• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.557-562
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• 2009

A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about $C_{11}$ and SIP-modules.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-257
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• 1995

In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.973-990
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• 2020

For the question "when is E(_RR) a flat left R-module for any ring R?", in this paper, we deal with a class of modules partaking in the hierarchy of injective and cotorsion modules, so-called Harmanci injective modules, which turn out by the motivation of relations among the concepts of injectivity, flatness and cotorsionness. We give some characterizations and properties of this class of modules. It is shown that the class of all Harmanci injective modules is enveloping, and forms a perfect cotorsion theory with the class of modules whose character modules are Matlis injective. For the objective we pursue, we characterize when the injective envelope of a ring as a module over itself is a flat module.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.691-707
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• 2020

In this paper, we introduce and study the notions of weakly ⊕-supplemented modules, weakly D2 modules and weakly D2-covers. A right R-module M is called weakly ⊕-supplemented if every non-small submodule of M has a supplement that is not essential in M, and module M_R is called weakly D2 if it satisfies the condition: for every s ∈ S and s ≠ 0, if there exists n ∈ ℕ such that sⁿ ≠ 0 and Im(sⁿ) is a direct summand of M, then Ker(sⁿ) is a direct summand of M. The class of weakly ⊕-supplemented-modules and weakly D2 modules contains ⊕-supplemented modules and D2 modules, respectively, and they are equivalent in case M is uniform, and projective, respectively.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.163-165
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• 1994

Modules which satisfy the converse of Schur's lemma have been studied by many authors. In [6], R. Ware proved that a projective module P over a semiprime ring R is irreducible if and only if En $d_{R}$(P) is a division ring. Also, Y. Hirano and J.K. Park proved that a torsionless module M over a semiprime ring R is irreducible if and only if En $d_{R}$(M) is a division ring. In case R is a commutative ring, we obtain the following: An R-module M is irreducible if and only if En $d_{R}$(M) is a division ring and M is a multiplication R-module. Throughout this paper, R is commutative ring with identity and all modules are unital left R-modules. Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for each submodule N of M, there exists and ideal I of R such that N=IM. Cyclic R-modules are multiplication modules. In particular, irreducible R-modules are multiplication modules.dules.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.673-682
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• 2020

For the recently defined notion of strongly lifting modules, it has been shown that a direct sum is not, in general, strongly lifting. In this paper we investigate the question: When are the direct sums of strongly lifting modules, also strongly lifting? We introduce the notion of a relatively strongly projective module and use it to show if M = M1 ⊕ M2 is amply supplemented, then M is strongly lifting if and only if M1 and M2 are relatively strongly projective and strongly lifting. Also, we consider when an arbitrary direct sum of hollow (resp. local) modules is strongly lifting.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2005.05a
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• pp.283-287
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• 2005

In this paper, one general approach is proposed for the design of power system that can be applicable for next generation LEO satellite application. The power system consists of solar panels, battery, and power control and distribution unit(PCDU). The PCDU contains solar array modules, battery interface modules, low-voltage power distribution modules, high-voltage distribution modules, heater power distribution modules, on-board computer interface modules, and internal DC/DC converter modules. The PCDU plays roles of protection of battery against overcharge by active control of solar array generated power, distribution of unregulated electrical power via controlled outlets to bus and instrument units, distribution of regulated electrical power to selected bus and instrument units, and provision of status monitoring and telecommand interface allowing the system and ground operate the power system, evaluate its performance and initiate appropriate countermeasures in case of abnormal conditions. We review the functional schemes of the main constitutes of the PCDU such as the battery interface module, the auxiliary supply module, solar array regulators with maximum power point tracking(MPPT) technology, heater power distribution modules, spacecraft unit power distribution modules, and instrument power distribution module.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.561-569
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• 2018

In this paper, we introduce some notions of orthogonality in the setting of Finsler $C^*$-modules and investigate their relations with the Birkhoff-James orthogonality. Suppose that ($E,{\rho}$) and ($F,{\rho}^{\prime}$) are Finsler modules over $C^*$-algebras $\mathcal{A}$ and $\mathcal{B}$, respectively, and ${\varphi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a *-homomorphism. A map ${\Psi}:E{\rightarrow}F$ is said to be a ${\varphi}$-morphism of Finsler modules if ${\rho}^{\prime}({\Psi}(x))={\varphi}({\rho}(x))$ and ${\Psi}(ax)={\varphi}(a){\Psi}(x)$ for all $a{\in}{\mathcal{A}}$ and all $x{\in}E$. We show that each ${\varphi}$-morphism of Finsler $C^*$-modules preserves the Birkhoff-James orthogonality and conversely, each surjective linear map between Finsler $C^*$-modules preserving the Birkhoff-James orthogonality is a ${\varphi}$-morphism under certain conditions. In fact, we state a version of Wigner's theorem in the framework of Finsler $C^*$-modules.

• Journal of the Korea Institute of Building Construction
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• v.13 no.6
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• pp.609-618
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• 2013

The unit modular construction system is a building technique in which unit modules are manufactured at a factory and then assembled at the construction site. It has many benefits, including reduction of the construction period and improvement in quality. For this reason, it is utilized for various purposes in Japan and England. While it has been introduced in Korea, there have been few Korean studies conducted on the unit modular system. In particular, little research has been done on the method of safely fixating the unit modules to a truck. Therefore, this study reviewed the fixation methods of unit modules for transport, analyzed the problems, and designed a fixation device for unit modules. In addition, a device for the fixation of unit modules to a truck was developed, and a structural simulation was implemented for a safety test by considering the maximum stress generated during the transport of the unit modules fixed on a truck. When the device for the fixation of unit modules is manufactured based on the results of the structural simulation done in this study, it is expected to aid the development of a more practical fixation device for unit modules.

• Journal of the Korean Solar Energy Society
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• v.40 no.5
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• pp.1-12
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• 2020

To assess the performance and characteristics of colored building-integrated photovoltaic (BIPV) modules, a comparative assessment of empirical performance was conducted on colored BIPV modules (gray, blue, and orange) and general BIPV module. These modules were installed on the south-facing slope (30°) for comparative assessment through a field test. Monitoring data were collected every 10 min from December 20, 2019 to January 21, 2020 and used to performance and characteristics analysis. Performance ratio and module efficiency were utilized during performance indexing for comparative assessment. For general BIPV modules, the operational efficiency was analyzed at 16.63%, whereas for colored BIPV modules, 13.70% (gray), 15.12 % (blue), and 14.49% (orange) were analyzed. It was discovered that the efficiency reduction caused by transmission losses owing to the application of colored cover glasses were 17.74% (gray), 9.05% (blue), and 9.86 % (orange), under field testing conditions. These values turned on an additional 7% reduction in efficiency for gray BIPV modules, compared to the degradation resulting from transmission drop (gray: 10.87%, blue: 8.99%, and orange: 9.02%) calculated using the efficiency of each module in standard test conditions (STC). Performance ratio analysis resulted in the following values: 0.92 for general BIPV modules, and 0.85 (gray), 0.91 (blue), and 0.91 (orange) for colored BIPV modules. As demonstrated by the above results, modules with a colored cover glass may differ in their operational performance depending on their color, unlike general modules. Therefore, in addition to the performance evaluation under STC, additional factors of degradation require consideration through field test.