• Journal for History of Mathematics
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• v.11 no.2
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• pp.63-76
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• 1998

When teaching the linear regression analysis in the class, the power transformation must be introduced to fit the linear regression model for nonlinear data. Box and Cox (1964) proposed the attractive power transformation technique which is so called Box-Cox transformation. In this paper, an effective algorithm selecting an appropriate value for Box-Cox transformation is developed which is considered to find a value minimizing error sum of squares. When the proposed algorithm is used to find a value for transformation, the number of iterations needs to be considered. Thus, the number of iterations is examined through simulation study. Since SAS is one of most widely used packages and does not provide the procedure that performs iterative Box-Cox transformation, a SAS program automatically choosing the value for transformation is developed. Hence, the students could learn how the Box-Cox transformation works, moreover, researchers can use this for analysis of data.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1845-1847
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• 1991

In general, it is not easy to find the linearizing coordinate transformation map for a class of systems which are state equivalent to linear systems, because it is required to solve a set of partial differential equations. It is possible to construct an arbitrary nonlinear function with a backpropagation(BP) net. Utilizing this property of BP neural net, we construct a desired linearizing coordinate transformation map. That is, we implement a unknown coordinate transformation map through the training of neural weights. We have shown an example which supports this idea.

• Journal of Ocean Engineering and Technology
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• v.20 no.6 s.73
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• pp.35-40
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• 2006

In recent years, there's been strong demand for seawalls that havea gentle slope and permeability that serveswater affinity and disaster prevention from wave attack. The aim of this study is to examine wave transformation, including wave run-up that propagates on the coastal structures. A numerical model based on the weak nonlinear dispersive Boussinesq equation, together with the unsteady nonlinear Darcy law for fluid motion in permeable layer, is developed. The applicability of this numerical model is examined through Deguchi and Moriwaki's hydraulic model test on the permeable slopes. From this study, it is found that the proposed numerical model can predict wave transformation and run-up on the gentle slope with a permeable layer, but can't show accurate results for slopes steeper than about 1:10.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.1116-1121
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• 1991

In this paper the feedback linearization of the valve-controlled nonlinear hydraulic velocity control system and the Implementation of the digital state feedback controller is studied. The C.inf. nonlinear transformation to the electro-hydraulic velocity control system, which transforms nonlinear system to linear equivalent one, is obtained. It is shown that this transformation Is global one. The digital controller to this linearized model is obtained by using the one-step ahead state estimator and implemented to real plant. The proposed method In this paper is easier to implement than other proposed methods and it is possible to control in real tine. The experiment and simulation study show that the implementation of the digital state feedback controller based on the feedback linearized model is successful.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.405-412
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• 1992

The problem we consider in this paper is more demanding than the problem of input-output linearization with state equivalence recently solved by Cheng, Isidori, Respondek, and Tarn. We request that the MIMO nonlinear system, for which the problem of input-output linearization with state-equivalence is solvable, can be decoupled. In exchange for further requirement like this, our problem produces more usable and informative results than the problem of input-output linearization with state-equivalence. We present the necessary and sufficient conditions for our problem to be solvable. We characterize each of the nonlinear systems satisfying these conditions by a set of parameters which are invariant under the group action of state feedback and transformation. Using this set of parameters, we can determine directly the unique one, among the canonical forms of decouplable and controllable linear systems, to which a nonlinear system can be transformed via appropriate state feedback and transformation. Finally, we present the necessary and sufficient conditions for our problem to be solvable with internal stability, that is, for stable decoupling.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.142-145
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• 1997

This paper presents an modified orthogonal neural network(MONN) based on orthogonal functions and applies the network to nonlinear system control. The accuracy of orthogonal neural network is essentially dependent on the choice of basic orthogonal functions. Modified orthogonal neural network is modified model of orthogonal neural network with input transformation to adapt its basic orthogonal functions. The results show that the modified orthogonal neural network has the excellent performance of approximating and controlling nonlinear systems and the input transformation make the ability of modified orthogoneural neural network better than one of orthogonal neural network.

• Steel and Composite Structures
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• v.48 no.3
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.329-336
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• 2006

In the category of the group theoretic methods using invertible discrete group transformation, we give a useful relation between Emden-Fowler equations and nonlinear heat equation. In this paper, by means of appropriate transformations of discrete group analysis, the nonlinear hate equation transformed into the class of the Emden-Fowler equations. This approach shows that, under the group action, the solution of reference equation can be transformed into the solution of the transformed equation.

• Journal of KSNVE
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• v.9 no.1
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• pp.196-205
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• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.