• Macromolecular Research
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• 제16권1호
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• pp.51-56
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• 2008

Spherical micelles of poly(styrene-b-isoprene) (SI) diblock copolymers in selective solvents have been reported to pack onto either face-centered cubic (fcc) or body-centered cubic (bcc) lattices. The selection rule for fcc and bcc lattices has been understood in terms of the intermicellar potentials, and they have been quantified using the ratio of the corona layer thickness to the core radius, $L/R_c$, as suggested by McConnell and Gast. In order to test the validity of the McConnell-Gast criterion, this study compared the $L/R_c$ values from various solutions i.e. nine SI copolymers in several different selective solvents. The McConnell-Gast criterion was not found to be a determining factor, even though it could explain the fcc/bcc selection qualitatively. From the phase diagrams, the transition between fcc and bcc phases was also considered as a function of concentration and temperature, and their physical mechanisms are discussed based on the recent mean-field calculation reported by Grason.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권1호
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• pp.72-78
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• 2015

Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang's completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak's the rough set theory. It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang's definition.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.361-374
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• 2009

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its level set, show that a fuzzy totally ordered set is a distributive fuzzy lattice, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

• 한국분말재료학회지
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• 제5권4호
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• pp.324-328
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• 1998

This paper is aimed to study the computer simulation of sintering process for ceramics by Monte Carlo and molecular dynamics methods. Plural mechanisms of mass transfer were designed in the MC simulation of sintering process for micron size particles; the transfer of pore lattices for shrinkage and the transfer of solid lattices for grain growth ran in the calculation arrays. The MD simulation was performed in the case of nano size particles of ionic ceramics and showed the characteristic features in sintering process at atomic levels. The MC and MD simulations for sintering process are useful for microstructural design for ceramics.

• 대한수학회논문집
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• 제35권2호
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• pp.653-666
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• 2020

In this paper, when G is a connected and simply connected nilpotent Lie group of dimension less than or equal to four, we study the uniform lattices Γ of G up to isomorphism and then we study the structure of the automorphism group Aut(Γ) of Γ from the viewpoint of splitting as a natural extension.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권1호
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• pp.57-65
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• 2014

In this paper, we investigate the properties of L-lower approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We study relations lower (upper, join meet, meet join) approximation operators and Alexandrov L-topologies. Moreover, we give their examples as approximation operators induced by various L-fuzzy relations.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권2호
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• pp.119-130
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• 2016

In this paper, we introduce the notions of soft L-fuzzy preproximities in complete residuated lattices. We prove the existence of initial soft L-fuzzy preproximities. From this fact, we define subspaces and product spaces for soft L-fuzzy preproximity spaces. Moreover, we give their examples.

• Bulletin of the Korean Chemical Society
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• 제12권5호
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• pp.544-554
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• 1991

Using the Huckel method, we obtain the analytical expressions for eigenvalues and eigenvectors of s.c., f.c.c. and b.c.c. clusters of rectangular parallelepiped shape, and of an arbitrary size. Our formula converage to those derived from the Bloch sum, in the limit of infinite extension. DOS and LDOS reveal that the major contribution of the states near Fermi level originates from the surface atoms, also symmetry of DOS curves disappears by the introduction of 2nd nearest neighbor interactions, in all the cubic lattices. An accumulation of the negative charges on surface of cluster is observed.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.825-838
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• 2021

In this paper the concept of ordered fuzzy filters is introduced in Heyting almost distributive lattices and the properties of these ordered fuzzy filters are studied. We characterized and proved a set of theorems of ordered fuzzy filters. Some topological properties of prime ordered fuzzy filters are also studied.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.475-485
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• 2019

In this paper, we introduced the notions of right and left closure systems on generalized residuated lattices. In particular, we study the relations between right (left) closure (interior) operators and right (left) closure (interior) systems. We give their examples.