• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.4
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• pp.165-174
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• 2000

This paper presents the application of H$\infty$ control synthesis using LMI optimization method to power system stabilizer(PSS) design. Since power system is usually operated under circumstance of unmeasurable uncertainties and external disturbances, the improvement of small signal stability becomes one of the most important issue for securing system stability and preventing low frequency oscillation phenomena. The LMI optimized H$\infty$ PSS provides robust performance and guarantees the internal stability under these operating conditions. The global optimal H$\infty$ norm is found using LMI convex optimization method which is more systematic than standard two Riccati solution method. The design results are simulated for a case study. We verified that the LMI method shows the best performance characteristic smong standard Riccati method and conventional lead/lag method.

• Journal of Korea Multimedia Society
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• v.3 no.3
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• pp.298-308
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• 2000

We present an efficient algorithm for finding the sequence of extreme vortices of a moving regular convex polyhedron of with respect to a fixed plane H.. The algorithm utilizes the spherical Voronoi diagram that results from the outward unit normal vectors nF$_{i}$ 's of faces of P. It is well-known that the Voronoi diagram of n sites in the plane can be computed in 0(nlogn) time, and this bound is optimal. However. exploiting the convexity of P, we are able to construct the spherical Voronoi diagram of nF$_{i}$ ,'s in O(n) time. Using the spherical Voronoi diagram, we show that an extreme vertex problem can be transformed to a spherical point location problem. The extreme vertex problem can be solved in O(logn) time after O(n) time and space preprocessing. Moreover, the sequence of extreme vertices of a moving regular convex polyhedron with respect to H can be found in (equation omitted) time, where m$^{j}$ $_{k}$ (1$\leq$j$\leq$s) is the number of edges of a spherical Voronoi region sreg(equation omitted) such that (equation omitted) gives one or more extreme vertices.

• Restorative Dentistry and Endodontics
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• v.20 no.1
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• pp.316-327
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• 1995

The purpose of this study was to evaluate canal shaping ability and canal angulation change of K-file, straight endosonic K-file and pre curved endosonic K-file. Twenty staight canals and thirty curved canals were selected and divided into five groups according to canals curvature and canal instrumentation method. VI group was prepared by straight endosonic K-file and H1 group by K-file in straigt canals. V2 group was instrumented by straight endosonic K-file, V3 group by pre curved endosonic K-file and H2 group by precurved K-file in curved canals. Radiographs of canals were obtained before and after canal shaping. And postoperative radiographs were compared with preoperative radiographs using superimposition method. The results obtained were as follows ; l. In straight canals, K-file group demonstrated lager percentage of canal enlargement than endosonic K-file group on facial view, but reverse results exhibit on mesial view. 2. In curved canals, precurved K-file group showed largest percentage of canal enlargement, followed by precurved endosonic K-fine group and straight endosonic K-file group was smallest. 3. Percantage of canal enlargement at convex side was greater than at concave side in apical portion of each group. Especially in straight endosonic K-file group, percantage of canal enlargement at convex side and concave side showed sharply difference. 4. In angulation change, the straight endosonic K-file group exhibited the greatest its change, followed by precurved endosonic K-file group and precurved K-file group was the least. Above results suggest that K-file is more effective endodontic instrument than endosonic K-file, and that precurved file is effective for canal shaping in curved canal.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.105-123
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• 2015

Let $f_{\beta}=h_{\beta}+\bar{g}_{\beta}$ and $F_a=H_a+\bar{G}_a$ be harmonic mappings obtained by shearing of analytic mappings $h_{\beta}+g_{\beta}=1/(2isin{\beta})log\((1+ze^{i{\beta}})/(1+ze^{-i{\beta}})\)$, 0 < ${\beta}$ < ${\pi}$ and $H_a+G_a=z/(1-z)$, respectively. Kumar et al. [7] conjectured that if ${\omega}(z)=e^{i{\theta}}z^n({\theta}{\in}\mathbb{R},n{\in}\mathbb{N})$ and ${\omega}_a(z)=(a-z)/(1-az)$, $a{\in}(-1,1)$ are dilatations of $f_{\beta}$ and $F_a$, respectively, then $F_a\tilde{\ast}f_{\beta}{\in}S^0_H$ and is convex in the direction of the real axis, provided $a{\in}[(n-2)/(n+2),1)$. They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture, in the affirmative, for ${\beta}={\pi}/2$ and for all $n{\in}\mathbb{N}$.

• Korean Journal of Environment and Ecology
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• v.27 no.1
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• pp.11-21
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• 2013

We tried to find out the core feeding site of the Red-crowned Crane(Grus japonensis) in Cheorwon, Korea by using analysis techniques which are MCP(minimum convex polygon), KDE(kernel density estimation), LoCoH(local nearest-neighbor convex-hull). And, We discussed the difference and meaning of result among analysis methods. We choose the data of utilization distribution from distribution map of Red-crowned Crane in Cheorwon, Korea at $17^{th}$ February 2012. Extent of the distribution area was $140km^2$ by MCP analysis. Extents of core feeding area of the Red-crowned Crane were $33.3km^2$($KDE_{1000m}$), $25.7km^2$($KDE_{CVh}$), $19.7km^2$($KDE_{LSCVh}$), according to the 1000m, CVh, LSCVh in value of bandwidth. Extent, number and shape complexity of the core area has decreased, and size of each core area have decreased as small as the bandwidth size(default:1000m, CVh: 554.6m, LSCVh: 329.9). We would suggest the CVh value in KDE analysis as a proper bandwidth value for the Red-crowned crane's core area zoning. Extent of the distribution range and core area have increased and merged into the large core area as a increasing of k value in LoCoH analysis. Proper value for the selecting core area of Red-crowned Crane's distribution was k=24, and extent of the core area was $18.2km^2$, 16.5% area of total distribution area. Finally, the result of LoCoH analysis, we selected two core area, and number of selected core area was smaller than selected area of KDE analysis. Exact value of bandwidth have not been used in studies using KDE analysis in most articles and presentations of the Korea. As a result, it is needed to clarify the exact using bandwidth value in KDE studies.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.301-318
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• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.2
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• pp.117-125
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• 2016

This paper presents the internal oil leakage detection problem for a hydraulic double-rod cylinder. We represent the dynamics of the hydraulic cylinder as a convex combination of linear equations. To detect oil leakage, we propose a model-based fault detection observer design scheme. The observer is designed to be robust against disturbance. Sufficient design conditions are derived in the form of linear matrix inequalities. A numerical example is provided to verify the proposed techniques.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.702-704
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• 2004

This paper focuses on the problem of asymptotic stabilization for uncertain time-delay systems with saturating actuator. We propose a state feedback controller which maximizes the delay bound for guaranteeing stability of the system. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. The criterion is represented in terms of LMIs, which can be solved by various efficient convex optimization algorithm. Numerical examples are given to illustrate our main method.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.13-23
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• 2009

Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]