• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.651-684
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• 2022

Let G be an arbitrary, connected, simply connected and unimodular Lie group of dimension 3. On the space 𝔐(G) of left-invariant Lorentzian metrics on G, there exists a natural action of the group Aut(G) of automorphisms of G, so it yields an equivalence relation ≃ on 𝔐(G), in the following way: h₁ ≃ h₂ ⇔ h₂ = 𝜙^*(h₁) for some 𝜙 ∈ Aut(G). In this paper a procedure to compute the orbit space Aut(G)/𝔐(G) (so called moduli space of 𝔐(G)) is given.

• Journal of the Korea Fashion and Costume Design Association
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• v.6 no.3
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• pp.1-8
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• 2004

The purpose of this study was to investigate gather as decoration techniques of clothes. In this study, we defined 21st century as the modern fashion. And analyzed design that applied gather concerned with Milan, New York, London, Paris, Tokyo Woman's Collections. Data were used from Fashion News and Gap Press Magazine (2001-2004). The results of this study were as follows: 1. Gather was the most original techniques among decoration techniques of clothes and formed three-dimensional space. 2. There were many kinds of gather such as cluster gather, all gather, shirring, smoking, frill, flounce, ruffle. and it gave a different impression with Fabrics, cutting method, sewing method, parts that were used. 3. Gather had practical functions providing enough space in activity and was presented as new shape by three-dimension body motion when it was put on. 4. After analyzing design that applied gather showed in collections, there were various appearance according to designer's sensitivity.

• Korean Institute of Interior Design Journal
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• v.17 no.3
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• pp.148-155
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• 2008

The following research focuses on the formation method of digital space by organistic line extension among various digital formation methods. The paper reflects on the meaning and concept of today's digitalism which enables the application of complex organistic system on space through advanced technology. It also explores the concept of a line in topology which differs in assumptive meaning from traditional Euclidian geometry. The findings of the research are that first, digital space is not optimized, but is a tentative formation in process. A digital space encompasses characteristics such as infinity, possibility, potential, asymmetry, and the force of virtuality such characteristics are expressed through a moving surface constantly changing with direction. Second, a digital space formed by line extension is inseparable and durable since no measurement or dimension is predetermined. Furthermore, its sense of direction and flexibility gives it a feeling of a living organism. Third, a Euclidian methodology called 'NURBS' is being developed to express such a dynamic digital space; this is reflected through three elements, control point, weights, and knots to effectively reflect the characteristics of virtuality. The opportunities of digital space are infinite, and the possibilities of formation methods likewise vast.

• Journal of the Korean Society of Costume
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• v.62 no.2
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• pp.26-39
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• 2012

This study intends to reconsider pleat, which was undermined as something too simple to express the details for women's costume, by focusing on the aesthetic value of plea in men's costumes in the west before the 20th century. Furthermore, based on the aesthetic value of the pleat, diverse studies on contemporary men's costumes shall help to attempt to set up a basis for the new mode of men's costume. The pleat, a component in the costume since the ancient times, had unique characteristics including functionality, a sense of volume, directing effect that is caused by line repetitions and formativeness that results through elasticity. First, the aesthetics of the pleat before the 20th century shows rhythmic sense through the repetition of the pleat line as shown in the drape type costume, and it also shows a sense of volume as the pleat is moved along the motion of the body. Second, it shows functionality as the expansion of space moves in accordance with the motion of body sets up an internal space of the costume that facilitates body motion. Third, the pleat extends two dimension space into three dimension space using its elasticity. It exaggerates specific parts of the costume while ignoring body shape in order to symbolize status and authority of men. Fourth, it unifies the costume by wrapping the body by using quadrangle cloths with drapers, and expanding the silhouette with the pleat artificially to conceal the physical character and personality of the wearer. The physical character of the wearer disappears into the space made by the pleat. The pleat reveals the voluptuous beauty within.

