• East Asian mathematical journal
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• v.24 no.3
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• pp.213-221
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• 2008

In this paper, a new class of fuzzy topological spaces called ordered fuzzy pre-extremally disconnected spaces is introduced. Tietze extension theorem for ordered fuzzy pre-extremally disconnected spaces has been discussed as in [9] besides proving several other propositions and lemmas.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.529-540
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• 2024

In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear Hörmander class $BS^{m}_{1,1}$ in variable Triebel-Lizorkin spaces and variable Besov spaces.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.7 no.1
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• pp.113-131
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• 1997

This study was performed to evaluate the exposure levels of worker exposed to welding fume and metals in confined spaces of a shipyard. The airborne concentration of welding fumes and metal elements in confined spaces were compared with those in open working areas. Results of the study were as follows. 1. The geometric mean of welding fume concentration in a confined space was $16.6mg/m^3$, which contained $3.9mg/m^3$ Fe, $1.2mg/m^3$ Mg, $0.8mg/m^3$ Zn, $0.008mg/m^3$ Cu, $0.008mg/m^3$ Pb, $0.005mg/m^3$ Ni, $0.003mg/m^3$ Cr, $0.003mg/m^3$ Cd. The geometric mean of welding fume concentration in open working areas was $5.2mg/m^3$, which contained $1.1mg/m^3$ Fe, $0.3mg/m^3$ Mg, $0.3mg/m^3$ Zn, $0.004mg/m^3$ Cu, $0.008mg/m^3$ Pb, $0.005mg/m^3$ Ni, $0.003mg/m^3$ Cr, $0.0003mg/m^3$ Cd. The geometric mean of welding fume concentration in confined spaces was 3,2 times higher than that in open working areas. The geometric mean concentrations of such metals as Fe, Mg, Zn, or Cu within fume in confined spaces were 2-4 times higher than those in open working areas, while little difference made such metals as Pb, Ni, Cr, Cd. 2. In 32 samples out of a total of 39 samples (82.1%) collected in confined spaces, the concentrations of welding fume exceeded TLV. while so did 19 samples out of 33 samples (57.6%) in open working areas. As for the concentrations of metals in welding flume from confined spaces, Fe exceeded TLV in 14 out of a total of 38 samples (36.8%), Mn exceeded TLV in 23 out of a total of 38 samples (60.5%). As for the concentration of metals in welding fume from open working areas, Fe exceeded TLV in 3 out of a total of 34 samples (8.8%), Mn exceeded TLV in 6 out of a total of 34 samples (17.6%). Considering additive effect among metals, in 31 out of a total of 39 samples (79.5%) collected in confined spaces, the concentrations of welding fume exceeded TLV, while so did 14 out of 38 samples (55.6%) in open working areas. 3. In respect of base metal and welding type the concentration of total welding fume by $CO_2$ gas W./mild steel was the highest, followed by semiauto MMA/mild steel, then followed by TIG or $CO_2$ gas W./stainless steel. ; as for concentration of metal within fume, a decreasing order was Fe, Zn, Mn, and Pb in $CO_2$ gas W./mild steel and semiauto MMA/mild steel, but Fe, Mn, Cr, and Ni in TIG or $CO_2$ gas W./stainless steel. 4. In case of welding base metal covered by paint, contents of Zn within red paint chip and within gray paint chip were 14.0% and 0.08% respectively, which showed a little difference, while the airborne concentrations of Zn within fume during welding base metal covered red paint and gray paint were $1.351mg/m^3$ and $1.018mg/m^3$ respectively, which showed little difference. As for Pb, contents of red paint chip and gray paint chip were 0.14% and 0.08% respectively, and the airborne concentrations within fume during welding base metal covered red paint and gray paint were $0.009mg/m^3$ and $0.007mg/m^3$ respectively, both of which showed little difference.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.333-352
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• 2017

In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.413-425
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• 2001

We use the branching rules on SU(3) to show that if two Aloff-Wallach spaces $M_{k,l}\;and\;M_{k',l'}$ are isospectral for the Laplacian acting on smooth functions, they are isometric. We also show that 1 is the non-zero smallest eigenvalue among all Aloff-Wallach spaces and compute the multiplicities.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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• pp.255-263
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• 2006

In this paper, we introduce the concepts of ${\gamma}$-fuzzy feebly open and ${\gamma}$-fuzzy feebly closed sets in Sostak's fuzzy topological spaces and by using them, we explain the notions of ${\gamma}$-fuzzy F-closed spaces. Also, we give some characterization of ${\gamma}$-fuzzy F-closedness in terms of fuzzy filterbasis and ${\gamma}$-fuzzy feebly-${\theta}$-cluster points.

• East Asian mathematical journal
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• v.29 no.3
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• pp.315-326
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• 2013

In this paper, a new monotonicity, $M({\cdot},{\cdot})$-monotonicity, is introduced in Banach spaces, and the resolvent operator of an $M({\cdot},{\cdot})$-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with $M({\cdot},{\cdot})$-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.45-52
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• 2004

The theory of m-th root metric has been developed by H. Shimada [8], and applied to the biology [1] as an ecological metric. The purpose of this paper is to introduce the m-th root Finsler metrics which admit ($\alpha,\;\beta$)-types. Especially in cases of m = 3, 4, we give the condition for Finsler spaces with such metrics to be locally Minkowski spaces.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.761-765
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• 2012

We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.54-58
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• 2010

We introduce the concepts of interval-valued fuzzy $m{\alpha}$-open sets and interval-valued fuzzy $m{\alpha}$-continuous mappings. And we study some characterizations and properties of such concepts.