• Title, Summary, Keyword: quantum group

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A ROLE OF SINGLETONS IN QUANTUM CENTRAL LIMIT THEOREMS

  • Accardi, Luigi;Hashimoto, Yukihiro;Obata, Nobuaki
    • 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.

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Interband optical properties in wide band gap group-III nitride quantum dots

  • Bala, K. Jaya;Peter, A. John
    • Advances in nano research
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    • v.3 no.1
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    • pp.13-27
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    • 2015
  • Size dependent emission properties and the interband optical transition energies in group-III nitride based quantum dots are investigated taking into account the geometrical confinement. Exciton binding energy and the optical transition energy in $Ga_{0.9}In_{0.1}N$/GaN and $Al_{0.395}In_{0.605}N$/AlN quantum dots are studied. The largest intersubband transition energies of electron and heavy hole with the consideration of geometrical confinement are brought out. The interband optical transition energies in the quantum dots are studied. The exciton oscillator strength as a function of dot radius in the quantum dots is computed. The interband optical absorption coefficients in GaInN/GaN and AlInN/AlN quantum dots, for the constant radius, are investigated. The result shows that the largest intersubband energy of 41% (10%) enhancement has been observed when the size of the dot radius is reduced from $50{\AA}$ to $25{\AA}$ of $Ga_{0.9}In_{0.1}N$/GaN ($Al_{0.395}In_{0.605}N$/AlN) quantum dot.

QUANTUM DYNAMICAL SEMIGROUP AND ITS ASYMPTOTIC BEHAVIORS

  • Choi, Veni
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.1
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    • pp.189-198
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    • 2004
  • In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.

ON HOPF ALGEBRAS IN ENTROPIC JÓNSSON-TARSKI VARIETIES

  • ROMANOWSKA, ANNA B.;SMITH, JONATHAN D.H.
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1587-1606
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    • 2015
  • Comonoid, bi-algebra, and Hopf algebra structures are studied within the universal-algebraic context of entropic varieties. Attention focuses on the behavior of setlike and primitive elements. It is shown that entropic $J{\acute{o}}nsson$-Tarski varieties provide a natural universal-algebraic setting for primitive elements and group quantum couples (generalizations of the group quantum double). Here, the set of primitive elements of a Hopf algebra forms a Lie algebra, and the tensor algebra on any algebra is a bi-algebra. If the tensor algebra is a Hopf algebra, then the underlying $J{\acute{o}}nsson$-Tarski monoid of the generating algebra is cancellative. The problem of determining when the $J{\acute{o}}nsson$-Tarski monoid forms a group is open.

Formation of Quantum Dot Fluorescent Monolayer Film using Peptide Bond

  • Inami, Watau;Nanbu, Koichi;Miyakawa, Atsuo;Kawata, Yoshimasa
    • 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.

Quantum group $X_q(2)$

  • Oh, Sei-Qwon;Shin, Yong-Yeon
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.575-581
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    • 1995
  • The simple modules and the simple comodules of the quantum group $X)q(2)$ defined by M. L. Ge, N. H. Jing and Y. S. Wu, are classified.

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REPRESENTATION AND DUALITY OF UNIMODULAR C*-DISCRETE QUANTUM GROUPS

  • Lining, Jiang
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.575-585
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    • 2008
  • Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

INTEGRABLE MODULES OVER QUANTUM GROUPS AT ROOTS OF 1

  • Cho, Young-Hyun;Kwon, Sae-Ran;Lee, In-Sok
    • 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 $z \in (Z^+)^n$.

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WEAK HOPF ALGEBRAS CORRESPONDING TO NON-STANDARD QUANTUM GROUPS

  • Cheng, Cheng;Yang, Shilin
    • 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 $wX_q(A_1)$.