• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1827-1838
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• 2015

We give some results on hyperstability for the general linear equation. Namely, we show that a function satisfying the linear equation approximately (in some sense) must be actually the solution of it.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.165-180
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• 2017

In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.

• Korean Journal of Veterinary Research
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• v.50 no.1
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• pp.11-17
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• 2010

Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.215-224
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• 2017

In this paper, we propose a method of order two for the computation of positive solutions to a boundary value problem of the linear beam equation. The method is based on the Power method for the eigenvector associated with the dominant eigenvalue and the Crout-like factorization algorithm for the banded system of linear equations. It is extremely fast due to the linear complexity of the linear system solver. Numerical result of a test problem is included.

• Journal of The Korean Astronomical Society
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• v.36 no.3
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• pp.75-80
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• 2003

When a bright astronomical object (source) is gravitationally lensed by a foreground mass (lens), its image appears to be located at different positions. The lens equation describes the relations between the locations of the lens, source, and images. The lens equation used for the description of the lensing behavior caused by a lens system composed of multiple masses has a form with a linear combination of the individual single lens equations. In this paper, we examine the validity of the linear nature of the multi-lens equation based on the general relativistic point of view.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.208-213
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• 1992

In this paper we are concerned with optimal control problems whose costs am quadratic and whose states are governed by linear delay equations and general boundary conditions. The basic new idea of this paper is to Introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• 전기의세계
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• v.21 no.4
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• pp.7-14
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• 1972

The author has established a general equation for the travelling magnetic field in air gap with the end effect taken into consideration, which constitutes the basics for the analysis of characteristics of linear induction motor. This equation is verified by comparison of the experimental values with the theoretically calculated values. The properties of the travelling wave with attenuation, which is contained in the travelling magnetic field of linear induction motor, have been verified, and consequently the practicable equation is established with these effects taken into consideration. This provides the solid foundation for the theoretical analysis of the characteristics of the linear induction motor.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.35-41
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• 2002

In this paper, we prove the stability of a Jensen's functional equation on a normed almost linear space.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2001-2010
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• 2015

In this paper, we give explicit and new identities for the Bernoulli numbers of the second kind which are derived from a non-linear differential equation.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.253-263
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• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.