• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• Journal of Pathology and Translational Medicine
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• v.52 no.6
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• pp.396-403
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• 2018

Background: In the current American Joint Committee on Cancer staging system of breast cancer, only tumor size determines T-category regardless of whether the tumor is single or multiple. This study evaluated if tumor multiplicity has prognostic value and can be used to subclassify breast cancer. Methods: We included 5,758 patients with invasive breast cancer who underwent surgery at Samsung Medical Center, Seoul, Korea, from 1995 to 2012. Results: Patients were divided into two groups according to multiplicity (single, n=4,744; multiple, n=1,014). Statistically significant differences in lymph node involvement and lymphatic invasion were found between the two groups (p<.001). Patients with multiple masses tended to have luminal A molecular subtype (p<.001). On Kaplan-Meier survival analysis, patients with multiple masses had significantly poorer disease-free survival (DFS) (p=.016). The prognostic significance of multiplicity was seen in patients with anatomic staging group I and prognostic staging group IA (p=.019 and p=.032, respectively). When targeting patients with T1-2 N0 M0, hormone receptor-positive, and human epidermal growth factor receptor 2 (HER2)-negative cancer, Kaplan-Meier survival analysis also revealed significantly reduced DFS with multiple cancer (p=.031). The multivariate analysis indicated that multiplicity was independently correlated with worse DFS (hazard ratio, 1.23; 95% confidence interval, 1.03 to 1.47; p=.025). The results of this study indicate that tumor multiplicity is frequently found in luminal A subtype, is associated with frequent lymph node metastasis, and is correlated with worse DFS. Conclusions: Tumor multiplicity has prognostic value and could be used to subclassify invasive breast cancer at early stages. Adjuvant chemotherapy would be necessary for multiple masses of T1-2 N0 M0, hormone-receptor-positive, and HER2-negative cancer.

• Journal of Pathology and Translational Medicine
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• v.52 no.6
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• pp.386-395
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• 2018

Background: Previous studies on synchronous colorectal carcinoma (SCRC) have reported inconsistent results about its clinicopathologic and molecular features and prognostic significance. Methods: Forty-six patients with multiple advanced tumors (T2 or higher category) who did not receive neoadjuvant chemotherapy and/or radiotherapy and who are not associated with familial adenomatous polyposis were selected and 99 tumors from them were subjected to clinicopathologic and molecular analysis. Ninety-two cases of solitary colorectal carcinoma (CRC) were selected as a control considering the distributions of types of surgeries performed on patients with SCRC and T categories of individual tumors from SCRC. Results: SCRC with multiple advanced tumors was significantly associated with more frequent nodal metastasis (p=.003) and distant metastasis (p=.001) than solitary CRC. KRAS mutation, microsatellite instability, and CpG island methylator phenotype statuses were not different between SCRC and solitary CRC groups. In univariate survival analysis, overall and recurrence-free survival were significantly lower in patients with SCRC than in patients with solitary CRC, even after adjusting for the extensiveness of surgical procedure, adjuvant chemotherapy, or staging. Multivariate Cox regression analysis revealed that tumor multiplicity was an independent prognostic factor for overall survival (hazard ratio, 4.618; 95% confidence interval, 2.126 to 10.030; p<.001), but not for recurrence-free survival (p=.151). Conclusions: Findings suggested that multiplicity of advanced T category-tumors might be associated with an increased risk of nodal metastasis and a risk factor for poor survival, which raises a concern about the guideline of American Joint Committee on Cancer's tumor-node-metastasis staging that T staging of an index tumor determines T staging of SCRC.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.309-312
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• 1997

The dynamic characteristics of a continuous MMA/MA free-radical solution copolymerization reactor were studied. A mathematical model was developed and kinetic parameters which had been estimated in the previous work were used. With this model, bifurcation diagrams were constructed with various parameters as the bifurcation parameter to predict the region of stable operating conditions and to enhance the controller performance. It was shown that the steady-state multiplicity existed over wide ranges of residence time and jacket inlet temperature. Periodic solution branches were found to emanated from Hopf bifurcation points. Under certain conditions isola was also observed, which would result in poor performance of feedback controllers.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1187-1237
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• 2020

Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic 2, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the Clebsch-Gordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.713-724
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• 2011

We study the dynamics of transcendental entire functions with Siegel disks whose singular values are just two points. One of the two singular values is not only a superattracting fixed point with multiplicity more than two but also an asymptotic value. Another one is a critical value with free dynamics under iterations. We prove that if the multiplicity of the superattracting fixed point is large enough, then the restriction of the transcendental entire function near the Siegel point is a quadratic-like map. Therefore the Siegel disk and its boundary correspond to those of some quadratic polynomial at the level of quasiconformality. As its applications, the logarithmic lift of the above transcendental entire function has a wandering domain whose shape looks like a Siegel disk of a quadratic polynomial.

