• Journal of the Korean Electrochemical Society
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• v.4 no.1
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• pp.21-25
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• 2001

This article is concerned with the application of the fractal geometry to interfacial electrochemistry. Especially, we dealt with diffusion kinetics at the fractal electrodes. This article first explained the basic concepts of the Sacral geometry which has proven to be fruitful for modelling rough and irregular surfaces. Finally this article examined the electrochemical responses to various signals under diffusion-limited reactions during diffusion towards the fractal interfaces: The generalised forms, including the fractal dimension of the electrode surfaces, of Cottrell, Sand and Randles-Sevcik equations were theoretically derived and explained in chronoamperomety, chronopotentiometry and linear sweep/cyclic voltammetry, respectively.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.1
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• pp.124-129
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• 2010

When a phenolic resin is carbonized by the leakage current flowing along its surface, the carbonization pattern is one of the most important factors to determine its carbonization characteristics. However, the typical carbonization pattern of a phenolic resin is too complicated to be analyzed by conventional Euclidean geometry. In most cases, such a complicated shape shows a fractal structure. It is possible, therefore, to examine the characteristics of the carbonization pattern regarding a given phenolic resin. In order to quantitatively investigate the carbonization pattern of the phenolic resin carbonized by a leakage current, in this paper, the fractal dimension of the carbonization pattern has been calculated as a function of the magnitude of a leakage current and the distance between two electrodes. For reliability of calculation, the correlation function as well as the box counting method has been used to calculate the fractal dimension. According to the result of calculation, the fractal dimension increases as the current increases at the constant electrode gap distance. However, there is no significant relation between the fractal dimension and the electrode gap distance at a constant current.

• Journal of the Korean Society of Costume
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• v.60 no.5
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• pp.117-127
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• 2010

In this study, hyperspace is a result of imagination created by means of facts and fiction, represents a transfer to determination and indetermination, and means an extension to an open form. In other words, hyperspace is a high dimensional space expanded to imagination through the combination of the viewpoint on facts in this dimension and fiction. When the 2D plane surface or 3D symmetry is destroyed, or when the frame is twisted or entangled, the non-Euclidean geometry is created eventually. And when the twisting leads to transmutation and the destruction of the form reaches the extreme; this in turn became the twisting like Mbius band. Likewise, the non-Euclidean geometry is co-related to the asymmetry of the Higgs mechanism. When the 'destruction of symmetry' is considered, symmetric theory and asymmetric world can be connected. The asymmetry in turn can maintain balance by arranging the uneven weights at different distances from the shaft. Moreover, at this the concept of the upper, lower, left and right, which was included in the original form, may be crumbled down. The destruction of the symmetry is essential in order to present forecast that coincides with the phenomenon of the real world. Non-Euclidean geometry characteristic is expressed by asymmetry, twists, and deconstruction and its representative characteristic is ambiguity. The boundary between the front, back, upper, lower, inner and outer is unclear, and it is difficult and vague to pinpoint specific location. The design that does not clearly define or determine the direction of wearing costume is indeed the non-oriented design that can be worn without getting restricted by specific direction such as front and back. Non-Euclidean geometry characteristic of hyperspace have been applied to create new shapes through the modification of the substance from traditional clothing of the eastern world to modern fashion. The way of thinking in the 'hyperspace' that used to be expressed in the costumes of the east and the west in the past became the forum for unlimited creation.

• Structural Engineering and Mechanics
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• v.82 no.1
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• pp.1-16
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• 2022

This work elaborately investigates the influences of the guideway geometry parameters and track irregularity on the dynamic performances of the suspended monorail vehicle-guideway system (SMVGS). Firstly, a spatial dynamic analysis model of the SMVGS is established by adopting ANSYS parameter design language. Then, the dynamic interaction between a vehicle with maximum design load and guideway is investigated by numerical simulation and field tests, revealing the vehicle-guideway dynamic features. Subsequently, the influences of the guideway geometry parameters and track irregularity on the dynamic performances of the SMVGS are analyzed and discussed in detail, and the reasonable ranges of several key geometry parameters of the guideway are also obtained. Results show that the vehicle-guideway dynamic responses change nonlinearly with an increase of the guideway span, and especially the guideway dynamic performances can be effectively improved by reducing the guideway span; based on a comprehensive consideration of all performance indices of the SMVGS, the deflection-span ratio of the suspended monorail guideway is finally recommended to be 1/1054~1/868. The train load could cause a large bending deformation of the pier, which would intensify the car-body lateral displacement and decrease the vehicle riding comfort; to well limit the bending deformation of the pier, its cross-section dimension is suggested to be more than 0.8 m×0.8 m. The addition of the track irregularity amplitude has small influences on the displacements and stress of the guideway; however, it would significantly increase the vehicle-guideway vibrations and rate of load reduction of the driving tyre.

• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.71-78
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• 1998

Real crack and fracture surfaces have irregularities producing zigzag contours. These irregularities are analysed by a fractal geometry which has been by a Mandelbrot. We obtained a fractal dimension which is one of the fractal characteristics. It is also estimated by an vertical section method that fractal characteristics in the fractured surfaces can be obtained as the crack grows. Moreover fractal fracture energy that corresponds to an energy release rate is shown to find relationships between fractal dimensions and crack behaviors. From these results, we concluded that a fractal characteristics analysis for a crack can be applied to a fracture mechanics.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.196-200
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• 1996

In general, cylinderical types of billet are use in the backward extrusion. It is difficult to obtain homogenious wall thickness by the backward extrusion using these. It is gradually increased that improving the accuracyand reducing the post machining of the final products. In manufacturing cup shaped parts by backward extrusion, it is very important to design optimal initial billet or preform. These can improve the accuracy of final products and remove the post machining processes. In this study, the influence of final parts geometry by the shape of initial billet as non machined types are discussed.

• Proceedings of the IEEK Conference
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• 2001.06b
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• pp.329-332
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• 2001

This paper proposes a capacitance extraction algorithm based on boundary element method and describes the implemented 2-dimension extractor based on the proposed algorithm. The proposed algorithm uses a generalized conjugate residual iterative algorithm with a hierarchical subdivision. The implemented 2-D extractor computes the capacitances of complicated 2-D geometry of ideal conductors in uniform dielectric and can be efficiently used in the VLSI layout designs due to its user-friendly GUI.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.329-342
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• 2002

We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.

• Journal for History of Mathematics
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• v.31 no.1
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• pp.1-17
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• 2018

In this expository paper, we present an abridged report on the max-plus eigenspaces of max-plus matrices with its brief history. At the end of our work, a number of examples are presented with maple codes, and then we make a claim from the observation of these examples, which is on the euclidean dimension of the max-plus eigenspaces of strongly definite matrices.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.149-160
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• 2024

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature.