• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.673-693
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• 2005

In this paper, we first find a necessary and sufficient condition for the existence of multiple orthogonal polynomials by the moments of a pair of measures $(d{\mu},\;dv)$ and then give representations for multiple orthogonal polynomials. We also prove four term recurrence relations for multiple orthogonal polynomials of type II and several interesting relations for multiple orthogonal polynomials are given. A generalized recurrence relation for multiple orthogonal polynomials of type I is found and then four term recurrence relations are obtained as a special case.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.463-474
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• 2001

We find Rodrigues type formula for multi-variate orthogonal polynomial solutions of second order partial differential equations.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.5
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• pp.85-95
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• 2021

Structure design sensitivity was evaluated using the orthogonal array experimental method for passive-type deck support frame (DSF) developed for float-over installation of the offshore plant. Moreover, approximation characteristics were also reviewed based on various meta-models. The minimum weight design of the DSF is significantly important for securing both maneuvering performance and buoyancy of a ship equipped with the DSF and guaranteeing structural design safety. The performance strength of the passive type DSF was evaluated through structure analysis based on the finite element method. The thickness of main structure members was applied to design factors, and output responses were considered structure weight and strength performances. Quantitative effects on the output responses for each design factor were evaluated using the orthogonal array experimental method and analysis of variance. The optimum design case was also identified from the orthogonal array experiment results. Various meta-models, such as Chebyshev orthogonal polynomial, Kriging, response surface method, and radial basis function-based neural network, were generated from the orthogonal array experiment results. The results of the orthogonal array experiment were validated using the meta-modeling results. It was found that the radial basis function-based neural network among the meta-models could approximate the design space of the passive type DSF with the highest accuracy.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.21 no.4
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• pp.80-87
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• 2007

This paper will suggest that the 1 cross orthogonal loop type sensor improves on the orthogonal loop form sensor-head, which is available a calibration of the linear birefringence, when a fiber optic current sensor was composed. An output characteristics of the 1 cross orthogonal loop form, a general closed loop form, the orthogonal loop form are compared by the IEC(International Electrotechnical Commission) 60044-8 standard, and the state of polarization is compared with three forms. As a result, when the closed loop form was changed to the orthogonal loop form, retardation decreased 15.3[%]. When the closed loop form was changed to the 1 cross orthogonal loop type, the retardation decreased 33.8[%]. As a result of the Faraday Effect measurement, the 1 cross orthogonal loop form has the highest output characteristic and the lowest error ratio. It met the 0.5 class of the IEC 60044-8 standard. Thus, in application of the 1cross orthogonal loop form, the possibility to develop high reliability fiber optic current sensors that have a high output and stable error ratio rises is increased.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.603-617
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• 1997

Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + <\tau,p'(x)q'(x)> $$ where $\tau$ is a moment functional and c and $\lambda$ are real constants. We investigate properties of orthogonal polynomials relative to $\phi(\cdot,\cdot)$ and give necessary and sufficient conditions under which such Sobolev orthogonal polynomials satisfy a spectral type differential equation with polynomial coefficients.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.677-688
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• 2017

The composition of Jacobi type finite classes of the classical orthogonal polynomials with two generalized Riemann-Liouville fractional derivatives are considered. The outcomes are expressed in terms of generalized Wright function or generalized hypergeometric function. Similar composition formulas are also obtained by considering the generalized Riemann-Liouville and $Erd{\acute{e}}yi-Kober$ fractional integral operators.

• Advances in Computational Design
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• v.7 no.1
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• pp.37-56
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• 2022

Phase-type distributions are the distributions of the time to absorption in finite and absorbing Markov chains. They generalize, while at the same time, retain the tractability of the exponential distributions and their family. They are widely used as stochastic models from queuing theory, reliability, dependability, and forecasting, to computer networks, security, and computational design. The ability to fit phase-type distributions to intractable or empirical distributions is, therefore, highly desirable for many practical purposes. Many methods and tools currently exist for this fitting problem. In this paper, we present the results of our investigation on using orthogonal-distance fitting as a method for fitting phase-type distributions, together with a comparison to the currently existing fitting methods and tools.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.4
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• pp.70-76
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• 2009

In this paper, we propose the design criteria of the pre-processing scheme used in ABAB type quasi-orthogonal space-time block code(QOSTBC) and derive. The proposed design criteria show how to obtain full-diversity and full-rate (FDFR) property, single-symbol decodability, and increased coding gam. We design an improved ABAB type QOSTBC using the proposed design criteria. The desinged QOSTBC has a superior performance to Dalton's QOSTBC and inherits the merits of Dalton's QOSTBC, which are FDFR property, and single symbol decodability for PAM signal constellation.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.408-413
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• 2001

The structural optimization is carried out in the continuous design space or discrete design space. Methods for discrete variables such as genetic algorithms are extremely expensive in computational cost. In this research, an iterative optimization algorithm using orthogonal arrays is developed for design in discrete space. An orthogonal array is selected on a discrete design space and levels are selected from candidate values. Matrix experiments with the orthogonal array are conducted. New results of matrix experiments are obtained with penalty functions for constraints. A new design is determined from analysis of means(ANOM). An orthogonal array is defined around the new values and matrix experiments are conducted. The final optimum design is found from iterative process. The suggested algorithm has been applied to various problems such as truss and frame type structures. The results are compared with those from a genetic algorithm and discussed.

• Journal of the Korea Convergence Society
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• v.12 no.3
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• pp.187-196
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• 2021

The paper deals with comparative study for characteristics of approximation of design space according to various approximate models and sensitivity analysis using orthogonal array experiments in structure design of active type DSF which was developed for float-over installation of offshore plant. This study aims to propose the orthogonal array experiments based design methodology which is able to efficiently explore an optimum design case and to generate the accurate approximate model. Thickness sizes of main structure member were applied to the design factors, and output responses were considered structure weight and strength performances. Quantitative effects on the output responses for each design factor were evaluated using the orthogonal array experiment. Best design case was also identified to improve the structure design with weight minimization. From the orthogonal array experiment results, various approximate models such as response surface model, Kriging model, Chebyshev orthogonal polynomial model, and radial basis function based neural network model were generated. The experiment results from orthogonal array method were validated by the approximate modeling results. It was found that the radial basis function based neural network model among the approximate models was able to approximate the design space of the active type DSF with the highest accuracy.