• Korean Journal of Mathematics
• /
• v.19 no.2
• /
• pp.171-180
• /
• 2011

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations $$g(x+y)f(x-y)=f(x)^2-f(y)^2 \\ f(x+y)g(x-y)=f(x)^2-f(y)^2 \\ g(x+y)g(x-y)=f(x)^2-f(y)^2$$, which does not use his iteration method.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.931-950
• /
• 2006

We study the identification problems of constant parameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parameters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions [13].

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.87-97
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.14 no.1 s.35
• /
• pp.7-14
• /
• 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).

• The Pure and Applied Mathematics
• /
• v.17 no.4
• /
• pp.397-411
• /
• 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.

• Journal of the Korea Computer Industry Society
• /
• v.3 no.5
• /
• pp.569-574
• /
• 2002

We model the torsional oscillation of a suspension bridge, which is the forced sine-Cordon equation on a bounded domain. We use finite difference method to solve nonlinear partial differential equation numerically. The partial differential equation has multiple periodic solutions. Whether the span oscillates with small or large amplitude depends oかy on its initial displacement and velocity. Moreover, we observe that the qualitative properties are consistent with the behavior observed at the Tacoma Narrows Bridge on the day of its collapse.

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

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10b
• /
• pp.173-176
• /
• 1996

The transient behavior of the complex-LMS adaptive filter is studied when the adaptive filter is operating on a fixed or sweeping complex frequency sine-wave signal. The first-order difference equation is derived for the mean weights and its closed form solution is obtained. The transient response is represented as a function of the eigenvectors and eigenvalues of input correlation matrix. The mean-square error of the algorithm is evaluated as well. An optimal convergence parameter and filter length can be determined for sweeping frequency sine-wave signals as a function of frequency change rate and signal and noise powers.

• Korean Journal of Mathematics
• /
• v.16 no.1
• /
• pp.103-114
• /
• 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 Industrial Technology
• /
• v.14
• /
• pp.19-28
• /
• 1994

We can get a tridiagonal block Toeplitz linear system by the finite difference approximation of 2-D Poisson equation. To exploit the nice property of this linear equation, we transform the equation into a Lyapunov equation and apply DST (discrete sine transform) to get diagonal matrix based Lyapunov equation. DST can be performed using FFT, which enables high-speed computaion. All the computations are performed on an SIMD parallel computer, the MasPar MP-2 with 4,096 processing elements. In this paper, parallel algorithm, mapping method of the algorithm onto the MP-2, and timing results are presented.