• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

• Journal of the Korea institute for structural maintenance and inspection
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• v.27 no.1
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• pp.95-102
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• 2023

This study investigated the structural performance of wire-integrated steel decks with varied lattice end support conditions through finite element analysis. The results indicated that the steel decks with the lattice foots positioned above the supporting structural member have the higher system stiffness compared to the cases with the lattice foots shifted away from the support. It is also observed that the contribution of the end vertical bars on both the system stiffness and the strength is negligible when the lattice foots are located on the support. It is, especially, revealed that the end vertical bars can be eliminated when the lattice foot length is not smaller than 40mm. The ultimate load-carrying capacity of the system is not significantly affected by the lattice end support condition. The failure mode of the system is the top bar buckling at the center of the deck plate, the lattice end buckling, and the combination of both depending of design intention.

• Architectural research
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• v.10 no.1
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• pp.25-32
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• 2008

Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method to study parametrical instability of lattice dome structures, which is subjected to harmonically pulsating load. We consider elastic stiffness and geometrical stiffness simultaneously during the calculation of stiffness matrix, and adopt consistent mass matrix to make the solution more correct. In order to obtain instability regions, we represent displacements and accelerations in dynamic equation by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability regions eventually. Finally, we take 24-bar star dome and 90-bar lamella dome as examples to investigate dynamic instability phenomena.

• 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.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.55-60
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• 2007

Given operators X and Y acting on a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we showed the following : Let $\cal{L}$ be a subspace lattice acting on a Hilbert space $\cal{H}$ and let X and Y be operators in $\cal{B}(\cal{H})$. Let P be the projection onto $\bar{rangeX}$. If FE = EF for every $E\in\cal{L}$, then the following are equivalent: (1) $sup\{{{\parallel}E^{\perp}Yf\parallel\atop \parallel{E}^{\perp}Xf\parallel}\;:\;f{\in}\cal{H},\;E\in\cal{L}\}\$ < $\infty$, $\bar{range\;Y}\subset\bar{range\;X}$, and < Xf, Yg >=< Yf,Xg > for any f and g in $\cal{H}$. (2) There exists a self-adjoint operator A in Alg$\cal{L}$ such that AX = Y.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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• pp.17-20
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• 2006

A flat plate-column connection is susceptible to brittle punching shear failure, which may result in the necessity of shear reinforcement. In previous, experimental tests were performed to study the capacity of slab-column connections strengthened with various shear reinforcement, and the capacity of the specimens with lattice reinforcement are superior to the others. In present study, to study for effects of details of lattice reinforcement, experimental studies was performed. Main parameters are the amount of lattice shear reinforcement, arrangement of lattice and the effect of flexural re-bar. And capacity of the specimen with small amount of lattice reinforcement was higher than the capacity of other shear reinforcement.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.26-29
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• 2006

A flat plate-column connection is susceptible to brittle punching shear failure, which may result in the necessity of shear reinforcement. In present study, experimental tests were performed to study the capacity of slab-column connections strengthened with lattice, stud rail, shear band and stirrup under gravity and cyclic lateral load. Among them, the capacity of the specimens with lattice are superior to the others due to the truss action of the lattice bars and dowel action of the longitudinal bars as well as the shear resistance of the web re-bar. On the other hand, the strengths of the specimens with stud rail, shear band and stirrup are lower than the estimated strength by the ACI, therefore design formulas of the ACI are needed to revise.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.161-166
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• 2007

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for i = 1,2,...,n. In this article, we showed the following: Let L, be a subspace lattice on a Hilbert space H and let X and Y be operators in B(H). Then the following are equivalent: (1) $$sup\{\frac{{\parallel}E^{\bot}Yf{\parallel}}{{\overline}{\parallel}E^{\bot}Xf{\parallel}}\;:\;f{\epsilon}H,\;E{\epsilon}L}\}\;<\;{\infty},\;sup\{\frac{{\parallel}Xf{\parallel}}{{\overline}{\parallel}Yf{\parallel}}\;:\;f{\epsilon}H\}\;<\;{\infty}$$ and $\bar{range\;X}=H=\bar{range\;Y}$. (2) There exists an invertible operator A in AlgL such that AX=Y.

• Journal of the Korea Concrete Institute
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• v.23 no.5
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• pp.657-665
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• 2011

LB-DECK, a precast concrete panel type, is a permanent concrete deck form used as a formwork for cast-in-place concrete pouring at bridge construction site. LB-DECK consists of 60 mm thick concrete slab and 125 mm height Lattice-girders partly embedded in the concrete slab. These decks have been applied to the bridges, which girder spacings are short enough to resist longitudinal cracking caused by construction loads. This paper presents experimental research work conducted to evaluate the cracking load of LB-DECKs designed for long span bridge decks. Twenty four non-composite beams and four composite beams are fabricated considering three design variables of thickness of concrete slab, height of lattice-girder, and diameter of top-bar. Static loads controlled by displacements are applied to test beams to obtain cracking and ultimate loads. Vertical displacements at the center of beams, strains of top-bar, crack propagation in concrete slab, and final failure modes are carefully monitored. The obtained cracking loads are compared to the analytical results obtained by elastic analyses. Long-term analyses using age-adjusted effective modulus method (AEMM) are also conducted to investigate the effects of concrete shrinkage on the cracking loads. Based on the test results, the tensile strength and the design details of LB-DECKs are discussed to prevent longitudinal cracking of long span bridge decks.

• Journal of the Korea institute for structural maintenance and inspection
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• v.17 no.5
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• pp.21-30
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• 2013

LB-Deck is one of the widely used member in interior part of girders as a permanent formwork in structures, but it is not easy to apply to the exterior part of girder due to the overturning and excessive deflection. Considering allowable deflection and safety of the exterior part, Precast Concrete Cantilever Deck (PCC-Deck) is proposed with normal LB-Deck in inner part and extended bars of LB-Deck in outer part. Both numerical analyses and experimental tests were compared to check the safety and allowable deflection for 6 types of PCC-Deck, and D-type (with 16 mm top bar, 6 mm lattice bar, 12 mm bottom bar) is suggested as an optimal structural reinforcement to the 28 kN of maximum load and 27.49 mm of final deflection. The load resisting ratio of D-type under working load of 10 kN was about 2.8 times and 77.5% of improvement was observed.