• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1333-1338
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• 2018

A ${\ast}-ring$ R is called ${\ast}-regular$ if every principal one-sided ideal of R is generated by a projection. In this note, several characterizations of ${\ast}-regular$ rings are provided. In particular, it is shown that a matrix ring $M_n(R)$ is ${\ast}-regular$ if and only if R is regular and $1+x^*_1x_1+{\cdots}+x^*_{n-1}x_{n-1}$ is a unit for all $x_i$ of R; which answers a question raised in the literature recently.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1271-1290
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• 2013

Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, it coincides with prime (resp. semiprime) submodule of X. Other concepts encountered in the general theory are M-$m$-system sets, M-$n$-system sets, M-prime radical and M-Baer's lower nilradical of modules. Relationships between these concepts and basic properties are established. In particular, we identify certain submodules of M, called "primeM-ideals", that play a role analogous to that of prime (two-sided) ideals in the ring R. Using this definition, we show that if M satisfies condition H (defined later) and $Hom_R(M,X){\neq}0$ for all modules X in the category ${\sigma}[M]$, then there is a one-to-one correspondence between isomorphism classes of indecomposable M-injective modules in ${\sigma}[M]$ and prime M-ideals of M. Also, we investigate the prime M-ideals, M-prime submodules and M-prime radical of Artinian modules.

• Journal of the Korean Chemical Society
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• v.53 no.5
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• pp.491-498
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• 2009

The critical micelle concentration (CMC) and the counter ion binding constant (B) for the mixed micellizations of DBS (sodium dodecylbenzenesulfonate) with Brij 30 (polyoxyethylene(4) lauryl ether) and Brij 35 (polyoxyethylene (23) lauryl ehter) at 25 ${^{\circ}C}$ in pure water and in aqueous solutions of n-butanol were determined as a function of $\alpha$1 (the overall mole fraction of DBS) by the use of electric conductivity method. Various thermodynamic parameters (Xi, $\gamma$i, Ci, aiM, $\beta$, and ${\Delta}H_{mix}$) were calculated and compared for each mixed surfactant system by means of the equations derived from the nonideal mixed micellar model. There sults show that the molecules of DBS interact more strongly with Brij 35 than Brij 30 and that the DBS/Brij35 mixed system has greater negative deviation from the ideal mixed micellar model than the DBS/Brij 30mixed system.

• Korean Journal of Materials Research
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• v.33 no.5
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• pp.189-194
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• 2023

This study uses first-principles calculations to investigate the mechanical properties and effect of strain on the electronic properties of the 2D material 1H-PbX₂ (X: S, Se). Firstly, the stability of the 1H Pb-dichalcogenide structures was evaluated using Born's criteria. The obtained results show that the 1H-PbS₂ material possesses the greatest ideal strength of 3.48 N/m, with 3.68 N/m for 1H-PbSe₂ in biaxial strain. In addition, 1H-PbS₂ and 1H-PbSe₂ are direct semiconductors at equilibrium with band gaps of 2.30 eV and 1.90 eV, respectively. The band gap was investigated and remained almost unchanged under the strain ε_xx but altered significantly at strains ε_yy and ε_bia. At the fracture strain in the biaxial direction (19 %), the band gap of 1H-PbS₂ decreases about 60 %, and that of 1H-PbSe₂ decreases about 50 %. 1H-PbS₂ and 1H-PbSe₂ can convert from direct to indirect semiconductor under the strain ε_yy. Our findings reveal that the two structures have significant potential for application in nanoelectronic devices.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.723-735
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• 2006

In [2] it was shown that a 1-generator quasi-cyclic code C of length n = ml of index l over $\mathbb{Z}_4$ is free if C is generated by a polynomial which divides $X^m-1$. In this paper, we prove that a necessary and sufficient condition for a cyclic code over $\mathbb{Z}_pk$ of length m to be free is that it is generated by a polynomial which divides $X^m-1$. We also show that this can be extended to finite local rings with a principal maximal ideal.

