• 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 ${\parallel}||A{\parallel}=K$.

• 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.

• 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.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2013년도 춘계 종합학술대회 논문집
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• pp.369-370
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• 2013

Orthomodular lattice is a mathematical description of quantum theory which is based on the family CS(H) of all closed subspaces of a Hilbert space H. A partial multiplier is a function F from a non-empty subset D of a commutative semigroup A into A such that F(x)y = xF(y) for every elements x, y in A. In this paper, we define the notion of multipliers on orthomodular lattices and give some properties of multipliers. Also, we characterize some properties of orthomodular lattices by multipliers.

• 대한전기학회논문지
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• 제41권5호
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• pp.525-532
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• 1992

Fluorine-doped YBaS12TCuS13TOS17-xTFS1yT superconducting materials with y varing two orders of magnitude form 0.02 to 2.0 have been prepared by a sol-gel process by using metal nitrate salts, sodium hydroxide and sodium fluoride. Fluorine contents have been measured using an ion-selective electrode. All fluorine doped as reactant were found to be present in the resulted samples. From the observation of XRD it has been concluded that the samples with y 0.2 formed simply the single phase of perovskite structure, whereas those with y 0.5 yielded together some compounds such as BaFS12T, YFS13T and CuO in the resulted samples. The observation of solid state S019TF NMR has been carried out in order to check whether fluorine was actually incorporated into the lattice sites, and the experimental results revealed that the mole ratio of fluorine incorporated into the lattice sites of YBaS12TCuS13TOS17-xT was approximately 0.2 per mole of the compound. Also electrical resistivity measurement indicated that onset transition temperature has the tendency to increase slightly with increasing y in the dilute region as y 0.2.

• 호남수학학술지
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• 제31권2호
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• pp.259-265
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• 2009

Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$. Let x and y be vectors in $\mathcal{H}$ and let $P_x$ be the projection onto sp(x). If $P_xE$ = $EP_x$ for each E ${\in}\;\mathcal{L}$, then the following are equivalent. (1) There exists an operator A in Alg$\mathcal{L}$ such that Ax = y, Af = 0 for all f in $sp(x)^{\perp}$ and A ${\geq}$ 0. (2) sup ${\frac{{\parallel}E^{\perp}y{\parallel}}{{\parallel}E^{\perp}x{\parallel}}:E{\in}\mathcal{L}}$ < ${\infty}$ < x, y > ${\geq}$ 0. Let X and Y be operators in $\mathcal{B}(\mathcal{H})$. Let P be the projection onto $\overline{rangeX}$. If PE = EP for each E ${\in}\;\mathcal{L}$, then the following are equivalent: (1) sup ${\frac{{\parallel}E^{\perp}Yf{\parallel}}{{\parallel}E^{\perp}Xf{\parallel}}:f{\in}\mathcal{H},E{\in}\mathcal{L}}$ < ${\infty}$ and < Xf, Yf > ${\geq}$ 0 for all f in H. (2) There exists a positive operator A in Alg$\mathcal{L}$ such that AX = Y.

• Bulletin of the Korean Chemical Society
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• 제16권12호
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• pp.1184-1189
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• 1995

The rapid quenching dynamics of F center excitation by OH- defects in KCl crystals are investigated by monitoring ground state absorption bleach recovery, using a picosecond streak camera absorption spectrometer. F center absorption bleach in OH--doped crystals shows three distinguishable recovery components with the current temporal resolution, designated as slow, medium and fast components. The slow one is due to the normal relaxation process of F* centers as found in OH--free crystals. The others are consequent on energy transfer from electronically excited F centers to OH--vibrational levels. The fast component is a minor energy transfer process and resulting from the relaxation of somewhat distant, not the closest, associated pairs of F* and OH- defects. The energy transfer between widely separated F* and OH- defects opens up a recovery process via the medium component which is assisted by OH- librations, lattice vibrations and OH- dipole reorientations. The quenching behaviors of F* luminescence and photoionization by OH- are explained well by the relaxation process of the medium component.

