• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.83-89
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• 1993

Applications of the classical Knaster-Kuratowski-Mazurkiewicz theorem [KKM] and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde[L]. Recently, this concept has been extended to pseudo-convex spaces, contractible spaces, or spaces having certain families of contractible subsets by Horvath[H1-4]. In the present paper we give a far-reaching generalization of the best approximation theorem of Ky Fan[F1, 2] to pseudo-metric spaces and improved versions of the well-known fixed point theorems due to Brouwer [B] and Schauder [S] for spaces having certain families of contractible subsets. Our basic tool is a generalized Fan-Browder type fixed point theorem in our previous works [P3, 4].

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.493-499
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• 2021

Every closed subset of a compact topological space is compact. Also every compact subset of a Hausdorff topological space is closed. It follows that compact subsets are precisely the closed subsets in a compact Hausdorff space. It is also proved that a topological space is maximal compact if and only if its compact subsets are precisely the closed subsets. A locale is a categorical extension of topological spaces and a frame is an object in its opposite category. We investigate to find whether the closed sublocales are exactly the compact sublocales of a compact Hausdorff frame. We also try to investigate whether the closed sublocales are exactly the compact sublocales of a maximal compact frame.

• IMMUNE NETWORK
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• v.14 no.6
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• pp.289-295
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• 2014

Flow cytometric immunophenotyping of peripheral blood lymphocyte subsets is a powerful tool for evaluating cellular immunity and monitoring immune-mediated diseases. The numbers and proportions of blood lymphocyte subsets are influenced by factors such as gender, age, ethnicity, and lifestyle. This study aimed to establish reference ranges for peripheral blood lymphocyte subsets in a healthy Korean population. Blood samples from 294 healthy adults were collected. Lymphocyte subsets were analyzed using a single-platform method with a flow cytometer; white blood cells and lymphocytes were analyzed using an automated hematology analyzer. The mean value of the white blood cell count was $5,665cells/{\mu}l$, and the mean values of the subtype counts (percentages) were as follows: lymphocytes, $1,928cells/{\mu}l$ (35.08%); $CD3^+$ cells, $1,305cells/{\mu}l$ (67.53%); $CD3^+CD4^+$ cells, $787cells/{\mu}l$ (40.55%); $CD3^+CD8^+$ cells, $479cells/{\mu}l$ (25.23%); $CD3^-CD19^+$ cells, $203cells/{\mu}l$ (10.43%); and $CD3^-CD56^+$ cells, $300cells/{\mu}l$ (15.63%). Additionally, the $CD4^+/CD8^+$ ratio was 1.81. In this study, gender and age significantly influenced blood lymphocyte subsets. Our results demonstrate that, as with other populations, a healthy Korean population has its own, region-specific, lymphocyte subset reference ranges.

• Biomedical Science Letters
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• v.2 no.2
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• pp.211-222
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• 1996

The conceptus which are resulted by mating between two genetically non-identical partners can be considered to be an allograft to the mother science which is not rejected by the mother's immunological attack. The present studies have been, therefore, attempted in order to elucidate the mechanism by which protection of the fete-placental allograft, between the C3H/HeJ female mouse and DBA/2 male mouse occurred. For this purpose, firstly systemic immunity was investigated by measuring T and B lymphocytes subsets. Natural killer cell activity in maternal splenic tissue and by observing the effects of pregnancy serums, progesterone and hCG on immune systems. Secondly, local immunity also investigated by measuring T lymphocytes subsets, natural killer cell activity in lymph nodes draining the uterus. The subsets of Thy-1.2$^+$ cells and L 3T4$^+$ cells decreased slightly while the subsets of Ly2$^+$ cell increased significantly compared with those of the control group beyond the mid-gestational stage. The subsets of B cell gradually in-creased from the mid-gestational stage untill delivery. The natural killer cell activity in the maternal splenic tissue significantly increased during the period of 5th to 8th day of gestation. The natural killer cell activity was significantly suppressed by the pregnancy serums and non-pregnant serums compared with those of serum-free group. The treatment of hCG significantly suppressed natural killer cell activity in the dose dependent manner (1 unit/ml-1000 unit/ml) while pro-gesterone increased the natural killer cell activity at phamarcological dose only. In the lymph nodes draining the uterus, the subsets of Thy-1.2$^+$ cells significantly increased during the period of implantation and L3T4$^+$ cell subsets slightly increased during the mid-gestational stage. The subsets of Ly2$^+$ cell increased significantly during the mid-gestational stage, but decreasing slightly be-fore delivery. The natural killer cell activity was significantly elevated after the implantation period in the lymph nodes draining the uterus. The natural killer cell activity of the lymph nodes draining the uterus was higher than those of splenic tissue during the same periods of gestation. It is therefore, concluded that during the pregnancy, the phenomena which the fete-placental allograft has not been rejected and rather protected from the maternal immunological attack might be due to local immune suppression in fete-maternal interface tissues rather than systemic immune suppression. And the subsets of Thy-1.2$^+$ cells and L3T4$^+$ cells mainly contribute to accepting allograft in early stage of pregnancy, while the subsets of Ly2$^+$ cell and the subsets of B cell increased significantly compared with those of the control group beyond the mid-gestational stage, so their role in systemic immunity and local immunity gradually increased from the mid-gestational stage until delivery.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.17-25
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• 1996

