• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1213-1222
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• 2013

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group G over a field $\mathbb{K}$ where the group G is a semidirect product of a normal abelian subgroup N and a subgroup H. The main results are proved with the assumption that char $\mathbb{K}$ does not divide |G| but there is no assumption made of $\mathbb{K}$ being algebraically closed.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.693-699
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• 2010

In this paper we show that the flat property of a left R-module does not imply (carry over) to the corresponding inverse polynomial module. Then we define an induced inverse polynomial module as an R[x]-module, i.e., given an R-linear map f : M $\rightarrow$ N of left R-modules, we define $N+x^{-1}M[x^{-1}]$ as a left R[x]-module. Given an exact sequence of left R-modules $$0\;{\rightarrow}\;N\;{\rightarrow}\;E^0\;{\rightarrow}\;E^1\;{\rightarrow}\;0$$, where $E^0$, $E^1$ injective, we show $E^1\;+\;x^{-1}E^0[[x^{-1}]]$ is not an injective left R[x]-module, while $E^0[[x^{-1}]]$ is an injective left R[x]-module. Make a left R-module N as a left R[x]-module by xN = 0. We show inj $dim_R$ N = n implies inj $dim_{R[x]}$ N = n + 1 by using the induced inverse polynomial modules and their properties.

• Korean Journal of Materials Research
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• v.24 no.6
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• pp.326-337
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• 2014

The use of solar energy generation is steadily increasing, and photovoltaic modules are connected in series to generate higher voltage and power. However, solar panels are exposed to high-voltage stress (up to several hundreds of volts) between grounded module frames and the solar cells. Frequent high-voltage stress causes a power-drop in the modules, and this kind of degradation is called potential induced degradation (PID). Due to PID, a significant loss of power and performance has been reported in recent years. Many groups have suggested how to prevent or reduce PID, and have tried to determine the origin and mechanism of PID. Even so, the mechanism of PID is still unclear. This paper is focused on understanding the PID of crystalline-silicon solar cells and modules. A background for PID, as well as overviews of research on factors accelerating PID, mechanisms involving sodium ions, PID test methods, and possible solutions to the problem of PID, are covered in this paper.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1617-1642
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• 2019

In this paper, we study a theory for the structure of ${\tau}_w$-Loewy series of modules over commutative rings, where ${\tau}_w$ is the hereditary torsion theory induced by the so-called w-operation, and explore the relationship between ${\tau}_w$-Loewy modules and w-Artinian modules.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.1-12
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• 2024

In this paper, we introduce the notion of Gorenstein (m, n)-flat modules as an extension of (m, n)-flat left R-modules over a ring R, where m and n are two fixed positive integers. We demonstrate that the class of all Gorenstein (m, n)-flat modules forms a Kaplansky class and establish that (𝓖𝓕_m,n(R),𝓖𝓒_m,n(R)) constitutes a hereditary perfect cotorsion pair (where 𝓖𝓕_m,n(R) denotes the class of Gorenstein (m, n)-flat modules and 𝓖𝓒_m,n(R) refers to the class of Gorenstein (m, n)-cotorsion modules) over slightly (m, n)-coherent rings.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1389-1421
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• 2018

In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where R and S are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of C-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.307-314
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• 2012

Let M be a left R-module and R be a ring with unity, and $S=\{0,2,3,4,{\ldots}\}$ be a submonoid. Then $M[x^{-s}]=\{a_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ is an $R[x^s]$-module. In this paper we show some properties of $M[x^{-s}]$ as an $R[x^s]$-module. Let $f:M{\rightarrow}N$ be an R-linear map and $\overline{M}[x^{-s}]=\{a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ and define $N+\overline{M}[x^{-s}]=\{b_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}b_0{\in}N,\;a_i{\in}M}$. Then $N+\overline{M}[x^{-s}]$ is an $R[x^s]$-module. We show that given a short exact sequence $0{\rightarrow}L{\rightarrow}M{\rightarrow}N{\rightarrow}0$ of R-modules, $0{\rightarrow}L{\rightarrow}M[x^{-s}]{\rightarrow}N+\overline{M}[x^{-s}]{\rightarrow}0$ is a short exact sequence of $R[x^s]$-module. Then we show $E_1+\overline{E_0}[x^{-s}]$ is not an injective left $R[x^s]$-module, in general.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.405-423
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• 2023

Let (𝓛, 𝒜) be a complete duality pair. We give some equivalent characterizations of Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures and recollements associated to them.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.7
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• pp.1-14
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• 1996

Effects of the external optical feedback on the optical transmission characteristics were evaluated for 3 kinds of commercialized DFB-LD modules for 2.5Gbps optical communication systems. As a result, intensity noise induced by external optical feedback via generating the external cavity modes deteriorated the transmission performances of sthe DFB-LD modules as much as 1.5dB, 1.2dB, and 1.0dB for the maximum feedback ratio of -8.8dB which corresponds to the worst reflection along the fiber transmission line. Additional penalty of 0.5dB was occurrred when state of polarization of feedback light was adjusted. From the experiments evaluating the isolation ratio of the single polarization optical isolator, decrease of the polarization dependent isolation ratio as much as 10dB from that of specification and the effective isolation ratio as much as 20dB from that of specification was mjor cause of high sensitivity of DFB-LD modules to external feedback. It was suggested that polarization independent optical isolator or single polarization optical isolator with isolation ratio specification of more than 40dB is required for 2.5Gbps DFB-LD modules with complete suppression of external feedback effects.

• Laser Solutions
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• v.11 no.2
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• pp.33-38
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• 2008

Laser micromachining has increasingly been adopted in various advanced industries where the high-precision machining of large-area, high-density and multi-layered components is in a strong demand. To effectively meet the requirements, the laser micromachining process must be carefully monitored. In order to facilitate the development of a new laser micromachining process and/or a new system, we have fabricated a UV laser micromachining platform that is equipped with optical modules for monitoring the process online. They include a laser power stabilizing module, a module for laser-induced breakdown spectroscopy, and an auto-focusing module.