• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.749-755
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• 2008

In this paper, we introduce the relatively new notion of fuzzy ${\omega}^O$-open set. We prove that the collection of all fuzzy ${\omega}^O$-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known "fuzzy generalized open" subsets.

• East Asian mathematical journal
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• v.22 no.2
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• pp.207-213
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• 2006

Using the notion of nilpotent elements, the concept of nil subsets is introduced, and related properties are investigated. We show that a nil subset on a subalgebra (resp. (closed) ideal) is a subalgebra (resp. (closed) ideal). We also prove that in a nil algebra every ideal is a subalgebra.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.41-51
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• 2017

In this note, we deal with some characterizations of relative compactness on the $L_p$ metric space of fuzzy sets. And then, we point out that a characterization of relative compact subsets of fuzzy numbers with sendograph metric can be improved.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.14-17
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• 2003

By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.79-82
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• 1988

This paper investigates the relationship between compactness and pseudo-compactness in subsets of C(X) where X is locally compact and first countable. Two primary theorems are proven. First, equicontinuity at a point is proven to be equivalent to the existence of a certain open cover of a pseudo-compact subset of C(X). The second theorem proves the equivalence of compactness and pseudo-compctness for closed subsets F of C(X).

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.243-252
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• 2018

In this paper, we study the sequentially open and closed subsets of sequential topological groups determined by sequentially continuous group homomorphism. In particular, we investigate the sequentially openness (closedness) and sequentially compactness of subsets of sequential topological groups by the aid of sequentially continuity, sequentially interior or closure operators. Moreover, we explore subgroup and sequential quotient group of a sequential topological group.

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.31-32
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• 1980

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.2219-2224
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• 2012

Background: Circulating lymphocyte subsets reflect the immunological status and might therefore be a prognostic indicator in cancer patients. Our aim was to evaluate the clinical significance of circulating lymphocyte subset in gastric cancer (GC) cases. Methods: A retrospective study on a prevalent cohort of 846 GC patients hospitalized at Hospital from Aug 2006 to Jul 2010 was conducted. We calculated the patient's disease free survival (DFS) after first hospital admission, and hazard ratios (HR) from the Cox proportional hazards model. Results: Our findings indicated a significantly decreased percentage of CD3+, and CD8+ cells, a significantly increased proportion of $CD4^+$, $CD19^+$, $CD44^+$, $CD25^+$, NK cells, and an increased $CD4^+/CD8^+$ ratio in GC patients as compared with healthy controls (all P < 0.05). Alteration of lymphocyte subsets was positively correlated with sex, age, smoking, tumor stage and distant metastasis of GC patients (all P<0.05). Follow-up analysis indicated significantly higher DFS for patients with high circulating $CD19^+$ lymphocytes compared to those with low $CD19^+$ lymphocytes (P=0.037), with $CD19^+$ showing an important cutoff of $7.91{\pm}2.98%$ Conclusion: Circulating lymphocyte subsets in GC patients are significantly changed, and elevated CD19+ cells may predict a favorable survival.

• Genomics & Informatics
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• v.12 no.2
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• pp.71-75
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• 2014

The tRNA structure contains conserved modifications that are responsible for its stability and are involved in the initiation and accuracy of the translation process. tRNA modification enzymes are prevalent in bacteria, archaea, and eukaryotes. tRNA Gm18 methyltransferase (TrmH) and tRNA $m^1G37$ methyltransferase (TrmD) are prevalent and essential enzymes in bacterial populations. TrmH involves itself in methylation process at the 2'-OH group of ribose at the 18th position of guanosine (G) in tRNAs. TrmD methylates the G residue next to the anticodon in selected tRNA subsets. Initially, $m^1G37$ modification was reported to take place on three conserved tRNA subsets ($tRNA^{Arg}$, $tRNA^{Leu}$, $tRNA^{Pro}$); later on, few archaea and eukaryotes organisms revealed that other tRNAs also have the $m^1G37$ modification. The present study reveals Gm18, $m^1G37$ modification, and positions of $m^1G$ that take place next to the anticodon in tRNA sequences. We selected extremophile organisms and attempted to retrieve the $m^1G$ and Gm18 modification bases in tRNA sequences. Results showed that the Gm18 modification G residue occurs in all tRNA subsets except three tRNAs ($tRNA^{Met}$, $tRNA^{Pro}$, $tRNA^{Val}$). Whereas the $m^1G37$ modification base G is formed only on $tRNA^{Arg}$, $tRNA^{Leu}$, $tRNA^{Pro}$, and $tRNA^{His}$, the rest of the tRNAs contain adenine (A) next to the anticodon. Thus, we hypothesize that Gm18 modification and $m^1G$ modification occur irrespective of a G residue in tRNAs.

• IMMUNE NETWORK
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• v.16 no.1
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• pp.61-74
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• 2016

Dendritic cells (DCs) are professional antigen-presenting cells that sample their environment and present antigens to naïve T lymphocytes for the subsequent antigen-specific immune responses. DCs exist in a range of distinct subpopulations including plasmacytoid DCs (pDCs) and classical DCs (cDCs), with the latter consisting of the cDC1 and cDC2 lineages. Although the roles of DC-specific transcription factors across the DC subsets have become understood, the posttranscriptional mechanisms that regulate DC development are yet to be elucidated. MicroRNAs (miRNAs) are pivotal posttranscriptional regulators of gene expression in a myriad of biological processes, but their contribution to the immune system is just beginning to surface. In this study, our in-house probe collection was screened to identify miRNAs possibly involved in DC development and function by targeting the transcripts of relevant mouse transcription factors. Examination of DC subsets from the culture of mouse bone marrow with Flt3 ligand identified high expression of miR-124 which was able to target the transcript of TCF4, a transcription factor critical for the development and homeostasis of pDCs. Further expression profiling of mouse DC subsets isolated from in vitro culture as well as via ex vivo purification demonstrated that miR-124 was outstandingly expressed in CD24⁺ cDC1 cells compared to in pDCs and CD172α⁺ cDC2 cells. These results imply that miR-124 is likely involved in the processes of DC subset development by posttranscriptional regulation of a transcription factor(s).