• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.913-920
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• 2018

Let R be a 2-primal strongly 2-nil-clean ring. We prove that every square matrix over R is the sum of a tripotent and a nilpotent matrices. The similar result for rings of bounded index is proved. We thereby provide a large class of rings over which every matrix is the sum of a tripotent and a nilpotent matrices.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.475-484
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• 2023

Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.

• Journal of Powder Materials
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• v.20 no.2
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• pp.125-128
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• 2013

Magnetic and dielectric properties of rubber composites are controlled by using two kinds of high-permeability metal particles with different electrical conductivity (Sendust, Permalloy), and their effect on microwave absorbance has been investigated, focusing on the quasi-microwave frequency band (0.8-2 GHz). Noise absorbing sheets are composite materials of magnetic flake particles of high aspect ratio dispersed in polymer matrix with various filler amount of 80-90 wt.%. The frequency dispersion and magnitude of complex permeability is almost the same for Sendust and Permalloy composite specimens. However, the complex permittivity of the Permalloy composite (${{\varepsilon}_r}^{\prime}{\simeq}250$, ${{\varepsilon}_r}^{{\prime}{\prime}}{\simeq}50$) is much greater than that of Sendust composite (${{\varepsilon}_r}^{\prime}{\simeq}70$, ${{\varepsilon}_r}^{{\prime}{\prime}}{\simeq}0$). Due to the large dielectric permittivity of Permalloy composite, the absorbing band is shifted to lower frequency region. However, the investigation of impedance matching reveals that the magnetic permeability is still small to satisfy the zero-reflected condition at the quasi-microwave frequency band, resulting in a small microwave absorbance lower than 10 dB.

• Elastomers and Composites
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• v.49 no.4
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• pp.323-329
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• 2014

In order to select polymer matrix for MIF (Molded-In Foaming) process, in this study, we investigated rheological properties of commercial polymers, SBC (Styrene-Butadiene Copolymers, K-resin KK38) and SBS (Styrene- Butadiene-Styrene, KTR 101 and KTR 301). In time sweep test, the rheological properties ($G^{\prime}$, $G^{{\prime}{\prime}}$, ${\eta}^*$) of SBS at 155 and $170^{\circ}C$ display almost constant value as a function of time from 0 s to 1800 s. On contrast, the rheological properties of SBS at 185 and $200^{\circ}C$ exponentially increase as a function of time. It could be due to gelation of SBS at high temperature conditions. These increment of rheological properties are not observed in SBC. From LAOS (large amplitude oscillatory shear) test, the nonlinear rheological properties of SBS at 155 and $200^{\circ}C$ after 1800 s are compared. The nonlinear rheological properties at $155^{\circ}C$ show simple strain thinning behavior such as linear homopolymer, however, the nonlinear rheological properties at $200^{\circ}C$ show 2 times strain thinning behavior (Payne effect). It well match with the gelation of SBS at $200^{\circ}C$. From rheological studies, it is confirmed that the proper polymer matrix for MIF process (low rheological properties at initial time and high rheological properties after process) is SBS KTR 301.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.1-13
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• 2016

This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1069-1078
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• 2019

Let R be a ring with identity and P(R) denote the prime radical of R. An element r of a ring R is called strongly P-clean, if there exists an idempotent e such that $r-e=p{\in}P$(R) with ep = pe. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly P-clean.

• Korean Journal of Metals and Materials
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• v.49 no.2
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• pp.137-144
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• 2011

Strengthening mechanisms in an ordered intermetallic compound containing coherent precipitates of lower antiphase boundary energy than the matrix were investigated on the basis of the interaction between the deformation induced dislocations and the disordered precipitates in an $Ll_2$ ordered $Ni_3Al$-based alloy. Extra work was needed to pull out the dislocations from the precipitate, which was dependent on the difference in the antiphase boundary energy between the matrix and the precipitate, as well as the size and volume fraction of the precipitate. The strength of the $Ll_2$ ordered ${\gamma}^{\prime}$ phase containing fine precipitates of the disordered ${\gamma}$ phase was examined using the proposed model. The model can explain almost quantitatively the age hardening behavior of the $Ll_2$ ordered ${\gamma}^{\prime}$ phase.

• Analytical Science and Technology
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• v.6 no.5
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• pp.515-520
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• 1993

By the real use of Rene 80 cast blades at high temperature ${\gamma}^{\prime}$ precipitates in the matrix(${\gamma}$) mainly due to the operating temperature. These precipitates play main role for strenthening of the blades. Generally known that dislocation density increases due to ${\gamma}-{\gamma}^{\prime}$ mismatch by the generation and growth of the precipitates, because the lattice parameter of ${\gamma}^{\prime}$ is higher than that of ${\gamma}$. These lattice parameters of ${\gamma}$ and ${\gamma}^{\prime}$ are determined through the CBED(Convergent Beam Electron Diffraction) method by STEM(Scanning Transmission Electron Microscope) in this work. And also studied, whether and how much the dislocation density increases by the generation and growth of the precipitates.

• Journal of the Korean Society for Heat Treatment
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• v.4 no.2
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• pp.38-46
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• 1991

Effects of aging treatment on the microstructures and microhardness of a rapidly solidified Al-Li-Cu-Mg-Zr alloy were investigated by differential scanning calorimetry(DSC) and transmission electron microscopy(TEM). The as-melt-spun ribbon was consisted of fine ${\delta}^{\prime}$ and icosahedral intermetallic compound which were precipitated in the matrix. Two exothermic peaks with the range of $120^{\circ}C-190^{\circ}C$ and $280^{\circ}C-344^{\circ}C$ corresponded to ${\delta}^{\prime}$ and ${\theta}^{\prime}$, S', $T_1$ precipitating reaction respectively, and two endothermic peaks with the range of $190^{\circ}C-280^{\circ}C$ and $344^{\circ}C-550^{\circ}C$ corresponded to dissolution of ${\delta}^{\prime}$ and ${\theta}^{\prime}$, S', $T_1$ respectively in DSC curves. Peak hardness value was obtained at $210^{\circ}C$ for 1 hr aging treatment.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.925-942
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• 2016

We study the structure of rings whose principal right ideals contain a sort of two-sided ideals, introducing right ${\pi}$-duo as a generalization of (weakly) right duo rings. Abelian ${\pi}$-regular rings are ${\pi}$-duo, which is compared with the fact that Abelian regular rings are duo. For a right ${\pi}$-duo ring R, it is shown that every prime ideal of R is maximal if and only if R is a (strongly) ${\pi}$-regular ring with $J(R)=N_*(R)$. This result may be helpful to develop several well-known results related to pm rings (i.e., rings whose prime ideals are maximal). We also extend the right ${\pi}$-duo property to several kinds of ring which have roles in ring theory.