• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.641-645
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• 2013

In this article, we show that the modular equation ${\Phi}_p^{T_q}(X,Y)$ of Thompson series $T_q$ corresponding to ${\Gamma}_0(q)+q$ gives an affine model of a modular curve $X_0(pq)+q$.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.337-343
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• 2010

We study affine translation surfaces in $\mathbb{R}^3$ and get a complete classification of such surfaces with constant Gauss-Kronecker curvature.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.173-190
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• 2011

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step length along this direction which makes the iterate point strictly feasible and the objective function nonmonotonically decreasing. Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, we present some numerical results to illustrate the effectiveness of the proposed algorithm.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.877-880
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• 2000

In this paper, we develop an algorithm of soccer image sequences mosaicing using reverse affine transform. The continuous mosaic images of soccer ground field allows the user/viewer to view a “wide picture” of the player’s actions The first step of our algorithm is to automatic detection and tracking player, ball and some lines such as center circle, sideline, penalty line and so on. For this purpose, we use the ground field extraction algorithm using color information and player and line detection algorithm using four P-rules and two L-rules. The second step is Affine transform to map the points from image to model coordinate using predefined and pre-detected four points. General Affine transformation has many holes in target image. In order to delete these holes, we use reverse Affine transform. We tested our method in real image sequence and the experimental results are given.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• The Journal of the Acoustical Society of Korea
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• v.33 no.6
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• pp.420-426
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• 2014

In this paper, we propose a new affine projection sign algorithm (APSA) to improve the convergence speed of the conventional APSA which has been proposed to enable the affine projection algorithm (APA) to operate robustly in impulsive noise environment. The conventional APSA has two advantages; it operates robustly against impulsive noise and does not need calculation for the inverse matrix. The proposed algorithm also has the conventional algorithm's advantages and furthermore, better convergence speed than the conventional algorithm. In the conventional algorithm, each input signal is normalized by $l_2$-norm of all input signals, but the proposed algorithm uses input signals normalized by their corresponding $l_2$-norm. We carried out a performance comparison of the proposed algorithm with the conventional algorithm using a system identification model. It is shown that the proposed algorithm has the faster convergence speed than the conventional algorithm.

• The Journal of the Acoustical Society of Korea
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• v.34 no.2
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• pp.130-137
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• 2015

In this paper, we propose a new Modified Filtered-x Affine Projection Sign Algorithm(MFxAPSA) to improve the convergence speed of the conventional MFxAPSA which has been proposed for active control of impulsive noise. Under the impulsive noise environment, the adaptive algorithms based on the second order moment such as the Filtered-x Least Mean Square(FxLMS) show slow convergence speed or diverge because the noise source tends to have infinite variance. The MFxAPSA is the algorithm derived by applying the Affine Projection Sign Algorithm(APSA) to active noise control. The APSA has an advantage that it does not need the calculation for the inverse matrix, so it may be suitable for the active noise control that requires low computational burden. The proposed MFxAPSA also has APSA's advantage and furthermore, better performance than the conventional MFxAPSA. We carried out a performance comparison of the proposed MFxAPSA with the conventional MFxAPSA. It is shown that the proposed MFxAPSA has the faster convergence speed than the conventional MFxAPSA.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.2
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• pp.45-55
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• 1994

In this paper, a block based image approximation technique using the Self Affine System(SAS) from the fractal theory is suggested. Each block of an image is divided into 4 tiles and 4 affine mapping coefficients are found for each tile. To find the affine mapping cefficients that minimize the error between the affine transformed image block and the reconstructed image block, the matrix euation is solved by setting each partial differential coefficients to aero. And to ensure the convergence of coding block. 4 uniformly partitioned affine transformation is applied. Variable block size technique is employed in order to applynatural image reconstruction property of fractal image coding. Large blocks are used for encoding smooth backgrounds to yield high compression efficiency and texture and edge blocks are divided into smaller blocks to preserve the block detail. Affine mapping coefficinets are found for each block having 16$\times$16, 8$\times$8 or 4$\times$4 size. Each block is classified as shade, texture or edge. Average gray level is transmitted for shade bolcks, and coefficients are found for texture and edge blocks. Coefficients are quantized and only 16 bytes per block are transmitted. Using the proposed algorithm, the computational load increases linearly in proportion to image size. PSNR of 31.58dB is obtained as the result using 512$\times$512, 8 bits per pixel Lena image.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.85-94
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• 2001

Let g=g(A) be an affine Lie algebra of type A(sub)2ι(sup)(2)(ι>1) and W be its Weyl group. In this paper, we find $\omega$$\in$W such that $\Delta$+U{1/2($\alpha$ι+$\delta$), 1/2($\alpha$ι+3$\delta$)}⊂$\Delta$+($\omega$).

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.485-498
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• 2005

In this article we show that every quasi-homogeneous convex affine domain whose boundary is everywhere differentiable except possibly at a finite number of points is either homogeneous or covers a compact affine manifold. Actually we show that such a domain must be a non-elliptic strictly convex cone if it is not homogeneous.