• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.187-193
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• 2010

In this paper, the moments of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs(RNT) distribution over a general interval [a, b] $\subset$ [0, 1], are found through the moments of the RNT distribution over the unit interval, [0, 1]. This is done using some special features of the distribution and the fact that [0, 1] is a self-similar set in a dynamical system generated by the RNT distribution. The results are important for the study of the orthogonal polynomials with respect to the RNT distribution over a general interval.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.584-586
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• 1997

The orthogonal polynomials have been widely employed to solve control problems, but the LQG(linear quadratic gaussian) problem remains unsolved. In this paper, we obtained the solutions of Riccati equation and covariance matrix Riccati equation by two point boundary problem and matrix fraction method using BPF(Block Pulse Function), respectively. This solutions are solved the problem of the LQG controller design.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.811-827
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• 2010

This paper deals with a density estimation method in binary choice models that can be regarded as a statistical inverse problem. We use an orthogonal basis to estimate density function and consider the choice of an appropriate truncation parameter to reflect the model complexity and the prediction accuracy. We propose a data-dependent rule to choose the truncation parameter in the context of binary choice models. A numerical simulation is provided to illustrate the performance of the proposed method.

• Proceedings of the KAIS Fall Conference
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• 2007.11a
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• pp.319-322
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• 2007

철도차량의 피로수명예측은 안전성과 신뢰성을 확보하고 높은 품질을 위한 중요한 관점이다. 이것은 최적설계 과정에서 추가의 제한조건으로 최소 피로수명값을 사용해서 접근할 수 있다. 하지만 피로수명은 회수의 함수이기 때문에 최적설계 적용에 제약이 따른다. 본 연구는 피로수명예측을 위한 최적설계에 대해 2단계 반응표면모델의 응용을 제안한다. 적용 예제로 컨테이너 화차의 제동 브라켓 엔드빔의 피로파손 문제에 대해 제안한 방법의 유효성을 설명한다.

• Asian-Australasian Journal of Animal Sciences
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• v.20 no.2
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• pp.160-165
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• 2007

Dispersion parameters for the number of piglets born alive were estimated using a repeatability and random regression model. Six sow breeds/lines were included in the analysis: Swedish Landrace, Large White and both crossbred lines between them, German Landrace and their cross with Large White. Fixed part of the model included sow genotype, mating season as month-year interaction, parity and weaning to conception interval as class effects. The age at farrowing was modelled as a quadratic regression nested within parity. The previous lactation length was fitted as a linear regression. Random regressions for parity on Legendre polynomials were included for direct additive genetic, permanent environmental, and common litter environmental effects. Orthogonal Legendre polynomials from the linear to the cubic power were fitted. In the repeatability model estimate of heritability was 0.07, permanent environmental effect as ratio was 0.04, and common litter environmental effect as ratio was 0.01. Estimates of genetic parameters with the random regression model were generally higher than in the repeatability model, except for the common litter environmental effect. Estimates of heritability ranged from 0.06 to 0.10. Permanent environmental effect as a ratio increased along a trajectory from 0.03 to 0.11. Magnitudes of common litter effect were small (around 0.01). The eigenvalues of covariance functions showed that between 7 and 8 % of genetic variability was explained by individual genetic curves of sows. This proportion was mainly covered by linear and quadratic coefficients. Results suggest that the random regression model could be used for genetic analysis of litter size.

• Asian-Australasian Journal of Animal Sciences
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• v.29 no.12
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• pp.1682-1687
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• 2016

The objective of this study was to estimate the genetic parameters of milk protein yields in Iranian Holstein dairy cattle. A total of 1,112,082 test-day milk protein yield records of 167,269 first lactation Holstein cows, calved from 1990 to 2010, were analyzed. Estimates of the variance components, heritability, and genetic correlations for milk protein yields were obtained using a random regression test-day model. Milking times, herd, age of recording, year, and month of recording were included as fixed effects in the model. Additive genetic and permanent environmental random effects for the lactation curve were taken into account by applying orthogonal Legendre polynomials of the fourth order in the model. The lowest and highest additive genetic variances were estimated at the beginning and end of lactation, respectively. Permanent environmental variance was higher at both extremes. Residual variance was lowest at the middle of the lactation and contrarily, heritability increased during this period. Maximum heritability was found during the 12th lactation stage ($0.213{\pm}0.007$). Genetic, permanent, and phenotypic correlations among test-days decreased as the interval between consecutive test-days increased. A relatively large data set was used in this study; therefore, the estimated (co)variance components for random regression coefficients could be used for national genetic evaluation of dairy cattle in Iran.

• Structural Engineering and Mechanics
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• v.29 no.2
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• pp.135-154
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• 2008

The moving vehicle loads on a bridge deck is one of the most important live loads of bridges. They should be understood, monitored and controlled before the bridge design as well as when the bridge is open for traffic. A MOM-based algorithm (MOMA) is proposed for identifying the timevarying moving vehicle loads from the responses of bridge deck in this paper. It aims at an acceptable solution to the ill-conditioning problem that often exists in the inverse problem of moving force identification. The moving vehicle loads are described as a combination of whole basis functions, such as orthogonal Legendre polynomials or Fourier series, and further estimated by solving the new system equations developed with the basis functions. A number of responses have been combined, some numerical simulations on single axle, two axle and multiple-axle loads, being either constant or timevarying, have been carried out and compared with the existing time domain method (TDM) in this paper. The illustrated results show that the MOMA has higher identification accuracy and robust noise immunity as well as producing an acceptable solution to ill-conditioning cases to some extent when it is used to identify the moving force from bridge responses.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.12
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• pp.1141-1150
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• 2012

This paper describes the shape optimization of impeller blades for an anti-heeling bidirectional axial flow pump used in ships. In general, a bidirectional axial pump has efficiency much lower than that of a classical unidirectional pump because of the symmetry of the blade type. In this study, by focusing on a pump impeller, the shape of the blades is redesigned to develop a bidirectional axial pump with higher efficiency. The commercial code employed in this simulation is CFX v.13. The CFD result of the pump torque, head, and hydraulic efficiency was compared. The orthogonal array (OA) and analysis of variance (ANOVA) techniques and surrogate-model-based optimization using orthogonal polynomials are employed to determine the main effects and their optimal design variables. According to the optimal design, we confirm an effective design variable for impeller blades and explain the optimal solution as well as the usefulness of satisfying the constraints of the pump torque and head.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.11
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• pp.1765-1771
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• 2010

In the case of micro.electro-mechanical system (MEMS) devices, the quality of punched via hole is one of the most important factors governing the performance of the device. The common features that affect the laser micromachining of via holes drilled by using Nd:$YVO_4$ laser are described, and efficient optimization methods to measure them are presented. The analysis methods involving an orthogonal array, analysis of variance (ANOVA), and response surface optimization are employed to determine the main effects and to determine the optimal laser process parameters. The significant laser process parameters were identified and their effects on the quality of via holes were studied. Finally, an experiment in which the optimal levels of the laser process parameters were used was carried out to demonstrate the effectiveness of the optimization method.