• 충청수학회지
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• 제31권3호
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• pp.281-285
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• 2018

Let $S_k(N)$ be the space of cusp forms of weight k for ${\Gamma}_0(N)$. We show that $S_k(N)$ is the direct sum of subspaces $S_k^+(N)$ and $S_k^-(N)$. Where $S_k^+(N)$ is the vector space of cusp forms of weight k for the group ${\Gamma}_0^+(N)$ generated by ${\Gamma}_0(N)$ and $W_N$ and $S_k^-(N)$ is the subspace consisting of elements f in $S_k(N)$ satisfying $f{\mid}_kW_N=-f$. We find generators spanning the space $S_k^-(N)$ from $Poincar{\acute{e}}$ series and give all linear relations among such generators.

• Architectural research
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• 제12권1호
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• pp.15-23
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• 2010

This paper will discuss three different ways of framing relationships between identity and built forms mainly through the theoretical frame works of David Harvey, Christine M. Boyer, Jane M. Jacobs, Doreen Massey, Paul Rabinow, and Michel Foucault. From these scholars, this paper will argue the relationships between identity and built forms are categorized as such: "Becoming", "Politics of Difference", and "Construction of Self". Besides these three approaches of framing identity and built forms, relevant ideas will be drawn from the work of other scholars in so far as their theoretical positions relate and support these three key frameworks. To approach the critical points of each debate, these three categories are further analyzed by juxtaposing the epistemological positions between them. Through the comparisons, this paper illustrates the interrelationships and interdependence of these three categories whose discursive power gains rapid popularity in Western scholarships. By incorporating the three ways to view the relationship between built form and the identity of social groups, drawn is a suggestion for a broader imagining of new spatial identity.

• 한국실내디자인학회논문집
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• 제14호
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• pp.10-18
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• 1998

This study aims to make clear visual quality of organic form and structural order that is immanent in nature about a form as formative principles of architectural space design the significanced of this study is to prove the application possibility in to functional form architectural space design. All organic forms in nature has a unique shape and pattern in structure to be self-controled and good in order. Such an order in nature comes from regular construction and ratio principles which has aesthetical order by mathmetics. The specialty of beauty in nature can be revealed not only visual form but also the ratio balance and rhythm of structural principles. As we examine the aesthetic source embodied some object can be developed in to basic principles. Furthermore through this study we can find out that the form construction theory in nature forms share the quality attribute with geometrical form to be shown in architectural space design. Natural forms are ultimate visual expression of power that effects on the architectural space design. The rule of power in nature as nature formal characteristics have a direct influence and can be also applied to architectural construction. Therefore I expect that this study will be linked and continued to another structural view.

• 대한수학회논문집
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• 제39권3호
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• pp.739-756
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• 2024

The ordinary mean curvature vector field 𝗛 on a submanifold M of a space form is said to be proper if it satisfies equality Δ𝗛 = a𝗛 for a constant real number a. It is proven that every hypersurface of an Riemannian space form with proper mean curvature vector field has constant mean curvature. In this manuscript, we study the Lorentzian hypersurfaces with proper second mean curvature vector field of four dimensional Lorentzian space forms. We show that the scalar curvature of such a hypersurface has to be constant. In addition, as a classification result, we show that each Lorentzian hypersurface of a Lorentzian 4-space form with proper second mean curvature vector field is C-biharmonic, C-1-type or C-null-2-type. Also, we prove that every 𝗛₂-proper Lorentzian hypersurface with constant ordinary mean curvature in a Lorentz 4-space form is 1-minimal.

• 대한지리학회지
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• 제40권4호
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• pp.454-472
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• 2005

본 연구는 지리교과를 통한 시민성 교육의 가능성을 탐색하기 위한 것으로서 '시민성'과 '시민성의 공간' 에 대한 내재적 정당화에 관한 논의이다. Peters의 지식의 형식과 입문으로서의 교육관에 따라 지리적 지식의 형식을 검토하여 시민성을 내재적으로 정당화하였다. 지리학은 탈실증주의 패러다임의 언어와 이데올로기의 도입을 통해 기존의 '공간' 중심에서 '인간'과 '사회'에 더욱 관심을 가지는 방향으로 나아가고 있는데 이는 다름아닌 시민성의 공간으로의 전환을 의미한다. 즉, 사회공간이론을 통해 가치중립적인 물리적 공간 개념을 거부하고, 가치내재적인 '시민성의 공간'으로 전환을 모색하고 있다. 이러한 지리적 지식의 형식의 변화가 지리교과의 내용지식의 변화를 주도한다고 볼 때, 시민성은 내재적으로 정당화될 수 있다. 이와 같이 지리교과의 내용지식으로서의 시민성은 사회과 교육목적을 그대로 수용하는 외재적 정당화가 아니라, 지리적 지식의 형식을 통해 내재적으로 정당화될 때 의미를 지닌다. 그리고 시민성 공간에 토대한 시민성이라는 가치와 신념으로의 입문으로서의 지리교육은 학생들로 하여금 어떤 목적지에 도달하도록 하는 것이 아니라, 다른 관점을 가지고 나아가도록 해야 한다는 것을 의미한다.

