• 대한수학회지
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• 제42권4호
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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.

• 대한수학회보
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• 제38권3호
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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.

• 한국기계가공학회지
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• 제20권5호
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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.

• 조명전기설비학회논문지
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• 제21권4호
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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.

• 대한수학회논문집
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• 제12권3호
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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.

• 대한수학회논문집
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• 제32권3호
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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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• 제7권1호
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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.

• 대한전자공학회논문지TC
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• 제46권4호
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• pp.70-76
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• 2009

본 논문에서는 ABAB 형 준직교 시공간 부호(Quasi-Orthogonal Space-Time Block Code; QOSTBC)에 사용되는 전처리 과정을 설계하는 조건을 제안하였다. 본 논문에서 제안한 설계 조건은 최대 다이버시티 및 최대 전송율(Full Diversity and Full Rate; FDFR), 단일 심볼 복호 능력, 향상된 부호 이득을 얻을 수 있는 방법을 제공한다. 또한 본 논문에서는 제안된 설계 조건을 이용하여 개선된 ABAB 형 QOSTBC를 설계하였다. 이 QOSTBC는 기존에 Dalton이 제안했던 ABAB 형 QOSTBC 부호 보다 뛰어난 성능을 가질 뿐 아니라, 동일하게 FDFR을 충족하며, PAM 신호 성좌가 사용되는 경우, 단일 심볼 복호가 가능하다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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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.

• 한국융합학회논문지
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• 제12권3호
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• pp.187-196
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• 2021

본 연구에서는 해양플랜트의 플로트오버 설치 작업을 위해 개발된 능동형 갑판지지 프레임(Deck support frame, DSF)의 구조설계에 대해 직교배열실험 방법을 이용한 민감도해석과 다양한 근사모델의 적용에 따른 설계공간의 근사화 특성에 관한 비교연구를 수행하였다. 본 연구의 목적은 효율적인 최적설계안 탐색과 높은 정확도의 근사모델을 생성할 수 있는 직교배열실험 기반의 설계 방법론을 제안하는 것이다. 설계인자는 주요 구조부재의 두께 치수를 적용하였고, 응답함수는 중량과 강도성능을 선정하였다. 직교배열실험을 이용하여 설계인자 별 응답함수에 대해 정량적인 영향도가 분석되었고, 최소중량설계를 실현할 수 있는 최상 설계조건이 탐색되었다. 직교배열실험 결과로부터 반응표면 모델, 크리깅 모델, 체비쇼프 직교 다항식 모델, 그리고 방사기저함수 신경망 모델과 같은 다양한 근사모델이 생성되었다. 근사모델의 결과를 통해 직교배열실험 결과의 타당성을 검증하였으며, 능동형 DSF의 설계공간에 대해 방사기저함수 신경망 모델이 가장 높은 정확도로 근사화할 수 있는 것으로 나타났다.