• East Asian mathematical journal
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• v.30 no.3
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• pp.327-334
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• 2014

In this paper, we construct extrapolated expanded mixed finite element approximations to approximate the scalar unknown, its gradient and its flux of semilinear Sobolev equations. To avoid the difficulty of solving the system of nonlinear equations, we use an extrapolated technique in our construction of the approximations. Some numerical examples are used to show the efficiency of our schemes.

• Journal of Ocean Engineering and Technology
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• v.15 no.1
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• pp.12-18
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• 2001

This study concentrates on the second-order diffraction problem around circular cylinders in multi-frequency waves. The method of solution is a time-domain Rankine panel method which adopts a higher-order approximation for the velocity potential and wave elevation. In the present study, the multiple second-order quadratic transfer functions are extracted from the second-order time signal generated in random waves, and the comparison with other bench-mark test results shows a good agreement. This approach is directly applicable to prediction of nonlinear forces on offshore structures in random ocean.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.895-902
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• 2022

The aim of this paper is to construct a new method for finding the zeros of the sum of two maximally monotone mappings in Hilbert spaces. We will define a simple function such that its set of zeros coincide with that of the sum of two maximal monotone operators. Moreover, we will use the Newton-Raphson algorithm to get an approximate zero. In addition, some illustrative examples are given at the end of this paper.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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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.

• International Journal of Control, Automation, and Systems
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• v.5 no.6
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• pp.621-629
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• 2007

In the adaptive fuzzy control field for affine nonlinear systems, there are two basic configurations: direct and indirect. It is well known that the direct configuration needs more restrictions on the control gain than the indirect configuration. In general, these restrictions are difficult to check in practice where mathematical models of plant are not available. In this paper, using a simple extension of the universal approximation theorem, we show that the only required constraint on the control gain is that its sign is known. The Lyapunov synthesis approach is used to guarantee the stability and convergence of the closed loop system. Finally, examples of an inverted pendulum and a magnet levitation system demonstrate the theoretical results.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.735-769
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• 2019

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with a viscoelastic term. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

• The Journal of Information Technology and Database
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• v.6 no.1
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• pp.73-88
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• 1999

There have been a series of debates to determine whether it would be possible to forecast dynamic systems such as stock markets. Recently the introduction of chaos theory has allowed many researchers to bring back this issue. Their main concern was whether the behavior of stock markets is chaotic or not. These studies, however, present divergent opinions on this question, depending upon the method applied and the data used. And the issue of predictability based on the nonlinear, chaotic nature was not dealt extensively. This paper is to test the nonlinear nature of the Korea stock market and accordingly attempts to predict its behavior. The result indicates that our stock market represents a chaotic behavior. We also found out based on our simulation that executing buy/sell transactions based upon forecasts which were derived using the local approximation method outperforms the decision of holding without a buy/sell transaction.

• Journal of KSNVE
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• v.9 no.4
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• pp.806-812
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• 1999

Dynamic behaviors are analyzed for a flexble spinning disk with angular acceleration, considering geometric nonlinearity. Based upon the Kirchhoff plate theory and the von Karman strain theory, the nonlinear governing equations are derived which are coupled equations with the in-plane and out-of-planedisplacements. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are computed by using the generalized-$\alpha$ method and the Newton-Raphson method. The analysis shows that the existence of angular acceleration increases the displacements of the spinning disk and makes the disk unstable.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.329-338
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• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

• Structural Engineering and Mechanics
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• v.40 no.3
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• pp.335-346
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• 2011

This paper deals with the bifurcations of non-semi-simple eigenvalues at critical point of Hopf bifurcation to understand the dynamic behavior of the system. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method.