• Bulletin of the Korean Chemical Society
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• 제19권10호
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• pp.1063-1068
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• 1998

The nature of F electronic excitation energy transfer to OH- vibrational levels in KCl crystals is the exchange interaction, although the transfer process exhibits three temporally distinguishable components depending on the distance between excited F center and OH-. The critical distance as well as rate of the major energy transfer process in randomly distributed samples increases rapidly as OH- librational motions become active with temperature rise. The excited state character introduced into the OH- ground electronic state by perturbation is essential for the exchange interaction. The perturbation is brought about by the expanded electron cloud of excited F center for OH- associated to F center, whereas by librations and lattice vibrations perpendicular to the bond axis for isolated OH- . F excitation quenching efficiency by OH- is dependent on the variation of the critical distance rather than the rate as the rate is much faster than the normal F bleach recovery rate.

• 한국통신학회논문지
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• 제3권1호
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• pp.18-25
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• 1978

반도체 소자에서 생기는 1/f 형의 잡음의 근원이 무엇인가에 대해 지금까지 여러 이론이 나왔다. 그중에도 Mcwhorter's Surface model이 대표적인 이론이었다. 그러나 Hooge는 이론에 반기를 들고 나왔다. Hooge의 이론에 의하면 thermo cell이나 Concentration cell에서의 1/f-형의 잡음이 표면효과(surface effect)가 아니라는 것이다. 본 논문에서는 이 두 대표적인 이론을 종합검토할 수 있는 Langenvin type의 Boltzmann transport equation에 입각하여 새로운 일반이론을 세웠다. 본 논문에서는 N형 채널을 갖고 있는 금속산화물반도체 전계효과 트랜지스터에서 단일준의 Shockley-Read-Hall recombination center에 의한 단락회로에서 드레인의 1/f-형 잡음스펙트럼을 계산하기 위해 시간에 따라 변화하는 양을 포함시키므로써 각 에너지대의 케리어에 대해 준-페르미준위를 정의할 수 없다고 가정했으므로, 1/f-형의 잡음은 다수케리어 효과에 기인한다고 가정했다. 이러한 가정하에서 유도된 1/f-형의 잡음은 금속산화물반도체 전계효과 트랜지스터에서 1/f-형의 잡음에 중요한 요인들을 모두 보여주었다. : 적주파에서 플렛티유를 나타내지 않았고 채널의 면적 A와 드레인 바이어스 전압 V에 비례하고 체널의 길이 L에 반비례한다. 본 논문의 모델에서는 1/f-응답에서 1/f2에 대한 잡음스트럼의 전이주파수와 P-n 합다이오우드의 surfact center에 관계되는 완화시간(relaxation time)에 대응하는 주파수 사이를 구별하여 설명할 수 있었다. 본 논문의 결과에서 1/f-형 잡음스펙트럼은 격자산란이 주원인이 된다. 금속산화물반도체 전계효과 트랜지스터를 살펴보면 격자산란이 주로 표면에서 일어나기 때문에 1/f-형 잡음이 표면효과라고 말할 수 있다.

• 한국결정성장학회:학술대회논문집
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• 한국결정성장학회 1998년도 PROCEEDINGS OF THE 14TH KACG TECHNICAL MEETING AND THE 5TH KOREA-JAPAN EMGS (ELECTRONIC MATERIALS GROWTH SYMPOSIUM)
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• pp.71-74
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• 1998

$Er^{3+}$ doped $NdF_{3}$ single crystalline thin films with smooth, microcrack-free, and high-crystalline quality were grown on $CaF_{2}(111)$ substrate at $500^{\circ}C$by molecular beem epitaxy(MBE). The relation-ship between subcell and supercell showing the reconstructed $3^{1/2} \times 3^{1/2}$ structure was studied by reflection high-energy electron diffraction(RHEED) investigation. The film surface and the growth mode were examined in studied by RHEED patterns and atomic force microscope(AFM) images ex situ. The crystallinity of film and the lattice mismatch between $NdF_{3}Er}^{3+}(0002)$ film and $CaF_{2}(111)$ substrate depending in the $Er^{3+}$ concentration were investigated by X-ray rocking curve analysis.