  • Koh, Heejeong
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제19권4호
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    • pp.397-407
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    • 2012
  • Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.

THE ENUMERATION OF ROOTED CUBIC C-NETS

  • CAI JUNLIANG;HAO RONGXIA;LID YANPEI
    • Journal of applied mathematics & informatics
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    • 제18권1_2호
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    • pp.329-337
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    • 2005
  • This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].