• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.11a
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• pp.563-564
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• 2007

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.987-1030
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• 2001

Some discrimination of modules whose endomorhism rings are prime is introduced, by means of structures of submodules inducing prime ideals of the endomorphism ring End(sub)R (M) of a left R-module (sub)RM over a ring R. Modules with non-prime endomorphism rings are contrapositively studied as well.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.803-804
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• 2013

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.797-798
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• 2009

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.85-94
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• 2011

The aim of this paper is to study the normality of fuzzy topological spaces in Kubiak-$\check{S}$ostak's sense. Also, some characterizations and the effects of some types of functions on these types of normality are studied.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.405-411
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• 2005

We use a congruence relation on deductive systems of a Hilbert algebra H, to define a uniform structure on H and investigate the corresponding topology.

• 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.21 no.2
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• pp.107-113
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• 1984

Throughout the paper let A be a semifinite, infinite von Neumann algebra acting on a Hilbert space H, .alpha. an infinite cardinal. The main purpose of our work is to give several characterizations of a class of closed ideals in A, by introducing the notions of relative ranks of elements in A and the relative .alpha.-topology on H. The relative .alphi.-topology is an analogue to the .alpha.-topology that we have defined in ([7], [8]). The present work is regarded as an extension of [7], [8] and motivated by works of M. Breuer ([1], [2]), V. Kaftal ([5], [6]) and M.G. Sonis [9].

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.659-667
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• 1994

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$. Note that the ultraweak operator topology coincides with the weak topology on $L(H) (cf. [6]). Several functional analysists have studied the problem of solving systems of simultaneous equations in the predual of a dual algebra (cf. [3]). This theory is applied to the study of invariant subspaces and dilation theory, which are deeply related to the classes $A_{m,n}$ (that will be defined below) (cf. [3]). An abstract geometric criterion for dual algebras with property $(A_{\aleph_0}, {\aleph_0})$ was first given in [1].

• Smart Structures and Systems
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• v.16 no.4
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• pp.607-621
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• 2015

Wireless sensor technology has been opened up numerous opportunities to advanced health and maintenance monitoring of civil infrastructure. Compare to the traditional tactics, it offers a better way of providing relevant information regarding the condition of building structure health at a lower price. Numerous domestic buildings, especially longer-span buildings have a low frequency response and challenging to measure using deployed numbers of sensors. The way the sensor nodes are connected plays an important role in providing the signals with required strengths. Out of many topologies, the dense and sparse topologies wireless sensor network were extensively used in sensor network applications for collecting health information. However, it is still unclear which topology is better for obtaining health information in terms of greatest components, node's size and degree. Theoretical and computational issues arising in the selection of the optimum topology sensor network for estimating coverage area with sensor placement in building structural monitoring are addressed. This work is an attempt to fill this gap in high-rise building structural health monitoring application. The result shows that, the sparse topology sensor network provides better performance compared with the dense topology network and would be a good choice for monitoring high-rise building structural health damage.