• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.571-575
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• 2023

Let D be an integral domain and let * be a star-operation on D. In this article, we give new characterizations of *_w-Noetherian domains and *_w-principal ideal domains. More precisely, we show that D is a *_w-Noetherian domain (resp., *_w-principal ideal domain) if and only if every *_w-countable type ideal of D is of *_w-finite type (resp., principal).

• Journal of the Korean Ceramic Society
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• v.47 no.4
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• pp.333-337
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• 2010

Domain structure and polarization switching in (001)-oriented $Pb(Mg_{1/3}Nb_{2/3})O_3-x%PbTiO_3$ (PMN-x%PT) crystals for x=20 and 35at% have been investigated in-situ by scanning force microscope (SFM) in a piezoresponse mode under a step DC electrical voltage. In the initial annealed condition, polar nano domains (PND) and domain striations oriented along {110} were observed in x=20 and x=35, respectively. For x=20, domain switching occurs by heterogeneous nucleation, where nucleation is not confined in the vicinity of domain boundaries, but rather can occur throughout the crystal volume. However, for x=35, domain switching tends to be preferentially initiated near pre-existing twin boundaries. With increasing the applying voltage, the nuclei density increased and assembled into {110} striations, indicating a stress-accommodated domain growth process. At higher voltage, nucleation occurs heterogeneously throughout the crystal volume.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.419-429
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• 2022

An integral domain R is an RTP domain (or has the radical trace property) (resp. an LTP domain) if I(R : I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R : I)R_P = PR_P for each minimal prime P of I(R : I)). Clearly each RTP domain is an LTP domain, but whether the two are equivalent is open except in certain special cases. In this paper, we study the descent of these notions from particular overrings of R to R itself.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1491-1499
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• 2020

We give a strong fundamental domain for the quotient of PGL₂(𝔽_q((t^-1))) by PGL₂(𝔽_q[t]) as a subset of distinct ordered triple points of ℙ¹(𝔽_q((t^-1))).

• Journal of the Korean Ceramic Society
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• v.51 no.3
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• pp.218-223
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• 2014

The domain structures, dielectric properties, and phase transformation of (001)-oriented $Pb(Mg_{1/3}Nb_{2/3})O_3-x%PbTiO_3$ (PMN-x%PT) crystals for x=20, 30, 35, and 40 mole% have been investigated. PMN-20%PT consists of polar nano-domains (PND) which do not self-assemble into macro-domain plates. PMN-30%PT consists of PNDs which begin to self-assemble into colonies along preferred {110} planes. PMN-35PT consists of miniature polar domains on the nm scale. PMN-40%PT consists of {001} oriented lamella domains on the mm scale that have internal nano-scale heterogeneities. The dielectric properties of poled (001) PMN-x%PT single crystals have been measured for orientations both parallel and perpendicular to the [001] poling direction. The results of the temperature dependence of the dielectric constant and mesh scans for the 30%PT sample demonstrate that the initial monoclinic phase changes to single domain tetragonal phase and to cubic phase with increasing temperature.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.139-145
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• 2009

Reduction scheme is remarkably useful in the case requiring the repeated calculation procedure. Recently, the efficiency of the reduction scheme has been improved by combining scheme of sub-domain method. But, when the global domain is partitioned into a few sub-domains, sub-domains without constraints can be produced. it is needed to extract the ritz vector from each sub-domain to construct the reduced system of each sub-domain. it is easy to extract the ritz vector from sub-domain with constraint. on the other hand, pseudo inverse method should be employed to extract the ritz vector from sub-domain without constraint. generally, the pseudo inverse takes a large number of computing time to obtain a reduced system of a sub-domain without boundary condition. This trouble can be overcome by the reduced pseudo inverse scheme which proposed in this study. This scheme is based on the static condensation that is not related with selection of the primary degrees of freedom. Numerical examples demonstrate that present method saves computational cost effectively and predicts the accurate eigenvalues.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.2
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• pp.173-179
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• 2009

