• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.623-669
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• 2018

In Donaldson-Thomas theory, moduli spaces are locally the critical locus of a holomorphic function defined on a complex manifold. In this paper, we develop a theory of critical virtual manifolds which are the gluing of critical loci of holomorphic functions. We show that a critical virtual manifold X admits a natural semi-perfect obstruction theory and a virtual fundamental class $[X]^{vir}$ whose degree $DT(X)=deg[X]^{vir}$ is the Euler characteristic ${\chi}_{\nu}$(X) weighted by the Behrend function ${\nu}$. We prove that when the critical virtual manifold is orientable, the local perverse sheaves of vanishing cycles glue to a perverse sheaf P whose hypercohomology has Euler characteristic equal to the Donaldson-Thomas type invariant DT(X). In the companion paper, we proved that a moduli space X of simple sheaves on a Calabi-Yau 3-fold Y is a critical virtual manifold whose perverse sheaf categorifies the Donaldson-Thomas invariant of Y and also gives us a mathematical theory of Gopakumar-Vafa invariants.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.237-260
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• 2001

The approximation properties for $L^2$-projection, Raviart-Thomas projection, and inverse inequality have been derived in 3 dimensional space. h-p-mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed in 3D. Solvability and convergence of the linearized problem have been shown through duality argument and fixed point argument. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example.

• The Korean Journal of Zoology
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• v.26 no.2
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• pp.123-134
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• 1983

Age variation and secondary sexual dimorphism in four external and 27 cranial characters of 102 specimens of striped firld mice, Apodemus agrarius coreae Thomas, from Cheongju, Korea, were analyzed statistically. Specimens were classified as subadults, young adults, middle-aged adults, and old adults, and variation of morphometric characters among the four age classes was evident. Significant secondary sexual dimorphism among sexes of the same age class was not revealed. Teh specimens of the same age class have to be used in further analyses to clarify geographic variation of morphometric characters in Apodemus agrarius from Korea.

• Proceedings of the Korea Port Economic Association Conference
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• 2006.08a
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• pp.13-24
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• 2006

• Journal of Environmental Science International
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• v.23 no.9
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• pp.1593-1600
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• 2014

Adsorption and desorption characteristics of the representative 10 kinds components consisting of gasoline vapor on activated carbon were investigated at the temperature range of $-30^{\circ}C{\sim}25^{\circ}C$. The breakthrough curves of each vapors obtained by the Thomas model were well described the breakthrough experimental results of this study. The breakthrough times of each vapors were correlated with the molecular weight, density, and vapor pressure. The breakthrough times had greater correlation with boiling point than molecular weight and density. The slope of the breakthrough curve was a proportional relationship with the rate constant (k) of Thomas model expression. The higher the slope of the breakthrough curve, the rate constant was larger. The biggest slope vapor had the smallest adsorption capacity ($q_e$). Adsorption and desorption characteristics of mixed vapor similar to the gasoline vapor were studied at room temperature ($25^{\circ}C$). The mixed vapor consisting of 9 components; group A (pentane, hexene, hexane), group B (benzene, toluene), group C (octane, ethylbenzene, xylene, nonane) was examined. Group A was not nearly adsorbed because of substitution by group C, and the desorption capacity of group A was smaller than group C. The adsorbed substances were confirmed to be Group C.

• Korean journal of applied entomology
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• v.47 no.3
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• pp.193-199
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• 2008

Fifty potato cultivars were screened for potato aphid, Macrosiphum euphorbiae Thomas infestation degree in the field. Aphid honey dew secretion and contents of foliar substances(glycoalkaloids, total nitrogen, Ca, K and Mg) of the cultivars were measured in the laboratory to analyze the correlation between infestation degrees and those factors. The number of aphids ranged from 4.1 to 31.4 per five leaves. The lower density(less than 5 aphids) was found on cvs. Jidose, Recent, and Sebago. The aphid secreted highest(40.3 droplets) and lowest(15.7 droplets) honeydew on cvs. Jopoong and Anco, respectively. Degree of infestation is positively correlated to glycoalkaloids and total nitrogen contents of the potato leaf.

• Journal of Gifted/Talented Education
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• v.23 no.5
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• pp.817-833
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• 2013

The study aims to analyze Thomas Young's problem solving processes of analogical reasoning during the formation of the interference theory of light, and to draw its implications for secondary science education, particularly for enhancing creativity in science. The research method employed in the study was literature review of the papers which Young himself had written about sound wave and property of light. His thinking processes and specific features in his thought that were obtained through analysis of his papers about light are as follows: Young reconsidered Newton's experiments and observations, and reinterpreted Newton's results in the new viewpoints. Through this analysis, Young discovered that Newton's interpretation about his own experiments and observations was faulty in a certain point of view and new interpretation is necessary. Based on the data, it is hypothesized that colors observed on thin plates and colors appeared repeatedly on Newton's ring are appeared because of the effect of light interference. Young used analogical reasoning during the process of inference of similarity between sound and light. And he formulated an hypothesis on the interference of light through using abductive reasoning from interference of water wave, and proved the hypothesis by constructing an creative experimental device, which is called a critical experiment. It is implicated that the analogical reasoning and experimental devices for explaining the light interference which Young created and used can be utilized for school science education enhancing creativity in science.

• Proceedings of the Korean Nuclear Society Conference
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• 2004.10a
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• pp.85-86
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• 2004

• Proceedings of the Zoological Society Korea Conference
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• 2001.04a
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• pp.46.1-46
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• 2001

No Abstract, See Full Text

• Communications of Mathematical Education
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• v.27 no.2
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• pp.165-177
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• 2013

Mathematics teaching is often more effective when teachers connect the contents of mathematics with history, culture, and social events. In the history of mathematics, the 'paradigm' theory from Thomas Kuhn's scientific revolution is very effective to explain the revolutionary process of development in mathematics, and his theory has been widely quoted in the history of science and economics. However, it has not been appropriate to use his theory in the other fields. This is due to the fact that the scope of Kuhn's paradigm theory is limited to mathematics and science. In this study, this researcher introduced pan-paradigm as a general concept that encompasses all, since through any relation in the field of mathematics and architecture, Thomas Kuhn's theory of paradigm does not explain the phenomena. That is, at the root of various cultures there exist always a 'collective unconsciousness' and 'demands of the times,' and these two factors by synergism form values and controlling principles common to various parts of the culture, and this synergism leads the cultural activities, the process of which is a phenomenon called pan-paradigm.