• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.351-360
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• 2022

We prove that a punctured-torus group of hyperbolic 4-space which keeps an embedded hyperbolic 2-plane invariant has a strictly parabolic commutator. More generally, this rigidity persists for a punctured-surface group.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1705-1714
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• 2023

We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the projective space at torus invariant points in codimension one by anti-flips.

• Korean Journal of Veterinary Research
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• v.36 no.2
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• pp.255-264
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• 1996

This studies were carried out to identify the characteristics of the tongue of Korean native goat(Capra hircus) by macroscopy, microscopy and scanning microscopy. Korean native goat had torus linguae, median lingual sulcus, lingual fossa and ventral median fissure but did not have glossoepiglottic fold and terminal sulcus in the tongue. The whole length of tongue was $11.51{\pm}0.76cm$. The length of tongue apex, tongue body, tongue root and the torus linguae were $2.62{\pm}0.28$, $7.39{\pm}0.27$, $1.56{\pm}0.26$ and $6.37{\pm}0.29cm$, respectively. The width of tongue apex, torus linguae and tongue root were $3.41{\pm}0.24$, $3.74{\pm}0.29$ and $3.68{\pm}0.11$, respectively. The thickness of tongue apex was $1.60{\pm}0.10$, and the height of torus linguae was $1.52{\pm}0.15cm$. Filiform papillae were present at the tongue apex and the tongue body rostral to torus linguae. Fungiform papillae were scattered from tongue apex to rostral portion of torus linguae, being in abundance at the tongue apex. Vallate papillae were showed at the lateral portion of torus linguae, while lentiform papillae were present at its central portion. Conical papillae were located between vallate and lentiform papillae. The numbers of filiform, fungiform, conical, vallate and lentiform papillae were $46,980{\pm}1070.98$, $446.8{\pm}36.97$, $818.4{\pm}43.99$, $34.8{\pm}2.77$, and $255.6{\pm}39.30$, respectively. The average numbers of taste bud were $8.3{\pm}2.04$ in a fungiform papilla and $247.3{\pm}37.44$ in a vallate papilla. The filiform papilla had secondary and tertiary papillae. The height of filiform papilla was about $150{\mu}m$ and the diameter was $100{\mu}m$. The diameters of fungiform papillae were 350 to $550{\mu}m$. The long and short diameters of maximum-sized lentiform papilla were 4000 and $3000{\mu}m$, respectively, while those of minimum-sized papilla were 700 and $600{\mu}m$, respectively. The height of conical papillae was 450 to $600{\mu}m$ and diameter was 250 to $450{\mu}m$. The vallate papilla was round or oval in shape and its diameter was 500 to $850{\mu}m$. It had well-developed papillary groove around itself. The modified conical papillae were not observed in the tongue of Korean native goat.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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• pp.37.2-38
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• 2015

According to the unified model of AGNs, type 1 and 2 AGNs are intrinsically the same objects but seem different due to an obscuring matter which can block lights from the central engine of the AGN depending on the viewing angle. The obscuring object is thought to be shaped in a toroidal form and thus the geometry of tori of AGNs is an important factor to determine the fraction of type 1 (or type 2) AGNs. Oh et al. (2015) provides a new catalog of type 1 AGNs from SDSS DR7 in the nearby universe (z < 0.2) and it contains nearly 50% more type 1 AGNs than previously known. Using this new catalog, we test the fraction of type 1 AGNs along the black hole mass (MBH) and the bolometric luminosity of AGNs (Lbol), which are regarded as key parameters of the AGNs. First of all, because the methods to derive the black hole mass and the bolometric luminosity bear uncertainties, we test how the different methods lead to different values of type 1 fraction. We found that the fraction of type 1 AGNs varies with both MBH and Lbol. The extensively-studied, "receding torus model" can only explain the trend along Lbol and hence fails to explain the trend. To understand the new trend, we test the geometry of the torus based on the "clumpy torus model". We present our results on the basic properties of the torus such as a column density or opening angle and compare with those from previous studies based on other wavelengths (e.g. Infrared or X-ray).

• The Bulletin of The Korean Astronomical Society
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• v.41 no.2
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• pp.33.2-34
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• 2016

The unification model of active galactic nuclei invokes the presence of a thick molecular torus that hides the broad emission line region from a line of sight toward observers with low latitude. It is expected that the illuminated side of the molecular torus may be photodissociated by strong far UV radiation from the central AGN, forming an H I region with a high neutral column density. We propose that the Rayleigh scattering optical depth of this HI region can be significant for most broad $Ly{\alpha}$ line photons with the Doppler factor not exceeding 104 km s-1. Rayleigh scattered $Ly{\alpha}$ photons can be characterized by strong linear polarization depending on their scattering optical depth. We performed Monte Carlo simulations of polarized radiative transfer of $Ly{\alpha}$ adopting simple scattering geometries relevant to the unification model of AGN. We find that for a low torus the Rayleigh scattered $Ly{\alpha}$ is polarized in the direction parallel to the symmetry axis with the polarization degree dependent on wavelength. In the case of a high torus, the core part of $Ly{\alpha}$ is polarized in the direction perpendicular to the symmetry axis whereas the wing part is parallelly polarized. We conclude that careful spectropolarimetry around $Ly{\alpha}$ can be useful in testing the AGN unification model.

