• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.433-439
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• 2017

It is well known that an integral domain D is a Dedekind domain if and only if D is a Noetherian almost Dedekind domain. In this paper, we show that an integral domain D is a Dedekind domain if and only if D is an almost Dedekind domain such that Max(D) is a Noetherian topological space as a subspace of Spec(D) with respect to the Zariski topology. We also give a new characterization of ZPI-rings.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.793-808
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• 2014

The goal of this study is to evaluate and design steel plates with optimal material distributions achieved through a specific material topology optimization by using a CCARAT (Computer Aided Research Analysis Tool) as an optimizer, topologically optimally updating node densities as design variables. In typical material topology optimization, optimal topology and layouts are described by distributing element densities (from almost 0 to 1), which are arithmetic means of node densities. The average element densities are employed as material properties of each element in finite element analysis. CCARAT may deal with material topology optimization to address the mean compliance problem of structural mechanical problems. This consists of three computational steps: finite element analysis, sensitivity analysis, and optimality criteria optimizer updating node densities. The present node density based design via CCARAT using node densities as design variables removes jagged optimal layouts and checkerboard patterns, which are disadvantages of classical material topology optimization using element densities as design variables. Numerical applications that topologically optimize reinforcement material distribution of steel plates of a cantilever type are studied to verify the numerical superiority of the present node density based design via CCARAT.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.457-475
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• 2010

In this paper, we have use a fuzzy bitopological space (X, $\tau_1$, $\tau_2$) to create a family $\tau_{ij}^s$ which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r-($\tau_i$, $\tau_j$)-generalized fuzzy regular closed, r-($\tau_i$, $\tau_j$)-generalized fuzzy strongly semi-closed and r-($\tau_i$, $\tau_j$)-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense of $\check{S}$ostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.688-693
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• 2007

Most frame structures cannot be manufactured in a single-piece form. Ideally, when a structure is built up by assembling multi pieces, assembly at the joints should be rigidly performed enough to have almost full stiffness, which is difficult for practical reasons such as manufacturing cost and time. In this research, we aim to develop a manufacturability-oriented compliance-minimizing topology optimization using a ground beam model incorporating additional zero-length elastic joint elements. In the present formulation, design variables control the stiffness of zero-length elastic joints, not the stiffness of beams. Because joint stiffness values at the converged state can be utilized to select candidate assembly locations and their strengths, the technique is extremely useful to design multi-piece frame structures. An optimal layout is also extracted based on the stiffness values.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.64-68
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• 2005

We introduce in Sostak's fuzzy topological spaces definitions of paracompactness, almost paracompactness, and near paracompactness all of which turn to be good extensions of their classical topological counterparts. Fuzzy semi-paracompact, para S-closed and weakly paracompact spaces are treated to a similar approach.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.291-296
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• 2011

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.245-250
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• 2019

In this paper, the notion of ${\gamma}$-operation on a supratopological space is introduced. We found that the ${\gamma}$-operation induces a supratopology (topology) containing a given supratopology. We also introduce the notions of (${\gamma}$, S)-continuous function and almost ${\Gamma}$-supracompact defined by ${\gamma}$-operation on a supratopological space and investigate some properties for such notions.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.445-460
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• 2022

In this paper, we studied on 𝛽-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of 𝛽-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any 𝛽-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime 𝛽-fuzzy filters and some topological concepts on the collection of prime 𝛽-fuzzy filters of a Stone ADL. Further we show that the collection 𝓣 = {X^𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec_𝛽(A) where X^𝛽(λ) = {𝜇 ∈ 𝓕Spec_𝛽(A) : λ ⊈ 𝜇}.

• Journal of Power Electronics
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• v.15 no.5
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• pp.1227-1234
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• 2015

The efficient electric power demand management in electric power supply industry is currently being changed by distributed generation. Meanwhile, small-scale distributed generation systems using renewable energy are being constructed worldwide. Several small-scale renewable distributed generation systems, which can supply electricity to the grid at peak load of the grid as per policy such as demand response programs, could help in the stability of the electric power demand management. In this case, the power quality of the small-scale renewable distributed generation system is more significant. Low prices of power semiconductors and multilevel inverters with high power quality have been recently investigated. However, the conventional multilevel inverter topology is unsuitable for the small-scale renewable distributed generation system, because the number of devices of such topology increases with increasing output voltage level. In this paper, a single-phase multilevel inverter based on H-bridge, with DC_Link divided by bi-directional switches, is proposed. The proposed topology has almost half the number of devices of the conventional multilevel inverter topology when these inverters have the same output voltage level. Double Fourier series solution is mainly used when comparing PWM output harmonic components of various inverter topologies. Harmonic components of the proposed multilevel inverter, which have been analyzed by double Fourier series, are compared with those of the conventional multilevel inverter. An inverter prototype is then developed to verify the validity of the theoretical analysis.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.77-81
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• 1979

Almost mathematicians wish to study on the classification of the objects within isomorphism and determination of effective and computable invariants to distinguish the isomorphism classes. In topology, the concepts of homotopy and homeomorphism are such examples. In this lecture I shall speak of with respect to (i) Thom's cobordism group (ii) Cobordism category (iii) finally, the semigroup in cobordism category is isomorphic to the Thom's cobordism group.