• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.66-70
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• 2007

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings ${\phi}$ on the class of Choquet integrable functions and m-convex mappings $T_{\phi}$, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.275-285
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• 1997

Let E be a uniformly convex Banach space with a uniformly G$\hat{a}teaux differentiable norm, C a nonempty closed convex subset of $E, T : C \to E$ a nonexpansive mapping, and Q a sunny nonexpansive retraction of E onto C. For $u \in C$ and $t \in (0,1)$, let $x_t$ be a unique fixed point of a contraction $R_t : C \to C$, defined by $R_tx = Q(tTx + (1-t)u), x \in C$. It is proved that if ${x_t}$ is bounded, then the strong $lim_{t\to1}x_t$ exists and belongs to the fixed point set of T. Furthermore, the strong convergence of ${x_t}$ in a reflexive and strictly convex Banach space with a uniformly G$\hat{a}$teaux differentiable norm is also given in case that the fixed point set of T is nonempty.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1311-1332
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• 2013

This paper concerns the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive power ${\beta}$ of the positive mean curvature. It is shown that the flow exists on a finite maximal interval, convexity by horospheres is preserved and the hypersurfaces shrink down to a single point as the final time is approached.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.409-421
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• 2018

Let X be a complex manifold of dimension n $n{\geqslant}2$ and let ${\Omega}{\Subset}X$ be a weakly q-convex domain with smooth boundary. Assume that E is a holomorphic line bundle over X and $E^{{\otimes}m}$ is the m-times tensor product of E for positive integer m. If there exists a strongly plurisubharmonic function on a neighborhood of $b{\Omega}$, then we solve the ${\bar{\partial}}$-problem with support condition in ${\Omega}$ for forms of type (r, s), $s{\geqslant}q$ with values in $E^{{\otimes}m}$. Moreover, the solvability of the ${\bar{\partial}}_b$-problem on boundaries of weakly q-convex domains with smooth boundary in $K{\ddot{a}}hler$ manifolds are given. Furthermore, we shall establish an extension theorem for the ${\bar{\partial}}_b$-closed forms.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.197-202
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• 1992

In this paper, we consider the synthesis of mixed H$_{2}$/H$_{\infty}$ controllers such that the closed-loop poles are located in a specified region in the complex plane. Using solution to a generalized Riccati equation and a change of variable technique, it is shown that this synthesis problem can be reduced to a convex optimization problem over a bounded subset of matrices. This convex programming can be further reduced to Generalized Eigenvalue Minimization Problem where Interior Point method has been recently developed to efficiently solve this problem..

• 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.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.273-281
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• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.211-217
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• 2006

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.1
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• pp.19-24
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• 2007

In this paper, we propose a 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 consists of the convex set of PID and PI-PD controller. PID-PD controller controls the closed-loop response to be located 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 Society for Precision Engineering
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• v.20 no.3
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• pp.97-104
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• 2003

This paper proposes a new parallel manipulator fur plane motion, and then discusses on the workspace and kinematical characteristics of the manipulator. The conventional planar parallel manipulators have some disadvantages which are complex non-closed type direct kinematics, workspaces containing useless voids, and concave type border tines of workspaces. The proposed planar parallel manipulator overcomes the above disadvantages, that is, the manipulator has simple closed type direct kinematics, a void-free workspace, and a convex type borderline of a workspace. This paper shows the simulation result of the workspace as well as performances indices using a homogeneous inverse Jacobian.