• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.131-135
• /
• 2011

It is shown that generalized GCD domains satisfy a certain property of injectivity and conversely this property characterizes generalized GCD domains.

• Journal of Korea Foundry Society
• /
• v.21 no.6
• /
• pp.350-358
• /
• 2001

The machinability of cast iron is closely related to its microstructural property. In this study, the effect of graphite mophology and matrix microstructure on machinability in several commercial cast irons(GC 25, GCD 45, GCD 50, GCD 70, GCD HSMo, GCMP) was investigated. To estimate the machinability, turning test was carried out under conditions of spindle speed 80m/min, depth of cut 0.25mm, feed 0.16mm/rev and cutting distance 1 km. Thrust force in turning test decreases in the order of GCMP, GCD 70, GCD 50, GC 25, GCD 45 and GCD HSMo. i.e. machinability increases in this order. The superior machinability of GC 25 is caused by flake type graphite which acts as chip braker and provides lubrication during machining. Consequently, soft ferritic cast irons exhibit superior machinability compared with pearlitic cast irons.

• Journal of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1057-1075
• /
• 2016

Let R be a ring in which Nil(R) is a divided prime ideal of R. Then, for a suitable property X of integral domains, we can define a ${\phi}$-X-ring if R/Nil(R) is an X-domain. This device was introduced by Badawi [8] to study rings with zero divisors with a homomorphic image a particular type of domain. We use it to introduce and study a number of concepts such as ${\phi}$-Schreier rings, ${\phi}$-quasi-Schreier rings, ${\phi}$-almost-rings, ${\phi}$-almost-quasi-Schreier rings, ${\phi}$-GCD rings, ${\phi}$-generalized GCD rings and ${\phi}$-almost GCD rings as rings R with Nil(R) a divided prime ideal of R such that R/Nil(R) is a Schreier domain, quasi-Schreier domain, almost domain, almost-quasi-Schreier domain, GCD domain, generalized GCD domain and almost GCD domain, respectively. We study some generalizations of these concepts, in light of generalizations of these concepts in the domain case, as well. Here a domain D is pre-Schreier if for all $x,y,z{\in}D{\backslash}0$, x | yz in D implies that x = rs where r | y and s | z. An integrally closed pre-Schreier domain was initially called a Schreier domain by Cohn in [15] where it was shown that a GCD domain is a Schreier domain.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.11 no.1
• /
• pp.82-87
• /
• 2012

For different ferrite-pearlite matrix structure, contain more than 90% spheroidal ratio of graphite, GCD 45-3, GCD 50, GCD 60 series and 70%, 80%, 90% spheroidal ratio of graphite, GCD 40, GCD 45-1, GCD 45-2 series, this paper has carried out rotary bending fatigue test, estimated maximum and mean size of spheroidal graphite, investigated correlation. It was concluded as follows. (1) Fatigue limit in $10^7$cycles and numbers of spheroidal graphite per 1$mm^2$ was linear relation. (2) projection area of graphite can be used to predict fatigue limit of Ductile Cast Iron. The Statistical distribution of extreme values of projection area of defects may be used as a guideline for the control of inclusion size in the steelmaking processes.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.4
• /
• pp.711-715
• /
• 2012

In terms of divisible-like modules, some equivalent conditions for an integral domain R to be a generalized GCD domain are given.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.4
• /
• pp.449-457
• /
• 2017

In this paper we study several generalizations of greatest common divisor of GCD domain with always the greatest common divisor.

• Tribology and Lubricants
• /
• v.19 no.1
• /
• pp.31-35
• /
• 2003

This paper reports the studies on the wear-corrosion behavior of ductile cast iron in the various pH environments. In the variety of pH solutions, corrosion and wear-corrosion loss of GCD 600 were investigated. Also, the anodic polarization test of GCD 600 using potentiostat/galvanostat was carried out. And rubbed surface of GCD 60 using scanning electron micrographs after immersion and wear-corrosion test was examined in the environment of various pH values. The main results are as following In alkali zone, the wear-corrosion loss of GCD 600 increases, but corrosion loss decreases. The unevenness and crack of wear-corrosion surface in neutral zone becomes duller than that in alkali zone. As the corrosive environment is acidified, wear-corrosion behavior of GCD 600 with passing immersion time becomes sensitive.

• Proceedings of the Korean Information Science Society Conference
• /
• 2007.06b
• /
• pp.476-481
• /
• 2007

큰 소수를 빠르게 생성하기 위한 다양한 소수 검사 방법이 개발되었으며, 가장 많이 쓰이는 소수 검사 방법은 trial division과 Fermat (또는 Miller-Rabin) 검사를 조합한 방법과 gcd 연산과 Fermat (또는 Miller-Rabin) 검사를 조합한 방법이다. 이 중 trial division과 조합한 방법에 대해서는 확률적 분석을 이용하여 수행시간을 예측하고 수행시간을 최적화 하는 방법이 개발되었다. 하지만, gcd 연산과 조합한 방법에 대해서는 아무런 연구결과도 제시되어 있지 않다. 본 논문에서는 gcd 연산을 이용한 조합 소수 검사 방법에 대해 확률적 분석을 이용하여 수행시간을 예측하고 수행시간을 최적화 하는 방법을 제안한다.

• Journal of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1689-1701
• /
• 2019

Let ${\star}$ be a semistar operation on the integral domain D. In this paper, we prove that D is a $G-{\tilde{\star}}-GCD$ domain if and only if D[X] is a $G-{\star}_1-GCD$ domain if and only if the Nagata ring of D with respect to the semistar operation ${\tilde{\star}}$, $Na(D,{\star}_f)$ is a G-GCD domain if and only if $Na(D,{\star}_f)$ is a GCD domain, where ${\star}_1$ is the semistar operation on D[X] introduced by G. Picozza [12].

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.601-607
• /
• 2011

Let D be an integral domain, X be an indeterminate over D, and D[X] be the polynomial ring over D. We show that D is an almost weakly factorial PvMD if and only if D + XDS[X] is an integrally closed almost GCD-domain for each (saturated) multiplicative subset S of D, if and only if $D+XD_1[X]$ is an integrally closed almost GCD-domain for any t-linked overring $D_1$ of D, if and only if $D_1+XD_2[X]$ is an integrally closed almost GCD-domain for all t-linked overrings $D_1{\subseteq}D_2$ of D.