• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.251-256
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• 2008

In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the sc-convex function and $s^*c$-convex function. Finally, we characterize sc-convex functions, $s^*$-convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.267-270
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• 2002

본 논문에서는 Support Vector Machines (SVM) 을 이용하여, 빠르고 정확한 두 convex한 클러스터 간의 거리 측정 방법을 제시한다 제시된 방법에서는, SVM에 의해서 생성되는 최적 다차원 평면이 두 클러스터간의 최소 거리를 계산하는데 사용된다. 또한, 본 논문에서는 이러한 두 클러스터 간의 최적의 거리를 사용하여, Fuzzy Convex Clustering (FCC) 방법 (1) 에 의해서 생성되는 Convex 클러스터들을 묶어주는 효과적인 클러스터 결합 알고리즘을 제시하였다. 그러므로, 데이터의 부적절한 표현을 유발하지 않고도 클러스터들의 개수를 좀 더 줄일 수 있었다. 제시한 방법의 타당성을 위하여 여러 실험 결과를 제시하였다

• Honam Mathematical Journal
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• v.44 no.3
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• pp.360-369
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• 2022

The aim of this study is to establish some new Jensen and Lazhar type inequalities for p-convex function that is a generalization of convex and harmonic convex functions. The results obtained here are reduced to the results obtained earlier in the literature for convex and harmonic convex functions in special cases.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.279-288
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• 2023

We obtain a Chandrabhan type fixed point theorem for a multimap having a non-compact domain and a weakly closed graph, and taking convex values only on a quasi-convex subset of Hausdorff locally convex topological vector space. We introduce the definition of Chandrabhan-set and find a sufficient condition for every countably condensing multimap to have a relatively compact Chandrabhan-set. Finally, we establish a new version of Sadovskii fixed point theorem for multimaps.

• Proceedings of the KSME Conference
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• 2007.05b
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.369-374
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• 2004

A cluster merging algorithm that merges convex clusters resulted by the Fuzzy Convex Clustering(FCC) method into non-convex clusters was proposed. This was achieved by proposing a fast and reliable distance measure between two convex clusters using Support Vector Machines(SVM) to improve accuracy and speed over other existing conventional methods. In doing so, it was possible to reduce cluster number without losing its representation of the data. In this paper, results for several data sets are given to show the validity of our distance measure and algorithm.

• International Journal of Air-Conditioning and Refrigeration
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• v.16 no.3
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• pp.100-107
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• 2008

The heat transfer and friction characteristics of heat exchangers having convex louver fins are experimentally investigated, and the results are compared with those of wave fin counterparts. Eighteen samples (nine convex louver fin samples and nine wave fin samples) which had different fm pitches (1.81 mm to 2.54 mm) and tube rows (one to four) were tested. The convex angle was $11.7^{\circ}$. The j factors are insensitive to fin pitch, while f factors increase as fin pitch increases. The effect of fin pitch on f factor is more significant for the wave fin compared with the convex louver fin. It appears that the complex fin pattern of the convex louver fin induces intense mixing of the flow, and thus reduces the effect of fin pitch. Both the j and f factors decrease as the number of tube row increases. However, as the Reynolds number increases, the effect of tube row diminishes. Comparison of the convex louver fin j factors with those of wave fin reveals that convex louver fin j factors are 18% to 29% higher than those of wave fin. The f factors are 16% to 34% higher for the convex louver fin. The difference increases as fin pitch decreases. Existing correlation fails to adequately predict the present data. More data is needed for a general correlation of the convex louver fin geometry.

• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.697-709
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• 2001

Generalized forms of the von neumann-Sion type minimax theorem, the Fan-Ma intersection theorem, the Fan-a type analytic alternative, and the Nash-Ma equilibrium theorem hold for generalized convex spaces without having any linear structure.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.387-395
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• 2002

In [11] Kim obtained fixed point theorems for maps defined on some “locally G-convex”subsets of a generalized convex space. Theorem 2 in Kim's article determines us to introduce, in this paper, the notion of K-G-convex space. In this framework we obtain fixed point theorems, section properties and minimax inequalities.