• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.239-247
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권6호
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• pp.1492-1511
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• 2013

A novel, chaotic map that is based on concatenated torus automorphisms is proposed in this paper. As we know, cat map, which is based on torus automorphism, is highly chaotic and is often used to encrypt information. But cat map is periodic, which decreases the security of the cryptosystem. In this paper, we propose a novel chaotic map that concatenates several torus automorphisms. The concatenated mechanism provides stronger chaos and larger key space for the cryptosystem. It is proven that the period of the concatenated torus automorphisms is the total sum of each one's period. By this means, the period of the novel automorphism is increased extremely. Based on the novel, concatenated torus automorphisms, two application schemes in image encryption are proposed, i.e., 2D and 3D concatenated chaotic maps. In these schemes, both the scrambling matrices and the iteration numbers act as secret keys. Security analysis shows that the proposed, concatenated, chaotic maps have strong chaos and they are very sensitive to the secret keys. By means of concatenating several torus automorphisms, the key space of the proposed cryptosystem can be expanded to $2^{135}$. The diffusion function in the proposed scheme changes the gray values of the transferred pixels, which makes the periodicity of the concatenated torus automorphisms disappeared. Therefore, the proposed cryptosystem has high security and they can resist the brute-force attacks and the differential attacks efficiently. The diffusing speed of the proposed scheme is higher, and the computational complexity is lower, compared with the existing methods.

• 한국컴퓨터그래픽스학회논문지
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• 제25권3호
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• pp.93-103
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• 2019

3차원상의 자유곡면에 대한 효율적인 기하 연산을 지원하기 위한 새로운 공간자료구조로서 토러스 패치 기반 정밀 근사를 이용한 자유곡면의 기하학적 처리 기법을 소개한다. 토러스는 곡률이 양이나 음인 경우뿐만 아니라, 0인 부분도 있으므로 자유곡면의 볼록, 오목 여부에 상관없이 곡면을 정밀하게 근사할 수 있다. 전통적인 기법과 달리 토러스 패치는 자유곡면의 법벡터 방향까지 쉽게 모델링할 수 있고, 토러스의 오프셋은 다시 토러스가 되므로 다양한 기하 연산의 가속화를 지원할 수 있다. 자유곡면과 이를 근사하는 토러스 패치 집합 사이의 양방향 하우스도르프 거 리의 상한을 계산하여 토러스 패치를 이용하여 자유곡면을 높은 정밀도로 근사할 수 있음을 보였다. 이 기법을 이용하여 두 자유곡면의 교차곡선 계산과 자유곡면의 오프셋 곡면 생성을 쉽게 처리할 수 있음을 보였다.

• Tribology and Lubricants
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• 제18권4호
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• pp.249-254
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• 2002

Adhesive contact characteristics of torus-shaped bumps were analyzed using the finite element technique considering the adhesive force. Analyses focused on the effect of rim and bump radii on the adhesive contact behavior such as the jump-to-contact behavior, adhesion hysteresis, pull-off forces, contact region and pressure, and surface and subsurface stresses. Analysis results in the absence of adhesive force were also included to examine the effect of adhesive force. The applicability of torus-shaped bumps to the MEMS structure for reduction of friction is discussed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.73-88
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• 2004

A punctured torus $\Sigma(1,1)$ is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let $\cal{C}$ be a matrix presentation of the boundary component of $\Sigma(1,1)$.In the level of the matrix group $\mathbb{SL}$($\mathbb2,R$) we shall show that the trace of $\cal{C}$ is always negative.

• 대한수학회보
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• 제57권1호
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• pp.1-30
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• 2020

In this paper, we classify all twisted torus knots which are middle/hyper doubly Seifert. By the definition of middle/hyper doubly Seifert knots, these knots admit Dehn surgery yielding either Seifert-fibered spaces or graph manifolds at a surface slope. We show that middle/hyper doubly Seifert twisted torus knots admit the latter, that is, non-Seifert-fibered graph manifolds whose decomposing pieces consist of two Seifert-fibered spaces over the disk with two exceptional fibers.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.275-288
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• 2010

A one-holed torus ${\Sigma}$(l, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus ${\Sigma}$(1, 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of ${\Sigma}$(1, 1).

• East Asian mathematical journal
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• 제16권1호
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• pp.61-69
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• 2000

We show that the intersection of two standard torus knots of type (${\lambda}_1$, ${\lambda}_2$) and (${\beta}_1$, ${\beta}_2$) induces an automorphism of the cyclic group ${\mathbb{Z}}_d$, where d is the intersection number of the two torus knots and give an elementary proof of the fact that all non-trivial torus knots are strongly invertiable knots. We also show that the intersection of two standard knots on the 3-torus $S^1{\times}S^1{\times}S^1$ induces an isomorphism of cyclic groups.

• 한국가구학회지
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• 제17권3호
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• pp.23-28
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• 2006

An experiment was conducted to investigate the pit structure of four kind of pine wood species grown in Korea. Torus diameter, margo width, margo lattice size, diameter of pit aperture and pit border width were taken under consideration for explaining the pit structure difference among Pinus densiflora, Pinus rigida, Pinus koraiensis and Larix kaempferi. Torus diameter was found highest in Pinus rigida and the lowest in Pinus densiflora. Margo lattice size varied with torus diameter. Wider torus lowered the margo lattice size. Highest margo width was found in Pinus rigida while the lowest one was found in Pinus koraiensis. Pit aperture diameter was found highest in Pinus densiflora and lowest in Pinus koraiensis. In Pinus rigida, pit border was found the highest and the lowest was found in Larix kaempferi. Pit aperture diameter and pit border were increased gradually from pith to bark while there was a decreasing trend in the margo lattice size measuring from the pith to bark.

• 정보처리학회논문지A
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• 제8A권2호
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• pp.157-166
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• 2001

A simulation package has been developed as an event-driven system that can handle the hardware configuration of STC104 and algorithm proposed in the sister paper of ‘Study on High Speed Routers(II).’After various STC104 topology of meshes, torus, and hypercubes are constructed using up to 512 switches, the performance of each topology has been analyzed under different message generation rate in terms of throughputs, latency, and packet blocking time. Modified multicast algorithms for STC104 have been proposed for STC104 after U-mesh and U-torus in order to overcome the multicasting difficulty because of the point-to-point communication method found in STC104. The performance of the multicast algorithms have been analyzed over meshes and torus configuration. Throughput gets higher in the order of mesh, torus, and hypercube. Throughput difference among topology were distinctive in the zone of high message generation rate. Latency and blocking time increased in the order of hypercube, torus, and mesh. U-mesh and U-torus of software multicast showed similar throughput, however, U-mesh peformed slightly better result. These algorithms showed eight to ten times better results compared to individual message pass for 90 destination nodes. Multi-link environment also showed better performance than single-link environment because multi-link network used the extra links for communication.