• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1069-1083
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• 2016

In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M: (1) M is e-local; (2) $Rad_e(M)$ is a maximal submodule of M and every proper essential submodule of M is contained in a maximal submodule; (3) M has a unique essential maximal submodule and every proper essential submodule of M is contained in a maximal submodule.

• Journal of Information Processing Systems
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• 제18권4호
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• pp.575-586
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• 2022

Uneven light in real-world causes visual degradation for underexposed regions. For these regions, insufficient consideration during enhancement procedure will result in over-/under-exposure, loss of details and color distortion. Confronting such challenges, an unsupervised low-light image enhancement network is proposed in this paper based on the guidance of the unpaired low-/normal-light images. The key components in our network include super-resolution module (SRM), a GAN-based low-light image enhancement network (LLIEN), and denoising-scaling module (DSM). The SRM improves the resolution of the low-light input images before illumination enhancement. Such design philosophy improves the effectiveness of texture details preservation by operating in high-resolution space. Subsequently, local lightness attention module in LLIEN effectively distinguishes unevenly illuminated areas and puts emphasis on low-light areas, ensuring the spatial consistency of illumination for locally underexposed images. Then, multiple discriminators, i.e., global discriminator, local region discriminator, and color discriminator performs assessment from different perspectives to avoid over-/under-exposure and color distortion, which guides the network to generate images that in line with human aesthetic perception. Finally, the DSM performs noise removal and obtains high-quality enhanced images. Both qualitative and quantitative experiments demonstrate that our approach achieves favorable results, which indicates its superior capacity on illumination and texture details restoration.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권3호
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• pp.1464-1480
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• 2019

Robust tracking of infrared (IR) pedestrian targets with various backgrounds, e.g. appearance changes, illumination variations, and background disturbances, is a great challenge in the infrared image processing field. In the paper, we address a new tracking method for IR pedestrian targets via multi-feature local sparse representation (SR), which consists of three important modules. In the first module, a multi-feature local SR model is constructed. Considering the characterization of infrared pedestrian targets, the gray and edge features are first extracted from all target templates, and then fused into the model learning process. In the second module, an effective tracker is proposed via the learned model. To improve the computational efficiency, a sliding window mechanism with multiple scales is first used to scan the current frame to sample the target candidates. Then, the candidates are recognized via sparse reconstruction residual analysis. In the third module, an adaptive dictionary update approach is designed to further improve the tracking performance. The results demonstrate that our method outperforms several classical methods for infrared pedestrian tracking.

• 대한수학회지
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• 제52권6호
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• 대한수학회보
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• 제54권1호
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• pp.319-329
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• 2017

Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module $H^c_I(M)$, c = grade(I, M). In particular there is a natural homomorphism $$Hom_{\hat{R}^I}({\hat{M}}^I,\;{\hat{M}}^I){\rightarrow}Hom_R(H^c_I(M),\;H^c_I(M))$$, $where{\hat{\cdot}}^I$ denotes the I-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J{\subset}I$ with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).

• 대한수학회보
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• 제53권5호
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• pp.1341-1352
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• 2016

Let R be a commutative Noetherian ring, ${\Phi}$ a system of ideals of R and $I{\in}{\Phi}$. In this paper among other things we prove that if M is finitely generated and $t{\in}\mathbb{N}$ such that the R-module $H^i_{\Phi}(M)$ is $FD_{{\leq}1}$ (or weakly Laskerian) for all i < t, then $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all i < t and for any $FD_{{\leq}0}$ (or minimax) submodule N of $H^t_{\Phi}(M)$, the R-modules $Hom_R(R/I,H^t_{\Phi}(M)/N)$ and $Ext^1_R(R/I,H^t_{\Phi}(M)/N)$ are finitely generated. Also it is shown that if cd I = 1 or $dimM/IM{\leq}1$ (e.g., $dim\;R/I{\leq}1$) for all $I{\in}{\Phi}$, then the local cohomology module $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all $i{\geq}0$. These generalize the main results of Aghapournahr and Bahmanpour [2], Bahmanpour and Naghipour [6, 7]. Also we study cominimaxness and weakly cofiniteness of local cohomology modules with respect to a system of ideals.

• 대한수학회보
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• 제32권2호
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• pp.349-357
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• 1995

In the theory of elliptic curves over a complete field with bad reduction (i.e. with nonintegral j-invariant) Tate elliptic curves play an important role. Likewise, in the theory of Drinfeld modules, Tate-Drinfeld modules replace Tate elliptic curves.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2019년도 학술발표회
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• pp.163-163
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• 2019

The rapidly growing global population increases the awareness of water, energy, and food security worldwide. The concept of Water, Energy, and Food nexus (hereafter, WEF nexus) has been widely introduced as a new resources management concept that integrate the water, energy, and food in a single management framework. Recently, WEF nexus analyzes not only the interconnections among the resources, but also considers the external factors (such as environment, climate change, policy, finance, etc) to enhance the resources sustainability by proper understanding of their relations. A nation-level resources management is quite complex task since multiple regions (e.g., watersheds, cities, and counties) with different characteristics are spatially interconnected and transfer the resources each other. This study proposes a multiple region WEF nexus simulation and transfer model. The model is equipped with three simulation modules, such as local nexus simulation module, regional resources transfer module, and optimal investment planning module. The model intends to determine an optimal capital investment plan (CIP), such as build-up of power plants, water/waste water treatment plants, farmland development and to determine W-E-F import/export decisions among areas. The objective is to maximize overall resources sustainability while minimize financial cost. For demonstration, the proposed model is applied to a semi-hypothetical study area with three different characterized cities. It is expected the model can be used as a decision support tool for a long-term resources management planning process.

• 대한수학회보
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• 제51권2호
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• pp.519-530
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• 2014

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. For an integer s > -1, we say that M is Cohen-Macaulay in dimension > s if every system of parameters of M is an M-sequence in dimension > s introduced by Brodmann-Nhan [1]. In this paper, we give some characterizations for Cohen-Macaulay modules in dimension > s in terms of the Noetherian dimension of the local cohomology modules $H^i_m(M)$, the polynomial type of M introduced by Cuong [5] and the multiplicity e($\underline{x}$;M) of M with respect to a system of parameters $\underline{x}$.

• 전산구조공학
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• 제9권4호
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• pp.141-154
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• 1996

드로네이 요소생성기법은 모델링 영역의 모양에 구애받지 않으면서 요소의 크기제어, 재편성, 국지요소생성 등에 있어서 탁월한 기능을 보여주고 있다. 그러나 생성되는 요소가 선형삼각형요소임으로해서 비압축성 또는 대변위거동의 근사나 복잡한 형상의 영역의 기하학적 근사에 한계를 갖고 있다. 이를 보완하기 위해 기제시된 드로네이 요소생성 알고리즘을 바탕으로한 6절점 삼각요소 생성알고리즘을 제시하여 본 기법의 완성도를 높이고 이를 성형문제에 적용해 보였다.