• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.737-767
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• 2016

This paper concerns closed hypersurfaces of dimension $n{\geq}2$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature evolving in direction of its normal vector, where the speed equals a power ${\beta}{\geq}1$ of the mean curvature. The main result is that if the initial closed, weakly h-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to 1, depending only on n and ${\beta}$, then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in ${\mathbb{H}}_{\kappa}^{n+1}$ in a maximal finite time, and when rescaling appropriately, the evolving hypersurfaces exponential convergence to a unit geodesic sphere of ${\mathbb{H}}_{\kappa}^{n+1}$.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.628-631
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• 2005

In this paper, we propose tuning method of PID-PD controller to satisfy design specifications in frequency domain as well as time domain. The proposed tuning method of PID-PD controller that consist of the convex set of PID and PI-PD controller controls the closed-loop response to locate between the step responses, and Bode magnitudes of closed-loop transfer functions controlled by PID and PI-PD controller. The controller is designed by the optimum tuning method to minimize the proposed specific cost function subject to sensor noise insensitivity and robust stability. Its effectiveness is examined by the case study and analysis.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.118-127
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• 1991

In this paper, criteria and algorithms for the optimal service rate in a closed queueing network have been established. The objective is to minimize total cost. It is shown that system throughput is increasing concave over the service rate of a node and cycle time is increasing convex over the set of service times with a single calss of cubsomers. This enables developing an algorithm using a steepest descent method when the cost function for service rate is convex. The efficiency of the algorithm rests on the fact that the steepest descent direction is readily obtained at each iteration from the MVA algorithm. Several numerical examples are presented. The major application of this research is optimization of facility capacity in a manufacturing system.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.135-145
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• 1998

In this paper, we focus on the convex-valued selection theorem out of four main selection theorems; zero-dimensional, convex-valued, compact-valued, finite-dimensional theorems based on Michael's papers. We prove some theorems about lower semi-continuous set-valued mappings, and derive some applications to closed continuous set-valued mappings and to functional analysis. We also give a partial solution to the open problem posed by Engelking, Heath, and Michael.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.131-143
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• 2004

Let Ε and F be locally convex spaces over C. We assume that Ε is a nuclear space and F is a Banach space. Let f be a holomorphic mapping from Ε into F. Then we show that f is of uniformly bounded type if and only if, for an arbitrary locally convex space G containing Ε as a closed subspace, f can be extended to a holomorphic mapping from G into F.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.17-35
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• 2005

Necessary conditions for a deterministic optimal control problem which involves states constraints are derived in the form of a maximum principle. The conditions are similar to those of F.H. Clarke, R.B. Vinter and G. Pappas who assume that the problem's data are Lipschitz. On the other hand, our data are not continuously differentiable but only differentiable. Fermat's rule and Rockafellar's duality theory of convex analysis are the basic techniques in this paper.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.351-365
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• 2011

In the present paper we introduce a new subclass of analytic functions in the unit disc defined by convolution $(f_{\mu})^{(-1)}*f(z)$; where $$f_{\mu}=(1-{\mu})z_2F_1(a,b;c;z)+{\mu}z(z_2F_1(a,b;c;z))^{\prime}$$. Several interesting properties of the class and integral preserving properties of the subclasses are also considered.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.545-556
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• 1996

In this paper, we introduce a new concept of partial ordering which permits us to compare pairs of the dependence structures of a new hitting times for POD multivariate vector process of interest as to their degree of POD-ness. We show that POD ordering is closed under convolution, limit in distribution, compound distribution, mixture of a certain type and convex combination. Finally, we present several examples of POD ordering processes.

• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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• pp.189-196
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• 1990

In this paper, we try to generalize ultraproducts in the category of locally convex spaces. To do so, we introduce D-ultracolimits. It is known [7] that the topology on a non-trivial ultraproduct in the category T $V^{ec}$ of topological vector spaces and continuous linear maps is trivial. To generalize the category Ba $n_{1}$ of Banach spaces and linear contractions, we introduce the category L $C_{1}$ of vector spaces endowed with families of semi-norms closed underfinite joints and linear contractions (see Definition 1.1) and its subcategory, L $C_{2}$ determined by Hausdorff objects of L $C_{1}$. It is shown that L $C_{1}$ contains the category LC of locally convex spaces and continuous linear maps as a coreflective subcategory and that L $C_{2}$ contains the category Nor $m_{1}$ of normed linear spaces and linear contractions as a coreflective subcategory. Thus L $C_{1}$ is a suitable category for the study of locally convex spaces. In L $C_{2}$, we introduce $l_{\infty}$(I. $E_{i}$ ) for a family ( $E_{i}$ )$_{i.mem.I}$ of objects in L $C_{2}$ and then for an ultrafilter u on I. we have a closed subspace $N_{u}$ . Using this, we construct ultraproducts in L $C_{2}$. Using the relationship between Nor $m_{1}$ and L $C_{2}$ and that between Nor $m_{1}$ and Ba $n_{1}$, we show thatour ultraproducts in Nor $m_{1}$ and Ba $n_{1}$ are exactly those in the literatures. For the terminology, we refer to [6] for the category theory and to [8] for ultraproducts in Ba $n_{1}$..

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1353-1362
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• 2003

This paper considers a simultaneous optimization problem of structure and control systems. The problem is generally formulated as a non-convex optimization problem for the design parameters of mechanical structure and controller. Therefore, it is not easy to obtain the global solutions for practical problems. In this paper, we parameterize all design parameters of the mechanical structure such that the parameters work in the control system as decentralized static output feedback gains. Using this parameterization, we have formulated a simultaneous optimization problem in which the design specification is defined by the Η$_2$and Η$\_$$\infty$/ norms of the closed loop transfer function. So as to lead to a convex problem we approximate the nonlinear terms of design parameters to the linear terms. Then, we propose a convex optimization method that is based on linear matrix inequality (LMI). Using this method, we can surely obtain suboptimal solution for the design specification. A numerical example is given to illustrate the effectiveness of the proposed method.