• 대한수학회보
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• 제61권1호
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• pp.29-44
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• 2024

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.67-77
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• 1999

For a orientation-shift model supported on the unit sphere, Euler angles are the conventional measure to parametrize orientation-shifts. The essential role which is played by rotationally symmetry of an underlying distribution is reviewed. In this paper we propose the inference procedure based on Euler angles for the rotationally symmetric spherical distribution. The likelihood ratio test(LRT) based on the Euler angles is worked out. The asymptotic distribution of the test under the null hypotheses and certain contiguous alternatives is obtained.

• 한국광학회지
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• 제1권2호
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• pp.217-222
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• 1990

A general ray tracing scheme has been developed for using a personal computer which trace finite rays through any non-rotationally symmetric system. This scheme may be used for the surface type such as conic section with or without aspherics, toric surfaces, sagittal and tangential cylindrical sections and axicons. Specially, any combinational of decentered, tilted and rotated surfaces has been considered. Before transfering to the next surfaces, the local coordinates are refered back to an initial reference coordinate system. We can get a mathmtical model of a non-rotationally symmetrical finite ray trace running on an inexpensive personal computer.

• 대한수학회보
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• 제48권2호
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• pp.335-342
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• 2011

In this paper, we prove that minimal hypersurfaces when n $\geq$ 3 and nonzero constant mean curvature hypersurfaces when n $\geq$ 2 foliated by spheres in parallel horizontal hyperplanes in $\mathbb{H}^n{\times}\mathbb{R}$ must be rotationally symmetric.

• 대한수학회보
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• 제58권1호
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• pp.21-30
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• 2021

In this paper, we prove some rigidity results about embedded minimal hypersurface M ⊂ ℝn+1 with compact ∂M that has one end which is regular at infinity. We first show that if M ⊂ ℝn+1 meets a hyperplane in a constant angle ≥ ��/2, then M is part of an n-dimensional catenoid. We show that if M meets a sphere in a constant angle and ∂M lies in a hemisphere determined by the hyperplane through the center of the sphere and perpendicular to the limit normal vector nM of the end, then M is part of either a hyperplane or an n-dimensional catenoid. We also show that if M is tangent to a C2 convex hypersurface S, which is symmetric about a hyperplane P and nM is parallel to P, then M is also symmetric about P. In special, if S is rotationally symmetric about the xn+1-axis and nM = en+1, then M is also rotationally symmetric about the xn+1-axis.

• 한국정밀공학회지
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• 제6권4호
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• pp.84-93
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• 1989

This paper describes some development of Computer-Aided Process Planning System for cold-forging of rotationally symmetric parts(soild shape and solid-can combined shape) produced by the presses or formers. Using the developed system, forming sequences for producing final product are generated as graphic forms and process names, preform dimensions and process parameters(load, punch pressure, die pressure) are generated as routing sheets. Konwledges for forming sequence and process parameters are extracted from process limitations, plasticity theories, handbooks, relevent refferences and empirical know-how of experts in cold forging companies. Among extracted knowldeges, general and consistent knowledges are represented as design rules and are constructed as knowledge base. The developed system provides more powerful tool for through checking the producibilities of design, conformation of appropriate forming sequences and discoveries of new possibility. The results of the developed system are in good agreement with the practical data.

• 한국정밀공학회지
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• 제7권2호
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• pp.95-104
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• 1990

This paper descirbes some research of Computer-aided Design of multi-stage cold forging die of rotationally symmetric parts produced by the press or former. An approach to the system is based on knowledge based system. Knowledges for tool design are extracted from the plasticity theory, handbooks, relevent references and empirical know-how of experts in cold forging companies. The deveoped system is composed of three main modules such as die design module, punch design module, tool elements design module which are sued independently or in all. Using this system, design parameters (types of dies, geometric shapes and dimensions of dies, types of punches, geometric shapes and dimensions of punches, geometric shapes and dimensions of tool elements) in each operation are determined and the output is generated in graphic form. The develpoed system, aids designer, provides powerful capability for designing dies, punches and tool elements.

• 대한수학회보
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• 제61권2호
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• pp.511-517
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• 2024

Let (M, p) denote a noncompact manifold M together with arbitrary basepoint p. In [7], Kondo-Tanaka show that (M, p) can be compared with a rotationally symmetric plane M_m in such a way that if M_m satisfies certain conditions, then M is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of M_m with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when M_m satisfies certain conditions, then M is homeomorphic to ℝⁿ.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 춘계 학술대회논문집
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• pp.45-50
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• 2000

We study a conceptual numerical model on shock-vortex interaction setting an impulsive shock in a compressible vertex. Navier-Stokes equations are solved for the investigation of interactive structure and acoustic wave propagation. The rotationally symmetric vortex enforces two compression-expansion pairs resultantly forming a quadrupolar shape. These compressive and expansive waves cylindrically propagate to the far field and turn to acoustic waves. Using a fine uniform Cartesian grid system and a TVD-high resolution method, the flow data irl: precisely obtained to extend our interest to the sound source.

• 충청수학회지
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• 제34권4호
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• pp.387-395
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• 2021

In this paper, we give a characterization of a Delaunay surface in ℝ³. Let Σ be a CMC-H surface in ℝ³ with H ≠ 0. If Σ meets a plane with constant contact angle along a circle, then it is rotationally symmetric, i.e., Σ is part of a Delaunay surface.