• 한국소음진동공학회논문집
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• 제16권7호
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• pp.769-776
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• 2006

A measured frequency response function can be represented as a ratio of two polynomials. A curve-fitting of frequency responses with Legendre polynomialis suggested in the paper. And the suggested curve-fitting algorithm is based on the least-square error method. Since the Legendre polynomials satisfy the orthogonality condition, the curve-fitting with the polynomials results to more reliable curve-fitting than ordinary polynomial method. Though the proposed curve-fitting with Legendre polynomials cannot cover all frequency range of interest, example shows that the suggested method is quite applicable in a limited frequency band.

• 대한수학회지
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• 제45권2호
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• pp.393-404
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• 2008

Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.

• 대한수학회보
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• 제47권6호
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• pp.1163-1170
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• 2010

We study finite type curve in $R^3$(-3) which lies in a cylinder $N^2$(c). Baikousis and Blair proved that a Legendre curve in $R^3$(-3) of constant curvature lies in cylinder $N^2$(c) and is a 1-type curve, conversely, a 1-type Legendre curve is of constant curvature. In this paper, we will prove that a 1-type curve lying in a cylinder $N^2$(c) has a constant curvature. Furthermore we will prove that a curve in $R^3$(-3) which lies in a cylinder $N^2$(c) is finite type if and only if the curve is 1-type.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• 응용통계연구
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• 제34권6호
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• pp.945-956
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• 2021

본 연구에서는 가중주성분분석으로부터 정준대응분석을 유도하는 Legendre와 Legendre (2012)의 알고리즘을 고찰하였다. 그리고, 가중주성분분석에 기반한 Legendre와 Legendre (2012)의 정준대응분석이 가우시안 반응모형에 기초한 Ter Braak (1986)의 정준대응분석과 동일함을 다루었다. 생태학에서 종의 발현 정도를 잘 설명할 수 있는 가우시안 반응곡선에서 도출된 Ter Braak (1986)의 정준대응분석은 종 패킹 모형(species packing model)이라는 기본 가정을 사용한 후 일반화선형모형과 정준상관분석을 결합시키는 방법으로 도출된다. 그런데 Legendre와 Legendre (2012)의 알고리즘은 이러한 가정없이 Benzecri의 대응분석과 상당히 유사한 방법으로 계산되는 특징을 지닌다. 그러므로 가중주성분석에 기초한 정준대응분석을 사용하면, 결과물 활용에 약간의 유연성을 지닐 수 있게 된다. 결론적으로 본 연구에서는 서로 다른 모형에서 출발한 두 방법이 장소점수(site score), 종 점수(species score) 그리고 환경변수와의 상관관계가 서로 동일함을 보인다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권2호
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• pp.83-96
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• 2020

In this paper we study Biharmonic curves, Legendre curves and Magnetic curves in three dimensional f-Kenmotsu manifolds. We also study 1-type curves in a three dimensional f-Kenmotsu manifold by using the mean curvature vector field of the curve. As a consequence we obtain for a biharmonic helix in a three dimensional f-Kenmotsu manifold with the curvature κ and the torsion τ, κ² + τ² = -(f² + f'). Also we prove that if a 1-type non-geodesic biharmonic curve γ is helix, then λ = -(f² + f').

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권3호
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• pp.109-124
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• 2017

The numerical solution of the Stokes equation with discontinuous viscosity and singular force term is challenging, due to the discontinuity of pressure, non-smoothness of velocity, and coupled discontinuities along interface.In this paper, we give an efficient algorithm to solve this problem by employing spectral Legendre and Chebyshev approximations.First, we present the algorithm for a problem defined in rectangular domain with straight line interface. Then it is generalized to a domain with smooth curve boundary and interface by employing spectral element method. Numerical experiments demonstrate the accuracy and efficiency of our algorithm and its spectral convergence.

• 대한수학회논문집
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• 제35권3호
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• pp.967-977
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• 2020

In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜³₁(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅² - 𝜏² = -1 + 𝜀₁(H + 1)𝜂(B)² in the Lorentzian Sasakian space forms x1D4DC³₁(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.485-489
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• 2006

In this paper, we slightly improve the Baby-step Giant-step for certain elliptic curves. This method gives the running time improvement of $200\%$ in precomputation (Baby-step) and requires half as much storage as the original Baby-step Giant-step method.

• Asian-Australasian Journal of Animal Sciences
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• 제29권12호
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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.