• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.905-913
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• 2023

Suppose that M is a strictly convex hypersurface in the (n + 1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with the origin o in its convex side and with the outward unit normal N. For a fixed point p ∈ M and a positive constant t, we put 𝚽_t the hyperplane parallel to the tangent hyperplane 𝚽 at p and passing through the point q = p - tN(p). We consider the region cut from M by the parallel hyperplane 𝚽_t, and denote by I_p(t) the (n + 1)-dimensional volume of the convex hull of the region and the origin o. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space 𝔼³, the ellipsoids are the only ones satisfying I_p(t) = 𝜙(p)t, where 𝜙 is a function defined on M. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in 𝔼ⁿ⁺¹ satisfying for a constant 𝛽, I_p(t) = 𝜙(p)t^𝛽. In this paper, we study the volume I_p(t) of a strictly convex and complete hypersurface in 𝔼ⁿ⁺¹ with the origin o in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.185-197
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• 2015

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(f_n)-Lipschitzian map- pings and an infinite family of g_n-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1019-1045
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• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• Journal of Electrical Engineering and information Science
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• v.3 no.3
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• pp.281-285
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• 1998

Consider the two-dimensional sorted-set convex hull problem: Given N points in a plane sorted by the x coordinates, compute the convex hull of the points. We propose an O(logNlog logN)-time algorithm that solves the sorted-set convex hull problem on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh. The best known algorithm for the problem on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh takes O(log\ulcornerN) time. Although there is a constant-time algorithm on an N${\times}$N reconfigurable mesh for general two-dimensional convex hull problem, the general convex hull problem requires Θ(N\ulcorner\ulcorner) time on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh due to bandwidth constraints.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.81-90
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• 2018

A bounded linear operator T on a Hilbert space ${\mathcal{H}}$ is convex, if for each $x{\in}{\mathcal{H}}$, ${\parallel}T^2x{\parallel}^2-2{\parallel}Tx{\parallel}^2+{\parallel}x{\parallel}^2{\geq}0$. In this paper, it is shown that if T is convex and supercyclic then it is a contraction or an expansion. We then present some examples of convex supercyclic operators. Also, it is proved that no convex composition operator induced by an automorphism of the disc on a weighted Hardy space is supercyclic.

• 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 Korean Society of Industrial and Systems Engineering
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• v.23 no.61
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• pp.127-135
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• 2000

This paper provides a new method of initializing neurons used in self-organizing neural networks and sequencing input nodes for applying to Euclidean traveling salesman problem. We use a general property that in any optimal solution for Euclidean traveling salesman problem, vertices located on the convex hull are visited in the order in which they appear on the convex hull boundary. We composite input nodes as number of convex hulls and initialize neurons as shape of the external convex hull. And then adapt input nodes as the convex hull unit and all convex hulls are adapted as same pattern, clockwise or counterclockwise. As a result of our experiments, we obtain l∼3 % improved solutions and these solutions can be used for initial solutions of any global search algorithms.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.1-28
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• 2000

In the present paper, we introduce fundamental results in the KKM theory for G-convex spaces which are equivalent to the Brouwer theorem, the Sperner lemma, and the KKM theorem. Those results are all abstract versions of known corresponding ones for convex subsets of topological vector spaces. Some earlier applications of those results are indicated. Finally, We give a new proof of the Himmelberg fixed point theorem and G-convex space versions of the von Neumann type minimax theorem and the Nash equilibrium theorem as typical examples of applications of our theory.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.279-289
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• 1999

Given n points in the plane the planar convex hull prob-lem in that of finding which of these points belong to the perimeter of the smallest convex region (a polygon) containing all n points. Here we suggest two kinds of methods. First we present a new sequential method for constructing the pla-nar convex hull O(1.5n) time in the quadratic decision tree model. Second using the sequential method we suggest a new parallel algo-rithm which solve the planar convex hull O(1.5n/p) time on a maspar Machine (CREW-PRAM) with O(n) processors. Also when we run on a maspar Machine we achieved a 37. 156-fold speedup with 64 pro-cessor.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.138-143
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• 2008

Recently, a new periodic cellular metal(PCM) named as Wire wove Bulk Kagome(WBK) was introduced. Based on the shape of tetrahedra composing a WBK, WBKs are classified into two types, namely, concave and convex type. They are easily differentiated by changing the assembling sequence. The effect of geometrical parameters such as the wire diameter, strut length and number of layers on the compressive behavior of concave type WBK has already been investigated. In this work, the similar works were performed with the convex type WBKs. It was shown that the compressive strength of the convex type WBK was quite similar to that of the concave type. The compressive strengths of convex type specimens also depend on the slenderness ratio, but a little different from those of concave type specimens in the detailed behavior. And densification occurs earlier than the concave type WBK.