• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.227-245
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• 2016

A generalized constant ratio surface (GCR surface) is defined by the property that the tangential component of the position vector is a principal direction at each point on the surface, see [8] for details. In this paper, by solving some differential equations, a complete classification of Lorentz GCR surfaces in the three-dimensional Minkowski space is presented. Moreover, it turns out that a flat Lorentz GCR surface is an open part of a cylinder, apart from a plane and a CMC Lorentz GCR surface is a surface of revolution.

• Journal of computational fluids engineering
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• v.4 no.2
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• pp.31-38
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• 1999

Numerical analysis is conducted on the deformation of free surface of magnetic fluid. Steady magnetic fields are induced by a circular current loop. Governing equations of magnetic fields are solved by using the concept of vector potential. The free surface of magnetic fluid is formed by the balance of surface force, gravity, pressure difference, magnetic normal pressure and magnetic body force. The deformations of free surface of magnetic fluid are qualitatively clarified. And, the patterns of steady non-uniform magnetic fields induced by a circular current loop are quantitatively presented. The shape of free surface attained by the polar fluid approach is rougher and higher than that attained by the quasi-steady approach.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.641-649
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• 2017

Multivariate confidence regions were defined using a chi-square distribution function under a normal assumption and were represented with ellipse and ellipsoid types of bivariate and trivariate normal distribution functions. In this work, an alternative confidence region using the multivariate quantile vectors is proposed to define the normal distribution as well as any other distributions. These lower and upper bounds could be obtained using quantile vectors, and then the appropriate region between two bounds is referred to as the quantile confidence region. It notes that the upper and lower bounds of the bivariate and trivariate quantile confidence regions are represented as a curve and surface shapes, respectively. The quantile confidence region is obtained for various types of distribution functions that are both symmetric and asymmetric distribution functions. Then, its coverage rate is also calculated and compared. Therefore, we conclude that the quantile confidence region will be useful for the analysis of multivariate data, since it is found to have better coverage rates, even for asymmetric distributions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.10
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• pp.917-924
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• 2012

Noise power of large machineries, such as textile looms, winders, and twisting machines, is often measured in a reverberant space because they cannot be installed and operated in an anechoic chamber due to their size, weight, and operating conditions. Factors affecting the measurement error of an in-situ noise power measurement include the nonuniform reverberation time and the direction of sound intensity vector which is usually regarded as normal to the measurement surface. In this study errors due to these factors are estimated with the aid of numerical simulation based on the ray-tracing technique. The averaging of reverberation times measured at several points on the measurement surface is suggested to reduce the errors from nonuniform absorption. Also the direction cosine of each surface element is taken into account, which as a whole is represented as a solid angle of the measurement surface.

• Journal of Korea Multimedia Society
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• v.5 no.5
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• pp.552-561
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• 2002

In this paper, a new watermarking algorithm for STL files which contains 3D geometric information as triangular facets is proposed. STL files are widely used in rapid prototyping industry as a standard interchange format. The proposed algorithm inserts multi-bit watermark information into the surface normal vector and vertex description area of STL file without distorting the original 3D geometric information. According to the watermark bits, the position of normal vector and the direction of vertex sequence are modulated. The proposed algorithm is robust to the attack of changing the order of the triangular meshes. In addition, the invisibility requirement is also satisfied. Experiment results show that the proposed algorithm can encode and decode watermark bits into the various STL files without any distortion of 3D shape.

• The Korean Journal of Ecology
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• v.8 no.2
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• pp.99-107
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• 1985

Photosynthetically Active Radiation (PAR) affects the growth of plants as well as their photosynthetic rates. A mathematical model for intercepted solar radiation on the tilted leaf with any azimuth angle was established and the leaf orientation in which receives the maximum solar radiation was determined each month, during the growing season, and for an year. PAR was maximized at the leaf elevation of 50。~60。 in the winter, at that of 20。~40。. On the whole the leaves of tilt angle 0。~40。 received much radiation comparing with those of other tilt angles. The theoretical tendencies were compared with the distribution of leaf orientation measused practically. The average leaf elevation of maple tree was 17.0。$\pm$12.0。, and that of ginkgo was 29.8。$\pm$16.0。. Several results from other literatures support our suggestion that cumulative effevct of the relationships between surface normal vector and a vector pointing in the direction of the radiation determine the leaf orientation.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.2
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• pp.50-64
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• 1994

Cutter deflections in the ball-end milling process is one of the main causes of the machining errors on a free-form surface. In order to avoid machining errors in this process, a methodology avoiding these machining errors on the free-form surfaces has been developed. In this method, feedrates in the finish cuts are adjusted for the prevention of machining errors. A model for the prediction of machining errors on the free-form surface is analytically derived as a function of feed and normal vector at the surface of contact point by the cutter. This model is applied to the dertermination of the adjusted feedrates which satisfy the machining tolerance of the surface. In the finish cuts of a simple curved surface, the suggested model is examined by the measurements of the generated machining error on this surface. And also, this surface is machined with the adjusted feedrates for the given machining tolerance. The measured machining errors on this surface are compared with the given tolerance. In this comparisons, it is shown that the predicted errors are fairly good agreement with the test results.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• Journal of ILASS-Korea
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• v.18 no.4
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• pp.209-214
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• 2013

The present study aims to determine the optimized shape for the maximum electric energy production of building integrated photovoltaic system (BIPV) noise barrier through numerical analysis. The shape of BIPV noise barrier is one of the important factors in determining angle difference between direction vector of the sun and normal vector of the sound barrier surface. This study simulated numerically the flow and thermal fields for different angles in the range from $90^{\circ}$ to $180^{\circ}$, and from the results, the amount of isolation onto noise barrier surface was estimated along the angle between ground and top side of noise barrier. The commercial CFD code (Fluent V. 13.0) was used for calculation. It was found that the maximum amount of insolation per unit area was 19.6 MJ for $105^{\circ}$ case during a day in summer and was estimated 12.4 MJ in $150^{\circ}$ case during a day in winter. The results of the summer and winter cases showed the different tendency and this result would be useful in determining the appropriate shape of noise barrier which can be mounted under various circumstances.

• KIEAE Journal
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• v.16 no.1
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• pp.89-94
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• 2016

This study is part of three-dimensional(3D) heat transfer analysis program developmental process. The program is being developed without it's own built in 3D-modeller. So 3D-model must be created from another 3D-modeller such as generic CAD programs and imported to the developed program. After that, according to the 3D-geometric data form imported model, 3D-mesh created for numerical calculation. But the 3D-model created from another 3D-modeller is likely to have errors in it's geometric data such as mismatch of position between vertexes or surfaces. these errors make it difficult to create 3D-mesh for calculation. These errors are must be detected and cured in the pre-process before creating 3D-mesh. So, in this study four kinds of filters and functions are developed and tested. Firstly, 'vertex error filter' is developed for detecting and curing for position data errors between vertexes. Secondly, 'normal vector error filter' is developed for errors of surface's normal vector in 3D-model. Thirdly, 'intersection filter' is developed for extracting and creating intersection surface between adjacent objects. fourthly, 'polygon-line filter' is developed for indicating outlines of object in 3D-model. the developed filters and functions were tested on several shapes of 3D-models. and confirmed applicability. these developed filters and functions will be applied to the developed program and tested and modified continuously for less errors and more accuracy.