• Journal of Korean Society of Steel Construction
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• v.19 no.1
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• pp.129-137
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• 2007

In this study, the elastic out-of-plane buckling load and the effective length factor of X-bracing systems were studied. Points of the intersection of diagonals were modeled as a rigid connection or a pinned connection depending on the connection method of diagonals. The boundary condition of the intersection influences the buckling load of X-bracing systems. For each boundary condition of the intersection, effective out-of-plane length factors of X-bracing systems were derived as a function of the length ratio of tension and compression diagonals $L_P$/$L_T$, the applied force ratio of tension and compression diagonals T/P, and the Euler buckling load ratio of tension and compression diagonals $P_{ET}$/$P_{EP}$. The proposed effective out-of-plane length factors of X-bracing systems were compared with the results of previous researchers and those of the finite element analysis and their properties were verified. Finally, the effects of the boundary condition of the intersection on the out-of-plane buckling load of X-bracing systems were investigated.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.127-136
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• 2017

For a quadrangle P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. If $G_0$ is equal to $G_1$ or $G_2$, then the quadrangle P is a parallelogram. We denote by M the intersection point of two diagonals of P. In this note, first of all, we show that if M is equal to $G_0$ or $G_2$, then the quadrangle P is a parallelogram. Next, we investigate various quadrangles whose perimeter centroid coincides with the intersection point M of diagonals. As a result, for an example, we show that among circumscribed quadrangles rhombi are the only ones whose perimeter centroid coincides with the intersection point M of diagonals.

• Honam Mathematical Journal
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• v.11 no.1
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• pp.15-19
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• 1989

A conjecture of E. T. H. Wang asserts that if every diagonal disjoint from m mutually disjoint zero diagonals of $A{\in}{\Omega}_n$ has a constant sum, then all entries off the m zero diagonals are equal to l/(n-m). E. T. H. Wang proved the conjecture for m=0, 1, n-2 and n-1. In the present paper, it is proved that the conjecture holds true for m=2.

• International Journal of High-Rise Buildings
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• v.12 no.4
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• pp.307-320
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• 2023

Tall buildings are built with an abundant amount of materials, including structural materials, coming from our limited natural resources. Tall buildings that began from about 10-story tall office towers have evolved to over 150-story tall mixed-use megastructures. As a building becomes taller, structural material requirement to resist lateral wind loads becomes exponentially larger. Therefore, it is crucial to employ efficient structural systems and optimize their design, which will contribute to sustainable vertical built environments through preservation of resources. Tube type structures with large perimeter diagonals are among the most efficient structural systems for tall buildings. Developments of braced tube, braced megatube, diagrid structures, and their optimal design strategies are reviewed. Superframed conjoined towers, produced by interconnecting multiple clustered braced tubes, are presented as a new design direction to achieve not only structural but also architectural and social sustainable design goals.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.1-19
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• 2024

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product ${\mathbb{K}}{\hat{\bigotimes}}{\mathbb{H}}$ via χ ⊗ η-σwc virtual diagonals, where χ ∈ 𝕂_* and η ∈ ℍ_* are linear functionals on dual Banach algebras 𝕂 and ℍ, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of 𝕂 ×_θ ℍ. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras 𝕂 ⊕ 𝕏, where 𝕏 is a normal Banach 𝕂-bimodule.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.35-38
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• 1996

The aim of this paper is to present a characterization of Hilbert spaces in terms of the lengths of four sides and two diagonals of a parallelogram.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.285-303
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• 2013

The asymptotic expansions of the Bergman kernels on the diagonals near the boundary points of exponentially-flat infinite type for pseudoconvex tube domain in $\mathbb{C}^2$ are obtained.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.723-734
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• 2019

We study the negative trinomial table T' of $(x^2+x+1)^{-n}$ and its t/u-slope diagonals for any t, u > 0. We investigate recurrence formula of the t/u-slope diagonal sums of T' and find interrelationships with t/u-slope diagonal sums of the trinomial table T.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.561-573
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• 2023

In this paper, we extend the medial triangle theorem and Varignon's theorem to generic two-dimensional polygons and highlight the role played by diagonals in this process. One of the results is a synthetic definition of the concept of median for an n-sided polygon.

• The KIPS Transactions:PartA
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• v.15A no.5
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• pp.295-300
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• 2008

In this paper, we consider a characterization of a Guard Sufficiency Set(GSS) in the hierarchy of simple polygons. we propose the diagonals of a arbitrary triangulation of a polygon as a GSS when guards see the diagonals with completely visibility and both sides of the diagonal. we show that this can be a GSS in convex polygons, unimodal polygons, spiral polygons but this can not be a GSS in star-shaped polygons, monotone polygons, completely external visible polygons.