• 대한수학회지
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• 제45권4호
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• pp.1075-1087
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• 2008

We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system ($\mathcal{A},{\tau},{\omega}$), where $\mathcal{A}$ is a quasi-local algebra, $\tau$ is a strongly continuous one parameter group of *-automorphisms of $\mathcal{A}$ and $\omega$ is a Gibbs state on $\mathcal{A}$. The semigroups can be considered as the extension of semi groups on the nontrivial abelian subalgebra. Let $\mathcal{H}$ be a Hilbert space corresponding to the GNS representation con structed from $\omega$. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}$. The semigroup $\{T_t\}{_t_\geq_0}$ acts separately on two subspaces $\mathcal{H}_d$ and $\mathcal{H}_{od}$ of $\mathcal{H}$, where $\mathcal{H}_d$ is the diagonal subspace and $\mathcal{H}_{od}$ is the off-diagonal subspace, $\mathcal{H}=\mathcal{H}_d\;{\bigoplus}\;\mathcal{H}_{od}$. The restriction of the semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}_d$ is Glauber dynamics, and for any ${\eta}{\in}\mathcal{H}_{od}$, $T_t{\eta}$, decays to zero exponentially fast as t approaches to the infinity.

• 대한수학회논문집
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• 제10권1호
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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 $z \in (Z^+)^n$.

• 대한수학회보
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• 제29권1호
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• pp.41-55
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• 1992

The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

• 대한치과교정학회지
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• 제44권2호
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• pp.62-68
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• 2014

Objective: The purpose of this study was to examine the symmetry and parallelism of the skeletal and soft-tissue poria by three-dimensional (3D) computed tomographic (CT) imaging. Methods: The locations of the bilateral skeletal and soft-tissue poria in 29 patients with facial asymmetry (asymmetric group) and 29 patients without facial asymmetry (symmetric group) were measured in 3D reconstructed models of CT images by using a 3D coordinate system. The mean intergroup differences in the anteroposterior and vertical angular deviations of the poria and their anteroposterior and vertical parallelism were statistically analyzed. Results: The symmetric and asymmetric groups showed significant anteroposterior angular differences in both the skeletal and the soft-tissue poria (p = 0.007 and 0.037, respectively; Mann-Whitney U-test). No significant differences in the anteroposterior and vertical parallelism of the poria were noted ($p{\leq}0.05$; Wilcoxon signed-rank test). Conclusions: In general, the skeletal poria are parallel to the soft-tissue poria. However, patients with facial asymmetry tend to have asymmetric poria.

• 대한영상의학회지
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• 제85권2호
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• pp.381-393
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• 2024

목적 간성뇌증(hepatic encephalopathy; 이하 HE)의 대사이상은 뇌부종 또는 탈수초성 질환을 일으켜 자기공명영상에서 대칭적인 지역 뇌부종을 유발한다. 본 연구에서 HE 환자의 뇌 자기공명영상에서 대칭적인 지역 뇌부종 패턴의 군집화 분석을 통해 뇌부전 발생 예측의 유용성을 조사하는 것을 목적으로 한다. 대상과 방법 연속적인 HE 환자 98명을 대상으로 MR 소견과 임상자료를 후향적으로 분석하였다. Symmetric regional cerebral edema (이하 SRCE)의 12개 영역 간의 상관관계는 파이(φ) 계수를 사용하여 계산하였고, φ² 거리 측정과 Ward의 방법을 사용하여 계층적 군집화를 사용하여 패턴을 분류하였다. SRCE의 분류된 패턴은 말기 간 질환 모델(model for endstage liver disease; 이하 MELD) 점수 및 HE 등급과 같은 임상과 상관관계를 조사하였다. 결과 적색 핵과 뇌량(φ = 0.81, p < 0.001), 대뇌 십자 및 적색 핵(φ = 0.72, p < 0.001), 적색핵과 치상핵(φ = 0.66, p < 0.001)을 포함한 22쌍의 관심영역 사이에 유의한 연관성이 발견되었다. 계층적 군집화 후 24건을 I군, 35건을 II군, 39건을 III군으로 분류하였다. 그룹 III은 그룹 I에 비해 MELD 점수(p = 0.04)와 HE 등급(p = 0.002)이 더 높았다. 결론 본 연구는 HE 환자에서 대칭적인 지역 뇌부종의 패턴은 간 보존 및 뇌부전 발생을 예측하는 데 유용할 수 있음을 보여주었다.

• 대한수학회지
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• 제35권3호
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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.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• 대한치과교정학회지
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• 제53권4호
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• pp.219-231
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• 2023

Objective: This study aimed to clarify differences in the positions of cone-beam computed tomography (CBCT) landmarks according to different midsagittal planes (MSPs) in patients with skeletal Class III facial asymmetry. Methods: Pre-treatment CBCT data from 60 patients with skeletal Class III were used. The patients were classified into symmetric (menton deviations of < 2 mm) or asymmetric (menton deviations of > 4 mm) groups. Six MSPs were established based on previous studies, and three-dimensional analyses were performed for the planes in both the groups. The measurement outcomes were compared statistically. Results: A statistically significant interaction (p < 0.01) was observed between MSPs and facial asymmetry. No significant differences were observed among MSPs in the symmetric group. However, significant differences in linear measurements were identified among MSPs in the asymmetric group. Specifically, the upper facial MSP revealed both maxillary and mandibular transverse asymmetries. On the other hand, anterior nasal spine (ANS)-associated MSP could not identify maxillary asymmetry. Furthermore, the menton deviation was approximately 3 mm lower when estimated using the ANS-associated MSP than that using upper facial MSP. Conclusions: The choice of MSP can significantly affect treatment outcomes while diagnosing patients with asymmetry. Therefore, care should be taken when selecting MSP in clinical practice.

• 한국해양공학회지
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• 제22권1호
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• pp.6-12
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• 2008

The dispersion and attenuation of Lamb and Leaky Lamb waves propagating in a 1 mm-thick steel plate were investigated. For acquiring a long(or large) range inspection capability, the fundamental symmetric and anti-symmetric wave modes(S0 and A0) over law frequencies were studied. Based on the dispersion curves, as well as pitch-catch and multi-mode simulations, it was shown that the S0 mode over law frequencies is the proper mode to minimize the dispersion and attenuation. In addition, it was shown that the S0 mode couldbe easily distinguished under multi-mode simulation since it has a larger group velocity than the A0 mode.

• Journal of information and communication convergence engineering
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• 제13권4호
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• pp.228-234
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• 2015

The system performance improvement in dispersion managed (DM) links combined with optical phase conjugator (OPC) for compensating for optical signal distortion due to group velocity dispersion and nonlinear fiber effects has been reported. However, in DM link combined OPC, the equalities of the lengths of single-mode fibers (SMFs), the length of dispersion compensating fibers (DCFs), the dispersion coefficient of DCF, and the residual dispersion per span (RDPS) with respect to an OPC restrict a flexible link configuration. Thus, in this paper, we propose a flexible optical link configuration with inequalities of link parameters, the so-called "pseudo-symmetric configuration." Simulation results show that, in the restricted RDPS range of 450 ps/nm to 800 ps/nm, the improvement in the system performance of the proposed pseudo-symmetrically configured optical links is better than that of the asymmetrically configured optical links. Consequently, we confirmed that the proposed pseudo-symmetric configuration is effective and useful for implementing a reconfigurable long-haul wavelength-division multiplexing (WDM) network.