• Proceedings of the Korean Society of Computer Information Conference
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• 2020.07a
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• pp.83-84
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• 2020

Sum Utility를 최적화하는 Convex Optimization Algorithm을 제안한다. 일반적으로, Sum Utility 최적화 문제는 Non Convex Optimization Problem이다. 하지만, '상대간섭'과 '간섭주요화'를 활용하여 Non Convex Optimization Problem이 간섭구간에 따라 Convex Optimization으로 해결할 수 있음을 확인하였다. 특히, 유틸리티 함수는 상대간섭 0.1 이하에서는 오목함수임을 확인하였다. 실험결과 상대간섭이 작아질수록 제안하는 알고리즘에 의한 Sum Utility는 증가함을 확인하였다.

• Journal of the Korea Society of Computer and Information
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• v.25 no.7
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• pp.75-83
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• 2020

We consider the D2D utility optimization problem in the cellular system. More specifically, we develop a concave function decision rule which reduces the complexity of non-convex optimization problem. Typically, utility function, which is a function of the signal and the interference, is non-convex. In this paper, we analyze the utility function from the interference perspective. We introduce the 'relative interference' and the 'interference majorization'. The relative interference captures the level of interference at D2D receiver's perspective. The interference majorization approximates the interference by applying the major interference. Accordingly, we propose a concave function decision rule, and the corresponding convex optimization solution. Simulation results show that the utility function is concave when the relative interference is less than 0.1, which is a typical D2D usage scenario. We also show that the proposed convex optimization solution can be applied for such relative interference cases.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.179-186
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• 2009

Generalizing the approximately convex function which is introduced by D.H. Hyers and S.M. Ulam we establish an approximately convex Schwartz distribution and prove that every approximately convex Schwartz distribution is an approximately convex function.

• Restorative Dentistry and Endodontics
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• v.17 no.1
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• pp.141-152
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• 1992

Four endodontic instruments from different manufacturers(K - file, Hedstrom - file, K - flex - file, Cavi - Endo) were used to shape 80 mesial canals of extracted posterior teeth. The instrument's ability to enlarge and shape the canals as the original canal shape was assessed by superimposing radiographs of canals obtained before and after canal shaping. The results were as follows 1. Hedstrom - file enlarged canals greater than K - file, K - flex - file, and Cavi - Endo(P<0.05). There are no differences in canal enlargement among K - flex, K - flex - file, and Cavi - Endo(P<0.05). 2. All the instruments showed no difference in canal enlargement between convex side and concave side of B point in proximal and clinical radiographic views, but at the concave side of C point canals were enlarged greater than at the convex side(proximal view of K - file: P<0.05, the others: P<0.01). 3. There was no difference m canal enlargement between convex side and concave side in proximal view of A and D points of K - file and K - flex - file(P<0.05). But in clinical view, canal enlargement at convex side of A point and concave side of D point was greater than that at concave side of A point and convex side of D point respectively. 4. Hedstrom - files showed greater canal enlargement at convex side of A points and concave side of D points (P<0.05 or P<0.01). Cavi - Endo showed no difference in canal enlargement between convex side and concave side at A and D points in proximal view(P<0.05). Bur canal enlargement was greater at concave side than at convex side of D point in clinical view. 5. K - file and Cavi - Endo showed no differences in canal enlargement between convex and concave side in proximal and clinical view (P<0.05). K - flex - file showed greater canal enlargement at concave side in proximal and clinical view(P<0.0:5). Hedstrom file showed no difference in canal enlargement between convex side and concave side in proximal view, but showed greater canal enlargement at concave side in clinical view(P<0.05).

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.975-981
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• 1996

Let $D \subset C^2$ be a bounded convex domain with real analytic boundary. We get some Lipschitz regularity of the Cauchy transform on the convex domain D.

• Journal of Korea Multimedia Society
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• v.4 no.4
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• pp.363-369
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• 2001

This paper proposes a convex hull algorithm for 2D patterns. The proposed algorithm is divided ito 2steps; candidate convex point extraction and final convex point extraction. First step removes as many points as possible that cannot be convex points using simple operation. Second step computes final convex hull of 2D patterns. This method accelerates execution time, since it consists of simple operations. Experimental results show that the proposed method is faster than other 2 methods in speed.

• Proceedings of the Korean Society of Computer Information Conference
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• 2020.07a
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• pp.81-82
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• 2020

Non-convex 최적화 문제의 복잡도를 완화하도록 해주는 오목함수 결정규칙을 제안한다. 전송용량을 나타내는 유틸리티 함수는 신호와 간섭의 함수이며, non-convex이다. 유틸리티 함수를 간섭관점에서 분석한다. '상대간섭'과 '간섭주요화'를 정의한다. 상대간섭은 D2D 수신단에서의 간섭레벨을 나타낸다. 간섭주요화는 간섭을 주요간섭으로 간략화한다. 간섭주요화를 기반으로 하는 오목함수 결정규칙을 제안한다. 실험결과를 통하여 유틸리티 함수는 상대간섭 0.1 이하에서는 오목함수임을 확인하였다.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11b
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• pp.213-220
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• 2000

Numerical modeling of cut slope has some limits in simulating the real slopes. In the case of 2D analysis of slope stability, it is assumed that slope is simply straight even when it is concave or convex in plan view. In this study, 3D analysis in curved shape slopes has been conducted for the comparison with 2D analysis in terms of failure mode and factor of safety. For this, 3D analysis by FLAC3D was compared with 2D analysis in plane strain condition and axi-symmetric model condition by FLAC. It was also observed how safety factors of slopes were affected by the variation of the tensile strength and cohesion, which are important variables to decide whether the slope fails or not. 2D analysis of concave slopes under plane strain condition showed much smaller safety factors by 16-40 % errors depending on the radius of curvature of slopes, compared to the more realistic values from 3D analysis. In case of convex slopes, the lower values by 7-10 % has been reported. 2D analysis of axi-symmetric model showed also smaller safety factors by 6-10 % and by 2-4 %, in case of concave and convex slopes, respectively. Such results are expected to contribute to the better understanding of failure process and could be applied for improved design of slopes.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.43 no.2 s.308
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• pp.81-92
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• 2006

This paper proposes a robustness watermarking for 3D mesh model based on projection onto convex sets (POCS). After designing the convex sets for robustness and invisibility among some requirements for watermarking system, a 3D-mesh model is projected alternatively onto two constraints convex sets until the convergence condition is satisfied. The robustness convex set are designed for embedding the watermark into the distance distribution of the vertices to robust against the attacks, such as mesh simplification, cropping, rotation, translation, scaling, and vertex randomization. The invisibility convex set are designed for the embedded watermark to be invisible. The decision values and index that the watermark was embedded with are used to extract the watermark without the original model. Experimental results verify that the watermarked mesh model has invisibility and robustness against the attacks, such as translation, scaling, mesh simplification, cropping, and vertex randomization.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.79-89
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• 2018

In this paper, we study the maximal property of the volume of the convex hull of d-dimensional independent random vectors. We show that the volume of the random convex hull from a multivariate location-scale family indexed by ${\Sigma}$ is stochastically maximized in simple stochastic order when ${\Sigma}$ is diagonal. The claim can be applied to a broad class of multivariate distributions that include skewed/unskewed multivariate t-distributions. We numerically investigate the proven stochastic relationship between the dependent and independent random convex hulls with the Gaussian random convex hull. The numerical results confirm our theoretical findings and the maximal property of the volume of the independent random convex hull.