• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1069-1083
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• 2016

In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M: (1) M is e-local; (2) $Rad_e(M)$ is a maximal submodule of M and every proper essential submodule of M is contained in a maximal submodule; (3) M has a unique essential maximal submodule and every proper essential submodule of M is contained in a maximal submodule.

• Journal of Power Electronics
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• v.17 no.5
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• pp.1308-1316
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• 2017

The distributed maximum power point tracking (DMPPT) concept is widely adopted in photovoltaic systems to avoid mismatch loss. However, the high cost and complexity of DMPPT hinder its further promotion in practice. Based on the concept of DMPPT, this paper presents an integrated submodule level half-bridge stack structure along with an optimal current point tracking (OCPT) control algorithm. In this full power processing integrated solution, the number of power switches and passive components is greatly reduced. On the other hand, only one current sensor and its related AD unit are needed to perform the ideal maximum power generation for all of the PV submodules in any irradiance case. The proposal can totally eliminate different small-scaled mismatch effects in real-word condition and the true maximum power point of each PV submodule can be achieved. As a result, the ideal maximum power output of the whole PV system can be achieved. Compared with current solutions, the proposal further develops the integration level of submodule DMPPT solutions with a lower cost and a smaller size. Moreover, the individual MPPT tracking for all of the submodules are guaranteed.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.445-453
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• 2005

We say that a module M is weak lifting if M is supplemented and every supplement submodule of M is a direct summand. The module M is called lifting, if it is weak lifting and amply supplemented. This paper investigates the structure of weak lifting modules and lifting modules having small radical over commutative noetherian rings.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.293-300
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• 2020

In this article, we define a (an amply) F_δ-supplemented module in category of R-Mod. The general properties of F_δ-supplemented modules are briefly discussed. Then, concentrating on the F_δ-small submodule, we find the necessary and sufficient condition for F_δ- supplemented modules. Also, we introduce ascending chain condition for F_δ-small submodules of any module and establish a basic theorem for amply F_δ-supplemented modules by using π-projectivity.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1305-1319
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• 2014

A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism $N{\rightarrow}S$ can be extended to a homomorphism $M{\rightarrow}S$. M is called coneat-flat if the kernel of any epimorphism $Y{\rightarrow}M{\rightarrow}0$ is coneat in Y. It is proven that (1) coneat submodules of any right R-module are coclosed if and only if R is right K-ring; (2) every right R-module is coneat-flat if and only if R is right V -ring; (3) coneat submodules of right injective modules are exactly the modules which have no maximal submodules if and only if R is right small ring. If R is commutative, then a module M is coneat-flat if and only if $M^+$ is m-injective. Every maximal left ideal of R is finitely generated if and only if every absolutely pure left R-module is m-injective. A commutative ring R is perfect if and only if every coneat-flat module is projective. We also study the rings over which coneat-flat and flat modules coincide.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.289-300
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• 2015

In [9], the author extends the definition of lifting and supplemented modules to ${\delta}$-lifting and ${\delta}$-supplemented by replacing "small submodule" with "${\delta}$-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of ${\delta}$-lifting and ${\delta}$-supplemented modules. Especially, we show that any finite direct sum of ${\delta}$-hollow modules is ${\delta}$-supplemented. On the other hand, the notion of amply ${\delta}$-supplemented modules is studied as a generalization of amply supplemented modules and several properties of these modules are given. We also prove that a module M is Artinian if and only if M is amply ${\delta}$-supplemented and satisfies Descending Chain Condition (DCC) on ${\delta}$-supplemented modules and on ${\delta}$-small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a ${\delta}$-semiperfect ring which satisfies DCC on ${\delta}$-small right ideals of R.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.30 no.5
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• pp.325-330
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• 2017

We fabricated 1-D and 2-D diffraction gratings of SiOx anti-reflection (AR) film grown on a quartz substrate and integrated them into a c-Si photovoltaic (PV) submodule. The light-trapping effect of the resulting submodules was studied in terms of the oblique optical incident angle, ${\theta}_i$. As the ${\theta}_i$ increased, solar conversion efficiency, ${\eta}$, was improved as expected by the increased optical transmission caused by the grating. For ${\theta}_i{\leq}30^{\circ}$, the relative solar conversion efficiency, ${\Delta}{\eta}$, of a 1-D SiOx (t=300 nm) grating, compared to that of a flat SiOx AR-coated integrated PV submodule, was improved very little, with a small variation of within 2%, but increased markedly for ${\theta}_i{\geq}40^{\circ}$. We observed a change of ${\Delta}{\eta}$ as large as 10.7% and 9.5% for the SiOx grating of period t=800 nm and 1200 nm, respectively. For a 2-D SiOx (t=300 nm) grating integrated PV submodule, however, the optical trapping behavior was similar in terms of ${\theta}_i$ but its variation was small, within ${\pm}1.0%$.

• Journal of the Korean Institute of Telematics and Electronics
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• v.18 no.3
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• pp.52-57
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• 1981

This paper deals with the development of a design approach to generate easily testable complex digital systems. As the technique is based on small testable building blocks (submodule) with the exhaustive testing circuits, it is not necessary for any automatic test equipment and signature analyzer. As a result ,the test time which is determined not by circuit complexity but sixte of the tarprest submodule, is not exhaustive and also, the circuit reliability is very high.

• 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.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.51-58
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• 2009

Let R be a ring. A right R-module M is called perfect if M possesses a projective cover. In this paper, we consider the relationship between the class of perfect modules and other classes of modules. Some known rings are characterized by these relationships.