• 충청수학회지
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• 제31권3호
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• pp.321-324
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• 2018

We present a new and simple proof of improved Carleson's inequality.

• 충청수학회지
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• 제24권3호
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• pp.583-586
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• 2011

A fractional Gagliardo-Nirenberg inequality is established. A sharp fractional Sobolev inequality is discussed as a direct consequence.

• 한국문헌정보학회지
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• 제55권2호
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• pp.263-287
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• 2021

한국사회의 불평등과 관련된 연구는 다양한 영역에서 산발적으로 진행되어 왔다. 이 연구에서는 불평등 관련 연구 동향을 한국학술지인용색인을 통해 수집한 논문 데이터를 활용하여 기초 통계 분석, 단어 동시 출현 분석, 주 경로 분석을 통해 통합적으로 분석하였다. 기초 통계 분석을 통해 핵심저자, 저널, 논문을 파악할 수 있었다. 동시출현 분석을 통해 소득불평등, 교육불평등, 복지불평등, 불평등 정책이 핵심 주제로 확인되었다. 주 경로 분석을 통해 2004년 이후의 불평등 연구 흐름은 두 가지로 나타났다. 하나는 경제적 불평등에 관한 연구이고, 다른 하나는 건강 불평등 및 사회 구조적 불평등과 관련된 연구로 나타났다.

• East Asian mathematical journal
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• 제34권4호
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• pp.359-369
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• 2018

This note, we first show that the famous Carleman's inequality can be improved if we find a positive sequence $\{c_n\}$ such that $c_n{\sum\limits_{j=n}^{\infty}}{\frac{1}{j\(\prod_{k=1}^{j}ck\)^{\frac{1}{j}}}}$ < e. Then we list a lot of known results in the literature improving Carleman's inequality by this method. These results can be a good source to a further research for interested students. We next consider about similar improvement of Polya-Knopp's inequality, which is a continuous version of Carleman's inequality. We show by a manner parallel to the case of Carleman's inequality that Polya-Knopp's inequality can be improved if we find a positive function c(x) such that $c(x){\int}_{x}^{\infty}\frac{1}{t\;{\exp}\(\frac{1}{t}{\int}_{0}^{t}{\ln}\;c(s)\;ds\)}dt$ < e. But there are no known results improving Polya-Knopp's inequality by this method. Suggesting to find a new method, we lastly show that there is no nice continuous function c(x) that satisfies the inequality.

• Asian Journal for Public Opinion Research
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• 제6권1호
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• pp.1-17
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• 2018

As societal interest in inequality increases in Korea, both public and academic discussion on inequality is also on the rise. In order to more effectively discuss the problems of rising inequality, however, it is essential to study the consequences and implications of inequality. This study examines one of the consequences of inequality, particularly on individuals - the relationship between an individual's perception of inequality and his/her evaluation of societal health, such as social trust and social mobility. According to a statistical analysis of the Korean Academic Multimode Open Survey for Social Sciences (KAMOS), those who perceive the level of income and wealth inequality in Korea as more unequal tend to have a lower level of trust toward Korean society and Korean people, as well as a lower expectation for both intra- and intergenerational social mobility. This study, which shows that rising inequality could have a negative impact at the individual level, not only extends the scope of the consequence-of-inequality studies from the society-oriented toward the individual-oriented, but it also has significant implications for the field, suggesting a new direction for future studies.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권1호
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• pp.93-101
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• 2008

In this article we shall characterize the Heinz-Kato-Furuta inequality in several ways, and the best bound for sharpening of the inequality is obtained by the method in [7].

• 대한수학회지
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• 제47권2호
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• pp.277-288
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• 2010

The mixed chord-integrals are defined. The Fenchel-Aleksandrov inequality and a general isoperimetric inequality for the mixed chordintegrals are established. Furthermore, the dual general Bieberbach inequality is presented. As an application of the dual form, a Brunn-Minkowski type inequality for mixed intersection bodies is given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권3호
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• pp.305-313
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• 2012

In this note we study Nesbitt's Inequality and modify it to make several inequalities. We prove some inequalities by using power series and Cauchy-Schwarz Inequality.

• 전기학회논문지
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• 제65권3호
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• pp.457-462
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• 2016

In this paper, we consider the stability of time-delayed linear systems. To derive an LMI form of result, the integral inequality is essential, and Jensen's integral inequality was the best in the last two decades until Seuret's integral inequality is appeared recently. However, these two are proportional to the inverse of integration interval, so another integral inequality is needed to make it in the form of LMI. In this paper, we derive an integral inequality which is proportional to the integration interval which can be easily converted into LMI form without any other inequality. Also, it is shown that Seuret's integral inequality is a special case of our result. Next, based on this new integral inequality, we derive a stability condition in the form of LMI. Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• 충청수학회지
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• 제23권1호
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• pp.137-147
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• 2010

In this paper we extend a differential inequality presented in Theorem 2.2 [6] to a dynamic inequality on time scales.