• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2035-2045
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• 2015

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.581-590
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• 2018

In this paper, we consider surfaces in the 3-dimensional Euclidean space $\mathbb{E}^3$ which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, namely, tubes in $\mathbb{E}^3$. We show that tubes are of infinite III-type.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.315-330
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• 1998

Chen and Piccinni [7] have classified all compact surfaces in a Euclidean space $R^{2＋p}$ with 1-type generalized Gauss map. Being motivated by this result, the purpose of this paper is to consider the Lorentz version of the classification theorem and to obtain a complete classification of space-like surfaces in indefinite Euclidean space $R_{p}$ $^{2＋p}$ with 1-type generalized Gauss map.p.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.251-260
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• 2020

In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵. Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵ are the locally product of two pseudo-Hermitian circles.

• 한국정보디스플레이학회:학술대회논문집
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• 2005.07a
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• pp.774-777
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• 2005

In this work, a soft embossing method is proposed to fabricate microgrooves on polyimide surfaces. Apply these resulting patterned micro-grooved polyimide surfaces as the liquid crystal alignment layers. The director of liquid crystal molecules aligns perfectly along the direction of microgrooves.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.909-928
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• 2016

Chen and Ishikawa studied the surfaces of revolution of the polynomial and the rational kind of finite type in Euclidean 3-space $E^3$ [10]. Here, the pedal of revolution surfaces of the polynomial and the rational kind are discussed. Also, as a special case of general revolution surfaces, the sphere and catenoid are studied for the kind of finite type.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.447-455
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• 2005

In this article, we introduce the notion of pointwise 1-type Gauss map of the first and second kinds and study surfaces of revolution with such Gauss map. Our main results state that surfaces of revolution with pointwise 1-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only rational surfaces of revolution with pointwise 1-type Gauss map of the second kind.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.151-160
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• 1995

The notion of finite type submanifold was introduced by B.-Y. Chen [1]. A lot of works were done in this field of study by many authors. B.-Y. Chen also extended this notion to pseudo-Riemannian submanifold of pseudo-Euclidean space ([2]).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.113-117
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• 1998

We propose a way to show the inherent learning complexity for the multilayer perceptron. We display the solution space and the error surfaces on the input space of a single neuron with two inputs. The evolution of its weights will follow one of the two error surfaces. We observe that when we use the back-propagation(BP) learning algorithm (1), the wight cam not jump to the lower error surface due to the implicit continuity constraint on the changes of weight. The self-relaxation approach is to explicity find out the best combination of all neurons' two error surfaces. The time complexity of training a multilayer perceptron by self-relaxationis exponential to the number of neurons.

• Current Optics and Photonics
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• v.3 no.3
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• pp.227-235
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• 2019

With slimmer, lighter and all-reflective imaging systems in high demand for consumer and military applications, coaxially folded optical image systems are widely considered because they can extend focal length and reduce track length. Most of these systems consist of multiple surfaces, and these surfaces are machined on one element or grouping processing on two elements. In this paper, we report and first experimentally demonstrate an all-aluminum all-reflective optical system which consists of two optical elements, with two high order aspherical surfaces in each element. The coaxially folded system is designed with Seidel aberration theory and advanced optimization with Zemax. The system is made of all-aluminum material processing by single point diamond turning (SPDT). On this basis, we completed the system integration and performed an imaging experiment. The final system has the advantages of short track length and long focal length and broad application prospects in the micro-unmanned aerial vehicle field.