• 호남수학학술지
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• 제27권1호
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• pp.43-49
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• 2005

Making use of a transparent way of convolution by tensor product of approximate identities we consider the cosine functional equation in several variables.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권1호
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• pp.7-14
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• 2007

The aim of this paper is to study the superstability problem of the cosine type functional equation f(x+y)+f(x+${\sigma}y$)=2g(x)g(y).

• Korean Journal of Mathematics
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• 제16권1호
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• pp.103-114
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• 2008

In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y) +f(x−y) = 2g(x)h(y), f(x + y) + g(x − y) = 2f(x)g(y), f(x + y) + g(x − y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine($d^{\prime}Alembert$) and the Wilson functional equations by J. Baker, $P.\;G{\check{a}}vruta$, R. Badora and R. Ger, and G.H. Kim.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.481-486
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• 2005

This paper introduces a numerical method for integration of the linear and nonlinear differential dynamic equation of motion. The variation of acceleration in two time steps is approximated as a combination of both trigonometric cosine and hyperbolic cosine functions with weighted coefficient. From which all necessary formulae are elaborated for the direct integration of the governing equation. A number of linear and nonlinear dynamic problems with various degrees of freedom are analysed using both the suggested method and Newmark method for the comparison. The numerical results show high advantages and effectiveness of the new method.

• 한국전산유체공학회지
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• 제9권3호
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• pp.8-17
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• 2004

A Semi-Lagrangian method based on CIP(Cubic Interpolated Pseudoparticle)method is proposed and it is applied to solve the two dimensional advection equation. Especially the attentions are given to settle the pole problem and to enhance the accuracy in solving the advection equation on the spherical coordinate system. Tn this algorithm, the CU method is employed as the Semi-Lagrangian method and extended to the spherical coordinate system. To enhance the accuracy of the solution, the spatial discretization is made by CIP method. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy and capability of proposed algorithm, two dimensional rotating cosine bell problem and the frontogenesis problem are simulated by the present scheme. As results, it is confirmed that the present scheme gives an accurate solution and settles the pole problem in the advection equation on the sphere.

• Journal of Applied and Pure Mathematics
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• 제5권5_6호
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• pp.389-406
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• 2023

In the pursuit of enhancing image fusion techniques, this research presents a novel approach for fusing multimodal images, specifically infrared (IR) and visible (VIS) images, utilizing a combination of partial differential equations (PDE) and discrete cosine transformation (DCT). The proposed method seeks to leverage the thermal and structural information provided by IR imaging and the fine-grained details offered by VIS imaging create composite images that are superior in quality and informativeness. Through a meticulous fusion process, which involves PDE-guided fusion, DCT component selection, and weighted combination, the methodology aims to strike a balance that optimally preserves essential features and minimizes artifacts. Rigorous evaluations, both objective and subjective, are conducted to validate the effectiveness of the approach. This research contributes to the ongoing advancement of multimodal image fusion, addressing applications in fields like medical imaging, surveillance, and remote sensing, where the marriage of IR and VIS data is of paramount importance.

• 대한수학회보
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• 제46권1호
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• pp.87-97
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• 2009

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.801-812
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• 2023

In this paper, we investigate the superstability for the p-power-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from an approximation of the p-power-radical functional equation: $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)h(y),$$ where p is an odd positive integer and f, g, h are complex valued functions. Furthermore, the obtained results are extended to Banach algebras.

• Korean Journal of Mathematics
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• 제29권4호
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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.