• Fashion & Textile Research Journal
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• v.11 no.4
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• pp.515-526
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• 2009

From traditional ceremony to science technology, origami was used as technique for artistic creativity and functionality based on formative characteristics. The purpose of this study is to analyze the expressive characteristics of functionality in fashion design using origami technique. The method of this study was to analyze recent documentaries, fashion books, fashion magazines, internet web site and so forth. The results were as follows: In various fields of design, the category of the expressive characteristics was classified as efficient correspondence of space, compositive convergence of function, variable potentiality of form and human ergonomic optimum. In recent origami fashion based on functionality, the efficient correspondence of space was expressed constructive or decorative pocket design, using on clothing surface and varied design by lifestyle. The compositive convergence of function was expressed innovative connection of fashion items or non-fashion items and deconstructed classical clothing pattern. The variable potentiality of form was expressed control of form by irregular fold, dynamic metamorphosis by organic fold and creation of varied clothing silhouette. The human ergonomic optimum was expressed metamorphosis mechanism from two dimension to three dimension, suitable construction to physical ability and limit and organic form based on articular folding. The functional origami fashion means reflection of nomadic lifestyle, maximum of usability, pursuit of playful sensibility, creation of new body aesthetic and pursuit of technology and humanism. And the result of these study may be used for creative inspiration in fashion design because of unique characteristics.

• Korean Institute of Interior Design Journal
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• v.20 no.6
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• pp.79-87
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• 2011

Spatial perception and spatial structure that focus on psychological effects produce a real force through the medium of space that can control human actions, even their psychology. The job of understanding the characteristics and effects of architectural spaces that recognize the relationship between architecture and human beings, including the psychological dimension, is an alternative search for quality spaces that can increase the mutual relationship between space and human beings. This paper introduces two propositions called "space" and "psychology" in order to discover a meta-pattern connecting space and the human mind with the aim of systematizing that internal network and establishing a new architectural system concerning space and human beings. This paper also proposes a method of accessing physical spaces that can affect psychological states through a conceptual substitution called "extension," with the aim of discovering the implications inherent in such extensive relationships and proposing a methodology of organizing psychological spaces based on the characteristics of that extensive connection. The means of extensively connecting psychological spaces were classified into the three categories of memory system, sensory system, and motor system, and their corresponding extensive connection characteristics called "simultaneous relativity," "non-mediated immediacy," and "purification process" were also derived. These characteristics accelerate the changes in psychological intensity and function as principles that organize psychological space.

• Korean Institute of Interior Design Journal
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• no.7
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• pp.79-86
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• 1996

This study is searching the characteristics of transferred element in composition of architectural spaces ; it is ultimate goal that frame of reference is arranged system about path of horizontal direction is two-dimension and stairs of vertical in three-dimension as transferred element in Architectural plan. With the exception of stylized discussion or rhetorical analysis about these, it is analysed as element in physical order of a whole architecture in relation to another elements in composition of architecture spaces. And one who is perceptible and cognitive through spaces is the subject. Consequently , these elements are classified concept of location and circulation. And it can't think that the formal is divided the latter for accept behavior of pedestrican and thinking system to consider verticality and time property is absolutely conceptual elements in space of architectural plan.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.215-222
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• 1997

This paper deals with the problem of generating a uniform tetrahedral mesh which fills a 3-D space with the tetrahedra which are close to the equilateral tetrahedra as possible. This problem is particularly interesting in finite element modeling where a fat triangulation minimizes the error of an analysis. Fat triangulation is defined as a scheme for generating an equilateral triangulation as possible in a given dimension. In finite element modeling, there are many algorithms for generating a mesh in 2-D and 3-D. One of the difficulties in generating a mesh in 3-D is that a 3-D object can not be filled with uniform equilateral tetrahedra only regardless of the shape of the boundary. Fat triangulation in 3-D has been proved to be the one which fills a 3-D space with the tetrahedra which are close to the equilateral as possible. Topological and geometrical properties of the fat triangulation and its application to meshing algorithm are investigated.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.11
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• pp.1398-1406
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• 2004

The nonlinear signals from an impedance meter for the area average void fraction in two-phase flow have been analyzed to construct a phase space trajectory. The pseudo phase space was constructed with the time delay and proper dimensions. The time delay and the embedding dimension were chosen by the average mutual information and by the false nearest neighborhood, respectively. The attractor-density-map of projected states was used to produce the two dimensional probability distribution functions (2D-PDF). Since the developed 2D-PDF showed clear distinction of the flow patterns, the flow regime identification was made with three rules and with the 2D-PDF. Also, the transition criteria of Mishima-Ishii agree well with the present results.