• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.257-266
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• 1999

We used Carleson and Chang's method to give another proof of the Moser-Trudinger inequality which was known as a limiting case of the Sobolev imbedding theorem and at the same time we get sharper information for the bound.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.905-915
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• 2022

This paper studies the boundedness of integral operators on the Cesàro function spaces. As applications of the main result, we obtain the Hilbert inequalities, the boundedness of the Erdélyi-Kober fractional integrals and the Mellin fractional integrals on the Cesàro function spaces.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.4
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• pp.69-78
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• 2008

We propose to analyze a weakness of quantum key distribution and quantum authentication which use entangled state were proposed by Bao-sen Shi(2001) and to improve the security of the protocol. The existing protocol had a weakness against an impersonation attack of an eavesdropper, because of a only process which authenticated a third party(Center) by users. In this paper, we propose improving the security of the protocol that authenticates users by a third party using check mode which applies CHSH inequality.

• Journal of Information Processing Systems
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• v.9 no.2
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• pp.315-332
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• 2013

This paper presents an approach for improving the use of VP-tree in video indexing and searching. A vantage-point tree or VP-tree is one of the metric space-based indexing methods used in multimedia database searches and data retrieval. Instead of relying on the Euclidean distance as a measure of search space, the proposed approach focuses on the trigonometric inequality for compressing the search range, which thus, improves the search performance. A test result of using 10,000 video files shows that this method reduced the search time by 5-12%, as compared to the existing method that uses the AESA algorithm.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.509-519
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• 2018

In this paper, we introduce a new class of reciprocal convex set which is called as relative reciprocal convex set. We establish a necessary and sufficient condition for the minimum of the differentiable relative reciprocal convex function. This condition can be viewed as a new class of variational inequality which is called relative reciprocal variational inequality. Using the auxiliary principle technique we discuss the existence criteria for the solution of relative reciprocal variational inequality. Some special cases which are naturally included in our main results are also discussed.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.191-201
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• 2008

In this paper, we consider an insurance risk model governed by a compound Binomial arrival claim process and by a compound Binomial arrival premium process. Some formulas for the probabilities of ruin and the distribution of ruin time are given, we also prove the integral equation of the ultimate ruin probability and obtain the Lundberg inequality by the discrete martingale approach.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.291-297
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• 2008

In this paper, new inequalities of Ostrowski type involving two functions and their derivatives for mapping whose derivations belong to $L^p$[a, b], p>1 are established.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.4
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• pp.251-263
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• 2003

This paper presents matrix inequality conditions for Η$_2$control and Η$_2$controller design method of linear time-invariant descriptor systems with parameter uncertainties in continuous and discrete time cases, respectively. First, the necessary and sufficient condition for Η$_2$control and Η$_2$ controller design method are expressed in terms of LMI(linear matrix inequality) with no equality constraints in continuous time case. Next, the sufficient condition for Hi control and Η$_2$controller design method are proposed by matrix inequality approach in discrete time case. Based on these conditions, we develop the robust Η$_2$controller design method for parameter uncertain descriptor systems and give a numerical example in each case.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.10
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• pp.949-954
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• 2010

Computing the rotation-invariant distance between image time-series is a time-consuming process that incurs a lot of Euclidean distances for all possible rotations. In this paper we propose an innovative solution that significantly reduces the number of Euclidean distances using the triangular inequality. To this end, we first present the notion of self rotation distance and show that, by using the self rotation distance with the triangular inequality, we can prune many unnecessary distance computations. We next present that only one self-rotation is enough for all self-rotation distances required. Experimental results show that our self rotation distance-based methods outperform the existing methods by up to an order of magnitude.

• Health Policy and Management
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• v.25 no.4
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• pp.277-284
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• 2015

Background: This study investigates the relationship of socioeconomic status with adverse birth outcomes (low birth weight, preterm birth) and the relationship of socioeconomic status with infant mortality, using the birth cohort in Korea, 1995-2010. Methods: 8,648,035 births from National Statistics Offics, 1995-2010 were studied with respect to social variation in adverse birth outcomes and infant mortality in Korea. The effect of social inequality was examined against adverse birth outcomes and infant mortality using multivariate logistic regression after controlling for other covariates. Results: Social inequality were observed in adverse birth outcomes: low birth weight (LBW, 1,500-2,499 g), very LBW (1,000-1,499 g), and extremely LBW (500-999 g) as well as moderately preterm birth (PTB, 33-36 weeks), very PTB (28-32 weeks), extremely PTB (22-27 weeks), and infant mortality. The effect of social inequality was higher among moderately LBW (1,500-2,499 g) and PTB (33-36 weeks) than very or extremely LBW and PTB. Conclusion: The social inequality in adverse birth outcomes (low birth weight and preterm) and infant mortality existed and increased in Korea from 1995 to 2010. The effect of maternal education on adverse birth outcomes as well as infant mortality was apparent in the study results. Especially, social inequailiy in infant mortality was greater among the sub-normal births (low birth weight [1,500-2,499 g] or preterm birth [33-36 weeks]), which suggests, social interventions should aim at more among the subnormal births. This study suggest that tackling inequality in births as well as infant mortality should be focused on the social inequality itself.