• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.509-525
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• 2014

Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and $R_m$ is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Pr$\ddot{u}$fer v-multiplication domain.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.799-812
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• 2019

We introduce flat e-covers of modules and define e-perfect rings as a generalization of perfect rings. We prove that a ring is right perfect if and only if it is semilocal and right e-perfect which generalizes a result due to N. Ding and J. Chen. Moreover, in the light of the fact that a ring R is right perfect if and only if flat covers of any R-module are projective covers, we study on the rings over which flat covers of modules are (generalized) locally projective covers, and obtain some characterizations of (semi) perfect, A-perfect and B-perfect rings.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.439-450
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• 2019

Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.3
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• pp.25-33
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• 1997

In the design of microwave multi-stage amplifiers composed of N amplifier modules, the variation of performances of amplifier as various connection length between modules has been studied. In addition, the methods, equations and conditions for the maximum gain or the most flat gain are presented. The results of sensitivity analysis for the connection length showed that the small change in phase of input, output reflection coefficients(S$_{11}$, S$_{22}$) of module itself is the most important in determination of connection length for the most flat gain. Th egain flatness of 2-module amplifier of which connection length between modules had been determined by presented methods was the best one out of performances with various arbitrary connectio lengths.s.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.1-6
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• 2002

In this paper, an Analog Flat Panel interface(AFPI) which supports for UXGa(Ultar extended Graphics Array)-Compatible TFT LCD Driver is designed. The Proposed AFPI is composed of 8-b ADC, Automatic Gain Control(AGC), Low-Jitter PLL. In order to obtain a high speed and low power consumption, an efficient architecture of 8-bit ADC is proposed, whose FR(Folding Rate) is 8, NFB(Number of Folding Block) is 2, and IR (Interpolating Rate) is 16. We can get high SNDR by adopting distributed track and hold circuits. Also a programmable AGC which is possible to control gain and clamp, and a low-jitter PLL are proposed. The chip has been fabricated with 0.25${\mu}{\textrm}{m}$ 1-poly S-metal n-well CMOS technology. The effective chip area is 3.6mm $\times$ 3.2mm and it dissipates about 602㎽ at 2.5V power supply. The INL and DNL are within $\pm$ 1LSB. The measured SNDR is about 43㏈, when the input frequency is 10MHz at 200MHz clock frequency.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.31-47
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• 2012

The so-called Ding-Chen ring is an n-FC ring which is both left and right coherent, and has both left and right self FP-injective dimensions at most n for some non-negative integer n. In this paper, we investigate the classes of the so-called Ding projective, Ding injective and Gorenstein at modules and show that some homological properties of modules over Gorenstein rings can be generalized to the modules over Ding-Chen rings. We first consider Gorenstein at and Ding injective dimensions of modules together with Ding injective precovers. We then discuss balance of functors Hom and tensor.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• Journal of Korean Society of Water and Wastewater
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• v.21 no.2
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• pp.195-201
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• 2007

A submerged flat-sheet membrane separation system integrated with PAC (powdered activated carbon) was used in this research in order to investigate the effects of PAC on the efficiencies of operation and treatment and to evaluate the performance of the system. The experiments were carried out under operating conditions of a filtration rate of 0.38 m/d, water temperature of $20-28^{\circ}C$, and PAC dose of 0 g/L (Run-A) and 20 g/L (Run-B). The influent concentrations of TOC (total organic carbon), $NH_4{^+}-N$ (ammonia nitrogen) and $UV_{254}$ (UV absorbance at 254 nm) were 2.48 mg/L, 1.4 mg/L and 2.53 1/m, respectively. TOC removal of 43.2 and 73.6%, ammonia nitrogen removal of 4.9 and 15.9%, and $UV_{254}$ removal of 20.6 and 31.6% were obtained for Run-A and Run-B, respectively. During an experimental period of 33 days, no change was found in TMP (Run-B), but the TMP in Run-A increased by 5 kPa after 29 days. This research showed that the filtrate quality and the performance efficiency were enhanced when PAC was introduced into the filtration system.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.45-58
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• 2024

Let R be a commutative ring with identity. If the nilpotent radical N il(R) of R is a divided prime ideal, then R is called a ϕ-ring. Let R be a ϕ-ring and S be a multiplicative subset of R. In this paper, we introduce and study the class of nonnil-S-coherent rings, i.e., the rings in which all finitely generated nonnil ideals are S-finitely presented. Also, we define the concept of ϕ-S-coherent rings. Among other results, we investigate the S-version of Chase's result and Chase Theorem characterization of nonnil-coherent rings. We next study the possible transfer of the nonnil-S-coherent ring property in the amalgamated algebra along an ideal and the trivial ring extension.