• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.977-1000
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• 2021

Consider the high dimensional torus 𝕋ⁿ and the set 𝜺 of its endomorphisms. We construct a map in 𝜺 that is robustly transitive if 𝜺 is endowed with the C² topology but is not robustly transitive if 𝜺 is endowed with the C¹ topology.

• Journal of the Korea Society of Computer and Information
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• v.19 no.9
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• pp.21-31
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• 2014

Singular value decomposition (SVD) has been widely used to identify unique features from a data set in various fields. However, a complex matrix calculation of SVD requires tremendous computation time. This paper improves the performance of a representative one-sided block Jacoby algorithm using a two-dimensional (2D) multi-core system. In addition, this paper explores an optimal multi-core system by varying the number of processing elements in the 2D multi-core system with the same 400MHz clock frequency and TSMC 28nm technology for each matrix-based one-sided block Jacoby algorithm ($128{\times}128$, $64{\times}64$, $32{\times}32$, $16{\times}16$). Moreover, this paper demonstrates the potential of the 2D multi-core system for the one-sided block Jacoby algorithm by comparing the performance of the multi-core system with a commercial high-performance graphics processing unit (GPU).

• Transactions of the Korean Society of Machine Tool Engineers
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• v.17 no.4
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• pp.8-14
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• 2008

This paper aims at finding out dominant robot configurations with maximal position errors, which can be attributed to the parameter errors, by using Monte-Carlo simulation for error analysis of a 3-axis SCARA(Selective Compliance Assembly Robot Arm) type robot. In particular, the Monte-Carlo simulation is used for virtually measuring on the position errors, instead of physical measurement. In order to measure the observability of the model parameters with respect to a set of robot configurations, we propose the observability index which is defined as the product of singular values for error propagation matrices. Thus the index can be used for discriminating dominant robot configurations from a set of simulated ones in conjunction with standard deviation of positional errors, This paper analyzed error by robot positional error.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.198-200
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• 1987

This paper presents the choice of appropriate sets of input variables for large-scale linear multivariable systems. It is shown that the selection of a good set of input variables for control may become important when both strong and weak input variables are available. The transmission of information from the inputs to the outputs is investigated and appropriate scaling procedures to derive a scaled input matrix are proposed. Singular value decomposition methods facilitate the quantification of the systems excitation stemming from the various input variables, and thus the selection of an appropriately strong and orthogonal set of input variables. The need for and the implementation and benefits of reducing the number of input variables are illustrated by a large-scale steam generator model of a real process.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.1
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• pp.1-8
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• 2010

The Fourier series uses a vibrating wave that possesses an amplitude that is like the one of the sine curve. Therefore, the functions used in the Fourier series do not change due to the value of the frequency and that set a limit to express irregular signals with rapid oscillations or with discontinuities in localized regions. However, the wavelet series analysis(WSA) method supplements these limits of the Fourier series by a linear combination of a suitable number of wavelets. By using the wavelet that is focused on time, it is able to give changes to the range in the cycle. Also, this enables to express a signal more efficiently that has singular configuration and that is flowing. The main objective of this study is to propose a scheme called wavelet series analysis for the application of wavelet theory to one-dimensional problems represented by the second-order elliptic equation and to evaluate theperformance of proposed scheme comparing with the finite element analysis. After a through evaluation of different types of wavelets, the HAT wavelet system is chosen as a wavelet function as well as a scaling function. It can be stated that the WSA method is as efficient as the FEA method in the case of axial bars with distributed loads, but the WSA method is more accurate than the FEA method at the singular points and its computation time is less.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1841-1850
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• 2014

It is known that the ranks of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{\ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $\mathcal{SOP}_n$ and $\mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $\mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{\leq}m{\leq}n-1$, the m-potent ranks of the semigroups $\mathcal{SOP}_n$ and $\mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $\mathcal{SSPOP}_n$ is n + 1.

• 한국해양학회지
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• v.30 no.6
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• pp.543-549
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• 1995

The inverse method has been used to estimate a surface velocity field from sequential AVHRR/SST data. In the model, equation system was composed of heat equation and horizontal divergence minimization and the velocity field contained in the advective term of the heat equation, which was linearized in grid system, was estimated. A constraint was the minimization of horizontal divergence with weighting factor and introduced to compensate the null space(Menke, 1984) of the velocity solutions for the heat equation. The experiments were carried out to set up the range of weighting factor and the matrix equation was solved by SVD(Singular Value Decomposion). In the experiment, the scales of horizontal temperature gradient and divergence of synthetic velocity field were approximated to those of real field. The neglected diffusive effect and the horizontal variation of heat flux in the heat equation were regarded as random temperature errors. According to the result of experiments, the minimum of relative error was more desirable than the minimum of misfit as the criteria of setting up the weighting factor and the error of estimated velocity field became small when the weighting factor was order of $10^{-1}$

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.159-165
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• 2005

This paper designs observers for matrix second-order linear systems on the basis of generalized eigenstructure assignment via unified parametric approach. It is shown that the problem is closely related with a type of so-called generalized matrix second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass system is utilized to show the effect of the proposed approaches.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1101-1123
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• 2011

Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.483-501
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• 2018

In this paper, we present some recent results on weighted pointwise convergence and the rate of pointwise convergence for the family of nonlinear double singular integral operators in the following form: $$T_{\eta}(f;x,y)={\int}{\int\limits_{{\mathbb{R}^2}}}K_{\eta}(t-x,\;s-y,\;f(t,s))dsdt,\;(x,y){\in}{\mathbb{R}^2},\;{\eta}{\in}{\Lambda}$$, where the function $f:{\mathbb{R}}^2{\rightarrow}{\mathbb{R}}$ is Lebesgue measurable on ${\mathbb{R}}^2$ and ${\Lambda}$ is a non-empty set of indices. Further, we provide an example to support these theoretical results.