• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.373-384
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• 2011

In this paper we introduce and give some characterizations of (m, n)-regular le-${\Gamma}$-semigroup in terms of (m, n)-ideal elements and (m, n)-quasi-ideal elements. Also, we give some characterizations of subidempotent (m, n)-ideal elements in terms of $r_{\alpha}$- and $l_{\alpha}$- closed elements.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.1-9
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• 2023

An le-module M over a commutative ring R is a complete lattice ordered additive monoid (M, ⩽, +) having the greatest element e together with a module like action of R. This article characterizes the le-modules _RM such that the pseudo-prime spectrum X_M endowed with the Zariski topology is a Noetherian topological space. If the ring R is Noetherian and the pseudo-prime radical of every submodule elements of _RM coincides with its Zariski radical, then X_M is a Noetherian topological space. Also we prove that if R is Noetherian and for every submodule element n of M there is an ideal I of R such that V (n) = V (Ie), then the topological space X_M is spectral.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1177-1190
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• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α₁, …, α_p and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and Ann_R(α^m) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αⁿ, bⁿ) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.366-371
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• 1995

High performance magnetic materials are characterized by the combination of outstanding magnetic properties and optimized microstructures, e.g., nanocrystalline composites of multilayers and small particle systems. The characteristic parameters of the hysteresis loops of these materials vary over more than a factor of $10^{6}$ with optimum values for the coercive field of several Tesla and permeabilities of $10^{6}$. Within the framework of the computational micromagnetism (nanomagnetism) using the finite element method the upper and lower bounds of the coercive field of different types of grain ensembles and multilayers have been determined. For the case of nanocrystalline composites the role of grain size, exchange and dipolar coupling between grains and the degree of grain alignment will be discusses in detail. It is shown that the largest coercivities are obtained for exchange decoupled grains, whereas remanence enhancing requires exchange coupled grains below 20 nm. For composite permanent magnets based on $Nd_{2}Fe_{14}B$ with an amount of ~ 50% soft $\alpha$-Fe-phase coercivities of ${\mu}_{0}H_{c}=0.75\;T$, a remanence of 1.5 T and an energy product of $400\;kJ/m^{3}$ is expected. In nanocrystalline systems the temperature dependence of the coercivity is well described by the relation ${\mu}_{0}H_{c}=(2\;K_{1}/M_{s}){\alpha}-N_{eff}{\mu}_{0}M_{s}$, where the microstructural parameters $\alpha$ and $N_{eff}$ take care of the short-range perturbations of the anisotropy and $N_{eff}$ is related to the long-range dipolar interactions. $N_{eff}$ is found to follow a logarithmic grain size size dependence ${\mu}_{0}H_{c}=(2\;K_{1}/M_{s}){\alpha}-N_{eff}(\beta1nD){\mu}_{0}M_{s}$. Several trends how to achieve the ideal situation $\alpha$->1 and $N_{eff}$->1->0 will be discussed.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.83-91
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• 2023

A ring R is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal I of a UN ring R. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring R, a matrix ring M_n(R) is UN if and only if R is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group G and a field K for the group algebra KG to be UN. Then we extend the results obtained for KG to the group ring RG over a ring R (which may not necessarily be a field).

• Coupled systems mechanics
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• v.12 no.2
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• pp.127-149
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• 2023

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

• Restorative Dentistry and Endodontics
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• v.20 no.2
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• pp.432-461
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• 1995

The basic principles in the design of Class II amalgam cavity preparations have been modified but not changed in essence over the last 90 years. The early essential principle was "extension for prevention". Most of the modifications have served to reduce the extent of preparation and, thus, increase the conservation of sound tooth structure. A more recent concept relating to conservative Class II cavity preparations involves elimination of occlusal preparation if no carious lesion exists in this area. To evaluate the ideal ClassII cavity preparation design, if carious lesion exists only in the interproximal area, three cavity design conditions were studied: Rodda's conventional cavity, simple proximal box cavity and proximal box cavity with retention grooves. In this study, MO amalgam cavity was prepared on maxillary first premolar. Three dimensional finite element models were made by serial photographic method. Linear, eight and six-nodal, isoparametric brick elements were used for the three dimensional finite element model. The periodontal ligament and alveolar bone surrounding the tooth were excluded in these models. Three types model(B option, Gap option and R option model) were developed. B option model was assumed perfect bonding between the restoration and cavty wall. Gap option model(Gap distance: $2{\mu}m$) was assumed the possibility of play at the interface simulated the lack of real bonding between the amalgam and cavity wall (enamel and dentin). R option model was assumed non-connection between the restoration and cavty wall. A load of 500N was applied vertically at the first node from the lingual slope of the buccal cusp tip. This study analysed the displacement, 1 and 2 direction normal stress and strain with FEM software ABAQUS Version 5.2 and hardware IRIS 4D/310 VGX Work-station. The results were as followed. 1. Rodda's cavity form model showed greater amount of displacement with other two models. 2. The stress and strain were increased on the distal marginal ridge and buccopulpal line angle in Rodda's cavity form model. 3. The stress and strain were increased on the central groove and a part of distal marginal ridge in simple proximal box model and proximal box model with retention grooves. 4. With Gap option, Rodda's cavity form model showed the greatest amount of the stress on distal marginal ridge followed by proximal box model with retention grooves and simple proximal box model in descending order. 5. With Gap option, simple proximal box model showed greater amount of stress on the central groove with proximal box model with retention grooves. 6. Retention grooves in the proximal box played the role of supporting the restorations opposing to loads.