• 대한수학회보
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• 제57권6호
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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.

• Nuclear Engineering and Technology
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• 제48권1호
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• pp.164-168
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• 2016

Lean duplex stainless steels with 0.087 wt.% gadolinium (Gd) were inert arc-melted and cast in molds of size $10mm{\times}10mm{\times}20mm$. The micro-hardnesses of the rolling direction (RD), transverse direction (TD) and short transverse (ST) direction were $258.5H_V$, $292.3H_V$, and $314.7H_V$, respectively. A 33% cold rolled specimen had the crystallographic texture that (100) pole was mainly concentrated to the normal direction (ND) and (110) pole was concentrated in the center of ND and RD. The corrosion potential and corrosion rate in artificial seawater and $0.1M\;H_2SO_4$ solution were in the range of $105.6-221.6mV_{SHE}$, $0.59-1.06mA/cm^2$, and $4.75-8.25mV_{SHE}$, $0.69-1.68mA/cm^2$, respectively. The friction coefficient and wear loss of the 0.087 w/o Gd-lean duplex stainless steels in artificial seawater were about 67% and 65% lower than in air, whereas the wear efficiency was 22% higher. The corrosion and wear behaviors of the 0.087 w/o Gd-lean duplex stainless steels significantly depended on the Gd phases.