• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.917-924
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• 1995

Let $P_I$ be the convex compact set of all unital positive linear maps between the $n \times n$ matrix algebra over the complex field. We find a necessary and sufficient condition for which two maximal faces of $\cap P_I$ intersect. In particular, we show that any pair of maximal faces of $P_I$ has the nonempty intersection, whenever $n \geq 3$.

• Korean Journal of Radiology
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• v.20 no.5
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• pp.812-822
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• 2019

Objective: To assess the diagnostic value of combining diffusion-weighted imaging (DWI) with conventional magnetic resonance imaging (MRI) for differentiating between pathologic and traumatic fractures at extremities from metastasis. Materials and Methods: Institutional Review Board approved this retrospective study and informed consent was waived. This study included 49 patients each with pathologic and traumatic fractures at extremities. The patients underwent conventional MRI combined with DWI. For qualitative analysis, two radiologists (R1 and R2) independently reviewed three imaging sets with a crossover design using a 5-point scale and a 3-scale confidence level: DWI plus non-enhanced MRI (NEMR; DW set), NEMR plus contrast-enhanced fat-saturated T1-weighted imaging (CEFST1; CE set), and DWI plus NEMR plus CEFST1 (combined set). McNemar's test was used to compare the diagnostic performances among three sets and perform subgroup analyses (single vs. multiple bone abnormality, absence/presence of extra-osseous mass, and bone enhancement at fracture margin). Results: Compared to the CE set, the combined set showed improved diagnostic accuracy (R1, 84.7 vs. 95.9%; R2, 91.8 vs. 95.9%, p < 0.05) and specificity (R1, 71.4% vs. 93.9%, p < 0.005; R2, 85.7% vs. 98%, p = 0.07), with no difference in sensitivities (p > 0.05). In cases of absent extra-osseous soft tissue mass and present fracture site enhancement, the combined set showed improved accuracy (R1, 82.9-84.4% vs. 95.6-96.3%, p < 0.05; R2, 90.2-91.1% vs. 95.1-95.6%, p < 0.05) and specificity (R1, 68.3-72.9% vs. 92.7-95.8%, p < 0.005; R2, 83.0-85.4% vs. 97.6-98.0%, p = 0.07). Conclusion: Combining DWI with conventional MRI improved the diagnostic accuracy and specificity while retaining sensitivity for differentiating between pathologic and traumatic fractures from metastasis at extremities.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.341-355
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• 2003

The fuzzification of ${\bigotimes}-closed$ set is considered, and its basic properties we investigated. Characterizations of fuazzy ${\bigotimes}-closed$ set we given. Using a collection of ${\bigotimes}-closed$ sets with additional conditions, a fuzzy ${\bigotimes}-closed$ set is stated. The theory of fuzzy topological ${\bigotimes}-closed$ sets is discussed.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.161-169
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• 2024

A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

• Journal of Plant Biotechnology
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• v.43 no.3
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• pp.293-301
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• 2016

High-quality gene sets are necessary for functional research of genes. Although Perilla is a commonly cultivated oil crop and vegetable crop in Southeast Asia, the quality of its available gene set is insufficient. To construct a high-quality Perilla gene set, we sequenced mRNAs extracted from different tissues of Perilla citriodora, the wild species (2n = 20) of Perilla. To make a high-quality gene set for P. citriodora, we compared the quality of assemblies produced by Velvet and Trinity, the two well-known de novo assemblers, and improved the de novo assembly pipeline by optimizing k-mers and removing redundant sequences. We then selected representative transcripts for loci according to several criteria. The improved assembly yielded a total of 86,396 transcripts and 38,413 representative transcripts. We evaluated the assembled transcripts by comparing them to 638 homologous Arabidopsis genes involved in fatty acid and TAG biosynthesis pathways. High proportions of full-length genes and transcripts in the assembled transcripts matched known genes in other species, indicating that the P. citriodora gene set can be applied in future functional studies. Our study provides a reference P. citriodora gene set for further studies. It will serve as valuable genetic resource to elucidate the molecular basis of various metabolisms.

• Research in Plant Disease
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• v.18 no.2
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• pp.73-79
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• 2012

Phytophthora katsurae is a fungal pathogen responsible for chestnut ink disease. We designed two duplex primer sets (SOPC 1F/1R+KatI 3F/5R, SOPC 1-1F/1-1R+KatI 3F/5R) to detect P. katsurae. SOPC 1F/1R and SOPC 1-1F/1-1R primer pairs were designed for sequence characteristic amplification regions (SCAR) marker, and KatI 3F/5R primer pair was used for P. katsurae-specific primer designed from internal transcribed spacer (ITS) region. To assess the sensitivity of duplex PCR, genomic DNA was serially diluted 10-fold to make the final concentrations from 1 mg/ml to 1 ng/ml. The sensitivity for two primer sets were 1 ${\mu}g/ml$ and 100 ng/ml, respectively. To find detection limits for zoospores of P. katsurae, each zoospore suspension was serially diluted 10-fold to make the final concentrations from $1{\times}10^6$ to $1{\times}10^2$ cells/ml, and then DNA was extracted. The limits of detection for all of two primer sets were $1{\times}10^5$ cells/ml. All of two primer sets were specific to P. katsurae in PCR detection and did not produce any P. katsurae-specific PCR amplicons from other 16 Phytophthora species used as the control. This study shows that duplex PCR using two primer sets might be a useful tool for rapid and efficient detection of P. katsurae.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.565-586
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• 2017

In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1,2,3,${\cdots}$,p+q} that induces for each vertex v the label defined by the rule $f^v(v)=Round\;\left({\frac{{\Sigma}_{e{\in}E_v}\;f(e)}{d(v)}}\right)$, where $E_v$ denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,${\cdots}$,p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.867-871
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• 2009

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.751-766
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• 2019

In these notes we introduce a numerical function which allows us to describe explicitly (and nonrecursively) the Betti numbers, and hence, the Hilbert function of a set Z of three fat points whose support is an almost complete intersection (ACI) in ${\mathbb{P}}^1{\times}{\mathbb{P}}^1$. A nonrecursively formula for the Betti numbers and the Hilbert function of these configurations is hard to give even for the corresponding set of five points on a special support in ${\mathbb{P}}^2$ and we did not find any kind of this result in the literature. Moreover, we also give a criterion that allows us to characterize the Hilbert functions of these special set of fat points.

• Genomics & Informatics
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• v.11 no.3
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• pp.135-141
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• 2013

Gene set analysis is a powerful tool for interpreting a genome-wide association study result and is gaining popularity these days. Comparison of the gene sets obtained for a variety of traits measured from a single genetic epidemiology dataset may give insights into the biological mechanisms underlying these traits. Based on the previously published single nucleotide polymorphism (SNP) genotype data on 8,842 individuals enrolled in the Korea Association Resource project, we performed a series of systematic genome-wide association analyses for 49 quantitative traits of basic epidemiological, anthropometric, or blood chemistry parameters. Each analysis result was subjected to subsequent gene set analyses based on Gene Ontology (GO) terms using gene set analysis software, GSA-SNP, identifying a set of GO terms significantly associated to each trait ($p_{corr}$ < 0.05). Pairwise comparison of the traits in terms of the semantic similarity in their GO sets revealed surprising cases where phenotypically uncorrelated traits showed high similarity in terms of biological pathways. For example, the pH level was related to 7 other traits that showed low phenotypic correlations with it. A literature survey implies that these traits may be regulated partly by common pathways that involve neuronal or nerve systems.