• Honam Mathematical Journal
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• v.41 no.3
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• pp.505-514
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• 2019

In this paper, some results are obtained from studying convolution on the spectrum of full transformation semigroup and some of its subsemigroups using Cayley's table. The shift of ${\alpha}$ determines its eigenvalues and one-dimensional linear convolution is complex in Symmetric group.

• Journal of the Optical Society of Korea
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• v.18 no.3
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• pp.207-216
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• 2014

In this work, we report detailed numerical analysis of the near-elliptic core index-guiding triangular-lattice and square-lattice photonic crystal fiber (PCFs); where we numerically characterize the birefringence, single mode, cut-off behavior and group velocity dispersion and effective area properties. By varying geometry and examining the modal field profile we find that for the same relative values of $d/{\Lambda}$, triangular-lattice PCFs show higher birefringence whereas the square-lattice PCFs show a wider range of single-mode operation. Square-lattice PCF was found to be endlessly single-mode for higher air-filling fraction ($d/{\Lambda}$). Dispersion comparison between the two structures reveal that we need smaller lengths of triangular-lattice PCF for dispersion compensation whereas PCFs with square-lattice with nearer relative dispersion slope (RDS) can better compensate the broadband dispersion. Square-lattice PCFs show zero dispersion wavelength (ZDW) red-shifted, making it preferable for mid-IR supercontinuum generation (SCG) with highly non-linear chalcogenide material. Square-lattice PCFs show higher dispersion slope that leads to compression of the broadband, thus accumulating more power in the pulse. On the other hand, triangular-lattice PCF with flat dispersion profile can generate broader SCG. Square-lattice PCF with low Group Velocity Dispersion (GVD) at the anomalous dispersion corresponds to higher dispersion length ($L_D$) and higher degree of solitonic interaction. The effective area of square-lattice PCF is always greater than its triangular-lattice counterpart making it better suited for high power applications. We have also performed a comparison of the dispersion properties of between the symmetric-core and asymmetric-core triangular-lattice PCF. While we need smaller length of symmetric-core PCF for dispersion compensation, broadband dispersion compensation can be performed with asymmetric-core PCF. Mid-Infrared (IR) SCG can be better performed with asymmetric core PCF with compressed and high power pulse, while wider range of SCG can be performed with symmetric core PCF. Thus, this study will be extremely useful for designing/realizing fiber towards a custom application around these characteristics.

• 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.

• 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 $z \in (Z^+)^n$.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.345-353
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• 2002

Three noded plate and shell finite element and 3D beam element in conjunction with Lanczos method are used for studying the effect of boat tail angle on the free vibration characteristics of a typical payload fairing for three different cylinder diameters with height to diameter ratio 1.5. Configurations without boat tail structural member are also studied. One half of the one side fairing structure is considered for the analysis and symmetric boundary conditions are used.

• Journal of the Korean Society of Radiology
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• v.85 no.2
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• pp.381-393
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• 2024

Purpose Metabolic abnormalities in hepatic encephalopathy (HE) cause brain edema or demyelinating disease, resulting in symmetric regional cerebral edema (SRCE) on MRI. This study aimed to investigate the usefulness of the clustering analysis of SRCE in predicting the development of brain failure. Materials and Methods MR findings and clinical data of 98 consecutive patients with HE were retrospectively analyzed. The correlation between the 12 regions of SRCE was calculated using the phi (φ) coefficient, and the pattern was classified using hierarchical clustering using the φ² distance measure and Ward's method. The classified patterns of SRCE were correlated with clinical parameters such as the model for end-stage liver disease (MELD) score and HE grade. Results Significant associations were found between 22 pairs of regions of interest, including the red nucleus and corpus callosum (φ = 0.81, p < 0.001), crus cerebri and red nucleus (φ = 0.72, p < 0.001), and red nucleus and dentate nucleus (φ = 0.66, p < 0.001). After hierarchical clustering, 24 cases were classified into Group I, 35 into Group II, and 39 into Group III. Group III had a higher MELD score (p = 0.04) and HE grade (p = 0.002) than Group I. Conclusion Our study demonstrates that the SRCE patterns can be useful in predicting hepatic preservation and the occurrence of cerebral failure in HE.

• The korean journal of orthodontics
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• v.44 no.2
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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.

• Kyungpook Mathematical Journal
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• v.62 no.1
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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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.25-40
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• 2018

We focus on the structure of the set of noncentral idempotents whose role is similar to one of central idempotents. We introduce the concept of quasi-Abelian rings which unit-regular rings satisfy. We first observe that the class of quasi-Abelian rings is seated between Abelian and direct finiteness. It is proved that a regular ring is directly finite if and only if it is quasi-Abelian. It is also shown that quasi-Abelian property is not left-right symmetric, but left-right symmetric when a given ring has an involution. Quasi-Abelian property is shown to do not pass to polynomial rings, comparing with Abelian property passing to polynomial rings.