• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(II)
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• pp.1073-1076
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• 1987

In this paper, a new ray tracing algorithm which uses space subdivision method is introduced. In order to reduce huge number of ray-surface intersection calculation, the space is subdivided as lattice that contains minimum number of objects. With lattice structure, the process that calculates unnecessary ray-surface intersection is eliminated.

• 대한수학회논문집
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• 제19권4호
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• pp.691-700
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• 2004

Let X and Y be operators acting on a Hilbert space and let (equation omitted) be a subspace lattice of orthogonal projections on the space containing 0 and I. We investigate normal interpolation problems in Alg(equation omitted): Given operators X and Y acting on a Hilbert space, when does there exist a normal operator A in Alg(equation omitted) such that AX = Y?

• 터널과지하공간
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• 제6권2호
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• pp.122-130
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• 1996

Generally the NATM technique uses shotcrete, rock bolts, H-beam steel ribs, and concrete lining for the tunnel support in Korea. Among them, H-beam steel ribs are extremely heavy and difficult for workers to handle. Therefore, especially in Europe, lattice girders are being used instead of H-beam steel ribs for tunnel support. Lattice girders have basically the same function as H-beam steel ribs in tunnelling. The main advantages of using lattice girders compared to H-beam steel rib supports are as follows: 1) lattice girders have relatively a low weight enough to be easily lifted and installed by labors and 2) they create a more effective bond with the shotcrete. The purpose of this study is to evaluate the effectiveness and applicability of lattice girders compared to H-beam steel ribs used in construction tunnel sites and to show that lattice girders can be adequately applied in domestic tunnel construction sites as a new tunnel support system.

• Korean Journal of Mathematics
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• 제28권3호
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• pp.439-447
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• 2020

Let M be a lattice module over a C-lattice L. Let Spec^s(M) be the collection of all second elements of M. In this paper, we consider a topology on Spec^s(M), called the second classical Zariski topology as a generalization of concepts in modules and investigate the interplay between the algebraic properties of a lattice module M and the topological properties of Spec^s(M). We investigate this topological space from the point of view of spectral spaces. We show that Spec^s(M) is always T₀-space and each finite irreducible closed subset of Spec^s(M) has a generic point.

• 한국터널지하공간학회 논문집
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• 제21권6호
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• pp.897-908
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• 2019

본 연구의 목적은 수치해석을 수행하여 고성능 격자지보재(BK-Lattice Girder)의 현장 지지성능을 평가하기 위한 것이다. 고속도로 2차로, 3차로와 4차로 터널 단면에 3가지 형태(50, 70, 95 타입)의 기존 및 고성능 격자지보재를 적용하여 지지성능을 비교하였다. 수치해석은 유한요소방법을 사용하였고 격자지보재는 탄소성 프레임으로 3차원으로 모델링하였다. 지반은 압축만을 받는 스프링으로 모델링하였다. 하중은 터널 단면의 중앙 천정부에 집중하중으로 적용하였다. 수치해석 결과로부터 격자지보재의 항복강도를 결정하여 지지성능을 비교하였다. 50타입의 경우, 고성능 격자지보재는 기존 격자지보재보다 항복강도가 6.7~10.0% 증가하였다. 70타입의 경우, 고성능 격자지보재는 기존 격자지보재보다 항복강도가 12.1~14.9% 증가하였다. 95타입의 경우에도, 고성능 격자지보재는 기존 격자지보재보다 항복강도가 13.3~20.0% 증가하였다. 수치해석을 수행한 결과, 격자지보재만 시공된 경우에 고성능 격자지보재는 기존 격자지보재보다 지지성능이 우수한 것으로 판단되었다.

• 대한수학회지
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• 제42권4호
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• pp.635-653
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• 2005

We study the distribution of a dense orbit of a lattice A acting by the right multiplication on the space $\Gamma/G$ where G is a connected simple Lie group and $\Gamma$ its lattice. We show that for $G=SL_n(\mathbb{R})$, every dense orbit is equidistributed with respect to the Euclidean norm.

• 한국공간구조학회논문집
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• 제18권4호
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• pp.113-121
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• 2018

U-flanged truss beam is composed of u-shaped upper steel flange, lower steel plate of 8mm or more thickness, and connecting lattice bars. Upper flange and lower plate are connected by the diagonal lattice bars welded on the upper and lower sides. In this study the structural experiments on the U-flanged truss beams with various shapes of upper flange were performed, and the flexural and shear capacities of U-flanged truss beam in the construction stage were evaluated. The principal test parameters were the shape of upper flange and the alignment space of diagonal lattice bars. In all the test specimens, the peak loads were determined by the buckling of lattice bar regardless of the upper flange shape. The test results have shown that the buckling of lattice bar is very important design factor and there is no need to reinforce the basic u-shaped upper flange. However, the early lattice buckling occurred in the truss beam with upper steel bars because of the insufficient strength and stiffness of upper chord, and the reinforcement in the upper chord is necessary. The formulae of Eurocode 3 (2005) have presented more exact evaluations of lattice buckling load than those of KBC 2016.

• 충청수학회지
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• 제28권3호
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• pp.431-441
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• 2015

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. Our purpose of this study is to give new topologies on the family ${\tau}(X)$ of all topologies induced by old one and its ${\theta}$ topology and to compare them.

• 대한수학회보
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• 제40권2호
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• pp.207-213
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. An interpolating operator for n-vectors satisfies the equation Ax$_{i}$=y$_{i}$. for i=1,2, …, n. In this article, we investigate unitary interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H. Let x and y be vectors in H. When does there exist a unitary operator A in AlgL such that Ax=y?

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.359-365
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. In this article, we investigate invertible interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H and x and y be vectors in H. When does there exist an invertible operator A in AlgL suth that An = ㅛ?