• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.293-306
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• 2022

In the present paper, we introduce the notation of 𝛿-convex rectangular metric spaces with the help of convex structure. We investigate fixed point results concerning Kannan-type contraction and Reich-type contraction in such spaces. We also propound an ingenious example in reference of given new notion.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.6
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• pp.1-9
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• 2003

In this paper, we propose a new fingerprint feature extraction method using the convex structure. A fingerprint minutiae flows along the uniform direction and is regarded as a sinusoidal signal across the normal direction. Local maxima of the signal represent coarse thinned one-pixel-wide ridges in which the convex region of the signal correspond to ridges. The proposed fingerprint feature extraction method detects the convex structure and local maxima. Finally fingerprint features are extracted from one-pixel-wide ridges. Because it has no parameter, it is efficient for various fingerprint identification systems.

• 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.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.2241-2242
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• 2008

Anisotropic TMAH etching is key processing step for the fabrication of pendulum structure. During the etching, convex corners are attacked, and a proper compensating structure design is required when fabricating pendulum structures with sharp convex corner. In this paper, we present four compensation structures for convex corner compensation with 30% wt TMAH-water solution at $89\pm1^{\circ}C$ temperature, and observe the etched convex corner by optical microscope. we compare the result of calculations and experiments about four convex corner compensation patterns.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.314-319
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• 2005

When a robot navigates in the real environment, it frequently meets various environments that can be expressed by simple geometrical shapes such as fiat floor, uneven floor, floor with obstacles, slopes, concave or convex corners, etc. Among them, the convex corner composed of two plain surfaces is the most difficult one for the robot to negotiate. In this paper, we propose a gait planning algorithm to help the robot overcome the convex environment. The trajectory of the body is derived from the maximum distance between the edge boundary of the corner and the bottom of the robot when it travels in the convex environment. Additionally, we find the relation between kinematical structure of the robot and its ability of avoiding collision. The relation is realized by considering the workspace and the best posture of the robot in the convex structure. To provide necessary information for the algorithm, we use an IR sensor attached in the leg of the robot to perceive the convex environment. The validity of the gait planning algorithm is verified through simulations and the performance is demonstrated using a quadruped walking robot, called "MRWALLSPECT III"( Multifunctional Robot for WALL inSPECTion version 3).

• 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.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.123-134
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• 2023

Since Knaster, Kuratowski, and Mazurkiewicz established their KKM theorem in 1929, it was first applied to topological vector spaces mainly by Fan and Granas. Later it was extended to convex spaces by Lassonde and to extensions of c-spaces by Horvath. In 1992, such study was called the KKM theory by ourselves. Then the theory was extended to generalized convex spaces or G-convex spaces. Motivated by such spaces, there have appeared several particular types of artificial spaces. In 2006 we introduced abstract convex spaces which contain all existing spaces appeared in the KKM theory. Later in 2014-2020, Khahn and Quan introduced "topologically based existence theorems" and the so-called KKM structure. In the present paper, we show that their structure is a particular type of already known KKM spaces.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.51-57
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• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• Geomechanics and Engineering
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• v.29 no.3
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• pp.339-348
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• 2022

The bored tunneling method is generally preferred for urban tunnel construction, However the cut & cover tunnel is still necessary for special conditions, such as metro station and access structures. In some case, deep excavation for cut & cover construction is planed of irregular and unusual shape, as a consequence, the convex and concave corner is often encountered during that excavation. In particular, discontinuity or imbalance of the support structure in the convex corner can lead to collapse, which may result in damages and casualties. In this study, the behavior of the convex corner of retaining structure were investigated using 3-dimensional numerical models established to be able to simulate the split-shaped behavior of convex corners. To improve the stability in the vicinity of the convex corner, several stabilizing measures were proposed and estimated numerically. It is found that linking two discretized wales at the convex corner can effectively perform the control of deformation. Furthermore, it was also confirmed that the stabilizing measures can be enhanced when the tie-material linking two discretized wales is installed at the depth of the maximum wall deflection.