• 한국디자인학회:학술대회논문집
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• 한국디자인학회 2001년도 Bulletin of The 5th Asian Design Conference International Symposium on Design Science
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• pp.22.1-22
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• 2001

• Kyungpook Mathematical Journal
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• 제52권3호
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• pp.271-278
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• 2012

We study some functions defined on the unit tangent space, which are formed with the second fundamental form of submanifolds of a real space form. These give an exact expression of isotropy of submanifolds in a real space form and a relationship between intrinsic invariants and extrinsic ones.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.781-791
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• 2016

Let $d_*(1,w)^2 ={\mathbb{R}}^2$ with the octagonal norm of weight w. It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on $d_*(1,w)^2$. We also show that the unit sphere of the space of symmetric bilinear forms on $d_*(1,w)^2$ is the disjoint union of the sets of smooth points, extreme points and the set A as follows: $$S_{{\mathcal{L}}_s(^2d_*(1,w)^2)}=smB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}extB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}A$$, where the set A consists of $ax_1x_2+by_1y_2+c(x_1y_2+x_2y_1)$ with (a = b = 0, $c={\pm}{\frac{1}{1+w^2}}$), ($a{\neq}b$, $ab{\geq}0$, c = 0), (a = b, 0 < ac, 0 < ${\mid}c{\mid}$ < ${\mid}a{\mid}$), ($a{\neq}{\mid}c{\mid}$, a = -b, 0 < ac, 0 < ${\mid}c{\mid}$), ($a={\frac{1-w}{1+w}}$, b = 0, $c={\frac{1}{1+w}}$), ($a={\frac{1+w+w(w^2-3)c}{1+w^2}}$, $b={\frac{w-1+(1-3w^2)c}{w(1+w^2)}}$, ${\frac{1}{2+2w}}$ < c < ${\frac{1}{(1+w)^2(1-w)}}$, $c{\neq}{\frac{1}{1+2w-w^2}}$), ($a={\frac{1+w(1+w)c}{1+w}}$, $b={\frac{-1+(1+w)c}{w(1+w)}}$, 0 < c < $\frac{1}{2+2w}$) or ($a={\frac{1=w(1+w)c}{1+w}}$, $b={\frac{1-(1+w)c}{1+w}}$, $\frac{1}{1+w}$ < c < $\frac{1}{(1+w)^2(1-w)}$).

• 한국실내디자인학회논문집
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• 제24권5호
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• pp.21-30
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• 2015

The visual expression system of space realized in Baroque aesthetics is basically grounded on the philosophical view to the world of the time, that is to say the changes of the thinking system in the Renaissance and ontology based on it. Structural aesthetics in Baroque freed from Plato's system of harmony but grounded on Leibniz's process philosophy formed a crucial background to highlight the formal nature of the whole and build a structure based on the inclusive principle of formativity. Also, to solve problems to realize the order and consistency of forms from the whole, Baroque adopted the nonlinear and nonphysical formative system as the principle of building space in works of art. Combining the order system of nature in the Renaissance with manneristic dynamicity as well as formative principle taking shape geometrically, it did establish a variety of aesthetic concepts based on the results of infiniteness and exaggeration expressed from the two forces, the Renaissance and mannerism. This study has found that such Baroque aesthetics did overcome classical planeness and draw continuous mobility from the structures and forms based on that with the transborder concepts of structures, the components of space, as an ultimate system of formative expression. Moreover, this author has drawn and analyzed with the cases of the 17th-century art and architecture the transborder elements manifesting the nature of diverse formative visual elements produced in artistic expressions with that principle of aesthetics, that is the intangible concept of Baroque. Based on that, this researcher intends to come up with technical solutions to solve a lot of environmental and architectural problems we are severely facing nowadays in terms of environmental, physical, and emotional aspects with the theoretical clues and results acceptable to this contemporary era.

• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.49-86
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• 2013

This article is a continuation of the paper [21]. In this paper we deal with Maass-Jacobi forms on the Siegel-Jacobi space $\mathbb{H}{\times}\mathbb{C}^m$, where H denotes the Poincar$\acute{e}$ upper half plane and $m$ is any positive integer.