We study the relationship between a property of a triangular subset and coassociated prime ideals of the module of generalized fractions induced by the triangular subset, and investigate coassociated prime ideals of modules of generalized fractions defined by some special triangular subsets.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.465-475
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• 2012

We characterize the fuzzy ideal generated by a fuzzy subset in a semigroup and the fuzzy interior ideal generated by a fuzzy subset in a semigroup. Our work generalizes the characterizations ([8]) of those fuzzy ideals generated by fuzzy subsets in semigroups with an identity element.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.853-867
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• 2013

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F be subsets of the d-dimensional vector space $\mathbb{F}^d_q$ over a finite field $\mathbb{F}_q$ with q elements. As a new result, we prove that if E and F are subsets of the paraboloid and ${\mid}E{\parallel}F{\mid}{\geq}Cq^d$ for some large C > 1, then ${\mid}{\Pi}(E,F){\mid}{\geq}cq$ for some 0 < c < 1. In particular, we find a connection between the size of the dot product set and the number of lines through both the origin and a nonzero point in the given set E. As an application of this observation, we obtain more sharpened results on the generalized dot product set problems. The discrete Fourier analysis and geometrical observation play a crucial role in proving our results.

• Journal of Periodontal and Implant Science
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• v.26 no.3
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• pp.725-734
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• 1996

The present study has been performed to revise the forms of early-onset periodontitis(EOP) into the homogeneous phenotypic subsets by cluster analysis using sets of clinical parameters. Retrospective radiographic interproximal alveolar bone levels were measured from cemento-enamel junctions on patients who have previously been diagnosed as having one of EOP during last 5 years. Mean interproximal bone levels(BL) and mesial bone level(Ratio) of 1st molars relative to mean interproximal bone levels of adjacent teeth(lst and 2nd premolars and canines)were calculated on each patient. Using parameters BL and Ratio(BR group) or BL, Ratio and age(BRA group), cluster analysis was performed to revise EOP patients into homogeneous subsets. At least three or four cluster could be homogeneously formed both in BR or BRA groups with statistically significant differences in parameters used among clusters as evidenced by MANOVA test. It was shown that the greater the BL, the smaller the Ratio was. It was also evident that mean interproximal bone levels were lowest aroud 1st molars and/or incisors regardless of cluster types. The results has provided cluster-based studies for identifying laboratory markers responsible for the development of EOP subsets.

• Journal of Korean Neurosurgical Society
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• v.58 no.2
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• pp.101-106
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• 2015

Objective : The aim of this study was to explore the immunity in rats transplanted with adipose-derived mesenchymal stem cells (ADSCs) and acellular nerve (ACN) for repairing sciatic nerve defects. Methods : ADSCs were isolated from the adipose tissues of Wistar rats. Sprague-Dawley rats were used to establish a sciatic nerve defect model and then divided into four groups, according to the following methods : Group A, allogenic nerve graft; Group B, allograft with ACN; Group C, allograft ADSCs+ACN, and Group D, nerve autograft. Results : At the day before transplantation and 3, 7, 14, and 28 days after transplantation, orbital venous blood of the Sprague-Dawley rats in each group was collected to detect the proportion of $CD3^+$, $CD4^+$, and $CD8^+$ subsets using flow cytometry and to determine the serum concentration of interleukin-2 (IL-2), tumor necrosis $factor-{\alpha}$ ($TNF-{\alpha}$) and $interferon-{\gamma}$ ($IFN-{\gamma}$) using enzyme-linked immunosorbent assay (ELISA). At each postoperative time point, the proportion of $CD3^+$, $CD4^+$, and $CD8^+$ subsets and the serum concentration of IL-2, $TNF-{\alpha}$, and $IFN-{\gamma}$ in group C were all near to those in group B and group D, in which no statistically significant difference was observed. As compared with group A, the proportion of $CD3^+$, $CD4^+$, and $CD8^+$ subsets and the serum concentration of IL-2, $TNF-{\alpha}$, and $IFN-{\gamma}$ were significantly reduced in group C (p<0.05). Conclusion : The artificial nerve established with ADSCs and ACN has no obvious allograft rejection for repairing rat nerve defects.

• The KIPS Transactions:PartB
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• v.8B no.5
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• pp.463-468
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• 2001

We propose a new similarity measure based on relative membership function (RMF). In this paper, the RMF is suggested to represent the relativity between fuzzy subsets easily. Since the shape of the RMF is determined according to the values of its parameters, we can easily represent the relativity between fuzzy subsets by adjusting only the values of its parameters. Hence, we can easily reflect the relativity among individuals or cultural differences when we represent the subjectivity by using the fuzzy subsets. In this case, these parameters may be regarded as feature points for determining the structure of fuzzy subset. In the sequel, the degree of similarity between fuzzy subsets can be quickly computed by using the parameters of the RMF. We use Euclidean distance to compute the degree of similarity between fuzzy subsets represented by the RMF. In the meantime, we present a new linguistic approximation method as an application area of the proposed similarity measure and show its numerical example.