• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.959-972
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• 2013

Rege-Chhawchharia, and Nielsen introduced the concept of right McCoy ring, based on the McCoy's theorem in 1942 for the annihilators in polynomial rings over commutative rings. In the present note we concentrate on a natural generalization of a right McCoy ring that is called a right nilpotent coefficient McCoy ring (simply, a right NC-McCoy ring). The structure and several kinds of extensions of right NC-McCoy rings are investigated, and the structure of minimal right NC-McCoy rings is also examined.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1629-1643
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• 2016

Let R be a ring with identity, X be the set of all nonzero, nonunits of R and G be the group of all units of R. A ring R is called unit-duo ring if $[x]_{\ell}=[x]_r$ for all $x{\in}X$ where $[x]_{\ell}=\{ux{\mid}u{\in}G\}$ (resp. $[x]_r=\{xu{\mid}u{\in}G\}$) which are equivalence classes on X. It is shown that for a semisimple unit-duo ring R (for example, a strongly regular ring), there exist a finite number of equivalence classes on X if and only if R is artinian. By considering the zero divisor graph (denoted ${\tilde{\Gamma}}(R)$) determined by equivalence classes of zero divisors of a unit-duo ring R, it is shown that for a unit-duo ring R such that ${\tilde{\Gamma}}(R)$ is a finite graph, R is local if and only if diam(${\tilde{\Gamma}}(R)$) = 2.

• KSTLE International Journal
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• v.2 no.1
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• pp.40-45
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• 2001

The paper deals with a non-linear finite element analysis of the thermomechanical distortions of an elastomeric O-ring seal including a temperature gradient. Axial compression of O-ring seals, as well as the influence of the temperature gradients and various O-ring seal models, are investigated based on the axisymmetric analysis. The highest temperature occurs near the interface of the O-ring between the dovetail groove bottom and the O-ring seal. The calculated FEM results indicate that the composite O-ring with the diametral ratio, 0.8 shows very stable and recommendable compared with other seal models far elevated temperatures and corrosive environments.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.715-726
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• 2010

We continue the study of fully idempotent rings initiated by Courter. It is shown that a (semi)prime ring, but not fully idempotent, can be always constructed from any (semi)prime ring. It is shown that the full idempotence is both Morita invariant and a hereditary radical property, obtaining $hs(Mat_n(R))\;=\;Mat_n(hs(R))$ for any ring R where hs(-) means the sum of all fully idempotent ideals. A non-semiprimitive fully idempotent ring with identity is constructed from the Smoktunowicz's simple nil ring. It is proved that the full idempotence is preserved by the classical quotient rings. More properties of fully idempotent rings are examined and necessary examples are found or constructed in the process.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.117-124
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• 2020

In 2013, Diesl defined a nil clean ring as a ring of which all elements can be expressed as the sum of an idempotent and a nilpotent. Furthermore, in 2017, Y. Zhou, S. Sahinkaya, G. Tang studied nil clean group rings, finding both necessary condition and sufficient condition for a group ring to be a nil clean ring. We have proposed a necessary and sufficient condition for a group ring to be a uniquely nil clean ring. Additionally, we provided theorems for general nil clean group rings, and some examples of trivial-center groups of which group ring is not nil clean over any strongly nil clean rings.

• Journal of Aerospace System Engineering
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• v.10 no.3
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• pp.52-58
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• 2016

The elastomeric O-ring is the most-commonly-used seal due to its excellent sealing capacity, and its availability in various costs and sizes; furthermore, its importance has lasted over a long duration. However, a dearth of research exists in Korea regarding the elastomeric O-ring and the corresponding techniques. The constituent parts of elastomeric rubber are important; to determine their properties, the uni-axial tension and equi-biaxial tension need to be tested. Also, the non-linear analysis method reduces the design cost. An O-ring failure causes leaks and vibration. In this paper, foreign objects are used to affect an O-ring and its performance so that all angles of the O-ring design can be considered. This paper presents a solution for the O-ring-failure problem using a finite-element analysis.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.421-428
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• 2013

We observe the basic structure of the products of coefficients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result for semi-Armendariz rings. We introduce the concept of ${\alpha}$-skew n-semi-Armendariz ring, where ${\alpha}$ is a ring endomorphism. We prove that a ring R is ${\alpha}$-rigid if and only if the n by n upper triangular matrix ring over R is $\bar{\alpha}$-skew n-semi-Armendariz. This result are applicable to several known results.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.163-165
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• 1994

Modules which satisfy the converse of Schur's lemma have been studied by many authors. In [6], R. Ware proved that a projective module P over a semiprime ring R is irreducible if and only if En $d_{R}$(P) is a division ring. Also, Y. Hirano and J.K. Park proved that a torsionless module M over a semiprime ring R is irreducible if and only if En $d_{R}$(M) is a division ring. In case R is a commutative ring, we obtain the following: An R-module M is irreducible if and only if En $d_{R}$(M) is a division ring and M is a multiplication R-module. Throughout this paper, R is commutative ring with identity and all modules are unital left R-modules. Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for each submodule N of M, there exists and ideal I of R such that N=IM. Cyclic R-modules are multiplication modules. In particular, irreducible R-modules are multiplication modules.dules.

• Membrane and Water Treatment
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• v.3 no.1
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• pp.51-62
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• 2012

The permeate flux declination along an ultrafilter membrane is due mainly to the concentration-polarization resistance increment and the decline in transmembrane pressure. It was found in previous works that the concentration polarization resistance could be reduced in a ring-rod tubular membrane ultrafilter using the turbulent behavior. In the present study, the performance was further improved by properly and gradually decreasing the baffled-ring distance along the cross-flow channel coupled with properly adjusting the number of baffled rings. This theoretical analysis is based on the mass and momentum balances as well as the application of the resistance-in-series model. The correlation predictions are confirmed with the experimental results for dextran T500 aqueous solution ultrafiltration.

• Structural Engineering and Mechanics
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• v.60 no.6
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• pp.1079-1092
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• 2016

In this paper, an electromechanical integrated harmonic piezodrive system is proposed. The operating principle of the drive system is introduced. The equation of the relationship between the displacements of the flexible ring and the rotating angle of the rotor is deduced. Using the equation, the displacements of the flexible ring for the drive system and their changes along with the system parameters are investigated. The results show that the displacements of the flexible ring changes periodically along with the rotation of the vibrator; there are abrupt changes in the displacements of the flexible ring at some points where there are abrupt changes in the number of the mesh teeth pair; the length of the flexible ring, the excitation voltage, and the speed ratio have obvious effects on the displacements of the flexible ring. The results are useful for the design of the drive system. ;