• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.867-875
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• 1998

In this paper we prove that any continuous function on a bounded closed interval of can be approximated by the superposition of a bounded sigmoidal function with a fixed weight. In addition we show that any continuous function over $\mathbb{R}$ which vanishes at infinity can be approximated by the superposition f a bounded sigmoidal function with a weighted norm. Our proof is constructive.

• 한국컴퓨터정보학회논문지
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• 제11권3호
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• pp.107-115
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• 2006

본 논문에서는 캐스케이드 코릴레이션 학습 알고리즘을 위한 새로운 클래스의 활성화 함수를 소개한다. 이 함수는 코사인으로 모듈화된 가우스 함수로서 편의상 이 활성화 함수를 코스가우스(CosGauss) 함수라고 칭하기로 한다. 이 함수는 기존의 시그모이드 함수(sigmoidal function), 하이퍼볼릭탄젠트 함수(hyperbolic tangent function), 가우스 함수(gaussian function)에 비해서 등성이(ridge)를 더 많이 얻을 수 있다. 이러한 등성이들로 인하여 빠른 속도로 수렴하고 패턴인식 속도를 향상 시켜서 학습 능력을 향상시킬 수 있다. 캐스케이드 코릴레이션 네트워크에 이 활성화 함수를 사용하여 중요한 기준 문제(benchmark problem)의 하나인 이중나선 문제(two spirals problem)에 대하여 실험하여 다른 활성화 함수들과 결과 값을 비교하였다.

• 한국도로학회논문집
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• 제10권4호
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• pp.31-40
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• 2008

아스팔트 콘크리트의 동탄성계수는 아스팔트 포장 해석 및 설계에 매우 중요하다. 동탄성계수의 메스터 곡선은 일반적으로 시그모이달 함수로 표현된다. Ramberg-Osgood 모델은 지반동역학분야에서 변형률 크기에 따른 정규화 탄성계수 감소 곡선에 대한 피팅모델로 널리 사용되고 있다. 동일한 동탄성계수 시험자료에 대하여 시그모이달 함수와 수정 Rambeyg-osgood 모델 모두를 사용하여 메스터 곡선을 획득하였으며, 두 피팅모델 모두 적용성이 우수함을 확인하였다. 시그모이달 함수의 계수들은 서로 연관되어 있어서 메스터 곡선의 절대값과 형상 특성을 서로 분리하는 것이 불가능하다. 그러나 Ramberg-Osgood 모델의 계수는 물리적 의미가 명확할 뿐 아니라 서로 분리되어 있어서 메스터 곡선에 대한 영향요소를 서로 분리하여 평가할 수 있음을 확인하였다.

• Nuclear Engineering and Technology
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• 제53권1호
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• pp.258-265
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• 2021

High levels for noise and a loss of true signal make the quantitative interpretation of nuclear medicine (NM) images difficult. An application of profile optimization using a sigmoidal function in this study was used to acquire the NM images with high quality. And the images were acquired by using three kinds of reconstruction method using each same sinogram: a standard filtered back-projection (FBP), an iterative reconstruction (IR) technique, and the sigmoidal function profile optimization (SFPO). Comparison of image according to reconstruction method was performed to show a superiority of the SFPO for imaging. The images reconstructed by using the SFPO showed an average of 1.49 times and of 1.17 times better in contrast than the results obtained using the standard FBP and the IR technique, respectively. Higher signal to noise ratios were obtained as an average of 12.30 times and of 3.77 times than results obtained using the standard FBP and the IR technique, respectively. This study confirms that reconstruction with SFPO (vs FBP and vs IR) can lead to better lesion detectability and characterization with noise reduction. It can be developed for future reconstruction technique for the NM imaging.

• 호남수학학술지
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• 제27권2호
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• pp.225-232
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• 2005

We obtain the approximation order to a smooth function on a compact subset of $\mathbb{R}$ by generalized translation networks. In our study, the activation function is infinitely many times continuously differentiable function but it does not have special properties around ${\infty}$ and $-{\infty}$ like a sigmoidal activation function. Using the Jackson's Theorem, we get the approximation order. Especially, we obtain the approximation order by a neural network with a fixed threshold.

