• 호남수학학술지
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• 제45권2호
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• pp.269-284
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• 2023

In this paper we study generalizations of the concept of pure-direct-projectivity from module categories to Grothendieck categories. We examine for which categories or under what conditions pure-direct-projective objects are direct-projective, quasi-projective, pure-projective, projective and flat. We investigate classes all of whose objects are pure-direct-projective. We give applications of some of the results to comodule categories.

• 대한수학회논문집
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• 제9권2호
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• pp.361-367
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• 1994

An elliptic module is an analogue of an elliptic curve over a function field [D]. The dual of an elliptic curve E is represented by Ext(E, $G_{m}$) and the Cartier dual of an affine group scheme G is represented by Hom(G, G$G_{m}$). In the category of elliptic modules the Carlitz module C plays the role of $G_{m}$. Taguchi [T] showed that a notion of duality of a finite t-module can be represented by Hom(G, C) in a suitable category. Our computation shows that the Ext-group as it stands is rather too "big" to represent a dual of an elliptic module.(omitted)

• 대한수학회보
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• 제32권2호
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• pp.251-257
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• 1995

In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.

• 대한수학회보
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• 제61권1호
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• pp.273-280
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• 2024

Let I be an ideal of a commutative Noetherian semi-local ring R and M be an R-module. It is shown that if dim M ≤ 2 and Supp_R M ⊆ V (I), then M is I-weakly cofinite if (and only if) the R-modules Hom_R(R/I, M) and Ext¹_R(R/I, M) are weakly Laskerian. As a consequence of this result, it is shown that the category of all I-weakly cofinite modules X with dim X ≤ 2, forms an Abelian subcategory of the category of all R-modules. Finally, it is shown that if dim R/I ≤ 2, then for each pair of finitely generated R-modules M and N and each pair of the integers i, j ≥ 0, the R-modules Tor^R_i(N, H^j_I(M)) and Extⁱ_R(N, H^j_I(M)) are I-weakly cofinite.

• 대한수학회논문집
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• 제29권1호
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• pp.9-22
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• 2014

In this paper we state some applications of Gr-category theory to the classification problem of crossed modules and to that of group extensions of the type of a crossed module.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.439-458
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• 2018

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category C of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in C. Further, we characterize the derivations of crossed modules in a category C and obtain new crossed modules using regular derivations of old one.

• 디자인학연구
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• 제15권3호
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• pp.115-126
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• 2002

현대의 복잡한 사회구조와 사회 구성원의 의식변화에 따라 사회 구성원의 직업수행방식과 능력도 바뀌어 가고 있다. 이러한 사회환경변화에 따른 사회구성원의 직업 수행능력과 적응력 제고를 위해 학습자의 자율적 학습체제의 필요성이 대두되었다. 이러한 해결점으로 모듈식 교재 개발의 체제적인 접근방법이 요구되었고, 특히 직업을 수행할 수 있는 능력을 중심으로 한 모듈식 교재체제를 개발하고 적용하는데 본 연구의 목적을 두고 있다. 본 연구는 광고디자인 직무분석을 토대로, 각 직무를 수행할 수 있는 학습 능력을 추출하고 각 능력별로 학습영역을 설정하여 각 영역별 지식, 기능, 태도를 추출하였다. 이러한 과정을 집대성한 것이 모듈식 교재체제 개발의 기초가 되는 것이다. 본 연구를 시작으로 광고디자인 분야뿐만 아닌 다른 분야에서도 적극적으로 모듈식 교육체제를 개발${\cdot}$적용하길 바란다.

• International Journal of Advanced Culture Technology
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• 제7권4호
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• pp.321-326
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• 2019

As AI technology is recently introduced into various fields, it is being applied to the fashion field. This paper proposes a system for recommending cody clothes suitable for a user's selected clothes. The proposed system consists of user app, cody recommendation module, and server interworking of each module and managing database data. Cody recommendation system classifies clothing images into 80 categories composed of feature combinations, selects multiple representative reference images for each category, and selects 3 full body cordy images for each representative reference image. Cody images of the representative reference image were determined by analyzing the user's preference using Google survey app. The proposed algorithm classifies categories the clothing image selected by the user into a category, recognizes the most similar image among the classification category reference images, and transmits the linked cody images to the user's app. The proposed system uses the ResNet-50 model to categorize the input image and measures similarity using ORB and HOG features to select a reference image in the category. We test the proposed algorithm in the Android app, and the result shows that the recommended system runs well.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.535-545
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• 2019

The main idea of this paper is to introduce the notion of $cat^1$-monoids and to prove that the category of crossed semimodules ${\mathcal{C}}=(A,B,{\partial})$ where A is a group is equivalent to the category of $cat^1$-monoids. This is a generalization of the well known equivalence between category of $cat^1$-groups and that of crossed modules over groups.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.803-808
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• 2007

LCCA module enabling to estimate LCC and analyze time-variant reliability index of a plate girder bridge was developed. The developed module was based on the designed data structure following the standardized methodology of ISO/STEP, LCCA module consisted of LCC estimation module, which is composed of six sub modules according to the cost category, and reliability index analysis module, which is composed of time-variant corrosion sub module, time-variant live load sub module, and element reliability analysis sub module, The effectiveness of the developed LCCA module was verified by estimating LCC and analyzing time-variant reliability index of a plate girder bridge on the basis of the constructed test database.