• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.215-219
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• 1995

The most fundamental examples of (combinatorial) geometries are projective geometries PG(n - 1,q) of dimension n - 1, representable over GF(q), where q is a prime power. Every upper interval of a projective geometry is a projective geometry. The Whitney numbers of the second kind are Gaussian coefficients. Every flat of a projective geometry is modular, so the projective geometry is supersolvable in the sense of Stanley [6].

• Journal for History of Mathematics
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• v.15 no.1
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• pp.1-14
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• 2002

This paper treats the history of the fundament of projective geometry Especially we introduce the essence of the framework of Karl Chirstian von Staudt's ‘Geometrie der Lage’. Von Staudt used axiomatical method to bum the system of the projective geometry, and proved the fundamental theorem of projective geometry. And he handled imaginary elements (or the first time in synthetic projective geometry.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1139-1171
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• 1996

The purpose of our research is to understand geometric and topological aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to $RP^2$ such that transition functions are restrictions of projective automorphisms of $RP^2$. Since such an atlas lifts projective geometry on $RP^2$ to the surface locally and consistently, one can study the global projective geometry of surfaces.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.49-61
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• 2006

Wu et al. (1992) constructed some general classes of tight asymmetric orthogonal arrays of strength 2 using the method of grouping. Rains et al. (2002) obtained asymmetric orthogonal arrays of strength 2 using the concept of mixed spread in finite projective geometry. In this paper, we obtain some new tight asymmetric orthogonal arrays of strength 2 using the concept of mixed partition in finite projective geometry.

• Kyungpook Mathematical Journal
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• v.1 no.1
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• pp.1-15
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• 1958

• Journal for History of Mathematics
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• v.18 no.4
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• pp.29-38
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• 2005

This Paper discusses the history of the conflicts between synthesis and analysis, from those in heuristic and logic development style in ancient Greek to those in projective geometric methods. The two methods, which originally displayed difference in heuristic, offer the base for the two fields of geometry, the analytic geometry and the synthetic geometry in the 18th century as they originated from the field of geometry. As to the 19th century, they even display antagonistic aspects derived by having other perspectives about the true nature of mathematic but finally lose the reason of conflict as the ancient times when the dialectical sublation of both had been proposed.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1743-1755
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• 2017

Let B be a simply-connected projective variety such that the first cohomology groups of all line bundles on B are zero. Let E be a vector bundle over B and $X={\mathbb{P}}(E)$. It is easily seen that a power of any endomorphism of X takes fibers to fibers. We prove that if X admits an endomorphism which is of degree greater than one on the fibers, then E splits into a direct sum of line bundles.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.391-394
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• 2005

In this paper, we present an approach that is able to reconstruct 3 dimensional metric models from un-calibrated images acquired by a freely moved camera system. If nothing is known of the calibration of either camera, nor the arrangement of one camera which respect to the other, then the projective reconstruction will have projective distortion which expressed by an arbitrary projective transformation. The distortion on the reconstruction is removed from projection to metric through self-calibration. The self-calibration requires no information about the camera matrices, or information about the scene geometry. Self-calibration is the process of determining internal camera parameters directly from multiply un-calibrated images. Self-calibration avoids the onerous task of calibrating cameras which needs to use special calibration objects. The root of the method is setting a uniquely fixed conic(absolute quadric) in 3D space. And it can make possible to figure out some way from the images. Once absolute quadric is identified, the metric geometry can be computed. We compared reconstruction image from calibrated images with the result by self-calibration method.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1095-1110
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• 2017

The t-wise intersection is a useful property of a linear code due to its many applications. Recently, the second author determined the t-wise intersection of a relative two-weight code. By using this result and generalizing the finite projective geometry method, we will present the t-wise intersection of a relative three-weight code and its applications in this paper.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1958-1959
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• 2006

This paper proposes a local path-planning algorithm that enables a mobile robot with vision sensor in a local area.The proposed method based on projective geometry and a wavefront method finds local-paths to avoid collisions using 3-D walls or obstacles map generated using projective geometry. Simulation results show the feasibility of the proposed method