• 대한수학회보
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• 제36권4호
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• pp.771-778
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• 1999

In this paper, we obtain some geometric inequalities for mixed volumes of a convex body and its polar dual. We also develop a lower bound of the product of quermassintegral of a convex body and its polar dual and give a lower bound for the product of the dual quermassintegral of any index of centrally symmetric convex body and that of its polar dual.

• 대한수학회논문집
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• 제23권2호
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• pp.241-250
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• 2008

In this article, we find a counter example which shows that the well-known necessary condition about the boundary regularity of a stable strictly convex body is not a sufficient condition.

• 호남수학학술지
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• 제34권3호
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• pp.403-408
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• 2012

In this paper, we prove that if K is a convex body in $E^n$ and $E_i$ and $E_o$ are inscribed ellipsoid and circumscribed ellipsoid of K respectively with ${\alpha}E_i=E_o$, then $\[({\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n{\geq}V(K)V({\Gamma}^{\ast}_pK){\geq}\[(\frac{1}{\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n$. Lutwak and Zhang[6] proved that if K is a convex body, ${\omega}^2_n=V(K)V({\Gamma}_pK)$ if and only if K is an ellipsoid. Our inequality provides very elementary proof for their result and this in turn gives a lower bound of the volume product for the sets of constant width.

• 대한수학회보
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• 제51권1호
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• pp.129-137
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• 2014

In this paper, a new proof of the following result is given: The product of the volumes of an origin-symmetric convex bodies K in $\mathbb{R}^2$ and of its polar body is minimal if and only if K is a parallelogram.

• 대한수학회보
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• 제55권1호
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• pp.139-148
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• 2018

In this paper, we prove a stability result for p-centroid bodies with respect to the Hausdorff distance. As its application, we show that the symmetric convex body is determined by its p-centroid body.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회B
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• pp.2757-2762
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• 2007

A cyclone design concept named Convex cyclone was developed to reduce pressure losses. Contrary to conventional cylinder-on-con type cyclone, inner wall of Convex cyclone are defined with a continuous curve and it has convex shape body. The discontinuity of inner diameter variation rate of cylinder-on-con type cyclone cause additional pressure loss. Continuous wall of Convex cyclone prevent additional pressure loss. In order to verify Convex cyclone design concept, we make a comparative experiments between Stairmand HE and Convex cyclone. Experimental Convex cyclone designed based on Stairmand HE model, and inner wall are defined with circular arch. The experimental result clearly shows that Convex cyclone can achieve maximum 50% pressure loss reduction with a few percent of collection efficiency drop. In addition, the experimental results indicated the existence of optimum convexity, minimum pressure loss, of cyclone wall.

• 대한수학회보
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• 제40권3호
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• pp.521-529
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• 2003

In this paper, we get the measure of strips and lines in the Minkowski plane $M^2$ that meet a fixed compact convex body in $M^2$. From this we also investigate the probability that strips and lines meet a fixed compact convex body in $M^2$.

• 대한수학회보
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• 제51권4호
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• pp.1023-1029
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• 2014

In the paper, we define a class of convex bodies in $\mathbb{R}^n$-parallel sections homothety bodies, and for some special parallel sections homothety bodies, we prove that n-cubes have the minimal Mahler volume.

• 한국방사선학회논문지
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• 제13권6호
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• pp.895-900
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• 2019

초음파는 인체에 무해하다고 알려져 산부인과에서 태아의 진단 및 발육상태 확인을 위해 널리 이용되고 있다. 진단 초음파의 장시간 사용은 체온 변화를 야기할 수 있지만 초음파로 인한 임신부의 자궁온도 변화에 대한 연구가 부족한 실정이다. 이에 본 연구에서는 자체 제작한 자궁모형팬텀을 이용하여 초음파 주사시간에 따른 온도 변화를 알아보고자 하였다. 조직등가 물질인 아크릴과 돼지 자궁을 이용하여 인체 자궁과 유사한 자궁모형팬텀을 자체 제작하였으며 초음파 장비와 4MHz convex probe를 사용하였다. 아크릴 수조 내부, 자궁내부, 대기온도 측정을 위해 3개의 탐침형 온도계를 설치하였고 측정대상의 온도를 분단위로 6시간, 총 361회 측정 한 결과 자궁모형팬텀의 온도가 상승되었음을 확인하였다. 본 연구를 통해 초음파로 인한 인체 체온 상승의 가능성을 확인 할 수 있었고 본 연구가 초음파 열 흡수효과 연구의 기초자료로 활용 될 것이라 사료된다.

• 대한수학회지
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• 제45권2호
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• pp.587-596
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• 2008

For convex bodies, chord power integrals were introduced and studied in several papers (see [3], [6], [14], [15], etc.). The aim of this article is to study them further, that is, we establish the Brunn-Minkowski-type inequalities and get the upper bound for chord power integrals of convex bodies. Finally, we get the famous Zhang projection inequality as a corollary. Here, it is deserved to mention that we make use of a completely distinct method, that is using the theory of inclusion measure, to establish the inequality.