• Communications of Mathematical Education
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• v.32 no.3
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• pp.257-273
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• 2018

In this paper, we deal with the isoprimetric problem of polygons from the point of view of learning materials for elementary gifted students. The isoperimetric problem of the polygon of odd degree can be solved by E-transformation(see Figure III-1) and M-transformation(see Figure III-3). But in the case of even degree's polygon, it is quite difficult to solve the problem because of the connected components of diagonals (here we consider the diagonals forming triangle with two adjacent sides of polygon). The primary purpose of this paper is to give an idea to solve the isoperimetric problem of polygons of even degree using the properties of ellipse. This idea is derived from the programs of the Institute of Science Education for Gifted Students in the Jeju National University.

• Steel and Composite Structures
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• v.52 no.1
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• pp.77-87
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• 2024

Analytical methods for assessment of the out-of-plane buckling of unbraced top chords of truss bridges may look obsolete while comparing them to finite element analysis. However they are, usually, superior when rapid assessment is necessary. Analytical methods consider the top chord as a bar on elastic supports provided by bracing (Holt, Timoshenko). Correct assessment of the support elasticity (stiffness) is crucial. In the case of truss bridge spans of traditional structural layout (cross-beams at the truss chord nodes only), the elasticity may be set based on the analysis of the, so called, U-frame stiffness. Here the analyses consider the U-frame itself (a pair of verticals and a cross-beam) or the U-frame with adjacent diagonals or the pair of diagonals (in the absence of verticals) and the members of the bottom chord in the adjacent panels. For all the cases, the stability analysis of the chord as a bar in compression is necessary. Unfortunately, the method cannot be applied to contemporary truss bridges without verticals, that usually have independent cross-beam decks (the cross-beams attached to truss chords at their nodes and between them). This is the motivation for the analysis resulting in the method of setting the stiffness of the equivalent U-frame for the aforementioned truss bridges. Truss girders of both, gussetless and gusseted, joints are taken into account.

• International Journal of High-Rise Buildings
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• v.5 no.4
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• pp.263-270
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• 2016

In this paper, the stability requirements for diagrid and mega braced structures are examined. The role of the secondary bracing system for the stability of a diagrid structure is discussed. A simple procedure is proposed for the design of the secondary bracing system when it is required. As a case study, the design of the Hearst Tower diagrid and its secondary bracing system are presented.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.1-11
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• 2024

In this paper, we introduce the notion of 𝜎-Jordan amenability of Banach algebras and some hereditary are investigated. Similar to Johnson's classic result, we give the notions of 𝜎-Jordan approximate and 𝜎-Jordan virtual diagonals, and find some relations between the existence of them and 𝜎-Jordan amenability.

• Earthquakes and Structures
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• v.8 no.5
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• pp.1215-1240
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• 2015

In this paper, the Theory of Plastic Mechanism Control (TPMC) is applied to the seismic design of dual systems composed by moment-resisting frames and Chevron braced frames. The application of TPMC is aimed at the design of dual systems able to guarantee, under seismic horizontal forces, the development of a collapse mechanism of global type. This design goal is of primary importance in seismic design of structures, because partial failure modes and soft-storey mechanisms have to be absolutely prevented due to the worsening of the energy dissipation capacity of structures and the resulting increase of the probability of failure during severe ground motions. With reference to the examined structural typology, diagonal and beam sections are assumed to be known quantities, because they are, respectively, designed to withstand the whole seismic actions and to withstand vertical loads and the net downward force resulting from the unbalanced axial forces acting in the diagonals. Conversely column sections are designed to assure the yielding of all the beam ends of moment-frames and the yielding and the buckling of tensile and compressed diagonals of the V-Braced part, respectively. In this work, a detailed designed example dealing with the application of TPMC to moment frame-chevron brace dual systems is provided with reference to an eight storey scheme and the design procedure is validated by means of non-linear static analyses aimed to check the actual pattern of yielding. The results of push-over analyses are compared with those obtained for the dual system designed according to Eurocode 8 provisions.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.431-442
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• 2017

For a quadrilateral 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. We denote by M the intersection point of two diagonals of P. If P is a parallelogram, then we have $G_0=G_1=G_2=M$. Conversely, one of $G_0=M$ and $G_2=M$ implies that P is a parallelogram. In this paper, we show that $G_1=M$ is also a characteristic property of parallelograms.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.135-145
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• 2017

For a polygon P, we consider the centroid $G_0$ of the vertices of P, the centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P. When P is a triangle, (1) we always have $G_0=G_2$ and (2) P satisfies $G_1=G_2$ if and only if it is equilateral. For a quadrangle P, one of $G_0=G_2$ and $G_0=G_1$ implies that P is a parallelogram. In this paper, we investigate the relationships between centroids of quadrangles. As a result, we establish some characterizations for rhombi and show that among convex quadrangles whose two diagonals are perpendicular to each other, rhombi and kites are the only ones satisfying $G_1=G_2$. Furthermore, we completely classify such quadrangles.

• International Journal of High-Rise Buildings
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• v.7 no.3
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• pp.215-221
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• 2018

Buckling-Restrained Braces (BRBs) have been widely applied to tall buildings in seismic areas in the world. In this paper the author summarizes representative types of BRB compositions and shows two cases of special applications of BRBs. In the first case, BRB diagonals for tall building were used to provide stable cyclic nonlinear hysteresis and also used to limit forces generated at columns, connections and walls. The top outriggers are pre-loaded by jacks to resolve long-term differential shortenings between the concrete core wall and concrete-filled steel box columns. The second case is the retrofit work for a communication tower by replacing the insufficiently strong members with BRBs in Japan.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.703-722
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• 2013

In this paper a study about concrete arch bridges built by lattice cantilevers is presented. Lattice cantilevers are partial structures composed of deck, arch, piers and provisional steel diagonals, organized as reticular cantilever girders, in order to build arch bridges without the use of centrings, supports or temporary towers. Characteristics of this construction methodology with its variants are explained together with their implications in the erection sequence. Partial elastic scheme method is implemented in order to find initial forces of temporary cables and a forward analysis is carried out to follow the actual sequence of construction, by extending a procedure already applied to concrete cable-stayed bridges and to arches built by the classical suspended cantilever method. A numerical application on a case-study of a concrete arch bridge is performed together with a comparison between different methodologies followed for its construction sequence. Differences between erection by lattice cantilevers and cable-stayed cantilevers, are discussed. Results can be useful for designers in conceptual design of concrete arch bridges.

• ETRI Journal
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• v.36 no.4
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• pp.545-553
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• 2014

This paper proposes an algorithm to sense orthogonal frequency-division multiplexing (OFDM) signals in cognitive radio (CR) systems. The basic idea behind this study is when a primary user is occupying a wireless channel, the covariance matrix is non-diagonal because of the time domain cross-correlation of the cyclic prefix (CP). In light of this property, a new decision metric that measures the power of the data found on two minor diagonals in the covariance matrix related to the CP is introduced. The impact of synchronization errors on the signal detection is analyzed. Besides this, a likelihood-ratio test is proposed according to the Neyman-Pearson criterion after deriving probability distribution functions of the decision metric under hypotheses of signal presence and absence. A threshold, subject to the requirement of probability of false alarm, is derived; also the probabilities of detection and false alarm are computed accordingly. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed algorithm.