• Honam Mathematical Journal
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• v.35 no.3
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• pp.541-550
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• 2013

In this paper, we strengthen the properties of approximation by points (AP) and weak approximation by points (WAP) considered by A. Pultr and A. Tozzi in 1993 to define ${\kappa}$-AP and ${\kappa}$-WAP for an infinite cardinal ${\kappa}$. We also strengthen the properties of radial and pseudoradial to define ${\kappa}$-radial and ${\kappa}$-pseudoradial for an infinite cardinal ${\kappa}$. These allow us to consider new cardinal functions related to almost closed sets; AP-number, WAP-number, radial number, and pseudoradial number. We study their properties and show the relationships between them. We also provide some examples around ${\kappa}$-AP and ${\kappa}$-WAP which are closely connected with ${\kappa}$-radial and ${\kappa}$-pseudoradial.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.655-663
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• 2017

In this paper we define $AP_c$ and $AP_{cc}$ spaces which are stronger than the property of approximation by points(AP). We investigate operations on their subspaces and study function theorems on $AP_c$ and $AP_{cc}$ spaces. Using those results, we prove that every continuous image of a countably compact Hausdorff space with AP is AP. Finally, we prove a theorem that every compact ${\kappa}$-WAP space is ${\kappa}$-pseudoradial, and prove a theorem that the product of a compact ${\kappa}$-radial space and a compact ${\kappa}$-WAP space is a ${\kappa}$-WAP space.

• Fisheries and Aquatic Sciences
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• v.17 no.4
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• pp.471-478
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• 2014

Genomic organization, including the structural characteristics of 5'-flanking regions of two 65-kDa protein (WAP65) isoform genes associated with warm temperature acclimation, were characterized and their transcriptional responses to immune challenges were examined in the intestine, kidney and spleen of the mud loach (Misgurnus mizolepis; Cypriniformes). Both mud loach Wap65 isoform genes displayed a 10-exon structure that is common to most teleostean Wap65 genes. The two mud loach Wap65 isoforms were predicted to possess various stress- and immune-related transcription factor binding sites in their regulatory regions; however, the predicted motif profiles differed between the two isoforms, and the inflammation-related transcription factor binding motifs, such as NF-${\kappa}B$ and CREBP sites, were more highlighted in the Wap65-2 isoform than the Wap65-1 isoform. The results of qRT-PCR indicated that experimental immune challenges using Edwardsiella tarda, lipopolysaccharide or polyI:C induced the Wap65-2 isoform more than Wap65-1 isoform, although modulation patterns in response to these challenges were tissue- and stimulant-dependent. This study confirms that functional diversification between the two mud loach Wap65 isoforms (i.e., closer involvement of Wap65-2 in the acute phase of inflammation and innate immunity) occurs at the mRNA level in multiple tissues, and suggests that such differential modulation patterns between the two isoforms are related to the different transcription factor binding profiles in their regulatory regions.