• 충청수학회지
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• 제20권4호
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• pp.457-463
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• 2007

We show that any filter of Tarski algebra can be de-composed into the union of some sets. Moreover, we introduce the notion of expansions of filters in Tarski algebras, and discuss the notion of ${\sigma}$-primary filters in Tarski algebras. Finally, we show that there is no non-trivial quadratic Tarski algebras on a field X with $|X|{\geq}3$.

• 대한수학회보
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• 제40권3호
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• pp.425-435
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• 2003

In this paper, a new kind of matrices, i.e., $level-{\kappa}$ II-circulant matrices is considered. Algorithms for computing minimal polynomial of this kind of matrices are presented by means of the algorithm for the Grobner basis of the ideal in the polynomial ring. Two algorithms for finding the inverses of such matrices are also presented based on the Buchberger's algorithm.

• 대한수학회지
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• 제44권6호
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• pp.1291-1312
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• 2007

We study some extremal problems on the Cartan-Hartogs domains. Through computing the minimal circumscribed Hermitian ellipsoid of the Cartan-Hartogs domains, we get the $Carath\acute{e}odory$ extremal mappings between the Cartan-Hartogs domains and the unit hyperball, and the explicit formulas for computing the $Carath\acute{e}odory$ extremal value.

• 대한수학회보
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• 제46권4호
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• pp.789-802
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• 2009

We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over $\mathbb{F}_p$ can be executed in $\mathbb{F}_{p2}$ or $\mathbb{F}_{p4}$ . Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.

• 충청수학회지
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• 제22권2호
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• pp.123-129
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• 2009

We introduce the notion of Smarandache GT-algebras, and the notion of Smarandache GT-filters of the Smarandache GT- algebra related to the Tarski algebra, and related some properties are investigated.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.127-139
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• 2007

In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.

• 대한수학회논문집
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• 제28권4호
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• pp.833-850
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• 2013

We present an algorithm for computing the Hausdorff distance between two parametric curves in $\mathbb{R}^n$, or more generally between two sets of parametric curves in $\mathbb{R}^n$. During repeated subdivision of the parameter space, we prune subintervals that cannot contain an optimal point. Typically, our algorithm costs O(logM) operations, compared with O(M) operations for a direct, brute-force method, to achieve an accuracy of $O(M^{-1})$.

• 대한수학회논문집
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• 제34권4호
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• pp.1353-1364
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• 2019

Modified Lagrange functional for solving an elastic problem with a crack is considered. Two formulations of a crack problem are investigated. The first formulation concerns a problem where a crack extending to the outer boundary of the domain. In the second formulation, we consider a problem with an internal crack. Duality ratio is established for initial and dual problem in both cases.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권7호
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• pp.2512-2529
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• 2015

Wireless mesh networks (WMNs) provide an efficient and flexible method to the field of wireless networking, but also bring many security issues. A mesh point may lose all of its available links during its movement. Thus, the mesh point needs to handover to a new mesh point in order to obtain access to the network again. For multi-domain WMNs, we proposed a new ID-based signcryption scheme and accordingly present a novel ID-based handover protocol for mesh points. The mutual authentication and key establishment of two mesh points which belong to different trust domains can be achieved by using a single one-round message exchange during the authentication phase. The authentication server is not involved in our handover authentication protocol so that mutual authentication can be completed directly by the mesh points. Meanwhile, the data transmitted between the two mesh points can be carried by the authentication messages. Moreover, there are no restrictions on the PKG system parameters in our proposed multi-domain ID-based signcryption scheme so our handover scheme can be easily applied to real WMNs circumstances. Security of the signcryption scheme is proved in the random oracle model. It shows that our protocol satisfies the basic security requirements and is resistant to existing attacks based on the security of the signcryption. The analysis of the performance demonstrates that the protocol is efficient and suitable for the multi-domain WMNs environment.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제7권1호
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• pp.15-29
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• 2003

The present study examined the 7th national elementary school mathematics curriculum from a perspective of mathematical creativity. The study investigated to what extent the activities in the Pattern and Function lessons in the national elementary school mathematics textbooks promoted the development of mathematical creativity. The results indicated that the current elementary school mathematics curriculum was limited in many ways to promote the development of mathematical creativity. Regarding the activities in Pattern lessons, for example, most activities presented closed tasks involving finding and extending patterns. The lesson provided little opportunities to explore the relationships among various patterns, apply patterns to different situations, or create ones own patterns. In regard to the Function lessons, the majority of activities were about computing the rate. This showed that the function was taught from an operational perspective, not a relational perspective. It was unlikely that students would develop the basic understanding of function through the activities involving the computing the rate. Further, the lessons had students use exclusively the numbers in representing the function. Students were provided little opportunities to use various representation methods involving pictures or graphs, explore the strengths and limitations of various representation methods, or to choose more effective representation methods in particular contexts. In conclusion, the lesson activities in the current elementary school mathematics textbooks were unlikely to promote the development of mathematical creativity.