• Title/Summary/Keyword: BCC

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HYPER BCC-ALGEBRAS

  • JUN, YOUNG BAE;ROH, EUN HWAN;HARIZAVI, HABIB
    • Honam Mathematical Journal
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    • v.28 no.1
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    • pp.57-67
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    • 2006
  • we apply the hyperstructures to BCC-algebras, and introduce the concept of a hyper BCC-algebra which is a generalization of a BCC-algebra, and investigates some related properties. We also introduce the notion of a hyper BCC-subalgebra, BCC-scalar element and a hyper BCC-ideal, and discuss related properties.

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SOFT IDEALS IN SOFT BCC-ALGEBRAS

  • Jun, Young-Bae;Lee, Kyoung-Ja
    • Honam Mathematical Journal
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    • v.31 no.3
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    • pp.335-349
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    • 2009
  • Soft set theory by Molodtsov is applied to ideals in BCC-algebras. The notion of soft BCC-ideals of soft BCC-algebras and idealistic soft BCC-algebras are introduced, and several examples are provided. Relations between a fuzzy BCC-ideal and an idealistic soft BCC-algebra are given, and the characterization of idealistic soft BCC-algebras is established.

POSITIVE IMPLICATIVE SMARANDACHE BCC-IDEALS IN SMARANDACHE BCC-ALGEBRAS

  • Jun, Young-Bae;Song, Seok-Zun;Kang, Kyung-Tae
    • Honam Mathematical Journal
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    • v.30 no.3
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    • pp.505-512
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    • 2008
  • The notion of positive implicative Smarandache BCC-ideals is introduced, and related properties are investigated. Relations between Smarandache BCC-ideals and positive implicative Smarandache BCC-ideals are discussed. The extension property of a positive implicative Smarandache BCC-ideals is given.

TOPOLOGICAL PROPERTIES IN BCC-ALGEBRAS

  • Ahn, Sun-Shin;Kwon, Seok-Hwan
    • Communications of the Korean Mathematical Society
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    • v.23 no.2
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    • pp.169-178
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    • 2008
  • In this paper, we show how to associate certain topologies with special ideals of BCC-algebras on these BCC-algebras. We show that it is natural for BCC-algebras to be topological BCC-algebras with respect to theses topologies. Furthermore, we show how certain standard properties may arise. In addition we demonstrate that it is natural for these topologies to have many clopen sets and thus to be highly connected via the ideal theory of BCC-algebras.

Quasi BCC-algebras

  • Jun, Young Bae;Song, Seok Zun
    • Kyungpook Mathematical Journal
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    • v.45 no.1
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    • pp.115-121
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    • 2005
  • Using the concept of fuzzy points, the notions of fuzzy point BCC-(sub) algebras, quasi BCC-(sub)algebras and quasi BCC-ideals are introduced. Some characterizations of them are discussed.

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IDEALS AND BRANCHES OF BCC-ALGEBRAS

  • Karamdin, Bushra;Bhatti, Shaban Ali
    • East Asian mathematical journal
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    • v.23 no.2
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    • pp.247-255
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    • 2007
  • Basic properties of branches of weak BCC-algebras and ideals of BCC-algebras containing only atoms are described.

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SOFT BCC-ALGEBRAS

  • Jun, Young-Bae;Lee, Kyoung-Ja;Ozturk, Mehmet Ali
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1293-1305
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    • 2009
  • Molodtsov [D. Molodtsov, Soft set theory First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCC-algebras. The notion of (trivial, whole) soft BCC-algebras and soft BCC-subalgebras are introduced, and several examples are provided. Relations between a fuzzy subalgebra and a soft BCC-algebra are given, and the characterization of soft BCC-algebras is established.

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Amorphous Cr-Ti Texture-inducing Layer Underlying (002) Textured bcc-Cr alloy Seed Layer for FePt-C Based Heat-assisted Magnetic Recording Media

  • Jeon, Seong-Jae;Hinata, Shintaro;Saito, Shin
    • Journal of Magnetics
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    • v.21 no.1
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    • pp.35-39
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    • 2016
  • $Cr_{100-x}Ti_x$ amorphous texture-inducing layers (TIL) were investigated to realize highly (002) oriented $L1_0$ FePt-C granular films through hetero-epitaxial growth on the (002) textured bcc-$Cr_{80}Mn_{20}$ seed layer (bcc-SL). As-deposited TILs showed the amorphous phase in Ti content of $30{\leq}x(at%){\leq}75$. Particularly, films with $40{\leq}x{\leq}60$ kept the amorphous phase against the heat treatment over $600^{\circ}C$. It was found that preference of the crystallographic texture for bcc-SLs is directly affected by the structural phase of TILs. (002) crystallographic texture was realized in bcc-SLs deposited on the amorphous TILs ($40{\leq}x{\leq}70$), whereas (110) texture was formed in bcc-SLs overlying on crystalline TILs (x < 30 and x > 70). Correlation between the angular distribution of (002) crystal orientation of bcc-SL evaluated by full width at half maximum of (002) diffraction (FWHM) and a grain diameter of bcc-SL indicated that while the development of the lateral growth for bcc-SL grain reduces FWHM, crystallization of amorphous TILs hinders FWHM. $L1_0$ FePt-C granular films were fabricated under the substrate heating process over $600^{\circ}C$ with having different FWHM of bcc-SL. Hysteresis loops showed that squareness ($M_r/M_s$) of the films increased from 0.87 to 0.95 when FWHM of bcc-SL decreased from $13.7^{\circ}$ to $3.8^{\circ}$. It is suggested that the reduction of (002) FWHM affects to the overlying MgO film as well as FePt-C granular film by means of the hetero-epitaxial growth.