• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• Korean Journal of Materials Research
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• v.29 no.11
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• pp.703-708
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• 2019

In this study, we investigate the relationship between the peeling behavior of the backsheet of a photovoltaic(PV) module and its surface temperature in order facilitate removal of the backsheet from the PV module. At low temperatures, the backsheet does not peel off whereas, at high temperatures, part of the backsheet remains on the surface of the PV module after the peeling process. The backsheet material remaining on the surface of the PV module is confirmed by X-ray diffraction(XRD) analysis to be poly-ethylene(PE). Differential scanning calorimetry(DSC) is also performed to investigate the interfacial characteristics of the layers of the PV module. In particular, DSC provides the melting temperature($T_m$) of laminated ethylene vinyl acetate(EVA) and of the backsheet on the PV module. It is found that the backsheet does not peel off below the $T_m$ of ethylene of EVA, while the PE layer of the backsheet remains on the surface of the PV module above the $T_m$ of the PE. Thus, the backsheet is best removed at a temperature between the $T_m$ of ethylene and that of PE layer.

• Journal of Korean Society of Water and Wastewater
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• v.31 no.4
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• pp.339-346
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• 2017

In this study, thermal performance test of VMD module was performed, prior to the construction of the demonstration plant using the vacuum membrane distillation (VMD) module of the capacity of $400m^3/day$ and to the commercialization of the VMD module. For the thermal performance test, the experimental equipment of capacity of $2m^3/day$ was constructed. The permeate flux test and thermal performance test according to feed water conditions such as temperature and flow rate were conducted. The VMD module used in the study was manufactured by ECONITY Co., LTD with PVDF hollow fiber membrane. As a result, the Performance Ratio (PR) of the VMD module showed the maximum value of 0.904 under the condition of feed water temperature of $75^{\circ}C$ and flow rate of $8m^3/h$. PR value of the VMD module using PVDF hollow fiber membrane showed linearly increasing relationship with feed water temperature and flow rate. Also, The permeate flux of the VMD module was analyzed to have maximum value of 18.25 LMH and the salt rejection was 99.99%.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.251-258
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• 2002

Let R be a commutative Noetherian ring and M an R-module. In this paper we will consider the asymptotic behaviour of ideals relative to an R-module E which is M-injective.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.153-164
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• 1994

Let A be a commutative ring with identity and M an A-module. When $U_n$ is a triangular subset of $A_n$, Sharp and Zakeri defined a module of generalized fractions $U_n^{-n}M$. In [SZ3], they described a relation of the Monomial Conjecture and a module of generalized fractions under the condition of a Noetherian local ring. In this paper, we investigate some properties of non-zero generalized fractions and give a generalization of results of Sharp and Zakeri for an arbitrary ring.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.273-280
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• 2024

Let I be an ideal of a commutative Noetherian semi-local ring R and M be an R-module. It is shown that if dim M ≤ 2 and Supp_R M ⊆ V (I), then M is I-weakly cofinite if (and only if) the R-modules Hom_R(R/I, M) and Ext¹_R(R/I, M) are weakly Laskerian. As a consequence of this result, it is shown that the category of all I-weakly cofinite modules X with dim X ≤ 2, forms an Abelian subcategory of the category of all R-modules. Finally, it is shown that if dim R/I ≤ 2, then for each pair of finitely generated R-modules M and N and each pair of the integers i, j ≥ 0, the R-modules Tor^R_i(N, H^j_I(M)) and Extⁱ_R(N, H^j_I(M)) are I-weakly cofinite.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.545-551
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• 2009

We investigate the behavior of maps in minimal injective resolution of an A-module M when ${\mu}_t$(m,M) = 1 for some t, and we develop slightly the fact that a module of type 1 is Cohen-Macaulay.

• Journal of Astronomy and Space Sciences
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• v.26 no.1
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• pp.127-140
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• 2009

COMS DATS C&M software is an integrated management system providing control and monitoring functionalities for COMS IDACS (Image Data Acquisition and Control System). DATS C&M S/W consists of a system management module, a control and monitoring module, a data management module, and a trend analysis module. COMS SOC is supposed to operate IDACS as a backup of MSC. Especially, for the backup operation, the control and monitoring module of DATS C&M S/W is designed to support the synchronization of the two IDACS systems. This paper describes design, implementation, and result of development of DATS C&M S/W.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.591-600
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• 2020

A module M is called ss-semilocal if every submodule U of M has a weak supplement V in M such that U∩V is semisimple. In this paper, we provide the basic properties of ss-semilocal modules. In particular, it is proved that, for a ring R, _RR is ss-semilocal if and only if every left R-module is ss-semilocal if and only if R is semilocal and Rad(R) ⊆ Soc(RR). We define projective ss-covers and prove the rings with the property that every (simple) module has a projective ss-cover are ss-semilocal.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.917-928
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• 2022

Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let M be a finitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension r^I(M, N) and artinianness dimension a^I(M, N) of M, N with respect to I by r^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not representable} and a^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not artinian} and we show that a^I(M, N) = r^I(M, N) = inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)} ≥ inf{a^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)}. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N/∩_t>0I^tN is artinian we prove that inf{i : H^I_i(M, N) is not minimax}=inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)＼Max(R)}.