• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.789-795
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• 1995

For nonintegrable weight $-\rho$, some weight multiplicities of the irreducible module $L(-\rho)$ over $A^{(1)}_{(1)}$ affine Lie algebras are expressed in terms of the colored partition functions. Also we find the multiplicity of $L(-\rho)$ in ther Verma module $M(-\rho)$ for any affine Lie algebras.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1567-1586
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• 2013

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifolds with constant scalar curvature. We also consider the multiply warped products with an affine connection with a zero torsion.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.7
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• pp.1690-1704
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• 2013

An affine invariant descriptor is proposed, which is able to well represent the affine covariant regions. Estimating main orientation is still problematic in many existing method, such as SIFT (scale invariant feature transform) and SURF (speeded up robust features). Instead of aligning the estimated main orientation, in this paper ellipse orientation is directly used. According to ellipse orientation, affine covariant regions are firstly divided into 4 sub-regions with equal angles. Since affine covariant regions are divided from the ellipse orientation, the divided sub-regions are rotation invariant regardless the rotation, if any, of ellipse. Meanwhile, the affine covariant regions are normalized into a circular region. In the end, the gradients of pixels in the circular region are calculated and the partition-based descriptor is created by using the gradients. Compared with the existing descriptors including MROGH, SIFT, GLOH, PCA-SIFT and spin images, the proposed descriptor demonstrates superior performance according to extensive experiments.

• Journal of the Korean Society of Industry Convergence
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• v.25 no.4_2
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• pp.707-714
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• 2022

Versatile Video Coding (VVC) is the most recent video coding standard, which had been developed by Joint Video Expert Team (JVET). It can improve significant coding performance compared to the previous standard, namely High Efficiency Video Coding (HEVC). Although VVC can achieve the powerful coding performance, it requires the tremendous computational complexity of VVC encoder. Especially, affine motion compensation (AMC) was adopted the block-based 4-parameter or 6-parameter affine prediction to overcome the limit of translational motion model while VVC require the cost of higher encoding complexity. In this paper, we proposed the early termination of AMC that determines whether the affine motion estimation for AMC is performed or not. Experimental results showed that the proposed method reduced the encoding complexity of affine motion estimation (AME) up to 16% compared to the VVC Test Model 17 (VTM17).

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.517-527
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• 2014

In this paper, we study affine transformations of normal bases and give an explicit formulation of the multiplication table of an affine transformation of a normal basis. We then discuss constructions of self-dual normal bases using affine transformations of traces of a type I optimal normal basis and of a Gauss period normal basis.

• ALGAE
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• v.34 no.3
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• pp.237-251
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• 2019

The dinoflagellate genus Alexandrium is known to often form harmful algal blooms causing human illness and large-scale mortality of marine organisms. Therefore, the population dynamics of Alexandrium species are of primary concern to scientists and aquaculture farmers. The growth rate of the Alexandrium species is the most important parameter in prediction models and nutrient conditions are critical parameters affecting the growth of phototrophic species. In Korean coastal waters, Alexandrium affine and Alexandrium fraterculus, of similar sizes, often form red-tide patches together. Thus, to understand bloom dynamics of A. affine and A. fraterculus, growth rates and nitrate uptake of each species as a function of nitrate ($NO_3$) concentration at $100{\mu}mol\;photons\;m^{-2}s^{-1}$ under 14-h light : 10-h dark and continuous light conditions were determined using a nutrient repletion method. With increasing $NO_3$ concentration, growth rates and $NO_3$ uptake of A. affine or A. fraterculus increased, but became saturated. Under light : dark conditions, the maximum growth rates of A. affine and A. fraterculus were 0.45 and $0.42d^{-1}$, respectively. However, under continuous light conditions, the maximum growth rate of A. affine slightly increased to $0.46d^{-1}$, but that of A. fraterculus largely decreased. Furthermore, the maximum nitrate uptake of A. affine and A. fraterculus under light : dark conditions were 12.9 and $30.1pM\;cell^{-1}d^{-1}$, respectively. The maximum nitrate uptake of A. affine under continuous light conditions was $16.4pM\;cell^{-1}d^{-1}$. Thus, A. affine and A. fraterculus have similar maximum growth rates at the given $NO_3$ concentration ranges, but they have different maximum nitrate uptake rates. A. affine may have a higher conversion rate of $NO_3$ to body nitrogen than A. fraterculus. Moreover, a longer exposure time to the light may confer an advantage to A. affine over A. fraterculus.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.425-430
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• 2012

In this paper, we will prove a social equilibrium existence theorem of a generalized Nash game with affine constraint correspondences which is comparable with Nash's equilibrium existence theorem in several aspects.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2019.06a
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• pp.216-217
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• 2019

Light Field (LF) image can be understood as a set of images captured by a multi-view camera array at the same time. The changes among views can be modeled by a general motion model such as affine motion model. In this paper, we study the impact of affine coding tool of Versatile Video Coding (VVC) on LF image compression. Our experimental results show a small contribution by affine coding tool in overall LF image compression of roughly 0.2% - 0.4%.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.157-161
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• 2001

In this paper, we prove that an affine manifold M is finitely covered by a manifold $\overline{M}$ where $\overline{M}$ is radiant or the tangent bundle of $\overline{M}$ has a conformally flat vector subbundle of the projective holonomy group of M admits an invariant probability Borel measure. This implies that$x^M$is zero.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.433-450
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• 2024

Using a Reilly type integral formula due to Li and Xia [23], we prove several geometric inequalities for affine connections on Riemannian manifolds. We obtain some general De Lellis-Topping type inequalities associated with affine connections. These not only permit to derive quickly many well-known De Lellis-Topping type inequalities, but also supply a new De Lellis-Topping type inequality when the 1-Bakry-Emery Ricci curvature is bounded from below by a negative function. On the other hand, we also achieve some Lichnerowicz type estimate for the first (nonzero) eigenvalue of the affine Laplacian with the Robin boundary condition on Riemannian manifolds.