• Title/Summary/Keyword: Cubic equation

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A General Uniqueness Theorem concerning the Stability of AQCQ Type Functional Equations

  • Lee, Yang-Hi;Jung, Soon-Mo
    • Kyungpook Mathematical Journal
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    • v.58 no.2
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    • pp.291-305
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    • 2018
  • In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY A MODULAR EQUATION OF DEGREE 9

  • PAEK, DAE HYUN;YI, JINHEE
    • The Pure and Applied Mathematics
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    • v.23 no.3
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    • pp.223-236
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    • 2016
  • We show how to evaluate the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for n = 4m, 4−m, 2 · 4m, and 2−1 · 4−m for some nonnegative integer m by using modular equations of degree 9. We then find some explicit values of them.

A NEW DESCRIPTION OF SPHERICAL IMAGES ASSOCIATED WITH MINIMAL CURVES IN THE COMPLEX SPACE ℂ4

  • Yilmaz, Suha;Unluturk, Yasin
    • Honam Mathematical Journal
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    • v.44 no.1
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    • pp.121-134
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    • 2022
  • In this study, we obtain the spherical images of minimal curves in the complex space in ℂ4 which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.

Effects of Swirl number and Recess length on Flame Structure of Supercritical Kerosene/LOx Double Swirl Coaxial Injector (선회수와 리세스 길이가 초임계상태 케로신/액체산소 이중 와류 동축형 분사기의 화염구조에 미치는 영향 해석)

  • Park, Sangwoon;Kim, Taehoon;Kim, Yongmo
    • 한국연소학회:학술대회논문집
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    • 2012.11a
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    • pp.33-35
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    • 2012
  • This study has been mainly motivated to numerically model the supercritical mixing and combustion processes encountered in the liquid propellant rocket engines. In the present approach, turbulence is represented by the extended k-e model. To account for the real fluid effects, the propellant mixture properties are calculated by using generalized cubic equation of state. In order to realistically represent the turbulence-chemistry interaction in the turbulent nonpremixed flames, the flamelet approach based on the real fluid flamelet library has been adopted. Based on numerical results, the detailed discussions are made for the effects of swirl number on flame structure of supercritical kerosene/LOx double swirl coaxial injector.

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Analysis of a Nonlinear Conservative Dynamical System Using VAXIMA (VAXIMA를 이용한 비선형 보존 동역학계의 해석)

  • 이원경
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.14 no.3
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    • pp.755-760
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    • 1990
  • VAXIMA is a computer software which gives us results in terms of parameters. We use VAXIMA to analyze quantitatively a conservative dynamical system with cubic and quintic nonlinear terms. The system is described by a nonlinear second-order autonomous ordinary differential equation. Using the Lindstedt-Poincare method, we obtain period-amplitude characteristics. In order to check the validity of the approximate solution, we integrate numerically the equation of motion.

Effects of Swirl number and Pressure on Flame Structure of Supercritical Kerosene Propellant Subscale Injector (선회수와 압력이 초임계상태 케로신 추진제 축소형 다중분사기의 화염구조에 미치는 영향 해석)

  • Park, Sangwoon;Kim, Taehoon;Kim, Yongmo
    • 한국연소학회:학술대회논문집
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    • 2013.06a
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    • pp.81-82
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    • 2013
  • This study has been mainly motivated to numerically model the supercritical mixing and combustion processes encountered in the liquid propellant rocket engines. In the present approach, turbulence is represented by the standard k-e model. To account for the real fluid effects, the propellant mixture properties are calculated by using generalized cubic equation of state. In order to realistically represent the turbulence-chemistry interaction in the turbulent nonpremixed flames, the flamelet approach based on the real fluid flamelet library has been adopted. Based on numerical results, the detailed discussions are made for the effects of swirl on flame structure of supercritical kerosene liquid propellant combustion.

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On the Generalized Hyers-Ulam-Rassias Stability for a Functional Equation of Two Types in p-Banach Spaces

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • Kyungpook Mathematical Journal
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    • v.48 no.1
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    • pp.45-61
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    • 2008
  • We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x+3y) + 6f(x-y) + 12f(2y) = 2f(x - 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated essentially with the Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.

HIGHER ORDER GALERKIN FINITE ELEMENT METHOD FOR THE GENERALIZED DIFFUSION PDE WITH DELAY

  • LUBO, GEMEDA TOLESSA;DURESSA, GEMECHIS FILE
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.603-618
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    • 2022
  • In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L2 and L error norms.

Free vibration analysis of clamped free circular cylindrical shells (일단고정-일단자유 원통 셸의 진동 해석)

  • 임정식
    • Journal of KSNVE
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    • v.6 no.1
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    • pp.45-56
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    • 1996
  • Frequency equation for clamped-free circular cylindrical thin shell is derived by the application of Rayleigh-Ritz method using the Sanders shell equation. The cubic frequency equation is solved for each axial and circumferential mode number. Integration of the beam characteristic funcitions was performed via Mathematica which results in more accurate integration of the beam functions that affect the accuracy of the frequency. The natural frequencies from this calculation are compared with existing results. It shows that this calculation predicts natural frequencies closer to the test results than existing results.

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우리나라 동남부 일강수량의 도수분포곡선

  • 김석중
    • Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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    • 2003.04a
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    • pp.207-210
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    • 2003
  • In this research analyzed the daily precipitation depths of 4 climatic stations in south eastern part of Korea. It aimed to present some indices for regionalization of the area. The items are frequency distributions of precipitation quantity and days and the longest days less than class limit set up by arithmetic differences. The regression analysis between class value and frequency show very good correlation coefficients better than 0.99 which are cubic equation for the precipitation, exponential equation for the precipitation days, and first degree equation for the longest day less than class limit.

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