• The Pure and Applied Mathematics
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• v.20 no.2
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• pp.117-127
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• 2013

As a generalization of fuzzy subsemigroups, the notion of ${\varepsilon}$-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ${\varepsilon}$-generalized fuzzy subsemigroups are established, and we show that the intersection of two ${\varepsilon}$-generalized fuzzy subsemigroups is also an ${\varepsilon}$-generalized fuzzy subsemigroup. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be ${\varepsilon}$-fuzzy idempotent is discussed. Using a given ${\varepsilon}$-generalized fuzzy subsemigroup, a new ${\varepsilon}$-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ${\varepsilon}$-generalized fuzzy subsemigroup is considered.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.571-577
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• 1997

We first show that if $\psi : M_n(B(H)) \to M_n (B(H))$ is a $D_n \otimes F(H)$-bimodule map, then there is a matrix $A \in M_n$ such that $\psi = S_A$. Secondly, we show that for an operator space $\varepsilon, A \in M_n$, the Schur product map $S_A : M_n(\varepsilon) \to M_n(\varepsilon)$ and $\phi_A : M_n(\varepsilon) \to \varepsilon$, defined by $\phi_A([x_{ij}]) = \sum^{n}_{i,j=1}{a_{ij}x_{ij}}$, we have $\Vert S_A \Vert = \Vert S_A \Vert_{cb} = \Vert A \Vert_S, \Vert \phi_A \Vert = \Vert \phi_A \Vert_{cb} = \Vert A \Vert_1$ and obtain some characterizations of A for which $S_A$ is contractive.

• Journal of the Korean Society for Heat Treatment
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• v.16 no.4
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• pp.211-215
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• 2003

In this work, a new way of measuring the volume fraction of e martensite in Fe-based alloys has been proposed. Since the specific volume of ${\varepsilon}$ martensite, depending on alloy composition, is smaller than that of austenite i.e ${\gamma}$ phase, volume expansion takes place during ${\varepsilon}{\rightarrow}{\gamma}$ reverse transformation. As the amount of the volume expansion is proportional to the product of specific volume difference times the volume fraction of ${\varepsilon}$ martensite, the volume fraction of ${\varepsilon}$ martensite can be calculated by measuring the volume expansion and the specific volume difference. Such a relationship was confirmed in Fe-21Mn and Fe-32Mn-6Si alloys which undergo ${\gamma}{\rightarrow}{\varepsilon}$ martensitic transformation on cooling and by cold rolling, respectively. It was also found that the former has isotropic ${\varepsilon}$ martensite while the latter has anisotropic ${\varepsilon}$ martensite.

• Journal of the Korean Ceramic Society
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• v.36 no.2
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• pp.151-158
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• 1999

$\varepsilon$-Caprolactame as organic monomer was intercalated in the interlayer space of montmorillonite and polymerized by polymerization reaction so that the inorganic polymer and organic polymer could be combined each other by chemical bonding. The results of X-ray and IR analysis showed that the polymerization reaction of $\varepsilon$-caprolactame between the interlayer spaces has been performed sucessfully. In order to study polymeric reaction product in detail we have isolated the polymerized material from the interlayer space and analyzed it by X-ray diffractometer and IR-Spectrocopy. The comparison of these results with them of the analyses for thee pure polymer which has been synthesized by polymeric reaction of $\varepsilon$-carolactame without montmorillonite showed that the obtained both polymeric materials are the same compounds.

• Journal of the Korean Ceramic Society
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• v.43 no.4 s.287
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• pp.207-212
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• 2006

[ ${\varepsilon}-caprolactam$ ] was polymerized in the layers of the [DEACOOH]-Montmorillonite intercalations complex at high temperatures ranging from 250% to 260% formed from Na-Montmorillonite and 10-Carboxy-n-decyldimethylethylammonium bromide to achieve [DEACOOH]-Polycaprolactam-Montmorillonite, in which an inorganic polymer (montmorillonite) is chemically combined with an organic polymer (polycaprolactam). The results of X-ray and IR analyses for the samples obtained after polymerization showed that the polymerization reaction was successfully accomplished. For the purpose of studying the polymeric reaction product more precisely, the polymerized product was separated from the silicate layers and analyzed with an X-ray diffractometer and an IR-spectrometer. A comparison of the results of the X-ray and IR analyses of the separated polymer and the polymer that was synthesized by the reaction of ${\varepsilon}-caprolactam$ solely with the organic cation without montmorillonite showed that the obtained both polymers are identical compounds.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.405-434
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• 2005

