• Bulletin of the Korean Chemical Society
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• v.12 no.1
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• pp.47-51
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• 1991

Spin-lattice relaxation of methyl protons in 2,6-dichlorotoluene and N-methyl phthalimide, each dissolved in CDCl$_3$, has been studied at 34$^{\circ}$C and the contribution from spin-rotation interaction to the relaxation process has been separated from that due to dipole-dipole interactions among methyl protons. The results show that the spin-rotational contributions to the initial rate of relaxation in 2,6-dichlorotoluene and N-methyl phthalimide amount to 18 and 31%, respectively, of the total relaxation rate at 34$^{\circ}$C. The method of separating the spin-rotational contribution from that of dipolar interactions adopted in this paper is based on the well known fact that in an A$_3$ spin system such as methyl protons in liquid phase dipolar relaxation mechanism gives non-exponential decay of the z-component of total magnetization of protons while the random field fluctuation such as spin-rotational mechanism causes exponential decay.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.379-389
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• 2004

Given operators X and Y acting on a Hilbert space ${\mathcal{H}}$, 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 $i=1,2,{\cdots},n$. In this article, we obtained the following : Let ${\mathcal{H}}$ be a Hilbert space and let ${\mathcal{L}}$ be a commutative subspace lattice on ${\mathcal{H}}$. Let X and Y be operators acting on ${\mathcal{H}}$. Then the following statements are equivalent. (1) There exists an operator A in $Alg{\mathcal{L}}$ such that AX = Y, A is positive and every E in ${\mathcal{L}}$ reduces A. (2) sup ${\frac{{\parallel}{\sum}^n_{i=1}\;E_iY\;f_i{\parallel}}{{\parallel}{\sum}^n_{i=1}\;E_iX\;f_i{\parallel}}}:n{\in}{\mathbb{N}},\;E_i{\in}{\mathcal{L}}$ and $f_i{\in}{\mathcal{H}}<{\infty}$ and <${\sum}^n_{i=1}\;E_iY\;f_i$, ${\sum}^n_{i=1}\;E_iX\;f_i>\;{\geq}0$, $n{\in}{\mathbb{N}}$, $E_i{\in}{\mathcal{L}}$ and $f_i{\in}H$.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.387-395
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• 2004

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 H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that range(X) is dense in H. Then the following statements are equivalent: (1) There exists an operator A in AlgL such that AX = Y, $A^{*}$ = A and every E in L reduces A. (2) sup ${\frac{$\mid$$\mid${\sum_{i=1}}^n\;E_iYf_i$\mid$$\mid$}{$\mid$$\mid${\sum_{i=1}}^n\;E_iXf_i$\mid$$\mid$}$:n{\epsilon}N,f_i{\epsilon}H\;and\;E_i{\epsilon}L}\;<\;{\infty}$ and = for all E in L and all f, g in H.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.421-428
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• 2009

Given operators X and Y acting on a Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this paper, we showed the following : Let $\mathcal{L}$ be a subspace lattice acting on a Hilbert space $\mathcal{H}$ and let $X_i$ and $Y_i$ be operators in B($\mathcal{H}$) for i = 1, 2, ${\cdots}$. Let $P_i$ be the projection onto $\overline{rangeX_i}$ for all i = 1, 2, ${\cdots}$. If $P_kE$ = $EP_k$ for some k in $\mathbb{N}$ and all E in $\mathcal{L}$, then the following are equivalent: (1) $sup\;\{{\frac{{\parallel}E^{\perp}({\sum}^n_{i=1}Y_if_i){\parallel}}{{\parallel}E^{\perp}({\sum}^n_{i=1}Y_if_i){\parallel}}:f{\in}H,n{\in}{\mathbb{N}},E{\in}\mathcal{L}}\}$ < ${\infty}$ range $\overline{rangeY_k}\;=\;\overline{rangeX_k}\;=\;\mathcal{H}$, and < $X_kf,\;X_kg$ >=< $Y_kf,\;Y_kg$ > for some k in $\mathbb{N}$ and for all f and g in $\mathcal{H}$. (2) There exists an operator A in Alg$\mathcal{L}$ such that $AX_i$ = $Y_i$ for i = 1, 2, ${\cdots}$ and AA$^*$ = I = A$^*$A.

• Journal of the Korean Magnetics Society
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• v.3 no.2
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• pp.87-93
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• 1993

Iron nitride (Fe-N) magnetic thin films were deposited using a DC magnetron sputtering system. Microstructures and magnetic properties were examined as a function of deposition power and nitrogen gas input ratio. The nitrogen content in the film was found to be the major factor determining the microstructure and the magnetic properties. The films deposited at low nitrogen input ratios have an $\alpha$-Fe structure of which the lattice is expanded due to the nitrogen atoms incorporated at the interstitial sites. As the nitrogen content in the film increases, the degree of lat-tice expansion increases and the value of saturation magnetization decreases linearly. The films with a high degree of lattice expansion give very low values of coercivity, which is attributed to the disturbance of colunmar growth and the decrease of surface roughness. Further increase in the nitrogen input ratio causes the phase transfonnation from $\alpha$-Fe to $Fe_{2-3}N$, resulting in the marked reduction in the saturation magnetization. The phase transformation occurs when, regardless of deposition conditions, the nitrogen content reaches at 15 at.% and the lattice is expanded by 5%.

