• Multiscale and Multiphysics Mechanics
• /
• 제1권1호
• /
• pp.15-33
• /
• 2016

In this paper, an asymptotic method is employed to formulate nano- or micro-beams based on strain gradient elasticity. Although a basic theory for the strain gradient elasticity has been well established in literature, a systematic approach is relatively rare because of its complexity and ambiguity of higher-order elasticity coefficients. In order to systematically identify the strain gradient effect, an asymptotic approach is adopted by introducing the small parameter which represents the beam geometric slenderness and/or the internal atomistic characteristic. The approach allows us to systematically split the two-dimensional strain gradient elasticity into the microscopic one-dimensional through-the-thickness analysis and the macroscopic one-dimensional beam analysis. The first-order beam problem turns out to be different from the classical elasticity in terms of the bending stiffness, which comes from the through-the-thickness strain gradient effect. This subsequently affects the second-order transverse shear stress in which the surface shear stress exists. It is demonstrated that a careful derivation of a first strain gradient elasticity embraces "Gurtin-Murdoch traction" as the surface effect of a one-dimensional Euler-Bernoulli-like beam model.

• Journal of the Korean Data and Information Science Society
• /
• 제28권6호
• /
• pp.1245-1255
• /
• 2017

온라인 학습은 자료가 실시간으로 혹은 배치 단위로 축적되는 상황에서 주어진 목적함수의 해를 계산하는 방법을 말한다. 온라인 학습 알고리즘 중 배치를 이용한 확률적 경사 하강법 (stochastic gradient decent method)은 가장 많이 사용되는 방법 중 하나다. 이 방법은 구현이 쉬울 뿐만 아니라 자료가 동질적인 분포를 따른다는 가정 하에서 그 해의 성질이 잘 연구되어 있다. 하지만 자료에 특이값이 있거나 임의의 배치가 확률적으로 이질적 성질을 가질 때, 확률적 경사 하강법이 주는 해는 큰 편이를 가질 수 있다. 본 연구에서는 이러한 비정상 배치 (abnormal batch) 있는 자료 하에서 효과적으로 온라인 학습을 수행할 수 있는 수정된 경사 하강 알고리즘 (modified gradient decent algorithm)을 제안하고, 그 알고리즘을 통해 계산된 해의 수렴성을 밝혔다. 뿐만 아니라 간단한 모의실험을 통해 제안한 방법의 이론적 성질을 실증하였다.

• Journal of applied mathematics & informatics
• /
• 제34권1_2호
• /
• pp.157-165
• /
• 2016

In this paper, we develop a new hybridization conjugate gradient method for solving the unconstrained optimization problem. Under mild assumptions, we get the sufficient descent property of the given method. The global convergence of the given method is also presented under the Wolfe-type line search and the general Wolfe line search. The numerical results show that the method is also efficient.

• Journal of Industrial and Engineering Chemistry
• /
• 제68권
• /
• pp.355-363
• /
• 2018

There are serious issues with the application of surfactant flooding as a third recovery method, such as surfactant slug losses. In this study,the impact of the salinity gradient on the remobilization of oiltrapped in Berea sandstone was investigated by emphasizing the surfactant adsorption gradient and phase behavior to determine the optimal salinity of the chosen surfactant concentration for investigating the salinity gradient. Three salinity-gradient schemes were applied to six cores saturated with light and heavy oils. The positive salinity gradient provided the best recovery results with an in situ microemulsion formation that could be observed in the fluid collector.

• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.367-376
• /
• 2007

In this paper we consider the global convergence of a new super memory gradient method for unconstrained optimization problems. New trust region radius is proposed to make the new method converge stably and averagely, and it will be suitable to solve large scale minimization problems. Some global convergence results are obtained under some mild conditions. Numerical results show that this new method is effective and stable in practical computation.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제12권4호
• /
• pp.1760-1778
• /
• 2018

For image segmentation with intensity inhomogeneity, many region-based level set methods have been proposed. Some of them however can't get the relatively ideal segmentation results under the severe intensity inhomogeneity and weak edges, and without use of the image gradient information. To improve that, we propose a new level set method combined with local direction gradient in this paper. Firstly, based on two assumptions on intensity inhomogeneity to images, the relationships between segmentation objects and image gradients to local minimum and maximum around a pixel are presented, from which a new pixel classification method based on weight of Euclidian distance is introduced. Secondly, to implement the model, variational level set method combined with image spatial neighborhood information is used, which enhances the anti-noise capacity of the proposed gradient information based model. Thirdly, a new diffusion process with an edge indicator function is incorporated into the level set function to classify the pixels in homogeneous regions of the same segmentation object, and also to make the proposed method more insensitive to initial contours and stable numerical implementation. To verify our proposed method, different testing images including synthetic images, magnetic resonance imaging (MRI) and real-world images are introduced. The image segmentation results demonstrate that our method can deal with the relatively severe intensity inhomogeneity and obtain the comparatively ideal segmentation results efficiently.

• Journal of applied mathematics & informatics
• /
• 제31권3_4호
• /
• pp.353-363
• /
• 2013

A variant of the global conjugate gradient method for solving general linear systems with multiple right-hand sides is proposed. This method is called as the global conjugate gradient linear least squares (Gl-CGLS) method since it is based on the conjugate gradient least squares method(CGLS). We present how this method can be implemented for the image deblurring problems with Neumann boundary conditions. Numerical experiments are tested on some blurred images for the purpose of comparing the computational efficiencies of Gl-CGLS with CGLS and Gl-LSQR. The results show that Gl-CGLS method is numerically more efficient than others for the ill-posed problems.

• 대한전자공학회논문지SP
• /
• 제47권1호
• /
• pp.120-127
• /
• 2010

본 논문은 높은 품질 SR 이미지를 획득하기 위해 국소 그라디언트를 기반으로 적응형 보간법을 이용하는 SR 방법을 제공한다. 이 방법에서, 내삽 화소와 인접하는 유효한 화소 사이에 거리는 국소 그라디언트 특징을 이용하여 고려되며, 보간 계수는 LR 이미지의 국소 그라디언트를 고려한다. 픽셀의 국소 그라디언트는 더 작을수록, 그리고 메디안 필터는 보간된 HR 이미지의 블러링과 노이즈를 감소시키기 위해 적용된다. 실험 결과는 특히 이미지의 에지 부분에서, 다른 방법과 비교하여 제안된 방법의 유효성을 보여준다.

• 대한수학회지
• /
• 제56권4호
• /
• pp.1001-1016
• /
• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• 한국지능시스템학회논문지
• /
• 제11권6호
• /
• pp.454-458
• /
• 2001

이 논문에서는 디지털 영상의 퍼지 시스템 표현으로부터 유도된 Edge 검출 알고리듬에 대하여 기술한다. 이 알고리듬은 Gradient을 기반으로 한 것으로 Convolution Kernel이 기존의 Roberts, Prewitt 또는 Sobel등이 제안한 Gradient Kernel과 다른 새로운 것이다. 사용한 퍼지시스템은 디지털 영상을 근사적으로 표현한 Bicubic Spline 함수를 퍼지시스템 화한것으로서 2차 도함수가 연속이기 때문에 Gradient나 Laplacian 연산이 가능하다. Grid 점들에서 이 함수의 Gradient는 두 개의 축 방향으로 각각 한개의 3$\times$3행렬과 영상과의 Covolution에 의하여 산출됨을 보였으며 이를 이용하여 검출된 Edge들은 기존의 다른 방법을 사용하여 검출된 Edge 영상보다 훨씬 선명함을 확인하였다. 이 알고리듬 적용사례 2개에 대한 기술에 포함되어 있다.