• 대한수학회지
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• 제41권3호
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• pp.423-433
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• 2004

In this paper we obtained the following: Let H. be a Hilbert space and (equation omitted) be a subspace lattice on H. Let X and Y be operators acting on H. If the range of X is dense in H, then the following are equivalent: (1) there exists an operator A in Alg(equation omitted) such that AX = Y, (2) sup (equation omitted) Moreover, if condition (2) holds, we may choose the operator A such that ∥A∥ = K.

• 전기의세계
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• 제16권4호
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• pp.11-16
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• 1967

A physical analysis is applied to the measured phenomena of aromatic organic compounds under the uniform electric field of 0.1MV/cm through 1.5MV/cm, when they are irradiated or non-irradiated respectively. Upon the observations about irradiation effects, space charge effects and their temperature dependance, the conditions of lattice defects act conspicuously on electric conductrivity, photo conductivity and dielectric breakdown. Although the qualitative agreement with Frohlich's high energy criterion theory for the above mechanisms is poor, it is concluded that the phenomena of aromatic compounds may possibly be due to the effect of lattice defects or impurity centers generated by .gamma.-ray irradiations.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.513-524
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• 2005

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. Let L be a subspace lattice on H. We obtained a necessary and sufficient condition for the existence of an interpolating operator A which is in AlgL.

• 한국터널지하공간학회 논문집
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• 제18권5호
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• pp.431-439
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• 2016

본 논문은 비파괴 기법을 활용한 격자지보재의 품질평가 기법에 대한 내용을 다루었다. 일반적인 격자지보재의 성능평가는 강재의 인장강도시험과 육안조사로 이루어진다. 강재의 인장강도시험은 현장에 반입되는 격자지보의 시편을 확보하여 수행하게 되는데 이때 시편 확보를 위해 격자지보재를 훼손시켜야하는 단점을 가지고 있고 대부분의 현장에서는 인장강도시험기를 보유하고 있지 않아 시험인증기관에 의뢰해야하는 불편함을 가지고 있다. 또한 강재 생산시 발행된 성적서(Mile sheet)로 대체하기도 하나 이는 신뢰성이 결여될 수 밖에 없다. 더욱이 현장에서의 육안조사는 신뢰성이 결여되는 문제점을 가지고 있기 때문에 현장에서 자재의 훼손없이, 쉽고 빠르게 격자지보재의 품질을 평가할 수 있는 방법이 필요하게 되었다. 따라서 본 연구에서는 동일 시편에 대한 인장강도시험의 항복강도와 계장화압입시험의 항복강도를 비교 분석하여 비파괴시험법의 적용성을 분석하였다. 시험결과 계장 화압입시험은 95%이상의 정밀도를 보였으며 현장에서 성능평가가 가능한 계장화압입시험에 의한 품질평가기법을 제안하고자 한다.

• 호남수학학술지
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• 제34권3호
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• pp.409-422
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• 2012

Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$. And let X and Y be operators acting on a Hilbert space $\mathcal{H}$. Let $sp(x)=\{{\alpha}x\;:\;{\alpha}{\in}\mathcal{C}\}$ $x{\in}\mathcal{H}$. Assume that $\mathcal{H}=\overline{range\;X}{\oplus}sp(h)$ for some $h{\in}\mathcal{H}$ and < $h$, $E^{\bot}Xf$ >= 0 for each $f{\in}\mathcal{H}$ and $E{\in}\mathcal{L}$. Then there exists an operator A in Alg$\mathcal{L}$ such that AX = Y if and only if $sup\{\frac{{\parallel}E^{\bot}Yf{\parallel}}{{\parallel}E^{\bot}Yf{\parallel}}\;:\;f{\in}H,\;E{\in}\mathcal{L}\}$ = K < ${\infty}$. Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}||A{\parallel}=K$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.29-36
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• 2004

Given vectors x and ｙ in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and ｙ be vectors in $\cal{H}$ and let $P_x$, be the projection onto sp(x). If $P_xE=EP_x$ for each $ E \in \cal{L}$ then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in ($sp(x)^\perp$) and $A=-A^\ast$. (2) (equation omitted)

• International Journal of Aeronautical and Space Sciences
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• 제13권2호
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• pp.199-209
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• 2012

An advanced aeroelastic formulation for flutter analyses is presented in this paper. Refined 1D structural models were coupled with the doublet lattice method, and the g-method was used for flutter analyses. Structural models were developed in the framework of the Carrera Unified Formulation (CUF). Higher-order 1D structural models were obtained by using Taylor-like expansions of the cross-section displacement field of the structure. The order (N) of the expansion was considered as a free parameter since it can be arbitrarily chosen as an input of the analysis. Convergence studies on the order of the structural model can be straightforwardly conducted in order to establish the proper 1D structural model for a given problem. Flutter analyses were conducted on several wing configurations and the results were compared to those from literature. Results show the enhanced capabilities of CUF 1D in dealing with the flutter analysis of typical wing structures with high accuracy and low computational costs.

• 호남수학학술지
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• 제29권1호
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• pp.55-60
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• 2007

Given operators X and Y acting on a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we showed the following : Let $\cal{L}$ be a subspace lattice acting on a Hilbert space $\cal{H}$ and let X and Y be operators in $\cal{B}(\cal{H})$. Let P be the projection onto $\bar{rangeX}$. If FE = EF for every $E\in\cal{L}$, then the following are equivalent: (1) $sup\{{{\parallel}E^{\perp}Yf\parallel\atop \parallel{E}^{\perp}Xf\parallel}\;:\;f{\in}\cal{H},\;E\in\cal{L}\}\$ < $\infty$, $\bar{range\;Y}\subset\bar{range\;X}$, and < Xf, Yg >=< Yf,Xg > for any f and g in $\cal{H}$. (2) There exists a self-adjoint operator A in Alg$\cal{L}$ such that AX = Y.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.1089-1093
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• 2003

The moving least square (MLS) basis is implemented for the real-space band-structure calculation of 2D photonic crystals. The value-periodic MLS shape function is thus used in order to represent the periodicity of crystal lattice. Any periodic function can properly be reproduced using this shape function. Matrix eigenequations, derived from the macroscopic Maxwell equations, are then solved to obtain photonic band structures. Through numerical examples of several lattice structures, the MLS-based method is proved to be a promising scheme for predicting band gaps of photonic crystals.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권3호
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• pp.161-166
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• 2007

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for i = 1,2,...,n. In this article, we showed the following: Let L, be a subspace lattice on a Hilbert space H and let X and Y be operators in B(H). Then the following are equivalent: (1) $$sup\{\frac{{\parallel}E^{\bot}Yf{\parallel}}{{\overline}{\parallel}E^{\bot}Xf{\parallel}}\;:\;f{\epsilon}H,\;E{\epsilon}L}\}\;<\;{\infty},\;sup\{\frac{{\parallel}Xf{\parallel}}{{\overline}{\parallel}Yf{\parallel}}\;:\;f{\epsilon}H\}\;<\;{\infty}$$ and $\bar{range\;X}=H=\bar{range\;Y}$. (2) There exists an invertible operator A in AlgL such that AX=Y.