• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.563-569
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• 2014

We investigate a minimal set of generators of a homogeneous ideal of a curve of degree d on a linearly normal smooth surface scroll W in $P^r$ whose arithmetic genus is maximal among curves of degree d on W.

• East Asian mathematical journal
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• v.35 no.1
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• pp.51-58
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• 2019

For a nondegenerate irreducible projective variety, it is a classical problem to describe its defining equations. In this paper we precisely determine the defining equations of some rational curves of maximal regularity in ${\mathbb{P}}^4$ according to their rational parameterizations.

• Honam Mathematical Journal
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• v.26 no.2
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• pp.237-246
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• 2004

In this paper, three kinds of minimal digital pseudotori $DT_6$, $DT^{\prime}_{18}$, $DT^{{\prime}{\prime}}_{26}$, which are derived from the minimal simple 4- and 8-curves, $MSC_4$ and $MSC^{\prime}_8$, are shown and are proved not to be digitally ${\kappa}$-homotopy equivalent to each other, where ${\kappa}{\in}\{6,\;18,\;26\}$. Furthermore, the digital topological properties of the minimal digital ${\kappa}$-pseudotori are investigated in the digital homotopical point of view, where ${\kappa}{\in}\{6,\;18,\;26\}$.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.41-62
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• 2010

In this article, we discuss a Grobner basis algorithm related to the stability of algebraic varieties in the sense of Geometric Invariant Theory. We implement the algorithm with Macaulay 2 and use it to prove the stability of certain curves that play an important role in the log minimal model program for the moduli space of curves.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.594-617
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• 2022

In this study, firstly Smarandache ruled surfaces whose base curves are Smarandache curves derived from Frenet vectors of the curve, and whose direction vectors are unit vectors plotting Smarandache curves, are created. Then, the Gaussian and mean curvatures of the obtained ruled surfaces are calculated separately, and the conditions to be developable or minimal for the surfaces are given. Finally, the examples are given for each surface and the graphs of these surfaces are drawn.

• Journal of the Korean Society of Costume
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• v.24
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• pp.157-176
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• 1995

The purpose of this treatise is to study external form and internal meaning of minimal expression fashion which appeared as a major stream in modern fashion trends to understand one aspect of modernism in fashion and also to gain insight into internal value of human beings through fashion. The results can be summarized as follows : Firstly , minimalism is a trend in art attempting to seek essence of the object by presenting simple and disciplined expressions by minimal formative means and minimal production process. Secondly, minimal expression in fashion means seeking simplicity an dpurity by using minimum design elements and minimal productive process. Thirdly, external from of minimal expression fashion can be created through application of following minimal expression techniques. 1. Minimal expression techniques in terms of line mean smooth curve flowing along body contours, straight lines of diagonal lines into desciplined silhouette or rendering internal contour lines. 2. Minimum expression techniques in terms of forms mean forms of smooth curves flowing along boyd or forms with simple geometric forms from qualitative aspects, In terms of volume it means quest for essence of pure body itself by revealing body as it is by minimizing the size of dress or its area and herein is contained using simple geometric pattern or utilizing textiles without any patterns.3. Minimal expression techniques by colors mean simple colors such as primary colors, colors without clear distinctions or natural colors and in terms of quantity it means quest for one color within one item of dress or combination of each items when getting dressed. 4. Minimal expression techniques in terms of fabrics mean fabrics with simple surfaced. In terms of quantity it means quest for essence of tight fitting thin textiles to human body or using transparent materials to human body thus exposing body contours as it is. 5. Minimal expression techniques in terms of productive process mean minimizing process of tailoring , sewing or ornamenting and seeking for simplicity and purity. 6. Minimal expression techniques in terms of manufacturing process mean selection of technique conveying simple image with disciplined simple image. Fourthly, minimal expression fashion with external expression as mentioned in the above lay body-priority style and its internal meaning can be asummed as quest for essence and purity of human body.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1329-1343
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• 2013

In this paper, we define translation surfaces in the 3-dimensional Heisenberg group $\mathcal{H}_3$ obtained as a product of two planar curves lying in planes, which are not orthogonal, and study minimal translation surfaces in $\mathcal{H}_3$.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.67-74
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• 2024

Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃³ in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.

• East Asian mathematical journal
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• v.34 no.1
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• pp.21-28
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• 2018

For a nondegenerate irreducible projective variety, it is a classical problem to study the defining equations of a variety with respect to the given embedding. In this paper we precisely determine the defining equations of certain types of rational curves in ${\mathbb{P}}^3$.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.679-683
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• 1997

We obtain new upper bound of the area of a constant breath curve. We estimate the area of a constant breadth curve in terms of its breadth and minimal radius and the arc length of its pedal curve.