• 대한수학회보
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• 제46권2호
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• pp.245-253
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• 2009

A new hard problem called the vector decomposition problem (VDP) was recently proposed by Yoshida et al., and it was asserted that the VDP is at least as hard as the computational Diffie-Hellman problem (CDHP) under certain conditions. Kwon and Lee showed that the VDP can be solved in polynomial time in the length of the input for a certain basis even if it satisfies Yoshida's conditions. Extending our previous result, we provide the general condition of the weak instance for the VDP in this paper. However, when the VDP is practically used in cryptographic protocols, a basis of the vector space ${\nu}$ is randomly chosen and publicly known assuming that the VDP with respect to the given basis is hard for a random vector. Thus we suggest the type of strong bases on which the VDP can serve as an intractable problem in cryptographic protocols, and prove that the VDP with respect to such bases is difficult for any random vector in ${\nu}$.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권1호
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• pp.25-45
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• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.

• East Asian mathematical journal
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• 제4권
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• pp.157-173
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• 1988

• 대한수학회논문집
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• 제4권2호
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• pp.321-329
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• 1989

• Kyungpook Mathematical Journal
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• 제8권1호
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• pp.1-4
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• 1968

• East Asian mathematical journal
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• 제7권2호
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• pp.171-178
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• 1992

• 터널과지하공간
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• 제4권2호
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• pp.156-169
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• 1994

• 한국측량학회:학술대회논문집
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• 한국측량학회 2004년도 춘계학술발표회논문집
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• pp.477-482
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• 2004

Due to the traffic congestion of the city and public transportation-oriented policies, public transportation is receiving more attention and being used increasingly However, relatively less research on the design and distribution of public transportation network and limitations in quantitative approaches have made implementation and operation practically difficult. Over- or under-supply of transportation routes caused unbalanced connectivity among areas and differences in time, expenses and metal burden of users. On the other hand, the Space Syntax theory, designed to calculate the connectivity of urban or architectural space, helps generate quantitative connectivity of whole space simply based on the spacial structure. This study modified the original Space Syntax algorithm to fit the public transportation problem and showed how it is appied to a network by creating an artificial network using the GIS.

• 호남수학학술지
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• 제31권3호
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• pp.279-292
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• 2009

As a survey-type article, the paper reviews some results on a regular covering space in digital covering theory. The recent paper [10](see also [12]) established the notion of regular covering space in digital covering theory and studied its various properties. Besides, the papers [14, 16] developed a discrete Deck's transformation group of a digital covering. In this paper we study further their properties. By using these properties, we can classify digital covering spaces. Finally, the paper proposes an open problem.

• 호남수학학술지
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• 제31권3호
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• pp.267-278
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• 2009

As a survey-type article, the paper reviews the recent results on a (generalized) universal covering space in digital covering theory. The recent paper [19] established the generalized universal (2, k)-covering property which improves the universal (2, k)-covering property of [3]. In algebraic topology it is well-known that a simply connected and locally path connected covering space is a universal covering space. Unlike this property, in digital covering theory we can propose that a generalized universal covering space has its intrinsic feature. This property can be useful in classifying digital covering spaces and in studying a shortest k-path problem in data structure.