• Journal of the Korean Mathematical Society
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• v.45 no.4
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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.

• The korean journal of orthodontics
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• v.53 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.489-501
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• 2015

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of right unit-duo. This newly introduced property is first observed to be not left-right symmetric, and we examine several conditions to ensure the symmetry. Right unit-duo rings are next proved to be Abelian, by help of which the class of noncommutative right unit-duo rings of minimal order is completely determined up to isomorphism. We also investigate some properties of right unit-duo rings which are concerned with annihilating conditions.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1015-1021
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• 2011

A point of a Riemann surface X is said to be its fixed point if it is a fixed point of one of its nontrivial holomorphic automorphisms. We start this note by proving that the set Fix(X) of fixed points of Riemann surface X of genus g${\geq}$2 has at most 82(g-1) elements and this bound is attained just for X having a Hurwitz group of automorphisms, i.e., a group of order 84(g-1). The set of such points is invariant under the group of holomorphic automorphisms of X and we study the corresponding symmetric representation. We show that its algebraic type is an essential invariant of the topological type of the holomorphic action and we study its kernel, to find in particular some sufficient condition for its faithfulness.

• Macromolecular Research
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• v.14 no.3
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• pp.306-311
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• 2006

New unsymmetrical ($\alpha$-Diimine)nickel(II) catalysts having different pendent groups at the ortho positions on aromatic rings were synthesized and subjected to propylene polymerizations with MAO (methylaluminoxane). Structural analyses of the resulting polypropylenes by $^1H\;and\;^{13}C\;NMR$ showed that the ortho substituents on aromatic rings of ($\alpha$-diimine)nickel(II) catalyst affected significantly the polypropylene microstructure. While $C_s$ symmetric catalyst afforded a syndiotactic polypropylene (rr triad content=66%) due to the syndiospecific chain end control, $C_1$ symmetric catalysts produced much less stereoregular polypropylenes (rr triads content <50%), presumably because of collision of the isospecific site control with the syndiospecific chain end control.

• Journal of KSNVE
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• v.9 no.2
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• pp.258-264
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• 1999

The purpose of this paper is to investigate the damping behavior of a flexible joint. The slip at a structrual joint is selected at the tips of two identical cantilever beams adjoining each other. Both the direction of normal force and its magnitude varies due to the global deformation of the structure from mode to mode in the friction model. The friction dependent on vibration displacements resultsin the same functional behavior of the hysteretic material damping. Linearized energy loss factors are obtained as functions of both linear and torsional spring stiffness for their groups of symmetric and anti-symmetric modes, respectively. Experimental measurements as made for comparisons with analytical estimations by controlling the magnitude of fastening torque in the fastener, Hi-Lite. Trends on damping levelsmeasured in a very common vibration test method make an excellent agreement on the estimated damping levels.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.45-52
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• 2006

Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $L_{[,]}$ with respect to its commutator. It is an interesting problem whether the equality $Aut{non}(L)=Aut_{semi-Lie}(L)$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ and $Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ where every automorphism of the automorphism groups is the composition of elementary maps [3], [4], [7], [8], [9], [10], [11]. The results of the paper show that the F-algebra automorphism groups of a polynomial ring and its Laurent extension make easy to find the automorphism groups of the algebras in the paper.

• The korean journal of orthodontics
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• v.43 no.5
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• pp.209-217
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• 2013

Objective: This study investigated whether temporomandibular joint (TMJ) condyle-fossa relationships are bilaterally symmetric in class III malocclusion patients with and without asymmetry and compared to those with normal occlusion. The hypothesis was a difference in condyle-fossa relationships exists in asymmetric patients. Methods: Group 1 comprised 40 Korean normal occlusion subjects. Groups 2 and 3 comprised patients diagnosed with skeletal class III malocclusion, who were grouped according to the presence of mandibular asymmetry: Group 2 included symmetric mandibles, while group 3 included asymmetric mandibles. Pretreatment three-dimensional cone-beam computed tomography (3D CBCT) images were obtained. Right- and left-sided TMJ spaces in groups 1 and 2 or deviated and non-deviated sides in group 3 were evaluated, and the axial condylar angle was compared. Results: The TMJ spaces demonstrated no significant bilateral differences in any group. Only group 3 had slightly narrower superior spaces (p < 0.001). The axial condylar angles between group 1 and 2 were not significant. However, group 3 showed a statistically significant bilateral difference (p < 0.001); toward the deviated side, the axial condylar angle was steeper. Conclusions: Even in the asymmetric group, the TMJ spaces were similar between deviated and non-deviated sides, indicating a bilateral condyle-fossa relationship in patients with asymmetry that may be as symmetrical as that in patients with symmetry. However, the axial condylar angle had bilateral differences only in asymmetric groups. The mean TMJ space value and the bilateral difference may be used for evaluating condyle-fossa relationships with CBCT.

• Physical Therapy Korea
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• v.27 no.3
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• pp.191-198
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• 2020

Background: Stroke patients experience multiple dysfunctions that include motor and sensory impairments. Therefore, new intervention methods require a gradational approach depending on functional levels of a stroke patient's activity and should include cognition treatment to allow for a patient's active participation in rehabilitation. Objects: This study investigates the effect of integrated revision of electrical sensory stimulation, which stimulates somatosensory and action observation training, which is synchronized cognition intervention method on stroke patients' functions. Methods: Twenty-one stroke patients were randomized into two groups. The two groups underwent twenty minutes of intervention five times a week for three weeks. This study used an electromyogram to evaluate symmetric muscle activation of lower extremities and muscle onset time when performing sit to stand before and after intervention. A weight-bearing ratio was used to evaluate the weight-bearing of the affected side in a sit to standing. To evaluate sit to stand performance ability, this study performed five timed sit to stand tests. Results: The two groups both showed statistically significant improvement in muscle onset time of lower extremity, static balance ability in a standing position, and sit to stand performance after the intervention (p < 0.05). In addition, the action observation and synchronized electrical sensory stimulation group showed significant improvement in symmetric muscle activation of lower extremities and weight-bearing ratio of the affected side (p < 0.05). Conclusion: action observation and synchronized electrical sensory stimulation (AOT with ESS) can have positive effects on a stroke patient's sit to stand performance, and the intervention method that provides integrated AOT with ESS can be used as new nervous system intervention program.