• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.651-684
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• 2022

Let G be an arbitrary, connected, simply connected and unimodular Lie group of dimension 3. On the space 𝔐(G) of left-invariant Lorentzian metrics on G, there exists a natural action of the group Aut(G) of automorphisms of G, so it yields an equivalence relation ≃ on 𝔐(G), in the following way: h₁ ≃ h₂ ⇔ h₂ = 𝜙^*(h₁) for some 𝜙 ∈ Aut(G). In this paper a procedure to compute the orbit space Aut(G)/𝔐(G) (so called moduli space of 𝔐(G)) is given.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.751-763
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• 2005

For a given gauge invariant state $\omega$ on the CAR algebra A isomorphic with the C$\ast$ -algebra of $2{\times}2$ complex matrices, we construct a family of quantum Markov semigroups on A which leave w invariant. By analyzing their generators, we decompose the algebra A into four eigenspaces of the semigroups and show some properties.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.149-156
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• 2007

This study suggests a new method for testing seasonal unit roots in a momentum threshold autoregressive (MTAR) process. This sign test is robust against heteroscedastic or heavy tailed errors and is invariant to monotone data transformation. The proposed test is a seasonal extension of the sign test of Park and Shin (2006). In the case of partial seasonal unit root in an MTAR model, a Monte-Carlo study shows that the proposed test has better power than the seasonal sign test developed for AR model.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.2
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• pp.178-183
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• 2013

In this study, we proposed a method for electroencephalogram (EEG) classification using invariant CSP at special channels for improving the accuracy of classification. Based on the naive EEG signals from left and right hand movement experiment, the noises of contaminated data set should be eliminate and the proposed method can deal with the de-noising of data set. The considering data set are collected from the special channels for right and left hand movements around the motor cortex area. The proposed method is based on the fit of the adjusted parameter to decline the affect of invariant parts in raw signals and can increase the classification accuracy. We have run the simulation for hundreds time for each parameter and get averaged value to get the last result for comparison. The experimental results show the accuracy is improved more than the original method, the highest result reach to 89.74%.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.287-295
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• 2014

In this paper, we prove that the image of the representation of the automorphism group of a supersingular K3 surface of Artin-invariant 1 over odd characteristic p on the global two forms is a finite cyclic group of order p + 1. Using this result, we deduce, for such a K3 surface, there exists an automorphism which cannot be lifted over a field of characteristic 0.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.701-707
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• 1998

An operator $T{\in} {{\mathcal L}(H)}$ is generalized k-quasihyponormal if there exist a constant M>0 such that $T^{\ast k}[M^2(T-z)^{\ast}(T-z)-(T-z)(T-z)^{\ast}]T^k{\geq}0$ for some integer $k{\geq}0$ and all $Z{\in} {\mathbf C}$. In this paper, we show that it T is a generalized k-quasihyponormal operator with the property $0{\not\in}{\sigma}(T)$, then T is subscalar of order 2. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum has interior in C.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.879-889
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• 2011

In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• Proceedings of the IEEK Conference
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• 2000.11d
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• pp.65-68
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• 2000

This paper describes an approach for extracting invariant features using a view-based representation and recognizing an object with a high speed search method in FLIR. In this paper, we use a reformulated eigenspace technique based on robust estimation for extracting features which are robust for outlier such as noise and clutter. After extracting feature, we recognize an object using a partial distance search method for calculating Euclidean distance. The experimental results show that the proposed method achieves the improvement of recognition rate compared with standard PCA.

• IEIE Transactions on Smart Processing and Computing
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• v.5 no.3
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• pp.178-184
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• 2016

This paper proposes a new path-finding scheme using viewpoint-invariant landmarks. The scheme introduces the concept of landmark detection in images captured with a vision sensor attached to a mobile robot, and provides landmark clues to determine a path. Experiment results show that the scheme efficiently detects landmarks with changes in scenes due to the robot's movement. The scheme accurately detects landmarks and reduces the overall landmark computation cost. The robot moves in the room to capture different images. It can efficiently detect landmarks in the room from different viewpoints of each scene. The outcome of the proposed scheme results in accurate and obstacle-free path estimation.