• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.141-154
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• 2022

Let R be a commutative ring with identity. Denote by w𝒫_w the class of weak w-projective R-modules and by w𝒫_w^⊥ the right orthogonal complement of w𝒫_w. It is shown that (w𝒫_w, w𝒫_w^⊥) is a hereditary and complete cotorsion theory, and so every R-module has a special weak w-projective precover. We also give some necessary and sufficient conditions for weak w-projective modules to be w-projective. Finally it is shown that when we discuss the existence of a weak w-projective cover of a module, it is enough to consider the w-envelope of the module.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.29 no.3
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• pp.184-191
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• 2018

Orthogonal frequency division multiplexing(OFDM) is a multicarrier modulation(MCM) system that enables high-speed communications using multiple carriers and has advantages of power and spectral efficiency. Therefore, this study aims to complement the existing shortcomings and to design an efficient MCM system. The proposed system uses the inverse discrete wavelet transform(IDWT) operation instead of the inverse fast Fourier transform(IFFT) operation. The bit error rate(BER), spectral efficiency, and peak-to-average power ratio(PAPR) performance were compared with the conventional OFDM system through the OFDM system design based on wavelet transform. Our results showed that the conventional OFDM and Wavelet-OFDM exhibited the same BER performance, and that the Wavelet-OFDM using the discrete Meyer wavelet had the same spectral efficiency as the conventional OFDM. In addition, all systems of Wavelet-OFDM based on various wavelets confirm a PAPR performance lower than that of conventional OFDM.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.86-100
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• 2008

Most of the previously employed dynamic modeling approaches, including Natural Orthogonal Complement Algorithm, have limitations on their application to the mobile robot, specifically at singular configurations. Also, in their dynamic modeling of mobile robots, wheel dynamics is usually ignored assuming that its dynamic effect is negligibly small. As a remedy for this, a singularity-free operational space dynamic modeling approach based on Lagrange's form of the D' Alembert principle is proposed, and the singularity-free characteristic of the proposed dynamic modeling is discussed in the process of analytical derivation of the proposed dynamic model. Then an accurate dynamic model taking into account the wheel dynamics of the omni-directional mobile robot is derived, and through simulation it is manifested that the effect of the wheel dynamics on the whole dynamic model of the mobile robot may not be negligible, but rather in some cases it is significantly large, possibly affecting the operational performances of dynamic model-based control algorithms. Lastly, the importance of its accurate dynamic model is further illustrated through impulse analysis and its simulation for the mobile robot.