• Transactions of the Korean Society of Automotive Engineers
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• v.24 no.6
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• pp.702-708
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• 2016

The torque converter is deformed according to the rotating speed and control pressure when engine power is transferred to the transmission. This deformation, which is called ballooning phenomenon, occurs mainly at the outer side by the centrifugal force of the automatic transmission fluid (ATF) and the control pressure from the valve body. Although the torque converter is slightly deformed when rotating, the ballooning phenomenon affects fluid performance, efficiency and durability. Thus, expansion characteristics analysis is important in determining torus size, control pressure and structure. In this paper, an analysis equation and FEM model was developed to investigate the expansion characteristics. Using this model, structural analysis was performed to investigate the relationships between deformation and the torus diameter. The results were confirmed by comparing with the test results.

• Journal of Korea Multimedia Society
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• v.19 no.8
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• pp.1487-1497
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• 2016

Explosively growing service of digital multimedia data increases the need for highly scalable low-cost storage. This paper proposes the new storage architecture based on torus network which does not need network switch and erasure coding for efficient storage usage for high scalability and efficient disk utilization. The proposed model has to compensate for the disadvantage of long network latency and network processing overhead of torus network. The proposed storage model was compared to two most popular distributed file system, GlusterFS and Ceph distributed file systems through a prototype implementation. The performance of prototype system shows outstanding results than erasure coding policy of two file systems and mostly even better results than replication policy of them.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.70.3-70.3
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• 2016

Active galactic nuclei (AGNs) typically show a non-thermal continuum locally represented by a power-law and many prominent emission lines in the UV and optical regions. AGNs are classified by two types, where Type I AGNs exhibit both broad and narrow lines and only narrow lines are observed in Type 2 AGNs. The unification models of AGNs invoke the existence of a molecular torus just outside of the broad line region. In the presence of a high column HI region associated with the molecular torus, we propose that significant fraction of broad line photons near Lyman series can be scattered by atomic hydrogen in the torus. In particular, $Ly{\alpha}$ being the strongest emission line, strong linear polarization may develop around $Ly{\alpha}$ through Rayleigh scattering. We adopt a Monte Carlo technique to investigate the polarized transfer of $Ly{\alpha}$ in a thick HI region with the shape of a torus. We consider the range of HI column density N_HI = 1020-23 with fixed geometric parameters of the torus such as the inner and outer radii and the height. We present the polarized spectra and angular distribution of Rayleigh scattered radiation around $Ly{\alpha}$. We find that the $Ly{\alpha}$ core part is polarized in the direction perpendicular to the symmetry axis whereas in the far wing part it is polarized in the parallel direction. It is concluded that the unification of AGNs implies that $Ly{\alpha}$ can be uniquely polarized through Rayleigh scattering.

• Archives of Plastic Surgery
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• v.37 no.4
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• pp.473-476
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• 2010

Purpose: Torus palatinus is a bony prominence at the middle of the hard palate. The size varies from barely discernible to very large, from flat to lobular. This oral exostosis is not a disease or a sign of disease, but if large, may be a problem. So, we present the clinical and histopathologic features and applied therapy and provide a comprehensive review of the rare case of the symptomatic exostoses. Methods: A 37-year-old woman had slowly growing exophytic nodular mass of the bone that arises the midline suture of the hard palate. The patient was concerned about discomfort associated with movement of her tongue and about frequent irritation of the palatal mucosa during mastification of the hard food. The patient had a large, unilobulated torus palatinus. It extended from the area adjacent to the canine to a point beyond the junction with the soft palate. The mass was oblong in shape, measuring about 3 cm long, 2 cm wide, and 0.8 cm in height. Results: Before surgical intervention a CT was obtained for the sake of estimating the thickness of the bone between the exostoses and the maxillary antrum and floor of the nose. The surgical procedure was performed with the patient under general anesthesia. Removal of the exostosis was performed after midline mucoperiosteal incision with osteotome and diamond burr. Histologic finding revealed decalcified dense bony tissue, the presence of lacunae, and normal osteocytes. Conclusion: Surgical removal is recommended when one or more of the following condition exist: interference with the construction of prosthesis, interference with oral function, irritation or pathology of the overlying tissue, inability of the patient to maintain proper oral hygiene, and fear of malignancy or other psychologic trauma. We report a rare case of the torus arising in hard palate with symptoms.