• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.65-72
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• 1992

All rings are commutative, Noetherian with identity and of prime characteristic p, unless otherwise specified. First, we describe the definition of tight closure of an ideal and the properties about the tight closure used frequently. The technique used here for the tight closure was introduced by M. Hochster and C. Huneke [4,5, or 6]. Using the concepts of the tight closure and its properties, we will prove that if R is a complete local domain and F-rational, then R is Cohen-Macaulay. Next, we study the properties of R$^{+}$, the integral closure of a domain in an algebraic closure of its field of fractions. In fact, if R is a complete local domain of characteristic p>0, then R$^{+}$ is Cohen-Macaulay [8]. But we do not know this fact is true or not if the characteristic of R is zero. For the special case we can show that if R is a non-Cohen-Macaulay normal domain containing the rationals Q, then R$^{+}$ is not Cohen-Macaulay. Finally we will prove that if R is an excellent local domain of characteristic p and F-ratiional, then R is Cohen-Macaulay.aulay.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.57-64
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• 2006

In this paper, we introduce the concepts of $r$-closure and $r$-interior defined by intuitionistic gradation of openness. We also introduce the concepts of $r$-gp-maps, weakly $r$-gp-maps, and obtain some characterizations in terms of $r$-closure and $r$-interior operators.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.6
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• pp.557-563
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• 2000

We introduce r-fuzzy $\delta$-cluster ($\theta$-cluster) points and r-fuzzy $\delta$-closure ($\theta$-closure) sets in smooth fuzzy topological spaces in a view of the definition of A.P. Sostak [13]. We study some properties of them.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.449-464
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• 2011

We show that, if R is a graded Noetherian ring and I is a proper ideal of R generated by n homogeneous elements, then any prime ideal of R minimal over I has h-height ${\leq}$ n, and that if R is a graded Noetherian domain with h-dim R ${\leq}$ 2, then the integral closure R' of R is also a graded Noetherian domain with h-dim R' ${\leq}$ 2. We also present a short improved proof of the result that, if R is a graded Noetherian domain, then the integral closure of R is a graded Krull domain.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.325-340
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• 2003

We introduce a fuzzy g-closure operator induced by a fuzzy topological space in view of the definition of Sostak [13]. We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of fuzzy g-closure operators.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.231-241
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• 2016

In this paper we will define the tight integral closure of a finite set of ideals of a ring relative to a module and we will study some related results.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.10
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• pp.166-173
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• 2020

The purpose of the present study was to validate the Need for Closure Scale-Short Form (NFCS-SF), which measures the need for cognitive closure. Participants completed questionnaires regarding need for cognitive closure, intolerance of uncertainty, depression, and anxiety. Of the 536 data collected between May and July 2017, data from a total of 495 participants were analyzed using SPSS 20.0 and M-Plus. The results of the study are as follows. First, a 15-item selection comprised three items from each facet scale via exploratory factor analysis. Second, the NFCS-SF demonstrated good internal consistency (Study 1, Cronbach's α=.85; Study 2, Cronbach's α=.84). Third, the results of the confirmatory factor analyses supported a 5-factor model (χ2(80)=178.34, p<.001; CFI=.87, TLI=.83, RMSEA=.07, SRMR=.08). Fourth, the NFCS-SF showed significant correlation with the measures of intolerance of uncertainty (r=.58, p<.01), depression (r=.16, p<.05), and anxiety (state anxiety, r=.31, p<.01; trait anxiety, r=.29, as well as the NFCS (r=.86, p<.01). Based on these findings, significance and limitations of the results as well as suggestions for further study are discussed.

• Clinical and Experimental Pediatrics
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• v.53 no.12
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• pp.1012-1017
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• 2010

Purpose: Transcatheter closure has become an effective therapy in most patients with patent ductus arteriosus (PDA). However, there are difficulties in transcatheter closure of PDA in small children. We reviewed clinical outcomes of transcatheter closure of PDA in children weighing less than 10 kg in a single center. Methods: Between January 2003 and December 2009, 314 patients with PDA underwent transcatheter closure in our institute. Among them, 115 weighed less than 10 kg. All of these patients underwent transcatheter closure of PDA using either COOK Detachable $Coil^{(R)}$, PFM Nit-$Occlud^{(R)}$, or Amplatzer duct $occluder^{(R)}$. A retrospective review of the treatment results and complications was performed. Results: The mean age of patients was $9.1{\pm}5.9$ months (median, 8 months), and mean weight was $7.6{\pm}1.8kg$ (median, 7.8 kg). The mean diameter of PDA was $3.2{\pm}1.4mm$ (median, 3 mm). Complete occlusion occurred in 113 patients (98%). One patient was sent to surgery because of a failed attempt at device closure, and another patient had a small residual shunt after device placement. The average mean length of hospital stay was $3.0{\pm}3.3$ days, and mean follow-up duration was $21.0{\pm}19.6$ months. There were no major complications in any of the patients. Conclusion: Transcatheter closure of PDA is considered safe and efficacious in infants weighing less than 10 kg. With sufficient experience and further effort, transcatheter closure of PDA can be accepted as the gold standard of treatment for this group of patients.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.5
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• pp.797-804
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• 2001

To obtain representative fatigue crack growth characteristic curve in residual stress field, fatigue crack growth test was carried out at various stress ratio and fatigue crack growth characteristic curve was represented using crack closure concept. Obtained results are as follows;K(sub)op/K(sub)max was independent of K(sub)max when R was lower than 0.5 and crack closure phenomenon was not observed when R is higher than 0.5. therefore neglecting crack closure behaviour, actual fatigue crack growth rate can be underestimated. Thus, considering crack closure phenomenon, fatigue crack growth characteristics curve of A 106 Gr B Steel weldment can be effectively estimated.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.653-666
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• 2007

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)