• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.729-741
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• 2019

In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.

• Journal of Broadcast Engineering
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• v.19 no.1
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• pp.64-74
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• 2014

The primary and ambient signal decomposition of a stereo sound is a key step to the stereo upmix. The principal component analysis (PCA) is one of the most widely used methods of primary-ambient signal decomposition. However, previous PCA-based decomposition algorithms assume that stereo sound sources are only amplitude-panned without any consideration of phase difference. So it occurs some performance degradation in case of live recorded stereo sound. In this paper, we propose a new PCA-based stereo decomposition algorithm that can consider the phase difference between the channel signals. The proposed algorithm overcomes limitation of conventional signal model using PCA with phase alignment. The phase alignment is realized by using inter-channel phase difference (IPD) which is widely used in parametric stereo coding. Moreover, Enhanced Modified PCA(EMPCA) is combined to solve the problem of conventional PCA caused by Primary to Ambient energy Ratio(PAR) and panning angle dependency. The simulation results are presented to show the improvements of the proposed algorithm.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.475-484
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• 2023

Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.475-483
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• 2017

In this paper we consider the tight closure of an ideal relative to a module whose its zero submodule has a primary decomposition.

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.4
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• pp.27-33
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• 1996

In this paper we introduce the notions of T-generalized state machines and primary submachines of T-generalized state machines and obtain a decomposition theorem for T-generalized state machine in terms of primary submachines.

• Smart Structures and Systems
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• v.11 no.1
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• pp.123-134
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• 2013

Identifying structural modal parameters, especially those modes within high frequency range, from ambient data is still a challenging problem due to various kinds of uncertainty involved in vibration measurements. A procedure applying an ensemble empirical mode decomposition (EEMD) method is proposed for accurate and robust structural modal identification. In the proposed method, the EEMD process is first implemented to decompose the original ambient data to a set of intrinsic mode functions (IMFs), which are zero-mean time series with energy in narrow frequency bands. Subsequently, a Sub-PolyMAX method is performed in narrow frequency bands by using IMFs as primary data for structural modal identification. The merit of the proposed method is that it performs structural identification in narrow frequency bands (take IMFs as primary data), unlike the traditional method in the whole frequency space (take original measurements as primary data), thus it produces more accurate identification results. A numerical example and a multiple-span continuous steel bridge have been investigated to verify the effectiveness of the proposed method.

• Journal of Wetlands Research
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• v.12 no.1
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• pp.15-22
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• 2010

We measured net primary productivity, annual accumulation of organic carbon and leaf decomposition of Salix community in the flood plain of the Han River and the Nakdong River. Net primary productivity, annual accumulation of organic carbon of the Salix community were 22.5ton/ha/yr(16.7ton/ha/yr-31.2ton/ha/yr) and 9.7ton C/ha/yr(7.5ton C/ha/yr-14.0ton C/ha/yr) respectively, which showed the highest values among the woody plant communities reported in the Korea. It means that planting Salix in the flood plain of the river is the best way to remove carbon dioxides. The faster leaf decomposition occurred around, under and the herb of Salix community in order. Leaf decomposition rate of Salix was higher than that of mesophytes, but lower than that of hydrophytes.

• East Asian mathematical journal
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• v.16 no.2
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• pp.277-301
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• 2000

• Journal of Broadcast Engineering
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• v.17 no.6
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• pp.924-932
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• 2012

Decomposition of a stereo signal into the primary and ambient components is a key step to the stereo upmix and it is often based on the principal component analysis (PCA). However, major shortcoming of the PCA-based method is that accuracy of the decomposed components is dependent on both the primary-to-ambient power ratio (PAR) and the panning angle. Previously, a modified PCA was suggested to solve the PAR-dependent problem. However, its performance is still dependent on the panning angle of the primary signal. In this paper, we proposed a new PCA-based primary-ambient decomposition algorithm whose performance is not affected by the PAR as well as the panning angle. The proposed algorithm finds scale factors based on a criterion that is set to preserve the powers of the mixed components, so that the original primary and ambient powers are correctly retrieved. Simulation results are presented to show the effectiveness of the proposed algorithm.

• Environmental and Resource Economics Review
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• v.23 no.2
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• pp.305-330
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• 2014

There has been a lot of studies to identify the driving forces of energy consumption. Many of them decomposed the final energy consumption into the intensity effect, structural effect, and production effect. Those approach, however, could not consider the transformation loss during the electric power generation. Therefore, in this study, we conducted a decomposition analysis on the primary energy use basis to reflect that transformation loss. Log mean Divisia index and refined Laspeyres methods were used for the index decomposition. As results, we could find out that the difference between two approaches were definite. The intensity effect in 2011 is -0.607 times against 1981 in the final energy case, but -0.236 times in the primary energy case. The structure effect in 2011 is 0.227 times against 1981 in the final energy case, but 0.434 times in the primary energy case. Therefore, an analysis on the primary energy basis is essential when conducting a decomposition analysis.