• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.127-132
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• 2004

$H_v$-rings first were introduced by Vougiouklis in 1990. The largest class of algebraic systems satisfying ring-like axioms is the $H_v$-ring. Let R be an $H_v$-ring and ${\gamma}_R$ the smallest equivalence relation on R such that the quotient $R/{\gamma}_R$, the set of all equivalence classes, is a ring. In this case $R/{\gamma}_R$ is called the fundamental ring. In this short communication, we study the fundamental rings with respect to the product of two fuzzy subsets.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.247-256
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• 2004

Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.689-699
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• 2001

We discuss the class of projective systems whose supports are the complement of the union of three linear subspaces in general position. We proves these codes are uniquely dtermined up to equivalence by their weight enumerators. Our result is a generalization of the result given in [1].

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.493-505
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• 2000

We discuss the class of projective systems whose supports are the complement of the union of two linear subspaces in general position. We express the weight enumerators of the codes generated by these projective systems using two simplex codes corresponding to given linear subspaces. We also prove these codes are uniquely determined upto equivalence by their weight enumerators.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.95-104
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• 2000

This paper is a sequel to [24]. It is well known that the order structure plays the important role in the study of various mathematical structures. In 1972, Scott has introduced a concept of continuous lattices and has shown the equivalence between continuous lattices and injective $T_0-spaces$. There have been many efforts made to generalize continuous lattices and extend corresponding properties to them. We introduce another class of frames, namely countably approximating frames, generalizing continuous frames and study its basic properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.479-484
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• 1998

입력된 영상으로부터 추론된 정보 표를 지식베이스에 저장하여 결정해를 구하는데는 많은 탐색시간이 소비된다. 본 논문에서는 탐색 시간을 감소시키기 위해서 러프집합의 식별(classification)과 근사(approximation) 개념을 이용하여 추론된 정보를 동치 클래스(equivalence class)로 분류하여 간략화한다. 감소된 규칙, 즉 Core와 Reduct 리스트를 구하여 결정해를 검색하는데 탐색 시간을 감소시키는데 있다.

• Fire Science and Engineering
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• v.27 no.5
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• pp.44-56
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• 2013

This research is to identify how much toxic combustion gases are produced from Korea standardized real fire test (Class A&B) by using Room Corner Tester (RCT) and how much those gases are possibly dangerous to testing personnel by estimating the level of carboxyhemoglobin (% COHb). It is confirmed that testing personnel can be affected as more than 40% COHb from Class A 9th and 10th rating in respiration minute volume (RMV) 2 and from Class A 5th to Class A 10th rating in RMV 3 during the time for initial three minutes. Also, in the case of Class B real fire tests, although it is considered rather safe for the initial 1 minute, testing personnel can be affected as more than 20% COHb from Class B 16th to 20th rating in RMV 3 during total test time. Currently, the Korea standard is only focusing on the protection measures against the heat, but the it is neglecting the protection measures against toxic combustion gases. Therefore, according to this study, it is strongly recommended that testing personnel should wear a self-contained breathing apparatus, or the equivalence depending on the real fire test rating.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.465-472
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• 2010

The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Communications for Statistical Applications and Methods
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• v.16 no.6
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• pp.989-995
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• 2009

Basu et al. (1998) proposed the minimum divergence estimating method which is free from using the painful kernel density estimator. Their proposed class of density power divergences is indexed by a single parameter $\alpha$ which controls the trade-off between robustness and efficiency. In this article, (1) we introduce a new large class the minimum squared distance which includes from the minimum Hellinger distance to the minimum $L_2$ distance. We also show that under certain conditions both the minimum density power divergence estimator(MDPDE) and the minimum squared distance estimator(MSDE) are asymptotically equivalent and (2) in finite samples the MDPDE performs better than the MSDE in general but there are some cases where the MSDE performs better than the MDPDE when estimating a location parameter or a proportion of mixed distributions.