• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.71-78
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• 2013

Let X be a space and $2^X$(C(X);K(X);$C_K$(X)) denote the hyperspace of nonempty closed subsets(connected closed subsets, compact subsets, subcontinua) of X with the Vietoris topology. We investigate the relationships between the space X and its hyperspaces concerning the properties of connectedness im kleinen. We obtained the following : Let X be a locally compact Hausdorff space. Let $x{\in}X$. Then the following statements are equivalent: (1) X is connected im kleinen at $x$. (2) $2^X$ is arcwise connected im kleinen at {$x$}. (3) K(X) is arcwise connected im kleinen at {$x$}. (4) $C_K$(X) is arcwise connected im kleinen at {$x$}. (5) C(X) is arcwise connected im kleinen at {$x$}.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.197-204
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• 2008

We study diameter preserving linear maps from C(X) into C(Y) where X and Y are compact Hausdorff spaces. By using the extreme points of $C(X)^*\;and\;C(Y)^*$ and a linear condition on them, we obtain that there exists a diameter preserving linear map from C(X) into C(Y) if and only if X is homeomorphic to a subspace of Y. We also consider the case when X and Y are noncompact but locally compact spaces.

• Proceedings of the Materials Research Society of Korea Conference
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• 2009.05a
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• pp.53.1-53.1
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• 2009

실리콘 다층박막 태양전지를 위한 초고효율 실리콘 양자점 박막을 연구하기 위해 Silicon target과 Carbon target을 동시에 스퍼터하여 Silicon Carbide 박막을 증착하였다. Silicon Carbide 박막의 조성비는 target에 인가되는 RF Power를 조절하여 Auger Electro Spectroscopy를 사용하여 Si, C, O, N원소의 양을 정량화하여 측정하였다. Si Power를 200W에 고정하고, C Power를 0W에서 400W까지 변화시킬 때, $Si_{1-x}$ $C_x$ 박막에서 조성비 x는 0 ~ 0.43 범위였다. 이 박막을 증착 한 후에 질소 분위기에서 600 ~ $1000^{\circ}C$ 온도로 열처리를 진행하였다. High resolution TEM과 Raman 분석을 통해, 박막의 열처리 후 $Si_{1-x}$ $C_x$ 박막 내에 실리콘 양자점이 형성되었음을 관찰할 수 있었고, 2 ~ 10 nm 의 크기를 가지는 것으로 확인할 수 있었다. 이 실리콘 양자점을 포함한 $Si_{1-x}$ $C_x$ 박막을 적층하여 UV-VIS-NIR spectroscopy, FTIR및 PL와 같은 측정을 통해 광학적 에너지 밴드갭의 변화와 그에 따른 특성을 확인하였다.

• Journal of Internet of Things and Convergence
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• v.6 no.4
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• pp.49-57
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• 2020

In this paper, I provided an approximation function Li*2,10(x) using logarithm integral for the counting function π*2,10(x) of consecutive deca primes. Several personal computers and Mathematica were used to validate the approximation function Li*2,10(x). I found the real value of π*2,10(x) and approximate value of Li*2,10(x) for various x ≤ 1011. By the result of theses calculations, most of the error rates are margins of error of 0.005%. Also, I proved that the sum C2,10(∞) of reciprocals of all primes with difference 10 between primes is finite. To find C2,10(∞), I computed the sum C2,10(x) of reciprocals of all consecutive deca primes for various x ≤ 1011 and I estimate that C2,10(∞) probably lies in the range C2,10(∞)=0.4176±2.1×10-3.

• Journal of the Korean Ceramic Society
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• v.34 no.9
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• pp.921-926
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• 1997

Two NbCx-C1-x/Y2O3/Ti sputter-coated Al2O3 substrates (L 5.5 cm$\times$W 0.5 cm) were diffusion bonded together using hot press method at 95$0^{\circ}C$ for 3 hours under 1 MPa of applied pressure. 4 points bending tests were used to evaluate the mechanical performance of these precracked laminate beams. Two types of mechanical responses were observed: crack penetration through the interface for x=0.75, 1 and crack deflection into an interface for x=0.25, 0.5. The Al2O3/NbCx-C1-x/Y2O3/Ti system suggested here has been proves to be effective for the thermokinetical stability and tailorability of the interfaces of Al2O3/Ti composites at 95$0^{\circ}C$.