We establish appropriate $L^p$ estimates for a class of maximal operators $S_{\Omega}^{(\gamma)}$ on the product space $R^n\;\times\;R^m\;when\;\Omega$ lacks regularity and $1\;\le\;\gamma\;\le\;2.\;Also,\;when\;\gamma\;=\;2$, we prove the $L^p\;(2\;{\le}\;P\;<\;\infty)\;boundedness\;of\;S_{\Omega}^{(\gamma)}\;whenever\;\Omega$ is a function in a certain block space $B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ (for some q > 1). Moreover, we show that the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is nearly optimal in the sense that the operator $S_{\Omega}^{(2)}$ may fail to be bounded on $L^2$ if the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is replaced by the weaker conditions $\Omega\;{\in}\;B_q^{(0,\varepsilon)}(S^{n-1}\;\times\;S^{m-1})\;for\;any\;-1\;<\;\varepsilon\;<\;0.$

• Journal of the Korean Society of Propulsion Engineers
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• v.4 no.4
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• pp.9-17
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• 2000

The crystal growth and dissolution rates were calculated by solving a model equation, which involved the dissolution of the metastable phase($\beta$-HNIW) and growth of the stable phase($\varepsilon$-HNIW), together with the mass balance equation. The model has been successfully used to simulate available kinetic data for the $\beta$$\longrightarrow$$\varepsilon$ polymorphic transformation via a solution phase. From the effectiveness factor based on the two-step model, it was found that the surface integration contribution to the process was comparatively small, and a diffusion dependency decreased with an increase of the mass fraction of chloroform in the mixed solvents of ethyl acetate and chloroform. Appling these kinetics in process simulation allowed for the prediction of the product size of $\varepsilon$-HNIW.

• Plant Resources
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• v.1 no.1
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• pp.33-37
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• 1998

Carotenoid compounds in embryos of wild-type(WT) and viviparous mutants of maize(Zea mays L.) were analyzed using high performance liquid ehromatography (HPLC) with a photodiode array detector. Zeaxanthin accumulates in WT embryos as the major carotenoid. Phytoene accumulates in vp2 and vp5. Phytofluene in w3 and ${\xi}$-carotene in the vp9 mutant embryos. This indicates that the vp2 and vp5 mutants impair phytoene desaturase from 15-cis-phytoene to 15-cis-phytofluene. The w3 mutant has neither an isomerase from 15-cis-phytofluene to all-trans-phytofuene nor phytofluene desaturase from phytofluene to ${\xi}$-carotene. The vp9 mutant does not have the ${\xi}$-carotene desaturase from ${\xi}$-carotene to lycopene. Our analysis shows that the terminal carotenoid. ${\gamma}$-carotene(${\beta},{\Psi}$-carotene), accumulates in the vp7 mutant embryos. The ${\varepsilon}$-carotene(${\varepsilon},{\varepsilon}$-carotene), a product of ${\delta}$-carotene(${\varepsilon},{\Psi}$-carotene) in some plants, however, has not been found in maize embryos. The vp7 mutant impairs a cyclization step from ${\gamma}$-carotene to both ${\beta}$-carotene and ${\alpha}$-carotene. We suggest that monocyclic ${\gamma}$-carotene is the sole precursor of both bicyclic ${\beta}$-carotene(${\beta},{\beta}$-carotene) and ${\alpha}$-carotene(${\beta},{\varepsilon}$-carotene) in maize.

• Current Research on Agriculture and Life Sciences
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• v.3
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• pp.21-27
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• 1985

A bacterium which utilizes ${\varepsilon}$-caprolactam as a sole source of carbon and nitrogen was isolated from sludge of Shinchun river in Taegu and identified as Arthrobacter globiformis N-2-l. The growth medium for the optimum culture condition was composed of 0.4% ${\varepsilon}$-caprolactam, 0.02% $K_2HPO_4$, 0.05% $KH_2PO_4$, 0.02% $MgSO_4{\cdot}7H_2O$, 0.01% $FeCl_3{\cdot}6H_2O$ and 0.05% yeast extract. The optimum pH and temperature for growth were 7.0 and $30^{\circ}C$ respectively. The bacterial growth on the ${\varepsilon}$-caprolactam medium did not require any other organic nitrogen source such as yeast extract, although it was remarkably stimulated by the yeast extract. The bacteria utilized wide range of sugars and organic acids such as ${\alpha}$-ketoglutarate, adipate and P-hydroxybenzoate. The bacteria could use all kind of amino acids, ${\varepsilon}$-Caprolactam in the medium was consumed completely in the timecourse culture at $30^{\circ}C$ for 60 hr on the shaker by the bacteria. Decomposition product of ${\varepsilon}$-caprolactam by Arthrobacter globiformis N-2-1 was ${\varepsilon}$-aminocaproic acid.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.265-271
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• 2003

The purpose of this paper is to present certain results arising from product between fuzzy $H_{v}$-submodules. In particular, we consider the fundamental relation $\varepsilon$* defined on an $H_{v}$-module and give a property of the fundamental relations and fundamental modules with respect to the fuzzy product of $H_{v}$-modules.