• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.965-977
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• 2016

The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained.

• East Asian mathematical journal
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• v.30 no.1
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• pp.1-14
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• 2014

The first purpose of this paper is to study contact CR submanifolds of Sasakian manifolds and investigate some properties concernig with ${\phi}$-holomorphic bisectional curvature. The second purpose is to show an existence theorem of mixed foliate proper contact CR submanifolds in the standard Sasakian space form $E^{2m+1}$(-3) with constant ${\phi}$-sectional curvature -3.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.215-222
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• 2015

We show that homology group on a contact CR-warped product submanifold in odd dimensional sphere is zero under certain conditions in terms of warping function and the dimension of the submanifold.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1101-1110
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• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.863-881
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• 2014

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1303-1313
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• 2019

Recently Hui et al. ([8,9]) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. The characterization for both these classes of warped product submanifolds have been studied here. It is also shown that there do not exists any proper warped product bi-slant submanifold of a $(LCS)_n$-manifold. Although the existence of a bi-slant submanifold of $(LCS)_n$-manifold is ensured by an example.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.08a
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• pp.207-215
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• 2004

There are various characteristics called for in work roll and intermediate rolls for cold rolling mills. Among these characteristics, the two main requirements are to ensure the quality of the rolled products and to reduce roll cost. To achieve these needs, resistance to wear, to thermal shock and to contact fatigue are especially important. This paper describes that new material(named DSR1) for intermediate rolls which greatly increases rolling campaign and improves resistance to wear has been developed. DSR1 was successfully manufactured and has been used in the cold rolling mill. It showed that Trial product was homogenous in hardness distribution and sufficient usable diameter. Also in service test, trial product is much more excellent rolling performance than conventional $5\%Cr$.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.40 no.2
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• pp.203-214
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• 2014

We measured the contact dermatitis-causing substances concentrations in 28 commercial oxidative hair-coloring products. This study was aimed to provide the fundamental data about oxidative hair-coloring products. We selected 10 oxidation dyes (p-phenylenediamine, toluene-2,5-diamine, m-phenylenediamine, nitro-p-phenylenediamine, p-aminophenol, m-aminophenol, o-aminophenol, p-methylaminophenol, N,N'-bis(2-hydroxyethyl)-p-phenylenediamine sulfate, 2-methyl-5-hydroxyethylaminophenol) and 4 heavy metal (nikel; Ni, chromium; Cr, cobalt; Co, copper; Cu) as contact dermatitis-causing substances. To identify 10 oxidation dyes, hexane-2% sodium sulfite was used for the rapid and simple extraction and ultra performance liquid chromatography (UPLC) analysis was used for simultaneous analysis in 12 minutes. 10 oxidative dyes were detected as indicated on the product packaging and each concentration was lower than prescribed upper concentration limit by pharmaceutical manufacturing standards. And we analysed inductively coupled plasma-optical emission spectrophotometer (ICP-OES) for content search of heavy metal after microwave digestion. The heavy metal average concentration in oxidative hair-coloring products was 0.572 ${\mu}g/g$ for Ni, 3.161 ${\mu}g/g$ for Cr, 2.029 ${\mu}g/g$ for Co, 0.420 ${\mu}g/g$ for Cu, respectively. The average of concentration in powder type (henna) was higher than those of other foam and cream type oxidative hair-coloring products as follows; 1.800 ${\mu}g/g$ for Ni, 10.127 ${\mu}g/g$ for Cr, 7.082 ${\mu}g/g$ for Co, 1.451 ${\mu}g/g$ for Cu. Hair coloring products were classified into the six colors - black, dark brown, brown, dark brown, light brown, red brown and analyzed. Brown color had the highest average concentration of Co and the others had the highest average concentration of Cr.

• Journal of Korean Society of Environmental Engineers
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• v.28 no.3
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• pp.329-336
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• 2006

Iron manufacturing process involves production of various by-product including slag, sludge, sintering and EAF(Electric Arc furnace dust). Some of the by-products such as EAF and sintering dust are disposed of as waste due to their high heavy metal contents. It has been notice for many years that the EAF dust also contain about 65% of Fe(0) and Fe(II) and then the possible utilization of the iron. One possibility is to apply the EAF as a lining material in conjunction with clay or HDPE liners, in waste landfill. The probable reaction between the leachate containing toxic elements such as TCE, PCE dioxine and $Cr^{6+}$ is reduction of the toxic materials in corresponding to the oxidation of the reduced iron and therefore diminishing the toxicity of the leachate. It is, however, prerequisite to evaluate the leaching characteristics of the EAF dust before application. Amelioration of the leachate would be archived only when the level of toxic elements in the treated leachate is less than that of in the untreated leachate. Several leaching techniques were selected to cover different conditions and variable environments including time, pH and contact method. The testing methods include availability test, pH-stat test and continuous column test. Cr and Zn are potentially leachable elements among the trace metals. The pH of the EAF dust is highly alkaline, recording around 12 and Zn is unlikely to be leached under the condition. On the contrary Cr is more leachable under alkaline environment. However, the released Cr should be reduced to $Cr^{3+}$ and then removed as $Cr(OH)_3$. Removal of the Cr is observed in the column test and further study on the specific reaction of Cr and EAF dust is underway.

• Journal of Welding and Joining
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• v.34 no.1
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• pp.26-34
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• 2016

Automotive today has been transforming to an electronic product by adopting a lot of convenience and safety features, suggesting that joining materials and their mechanical reliabilities are getting more important. In this study, a Sn-Cu-Cr-Ca solder composition having a high melting temperature ($>230^{\circ}C$) was fabricated and its joint properties and reliability was investigated with an aim to evaluate the suitability as a joining material for electronics of engine room. Furthermore, mechanical properties change under complex environment were compared with several existing solder compositions. As a result of contact angle measurement, favorable spreadability of 84% was shown and the average shear strength manufactured with corresponding composition solder paste was $1.9kg/mm^2$. Also, thermo-mechanical reliability by thermal shock and vibration test was compared with that of the representative high temperature solder materials such as Sn-3.5Ag, Sn-0.7Cu, and Sn-5.0Sb. In order to fabricate the test module, solder balls were made in joints with ENIG-finished BGA and then the BGA chip was reflowed on the OPS-finished PCB pattern. During the environmental tests, resistance change was continuously monitored and the joint strength was examined after tests. Sn-3.5Ag alloy exhibited the biggest degradation rate in resistance and shear stress and Sn-0.7Cu resulted in a relatively stable reliability against thermo-mechanical stress coming from thermal shock and vibration.