• 대한수학회보
• /
• 제53권1호
• /
• pp.227-245
• /
• 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.

• 한국전산유체공학회지
• /
• 제4권2호
• /
• pp.31-38
• /
• 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
• /
• 제24권6호
• /
• pp.641-649
• /
• 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.

• 한국소음진동공학회논문집
• /
• 제22권10호
• /
• pp.917-924
• /
• 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.

• 한국멀티미디어학회논문지
• /
• 제5권5호
• /
• pp.552-561
• /
• 2002

본 논문은 쾌속조형(rapid prototyping) 시스템에서 사용되며 3D 기하학적 형상을 가지는 STL 파일에 워터마크를 삽입하고 추출하는 방법에 관한 연구이다. 제안된 알고리즘은 3D 형상의 왜곡이 없도록 하기위해, 패싯의 법선 영역과 꼭지점 영역에 워터마크를 삽입한다. 워터마크 비트들은 법선의 위치와 꼭지점의 순서 정보를 이용하여 삽입된다 제안된 알고리즘은 패싯의 저장 순서에 대한 종속성이 없으며, 워터마크의 비가시성 (invisibility)을 충족한다. 제안된 알고리즘으로 3D 기하학적 형상에 워터마크를 삽입하고 추출하는 실험 결과들은 STL로 표현된 3D원형상에 영향을 주지 않고 워터마크의 삽입과 추출이 가능함을 보여준다.

• Korean Journal of Mathematics
• /
• 제32권2호
• /
• pp.259-284
• /
• 2024

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

• The Korean Journal of Ecology
• /
• 제8권2호
• /
• pp.99-107
• /
• 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.

• 한국정밀공학회지
• /
• 제11권2호
• /
• pp.50-64
• /
• 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.

• 대한수학회지
• /
• 제54권4호
• /
• pp.1331-1343
• /
• 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.

• 한국분무공학회지
• /
• 제18권4호
• /
• pp.209-214
• /
• 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.