• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.43-49
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• 2012

In this paper, we investigate the stability of a functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$ by using the fixed point theory in the sense of L. $C\breve{a}dariu$ and V. Radu.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.779-787
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• 2019

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

• East Asian mathematical journal
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• v.34 no.5
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• pp.661-681
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• 2018

In this paper, we discuss a reduced-order modeling for the Benjamin-Bona-Mahony-Burgers (BBMB) equation and its application to a distributed feedback control problem through the centroidal Voronoi tessellation (CVT). Spatial distcritization to the BBMB equation is based on the finite element method (FEM) using B-spline functions. To determine the basis elements for the approximating subspaces, we elucidate the CVT approaches to reduced-order bases with snapshots. For the purpose of comparison, a brief review of the proper orthogonal decomposition (POD) is provided and some numerical experiments implemented including full-order approximation, CVT based model, and POD based model. In the end, we apply CVT reduced-order modeling technique to a feedback control problem for the BBMB equation.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 1996.11a
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• pp.101-103
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• 1996

This Paper describes Peak load forecasting technique of pole transformers with correlation equation. While customers are demanding safe energy supply, current correlation equation that is used for load management of pole transformers has some problems. To get accurate correlation equation. several correlation equation were examined using past data and nu data collected using the measuring instrument developed for this study. It was recognized that the quadratic equation was the most accurate for peak load forecasting from working electrical energy.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.10-13
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• 1995

This paper considers the linear-quadratic optimal regulator problem for nonstandard singularly perturbed systems making use of the recursive technique. We first derive a generalized Riccati differential equation by the Hamilton-Jacobi equation. In order to obtain the feedback gain, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(.epsilon.). The existence of a bounded solution of error term can be proved by the implicit function theorem. It is enough to show that the corresponding Jacobian matrix is nonsingular at .epsilon. = 0. As a result, the solution of optimal regulator problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(.epsilon.$^{k}$ ). The proposed technique represents a significant improvement since the existing method for the standard singularly perturbed systems can not be applied to the nonstandard singularly perturbed systems.

• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.457-466
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• 1998

The dynamic response of an elastic torsion shaft of revolution is analysed by the Line-Loaded Integral Equation Method (LLIEM). A "Dynamic Point Ring Couple" (DPRC) is used as a fictitious fundamental load and is distributed in an elastic space along the axis of the shaft outside the shaft occupation. According to the boundary condition, our problem is reduced to a 1-D Fredholm integral equation of the first kind, which is simpler for solving than that of a 2-D singular integral equation of the same kind obtanied by Boundary Element Method (BEM), for steady periodically varied loading. Numerical example of a shaft with quadratic generator under sinusoidal type of torque is given. Formulas for stresses and dangerous frequency are mentioned.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.505-514
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• 2008

In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.

• Journal of Embryo Transfer
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• v.18 no.3
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• pp.215-225
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• 2003

This study was carried out to investigate the change of blood compositions by age in Hanwoo, and a total of 866 of Hanwoo, which consisted with 638 of steer and 228 of bulls, were used to measure serum concentrations. A multiple regression equation was estimated with collection age and blood composition as independent and dependent variables, respectively. Complicated regression equations for blood compositions in steer and bulls were IGF-I(cubic), calcium (linear), and IP(linear). Linear and cubic equations were fitted to testosterone in steer and creatinine in bulls, respectively. A cubic equation in steer and linear equation in bulls were fitted to HDLC. Equations of quadratic in steer and cubic in bulls were fitted to concentration of triglyceride, globulin, and A/G ratio. BUN was fitted by equations of cubic in steer and quadratic in bulls. TP and albumin were fitted by equations of quadratic in steer and linear in bulls. A cubic regression equation did not explain the change of cortisol by age in steer and bulls. A cubic regression equation did explain the change of glucose by age in steer, but not in bulls. Higher R-square values (R-SQUARE>0.1) were estimated to IGF-1, albumin, creatinine, Inorganic phosphorous(IP) and HDLC in steer, and testosterone, IGF-I, TP, albumin, glucose, creatinine, IP, and HDLC in bulls for the fitted regression equations of blood compositions. Therefore, IGF-I, albumin, creatinine, IP, and HDLC were regarded as comparatively large variation by age in steer and bulls.

• Bulletin of the Korean Space Science Society
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• 2005.10a
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• pp.65-65
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• 2005

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.415-426
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• 2020

In this paper, we will prove some uniqueness theorems that can be applied to the generalized Hyers-Ulam stability of some additive-quadratic-cubic functional equation in complete modular spaces without Δ₂-conditions.