• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.1-8
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• 2023

This study is on a Boolean B or Boolean lattice L in abstract algebra with closed binary operation *, complement and distributive properties. Both Binary operations and logic properties dominate this set. A lattice sheds light on binary operations and other algebraic structures. In particular, the construction of the elements of this L set from idempotent elements, our definition of k-order idempotent has led to the expanded definition of the definition of the lattice theory. In addition, a lattice offers clever solutions to vital problems in life with the concept of logic. The restriction on a lattice is clearly also limit such applications. The flexibility of logical theories adds even more vitality to practices. This is the main theme of the study. Therefore, the properties of the set elements resulting from the binary operation force the logic theory. According to the new definition given, some properties, lemmas and theorems of the lattice theory are examined. Examples of different situations are given.

• Journal of the Korean Ceramic Society
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• v.31 no.4
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• pp.420-426
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• 1994

A new method is proposed for the oxide lattice energy calculation. It is consisted of (1) setting a central and a computation domains in a real lattice, (2) calculation of inter-ionic potential producted by the associated portion of each ion to the relative domain, and (3) summing up the potential energies. Even with a slight expansion of the domain, the lattice energy converges to the published data. The method is superior than any other reported due to the simple and clear concept and the reduced computing.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.633-643
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• 2010

In this paper, the concept of maximal ideals relative to a filter on posets is introduced and examined. An intrinsic characterization of distributive lattices is obtained. In addition, we also give a characterization of pseudo primes in semicontinuous lattices and a characterization of semicontinuous lattices. Functions of semicontinuous lattices which are order preserving and semicontinuous are studied. A new concept of semiarithmetic lattices is introduced and examined.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.13-26
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• 1998

The purpose of this note is to study the relation between Heyting algebra and t-algebra which is the dual concept of BCK-algebra. We define t-algebra with binary operation ${\rhd}$ which is a generalization of the implication in the Heyting algebra, and define a bounded ness and commutativity of it, and then characterize a Heyting algebra and a Boolean algebra as a bounded commutative t-algebra X satisfying $x=(x{\rhd}y){\rhd}x$ for all $x,y{\in}X$.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.323-330
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• 2014

The notion of transitive filters is introduced in lattice implication algebras. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. The concept of absorbent filters is introduced and their properties are studied. A set of equivalent conditions is obtained for a filter to become an absorbent filter.

• Korean Journal of Materials Research
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• v.25 no.12
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• pp.713-718
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• 2015

A new method is proposed for the calculation of the unrelaxed surface energy of spinel ferrite. The surface energy calculation consists of (1) setting the central and computational domains in the semi-infinite real lattice, having a specific surface, and having an infinite real lattice; (2) calculation of the lattice energies produced by the associated portion of each ion in the relative domain; and (3) dividing the difference between the semi-infinite lattice energy and the infinite lattice energy on the exposed surface area in the central domain. The surface energy was found to converge with a slight expansion of the domain in the real lattice. This method is superior to any other so far reported due to its simple concept and reduced computing burden. The unrelaxed surface energies of the (100), (110), and (111) of $ZnFe_2O_4$ and $Fe_3O_4$ were evaluated by using in the semi-infinite real lattices containing only one surface. For the normal spinel $ZnFe_2O_4$, the(100), which consisted of tetrahedral coordinated $Zn^{2+}$ was electrostatically the most stable surface. But, for the inverses pinel $Fe_3O_4$, the(111), which consisted of tetrahedral coordinated $Fe^{3+}$ and octahedral coordinated $Fe^{2+}$ was electrostatically the most stable surface.

• Journal of the Korea Society of Computer and Information
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• v.21 no.4
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• pp.123-129
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• 2016

This study had a purpose to find the correlation between academic achievement and entrance examination score using FCA and framing a concept of university academic achievement and entrance examination score and then, building concept lattice. The subject for this analysis was admission materials of freshmen in computer engineering department at A university located in Chungcheong area in 2010. Also 56 students in total were subjects for the score analysis of their first semester from 2010 to 2014. The major findings of this study were as follows. We organized and extracted many-valued context, concept lattice, associated rules using FCA. And we analyzed the correlation between University academic achievement and entrance examination score using FCA. The conclusions were as follows. We could get meaningful analyzed results using FCA. University academic achievement had lower relativeness with entrance examination score and female students had higher university academic achievement than male students. The improvement points are summarized below. It is necessary to improve the ratio and application method of the university admission factors and to increase the regular admission for a university. And programs for completing College-preparatory programming for male students in low university academic achievement are necessary.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.683-690
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• 2013

In this paper, we introduce the concept of a right derivation in incline algebras and give some properties of incline algebras. Also, the concept of d-ideal is introduced in an incline algebra with respect to right derivation.

• Journal of Korea Multimedia Society
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• v.16 no.7
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• pp.802-809
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• 2013

In this paper, we propose the similarity measurement method between two program codes by counting the frequency and length of continuous patterns of specifiers and keywords, which exist in two program codes. In addition, we propose the visualization method of this analysis result by formal concept analysis. Proposed method considers adjacencies of specifiers or keywords, which have not been considered in the previous similarity measurements. Proposed method can detect the plagiarism by analyzing the pattern in each function regardless of the order of function call and execution. In addition, the result of the similarity measurement is visualized by the lattice of formal concept analysis to increase the user understanding about the relations between program codes. Experimental results showed that proposed method succeeded in 96% plagiarism detections. Our method could be applied into the analysis of general documents.

• Journal of KSNVE
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• v.8 no.5
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• pp.949-956
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• 1998

Complex and large lattice type structures are frequently used in design of bridge, tower, crane and aerospace structures. In general, in order to analyze these structures we have used the finite element method(FEM). This method is the most widely used and powerful method for structural analysis lately. However, it is necessary to use a large amount of computer memory and computational time because the FEM requires many degrees of freedom for solving dynamic problems exactly for these complex and large structures. For analyzing these structures on a personal computer, the authors developed the transfer stiffness coefficient method(TSCM). This method is based on the concept of the transfer of the nodal dynamic stiffness coefficient matrix which is related to force and displacement vector at each node. And we suggested TSCM for free vibration analysis of complex and large lattice type structures in the previous report. In this paper, we formulate forced vibration analysis algorithm for complex and large lattice type structures using extened TSCM. And we confirmed the validity of TSCM through computational results by the FEM and TSCM, and experimental results for lattice type structures with harmonic excitation.