• Journal of Korea Game Society
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• v.9 no.2
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• pp.95-104
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• 2009

The windows games and the console games that use DirectX occupied 20% or more of world game market and that are developed by C++ Language occupied 75% or more of the market. This study proposed that commonality and variability for code of the 20 projects based on DirectX and C++ is analysed and patternized, that common modules are created, and that modules are modeled. As a result of applying a case study, it is verified that the proposed model reduces effort in game development.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.17-53
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• 2014

Let ${\gamma}$ be a hyperbolic closed orbit of a $C^1$ vector field X on a compact boundaryless Riemannian manifold M, and let $C_X({\gamma})$ be the chain component of X which contains ${\gamma}$. We say that $C_X({\gamma})$ is $C^1$ robustly shadowable if there is a $C^1$ neighborhood $\mathcal{U}$ of X such that for any $Y{\in}\mathcal{U}$, $C_Y({\gamma}_Y)$ is shadowable for $Y_t$, where ${\gamma}_Y$ denotes the continuation of ${\gamma}$ with respect to Y. In this paper, we prove that any $C^1$ robustly shadowable chain component $C_X({\gamma})$ does not contain a hyperbolic singularity, and it is hyperbolic if $C_X({\gamma})$ has no non-hyperbolic singularity.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.161-173
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• 2013

This paper is concerned with the space $\mathcal{K}_{w^*}(X^*,Y)$ of $weak^*$ to weak continuous compact operators from the dual space $X^*$ of a Banach space X to a Banach space Y. We show that if $X^*$ or $Y^*$ has the Radon-Nikod$\acute{y}$m property, $\mathcal{C}$ is a convex subset of $\mathcal{K}_{w^*}(X^*,Y)$ with $0{\in}\mathcal{C}$ and T is a bounded linear operator from $X^*$ into Y, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\{S{\in}\mathcal{C}:{\parallel}S{\parallel}{\leq}{\parallel}T{\parallel}\}}^{{\tau}_{\mathcal{c}}}$, where ${\tau}_{\mathcal{c}}$ is the topology of uniform convergence on each compact subset of X, moreover, if $T{\in}\mathcal{K}_{w^*}(X^*, Y)$, here $\mathcal{C}$ need not to contain 0, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\mathcal{C}}$ in the topology of the operator norm. Some properties of $\mathcal{K}_{w^*}(X^*,Y)$ are presented.

• Corrosion Science and Technology
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• v.9 no.2
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• pp.81-86
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• 2010

The mechanisms of selective oxidation of intercritically annealed CMnAl TRIP steels in a Continuous Galvanizing Line (GCL) were studied by cross-sectional observation of the surface and sub-surface regions by means of High Resolution Transmission Electron Microscopy (HR-TEM). The selective oxidation and nitriding of an intercritically annealed CMnAl TRIP steel in a controlled dew point 10%$H_2+N_2$ atmosphere resulted in the formation of c-xMnO.$MnO_2$ (1${\leq}$x<3) and c-xMnO.$Al_2O_3$ ($x{\geq}1$) particles on the steel surface. Single crystal c-xMnO.$SiO_2$ ($2{\leq}x{\leq}4$) oxide particles were also observed on the surface. A thin film of crystalline c-xMnO.$SiO_2$ (2${\leq}$x<3) and c-xMnO.$Al_2O_3$ ($x{\geq}1$) was present between these particles. In the sub-surface region, internal oxidation, nitriding and intermetallic compound formation were observed. In the first region, large crystalline c-xMnO.$SiO_2$ ($1{\geq}x{\geq}2$) and c-xMnO.$Al_2O_3$ ($x{\geq}1$) oxides particles were present. In the second region, c-AlN particles were observed, and in a third region, small $MnAl_x$ (x>1) intermetallic compound particles were observed.