• Journal of the Korean Applied Science and Technology
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• v.23 no.4
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• pp.280-289
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• 2006

Multilayer adsorptions and BET adsorption are analyzed statistical-mechanically. Which ensemble is selected for the analysis is unimportant, because each ensemble yields the same results. However, the amount of mathematical manipulations and the matter of convenience vary from ensemble to ensemble. Hence, multilayer adsorptions and BET adsorption are examined using a canonical and a grand canonical ensembles, and an ensemble of subsystems. Also, the characteristics of multilayer and BET adsorptions are delineated.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.41 no.7
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• pp.773-783
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• 1992

There have been several control schemes for the single input systems with unmeasurable state variables using variable structure control(VSC) theory. However, each of them is a study on the systems which can be represented in the phase canonical form or non-phase canonical form dynamic equation separately. As these control algorithms have difficulties in practical application by its theoretical limitations, in this paper we propose a new VSC theory which overcomes those limitations, in this paper we propose a new VSC theory which overcomes those limitations of proposed schemes. This new control scheme can be realized for the general linear systems which have unmeasurable state variables. And the switching function of this VSS algorithm consists of measurable state variable function(reduced-order switching function) and its derivatives. Also in the construction of control imput only measurable state variables are used.

• Journal of the Korean Society of Clothing and Textiles
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• v.29 no.7 s.144
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• pp.978-986
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• 2005

The color of apparel products have a close relationship with the face skin colors of consumers. In order to extract the favorable colors which flatter to consumer's face skin colors, this study was carried our to classify the face skin colors of Korean females. The criteria that select new subjects who have the classified face skin colors have to be decided. With color spectrometer, JX-777, face skin colors of subjects were measured and classified into three clusters that had similar hue, value and chroma with Munsell Color System. Sample size was 324 Korean females and other new 10 college girls. Data were analyzed by K-means cluster analysis, ANOVA, Duncan multiple range test, Stepwise discriminant analysis using SPSS Win. 12. Findings were as follows: 1. 324 subjects who have YR colors were clustered into 3 face skin color groups. 2. Discriminant variables of face skin colors were 5 variables : b value of cheek, V value of forehead, L value of cheek, C value of forehead and H value of cheek by the standardized canonical discriminant function coefficient 1. 3. Hit ratio of type 1 was $96.8\%$, of type 2 was $94.9\%$, of type 3 was $100.0\%$ and mean of hit ratio was $96.9\%$ by canonical discriminant function of 5 variables. 4. With the unstandardized canonical discriminant function coefficient and constant, canonical discriminant function equation 1 and 2 were calculated. And cutting score and range of score of the classified types were computed. The criteria that select the new subjects were decided.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.237-243
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• 2024

A similarity transformation of a solution of the Cauchy problem for the linear difference equation in Hilbert space has been studied. In this manuscript, we obtain necessary and sufficient conditions for linear equivalence of the discrete semigroup of operators, generated by the solution of the difference equation utilizing four Canonical semigroups.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.403-409
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• 1997

Let X be a closed almost complex 4-manifold with $b_2^+(X) > 1$, and have its canonical line bundle as a basic class. Then the pseudo-holomorphic 2-dimensional submanifolds in X with nonnegative self-intersection minimize genus in their homology classes.

• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.355-370
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• 2013

Thomas Harriot has been introduced in middle school textbooks as a great mathematician who created the sign of inequality. This study is about Harriot's symbolism and the theory of equation. Harriot made symbols of mathematical concepts and operations and used the algebraic visual representation which were combinations of symbols. He also stated solving equations in numbers, canonical, and by reduction. His epoch-making inventions of algebraic equation using notation of operation and letters are similar to recent mathematical representation. This study which reveals Harriot's contribution to general and structural approach of mathematical solution shows many developments of algebra in 16th and 17th centuries from Viete to Harriot and from Harriot to Descartes.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.6
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• pp.521-532
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• 2007

In the derivation of mild slope equation, a Galerkin method is used to rigorously form the Sturm-Liouville problem of depth dependent functions. By use of the canonical transformation to the dependent variable of the equation a reduced Helmholtz equation is obtained which exclusively consists of terms proportional to wave number, bottom slope and bottom curvature. Through numerical studies the behavior of terms is shown to play an important role in wave transformations over variable depth and it is proved that their relative magnitudes limit applicability of the mild slope equation(MSE) against the modified mild slope equation(MMSE).

• East Asian mathematical journal
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• v.33 no.1
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• pp.37-44
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• 2017

We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the ${\bar{\partial}}$-equation. We use Delin's weighted $L^2$-estimate ([3], [6]) for it.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.12
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• pp.2001-2009
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• 1989

This study suggests the use of fuzzy model in the semiconductor devices modeling as a black box approach. When membership functions of fuzzy sets used in a fuzzy model are simple piecewise-linear functions, the fuzzy model can be reresented in a simple equation. To show that the fuzzy model can be very realistic and simple when used in semiconductor devices modeling, we construct fuzzy models for bipolar transistor, MOSFET and GaAs FET, and compare those with canonical piecewise-linear models.