• Proceedings of the KIEE Conference
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• 1987.07b
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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.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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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?

• Tunnel and Underground Space
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• v.6 no.2
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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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• v.28 no.3
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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.

• Journal of Korean Tunnelling and Underground Space Association
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• v.21 no.6
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• pp.897-908
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• 2019

The objective of this study is to evaluate the field support performance of highperformance lattice girder (BK-Lattice Girder) by using numerical analysis. Three types (50, 70, 95-type) of existing and high performance lattice girders were applied to the cross section of highway 2, 3, and 4 lane tunnels to compare the supporting performance. The numerical analysis was the finite element method and the lattice girder was modeled in three dimensions with an elasto-plastic frame. The ground was modeled as a spring receiving only compression. The load was applied as a concentrated load on the central ceiling of the tunnel section. The yield strengths of the lattice girders were determined from the numerical results to compare the supporting performance of lattice girder. In case of 50-type, the yield strengths of high-performance lattice girders were increased by 6.7~10.0% compared with those of the existing lattice girders. In the case of 70-type, the high-performance lattice girders increased yield strengths by 12.1~14.9% than the existing lattice girder. In the case of 95-type, the high-performance lattice girders increased yield strengths by 13.3~20.0% than the existing lattice girder. As a result of numerical analysis, it was considered that the high-performance lattice girder supported better than the existing lattice girder when only the lattice girders were constructed.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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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.

• Journal of Korean Association for Spatial Structures
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• v.18 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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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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• v.12 no.1_2
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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?