• Journal of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.1051-1066
• /
• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.743-755
• /
• 2019

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1067-1079
• /
• 2012

Let M be a right R-module, (S, ${\leq}$) a strictly totally ordered monoid which is also artinian and ${\omega}:S{\rightarrow}Aut(R)$ a monoid homomorphism, and let $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ denote the generalized inverse polynomial module over the skew generalized power series ring [[$R^{S,{\leq}},{\omega}$]]. In this paper, we prove that $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same uniform dimension as its coefficient module $M_R$, and that if, in addition, R is a right perfect ring and S is a chain monoid, then $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same couniform dimension as its coefficient module $M_R$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.207-222
• /
• 2011

Let R be a commutative ring and let M be a GV -torsionfree R-module. Then M is said to be a $\omega$-module if $Ext_R^1$(R/J, M) = 0 for any J $\in$ GV (R), and the w-envelope of M is defined by $M_{\omega}$ = {x $\in$ E(M) | Jx $\subseteq$ M for some J $\in$ GV (R)}. In this paper, $\omega$-modules over commutative rings are considered, and the theory of $\omega$-operations is developed for arbitrary commutative rings. As applications, we give some characterizations of $\omega$-Noetherian rings and Krull rings.

• Journal of the Korean Institute of Telematics and Electronics A
• /
• v.33A no.7
• /
• pp.216-222
• /
• 1996

Since many typical 2.5 Gbps optical transmitter modules use a 50$\Omega$ characteristic impedance, they require relatively high voltage and high power sources compared to the 25$\Omega$ module. However, simple replacement of the 50$\Omega$ internal matching impedance with 25$\Omega$ results in bandwidth reduction and consequent problem of data transmitter module is proposed in order to expand the modulator bandwidth. From the calculated resutls based on accurate 3-dimensional inductance analysis, we have found that the series parasitic inductance is a dominant element limiting the bandwidth and the insertion of a 2.5pF capacitor in parallel to the 20$\Omega$ matching resiter can increase the 3 dB bandwidth about 1.4GHz wider. The time-domain results show the rise time (140 psec) without the compensation is greatly improved to 63 psec with the compensation. This capacitive ocmpensation can be implemented easily and be compatible with common manufacturing process of the optical transmitter module.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.475-483
• /
• 2013

We give some characterizations of injective modules over ${\omega}$-Noetherian rings. It is also shown that each localization of a GV-torsion-free injective module over a ${\omega}$-Noetherian ring is injective.

• Journal of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.971-985
• /
• 2014

All modules considered in this note are over associative commutative rings with an identity element. We show that a ${\omega}$-local module M is Rad-supplemented if and only if M/P(M) is a local module, where P(M) is the sum of all radical submodules of M. We prove that ${\omega}$-local nonsmall submodules of a cyclic Rad-supplemented module are again Rad-supplemented. It is shown that commutative Noetherian rings over which every w-local Rad-supplemented module is supplemented are Artinian. We also prove that if a finitely generated Rad-supplemented module is cyclic or multiplication, then it is amply Rad-supplemented. We conclude the paper with a characterization of finitely generated amply Rad-supplemented left modules over any ring (not necessarily commutative).

• Journal of the Korean Society of Safety
• /
• v.33 no.1
• /
• pp.28-34
• /
• 2018

The purpose of this study is to fabricate a sensor module to detect the resistive leakage current (Igr) in real time that occurs to low voltage electric lines and to verify its reliability. In the case of the developed sensor module, wires are inserted into the zero current transformer (ZCT) and current transformer (CT) in advance and then the branch line is connected to the circuit breaker. The measurement result of the resistance of the distribution panel equipped with the developed sensor module shows that the resistance is $0.151m{\Omega}$ between the R and R phases, $0.169m{\Omega}$ between the S and S phases, and $0.178m{\Omega}$ between the T and T phases, respectively. The insulation resistance measured at AC 500 V and 1,000 V is $0.08m{\Omega}$ between the R, S, T and N phases, respectively. Then, the insulation resistance measured at DC 500 V is $83.3G{\Omega}$ between the R, S, T and G terminal, respectively. In addition, the applied withstanding voltage is AC 220 V/380 V/440 V and it was found that characteristics between all phases are good. This study measured the standby power by installing the developed sensor module at the rear of the MCCB and switching the circuit breaker on sequentially. The standby power is 1.350 W when one circuit breaker is turned on, 1.690 W when 2 circuit breakers are turned on, and 4.371 W when 10 circuit breakers are turned on. This study also verified the reliability of the standby power of the distribution panel equipped with the developed sensor module using the Minitab Program (Minitab PGM). Since the analysis shows the statistical average of 1.34627 in the reliable range of normal distribution, standard deviation of 0.001874, AD of 0.554, and P value of 0.140, it is found that the distribution panel equipped with the developed sensor module has high reliability.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.14 no.11
• /
• pp.1198-1206
• /
• 2003

In this paper, a MMIC waveguide mixer module based upon the novel suggested mode converter for wave-guide-to-microstrip transition was fabricated and measured. The insertion and return losses of the mode converter was optimized by compensating the discontinuity effect between ridge and microstrip with the modification of 50 $\Omega$ microstrip line pattern. Due to the low loss nature of the mode converter, a millimeter wave MMIC mixer chip can be successfully applied as a waveguide module for mmW waveguide communication system. The measured results of the module showed the successful MMIC chip application in waveguide and the negligible degradation of the supplied chip specification.

• Membrane Journal
• /
• v.6 no.2
• /
• pp.86-95
• /
• 1996

Rotary disc ultrafiltration module(RDM) was developed for the separation of oil e$$\mu$sions. This module was devised to reduce the gel polarization phenomenon by decoupling the operation pressure and the surface velocity of solution in ultrafiltration(UF) processes. The rotary disc membrane consists of 3mm-thick ABS plate covered with UF membrane (UOP, U.S.A.). When the angular velocity($\omega$) was increased, the pure water flux was slightly decreased due to pressure drop caused by centrifugal force and slip flow at the surface of membrane. The pressure drop was proportional to the square of linear velocity(${\omega}r$). When the angular velocity was changed from 52.36rad/s to 2.62rad/s, the flux decline for 5% cutting oil in one-shaft RDM at $25^{\circ}C$ and 0.1MPa was 30.16%. In the lower concentrations, angular velocity tends to give less effect on the flux. Flux(J; $kg/m^{2} \cdot s$) in a rotating disc module is mainly a function of the bulk concentration($C_{B}$; %), the linear velocity(${\omega}r$; m/s) and the effective transmembrane pressure($\Delta P_{T}$ ; Pa). Using a modified resistance-in-series model, the flux data of cutting oil experiments were fitted to give the following equation.