• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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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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• v.1 no.2
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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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• v.40 no.1
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.5A
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• pp.333-340
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• 2003

In this paper, we propose a new turbo-coded orthogonal frequency division multiplexing (OFDM) transmission scheme that can improve greatly the performance by making all the turbo-coded symbols have the same reliability for OFDM transmission over a frequency selective fading channel. The same reliability, that is, the same fading can be accomplished through multiplexing of turbo-coded symbols using distinct orthogonal codes and spreading over the whole effective subcarriers (hereafter, called as the orthogonal code multiplexing (OCM)). As for the orthogonal code selection, we choose the set of the discrete Fourier transform (DFT) basis sequences, since the code set holds the orthogonality irrespective of the length and also has the equal energy property. We perform computer simulations using the Log-maximum-a-posteriori (Log-MAP) algorithm for iterative decoding in order to assess the performance of the proposed transmission scheme.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.499-505
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• 2004

The Pareto diagram analysis of the experimental data by the two level orthogonal arrays has been used widely in practice since it is a graphical, quick and easy method to analyze experimental results, which does not use the analysis of variance to screen significant effects. For the analysis of the experimental data by $L_{18}(2 \times 3^7)$ orthogonal array, Park(1996) proposed Pareto ANOVA in which the size of effects is defined by the mean squares of effects and the Pareto principle is used. In this paper, a new approach of the Pareto diagram analysis of the experimental data by $L_{18}(2 \times 3^7)$ orthogonal array is proposed. The main idea is to partition the size of three level effects by that of linear and quadratic orthogonal contrasts of those effects.

• Journal of Convergence for Information Technology
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• v.10 no.7
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• pp.138-146
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• 2020

The paper deals with comparative study of characteristics of surrogate models and sensitivity evaluation using design of experiments in order to enhance and analysis the structure design of an automatic salt collector under various design load conditions. Orthogonal array design based on numerical analysis was used for the design of experiments. The thickness sizing variables of main structure member were considered the design factors, and the output responses were selected from the strength performances as well as the weight. The quantitative effects on responses for each design factor were evaluated from the orthogonal array experiment. Optimum design case was also identified to improve the strength performances with weight minimization. Using the orthogonal array experiment. various surrogate models such as response surface model, Kriging model, and Chebyshev orthogonal polynomial were generated. The orthogonal array experiment results were validated by the surrogate modeling results. The most suitable surrogate model was the response surface model for the exploration of design space of the automatic salt collector.

• Journal of Electrical Engineering and Technology
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• v.5 no.2
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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.

• 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.

• Proceedings of the KIEE Conference
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• 1998.07b
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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.