• Environmental Analysis Health and Toxicology
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• v.18 no.3
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• pp.165-174
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• 2003

Cr (Ⅵ) - containing compounds are well-established carcinogens, although the mechanism for chromium - induced carcinogenesis is still not well understood. The reduction of Cr (Ⅵ) to its lower oxidation states, par ticularly Cr (V) and Cr (IV), is an important step for the production of chromium-mediated reactive oxygen species (ROS). The persistent oxidative stress during the reduction process may play a key role in the mechanism of Cr (Ⅵ) -induced carcinogenesis. This paper summarizes recent studies on (1) the reduction of Cr (Ⅵ) to Cr (III) occur by a multiplicity of mechanisms depending on the nature of reducing agents including ascorbate, diol-and thiol-containing molecules, certain flavoenzymes, cell organelles, intact cells, and whole animals; (2) free-radical production with emphasis on hydroxy radical generation via Fenton or Haber-Weiss type reactions; and (3) free radical - induced cellular damage, such at DNA strand breaks, hydroxylation of 2'-deoxyguanosine, and activation of nuclear transcription factor kB.

• 한국생물공학회:학술대회논문집
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• 2005.04a
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• pp.203-206
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• 2005

TGE (Transmissible Gastroenteritis) caused by a virus belonging to family coronavirus, results in an acute infection of the small intestine of the pig. The optimum operation variables such as multiplicity of infection (MOI), infection time and harvest time were investigated for TGE vaccine production by immobilized ST(swine testicle) cells. In the culture supplemented with 5% serum, maximum virus titer of $1.2{\times}10^6pfu/ml$ was obtained at the conditions of 0.01 MOI, 2day infection time, and 1 day harvest time. Serum is a potential source of bacterial, mycoplasmal and viral contamination, and it has a possibility of the introduction of serum proteins, prion and pyrogens into the final product. For these reasons, much attention has been focused on the development of serum-free media. A new serum-free media (SFM) has been developed in order to produce TGE vaccine of high quality with low cost. The performance of SFM developed was compared with other commercially available serum-free media and serum supplemented media in terms of virus productivity. The cultures with serum-free media showed higher titer than that with serum supplemented media. Among various serum-free media tested, CHO-S-SFMII showed highest virus titer.

• KSBB Journal
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• v.9 no.3
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• pp.272-278
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• 1994

Attenuated varicella-zoster virus(VZV) was cultured in human embryonic lung cells. The effects of serum type and its concentration on the production of VZV were studied. Regardless of cell culture conditions, VZV yield was increased with multiplicity of infection, and the total cell concentration was decreased after virus infection. The newborn calf serum, calf serum, or horse serum was not as good as the fetal bovine serum or calf serum supplemented with iron for the propagation of VZV in the human embryonic lung cells. The yields of total VZV(cell-associated virus and cell-free virus) in the medium with calf serum containing iron were comparable to those in the medium supplemented with fetal bovine serum. Furthermore, some components of serum appear to be important for the maintenance of VZV infectivity.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.146-151
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• 1992

A two-compartment four-cell model is developed for the adiabatic autoclave slim type reactor for free radical polymerization of low density polyethylene(LDPE). The mass and energy balances give rise to a set of ordinary differential equations, and by analyzing the system it is possible to predict properly not only the reactor performance but also the properties of polymer product. The steady state multiplicity is found to exist and examined by constructing the bifurcation diagram. The effects of various operation parameters on the reactor performance and polymer properties are investigated systematically to show that the temperature distribution plays the central role for the properties of polymer product. Therefore, it is essential to establish a good control strategy for the temperature in each compartment. In this study it is shown that the reactor system can be adoptively controlled by pole-placement algorithm with conventional PID controller. To accomplish a satisfactory control, the estimator and controller are initialized during the period of start-up.