• Korean Journal of Mathematics
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• 제29권4호
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• pp.687-704
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• 2021

The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly (α, m)-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.

• 환경영향평가
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• 제29권4호
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• pp.272-285
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• 2020

본 연구에서는 3차원 기상 및 대기질 모델의 입출력 자료를 평가하는 데 필요한 통계 검증지표를 선별하고, 선정된 검증지표의 기준치를 조사하여 그 결과를 요약하였다. 여러 국내외 문헌과 최근 논문 검토를 통해 최종 선정된 통계 검증지표는 MB (Mean Bias), ME (Mean Error), MNB (Mean Normalized Bias Error), MNE (Mean Absolute Gross Error), RMSE (Root Mean Square Error), IOA (Index of Agreement), R (Correlation Coefficient), FE (Fractional Error), FB (Fractional Bias)로 총 9가지이며, 국내외 문헌을 통해 그 기준치를 확인하였다. 그 결과, 기상모델의 경우 대부분 MB와 ME가 주요 지표로 사용되어 왔고, 대기질 모델 결과는 NMB와 NME 지표가 주로 사용되었으며, 그 기준치의 차이를 분석하였다. 아울러 이들 통계 검증지표값을 이용하여 모델 예측 결과를 효과적으로 비교하기 위한 표출 도식으로 축구 도식, 테일러 도식, Q-Q (Quantile-Quantile) 도식의 장단점을 분석하였다. 나아가 본 연구 결과를 기반으로 우리나라의 산악지역의 특수성 등이 잘 고려된 통계 검증지표의 기준치 설정 등의 추가연구가 효과적으로 진행될 수 있기를 기대한다.

• Journal of Mechanical Science and Technology
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• 제20권5호
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• pp.658-667
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• 2006

Fractional derivative models, which are used to describe the viscoelastic behavior of material, have received considerable attention. Thus it is necessary to put forward the analysis solutions of dynamic systems containing a fractional derivative. Although previously reported such kind of fractional calculus-based constitutive models, it only handles the particularity of rational number in part, has great limitation by reason of only handling with particular rational number field. Simultaneously, the former study has great unreliability by reason of using the complementary error function which can't ensure uniform real number. In this paper, a new approach is proposed for an analytical scheme for dynamic system of a spring-mass-damper system of single-degree of freedom under general forcing conditions, whose damping is described by a fractional derivative of the order $0<{\alpha}<1$ which can be both irrational number and rational number. The new approach combines the fractional Green's function and Laplace transform of fractional derivative. Analytical examples of dynamic system under general forcing conditions obtained by means of this approach verify the feasibility very well with much higher reliability and universality.

• 한국음향학회지
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• 제22권8호
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• pp.680-686
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• 2003

디지털 도파관 모델은 악기의 물리적 모델링에 사용되는 일반적인 방법이다. 디지털 도파관 모델에서 파동의 움직임은 시간 또는 공간을 기준으로 해석 가능하다. 음의 샘플링이 시간을 기준으로 이루어지므로 악기 모델은 시간에 의한 파동의 움직임으로 묘사되는 것이 일반적이다. 본 논문에서는 현에 대한 공간 기준의 디지털 도파관 모델에 악기 몸체 모델을 추가해 악기 음을 합성하였다. 그렇게 함으로써 합성 음의 음질을 향상시키고 악기 모델의 음색 조절 변수들을 효과적으로 처리할 수 있었다. 공간 기준 샘플링에서 현 및 몸체에서 발생하는 미소 지연 오차에 대해 설명하고 FD (Fractional Delay) 필터를 이용해 미소 지연을 처리하는 방법을 보였다. 그리고 지연에 수에 따른 합성음의 변화를 설명하고 그 결과를 시간 기준 디지털 도파관 모델과 비교하였다.

• Journal of Power Electronics
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• 제18권3호
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• pp.723-735
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• 2018

Linear proportional-integral (PI) controllers are an attractive choice for controlling the speed of induction machines because of their simplicity and ease of implementation. Fractional-order PI (FO-PI) controllers, however, perform better than PI controllers because of their nonlinear nature and the underlying iso-damping property of fractional-order operators. In this work, an FO-PI controller based on the proposed first-order plus dead-time induction motor model and integer-order (IO) controllers, such as Ziegler-Nichols PI, Cohen-Coon PI, and a PI controller tuned via trial-and-error method, is designed. Simulation and experimental investigation on an indirect field-oriented induction motor drive system proves that the proposed FO-PI controller has better speed tracking, lesser settling time, better disturbance rejection, and lower speed tracking error compared with linear IO-PI controllers. Our experimental study also validates that the FO-PI controller maximizes the torque per ampere output of the induction machine and can effectively control the motor at low speed, in field-weakening regions, and under detuned conditions.

• 대한수학회지
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• 제61권4호
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2023년도 학술발표회
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• pp.25-25
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• 2023

The ensemble optimal interpolation (EnOI) scheme is a sub-optimal alternative to the ensemble Kalman filter (EnKF) with a reduced computational demand making it potentially more suitable for operational applications. Since only one model is integrated forward instead of an ensemble of model realizations, online estimation of the background error covariance matrix is not possible in the EnOI scheme. In this study, we investigate two Gaussian noise based ensemble generation strategies to produce dynamic covariance matrices for assimilation of water level observations into a distributed hydrological model. In the first approach, spatially correlated noise, sampled from a normal distribution with a fixed fractional error parameter (which controls its standard deviation), is added to the model forecast state vector to prepare the ensembles. In the second method, we use an adaptive error estimation technique based on the innovation diagnostics to estimate this error parameter within the assimilation framework. The results from a real and a set of synthetic experiments indicate that the EnOI scheme can provide better results when an optimal EnKF is not identified, but performs worse than the ensemble filter when the true error characteristics are known. Furthermore, while the adaptive approach is able to reduce the sensitivity to the fractional error parameter affecting the first (non-adaptive) approach, results are usually worse at ungauged locations with the former.

• 대한임베디드공학회논문지
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• 제15권5호
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• pp.235-242
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• 2020

This paper analyzes the effect of reduced output width of the truncated logarithmic multiplication and application to inferences using convolutional neural networks (CNNs). For small hardware overhead, output width is reduced in the truncated Mitchell multiplier, so that fractional bits in multiplication output are minimized in error-resilient applications. This analysis shows that when reducing output width in the truncated Mitchell multiplier, even though worst-case relative error increases, average relative error can be kept small. When adopting 8 fractional bits in multiplication output in the evaluations, there is no significant performance degradation in target CNNs compared to existing exact and original Mitchell multipliers.

• 응용통계연구
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• 제26권6호
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• pp.1053-1061
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• 2013

본 논문은, 장기기억 특성과 이분산성을 고려한 인터넷 트래픽 예측 모형을 제안하고자 한다. 트래픽 과부하를 대비하기 위해서, 트래픽 용량은 트래픽의 예측치와 트래픽의 변동 크기에 따라 트래픽의 최대용량을 설정하여야 한다. 이를 위하여 교내 트래픽 자료 중 교내로 들어오는 트래픽과 교외로 나가는 트래픽에 이분산성과 장기기억 모형의 유용성을 확인하였다. 이에 대하여 AR-GARCH 모형, ARMA-GARCH 모형과 장기기억모형인 Fractional ARIMA와 장기기억과 이분산성을 고려한 Fractional ARMA-GARCH 모형을 적용하여 모형의 예측성능을 비교하였다.

• 대한수학회지
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• 제51권1호
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• pp.203-224
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• 2014

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.