• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.9
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• pp.1827-1833
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• 2009

This paper deals with the trajectory tracking control of wheeled mobile robots with input constraint. The proposed method converts the trajectory tracking problem to the system stability problem using the control inputs composed of feedforward and feedback terms, and then, by using Taylor series, nonlinear terms in origin system are transformed into polynomial equations. The composed system model can make it possible to obtain the control inputs using numerical tool named as SOSTOOL. From the simulation results, the mobile robot can track the reference trajectory well and can have faster convergence rate of the trajectory errors than the existing nonlinear control method. By using the proposed method, we can easily obtain the control input for nonlinear systems with input constraint.

• Journal of Electrical Engineering and Technology
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• v.11 no.4
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• pp.1027-1034
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• 2016

This paper proposes a sum of squares (SOS) method for anti-swing control of overhead crane system using HOSM (High-Order Sliding-Mode) observer. By representing the dynamic equations of overhead crane as the polynomial dynamic equations via Taylor series expansion, the control input is obtained from the converted polynomial dynamic equations by numerical tool SOSTOOL. Since the actual crane systems include disturbance such as wind and friction, we propose a method to compensate for the disturbance by estimating the disturbance using HOSM observer. Numerical simulations show the effectiveness and the applicability of the proposed method.

• Journal of Information Technology Application
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• v.3 no.3
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• pp.25-40
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• 2001

This paper deals with the problem of generating optimal polynomials using Genetic Programming(GP). The polynomial should approximate nonlinear response surfaces. Also, there should be a consideration regarding the size of the polynomial, It is not desirable if the polynomial is too large. To build small or medium size of polynomials that enable to model nonlinear response surfaces, we use the low order Tailor series in the function set of GP, and put the constrain on generating GP tree during the evolving process in order to prevent GP trees from becoming too large size of polynomials. Also, GAGPT(Group of Additive Genetic Programming Trees) is adopted to help achieving such purpose. Two examples are given to demonstrate our method.

• Journal of Ship and Ocean Technology
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• v.11 no.4
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• pp.21-28
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• 2007

Recently the importance of the utilization of engineering data is gradually increasing. Engineering data contains the experiences and know-how of experts. Data mining technique is useful to extract knowledge or information from the accumulated existing data. This paper deals with generating optimal polynomials using genetic programming (GP) as the module of Data Mining system. Low order Taylor series are used to approximate the polynomial easily as a nonlinear function to fit the accumulated data. The overfitting problem is unavoidable because in real applications, the size of learning samples is minimal. This problem can be handled with the extended data set and function node stabilization method. The Data Mining system for the ship design based on polynomial genetic programming is presented.

• Journal of Korea Water Resources Association
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• v.33 no.1
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• pp.31-38
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• 2000

Relationships between hydrologic variables are often nonlinear. Usually the functional form of such a relationship is not known a priori. A multivariate, nonparametric regression methodology is provided here for approximating the underlying regression function using locally weighted polynomials. Locally weighted polynomials consider the approximation of the target function through a Taylor series expansion of the function in the neighborhood of the point of estimate. The utility of this nonparametric regression approach is demonstrated through an application to nonparametric short term forecasts of the biweekly Great Salt Lake volume.volume.

• Tunnel and Underground Space
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• v.31 no.6
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• pp.480-493
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• 2021

Since the generalized Hoek-Brown criterion (GHB) provides an efficient way of identifying its strength parameter values with the consideration of in-situ rock mass condition via Geological Strength Index (GSI), this criterion is recognized as one of the standard rock mass failure criteria in rock mechanics community. However, the nonlinear form of the GHB criterion makes its mathematical treatment inconvenient and limits the scope of its application. As an effort to overcome this disadvantage of the GHB criterion, the explicit approximate analytical equations for the minimum principal stress, which is associated with the maximum principal stress at failure, are formulated based on the Taylor polynomial approximation of the original GHB criterion. The accuracy of the derived approximate formula for the minimum principal stress is verified by comparing the resulting approximate minimum principal stress with the numerically calculated exact values. To provide an application example of the approximate formulation, the equivalent friction angle and cohesion for the expected plastic zone around a circular tunnel in a GHB rock mass are calculated by incorporating the formula for the approximate minimum principal stress. It is found that the simultaneous consideration of the values of mi, GSI and far-field stress is important for the accurate calculation of equivalent Mohr-Coulomb parameter values of the plastic zone.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.25-34
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• 2002

This paper explains methods of numerical analysis which appear on Cardano's Ars Magna and Newton's Principia. Cardano's method is secant method, but its actual al]plication is severely limited by technical difficulties. Newton's method is what nowadays called Newton-Raphson's method. But mysteriously, Newton's explanation had been forgotten for two hundred years, until Adams rediscovered it. Newton had even explained finding the root using the second degree Taylor's polynomial, which shows Newton's greatness.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.629-642
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• 2022

In a recent paper, Sakar and Güney introduced a new class of bi-close-to-convex functions and determined the estimates for the general Taylor-Maclaurin coefficients of functions therein. The main purpose of this note is to give a generalization of this class. Also we point out the proof by Sakar and Güney is incorrect and present a correct proof.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.12 no.6
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• pp.580-598
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• 1987

This paper presents a method to realize the sequential multiple-valued Logic on Galois field. First, We develop so that Taylor series can be corresponded the irreducible polynomial to realize over the finite field, and produce the matrix. This paper object expanded a basic concept of the conbinational Logic circuit so as to apply in the sequential Logic circuit. First of all, We suggest a theory for constructing sequential multiple-valued Logic circuit. Then, We realized the construction with the single input and the multi-output that expanded its function construction. In case of the multi-output, the circuit process by the partition function concept as the mutual independent. This method can be reduced a enormous computer course to need a traditional extention that designed the sequential multi-valued Logic circuit.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.