• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.9-16
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• 2006

The purpose of this paper is to define the symmetric $bi-(\sigma,\;\tau)$ derivations on prime and semi prime Gamma rings and to prove some results concerning symmetric $bi-(\sigma,\;\tau)$derivations on prime and semi prime Gamma rings.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1249-1260
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• 2023

In the present paper, we study a semi-symmetric recurrent metric connection and verify its various geometric properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.384-385
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• 1995

We study fuzzy symmetric subgroups and obtain some properties of fuzzy symmetric subgroups of symmetric groups.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.4
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• pp.36-42
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• 2004

The shaft with the circular cross section has symmetric structural combination parts to keep the rotating balance. Hence the crack usually initiates 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 a rotary bending tester and the specimen with symmetric defects in circular cross section. The characteristics of crack initiation and propagation on the symmetric surface cracks in circular cross section were examined. We also observed the internal crack using the oxidation coloring method and investigated the fatigue behavior using the relationship between the surface crack and the internal crack. As a result, the fatigue life of symmetric cracks was reduced by 35% compared to that of a single crack. We examined the characteristics of fatigue behavior of elements with symmetric cracks using internal crack propagation rate and maximum stress intensity factor range that were obtained from an approximation method.

• Journal of Welding and Joining
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• v.28 no.2
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• pp.60-65
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• 2010

Although two dimensional axi-symmetric modeling is useful for calculating the residual stresses of a cylindrical weldment such as a core barrel, this conventional axi-symmetric modeling can not express the behavior of shrinkage well in the locally heated weld zone. New technique of two dimensional axi-symmetric modeling using a virtual fixture is suggested to simulate the behavior of dimensional changes in the weld zone during the heating period of the welding. The virtual fixture in the model has a role to restrain the expansion of the high temperature heated region, which simulates equivalent intrinsic restraint effect of the weldment. In the restraint condition of the virtual fixture above the critical yield strength, the calculated shrinkages by using the suggested axi-symmetric model agreed well with those measured in a welded mock-up. The calculated residual stresses by using the suggested axi-symmetric model also agreed well with those calculated by using conventional axi-symmetric model which has beenused for calculating residual stresses in the weldment.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.209-227
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• 2021

In this paper, we deal with the question that what kind of properties does a ring gain when it satisfies symmetricity or reversibility by the way of nilpotent elements? By the motivation of this question, we approach to symmetric and reversible property of rings via nilpotents. For symmetricity, we call a ring R middle right-(resp. left-)nil symmetric (mr-nil (resp. ml-nil) symmetric, for short) if abc = 0 implies acb = 0 (resp. bac = 0) for a, c ∈ R and b ∈ nil(R) where nil(R) is the set of all nilpotent elements of R. It is proved that mr-nil symmetric rings are abelian and so directly finite. We show that the class of mr-nil symmetric rings strictly lies between the classes of symmetric rings and weak right nil-symmetric rings. For reversibility, we introduce left (resp. right) N-reversible ideal I of a ring R if for any a ∈ nil(R), b ∈ R, being ab ∈ I implies ba ∈ I (resp. b ∈ nil(R), a ∈ R, being ab ∈ I implies ba ∈ I). A ring R is called left (resp. right) N-reversible if the zero ideal is left (resp. right) N-reversible. Left N-reversibility is a generalization of mr-nil symmetricity. We exactly determine the place of the class of left N-reversible rings which is placed between the classes of reversible rings and CNZ rings. We also obtain that every left N-reversible ring is nil-Armendariz. It is observed that the polynomial ring over a left N-reversible Armendariz ring is also left N-reversible.

• East Asian mathematical journal
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• v.34 no.5
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• pp.615-621
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• 2018

Let R be a ring with the unity 1, and let e be an idempotent of R. In this paper, we discuss some symmetric property for the set $\{(a_1,a_2,{\cdots},a_n){\in}R^n:a_1a_2{\cdots}a_n=e\}$. We here investigate some properties of those rings with such a symmetric property for an arbitrary idempotent e; some of our results turn out to generalize some known results observed already when n = 2 and e = 0, 1 by several authors. We also focus especially on the case when n = 3 and e = 1. As consequences of our observation, we also give some equivalent conditions to the commutativity for some classes of rings, in terms of the symmetric property.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.10a
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• pp.277-280
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• 2003

It was investigated that the "ㄱ" type angle product could be bended with a curvature during extrusion by extru-bending process. The bending process for the "ㄱ" type angle product can be developed by the hot metal extru-bending machine with the two punches moving in the different velocity. Because of non-symmetry of product, it is important to design the ruled surface contour of dies cavity for the welding and bending with two billets. So it is designed that the multi-hole container has two non-symmetric holes and non-symmetric contour of dies entrance. The results of the experiment show that "ㄱ" type angle product can be bended by the extrusion process and that the curvature of the product can be controlled by the velocity of punch and that the defects such as the distortion of section and the thickness change of the product and the folding and wrinkling of the product did not happen after the bending processing by the extrusion bending machine.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.113-124
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• 2010

We consider matrix polynomial which has the form $P_1(X)=A_oX^m+A_1X^{m-1}+...+A_m=0$ where X and $A_i$ are $n{\times}n$ matrices with real elements. In this paper, we propose an iterative method for the symmetric and generalized centro-symmetric solution to the Newton step for solving the equation $P_1(X)$. Then we show that a symmetric and generalized centro-symmetric solvent of the matrix polynomial can be obtained by our Newton's method. Finally, we give some numerical experiments that confirm the theoretical results.

• 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.