• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.389-402
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• 2015

A symmetric union is a diagram of a knot, obtained from diagrams of a knot in the 3-space and its mirror image, which are symmetric with respect to an axis in the 2-plane, by connecting them with 2-tangles with twists along the axis and 2-tangles with no twists. This paper presents an invariant of knots with symmetric union presentations, which is called the minimal twisting number, and the minimal twisting number of $10_{42}$ is shown to be two. This paper also presents a sufficient condition for non-amphicheirality of a knot with a certain symmetric union presentation.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1229-1240
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• 2014

In this paper we provide three results involving large Schr$\ddot{o}$der paths. First, we enumerate the number of large Schr$\ddot{o}$der paths by type. Second, we prove that these numbers are the coefficients of a certain symmetric function defined on the staircase skew shape when expanded in elementary symmetric functions. Finally we define a symmetric function on a Fuss path associated with its low valleys and prove that when expanded in elementary symmetric functions the indices are running over the types of all Schr$\ddot{o}$der paths. These results extend their counterparts of Kreweras and Armstrong-Eu on Dyck paths respectively.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1089-1103
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• 2010

In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1309-1325
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• 2016

This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.11-19
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• 2010

In this paper, several common fixed degree theorems of a sequence of fuzzy mappings defined on symmetric spaces are established.

• Journal of computational fluids engineering
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• v.13 no.4
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• pp.39-44
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• 2008

Numerical simulations of laminar flow over a sphere are conducted to investigate the effect of the Reynolds number on the characteristics of vortex shedding. The Reynolds numbers considered are between 300 and 475, covering unsteady planar-symmetric and asymmetric flows. Results show that the unsteady planar-symmetric flow can be categorized into two different regimes: single-frequency regime and multiple-frequency regime. The former has a single frequency component due to periodic shedding of the vortices with the same strength in every shedding cycle, while the latter has multiple frequency components due to cycle-to-cycle variation in the strength of shed vortices with the shedding angle fixed. The multiple-frequency planar-symmetric flow, which is newly found in the present study, occurs at Re=330${\sim}$360 between the single-frequency planar-symmetric flow and the asymmetric flow. On the other hand, the asymmetric flow occurs at Re${\geq}$365, where the vortices shed from the sphere show variation both in strength and shedding angle unlike the planar-symmetric flow. Also, it is shown that the breaking of planar symmetry is closely related to the imbalance of vortical strength between a pair of streamwise vortices.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.10
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• pp.84-91
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• 2002

The shaft with the circular cross section have symmetric structural combination parts to keep the rotating balance. Hence the crack usually emanate from symmetric combination parts due to the stress concentration of these parts. In this study to estimate the fatigue behavior of symmetric cracks, the fatigue test was performed by using rotary bending tester and the specimen with symmetric defects in circular cross section. From the facts the characteristics of crack initiation and propagation on the symmetric surface cracks in circular cross section was examined. Also we observed the internal crack using oxidation coloring and investigated the fatigue behavior using the relationship between surface crack and internal crack. As a result of fatigue lift of symmetric cracks was reduced to 35% compared to single crack’s. We examined the characteristics of fatigue behavior in element with symmetric cracks using internal crack propagation rate and maximum stress intensity factor range obtained from approximation method.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.211-216
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• 2001

The components with the circular cross section have the symmetric combination parts for rotating balance and the crack emanates from the symmetric combination parts. The symmetric cracks from symmetric combination parts make a decrease in the component fatigue life more than single crack. In this study, to estimate the behavior of symmetric cracks, the fatigue test was performed using rotary bending tester on the specimen with a symmetric defects in circular cross section. The material used in this study is Ni-Cr-Mo steel alloy. Under the same stress, the result from the rotary bending fatigue test turned out that the symmetric cracks made a decrease in the fatigue life by 35% more than single crack and the relation between log a and cycle ratio $N/N_f$ obtained linearly.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.1
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• pp.69-77
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• 1996

To design high-effective profile in screw rotor profile using in screw compressor, we design the symmetric type changing the number of lobes and the non-symmetric type changing the neighbourhood of the top point of lobe. Then, we calculated the performance value of profile according to the scale of these non-symmetric's wrap angle. We had the results as follows. 1. About the non-symmetric case, the larger a wrap angle is the shorter seal line is and the smaller blow hole is, thus we know what the large wrap angle profile is better than the small one. 2. We know what the non-symmetric profile is better than the symmetric profile in the result of the compare of seal line's length, blow hole's area, volume curve. 3. About the non-symmetric case, the deformation of the neighbourhood of lobe's top point of the rotor profile has a large effect upon the increase of performance because the length of seal line became short and the area of blow hole is small.

• Korean Journal of Bronchoesophagology
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• v.4 no.1
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• pp.79-84
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• 1998

Benign symmetric lipomatosis was initially described in 1846 by Sir Benjamin Brodie. In 1888, Otto Madelung presented 33 cases of benign symmetric lipomatosis and described the classic“horse collar”cervical distribution of the lipomatous tissue. Launois and Bensaude described benign symmetric lipomatosis as a distint syndrome characterized by a diffuse, symmetric, fatty accumulation in the cervical region. This disease is rare condition affecting mostly middle aged alcoholic men and associated with many systemic diseases such as diabetes mellitus, hyperuricemia, renal tubular acidosis, liver enzyme abnormality etc. The condition does not spontaneously involute and surgical excision is the only proven method of treatment, and recurrence is frequent. We experienced six patients of benign symmetric lipomatosis who underwent surgical excision via collar incision which afford wide exposure of the entire cervical area. We report them with the review of literature.