• Journal of Institute of Control, Robotics and Systems
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• v.4 no.3
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• pp.308-314
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• 1998

This paper studies the problem of computing the Hankel singular values and vectors in the input delay systems. It is shown that the Hankel singular values are solutions to a transcendental equation and the Hankel singular vectors are obtained from the kernel of the matrix. The computation is carried out in state space framework. Finally, Hankel approximation of a simple example shows the usefulness of this study.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.5
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• pp.928-938
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• 1997

We propose an algorithm for extracting singular points of fingerprint image using directional information. First, we extract the candidates of singular points using Poincare index in two(lower and higher) resolutional directional images. Then we remove the false singular points using smoothing technique from lower resolutional directional image. And finally we select the singular points in higher resolution corresponding to those in lower resolution. The possible missing points in lower resolution are found by computing Poincare index algong the proposed small curve. And the reliable points are selected from analysis around them. We also propose a method for segmentation of fingerprint as preprocessing step to enhance the computational speed and the performance of system.

• Journal of Ocean Engineering and Technology
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• v.33 no.1
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• pp.17-25
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• 2019

A numerical method is suggested for evaluating the singular integral of curved panels in the higher-order boundary element method. Two-step mapping procedures that are significantly related to the physical properties of singular behaviors were developed and illustrated. As a result, the singular behaviors were significantly alleviated, and the efficiency and robustness of the present method for tangentially and axially deformed elements were proven. However, inaccuracies and numerical instabilities of twisted elements were discovered as a result of nonlinearities.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.109-122
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• 2021

In this paper, we consider the problem of finding the hypersurface Mn in the Euclidean (n + 1)-space ℝn+1 that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the surfaces in the upper half-space ℝ+3 (u) with lowest gravity center, for a fixed unit vector u ∈ ℝ3. We first state that a singular minimal cylinder Mn in ℝn+1 is either a hyperplane or a α-catenary cylinder. It is also shown that this result remains true when Mn is a translation hypersurface and u is a horizantal vector. As a further application, we prove that a singular minimal translation graph in ℝ3 of the form z = f(x) + g(y + cx), c ∈ ℝ - {0}, with respect to a certain horizantal vector u is either a plane or a α-catenary cylinder.

• Current Optics and Photonics
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• v.4 no.6
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• pp.540-544
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• 2020

Current two-dimensional (2D) augmented reality (AR) devices present virtual image and information to a fixed focal plane, regardless of the various locations of ambient objects of interest around the observer. This limitation can lead to a visual discomfort caused by misalignments between the view of the ambient object of interest and the visual representation on the AR device due to a failing of the singular fusion. Since the misalignment becomes more severe as the depth difference gets greater, it can hamper visual understanding of the scene, interfering with task performance of the viewer. Thus, we analyzed the range of singular fusion (RSF) of AR images within which viewers can perceive the shape of an object presented on two different depth planes without difficulty due to the failure of singular fusion. It is expected that our analysis can inspire the development of advanced AR systems with low visual discomfort.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.3
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• pp.194-206
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• 2023

We present families of nonlinear transformations useful for numerical evaluation of weakly singular integrals. First, for end-point singular integrals, we define a prototype function with some appropriate features and then suggest a family of transformations. In addition, for interior-point singular integrals, we develop a family of nonlinear transformations based on the aforementioned prototype function. We take some examples to explore the efficiency of the proposed nonlinear transformations in using the Gauss-Legendre quadrature rule. From the numerical results, we can find the superiority of the proposed transformations compared to some existing transformations, especially for the integrals with high singularity strength.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.1067-1086
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• 2024

For a foliation 𝓕 of degree r over ℙ², we can regard it as a maximal invertible sheaf N^∨_𝓕 of Ω_ℙ², which is represented by a section s ∈ H⁰(Ω_ℙ² (r+2)). The singular locus Sing𝓕 of 𝓕 is the zero dimensional subscheme Z(s) of ℙ² defined by s. Campillo and Olivares have given some characterizations of the singular locus by using some cohomology groups. In this paper, we will give some different characterizations. For example, the singular locus of a foliation over ℙ² can be characterized as the residual subscheme of r collinear points in a complete intersection of two curves of degree r + 1.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.5
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• pp.22-28
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• 2009

In this paper, we consider the problem of $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays. The aim of designed filter is to guarantee regularity, impulse-free, asymptotic stability and $H_{\infty}$ norm bound of filtering error singular system. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent BRL (bounded real lemma) for singular systems with multiple state-delays is derived. Based on the result, the existence condition of $H_{\infty}$ filter and filter design method are proposed in terms of LMI (linear matrix inequality). Finally, a numerical example is provided to show the validity of the design methods.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.6
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• pp.2634-2648
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• 2020

In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.2
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• pp.883-900
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• 2017

In this paper block based blind secure gray image watermarking scheme based on discrete wavelet transform and singular value decomposition is proposed. In devising the proposed scheme, security is given high importance along with other two requirements: robustness and imperceptibility. The use of discrete wavelet transform not only improves robustness but the selection of bands with high tolerance towards noise caused an improvement in terms of imperceptibility. The robustness further improved due to the involvement of singular vectors along with singular values in watermark embedding and extraction process. Finally, to achieve security, the selected DWT band is decomposed into smaller blocks and random blocks are chosen for modification. Furthermore, the elements of left and right singular vectors of selected blocks are chosen based on their dependence upon each other for watermark embedding. Various experiments using different images as host and watermark were conducted to examine and validate the proposed technique. Additionally, the proposed technique is tested against various attacks like compression, affine transformation, cropping, translation, X shearing, scaling, Y shearing, filtering, blurring, different kinds of noises, histogram equalization, rotation, etc. Lastly, the proposed technique is compared with state-of-the-art watermarking techniques and their comparison shows significant improvement of proposed scheme over existing techniques.