• 충청수학회지
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• 제34권3호
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• pp.271-283
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• 2021

The asymptotics behavior orthogonal polynomials have been in the spotlight since the result of G. Szegő in 1921. In this paper we study the pointwise asymptotics inside the unit disk for orthogonal polynomials with respect to a polynomial Szegő measure with an infinite masses points.

• 대한수학회보
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• 제33권1호
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• pp.135-170
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• 1996

Recently many people have studied the Sobolev orthogonal polynomials, that is, polynomials which are orthogonal relative to a symmetric bilinear form $\phi(\cdot,\cdot)$ defined by $$ (1.1) $\phi(p,q) := (p,q)_N = \sum_{k=0}^{N} \int_{R}p^(k) (x)q^(k) (x) d\mu_k, $$ where each $d\mu_k$ is a signed Borel measure on the real line $R$ with finite moments of all orders. For the brief history on this subject, we refer to the survey article Ronveaux [13] and Marcellan and et al [10].

• Journal of Electrical Engineering and information Science
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• 제1권2호
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• pp.125-133
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• 1996

In this paper, we dicuss on the properties related to the circular filtering in orthogonal transform domain. The efficient filtering schemes in six orthogonal transform domains are presented by generalizing the convolution-multiplication property of the DFT. In brief, the circular filtering can be accomplished by multiplying the transform domain filtering matrix W, which is shown to be very sparse, yielding the computational gains compared with the time domain processing. As an application, decimation and interpolation techniques in orthogonal transform domains are also investigated.

• East Asian mathematical journal
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• 제40권1호
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• pp.25-36
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• 2024

Full univariate moment problems have been studied using continued fractions, orthogonal polynomials, spectral measures, and so on. On the other hand, the truncated moment problem has been mainly studied through confirming the existence of the extension of the moment matrix. A few articles on the multivariate moment problem implicitly presented about some results of this note, but we would like to rearrange the important results for the existence of a representing measure of a moment sequence. In addition, new techniques with orthogonal polynomials will be introduced to expand the means of studying truncated moment problems.

• 한국통신학회논문지
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• 제28권5A호
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• pp.333-340
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• 2003

본 논문에서는 주파수 선택적 페이딩 환경에서도 터보부호화된 모든 정보심벌들이 수신단에서 동일한 신뢰도를 갖도록 전송함으로써, 터보부호화된 OFDM (orthogonal frequency division multiplexing) 시스템의 성능을 크게 향상시키는 새로운 전송 방식을 제안한다. 모든 정보심벌들이 동일한 신뢰도를 갖는다는 것은 페이딩의 영향을 동일하게 받는다는 것을 의미한다. 이를 위하여 각 정보심벌에 서로 다른 직교코드를 할당하여 다중화하고, 이를 전송 가능한 모든 부채널들로 확산시켜 전송한다 (이후, 이 과정은 직교코드 다중화 (orthogonal code multiplexing: OCM) 라고 한다.). 다중화를 위한 직교코드로는 코드의 길이에 상관없이 코드들 상호간의 직교성을 유지하며 코드간 동일한 에너지를 갖는 DFT (discrete Fourier transform) 기본 시퀀스 (basis sequence)를 사용한다. 모의실험을 통하여 제안된 시스템의 성능분석이 이루어지며, 반복 복호를 위해서는 Log-MAP(Log-maximum a posteriori) 알고리즘을 사용한다.

• 응용통계연구
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• 제17권3호
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• pp.499-505
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• 2004

2수준 직교배열표를 이용한 실험자료에 대한 파레토 그림에 의한 분석 방법은 실무에서 많이 활용되고 있는데, 그 이유는 유의한 요인을 선별하기 위해서 분산분석법을 사용하지 않고 시각적이고 간결한 방법에 의하여 실험자료를 분석하기 때문이다. $L_{18}(2 \times 3^7)$ 직교배열표를 이용한 실험자료에 대한 분석방법으로 Park(1996)은 효과의 크기를 각 효과의 평균제곱으로 정의하고 파레토 원칙을 사용한 Pareto ANOVA를 제안하였다. 이 논문에서는 $L_{18}(2 \times 3^7)$ 실험자료에 대한 새로운 파레토 그림에 의한 분석 방법이 제시된다. 주요 요점은 3수준 효과의 크기를 일차와 이차 직교대비의 크기에 의해 분할하는 것이다.

• 융합정보논문지
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• 제10권7호
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• pp.138-146
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• 2020

본 논문은 다양한 설계하중조건 상태에서 자동채염기 구조설계의 성능분석과 개선을 위해 실험계획법을 이용한 설계민감도 평가와 대리모델의 특성에 대한 비교연구를 수행하였다. 실험계획법은 수치해석 기반의 직교배열설계 방법을 이용하였다. 설계인자는 주요 구조부재의 두께치수 변수를 고려하였고, 응답치는 중량과 강도성능을 선정하였다. 직교배열실험을 통해 설계인자 별 응답치에 대한 정량적인 영향도를 분석하였다. 또한 최소의 중량증감으로 구조성능을 개선할 수 있는 최적의 설계조건을 탐색하였다. 직교배열실험 결과를 이용하여 반응표면모델, 크리깅모델, 그리고 체비쇼프 직교 다항식과 같은 다양한 대리모델을 생성하였다. 대리모델의 결과를 통해 직교배열실험 결과의 타당성을 검증하였다. 자동채염기 구조설계 공간 탐색에는 반응표면모델이 가장 적합한 대리모델로 평가되었다.

• Journal of Electrical Engineering and Technology
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• 제5권2호
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• pp.337-341
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• 2010

In this paper, an extremely low voltage operated micro corner cube retroreflector (CCR) was fabricated for free-space optical communication applications by using bulk silicon micromachining technologies. The CCR was comprised of an orthogonal vertical mirror and a horizontal actuated mirror. For low voltage operation, the horizontal actuated mirror was designed with two PZT cantilever actuators, torsional bars, hinges, and a mirror plate with a size of $400{\mu}m{\times}400{\mu}m$. In particular, the torsional bars and hinges were carefully simulated and designed to secure the flatness of the mirror plate by using a finite element method (FEM) simulator. The measured tilting angle was approximately $2^{\circ}$ at the applied voltage of 5 V. An orthogonal vertical mirror with an extremely smooth surface texture was fabricated using KOH wet etching and a double-SOI (silicon-on-insulator) wafer with a (110) silicon wafer. The fabricated orthogonal vertical mirror was comprised of four pairs of two mutually orthogonal flat mirrors with $400{\mu}m4 (length) $\times400{\mu}m$ (height) $\times30{\mu}m$ (thickness). The cross angles and surface roughness of the orthogonal vertical mirror were orthogonal, almost $90^{\circ}$ and 3.523 nm rms, respectively. The proposed CCR was completed by combining the orthogonal vertical and horizontal actuated mirrors. Data transmission and modulation at a frequency of 10 Hz was successfully demonstrated using the fabricated CCR at a distance of approximately 50 cm.

• 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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 B
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• pp.468-470
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• 1998

We have studied system identification model reduction method, optimal control by orthogonal functions. This paper presents the easy method that solves algebra equations instead of differential equations using Walsh, Haar, Block pulse function of orthogonal functions in state equation. The proposed algorithm is verified through some examples.