• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.183-203
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• 2014

We examine fundamental units of quadratic function fields from continued fraction of $\sqrt{D}$. As a consequence, we give another proof of geometric analog of Ankeny-Artin-Chowla-Mordell conjecture and bounds for class number, and study real quadratic function fields of minimal type with quasi-period 4.

• East Asian mathematical journal
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• v.36 no.5
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• pp.561-570
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• 2020

We compute the extended four operations of the 2-dimensional quadratic fuzzy numbers. Then we calculate the intersection between a plane perpendicular to the x-axis, which passes through each vertex, and the resulting 2-dimensional quadratic fuzzy number. We confirm that the equations of the two intersections acquired in this way and the graphs are actually identical, respectively.

• Journal of KSNVE
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• v.7 no.4
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• pp.605-612
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• 1997

A state feedback controller and an observer have been developed and analyzed for an aircraft's safe landing in the windshear called microburst. The observer estimates the ambient wind field as well as the full-order longitudinal state vector. The controller uses the wind and state estimates for guiding the control inputs for safe landing. For the observer and controller gains, the design methodologies of linear quadratic estimation and linear quadratic regulation have been exploited. Analysis shows that some of the microburst-induced aircraft accidents in the past might have been avoided with the designed autopilot.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.67-76
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• 2008

Limit cycle oscillations of a two-dimensional airfoil with quadratic and cubic pitching nonlinearities are investigated. The equivalent stiffness of the pitching stiffness is obtained by combining the linearization and harmonic balance method. With the equivalent stiffness, the equivalent linearization method for nonlinear flutter analysis is generalized to address aeroelastic system with quadratic nonlinearity. Numerical example shows that good approximation of the limit cycle can be obtained by the generalized method. Furthermore, the proposed method is capable of revealing the unsymmetry of the limit cycle; however the ordinary equivalent linearization method fails to do so.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.607-618
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• 2017

In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set [0, 1]. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.489-508
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• 2020

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

• East Asian mathematical journal
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• v.36 no.1
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• pp.35-53
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.623-630
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• 2003

Recently, Tanaka(1988) derived two influence functions related to an eigenvalue problem $(A-\lambda_sI)\upsilon_s=0$ of real symmetric matrix A and used them for sensitivity analysis in principal component analysis. In this paper, we deal with the perturbation expansions up to quadratic terms of the same functions and discuss the application to sensitivity analysis in principal component regression analysis(PCRA). Numerical example is given to show how the approximation improves with the quadratic term.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.52-54
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• 1991

In this paper, the robust stability, and the quadratic performance of linear uncertain systems are studied. A quadratic Lyapunov function candidate with time-varying matrix is derived to provide robust stability bounds. Also upper bounds of a quadratic performance is given under the assumption that the uncertain system is stable. Both the robust stability bounds and the upper bounds of a quadratic performance are obtained as solutions of a class of modified Lyapunov equations.