• Advances in materials Research
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• 제12권1호
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• pp.43-65
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• 2023

Free vibration analysis of power law and sigmoidal sandwich plates made up of functionally graded materials (FGMs) has been carried out using finite element based higher-order zigzag theory. The present model satisfies all-important conditions such as transverse shear stress-free conditions at the plate's top and bottom surface along with continuity condition for transverse stresses at the interface. A Nine-noded C0 finite element having eleven degrees of freedom per node is used during the study. The present model is free from the requirement of any penalty function or post-processing technique and hence is computationally efficient. The present model's effectiveness is demonstrated by comparing the present results with available results in the literature. Several new results have been proposed in the present work, which will serve as a benchmark for future works. It has been observed that the material variation law, power-law exponent, skew angle, and boundary condition of the plate widely determines the free vibration behavior of sandwich functionally graded (FG) plate.

• 한국콘텐츠학회논문지
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• 제9권2호
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• pp.97-105
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• 2009

본 논문에서는 일반화된 캐스케이드 코릴레이션 학습 알고리즘과 일반화된 순환 캐스케이드 코릴레이션 학습 알고리즘의 결합을 통한 새로운 알고리즘을 소개한다. 이 새로운 알고리즘은 패턴분류문제(pattern classification problem)의 신속한 해결을 위하여 비순환 뉴런이 유리한지 순환 뉴런이 유리한지 또는 수직성장이 유리한지 수평성장이 유리한지 고민할 필요 없이 후보뉴런의 학습 중에 네트워크의 구성을 스스로 결정한다. 이 알고리즘의 성능평가를 위하여 학습 알고리즘에서 중요한 기준 문제(benchmark problem) 중의 하나인 콘택트렌즈 문제(Contact lens problem)와 밸런스 스케일 문제 (Balance scale problem)에 대하여 실험하였고 기존의 캐스케이드 코릴레이션 알고리즘 및 순환 캐스케이드 코릴레이션 알고리즘과 성능을 비교 하였다. 이 실험에서 활성화 함수는 일반적으로 많이 사용하는 시그모이드 함수(sigmoidal function) 와 하이퍼볼릭탄젠트 함수(hyperbolic tangent function)를 사용하였다. 이 새로운 알고리즘은 학습을 통하여 기존의 알고리즘보다 적은 수의 은닉뉴런을 생성하여 보다 빠른 학습 속도를 보여주었다.

• 호남수학학술지
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• 제28권1호
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• pp.125-133
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• 2006

We investigate the approximation order to a function in $L_p$[-1, 1] for $0{\leq}p<{\infty}$ by generalized translation networks. In most papers related to neural network approximation, sigmoidal functions are adapted as an activation function. In our research, we choose an infinitely many times continuously differentiable function as an activation function. Using the integral modulus of continuity and the divided difference formula, we get the approximation order to a function in $L_p$[-1, 1].

• Korean Journal of Mathematics
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• 제23권3호
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• pp.327-336
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• 2015

In this paper, we study a constructive approximation by neural networks with positive integer weights. Like neural networks with real weights, we show that neural networks with positive integer weights can even approximate arbitrarily well for any continuous functions on compact subsets of $\mathbb{R}$. We give a numerical result to justify our theoretical result.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.85-96
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• 2018

This study investigates the response of functionally graded (FG) gas pipe under unsteady internal pressure and temperature. The pipe is proposed to be manufactured from FGMs rather than custom carbon steel, to reduce the erosion, corrosion, pressure surge and temperature variation effects caused by conveying of gases. The distribution of material graduations are obeying power and sigmoidal functions varying with the pipe thickness. The sigmoidal distribution is proposed for the 1st time in analysis of FG pipe structure. A Two-dimensional (2D) plane strain problem is proposed to model the pipe cross-section. The Fourier law is applied to describe the heat flux and temperature variation through the pipe thickness. The time variation of internal pressure is described by using exponential-harmonic function. The proposed problem is solved numerically by a two-dimensional (2D) plane strain finite element ABAQUS software. Nine-node isoparametric element is selected. The proposed model is verified with published results. The effects of material graduation, material function, temperature and internal pressures on the response of FG gas pipe are investigated. The coupled temperature and displacement FEM solution is used to find a solution for the stress displacement and temperature fields simultaneously because the thermal and mechanical solutions affected greatly by each other. The obtained results present the applicability of alternative FGM materials rather than classical A106Gr.B steel. According to proposed model and numerical results, the FGM pipe is more effective in natural gas application, especially in eliminating the corrosion, erosion and reduction of stresses.