• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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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.

• Bulletin of the Korean Chemical Society
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• 제18권9호
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• pp.965-972
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• 1997

An approximate molecular theory of classical fluids based on the nonrandom lattice statistical-mechanical theory is presented. To obtain configurational Helmholtz free energy and equation of state (EOS), the lattice-hole theory of the Guggenheim combinatorics is approximated by introducing the nonrandom two-fluid theory. The approximate nature in the derivation makes the model possible to unify the classical lattice-hole theory and to describe correctly the configurational properties of real fluids including macromolecules. The theory requires only two molecular parameters for a pure fluid. Results obtained to date have demonstrated that the model correlates quantitatively the first- and second-order thermodynamic properties of real fluids. The basic simplicity of the model can readily be generalized to multicomponent systems. The model is especially relevant to (multi) phase equilibria of systems containing molecularly complex species.

• Journal of the Korean Chemical Society
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• 제46권6호
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• pp.545-549
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• 2002

Many theories for polymeric liquids are based on the concepts of cell, hole, free volume or lattice etc. In the theories, van der Waals potential, Lennard-Jones 6-12 potential and their modified potentials are commonly used.In this work, Mie(p, 6) potential was applied to the Continuous Lattice Fluid Theory (which extends the discrete lattices of Lattice Fluid Theory to classically continuous lattices) and Dee-Walsch's Cell Theory (which modifies Flory's Equa-tion of State Theory). Both of them are known to be successful theories for polymeric liquids. Thus, PVT values chang-ing with p (the exponent in the repulsion potential) were calculated and compared with experimental values. And, calculated values of Lattice Fluid Theory, Flory's Equation of State Theory and Cho-Sanchez Theory using pertubation method were also compared. Through the calculated results, van der Waals potential, Lennard-Jones 6-12 potential and Mie(p, 6) potential for polymeric liquids were compared with each other.

• Journal for History of Mathematics
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• 제15권2호
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• pp.175-181
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• 2002

Since Noether has consolidated the structural approach to the study of algebra, the lattice theory has reemerged as a tool for the structural study for algebra and its own right as well in 1930s. We investigate the process which the mathematical structures made their foundations in Mathematics through the lattice theory in the period.

• Kyungpook Mathematical Journal
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• 제43권4호
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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.

• Journal of the Computational Structural Engineering Institute of Korea
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• 제28권1호
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• pp.53-61
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• 2015

This paper presented the nonlinear behaviors of the single-layered lattice dome, which is widely used for the long-span structure system. The behaviors were analysed through the classical shell buckling theory as the single-layered lattice dome behaves like continum thin shell due to its geometric characteristics, and finite element analysis method using the software program Nastran. Shell buckling theory provides two types of buckling loads, the global- and member buckling, and finite element analysis provides the ultimate load of geometric nonlinear analysis as well as the buckling load of Eigen value solution. Two types of models for the lattice dome were analysed, that is rigid- and pin-jointed structure. Buckling load using the shell buckling theory for each type of lattice dome, governed by the minimum value of global buckling or member buckling load, resulted better estimation than the buckling load with Eigen value analysis. And it is useful to predict the buckling pattern, that is global buckling or member buckling.

• Bulletin of the Korean Chemical Society
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• 제6권3호
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• pp.132-135
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• 1985

Four types of the phase diagrams indicating the partial miscibilities in polymer-polymer or polymer-solvent systems have been explained in terms of the extended Flory-Huggins lattice theory. In this article, the term $kT_{\chi}$ in the theory is expressed as a function of temperature. Using such $a_{\chi}$-parameter, the simplest forms of geometrical conditions are derived for each type of the four partial miscibilities in polymer systems. The calculated partial miscibilities are in good agreement with the experiment.

• Honam Mathematical Journal
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• 제40권3호
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• pp.457-486
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• 2018

In several fields the soft set theory has a very vast range uses and applications. A soft group is a proper family of subgroups and a fuzzy soft group is a proper family of fuzzy subgroups. Here in this paper the concept of lattice ordered fuzzy soft groups is introduced. Also its some properties are studied and discussed. In addition, the defintion of lattice order fuzzy soft right (left) cosets and lattice order soft product of fuzzy soft subgroups and some related results are discussed to clear these ideas.

• Journal of Ocean Engineering and Technology
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• 제25권4호
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• pp.48-53
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• 2011

Current trends in propeller design have led to the need for extremely complex blade shapes, which place great demands on the accuracy of design and analysis methods. This paper presents a new proposal for improving the prediction of propeller performance with a vortex lattice method using the lifting surface theory. The paper presents a review of the theory and a description of the numerical methods employed. For 8 different propellers, the open water characteristics are calculated and compared with experimental data. The results are in good agreement in the region of a high advanced velocity, but there are differences in the other case. We have corrected the parameters for the trailing wake modeling in this paper, and repeated the calculation. The new calculation results are more in agreement with the experimental data.

• Journal of the Semiconductor & Display Technology
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• 제6권4호
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• pp.65-68
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• 2007

An epitaxial NiSi structure on Si (001) substrate was studied by using density functional theory (DFT). Orhorhombic and B2-NiSi structures were compared first. B2 structure was further considered as it has same crystal structure as Si and the lattice mismatch between B2 and Si is small, compared to orthorhombic-NiSi. The lattice parameters of x- and y-direction in B2-NiSi structure were modified to match with those in Si (001). The size reduction of the lattice parameter of B2-NiSi to match with that of Si increased the lattice parameter of z-direction by 10.5%. Therefore, we propose that an optimum structure of NiSi for epitaxial growth on Si (001) is a tetragonal structure.