• 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.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.247-258
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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. It is well known that P satisfies $G_0=G_1$ or $G_0=G_2$ if and only if it is a parallelogram. In this note, we investigate various quadrilaterals satisfying $G_1=G_2$. As a result, for example, we show that among circumscribed quadrilaterals kites are the only ones satisfying $G_1=G_2$. Furthermore, such kites are completely classified.

• Journal of Korean Association for Spatial Structures
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• v.6 no.3 s.21
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• pp.87-92
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• 2006

This paper is a study on the experiment and elasto-plastic discrete limit analysis of reinforced concrete circular cylindrical shell by the rigid-bodies spring model. In the rigid bodies-spring model, each collapsed part or piece of structures at the limiting state of loading is assumed to behave like rigid bodies. The present author propose new discrete elements for elasto-plastic analysis of cylindrical shell structures, that is, a rectangular-shaped cylindrical element and a rhombus-shaped cylindrical element for the improvement and expansion of this rigid-bodies spring model. In this study, it is proposed how this rigid element-bodies spring model can be applied to the elasto-plastic discrete limit analysis of cylindrical shell structures. Some numerical results of elasto-plastic discrete limit analysis and experimental results such as the curve of load-displacement and the yielding and fracturing pattern of circular cylindrical shell under horizontal load are shown.

• Journal of Korean Association for Spatial Structures
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• v.16 no.4
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• pp.67-73
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• 2016

This paper is a study on Development of polyhedral surfaces Quasicrystal System. Quasicrystal is the quasi-crystalline material, which is the intermediate material of the crystalline material and non-crystalline material. Quasicrystal is a structures that is ordered but not periodic, the basic form is a rhombus. These studies in the field of chemistry will proceed actively studied, in the field of construction a situation that still insufficient research. Therefore, in this paper, we presents the analysis of Quasicrystal system, and the research on the applicability of as dome structures. This paper described some examples of polyhedron form, and method of applying Quasicrystal system.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.5
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• pp.186-193
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• 1999

In this paper, a full vehicle model is developed to analyze toe and camber changes due to rack height variation and compliance. The AutoDyn7 program developed in G7 project is used for the computer simulation. Steady state cornering test was done to find the understeer gradient. Imposing a pulse steer input, Frequency Response Function(FRF) of yaw rate and lateral accelerations were evaluated. To verify the stability, the rhombus using four parameters is employed. Steer characteristics were evaluated by changing the rack height and the bushing lateral stiffiness. which installed between the low control arm and the chassis.

• 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.

• Journal of Environmental Science International
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• v.16 no.3
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• pp.255-260
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• 2007

The photocatalytic decolorization of Rhodamine B (RhB) was studied using packed-bed reactor and immobilized $TiO_2/UV$ System. The 20 W UV-A, UV-B and UV-C lamps were employed as the light source. The effect of shape and surface polishing extent of reflector, distance between the reactor and reflector, reactor material were investigated. The results showed that the order of the initial reaction constant with reflector shape was round > polygon > W > rhombus. The optimum distance between the reactor and reflector was 2 cm. The initial reaction constant of quartz reactor was 1.46 times higher than that of tile PVDF reactor.

• Journal of Navigation and Port Research
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• v.26 no.2
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• pp.209-213
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• 2002

MRA(Multi-resolution analysis) algorithm by Wavelet and morphology with $3{\times}3$ SQ(square) SE(structure element) is efficient to remove ship's radar clutter progressively and enhances detecting performance. Smoothing efficiency of RMM (Recursive mathematical Morphology) is better than that of Morphology. So, to get a better result than that of old algorithms, this paper proposes a new MRA algorithm which uses Wavelet and Recursive mathematical Morphology with $3{\times}3$ RHR(rhombus) SE. Simulation result of the proposed algorithm shows that PSNR is 0.65~1.50db better than that of old method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.12
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• pp.3100-3116
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• 2012

Reversible data hiding enables the embedding of messages in a host image without any loss of host content, which is proposed for image authentication that if the watermarked image is deemed authentic, we can revert it to the exact copy of the original image before the embedding occurred. In this paper, we present an improved histogram-based reversible data hiding scheme based on prediction and sorting. A rhombus prediction is employed to explore the prediction for histogram-based embedding. Sorting the prediction has a good influence on increasing the embedding capacity. Characteristics of the pixel difference are used to achieve large hiding capacity while keeping low distortion. The proposed scheme exploits a two-stage embedding strategy to solve the problem about communicating peak points. We also present a histogram shifting technique to prevent overflow and underflow. Performance comparisons with other existing reversible data hiding schemes are provided to demonstrate the superiority of the proposed scheme.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.469-480
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• 2019

A generalized tiling is defined as a generalization of the properties of tiling a region of ${\mathbb{Z}}^2$ with dominoes, and comprises tiling with rhombus and any other tilings that admits height functions which can be ordered into a distributive lattice. By using properties of the distributive lattice, we prove that the Markov chain consisting of moving from one height function to the next by a flip is fast mixing and the mixing time ${\tau}({\epsilon})$ is given by ${\tau}({\epsilon}){\leq}(kmn)^3(mn\;{\ln}\;k+{\ln}\;{\epsilon}^{-1})$, where mn is the area of the grid ${\Gamma}$ that is a k-regular polycell. This result generalizes the result of the authors (T-tetromino tiling Markov chain is fast mixing, Theor. Comp. Sci. (2018)) and improves on the mixing time obtained by using coupling arguments by N. Destainville and by M. Luby, D. Randall, A. Sinclair.