• Kyungpook Mathematical Journal
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• 제23권1호
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• pp.85-89
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• 1983

• 한국광학회지
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• 제33권6호
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• pp.275-286
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• 2022

광학설계 과정의 첫 단계에서 근축 광선이 만족하는 Gauss 방정식에 대한 해를 구할 수 있는 재귀적 수치 계산법을 도출하였다. 설계 사양으로 렌즈 모듈의 굴절력, 렌즈 제1 주요면으로의 입사각과 제2 주요면으로부터의 출사각이 주어지면 렌즈의 주요면 사이의 거리를 선택한 후, 재귀적 수치 계산법을 적용하여 렌즈의 두께, 렌즈 앞면의 곡률 반경과 뒷면의 곡률 반경을 구할 수 있다. 즉, 설계 사양을 만족하는 두께가 다른 여러 등가렌즈를 얻을 수 있다. 모듈이 2개 이상의 렌즈로 구성되는 경우에도 렌즈의 개수를 하나씩 증가하면서 렌즈의 주요면 사이의 거리를 설계 사양에 맞추어 선택한 후 각 렌즈의 두께와 곡률 반경을 결정할 수 있다.

• 대한수학회보
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• 제53권1호
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• pp.83-90
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• 2016

We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권1호
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• pp.43-53
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• 2021

We study translation surfaces in the Euclidean 3-space ��3 and the Gauss map N with respect to the so-called Cheng-Yau operator ☐. As a result, we prove that the only translation surfaces with Gauss map N satisfying ☐N = AN for some 3 × 3 matrix A are the flat ones. We also show that the only translation surfaces with Gauss map N satisfying ☐N = AN for some nonzero 3 × 3 matrix A are the cylindrical surfaces.

• 호남수학학술지
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• 제46권2호
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• pp.279-290
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• 2024

In this study, tubular surfaces were introduced according to the modified orthogonal frame defined at the points where the torsion is different from zero in the 3-dimensional Euclidean space. First, the relations between the Frenet frame and the modified orthogonal frame with torsion are given. Then, the singularity, Gaussian curvature, mean curvature and basic forms of the tubular surface given according to the modified orthogonal frame with torsion were calculated. In addition, the conditions for the parameter curves of the tubular surface to be geodesic, asymptotic and line of curvature were examined. Finally, tubular surface examples based on both the Frenet frame and the modified orthogonal frame with torsion were given to support the study.

• 한국해양공학회지
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• 제20권4호
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• pp.24-30
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• 2006

Different methods exist for the estimation of thermaldeformation of plates in the line heating process. These are based on the assumption of residual strains in the heat-affected zone, known as the method of inherent strains, or simulated relations between heating conditions and residual deformations. The purpose of this paper is to develop a simulator of thermal deformation in the line heating, using the artificial neural network. Curvature deformations for the plate-forming are investigated, which can be used as a prime deformation parameter in the process. The curvature of plates are calculated using the approximation of plate surface by NURBS. Line heating experiments for 11 specimens of different thickness and heating conditions were performed. Two neural networks predicting the maximum temperature and curvature deformations at the heating line are studied. It was concluded that the thermal deformations predicted by the neural network can be used in a line heating simulator, which is considered an attractive and practical alternative to the existing methods.

• 대한수학회보
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• 제50권3호
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• pp.935-949
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• 2013

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.

• 호남수학학술지
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• 제41권4호
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• pp.683-695
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• 2019

In the present paper, we study curves in 𝔼³ with density $e^{ax^2+by^2}$, where a, b ∈ ℝ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.81-92
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• 2008

In this paper, the trajectory scroll in 3-dimensional Minkowski space-time $E_1^3$ is given by a firmly connected oriented line moving with Cartan frame along curve. Some theorems and results between curvatures of base curve and distribution parameter of this surface are obtained. Moreover, some theorems and results related to being developable and minimal of this surface are given. And also, some relationships among geodesic curvature, geodesic torsion and the curvatures of base curve of trajectory scroll are found.

• 호남수학학술지
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• 제43권3호
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• pp.453-463
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• 2021

In this study, tubular surfaces that play an important role in technological designs in various branches are examined for the case of the base curve is not satisfying the fundamental theorem of the differential geometry. In order to give an alternative perspective to the researches on tubular surfaces, the modified orthogonal frame is used in this study. Firstly, the relationships between the Serret-Frenet frame and the modified orthogonal frame are summarized. Then the definitions of the tubular surfaces, some theorems, and results are given. Moreover, the fundamental forms, the mean curvature, and the Gaussian curvature of the tubular surface are calculated according to the modified orthogonal frame. Finally, the properties of parameter curves of the tubular surface with modified orthogonal frame are expressed and the tubular surface is drawn according to the Frenet frame and the modified orthogonal frame.