• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.241-254
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• 2007

This paper propose a new short-term interest rate model having a different nonlinear drift function and the same diffusion coefficient with Chan et al. (1992) model. The fractional polynomial power of the drift function in our model is linked to the local volatility elasticity of the diffusion coefficient. While the nonlinear drift function estimated by $A\"{\i}t$-Sahalia (1996a) and others has a feature that higher interest rates tend to revert downward and low rates upward, the drift function estimated by our nonlinear model shows that higher interest rate mean-reverts strongly, but, medium rates has almost zero drift and low rates has a very small drift. This characteristic coincides the empirical result based on the nonparametric methodology by Stanton (1997) and the implication by the scatter plot of the short rate data.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.501-516
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• 2013

The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall's inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.

• Proceedings of the Korean Geotechical Society Conference
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• 2001.03a
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• pp.33-40
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• 2001

In this research, the cracking of tunnel concrete lining was investigated and analyzed through long-term measurement and nonlinear numerical analysis. For one year after the casting of lining, the stresses and strains were measured by the sensors installed in hard rock tunnel lining. The measurements showed that only small stresses which were less than cracking stress occurred in every survey sections regardless of sensor directions. It could be induced that the external load applied to the lining was small or ignorable. Also, it was carried out short-term numerical analysis based on such site condition as ambient temperature, the- degree of overbreak and mold staying period. Long-term numerical analysis based on creep & shrinkage and nonlinear cracking was carried out. The output showed that construction condition and ambient environments could make the lining concrete crack without external loads. The cracks formed in this process does not indicate the structural instability of the tunnel.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.57 no.2
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• pp.115-120
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• 2008

The EKF(Extended Kalman filter) method which is the state estimation algorithm of nonlinear stochastic system depends on the initial error and the estimated states. Therefore, the divergence of the estimated state can be caused if the initial values of the estimated states are not chosen as approximate real state values. In this paper, the demerit of the existing EKF method is improved using the EKF algorithm transformated by STWS(Single Term Walsh Series). This method linearizes each sampling interval of continous-time system through the derivation of an algebraic iterative equation without discretizing continuous system by the characteristic of STWS, the convergence of the estimated states can be improved. The validity of the proposed method is checked through comparison with the existing EKF method in simulation.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.113-131
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• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

• The Journal of the Acoustical Society of Korea
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• v.21 no.6
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• pp.522-530
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• 2002

This paper introduces a neural network (NN) -based nonlinear predictor for the LP (Linear Prediction) residual. To evaluate the effectiveness of the NN-based nonlinear predictor for LP-residual, we first compared the average prediction gain of the linear long-term predictor with that of the NN-based nonlinear long-term predictor. Then, the effects on the quantization noise of the nonlinear prediction residuals were investigated for the NN-based nonlinear predictor A new NN predictor takes into consideration not only prediction error but also quantization effects. To increase robustness against the quantization noise of the nonlinear prediction residual, a constrained back propagation learning algorithm, which satisfies a Kuhn-Tucker inequality condition is proposed. Experimental results indicate that the prediction gain of the proposed NN predictor was not seriously decreased even when the constrained optimization algorithm was employed.

• International Journal of Vascular Biomedical Engineering
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• v.3 no.1
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• pp.14-22
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• 2005

In the present study, our aim is to investigate whether responses to the head-up tilt (HUT) on nonlinear properties of heart rate variability (HRV) in young and elderly subjects are different or not. Thirteen young-healthy subjects ($24.5{\pm}3.7$ years) and 18 old-aged healthy subjects ($74.5{\pm}7.4$ years) participated in this study. An electrocardiogram (ECG) in the supine posture, at $0^{\circ}$, and in the standing posture, at $70^{\circ}$ of head-up tilt, was recorded. Detrended fluctuation analysis (DFA) and approximate entropy (ApEn), measures of short-/long-term correlation properties and overall complexity of heart rate (HR) respectively, along with spectral components of HR variability (HRV) were analyzed for both the supine and HUT postures. We observed that the short-term fractal exponent ${\alpha}_1$ increased during HUT posture (F(1, 29) = 39.79, P = 0.000), especially, the young subjects showed a significantly higher values compared to the elderly subjects. ApEn significantly decreased (F(1, 29) = 8.61, P = 0.006) during HUT posture. HUT posture decreased the complexity in HR dynamics and increased short-term fractal exponent values in young subjects but not in elderly subjects. These results imply that there are differences of response to HUT on nonlinear properties between young and elderly subjects.

• Journal of Ocean Engineering and Technology
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• v.4 no.1
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• pp.49-54
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• 1990

This study describes the application of a two dimensional depth integrated numerical model. The explict scheme of finite difference method had been applied to the model of circulation. The nonlinear terms showed a slight difference for the variations of water elevation when calculated grid was small. They were also found to be minor when calculated grid size was increased. For verification of the numerical model, numerical results were compared with predicted values and field data. In the model, the effect of nonlinear advective terms proved not to be significant.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.10a
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• pp.116-122
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• 2001

A novel approach based on WaveARX neural network observer is proposed far the fault detect of a class of nonlinear systems which consist of known linear part and unknown nonlinear part. A linear observer is first designed, then a nonlinear compensation term in the nonlinear observer is estimated by using a deconvolution method. The WaveARX network is used to model the obtained compensation term. At last, the residual fur fault detection is generated based on the analysis of the upper bound approximate error. Simulation results have shown the feasibility and effectiveness of the method.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.227-238
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• 2017

The existence of solutions for nonlinear elliptic partial differential equations with general flux and damping terms is investigated.