• 대한수학회보
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• 제29권1호
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• pp.125-135
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• 1992

In various viscus flow problems it has been the custom to replace the convective derivative by the ordinary partial derivative in problems for which the data are small. In this paper we consider the Benard Convection problem with small data and compare the solution of this problem (assumed to exist) with that of the linearized system resulting from dropping the nonlinear terms in the expression for the convective derivative. The objective of the present work is to derive an estimate for the error introduced in neglecting the convective inertia terms. In fact, we derive an explicit bound for the L$_{2}$ error. Indeed, if the initial data are O(.epsilon.) where .epsilon. << 1, and the Rayleigh number is sufficiently small, we show that this error is bounded by the product of a term of O(.epsilon.$^{2}$) times a decaying exponential in time. The results of the present paper then give a justification for linearizing the Benard Convection problem. We remark that although our results are derived for classical solutions, extensions to appropriately defined weak solutions are obvious. Throughout this paper we will make use of a comma to denote partial differentiation and adopt the summation convention of summing over repeated indices (in a term of an expression) from one to three. As reference to work of continuous dependence on modelling and initial data, we mention the papers of Payne and Sather [8], Ames [2] Adelson [1], Bennett [3], Payne et al. [9], and Song [11,12,13,14]. Also, a similar analysis of a micropolar fluid problem backward in time (an ill-posed problem) was given by Payne and Straughan [10] and Payne [7].

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권10호
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• pp.5129-5152
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• 2016

Multi-view super-resolution (MVSR) aims to estimate a high-resolution (HR) image from a set of low-resolution (LR) images that are captured from different viewpoints (typically by different cameras). MVSR is usually applied in camera array imaging. Given that MVSR is an ill-posed problem and is typically computationally costly, we super-resolve multi-view LR images of the original scene via image fusion (IF) and blind deblurring (BD). First, we reformulate the MVSR problem into two easier problems: an IF problem and a BD problem. We further solve the IF problem on the premise of calculating the depth map of the desired image ahead, and then solve the BD problem, in which the optimization problems with respect to the desired image and with respect to the unknown blur are efficiently addressed by the alternating direction method of multipliers (ADMM). Our approach bridges the gap between MVSR and BD, taking advantages of existing BD methods to address MVSR. Thus, this approach is appropriate for camera array imaging because the blur kernel is typically unknown in practice. Corresponding experimental results using real and synthetic images demonstrate the effectiveness of the proposed method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권12호
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• pp.4420-4438
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• 2021

Image dehazing is an ill-posed problem which is far from being solved. Traditional image dehazing methods often yield mediocre effects and possess substandard processing speed, while modern deep learning methods perform best only in certain datasets. The haze removal effect when processed by said methods is unsatisfactory, meaning the generalization performance fails to meet the requirements. Concurrently, due to the limited processing speed, most dehazing algorithms cannot be employed in the industry. To alleviate said problems, a lightweight fast dehazing network based on a multiple scale-patch framework (MSP) is proposed in the present paper. Firstly, the multi-scale structure is employed as the backbone network and the multi-patch structure as the supplementary network. Dehazing through a single network causes problems, such as loss of object details and color in some image areas, the multi-patch structure was employed for MSP as an information supplement. In the algorithm image processing module, the image is segmented up and down for processed separately. Secondly, MSP generates a clear dehazing effect and significant robustness when targeting real-world homogeneous and nonhomogeneous hazy maps and different datasets. Compared with existing dehazing methods, MSP demonstrated a fast inference speed and the feasibility of real-time processing. The overall size and model parameters of the entire dehazing model are 20.75M and 6.8M, and the processing time for the single image is 0.026s. Experiments on NTIRE 2018 and NTIRE 2020 demonstrate that MSP can achieve superior performance among the state-of-the-art methods, such as PSNR, SSIM, LPIPS, and individual subjective evaluation.

• 지구물리와물리탐사
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• 제7권3호
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• pp.207-212
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• 2004

자기지전류(MT) 자료의 3차원 역산에 대해 소개한다. MT 자료의 역산 문제는 기본적으로 악조건이므로 유일한 해가 존재하지 않는다. 이러한 비유일성을 줄이고 정확한 역산해를 구하기 위해서는 역산 시 사전정보를 추가하는 제약조건을 가해야 한다. 물리탐사 분야에서 비선형 역산에 사용되는 가장 일반적인 방법은 일련의 선형화된 역산문제를 푸는 Gauss-Newton법이다. 이 알고리듬은 수렴 시, 모델 공간에서 역산문제에 대한 목적함수를 최소화하는 최적해를 준다. 그러나 이러한 반복적 선형화기법은 3차원 MT 역산의 경우 Jacobian 행렬을 구하기 힘들기 때문에 그 유용성에 한계가 있다. 이러한 어려움은 CG법에 의해 완화할 수 있다. 선형 CG법은 Gauss-Newton 반복의 각 단계를 근사적으로 풀기 위해서 사용된다. 한편 비선형 CG법은 목적함수의 최소화에 직접적으로 적용된다. 이들 CG법은 Jacobian 행렬의 계산 및 대형 선형방정식의 해를 반복 당 세 번의 모델링으로 대치할 수 있어서 3차원 역산에 적합하다.

• 국제지역연구
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• 제14권4호
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• pp.27-52
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• 2011

키르기스스탄은 다자간 안보시스템에 의존한 군사안보 확보와 등거리 외교를 통한 국가안보를 국가정책의 주요 목표로 두고 추진하고 있다. 부연하자면, 중앙아시아의 소국으로서 자주권의 확립과 국가발전이라는 과제를 추진하기 위하여 나름의 군사안보정책을 통하여 해결점을 찾으려 한다는 것이다. 그러나 한 국가가 단순히 외교와 외부의 안보시스템에 의존하여 국가의 자주성과 발전을 담보할 수는 없을 것이다. 이 논문에서는 키르기스스탄의 국방력과 군사력을 해부해 봄으로써 키르기스스탄이 최소한의 자위적 차원의 국방력을 가지고 있는가를 살펴보는 것과 국방력 증강에 대한 가능성을 살펴보는 것이 중요하다고 본다. 해양세력과 대륙세력, 그 양대 세력의 신-그레이트 게임속에서 등거리외교와 다자간 안보협력기구를 통하여 국가자주성을 확보해 나가는 균형 외교전략의 한계와 미래를 살펴봄으로서 앞으로의 키르기스스탄 독립과 자주 문제를 파악, 예측 해 보는 것이 본 논문의 목적이다.