• Nuclear Engineering and Technology
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• v.49 no.1
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• pp.209-215
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• 2017

Fast neutron irradiation was used to improve the switching speed of a 600-V nonpunch-through insulated gate bipolar transistor. Fast neutron irradiation was carried out at 30-MeV energy in doses of $1{\times}10^8n/cm^2$, $1{\times}10^9n/cm^2$, $1{\times}10^{10}n/cm^2$, and $1{\times}10^{11}n/cm^2$. Electrical characteristics such as current-voltage, forward on-state voltage drop, and switching speed of the device were analyzed and compared with those prior to irradiation. The on-state voltage drop of the initial devices prior to irradiation was 2.08 V, which increased to 2.10 V, 2.20 V, 2.3 V, and 2.4 V, respectively, depending on the irradiation dose. This effect arises because of the lattice defects generated by the fast neutrons. In particular, the turnoff delay time was reduced to 92 nanoseconds, 45% of that prior to irradiation, which means there is a substantial improvement in the switching speed of the device.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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• pp.279.2-279.2
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• 2016

InGaN/GaN multiple quantum wells (MQWs) have been attracted much attention as light-emitting diodes (LEDs) in the visible and UV regions. Particularly, quantum efficiency of green LEDs is decreased dramatically as approaching to the green wavelength (~500 nm). This low efficiency has been explained by quantum confined Stark effect (QCSE) induced by piezoelectric field caused from a large lattice mismatch between InGaN and GaN. To improve the quantum efficiency of green LED, several ways including epitaxial lateral overgrowth that reduces differences of lattice constant between GaN and sapphire substrates, and non-polar method that uses non- or semi-polar substrates to reduce QCSE were proposed. In this study, graded short-period InGaN/GaN superlattice (GSL) was grown below the 5-period InGaN/GaN MQWs. InGaN/GaN MQWs were grown on the patterned sapphire substrates by vertical-metal-organic chemical-vapor deposition system. Five-period InGaN/GaN MQWs without GSL structure (C-LED) were also grown to compare with an InGaN/GaN GSL sample. The luminescence properties of green InGaN/GaN LEDs have been investigated by using photoluminescence (PL) and time-resolved PL (TRPL) measurements. The PL intensities of the GSL sample measured at 10 and 300 K increase about 1.2 and 2 times, respectively, compared to those of the C-LED sample. Furthermore, the PL decay of the GSL sample measured at 10 and 300 K becomes faster and slower than that of the C-LED sample, respectively. By inserting the GSL structures, the difference of lattice constant between GaN and sapphire substrates is reduced, resulting that the overlap between electron and hole wave functions is increased due to the reduced piezoelectric field and the reduction in dislocation density. As a results, the GSL sample exhibits the increased PL intensity and faster PL decay compared with those for the C-LED sample. These PL and TRPL results indicate that the green emission of InGaN/GaN LEDs can be improved by inserting the GSL structures.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.33-39
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• 2000

Well known is the directed self-avoiding walk model on the square lattice with reflecting and absorbing barriers. We consider two models, namely, a pyramid self-avoiding polygon model and a top and bottom pyramid polygon model, as subcollections of the model. We derive explicit formulas for the number of 2N-step polygons in these models.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.159-178
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• 2024

We continue the investigations in [7] extending the Bruhat order on n × n alternating sign matrices to a more general setting. We show that the resulting partially ordered set is a lattice and also investigate its rank.

• Journal of the Korean Ceramic Society
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• v.53 no.4
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• pp.463-467
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• 2016

$Si^{4+}-N^{3-}$ was incorporated into $Ce^{3+}-doped$ lutetium aluminum garnet ($Lu_{2.965}Ce_{0.035}Al_5O_{12}$, $LuAG:Ce^{3+}$) lattices, resulting in the formation of $Lu_{2.965}Ce_{0.035}Al_{5-x}Si_xO_{12-x}N_x$ [(Lu,Ce)AG:xSN]. For x = 0-0.25, the synthesized powders consisted of the LuAG single phase, and the lattice constant decreased owing to the smaller $Si^{4+}$ ions. However, for x > 0.25, a small amount of unknown impurity phases was observed, and the lattice constant increased. Under 450 nm excitation, the PL spectrum of $LuAG:Ce^{3+}$ exhibited the green band, peaking at 505 nm. The incorporation of $Si^{4+}-N^{3-}$ into the $Al^{3+}-O^{2-}$ sites of $LuAG:Ce^{3+}$ led to a red-shift of the emission peak wavelength from 505 to 570 nm with increasing x. Corresponding CIE chromaticity coordinates varied from the green to yellow regions. These behaviors were discussed based on the modification of the $5d^1$ split levels and crystal field surroundings of $Ce^{3+}$, which arose from the Ce-(O,N)8 bonds.