Reduction scheme is remarkably useful in the case requiring the repeated calculation procedure. Recently, the efficiency of the reduction scheme has been improved by combining scheme of sub-domain method. But, when the global domain is partitioned into a few sub-domains, sub-domains without constraints can be produced. it is needed to extract the ritz vector from each sub-domain to construct the reduced system of each sub-domain. it is easy to extract the ritz vector from sub-domain with constraint. on the other hand, pseudo inverse method should be employed to extract the ritz vector from sub-domain without constraint. generally, the pseudo inverse takes a large number of computing time to obtain a reduced system of a sub-domain without boundary condition. This trouble can be overcome by the reduced pseudo inverse scheme which proposed in this study. This scheme is based on the static condensation that is not related with selection of the primary degrees of freedom. Numerical examples demonstrate that present method saves computational cost effectively. In addition, it is shown that the reduced system based on the proposed scheme predicts the accurate eigenvalues of global system.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1351-1365
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• 2020

Let S and T be w-linked extension domains of a domain R with S ⊆ T. In this paper, we define what satisfying the w_R-GD property for S ⊆ T means and what being w_R- or w-GD domains for T means. Then some sufficient conditions are given for the w_R-GD property and w_R-GD domains. For example, if T is w_R-integral over S and S is integrally closed, then the w_R-GD property holds. It is also given that S is a w_R-GD domain if and only if S ⊆ T satisfies the w_R-GD property for each w_R-linked valuation overring T of S, if and only if S ⊆ (S[u])_w satisfies the w_R-GD property for each element u in the quotient field of S, if and only if S_𝔪 is a GD domain for each maximal w_R-ideal 𝔪 of S. Then we focus on discussing the relationship among GD domains, w-GD domains, w_R-GD domains, Prüfer domains, PνMDs and Pw_RMDs, and also provide some relevant counterexamples. As an application, we give a new characterization of Pw_RMDs. We show that S is a Pw_RMD if and only if S is a w_R-GD domain and every w_R-linked overring of S that satisfies the w_R-GD property is w_R-flat over S. Furthermore, examples are provided to show these two conditions are necessary for Pw_RMDs.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.571-594
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• 2022

Let D be an integral domain with quotient field K, Pic(D) be the ideal class group of D, and X be an indeterminate. A polynomial overring of D means a subring of K[X] containing D[X]. In this paper, we study almost Dedekind domains which are polynomial overrings of a principal ideal domain D, defined by the intersection of K[X] and rank-one discrete valuation rings with quotient field K(X), and their ideal class groups. Next, let ℤ be the ring of integers, ℚ be the field of rational numbers, and 𝔊f be the set of finitely generated abelian groups (up to isomorphism). As an application, among other things, we show that there exists an overring R of ℤ[X] such that (i) R is a Bezout domain, (ii) R∩ℚ[X] is an almost Dedekind domain, (iii) Pic(R∩ℚ[X]) = $\oplus_{G{\in}G_{f}}$ G, (iv) for each G ∈ 𝔊f, there is a multiplicative subset S of ℤ such that RS ∩ ℚ[X] is a Dedekind domain with Pic(RS ∩ ℚ[X]) = G, and (v) every invertible integral ideal I of R ∩ ℚ[X] can be written uniquely as I = XnQe11···Qekk for some integer n ≥ 0, maximal ideals Qi of R∩ℚ[X], and integers ei ≠ 0. We also completely characterize the almost Dedekind polynomial overrings of ℤ containing Int(ℤ).

• Journal of Magnetics
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• v.13 no.3
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• pp.102-105
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• 2008

This study examined the feasibility of the combining HDDR-process (hydrogenation, disproportionation, desorption and recombination) with mechanical milling to prepare single domain $Nd_2Fe_{14}B$ particles from a Nd-Fe-B alloy ingot. The $Nd_{15}Fe_{77}B_8$ alloy was HDDR-treated and then subjected to a roller-milling. In the HDDR-treated $Nd_{15}Fe_{77}B_8$ alloy, very small $Nd_2Fe_{14}B$ grains comparable to their critical single domain size(0.3 ${\mu}m$) were observed. These fine individual grains were separated successfully along the grain boundaries by a roller-milling. The separated $Nd_2Fe_{14}B$ grains were found to be single domain particles. These results suggest that single domain particles of the $Nd_2Fe_{14}B$ phase can be prepared from a Nd-Fe-B ingot alloy by combining a HDDR-process with mechanical milling.