• Journal of the Korean Chemical Society
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• v.46 no.6
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• pp.495-501
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• 2002

The critical micelle concentration(CMC) and the counterion binding constant(B) for the mixed micel-lization of sodium n-octanoate(SOC) with n-octylammonium chloride(OAC) were determined as a function of the overall mole fraction of $SOC({\alpha}_1).$ Various thermodynamic parameters($x_i$, $Y_i$, $C_i$, $${\alpha}_i^M$$, and $\Delta$$H_{mix}$) for the mixed micellization of the SOC/OAC systems have been calculated and analyzed by means of the equations derived from the nonideal mixed micellar model. The results show that there are great deviations from the ideal behavior for the mixed micellization of these systems. And other thermodynamic parameters(${\Delta}$$G^0_m$, ${\Delta}$$H^0_m$, and ${\Delta}$$S^0_m$) associated with the micellization of SOC,OAC, and their $mixture({\alpha}_1=0.5)$ have been also estimated from the temperature dependence of CMC and B values, and the significance of these parameters and their relation to the theory of the micelle formation have been considered and analyzed by comparing each other.

• Applied Chemistry for Engineering
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• v.9 no.2
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• pp.306-310
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• 1998

The soluble polyimides(PMDA/diamine/dianhydride) were prepared and investigated. After coating the prepared PMDA/diamine/dianhydride solution into the commercial tubular alumina ceramic membranes, gas permeation characteristics was investigated. $T_g{\prime}s$ of the polyimides were in the range of $337{\sim}358^{\circ}C$ and thermal stability was good. The polymer was soluble in NMP, DMAc, DMSO, THF, and m-cresol. The adhesion between the alumina membrane and the soluble polyimide was excellent. The soluble polyimide/alumina membranes containing 6FDA showed the highest permeability among others. The permeability of nitrogen of PMDA/1,3PDA/6FDA-alumina membrane was about $7.6{\times}10^{-7}(mol/m^2{\cdot}Pa{\cdot}s)$ in the gas permeation experiments. The ideal separation factor of $O_2/N_2$ and $H_2/N_2$ in PMDA/1,3PDA/6FDA-alumina membrane were 6.19, and 70.0, respectively.

• Korean Chemical Engineering Research
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• v.44 no.6
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• pp.588-596
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• 2006

The surface of polystyrene membrane treated by Ar, $O_2$ plasma, and the effects were observed before and after the treatment and permeability of $CO_2$, $N_2$ and selectivity of $CO_2$ relative to $N_2$ was measured using continuous flow gas permeation analyzer (GPA). The mole ratio of O over C in the surface was increased from 0 to 0.179 with Ar plasma treatment and route mean square of surface was increased from $15.86{\AA}$ to $71.64{\AA}$. Therefore the contact angle was decreased from $89.16^{\circ}$ to $18.1^{\circ}$. Thus Plasma treatments made surface of membrane tend to be highly hydrophilic. The optimum condition for the $CO_2$ permeability and ideal selectivity of the plasma treated membrane was as follows: the measurement of Ar (60 W, 2 min, $70^{\circ}C$) plasma treatment was $1.14{\times}10^{-12}[m^3(STP){\cdot}m/m^2{\cdot}sec{\cdot}atm]$ and 4.22. In the case of $O_2$ plasma treatment, the contact angle was decreased at $13.56^{\circ}$ with increase of O/C ratio ($0.189{\AA}$) and route mean square of surface ($57.10{\AA}$). The optimum condition for the $CO_2$ permeability and ideal selectivity of the plasma treated membrane was as follows: the measurement of $O_2$ (90 W, 2 min, $70^{\circ}C$) plasma treatment was $7.1{\times}10^{-12}[m^3(STP){\cdot}m/m^2{\cdot}sec{\cdot}atm]$ and 11.5. After plasma treatment, the changes of membrane surface were all subtly linked with both cross-linking and etching effects. Finally, it was confirmed that the gas permeation capacity and selectivity of the modified membrane with plasma could be improved by an appropriate control of the plasma conditions such as treatment time, the power input and sort of plasma gas.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.275-280
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• 2020

Let (R, m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that β_R(I, R) denotes the constant value of depth_R(R/Iⁿ) for n ≫ 0. In this paper we introduce the new notion γ_R(I, R) and then we prove the following inequalities: β_R(I, R) ≤ γ_R(I, R) ≤ dim R - cd(I, R) ≤ dim R/I. Also, some applications of these inequalities will be included.