• Title, Summary, Keyword: lattice embedding

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Remarks on the Valid Equations in Lattice Implication Algebras

  • JEONG, JOOHEE
    • Kyungpook Mathematical Journal
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    • v.43 no.4
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    • pp.539-545
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    • 2003
  • We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.

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Characteristic Genera of Closed Orientable 3-Manifolds

  • KAWAUCHI, AKIO
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.753-771
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    • 2015
  • A complete invariant defined for (closed connected orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself can be reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In a previous work, a characteristic lattice point invariant defined for the 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points. In this paper, a characteristic rational invariant defined for the 3-manifolds called the characteristic genus defined for the 3-manifolds is constructed by using an embedding of a set of lattice points called the PDelta set into the set of rational numbers. The characteristic genus defined for the 3-manifolds is also compared with the Heegaard genus, the bridge genus and the braid genus defined for the 3-manifolds. By using this characteristic rational invariant defined for the 3-manifolds, a smooth real function with the definition interval (-1, 1) called the characteristic genus function is constructed as a characteristic invariant defined for the 3-manifolds.

A NOTE ON JANOWITZ'S HULLS OF GENERALIZED ORTHOMODULAR LATTICES

  • Park, Eun-Soon;Chung, Jin-Young
    • Communications of the Korean Mathematical Society
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    • v.15 no.3
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    • pp.511-519
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    • 2000
  • If G is a strict generalized orthomodular lattice and H={I|I=[0, $\chi$, $\chi$$\in$G}, then H is prime ideal of the Janowitz's hull J(G) of G. If f is the janowitz's embedding, then the set of all commutatiors of f(G) equals the set of all commutators of the Janowitz's hull J(G) of G. Let L be an OML. Then L J(G) for a strict GOML G if and only if ther exists a proper nonprincipal prime ideal G in L.

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On the Representations of Finite Distributive Lattices

  • Siggers, Mark
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.1-20
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    • 2020
  • A simple but elegant result of Rival states that every sublattice L of a finite distributive lattice 𝒫 can be constructed from 𝒫 by removing a particular family 𝒥L of its irreducible intervals. Applying this in the case that 𝒫 is a product of a finite set 𝒞 of chains, we get a one-to-one correspondence L ↦ 𝒟𝒫(L) between the sublattices of 𝒫 and the preorders spanned by a canonical sublattice 𝒞 of 𝒫. We then show that L is a tight sublattice of the product of chains 𝒫 if and only if 𝒟𝒫(L) is asymmetric. This yields a one-to-one correspondence between the tight sublattices of 𝒫 and the posets spanned by its poset J(𝒫) of non-zero join-irreducible elements. With this we recover and extend, among other classical results, the correspondence derived from results of Birkhoff and Dilworth, between the tight embeddings of a finite distributive lattice L into products of chains, and the chain decompositions of its poset J(L) of non-zero join-irreducible elements.

The Embedded Atom Method Analysis of the Nickel (Nickel의 Embedded Atom Method 해석)

  • 정영관;김경훈;이근진;김종수
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.572-575
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    • 1997
  • The embedded atom method based on density functional theory was developed as a new means for calculating ground state properties of realistic metal system by Murray S. Daw, Stephen M. Foiles and Michael I. Baskes. In the paper, we had corrected constitutive formulae and parameters on the nickel for the purpose of doing Embedded Atom Method analysis. And then we have computed the properties of the nickel on the fundamental scale of the atomic structure. In result, simulated ground state properties, such as the lattice constant, elastics constants and sublimation energy, show good agreement with Daw's simulation data and with experimental data.

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The Embedded Atom Method Analysis of the Palldium (Palladium의 Embedded Atom Method 개발)

  • 정영관;김경훈;김세웅;이성희;이근진;박규섭
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.652-655
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    • 2002
  • The embedded atom method based on the density functional theory is used for calculating ground state properties of realistic metal systems. In this paper, we had corrected constitutive formulae and parameters on the palladium for the purpose of doing Embedded Atom Method analysis. And then we have computed the properties of the palladium on the fundamental scale of the atomic structure. In result, simulated ground state properties, such as the lattice constant, elastics constants and the sublimation energy, show good agreement with Daw's simulation data and with experimental data.

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Numerical Study on Properties of Metals and Expansion of Metal Hydrides (금속의 특성 및 금속수소화물의 팽창에 관한 수치해석)

  • Jung, Y.G.;Park, K.S.
    • Transactions of the Korean hydrogen and new energy society
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    • v.15 no.4
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    • pp.257-265
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    • 2004
  • Numerical analysis, as EAM(Embedded Atom Method), in the atomic level is necessary to analyze the relation between the hydrogen and hydrogen absorption metals. EAM established on density functional theory was developed as a new means for calculating various properties and phenomena of realistic metal systems. In this study, we had constructed the EAM program from constitutive formulae and parameters of the hydrogen, nickel and palladium for the purpose of predicting the expansion behavior on hydrogen absorbing. In result, not only the ground state properties of metals but also lattice constants and the volume expansion ratio of metal hydrides show good agreement with Daw's data and experiment data.