• Journal of Electrochemical Science and Technology
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• v.7 no.4
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• pp.293-297
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• 2016

Here we propose a new equation by which we can estimate the baseline for measuring the peak current of the reverse curve in a cyclic voltammogram. A similar equation already exists, but it is a linear algebraic equation that over-simplifies the voltammetric curve and may cause unpredictable errors when calculating the baseline. In our study, we find a quadratic algebraic equation that acceptably reflects the complexity included in a voltammetric curve. The equation is obtained from a laborious numerical analysis of cyclic voltammetry simulations using the finite element method, and not from the closed form of the mathematical equation. This equation is utilized to provide a virtual baseline current for the reverse peak current. We compare the results obtained using the old linear and new quadratic equations with the theoretical values in terms of errors to ascertain the degree to which accuracy is improved by the new equation. Finally, the equations are applied to practical cyclic voltammograms of ferricyanide in order to confirm the improved accuracy.

• Journal of The Korean Society of Agricultural Engineers
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• v.65 no.2
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• pp.35-45
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• 2023

The DOR (Drainage outlet raising) in the paddy field has been suggested as one of the most important best management practices for the TMDL (Total maximum daily load) management in the technical guidelines by the NIER (National institute of environmental research). However, this method is underestimated and is not well adopted by local governments for the TMDL. The purpose of this study is to evaluate the unit load reduction equation according to the application of DOR in order to expand this equation. The original equation in the guideline was derived using the HSPF (Hydrological Simulation Program-Fortran) model for 1 year in Changnyeong. We analyzed the reduction effect of the original equation application by collecting additional long-term monitoring data from the Buan, Icheon, Iksan, and Jeonju. When comparing the reduction loads between the original equation and monitoring results, the evaluation results of the original equation were 11% of the monitoring analysis results, which was underestimated. This means that the original equation needs to be improved. For assessing the equation, the HSPF Paddy-RCH model was established according to the NI ER guideline and evaluated for applicability. The performance results of the model showed a reasonable range by the statistical criteria. Modified equations 1 and 2 were proposed based on the monitoring and modeling results. Modified equation 1 was the method of modifying the original equation's main factors, and modified equation 2 was the method of applying the non-point pollution reduction efficiency according to the rainfall class using the long-term modeling results. At the level of 58.6~64.6% of monitoring data, the difference between them could be further reduced compared to the original equation. The suggested approach will be more reasonable and practicable for decision-makers and will contribute to the TMDL management plans.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.599-605
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• 2003

For practical calculations, the Reynolds equation is frequently used to analyze the lubricating flow. The full Navier-Stokes Equations are used to find validity limits of Reynolds equation in a lubricating flow regime by result comparison. As the amplitude of wavy upper wall increased at a given average channel height, the difference between Navier-Stokes and lubrication theory decreased slightly : however, as the minimum distance in channel throat increased, the differences in the maximum pressure between Navier-Stokes and lubrication theory became large.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.393-399
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• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.6
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• pp.8-14
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• 1998

The derivation of the dual integral equation in the spectral domain, which has total fields of the interfaces as unknowns, is investigated. It is analytically shown that the derivation of the dual integral equation is equivalent to deriving the Helmholtz-Kirchhoff integral equation from the Wiener-Hopf integral equation.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.193-198
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• 2012

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.265-277
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• 2004

This article deals with the number of periodic solutions of the second order polynomial differential equation using the Riccati equation, and applies the property of the solutions of the Riccati equation to study the property of the solutions of the more complicated differential equations. Many valuable criterions are obtained to determine the number of the periodic solutions of these complex differential equations.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.697-710
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• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.477-486
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• 2000

In this paper, we investigate the Hyers-Ulam-Rassias stability of a quadratic functional equation f(x+y+z)+f(x+y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on restricted (unbounded) domains.