• 한국수학사학회지
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• 제10권1호
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• pp.19-32
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• 1997

This paper deals with the relationship between the order structure and topological structure in the historical point of view. We first investigate how the order structure has developed along with the set theory and logic in the second half of the nineteenth century. After the general topology has emerged in the beginning of the twentieth century, two disciplines of the order theory and topology give each other a great deal of effect for their development via various dualities, compactifications by maximal filter spaces and Alexandroff's specialization order, which form eventually a fundamental setting for the development of the category theory or functor theory.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.515-540
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• 2013

Let $G=O(2){\times}O(2){\times}O(2)$. Then a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$ is a product of spheres, i.e., the square norm of its second fundamental form, S = 4.

• East Asian mathematical journal
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• 제31권1호
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• pp.27-32
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• 2015

In this paper, we study lightlike hypersurfaces M of a Lorentz manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the screen distribution S(TM) is totally geodesic in M, and (2) the second fundamental form B of M is parallel.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.547-557
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• 2018

We establish some characterizations of isoparametric surfaces in the three-dimensional Euclidean space, which are associated with the Laplacian operator defined by the so-called II-metric on surfaces with non-degenerate second fundamental form and the elliptic linear Weingarten metric on surfaces in the three-dimensional Euclidean space. We also study a Ricci soliton associated with the elliptic linear Weingarten metric.

• 호남수학학술지
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• 제42권4호
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• pp.829-841
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• 2020

The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geodesic if the second fundamental form is any one of (i) symmetric, (ii) recurrent, (iii) pseudo symmetric, (iv) almost pseudo symmetric and (v) weakly pseudo symmetric.

• 대한수학회논문집
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• 제37권2호
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• pp.595-606
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• 2022

In this paper, we have studied f-biharmonic submanifolds in locally conformal almost cosymplectic space forms and have derived condition on second fundamental form for f-biharmonic submanifolds. Also, we have discussed its integral submanifolds in locally conformal almost cosymplectic space forms.

• 호남수학학술지
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• 제44권1호
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• pp.1-16
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• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• 한국실내디자인학회논문집
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• 제19권5호
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• pp.56-66
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• 2010

This study proposes a thesis of architectural concepts and visual dimension systems, and the comparison between steps of spatial formation and dimensional alteration. The second chapter, to form the basis of this study, explains the dimensional alterations and changes of fundamental notion of space. In the third chapter, history of space, architectural formations, and changes of the viewpoint are analyzed as objects of study. The forth chapter presents the interrelation between dimensional alteration and the transition in fundamental notion of space, demonstrating that modern architecture has been born from these cultural movements. Lastly, the fifth chapter suggests possibilities on further studies and the following conclusions: First, architectural spaces have been changed, in accordance with the changes of culture, art and the tools that regulate architectural design. Proportional regulations by two-dimensional tools and depth through three-dimensional drawings are created. Second, architectural spaces gained depth by recognizing movement and time that have induced formations to change, creating various aesthetic backgrounds and attempts. Third, the aesthetic background and cosmologic spatial concept have led the visualization and changes of architectural experience. It created the design tools and shapes originated in dynamism and vitality. Forth, diversification of fundamental spatial concepts has become palimpsest and complex, and been divided into four dimensions; expressional two-dimensional space, perspective three-dimensional space, forth-dimensional space of time and experience, and imagery space formed by body movement. Fifth, architecture has been influenced by the elevated viewpoint that understands the whole world as a space. It has evolved from the two-dimensional proportion principle, change of depth and vanishing point to multidimensional space of movement and time. Sixth, changes of fundamental notion of space have arisen from changes of visual dimensions in times. In other words, space has been developed from two-dimensional space to multidimensional space by accepting visual dimension, grasping distance, direction, depth, height, velocity, movement, gravity, power and structure.

• Structural Engineering and Mechanics
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• 제32권3호
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• pp.407-427
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• 2009

A fundamental solution for the transient, quasi-static, plane problems of linear viscoelasticity is introduced for a specific material. An integral equation has been found for any problem as a result of dynamic reciprocal identity which is written between this fundamental solution and the problem to be solved. The formulation is valid for the first, second and mixed boundary-value problems. This integral equation has been solved by BEM and algorithm of the BEM solution is explained on a sample, mixed boundary-value problem. The forms of time-displacement curves coincide with literature while time-surface traction curves being quite different in the results. The formulation does not have any singularity. Generalized functions and the integrals of them are used in a different form.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.965-977
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• 2016

The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained.