• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.65-72
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• 2015

The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve $x_t$ ($t{\in}[0,1]$) in M into the affine tangent space at $x_0$ (${\in}M$) with respect to a given generalized affine connection in the bundle of affine frames over M.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1135-1202
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• 2008

We construct the Fock space representations of classical quantum affine algebras using combinatorics of Young walls. We also show that the crystal graphs of the Fock space representations can be realized as the crystal consisting of proper Young walls. Finally, we give a generalized version of Lascoux-Leclerc-Thibon algorithm for computing the global bases of the basic representations of classical quantum affine algebras.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.203-207
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• 1999

In this paper, we find a condition of an open subset of the affine space which admits a cocompact affine action. To do it, the asymptotic flag of an open convex subset is introduced and some applications to affine manifolds are presented.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.461-464
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• 1998

We generalize the Artin-Rees Theorem about the AR-property and study linking diagram in the set of prime ideals of the coordinate ring of quantum affine space.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.825-832
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• 2011

In this paper, we make a minute and detailed proof of a part which is omitted in the process of obtaining the value of the curvature tensor for an invariant affine connection at the point {H} of a reductive homogeneous space G/H in the paper 'Invariant affine connections on homogeneous spaces' by K. Nomizu.

• Korean Journal of Geomatics
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• v.4 no.1
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• pp.31-37
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• 2004

The aim of this research is comparing the existing approximation models (e.g. Affine Transformation and Direct Linear Transformation) with Rational Function Model as a substitute of rigorous sensor model of linear array scanner, especially push-broom sensor. To do so, this research investigates the mathematical model of each approximation method. This is followed by the assessments of accuracy of transformation from object space to image space by using simulated data generated by collinearity equations which incorporate or depict the physical aspects of linear array sensor.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.13-22
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• 2019

We compute the second cohomology of the affine Lie algebra aff(1) on the dimensional real space with coefficients in the space ${\mathcal{D}}^n_{{\underline{\lambda}},{\mu}}$ of n-ary linear differential operators acting on weighted densities where ${\underline{\lambda}}=({\lambda}_1,{\ldots},{\lambda}_n)$. We explicitly give 2-cocycles spanning these cohomology.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.367-370
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• 2005

This paper proposes a novel method for content-based watermarking based on feature points of an image. At each feature point, watermark is embedded after affine normalization according to the local characteristic scale and orientation. The characteristic scale is the scale at which the normalized scale-space representation of an image attains a maximum value, and the characteristic orientation is the angle of the principal axis of an image. By binding watermarking with the local characteristics of an image, resilience against affine transformations can be obtained. Experimental results show that the proposed method is robust against various image processing steps including affine transformations, cropping, filtering, and JPEG compression.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1894-1905
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• 1996

Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.