• Transactions of the Society of Information Storage Systems
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• v.8 no.1
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• pp.1-5
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• 2012

We present a method for preparing a quantum dot fluorescent monolayer film on a glass substrate. Since nanoparticles aggregate easily, it is difficult to prepare a nanoparticle monolayer film. We have used a covalent bond, the peptide bond, to fix quantum dots on the glass substrate. The surface of the quantum dot was functionalized with carboxyl groups, and the glass substrate was also functionalized with amino groups using a silane coupling agent. The carboxyl group can be strongly coupled to the amino group. We were able to successfully prepare a monolayer film of CdSe quantum dots on the glass substrate.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1785-1801
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• 2008

Noncommutative extensions of the Gross and Beltrami Laplacians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Fourier- Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.675-690
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• 1998

A role of singletons in quantum central limit theorems is studied. A common feature of quantum central limit distributions, the singleton condition which guarantees the symmetry of the limit distributions, is revisited in the category of discrete groups and monoids. Introducing a general notion of quantum independence, the singleton independence which include the singleton condition as an extremal case, we clarify the role of singletons and investigate the mechanism of arising non-symmetric limit distributions.

• Proceedings of the Korean Vacuum Society Conference
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• 2015.08a
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• pp.222.1-222.1
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• 2015

Recently, graphene quantum dots (GQDs) have attracted great attention due to various properties including cost-effectiveness of synthesis, low toxicity, and high photostability. Nevertheless, the origins of photoluminescence (PL) from GQDs are unclear because of extrinsic states of the impurities, disorder structures, and oxygen-functional groups. Therefore, to utilize GQDs in various applications, their optical properties generated from the extrinsic states should be understood. In this work, we have focused on the effect of oxygen-functional groups in PL of the GQDs. The GQDs with nanoscale and single layer are synthesized by employing graphite nanoparticles (GNPs) with 4 nm. The series of GQDs with different amount of oxygen-functional groups were prepared by the chain of chemical oxidation and reduction process. The fabrication of a series of graphene oxide QDs (GOQDs) with different amounts of oxygen-contents is first reported by a direct oxidation route of GNPs. In addition, for preparing a series of reduced GOQDs (rGOQDs), we employed the conventional chemical reduction to GOQDs solution and controlled the amount of reduction agents. The GOQDs and rGOQDs showed irreversible PL properties even though both routes have similar amount of oxyen-functional groups. In the case of a series of GOQDs, the PL spectrum was clearly redshifted into blue and green-yellowish color. On the other hand, the PL spectrum of rGOQDs did not change significantly. By various optical measurement such as the PL excitation, UV-vis absorbance, and time-resolved PL, we could verify that their PL mechanisms of GOQDs and rGOQDs are closely associated with different atomic structures formed by chemical oxidation and reduction. Our study provides an important insights for understanding the optical properties of GQDs affected by oxygen-functional groups. [1]

• Proceedings of the Korean Vacuum Society Conference
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• 2012.02a
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• pp.531-531
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• 2012

So many groups have been researching the green quantum dots such as InP, InP/ZnS for overcoming the semiconductor nanoparticles composed with heavy metals like as Cd and Pb so on. In spite of much effort to keep up CdSe quantum dots, it does not reach the good properties compared with CdSe/ZnS quantum dots. This quantum dot has improved its properties through the generation of core/shell CdSe/ZnS structure or core/multi-shell structures like as CdSe/CdS/ZnS and CdSe/CdS/ CdZnS/ZnS. In this research, we try to synthesize the InP multi-shell structure by the successiveion layer absorption reaction (SILAR) in the one pot. The synthesized multi-shell structure has improved quantum yield and photo-stability. To generate white light, highly luminescent InP multi-shell quantum dots were mixed with yellow phosphor and integrated on the blue LED chip. This InP multi-shell improved red region of the LEDs and generated high CRI.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1231-1249
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• 2005

By employing Chebotarev and Fagnola's sufficient conditions for conservativity of minimal quantum dynamical semigroups [7, 8], we construct the conservative minimal quantum dynamical semigroups generated by noncommutative elliptic operators in the sense of [2]. We apply our results to concrete examples.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.35-38
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• 1995

Let A be a symmetric positive definite Cartan matrix. As in [4], we denote by U the quantum group arising from A and $U_\lambda$ be the corresponding quantum group at a root of unity $\lambda$. In [4], Lusztig constructed irreducible highest weight $U_\lambda$-modules $L_\lambda(z)$ for $z \in Z^n$ and showed that $L_\lambda(z)$ is of finite dimension over C if and only if $z \in (Z^+)^n$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.463-484
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• 2017

We construct a weak Hopf algebra $wX_q(A_1)$ corresponding to non-standard quantum group $X_q(A_1)$. The PBW basis of $wX_q(A_1)$ is described and all the highest weight modules of $wX_q(A_1)$ are classified. Finally we give the Clebsch-Gordan decomposition of the tensor product of two highest weight modules of $wX_q(A_1)$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.557-570
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• 2015

Let $\mathbb{G}$ be a von Neumann algebraic locally compact quantum group, in the sense of Kustermans and Vaes. In this paper, as a consequence of a notion of amenability for actions of Lau algebras, we show that $\hat{\mathbb{G}}$, the dual of $\mathbb{G}$, is co-amenable if and only if there is a state $m{\in}L^{\infty}(\hat{\mathbb{G}})^*$ which is invariant under a left module action of $L^1(\mathbb{G})$ on $L^{\infty}(\hat{\mathbb{G}})^*$. This is the quantum group version of a result by Stokke [17]. We also characterize amenable action of Lau algebras by several properties such as fixed point property. This yields in particular, a fixed point characterization of amenable groups and H-amenable representation of groups.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2010.06a
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• pp.254-254
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• 2010

We report aqueous synthesis of cadmium telluride (CdTe) quantum dots(QDs) using imidazolium-based ionic liquids with various functional groups. The functinalized ionic liquids were designed to have thiol groups, and then phase transfer with aqueous or organic solvents can be adjusted by changing side chain lengths of the cation and the choice of anion. The quantum yield was obtained IL-functionalized CdTe QDs reached up to 40% by post-treatment method.